Finite Group Databasebeta

← #33249526

Subgroups — #33249526

Order 18688.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989175C211yesmaximal, characteristic
2#22613119C211yesmaximal, characteristic, complemented
3#22613104C211yesmaximal, characteristic, complemented
4#22613087C211yesmaximal, characteristic, complemented
5#22613080C211yesmaximal, characteristic, complemented
6#22613046C211yesmaximal, characteristic, complemented
7#22613011C211yesmaximal, characteristic, complemented
8#22612999C211yesmaximal, characteristic, complemented
9#22612978C211yesmaximal, characteristic, complemented
10#22612950C211yesmaximal, characteristic, complemented
11#22612947C211yesmaximal, characteristic, complemented
12#22612936C211yesmaximal, characteristic, complemented
13#22612926C211yesmaximal, characteristic, complemented
14#22612867C211yesmaximal, characteristic, complemented
15#22612856C211yesmaximal, characteristic, complemented
16#22612838C211yesmaximal, characteristic, complemented
17C4⋊C4×C22⋊D73C211yesmaximal, characteristic, complemented
18#22612745C211yesmaximal, characteristic, complemented
19#22612716C211yesmaximal, characteristic, complemented
20#22612707C211yesmaximal, characteristic, complemented
21#22612701C211yesmaximal, characteristic, complemented
22#22612637C211yesmaximal, characteristic, complemented
23#22612628C211yesmaximal, characteristic, complemented
24#22612623C211yesmaximal, characteristic, complemented
25#22612598C211yesmaximal, characteristic, complemented
26#22612589C211yesmaximal, characteristic, complemented
27#22612589C211yesmaximal, characteristic, complemented
28#22612529C211yesmaximal, characteristic, complemented
29C4×#14556560C211yesmaximal, characteristic, complemented
30C4×#14556560C211yesmaximal, characteristic, complemented
31C2×#385×C73C211yesmaximal, characteristic, complemented
32#17989175C4116yescomplemented
33C2×#14556584C2211yescharacteristic
34C2×#14556584C2211yescharacteristic
35C2×#14556577C2211yescharacteristic
36C2×#14556577C2211yescharacteristic
37C2×#14556573C2211yescharacteristic
38C2×#14556573C2211yescharacteristic
39C2×#14556570C2211yescharacteristic
40C2×#14556565C2211yescharacteristic
41C2×#14556564C2211yescharacteristic
42C2×#14556564C2211yescharacteristic
43C2×#14556560C2211yescharacteristic
44C2×#14556560C2211yescharacteristic
45C2×#14556556C2211yescharacteristic, complemented
46C2×#14556553C2211yescharacteristic, complemented
47C2×C4×C22⋊D73C2211yescharacteristic
48C2×C4×C22⋊D73C2211yescharacteristic
49C2×C4×C22⋊D73C2211yescharacteristic
50C2×C4×C22⋊D73C2211yescharacteristic
51C2×C4×C22⋊D73C2211yescharacteristic
52C2×C4×C22⋊D73C2211yescharacteristic
53C2×C4×C22⋊D73C2211yescharacteristic
54C2×C4×C22⋊D73C2211yescharacteristic
55C2×C4×C22⋊D73C2211yescharacteristic
56C2×C4×C22⋊D73C2211yescharacteristic
57C2×#14556549C2211yescharacteristic, complemented
58C2×C4⋊C4×D73C2211yescharacteristic, complemented
59#17988492C2211yescharacteristic, complemented
60#17988491C2211yescharacteristic, complemented
61#17988491C2211yescharacteristic, complemented
62#17988488C2211yescharacteristic, complemented
63#17988487C2211yescharacteristic
64#17988487C2211yescharacteristic
65#17988487C2211yescharacteristic
66#17988487C2211yescharacteristic
67#17988484C2211yescharacteristic, complemented
68#17988484C2211yescharacteristic, complemented
69#17988483C2211yescharacteristic, complemented
70#17988483C2211yescharacteristic, complemented
71#17988482C2211yescharacteristic, complemented
72#17988482C2211yescharacteristic, complemented
73#17988482C2211yescharacteristic, complemented
74#17988482C2211yescharacteristic, complemented
75#17988481C2211yescharacteristic
76#17988481C2211yescharacteristic
77#17988481C2211yescharacteristic
78#17988481C2211yescharacteristic
79#17988480C2211yescharacteristic
80#17988480C2211yescharacteristic
81#17988480C2211yescharacteristic
82#17988480C2211yescharacteristic
83#17988480C2211yescharacteristic
84#17988480C2211yescharacteristic
85#17988480C2211yescharacteristic
86#17988480C2211yescharacteristic
87#17988479C2211yescharacteristic, complemented
88#17988479C2211yescharacteristic, complemented
89#17988477C2211yescharacteristic, complemented
90#17988477C2211yescharacteristic, complemented
91#17988477C2211yescharacteristic, complemented
92#17988477C2211yescharacteristic, complemented
93#17988476C2211yescharacteristic, complemented
94#17988476C2211yescharacteristic, complemented
95#17988475C2211yescharacteristic
96#17988475C2211yescharacteristic
97#17988475C2211yescharacteristic
98#17988475C2211yescharacteristic
99#17988474C2211yescharacteristic, complemented
100#17988474C2211yescharacteristic, complemented
101#17988472C2211yescharacteristic, complemented
102#17988472C2211yescharacteristic, complemented
103#17988470C2211yescharacteristic, complemented
104#17988470C2211yescharacteristic, complemented
105#17988469C2211yescharacteristic, complemented
106#17988469C2211yescharacteristic, complemented
107#17988468C2211yescharacteristic, complemented
108#17988468C2211yescharacteristic, complemented
109#17988468C2211yescharacteristic, complemented
110#17988468C2211yescharacteristic, complemented
111#17988466C2211yescharacteristic
112#17988466C2211yescharacteristic
113#17988466C2211yescharacteristic
114#17988466C2211yescharacteristic
115#17988466C2211yescharacteristic
116#17988466C2211yescharacteristic
117#17988466C2211yescharacteristic
118#17988466C2211yescharacteristic
119#17988465C2211yescharacteristic, complemented
120#17988465C2211yescharacteristic, complemented
121#17988463C2211yescharacteristic
122#17988463C2211yescharacteristic
123#17988463C2211yescharacteristic
124#17988463C2211yescharacteristic
125#17988461C2211yescharacteristic, complemented
126#17988461C2211yescharacteristic, complemented
127#17988460C2211yescharacteristic
128#17988460C2211yescharacteristic
129#17988460C2211yescharacteristic
130#17988460C2211yescharacteristic
131#17988460C2211yescharacteristic
132#17988460C2211yescharacteristic
133#17988460C2211yescharacteristic
134#17988460C2211yescharacteristic
135#17988458C2211yescharacteristic, complemented
136#17988458C2211yescharacteristic, complemented
137#17988458C2211yescharacteristic, complemented
138#17988458C2211yescharacteristic, complemented
139#17988456C2211yescharacteristic, complemented
140#17988454C2211yescharacteristic, complemented
141#17988452C2211yescharacteristic, complemented
142#17988451C2211yescharacteristic, complemented
143#17988449C2211yescharacteristic, complemented
144#17988447C2211yescharacteristic
145#17988447C2211yescharacteristic
146#17988446C2211yescharacteristic, complemented
147#17988444C2211yescharacteristic, complemented
148#17988444C2211yescharacteristic, complemented
149#17988443C2211yescharacteristic
150#17988443C2211yescharacteristic
151C4⋊C4×Dic73C2211yescharacteristic, complemented
152C4⋊C4×Dic73C2211yescharacteristic, complemented
153C4⋊C4×Dic73C2211yescharacteristic, complemented
154C4⋊C4×Dic73C2211yescharacteristic, complemented
155#17988438C2211yescharacteristic, complemented
156#17988438C2211yescharacteristic, complemented
157#17988438C2211yescharacteristic, complemented
158C4×C22⋊Dic73C2211yescharacteristic
159C4×C22⋊Dic73C2211yescharacteristic
160C4×C22⋊Dic73C2211yescharacteristic
161C4×C22⋊Dic73C2211yescharacteristic
162C4×C22⋊Dic73C2211yescharacteristic
163C4×C22⋊Dic73C2211yescharacteristic
164C4×C22⋊Dic73C2211yescharacteristic
165C4×C22⋊Dic73C2211yescharacteristic
166C4×C22⋊Dic73C2211yescharacteristic
167C4×C22⋊Dic73C2211yescharacteristic
168#17988434C2211yescharacteristic, complemented
169#17988434C2211yescharacteristic, complemented
170#17988434C2211yescharacteristic, complemented
171#17988432C2211yescharacteristic, complemented
172#95×D73C2211yescharacteristic, complemented
173C24×C4×C73C2211yescharacteristic
174C22×C4⋊C4×C73C2211yescharacteristic
175C22×C4⋊C4×C73C2211yescharacteristic
176C22×C22⋊C4×C73C2211yescharacteristic
177C22×C22⋊C4×C73C2211yescharacteristic
178#385×C73C2211yescharacteristic
179#385×C73C2211yescharacteristic
180#385×C73C2211yescharacteristic
181#385×C73C2211yescharacteristic
182#385×C73C2211yescharacteristic
183#385×C73C2211yescharacteristic
184#385×C73C2211yescharacteristic
185#385×C73C2211yescharacteristic
186C2×#95×C73C2211yescharacteristic
187C2×#95×C73C2211yescharacteristic
188C22×Dic146C2311yescharacteristic
189C22×D292C2311yescharacteristic
190C22×C22⋊D73C2311yescharacteristic
191C22×C22⋊D73C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C22×C4×D73C2311yescharacteristic
197C22×C4×D73C2311yescharacteristic
198C22×C4×D73C2311yescharacteristic
199C22×C4×D73C2311yescharacteristic
200C22×C4×D73C2311yescharacteristic
201C22×C4×D73C2311yescharacteristic
202#14556584C2×C418yescomplemented
203#14556584C2×C418yescomplemented
204#14556577C2×C418yescomplemented
205#14556577C2×C418yescomplemented
206#14556573C2×C418yescomplemented
207#14556573C2×C418yescomplemented
208#14556570C2×C418yescomplemented
209#14556565C2×C418yescomplemented
210#14556564C2×C418yescomplemented
211#14556564C2×C418yescomplemented
212#14556560C2×C418yescomplemented
213#14556560C2×C418yescomplemented
214#14556556—42no—
215#14556553—42no—
216C4×C22⋊D73—42no—
217C4×C22⋊D73—42no—
218C4×C22⋊D73—42no—
219C4×C22⋊D73—42no—
220C4×C22⋊D73—42no—
221C4×C22⋊D73—42no—
222C4×C22⋊D73—42no—
223C4×C22⋊D73—42no—
224C4×C22⋊D73C2×C418yescomplemented
225C4×C22⋊D73C2×C418yescomplemented
226#14556549—42no—
227C2×C4⋊Dic73C2311yescharacteristic
228C2×C4⋊Dic73C2311yescharacteristic
229C2×C4⋊Dic73C2311yescharacteristic
230C2×C4⋊Dic73C2311yescharacteristic
231C2×C4⋊Dic73C2311yescharacteristic
232C2×C4⋊Dic73C2311yescharacteristic
233C2×#11924007C2311yescharacteristic
234C2×#11924007C2311yescharacteristic
235C2×#11924007C2311yescharacteristic
236C2×#11924007C2311yescharacteristic
237C2×#11924007C2311yescharacteristic
238C2×#11924007C2311yescharacteristic
239C2×#11924007C2311yescharacteristic
240C2×#11924007C2311yescharacteristic
241C2×#11924007C2311yescharacteristic
242C2×#11924007C2311yescharacteristic
243C2×#11924007C2311yescharacteristic
244C2×#11924007C2311yescharacteristic
245C2×#11924007C2311yescharacteristic
246C2×#11924007C2311yescharacteristic
247C2×#11924007C2311yescharacteristic
248C2×#11924007C2311yescharacteristic
249C4⋊C4×D73—42no—
250C2×C22⋊Dic73C2311yescharacteristic
251C2×C22⋊Dic73C2311yescharacteristic
252C2×C22⋊Dic73C2311yescharacteristic
253C2×C22⋊Dic73C2311yescharacteristic
254C2×C22⋊Dic73C2311yescharacteristic
255C2×C22⋊Dic73C2311yescharacteristic
256C2×C22⋊Dic73C2311yescharacteristic
257C2×C22⋊Dic73C2311yescharacteristic
258C2×C22⋊Dic73C2311yescharacteristic
259C2×C22⋊Dic73C2311yescharacteristic
260C2×C22⋊Dic73C2311yescharacteristic
261C2×C22⋊Dic73C2311yescharacteristic
262C2×C22⋊Dic73C2311yescharacteristic
263C2×C22⋊Dic73C2311yescharacteristic
264C2×C22⋊Dic73C2311yescharacteristic
265C2×C22⋊Dic73C2311yescharacteristic
266C2×C22⋊Dic73C2311yescharacteristic
267C2×C22⋊Dic73C2311yescharacteristic
268C2×#11924005C2311yescharacteristic
269C2×#11924005C2311yescharacteristic
270C2×#11924005C2311yescharacteristic
271C2×#11924005C2311yescharacteristic
272C2×#11924005C2311yescharacteristic
273C2×#11924005C2311yescharacteristic
274C2×#11924005C2311yescharacteristic
275C2×#11924005C2311yescharacteristic
276C2×#11924005C2311yescharacteristic
277C2×#11924005C2311yescharacteristic
278C2×#11924005C2311yescharacteristic
279C2×#11924005C2311yescharacteristic
280C2×#11924005C2311yescharacteristic
281C2×#11924005C2311yescharacteristic
282C2×#11924005C2311yescharacteristic
283C2×#11924005C2311yescharacteristic
284C2×C4×Dic73C2311yescharacteristic
285C2×C4×Dic73C2311yescharacteristic
286C2×C4×Dic73C2311yescharacteristic
287C2×C4×Dic73C2311yescharacteristic
288C2×C4×Dic73C2311yescharacteristic
289C2×C4×Dic73C2311yescharacteristic
290C2×C4×Dic73C2311yescharacteristic
291C2×C4×Dic73C2311yescharacteristic
292C2×C4×Dic73C2311yescharacteristic
293C2×C4×Dic73C2311yescharacteristic
294C2×C4×Dic73C2311yescharacteristic
295C2×C4×Dic73C2311yescharacteristic
296C2×C4×Dic73C2311yescharacteristic
297C2×C4×Dic73C2311yescharacteristic
298C2×C4×Dic73C2311yescharacteristic
299C2×C4×Dic73C2311yescharacteristic
300C2×C4×Dic73C2311yescharacteristic
301C2×C4×Dic73C2311yescharacteristic
302#14556498C2311yescharacteristic
303#14556498C2311yescharacteristic
304#14556498C2311yescharacteristic
305#14556498C2311yescharacteristic
306#14556498C2311yescharacteristic
307#14556498C2311yescharacteristic
308#14556498C2311yescharacteristic
309#14556498C2311yescharacteristic
310#14556498C2311yescharacteristic
311#14556498C2311yescharacteristic
312#14556498C2311yescharacteristic
313#14556498C2311yescharacteristic
314#14556498C2311yescharacteristic
315#14556498C2311yescharacteristic
316#14556498C2311yescharacteristic
317#14556498C2311yescharacteristic
318#14556498C2311yescharacteristic
319#14556498C2311yescharacteristic
320#14556498C2311yescharacteristic
321#14556498C2311yescharacteristic
322#14556498C2311yescharacteristic
323#14556498C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330#14556498C2311yescharacteristic
331#14556498C2311yescharacteristic
332#14556498C2311yescharacteristic
333#14556498C2311yescharacteristic
334C25×C73C2311yescharacteristic
335C23×C4×C73—42no—
336C23×C4×C73—42no—
337C23×C4×C73—42no—
338C23×C4×C73C2311yescharacteristic
339C23×C4×C73C2311yescharacteristic
340C23×C4×C73C2311yescharacteristic
341C23×C4×C73C2311yescharacteristic
342C23×C4×C73C2311yescharacteristic
343C23×C4×C73C2311yescharacteristic
344C23×C4×C73C2311yescharacteristic
345C23×C4×C73C2311yescharacteristic
346C23×C4×C73C2311yescharacteristic
347C23×C4×C73C2311yescharacteristic
348C2×C4⋊C4×C73—42no—
349C2×C4⋊C4×C73—42no—
350C2×C4⋊C4×C73C2311yescharacteristic
351C2×C4⋊C4×C73C2311yescharacteristic
352C2×C4⋊C4×C73C2311yescharacteristic
353C2×C4⋊C4×C73C2311yescharacteristic
354C2×C4⋊C4×C73C2311yescharacteristic
355C2×C4⋊C4×C73C2311yescharacteristic
356C2×C4⋊C4×C73C2311yescharacteristic
357C2×C4⋊C4×C73C2311yescharacteristic
358C2×C22⋊C4×C73—42no—
359C2×C22⋊C4×C73C2×C418yescomplemented
360C2×C22⋊C4×C73C2311yescharacteristic
361C2×C22⋊C4×C73C2311yescharacteristic
362C2×C22⋊C4×C73C2311yescharacteristic
363C2×C22⋊C4×C73C2311yescharacteristic
364C2×C22⋊C4×C73C2311yescharacteristic
365C2×C22⋊C4×C73C2311yescharacteristic
366C2×C22⋊C4×C73C2311yescharacteristic
367C2×C22⋊C4×C73C2311yescharacteristic
368#95×C73C2311yescharacteristic
369#95×C73C2311yescharacteristic
370#95×C73C2311yescharacteristic
371#95×C73C2311yescharacteristic
372#95×C73C2311yescharacteristic
373#95×C73C2311yescharacteristic
374#95×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376C23×D73C2411yescharacteristic
377C23×D73C2411yescharacteristic
378C2×Dic146—41no—
379C2×Dic146—41no—
380C2×Dic146C22×C414yescomplemented
381C2×D292—41no—
382C2×D292—41no—
383C2×D292C22×C414yescomplemented
384C2×C22⋊D73—22no—
385C2×C22⋊D73—22no—
386C2×C22⋊D73—22no—
387C2×C22⋊D73—22no—
388C2×C22⋊D73—41no—
389C2×C22⋊D73—41no—
390C2×C22⋊D73—41no—
391C2×C22⋊D73—41no—
392C2×C22⋊D73—41no—
393C2×C22⋊D73—41no—
394C2×C22⋊D73—41no—
395C2×C22⋊D73—41no—
396C2×C22⋊D73C22×C414yes—
397C2×C22⋊D73C22×C414yes—
398C2×C22⋊D73C22×C414yes—
399C2×C22⋊D73C22×C414yes—
400C2×C22⋊D73C22×C414yes—
401C2×C22⋊D73C22×C414yes—
402C22×Dic73C2411yescharacteristic
403C22×Dic73C2411yescharacteristic
404C22×Dic73C2411yescharacteristic
405C22×Dic73C2411yescharacteristic
406C22×Dic73C2411yescharacteristic
407C22×Dic73C2411yescharacteristic
408C22×Dic73C2411yescharacteristic
409C22×Dic73C2411yescharacteristic
410C22×Dic73C2411yescharacteristic
411C22×Dic73C2411yescharacteristic
412C22×Dic73C2411yescharacteristic
413C22×Dic73C2411yescharacteristic
414C22×Dic73C2411yescharacteristic
415C22×Dic73C2411yescharacteristic
416C2×C4×D73—22no—
417C2×C4×D73—22no—
418C2×C4×D73—41no—
419C2×C4×D73—41no—
420C2×C4×D73—41no—
421C2×C4×D73—41no—
422C2×C4×D73—41no—
423C2×C4×D73—41no—
424C2×C4×D73—41no—
425C2×C4×D73—41no—
426C2×C4×D73—41no—
427C2×C4×D73—41no—
428C2×C4×D73—41no—
429C2×C4×D73—41no—
430C2×C4×D73—41no—
431C2×C4×D73—41no—
432C2×C4×D73C22×C414yescomplemented
433C2×C4×D73C22×C414yescomplemented
434C4⋊Dic73—41no—
435C4⋊Dic73—41no—
436C4⋊Dic73—41no—
437C4⋊Dic73—41no—
438C4⋊Dic73C22×C414yescomplemented
439C4⋊Dic73C22×C414yescomplemented
440#11924007—22no—
441#11924007—22no—
442#11924007—41no—
443#11924007—41no—
444#11924007—41no—
445#11924007—41no—
446#11924007—41no—
447#11924007—41no—
448#11924007—41no—
449#11924007—41no—
450#11924007—41no—
451#11924007—41no—
452#11924007C22×C414yescomplemented
453#11924007C22×C414yescomplemented
454#11924007C22×C414yescomplemented
455#11924007C22×C414yescomplemented
456C22⋊Dic73—22no—
457C22⋊Dic73—22no—
458C22⋊Dic73—22no—
459C22⋊Dic73—22no—
460C22⋊Dic73—41no—
461C22⋊Dic73—41no—
462C22⋊Dic73—41no—
463C22⋊Dic73—41no—
464C22⋊Dic73—41no—
465C22⋊Dic73—41no—
466C22⋊Dic73—41no—
467C22⋊Dic73—41no—
468C22⋊Dic73C22×C414yes—
469C22⋊Dic73C22×C414yes—
470C22⋊Dic73C22×C414yes—
471C22⋊Dic73C22×C414yes—
472C22⋊Dic73C22×C414yes—
473C22⋊Dic73C22×C414yes—
474#11924005—22no—
475#11924005—22no—
476#11924005—41no—
477#11924005—41no—
478#11924005—41no—
479#11924005—41no—
480#11924005—41no—
481#11924005—41no—
482#11924005—41no—
483#11924005—41no—
484#11924005—41no—
485#11924005—41no—
486#11924005C22×C414yescomplemented
487#11924005C22×C414yescomplemented
488#11924005C22×C414yescomplemented
489#11924005C22×C414yescomplemented
490C4×Dic73—22no—
491C4×Dic73—22no—
492C4×Dic73—41no—
493C4×Dic73—41no—
494C4×Dic73—41no—
495C4×Dic73—41no—
496C4×Dic73—41no—
497C4×Dic73—41no—
498C4×Dic73—41no—
499C4×Dic73—41no—
500C4×Dic73—41no—
501C4×Dic73—41no—
502C4×Dic73—41no—
503C4×Dic73—41no—
504C4×Dic73—41no—
505C4×Dic73—41no—
506C4×Dic73C22×C414yescomplemented
507C4×Dic73C22×C414yescomplemented
508C24×C73—22no—
509C24×C73—22no—
510C24×C73—41no—
511C24×C73—41no—
512C24×C73—41no—
513C24×C73—41no—
514C24×C73C22×C414yes—
515C24×C73C2411yescharacteristic
516C24×C73C2411yescharacteristic
517C24×C73C2411yescharacteristic
518C22×C4×C73—22no—
519C22×C4×C73—22no—
520C22×C4×C73—22no—
521C22×C4×C73—22no—
522C22×C4×C73—22no—
523C22×C4×C73—22no—
524C22×C4×C73—22no—
525C22×C4×C73—22no—
526C22×C4×C73—22no—
527C22×C4×C73—22no—
528C22×C4×C73—41no—
529C22×C4×C73—41no—
530C22×C4×C73—41no—
531C22×C4×C73—41no—
532C22×C4×C73—41no—
533C22×C4×C73—41no—
534C22×C4×C73—41no—
535C22×C4×C73—41no—
536C22×C4×C73—41no—
537C22×C4×C73—41no—
538C22×C4×C73—41no—
539C22×C4×C73—41no—
540C22×C4×C73—41no—
541C22×C4×C73—41no—
542C22×C4×C73—41no—
543C22×C4×C73—41no—
544C22×C4×C73—41no—
545C22×C4×C73—41no—
546C22×C4×C73—416no—
547C22×C4×C73C22×C414yes—
548C22×C4×C73C22×C414yes—
549C22×C4×C73C2411yescharacteristic
550C22×C4×C73C2411yescharacteristic
551C22×C4×C73C2411yescharacteristic
552C22×C4×C73C2411yescharacteristic
553C22×C4×C73C2411yescharacteristic
554C22×C4×C73C2411yescharacteristic
555C22×C4×C73C2411yescharacteristic
556C22×C4×C73C2411yescharacteristic
557C22×C4×C73C2411yescharacteristic
558C22×C4×C73C2411yescharacteristic
559C22×C4×C73C2411yescharacteristic
560C22×C4×C73C2411yescharacteristic
561C4⋊C4×C73—22no—
562C4⋊C4×C73—22no—
563C4⋊C4×C73—22no—
564C4⋊C4×C73—22no—
565C4⋊C4×C73—41no—
566C4⋊C4×C73—41no—
567C4⋊C4×C73—41no—
568C4⋊C4×C73—41no—
569C22⋊C4×C73—41no—
570C22⋊C4×C73—41no—
571C22⋊C4×C73—41no—
572C22⋊C4×C73—41no—
573C22⋊C4×C73C22×C414yes—
574C22⋊C4×C73C22×C414yes—
575C22⋊C4×C73C22×C414yes—
576C22⋊C4×C73C22×C414yes—
577C23×C73—21no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—28no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—21no—
587C23×C73—21no—
588C23×C73—21no—
589C23×C73—21no—
590C23×C73—21no—
591C23×C73—21no—
592C23×C73—21no—
593C23×C73—21no—
594C23×C73—44no—
595C23×C73—44no—
596C23×C73—44no—
597C23×C73—44no—
598C23×C73—44no—
599C23×C73—44no—
600C23×C73C23×C412yes—
601C23×C73C23×C412yes—
602C23×C73C23×C412yes—
603C23×C73H(5,𝔽2)12yes—
604C23×C732−1+412yes—
605C23×C73C2511yescharacteristic
606C22×D73—21no—
607C22×D73—21no—
608C22×D73—21no—
609C22×D73—21no—
610C22×D73—21no—
611C22×D73—21no—
612C22×D73—21no—
613C22×D73—21no—
614C22×D73—21no—
615C22×D73—21no—
616C22×D73—21no—
617C22×D73—21no—
618C22×D73C23×C412yes—
619C22×D73C23×C412yes—
620C2×C4×C73—21no—
621C2×C4×C73—21no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—44no—
651C2×C4×C73—44no—
652C2×C4×C73—44no—
653C2×C4×C73—44no—
654C2×C4×C73—44no—
655C2×C4×C73—44no—
656C2×C4×C73—44no—
657C2×C4×C73—44no—
658C2×C4×C73—82no—
659C2×C4×C73—82no—
660C2×C4×C73C23×C412yes—
661C2×C4×C73C23×C412yes—
662C2×C4×C73C23×C412yes—
663C2×C4×C73C23×C412yes—
664C2×C4×C73H(5,𝔽2)12yes—
665C2×C4×C73H(5,𝔽2)12yes—
666C22⋊D73—28no—
667C22⋊D73—28no—
668C22⋊D73—44no—
669C22⋊D73—44no—
670C22⋊D73—44no—
671C22⋊D73—44no—
672C2×Dic73—21no—
673C2×Dic73—21no—
674C2×Dic73—21no—
675C2×Dic73—21no—
676C2×Dic73—21no—
677C2×Dic73—21no—
678C2×Dic73—21no—
679C2×Dic73—21no—
680C2×Dic73—21no—
681C2×Dic73—21no—
682C2×Dic73—21no—
683C2×Dic73—21no—
684C2×Dic73—21no—
685C2×Dic73—21no—
686C2×Dic73—21no—
687C2×Dic73—21no—
688C2×Dic73—21no—
689C2×Dic73—21no—
690C2×Dic73—21no—
691C2×Dic73—21no—
692C2×Dic73—21no—
693C2×Dic73—21no—
694C2×Dic73—21no—
695C2×Dic73—21no—
696C2×Dic73—21no—
697C2×Dic73—21no—
698C2×Dic73—21no—
699C2×Dic73—21no—
700C2×Dic73—21no—
701C2×Dic73—21no—
702C2×Dic73—21no—
703C2×Dic73—21no—
704C2×Dic73—21no—
705C2×Dic73—21no—
706C2×Dic73—21no—
707C2×Dic73—21no—
708C2×Dic73C23×C412yes—
709C2×Dic73C23×C412yes—
710C2×Dic73C23×C412yes—
711C2×Dic73C23×C412yes—
712C2×Dic73C23×C412yes—
713C2×Dic73C23×C412yes—
714D292—44no—
715C4×D73—44no—
716C4×D73—44no—
717C4×D73—82no—
718C4×D73—82no—
719C4×D73—82no—
720C4×D73—82no—
721Dic146—44no—
722C22×C73—22no—
723C22×C73—22no—
724C22×C73—22no—
725C22×C73—22no—
726C22×C73—22no—
727C22×C73—22no—
728C22×C73—22no—
729C22×C73—22no—
730C22×C73—22no—
731C22×C73—22no—
732C22×C73—22no—
733C22×C73—22no—
734C22×C73—416no—
735C22×C73—41no—
736C22×C73—41no—
737C22×C73—41no—
738C22×C73—41no—
739C22×C73—41no—
740C22×C73—41no—
741C22×C73—41no—
742C22×C73—41no—
743C22×C73#52014yes—
744C22×C73C24×C411yescharacteristic
745C22×C73C2×H(5,𝔽2)11yescharacteristic
746C22×C73C2×H(5,𝔽2)11yescharacteristic
747C22×C73C2×H(5,𝔽2)11yescharacteristic
748C22×C73C2×2−1+411yescharacteristic
749C22×C73#58511yescharacteristic
750C22×C73#58511yescharacteristic
751C2×D73—22no—
752C2×D73—22no—
753C2×D73—22no—
754C2×D73—22no—
755C2×D73—22no—
756C2×D73—22no—
757C2×D73—41no—
758C2×D73—41no—
759C2×D73—41no—
760C2×D73—41no—
761C2×D73—41no—
762C2×D73—41no—
763C2×D73—41no—
764C2×D73—41no—
765C4×C73—22no—
766C4×C73—22no—
767C4×C73—22no—
768C4×C73—22no—
769C4×C73—22no—
770C4×C73—22no—
771C4×C73—41no—
772C4×C73—41no—
773C4×C73—41no—
774C4×C73—41no—
775C4×C73—41no—
776C4×C73—41no—
777Dic73—22no—
778Dic73—22no—
779Dic73—22no—
780Dic73—22no—
781Dic73—22no—
782Dic73—22no—
783Dic73—41no—
784Dic73—41no—
785Dic73—41no—
786Dic73—41no—
787Dic73—41no—
788Dic73—41no—
789Dic73—41no—
790Dic73—41no—
791#34416—731nomaximal, Sylow
792C2×C73—24no—
793C2×C73—42no—
794C2×C73—42no—
795C2×C73C2×#52011yescharacteristic
796C2×C73C4×H(5,𝔽2)11yescharacteristic
797C2×C73C4×H(5,𝔽2)11yescharacteristic
798C2×C73#353211yescharacteristic
799C2×C73#353311yescharacteristic
800C2×C73#354111yescharacteristic
801C2×C73#354111yescharacteristic
802D73—42no—
803D73—42no—
804C2×#538—731no—
805#2383—731no—
806#2379—731no—
807#2377—731no—
808#2376—731no—
809#2373—731no—
810#2368—731no—
811#2367—731no—
812#2364—731no—
813#2361—731no—
814#2361—731no—
815#2360—731no—
816#2359—731no—
817#2353—731no—
818#2352—731no—
819#2349—731no—
820D4×C4⋊C4—731no—
821#2337—731no—
822#2335—731no—
823#2334—731no—
824#2334—731no—
825#2326—731no—
826#2325—731no—
827#2324—731no—
828#2322—731no—
829#2321—731no—
830#2321—731no—
831#2312—731no—
832C4×#120—731no—
833C4×#120—731no—
834C2×#385D7311yescharacteristic, complemented
835C73#3441611yescharacteristic, complemented, Sylow
836C24×C4C2×D7311yescharacteristic
837#538—7316no—
838C2×#126—731no—
839C2×#126—731no—
840C2×#124—731no—
841C2×#124—731no—
842C2×#123—731no—
843C2×#123—731no—
844C2×C22⋊Q8—731no—
845C2×#121—731no—
846C2×#121—731no—
847C2×#121—731no—
848C2×#120—731no—
849C2×#120—731no—
850C2×C4×Q8—731no—
851C2×C4×D4—731no—
852C2×C4×D4—731no—
853C2×C4×D4—731no—
854C2×C4×D4—731no—
855C2×C4×D4—731no—
856C2×C4×D4—731no—
857C2×C4×D4—731no—
858C2×C4×D4—731no—
859C2×C4×D4—731no—
860C2×C4×D4—731no—
861C2×C4×D4—731no—
862C2×#117—731no—
863C22×C4⋊C4—731no—
864C22×C4⋊C4C2×D7311yescharacteristic
865C22×C4⋊C4C2×D7311yescharacteristic
866C22×C22⋊C4C2×D7311yescharacteristic
867C22×C22⋊C4C2×D7311yescharacteristic
868#391—731no—
869#391—731no—
870#391—731no—
871#390—731no—
872#390—731no—
873#390—731no—
874#390—731no—
875#390—731no—
876#389—731no—
877#389—731no—
878#389—731no—
879#389—731no—
880#389—731no—
881#389—731no—
882#389—731no—
883#389—731no—
884#388—731no—
885#388—731no—
886#388—731no—
887#388—731no—
888#388—731no—
889#388—731no—
890#388—731no—
891#388—731no—
892#388—731no—
893#388—731no—
894#388—731no—
895#388—731no—
896#388—731no—
897#388—731no—
898#388—731no—
899#388—731no—
900#388—731no—
901#388—731no—
902#388—731no—
903#388—731no—
904#388—731no—
905#388—731no—
906#388—731no—
907#388—731no—
908#387—731no—
909#387—731no—
910#387—731no—
911#387—731no—
912#387—731no—
913#387—731no—
914#387—731no—
915#387—731no—
916#387—731no—
917#387—731no—
918#387—731no—
919#387—731no—
920#386—731no—
921#386—731no—
922#386—731no—
923#386—731no—
924#386—731no—
925#386—731no—
926#386—731no—
927#386—731no—
928#386—731no—
929#386—731no—
930#386—731no—
931#386—731no—
932#386—731no—
933#386—731no—
934#385—731no—
935#385—731no—
936#385—731no—
937#385—731no—
938#385—731no—
939#385—731no—
940#385—731no—
941#385—731no—
942#385—731no—
943#385—731no—
944#385—731no—
945#385—731no—
946#385—731no—
947#385—731no—
948#385C2×D7311yescharacteristic
949#385C2×D7311yescharacteristic
950#385C2×D7311yescharacteristic
951#385C2×D7311yescharacteristic
952#385C2×D7311yescharacteristic
953#385C2×D7311yescharacteristic
954#385C2×D7311yescharacteristic
955#385C2×D7311yescharacteristic
956#384—731no—
957#383—731no—
958#382—731no—
959#382—731no—
960#381—731no—
961#380—731no—
962#380—731no—
963#380—731no—
964#380—731no—
965#380—731no—
966#379—731no—
967#379—731no—
968C4×C4⋊C4—731no—
969C4×C4⋊C4—731no—
970C4×C4⋊C4—731no—
971C4×C4⋊C4—731no—
972C4×C4⋊C4—731no—
973C4×C4⋊C4—731no—
974C4×C4⋊C4—731no—
975C4×C22⋊C4—731no—
976C4×C22⋊C4—731no—
977C4×C22⋊C4—731no—
978C4×C22⋊C4—731no—
979C4×C22⋊C4—731no—
980C4×C22⋊C4—731no—
981C4×C22⋊C4—731no—
982C4×C22⋊C4—731no—
983C4×C22⋊C4—731no—
984C4×C22⋊C4—731no—
985C4×C22⋊C4—731no—
986C4×C22⋊C4—731no—
987C4×C22⋊C4—731no—
988#376—731no—
989C2×#95—731no—
990C2×#95C2×D7311yescharacteristic
991C2×#95C2×D7311yescharacteristic
992C25C22×D7311yescharacteristic
993C22×Q8—731no—
994C22×D4—731no—
995C22×D4—731no—
996C22×D4—731no—
997C22×D4—731no—
998C22×D4—731no—
999C22×D4—731no—
1000C22×D4—731no—
1001C23×C4—42no—
1002C23×C4—42no—
1003C23×C4—42no—
1004C23×C4—731no—
1005C23×C4—731no—
1006C23×C4—731no—
1007C23×C4—731no—
1008C23×C4—731no—
1009C23×C4—731no—
1010C23×C4C22×D7311yescharacteristic
1011C23×C4C22×D7311yescharacteristic
1012C23×C4C22×D7311yescharacteristic
1013C23×C4C22×D7311yescharacteristic
1014C23×C4C22×D7311yescharacteristic
1015C23×C4C22×D7311yescharacteristic
1016C23×C4C22×D7311yescharacteristic
1017C23×C4C22×D7311yescharacteristic
1018C23×C4C22×D7311yescharacteristic
1019C23×C4C22×D7311yescharacteristic
1020#126—738no—
1021#126—738no—
1022#124—738no—
1023#124—738no—
1024#123—738no—
1025#123—738no—
1026C22⋊Q8—738no—
1027#121—738no—
1028#121—738no—
1029#121—738no—
1030#120—738no—
1031#120—738no—
1032C4×Q8—2922no—
1033C4×D4—2922no—
1034C4×D4—2922no—
1035C4×D4—2922no—
1036C4×D4—2922no—
1037C4×D4—2922no—
1038C4×D4—2922no—
1039C4×D4—2922no—
1040C4×D4—2922no—
1041C4×D4—2922no—
1042C4×D4—738no—
1043C4×D4—738no—
1044#117—2922no—
1045C2×C4⋊C4—42no—
1046C2×C4⋊C4—42no—
1047C2×C4⋊C4—2922no—
1048C2×C4⋊C4—731no—
1049C2×C4⋊C4—731no—
1050C2×C4⋊C4—731no—
1051C2×C4⋊C4—731no—
1052C2×C4⋊C4—731no—
1053C2×C4⋊C4—731no—
1054C2×C4⋊C4—731no—
1055C2×C4⋊C4—731no—
1056C2×C4⋊C4—731no—
1057C2×C4⋊C4—731no—
1058C2×C4⋊C4—731no—
1059C2×C4⋊C4—731no—
1060C2×C4⋊C4—731no—
1061C2×C4⋊C4—731no—
1062C2×C4⋊C4—731no—
1063C2×C4⋊C4—731no—
1064C2×C4⋊C4—731no—
1065C2×C4⋊C4—731no—
1066C2×C4⋊C4—731no—
1067C2×C4⋊C4—731no—
1068C2×C4⋊C4—731no—
1069C2×C4⋊C4—731no—
1070C2×C4⋊C4C22×D7311yescharacteristic
1071C2×C4⋊C4C22×D7311yescharacteristic
1072C2×C4⋊C4C22×D7311yescharacteristic
1073C2×C4⋊C4C22×D7311yescharacteristic
1074C2×C4⋊C4C22×D7311yescharacteristic
1075C2×C4⋊C4C22×D7311yescharacteristic
1076C2×C4⋊C4C22×D7311yescharacteristic
1077C2×C4⋊C4C22×D7311yescharacteristic
1078C2×C22⋊C4—42no—
1079C2×C22⋊C4—731no—
1080C2×C22⋊C4—731no—
1081C2×C22⋊C4—731no—
1082C2×C22⋊C4—731no—
1083C2×C22⋊C4—731no—
1084C2×C22⋊C4—731no—
1085C2×C22⋊C4—731no—
1086C2×C22⋊C4—731no—
1087C2×C22⋊C4—731no—
1088C2×C22⋊C4—731no—
1089C2×C22⋊C4—731no—
1090C2×C22⋊C4—731no—
1091C2×C22⋊C4—731no—
1092C2×C22⋊C4—731no—
1093C2×C22⋊C4—731no—
1094C2×C22⋊C4—731no—
1095C2×C22⋊C4—731no—
1096C2×C22⋊C4—731no—
1097C2×C22⋊C4—731no—
1098C2×C22⋊C4—731no—
1099C2×C22⋊C4—731no—
1100C2×C22⋊C4—731no—
1101C2×C22⋊C4—731no—
1102C2×C22⋊C4—731no—
1103C2×C22⋊C4—731no—
1104C2×C22⋊C4—731no—
1105C2×C22⋊C4—731no—
1106C2×C22⋊C4—731no—
1107C2×C22⋊C4—731no—
1108C2×C22⋊C4—731no—
1109C2×C22⋊C4—731no—
1110C2×C22⋊C4—731no—
1111C2×C22⋊C4—731no—
1112C2×C22⋊C4—731no—
1113C2×C22⋊C4C4×D7318yescomplemented
1114C2×C22⋊C4C22×D7311yescharacteristic
1115C2×C22⋊C4C22×D7311yescharacteristic
1116C2×C22⋊C4C22×D7311yescharacteristic
1117C2×C22⋊C4C22×D7311yescharacteristic
1118C2×C22⋊C4C22×D7311yescharacteristic
1119C2×C22⋊C4C22×D7311yescharacteristic
1120C2×C22⋊C4C22×D7311yescharacteristic
1121C2×C22⋊C4C22×D7311yescharacteristic
1122C2×C42—731no—
1123C2×C42—731no—
1124C2×C42—731no—
1125C2×C42—731no—
1126C2×C42—731no—
1127C2×C42—731no—
1128C2×C42—731no—
1129C2×C42—731no—
1130C2×C42—731no—
1131C2×C42—731no—
1132C2×C42—731no—
1133C2×C42—731no—
1134C2×C42—731no—
1135C2×C42—731no—
1136C2×C42—731no—
1137C2×C42—731no—
1138C2×C42—731no—
1139C2×C42—731no—
1140#95—731no—
1141#95—731no—
1142#95—731no—
1143#95—731no—
1144#95—731no—
1145#95—731no—
1146#95—731no—
1147#95—731no—
1148#95—731no—
1149#95—731no—
1150#95—731no—
1151#95—731no—
1152#95—731no—
1153#95—731no—
1154#95—731no—
1155#95—731no—
1156#95—731no—
1157#95—731no—
1158#95—731no—
1159#95—731no—
1160#95—731no—
1161#95—731no—
1162#95—731no—
1163#95—731no—
1164#95—731no—
1165#95—731no—
1166#95—731no—
1167#95—731no—
1168#95—731no—
1169#95—731no—
1170#95—731no—
1171#95—731no—
1172#95C22×D7311yescharacteristic
1173#95C22×D7311yescharacteristic
1174#95C22×D7311yescharacteristic
1175#95C22×D7311yescharacteristic
1176#95C22×D7311yescharacteristic
1177#95C22×D7311yescharacteristic
1178#95C22×D7311yescharacteristic
1179#95C22×D7311yescharacteristic
1180C24—22no—
1181C24—22no—
1182C24—41no—
1183C24—41no—
1184C24—41no—
1185C24—41no—
1186C24—731no—
1187C24—731no—
1188C24C2×C4×D7314yes—
1189C24C23×D7311yescharacteristic
1190C24C23×D7311yescharacteristic
1191C24C23×D7311yescharacteristic
1192C2×Q8—2921no—
1193C2×Q8—2921no—
1194C2×Q8—734no—
1195C2×D4—2921no—
1196C2×D4—2921no—
1197C2×D4—2921no—
1198C2×D4—2921no—
1199C2×D4—2921no—
1200C2×D4—2921no—
1201C2×D4—2921no—
1202C2×D4—2921no—
1203C2×D4—2921no—
1204C2×D4—2921no—
1205C2×D4—734no—
1206C2×D4—734no—
1207C2×D4—734no—
1208C2×D4—734no—
1209C2×D4—734no—
1210C2×D4—734no—
1211C2×D4—734no—
1212C2×D4—1462no—
1213C2×D4—1462no—
1214C2×D4—1462no—
1215C2×D4—1462no—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—22no—
1221C22×C4—22no—
1222C22×C4—22no—
1223C22×C4—22no—
1224C22×C4—22no—
1225C22×C4—22no—
1226C22×C4—41no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—41no—
1232C22×C4—41no—
1233C22×C4—41no—
1234C22×C4—41no—
1235C22×C4—41no—
1236C22×C4—41no—
1237C22×C4—41no—
1238C22×C4—41no—
1239C22×C4—41no—
1240C22×C4—41no—
1241C22×C4—41no—
1242C22×C4—41no—
1243C22×C4—41no—
1244C22×C4—416no—
1245C22×C4—2921no—
1246C22×C4—2921no—
1247C22×C4—2921no—
1248C22×C4—2921no—
1249C22×C4—2921no—
1250C22×C4—2921no—
1251C22×C4—2921no—
1252C22×C4—2921no—
1253C22×C4—2921no—
1254C22×C4—2921no—
1255C22×C4—2921no—
1256C22×C4—2921no—
1257C22×C4—2921no—
1258C22×C4—2921no—
1259C22×C4—734no—
1260C22×C4—734no—
1261C22×C4—731no—
1262C22×C4—731no—
1263C22×C4—731no—
1264C22×C4—731no—
1265C22×C4—731no—
1266C22×C4—731no—
1267C22×C4—731no—
1268C22×C4—731no—
1269C22×C4—731no—
1270C22×C4—731no—
1271C22×C4—731no—
1272C22×C4—731no—
1273C22×C4—731no—
1274C22×C4—731no—
1275C22×C4—1462no—
1276C22×C4—1462no—
1277C22×C4C2×C4×D7314yes—
1278C22×C4C2×C4×D7314yes—
1279C22×C4C23×D7311yescharacteristic
1280C22×C4C23×D7311yescharacteristic
1281C22×C4C23×D7311yescharacteristic
1282C22×C4C23×D7311yescharacteristic
1283C22×C4C23×D7311yescharacteristic
1284C22×C4C23×D7311yescharacteristic
1285C22×C4C23×D7311yescharacteristic
1286C22×C4C23×D7311yescharacteristic
1287C22×C4C23×D7311yescharacteristic
1288C22×C4C23×D7311yescharacteristic
1289C22×C4C23×D7311yescharacteristic
1290C22×C4C23×D7311yescharacteristic
1291C4⋊C4—22no—
1292C4⋊C4—22no—
1293C4⋊C4—22no—
1294C4⋊C4—22no—
1295C4⋊C4—41no—
1296C4⋊C4—41no—
1297C4⋊C4—41no—
1298C4⋊C4—41no—
1299C4⋊C4—2921no—
1300C4⋊C4—2921no—
1301C4⋊C4—2921no—
1302C4⋊C4—2921no—
1303C4⋊C4—2921no—
1304C4⋊C4—2921no—
1305C4⋊C4—2921no—
1306C4⋊C4—2921no—
1307C4⋊C4—2921no—
1308C4⋊C4—2921no—
1309C4⋊C4—2921no—
1310C4⋊C4—2921no—
1311C4⋊C4—2921no—
1312C4⋊C4—2921no—
1313C4⋊C4—734no—
1314C4⋊C4—734no—
1315C4⋊C4—734no—
1316C4⋊C4—734no—
1317C4⋊C4—734no—
1318C4⋊C4—734no—
1319C4⋊C4—1462no—
1320C4⋊C4—1462no—
1321C22⋊C4—41no—
1322C22⋊C4—41no—
1323C22⋊C4—41no—
1324C22⋊C4—41no—
1325C22⋊C4—2921no—
1326C22⋊C4—2921no—
1327C22⋊C4—2921no—
1328C22⋊C4—2921no—
1329C22⋊C4—2921no—
1330C22⋊C4—2921no—
1331C22⋊C4—2921no—
1332C22⋊C4—2921no—
1333C22⋊C4—2921no—
1334C22⋊C4—2921no—
1335C22⋊C4—2921no—
1336C22⋊C4—2921no—
1337C22⋊C4—2921no—
1338C22⋊C4—2921no—
1339C22⋊C4—2921no—
1340C22⋊C4—2921no—
1341C22⋊C4—2921no—
1342C22⋊C4—2921no—
1343C22⋊C4—734no—
1344C22⋊C4—734no—
1345C22⋊C4—734no—
1346C22⋊C4—734no—
1347C22⋊C4—734no—
1348C22⋊C4—734no—
1349C22⋊C4—734no—
1350C22⋊C4—734no—
1351C22⋊C4—734no—
1352C22⋊C4—734no—
1353C22⋊C4—1462no—
1354C22⋊C4—1462no—
1355C22⋊C4—1462no—
1356C22⋊C4—1462no—
1357C22⋊C4—1462no—
1358C22⋊C4—1462no—
1359C22⋊C4C2×C4×D7314yes—
1360C22⋊C4C2×C4×D7314yes—
1361C22⋊C4C2×C4×D7314yes—
1362C22⋊C4C2×C4×D7314yes—
1363C42—2921no—
1364C42—2921no—
1365C42—2921no—
1366C42—2921no—
1367C42—2921no—
1368C42—2921no—
1369C42—2921no—
1370C42—2921no—
1371C42—2921no—
1372C42—2921no—
1373C42—2921no—
1374C42—2921no—
1375C42—2921no—
1376C42—2921no—
1377C42—734no—
1378C42—734no—
1379C42—1462no—
1380C42—1462no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—28no—
1398C23—44no—
1399C23—44no—
1400C23—44no—
1401C23—44no—
1402C23—44no—
1403C23—44no—
1404C23—732no—
1405C23—732no—
1406C23—1461no—
1407C23—1461no—
1408C23—1461no—
1409C23—1461no—
1410C23—1461no—
1411C23—1461no—
1412C23—1461no—
1413C23—1461no—
1414C23—1461no—
1415C23—1461no—
1416C23—1461no—
1417C23—1461no—
1418C23C22×C4×D7312yes—
1419C23C22×C4×D7312yes—
1420C23C22×C4×D7312yes—
1421C23#1455663612yes—
1422C23#1455663912yes—
1423C23C24×D7311yescharacteristic
1424Q8—2924no—
1425D4—2924no—
1426D4—2924no—
1427D4—2924no—
1428D4—2924no—
1429D4—2924no—
1430D4—1468no—
1431D4—1468no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—44no—
1463C2×C4—44no—
1464C2×C4—44no—
1465C2×C4—44no—
1466C2×C4—44no—
1467C2×C4—44no—
1468C2×C4—44no—
1469C2×C4—44no—
1470C2×C4—82no—
1471C2×C4—82no—
1472C2×C4—2924no—
1473C2×C4—2924no—
1474C2×C4—5842no—
1475C2×C4—5842no—
1476C2×C4—5842no—
1477C2×C4—5842no—
1478C2×C4—732no—
1479C2×C4—732no—
1480C2×C4—732no—
1481C2×C4—732no—
1482C2×C4—732no—
1483C2×C4—732no—
1484C2×C4—1461no—
1485C2×C4—1461no—
1486C2×C4—1461no—
1487C2×C4—1461no—
1488C2×C4—1461no—
1489C2×C4—1461no—
1490C2×C4—1461no—
1491C2×C4—1461no—
1492C2×C4—1461no—
1493C2×C4—1461no—
1494C2×C4—1461no—
1495C2×C4—1461no—
1496C2×C4—1461no—
1497C2×C4—1461no—
1498C2×C4—1461no—
1499C2×C4—1461no—
1500C2×C4—1461no—
1501C2×C4—1461no—
1502C2×C4—1461no—
1503C2×C4—1461no—
1504C2×C4—1461no—
1505C2×C4—1461no—
1506C2×C4—1461no—
1507C2×C4—1461no—
1508C2×C4—1461no—
1509C2×C4—1461no—
1510C2×C4—1461no—
1511C2×C4—1461no—
1512C2×C4—1461no—
1513C2×C4—1461no—
1514C2×C4—1461no—
1515C2×C4—1461no—
1516C2×C4—1461no—
1517C2×C4—1461no—
1518C2×C4—1461no—
1519C2×C4—1461no—
1520C2×C4C22×C4×D7312yes—
1521C2×C4C22×C4×D7312yes—
1522C2×C4C22×C4×D7312yes—
1523C2×C4C22×C4×D7312yes—
1524C2×C4#1455663612yes—
1525C2×C4#1455663612yes—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—22no—
1534C22—22no—
1535C22—22no—
1536C22—22no—
1537C22—22no—
1538C22—416no—
1539C22—41no—
1540C22—41no—
1541C22—41no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—2921no—
1548C22—2921no—
1549C22—2921no—
1550C22—2921no—
1551C22—2921no—
1552C22—2921no—
1553C22—2921no—
1554C22—2921no—
1555C22—1462no—
1556C22—1462no—
1557C22—1462no—
1558C22—1462no—
1559C22—1462no—
1560C22—1462no—
1561C22#1798906814yes—
1562C22C23×C4×D7311yescharacteristic
1563C22C2×#1455663611yescharacteristic
1564C22C2×#1455663611yescharacteristic
1565C22C2×#1455663611yescharacteristic
1566C22C2×#1455663911yescharacteristic
1567C22#1798942311yescharacteristic
1568C22#1798942311yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—22no—
1574C4—22no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—41no—
1581C4—2921no—
1582C4—2921no—
1583C4—2921no—
1584C4—2921no—
1585C4—2921no—
1586C4—2921no—
1587C4—2921no—
1588C4—2921no—
1589C4—1462no—
1590C4—1462no—
1591C4—1462no—
1592C4—1462no—
1593C4—1462no—
1594C4—1462no—
1595C2—24no—
1596C2—42no—
1597C2—42no—
1598C2—2922no—
1599C2—2922no—
1600C2C2×#1798906811yescharacteristic
1601C2C4×#1455663611yescharacteristic
1602C2C4×#1455663611yescharacteristic
1603C2#2262408611yescharacteristic
1604C2#2262410211yescharacteristic
1605C2#2262422811yescharacteristic
1606C2#2262422811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC2×#385×C73C2
socle, cosocleC23×C73C25
prime radicalC2×#17989175C2
hypercenterC2×#385D73
hypocenterC73#34416
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#385

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22613119C2semidirect
3. #22613104C2semidirect
4. #22613087C2semidirect
5. #22613080C2semidirect
6. #22613046C2semidirect
7. #22613011C2semidirect
8. #22612999C2semidirect
9. #22612978C2semidirect
10. #22612950C2semidirect
11. #22612947C2semidirect
12. #22612936C2semidirect
13. #22612926C2semidirect
14. #22612867C2semidirect
15. #22612856C2semidirect
16. #22612838C2semidirect
17. C4⋊C4×C22⋊D73C2semidirect
18. #22612745C2semidirect
19. #22612716C2semidirect
20. #22612707C2semidirect
21. #22612701C2semidirect
22. #22612637C2semidirect
23. #22612628C2semidirect
24. #22612623C2semidirect
25. #22612598C2semidirect
26. #22612589C2semidirect
27. #22612589C2semidirect
28. #22612529C2semidirect
29. C4×#14556560C2semidirect
30. C4×#14556560C2semidirect
31. C2×#385×C73C2semidirect
32. #17989175C4semidirect
45. C2×#14556556C22semidirect
46. C2×#14556553C22semidirect
57. C2×#14556549C22semidirect
58. C2×C4⋊C4×D73C22semidirect
59. #17988492C22semidirect
60. #17988491C22semidirect
61. #17988491C22semidirect
62. #17988488C22semidirect
67. #17988484C22semidirect
68. #17988484C22semidirect
69. #17988483C22semidirect
70. #17988483C22semidirect
71. #17988482C22semidirect
72. #17988482C22semidirect
73. #17988482C22semidirect
74. #17988482C22semidirect
87. #17988479C22semidirect
88. #17988479C22semidirect
89. #17988477C22semidirect
90. #17988477C22semidirect
91. #17988477C22semidirect
92. #17988477C22semidirect
93. #17988476C22semidirect
94. #17988476C22semidirect
99. #17988474C22semidirect
100. #17988474C22semidirect
101. #17988472C22semidirect
102. #17988472C22semidirect
103. #17988470C22semidirect
104. #17988470C22semidirect
105. #17988469C22semidirect
106. #17988469C22semidirect
107. #17988468C22semidirect
108. #17988468C22semidirect
109. #17988468C22semidirect
110. #17988468C22semidirect
119. #17988465C22semidirect
120. #17988465C22semidirect
125. #17988461C22semidirect
126. #17988461C22semidirect
135. #17988458C22semidirect
136. #17988458C22semidirect
137. #17988458C22semidirect
138. #17988458C22semidirect
139. #17988456C22semidirect
140. #17988454C22semidirect
141. #17988452C22semidirect
142. #17988451C22semidirect
143. #17988449C22semidirect
146. #17988446C22semidirect
147. #17988444C22semidirect
148. #17988444C22semidirect
151. C4⋊C4×Dic73C22semidirect
152. C4⋊C4×Dic73C22semidirect
153. C4⋊C4×Dic73C22semidirect
154. C4⋊C4×Dic73C22semidirect
155. #17988438C22semidirect
156. #17988438C22semidirect
157. #17988438C22semidirect
168. #17988434C22semidirect
169. #17988434C22semidirect
170. #17988434C22semidirect
171. #17988432C22semidirect
172. #95×D73C22semidirect
202. #14556584C2×C4semidirect
203. #14556584C2×C4semidirect
204. #14556577C2×C4semidirect
205. #14556577C2×C4semidirect
206. #14556573C2×C4semidirect
207. #14556573C2×C4semidirect
208. #14556570C2×C4semidirect
209. #14556565C2×C4semidirect
210. #14556564C2×C4semidirect
211. #14556564C2×C4semidirect
212. #14556560C2×C4semidirect
213. #14556560C2×C4semidirect
224. C4×C22⋊D73C2×C4semidirect
225. C4×C22⋊D73C2×C4semidirect
359. C2×C22⋊C4×C73C2×C4semidirect
380. C2×Dic146C22×C4semidirect
383. C2×D292C22×C4semidirect
432. C2×C4×D73C22×C4semidirect
433. C2×C4×D73C22×C4semidirect
438. C4⋊Dic73C22×C4semidirect
439. C4⋊Dic73C22×C4semidirect
452. #11924007C22×C4semidirect
453. #11924007C22×C4semidirect
454. #11924007C22×C4semidirect
455. #11924007C22×C4semidirect
486. #11924005C22×C4semidirect
487. #11924005C22×C4semidirect
488. #11924005C22×C4semidirect
489. #11924005C22×C4semidirect
506. C4×Dic73C22×C4semidirect
507. C4×Dic73C22×C4semidirect
834. C2×#385D73semidirect
835. C73#34416semidirect
1113. C2×C22⋊C4C4×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179891752
#226131192
#226131042
#226130872
#226130802
#226130462
#226130112
#226129992
#226129782
#226129502
#226129472
#226129362
#226129262
#226128672
#226128562
#226128382
C4⋊C4×C22⋊D732
#226127452
#226127162
#226127072
#226127012
#226126372
#226126282
#226126232
#226125982
#226125892
#226125292
C4×#145565602
C2×#385×C732
#3441673