Finite Group Databasebeta

← #33250366

Subgroups — #33250366

Order 18688.

2314 conjugacy classes of subgroups.

The subgroup lattice has 1570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989172C211yesmaximal, characteristic
2#22613119C211yesmaximal, characteristic, complemented
3#22613098C211yesmaximal, characteristic, complemented
4#22613073C211yesmaximal, characteristic, complemented
5#22613070C211yesmaximal, characteristic, complemented
6#22613058C211yesmaximal, characteristic, complemented
7#22613052C211yesmaximal, characteristic, complemented
8#22613048C211yesmaximal, characteristic, complemented
9#22613039C211yesmaximal, characteristic, complemented
10#22612999C211yesmaximal, characteristic, complemented
11#22612955C211yesmaximal, characteristic, complemented
12#22612920C211yesmaximal, characteristic, complemented
13#22612910C211yesmaximal, characteristic, complemented
14#22612877C211yesmaximal, characteristic, complemented
15#22612866C211yesmaximal, characteristic, complemented
16#22612782C211yesmaximal, characteristic, complemented
17#22612776C211yesmaximal, characteristic, complemented
18#22612740C211yesmaximal, characteristic, complemented
19#22612722C211yesmaximal, characteristic, complemented
20#22612697C211yesmaximal, characteristic, complemented
21#22612690C211yesmaximal, characteristic, complemented
22#22612641C211yesmaximal, characteristic, complemented
23#22612633C211yesmaximal, characteristic, complemented
24#22612618C211yesmaximal, characteristic, complemented
25#22612617C211yesmaximal, characteristic, complemented
26#22612592C211yesmaximal, characteristic, complemented
27#22612568C211yesmaximal, characteristic, complemented
28C4×#14556572C211yesmaximal, characteristic, complemented
29#22612441C211yesmaximal, characteristic, complemented
30#22612371C211yesmaximal, characteristic, complemented
31C73×#2321C211yesmaximal, characteristic, complemented
32#17989172C4116yescomplemented
33C2×#14556584C2211yescharacteristic
34C2×#14556584C2211yescharacteristic
35C2×#14556578C2211yescharacteristic
36C2×#14556577C2211yescharacteristic
37C2×#14556573C2211yescharacteristic
38C2×#14556572C2211yescharacteristic
39C2×#14556568C2211yescharacteristic
40C2×#14556563C2211yescharacteristic
41C2×#14556563C2211yescharacteristic
42C2×#14556562C2211yescharacteristic
43C2×#14556560C2211yescharacteristic
44C2×#14556556C2211yescharacteristic, complemented
45C2×D4×Dic73C2211yescharacteristic
46C2×D4×Dic73C2211yescharacteristic
47C2×C4×C22⋊D73C2211yescharacteristic
48C2×#14556551C2211yescharacteristic
49C2×#14556551C2211yescharacteristic
50C2×#14556551C2211yescharacteristic, complemented
51C2×#14556548C2211yescharacteristic, complemented
52C2×#14556547C2211yescharacteristic
53C2×#14556547C2211yescharacteristic
54C22×C22⋊Dic73C2211yescharacteristic
55C22×C22⋊Dic73C2211yescharacteristic
56C22×C4×Dic73C2211yescharacteristic, complemented
57#17988493C2211yescharacteristic, complemented
58#17988491C2211yescharacteristic, complemented
59#17988491C2211yescharacteristic, complemented
60#17988490C2211yescharacteristic
61#17988490C2211yescharacteristic
62#17988487C2211yescharacteristic
63#17988487C2211yescharacteristic
64#17988487C2211yescharacteristic
65#17988487C2211yescharacteristic
66#17988487C2211yescharacteristic, complemented
67#17988485C2211yescharacteristic, complemented
68#17988484C2211yescharacteristic, complemented
69#17988484C2211yescharacteristic, complemented
70#17988483C2211yescharacteristic, complemented
71#17988483C2211yescharacteristic, complemented
72#17988482C2211yescharacteristic, complemented
73#17988481C2211yescharacteristic
74#17988481C2211yescharacteristic
75#17988481C2211yescharacteristic
76#17988481C2211yescharacteristic
77#17988481C2211yescharacteristic
78#17988481C2211yescharacteristic
79#17988481C2211yescharacteristic
80#17988481C2211yescharacteristic
81#17988481C2211yescharacteristic, complemented
82#17988481C2211yescharacteristic, complemented
83#17988481C2211yescharacteristic, complemented
84#17988480C2211yescharacteristic
85#17988480C2211yescharacteristic
86#17988480C2211yescharacteristic
87#17988480C2211yescharacteristic
88#17988479C2211yescharacteristic, complemented
89#17988479C2211yescharacteristic, complemented
90#17988478C2211yescharacteristic, complemented
91#17988477C2211yescharacteristic, complemented
92#17988475C2211yescharacteristic
93#17988475C2211yescharacteristic
94#17988475C2211yescharacteristic
95#17988475C2211yescharacteristic
96#17988475C2211yescharacteristic
97#17988475C2211yescharacteristic
98#17988475C2211yescharacteristic
99#17988475C2211yescharacteristic
100#17988475C2211yescharacteristic, complemented
101#17988474C2211yescharacteristic, complemented
102#17988474C2211yescharacteristic, complemented
103#17988472C2211yescharacteristic, complemented
104#17988472C2211yescharacteristic, complemented
105#17988471C2211yescharacteristic, complemented
106#17988470C2211yescharacteristic, complemented
107#17988470C2211yescharacteristic, complemented
108#17988469C2211yescharacteristic, complemented
109#17988469C2211yescharacteristic, complemented
110#17988468C2211yescharacteristic, complemented
111#17988468C2211yescharacteristic, complemented
112#17988468C2211yescharacteristic, complemented
113#17988467C2211yescharacteristic
114#17988467C2211yescharacteristic
115#17988467C2211yescharacteristic
116#17988466C2211yescharacteristic
117#17988466C2211yescharacteristic, complemented
118#17988464C2211yescharacteristic
119#17988463C2211yescharacteristic
120#17988463C2211yescharacteristic
121#17988463C2211yescharacteristic
122#17988463C2211yescharacteristic
123#17988463C2211yescharacteristic, complemented
124#17988462C2211yescharacteristic
125#17988460C2211yescharacteristic
126#17988460C2211yescharacteristic
127#17988460C2211yescharacteristic
128#17988460C2211yescharacteristic, complemented
129#17988459C2211yescharacteristic
130#17988459C2211yescharacteristic
131#17988459C2211yescharacteristic
132#17988459C2211yescharacteristic, complemented
133#17988459C2211yescharacteristic, complemented
134#17988458C2211yescharacteristic, complemented
135#17988456C2211yescharacteristic, complemented
136#17988454C2211yescharacteristic, complemented
137#17988448C2211yescharacteristic
138#17988448C2211yescharacteristic
139#17988448C2211yescharacteristic, complemented
140#17988446C2211yescharacteristic, complemented
141#17988445C2211yescharacteristic
142#17988445C2211yescharacteristic
143#17988445C2211yescharacteristic, complemented
144#17988444C2211yescharacteristic, complemented
145#17988443C2211yescharacteristic
146C4⋊C4×Dic73C2211yescharacteristic, complemented
147C4×#11924007C2211yescharacteristic, complemented
148C4×#11924007C2211yescharacteristic, complemented
149C4×#11924007C2211yescharacteristic, complemented
150C4×C4⋊Dic73C2211yescharacteristic, complemented
151#17988438C2211yescharacteristic, complemented
152#17988438C2211yescharacteristic, complemented
153#17988438C2211yescharacteristic, complemented
154#17988438C2211yescharacteristic, complemented
155C22⋊C4×Dic73C2211yescharacteristic
156C22⋊C4×Dic73C2211yescharacteristic
157C22⋊C4×Dic73C2211yescharacteristic
158C22⋊C4×Dic73C2211yescharacteristic
159C22⋊C4×Dic73C2211yescharacteristic
160C22⋊C4×Dic73C2211yescharacteristic
161C22⋊C4×Dic73C2211yescharacteristic, complemented
162C4×#11924005C2211yescharacteristic, complemented
163C4×C22⋊Dic73C2211yescharacteristic
164C4×C22⋊Dic73C2211yescharacteristic
165C4×C22⋊Dic73C2211yescharacteristic
166C4×C22⋊Dic73C2211yescharacteristic, complemented
167#17988434C2211yescharacteristic, complemented
168#17988434C2211yescharacteristic, complemented
169#17988433C2211yescharacteristic, complemented
170#17988433C2211yescharacteristic, complemented
171#17988432C2211yescharacteristic, complemented
172#95×D73C2211yescharacteristic, complemented
173C2×#120×C73C2211yescharacteristic
174C2×C4×D4×C73C2211yescharacteristic
175C22×C22⋊C4×C73C2211yescharacteristic
176#390×C73C2211yescharacteristic
177#390×C73C2211yescharacteristic
178#388×C73C2211yescharacteristic
179#388×C73C2211yescharacteristic
180#388×C73C2211yescharacteristic
181#388×C73C2211yescharacteristic
182#386×C73C2211yescharacteristic
183#386×C73C2211yescharacteristic
184#386×C73C2211yescharacteristic
185#385×C73C2211yescharacteristic
186#379×C73C2211yescharacteristic
187C4×C22⋊C4×C73C2211yescharacteristic
188C22×Dic146C2311yescharacteristic
189C22×C22⋊D73C2311yescharacteristic
190C22×C22⋊D73C2311yescharacteristic
191C22×C22⋊D73C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C23×Dic73C2311yescharacteristic
194C23×Dic73C2311yescharacteristic
195C23×Dic73C2311yescharacteristic
196C23×Dic73C2311yescharacteristic
197C23×Dic73C2311yescharacteristic
198C23×Dic73C2311yescharacteristic
199C22×C4×D73C2311yescharacteristic
200C22×C4×D73C2311yescharacteristic
201C22×C4×D73C2311yescharacteristic
202#14556584C2×C418yescomplemented
203#14556584C2×C418yescomplemented
204#14556578C2×C418yescomplemented
205#14556577C2×C418yescomplemented
206#14556573C2×C418yescomplemented
207#14556572C2×C418yescomplemented
208#14556568C2×C418yescomplemented
209#14556563C2×C418yescomplemented
210#14556563C2×C418yescomplemented
211#14556562C2×C418yescomplemented
212#14556560C2×C418yescomplemented
213#14556556—42no—
214D4×Dic73—42no—
215D4×Dic73C2×C418yescomplemented
216C4×C22⋊D73—42no—
217#14556551—42no—
218#14556551—42no—
219#14556551C2×C418yescomplemented
220#14556548—42no—
221#14556547—42no—
222#14556547—42no—
223C2×C4⋊Dic73C2311yescharacteristic
224C2×C4⋊Dic73C2311yescharacteristic
225C2×C4⋊Dic73C2311yescharacteristic
226C2×C4⋊Dic73C2311yescharacteristic
227C2×C4⋊Dic73C2311yescharacteristic
228C2×#11924007C2311yescharacteristic
229C2×#11924007C2311yescharacteristic
230C2×#11924007C2311yescharacteristic
231C2×#11924007C2311yescharacteristic
232C2×#11924007C2311yescharacteristic
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×C22⋊Dic73—42no—
247C2×C22⋊Dic73C2×C418yescomplemented
248C2×C22⋊Dic73C2311yescharacteristic
249C2×C22⋊Dic73C2311yescharacteristic
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×C22⋊Dic73C2311yescharacteristic
269C2×C22⋊Dic73C2311yescharacteristic
270C2×#11924005C2311yescharacteristic
271C2×#11924005C2311yescharacteristic
272C2×#11924005C2311yescharacteristic
273C2×#11924005C2311yescharacteristic
274C2×#11924005C2311yescharacteristic
275C2×#11924005C2311yescharacteristic
276C2×#11924005C2311yescharacteristic
277C2×#11924005C2311yescharacteristic
278C2×C4×Dic73—42no—
279C2×C4×Dic73C2311yescharacteristic
280C2×C4×Dic73C2311yescharacteristic
281C2×C4×Dic73C2311yescharacteristic
282C2×C4×Dic73C2311yescharacteristic
283C2×C4×Dic73C2311yescharacteristic
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
298#14556498C2311yescharacteristic
299#14556498C2311yescharacteristic
300#14556498C2311yescharacteristic
301#14556498C2311yescharacteristic
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
332C25×C73C2311yescharacteristic
333C22×D4×C73C2311yescharacteristic
334C22×D4×C73C2311yescharacteristic
335C22×D4×C73C2311yescharacteristic
336C23×C4×C73C2311yescharacteristic
337C23×C4×C73C2311yescharacteristic
338C23×C4×C73C2311yescharacteristic
339#120×C73C2×C418yescomplemented
340C4×D4×C73—42no—
341C2×C4⋊C4×C73C2311yescharacteristic
342C2×C4⋊C4×C73C2311yescharacteristic
343C2×C4⋊C4×C73C2311yescharacteristic
344C2×C22⋊C4×C73—42no—
345C2×C22⋊C4×C73C2311yescharacteristic
346C2×C22⋊C4×C73C2311yescharacteristic
347C2×C22⋊C4×C73C2311yescharacteristic
348C2×C22⋊C4×C73C2311yescharacteristic
349C2×C22⋊C4×C73C2311yescharacteristic
350C2×C22⋊C4×C73C2311yescharacteristic
351C2×C22⋊C4×C73C2311yescharacteristic
352C2×C22⋊C4×C73C2311yescharacteristic
353C2×C22⋊C4×C73C2311yescharacteristic
354C2×C22⋊C4×C73C2311yescharacteristic
355C2×C22⋊C4×C73C2311yescharacteristic
356C2×C22⋊C4×C73C2311yescharacteristic
357C2×C22⋊C4×C73C2311yescharacteristic
358C2×C22⋊C4×C73C2311yescharacteristic
359C2×C22⋊C4×C73C2311yescharacteristic
360C2×C22⋊C4×C73C2311yescharacteristic
361C2×C42×C73C2311yescharacteristic
362C2×C42×C73C2311yescharacteristic
363C2×C42×C73C2311yescharacteristic
364#95×C73C2311yescharacteristic
365#95×C73C2311yescharacteristic
366#95×C73C2311yescharacteristic
367#95×C73C2311yescharacteristic
368#95×C73C2311yescharacteristic
369#95×C73C2311yescharacteristic
370C23×D73C2411yescharacteristic
371C2×Dic146—41no—
372C2×Dic146—41no—
373C2×Dic146C22×C414yes—
374C2×C22⋊D73—41no—
375C2×C22⋊D73—41no—
376C2×C22⋊D73—41no—
377C2×C22⋊D73—41no—
378C2×C22⋊D73—41no—
379C2×C22⋊D73—41no—
380C2×C22⋊D73—41no—
381C2×C22⋊D73—41no—
382C2×C22⋊D73C22×C414yes—
383C2×C22⋊D73C22×C414yes—
384C2×C22⋊D73C22×C414yes—
385C2×C22⋊D73C22×C414yes—
386C22×Dic73—22no—
387C22×Dic73—22no—
388C22×Dic73—41no—
389C22×Dic73—41no—
390C22×Dic73—41no—
391C22×Dic73—41no—
392C22×Dic73—41no—
393C22×Dic73—41no—
394C22×Dic73—41no—
395C22×Dic73—41no—
396C22×Dic73—41no—
397C22×Dic73—41no—
398C22×Dic73—41no—
399C22×Dic73—41no—
400C22×Dic73—41no—
401C22×Dic73C22×C414yes—
402C22×Dic73C22×C414yes—
403C22×Dic73C22×C414yes—
404C22×Dic73C2411yescharacteristic
405C22×Dic73C2411yescharacteristic
406C22×Dic73C2411yescharacteristic
407C22×Dic73C2411yescharacteristic
408C22×Dic73C2411yescharacteristic
409C22×Dic73C2411yescharacteristic
410C22×Dic73C2411yescharacteristic
411C22×Dic73C2411yescharacteristic
412C22×Dic73C2411yescharacteristic
413C22×Dic73C2411yescharacteristic
414C22×Dic73C2411yescharacteristic
415C22×Dic73C2411yescharacteristic
416C22×Dic73C2411yescharacteristic
417C22×Dic73C2411yescharacteristic
418C22×Dic73C2411yescharacteristic
419C2×C4×D73—22no—
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×D73C22×C414yes—
428C4⋊Dic73—41no—
429C4⋊Dic73—41no—
430C4⋊Dic73—41no—
431C4⋊Dic73C22×C414yes—
432C4⋊Dic73C22×C414yes—
433#11924007—22no—
434#11924007—22no—
435#11924007—22no—
436#11924007—41no—
437#11924007—41no—
438#11924007—41no—
439#11924007—41no—
440#11924007—41no—
441#11924007—41no—
442#11924007—41no—
443#11924007—41no—
444#11924007—41no—
445#11924007—41no—
446#11924007—41no—
447#11924007C22×C414yes—
448#11924007C22×C414yes—
449#11924007C22×C414yes—
450#11924007C22×C414yes—
451C22⋊Dic73—22no—
452C22⋊Dic73—22no—
453C22⋊Dic73—41no—
454C22⋊Dic73—41no—
455C22⋊Dic73—41no—
456C22⋊Dic73—41no—
457C22⋊Dic73—41no—
458C22⋊Dic73—41no—
459C22⋊Dic73—41no—
460C22⋊Dic73—41no—
461C22⋊Dic73—41no—
462C22⋊Dic73—41no—
463C22⋊Dic73—41no—
464C22⋊Dic73C22×C414yes—
465C22⋊Dic73C22×C414yes—
466C22⋊Dic73C22×C414yes—
467C22⋊Dic73C22×C414yes—
468C22⋊Dic73C22×C414yes—
469C22⋊Dic73C22×C414yes—
470C22⋊Dic73C22×C414yes—
471C22⋊Dic73C22×C414yes—
472C22⋊Dic73C22×C414yes—
473#11924005—22no—
474#11924005—41no—
475#11924005—41no—
476#11924005—41no—
477#11924005—41no—
478#11924005—41no—
479#11924005C22×C414yes—
480#11924005C22×C414yes—
481C4×Dic73—22no—
482C4×Dic73—22no—
483C4×Dic73—22no—
484C4×Dic73—22no—
485C4×Dic73—41no—
486C4×Dic73—41no—
487C4×Dic73—41no—
488C4×Dic73—41no—
489C4×Dic73—41no—
490C4×Dic73—41no—
491C4×Dic73—41no—
492C4×Dic73—41no—
493C4×Dic73—41no—
494C4×Dic73—41no—
495C4×Dic73—41no—
496C4×Dic73—41no—
497C4×Dic73—41no—
498C4×Dic73C22×C414yes—
499C4×Dic73C22×C414yes—
500C24×C73—41no—
501C24×C73—41no—
502C24×C73—41no—
503C24×C73—41no—
504C24×C73—41no—
505C24×C73—41no—
506C24×C73C22×C414yes—
507C24×C73C2411yescharacteristic
508C24×C73C2411yescharacteristic
509C24×C73C2411yescharacteristic
510C24×C73C2411yescharacteristic
511C2×D4×C73—41no—
512C2×D4×C73—41no—
513C2×D4×C73—41no—
514C2×D4×C73—41no—
515C2×D4×C73—41no—
516C2×D4×C73—41no—
517C2×D4×C73C22×C414yes—
518C2×D4×C73C22×C414yes—
519C2×D4×C73C22×C414yes—
520C22×C4×C73—22no—
521C22×C4×C73—22no—
522C22×C4×C73—41no—
523C22×C4×C73—41no—
524C22×C4×C73—41no—
525C22×C4×C73—41no—
526C22×C4×C73—41no—
527C22×C4×C73—41no—
528C22×C4×C73—41no—
529C22×C4×C73C2411yescharacteristic
530C22×C4×C73C2411yescharacteristic
531C22×C4×C73C2411yescharacteristic
532C22×C4×C73C2411yescharacteristic
533C22×C4×C73C2411yescharacteristic
534C22×C4×C73C2411yescharacteristic
535C22×C4×C73C2411yescharacteristic
536C22×C4×C73C2411yescharacteristic
537C22×C4×C73C2411yescharacteristic
538C22×C4×C73C2411yescharacteristic
539C22×C4×C73C2411yescharacteristic
540C4⋊C4×C73—41no—
541C4⋊C4×C73—41no—
542C4⋊C4×C73—41no—
543C22⋊C4×C73—22no—
544C22⋊C4×C73—22no—
545C22⋊C4×C73—41no—
546C22⋊C4×C73—41no—
547C22⋊C4×C73—41no—
548C22⋊C4×C73—41no—
549C22⋊C4×C73—41no—
550C22⋊C4×C73—41no—
551C22⋊C4×C73—41no—
552C22⋊C4×C73—41no—
553C22⋊C4×C73—41no—
554C22⋊C4×C73—41no—
555C22⋊C4×C73—41no—
556C22⋊C4×C73C22×C414yes—
557C22⋊C4×C73C22×C414yes—
558C22⋊C4×C73C22×C414yes—
559C42×C73—22no—
560C42×C73—41no—
561C42×C73—41no—
562C23×C73—21no—
563C23×C73—21no—
564C23×C73—21no—
565C23×C73—21no—
566C23×C73—21no—
567C23×C73—21no—
568C23×C73—21no—
569C23×C73—21no—
570C23×C73—21no—
571C23×C73—21no—
572C23×C73—21no—
573C23×C73—21no—
574C23×C73—21no—
575C23×C73—21no—
576C23×C73—21no—
577C23×C73—21no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—44no—
587C23×C73—44no—
588C23×C73—44no—
589C23×C73—82no—
590C23×C73—82no—
591C23×C73—82no—
592C23×C73—82no—
593C23×C73C23×C412yes—
594C23×C73C23×C412yes—
595C23×C73C23×C412yes—
596C23×C73C23×C412yes—
597C23×C73C2511yescharacteristic
598C22×D73—21no—
599C22×D73—21no—
600C22×D73—21no—
601C22×D73—21no—
602C22×D73—21no—
603C22×D73—21no—
604C22×D73C23×C412yes—
605D4×C73—44no—
606D4×C73—44no—
607D4×C73—44no—
608C2×C4×C73—21no—
609C2×C4×C73—21no—
610C2×C4×C73—21no—
611C2×C4×C73—21no—
612C2×C4×C73—21no—
613C2×C4×C73—21no—
614C2×C4×C73—21no—
615C2×C4×C73—21no—
616C2×C4×C73—21no—
617C2×C4×C73—21no—
618C2×C4×C73—21no—
619C2×C4×C73—21no—
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—44no—
638C2×C4×C73—82no—
639C2×C4×C73—82no—
640C2×C4×C73C23×C412yes—
641C2×C4×C73C23×C412yes—
642C2×C4×C73C23×C412yes—
643C2×C4×C73H(5,𝔽2)12yes—
644C22⋊D73—44no—
645C22⋊D73—44no—
646C22⋊D73—44no—
647C22⋊D73—44no—
648C2×Dic73—21no—
649C2×Dic73—21no—
650C2×Dic73—21no—
651C2×Dic73—21no—
652C2×Dic73—21no—
653C2×Dic73—21no—
654C2×Dic73—21no—
655C2×Dic73—21no—
656C2×Dic73—21no—
657C2×Dic73—21no—
658C2×Dic73—21no—
659C2×Dic73—21no—
660C2×Dic73—21no—
661C2×Dic73—21no—
662C2×Dic73—21no—
663C2×Dic73—21no—
664C2×Dic73—21no—
665C2×Dic73—21no—
666C2×Dic73—21no—
667C2×Dic73—21no—
668C2×Dic73—21no—
669C2×Dic73—21no—
670C2×Dic73—21no—
671C2×Dic73—21no—
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—44no—
686C2×Dic73—44no—
687C2×Dic73—44no—
688C2×Dic73—44no—
689C2×Dic73—82no—
690C2×Dic73—82no—
691C2×Dic73C23×C412yes—
692C2×Dic73C23×C412yes—
693C2×Dic73C23×C412yes—
694C2×Dic73C23×C412yes—
695C2×Dic73C23×C412yes—
696C2×Dic73C23×C412yes—
697C2×Dic73C23×C412yes—
698C2×Dic73H(5,𝔽2)12yes—
699C4×D73—44no—
700C4×D73—82no—
701C4×D73—82no—
702Dic146—44no—
703C22×C73—22no—
704C22×C73—22no—
705C22×C73—22no—
706C22×C73—22no—
707C22×C73—22no—
708C22×C73—22no—
709C22×C73—22no—
710C22×C73—22no—
711C22×C73—22no—
712C22×C73—22no—
713C22×C73—22no—
714C22×C73—22no—
715C22×C73—41no—
716C22×C73—41no—
717C22×C73—41no—
718C22×C73—41no—
719C22×C73—41no—
720C22×C73—41no—
721C22×C73—41no—
722C22×C73—41no—
723C22×C73—41no—
724C22×C73—41no—
725C22×C73—41no—
726C22×C73—41no—
727C22×C73—41no—
728C22×C73—41no—
729C22×C73—41no—
730C22×C73—41no—
731C22×C73—88no—
732C22×C73C24×C411yescharacteristic
733C22×C73C2×H(5,𝔽2)11yescharacteristic
734C22×C73C2×H(5,𝔽2)11yescharacteristic
735C22×C73#58511yescharacteristic
736C22×C73#58511yescharacteristic
737C22×C73#58511yescharacteristic
738C22×C73#58511yescharacteristic
739C2×D73—22no—
740C2×D73—22no—
741C2×D73—22no—
742C2×D73—41no—
743C2×D73—41no—
744C2×D73—41no—
745C2×D73—41no—
746C4×C73—22no—
747C4×C73—22no—
748C4×C73—22no—
749C4×C73—22no—
750C4×C73—41no—
751C4×C73—41no—
752C4×C73—41no—
753C4×C73—41no—
754C4×C73—41no—
755C4×C73—41no—
756C4×C73—41no—
757Dic73—22no—
758Dic73—22no—
759Dic73—22no—
760Dic73—22no—
761Dic73—22no—
762Dic73—22no—
763Dic73—22no—
764Dic73—22no—
765Dic73—41no—
766Dic73—41no—
767Dic73—41no—
768Dic73—41no—
769Dic73—41no—
770Dic73—41no—
771Dic73—41no—
772#34451—731nomaximal, Sylow
773C2×C73—42no—
774C2×C73—42no—
775C2×C73—42no—
776C2×C73—42no—
777C2×C73#342811yescharacteristic
778C2×C73C4×H(5,𝔽2)11yescharacteristic
779C2×C73C4×H(5,𝔽2)11yescharacteristic
780C2×C73#353311yescharacteristic
781C2×C73#354211yescharacteristic
782C2×C73#355111yescharacteristic
783C2×C73#356811yescharacteristic
784D73—42no—
785C2×#538—731no—
786#2383—731no—
787#2378—731no—
788#2376—731no—
789#2375—731no—
790#2373—731no—
791#2373—731no—
792#2373—731no—
793#2372—731no—
794#2367—731no—
795#2362—731no—
796#2359—731no—
797#2358—731no—
798#2354—731no—
799#2353—731no—
800#2342—731no—
801#2342—731no—
802#2337—731no—
803#2335—731no—
804#2333—731no—
805#2333—731no—
806#2326—731no—
807#2325—731no—
808#2324—731no—
809#2324—731no—
810#2321—731no—
811#2321D7311yescharacteristic, complemented
812#2319—731no—
813C4×#123—731no—
814C4×#121—731no—
815#2290—731no—
816C73#3445111yescharacteristic, complemented, Sylow
817#538—7316no—
818C2×#126—731no—
819C2×#126—731no—
820C2×#124—731no—
821C2×#124—731no—
822C2×#123—731no—
823C2×#123—731no—
824C2×C22⋊Q8—731no—
825C2×#121—731no—
826C2×#121—731no—
827C2×#121—731no—
828C2×#120—731no—
829C2×#120C2×D7311yescharacteristic
830C2×C4×Q8—731no—
831C2×C4×D4—731no—
832C2×C4×D4—731no—
833C2×C4×D4—731no—
834C2×C4×D4—731no—
835C2×C4×D4—731no—
836C2×C4×D4—731no—
837C2×C4×D4C2×D7311yescharacteristic
838C2×#117—731no—
839C2×#117—731no—
840C2×#117—731no—
841C22×C22⋊C4—731no—
842C22×C22⋊C4—731no—
843C22×C22⋊C4C2×D7311yescharacteristic
844C22×C42—731no—
845#391—731no—
846#391—731no—
847#391—731no—
848#390—731no—
849#390—731no—
850#390—731no—
851#390—731no—
852#390—731no—
853#390—731no—
854#390—731no—
855#390C2×D7311yescharacteristic
856#390C2×D7311yescharacteristic
857#389—731no—
858#389—731no—
859#389—731no—
860#389—731no—
861#389—731no—
862#389—731no—
863#388—731no—
864#388—731no—
865#388—731no—
866#388—731no—
867#388—731no—
868#388—731no—
869#388—731no—
870#388—731no—
871#388—731no—
872#388—731no—
873#388—731no—
874#388—731no—
875#388—731no—
876#388—731no—
877#388—731no—
878#388—731no—
879#388—731no—
880#388—731no—
881#388—731no—
882#388—731no—
883#388—731no—
884#388—731no—
885#388—731no—
886#388—731no—
887#388—731no—
888#388—731no—
889#388—731no—
890#388—731no—
891#388C2×D7311yescharacteristic
892#388C2×D7311yescharacteristic
893#388C2×D7311yescharacteristic
894#388C2×D7311yescharacteristic
895#387—731no—
896#387—731no—
897#387—731no—
898#387—731no—
899#387—731no—
900#387—731no—
901#387—731no—
902#387—731no—
903#387—731no—
904#387—731no—
905#387—731no—
906#387—731no—
907#386—731no—
908#386—731no—
909#386—731no—
910#386—731no—
911#386—731no—
912#386—731no—
913#386—731no—
914#386—731no—
915#386—731no—
916#386—731no—
917#386—731no—
918#386C2×D7311yescharacteristic
919#386C2×D7311yescharacteristic
920#386C2×D7311yescharacteristic
921#385—731no—
922#385—731no—
923#385—731no—
924#385—731no—
925#385—731no—
926#385—731no—
927#385—731no—
928#385—731no—
929#385—731no—
930#385—731no—
931#385—731no—
932#385C2×D7311yescharacteristic
933#384—731no—
934#383—731no—
935#381—731no—
936#381—731no—
937#381—731no—
938#380—731no—
939#380—731no—
940#380—731no—
941#380—731no—
942#380—731no—
943#379—731no—
944#379C2×D7311yescharacteristic
945C4×C4⋊C4—731no—
946C4×C4⋊C4—731no—
947C4×C4⋊C4—731no—
948C4×C4⋊C4—731no—
949C4×C4⋊C4—731no—
950C4×C4⋊C4—731no—
951C4×C4⋊C4—731no—
952C4×C4⋊C4—731no—
953C4×C4⋊C4—731no—
954C4×C22⋊C4—731no—
955C4×C22⋊C4—731no—
956C4×C22⋊C4—731no—
957C4×C22⋊C4—731no—
958C4×C22⋊C4—731no—
959C4×C22⋊C4—731no—
960C4×C22⋊C4—731no—
961C4×C22⋊C4—731no—
962C4×C22⋊C4—731no—
963C4×C22⋊C4—731no—
964C4×C22⋊C4—731no—
965C4×C22⋊C4—731no—
966C4×C22⋊C4—731no—
967C4×C22⋊C4—731no—
968C4×C22⋊C4C2×D7311yescharacteristic
969#376—731no—
970#376—731no—
971#376—731no—
972C2×#95—731no—
973C25C22×D7311yescharacteristic
974C22×Q8—731no—
975C22×D4—731no—
976C22×D4—731no—
977C22×D4—731no—
978C22×D4—731no—
979C22×D4C22×D7311yescharacteristic
980C22×D4C22×D7311yescharacteristic
981C22×D4C22×D7311yescharacteristic
982C23×C4—731no—
983C23×C4—731no—
984C23×C4—731no—
985C23×C4—731no—
986C23×C4—731no—
987C23×C4—731no—
988C23×C4—731no—
989C23×C4—731no—
990C23×C4—731no—
991C23×C4C22×D7311yescharacteristic
992C23×C4C22×D7311yescharacteristic
993C23×C4C22×D7311yescharacteristic
994#126—738no—
995#126—738no—
996#124—738no—
997#124—738no—
998#123—738no—
999#123—738no—
1000C22⋊Q8—738no—
1001#121—738no—
1002#121—738no—
1003#121—738no—
1004#120—738no—
1005#120C4×D7318yescomplemented
1006C4×Q8—2922no—
1007C4×D4—42no—
1008C4×D4—2922no—
1009C4×D4—2922no—
1010C4×D4—2922no—
1011C4×D4—2922no—
1012C4×D4—738no—
1013C4×D4—738no—
1014#117—2922no—
1015#117—2922no—
1016#117—2922no—
1017C2×C4⋊C4—731no—
1018C2×C4⋊C4—731no—
1019C2×C4⋊C4—731no—
1020C2×C4⋊C4—731no—
1021C2×C4⋊C4—731no—
1022C2×C4⋊C4—731no—
1023C2×C4⋊C4—731no—
1024C2×C4⋊C4—731no—
1025C2×C4⋊C4—731no—
1026C2×C4⋊C4—731no—
1027C2×C4⋊C4—731no—
1028C2×C4⋊C4—731no—
1029C2×C4⋊C4—731no—
1030C2×C4⋊C4—731no—
1031C2×C4⋊C4—731no—
1032C2×C4⋊C4—731no—
1033C2×C4⋊C4—731no—
1034C2×C4⋊C4—731no—
1035C2×C4⋊C4—731no—
1036C2×C4⋊C4—731no—
1037C2×C4⋊C4—731no—
1038C2×C4⋊C4—731no—
1039C2×C4⋊C4—731no—
1040C2×C4⋊C4C22×D7311yescharacteristic
1041C2×C4⋊C4C22×D7311yescharacteristic
1042C2×C4⋊C4C22×D7311yescharacteristic
1043C2×C22⋊C4—42no—
1044C2×C22⋊C4—2922no—
1045C2×C22⋊C4—731no—
1046C2×C22⋊C4—731no—
1047C2×C22⋊C4—731no—
1048C2×C22⋊C4—731no—
1049C2×C22⋊C4—731no—
1050C2×C22⋊C4—731no—
1051C2×C22⋊C4—731no—
1052C2×C22⋊C4—731no—
1053C2×C22⋊C4—731no—
1054C2×C22⋊C4—731no—
1055C2×C22⋊C4—731no—
1056C2×C22⋊C4—731no—
1057C2×C22⋊C4—731no—
1058C2×C22⋊C4—731no—
1059C2×C22⋊C4—731no—
1060C2×C22⋊C4—731no—
1061C2×C22⋊C4—738no—
1062C2×C22⋊C4—731no—
1063C2×C22⋊C4—731no—
1064C2×C22⋊C4—731no—
1065C2×C22⋊C4—731no—
1066C2×C22⋊C4—731no—
1067C2×C22⋊C4—731no—
1068C2×C22⋊C4—731no—
1069C2×C22⋊C4—731no—
1070C2×C22⋊C4—731no—
1071C2×C22⋊C4—731no—
1072C2×C22⋊C4—731no—
1073C2×C22⋊C4—731no—
1074C2×C22⋊C4—731no—
1075C2×C22⋊C4—731no—
1076C2×C22⋊C4C22×D7311yescharacteristic
1077C2×C22⋊C4C22×D7311yescharacteristic
1078C2×C22⋊C4C22×D7311yescharacteristic
1079C2×C22⋊C4C22×D7311yescharacteristic
1080C2×C22⋊C4C22×D7311yescharacteristic
1081C2×C22⋊C4C22×D7311yescharacteristic
1082C2×C22⋊C4C22×D7311yescharacteristic
1083C2×C22⋊C4C22×D7311yescharacteristic
1084C2×C22⋊C4C22×D7311yescharacteristic
1085C2×C22⋊C4C22×D7311yescharacteristic
1086C2×C22⋊C4C22×D7311yescharacteristic
1087C2×C22⋊C4C22×D7311yescharacteristic
1088C2×C22⋊C4C22×D7311yescharacteristic
1089C2×C22⋊C4C22×D7311yescharacteristic
1090C2×C22⋊C4C22×D7311yescharacteristic
1091C2×C22⋊C4C22×D7311yescharacteristic
1092C2×C42—2922no—
1093C2×C42—731no—
1094C2×C42—731no—
1095C2×C42—731no—
1096C2×C42—731no—
1097C2×C42—731no—
1098C2×C42—731no—
1099C2×C42—731no—
1100C2×C42—731no—
1101C2×C42—731no—
1102C2×C42—731no—
1103C2×C42—731no—
1104C2×C42—731no—
1105C2×C42—731no—
1106C2×C42—731no—
1107C2×C42—731no—
1108C2×C42—731no—
1109C2×C42—731no—
1110C2×C42—731no—
1111C2×C42—731no—
1112C2×C42C22×D7311yescharacteristic
1113C2×C42C22×D7311yescharacteristic
1114C2×C42C22×D7311yescharacteristic
1115#95—731no—
1116#95—731no—
1117#95—731no—
1118#95—731no—
1119#95—731no—
1120#95—731no—
1121#95—731no—
1122#95—731no—
1123#95—731no—
1124#95—731no—
1125#95—731no—
1126#95—731no—
1127#95—731no—
1128#95—731no—
1129#95—731no—
1130#95—731no—
1131#95—731no—
1132#95—731no—
1133#95—731no—
1134#95—731no—
1135#95—731no—
1136#95—731no—
1137#95—731no—
1138#95—731no—
1139#95—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#95C22×D7311yescharacteristic
1150#95C22×D7311yescharacteristic
1151#95C22×D7311yescharacteristic
1152#95C22×D7311yescharacteristic
1153#95C22×D7311yescharacteristic
1154#95C22×D7311yescharacteristic
1155C24—41no—
1156C24—41no—
1157C24—41no—
1158C24—41no—
1159C24—41no—
1160C24—41no—
1161C24—731no—
1162C24C2×C4×D7314yes—
1163C24C23×D7311yescharacteristic
1164C24C23×D7311yescharacteristic
1165C24C23×D7311yescharacteristic
1166C24C23×D7311yescharacteristic
1167C2×Q8—2921no—
1168C2×Q8—2921no—
1169C2×Q8—734no—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—41no—
1173C2×D4—41no—
1174C2×D4—41no—
1175C2×D4—41no—
1176C2×D4—2921no—
1177C2×D4—2921no—
1178C2×D4—2921no—
1179C2×D4—2921no—
1180C2×D4—2921no—
1181C2×D4—2921no—
1182C2×D4—2921no—
1183C2×D4—2921no—
1184C2×D4—734no—
1185C2×D4—734no—
1186C2×D4—734no—
1187C2×D4—734no—
1188C2×D4C2×C4×D7314yes—
1189C2×D4C2×C4×D7314yes—
1190C2×D4C2×C4×D7314yes—
1191C22×C4—22no—
1192C22×C4—22no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—41no—
1198C22×C4—41no—
1199C22×C4—41no—
1200C22×C4—2921no—
1201C22×C4—2921no—
1202C22×C4—2921no—
1203C22×C4—2921no—
1204C22×C4—2921no—
1205C22×C4—2921no—
1206C22×C4—2921no—
1207C22×C4—2921no—
1208C22×C4—2921no—
1209C22×C4—2921no—
1210C22×C4—2921no—
1211C22×C4—2921no—
1212C22×C4—2921no—
1213C22×C4—2921no—
1214C22×C4—2921no—
1215C22×C4—2921no—
1216C22×C4—2921no—
1217C22×C4—2921no—
1218C22×C4—2921no—
1219C22×C4—2921no—
1220C22×C4—734no—
1221C22×C4—734no—
1222C22×C4—734no—
1223C22×C4—734no—
1224C22×C4—731no—
1225C22×C4—731no—
1226C22×C4—731no—
1227C22×C4—731no—
1228C22×C4—731no—
1229C22×C4—731no—
1230C22×C4—731no—
1231C22×C4—731no—
1232C22×C4—731no—
1233C22×C4—731no—
1234C22×C4—731no—
1235C22×C4—731no—
1236C22×C4—731no—
1237C22×C4—731no—
1238C22×C4—731no—
1239C22×C4—1462no—
1240C22×C4—1462no—
1241C22×C4—1462no—
1242C22×C4C23×D7311yescharacteristic
1243C22×C4C23×D7311yescharacteristic
1244C22×C4C23×D7311yescharacteristic
1245C22×C4C23×D7311yescharacteristic
1246C22×C4C23×D7311yescharacteristic
1247C22×C4C23×D7311yescharacteristic
1248C22×C4C23×D7311yescharacteristic
1249C22×C4C23×D7311yescharacteristic
1250C22×C4C23×D7311yescharacteristic
1251C22×C4C23×D7311yescharacteristic
1252C22×C4C23×D7311yescharacteristic
1253C4⋊C4—41no—
1254C4⋊C4—41no—
1255C4⋊C4—41no—
1256C4⋊C4—2921no—
1257C4⋊C4—2921no—
1258C4⋊C4—2921no—
1259C4⋊C4—2921no—
1260C4⋊C4—2921no—
1261C4⋊C4—2921no—
1262C4⋊C4—2921no—
1263C4⋊C4—2921no—
1264C4⋊C4—2921no—
1265C4⋊C4—2921no—
1266C4⋊C4—2921no—
1267C4⋊C4—2921no—
1268C4⋊C4—2921no—
1269C4⋊C4—2921no—
1270C4⋊C4—734no—
1271C4⋊C4—734no—
1272C4⋊C4—734no—
1273C4⋊C4—734no—
1274C4⋊C4—734no—
1275C4⋊C4—734no—
1276C4⋊C4—1462no—
1277C4⋊C4—1462no—
1278C4⋊C4—1462no—
1279C22⋊C4—22no—
1280C22⋊C4—22no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—2921no—
1293C22⋊C4—2921no—
1294C22⋊C4—2921no—
1295C22⋊C4—2921no—
1296C22⋊C4—2921no—
1297C22⋊C4—2921no—
1298C22⋊C4—2921no—
1299C22⋊C4—2921no—
1300C22⋊C4—2921no—
1301C22⋊C4—2921no—
1302C22⋊C4—2921no—
1303C22⋊C4—2921no—
1304C22⋊C4—2921no—
1305C22⋊C4—2921no—
1306C22⋊C4—2921no—
1307C22⋊C4—2921no—
1308C22⋊C4—734no—
1309C22⋊C4—734no—
1310C22⋊C4—734no—
1311C22⋊C4—734no—
1312C22⋊C4—734no—
1313C22⋊C4—734no—
1314C22⋊C4—734no—
1315C22⋊C4—734no—
1316C22⋊C4—734no—
1317C22⋊C4—734no—
1318C22⋊C4—734no—
1319C22⋊C4—1462no—
1320C22⋊C4—1462no—
1321C22⋊C4—1462no—
1322C22⋊C4C2×C4×D7314yes—
1323C22⋊C4C2×C4×D7314yes—
1324C22⋊C4C2×C4×D7314yes—
1325C42—22no—
1326C42—41no—
1327C42—41no—
1328C42—2921no—
1329C42—2921no—
1330C42—2921no—
1331C42—2921no—
1332C42—2921no—
1333C42—2921no—
1334C42—2921no—
1335C42—2921no—
1336C42—2921no—
1337C42—2921no—
1338C42—2921no—
1339C42—2921no—
1340C42—2921no—
1341C42—734no—
1342C42—734no—
1343C42—1462no—
1344C42—1462no—
1345C42—1462no—
1346C42—1462no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—21no—
1353C23—21no—
1354C23—21no—
1355C23—21no—
1356C23—21no—
1357C23—21no—
1358C23—21no—
1359C23—21no—
1360C23—21no—
1361C23—21no—
1362C23—21no—
1363C23—21no—
1364C23—21no—
1365C23—21no—
1366C23—21no—
1367C23—21no—
1368C23—21no—
1369C23—21no—
1370C23—21no—
1371C23—44no—
1372C23—44no—
1373C23—44no—
1374C23—82no—
1375C23—82no—
1376C23—82no—
1377C23—82no—
1378C23—732no—
1379C23—1461no—
1380C23—1461no—
1381C23—1461no—
1382C23—1461no—
1383C23—1461no—
1384C23—1461no—
1385C23C22×C4×D7312yes—
1386C23C22×C4×D7312yes—
1387C23C22×C4×D7312yes—
1388C23C22×C4×D7312yes—
1389C23C24×D7311yescharacteristic
1390Q8—2924no—
1391D4—44no—
1392D4—44no—
1393D4—44no—
1394D4—2924no—
1395D4—2924no—
1396D4—2924no—
1397D4—2924no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—44no—
1428C2×C4—82no—
1429C2×C4—82no—
1430C2×C4—2924no—
1431C2×C4—2924no—
1432C2×C4—2924no—
1433C2×C4—2924no—
1434C2×C4—2924no—
1435C2×C4—5842no—
1436C2×C4—5842no—
1437C2×C4—5842no—
1438C2×C4—5842no—
1439C2×C4—732no—
1440C2×C4—732no—
1441C2×C4—732no—
1442C2×C4—732no—
1443C2×C4—732no—
1444C2×C4—732no—
1445C2×C4—732no—
1446C2×C4—732no—
1447C2×C4—1461no—
1448C2×C4—1461no—
1449C2×C4—1461no—
1450C2×C4—1461no—
1451C2×C4—1461no—
1452C2×C4—1461no—
1453C2×C4—1461no—
1454C2×C4—1461no—
1455C2×C4—1461no—
1456C2×C4—1461no—
1457C2×C4—1461no—
1458C2×C4—1461no—
1459C2×C4—1461no—
1460C2×C4—1461no—
1461C2×C4—1461no—
1462C2×C4—1461no—
1463C2×C4—1461no—
1464C2×C4—1461no—
1465C2×C4—1461no—
1466C2×C4—1461no—
1467C2×C4—1461no—
1468C2×C4—1461no—
1469C2×C4—1461no—
1470C2×C4—1461no—
1471C2×C4—1461no—
1472C2×C4—1461no—
1473C2×C4—1461no—
1474C2×C4—1461no—
1475C2×C4—1461no—
1476C2×C4—1461no—
1477C2×C4—1461no—
1478C2×C4—1461no—
1479C2×C4—1461no—
1480C2×C4—1461no—
1481C2×C4—1461no—
1482C2×C4—1461no—
1483C2×C4—1461no—
1484C2×C4C22×C4×D7312yes—
1485C2×C4C22×C4×D7312yes—
1486C2×C4C22×C4×D7312yes—
1487C2×C4#1455663612yes—
1488C22—22no—
1489C22—22no—
1490C22—22no—
1491C22—22no—
1492C22—22no—
1493C22—22no—
1494C22—22no—
1495C22—22no—
1496C22—22no—
1497C22—22no—
1498C22—22no—
1499C22—22no—
1500C22—41no—
1501C22—41no—
1502C22—41no—
1503C22—41no—
1504C22—41no—
1505C22—41no—
1506C22—41no—
1507C22—41no—
1508C22—41no—
1509C22—41no—
1510C22—41no—
1511C22—41no—
1512C22—41no—
1513C22—41no—
1514C22—41no—
1515C22—41no—
1516C22—88no—
1517C22—2921no—
1518C22—2921no—
1519C22—2921no—
1520C22—2921no—
1521C22—1462no—
1522C22—1462no—
1523C22—1462no—
1524C22C23×C4×D7311yescharacteristic
1525C22H(5,𝔽2)×D7311yescharacteristic
1526C22C2×#1455663611yescharacteristic
1527C22#1798942211yescharacteristic
1528C22#1798942211yescharacteristic
1529C22#1798942211yescharacteristic
1530C22#1798942311yescharacteristic
1531C4—22no—
1532C4—22no—
1533C4—22no—
1534C4—22no—
1535C4—41no—
1536C4—41no—
1537C4—41no—
1538C4—41no—
1539C4—41no—
1540C4—41no—
1541C4—41no—
1542C4—2921no—
1543C4—2921no—
1544C4—2921no—
1545C4—2921no—
1546C4—2921no—
1547C4—2921no—
1548C4—2921no—
1549C4—1462no—
1550C4—1462no—
1551C4—1462no—
1552C4—1462no—
1553C4—1462no—
1554C4—1462no—
1555C4—1462no—
1556C4—1462no—
1557C2—42no—
1558C2—42no—
1559C2—42no—
1560C2—42no—
1561C2—2922no—
1562C2#2262312911yescharacteristic
1563C2#2262313511yescharacteristic
1564C2C4×#1455663611yescharacteristic
1565C2#2262409211yescharacteristic
1566C2#2262424911yescharacteristic
1567C2#2262434811yescharacteristic
1568C2#2262462411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2321C2
socle, cosocleC23×C73C25
prime radicalC2×#17989172C2
hypercenter#2321D73
hypocenterC73#34451
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2321

Complements

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

NH ≅ G/Ntype
2. #22613119C2semidirect
3. #22613098C2semidirect
4. #22613073C2semidirect
5. #22613070C2semidirect
6. #22613058C2semidirect
7. #22613052C2semidirect
8. #22613048C2semidirect
9. #22613039C2semidirect
10. #22612999C2semidirect
11. #22612955C2semidirect
12. #22612920C2semidirect
13. #22612910C2semidirect
14. #22612877C2semidirect
15. #22612866C2semidirect
16. #22612782C2semidirect
17. #22612776C2semidirect
18. #22612740C2semidirect
19. #22612722C2semidirect
20. #22612697C2semidirect
21. #22612690C2semidirect
22. #22612641C2semidirect
23. #22612633C2semidirect
24. #22612618C2semidirect
25. #22612617C2semidirect
26. #22612592C2semidirect
27. #22612568C2semidirect
28. C4×#14556572C2semidirect
29. #22612441C2semidirect
30. #22612371C2semidirect
31. C73×#2321C2semidirect
32. #17989172C4semidirect
44. C2×#14556556C22semidirect
50. C2×#14556551C22semidirect
51. C2×#14556548C22semidirect
56. C22×C4×Dic73C22semidirect
57. #17988493C22semidirect
58. #17988491C22semidirect
59. #17988491C22semidirect
66. #17988487C22semidirect
67. #17988485C22semidirect
68. #17988484C22semidirect
69. #17988484C22semidirect
70. #17988483C22semidirect
71. #17988483C22semidirect
72. #17988482C22semidirect
81. #17988481C22semidirect
82. #17988481C22semidirect
83. #17988481C22semidirect
88. #17988479C22semidirect
89. #17988479C22semidirect
90. #17988478C22semidirect
91. #17988477C22semidirect
100. #17988475C22semidirect
101. #17988474C22semidirect
102. #17988474C22semidirect
103. #17988472C22semidirect
104. #17988472C22semidirect
105. #17988471C22semidirect
106. #17988470C22semidirect
107. #17988470C22semidirect
108. #17988469C22semidirect
109. #17988469C22semidirect
110. #17988468C22semidirect
111. #17988468C22semidirect
112. #17988468C22semidirect
117. #17988466C22semidirect
123. #17988463C22semidirect
128. #17988460C22semidirect
132. #17988459C22semidirect
133. #17988459C22semidirect
134. #17988458C22semidirect
135. #17988456C22semidirect
136. #17988454C22semidirect
139. #17988448C22semidirect
140. #17988446C22semidirect
143. #17988445C22semidirect
144. #17988444C22semidirect
146. C4⋊C4×Dic73C22semidirect
147. C4×#11924007C22semidirect
148. C4×#11924007C22semidirect
149. C4×#11924007C22semidirect
150. C4×C4⋊Dic73C22semidirect
151. #17988438C22semidirect
152. #17988438C22semidirect
153. #17988438C22semidirect
154. #17988438C22semidirect
161. C22⋊C4×Dic73C22semidirect
162. C4×#11924005C22semidirect
166. C4×C22⋊Dic73C22semidirect
167. #17988434C22semidirect
168. #17988434C22semidirect
169. #17988433C22semidirect
170. #17988433C22semidirect
171. #17988432C22semidirect
172. #95×D73C22semidirect
202. #14556584C2×C4semidirect
203. #14556584C2×C4semidirect
204. #14556578C2×C4semidirect
205. #14556577C2×C4semidirect
206. #14556573C2×C4semidirect
207. #14556572C2×C4semidirect
208. #14556568C2×C4semidirect
209. #14556563C2×C4semidirect
210. #14556563C2×C4semidirect
211. #14556562C2×C4semidirect
212. #14556560C2×C4semidirect
215. D4×Dic73C2×C4semidirect
219. #14556551C2×C4semidirect
247. C2×C22⋊Dic73C2×C4semidirect
339. #120×C73C2×C4semidirect
811. #2321D73semidirect
816. C73#34451semidirect
1005. #120C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891722
#226131192
#226130982
#226130732
#226130702
#226130582
#226130522
#226130482
#226130392
#226129992
#226129552
#226129202
#226129102
#226128772
#226128662
#226127822
#226127762
#226127402
#226127222
#226126972
#226126902
#226126412
#226126332
#226126182
#226126172
#226125922
#226125682
C4×#145565722
#226124412
#226123712
C73×#23212
#3445173