Finite Group Databasebeta

← #33258991

Subgroups — #33258991

Order 18688.

2404 conjugacy classes of subgroups.

The subgroup lattice has 1668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989180C211yesmaximal, characteristic, complemented
2C2×#17989171C211yesmaximal, characteristic, complemented
3#22618305C211yesmaximal, characteristic, complemented
4#22618295C211yesmaximal, characteristic, complemented
5#22618259C211yesmaximal, characteristic, complemented
6#22618228C211yesmaximal, characteristic, complemented
7#22616099C211yesmaximal, characteristic, complemented
8#22616080C211yesmaximal, characteristic, complemented
9#22616077C211yesmaximal, characteristic, complemented
10#22616056C211yesmaximal, characteristic, complemented
11#22615075C211yesmaximal, characteristic, complemented
12#22615054C211yesmaximal, characteristic, complemented
13#22615047C211yesmaximal, characteristic, complemented
14#22614940C211yesmaximal, characteristic, complemented
15#22614890C211yesmaximal, characteristic, complemented
16#22614860C211yesmaximal, characteristic, complemented
17#22614819C211yesmaximal, characteristic, complemented
18#22614631C211yesmaximal, characteristic, complemented
19#22614609C211yesmaximal, characteristic, complemented
20#22614250C211yesmaximal, characteristic, complemented
21#22614050C211yesmaximal, characteristic, complemented
22#22613934C211yesmaximal, characteristic, complemented
23#22613903C211yesmaximal, characteristic, complemented
24#22613485C211yesmaximal, characteristic, complemented
25#22613470C211yesmaximal, characteristic, complemented
26#22612604C211yesmaximal, characteristic, complemented
27#22612587C211yesmaximal, characteristic, complemented
28C4×#14556564C211yesmaximal, characteristic, complemented
29#388×D73C211yesmaximal, characteristic, complemented
30C4×#14556551C211yesmaximal, characteristic, complemented
31C73×#2557C211yesmaximal, characteristic, complemented
32#17989180—28no—
33#17989171—28no—
34C2×#14556585C2211yescharacteristic
35C2×#14556584C2211yescharacteristic
36C2×#14556584C2211yescharacteristic, complemented
37C2×#14556584C2211yescharacteristic, complemented
38C2×#14556582C2211yescharacteristic, complemented
39C2×#14556581C2211yescharacteristic, complemented
40C2×#14556580C2211yescharacteristic
41C2×#14556577C2211yescharacteristic
42C2×#14556576C2211yescharacteristic
43C2×#14556575C2211yescharacteristic
44C2×#14556573C2211yescharacteristic
45C2×#14556573C2211yescharacteristic
46C2×#14556573C2211yescharacteristic
47C2×#14556572C2211yescharacteristic, complemented
48C2×#14556570C2211yescharacteristic, complemented
49C2×#14556569C2211yescharacteristic
50C2×#14556568C2211yescharacteristic, complemented
51C2×#14556567C2211yescharacteristic
52C2×#14556564C2211yescharacteristic
53C2×#14556564C2211yescharacteristic
54C2×#14556564C2211yescharacteristic
55C2×#14556563C2211yescharacteristic
56C2×#14556563C2211yescharacteristic
57C2×#14556562C2211yescharacteristic
58C2×#14556561C2211yescharacteristic
59C2×#14556559C2211yescharacteristic
60C2×#14556559C2211yescharacteristic
61C2×C4×D292C2211yescharacteristic
62C2×C4×C22⋊D73C2211yescharacteristic
63C2×C4×C22⋊D73C2211yescharacteristic
64C2×C4×C22⋊D73C2211yescharacteristic, complemented
65C2×#14556551C2211yescharacteristic
66C2×#14556551C2211yescharacteristic
67C2×C4⋊C4×D73C2211yescharacteristic
68C2×C22⋊C4×D73C2211yescharacteristic
69C2×C22⋊C4×D73C2211yescharacteristic
70C2×C22⋊C4×D73C2211yescharacteristic
71C22×C4×Dic73C2211yescharacteristic, complemented
72C2×C42×D73C2211yescharacteristic
73#17988529C2211yescharacteristic, complemented
74#17988527C2211yescharacteristic, complemented
75#17988523C2211yescharacteristic
76#17988522C2211yescharacteristic
77#17988521C2211yescharacteristic, complemented
78#17988521C2211yescharacteristic, complemented
79#17988521C2211yescharacteristic, complemented
80#17988518C2211yescharacteristic, complemented
81#17988515C2211yescharacteristic, complemented
82#17988515C2211yescharacteristic, complemented
83#17988511C2211yescharacteristic
84#17988511C2211yescharacteristic, complemented
85#17988510C2211yescharacteristic
86#17988510C2211yescharacteristic
87#17988508C2211yescharacteristic, complemented
88#17988506C2211yescharacteristic, complemented
89#17988505C2211yescharacteristic
90#17988503C2211yescharacteristic
91#17988503C2211yescharacteristic, complemented
92#17988502C2211yescharacteristic
93#17988502C2211yescharacteristic
94#17988502C2211yescharacteristic
95#17988502C2211yescharacteristic, complemented
96#17988501C2211yescharacteristic
97#17988500C2211yescharacteristic
98#17988496C2211yescharacteristic
99#17988495C2211yescharacteristic
100#17988495C2211yescharacteristic, complemented
101#17988494C2211yescharacteristic, complemented
102#17988491C2211yescharacteristic, complemented
103#17988490C2211yescharacteristic
104#17988490C2211yescharacteristic
105#17988489C2211yescharacteristic
106#17988488C2211yescharacteristic
107#17988487C2211yescharacteristic
108#17988487C2211yescharacteristic
109#17988487C2211yescharacteristic
110#17988487C2211yescharacteristic, complemented
111#17988486C2211yescharacteristic, complemented
112#17988485C2211yescharacteristic, complemented
113#17988484C2211yescharacteristic, complemented
114#17988484C2211yescharacteristic, complemented
115#17988484C2211yescharacteristic, complemented
116#17988483C2211yescharacteristic, complemented
117#17988481C2211yescharacteristic
118#17988481C2211yescharacteristic
119#17988481C2211yescharacteristic, complemented
120#17988480C2211yescharacteristic
121#17988480C2211yescharacteristic, complemented
122#17988480C2211yescharacteristic, complemented
123#17988479C2211yescharacteristic
124#17988479C2211yescharacteristic
125#17988479C2211yescharacteristic
126#17988479C2211yescharacteristic
127#17988479C2211yescharacteristic, complemented
128#17988479C2211yescharacteristic, complemented
129#17988479C2211yescharacteristic, complemented
130#17988478C2211yescharacteristic
131#17988477C2211yescharacteristic
132#17988476C2211yescharacteristic
133#17988476C2211yescharacteristic
134#17988476C2211yescharacteristic
135#17988476C2211yescharacteristic, complemented
136#17988476C2211yescharacteristic, complemented
137#17988475C2211yescharacteristic
138#17988475C2211yescharacteristic
139#17988475C2211yescharacteristic
140#17988475C2211yescharacteristic
141#17988475C2211yescharacteristic, complemented
142#17988471C2211yescharacteristic, complemented
143#17988467C2211yescharacteristic
144#17988466C2211yescharacteristic
145#17988466C2211yescharacteristic
146#17988466C2211yescharacteristic, complemented
147#17988465C2211yescharacteristic
148#17988465C2211yescharacteristic
149#17988464C2211yescharacteristic, complemented
150#17988463C2211yescharacteristic
151#17988463C2211yescharacteristic
152#17988461C2211yescharacteristic
153#17988461C2211yescharacteristic
154#17988461C2211yescharacteristic, complemented
155#17988458C2211yescharacteristic, complemented
156#17988451C2211yescharacteristic, complemented
157#17988449C2211yescharacteristic
158#17988446C2211yescharacteristic
159#17988445C2211yescharacteristic, complemented
160#17988442C2211yescharacteristic
161C4×#11924007C2211yescharacteristic, complemented
162C4×#11924007C2211yescharacteristic, complemented
163#17988438C2211yescharacteristic, complemented
164#17988438C2211yescharacteristic, complemented
165C22⋊C4×Dic73C2211yescharacteristic, complemented
166C22⋊C4×Dic73C2211yescharacteristic, complemented
167C4×#11924005C2211yescharacteristic
168C4×#11924005C2211yescharacteristic, complemented
169#17988434C2211yescharacteristic
170#17988434C2211yescharacteristic
171#95×D73C2211yescharacteristic
172#95×D73C2211yescharacteristic
173C42×Dic73C2211yescharacteristic, complemented
174C2×#124×C73C2211yescharacteristic
175C2×#123×C73C2211yescharacteristic, complemented
176#397×C73C2211yescharacteristic
177#397×C73C2211yescharacteristic, complemented
178#393×C73C2211yescharacteristic, complemented
179#392×C73C2211yescharacteristic
180#391×C73C2211yescharacteristic, complemented
181#390×C73C2211yescharacteristic
182#388×C73C2211yescharacteristic
183#387×C73C2211yescharacteristic, complemented
184#386×C73C2211yescharacteristic
185#386×C73C2211yescharacteristic
186#386×C73C2211yescharacteristic, complemented
187C4×C22⋊C4×C73C2211yescharacteristic, complemented
188C4×C22⋊C4×C73C2211yescharacteristic, complemented
189C24×D73C2311yescharacteristic
190C22×Dic146C2311yescharacteristic
191C22×D292C2311yescharacteristic
192C22×D292C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C22×C22⋊D73C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C22×C22⋊D73C2311yescharacteristic
197C22×C22⋊D73C2311yescharacteristic
198C22×C22⋊D73C2311yescharacteristic
199C22×C22⋊D73C2311yescharacteristic
200C23×Dic73C2311yescharacteristic
201C23×Dic73C2311yescharacteristic
202C22×C4×D73C2311yescharacteristic
203C22×C4×D73C2311yescharacteristic
204C22×C4×D73C2311yescharacteristic
205C22×C4×D73C2311yescharacteristic
206C22×C4×D73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209#14556585—24no—
210#14556584—24no—
211#14556584—24no—
212#14556584—24no—
213#14556582—24no—
214#14556581—24no—
215#14556580—24no—
216#14556577—42no—
217#14556576—24no—
218#14556575—24no—
219#14556573—24no—
220#14556573—24no—
221#14556573—24no—
222#14556572—24no—
223#14556570—24no—
224#14556569—24no—
225#14556568—24no—
226#14556567—24no—
227#14556564—24no—
228#14556564—24no—
229#14556564—24no—
230#14556563—24no—
231#14556563—42no—
232#14556562—24no—
233#14556561—24no—
234#14556559—24no—
235#14556559—24no—
236C4×D292—24no—
237C4×C22⋊D73—24no—
238C4×C22⋊D73—24no—
239C4×C22⋊D73—42no—
240#14556551—24no—
241#14556551D418yescomplemented
242C2×C4⋊Dic73C2311yescharacteristic
243C2×C4⋊Dic73C2311yescharacteristic
244C2×C4⋊Dic73C2311yescharacteristic
245C2×C4⋊Dic73C2311yescharacteristic
246C2×C4⋊Dic73C2311yescharacteristic
247C2×C4⋊Dic73C2311yescharacteristic
248C2×C4⋊Dic73C2311yescharacteristic
249C2×C4⋊Dic73C2311yescharacteristic
250C2×#11924007C2311yescharacteristic
251C2×#11924007C2311yescharacteristic
252C2×#11924007C2311yescharacteristic
253C2×#11924007C2311yescharacteristic
254C2×#11924007C2311yescharacteristic
255C2×#11924007C2311yescharacteristic
256C2×#11924007C2311yescharacteristic
257C2×#11924007C2311yescharacteristic
258C2×#11924007C2311yescharacteristic
259C2×#11924007C2311yescharacteristic
260C2×#11924007C2311yescharacteristic
261C2×#11924007C2311yescharacteristic
262C2×#11924007C2311yescharacteristic
263C2×#11924007C2311yescharacteristic
264C2×#11924007C2311yescharacteristic
265C2×#11924007C2311yescharacteristic
266C2×#11924007C2311yescharacteristic
267C2×#11924007C2311yescharacteristic
268C2×#11924007C2311yescharacteristic
269C4⋊C4×D73—24no—
270C2×C22⋊Dic73C2311yescharacteristic
271C2×C22⋊Dic73C2311yescharacteristic
272C2×C22⋊Dic73C2311yescharacteristic
273C2×C22⋊Dic73C2311yescharacteristic
274C2×C22⋊Dic73C2311yescharacteristic
275C2×C22⋊Dic73C2311yescharacteristic
276C2×C22⋊Dic73C2311yescharacteristic
277C2×C22⋊Dic73C2311yescharacteristic
278C2×C22⋊Dic73C2311yescharacteristic
279C2×C22⋊Dic73C2311yescharacteristic
280C2×C22⋊Dic73C2311yescharacteristic
281C2×C22⋊Dic73C2311yescharacteristic
282C2×C22⋊Dic73C2311yescharacteristic
283C2×C22⋊Dic73C2311yescharacteristic
284C2×#11924005C2311yescharacteristic
285C2×#11924005C2311yescharacteristic
286C2×#11924005C2311yescharacteristic
287C2×#11924005C2311yescharacteristic
288C2×#11924005C2311yescharacteristic
289C2×#11924005C2311yescharacteristic
290C2×#11924005C2311yescharacteristic
291C2×#11924005C2311yescharacteristic
292C2×#11924005C2311yescharacteristic
293C2×#11924005C2311yescharacteristic
294C2×#11924005C2311yescharacteristic
295C2×#11924005C2311yescharacteristic
296C2×#11924005C2311yescharacteristic
297C2×#11924005C2311yescharacteristic
298C2×#11924005C2311yescharacteristic
299C2×#11924005C2311yescharacteristic
300C2×#11924005C2311yescharacteristic
301C2×#11924005C2311yescharacteristic
302C2×#11924005C2311yescharacteristic
303C2×#11924005C2311yescharacteristic
304C2×#11924005C2311yescharacteristic
305C2×#11924005C2311yescharacteristic
306C2×#11924005C2311yescharacteristic
307C2×#11924005C2311yescharacteristic
308C2×#11924005C2311yescharacteristic
309C22⋊C4×D73—24no—
310C22⋊C4×D73—24no—
311C22⋊C4×D73—42no—
312C2×C4×Dic73—42no—
313C2×C4×Dic73C2311yescharacteristic
314C2×C4×Dic73C2311yescharacteristic
315C2×C4×Dic73C2311yescharacteristic
316C2×C4×Dic73C2311yescharacteristic
317C2×C4×Dic73C2311yescharacteristic
318C2×C4×Dic73C2311yescharacteristic
319C2×C4×Dic73C2311yescharacteristic
320C2×C4×Dic73C2311yescharacteristic
321C2×C4×Dic73C2311yescharacteristic
322C2×C4×Dic73C2311yescharacteristic
323C2×C4×Dic73C2311yescharacteristic
324C2×C4×Dic73C2311yescharacteristic
325C42×D73—42no—
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330#14556498C2311yescharacteristic
331#14556498C2311yescharacteristic
332#14556498C2311yescharacteristic
333#14556498C2311yescharacteristic
334#14556498C2311yescharacteristic
335#14556498C2311yescharacteristic
336#14556498C2311yescharacteristic
337#14556498C2311yescharacteristic
338#14556498C2311yescharacteristic
339#14556498C2311yescharacteristic
340#14556498C2311yescharacteristic
341#14556498C2311yescharacteristic
342#14556498C2311yescharacteristic
343#14556498C2311yescharacteristic
344#14556498C2311yescharacteristic
345#14556498C2311yescharacteristic
346#14556498C2311yescharacteristic
347#14556498C2311yescharacteristic
348C22×Q8×C73C2311yescharacteristic
349C22×D4×C73C2311yescharacteristic
350C22×D4×C73C2311yescharacteristic
351C22×D4×C73C2311yescharacteristic
352C23×C4×C73C2311yescharacteristic
353C23×C4×C73C2311yescharacteristic
354#124×C73—24no—
355#123×C73—24no—
356C2×C4⋊C4×C73C2311yescharacteristic
357C2×C4⋊C4×C73C2311yescharacteristic
358C2×C4⋊C4×C73C2311yescharacteristic
359C2×C22⋊C4×C73C2311yescharacteristic
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
368C2×C22⋊C4×C73C2311yescharacteristic
369C2×C22⋊C4×C73C2311yescharacteristic
370C2×C22⋊C4×C73C2311yescharacteristic
371C2×C22⋊C4×C73C2311yescharacteristic
372C2×C42×C73C2311yescharacteristic
373C2×C42×C73C2311yescharacteristic
374C2×C42×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376#95×C73C2311yescharacteristic
377#95×C73C2311yescharacteristic
378#95×C73C2311yescharacteristic
379#95×C73C2311yescharacteristic
380#95×C73C2311yescharacteristic
381#95×C73C2311yescharacteristic
382#95×C73C2311yescharacteristic
383#95×C73C2311yescharacteristic
384#95×C73C2311yescharacteristic
385C23×D73—22no—
386C23×D73—22no—
387C23×D73—22no—
388C23×D73—41no—
389C23×D73—41no—
390C23×D73—41no—
391C23×D73—41no—
392C23×D73C2411yescharacteristic
393C23×D73C2411yescharacteristic
394C23×D73C2411yescharacteristic
395C2×Dic146—22no—
396C2×Dic146—41no—
397C2×Dic146—41no—
398C2×D292—22no—
399C2×D292—22no—
400C2×D292—22no—
401C2×D292—22no—
402C2×D292—41no—
403C2×D292—41no—
404C2×C22⋊D73—22no—
405C2×C22⋊D73—22no—
406C2×C22⋊D73—22no—
407C2×C22⋊D73—22no—
408C2×C22⋊D73—22no—
409C2×C22⋊D73—22no—
410C2×C22⋊D73—22no—
411C2×C22⋊D73—22no—
412C2×C22⋊D73—22no—
413C2×C22⋊D73—22no—
414C2×C22⋊D73—41no—
415C2×C22⋊D73—41no—
416C2×C22⋊D73—41no—
417C2×C22⋊D73—41no—
418C2×C22⋊D73—41no—
419C2×C22⋊D73—41no—
420C2×C22⋊D73—41no—
421C2×C22⋊D73—41no—
422C2×C22⋊D73—41no—
423C2×C22⋊D73—41no—
424C2×C22⋊D73C2×D414yes—
425C22×Dic73—22no—
426C22×Dic73—22no—
427C22×Dic73—41no—
428C22×Dic73—41no—
429C22×Dic73—41no—
430C22×Dic73C2×D414yes—
431C22×Dic73C2411yescharacteristic
432C22×Dic73C2411yescharacteristic
433C22×Dic73C2411yescharacteristic
434C22×Dic73C2411yescharacteristic
435C22×Dic73C2411yescharacteristic
436C22×Dic73C2411yescharacteristic
437C22×Dic73C2411yescharacteristic
438C22×Dic73C2411yescharacteristic
439C22×Dic73C2411yescharacteristic
440C22×Dic73C2411yescharacteristic
441C22×Dic73C2411yescharacteristic
442C22×Dic73C2411yescharacteristic
443C22×Dic73C2411yescharacteristic
444C2×C4×D73—22no—
445C2×C4×D73—22no—
446C2×C4×D73—22no—
447C2×C4×D73—22no—
448C2×C4×D73—22no—
449C2×C4×D73—22no—
450C2×C4×D73—22no—
451C2×C4×D73—22no—
452C2×C4×D73—41no—
453C2×C4×D73—41no—
454C2×C4×D73—41no—
455C2×C4×D73—41no—
456C2×C4×D73—41no—
457C2×C4×D73—41no—
458C2×C4×D73—41no—
459C2×C4×D73—41no—
460C2×C4×D73—41no—
461C2×C4×D73—41no—
462C2×C4×D73—41no—
463C2×C4×D73C2×D414yes—
464C2×C4×D73#4114yes—
465C4⋊Dic73—22no—
466C4⋊Dic73—22no—
467C4⋊Dic73—22no—
468C4⋊Dic73—22no—
469C4⋊Dic73—22no—
470C4⋊Dic73—22no—
471C4⋊Dic73—41no—
472C4⋊Dic73—41no—
473#11924007—22no—
474#11924007—22no—
475#11924007—22no—
476#11924007—22no—
477#11924007—22no—
478#11924007—22no—
479#11924007—22no—
480#11924007—22no—
481#11924007—22no—
482#11924007—22no—
483#11924007—22no—
484#11924007—22no—
485#11924007—22no—
486#11924007—22no—
487#11924007—41no—
488#11924007—41no—
489#11924007—41no—
490#11924007—41no—
491#11924007C2×D414yes—
492C22⋊Dic73—22no—
493C22⋊Dic73—22no—
494C22⋊Dic73—22no—
495C22⋊Dic73—22no—
496C22⋊Dic73—22no—
497C22⋊Dic73—22no—
498C22⋊Dic73—22no—
499C22⋊Dic73—22no—
500C22⋊Dic73—22no—
501C22⋊Dic73—22no—
502C22⋊Dic73—22no—
503C22⋊Dic73—22no—
504C22⋊Dic73—41no—
505C22⋊Dic73—41no—
506#11924005—22no—
507#11924005—22no—
508#11924005—22no—
509#11924005—22no—
510#11924005—22no—
511#11924005—22no—
512#11924005—22no—
513#11924005—22no—
514#11924005—22no—
515#11924005—22no—
516#11924005—22no—
517#11924005—22no—
518#11924005—22no—
519#11924005—22no—
520#11924005—22no—
521#11924005—22no—
522#11924005—22no—
523#11924005—41no—
524#11924005—41no—
525#11924005—41no—
526#11924005—41no—
527#11924005—41no—
528#11924005—41no—
529#11924005C2×D414yes—
530#11924005#4114yes—
531C4×Dic73—22no—
532C4×Dic73—22no—
533C4×Dic73—22no—
534C4×Dic73—22no—
535C4×Dic73—22no—
536C4×Dic73—22no—
537C4×Dic73—41no—
538C4×Dic73—41no—
539C4×Dic73—41no—
540C4×Dic73—41no—
541C4×Dic73—41no—
542C4×Dic73C2×D414yes—
543C24×C73C2411yescharacteristic
544C24×C73C2411yescharacteristic
545C24×C73C2411yescharacteristic
546C2×Q8×C73—22no—
547C2×Q8×C73—41no—
548C2×Q8×C73—41no—
549C2×D4×C73—22no—
550C2×D4×C73—22no—
551C2×D4×C73—22no—
552C2×D4×C73—41no—
553C2×D4×C73—41no—
554C2×D4×C73—41no—
555C2×D4×C73—41no—
556C2×D4×C73—41no—
557C2×D4×C73—41no—
558C22×C4×C73—22no—
559C22×C4×C73—22no—
560C22×C4×C73—41no—
561C22×C4×C73—41no—
562C22×C4×C73—41no—
563C22×C4×C73—41no—
564C22×C4×C73C2411yescharacteristic
565C22×C4×C73C2411yescharacteristic
566C22×C4×C73C2411yescharacteristic
567C22×C4×C73C2411yescharacteristic
568C22×C4×C73C2411yescharacteristic
569C22×C4×C73C2411yescharacteristic
570C22×C4×C73C2411yescharacteristic
571C22×C4×C73C2411yescharacteristic
572C22×C4×C73C2411yescharacteristic
573C22×C4×C73C2411yescharacteristic
574C22×C4×C73C2411yescharacteristic
575C22×C4×C73C2411yescharacteristic
576C4⋊C4×C73—22no—
577C4⋊C4×C73—22no—
578C4⋊C4×C73—22no—
579C22⋊C4×C73—22no—
580C22⋊C4×C73—22no—
581C22⋊C4×C73—22no—
582C22⋊C4×C73—22no—
583C22⋊C4×C73—22no—
584C22⋊C4×C73—22no—
585C22⋊C4×C73—22no—
586C22⋊C4×C73—22no—
587C22⋊C4×C73—41no—
588C22⋊C4×C73—41no—
589C22⋊C4×C73—41no—
590C22⋊C4×C73—41no—
591C22⋊C4×C73C2×D414yes—
592C42×C73—22no—
593C42×C73—41no—
594C42×C73—41no—
595C23×C73—21no—
596C23×C73—21no—
597C23×C73—21no—
598C23×C73—21no—
599C23×C73—21no—
600C23×C73—21no—
601C23×C73—21no—
602C23×C73—21no—
603C23×C73—21no—
604C23×C73—21no—
605C23×C73—21no—
606C23×C73—21no—
607C23×C73—21no—
608C23×C73—21no—
609C23×C73—21no—
610C23×C73—21no—
611C23×C73—21no—
612C23×C73—21no—
613C23×C73—21no—
614C23×C73—21no—
615C23×C73C22×D412yes—
616C23×C73C2511yescharacteristic
617C22×D73—21no—
618C22×D73—21no—
619C22×D73—21no—
620C22×D73—21no—
621C22×D73—21no—
622C22×D73—21no—
623C22×D73—21no—
624C22×D73—21no—
625C22×D73—21no—
626C22×D73—21no—
627C22×D73—21no—
628C22×D73—21no—
629C22×D73—21no—
630C22×D73—21no—
631C22×D73—21no—
632C22×D73—21no—
633C22×D73—21no—
634C22×D73—21no—
635C22×D73—44no—
636C22×D73—44no—
637C22×D73—44no—
638C22×D73—82no—
639C22×D73—82no—
640C22×D73—82no—
641C22×D73—82no—
642C22×D73C22×D412yes—
643C22×D73C2×#4112yes—
644C22×D73C2×#4112yes—
645Q8×C73—82no—
646D4×C73—82no—
647D4×C73—82no—
648D4×C73—82no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—21no—
654C2×C4×C73—21no—
655C2×C4×C73—21no—
656C2×C4×C73—21no—
657C2×C4×C73—21no—
658C2×C4×C73—21no—
659C2×C4×C73—21no—
660C2×C4×C73—21no—
661C2×C4×C73—21no—
662C2×C4×C73—21no—
663C2×C4×C73—21no—
664C2×C4×C73—21no—
665C2×C4×C73—21no—
666C2×C4×C73—21no—
667C2×C4×C73—21no—
668C2×C4×C73—21no—
669C2×C4×C73—21no—
670C2×C4×C73—21no—
671C2×C4×C73—21no—
672C2×C4×C73—21no—
673C2×C4×C73—21no—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—44no—
682C2×C4×C73—82no—
683C2×C4×C73C22×D412yes—
684C2×C4×C73C22×D412yes—
685C2×C4×C73C2×#4112yes—
686C2×C4×C73C2×#4112yes—
687C22⋊D73—28no—
688C22⋊D73—44no—
689C22⋊D73—44no—
690C22⋊D73—82no—
691C22⋊D73—82no—
692C22⋊D73—82no—
693C22⋊D73—82no—
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×Dic73—21no—
709C2×Dic73—21no—
710C2×Dic73—21no—
711C2×Dic73—21no—
712C2×Dic73—21no—
713C2×Dic73—21no—
714C2×Dic73—21no—
715C2×Dic73—21no—
716C2×Dic73—21no—
717C2×Dic73—21no—
718C2×Dic73—21no—
719C2×Dic73—21no—
720C2×Dic73—21no—
721C2×Dic73—21no—
722C2×Dic73—21no—
723C2×Dic73—21no—
724C2×Dic73—21no—
725C2×Dic73—21no—
726C2×Dic73—21no—
727C2×Dic73—44no—
728C2×Dic73—44no—
729C2×Dic73C22×D412yes—
730C2×Dic73C22×D412yes—
731C2×Dic73C22×D412yes—
732C2×Dic73C2×#4112yes—
733C2×Dic73C2×#4112yes—
734C2×Dic73H(5,𝔽2)12yes—
735D292—44no—
736D292—82no—
737C4×D73—44no—
738C4×D73—44no—
739C4×D73—44no—
740C4×D73—44no—
741C4×D73—82no—
742C4×D73—82no—
743C4×D73—82no—
744Dic146—82no—
745C22×C73—22no—
746C22×C73—22no—
747C22×C73—22no—
748C22×C73—41no—
749C22×C73—41no—
750C22×C73—41no—
751C22×C73—41no—
752C22×C73—41no—
753C22×C73—41no—
754C22×C73—41no—
755C22×C73—41no—
756C22×C73—41no—
757C22×C73—41no—
758C22×C73—41no—
759C22×C73—41no—
760C22×C73—41no—
761C22×C73—41no—
762C22×C73—41no—
763C22×C73—41no—
764C22×C73—41no—
765C22×C73—41no—
766C22×C73C23×D411yescharacteristic
767C22×C73C22×#4111yescharacteristic
768C22×C73C22×#4111yescharacteristic
769C22×C73C2×H(5,𝔽2)11yescharacteristic
770C22×C73#58511yescharacteristic
771C22×C73#58511yescharacteristic
772C22×C73#58511yescharacteristic
773C2×D73—22no—
774C2×D73—22no—
775C2×D73—22no—
776C2×D73—22no—
777C2×D73—22no—
778C2×D73—22no—
779C2×D73—41no—
780C2×D73—41no—
781C2×D73—41no—
782C2×D73—41no—
783C2×D73—41no—
784C2×D73—41no—
785C2×D73—41no—
786C2×D73—41no—
787C2×D73—41no—
788C2×D73—41no—
789C2×D73—41no—
790C2×D73—41no—
791C2×D73—41no—
792C2×D73—41no—
793C2×D73—88no—
794C2×D73#53214yes—
795C4×C73—22no—
796C4×C73—22no—
797C4×C73—22no—
798C4×C73—22no—
799C4×C73—41no—
800C4×C73—41no—
801C4×C73—41no—
802C4×C73—41no—
803C4×C73—41no—
804C4×C73—41no—
805C4×C73—41no—
806C4×C73—41no—
807Dic73—22no—
808Dic73—22no—
809Dic73—22no—
810Dic73—22no—
811Dic73—22no—
812Dic73—22no—
813Dic73—41no—
814Dic73—41no—
815Dic73—41no—
816Dic73—41no—
817Dic73—41no—
818Dic73—41no—
819Dic73—41no—
820#35009—731nomaximal, Sylow
821C2×C73—42no—
822C2×C73—81no—
823C2×C73—81no—
824C2×C73C2×#53211yescharacteristic
825C2×C73#345511yescharacteristic
826C2×C73#345911yescharacteristic
827C2×C73#349611yescharacteristic
828C2×C73#350011yescharacteristic
829C2×C73#351311yescharacteristic
830C2×C73#352111yescharacteristic
831D73—24no—
832D73—81no—
833D73—81no—
834C2×#539—731no—
835C2×#538—731no—
836#2861—731no—
837#2860—731no—
838#2854—731no—
839#2850—731no—
840#2664—731no—
841#2663—731no—
842#2662—731no—
843#2661—731no—
844#2560—731no—
845#2559—731no—
846#2558—731no—
847#2557D7311yescharacteristic, complemented
848#2549—731no—
849#2543—731no—
850#2539—731no—
851#2534—731no—
852#2521—731no—
853#2519—731no—
854#2488—731no—
855#2472—731no—
856#2464—731no—
857#2461—731no—
858#2425—731no—
859#2424—731no—
860#2322—731no—
861#2321—731no—
862C4×#121—731no—
863C2×#388—731no—
864C42×D4—731no—
865C73#3500911yescharacteristic, complemented, Sylow
866#539—1468no—
867#538—1468no—
868C2×#126—731no—
869C2×#126—731no—
870C2×#126—731no—
871C2×#126—731no—
872C2×#125—731no—
873C2×#125—731no—
874C2×#124—731no—
875C2×#124—731no—
876C2×#124C2×D7311yescharacteristic
877C2×#123—731no—
878C2×#123—731no—
879C2×#123—731no—
880C2×#123—731no—
881C2×#123—731no—
882C2×#123—731no—
883C2×#123C2×D7311yescharacteristic, complemented
884C2×C22⋊Q8—731no—
885C2×C22⋊Q8—731no—
886C2×C22⋊Q8—731no—
887C2×C22⋊Q8—731no—
888C2×#121—731no—
889C2×#121—731no—
890C2×#121—731no—
891C2×#121—731no—
892C2×#121—731no—
893C2×#121—731no—
894C2×#120—731no—
895C2×#120—731no—
896C2×#120—731no—
897C2×C4×D4—731no—
898C2×C4×D4—731no—
899C2×C4×D4—731no—
900C2×C4×D4—731no—
901C2×C4×D4—731no—
902C2×C4×D4—731no—
903C22×C4⋊C4—731no—
904C22×C22⋊C4—731no—
905C22×C22⋊C4—731no—
906C22×C22⋊C4—731no—
907C22×C42—731no—
908C22×C42—731no—
909#400—731no—
910#400—731no—
911#399—731no—
912#399—731no—
913#398—731no—
914#398—731no—
915#398—731no—
916#398—731no—
917#397—731no—
918#397—731no—
919#397C2×D7311yescharacteristic
920#397C2×D7311yescharacteristic, complemented
921#396—731no—
922#396—731no—
923#396—731no—
924#396—731no—
925#395—731no—
926#395—731no—
927#394—731no—
928#394—731no—
929#394—731no—
930#394—731no—
931#394—731no—
932#394—731no—
933#394—731no—
934#394—731no—
935#393—731no—
936#393C2×D7311yescharacteristic, complemented
937#392—731no—
938#392—731no—
939#392—731no—
940#392C2×D7311yescharacteristic
941#391—731no—
942#391—731no—
943#391C2×D7311yescharacteristic, complemented
944#390—731no—
945#390—731no—
946#390—731no—
947#390—731no—
948#390—731no—
949#390—731no—
950#390—731no—
951#390—731no—
952#390C2×D7311yescharacteristic
953#389—731no—
954#389—731no—
955#389—731no—
956#389—731no—
957#389—731no—
958#389—731no—
959#388—731no—
960#388—731no—
961#388—731no—
962#388—731no—
963#388—731no—
964#388—731no—
965#388—731no—
966#388—731no—
967#388—731no—
968#388—731no—
969#388—731no—
970#388—731no—
971#388—731no—
972#388—731no—
973#388—731no—
974#388—731no—
975#388—731no—
976#388—731no—
977#388—731no—
978#388—731no—
979#388—731no—
980#388—731no—
981#388—731no—
982#388—731no—
983#388—731no—
984#388C2×D7311yescharacteristic
985#387—731no—
986#387C2×D7311yescharacteristic, complemented
987#386—731no—
988#386—731no—
989#386—731no—
990#386—731no—
991#386—731no—
992#386—731no—
993#386—731no—
994#386—731no—
995#386—731no—
996#386C2×D7311yescharacteristic
997#386C2×D7311yescharacteristic
998#386C2×D7311yescharacteristic, complemented
999#385—731no—
1000#385—731no—
1001#385—731no—
1002#385—731no—
1003#382—731no—
1004#381—731no—
1005#380—731no—
1006#380—731no—
1007#379—731no—
1008C4×C4⋊C4—731no—
1009C4×C4⋊C4—731no—
1010C4×C4⋊C4—731no—
1011C4×C4⋊C4—731no—
1012C4×C22⋊C4—731no—
1013C4×C22⋊C4—731no—
1014C4×C22⋊C4—731no—
1015C4×C22⋊C4—731no—
1016C4×C22⋊C4—731no—
1017C4×C22⋊C4—731no—
1018C4×C22⋊C4C2×D7311yescharacteristic, complemented
1019C4×C22⋊C4C2×D7311yescharacteristic, complemented
1020C2×#95—731no—
1021C2×#95—731no—
1022C43—731no—
1023C25—731no—
1024C22×Q8—731no—
1025C22×Q8C22×D7311yescharacteristic
1026C22×D4—731no—
1027C22×D4—731no—
1028C22×D4—731no—
1029C22×D4—731no—
1030C22×D4—731no—
1031C22×D4—731no—
1032C22×D4—731no—
1033C22×D4—731no—
1034C22×D4—731no—
1035C22×D4C22×D7311yescharacteristic
1036C22×D4C22×D7311yescharacteristic
1037C22×D4C22×D7311yescharacteristic
1038C23×C4—731no—
1039C23×C4—731no—
1040C23×C4—731no—
1041C23×C4—731no—
1042C23×C4—731no—
1043C23×C4—731no—
1044C23×C4—731no—
1045C23×C4—731no—
1046C23×C4—731no—
1047C23×C4C22×D7311yescharacteristic
1048C23×C4C22×D7311yescharacteristic
1049#126—1464no—
1050#126—1464no—
1051#126—1464no—
1052#126—1464no—
1053#125—1464no—
1054#125—1464no—
1055#124—24no—
1056#124—2922no—
1057#124—1464no—
1058#123—24no—
1059#123—1464no—
1060#123—1464no—
1061#123—1464no—
1062#123—1464no—
1063#123—1464no—
1064#123—1464no—
1065C22⋊Q8—1464no—
1066C22⋊Q8—1464no—
1067C22⋊Q8—1464no—
1068C22⋊Q8—1464no—
1069#121—2922no—
1070#121—1464no—
1071#121—1464no—
1072#121—1464no—
1073#121—1464no—
1074#121—1464no—
1075#120—1464no—
1076#120—1464no—
1077#120—1464no—
1078C4×D4—2922no—
1079C4×D4—738no—
1080C4×D4—1464no—
1081C4×D4—1464no—
1082C4×D4—1464no—
1083C4×D4—1464no—
1084C2×C4⋊C4—731no—
1085C2×C4⋊C4—731no—
1086C2×C4⋊C4—731no—
1087C2×C4⋊C4—731no—
1088C2×C4⋊C4—731no—
1089C2×C4⋊C4—731no—
1090C2×C4⋊C4—731no—
1091C2×C4⋊C4—731no—
1092C2×C4⋊C4—731no—
1093C2×C4⋊C4—731no—
1094C2×C4⋊C4—731no—
1095C2×C4⋊C4—731no—
1096C2×C4⋊C4—731no—
1097C2×C4⋊C4—731no—
1098C2×C4⋊C4—731no—
1099C2×C4⋊C4—731no—
1100C2×C4⋊C4—731no—
1101C2×C4⋊C4—731no—
1102C2×C4⋊C4—731no—
1103C2×C4⋊C4—731no—
1104C2×C4⋊C4—731no—
1105C2×C4⋊C4—731no—
1106C2×C4⋊C4—731no—
1107C2×C4⋊C4—731no—
1108C2×C4⋊C4—731no—
1109C2×C4⋊C4—731no—
1110C2×C4⋊C4—731no—
1111C2×C4⋊C4—1464no—
1112C2×C4⋊C4C22×D7311yescharacteristic
1113C2×C4⋊C4C22×D7311yescharacteristic
1114C2×C4⋊C4C22×D7311yescharacteristic
1115C2×C22⋊C4—2922no—
1116C2×C22⋊C4—731no—
1117C2×C22⋊C4—731no—
1118C2×C22⋊C4—731no—
1119C2×C22⋊C4—731no—
1120C2×C22⋊C4—731no—
1121C2×C22⋊C4—731no—
1122C2×C22⋊C4—731no—
1123C2×C22⋊C4—731no—
1124C2×C22⋊C4—731no—
1125C2×C22⋊C4—731no—
1126C2×C22⋊C4—731no—
1127C2×C22⋊C4—731no—
1128C2×C22⋊C4—731no—
1129C2×C22⋊C4—731no—
1130C2×C22⋊C4—731no—
1131C2×C22⋊C4—731no—
1132C2×C22⋊C4—731no—
1133C2×C22⋊C4—731no—
1134C2×C22⋊C4—731no—
1135C2×C22⋊C4—731no—
1136C2×C22⋊C4—731no—
1137C2×C22⋊C4—731no—
1138C2×C22⋊C4—731no—
1139C2×C22⋊C4—731no—
1140C2×C22⋊C4—731no—
1141C2×C22⋊C4—731no—
1142C2×C22⋊C4—731no—
1143C2×C22⋊C4—731no—
1144C2×C22⋊C4—731no—
1145C2×C22⋊C4—731no—
1146C2×C22⋊C4—731no—
1147C2×C22⋊C4—731no—
1148C2×C22⋊C4—731no—
1149C2×C22⋊C4—731no—
1150C2×C22⋊C4—731no—
1151C2×C22⋊C4—731no—
1152C2×C22⋊C4—731no—
1153C2×C22⋊C4—731no—
1154C2×C22⋊C4—731no—
1155C2×C22⋊C4—1464no—
1156C2×C22⋊C4—1464no—
1157C2×C22⋊C4C22×D7311yescharacteristic
1158C2×C22⋊C4C22×D7311yescharacteristic
1159C2×C22⋊C4C22×D7311yescharacteristic
1160C2×C22⋊C4C22×D7311yescharacteristic
1161C2×C22⋊C4C22×D7311yescharacteristic
1162C2×C22⋊C4C22×D7311yescharacteristic
1163C2×C22⋊C4C22×D7311yescharacteristic
1164C2×C22⋊C4C22×D7311yescharacteristic
1165C2×C22⋊C4C22×D7311yescharacteristic
1166C2×C22⋊C4C22×D7311yescharacteristic
1167C2×C22⋊C4C22×D7311yescharacteristic
1168C2×C22⋊C4C22×D7311yescharacteristic
1169C2×C22⋊C4C22×D7311yescharacteristic
1170C2×C42—2922no—
1171C2×C42—2922no—
1172C2×C42—731no—
1173C2×C42—731no—
1174C2×C42—731no—
1175C2×C42—731no—
1176C2×C42—731no—
1177C2×C42—731no—
1178C2×C42—731no—
1179C2×C42—731no—
1180C2×C42—731no—
1181C2×C42—731no—
1182C2×C42—731no—
1183C2×C42—731no—
1184C2×C42C22×D7311yescharacteristic
1185C2×C42C22×D7311yescharacteristic
1186C2×C42C22×D7311yescharacteristic
1187#95—731no—
1188#95—731no—
1189#95—731no—
1190#95—731no—
1191#95—731no—
1192#95—731no—
1193#95—731no—
1194#95—731no—
1195#95—731no—
1196#95—731no—
1197#95—731no—
1198#95—731no—
1199#95—731no—
1200#95—731no—
1201#95—731no—
1202#95—731no—
1203#95—731no—
1204#95—731no—
1205#95—731no—
1206#95—731no—
1207#95—731no—
1208#95—731no—
1209#95C22×D7311yescharacteristic
1210#95C22×D7311yescharacteristic
1211#95C22×D7311yescharacteristic
1212#95C22×D7311yescharacteristic
1213#95C22×D7311yescharacteristic
1214#95C22×D7311yescharacteristic
1215#95C22×D7311yescharacteristic
1216#95C22×D7311yescharacteristic
1217#95C22×D7311yescharacteristic
1218#95C22×D7311yescharacteristic
1219C24—2921no—
1220C24—2921no—
1221C24—2921no—
1222C24—2921no—
1223C24—731no—
1224C24—731no—
1225C24—731no—
1226C24—1462no—
1227C24—1462no—
1228C24—1462no—
1229C24C23×D7311yescharacteristic
1230C24C23×D7311yescharacteristic
1231C24C23×D7311yescharacteristic
1232C2×Q8—22no—
1233C2×Q8—41no—
1234C2×Q8—41no—
1235C2×Q8—2921no—
1236C2×Q8—2921no—
1237C2×Q8—1462no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—22no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—41no—
1244C2×D4—41no—
1245C2×D4—41no—
1246C2×D4—41no—
1247C2×D4—2921no—
1248C2×D4—2921no—
1249C2×D4—2921no—
1250C2×D4—2921no—
1251C2×D4—2921no—
1252C2×D4—2921no—
1253C2×D4—2921no—
1254C2×D4—2921no—
1255C2×D4—2921no—
1256C2×D4—2921no—
1257C2×D4—2921no—
1258C2×D4—2921no—
1259C2×D4—734no—
1260C2×D4—1462no—
1261C2×D4—1462no—
1262C2×D4—1462no—
1263C2×D4—1462no—
1264C2×D4—1462no—
1265C2×D4—1462no—
1266C2×D4—1462no—
1267C2×D4—1462no—
1268C2×D4—1462no—
1269C2×D4—1462no—
1270C2×D4—1462no—
1271C2×D4—1462no—
1272C2×D4—1462no—
1273C2×D4—1462no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—41no—
1277C22×C4—41no—
1278C22×C4—41no—
1279C22×C4—41no—
1280C22×C4—2921no—
1281C22×C4—2921no—
1282C22×C4—2921no—
1283C22×C4—2921no—
1284C22×C4—2921no—
1285C22×C4—2921no—
1286C22×C4—2921no—
1287C22×C4—2921no—
1288C22×C4—2921no—
1289C22×C4—2921no—
1290C22×C4—2921no—
1291C22×C4—2921no—
1292C22×C4—2921no—
1293C22×C4—2921no—
1294C22×C4—734no—
1295C22×C4—734no—
1296C22×C4—734no—
1297C22×C4—731no—
1298C22×C4—731no—
1299C22×C4—731no—
1300C22×C4—731no—
1301C22×C4—731no—
1302C22×C4—731no—
1303C22×C4—731no—
1304C22×C4—731no—
1305C22×C4—731no—
1306C22×C4—731no—
1307C22×C4—731no—
1308C22×C4—731no—
1309C22×C4—731no—
1310C22×C4—1462no—
1311C22×C4—1462no—
1312C22×C4—1462no—
1313C22×C4—1462no—
1314C22×C4—1462no—
1315C22×C4—1462no—
1316C22×C4—1462no—
1317C22×C4—1462no—
1318C22×C4—1462no—
1319C22×C4—1462no—
1320C22×C4C23×D7311yescharacteristic
1321C22×C4C23×D7311yescharacteristic
1322C22×C4C23×D7311yescharacteristic
1323C22×C4C23×D7311yescharacteristic
1324C22×C4C23×D7311yescharacteristic
1325C22×C4C23×D7311yescharacteristic
1326C22×C4C23×D7311yescharacteristic
1327C22×C4C23×D7311yescharacteristic
1328C22×C4C23×D7311yescharacteristic
1329C22×C4C23×D7311yescharacteristic
1330C22×C4C23×D7311yescharacteristic
1331C22×C4C23×D7311yescharacteristic
1332C4⋊C4—22no—
1333C4⋊C4—22no—
1334C4⋊C4—22no—
1335C4⋊C4—2921no—
1336C4⋊C4—2921no—
1337C4⋊C4—2921no—
1338C4⋊C4—2921no—
1339C4⋊C4—2921no—
1340C4⋊C4—2921no—
1341C4⋊C4—734no—
1342C4⋊C4—1462no—
1343C4⋊C4—1462no—
1344C4⋊C4—1462no—
1345C4⋊C4—1462no—
1346C4⋊C4—1462no—
1347C4⋊C4—1462no—
1348C4⋊C4—1462no—
1349C4⋊C4—1462no—
1350C4⋊C4—1462no—
1351C4⋊C4—1462no—
1352C4⋊C4—1462no—
1353C4⋊C4—1462no—
1354C4⋊C4—1462no—
1355C4⋊C4—1462no—
1356C4⋊C4—1462no—
1357C4⋊C4—1462no—
1358C4⋊C4—1462no—
1359C4⋊C4—1462no—
1360C4⋊C4—1462no—
1361C4⋊C4—1462no—
1362C22⋊C4—22no—
1363C22⋊C4—22no—
1364C22⋊C4—22no—
1365C22⋊C4—22no—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—22no—
1369C22⋊C4—22no—
1370C22⋊C4—41no—
1371C22⋊C4—41no—
1372C22⋊C4—41no—
1373C22⋊C4—41no—
1374C22⋊C4—2921no—
1375C22⋊C4—2921no—
1376C22⋊C4—2921no—
1377C22⋊C4—2921no—
1378C22⋊C4—2921no—
1379C22⋊C4—2921no—
1380C22⋊C4—2921no—
1381C22⋊C4—2921no—
1382C22⋊C4—734no—
1383C22⋊C4—734no—
1384C22⋊C4—1462no—
1385C22⋊C4—1462no—
1386C22⋊C4—1462no—
1387C22⋊C4—1462no—
1388C22⋊C4—1462no—
1389C22⋊C4—1462no—
1390C22⋊C4—1462no—
1391C22⋊C4—1462no—
1392C22⋊C4—1462no—
1393C22⋊C4—1462no—
1394C22⋊C4—1462no—
1395C22⋊C4—1462no—
1396C22⋊C4—1462no—
1397C22⋊C4—1462no—
1398C22⋊C4—1462no—
1399C22⋊C4—1462no—
1400C22⋊C4—1462no—
1401C22⋊C4—1462no—
1402C22⋊C4—1462no—
1403C22⋊C4—1462no—
1404C22⋊C4—1462no—
1405C22⋊C4—1462no—
1406C22⋊C4—1462no—
1407C22⋊C4—1462no—
1408C22⋊C4—1462no—
1409C22⋊C4—1462no—
1410C22⋊C4—1462no—
1411C22⋊C4—1462no—
1412C22⋊C4—1462no—
1413C22⋊C4D4×D7314yes—
1414C42—22no—
1415C42—41no—
1416C42—41no—
1417C42—2921no—
1418C42—2921no—
1419C42—2921no—
1420C42—2921no—
1421C42—2921no—
1422C42—734no—
1423C42—1462no—
1424C42—1462no—
1425C42—1462no—
1426C42—1462no—
1427C42—1462no—
1428C42—1462no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—2924no—
1450C23—2924no—
1451C23—2924no—
1452C23—5842no—
1453C23—5842no—
1454C23—5842no—
1455C23—5842no—
1456C23—732no—
1457C23—732no—
1458C23—732no—
1459C23—1461no—
1460C23—1461no—
1461C23—1461no—
1462C23—1461no—
1463C23—1461no—
1464C23—1461no—
1465C23—1461no—
1466C23—1461no—
1467C23—1461no—
1468C23—1461no—
1469C23—1461no—
1470C23—1461no—
1471C23—1461no—
1472C23—1461no—
1473C23—1461no—
1474C23—1461no—
1475C23—1461no—
1476C23—1461no—
1477C23C2×D4×D7312yes—
1478C23C24×D7311yescharacteristic
1479Q8—82no—
1480Q8—5842no—
1481D4—82no—
1482D4—82no—
1483D4—82no—
1484D4—2924no—
1485D4—2924no—
1486D4—2924no—
1487D4—5842no—
1488D4—5842no—
1489D4—5842no—
1490D4—5842no—
1491D4—5842no—
1492D4—1468no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—44no—
1526C2×C4—82no—
1527C2×C4—2924no—
1528C2×C4—2924no—
1529C2×C4—2924no—
1530C2×C4—2924no—
1531C2×C4—2924no—
1532C2×C4—2924no—
1533C2×C4—5842no—
1534C2×C4—5842no—
1535C2×C4—5842no—
1536C2×C4—732no—
1537C2×C4—732no—
1538C2×C4—732no—
1539C2×C4—732no—
1540C2×C4—732no—
1541C2×C4—732no—
1542C2×C4—1461no—
1543C2×C4—1461no—
1544C2×C4—1461no—
1545C2×C4—1461no—
1546C2×C4—1461no—
1547C2×C4—1461no—
1548C2×C4—1461no—
1549C2×C4—1461no—
1550C2×C4—1461no—
1551C2×C4—1461no—
1552C2×C4—1461no—
1553C2×C4—1461no—
1554C2×C4—1461no—
1555C2×C4—1461no—
1556C2×C4—1461no—
1557C2×C4—1461no—
1558C2×C4—1461no—
1559C2×C4—1461no—
1560C2×C4—1461no—
1561C2×C4—1461no—
1562C2×C4—1461no—
1563C2×C4—1461no—
1564C2×C4—1461no—
1565C2×C4—1461no—
1566C2×C4—1461no—
1567C2×C4—1461no—
1568C2×C4—1461no—
1569C2×C4—1461no—
1570C2×C4—1461no—
1571C2×C4—1461no—
1572C2×C4—1461no—
1573C2×C4—1461no—
1574C2×C4—1461no—
1575C2×C4C2×D4×D7312yes—
1576C2×C4C2×D4×D7312yes—
1577C2×C4#41×D7312yes—
1578C2×C4#41×D7312yes—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—41no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—2921no—
1601C22—2921no—
1602C22—2921no—
1603C22—2921no—
1604C22—2921no—
1605C22—2921no—
1606C22—2921no—
1607C22—2921no—
1608C22—2921no—
1609C22—2921no—
1610C22—2921no—
1611C22—2921no—
1612C22—2921no—
1613C22—2921no—
1614C22—5848no—
1615C22—734no—
1616C22—1462no—
1617C22—1462no—
1618C22—1462no—
1619C22—1462no—
1620C22—1462no—
1621C22—1462no—
1622C22C22×D4×D7311yescharacteristic
1623C22C2×#41×D7311yescharacteristic
1624C22C2×#41×D7311yescharacteristic
1625C22H(5,𝔽2)×D7311yescharacteristic
1626C22#1798942211yescharacteristic
1627C22#1798942311yescharacteristic
1628C22#1798942311yescharacteristic
1629C4—22no—
1630C4—22no—
1631C4—22no—
1632C4—22no—
1633C4—41no—
1634C4—41no—
1635C4—41no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—2921no—
1642C4—2921no—
1643C4—2921no—
1644C4—2921no—
1645C4—2921no—
1646C4—2921no—
1647C4—2921no—
1648C4—1462no—
1649C4—1462no—
1650C4—1462no—
1651C4—1462no—
1652C4—1462no—
1653C4—1462no—
1654C2—42no—
1655C2—81no—
1656C2—81no—
1657C2—5841no—
1658C2—5841no—
1659C2—1464no—
1660C2#532×D7311yescharacteristic
1661C2#2262331411yescharacteristic
1662C2#2262334211yescharacteristic
1663C2#2262369111yescharacteristic
1664C2#2262371711yescharacteristic
1665C2#2262387011yescharacteristic
1666C2#2262399611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2557C2
hypercenter#2557D73
hypocenterC73#35009
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2557

Complements

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

NH ≅ G/Ntype
1. C2×#17989180C2semidirect
2. C2×#17989171C2semidirect
3. #22618305C2semidirect
4. #22618295C2semidirect
5. #22618259C2semidirect
6. #22618228C2semidirect
7. #22616099C2semidirect
8. #22616080C2semidirect
9. #22616077C2semidirect
10. #22616056C2semidirect
11. #22615075C2semidirect
12. #22615054C2semidirect
13. #22615047C2semidirect
14. #22614940C2semidirect
15. #22614890C2semidirect
16. #22614860C2semidirect
17. #22614819C2semidirect
18. #22614631C2semidirect
19. #22614609C2semidirect
20. #22614250C2semidirect
21. #22614050C2semidirect
22. #22613934C2semidirect
23. #22613903C2semidirect
24. #22613485C2semidirect
25. #22613470C2semidirect
26. #22612604C2semidirect
27. #22612587C2semidirect
28. C4×#14556564C2semidirect
29. #388×D73C2semidirect
30. C4×#14556551C2semidirect
31. C73×#2557C2semidirect
36. C2×#14556584C22semidirect
37. C2×#14556584C22semidirect
38. C2×#14556582C22semidirect
39. C2×#14556581C22semidirect
47. C2×#14556572C22semidirect
48. C2×#14556570C22semidirect
50. C2×#14556568C22semidirect
64. C2×C4×C22⋊D73C22semidirect
71. C22×C4×Dic73C22semidirect
73. #17988529C22semidirect
74. #17988527C22semidirect
77. #17988521C22semidirect
78. #17988521C22semidirect
79. #17988521C22semidirect
80. #17988518C22semidirect
81. #17988515C22semidirect
82. #17988515C22semidirect
84. #17988511C22semidirect
87. #17988508C22semidirect
88. #17988506C22semidirect
91. #17988503C22semidirect
95. #17988502C22semidirect
100. #17988495C22semidirect
101. #17988494C22semidirect
102. #17988491C22semidirect
110. #17988487C22semidirect
111. #17988486C22semidirect
112. #17988485C22semidirect
113. #17988484C22semidirect
114. #17988484C22semidirect
115. #17988484C22semidirect
116. #17988483C22semidirect
119. #17988481C22semidirect
121. #17988480C22semidirect
122. #17988480C22semidirect
127. #17988479C22semidirect
128. #17988479C22semidirect
129. #17988479C22semidirect
135. #17988476C22semidirect
136. #17988476C22semidirect
141. #17988475C22semidirect
142. #17988471C22semidirect
146. #17988466C22semidirect
149. #17988464C22semidirect
154. #17988461C22semidirect
155. #17988458C22semidirect
156. #17988451C22semidirect
159. #17988445C22semidirect
161. C4×#11924007C22semidirect
162. C4×#11924007C22semidirect
163. #17988438C22semidirect
164. #17988438C22semidirect
165. C22⋊C4×Dic73C22semidirect
166. C22⋊C4×Dic73C22semidirect
168. C4×#11924005C22semidirect
173. C42×Dic73C22semidirect
175. C2×#123×C73C22semidirect
177. #397×C73C22semidirect
178. #393×C73C22semidirect
180. #391×C73C22semidirect
183. #387×C73C22semidirect
186. #386×C73C22semidirect
187. C4×C22⋊C4×C73C22semidirect
188. C4×C22⋊C4×C73C22semidirect
241. #14556551D4semidirect
847. #2557D73semidirect
865. C73#35009semidirect
883. C2×#123C2×D73semidirect
920. #397C2×D73semidirect
936. #393C2×D73semidirect
943. #391C2×D73semidirect
986. #387C2×D73semidirect
998. #386C2×D73semidirect
1018. C4×C22⋊C4C2×D73semidirect
1019. C4×C22⋊C4C2×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891802
C2×#179891712
#226183052
#226182952
#226182592
#226182282
#226160992
#226160802
#226160772
#226160562
#226150752
#226150542
#226150472
#226149402
#226148902
#226148602
#226148192
#226146312
#226146092
#226142502
#226140502
#226139342
#226139032
#226134852
#226134702
#226126042
#226125872
C4×#145565642
#388×D732
C4×#145565512
C73×#25572
#3500973