Finite Group Databasebeta

← #33949293

Subgroups — #33949293

Order 18688.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22617750C211yesmaximal, characteristic, complemented
2#22616917C211yesmaximal, characteristic, complemented
3#22616913C211yesmaximal, characteristic, complemented
4#22616268C211yesmaximal, characteristic
5#22615590C211yesmaximal, characteristic, complemented
6#22615585C211yesmaximal, characteristic, complemented
7#22615508C211yesmaximal, characteristic, complemented
8#22615505C211yesmaximal, characteristic, complemented
9#22615344C211yesmaximal, characteristic, complemented
10#22615296C211yesmaximal, characteristic, complemented
11#22615182C211yesmaximal, characteristic
12#22614840C211yesmaximal, characteristic
13#22614767C211yesmaximal, characteristic, complemented
14#22614763C211yesmaximal, characteristic, complemented
15#22614672C211yesmaximal, characteristic, complemented
16#22614667C211yesmaximal, characteristic, complemented
17#22614555C211yesmaximal, characteristic, complemented
18#22614550C211yesmaximal, characteristic, complemented
19#22614024C211yesmaximal, characteristic
20#22614023C211yesmaximal, characteristic
21#22613607C211yesmaximal, characteristic, complemented
22#22613605C211yesmaximal, characteristic, complemented
23#22613014C211yesmaximal, characteristic, complemented
24#22613011C211yesmaximal, characteristic, complemented
25#22612958C211yesmaximal, characteristic, complemented
26#22612955C211yesmaximal, characteristic, complemented
27#22612917C211yesmaximal, characteristic
28C4×#14556590C211yesmaximal, characteristic, complemented
29#22612427C211yesmaximal, characteristic, complemented
30#22612425C211yesmaximal, characteristic, complemented
31C73×#2359C211yesmaximal, characteristic
32C2×#14556590C2211yescharacteristic
33C2×#14556572C2211yescharacteristic
34C2×#14556570C2211yescharacteristic
35C2×#14556570C2211yescharacteristic
36C2×#14556570C2211yescharacteristic
37C2×#14556568C2211yescharacteristic
38C2×C4×Dic146C2211yescharacteristic
39C2×C4×Dic146C2211yescharacteristic
40C2×#14556556C2211yescharacteristic
41C2×#14556550C2211yescharacteristic
42C2×#14556547C2211yescharacteristic
43C2×#14556547C2211yescharacteristic
44#17988529C2211yescharacteristic
45#17988529C2211yescharacteristic
46#17988529C2211yescharacteristic
47#17988528C2211yescharacteristic
48#17988527C2211yescharacteristic
49#17988527C2211yescharacteristic
50#17988526C2211yescharacteristic
51#17988525C2211yescharacteristic
52#17988521C2211yescharacteristic
53#17988521C2211yescharacteristic
54#17988520C2211yescharacteristic
55#17988519C2211yescharacteristic
56#17988518C2211yescharacteristic
57#17988518C2211yescharacteristic
58#17988518C2211yescharacteristic
59#17988518C2211yescharacteristic
60#17988517C2211yescharacteristic
61#17988517C2211yescharacteristic
62#17988515C2211yescharacteristic
63#17988515C2211yescharacteristic
64#17988512C2211yescharacteristic
65#17988512C2211yescharacteristic
66#17988510C2211yescharacteristic
67#17988510C2211yescharacteristic
68#17988508C2211yescharacteristic
69#17988507C2211yescharacteristic
70#17988507C2211yescharacteristic
71#17988507C2211yescharacteristic
72#17988501C2211yescharacteristic
73#17988501C2211yescharacteristic
74#17988499C2211yescharacteristic
75#17988499C2211yescharacteristic
76#17988492C2211yescharacteristic
77#17988491C2211yescharacteristic
78#17988491C2211yescharacteristic
79#17988491C2211yescharacteristic
80#17988491C2211yescharacteristic
81#17988491C2211yescharacteristic
82#17988486C2211yescharacteristic
83#17988484C2211yescharacteristic
84#17988484C2211yescharacteristic
85#17988484C2211yescharacteristic
86#17988484C2211yescharacteristic
87#17988483C2211yescharacteristic
88#17988483C2211yescharacteristic
89#17988482C2211yescharacteristic
90#17988482C2211yescharacteristic
91#17988481C2211yescharacteristic
92#17988481C2211yescharacteristic
93#17988481C2211yescharacteristic
94#17988481C2211yescharacteristic
95#17988480C2211yescharacteristic
96#17988480C2211yescharacteristic
97#17988475C2211yescharacteristic
98#17988475C2211yescharacteristic
99#17988475C2211yescharacteristic
100#17988475C2211yescharacteristic
101#17988475C2211yescharacteristic
102#17988475C2211yescharacteristic
103#17988475C2211yescharacteristic
104#17988475C2211yescharacteristic
105#17988474C2211yescharacteristic
106#17988473C2211yescharacteristic
107#17988472C2211yescharacteristic
108#17988472C2211yescharacteristic
109#17988472C2211yescharacteristic
110#17988472C2211yescharacteristic
111#17988471C2211yescharacteristic
112#17988471C2211yescharacteristic
113#17988471C2211yescharacteristic
114#17988471C2211yescharacteristic
115#17988471C2211yescharacteristic
116#17988471C2211yescharacteristic
117#17988471C2211yescharacteristic
118#17988471C2211yescharacteristic
119#17988470C2211yescharacteristic
120#17988470C2211yescharacteristic
121#17988470C2211yescharacteristic
122#17988470C2211yescharacteristic
123#17988470C2211yescharacteristic
124#17988469C2211yescharacteristic
125#17988469C2211yescharacteristic
126#17988469C2211yescharacteristic
127#17988469C2211yescharacteristic
128#17988468C2211yescharacteristic
129#17988468C2211yescharacteristic
130#17988468C2211yescharacteristic
131#17988468C2211yescharacteristic
132#17988468C2211yescharacteristic
133#17988467C2211yescharacteristic
134#17988462C2211yescharacteristic
135#17988460C2211yescharacteristic
136#17988460C2211yescharacteristic
137#17988460C2211yescharacteristic
138#17988460C2211yescharacteristic
139#17988460C2211yescharacteristic
140#17988459C2211yescharacteristic
141#17988459C2211yescharacteristic
142#17988456C2211yescharacteristic
143#17988455C2211yescharacteristic
144#17988454C2211yescharacteristic
145#17988454C2211yescharacteristic
146#17988454C2211yescharacteristic
147#17988453C2211yescharacteristic
148#17988451C2211yescharacteristic
149#17988450C2211yescharacteristic
150#17988448C2211yescharacteristic
151#17988447C2211yescharacteristic
152#17988447C2211yescharacteristic
153C4⋊C4×Dic73C2211yescharacteristic
154C4×#11924007C2211yescharacteristic
155C4×#11924007C2211yescharacteristic
156C4×#11924007C2211yescharacteristic
157C4×#11924007C2211yescharacteristic
158C4×#11924007C2211yescharacteristic
159C4×C4⋊Dic73C2211yescharacteristic
160#17988438C2211yescharacteristic
161#17988438C2211yescharacteristic
162C22⋊C4×Dic73C2211yescharacteristic
163C22⋊C4×Dic73C2211yescharacteristic
164C22⋊C4×Dic73C2211yescharacteristic
165C4×C22⋊Dic73C2211yescharacteristic
166C4×C22⋊Dic73C2211yescharacteristic
167C4×C22⋊Dic73C2211yescharacteristic
168#17988433C2211yescharacteristic
169#17988432C2211yescharacteristic
170C2×#14556498C2211yescharacteristic
171C42×Dic73C2211yescharacteristic
172C2×#123×C73C2211yescharacteristic
173C2×C4×D4×C73C2211yescharacteristic
174C2×#117×C73C2211yescharacteristic
175#389×C73C2211yescharacteristic
176#388×C73C2211yescharacteristic
177#388×C73C2211yescharacteristic
178#387×C73C2211yescharacteristic
179#387×C73C2211yescharacteristic
180#386×C73C2211yescharacteristic
181#385×C73C2211yescharacteristic
182#385×C73C2211yescharacteristic
183C4×C4⋊C4×C73C2211yescharacteristic
184C4×C22⋊C4×C73C2211yescharacteristic
185C4×C22⋊C4×C73C2211yescharacteristic
186C2×#95×C73C2211yescharacteristic
187C22×Dic146C2311yescharacteristic
188C22×Dic146C2311yescharacteristic
189C22×Dic146C2311yescharacteristic
190C23×Dic73C2311yescharacteristic
191C23×Dic73C2311yescharacteristic
192#14556590—24no—
193#14556572—24no—
194#14556570—24no—
195#14556570—24no—
196#14556570—24no—
197#14556568—24no—
198C4×Dic146—42no—
199C4×Dic146—42no—
200#14556556—42no—
201#14556550—24no—
202#14556547—24no—
203#14556547—42no—
204C2×C4⋊Dic73C2311yescharacteristic
205C2×C4⋊Dic73C2311yescharacteristic
206C2×C4⋊Dic73C2311yescharacteristic
207C2×C4⋊Dic73C2311yescharacteristic
208C2×C4⋊Dic73C2311yescharacteristic
209C2×C4⋊Dic73C2311yescharacteristic
210C2×C4⋊Dic73C2311yescharacteristic
211C2×C4⋊Dic73C2311yescharacteristic
212C2×C4⋊Dic73C2311yescharacteristic
213C2×#11924007C2311yescharacteristic
214C2×#11924007C2311yescharacteristic
215C2×#11924007C2311yescharacteristic
216C2×#11924007C2311yescharacteristic
217C2×#11924007C2311yescharacteristic
218C2×#11924007C2311yescharacteristic
219C2×#11924007C2311yescharacteristic
220C2×#11924007C2311yescharacteristic
221C2×#11924007C2311yescharacteristic
222C2×#11924007C2311yescharacteristic
223C2×#11924007C2311yescharacteristic
224C2×#11924007C2311yescharacteristic
225C2×#11924007C2311yescharacteristic
226C2×#11924007C2311yescharacteristic
227C2×#11924007C2311yescharacteristic
228C2×#11924007C2311yescharacteristic
229C2×#11924007C2311yescharacteristic
230C2×#11924007C2311yescharacteristic
231C2×#11924007C2311yescharacteristic
232C2×#11924007C2311yescharacteristic
233C2×#11924007C2311yescharacteristic
234C2×#11924007C2311yescharacteristic
235C2×#11924007C2311yescharacteristic
236C2×#11924007C2311yescharacteristic
237C2×#11924007C2311yescharacteristic
238C2×#11924007C2311yescharacteristic
239C2×C22⋊Dic73C2311yescharacteristic
240C2×C22⋊Dic73C2311yescharacteristic
241C2×C22⋊Dic73C2311yescharacteristic
242C2×C22⋊Dic73C2311yescharacteristic
243C2×C22⋊Dic73C2311yescharacteristic
244C2×C22⋊Dic73C2311yescharacteristic
245C2×C22⋊Dic73C2311yescharacteristic
246C2×C22⋊Dic73C2311yescharacteristic
247C2×C22⋊Dic73C2311yescharacteristic
248C2×C22⋊Dic73C2311yescharacteristic
249C2×C22⋊Dic73C2311yescharacteristic
250C2×C22⋊Dic73C2311yescharacteristic
251C2×C22⋊Dic73C2311yescharacteristic
252C2×C22⋊Dic73C2311yescharacteristic
253C2×C4×Dic73C2311yescharacteristic
254C2×C4×Dic73C2311yescharacteristic
255C2×C4×Dic73C2311yescharacteristic
256C2×C4×Dic73C2311yescharacteristic
257C2×C4×Dic73C2311yescharacteristic
258C2×C4×Dic73C2311yescharacteristic
259C2×C4×Dic73C2311yescharacteristic
260C2×C4×Dic73C2311yescharacteristic
261C2×C4×Dic73C2311yescharacteristic
262C2×C4×Dic73C2311yescharacteristic
263C2×C4×Dic73C2311yescharacteristic
264C2×C4×Dic73C2311yescharacteristic
265C2×C4×Dic73C2311yescharacteristic
266C2×C4×Dic73C2311yescharacteristic
267C2×C4×Dic73C2311yescharacteristic
268C2×C4×Dic73C2311yescharacteristic
269#14556498C2311yescharacteristic
270#14556498C2311yescharacteristic
271#14556498C2311yescharacteristic
272#14556498C2311yescharacteristic
273#14556498C2311yescharacteristic
274#14556498C2311yescharacteristic
275#14556498C2311yescharacteristic
276#14556498C2311yescharacteristic
277#14556498C2311yescharacteristic
278#14556498C2311yescharacteristic
279#14556498C2311yescharacteristic
280#14556498C2311yescharacteristic
281#14556498C2311yescharacteristic
282#14556498C2311yescharacteristic
283#14556498C2311yescharacteristic
284#14556498C2311yescharacteristic
285#14556498C2311yescharacteristic
286#14556498C2311yescharacteristic
287#14556498C2311yescharacteristic
288#14556498C2311yescharacteristic
289#14556498C2311yescharacteristic
290#14556498C2311yescharacteristic
291#14556498C2311yescharacteristic
292#14556498C2311yescharacteristic
293#14556498C2311yescharacteristic
294#14556498C2311yescharacteristic
295#14556498C2311yescharacteristic
296#14556498C2311yescharacteristic
297#14556498C2311yescharacteristic
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
319C22×D4×C73C2311yescharacteristic
320C23×C4×C73C2311yescharacteristic
321C23×C4×C73C2311yescharacteristic
322C23×C4×C73C2311yescharacteristic
323C23×C4×C73C2311yescharacteristic
324#123×C73—24no—
325C4×D4×C73—42no—
326#117×C73—42no—
327C2×C4⋊C4×C73C2311yescharacteristic
328C2×C4⋊C4×C73C2311yescharacteristic
329C2×C4⋊C4×C73C2311yescharacteristic
330C2×C4⋊C4×C73C2311yescharacteristic
331C2×C4⋊C4×C73C2311yescharacteristic
332C2×C4⋊C4×C73C2311yescharacteristic
333C2×C4⋊C4×C73C2311yescharacteristic
334C2×C22⋊C4×C73C2311yescharacteristic
335C2×C22⋊C4×C73C2311yescharacteristic
336C2×C22⋊C4×C73C2311yescharacteristic
337C2×C22⋊C4×C73C2311yescharacteristic
338C2×C22⋊C4×C73C2311yescharacteristic
339C2×C22⋊C4×C73C2311yescharacteristic
340C2×C22⋊C4×C73C2311yescharacteristic
341C2×C22⋊C4×C73C2311yescharacteristic
342C2×C42×C73C2311yescharacteristic
343C2×C42×C73C2311yescharacteristic
344C2×C42×C73C2311yescharacteristic
345C2×C42×C73C2311yescharacteristic
346C2×C42×C73C2311yescharacteristic
347#95×C73C2311yescharacteristic
348#95×C73C2311yescharacteristic
349#95×C73C2311yescharacteristic
350#95×C73C2311yescharacteristic
351#95×C73C2311yescharacteristic
352#95×C73C2311yescharacteristic
353#95×C73C2311yescharacteristic
354#95×C73C2311yescharacteristic
355#95×C73C2311yescharacteristic
356#95×C73C2311yescharacteristic
357C2×Dic146—22no—
358C2×Dic146—22no—
359C2×Dic146—22no—
360C2×Dic146—41no—
361C2×Dic146—41no—
362C2×Dic146—41no—
363C2×Dic146—41no—
364C2×Dic146—41no—
365C2×Dic146#4114yes—
366C22×Dic73—22no—
367C22×Dic73—22no—
368C22×Dic73—22no—
369C22×Dic73—22no—
370C22×Dic73—41no—
371C22×Dic73—41no—
372C22×Dic73C2411yescharacteristic
373C22×Dic73C2411yescharacteristic
374C22×Dic73C2411yescharacteristic
375C22×Dic73C2411yescharacteristic
376C22×Dic73C2411yescharacteristic
377C22×Dic73C2411yescharacteristic
378C22×Dic73C2411yescharacteristic
379C22×Dic73C2411yescharacteristic
380C22×Dic73C2411yescharacteristic
381C22×Dic73C2411yescharacteristic
382C22×Dic73C2411yescharacteristic
383C22×Dic73C2411yescharacteristic
384C22×Dic73C2411yescharacteristic
385C22×Dic73C2411yescharacteristic
386C22×Dic73C2411yescharacteristic
387C22×Dic73C2411yescharacteristic
388C4⋊Dic73—22no—
389C4⋊Dic73—22no—
390C4⋊Dic73—22no—
391C4⋊Dic73—22no—
392C4⋊Dic73—22no—
393C4⋊Dic73—22no—
394C4⋊Dic73—22no—
395C4⋊Dic73—41no—
396C4⋊Dic73—41no—
397#11924007—22no—
398#11924007—22no—
399#11924007—22no—
400#11924007—22no—
401#11924007—22no—
402#11924007—22no—
403#11924007—22no—
404#11924007—22no—
405#11924007—22no—
406#11924007—22no—
407#11924007—22no—
408#11924007—22no—
409#11924007—22no—
410#11924007—22no—
411#11924007—22no—
412#11924007—22no—
413#11924007—22no—
414#11924007—41no—
415#11924007—41no—
416#11924007—41no—
417#11924007—41no—
418#11924007—41no—
419#11924007—41no—
420#11924007—41no—
421#11924007—41no—
422#11924007—41no—
423C22⋊Dic73—22no—
424C22⋊Dic73—22no—
425C22⋊Dic73—22no—
426C22⋊Dic73—22no—
427C22⋊Dic73—22no—
428C22⋊Dic73—22no—
429C22⋊Dic73—22no—
430C22⋊Dic73—22no—
431C22⋊Dic73—22no—
432C22⋊Dic73—22no—
433C22⋊Dic73—22no—
434C22⋊Dic73—41no—
435C22⋊Dic73—41no—
436C22⋊Dic73#4114yes—
437C4×Dic73—22no—
438C4×Dic73—22no—
439C4×Dic73—22no—
440C4×Dic73—22no—
441C4×Dic73—22no—
442C4×Dic73—22no—
443C4×Dic73—22no—
444C4×Dic73—22no—
445C4×Dic73—22no—
446C4×Dic73—22no—
447C4×Dic73—22no—
448C4×Dic73—41no—
449C4×Dic73—41no—
450C4×Dic73—41no—
451C4×Dic73—41no—
452C4×Dic73—41no—
453C24×C73C2411yescharacteristic
454C24×C73C2411yescharacteristic
455C2×D4×C73—22no—
456C2×D4×C73—22no—
457C2×D4×C73—41no—
458C22×C4×C73—22no—
459C22×C4×C73—22no—
460C22×C4×C73—22no—
461C22×C4×C73—22no—
462C22×C4×C73—22no—
463C22×C4×C73—22no—
464C22×C4×C73—41no—
465C22×C4×C73—41no—
466C22×C4×C73—41no—
467C22×C4×C73—41no—
468C22×C4×C73—41no—
469C22×C4×C73—41no—
470C22×C4×C73C2411yescharacteristic
471C22×C4×C73C2411yescharacteristic
472C22×C4×C73C2411yescharacteristic
473C22×C4×C73C2411yescharacteristic
474C22×C4×C73C2411yescharacteristic
475C22×C4×C73C2411yescharacteristic
476C22×C4×C73C2411yescharacteristic
477C22×C4×C73C2411yescharacteristic
478C22×C4×C73C2411yescharacteristic
479C22×C4×C73C2411yescharacteristic
480C22×C4×C73C2411yescharacteristic
481C22×C4×C73C2411yescharacteristic
482C22×C4×C73C2411yescharacteristic
483C4⋊C4×C73—22no—
484C4⋊C4×C73—22no—
485C4⋊C4×C73—22no—
486C4⋊C4×C73—22no—
487C4⋊C4×C73—41no—
488C4⋊C4×C73—41no—
489C4⋊C4×C73—41no—
490C22⋊C4×C73—22no—
491C22⋊C4×C73—22no—
492C22⋊C4×C73—22no—
493C22⋊C4×C73—22no—
494C22⋊C4×C73—22no—
495C22⋊C4×C73—41no—
496C22⋊C4×C73—41no—
497C22⋊C4×C73#4114yes—
498C42×C73—22no—
499C42×C73—22no—
500C42×C73—22no—
501C42×C73—41no—
502C42×C73—41no—
503C23×C73—21no—
504C23×C73—21no—
505C23×C73—21no—
506C23×C73—21no—
507C23×C73—21no—
508C23×C73—21no—
509C23×C73—21no—
510C23×C73—21no—
511C23×C73—21no—
512C23×C73—21no—
513C23×C73—21no—
514C23×C73—21no—
515C23×C73C2×#4112yes—
516C23×C73C2×#4112yes—
517C23×C73C2511yescharacteristic
518D4×C73—44no—
519C2×C4×C73—21no—
520C2×C4×C73—21no—
521C2×C4×C73—21no—
522C2×C4×C73—21no—
523C2×C4×C73—21no—
524C2×C4×C73—21no—
525C2×C4×C73—21no—
526C2×C4×C73—21no—
527C2×C4×C73—21no—
528C2×C4×C73—21no—
529C2×C4×C73—21no—
530C2×C4×C73—21no—
531C2×C4×C73—21no—
532C2×C4×C73—21no—
533C2×C4×C73—21no—
534C2×C4×C73—21no—
535C2×C4×C73—21no—
536C2×C4×C73—21no—
537C2×C4×C73—21no—
538C2×C4×C73—21no—
539C2×C4×C73—21no—
540C2×C4×C73—21no—
541C2×C4×C73—21no—
542C2×C4×C73—21no—
543C2×C4×C73—21no—
544C2×C4×C73—21no—
545C2×C4×C73—21no—
546C2×C4×C73—21no—
547C2×C4×C73—21no—
548C2×C4×C73—21no—
549C2×C4×C73—21no—
550C2×C4×C73—21no—
551C2×C4×C73—21no—
552C2×C4×C73—21no—
553C2×C4×C73—44no—
554C2×C4×C73—44no—
555C2×C4×C73—82no—
556C2×C4×C73—82no—
557C2×C4×C73C2×#4112yes—
558C2×C4×C73C2×#4112yes—
559C2×C4×C73C2×#4112yes—
560C2×C4×C73H(5,𝔽2)12yes—
561C2×C4×C732−1+412yes—
562C2×Dic73—21no—
563C2×Dic73—21no—
564C2×Dic73—21no—
565C2×Dic73—21no—
566C2×Dic73—21no—
567C2×Dic73—21no—
568C2×Dic73—21no—
569C2×Dic73—21no—
570C2×Dic73—21no—
571C2×Dic73—21no—
572C2×Dic73—21no—
573C2×Dic73—21no—
574C2×Dic73—21no—
575C2×Dic73—21no—
576C2×Dic73—21no—
577C2×Dic73—21no—
578C2×Dic73—21no—
579C2×Dic73—21no—
580C2×Dic73—21no—
581C2×Dic73—21no—
582C2×Dic73—21no—
583C2×Dic73—21no—
584C2×Dic73—21no—
585C2×Dic73—21no—
586C2×Dic73—21no—
587C2×Dic73—21no—
588C2×Dic73—21no—
589C2×Dic73—21no—
590C2×Dic73—21no—
591C2×Dic73—21no—
592C2×Dic73—21no—
593C2×Dic73—21no—
594C2×Dic73—21no—
595C2×Dic73—21no—
596C2×Dic73—21no—
597C2×Dic73—21no—
598C2×Dic73—21no—
599C2×Dic73—21no—
600C2×Dic73—21no—
601C2×Dic73—21no—
602C2×Dic73—21no—
603C2×Dic73—21no—
604C2×Dic73—21no—
605C2×Dic73—44no—
606C2×Dic73—44no—
607C2×Dic73C2×#4112yes—
608C2×Dic73C2×#4112yes—
609C2×Dic73C2×#4112yes—
610C2×Dic73C2×#4112yes—
611C2×Dic732−1+412yes—
612Dic146—44no—
613Dic146—44no—
614Dic146—44no—
615C22×C73—22no—
616C22×C73—22no—
617C22×C73—22no—
618C22×C73—22no—
619C22×C73—22no—
620C22×C73—22no—
621C22×C73—41no—
622C22×C73—41no—
623C22×C73—41no—
624C22×C73—41no—
625C22×C73—41no—
626C22×C73—41no—
627C22×C73—41no—
628C22×C73—41no—
629C22×C73C22×#4111yescharacteristic
630C22×C73C22×#4111yescharacteristic
631C22×C73C22×#4111yescharacteristic
632C22×C73C2×H(5,𝔽2)11yescharacteristic
633C22×C73C2×2−1+411yescharacteristic
634C22×C73C2×2−1+411yescharacteristic
635C22×C73#58511yescharacteristic
636C4×C73—22no—
637C4×C73—22no—
638C4×C73—22no—
639C4×C73—22no—
640C4×C73—22no—
641C4×C73—41no—
642C4×C73—41no—
643C4×C73—41no—
644C4×C73—41no—
645C4×C73—41no—
646C4×C73—41no—
647C4×C73—41no—
648C4×C73—41no—
649Dic73—22no—
650Dic73—22no—
651Dic73—22no—
652Dic73—22no—
653Dic73—22no—
654Dic73—41no—
655Dic73—41no—
656Dic73—41no—
657Dic73—41no—
658Dic73—41no—
659Dic73—41no—
660Dic73—41no—
661Dic73—41no—
662Dic73—41no—
663Dic73—41no—
664Dic73—41no—
665#60043—731nomaximal, Sylow
666C2×C73—42no—
667C2×C73—42no—
668C2×C73#348111yescharacteristic
669C2×C73#348211yescharacteristic
670C2×C73#348211yescharacteristic
671C2×C73#349511yescharacteristic
672C2×C73#349511yescharacteristic
673C2×C73#350511yescharacteristic
674C2×C73#354411yescharacteristic
675#2794—731no—
676#2729—731no—
677#2729—731no—
678#2680—731no—
679#2606—731no—
680#2606—731no—
681#2599—731no—
682#2599—731no—
683#2586—731no—
684#2581—731no—
685#2572—731no—
686#2536—731no—
687#2530—731no—
688#2530—731no—
689#2524—731no—
690#2524—731no—
691#2515—731no—
692#2515—731no—
693#2470—731no—
694#2470—731no—
695#2438—731no—
696#2438—731no—
697#2368—731no—
698#2368—731no—
699#2362—731no—
700#2362—731no—
701#2359—731no—
702#2359D7311yescharacteristic
703C4×C4⋊Q8—731no—
704#2298—731no—
705#2298—731no—
706C73#6004311yescharacteristic, complemented, Sylow
707C2×C4⋊Q8—731no—
708C2×#123—731no—
709C2×#123C2×D7311yescharacteristic
710C2×C22⋊Q8—731no—
711C2×C22⋊Q8—731no—
712C2×C22⋊Q8—731no—
713C2×C22⋊Q8—731no—
714C2×C4×Q8—731no—
715C2×C4×Q8—731no—
716C2×C4×Q8—731no—
717C2×C4×D4C2×D7311yescharacteristic
718C2×#117—731no—
719C2×#117—731no—
720C2×#117—731no—
721C2×#117C2×D7311yescharacteristic
722#400—731no—
723#400—731no—
724#400—731no—
725#400—731no—
726#400—731no—
727#400—731no—
728#400—731no—
729#400—731no—
730#398—731no—
731#398—731no—
732#398—731no—
733#398—731no—
734#398—731no—
735#398—731no—
736#398—731no—
737#398—731no—
738#398—731no—
739#398—731no—
740#397—731no—
741#397—731no—
742#397—731no—
743#397—731no—
744#396—731no—
745#396—731no—
746#395—731no—
747#395—731no—
748#395—731no—
749#395—731no—
750#394—731no—
751#394—731no—
752#393—731no—
753#393—731no—
754#391—731no—
755#391—731no—
756#391—731no—
757#391—731no—
758#391—731no—
759#391—731no—
760#389—731no—
761#389—731no—
762#389—731no—
763#389—731no—
764#389—731no—
765#389—731no—
766#389—731no—
767#389—731no—
768#389—731no—
769#389C2×D7311yescharacteristic
770#388—731no—
771#388—731no—
772#388—731no—
773#388—731no—
774#388—731no—
775#388—731no—
776#388—731no—
777#388—731no—
778#388—731no—
779#388—731no—
780#388—731no—
781#388—731no—
782#388—731no—
783#388—731no—
784#388C2×D7311yescharacteristic
785#388C2×D7311yescharacteristic
786#387—731no—
787#387—731no—
788#387—731no—
789#387—731no—
790#387—731no—
791#387—731no—
792#387—731no—
793#387—731no—
794#387—731no—
795#387—731no—
796#387—731no—
797#387—731no—
798#387—731no—
799#387—731no—
800#387—731no—
801#387—731no—
802#387—731no—
803#387—731no—
804#387—731no—
805#387—731no—
806#387—731no—
807#387—731no—
808#387—731no—
809#387—731no—
810#387—731no—
811#387—731no—
812#387—731no—
813#387—731no—
814#387C2×D7311yescharacteristic
815#387C2×D7311yescharacteristic
816#386—731no—
817#386C2×D7311yescharacteristic
818#385—731no—
819#385—731no—
820#385—731no—
821#385—731no—
822#385—731no—
823#385—731no—
824#385—731no—
825#385—731no—
826#385C2×D7311yescharacteristic
827#385C2×D7311yescharacteristic
828#384—731no—
829#383—731no—
830#383—731no—
831#383—731no—
832#383—731no—
833#382—731no—
834#382—731no—
835#381—731no—
836#381—731no—
837#380—731no—
838#380—731no—
839C4×C4⋊C4—731no—
840C4×C4⋊C4—731no—
841C4×C4⋊C4—731no—
842C4×C4⋊C4—731no—
843C4×C4⋊C4—731no—
844C4×C4⋊C4—731no—
845C4×C4⋊C4—731no—
846C4×C4⋊C4—731no—
847C4×C4⋊C4—731no—
848C4×C4⋊C4C2×D7311yescharacteristic
849C4×C22⋊C4—731no—
850C4×C22⋊C4—731no—
851C4×C22⋊C4—731no—
852C4×C22⋊C4—731no—
853C4×C22⋊C4—731no—
854C4×C22⋊C4—731no—
855C4×C22⋊C4C2×D7311yescharacteristic
856C4×C22⋊C4C2×D7311yescharacteristic
857#376—731no—
858#376—731no—
859C2×#95—731no—
860C2×#95C2×D7311yescharacteristic
861C43—731no—
862C22×Q8—731no—
863C22×Q8—731no—
864C22×Q8—731no—
865C22×D4C22×D7311yescharacteristic
866C23×C4—731no—
867C23×C4—731no—
868C23×C4C22×D7311yescharacteristic
869C23×C4C22×D7311yescharacteristic
870C23×C4C22×D7311yescharacteristic
871C23×C4C22×D7311yescharacteristic
872C4⋊Q8—1464no—
873#123—24no—
874#123—1464no—
875C22⋊Q8—1464no—
876C22⋊Q8—1464no—
877C22⋊Q8—1464no—
878C22⋊Q8—1464no—
879C4×Q8—2922no—
880C4×Q8—2922no—
881C4×Q8—2922no—
882C4×D4—42no—
883#117—42no—
884#117—2922no—
885#117—1464no—
886#117—1464no—
887C2×C4⋊C4—731no—
888C2×C4⋊C4—731no—
889C2×C4⋊C4—731no—
890C2×C4⋊C4—731no—
891C2×C4⋊C4—731no—
892C2×C4⋊C4—731no—
893C2×C4⋊C4—731no—
894C2×C4⋊C4—731no—
895C2×C4⋊C4—731no—
896C2×C4⋊C4—731no—
897C2×C4⋊C4—731no—
898C2×C4⋊C4—731no—
899C2×C4⋊C4—731no—
900C2×C4⋊C4—731no—
901C2×C4⋊C4—731no—
902C2×C4⋊C4—731no—
903C2×C4⋊C4—731no—
904C2×C4⋊C4—731no—
905C2×C4⋊C4—731no—
906C2×C4⋊C4—731no—
907C2×C4⋊C4—731no—
908C2×C4⋊C4—731no—
909C2×C4⋊C4—731no—
910C2×C4⋊C4—731no—
911C2×C4⋊C4—731no—
912C2×C4⋊C4—731no—
913C2×C4⋊C4—731no—
914C2×C4⋊C4—731no—
915C2×C4⋊C4—731no—
916C2×C4⋊C4—731no—
917C2×C4⋊C4—731no—
918C2×C4⋊C4—731no—
919C2×C4⋊C4—731no—
920C2×C4⋊C4—731no—
921C2×C4⋊C4—731no—
922C2×C4⋊C4C22×D7311yescharacteristic
923C2×C4⋊C4C22×D7311yescharacteristic
924C2×C4⋊C4C22×D7311yescharacteristic
925C2×C4⋊C4C22×D7311yescharacteristic
926C2×C4⋊C4C22×D7311yescharacteristic
927C2×C4⋊C4C22×D7311yescharacteristic
928C2×C4⋊C4C22×D7311yescharacteristic
929C2×C22⋊C4—731no—
930C2×C22⋊C4—731no—
931C2×C22⋊C4—731no—
932C2×C22⋊C4—731no—
933C2×C22⋊C4—731no—
934C2×C22⋊C4—731no—
935C2×C22⋊C4—731no—
936C2×C22⋊C4—731no—
937C2×C22⋊C4—731no—
938C2×C22⋊C4—731no—
939C2×C22⋊C4—731no—
940C2×C22⋊C4—731no—
941C2×C22⋊C4—731no—
942C2×C22⋊C4—731no—
943C2×C22⋊C4C22×D7311yescharacteristic
944C2×C22⋊C4C22×D7311yescharacteristic
945C2×C22⋊C4C22×D7311yescharacteristic
946C2×C22⋊C4C22×D7311yescharacteristic
947C2×C22⋊C4C22×D7311yescharacteristic
948C2×C22⋊C4C22×D7311yescharacteristic
949C2×C22⋊C4C22×D7311yescharacteristic
950C2×C22⋊C4C22×D7311yescharacteristic
951C2×C42—731no—
952C2×C42—731no—
953C2×C42—731no—
954C2×C42—731no—
955C2×C42—731no—
956C2×C42—731no—
957C2×C42—731no—
958C2×C42—731no—
959C2×C42—731no—
960C2×C42—731no—
961C2×C42—731no—
962C2×C42—731no—
963C2×C42—731no—
964C2×C42—731no—
965C2×C42—731no—
966C2×C42—731no—
967C2×C42C22×D7311yescharacteristic
968C2×C42C22×D7311yescharacteristic
969C2×C42C22×D7311yescharacteristic
970C2×C42C22×D7311yescharacteristic
971C2×C42C22×D7311yescharacteristic
972#95—731no—
973#95—731no—
974#95—731no—
975#95—731no—
976#95—731no—
977#95—731no—
978#95—731no—
979#95—731no—
980#95—731no—
981#95—731no—
982#95—731no—
983#95—731no—
984#95—731no—
985#95—731no—
986#95—731no—
987#95—731no—
988#95—731no—
989#95—731no—
990#95—731no—
991#95—731no—
992#95—731no—
993#95—731no—
994#95—731no—
995#95—731no—
996#95—731no—
997#95—731no—
998#95—731no—
999#95—731no—
1000#95—731no—
1001#95—731no—
1002#95—731no—
1003#95—731no—
1004#95—731no—
1005#95—731no—
1006#95—731no—
1007#95—731no—
1008#95—731no—
1009#95—731no—
1010#95—731no—
1011#95—731no—
1012#95—731no—
1013#95—731no—
1014#95—731no—
1015#95—731no—
1016#95—731no—
1017#95—731no—
1018#95—731no—
1019#95—731no—
1020#95—731no—
1021#95—731no—
1022#95C22×D7311yescharacteristic
1023#95C22×D7311yescharacteristic
1024#95C22×D7311yescharacteristic
1025#95C22×D7311yescharacteristic
1026#95C22×D7311yescharacteristic
1027#95C22×D7311yescharacteristic
1028#95C22×D7311yescharacteristic
1029#95C22×D7311yescharacteristic
1030#95C22×D7311yescharacteristic
1031#95C22×D7311yescharacteristic
1032C24C23×D7311yescharacteristic
1033C24C23×D7311yescharacteristic
1034C2×Q8—2921no—
1035C2×Q8—2921no—
1036C2×Q8—2921no—
1037C2×Q8—2921no—
1038C2×Q8—2921no—
1039C2×Q8—734no—
1040C2×Q8—1462no—
1041C2×Q8—1462no—
1042C2×Q8—1462no—
1043C2×D4—22no—
1044C2×D4—22no—
1045C2×D4—41no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—22no—
1049C22×C4—22no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—41no—
1053C22×C4—41no—
1054C22×C4—41no—
1055C22×C4—41no—
1056C22×C4—41no—
1057C22×C4—41no—
1058C22×C4—2921no—
1059C22×C4—2921no—
1060C22×C4—731no—
1061C22×C4—731no—
1062C22×C4—731no—
1063C22×C4—731no—
1064C22×C4—731no—
1065C22×C4—731no—
1066C22×C4—731no—
1067C22×C4—731no—
1068C22×C4—731no—
1069C22×C4—731no—
1070C22×C4—731no—
1071C22×C4—731no—
1072C22×C4—731no—
1073C22×C4—731no—
1074C22×C4—731no—
1075C22×C4—731no—
1076C22×C4—1462no—
1077C22×C4—1462no—
1078C22×C4—1462no—
1079C22×C4—1462no—
1080C22×C4C23×D7311yescharacteristic
1081C22×C4C23×D7311yescharacteristic
1082C22×C4C23×D7311yescharacteristic
1083C22×C4C23×D7311yescharacteristic
1084C22×C4C23×D7311yescharacteristic
1085C22×C4C23×D7311yescharacteristic
1086C22×C4C23×D7311yescharacteristic
1087C22×C4C23×D7311yescharacteristic
1088C22×C4C23×D7311yescharacteristic
1089C22×C4C23×D7311yescharacteristic
1090C22×C4C23×D7311yescharacteristic
1091C22×C4C23×D7311yescharacteristic
1092C22×C4C23×D7311yescharacteristic
1093C4⋊C4—22no—
1094C4⋊C4—22no—
1095C4⋊C4—22no—
1096C4⋊C4—22no—
1097C4⋊C4—41no—
1098C4⋊C4—41no—
1099C4⋊C4—41no—
1100C4⋊C4—2921no—
1101C4⋊C4—2921no—
1102C4⋊C4—2921no—
1103C4⋊C4—2921no—
1104C4⋊C4—2921no—
1105C4⋊C4—2921no—
1106C4⋊C4—2921no—
1107C4⋊C4—2921no—
1108C4⋊C4—2921no—
1109C4⋊C4—2921no—
1110C4⋊C4—2921no—
1111C4⋊C4—1462no—
1112C4⋊C4—1462no—
1113C4⋊C4—1462no—
1114C4⋊C4—1462no—
1115C4⋊C4—1462no—
1116C4⋊C4—1462no—
1117C4⋊C4—1462no—
1118C4⋊C4—1462no—
1119C4⋊C4—1462no—
1120C4⋊C4—1462no—
1121C4⋊C4—1462no—
1122C4⋊C4—1462no—
1123C4⋊C4—1462no—
1124C4⋊C4—1462no—
1125C4⋊C4—1462no—
1126C4⋊C4—1462no—
1127C4⋊C4—1462no—
1128C4⋊C4—1462no—
1129C4⋊C4—1462no—
1130C4⋊C4—1462no—
1131C4⋊C4—1462no—
1132C4⋊C4—1462no—
1133C4⋊C4—1462no—
1134C4⋊C4—1462no—
1135C22⋊C4—22no—
1136C22⋊C4—22no—
1137C22⋊C4—22no—
1138C22⋊C4—22no—
1139C22⋊C4—22no—
1140C22⋊C4—41no—
1141C22⋊C4—41no—
1142C22⋊C4—2921no—
1143C22⋊C4—2921no—
1144C22⋊C4—734no—
1145C22⋊C4—1462no—
1146C22⋊C4—1462no—
1147C22⋊C4—1462no—
1148C22⋊C4—1462no—
1149C22⋊C4—1462no—
1150C22⋊C4—1462no—
1151C22⋊C4—1462no—
1152C22⋊C4—1462no—
1153C22⋊C4—1462no—
1154C22⋊C4—1462no—
1155C22⋊C4—1462no—
1156C22⋊C4#1192402814yes—
1157C42—22no—
1158C42—22no—
1159C42—22no—
1160C42—41no—
1161C42—41no—
1162C42—2921no—
1163C42—2921no—
1164C42—2921no—
1165C42—2921no—
1166C42—2921no—
1167C42—1462no—
1168C42—1462no—
1169C42—1462no—
1170C42—1462no—
1171C42—1462no—
1172C42—1462no—
1173C42—1462no—
1174C42—1462no—
1175C42—1462no—
1176C42—1462no—
1177C42—1462no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—21no—
1182C23—21no—
1183C23—21no—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23#41×D7312yes—
1191C23C2×#1192402812yes—
1192C23C24×D7311yescharacteristic
1193Q8—2924no—
1194Q8—2924no—
1195Q8—2924no—
1196D4—44no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—82no—
1234C2×C4—82no—
1235C2×C4—2924no—
1236C2×C4—2924no—
1237C2×C4—732no—
1238C2×C4—732no—
1239C2×C4—732no—
1240C2×C4—732no—
1241C2×C4—732no—
1242C2×C4—1461no—
1243C2×C4—1461no—
1244C2×C4—1461no—
1245C2×C4—1461no—
1246C2×C4—1461no—
1247C2×C4—1461no—
1248C2×C4—1461no—
1249C2×C4—1461no—
1250C2×C4—1461no—
1251C2×C4—1461no—
1252C2×C4—1461no—
1253C2×C4—1461no—
1254C2×C4—1461no—
1255C2×C4—1461no—
1256C2×C4—1461no—
1257C2×C4—1461no—
1258C2×C4—1461no—
1259C2×C4—1461no—
1260C2×C4—1461no—
1261C2×C4—1461no—
1262C2×C4—1461no—
1263C2×C4—1461no—
1264C2×C4—1461no—
1265C2×C4—1461no—
1266C2×C4—1461no—
1267C2×C4—1461no—
1268C2×C4—1461no—
1269C2×C4—1461no—
1270C2×C4—1461no—
1271C2×C4—1461no—
1272C2×C4—1461no—
1273C2×C4—1461no—
1274C2×C4—1461no—
1275C2×C4—1461no—
1276C2×C4—1461no—
1277C2×C4—1461no—
1278C2×C4—1461no—
1279C2×C4—1461no—
1280C2×C4—1461no—
1281C2×C4—1461no—
1282C2×C4—1461no—
1283C2×C4—1461no—
1284C2×C4—1461no—
1285C2×C4#41×D7312yes—
1286C2×C4C2×#1192402812yes—
1287C2×C4C2×#1192402812yes—
1288C2×C4#1455663612yes—
1289C2×C4#1455663812yes—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22C2×#41×D7311yescharacteristic
1305C22C2×#41×D7311yescharacteristic
1306C22C22×#1192402811yescharacteristic
1307C22C2×#1455663611yescharacteristic
1308C222−1+4×D7311yescharacteristic
1309C22C2×#1455663811yescharacteristic
1310C22#1798942211yescharacteristic
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—22no—
1315C4—22no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—2921no—
1325C4—2921no—
1326C4—2921no—
1327C4—2921no—
1328C4—2921no—
1329C4—2921no—
1330C4—2921no—
1331C4—2921no—
1332C4—2921no—
1333C4—2921no—
1334C4—2921no—
1335C4—1462no—
1336C4—1462no—
1337C4—1462no—
1338C4—1462no—
1339C4—1462no—
1340C2—42no—
1341C2—42no—
1342C2#2262353511yescharacteristic
1343C2#2262354511yescharacteristic
1344C2#2262354611yescharacteristic
1345C2#2262367011yescharacteristic
1346C2#2262368411yescharacteristic
1347C2#2262375811yescharacteristic
1348C2#2262426711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2359C2
prime radicalC22×D4×C73C23
hypercenter#2359D73
hypocenterC73#60043
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2359

Complements

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

NH ≅ G/Ntype
1. #22617750C2semidirect
2. #22616917C2semidirect
3. #22616913C2semidirect
5. #22615590C2semidirect
6. #22615585C2semidirect
7. #22615508C2semidirect
8. #22615505C2semidirect
9. #22615344C2semidirect
10. #22615296C2semidirect
13. #22614767C2semidirect
14. #22614763C2semidirect
15. #22614672C2semidirect
16. #22614667C2semidirect
17. #22614555C2semidirect
18. #22614550C2semidirect
21. #22613607C2semidirect
22. #22613605C2semidirect
23. #22613014C2semidirect
24. #22613011C2semidirect
25. #22612958C2semidirect
26. #22612955C2semidirect
28. C4×#14556590C2semidirect
29. #22612427C2semidirect
30. #22612425C2semidirect
706. C73#60043semidirect

Maximal subgroups

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

subgroupindex
#226177502
#226169172
#226169132
#226162682
#226155902
#226155852
#226155082
#226155052
#226153442
#226152962
#226151822
#226148402
#226147672
#226147632
#226146722
#226146672
#226145552
#226145502
#226140242
#226140232
#226136072
#226136052
#226130142
#226130112
#226129582
#226129552
#226129172
C4×#145565902
#226124272
#226124252
C73×#23592
#6004373