Finite Group Databasebeta

← #33949273

Subgroups — #33949273

Order 18688.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22616964C211yesmaximal, characteristic, complemented
2#22616942C211yesmaximal, characteristic
3#22616821C211yesmaximal, characteristic, complemented
4#22615641C211yesmaximal, characteristic, complemented
5#22615635C211yesmaximal, characteristic, complemented
6#22615567C211yesmaximal, characteristic, complemented
7#22615565C211yesmaximal, characteristic, complemented
8#22615208C211yesmaximal, characteristic, complemented
9#22615198C211yesmaximal, characteristic, complemented
10#22615117C211yesmaximal, characteristic, complemented
11#22614906C211yesmaximal, characteristic
12#22614754C211yesmaximal, characteristic, complemented
13#22614741C211yesmaximal, characteristic, complemented
14#22614629C211yesmaximal, characteristic
15#22614627C211yesmaximal, characteristic
16#22614599C211yesmaximal, characteristic, complemented
17#22614597C211yesmaximal, characteristic, complemented
18#22614165C211yesmaximal, characteristic
19#22614158C211yesmaximal, characteristic
20#22613640C211yesmaximal, characteristic, complemented
21#22613637C211yesmaximal, characteristic, complemented
22#22613055C211yesmaximal, characteristic, complemented
23#22613044C211yesmaximal, characteristic, complemented
24#22613038C211yesmaximal, characteristic
25#22613037C211yesmaximal, characteristic, complemented
26#22613033C211yesmaximal, characteristic, complemented
27#22613017C211yesmaximal, characteristic, complemented
28#22612498C211yesmaximal, characteristic, complemented
29#22612425C211yesmaximal, characteristic, complemented
30#22612423C211yesmaximal, characteristic, complemented
31C73×#2721C211yesmaximal, characteristic, complemented
32C2×#14556591C2211yescharacteristic
33C2×#14556590C2211yescharacteristic
34C2×#14556586C2211yescharacteristic
35C2×#14556586C2211yescharacteristic
36C2×#14556584C2211yescharacteristic
37C2×#14556581C2211yescharacteristic
38C2×#14556581C2211yescharacteristic
39C2×#14556577C2211yescharacteristic
40C2×#14556577C2211yescharacteristic
41C2×#14556556C2211yescharacteristic
42C2×#14556556C2211yescharacteristic
43C2×#14556549C2211yescharacteristic
44C2×#14556547C2211yescharacteristic
45#17988529C2211yescharacteristic
46#17988528C2211yescharacteristic
47#17988523C2211yescharacteristic
48#17988522C2211yescharacteristic
49#17988522C2211yescharacteristic
50#17988522C2211yescharacteristic
51#17988521C2211yescharacteristic
52#17988520C2211yescharacteristic
53#17988520C2211yescharacteristic
54#17988519C2211yescharacteristic
55#17988518C2211yescharacteristic
56#17988517C2211yescharacteristic
57#17988513C2211yescharacteristic
58#17988510C2211yescharacteristic
59#17988510C2211yescharacteristic
60#17988509C2211yescharacteristic
61#17988509C2211yescharacteristic
62#17988509C2211yescharacteristic
63#17988508C2211yescharacteristic
64#17988508C2211yescharacteristic
65#17988508C2211yescharacteristic
66#17988507C2211yescharacteristic
67#17988503C2211yescharacteristic
68#17988503C2211yescharacteristic
69#17988500C2211yescharacteristic
70#17988499C2211yescharacteristic
71#17988492C2211yescharacteristic
72#17988492C2211yescharacteristic
73#17988492C2211yescharacteristic
74#17988491C2211yescharacteristic
75#17988491C2211yescharacteristic
76#17988491C2211yescharacteristic
77#17988491C2211yescharacteristic
78#17988487C2211yescharacteristic
79#17988486C2211yescharacteristic
80#17988485C2211yescharacteristic
81#17988484C2211yescharacteristic
82#17988483C2211yescharacteristic
83#17988483C2211yescharacteristic
84#17988483C2211yescharacteristic
85#17988483C2211yescharacteristic
86#17988483C2211yescharacteristic
87#17988482C2211yescharacteristic
88#17988482C2211yescharacteristic
89#17988482C2211yescharacteristic
90#17988481C2211yescharacteristic
91#17988481C2211yescharacteristic
92#17988481C2211yescharacteristic
93#17988481C2211yescharacteristic
94#17988480C2211yescharacteristic
95#17988480C2211yescharacteristic
96#17988480C2211yescharacteristic
97#17988480C2211yescharacteristic
98#17988479C2211yescharacteristic
99#17988479C2211yescharacteristic
100#17988479C2211yescharacteristic
101#17988478C2211yescharacteristic
102#17988478C2211yescharacteristic
103#17988477C2211yescharacteristic
104#17988477C2211yescharacteristic
105#17988477C2211yescharacteristic
106#17988476C2211yescharacteristic
107#17988476C2211yescharacteristic
108#17988476C2211yescharacteristic
109#17988476C2211yescharacteristic
110#17988475C2211yescharacteristic
111#17988475C2211yescharacteristic
112#17988474C2211yescharacteristic
113#17988474C2211yescharacteristic
114#17988474C2211yescharacteristic
115#17988473C2211yescharacteristic
116#17988473C2211yescharacteristic
117#17988473C2211yescharacteristic
118#17988473C2211yescharacteristic
119#17988473C2211yescharacteristic
120#17988473C2211yescharacteristic
121#17988473C2211yescharacteristic
122#17988473C2211yescharacteristic
123#17988473C2211yescharacteristic
124#17988473C2211yescharacteristic
125#17988472C2211yescharacteristic
126#17988472C2211yescharacteristic
127#17988471C2211yescharacteristic
128#17988470C2211yescharacteristic
129#17988470C2211yescharacteristic
130#17988469C2211yescharacteristic
131#17988469C2211yescharacteristic
132#17988469C2211yescharacteristic
133#17988468C2211yescharacteristic
134#17988468C2211yescharacteristic
135#17988464C2211yescharacteristic
136#17988463C2211yescharacteristic
137#17988462C2211yescharacteristic
138#17988458C2211yescharacteristic
139#17988456C2211yescharacteristic
140#17988452C2211yescharacteristic
141#17988451C2211yescharacteristic
142#17988451C2211yescharacteristic
143#17988445C2211yescharacteristic
144#17988444C2211yescharacteristic
145C4⋊C4×Dic73C2211yescharacteristic
146C4⋊C4×Dic73C2211yescharacteristic
147C4⋊C4×Dic73C2211yescharacteristic
148C4⋊C4×Dic73C2211yescharacteristic
149C4⋊C4×Dic73C2211yescharacteristic
150C4⋊C4×Dic73C2211yescharacteristic
151C4⋊C4×Dic73C2211yescharacteristic
152C4⋊C4×Dic73C2211yescharacteristic
153C4⋊C4×Dic73C2211yescharacteristic
154C4×#11924007C2211yescharacteristic
155C4×C4⋊Dic73C2211yescharacteristic
156#17988438C2211yescharacteristic
157#17988438C2211yescharacteristic
158#17988438C2211yescharacteristic
159C22⋊C4×Dic73C2211yescharacteristic
160C22⋊C4×Dic73C2211yescharacteristic
161C22⋊C4×Dic73C2211yescharacteristic
162C4×#11924005C2211yescharacteristic
163#17988434C2211yescharacteristic
164#17988434C2211yescharacteristic
165#17988433C2211yescharacteristic
166#17988433C2211yescharacteristic
167#17988433C2211yescharacteristic
168#17988432C2211yescharacteristic
169#17988432C2211yescharacteristic
170#17988432C2211yescharacteristic
171C42×Dic73C2211yescharacteristic
172C2×#126×C73C2211yescharacteristic
173C2×#125×C73C2211yescharacteristic
174#399×C73C2211yescharacteristic
175#399×C73C2211yescharacteristic
176#398×C73C2211yescharacteristic
177#398×C73C2211yescharacteristic
178#397×C73C2211yescharacteristic
179#396×C73C2211yescharacteristic
180#389×C73C2211yescharacteristic
181#388×C73C2211yescharacteristic
182#388×C73C2211yescharacteristic
183#387×C73C2211yescharacteristic
184#387×C73C2211yescharacteristic
185#387×C73C2211yescharacteristic
186#384×C73C2211yescharacteristic
187C22×Dic146C2311yescharacteristic
188C22×Dic146C2311yescharacteristic
189C22×Dic146C2311yescharacteristic
190C22×C22⋊D73C2311yescharacteristic
191C23×Dic73C2311yescharacteristic
192C22×C4×D73C2311yescharacteristic
193#14556591—24no—
194#14556590—24no—
195#14556586—24no—
196#14556586—42no—
197#14556584—42no—
198#14556581—24no—
199#14556581—42no—
200#14556577—24no—
201#14556577—42no—
202#14556556—42no—
203#14556556—42no—
204#14556549—24no—
205#14556547—24no—
206C2×C4⋊Dic73C2311yescharacteristic
207C2×C4⋊Dic73C2311yescharacteristic
208C2×C4⋊Dic73C2311yescharacteristic
209C2×C4⋊Dic73C2311yescharacteristic
210C2×C4⋊Dic73C2311yescharacteristic
211C2×C4⋊Dic73C2311yescharacteristic
212C2×C4⋊Dic73C2311yescharacteristic
213C2×C4⋊Dic73C2311yescharacteristic
214C2×C4⋊Dic73C2311yescharacteristic
215C2×C4⋊Dic73C2311yescharacteristic
216C2×C4⋊Dic73C2311yescharacteristic
217C2×C4⋊Dic73C2311yescharacteristic
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×C22⋊Dic73C2311yescharacteristic
238C2×C22⋊Dic73C2311yescharacteristic
239C2×C22⋊Dic73C2311yescharacteristic
240C2×C22⋊Dic73C2311yescharacteristic
241C2×C22⋊Dic73C2311yescharacteristic
242C2×C22⋊Dic73C2311yescharacteristic
243C2×#11924005C2311yescharacteristic
244C2×#11924005C2311yescharacteristic
245C2×#11924005C2311yescharacteristic
246C2×#11924005C2311yescharacteristic
247C2×#11924005C2311yescharacteristic
248C2×#11924005C2311yescharacteristic
249C2×#11924005C2311yescharacteristic
250C2×#11924005C2311yescharacteristic
251C2×#11924005C2311yescharacteristic
252C2×#11924005C2311yescharacteristic
253C2×#11924005C2311yescharacteristic
254C2×#11924005C2311yescharacteristic
255C2×#11924005C2311yescharacteristic
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
269C2×C4×Dic73C2311yescharacteristic
270C2×C4×Dic73C2311yescharacteristic
271C2×C4×Dic73C2311yescharacteristic
272C2×C4×Dic73C2311yescharacteristic
273C2×C4×Dic73C2311yescharacteristic
274C2×C4×Dic73C2311yescharacteristic
275C2×C4×Dic73C2311yescharacteristic
276C2×C4×Dic73C2311yescharacteristic
277C2×C4×Dic73C2311yescharacteristic
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
319#14556498C2311yescharacteristic
320#126×C73—24no—
321#125×C73—24no—
322C2×C4⋊C4×C73C2311yescharacteristic
323C2×C4⋊C4×C73C2311yescharacteristic
324C2×C4⋊C4×C73C2311yescharacteristic
325C2×C4⋊C4×C73C2311yescharacteristic
326C2×C4⋊C4×C73C2311yescharacteristic
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×C4⋊C4×C73C2311yescharacteristic
335C2×C4⋊C4×C73C2311yescharacteristic
336C2×C4⋊C4×C73C2311yescharacteristic
337C2×C22⋊C4×C73C2311yescharacteristic
338C2×C22⋊C4×C73C2311yescharacteristic
339C2×C22⋊C4×C73C2311yescharacteristic
340C2×C22⋊C4×C73C2311yescharacteristic
341C2×C22⋊C4×C73C2311yescharacteristic
342C2×C22⋊C4×C73C2311yescharacteristic
343C2×C22⋊C4×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
357C23×D73C2411yescharacteristic
358C2×Dic146—22no—
359C2×Dic146—22no—
360C2×Dic146—41no—
361C2×Dic146—41no—
362C2×Dic146—41no—
363C2×Dic146—41no—
364C2×Dic146—41no—
365C2×Dic146—41no—
366C2×Dic146#4114yes—
367C2×C22⋊D73—22no—
368C2×C22⋊D73—41no—
369C2×C22⋊D73—41no—
370C22×Dic73—22no—
371C22×Dic73—22no—
372C22×Dic73—41no—
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
388C2×C4×D73—22no—
389C2×C4×D73—22no—
390C2×C4×D73—41no—
391C4⋊Dic73—22no—
392C4⋊Dic73—22no—
393C4⋊Dic73—22no—
394C4⋊Dic73—22no—
395C4⋊Dic73—22no—
396C4⋊Dic73—22no—
397C4⋊Dic73—22no—
398C4⋊Dic73—22no—
399C4⋊Dic73—22no—
400C4⋊Dic73—22no—
401C4⋊Dic73—41no—
402C4⋊Dic73—41no—
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—41no—
412#11924007—41no—
413#11924007—41no—
414#11924007—41no—
415#11924007—41no—
416#11924007—41no—
417#11924007—41no—
418#11924007—41no—
419#11924007—41no—
420#11924007—41no—
421#11924007#4114yes—
422C22⋊Dic73—22no—
423C22⋊Dic73—22no—
424C22⋊Dic73—22no—
425C22⋊Dic73—22no—
426C22⋊Dic73—41no—
427C22⋊Dic73—41no—
428#11924005—22no—
429#11924005—22no—
430#11924005—22no—
431#11924005—22no—
432#11924005—22no—
433#11924005—22no—
434#11924005—22no—
435#11924005—22no—
436#11924005—22no—
437#11924005—41no—
438#11924005—41no—
439#11924005—41no—
440#11924005—41no—
441C4×Dic73—22no—
442C4×Dic73—22no—
443C4×Dic73—22no—
444C4×Dic73—22no—
445C4×Dic73—22no—
446C4×Dic73—22no—
447C4×Dic73—22no—
448C4×Dic73—22no—
449C4×Dic73—22no—
450C4×Dic73—22no—
451C4×Dic73—22no—
452C4×Dic73—22no—
453C4×Dic73—22no—
454C4×Dic73—22no—
455C4×Dic73—22no—
456C4×Dic73—22no—
457C4×Dic73—22no—
458C4×Dic73—41no—
459C4×Dic73—41no—
460C4×Dic73—41no—
461C4×Dic73—41no—
462C4×Dic73—41no—
463C24×C73C2411yescharacteristic
464C22×C4×C73C2411yescharacteristic
465C22×C4×C73C2411yescharacteristic
466C22×C4×C73C2411yescharacteristic
467C22×C4×C73C2411yescharacteristic
468C22×C4×C73C2411yescharacteristic
469C22×C4×C73C2411yescharacteristic
470C22×C4×C73C2411yescharacteristic
471C22×C4×C73C2411yescharacteristic
472C22×C4×C73C2411yescharacteristic
473C22×C4×C73C2411yescharacteristic
474C22×C4×C73C2411yescharacteristic
475C22×C4×C73C2411yescharacteristic
476C22×C4×C73C2411yescharacteristic
477C22×C4×C73C2411yescharacteristic
478C4⋊C4×C73—22no—
479C4⋊C4×C73—22no—
480C4⋊C4×C73—22no—
481C4⋊C4×C73—22no—
482C4⋊C4×C73—22no—
483C4⋊C4×C73—22no—
484C4⋊C4×C73—22no—
485C4⋊C4×C73—22no—
486C4⋊C4×C73—22no—
487C4⋊C4×C73—22no—
488C4⋊C4×C73—41no—
489C4⋊C4×C73—41no—
490C4⋊C4×C73—41no—
491C4⋊C4×C73—41no—
492C4⋊C4×C73#4114yes—
493C22⋊C4×C73—22no—
494C22⋊C4×C73—22no—
495C22⋊C4×C73—22no—
496C22⋊C4×C73—22no—
497C22⋊C4×C73—22no—
498C22⋊C4×C73—41no—
499C22⋊C4×C73—41no—
500C42×C73—22no—
501C42×C73—22no—
502C42×C73—22no—
503C23×C73—21no—
504C23×C73—21no—
505C23×C73—21no—
506C23×C73—21no—
507C23×C73—21no—
508C23×C73—21no—
509C23×C73—21no—
510C23×C73C2511yescharacteristic
511C22×D73—21no—
512C22×D73—21no—
513C22×D73—21no—
514C22×D73—21no—
515C22×D73—21no—
516C22×D73—21no—
517C22×D73—21no—
518C2×C4×C73—21no—
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—21no—
554C2×C4×C73—21no—
555C2×C4×C73C2×#4112yes—
556C2×C4×C73C2×#4112yes—
557C2×C4×C73C2×#4112yes—
558C2×C4×C73C2×#4112yes—
559C2×C4×C73C2×#4112yes—
560C22⋊D73—82no—
561C2×Dic73—21no—
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—44no—
600C2×Dic73C2×#4112yes—
601C2×Dic73C2×#4112yes—
602C2×Dic73C2×#4112yes—
603C2×Dic73C2×#4112yes—
604C2×Dic73H(5,𝔽2)12yes—
605C2×Dic732−1+412yes—
606C2×Dic732−1+412yes—
607C4×D73—44no—
608Dic146—44no—
609Dic146—44no—
610Dic146—82no—
611C22×C73—41no—
612C22×C73—41no—
613C22×C73—41no—
614C22×C73—41no—
615C22×C73—41no—
616C22×C73—41no—
617C22×C73—41no—
618C22×C73C22×#4111yescharacteristic
619C22×C73C22×#4111yescharacteristic
620C22×C73C22×#4111yescharacteristic
621C22×C73C2×H(5,𝔽2)11yescharacteristic
622C22×C73C2×2−1+411yescharacteristic
623C22×C73C2×2−1+411yescharacteristic
624C22×C73#58511yescharacteristic
625C2×D73—41no—
626C2×D73—41no—
627C2×D73—41no—
628C2×D73—41no—
629C2×D73—41no—
630C2×D73—41no—
631C2×D73—41no—
632C4×C73—22no—
633C4×C73—22no—
634C4×C73—22no—
635C4×C73—22no—
636C4×C73—22no—
637C4×C73—41no—
638C4×C73—41no—
639C4×C73—41no—
640C4×C73—41no—
641C4×C73—41no—
642C4×C73—41no—
643C4×C73—41no—
644C4×C73—41no—
645C4×C73—41no—
646Dic73—22no—
647Dic73—22no—
648Dic73—22no—
649Dic73—22no—
650Dic73—22no—
651Dic73—22no—
652Dic73—22no—
653Dic73—41no—
654Dic73—41no—
655Dic73—41no—
656Dic73—41no—
657Dic73—41no—
658Dic73—41no—
659Dic73—41no—
660Dic73—41no—
661#60042—731nomaximal, Sylow
662C2×C73—81no—
663C2×C73#348211yescharacteristic
664C2×C73#348211yescharacteristic
665C2×C73#348311yescharacteristic
666C2×C73#349511yescharacteristic
667C2×C73#349511yescharacteristic
668C2×C73#350511yescharacteristic
669C2×C73#354411yescharacteristic
670D73—81no—
671#2734—731no—
672#2731—731no—
673#2721—731no—
674#2721D7311yescharacteristic, complemented
675#2612—731no—
676#2612—731no—
677#2604—731no—
678#2604—731no—
679#2574—731no—
680#2574—731no—
681#2565—731no—
682#2545—731no—
683#2529—731no—
684#2529—731no—
685#2521—731no—
686#2521—731no—
687#2519—731no—
688#2519—731no—
689#2479—731no—
690#2479—731no—
691#2441—731no—
692#2441—731no—
693#2373—731no—
694#2373—731no—
695#2372—731no—
696#2371—731no—
697#2371—731no—
698#2369—731no—
699C4×C4⋊Q8—731no—
700#2298—731no—
701#2298—731no—
702C73#6004211yescharacteristic, complemented, Sylow
703C2×C4⋊Q8—731no—
704C2×C4⋊Q8—731no—
705C2×#126—731no—
706C2×#126—731no—
707C2×#126—731no—
708C2×#126C2×D7311yescharacteristic
709C2×#125—731no—
710C2×#125—731no—
711C2×#125C2×D7311yescharacteristic
712C2×#124—731no—
713C2×#124—731no—
714C2×C4×Q8—731no—
715C2×C4×Q8—731no—
716C2×#117—731no—
717C2×#117—731no—
718#400—731no—
719#400—731no—
720#399—731no—
721#399—731no—
722#399—731no—
723#399—731no—
724#399C2×D7311yescharacteristic
725#399C2×D7311yescharacteristic
726#398—731no—
727#398—731no—
728#398—731no—
729#398—731no—
730#398—731no—
731#398—731no—
732#398C2×D7311yescharacteristic
733#398C2×D7311yescharacteristic
734#397—731no—
735#397C2×D7311yescharacteristic
736#396—731no—
737#396—731no—
738#396—731no—
739#396—731no—
740#396—731no—
741#396C2×D7311yescharacteristic
742#395—731no—
743#395—731no—
744#395—731no—
745#395—731no—
746#394—731no—
747#394—731no—
748#393—731no—
749#393—731no—
750#391—731no—
751#391—731no—
752#391—731no—
753#391—731no—
754#391—731no—
755#391—731no—
756#391—731no—
757#390—731no—
758#389—731no—
759#389—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#388—731no—
785#388—731no—
786#388—731no—
787#388—731no—
788#388—731no—
789#388—731no—
790#388—731no—
791#388—731no—
792#388C2×D7311yescharacteristic
793#388C2×D7311yescharacteristic
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#387—731no—
815#387—731no—
816#387—731no—
817#387C2×D7311yescharacteristic
818#387C2×D7311yescharacteristic
819#387C2×D7311yescharacteristic
820#386—731no—
821#386—731no—
822#385—731no—
823#385—731no—
824#384—731no—
825#384C2×D7311yescharacteristic
826#382—731no—
827#382—731no—
828#382—731no—
829#380—731no—
830#380—731no—
831C4×C4⋊C4—731no—
832C4×C4⋊C4—731no—
833C4×C4⋊C4—731no—
834C4×C4⋊C4—731no—
835C4×C4⋊C4—731no—
836C4×C4⋊C4—731no—
837C4×C4⋊C4—731no—
838C4×C4⋊C4—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×C22⋊C4—731no—
846C4×C22⋊C4—731no—
847C4×C22⋊C4—731no—
848C4×C22⋊C4—731no—
849C4×C22⋊C4—731no—
850C4×C22⋊C4—731no—
851#376—731no—
852#376—731no—
853#376—731no—
854#376—731no—
855#376—731no—
856#376—731no—
857C43—731no—
858C22×Q8—731no—
859C22×Q8—731no—
860C22×Q8—731no—
861C22×D4—731no—
862C23×C4—731no—
863C23×C4—731no—
864C4⋊Q8—1464no—
865C4⋊Q8—1464no—
866#126—24no—
867#126—2922no—
868#126—2922no—
869#126—1464no—
870#125—24no—
871#125—2922no—
872#125—1464no—
873#124—2922no—
874#124—1464no—
875C4×Q8—2922no—
876C4×Q8—2922no—
877#117—1464no—
878#117—1464no—
879C2×C4⋊C4—731no—
880C2×C4⋊C4—731no—
881C2×C4⋊C4—731no—
882C2×C4⋊C4—731no—
883C2×C4⋊C4—731no—
884C2×C4⋊C4—731no—
885C2×C4⋊C4—731no—
886C2×C4⋊C4—731no—
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⋊C4C22×D7311yescharacteristic
911C2×C4⋊C4C22×D7311yescharacteristic
912C2×C4⋊C4C22×D7311yescharacteristic
913C2×C4⋊C4C22×D7311yescharacteristic
914C2×C4⋊C4C22×D7311yescharacteristic
915C2×C4⋊C4C22×D7311yescharacteristic
916C2×C4⋊C4C22×D7311yescharacteristic
917C2×C4⋊C4C22×D7311yescharacteristic
918C2×C4⋊C4C22×D7311yescharacteristic
919C2×C4⋊C4C22×D7311yescharacteristic
920C2×C4⋊C4C22×D7311yescharacteristic
921C2×C4⋊C4C22×D7311yescharacteristic
922C2×C4⋊C4C22×D7311yescharacteristic
923C2×C4⋊C4C22×D7311yescharacteristic
924C2×C4⋊C4C22×D7311yescharacteristic
925C2×C22⋊C4—731no—
926C2×C22⋊C4—731no—
927C2×C22⋊C4—731no—
928C2×C22⋊C4—731no—
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⋊C4—731no—
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×C42—731no—
968C2×C42—731no—
969C2×C42—731no—
970C2×C42—731no—
971C2×C42—731no—
972C2×C42—731no—
973C2×C42C22×D7311yescharacteristic
974C2×C42C22×D7311yescharacteristic
975C2×C42C22×D7311yescharacteristic
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#95C22×D7311yescharacteristic
1019#95C22×D7311yescharacteristic
1020#95C22×D7311yescharacteristic
1021#95C22×D7311yescharacteristic
1022#95C22×D7311yescharacteristic
1023#95C22×D7311yescharacteristic
1024#95C22×D7311yescharacteristic
1025#95C22×D7311yescharacteristic
1026#95C22×D7311yescharacteristic
1027#95C22×D7311yescharacteristic
1028C24—731no—
1029C24C23×D7311yescharacteristic
1030C2×Q8—2921no—
1031C2×Q8—2921no—
1032C2×Q8—2921no—
1033C2×Q8—2921no—
1034C2×Q8—2921no—
1035C2×Q8—2921no—
1036C2×Q8—734no—
1037C2×Q8—1462no—
1038C2×Q8—1462no—
1039C2×D4—2921no—
1040C2×D4—2921no—
1041C2×D4—1462no—
1042C22×C4—2921no—
1043C22×C4—2921no—
1044C22×C4—731no—
1045C22×C4—731no—
1046C22×C4—731no—
1047C22×C4—731no—
1048C22×C4—731no—
1049C22×C4—731no—
1050C22×C4—731no—
1051C22×C4—731no—
1052C22×C4—731no—
1053C22×C4—731no—
1054C22×C4—731no—
1055C22×C4—731no—
1056C22×C4—731no—
1057C22×C4—731no—
1058C22×C4—731no—
1059C22×C4—1462no—
1060C22×C4—1462no—
1061C22×C4—1462no—
1062C22×C4—1462no—
1063C22×C4C23×D7311yescharacteristic
1064C22×C4C23×D7311yescharacteristic
1065C22×C4C23×D7311yescharacteristic
1066C22×C4C23×D7311yescharacteristic
1067C22×C4C23×D7311yescharacteristic
1068C22×C4C23×D7311yescharacteristic
1069C22×C4C23×D7311yescharacteristic
1070C22×C4C23×D7311yescharacteristic
1071C22×C4C23×D7311yescharacteristic
1072C22×C4C23×D7311yescharacteristic
1073C22×C4C23×D7311yescharacteristic
1074C22×C4C23×D7311yescharacteristic
1075C22×C4C23×D7311yescharacteristic
1076C22×C4C23×D7311yescharacteristic
1077C4⋊C4—22no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—22no—
1081C4⋊C4—22no—
1082C4⋊C4—22no—
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—22no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—2921no—
1092C4⋊C4—2921no—
1093C4⋊C4—2921no—
1094C4⋊C4—2921no—
1095C4⋊C4—2921no—
1096C4⋊C4—2921no—
1097C4⋊C4—2921no—
1098C4⋊C4—2921no—
1099C4⋊C4—2921no—
1100C4⋊C4—2921no—
1101C4⋊C4—2921no—
1102C4⋊C4—2921no—
1103C4⋊C4—734no—
1104C4⋊C4—1462no—
1105C4⋊C4—1462no—
1106C4⋊C4—1462no—
1107C4⋊C4—1462no—
1108C4⋊C4—1462no—
1109C4⋊C4—1462no—
1110C4⋊C4—1462no—
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#1192402714yes—
1123C22⋊C4—22no—
1124C22⋊C4—22no—
1125C22⋊C4—22no—
1126C22⋊C4—22no—
1127C22⋊C4—22no—
1128C22⋊C4—41no—
1129C22⋊C4—41no—
1130C22⋊C4—2921no—
1131C22⋊C4—2921no—
1132C22⋊C4—2921no—
1133C22⋊C4—2921no—
1134C22⋊C4—2921no—
1135C22⋊C4—2921no—
1136C22⋊C4—1462no—
1137C22⋊C4—1462no—
1138C22⋊C4—1462no—
1139C22⋊C4—1462no—
1140C22⋊C4—1462no—
1141C22⋊C4—1462no—
1142C22⋊C4—1462no—
1143C22⋊C4—1462no—
1144C22⋊C4—1462no—
1145C22⋊C4—1462no—
1146C22⋊C4—1462no—
1147C22⋊C4—1462no—
1148C22⋊C4—1462no—
1149C42—22no—
1150C42—22no—
1151C42—22no—
1152C42—2921no—
1153C42—2921no—
1154C42—2921no—
1155C42—2921no—
1156C42—2921no—
1157C42—1462no—
1158C42—1462no—
1159C42—1462no—
1160C42—1462no—
1161C42—1462no—
1162C42—1462no—
1163C42—1462no—
1164C42—1462no—
1165C42—1462no—
1166C42—1462no—
1167C42—1462no—
1168C42—1462no—
1169C42—1462no—
1170C42—1462no—
1171C42—1462no—
1172C42—1462no—
1173C42—1462no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—21no—
1180C23—21no—
1181C23—1461no—
1182C23—1461no—
1183C23—1461no—
1184C23—1461no—
1185C23—1461no—
1186C23—1461no—
1187C23—1461no—
1188C23C24×D7311yescharacteristic
1189Q8—2924no—
1190Q8—2924no—
1191Q8—5842no—
1192D4—5842no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
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—2924no—
1231C2×C4—2924no—
1232C2×C4—732no—
1233C2×C4—732no—
1234C2×C4—732no—
1235C2×C4—732no—
1236C2×C4—732no—
1237C2×C4—732no—
1238C2×C4—732no—
1239C2×C4—1461no—
1240C2×C4—1461no—
1241C2×C4—1461no—
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#41×D7312yes—
1278C2×C4#41×D7312yes—
1279C2×C4C2×#1192402712yes—
1280C2×C4C2×#1192402712yes—
1281C2×C4C2×#1192402712yes—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—2921no—
1290C22—2921no—
1291C22—2921no—
1292C22—2921no—
1293C22—2921no—
1294C22—2921no—
1295C22—2921no—
1296C22C2×#41×D7311yescharacteristic
1297C22C2×#41×D7311yescharacteristic
1298C22C22×#1192402711yescharacteristic
1299C22H(5,𝔽2)×D7311yescharacteristic
1300C222−1+4×D7311yescharacteristic
1301C222−1+4×D7311yescharacteristic
1302C22#1798942411yescharacteristic
1303C4—22no—
1304C4—22no—
1305C4—22no—
1306C4—22no—
1307C4—22no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—2921no—
1318C4—2921no—
1319C4—2921no—
1320C4—2921no—
1321C4—2921no—
1322C4—2921no—
1323C4—2921no—
1324C4—2921no—
1325C4—1462no—
1326C4—1462no—
1327C4—1462no—
1328C4—1462no—
1329C4—1462no—
1330C4—1462no—
1331C4—1462no—
1332C2—81no—
1333C2—5841no—
1334C2#2262354311yescharacteristic
1335C2#2262354511yescharacteristic
1336C2#2262355411yescharacteristic
1337C2#2262367511yescharacteristic
1338C2#2262368011yescharacteristic
1339C2#2262376311yescharacteristic
1340C2#2262427011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2721C2
prime radicalC22×C22⋊D73C23
hypercenter#2721D73
hypocenterC73#60042
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2721

Complements

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

NH ≅ G/Ntype
1. #22616964C2semidirect
3. #22616821C2semidirect
4. #22615641C2semidirect
5. #22615635C2semidirect
6. #22615567C2semidirect
7. #22615565C2semidirect
8. #22615208C2semidirect
9. #22615198C2semidirect
10. #22615117C2semidirect
12. #22614754C2semidirect
13. #22614741C2semidirect
16. #22614599C2semidirect
17. #22614597C2semidirect
20. #22613640C2semidirect
21. #22613637C2semidirect
22. #22613055C2semidirect
23. #22613044C2semidirect
25. #22613037C2semidirect
26. #22613033C2semidirect
27. #22613017C2semidirect
28. #22612498C2semidirect
29. #22612425C2semidirect
30. #22612423C2semidirect
31. C73×#2721C2semidirect
674. #2721D73semidirect
702. C73#60042semidirect

Maximal subgroups

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

subgroupindex
#226169642
#226169422
#226168212
#226156412
#226156352
#226155672
#226155652
#226152082
#226151982
#226151172
#226149062
#226147542
#226147412
#226146292
#226146272
#226145992
#226145972
#226141652
#226141582
#226136402
#226136372
#226130552
#226130442
#226130382
#226130372
#226130332
#226130172
#226124982
#226124252
#226124232
C73×#27212
#6004273