Finite Group Databasebeta

← #34034932

Subgroups — #34034932

Order 18688.

574 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22627147C211yesmaximal, characteristic, complemented
2#22627145C211yesmaximal, characteristic, complemented
3#22627144C211yesmaximal, characteristic, complemented
4#22627143C211yesmaximal, characteristic, complemented
5#22627143C211yesmaximal, characteristic, complemented
6#22627141C211yesmaximal, characteristic, complemented
7#22627139C211yesmaximal, characteristic, complemented
8D4×#11924040C211yesmaximal, characteristic, complemented
9#22627136C211yesmaximal, characteristic, complemented
10#22627136C211yesmaximal, characteristic, complemented
11#22627102C211yesmaximal, characteristic, complemented
12#22627101C211yesmaximal, characteristic, complemented
13#22627098C211yesmaximal, characteristic, complemented
14C2×C22⋊#11924040C211yesmaximal, characteristic, complemented
15#22626646C211yesmaximal, characteristic
16C2×#14556688C2211yescharacteristic, complemented
17C2×#14556687C2211yescharacteristic
18C2×#14556687C2211yescharacteristic
19C2×#14556687C2211yescharacteristic, complemented
20C2×#14556686C2211yescharacteristic, complemented
21C22×#11924040C2211yescharacteristic
22C22×#11924040C2211yescharacteristic
23C22×#11924040C2211yescharacteristic, complemented
24#17989690C2211yescharacteristic, complemented
25#17989690C2211yescharacteristic, complemented
26C4⋊#11924040C2211yescharacteristic, complemented
27C4⋊#11924040C2211yescharacteristic, complemented
28#17989684C2211yescharacteristic, complemented
29#17989684C2211yescharacteristic, complemented
30C22⋊#11924040C2211yescharacteristic
31C22⋊#11924040C2211yescharacteristic
32C22⋊#11924040C2211yescharacteristic
33C22⋊#11924040C2211yescharacteristic
34C22⋊#11924040C2211yescharacteristic
35C22⋊#11924040C2211yescharacteristic
36C22⋊#11924040C2211yescharacteristic
37C22⋊#11924040C2211yescharacteristic
38C22⋊#11924040C2211yescharacteristic, complemented
39C22⋊#11924040C2211yescharacteristic, complemented
40#17989681C2211yescharacteristic, complemented
41#17989681C2211yescharacteristic, complemented
42C4×#11924040C2211yescharacteristic, complemented
43C4×#11924040C2211yescharacteristic, complemented
44C2×#14556678C2211yescharacteristic
45C23×#10596833C2211yescharacteristic
46#17989618C411yescharacteristic
47#17989618C411yescharacteristic
48#17989616C411yescharacteristic
49#17989616C411yescharacteristic
50#17989614C2211yescharacteristic
51#17989614C2211yescharacteristic
52D4×#10596833C2211yescharacteristic
53D4×#10596833C2211yescharacteristic
54#17989593C411yescharacteristic
55#17989560C411yescharacteristic
56#17989557C411yescharacteristic
57#17989551C2211yescharacteristic
58#17989093C411yescharacteristic
59#14556688—41no—
60#14556687—41no—
61#14556687—41no—
62#14556687—41no—
63#14556686—41no—
64C2×#11924040—41no—
65C2×#11924040—41no—
66C2×#11924040—41no—
67C2×#11924040C2311yescharacteristic
68C2×#11924040C2311yescharacteristic
69C2×#11924040C2311yescharacteristic
70C2×#11924040C2311yescharacteristic
71C2×#11924040C2311yescharacteristic
72C2×#11924040C2311yescharacteristic
73C2×#11924040C2311yescharacteristic
74C2×#11924040C2311yescharacteristic
75#14556678—41no—
76#14556678—41no—
77C2×#11924038C2×C411yescharacteristic
78C2×#11924037C2×C411yescharacteristic
79C2×#11924037C2×C411yescharacteristic
80C2×#11924037C2×C411yescharacteristic
81C2×#11924036C2311yescharacteristic
82C22×#10596833—41no—
83C22×#10596833—41no—
84C22×#10596833C2×C411yescharacteristic
85C22×#10596833C2×C411yescharacteristic
86C22×#10596833C2×C411yescharacteristic
87C22×#10596833C2311yescharacteristic
88C22×#10596833C2311yescharacteristic
89C22×#10596833C2311yescharacteristic
90C22×#10596833C2311yescharacteristic
91#14556658C2×C411yescharacteristic
92#14556658C2×C411yescharacteristic
93C4⋊#10596833C2×C411yescharacteristic
94C4⋊#10596833C2×C411yescharacteristic
95#14556648C2×C411yescharacteristic
96#14556648C2×C411yescharacteristic
97C22⋊#10596833C2×C411yescharacteristic
98C22⋊#10596833C2×C411yescharacteristic
99C22⋊#10596833C2×C411yescharacteristic
100C22⋊#10596833C2×C411yescharacteristic
101C22⋊#10596833C2×C411yescharacteristic
102C22⋊#10596833C2×C411yescharacteristic
103#14556646C2×C411yescharacteristic
104#14556646C2×C411yescharacteristic
105C4×#10596833C2311yescharacteristic
106C4×#10596833C2311yescharacteristic
107C2×#11924027C2×C411yescharacteristic
108C23×Dic73C2×C411yescharacteristic
109#14556575C811yescharacteristic
110#14556572C811yescharacteristic
111#14556568C811yescharacteristic
112#14556568C811yescharacteristic
113#14556563C811yescharacteristic
114#14556563C811yescharacteristic
115#14556560C811yescharacteristic
116D4×Dic73C2×C411yescharacteristic
117D4×Dic73C2×C411yescharacteristic
118#14556551C2×C411yescharacteristic
119#14556551C2×C411yescharacteristic
120#14556547C2×C411yescharacteristic
121#120×C73C811yescharacteristic
122#11924040—21no—
123#11924040—21no—
124#11924040—21no—
125#11924040—21no—
126#11924040—21no—
127#11924040—21no—
128#11924040—21no—
129#11924040—21no—
130#11924038—41no—
131#11924037—41no—
132#11924037—41no—
133#11924037—41no—
134#11924036—21no—
135#11924036—21no—
136C2×#10596833—21no—
137C2×#10596833—21no—
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—41no—
145C2×#10596833—41no—
146C2×#10596833—41no—
147C2×#10596833C22×C411yescharacteristic
148C2×#10596833C22×C411yescharacteristic
149C2×#10596833C22×C411yescharacteristic
150C2×#10596833C22×C411yescharacteristic
151C2×#10596833C22×C411yescharacteristic
152C2×#10596833C22×C411yescharacteristic
153C2×#10596833C22×C411yescharacteristic
154C2×#10596833C2411yescharacteristic
155#11924027—41no—
156#11924027—41no—
157C2×Dic146C2×C811yescharacteristic
158C2×C22⋊D73C2×C811yescharacteristic
159C2×C22⋊D73C2×C811yescharacteristic
160C2×C22⋊D73C2×C811yescharacteristic
161C2×C22⋊D73C2×C811yescharacteristic
162C22×Dic73—41no—
163C22×Dic73—41no—
164C22×Dic73C2×C811yescharacteristic
165C22×Dic73C2×C811yescharacteristic
166C22×Dic73C2×C811yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C22×C411yescharacteristic
169C22×Dic73C22×C411yescharacteristic
170C22×Dic73C22×C411yescharacteristic
171C2×C4×D73C22×C411yescharacteristic
172C4⋊Dic73C2×C811yescharacteristic
173C4⋊Dic73C2×C811yescharacteristic
174#11924007C2×C811yescharacteristic
175#11924007C2×C811yescharacteristic
176#11924007C2×C811yescharacteristic
177#11924007C2×C811yescharacteristic
178C22⋊Dic73C2×C811yescharacteristic
179C22⋊Dic73C2×C811yescharacteristic
180C22⋊Dic73C2×C811yescharacteristic
181C22⋊Dic73C2×C811yescharacteristic
182C22⋊Dic73C2×C811yescharacteristic
183#11924005C2×C811yescharacteristic
184#11924005C2×C811yescharacteristic
185C4×Dic73C22×C411yescharacteristic
186C4×Dic73C22×C411yescharacteristic
187C24×C73C2×C811yescharacteristic
188C2×D4×C73C2×C811yescharacteristic
189C2×D4×C73C2×C811yescharacteristic
190C2×D4×C73C2×C811yescharacteristic
191C22⋊C4×C73C2×C811yescharacteristic
192C22⋊C4×C73C2×C811yescharacteristic
193C22⋊C4×C73C2×C811yescharacteristic
194C23×C73—22no—
195C23×C73—41no—
196C23×C73—41no—
197C23×C73C22×C811yescharacteristic
198C23×C73C22×C811yescharacteristic
199C23×C73C22×C811yescharacteristic
200C23×C73C22×C811yescharacteristic
201C22×D73C22×C811yescharacteristic
202D4×C73—22no—
203D4×C73—41no—
204D4×C73—41no—
205C2×C4×C73C22×C811yescharacteristic
206C2×C4×C73C22×C811yescharacteristic
207C2×C4×C73C22×C811yescharacteristic
208C22⋊D73—22no—
209C22⋊D73—41no—
210C22⋊D73—41no—
211C22⋊D73—41no—
212C2×Dic73—21no—
213C2×Dic73—21no—
214C2×Dic73—21no—
215C2×Dic73—21no—
216C2×Dic73—21no—
217C2×Dic73—21no—
218C2×Dic73—21no—
219C2×Dic73—21no—
220C2×Dic73—41no—
221C2×Dic73—41no—
222C2×Dic73—41no—
223C2×Dic73C22×C811yescharacteristic
224C2×Dic73C22×C811yescharacteristic
225C2×Dic73C22×C811yescharacteristic
226C2×Dic73C22×C811yescharacteristic
227C2×Dic73C22×C811yescharacteristic
228C2×Dic73C22×C811yescharacteristic
229C2×Dic73C23×C411yescharacteristic
230C4×D73—21no—
231C4×D73—21no—
232Dic146—41no—
233#10596833—21no—
234#10596833—21no—
235#10596833—21no—
236#10596833—21no—
237#10596833—21no—
238#10596833—21no—
239#10596833—21no—
240#10596833H(5,𝔽2)11yescharacteristic
241#10596833H(5,𝔽2)11yescharacteristic
242C22×C73—21no—
243C22×C73—21no—
244C22×C73—21no—
245C22×C73—21no—
246C22×C73—21no—
247C22×C73—21no—
248C22×C73—21no—
249C22×C73—21no—
250C22×C73—21no—
251C22×C73—21no—
252C22×C73—21no—
253C22×C73—44no—
254C22×C73#50412yes—
255C22×C73C23×C811yescharacteristic
256C2×D73—21no—
257C2×D73—21no—
258C2×D73—21no—
259C4×C73—21no—
260C4×C73—21no—
261C4×C73—21no—
262Dic73—21no—
263Dic73—21no—
264Dic73—21no—
265Dic73—21no—
266Dic73—21no—
267Dic73—21no—
268Dic73#51811yescharacteristic
269Dic73#56811yescharacteristic
270#33490—731nomaximal, Sylow
271C2×C73—22no—
272C2×C73—41no—
273C2×C73—41no—
274C2×C73—41no—
275C2×C73#297211yescharacteristic
276C2×C73C2×#50411yescharacteristic
277C2×C73#340711yescharacteristic
278D73—41no—
279#2929—731no—
280#2169—731no—
281#2169—731no—
282#2168—731no—
283#2168—731no—
284#2168—731no—
285#2168—731no—
286D4×C16—731no—
287D4×C16—731no—
288#2164—731no—
289#2164—731no—
290#2113—731no—
291#2113—731no—
292#2112—731no—
293C2×C22⋊C16—731no—
294C73#3349011yescharacteristic, complemented, Sylow
295C2×#131—731no—
296C23×C8—731no—
297#525—731no—
298C2×M32—731no—
299C2×M32—731no—
300C2×M32—731no—
301C2×M32—731no—
302C22×C16—731no—
303C22×C16—731no—
304C22×C16—731no—
305C22×C16—731no—
306#435—731no—
307#435—731no—
308#435—731no—
309#435—731no—
310C8×D4—731no—
311C8×D4—731no—
312C8×D4—731no—
313C8×D4—731no—
314#424—731no—
315#408—731no—
316#407—731no—
317#405—731no—
318C4⋊C16—731no—
319C4⋊C16—731no—
320C4⋊C16—731no—
321C4⋊C16—731no—
322C22⋊C16—731no—
323C22⋊C16—731no—
324C22⋊C16—731no—
325C22⋊C16—731no—
326C22⋊C16—731no—
327C22⋊C16—731no—
328C22⋊C16—731no—
329C22⋊C16—731no—
330C22⋊C16—731no—
331C22⋊C16—731no—
332C22⋊C16—731no—
333C22⋊C16—731no—
334#346—731no—
335#346—731no—
336C4×C16—731no—
337C4×C16—731no—
338C2×#41—731no—
339C23×C4—731no—
340#131—2921no—
341#131—2921no—
342C2×M16—731no—
343C2×M16—731no—
344C2×M16—731no—
345C2×M16—731no—
346C22×C8—2921no—
347C22×C8—2921no—
348C22×C8—731no—
349C22×C8—731no—
350C22×C8—731no—
351C22×C8—731no—
352C22×C8—731no—
353C22×C8—731no—
354C22×C8—731no—
355C22×C8—731no—
356#123—731no—
357#123—731no—
358C22⋊Q8—731no—
359C22⋊Q8—731no—
360#121—731no—
361#121—731no—
362#120—731no—
363#120#1059684211yescharacteristic
364C4×D4—731no—
365C4×D4—731no—
366C4×D4—731no—
367C4×D4—731no—
368#117—731no—
369M32—2921no—
370M32—2921no—
371M32—2921no—
372M32—2921no—
373C2×C16—2921no—
374C2×C16—2921no—
375C2×C16—2921no—
376C2×C16—2921no—
377C2×C16—731no—
378C2×C16—731no—
379C2×C16—731no—
380C2×C16—731no—
381C2×C16—731no—
382C2×C16—731no—
383C2×C16—731no—
384C2×C16—731no—
385C4⋊C8—731no—
386C4⋊C8—731no—
387C4⋊C8—731no—
388C4⋊C8—731no—
389C22⋊C8—731no—
390C22⋊C8—731no—
391C22⋊C8—731no—
392C22⋊C8—731no—
393C22⋊C8—731no—
394C22⋊C8—731no—
395C22⋊C8—731no—
396C22⋊C8—731no—
397#97—731no—
398#97—731no—
399C4×C8—731no—
400C4×C8—731no—
401C24C2×#1059684211yescharacteristic
402#41—2921no—
403#41—2921no—
404C2×Q8—731no—
405C2×D4—731no—
406C2×D4—731no—
407C2×D4—731no—
408C2×D4—731no—
409C2×D4C2×#1059684211yescharacteristic
410C2×D4C2×#1059684211yescharacteristic
411C2×D4C2×#1059684211yescharacteristic
412C22×C4—2921no—
413C22×C4—2921no—
414C22×C4—731no—
415C22×C4—731no—
416C22×C4—731no—
417C22×C4—731no—
418C22×C4—731no—
419C22×C4—731no—
420C22×C4—731no—
421C22×C4—731no—
422M16—2921no—
423M16—2921no—
424M16—2921no—
425M16—2921no—
426C2×C8—2921no—
427C2×C8—2921no—
428C2×C8—2921no—
429C2×C8—731no—
430C2×C8—731no—
431C2×C8—731no—
432C2×C8—731no—
433C2×C8—731no—
434C2×C8—731no—
435C2×C8—731no—
436C2×C8—731no—
437C2×C8—1461no—
438C2×C8—1461no—
439C2×C8—1461no—
440C2×C8—1461no—
441C2×C8—1461no—
442C2×C8—1461no—
443C2×C8—1461no—
444C2×C8—1461no—
445C2×C8—1461no—
446C2×C8—1461no—
447C4⋊C4—731no—
448C4⋊C4—731no—
449C4⋊C4—731no—
450C4⋊C4—731no—
451C4⋊C4—731no—
452C4⋊C4—731no—
453C22⋊C4—731no—
454C22⋊C4—731no—
455C22⋊C4—731no—
456C22⋊C4—731no—
457C22⋊C4—731no—
458C22⋊C4—731no—
459C22⋊C4—731no—
460C22⋊C4C2×#1059684211yescharacteristic
461C22⋊C4C2×#1059684211yescharacteristic
462C22⋊C4C2×#1059684211yescharacteristic
463C42—731no—
464C42—731no—
465C16—1461no—
466C16—1461no—
467C16—1461no—
468C16—1461no—
469C16—1461no—
470C16—1461no—
471C16—1461no—
472C16—1461no—
473C23—22no—
474C23—41no—
475C23—41no—
476C23—731no—
477C23C22×#1059684211yescharacteristic
478C23C22×#1059684211yescharacteristic
479C23C22×#1059684211yescharacteristic
480C23C22×#1059684211yescharacteristic
481Q8—2921no—
482D4—22no—
483D4—41no—
484D4—41no—
485D4—2921no—
486D4—2921no—
487D4—2921no—
488D4—1462no—
489C2×C4—2921no—
490C2×C4—2921no—
491C2×C4—2921no—
492C2×C4—731no—
493C2×C4—731no—
494C2×C4—731no—
495C2×C4—731no—
496C2×C4—731no—
497C2×C4—731no—
498C2×C4—731no—
499C2×C4—1461no—
500C2×C4—1461no—
501C2×C4—1461no—
502C2×C4—1461no—
503C2×C4—1461no—
504C2×C4—1461no—
505C2×C4—1461no—
506C2×C4—1461no—
507C2×C4—1461no—
508C2×C4—1461no—
509C2×C4C22×#1059684211yescharacteristic
510C2×C4C22×#1059684211yescharacteristic
511C2×C4C22×#1059684211yescharacteristic
512C8—731no—
513C8—731no—
514C8—1461no—
515C8—1461no—
516C8—1461no—
517C8—1461no—
518C8—1461no—
519C8—1461no—
520C8—1461no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—44no—
533C22—1461no—
534C22—1461no—
535C22—1461no—
536C22#1798970812yes—
537C22C23×#1059684211yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—731no—
542C4—731no—
543C4—1461no—
544C4—1461no—
545C4—1461no—
546C4—1461no—
547C4—1461no—
548C4—1461no—
549C2—22no—
550C2—41no—
551C2—41no—
552C2—41no—
553C2—2921no—
554C2#2262717311yescharacteristic
555C2C2×#1798970811yescharacteristic
556C2#2262718411yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10596842
commutator, socleC22×C73C23×C8
Fitting#120×C73C8
prime radical#17989093C4
cosocleC2×#10596833C24
hypercenter#120#10596842
hypocenterC73#33490
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #22627147C2semidirect
2. #22627145C2semidirect
3. #22627144C2semidirect
4. #22627143C2semidirect
5. #22627143C2semidirect
6. #22627141C2semidirect
7. #22627139C2semidirect
8. D4×#11924040C2semidirect
9. #22627136C2semidirect
10. #22627136C2semidirect
11. #22627102C2semidirect
12. #22627101C2semidirect
13. #22627098C2semidirect
14. C2×C22⋊#11924040C2semidirect
16. C2×#14556688C22semidirect
19. C2×#14556687C22semidirect
20. C2×#14556686C22semidirect
23. C22×#11924040C22semidirect
24. #17989690C22semidirect
25. #17989690C22semidirect
26. C4⋊#11924040C22semidirect
27. C4⋊#11924040C22semidirect
28. #17989684C22semidirect
29. #17989684C22semidirect
38. C22⋊#11924040C22semidirect
39. C22⋊#11924040C22semidirect
40. #17989681C22semidirect
41. #17989681C22semidirect
42. C4×#11924040C22semidirect
43. C4×#11924040C22semidirect
294. C73#33490semidirect

Maximal subgroups

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

subgroupindex
#226271472
#226271452
#226271442
#226271432
#226271412
#226271392
D4×#119240402
#226271362
#226271022
#226271012
#226270982
C2×C22⋊#119240402
#226266462
#3349073