Finite Group Databasebeta

← #11888575

Subgroups — #11888575

Order 1152.

1182 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#547C211yesmaximal, characteristic, complemented
2#10596036C211yesmaximal, characteristic, complemented
3#10592937C211yesmaximal, characteristic, complemented
4#10592937C211yesmaximal, characteristic, complemented
5#10592932C211yesmaximal, characteristic, complemented
6#10592931C211yesmaximal, characteristic, complemented
7#10592782C211yesmaximal, characteristic, complemented
8#10592781C211yesmaximal, characteristic, complemented
9#10592748C211yesmaximal, characteristic, complemented
10#10592747C211yesmaximal, characteristic, complemented
11#10592744C211yesmaximal, characteristic, complemented
12#10592742C211yesmaximal, characteristic, complemented
13#10592713C211yesmaximal, characteristic, complemented
14#10592710C211yesmaximal, characteristic, complemented
15#10592708C211yesmaximal, characteristic, complemented
16#83512—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×C32×#41C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic
20C32×#123—21no—
21C32×#123—21no—
22C32×C22⋊Q8C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24C32×#121—21no—
25C32×C4×D4C2211yescharacteristic
26C32×C4×D4C2211yescharacteristic
27C2×C32×C4⋊C4—21no—
28C2×#3755C2211yescharacteristic
29C2×#3755C2211yescharacteristic
30#64148—21no—
31C2×#3753C2211yescharacteristic
32#64139C2211yescharacteristic
33#64139C2211yescharacteristic
34#64135C2211yescharacteristic
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
36C2×#3748C2211yescharacteristic
37C22×C3⋊(C3⋊C8)C2211yescharacteristic
38#64107—21no—
39#64092—21no—
40#64090—21no—
41C4×C4⋊(C3⋊D3)C2211yescharacteristic
42#64079C2211yescharacteristic
43#63662C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48#63662C2211yescharacteristic
49#63659C2211yescharacteristic
50#63659C2211yescharacteristic
51#63659C2211yescharacteristic
52#63657C2211yescharacteristic
53#63657C2211yescharacteristic
54#63636C2211yescharacteristic
55#63635C2211yescharacteristic
56#63635C2211yescharacteristic
57#63634C2211yescharacteristic
58C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
59#63630C2211yescharacteristic
60C3×#547D314yescomplemented
61#5565—34no—
62#5238—34no—
63#5238—34no—
64#5233—34no—
65#5232—34no—
66#5083—34no—
67#5082—34no—
68#5049—34no—
69#5048—34no—
70#5045—34no—
71#5043—34no—
72#5014—34no—
73#5011—34no—
74#5009—34no—
75C32×#41—22no—
76C32×#41—22no—
77C32×#41—41no—
78C32×#41—41no—
79C2×C32×Q8C2311yescharacteristic
80C2×C32×Q8C2311yescharacteristic
81C2×C32×D4—21no—
82C2×C32×D4—21no—
83C2×C32×D4D411yescharacteristic
84C2×C32×D4C2311yescharacteristic
85C22×C32×C4—21no—
86C22×C32×C4—21no—
87C22×C32×C4—21no—
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C2×#638—21no—
91C2×#638—21no—
92C22×C3⋊Dic3—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C32×C4⋊C4—21no—
96C32×C4⋊C4—21no—
97C32×C4⋊C4—21no—
98C32×C4⋊C4—21no—
99C32×C4⋊C4D411yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C22⋊C4—21no—
102C32×C22⋊C4—21no—
103C32×C22⋊C4—21no—
104C32×C22⋊C4D411yescharacteristic
105C32×C22⋊C4D411yescharacteristic
106C32×C42C2311yescharacteristic
107#3757—21no—
108#3755—41no—
109#3755—41no—
110#3753—22no—
111#3752—21no—
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3—21no—
121#3748—41no—
122C2×C3⋊(C3⋊C8)—41no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3307—91noSylow
128C2×C3×#41C2×D314yes—
129C2×C3×#41C2×D314yes—
130C3×C4⋊Q8C2×D314yes—
131C3×#123—24no—
132C3×#123—24no—
133C3×C22⋊Q8C2×D314yes—
134C3×C22⋊Q8C2×D314yes—
135C3×#121—24no—
136C3×C4×D4C2×D314yes—
137C3×C4×D4C2×D314yes—
138C2×C3×C4⋊C4—24no—
139C2×#215—34no—
140C2×#215—34no—
141#939—64no—
142C2×#213—34no—
143#930—34no—
144#930—34no—
145#926—34no—
146C2×C4⋊Dic3—34no—
147C2×#208—34no—
148C22×C3⋊C8—34no—
149#898—64no—
150#883—64no—
151#67⋊C4—64no—
152C4×D12—34no—
153#870—34no—
154#835—34no—
155#835—34no—
156#835—34no—
157#835—34no—
158#835—34no—
159#835—34no—
160#832—34no—
161#832—34no—
162#832—34no—
163#830—34no—
164#830—34no—
165#809—34no—
166#808—34no—
167#808—34no—
168#807—34no—
169C4⋊(C3⋊C8)—34no—
170#803—34no—
171C23×C32—21no—
172C23×C32C2×D411yescharacteristic
173C23×C32C2×D411yescharacteristic
174C22×C3⋊D3—21no—
175C32×Q8—21no—
176C32×Q8—21no—
177C32×Q8—21no—
178C32×Q8—21no—
179C32×D4—21no—
180C32×D4—41no—
181C32×D4—42no—
182C32×D4—42no—
183C32×D4#4112yes—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—42no—
192C2×C32×C4—42no—
193C2×C32×C4—42no—
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2×D411yescharacteristic
197C2×C32×C4C2×D411yescharacteristic
198C2×C32×C4C2411yescharacteristic
199#638—42no—
200#638—81no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—81no—
205C4⋊(C3⋊D3)—21no—
206C4⋊(C3⋊D3)—21no—
207C4×C3⋊D3—81no—
208C3⋊(C3⋊C8)—21no—
209C3⋊(C3⋊C8)—21no—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)—21no—
212#553—91no—
213#547C3⋊D311yescharacteristic, complemented
214#491—91no—
215#485—91no—
216#483—91no—
217#478—91no—
218#468—91no—
219#465—91no—
220#461—91no—
221#449—91no—
222#449—91no—
223#442—91no—
224#435—91no—
225#417—91no—
226#416—91no—
227C3×#41—28no—
228C3×#41—28no—
229C3×#41—44no—
230C3×#41—44no—
231C2×C3×Q8C22×D314yes—
232C2×C3×Q8C22×D314yes—
233C2×C3×D4—24no—
234C2×C3×D4—24no—
235C2×C3×D4#6714yes—
236C2×C3×D4C22×D314yes—
237C22×C3×C4—24no—
238C22×C3×C4—24no—
239C22×C3×C4—24no—
240C22×C3×C4C22×D314yes—
241C22×C3×C4C22×D314yes—
242C2×#67—64no—
243C2×#67—64no—
244C22×Dic3—64no—
245C2×D12—34no—
246C2×C4×D3—64no—
247C3×C4⋊C4—24no—
248C3×C4⋊C4—24no—
249C3×C4⋊C4—24no—
250C3×C4⋊C4—24no—
251C3×C4⋊C4#6714yes—
252C3×C4⋊C4C22×D314yes—
253C3×C22⋊C4—24no—
254C3×C22⋊C4—24no—
255C3×C22⋊C4—24no—
256C3×C22⋊C4#6714yes—
257C3×C22⋊C4#6714yes—
258C3×C42C22×D314yes—
259#217—64no—
260#215—124no—
261#215—124no—
262#213—68no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—64no—
266C4⋊Dic3—34no—
267C4⋊Dic3—34no—
268C4⋊Dic3—34no—
269C4⋊Dic3—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—64no—
272C4×Dic3—64no—
273#208—124no—
274C2×C3⋊C8—34no—
275C2×C3⋊C8—34no—
276C2×C3⋊C8—34no—
277C2×C3⋊C8—34no—
278C2×C3⋊C8—124no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32—22no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32—21no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—41no—
292C32×C4—21no—
293C32×C4—21no—
294C32×C4—21no—
295C32×C4—21no—
296C32×C4—41no—
297C32×C4—41no—
298C32×C4—41no—
299C32×C4C2×#4111yescharacteristic
300C32×C4H(5,𝔽2)11yescharacteristic
301C3⋊Dic3—41no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C2×#41C2×C3⋊D311yescharacteristic
305C2×#41C2×C3⋊D311yescharacteristic
306C2×SD16—91no—
307C2×SD16—91no—
308C2×D8—91no—
309C2×M16—91no—
310C22×C8—91no—
311C4⋊Q8C2×C3⋊D311yescharacteristic
312#126—181no—
313#125—91no—
314#123—21no—
315#123—21no—
316#123—181no—
317C22⋊Q8C2×C3⋊D311yescharacteristic
318C22⋊Q8C2×C3⋊D311yescharacteristic
319#121—21no—
320#121—91no—
321#121—91no—
322#121—181no—
323C4×D4—91no—
324C4×D4—181no—
325C4×D4C2×C3⋊D311yescharacteristic
326C4×D4C2×C3⋊D311yescharacteristic
327#117—91no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—91no—
330#107—91no—
331#106—91no—
332#106—91no—
333C4⋊C8—91no—
334#103—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103—91no—
339#103—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102—91no—
344C22⋊C8—91no—
345C22⋊C8—91no—
346#97—91no—
347C23×C3—24no—
348C23×C3C2×#6714yes—
349C23×C3C2×#6714yes—
350C22×D3—64no—
351C3×Q8—24no—
352C3×Q8—24no—
353C3×Q8—24no—
354C3×Q8—24no—
355C3×D4—24no—
356C3×D4—44no—
357C3×D4—48no—
358C3×D4—48no—
359C3×D4#23718yes—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—24no—
364C2×C3×C4—24no—
365C2×C3×C4—24no—
366C2×C3×C4—24no—
367C2×C3×C4—48no—
368C2×C3×C4—48no—
369C2×C3×C4—48no—
370C2×C3×C4C2×#6714yes—
371C2×C3×C4C2×#6714yes—
372C2×C3×C4C2×#6714yes—
373C2×C3×C4C2×#6714yes—
374C2×C3×C4C23×D314yes—
375#67—128no—
376#67—244no—
377C2×Dic3—64no—
378C2×Dic3—64no—
379C2×Dic3—64no—
380C2×Dic3—244no—
381D12—64no—
382D12—64no—
383C4×D3—244no—
384C3⋊C8—64no—
385C3⋊C8—64no—
386C3⋊C8—64no—
387C3⋊C8—64no—
388C2×C32—41no—
389C2×C32—41no—
390C2×C32—42no—
391C2×C32#54611yescharacteristic
392C2×C32#57511yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—81no—
395#41—22no—
396#41—22no—
397#41—41no—
398#41—41no—
399C2×Q8C22×C3⋊D311yescharacteristic
400C2×Q8C22×C3⋊D311yescharacteristic
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—91no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4#63811yescharacteristic
407C2×D4C22×C3⋊D311yescharacteristic
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×C3⋊D311yescharacteristic
414C22×C4C22×C3⋊D311yescharacteristic
415SD16—361no—
416SD16—361no—
417D8—182no—
418M16—361no—
419C2×C8—91no—
420C2×C8—91no—
421C2×C8—91no—
422C2×C8—91no—
423C2×C8—361no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—91no—
429C4⋊C4—91no—
430C4⋊C4—91no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4—181no—
434C4⋊C4#63811yescharacteristic
435C4⋊C4C22×C3⋊D311yescharacteristic
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—21no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4#63811yescharacteristic
444C22⋊C4#63811yescharacteristic
445C42—181no—
446C42C22×C3⋊D311yescharacteristic
447C22×C3—24no—
448C22×C3—24no—
449C22×C3—28no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—24no—
453C22×C3—24no—
454C22×C3—44no—
455C22×C3—44no—
456C22×C3C22×#6714yes—
457C2×D3—124no—
458C2×D3—124no—
459C2×D3—124no—
460C3×C4—24no—
461C3×C4—24no—
462C3×C4—24no—
463C3×C4—24no—
464C3×C4—44no—
465C3×C4—44no—
466C3×C4—44no—
467C3×C4C2×#23714yes—
468C3×C4#100414yes—
469Dic3—124no—
470Dic3—124no—
471Dic3—124no—
472C32#330711yescharacteristic, complemented, Sylow
473C23—21no—
474C23—181no—
475C23C2×#63811yescharacteristic
476C23C2×#63811yescharacteristic
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481D4—21no—
482D4—41no—
483D4—42no—
484D4—42no—
485D4—181no—
486D4—181no—
487D4—362no—
488D4—721no—
489D4#383012yes—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—721no—
504C2×C4—721no—
505C2×C4C2×#63811yescharacteristic
506C2×C4C2×#63811yescharacteristic
507C2×C4C2×#63811yescharacteristic
508C2×C4C2×#63811yescharacteristic
509C2×C4C23×C3⋊D311yescharacteristic
510C8—181no—
511C8—181no—
512C8—181no—
513C8—181no—
514C2×C3—44no—
515C2×C3—44no—
516C2×C3—48no—
517C2×C3#580614yes—
518C2×C3#582214yes—
519C2×C3#583714yes—
520D3—244no—
521C22—21no—
522C22—21no—
523C22—22no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—41no—
529C22—41no—
530C22—361no—
531C22—361no—
532C22—361no—
533C22C22×#63811yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—361no—
542C4—361no—
543C4—361no—
544C4C2×#383011yescharacteristic
545C4#6436111yescharacteristic
546C3#8351214yescomplemented
547C2—41no—
548C2—41no—
549C2—42no—
550C2—721no—
551C2#1059627711yescharacteristic
552C2#1059629311yescharacteristic
553C2#1059630811yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#547C2
socleC22×C32C22×D4
hypercenter#547C3⋊D3
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C32×#547C2semidirect
2. #10596036C2semidirect
3. #10592937C2semidirect
4. #10592937C2semidirect
5. #10592932C2semidirect
6. #10592931C2semidirect
7. #10592782C2semidirect
8. #10592781C2semidirect
9. #10592748C2semidirect
10. #10592747C2semidirect
11. #10592744C2semidirect
12. #10592742C2semidirect
13. #10592713C2semidirect
14. #10592710C2semidirect
15. #10592708C2semidirect
60. C3×#547D3semidirect
213. #547C3⋊D3semidirect
472. C32#3307semidirect
546. C3#83512semidirect

Maximal subgroups

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

subgroupindex
C32×#5472
#105960362
#105929372
#105929322
#105929312
#105927822
#105927812
#105927482
#105927472
#105927442
#105927422
#105927132
#105927102
#105927082
#835123