Finite Group Databasebeta

← #11888557

Subgroups — #11888557

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×#553C211yesmaximal, characteristic, complemented
2#10596022C211yesmaximal, characteristic, complemented
3#10592768C211yesmaximal, characteristic, complemented
4#10592765C211yesmaximal, characteristic, complemented
5#10592741C211yesmaximal, characteristic, complemented
6#10592740C211yesmaximal, characteristic, complemented
7#10592736C211yesmaximal, characteristic, complemented
8#10592736C211yesmaximal, characteristic, complemented
9#10592718C211yesmaximal, characteristic, complemented
10#10592713C211yesmaximal, characteristic, complemented
11#10592710C211yesmaximal, characteristic, complemented
12#10592701C211yesmaximal, characteristic, complemented
13#10592695C211yesmaximal, characteristic, complemented
14#10592670C211yesmaximal, characteristic, complemented
15#10592665C211yesmaximal, characteristic, complemented
16#83615—34nomaximal
17C2×#3828C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C32×#126—21no—
20C32×#125C2211yescharacteristic
21C32×#123—21no—
22C32×#121—21no—
23C32×#121C2211yescharacteristic
24C32×#121C2211yescharacteristic
25C32×C4×D4—21no—
26C32×C4×D4C2211yescharacteristic
27C32×C4×D4C2211yescharacteristic
28C32×#117C2211yescharacteristic
29C2×C32×C4⋊C4C2211yescharacteristic
30#64147—21no—
31C2×#3754C2211yescharacteristic
32C2×#3754C2211yescharacteristic
33C2×#3753C2211yescharacteristic
34#64133C2211yescharacteristic
35#64133C2211yescharacteristic
36C2×#3748C2211yescharacteristic
37C22×C3⋊(C3⋊C8)C2211yescharacteristic
38C4⋊C4×C3⋊D3—21no—
39#64092—21no—
40#64092—21no—
41C4×C4⋊(C3⋊D3)C2211yescharacteristic
42#64078C2211yescharacteristic
43#63659C2211yescharacteristic
44#63657C2211yescharacteristic
45#63657C2211yescharacteristic
46#63637C2211yescharacteristic
47#63637C2211yescharacteristic
48#63637C2211yescharacteristic
49#63637C2211yescharacteristic
50#63637C2211yescharacteristic
51#63637C2211yescharacteristic
52#63636C2211yescharacteristic
53#63636C2211yescharacteristic
54#63636C2211yescharacteristic
55#63635C2211yescharacteristic
56#63635C2211yescharacteristic
57#63634C2211yescharacteristic
58C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
59#63630C2211yescharacteristic
60C3×#553D314yescomplemented
61#5551—34no—
62#5069—34no—
63#5066—34no—
64#5042—34no—
65#5041—34no—
66#5037—34no—
67#5037—34no—
68#5019—34no—
69#5014—34no—
70#5011—34no—
71#5002—34no—
72#4996—34no—
73#4971—34no—
74#4966—34no—
75C2×C32×D4—21no—
76C2×C32×D4—21no—
77C2×C32×D4D411yescharacteristic
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C22×C32×C4—21no—
81C22×C32×C4C2311yescharacteristic
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C2×#638—21no—
85#3828—22no—
86#3828—22no—
87#3828—41no—
88#3828—41no—
89C2×C4⋊(C3⋊D3)C2311yescharacteristic
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—21no—
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C32×C4⋊C4—21no—
96C32×C4⋊C4—21no—
97C32×C4⋊C4—21no—
98C32×C4⋊C4D411yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C4⋊C4C2311yescharacteristic
102C32×C22⋊C4—21no—
103C32×C22⋊C4—21no—
104C32×C22⋊C4—21no—
105C32×C22⋊C4—21no—
106C32×C22⋊C4D411yescharacteristic
107C32×C22⋊C4D411yescharacteristic
108C32×C42—21no—
109C32×C42C2311yescharacteristic
110#3757—21no—
111#3757—21no—
112#3754—41no—
113#3754—41no—
114#3753—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3750—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×#235—34no—
129C2×#235—34no—
130C3×#126—24no—
131C3×#125C2×D314yes—
132C3×#123—24no—
133C3×#121—24no—
134C3×#121C2×D314yes—
135C3×#121C2×D314yes—
136C3×C4×D4—24no—
137C3×C4×D4C2×D314yes—
138C3×C4×D4C2×D314yes—
139C3×#117C2×D314yes—
140C2×C3×C4⋊C4C2×D314yes—
141#938—64no—
142C2×#214—34no—
143C2×#214—34no—
144C2×#213—34no—
145#924—34no—
146#924—34no—
147C2×#208—34no—
148C22×C3⋊C8—34no—
149D3×C4⋊C4—64no—
150#883—64no—
151#883—64no—
152C4×D12—34no—
153#869—34no—
154#832—34no—
155#830—34no—
156#830—34no—
157#810—34no—
158#810—34no—
159#810—34no—
160#810—34no—
161#810—34no—
162#810—34no—
163#809—34no—
164#809—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×D4—21no—
176C32×D4—21no—
177C32×D4—41no—
178C32×D4—42no—
179C32×D4—81no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—81no—
188C2×C32×C4—81no—
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194#638—42no—
195#638—42no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C4⋊(C3⋊D3)—21no—
200C4⋊(C3⋊D3)#4112yes—
201C4×C3⋊D3—42no—
202C4×C3⋊D3—42no—
203C4×C3⋊D3—42no—
204#634—21no—
205#634—21no—
206#634—21no—
207#634—21no—
208C3⋊(C3⋊C8)—21no—
209C3⋊(C3⋊C8)—21no—
210C3⋊(C3⋊C8)—21no—
211C3⋊(C3⋊C8)—21no—
212#553C3⋊D311yescharacteristic, complemented
213#547—91no—
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—
227C2×C3×D4—24no—
228C2×C3×D4—24no—
229C2×C3×D4#6714yes—
230C2×C3×D4C22×D314yes—
231C22×C3×C4—24no—
232C22×C3×C4—24no—
233C22×C3×C4C22×D314yes—
234C22×C3×C4C22×D314yes—
235C2×#67—64no—
236C2×#67—64no—
237#235—68no—
238#235—68no—
239#235—124no—
240#235—124no—
241C2×D12—34no—
242C2×C4×D3—64no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×Dic6—34no—
246C2×Dic6—34no—
247C3×C4⋊C4—24no—
248C3×C4⋊C4—24no—
249C3×C4⋊C4—24no—
250C3×C4⋊C4#6714yes—
251C3×C4⋊C4C22×D314yes—
252C3×C4⋊C4C22×D314yes—
253C3×C4⋊C4C22×D314yes—
254C3×C22⋊C4—24no—
255C3×C22⋊C4—24no—
256C3×C22⋊C4—24no—
257C3×C22⋊C4—24no—
258C3×C22⋊C4#6714yes—
259C3×C22⋊C4#6714yes—
260C3×C42—24no—
261C3×C42C22×D314yes—
262#217—64no—
263#217—64no—
264#214—124no—
265#214—124no—
266#213—68no—
267(C2×D3)⋊C4—64no—
268C4⋊Dic3—34no—
269C4⋊Dic3—64no—
270C4⋊Dic3—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—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—21no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—22no—
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×#41—91no—
305C2×#41—91no—
306C2×SD16—91no—
307C2×SD16—91no—
308C2×D8—91no—
309C2×M16—91no—
310C22×C8—91no—
311C4⋊Q8—91no—
312#126—21no—
313#125C2×C3⋊D311yescharacteristic
314#123—21no—
315#123—181no—
316#123—181no—
317C22⋊Q8—91no—
318C22⋊Q8—91no—
319#121—21no—
320#121—181no—
321#121C2×C3⋊D311yescharacteristic
322#121C2×C3⋊D311yescharacteristic
323C4×D4—21no—
324C4×D4—91no—
325C4×D4C2×C3⋊D311yescharacteristic
326C4×D4C2×C3⋊D311yescharacteristic
327#117C2×C3⋊D311yescharacteristic
328C2×C4⋊C4—181no—
329C2×C4⋊C4C2×C3⋊D311yescharacteristic
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×D4—24no—
352C3×D4—24no—
353C3×D4—44no—
354C3×D4—48no—
355C3×D4—84no—
356C2×C3×C4—24no—
357C2×C3×C4—24no—
358C2×C3×C4—24no—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—84no—
364C2×C3×C4—84no—
365C2×C3×C4C2×#6714yes—
366C2×C3×C4C2×#6714yes—
367C2×C3×C4C2×#6714yes—
368C2×C3×C4C2×#6714yes—
369C2×C3×C4C23×D314yes—
370#67—128no—
371#67—128no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3—64no—
375D12—38no—
376D12—64no—
377C4×D3—128no—
378C4×D3—128no—
379C4×D3—128no—
380Dic6—64no—
381Dic6—64no—
382Dic6—64no—
383Dic6—64no—
384C3⋊C8—64no—
385C3⋊C8—64no—
386C3⋊C8—64no—
387C3⋊C8—64no—
388C2×C32—41no—
389C2×C32—41no—
390C2×C32—81no—
391C2×C32#54611yescharacteristic
392C2×C32#57511yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—42no—
395#41—182no—
396#41—182no—
397#41—361no—
398#41—361no—
399C2×Q8—91no—
400C2×Q8—91no—
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—181no—
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—91no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4#63811yescharacteristic
433C4⋊C4C22×C3⋊D311yescharacteristic
434C4⋊C4C22×C3⋊D311yescharacteristic
435C4⋊C4C22×C3⋊D311yescharacteristic
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—21no—
439C22⋊C4—21no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4#63811yescharacteristic
444C22⋊C4#63811yescharacteristic
445C42—21no—
446C42C22×C3⋊D311yescharacteristic
447C22×C3—24no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—24no—
453C22×C3—44no—
454C22×C3—44no—
455C22×C3—44no—
456C22×C3C22×#6714yes—
457C2×D3—68no—
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×C4D3×#4114yes—
468C3×C4#100914yes—
469Dic3—124no—
470Dic3—124no—
471Dic3—124no—
472C32#330711yescharacteristic, complemented, Sylow
473C23—21no—
474C23—181no—
475C23C2×#63811yescharacteristic
476C23C2×#63811yescharacteristic
477Q8—181no—
478Q8—181no—
479Q8—181no—
480Q8—181no—
481D4—21no—
482D4—21no—
483D4—41no—
484D4—42no—
485D4—81no—
486D4—92no—
487D4—181no—
488D4—362no—
489D4—362no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—81no—
498C2×C4—81no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—362no—
503C2×C4—362no—
504C2×C4—362no—
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—84no—
517C2×C3#582214yes—
518C2×C3#582914yes—
519C2×C3#583614yes—
520D3—128no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—182no—
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—
544C4#41×C3⋊D311yescharacteristic
545C4#6436611yescharacteristic
546C3#8361514yescomplemented
547C2—41no—
548C2—41no—
549C2—81no—
550C2—362no—
551C2#1059629311yescharacteristic
552C2#1059630011yescharacteristic
553C2#1059630711yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#553C2
socleC22×C32C22×D4
hypercenter#553C3⋊D3
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. C32×#553C2semidirect
2. #10596022C2semidirect
3. #10592768C2semidirect
4. #10592765C2semidirect
5. #10592741C2semidirect
6. #10592740C2semidirect
7. #10592736C2semidirect
8. #10592736C2semidirect
9. #10592718C2semidirect
10. #10592713C2semidirect
11. #10592710C2semidirect
12. #10592701C2semidirect
13. #10592695C2semidirect
14. #10592670C2semidirect
15. #10592665C2semidirect
60. C3×#553D3semidirect
212. #553C3⋊D3semidirect
472. C32#3307semidirect
546. C3#83615semidirect

Maximal subgroups

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

subgroupindex
C32×#5532
#105960222
#105927682
#105927652
#105927412
#105927402
#105927362
#105927182
#105927132
#105927102
#105927012
#105926952
#105926702
#105926652
#836153