Finite Group Databasebeta

← #11787779

Subgroups — #11787779

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic, complemented
2#10595029C211yesmaximal, characteristic
3#10592838C211yesmaximal, characteristic, complemented
4#10591231C211yesmaximal, characteristic, complemented
5#10591113C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#72021—31nomaximal
9#68777—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20#63978—22no—
21#63911C411yescharacteristic, complemented
22C4×#626—22no—
23#63866C411yescharacteristic, complemented
24#63864C411yescharacteristic, complemented
25#63860C411yescharacteristic, complemented
26#63652—22no—
27#63580—22no—
28#63570—22no—
29C3×#568—31no—
30#5832—31no—
31#5745D311yescharacteristic, complemented
32#5477—31no—
33#5240—31no—
34#5139—31no—
35#5139—31no—
36#5139—31no—
37#5139—61no—
38#5006—31no—
39#5005—31no—
40C3×#339—31no—
41#4555—31no—
42#4555D311yescharacteristic, complemented
43#4523—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634C2×C411yescharacteristic
53C2×C3×#67D412yes—
54C22×C3×Dic3—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C2×C3×D12C2×C411yescharacteristic
60C2×C3×C4×D3D412yes—
61C2×C3×Dic6C2×C411yescharacteristic
62C2×#626—22no—
63C32×M16—21no—
64C32×M16D412yescomplemented
65C2×C32×C8—21no—
66#3757—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4×C3⋊Dic3—21no—
69C3×#217—21no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3C2×C411yescharacteristic
74C3×C4×Dic3C2×C411yescharacteristic
75C3×#208—21no—
76C3×#208D412yescomplemented
77C2×C3×C3⋊C8—21no—
78C3×ΓL(1,𝔽25)—24no—
79C3×D3×C8—24no—
80Dic3⋊Dic3—22no—
81#3722—22no—
82(C2×D3)⋊Dic3—22no—
83#1884—91noSylow
84C2×C3×#41—31no—
85C2×#235—31no—
86C2×#235—31no—
87C2×#235—61no—
88C2×#235C2×D311yescharacteristic
89C3×#131—62no—
90C3×#131—62no—
91C2×C3×M16—21no—
92C2×C3×M16—31no—
93C2×C3×M16—62no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C2×D311yescharacteristic
96C3×#117—31no—
97C2×C3×C42—31no—
98#947—31no—
99#944—31no—
100#940—31no—
101#939—62no—
102#936—31no—
103#930—62no—
104C4×#67—62no—
105#926—31no—
106#926—31no—
107#926—61no—
108#926C2×D311yescharacteristic
109C2×C4×Dic3C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111#907—22no—
112D3×M16—22no—
113#901—22no—
114#875—31no—
115#875—31no—
116#874—31no—
117C4×D12—62no—
118#869—31no—
119#834—62no—
120#825—62no—
121#825—64no—
122#825—62no—
123#825—62no—
124#806—62no—
125#805—62no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—21no—
128C22×C3×D3C22⋊C412yes—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135#638—41no—
136#638—41no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—41no—
139C4⋊(C3⋊D3)—21no—
140C4⋊(C3⋊D3)—21no—
141C4×C3⋊D3—41no—
142C4×C3⋊D3—41no—
143#634—21no—
144#634—21no—
145C3×#67—22no—
146C3×#67—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3C22⋊C412yes—
152C3×D12—21no—
153C3×D12—21no—
154C3×C4×D3—22no—
155C3×C4×D3—22no—
156C3×Dic6—21no—
157C3×Dic6—21no—
158#626—44no—
159C32×C8—22no—
160C3×C3⋊C8—22no—
161#568—31no—
162#532—91no—
163#421—91no—
164#421—91no—
165#410—91no—
166#339—31no—
167#339—91no—
168C3×#41—61no—
169C3×#41—61no—
170C3×#41—61no—
171C3×#41—61no—
172C2×C3×Q8—31no—
173C2×C3×D4—32no—
174C2×C3×D4—31no—
175C22×C3×C4—21no—
176C22×C3×C4—32no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C2×#67—62no—
181C2×#67—61no—
182C2×#67—61no—
183C2×#67—121no—
184C2×#67D1212yes—
185C22×Dic3—21no—
186#235—21no—
187#235—21no—
188#235—21no—
189#235—21no—
190#235—62no—
191#235—62no—
192#235—61no—
193#235—61no—
194#235—61no—
195#235—61no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—121no—
201#235—121no—
202C2×D12—31no—
203C2×D12—31no—
204C2×D12—61no—
205C2×D12—62no—
206C2×D12C4×D311yescharacteristic
207C2×C4×D3—61no—
208C2×C4×D3—61no—
209C2×C4×D3—121no—
210C2×C4×D3#6712yes—
211C2×Dic6—31no—
212C2×Dic6—31no—
213C2×Dic6—61no—
214C2×Dic6C4×D311yescharacteristic
215C3×M16—21no—
216C3×M16—21no—
217C3×M16—22no—
218C3×M16—32no—
219C3×M16—41no—
220C3×M16—64no—
221C3×M16—61no—
222C3×M16D1212yescomplemented
223C3×M16#6712yescomplemented
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—41no—
227C2×C3×C8—64no—
228C2×C3×C8—61no—
229C3×C4⋊C4—61no—
230C3×C22⋊C4—61no—
231C3×C42—31no—
232C3×C42—31no—
233C3×C42—61no—
234C3×C42—61no—
235#217—21no—
236#217—62no—
237#217—61no—
238#217—61no—
239#217—121no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—21no—
244C4⋊Dic3—62no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247C4⋊Dic3—121no—
248Dic3⋊C4—62no—
249C4×Dic3—21no—
250C4×Dic3—21no—
251C4×Dic3—62no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3C4×D311yescharacteristic
255C4×Dic3C4×D311yescharacteristic
256#208—21no—
257#208#6712yescomplemented
258C2×C3⋊C8—21no—
259ΓL(1,𝔽25)—24no—
260D3×C8—24no—
261C22×C32—41no—
262C22×C32C2×C22⋊C411yescharacteristic
263C22×C32#12111yescharacteristic
264C22×C32#12111yescharacteristic
265C2×C3⋊D3—41no—
266C2×C3⋊D3—42no—
267C2×C3×D3—22no—
268C2×C3×D3—42no—
269C32×C4C4×D411yescharacteristic
270C32×C4C4×D411yescharacteristic
271C32×C4#12011yescharacteristic
272C32×C4#12311yescharacteristic
273C3⋊Dic3—41no—
274C3⋊Dic3—81no—
275C3×Dic3—22no—
276C3×Dic3—22no—
277C3×Dic3—41no—
278C3×Dic3—81no—
279C2×#41—31no—
280C2×#41—91no—
281#131—62no—
282#131—62no—
283C2×M16—31no—
284C2×M16—62no—
285C2×M16D3211yescharacteristic
286C4⋊Q8—91no—
287#127—91no—
288#124—91no—
289#124—91no—
290#121—182no—
291C4×D4—182no—
292#117—31no—
293#117—91no—
294C2×C42—31no—
295#104—182no—
296#104—182no—
297#99—182no—
298C23×C3—21no—
299C23×C3—32no—
300C23×C3C2×D1211yescharacteristic
301C23×C3D3×D411yescharacteristic
302C22×D3—61no—
303C22×D3—61no—
304C22×D3—121no—
305C22×D3(C2×D3)⋊C412yes—
306C3×Q8—61no—
307C3×Q8—61no—
308C3×D4—62no—
309C3×D4—62no—
310C3×D4—61no—
311C3×D4—61no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—32no—
319C2×C3×C4—61no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—61no—
323C2×C3×C4—122no—
324C2×C3×C4—121no—
325C2×C3×C4C2×C4×D311yescharacteristic
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4#23511yescharacteristic
329C2×C3×C4#23511yescharacteristic
330C2×C3×C4#23511yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4#23911yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337#67—22no—
338#67—22no—
339#67—124no—
340#67—122no—
341#67—122no—
342#67—121no—
343#67—121no—
344#67—121no—
345#67—121no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—42no—
349C2×Dic3—41no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—121no—
353C2×Dic3—122no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3(C2×D3)⋊C412yes—
357D12—21no—
358D12—21no—
359D12—62no—
360D12—61no—
361D12—61no—
362D12—61no—
363D12—61no—
364D12—121no—
365D12—124no—
366C4×D3—22no—
367C4×D3—22no—
368C4×D3—122no—
369C4×D3—122no—
370C4×D3—121no—
371C4×D3—121no—
372C4×D3—121no—
373C4×D3—121no—
374Dic6—21no—
375Dic6—21no—
376Dic6—62no—
377Dic6—61no—
378Dic6—61no—
379Dic6—61no—
380Dic6—61no—
381Dic6—121no—
382C3×C8—22no—
383C3×C8—22no—
384C3×C8—42no—
385C3×C8—62no—
386C3⋊C8—22no—
387C2×C32—21no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32#38611yescharacteristic
391C3⋊D3—81no—
392C3×D3—42no—
393#41—61no—
394#41—61no—
395#41—61no—
396#41—61no—
397#41—181no—
398#41—181no—
399#41—181no—
400#41—181no—
401C2×Q8—31no—
402C2×Q8—91no—
403C2×D4—32no—
404C2×D4—31no—
405C2×D4—91no—
406C2×D4—182no—
407C2×D4—181no—
408C22×C4—32no—
409C22×C4—61no—
410C22×C4—181no—
411C22×C4C2×D3211yescharacteristic
412M16—21no—
413M16—32no—
414M16—64no—
415M16—61no—
416M16#62612yescomplemented
417C2×C8—21no—
418C2×C8—64no—
419C2×C8—61no—
420C4⋊C4—61no—
421C4⋊C4—182no—
422C4⋊C4—181no—
423C22⋊C4—61no—
424C22⋊C4—182no—
425C22⋊C4—182no—
426C22⋊C4—181no—
427C42—31no—
428C42—31no—
429C42—61no—
430C42—61no—
431C42—181no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—62no—
438C22×C3—81no—
439C22×C3—122no—
440C22×C3D3×C22⋊C411yescharacteristic
441C22×C3#88411yescharacteristic
442C22×C3#89511yescharacteristic
443C22×C3C2×(C2×D3)⋊C411yescharacteristic
444C22×C3#93011yescharacteristic
445C22×C3#93011yescharacteristic
446C2×D3—22no—
447C2×D3—42no—
448C2×D3—122no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—121no—
452C2×D3—121no—
453C2×D3—242no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—62no—
459C3×C4—62no—
460C3×C4—121no—
461C3×C4—241no—
462C3×C4C4×D1211yescharacteristic
463C3×C4#88211yescharacteristic
464C3×C4#89311yescharacteristic
465C3×C4#89411yescharacteristic
466C3×C4C4×#6711yescharacteristic
467C3×C4C4×#6711yescharacteristic
468C3×C4#92911yescharacteristic
469C3×C4#95311yescharacteristic
470Dic3—22no—
471Dic3—22no—
472Dic3—41no—
473Dic3—81no—
474Dic3—122no—
475Dic3—121no—
476Dic3—121no—
477Dic3—241no—
478Dic3—241no—
479Dic3—242no—
480C32#188411yescharacteristic, complemented, Sylow
481C23—32no—
482C23—181no—
483C23D3×D1211yescharacteristic
484Q8—61no—
485Q8—61no—
486Q8—181no—
487Q8—181no—
488D4—62no—
489D4—62no—
490D4—61no—
491D4—61no—
492D4—181no—
493D4—181no—
494D4—364no—
495D4—361no—
496D4—361no—
497C2×C4—32no—
498C2×C4—61no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—61no—
502C2×C4—122no—
503C2×C4—121no—
504C2×C4—181no—
505C2×C4—361no—
506C2×C4—361no—
507C2×C4—361no—
508C2×C4#379811yescharacteristic
509C2×C4#379911yescharacteristic
510C2×C4C4×D3211yescharacteristic
511C2×C4C2×#62611yescharacteristic
512C2×C4D3×#6711yescharacteristic
513C2×C4D3×#6711yescharacteristic
514C8—22no—
515C8—62no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3—41no—
526C2×C3—122no—
527C2×C3#466511yescharacteristic
528C2×C3#521311yescharacteristic
529D3—42no—
530D3—242no—
531D3—241no—
532D3—241no—
533C22—41no—
534C22—62no—
535C22—122no—
536C22—362no—
537C22—361no—
538C22#6390611yescharacteristic
539C22#6390911yescharacteristic
540C22D3×(C2×D3)⋊C411yescharacteristic
541C4—62no—
542C4—62no—
543C4—121no—
544C4—241no—
545C4—361no—
546C4—721no—
547C4#6385011yescharacteristic
548C4C4×#62611yescharacteristic
549C4#6390411yescharacteristic
550C4#6397711yescharacteristic
551C3—21no—
552C3#6877711yescharacteristic, complemented
553C3#7202111yescharacteristic, complemented
554C2—21no—
555C2—21no—
556C2—21no—
557C2—122no—
558C2—721no—
559C2#1059138211yescharacteristic
subgroupG/H
centerC4#63977
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10595029C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5745C2semidirect
3. #10592838C2semidirect
4. #10591231C2semidirect
5. #10591113C2semidirect
6. C3×#4555C2semidirect
7. #10589162C2semidirect
21. #63911C4semidirect
23. #63866C4semidirect
24. #63864C4semidirect
25. #63860C4semidirect
31. #5745D3semidirect
42. #4555D3semidirect
64. C32×M16D4semidirect
76. C3×#208D4semidirect
222. C3×M16D12semidirect
223. C3×M16#67semidirect
257. #208#67semidirect
416. M16#626semidirect
480. C32#1884semidirect
552. C3#68777semidirect
553. C3#72021semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105950292
#105928382
#105912312
#105911132
C3×#45552
#105891622
#720213
#687773