Finite Group Databasebeta

← #11787780

Subgroups — #11787780

Order 1152.

793 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596216C211yesmaximal, characteristic, complemented
2#10595029C211yesmaximal, characteristic
3C3×#5139C211yesmaximal, characteristic, complemented
4#10591232C211yesmaximal, characteristic, complemented
5#10591111C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70417—31nomaximal
9#68777—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14#64116—22no—
15M16×C3⋊D3—22no—
16#64110—22no—
17C3×#926C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20#63978—22no—
21#63911C411yescharacteristic, complemented
22C4×#626—22no—
23#63866C411yescharacteristic, complemented
24#63864C411yescharacteristic, complemented
25#63860C411yescharacteristic, complemented
26C3×#825—22no—
27#63581—22no—
28#63569—22no—
29#5832—31no—
30#5745—31no—
31#5745—31no—
32#5745—61no—
33#5477—31no—
34C3×#421—31no—
35#5236—31no—
36#5139D311yescharacteristic, complemented
37#5006—31no—
38#5006—31no—
39#5005—31no—
40C3×#339—31no—
41#4555D311yescharacteristic, complemented
42#4532—31no—
43#4523—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638D412yes—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
51C2×C4×C3⋊D3D412yes—
52C2×#634C2×C411yescharacteristic
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C2×C3×D12C2×C411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×Dic6C2×C411yescharacteristic
62C2×#626—22no—
63C32×M16—21no—
64C32×M16D412yescomplemented
65C2×C32×C8—21no—
66#3748—21no—
67#3748D412yescomplemented
68C2×C3⋊(C3⋊C8)—21no—
69#3743—24no—
70C8×C3⋊D3—24no—
71C3×#217—21no—
72C3×#217—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3C2×C411yescharacteristic
79C3×C4×Dic3C2×C411yescharacteristic
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
89C2×C3×M16—21no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C3×#117—31no—
93C3×#117—31no—
94C2×C3×C42—31no—
95#947—31no—
96#944—31no—
97#940—31no—
98#939—62no—
99#936—31no—
100#930—62no—
101C4×#67—62no—
102#926C2×D311yescharacteristic
103#926C2×D311yescharacteristic
104C2×C4×Dic3C2×D311yescharacteristic
105C2×#208—31no—
106C2×#208—31no—
107C2×#208—61no—
108#907—64no—
109#907—62no—
110#907—62no—
111D3×M16—62no—
112D3×M16—62no—
113D3×M16—64no—
114#901—62no—
115#901—62no—
116#901—64no—
117#875—31no—
118#875—31no—
119#874—31no—
120C4×D12—62no—
121#869—31no—
122C3×#104—62no—
123#837—62no—
124#825—22no—
125#806—62no—
126#806—62no—
127#805—62no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3C22⋊C412yes—
130C22×C3×D3—21no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137#638—22no—
138#638—22no—
139C2×C3⋊Dic3C22⋊C412yes—
140C4⋊(C3⋊D3)—21no—
141C4⋊(C3⋊D3)—21no—
142C4×C3⋊D3—22no—
143C4×C3⋊D3—22no—
144#634—21no—
145#634—21no—
146C3×#67—41no—
147C3×#67—41no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C3×D12—21no—
155C3×D12—21no—
156C3×C4×D3—41no—
157C3×C4×D3—41no—
158C3×Dic6—21no—
159C3×Dic6—21no—
160#626—44no—
161C32×C8—22no—
162C3⋊(C3⋊C8)—22no—
163#568—91no—
164#532—91no—
165#421—31no—
166#421—91no—
167#410—91no—
168#339—31no—
169#339—91no—
170C3×#41—61no—
171C3×#41—61no—
172C3×#41—61no—
173C3×#41—61no—
174C2×C3×Q8—31no—
175C2×C3×D4—31no—
176C2×C3×D4—61no—
177C22×C3×C4—21no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C2×#67—21no—
183C2×#67—32no—
184C2×#67—32no—
185C2×#67—62no—
186C2×#67—62no—
187C22×Dic3—21no—
188#235—21no—
189#235—21no—
190#235—21no—
191#235—21no—
192#235—62no—
193#235—62no—
194#235—62no—
195#235—62no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—61no—
202#235—61no—
203#235—61no—
204C2×D12—31no—
205C2×D12—31no—
206C2×D12—61no—
207C2×D12—62no—
208C2×D12C4×D311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—32no—
211C2×C4×D3—32no—
212C2×C4×D3—62no—
213C2×Dic6—31no—
214C2×Dic6—31no—
215C2×Dic6—61no—
216C2×Dic6C4×D311yescharacteristic
217C3×M16—22no—
218C3×M16—21no—
219C3×M16—21no—
220C3×M16—22no—
221C3×M16D1212yescomplemented
222C3×M16#6712yescomplemented
223C2×C3×C8—22no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C22⋊C4—61no—
229C3×C22⋊C4—61no—
230C3×C42—31no—
231C3×C42—31no—
232C3×C42—61no—
233C3×C42—61no—
234C3×C42—61no—
235#217—21no—
236#217—21no—
237#217—62no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—62no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3—62no—
244Dic3⋊C4—62no—
245C4×Dic3—21no—
246C4×Dic3—21no—
247C4×Dic3—21no—
248C4×Dic3C4×D311yescharacteristic
249C4×Dic3C4×D311yescharacteristic
250#208—32no—
251#208—32no—
252#208—62no—
253#208—62no—
254#208—61no—
255#208—61no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259ΓL(1,𝔽25)—68no—
260ΓL(1,𝔽25)—64no—
261ΓL(1,𝔽25)—64no—
262D3×C8—68no—
263D3×C8—64no—
264D3×C8—64no—
265C22×C32—41no—
266C22×C32C2×C22⋊C411yescharacteristic
267C22×C32#12111yescharacteristic
268C22×C32#12111yescharacteristic
269C2×C3⋊D3—22no—
270C2×C3⋊D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—41no—
273C32×C4C4×D411yescharacteristic
274C32×C4C4×D411yescharacteristic
275C32×C4#12011yescharacteristic
276C32×C4#12311yescharacteristic
277C3⋊Dic3—22no—
278C3×Dic3—22no—
279C3×Dic3—41no—
280C3×Dic3—41no—
281C3×Dic3—81no—
282C3×Dic3—81no—
283C2×#41—31no—
284C2×#41—91no—
285#131—182no—
286#131—182no—
287C2×M16—91no—
288C2×M16—182no—
289C2×M16D3211yescharacteristic
290C4⋊Q8—91no—
291#127—91no—
292#124—91no—
293#124—91no—
294#121—182no—
295C4×D4—182no—
296#117—31no—
297#117—31no—
298C2×C42—31no—
299#104—62no—
300#104—182no—
301#99—182no—
302C23×C3—21no—
303C23×C3—61no—
304C23×C3D3×D411yescharacteristic
305C23×C3D3×D411yescharacteristic
306C22×D3—21no—
307C22×D3—32no—
308C22×D3—32no—
309C22×D3—62no—
310C3×Q8—61no—
311C3×Q8—61no—
312C3×D4—61no—
313C3×D4—61no—
314C3×D4—121no—
315C3×D4—121no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—61no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—122no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4#23511yescharacteristic
334C2×C3×C4#23511yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4#23711yescharacteristic
340C2×C3×C4#23911yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342#67—41no—
343#67—41no—
344#67—64no—
345#67—64no—
346#67—62no—
347#67—62no—
348#67—62no—
349#67—62no—
350#67—124no—
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—21no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—42no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3—62no—
360D12—21no—
361D12—21no—
362D12—62no—
363D12—62no—
364D12—61no—
365D12—61no—
366D12—61no—
367D12—61no—
368D12—124no—
369C4×D3—41no—
370C4×D3—41no—
371C4×D3—64no—
372C4×D3—64no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—62no—
377Dic6—21no—
378Dic6—21no—
379Dic6—62no—
380Dic6—62no—
381Dic6—61no—
382Dic6—61no—
383Dic6—61no—
384Dic6—61no—
385C3×C8—24no—
386C3×C8—22no—
387C3×C8—22no—
388C3⋊C8—64no—
389C3⋊C8—62no—
390C3⋊C8—62no—
391C2×C32—21no—
392C2×C32—21no—
393C2×C32—21no—
394C2×C32#38611yescharacteristic
395C3⋊D3—42no—
396C3×D3—81no—
397#41—61no—
398#41—61no—
399#41—61no—
400#41—61no—
401#41—181no—
402#41—181no—
403#41—181no—
404#41—181no—
405C2×Q8—31no—
406C2×Q8—91no—
407C2×D4—31no—
408C2×D4—61no—
409C2×D4—92no—
410C2×D4—91no—
411C2×D4—182no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—92no—
415C22×C4C2×D3211yescharacteristic
416M16—21no—
417M16—92no—
418M16—184no—
419M16—181no—
420M16#62612yescomplemented
421C2×C8—21no—
422C2×C8—184no—
423C2×C8—181no—
424C4⋊C4—61no—
425C4⋊C4—61no—
426C4⋊C4—182no—
427C22⋊C4—61no—
428C22⋊C4—61no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C42—31no—
432C42—31no—
433C42—61no—
434C42—61no—
435C42—61no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—81no—
442C22×C3—122no—
443C22×C3—121no—
444C22×C3D3×C22⋊C411yescharacteristic
445C22×C3D3×C22⋊C411yescharacteristic
446C22×C3#88411yescharacteristic
447C22×C3#88411yescharacteristic
448C22×C3#89511yescharacteristic
449C22×C3#93811yescharacteristic
450C2×D3—42no—
451C2×D3—41no—
452C2×D3—64no—
453C2×D3—62no—
454C2×D3—62no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—242no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—62no—
463C3×C4—121no—
464C3×C4—121no—
465C3×C4—241no—
466C3×C4—241no—
467C3×C4C4×D1211yescharacteristic
468C3×C4#67⋊C411yescharacteristic
469C3×C4#88211yescharacteristic
470C3×C4#88311yescharacteristic
471C3×C4#89311yescharacteristic
472C3×C4#89411yescharacteristic
473C3×C4C4×#6711yescharacteristic
474C3×C4#93711yescharacteristic
475Dic3—22no—
476Dic3—41no—
477Dic3—41no—
478Dic3—64no—
479Dic3—62no—
480Dic3—62no—
481Dic3—81no—
482Dic3—81no—
483C32#188411yescharacteristic, complemented, Sylow
484C23—61no—
485C23—92no—
486C23#380211yescharacteristic
487Q8—61no—
488Q8—61no—
489Q8—181no—
490Q8—181no—
491D4—61no—
492D4—61no—
493D4—121no—
494D4—121no—
495D4—182no—
496D4—182no—
497D4—181no—
498D4—181no—
499D4—364no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—92no—
504C2×C4—122no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4—121no—
508C2×C4—121no—
509C2×C4—182no—
510C2×C4—182no—
511C2×C4#379611yescharacteristic
512C2×C4#379811yescharacteristic
513C2×C4C4×D3211yescharacteristic
514C2×C4C2×#62611yescharacteristic
515C2×C4#381111yescharacteristic
516C2×C4#381111yescharacteristic
517C8—22no—
518C8—182no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—41no—
527C2×C3—41no—
528C2×C3—41no—
529C2×C3—241no—
530C2×C3#466511yescharacteristic
531C2×C3#495611yescharacteristic
532D3—81no—
533D3—124no—
534D3—122no—
535D3—122no—
536C22—41no—
537C22—122no—
538C22—121no—
539C22—182no—
540C22—362no—
541C22#6391211yescharacteristic
542C22#6391611yescharacteristic
543C22#6392111yescharacteristic
544C4—62no—
545C4—121no—
546C4—121no—
547C4—182no—
548C4—241no—
549C4—241no—
550C4#6385311yescharacteristic
551C4#6388111yescharacteristic
552C4C4×#62611yescharacteristic
553C4#6398111yescharacteristic
554C3—21no—
555C3#6877711yescharacteristic, complemented
556C3#7041711yescharacteristic, complemented
557C2—21no—
558C2—21no—
559C2—21no—
560C2—241no—
561C2—362no—
562C2#1059138711yescharacteristic
subgroupG/H
centerC4#63981
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. #10596216C2semidirect
3. C3×#5139C2semidirect
4. #10591232C2semidirect
5. #10591111C2semidirect
6. C3×#4555C2semidirect
7. #10589161C2semidirect
21. #63911C4semidirect
23. #63866C4semidirect
24. #63864C4semidirect
25. #63860C4semidirect
36. #5139D3semidirect
41. #4555D3semidirect
64. C32×M16D4semidirect
67. #3748D4semidirect
221. C3×M16D12semidirect
222. C3×M16#67semidirect
420. M16#626semidirect
483. C32#1884semidirect
555. C3#68777semidirect
556. C3#70417semidirect

Maximal subgroups

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

subgroupindex
#105962162
#105950292
C3×#51392
#105912322
#105911112
C3×#45552
#105891612
#704173
#687773