Finite Group Databasebeta

← #11787776

Subgroups — #11787776

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
1#10595029C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic, complemented
3#10592704C211yesmaximal, characteristic, complemented
4C3×#5006C211yesmaximal, characteristic, complemented
5#10591113C211yesmaximal, characteristic, complemented
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#70045—31nomaximal
9#68777—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63978—22no—
18#63911C411yescharacteristic, complemented
19C4×#626—22no—
20#63866C411yescharacteristic, complemented
21#63864C411yescharacteristic, complemented
22#63860C411yescharacteristic, complemented
23#63815—22no—
24#63814—22no—
25D3×#208—22no—
26#63632—22no—
27C3×#806—22no—
28#63570—22no—
29#5832—31no—
30#5819—31no—
31#5745—31no—
32#5477—31no—
33C3×#410—31no—
34#5139—31no—
35#5006D311yescharacteristic, complemented
36#5005—31no—
37#5005—31no—
38#5005—31no—
39#5005—61no—
40C3×#339—31no—
41#4532—31no—
42#4532D311yescharacteristic, 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×C4⋊C4—21no—
64C32×C22⋊C4—21no—
65C32×C42—21no—
66#3748—21no—
67#3748D412yescomplemented
68C2×C3⋊(C3⋊C8)—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—
78Dic3⋊Dic3—22no—
79#3722—22no—
80(C2×D3)⋊Dic3—22no—
81#3711—24no—
82D3×C3⋊C8—24no—
83#1884—91noSylow
84C2×C3×#41—31no—
85C2×#235—31no—
86C2×#235—31no—
87C2×#235—61no—
88C2×#235C2×D311yescharacteristic
89C2×C3×M16—31no—
90C3×#117—21no—
91C3×#117—31no—
92C3×#117C2×D311yescharacteristic
93C3×#117C2×D311yescharacteristic
94C2×C3×C42—31no—
95#948—62no—
96#948—62no—
97#947—31no—
98#944—31no—
99#940—31no—
100#939—62no—
101#936—31no—
102#930—62no—
103C4×#67—62no—
104#926C2×D311yescharacteristic
105C2×C4×Dic3C2×D311yescharacteristic
106C2×#208—31no—
107C2×#208—31no—
108C2×#208—61no—
109C2×#208—62no—
110C2×#208C2×D311yescharacteristic
111#907—62no—
112D3×M16—62no—
113#901—62no—
114#875—31no—
115#875—31no—
116#874—31no—
117C4×D12—62no—
118#869—31no—
119C3×#99—62no—
120#825—62no—
121#806—22no—
122#805—62no—
123#805—62no—
124#805—64no—
125#805—62no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—21no—
128C22×C3×D3C22⋊C412yes—
129C2×C32×C4—41no—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136#638—41no—
137#638—41no—
138C2×C3⋊Dic3—21no—
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—
159C3⋊(C3⋊C8)—22no—
160C3×C3⋊C8—22no—
161#568—91no—
162#532—91no—
163#421—91no—
164#421—91no—
165#410—31no—
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×#67#6712yes—
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×D3D1212yes—
211C2×Dic6—31no—
212C2×Dic6—31no—
213C2×Dic6—61no—
214C2×Dic6C4×D311yescharacteristic
215C3×M16—32no—
216C3×M16—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—41no—
221C3×C4⋊C4—61no—
222C3×C22⋊C4—21no—
223C3×C22⋊C4—21no—
224C3×C22⋊C4—41no—
225C3×C22⋊C4—61no—
226C3×C42—22no—
227C3×C42—21no—
228C3×C42—21no—
229C3×C42—31no—
230C3×C42—31no—
231C3×C42—61no—
232C3×C42—61no—
233#217—21no—
234#217—62no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238C4⋊Dic3—21no—
239C4⋊Dic3—62no—
240Dic3⋊C4—62no—
241C4×Dic3—21no—
242C4×Dic3—21no—
243C4×Dic3C4×D311yescharacteristic
244C4×Dic3C4×D311yescharacteristic
245#208—21no—
246#208—32no—
247#208—32no—
248#208—62no—
249#208—64no—
250#208—61no—
251#208—61no—
252#208—121no—
253#208D1212yescomplemented
254C2×C3⋊C8—21no—
255C2×C3⋊C8—64no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—121no—
259ΓL(1,𝔽25)—64no—
260D3×C8—64no—
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×C4—81no—
270C32×C4C4×D411yescharacteristic
271C32×C4C4×D411yescharacteristic
272C32×C4#12011yescharacteristic
273C32×C4#12311yescharacteristic
274C3⋊Dic3—41no—
275C3×Dic3—22no—
276C3×Dic3—22no—
277C3×Dic3—41no—
278C3×Dic3—81no—
279C2×#41—31no—
280C2×#41—91no—
281#131—182no—
282#131—182no—
283C2×M16—31no—
284C2×M16—91no—
285C2×M16—182no—
286C4⋊Q8—91no—
287#127—91no—
288#124—91no—
289#124—91no—
290#121—182no—
291C4×D4—182no—
292#117—31no—
293#117D3211yescharacteristic
294C2×C42—31no—
295#104—182no—
296#104—182no—
297#99—62no—
298C23×C3—21no—
299C23×C3—32no—
300C23×C3D3×D411yescharacteristic
301C23×C3C2×#6711yescharacteristic
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—42no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—61no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—61no—
326C2×C3×C4—122no—
327C2×C3×C4—121no—
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23711yescharacteristic
338C2×C3×C4#23711yescharacteristic
339C2×C3×C4#23911yescharacteristic
340#67—22no—
341#67—22no—
342#67—124no—
343#67—122no—
344#67—122no—
345#67—121no—
346#67—121no—
347#67—121no—
348#67—121no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—42no—
352C2×Dic3—41no—
353C2×Dic3—61no—
354C2×Dic3—61no—
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—62no—
383C3⋊C8—22no—
384C3⋊C8—62no—
385C3⋊C8—62no—
386C3⋊C8—122no—
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—32no—
413M16—61no—
414M16—92no—
415M16—184no—
416M16—181no—
417C2×C8—61no—
418C2×C8—184no—
419C2×C8—181no—
420C4⋊C4—21no—
421C4⋊C4—61no—
422C4⋊C4—182no—
423C22⋊C4—21no—
424C22⋊C4—61no—
425C22⋊C4—182no—
426C22⋊C4—182no—
427C42—21no—
428C42—31no—
429C42—31no—
430C42—61no—
431C42—61no—
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#93911yescharacteristic
445C22×C3#93911yescharacteristic
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—81no—
461C3×C4—81no—
462C3×C4—82no—
463C3×C4—121no—
464C3×C4—241no—
465C3×C4C4×D1211yescharacteristic
466C3×C4#67⋊C411yescharacteristic
467C3×C4#67⋊C411yescharacteristic
468C3×C4#88211yescharacteristic
469C3×C4#88211yescharacteristic
470C3×C4#88611yescharacteristic
471C3×C4#89311yescharacteristic
472C3×C4#89411yescharacteristic
473Dic3—22no—
474Dic3—22no—
475Dic3—41no—
476Dic3—81no—
477Dic3—122no—
478Dic3—121no—
479Dic3—121no—
480C32#188411yescharacteristic, complemented, Sylow
481C23—32no—
482C23—181no—
483C23D3×#6711yescharacteristic
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—41no—
499C2×C4—61no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—61no—
503C2×C4—122no—
504C2×C4—121no—
505C2×C4—181no—
506C2×C4—361no—
507C2×C4—361no—
508C2×C4#379611yescharacteristic
509C2×C4C4×D3211yescharacteristic
510C2×C4D3×D1211yescharacteristic
511C2×C4D3×D1211yescharacteristic
512C2×C4#380411yescharacteristic
513C2×C4#381111yescharacteristic
514C8—62no—
515C8—182no—
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#495811yescharacteristic
529D3—42no—
530D3—242no—
531D3—241no—
532D3—241no—
533C22—41no—
534C22—62no—
535C22—122no—
536C22—362no—
537C22—361no—
538C22#6388611yescharacteristic
539C22D3×(C2×D3)⋊C411yescharacteristic
540C22#6397111yescharacteristic
541C4—62no—
542C4—62no—
543C4—81no—
544C4—121no—
545C4—241no—
546C4—361no—
547C4#6388011yescharacteristic
548C4#6388111yescharacteristic
549C4#6389011yescharacteristic
550C4#6392311yescharacteristic
551C3—21no—
552C3#6877711yescharacteristic, complemented
553C3#7004511yescharacteristic, complemented
554C2—21no—
555C2—21no—
556C2—21no—
557C2—122no—
558C2—721no—
559C2#1059136411yescharacteristic
subgroupG/H
centerC4#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radical#10595029C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10594776C2semidirect
3. #10592704C2semidirect
4. C3×#5006C2semidirect
5. #10591113C2semidirect
6. C3×#4532C2semidirect
7. #10589161C2semidirect
18. #63911C4semidirect
20. #63866C4semidirect
21. #63864C4semidirect
22. #63860C4semidirect
35. #5006D3semidirect
42. #4532D3semidirect
67. #3748D4semidirect
76. C3×#208D4semidirect
253. #208D12semidirect
480. C32#1884semidirect
552. C3#68777semidirect
553. C3#70045semidirect

Maximal subgroups

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

subgroupindex
#105950292
#105947762
#105927042
C3×#50062
#105911132
C3×#45322
#105891612
#700453
#687773