Finite Group Databasebeta

← #11860626

Subgroups — #11860626

Order 1152.

1087 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595994C211yesmaximal, characteristic
2C3×#5516C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic
4C3×#4997C211yesmaximal, characteristic, complemented
5#10591131C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590383C212yesmaximal, complemented
9C4×#3719C212yesmaximal, complemented
10#10590362C212yesmaximal, complemented
11C4×#3717C212yesmaximal, complemented
12#82547—31nomaximal
13#78571—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18#64101—21no—
19C4⋊C4×C3⋊D3—21no—
20#64090—22no—
21C4×C4⋊(C3⋊D3)C2212yes—
22C4×#634C2212yes—
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#887—21no—
27C3×#887—21no—
28C3×#877—22no—
29C3×C4×Dic6C2212yes—
30C3×C4×Dic6C2212yes—
31C2×#3719C2212yes—
32#63833C418yescomplemented
33C2×#3717C2212yes—
34C3×#803C2212yes—
35C3×C4×C3⋊C8C2212yes—
36#63575C2212yes—
37#63573C2212yes—
38#63567C2211yescharacteristic
39#63567C2211yescharacteristic
40#63566C2212yes—
41#63566C2212yes—
42#63564C2211yescharacteristic
43#63564C2211yescharacteristic
44C3×#519—31no—
45C2×#942—31no—
46C2×#909—31no—
47#5523—31no—
48#5523—31no—
49#5523—61no—
50#5516D311yescharacteristic, complemented
51C3×#405—31no—
52C2×#835—31no—
53#5121—31no—
54#5113—31no—
55C2×#816—31no—
56#5030—32no—
57C4×#216—32no—
58#5026—32no—
59C4×#215—32no—
60#5002—31no—
61#4997D311yescharacteristic, complemented
62#4995—31no—
63#4716—32no—
64#4710—32no—
65C4×Dic12—32no—
66C4×#204—32no—
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69C22×C3⋊Dic3—21no—
70#3828—22no—
71#3828C2×C414yes—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—22no—
75C2×#634C2311yescharacteristic
76C22×C3×Dic3—21no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6C2×C414yescomplemented
80C2×C3×Dic6C2312yes—
81C32×C4⋊C4D411yescharacteristic
82C32×C4⋊C4D411yescharacteristic
83C32×C22⋊C4D412yes—
84C32×C42C2312yes—
85#3752—22no—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88#3750—22no—
89C4×C3⋊Dic3—22no—
90C3×#217—21no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3—22no—
97C3×C4×Dic3—21no—
98C3×#208C2×C414yescomplemented
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8C2311yescharacteristic
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103#3719C2×C418yescomplemented
104#3717C2×C418yescomplemented
105#2947—91noSylow
106C22×C3×Q8—31no—
107C2×#235—31no—
108C2×#235—31no—
109C2×#235—61no—
110C22×Dic6C2×D311yescharacteristic
111C2×C3×M16—31no—
112C22×C3×C8—31no—
113C3×C4×Q8—32no—
114C3×C4×Q8—32no—
115C3×C4×Q8—61no—
116C3×C4×Q8—61no—
117C3×#117—21no—
118C3×#117—31no—
119C3×#117—62no—
120C3×#117C2×D311yescharacteristic
121C3×#117C2×D311yescharacteristic
122C2×#216—32no—
123#942—38no—
124C2×#215—32no—
125#926C2×D311yescharacteristic
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—61no—
129C2×#208C2×D311yescharacteristic
130C22×C3⋊C8C2×D311yescharacteristic
131#909—38no—
132C2×Dic12—32no—
133C2×#204—32no—
134#892—62no—
135#892—61no—
136#892—61no—
137D3×C4⋊C4—62no—
138D3×C4⋊C4—61no—
139D3×C4⋊C4—61no—
140#887—21no—
141#887—21no—
142#67⋊C4—64no—
143#67⋊C4—62no—
144#67⋊C4—62no—
145#877—22no—
146C4×D12—32no—
147C4×D12—32no—
148C4×D12—62no—
149C4×Dic6—32no—
150C4×Dic6—32no—
151C4×Dic6—62no—
152C4×Dic6C2×D312yes—
153C4×Dic6C2×D312yes—
154C3×#97—32no—
155C3×C4×C8—32no—
156#835—32no—
157#835—32no—
158#821—31no—
159#821—31no—
160#818—32no—
161#817—32no—
162#816—32no—
163#816—32no—
164#816—31no—
165#816—31no—
166#810—31no—
167#810—31no—
168#809—31no—
169#809—31no—
170#808—32no—
171#807—32no—
172#803C2×D312yes—
173C4×C3⋊C8C2×D312yes—
174C23×C32C2×D411yescharacteristic
175C22×C3⋊D3—21no—
176C2×C32×C4C22×C412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182#638—24no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—81no—
186C4⋊(C3⋊D3)—21no—
187C4⋊(C3⋊D3)C22×C412yes—
188C4×C3⋊D3—24no—
189C4×C3⋊D3—82no—
190#634—21no—
191#634C22×C412yes—
192C2×C3×Dic3—24no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C3×Dic6—24no—
197C3×Dic6—22no—
198C3×Dic6C22×C414yes—
199C3×C3⋊C8—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8C22×C414yes—
202C2×#137—91no—
203#520—91no—
204#519—31no—
205#441—92no—
206#440—92no—
207C4×Q16—92no—
208C4×SD16—92no—
209#428—91no—
210#416—91no—
211C2×#103—91no—
212#405—31no—
213C2×C3×Q8—34no—
214C2×C3×Q8—32no—
215C2×C3×Q8—61no—
216C2×C3×Q8—62no—
217C22×C3×C4—21no—
218C22×C3×C4—61no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C2×#67—62no—
222C2×#67—61no—
223C2×#67—61no—
224C22×Dic3—21no—
225C22×Dic3—62no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228#235—34no—
229#235—34no—
230#235—64no—
231#235—64no—
232#235—62no—
233#235—62no—
234C2×D12—31no—
235C2×D12—31no—
236C2×D12—61no—
237C2×C4×D3—62no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—64no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×Dic6—22no—
244C2×Dic6—21no—
245C2×Dic6—31no—
246C2×Dic6—31no—
247C2×Dic6—61no—
248C2×Dic6C4×D314yescomplemented
249C2×Dic6C22×D312yes—
250C3×M16—34no—
251C2×C3×C8—32no—
252C2×C3×C8—31no—
253C2×C3×C8—31no—
254C2×C3×C8—62no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—31no—
258C3×C4⋊C4—31no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4—62no—
261C3×C4⋊C4D1211yescharacteristic
262C3×C4⋊C4D1211yescharacteristic
263C3×C4⋊C4#6711yescharacteristic
264C3×C4⋊C4#6711yescharacteristic
265C3×C22⋊C4—22no—
266C3×C22⋊C4—61no—
267C3×C22⋊C4D1212yes—
268C3×C22⋊C4#6712yes—
269C3×C42—22no—
270C3×C42—61no—
271C3×C42—62no—
272C3×C42—62no—
273C3×C42C22×D312yes—
274C3×C42C22×D312yes—
275#217—21no—
276#216—38no—
277#215—38no—
278(C2×D3)⋊C4—64no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281C4⋊Dic3—32no—
282C4⋊Dic3—32no—
283C4⋊Dic3—62no—
284C4⋊Dic3—62no—
285C4⋊Dic3—61no—
286C4⋊Dic3—61no—
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D311yescharacteristic
289Dic3⋊C4—22no—
290Dic3⋊C4—22no—
291Dic3⋊C4—64no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294C4×Dic3—22no—
295C4×Dic3—22no—
296C4×Dic3—21no—
297C4×Dic3—64no—
298C4×Dic3—62no—
299C4×Dic3—62no—
300#208C4×D314yescomplemented
301C2×C3⋊C8—22no—
302C2×C3⋊C8C22×D311yescharacteristic
303C2×C3⋊C8C22×D311yescharacteristic
304C2×C3⋊C8C22×D312yes—
305Dic12—38no—
306#204—38no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C4×D412yes—
310C22×C32C22×D411yescharacteristic
311C2×C3⋊D3—22no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C32×C4—22no—
315C32×C4—22no—
316C32×C4C4×D412yes—
317C32×C4C23×C411yescharacteristic
318C32×C4C2×#4111yescharacteristic
319C3⋊Dic3—22no—
320C3⋊Dic3—42no—
321C3×Dic3—24no—
322C3×Dic3—41no—
323C3×Dic3—41no—
324C2×#41—91no—
325C22×Q8—31no—
326#137—98no—
327C2×Q16—92no—
328C2×SD16—92no—
329C2×M16—31no—
330C22×C8—31no—
331C4×Q8—32no—
332C4×Q8—32no—
333C4×Q8—61no—
334C4×Q8—61no—
335C4×Q8—92no—
336C4×D4—92no—
337C4×D4—182no—
338#117—31no—
339#117—62no—
340#117—181no—
341#117D3211yescharacteristic
342C2×C4⋊C4—91no—
343C2×C4⋊C4—181no—
344#107—92no—
345#106—92no—
346#103—91no—
347#103—91no—
348#103—92no—
349#103—92no—
350#102—91no—
351#102—91no—
352#97—32no—
353C4×C8—32no—
354C23×C3—21no—
355C23×C3C2×D1211yescharacteristic
356C23×C3C2×#6711yescharacteristic
357C22×D3—62no—
358C22×D3—61no—
359C22×D3—61no—
360C3×Q8—34no—
361C3×Q8—64no—
362C3×Q8—62no—
363C2×C3×C4—21no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—21no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—64no—
370C2×C3×C4—62no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4C2×C4×D312yes—
374C2×C3×C4C2×C4×D312yes—
375C2×C3×C4C2×D1212yes—
376C2×C3×C4C2×D1212yes—
377C2×C3×C4C2×D1211yescharacteristic
378C2×C3×C4#23512yes—
379C2×C3×C4#23512yes—
380C2×C3×C4C2×#6712yes—
381C2×C3×C4C2×#6712yes—
382C2×C3×C4C2×#6711yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385#67—68no—
386#67—64no—
387#67—64no—
388C2×Dic3—24no—
389C2×Dic3—22no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—62no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—64no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—241no—
399C2×Dic3—241no—
400C2×Dic3—242no—
401D12—32no—
402D12—32no—
403D12—62no—
404D12—62no—
405D12—61no—
406D12—61no—
407C4×D3—68no—
408C4×D3—64no—
409C4×D3—64no—
410C4×D3—242no—
411C4×D3—242no—
412C4×D3—244no—
413Dic6—24no—
414Dic6—22no—
415Dic6—32no—
416Dic6—32no—
417Dic6—62no—
418Dic6—62no—
419Dic6—61no—
420Dic6—61no—
421Dic6C2×C4×D314yes—
422C3×C8—34no—
423C3×C8—61no—
424C3×C8—61no—
425C3⋊C8—21no—
426C3⋊C8—21no—
427C3⋊C8C2×C4×D314yes—
428C2×C32—22no—
429C2×C32C2×C4×D411yescharacteristic
430C2×C32#57711yescharacteristic
431C2×C32#57811yescharacteristic
432C3⋊D3—42no—
433#41—94no—
434#41—182no—
435C2×Q8—32no—
436C2×Q8—34no—
437C2×Q8—62no—
438C2×Q8—61no—
439C2×Q8—91no—
440C2×D4—91no—
441C2×D4—181no—
442C22×C4—61no—
443C22×C4—181no—
444C22×C4—181no—
445C22×C4—182no—
446C22×C4C2×D3211yescharacteristic
447Q16—98no—
448SD16—98no—
449M16—34no—
450C2×C8—32no—
451C2×C8—31no—
452C2×C8—31no—
453C2×C8—62no—
454C4⋊C4—31no—
455C4⋊C4—31no—
456C4⋊C4—62no—
457C4⋊C4—62no—
458C4⋊C4—92no—
459C4⋊C4—181no—
460C4⋊C4—182no—
461C4⋊C4#62611yescharacteristic
462C4⋊C4#62611yescharacteristic
463C22⋊C4—61no—
464C22⋊C4—182no—
465C22⋊C4#62612yes—
466C42—61no—
467C42—62no—
468C42—62no—
469C42—182no—
470C42C2×D3212yes—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—22no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3C4×D1212yes—
480C22×C3C4×#6712yes—
481C22×C3C22×D1211yescharacteristic
482C22×C3C22×#6711yescharacteristic
483C2×D3—64no—
484C2×D3—62no—
485C2×D3—62no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—121no—
489C2×D3—121no—
490C2×D3—121no—
491C2×D3—121no—
492C3×C4—22no—
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—22no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—22no—
499C3×C4—42no—
500C3×C4—42no—
501C3×C4—64no—
502C3×C4—121no—
503C3×C4—121no—
504C3×C4C4×D1212yes—
505C3×C4C4×#6712yes—
506C3×C4C22×C4×D311yescharacteristic
507C3×C4C22×C4×D311yescharacteristic
508C3×C4C2×#23511yescharacteristic
509C3×C4C2×#23511yescharacteristic
510Dic3—24no—
511Dic3—41no—
512Dic3—41no—
513Dic3—64no—
514Dic3—62no—
515Dic3—62no—
516Dic3—124no—
517Dic3—122no—
518Dic3—122no—
519C32#294711yescharacteristic, complemented, Sylow
520C23—181no—
521C23C2×#62611yescharacteristic
522Q8—34no—
523Q8—62no—
524Q8—64no—
525Q8—92no—
526Q8—181no—
527D4—92no—
528D4—184no—
529D4—181no—
530C2×C4—62no—
531C2×C4—64no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—181no—
535C2×C4—184no—
536C2×C4—182no—
537C2×C4—722no—
538C2×C4—721no—
539C2×C4#379812yes—
540C2×C4C4×D3212yes—
541C2×C4C2×#62612yes—
542C2×C4C2×#62612yes—
543C2×C4C2×#62611yescharacteristic
544C2×C4C22×D3211yescharacteristic
545C8—34no—
546C8—61no—
547C8—61no—
548C2×C3—22no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—42no—
554C2×C3C2×C4×D1211yescharacteristic
555C2×C3#575111yescharacteristic
556C2×C3#575311yescharacteristic
557C2×C3C2×C4×#6711yescharacteristic
558C2×C3#583711yescharacteristic
559C2×C3#583811yescharacteristic
560D3—124no—
561D3—122no—
562D3—122no—
563C22—21no—
564C22—21no—
565C22—182no—
566C22—361no—
567C22—361no—
568C22C4×#62612yes—
569C22C22×#62611yescharacteristic
570C4—22no—
571C4—22no—
572C4—64no—
573C4—121no—
574C4—121no—
575C4—182no—
576C4—362no—
577C4C4×#62612yes—
578C4C2×#379811yescharacteristic
579C4C2×C4×D3211yescharacteristic
580C3—21no—
581C3#7857111yescharacteristic, complemented
582C3#8254711yescharacteristic, complemented
583C2—22no—
584C2—362no—
585C2C2×C4×#62611yescharacteristic
586C2#1059544811yescharacteristic
587C2#1059545011yescharacteristic
subgroupG/H
centerC22C22×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5516C2semidirect
4. C3×#4997C2semidirect
5. #10591131C2semidirect
7. C2×#63566C2semidirect
8. #10590383C2semidirect
9. C4×#3719C2semidirect
10. #10590362C2semidirect
11. C4×#3717C2semidirect
32. #63833C4semidirect
50. #5516D3semidirect
61. #4997D3semidirect
79. C2×C3×Dic6C2×C4semidirect
98. C3×#208C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
248. C2×Dic6C4×D3semidirect
300. #208C4×D3semidirect
519. C32#2947semidirect
581. C3#78571semidirect
582. C3#82547semidirect

Maximal subgroups

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

subgroupindex
#105959942
C3×#55162
C2×#638332
C3×#49972
#105911312
#105911052
C2×#635662
#105903832
C4×#37192
#105903622
C4×#37172
#825473
#785713