Finite Group Databasebeta

← #11897680

Subgroups — #11897680

Order 1152.

734 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594470C211yesmaximal, characteristic
2#10594312C211yesmaximal, characteristic, complemented
3#10592589C211yesmaximal, characteristic
4C3×#4876C211yesmaximal, characteristic, complemented
5C3×#4875C211yesmaximal, characteristic, complemented
6#10590820C211yesmaximal, characteristic, complemented
7#10590795C211yesmaximal, characteristic
8#10590786C211yesmaximal, characteristic, complemented
9#10590759C211yesmaximal, characteristic
10#10590546C211yesmaximal, characteristic, complemented
11#10590493C211yesmaximal, characteristic, complemented
12#10590484C211yesmaximal, characteristic
13#10590464C211yesmaximal, characteristic
14#10590458C211yesmaximal, characteristic
15#10590411C211yesmaximal, characteristic, complemented
16#81965—31nomaximal
17#81137—31nomaximal
18#64102C2211yescharacteristic
19#64097C2211yescharacteristic
20C3×#890C2211yescharacteristic
21C3×#888C2211yescharacteristic
22C3×#888C2211yescharacteristic
23C3×#887C2211yescharacteristic
24#63918C2211yescharacteristic
25C4×#627C2211yescharacteristic
26#63895—21no—
27#63894C2211yescharacteristic
28#63894C2211yescharacteristic
29#63888—21no—
30#63883—21no—
31#63872C2211yescharacteristic
32#63871—21no—
33#63866—21no—
34#63843C2211yescharacteristic
35Dic3×Dic6C2211yescharacteristic
36#63840—21no—
37#63839—21no—
38#63837—21no—
39C2×#3717C2211yescharacteristic
40C32×#107C2211yescharacteristic
41#63648C2211yescharacteristic
42#63641C2211yescharacteristic
43#63636C2211yescharacteristic
44#63634C2211yescharacteristic
45C3×#817C2211yescharacteristic
46C3×#816C2211yescharacteristic
47C3×#815C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59#63555C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5730—31no—
62#5722—31no—
63#5690—31no—
64Q8×Dic6—31no—
65C3×#501—31no—
66C3×#477—31no—
67#5087—31no—
68#5078—31no—
69#5063—31no—
70C4×#215—31no—
71#4890—31no—
72#4890—31no—
73#4890—31no—
74#4890—61no—
75#4889—31no—
76#4876—31no—
77#4876D311yescharacteristic, complemented
78#4875D311yescharacteristic, complemented
79#4874—31no—
80#4870—31no—
81#4857—31no—
82#4856—31no—
83#4852—31no—
84#4842—31no—
85#4831—31no—
86#4817—31no—
87#4817—31no—
88#4799—31no—
89#4799—31no—
90#4710—31no—
91#4701—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#627D411yescharacteristic
100C2×#624—21no—
101C2×#624—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105#3752—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C3×C4⋊Dic3—21no—
111C3×C4⋊Dic3C2311yescharacteristic
112C3×C4⋊Dic3C2311yescharacteristic
113C3×C4⋊Dic3C2311yescharacteristic
114C3×Dic3⋊C4—21no—
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123#3724D411yescharacteristic
124Dic3⋊Dic3—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3D411yescharacteristic
130Dic3⋊Dic3D411yescharacteristic
131#3722—21no—
132#3722—21no—
133Dic32—21no—
134Dic32—21no—
135#3717Q814yescomplemented
136#3385—91noSylow
137C3×C4⋊Q8—31no—
138C3×C4⋊Q8—31no—
139C3×#125—31no—
140C3×C4×Q8—31no—
141#946—61no—
142#946—61no—
143Q8×Dic3—31no—
144Q8×Dic3—31no—
145#944—61no—
146#944—61no—
147C2×#215—31no—
148C2×#204—31no—
149#897—61no—
150#897—61no—
151#896—61no—
152#896—61no—
153#893—31no—
154#893—31no—
155#893—31no—
156#893—31no—
157#893—61no—
158D3×C4⋊C4—61no—
159D3×C4⋊C4—61no—
160#890—31no—
161#890—31no—
162#890C2×D311yescharacteristic
163#888—31no—
164#888—31no—
165#888—31no—
166#888—61no—
167#888—61no—
168#888—61no—
169#888—61no—
170#888C2×D311yescharacteristic
171#888C2×D311yescharacteristic
172#887—31no—
173#887—61no—
174#887C2×D311yescharacteristic
175C4×D12—31no—
176C4×D12—31no—
177#869—31no—
178#869—61no—
179C4×Dic6—31no—
180C4×Dic6—31no—
181C4×Dic6—31no—
182C4×Dic6—61no—
183C3×#107—21no—
184C3×#107—31no—
185C3×#107—31no—
186C3×#107C2×D311yescharacteristic
187C3×#107C2×D311yescharacteristic
188C3×#106—31no—
189C3×#106—31no—
190C3×C4⋊C8—31no—
191C3×#103—31no—
192C3×#103—31no—
193C3×#97—31no—
194#835—31no—
195#821—31no—
196#821—31no—
197#821—31no—
198#821—61no—
199#818—31no—
200#817—31no—
201#817C2×D311yescharacteristic
202#816C2×D311yescharacteristic
203#815—31no—
204#815—31no—
205#815C2×D311yescharacteristic
206Dic3⋊C8—31no—
207Dic3⋊C8—31no—
208Dic3⋊C8—31no—
209Dic3⋊C8—61no—
210Dic3⋊C8C2×D311yescharacteristic
211C8×Dic3—31no—
212#810—31no—
213#810C2×D311yescharacteristic
214#809—31no—
215#809—31no—
216#809—31no—
217#809—61no—
218#808—31no—
219#808C2×D311yescharacteristic
220#807—31no—
221#807—31no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—61no—
226#807C2×D311yescharacteristic
227#807C2×D311yescharacteristic
228C4⋊(C3⋊C8)—31no—
229C4×C3⋊C8—31no—
230C22×C3⋊D3—21no—
231C2×C32×C4—21no—
232C2×C32×C4—21no—
233C2×C32×C4C2411yescharacteristic
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3C2×D411yescharacteristic
236C2×C3⋊Dic3C2×D411yescharacteristic
237C4⋊(C3⋊D3)—21no—
238C4⋊(C3⋊D3)C2×Q812yes—
239C4×C3⋊D3—81no—
240#634—81no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3C2×D411yescharacteristic
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C3×Dic6—21no—
250C3×Dic6—81no—
251C3×Dic6—81no—
252C3×Dic6C2×Q812yes—
253#627—22no—
254#627—81no—
255#624—42no—
256#624—81no—
257C32×C8—21no—
258C3⋊(C3⋊C8)—21no—
259C3×C3⋊C8—21no—
260C3×C3⋊C8C2×Q812yes—
261Q82—91no—
262#554—91no—
263#501—31no—
264#501—91no—
265#500—91no—
266#479—91no—
267#479—91no—
268#477—31no—
269#476—91no—
270#474—91no—
271#474—91no—
272#446—91no—
273#440—91no—
274#440—91no—
275C4×SD16—91no—
276C2×C3×Q8—31no—
277C2×C3×Q8—61no—
278C2×C3×Q8—61no—
279C2×D12—31no—
280C2×D12—31no—
281C2×D12—61no—
282C2×C4×D3—61no—
283C2×C4×D3—61no—
284C2×C4×D3—61no—
285C2×C4×D3—61no—
286C2×C4×D3—61no—
287C2×C4×D3—61no—
288C2×C4×D3—121no—
289C2×Dic6—21no—
290C2×Dic6—21no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—121no—
298C2×Dic6C22×D311yescharacteristic
299C2×C3×C8—21no—
300C2×C3×C8—31no—
301C2×C3×C8—31no—
302C2×C3×C8C22×D311yescharacteristic
303C2×C3×C8C22×D311yescharacteristic
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C42—31no—
319C3×C42—31no—
320C3×C42—61no—
321#215—34no—
322(C2×D3)⋊C4—61no—
323(C2×D3)⋊C4—61no—
324(C2×D3)⋊C4—61no—
325(C2×D3)⋊C4—61no—
326(C2×D3)⋊C4—61no—
327(C2×D3)⋊C4—61no—
328(C2×D3)⋊C4—121no—
329C4⋊Dic3—21no—
330C4⋊Dic3—31no—
331C4⋊Dic3—31no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—61no—
335C4⋊Dic3—61no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3C22×D311yescharacteristic
341C4⋊Dic3C22×D311yescharacteristic
342C4⋊Dic3C22×D311yescharacteristic
343Dic3⋊C4—21no—
344Dic3⋊C4—21no—
345Dic3⋊C4—21no—
346Dic3⋊C4—21no—
347Dic3⋊C4—31no—
348Dic3⋊C4—31no—
349Dic3⋊C4—31no—
350Dic3⋊C4—31no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—121no—
359C4×Dic3—21no—
360C4×Dic3—31no—
361C4×Dic3—31no—
362C4×Dic3—61no—
363C4×Dic3—61no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3C22×D311yescharacteristic
368C4×Dic3C22×D311yescharacteristic
369C2×C3⋊C8—31no—
370C2×C3⋊C8—31no—
371C2×C3⋊C8—61no—
372C2×C3⋊C8C22×D311yescharacteristic
373C2×C3⋊C8C22×D311yescharacteristic
374#204—34no—
375C22×C32C22×D411yescharacteristic
376C2×C3⋊D3—22no—
377C2×C3⋊D3—41no—
378C2×C3⋊D3—41no—
379C32×C4—41no—
380C32×C4—41no—
381C32×C4C22×Q811yescharacteristic
382C32×C42−1+411yescharacteristic
383C3⋊Dic3—21no—
384C3⋊Dic3—21no—
385C3⋊Dic3—41no—
386C3×Dic3—22no—
387C3×Dic3—21no—
388C3×Dic3—21no—
389C3×Dic3—21no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3#13712yes—
394C2×SD16—91no—
395C4⋊Q8—31no—
396C4⋊Q8—31no—
397C4⋊Q8—91no—
398C4⋊Q8—91no—
399C4⋊Q8—181no—
400C4⋊Q8—181no—
401C4⋊Q8—181no—
402#125—31no—
403#125—91no—
404C22⋊Q8—181no—
405C22⋊Q8—181no—
406C22⋊Q8—181no—
407C4×Q8—31no—
408C4×Q8—91no—
409C4×Q8—91no—
410C4×Q8—91no—
411C4×Q8—181no—
412C4×D4—91no—
413C4×D4—91no—
414C4×D4—91no—
415C2×C4⋊C4—181no—
416#107—31no—
417#107—31no—
418#107—91no—
419#107—91no—
420#107—91no—
421#107D3211yescharacteristic
422#106—31no—
423#106—31no—
424#106—91no—
425C4⋊C8—31no—
426C4⋊C8—91no—
427C4⋊C8—91no—
428#103—31no—
429#103—31no—
430#103—91no—
431#102—91no—
432#102—91no—
433#102—91no—
434#97—31no—
435#97—91no—
436C4×C8—91no—
437C22×D3—61no—
438C22×D3—61no—
439C22×D3—121no—
440C3×Q8—32no—
441C3×Q8—61no—
442C3×Q8—241no—
443C3×Q8—241no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—31no—
450C2×C3×C4—31no—
451C2×C3×C4—31no—
452C2×C3×C4—31no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4C23×D311yescharacteristic
460C2×C3×C4C23×D311yescharacteristic
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—31no—
466C2×Dic3—31no—
467C2×Dic3—31no—
468C2×Dic3—31no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—121no—
474C2×Dic3D3×D411yescharacteristic
475C2×Dic3D3×D411yescharacteristic
476C2×Dic3D3×D411yescharacteristic
477C2×Dic3D3×D411yescharacteristic
478D12—32no—
479D12—32no—
480D12—62no—
481D12—61no—
482D12—61no—
483D12—121no—
484C4×D3—122no—
485C4×D3—122no—
486C4×D3—241no—
487C4×D3—241no—
488C4×D3—241no—
489C4×D3—241no—
490C4×D3—242no—
491Dic6—21no—
492Dic6—62no—
493Dic6—62no—
494Dic6—81no—
495Dic6—81no—
496Dic6—241no—
497Dic6—241no—
498Dic6—241no—
499Dic6—241no—
500Dic6—242no—
501Dic6D3×Q812yes—
502C3×C8—21no—
503C3×C8—21no—
504C3×C8—32no—
505C3×C8—41no—
506C3×C8—61no—
507C3⋊C8—21no—
508C3⋊C8—61no—
509C3⋊C8—61no—
510C3⋊C8—121no—
511C3⋊C8D3×Q812yes—
512C2×C32D4×Q811yescharacteristic
513C2×C32C2×#13711yescharacteristic
514C2×C32#57611yescharacteristic
515C3⋊D3—42no—
516C2×Q8—31no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8—91no—
520C2×Q8—181no—
521C2×Q8—181no—
522C2×D4—91no—
523C22×C4—181no—
524C22×C4—181no—
525C22×C4—181no—
526SD16—94no—
527C2×C8—31no—
528C2×C8—31no—
529C2×C8—91no—
530C2×C8C2×D3211yescharacteristic
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—61no—
535C4⋊C4—61no—
536C4⋊C4—61no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—91no—
540C4⋊C4—91no—
541C4⋊C4—91no—
542C4⋊C4—91no—
543C4⋊C4—181no—
544C4⋊C4—181no—
545C4⋊C4—181no—
546C4⋊C4—181no—
547C4⋊C4—181no—
548C4⋊C4—181no—
549C4⋊C4C2×D3211yescharacteristic
550C4⋊C4C2×D3211yescharacteristic
551C22⋊C4—181no—
552C22⋊C4—181no—
553C22⋊C4—181no—
554C42—31no—
555C42—31no—
556C42—61no—
557C42—91no—
558C42—181no—
559C42—181no—
560C22×C3—21no—
561C22×C3C2×D3×D411yescharacteristic
562C22×C3C2×D3×D411yescharacteristic
563C2×D3—62no—
564C2×D3—62no—
565C2×D3—122no—
566C2×D3—121no—
567C2×D3—121no—
568C2×D3—121no—
569C2×D3—121no—
570C2×D3—241no—
571C2×D3—241no—
572C3×C4—21no—
573C3×C4—21no—
574C3×C4—32no—
575C3×C4—41no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—41no—
579C3×C4—62no—
580C3×C4—61no—
581C3×C4—61no—
582C3×C4—61no—
583C3×C4—81no—
584C3×C4—81no—
585C3×C4—121no—
586C3×C4—121no—
587C3×C4—121no—
588C3×C4C2×D3×Q811yescharacteristic
589C3×C4C2×D3×Q811yescharacteristic
590C3×C4#100711yescharacteristic
591C3×C4#101011yescharacteristic
592Dic3—22no—
593Dic3—21no—
594Dic3—21no—
595Dic3—21no—
596Dic3—41no—
597Dic3—41no—
598Dic3—41no—
599Dic3—62no—
600Dic3—61no—
601Dic3—61no—
602Dic3—61no—
603Dic3—61no—
604Dic3—121no—
605Dic3—121no—
606Dic3—121no—
607Dic3—241no—
608Dic3#91812yes—
609C32#338511yescharacteristic, complemented, Sylow
610C23—181no—
611Q8—32no—
612Q8—61no—
613Q8—182no—
614Q8—241no—
615Q8—241no—
616Q8—721no—
617Q8—721no—
618D4—92no—
619D4—181no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—31no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—91no—
631C2×C4—91no—
632C2×C4—181no—
633C2×C4—362no—
634C2×C4—721no—
635C2×C4—721no—
636C2×C4C22×D3211yescharacteristic
637C8—21no—
638C8—32no—
639C8—61no—
640C8—181no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3#563211yescharacteristic
645C2×C3#572711yescharacteristic
646C2×C3C2×#91811yescharacteristic
647C2×C3#577411yescharacteristic
648C2×C3#577411yescharacteristic
649C2×C3D3×#13711yescharacteristic
650D3—122no—
651D3—122no—
652D3—242no—
653C22—182no—
654C22—361no—
655C22—361no—
656C22D32×D411yescharacteristic
657C4—32no—
658C4—41no—
659C4—41no—
660C4—62no—
661C4—61no—
662C4—61no—
663C4—61no—
664C4—121no—
665C4—121no—
666C4—121no—
667C4—181no—
668C4—181no—
669C4—361no—
670C4#6429711yescharacteristic
671C4D32×Q811yescharacteristic
672C3—21no—
673C3#8113711yescharacteristic, complemented
674C3#8196511yescharacteristic, complemented
675C2—362no—
676C2#1059437811yescharacteristic
677C2#1059473511yescharacteristic
678C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenter#107D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594312C2semidirect
4. C3×#4876C2semidirect
5. C3×#4875C2semidirect
6. #10590820C2semidirect
8. #10590786C2semidirect
10. #10590546C2semidirect
11. #10590493C2semidirect
15. #10590411C2semidirect
77. #4876D3semidirect
78. #4875D3semidirect
135. #3717Q8semidirect
609. C32#3385semidirect
673. C3#81137semidirect
674. C3#81965semidirect

Maximal subgroups

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

subgroupindex
#105944702
#105943122
#105925892
C3×#48762
C3×#48752
#105908202
#105907952
#105907862
#105907592
#105905462
#105904932
#105904842
#105904642
#105904582
#105904112
#819653
#811373