Finite Group Databasebeta

← #11897682

Subgroups — #11897682

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594460C211yesmaximal, characteristic
2#10594312C211yesmaximal, characteristic, complemented
3#10592575C211yesmaximal, characteristic, complemented
4C3×#4890C211yesmaximal, characteristic
5C3×#4875C211yesmaximal, characteristic, complemented
6#10590815C211yesmaximal, characteristic, complemented
7#10590757C211yesmaximal, characteristic
8#10590743C211yesmaximal, characteristic
9#10590646C211yesmaximal, characteristic, complemented
10#10590494C211yesmaximal, characteristic, complemented
11#10590478C211yesmaximal, characteristic
12#10590471C211yesmaximal, characteristic
13#10590453C211yesmaximal, characteristic
14#10590420C211yesmaximal, characteristic, complemented
15#10590411C211yesmaximal, characteristic, complemented
16#81137—31nomaximal
17#80960—31nomaximal
18#64099C2211yescharacteristic
19#64097C2211yescharacteristic
20C3×#893C2211yescharacteristic
21C3×#888C2211yescharacteristic
22C3×#888C2211yescharacteristic
23C3×#887C2211yescharacteristic
24#63918C2211yescharacteristic
25C4×#627C2211yescharacteristic
26#63898C2211yescharacteristic
27#63893—21no—
28Dic3×D12C2211yescharacteristic
29#63887—21no—
30D3×Dic3⋊C4—21no—
31#63869C2211yescharacteristic
32#63866—21no—
33#63856—21no—
34#63843C2211yescharacteristic
35Dic3×Dic6C2211yescharacteristic
36#63840—21no—
37#63839—21no—
38#63837—21no—
39C2×#3715C2211yescharacteristic
40C32×#107C2211yescharacteristic
41#63644C2211yescharacteristic
42#63642C2211yescharacteristic
43#63635C2211yescharacteristic
44#63634C2211yescharacteristic
45C3×#821C2211yescharacteristic
46C3×#816C2211yescharacteristic
47C3×Dic3⋊C8C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63566C2211yescharacteristic
58#63563C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5730—31no—
62#5722—31no—
63Q8×Dic6—31no—
64#5539—31no—
65C3×#477—31no—
66C3×#474—31no—
67#5081—31no—
68#5078—31no—
69C4×#215—31no—
70#5018—31no—
71#4890—31no—
72#4890D311yescharacteristic
73#4877—31no—
74#4876—31no—
75#4876—31no—
76#4876—31no—
77#4876—61no—
78#4875D311yescharacteristic, complemented
79#4874—31no—
80#4842—31no—
81#4831—31no—
82#4829—31no—
83#4828—31no—
84#4817—31no—
85#4817—31no—
86#4799—31no—
87#4799—31no—
88#4761—31no—
89#4759—31no—
90#4758—31no—
91#4757—31no—
92C2×#634—21no—
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#627D411yescharacteristic
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109#3750—21no—
110C4×C3⋊Dic3C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
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#3724—21no—
124#3724D411yescharacteristic
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3D411yescharacteristic
130Dic3⋊Dic3D411yescharacteristic
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133Dic32—21no—
134Dic32—21no—
135#3715Q814yescomplemented
136#3385—91noSylow
137C3×C4⋊Q8—31no—
138C3×C4⋊Q8—31no—
139C3×C4×Q8—31no—
140C3×C4×D4—31no—
141#946—61no—
142#946—61no—
143Q8×Dic3—31no—
144Q8×Dic3—31no—
145#944—61no—
146#944—61no—
147C2×#215—31no—
148D4×Dic3—31no—
149D4×Dic3—31no—
150C2×#214—31no—
151#924—61no—
152C2×Dic3⋊C4—61no—
153#897—61no—
154#893—31no—
155#893C2×D311yescharacteristic
156D3×C4⋊C4—61no—
157#890—31no—
158#890—31no—
159#890—31no—
160#890—61no—
161#888—31no—
162#888—31no—
163#888—31no—
164#888—61no—
165#888—61no—
166#888—61no—
167#888—61no—
168#888C2×D311yescharacteristic
169#888C2×D311yescharacteristic
170#887—31no—
171#887—61no—
172#887C2×D311yescharacteristic
173#878—61no—
174#878—61no—
175C4×D12—31no—
176#870—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×C4⋊C8—31no—
189C3×C4⋊C8—31no—
190C3×#103—31no—
191C3×#103—31no—
192C3×#102—31no—
193C3×#102—31no—
194#835—31no—
195#832—31no—
196#821—31no—
197#821C2×D311yescharacteristic
198#818—31no—
199#817—31no—
200#817—31no—
201#817—31no—
202#817—61no—
203#816—31no—
204#816C2×D311yescharacteristic
205#815—31no—
206#815—31no—
207#815—31no—
208#815—61no—
209Dic3⋊C8—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8C2×D311yescharacteristic
212Dic3⋊C8C2×D311yescharacteristic
213C8×Dic3—31no—
214#810C2×D311yescharacteristic
215#809C2×D311yescharacteristic
216#808—31no—
217#808—31no—
218#808—31no—
219#808—61no—
220#807—31no—
221#807—31no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—61no—
226#807C2×D311yescharacteristic
227#807C2×D311yescharacteristic
228#803—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⋊Dic3—21no—
236C2×C3⋊Dic3C2×D411yescharacteristic
237C2×C3⋊Dic3C2×D411yescharacteristic
238#634—81no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3C2×D411yescharacteristic
243C2×C3×Dic3C2×D411yescharacteristic
244C2×C3×Dic3C2×D411yescharacteristic
245C2×C3×Dic3C2×D411yescharacteristic
246C3×D12—21no—
247C3×D12C2×Q812yes—
248C3×C4×D3—81no—
249C3×Dic6—21no—
250C3×Dic6—81no—
251C3×Dic6—81no—
252C3×Dic6C2×Q812yes—
253#627—22no—
254#627—81no—
255D3×Dic3—42no—
256D3×Dic3—81no—
257C32×C8—21no—
258C3⋊(C3⋊C8)C2×Q812yes—
259C3×C3⋊C8—21no—
260C3×C3⋊C8—21no—
261Q82—91no—
262#554—91no—
263#501—91no—
264#501—91no—
265#500—91no—
266#479—91no—
267#479—91no—
268#477—31no—
269#476—91no—
270#474—31no—
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×C3×D4—31no—
280C22×C3×C4—61no—
281C22×Dic3—61no—
282C22×Dic3—61no—
283C2×D12C22×D311yescharacteristic
284C2×C4×D3—21no—
285C2×C4×D3—61no—
286C2×C4×D3—61no—
287C2×Dic6—21no—
288C2×Dic6—21no—
289C2×Dic6—31no—
290C2×Dic6—31no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—121no—
296C2×Dic6C22×D311yescharacteristic
297C2×C3×C8—21no—
298C2×C3×C8—31no—
299C2×C3×C8—31no—
300C2×C3×C8C22×D311yescharacteristic
301C2×C3×C8C22×D311yescharacteristic
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—61no—
307C3×C4⋊C4—61no—
308C3×C4⋊C4—61no—
309C3×C4⋊C4C22×D311yescharacteristic
310C3×C4⋊C4C22×D311yescharacteristic
311C3×C4⋊C4C22×D311yescharacteristic
312C3×C4⋊C4C22×D311yescharacteristic
313C3×C22⋊C4—61no—
314C3×C42—31no—
315C3×C42—31no—
316C3×C42—61no—
317#217—61no—
318#217—61no—
319#215—34no—
320#214—34no—
321(C2×D3)⋊C4—21no—
322(C2×D3)⋊C4—61no—
323(C2×D3)⋊C4—61no—
324C4⋊Dic3—31no—
325C4⋊Dic3—31no—
326C4⋊Dic3—31no—
327C4⋊Dic3—31no—
328C4⋊Dic3—31no—
329C4⋊Dic3—31no—
330C4⋊Dic3—61no—
331C4⋊Dic3—61no—
332C4⋊Dic3—61no—
333C4⋊Dic3—61no—
334C4⋊Dic3—61no—
335C4⋊Dic3—61no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—121no—
339C4⋊Dic3C22×D311yescharacteristic
340C4⋊Dic3C22×D311yescharacteristic
341Dic3⋊C4—21no—
342Dic3⋊C4—21no—
343Dic3⋊C4—21no—
344Dic3⋊C4—31no—
345Dic3⋊C4—31no—
346Dic3⋊C4—31no—
347Dic3⋊C4—31no—
348Dic3⋊C4—61no—
349Dic3⋊C4—61no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—121no—
359Dic3⋊C4—121no—
360C4×Dic3—21no—
361C4×Dic3—31no—
362C4×Dic3—31no—
363C4×Dic3—61no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3C22×D311yescharacteristic
369C4×Dic3C22×D311yescharacteristic
370C2×C3⋊C8—31no—
371C2×C3⋊C8—31no—
372C2×C3⋊C8—61no—
373C2×C3⋊C8C22×D311yescharacteristic
374C2×C3⋊C8C22×D311yescharacteristic
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—41no—
387C3×Dic3—22no—
388C3×Dic3—21no—
389C3×Dic3—21no—
390C3×Dic3—21no—
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—91no—
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—31no—
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—91no—
423#106—91no—
424#106—91no—
425C4⋊C8—31no—
426C4⋊C8—31no—
427C4⋊C8—91no—
428#103—31no—
429#103—31no—
430#103—91no—
431#102—31no—
432#102—31no—
433#102—91no—
434#97—91no—
435#97—91no—
436C4×C8—91no—
437C23×C3—61no—
438C22×D3—21no—
439C3×Q8—32no—
440C3×Q8—61no—
441C3×Q8—241no—
442C3×Q8—241no—
443C3×D4—32no—
444C3×D4—61no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—31no—
451C2×C3×C4—31no—
452C2×C3×C4—31no—
453C2×C3×C4—31no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—241no—
460C2×C3×C4C23×D311yescharacteristic
461C2×C3×C4C23×D311yescharacteristic
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—61no—
474C2×Dic3—61no—
475C2×Dic3—121no—
476C2×Dic3—121no—
477C2×Dic3—122no—
478C2×Dic3—241no—
479C2×Dic3D3×D411yescharacteristic
480C2×Dic3D3×D411yescharacteristic
481C2×Dic3D3×D411yescharacteristic
482C2×Dic3D3×D411yescharacteristic
483D12—21no—
484D12D3×Q812yes—
485C4×D3—81no—
486C4×D3—122no—
487C4×D3—241no—
488Dic6—21no—
489Dic6—62no—
490Dic6—62no—
491Dic6—81no—
492Dic6—81no—
493Dic6—241no—
494Dic6—241no—
495Dic6—241no—
496Dic6—241no—
497Dic6—242no—
498Dic6D3×Q812yes—
499C3×C8—22no—
500C3×C8—21no—
501C3×C8—21no—
502C3×C8—61no—
503C3×C8—61no—
504C3⋊C8—21no—
505C3⋊C8—21no—
506C3⋊C8—32no—
507C3⋊C8—32no—
508C3⋊C8—62no—
509C2×C32D4×Q811yescharacteristic
510C2×C32C2×#13711yescharacteristic
511C2×C32#57611yescharacteristic
512C3×D3—42no—
513C2×Q8—31no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—91no—
517C2×Q8—181no—
518C2×Q8—181no—
519C2×D4—31no—
520C22×C4—61no—
521C22×C4—181no—
522C22×C4—181no—
523SD16—94no—
524C2×C8—31no—
525C2×C8—31no—
526C2×C8—91no—
527C2×C8C2×D3211yescharacteristic
528C4⋊C4—31no—
529C4⋊C4—31no—
530C4⋊C4—61no—
531C4⋊C4—61no—
532C4⋊C4—61no—
533C4⋊C4—91no—
534C4⋊C4—91no—
535C4⋊C4—91no—
536C4⋊C4—91no—
537C4⋊C4—91no—
538C4⋊C4—181no—
539C4⋊C4—181no—
540C4⋊C4—181no—
541C4⋊C4—181no—
542C4⋊C4—181no—
543C4⋊C4—181no—
544C4⋊C4—181no—
545C4⋊C4—181no—
546C4⋊C4C2×D3211yescharacteristic
547C4⋊C4C2×D3211yescharacteristic
548C22⋊C4—61no—
549C22⋊C4—181no—
550C22⋊C4—181no—
551C42—31no—
552C42—31no—
553C42—61no—
554C42—91no—
555C42—181no—
556C42—181no—
557C22×C3—21no—
558C22×C3—62no—
559C22×C3—121no—
560C22×C3—121no—
561C22×C3C2×D3×D411yescharacteristic
562C22×C3C2×D3×D411yescharacteristic
563C2×D3—22no—
564C2×D3—41no—
565C2×D3—41no—
566C3×C4—21no—
567C3×C4—21no—
568C3×C4—32no—
569C3×C4—41no—
570C3×C4—41no—
571C3×C4—41no—
572C3×C4—41no—
573C3×C4—62no—
574C3×C4—61no—
575C3×C4—61no—
576C3×C4—61no—
577C3×C4—81no—
578C3×C4—81no—
579C3×C4—121no—
580C3×C4—121no—
581C3×C4C2×D3×Q811yescharacteristic
582C3×C4C2×D3×Q811yescharacteristic
583C3×C4#101011yescharacteristic
584C3×C4#101011yescharacteristic
585Dic3—22no—
586Dic3—21no—
587Dic3—21no—
588Dic3—21no—
589Dic3—41no—
590Dic3—41no—
591Dic3—61no—
592Dic3—61no—
593Dic3—61no—
594Dic3—61no—
595Dic3—121no—
596Dic3—121no—
597Dic3—121no—
598Dic3—121no—
599Dic3—121no—
600Dic3—121no—
601Dic3—241no—
602Dic3—241no—
603Dic3#91812yes—
604C32#338511yescharacteristic, complemented, Sylow
605C23—61no—
606Q8—32no—
607Q8—61no—
608Q8—182no—
609Q8—241no—
610Q8—241no—
611Q8—721no—
612Q8—721no—
613D4—32no—
614D4—61no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—31no—
618C2×C4—31no—
619C2×C4—31no—
620C2×C4—31no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—91no—
625C2×C4—91no—
626C2×C4—181no—
627C2×C4—181no—
628C2×C4—241no—
629C2×C4—362no—
630C2×C4—721no—
631C2×C4C22×D3211yescharacteristic
632C8—21no—
633C8—61no—
634C8—61no—
635C8—92no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—122no—
640C2×C3#563211yescharacteristic
641C2×C3#563211yescharacteristic
642C2×C3#575711yescharacteristic
643C2×C3C2×#91811yescharacteristic
644C2×C3#577411yescharacteristic
645C2×C3D3×#13711yescharacteristic
646D3—42no—
647C22—62no—
648C22—121no—
649C22—121no—
650C22D32×D411yescharacteristic
651C4—32no—
652C4—41no—
653C4—41no—
654C4—62no—
655C4—61no—
656C4—61no—
657C4—61no—
658C4—121no—
659C4—121no—
660C4—181no—
661C4—181no—
662C4—361no—
663C4—361no—
664C4#6429811yescharacteristic
665C4D32×Q811yescharacteristic
666C3—21no—
667C3#8096011yescharacteristic, complemented
668C3#8113711yescharacteristic, complemented
669C2—122no—
670C2#1059437711yescharacteristic
671C2#1059473211yescharacteristic
672C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
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
3. #10592575C2semidirect
5. C3×#4875C2semidirect
6. #10590815C2semidirect
9. #10590646C2semidirect
10. #10590494C2semidirect
14. #10590420C2semidirect
15. #10590411C2semidirect
78. #4875D3semidirect
135. #3715Q8semidirect
604. C32#3385semidirect
667. C3#80960semidirect
668. C3#81137semidirect

Maximal subgroups

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

subgroupindex
#105944602
#105943122
#105925752
C3×#48902
C3×#48752
#105908152
#105907572
#105907432
#105906462
#105904942
#105904782
#105904712
#105904532
#105904202
#105904112
#811373
#809603