Finite Group Databasebeta

← #11897656

Subgroups — #11897656

Order 1152.

740 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595272C211yesmaximal, characteristic
2#10594313C211yesmaximal, characteristic, complemented
3#10592456C211yesmaximal, characteristic
4C3×#4761C211yesmaximal, characteristic
5C3×#4759C211yesmaximal, characteristic
6#10591494C211yesmaximal, characteristic
7#10591405C211yesmaximal, characteristic
8#10591401C211yesmaximal, characteristic
9#10590903C211yesmaximal, characteristic, complemented
10#10590809C211yesmaximal, characteristic, complemented
11#10590805C211yesmaximal, characteristic, complemented
12#10590646C211yesmaximal, characteristic, complemented
13#10590434C211yesmaximal, characteristic, complemented
14#10590421C211yesmaximal, characteristic, complemented
15#10590411C211yesmaximal, characteristic, complemented
16#81056—31nomaximal
17#80960—31nomaximal
18D4×C3⋊Dic3C2211yescharacteristic
19C2×#3754C2211yescharacteristic
20#64096C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×#888C2211yescharacteristic
24C3×#888C2211yescharacteristic
25#63982—21no—
26C2×Dic3⋊Dic3—21no—
27#63964—21no—
28#63964—21no—
29#63919C2211yescharacteristic
30#63918C2211yescharacteristic
31C4×#627C2211yescharacteristic
32#63873—21no—
33#63872C2211yescharacteristic
34#63869C2211yescharacteristic
35#63844C2211yescharacteristic
36#63844C2211yescharacteristic
37#63839—21no—
38#63839—21no—
39#63838—21no—
40C32×#102C2211yescharacteristic
41#63643C2211yescharacteristic
42#63642C2211yescharacteristic
43#63634C2211yescharacteristic
44C3×#832C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#818C2211yescharacteristic
47C3×#817C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52#63576C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63574C2211yescharacteristic
56#63572C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5722—31no—
62#5722—31no—
63#5543—31no—
64#5539—31no—
65C3×#476—31no—
66C3×#474—31no—
67#5081—31no—
68#5078—31no—
69#5018—31no—
70C4×#214—31no—
71#4877—31no—
72#4876—31no—
73#4875—31no—
74#4874—31no—
75#4857—31no—
76#4857—31no—
77#4856—31no—
78#4856—31no—
79#4850—31no—
80#4831—31no—
81#4829—31no—
82#4828—31no—
83#4761D311yescharacteristic
84#4759—31no—
85#4759—31no—
86#4759D311yescharacteristic
87#4758—31no—
88#4757—31no—
89#4757—31no—
90#4757—31no—
91#4757—61no—
92C2×C32×D4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634C2311yescharacteristic
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6—21no—
99C2×#627—21no—
100C2×#627—21no—
101C2×#627D411yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104#3757—21no—
105#3754Q814yescomplemented
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123#3724—21no—
124#3724—21no—
125#3724—21no—
126#3724—21no—
127#3724D411yescharacteristic
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134Dic32—21no—
135Dic32—21no—
136#3385—91noSylow
137C3×C4⋊Q8—31no—
138C3×C4⋊Q8—31no—
139C3×C4×D4—31no—
140C3×C4×D4—31no—
141#944—61no—
142#944—61no—
143#944—61no—
144#944—61no—
145D4×Dic3—31no—
146D4×Dic3—31no—
147D4×Dic3—61no—
148D4×Dic3C2×D311yescharacteristic
149D4×Dic3C2×D311yescharacteristic
150C2×#214—31no—
151C2×#214—31no—
152C2×#214—61no—
153C2×C4⋊Dic3—61no—
154#924—61no—
155#924—61no—
156C2×Dic3⋊C4—61no—
157#890—31no—
158#890—31no—
159#890—31no—
160#888—31no—
161#888—31no—
162#888—31no—
163#888—61no—
164#888—61no—
165#888C2×D311yescharacteristic
166#888C2×D311yescharacteristic
167#887—31no—
168#887—31no—
169#887—31no—
170#887—31no—
171#887—61no—
172#887—61no—
173#887—61no—
174#878—61no—
175#878—61no—
176#878—61no—
177#878—61no—
178#870—31no—
179#869—31no—
180C4×Dic6—31no—
181C4×Dic6—31no—
182C4×Dic6—31no—
183C4×Dic6—31no—
184C3×#107—31no—
185C3×#107—31no—
186C3×#106—31no—
187C3×#106—31no—
188C3×C4⋊C8—31no—
189C3×C4⋊C8—31no—
190C3×#102—21no—
191C3×#102—31no—
192C3×#102—31no—
193C3×#102C2×D311yescharacteristic
194C3×#102C2×D311yescharacteristic
195#832C2×D311yescharacteristic
196#832C2×D311yescharacteristic
197#818—31no—
198#818—31no—
199#818C2×D311yescharacteristic
200#817C2×D311yescharacteristic
201#816—31no—
202#816—31no—
203#816—31no—
204#816—31no—
205#816—61no—
206#815—31no—
207#815—31no—
208#815—31no—
209#815—61no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8C2×D311yescharacteristic
213Dic3⋊C8C2×D311yescharacteristic
214C8×Dic3—31no—
215#810—31no—
216#810—31no—
217#808—31no—
218#808—31no—
219#808C2×D311yescharacteristic
220#807—31no—
221#807—31no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—31no—
226#807—61no—
227#807C2×D311yescharacteristic
228#803—31no—
229C4×C3⋊C8—31no—
230C23×C32—21no—
231C32×D4—21no—
232C32×D4C2×Q812yes—
233C2×C32×C4—21no—
234C2×C32×C4C2411yescharacteristic
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—81no—
238C2×C3⋊Dic3C2×D411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
240#634—21no—
241#634C2×Q812yes—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—42no—
247C2×C3×Dic3—81no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×Dic6—81no—
253C3×Dic6—81no—
254#627—22no—
255#627—81no—
256#627—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—91no—
269#476—31no—
270#474—31no—
271#474—91no—
272#446—91no—
273#440—91no—
274#440—91no—
275C4×SD16—91no—
276C2×C3×Q8—61no—
277C2×C3×Q8—61no—
278C2×C3×D4—21no—
279C2×C3×D4C22×D311yescharacteristic
280C2×C3×D4C22×D311yescharacteristic
281C22×C3×C4—61no—
282C22×C3×C4—61no—
283C22×Dic3—21no—
284C22×Dic3—21no—
285C22×Dic3—61no—
286C22×Dic3—61no—
287C22×Dic3—121no—
288C2×Dic6—21no—
289C2×Dic6—21no—
290C2×Dic6—31no—
291C2×Dic6—31no—
292C2×Dic6—31no—
293C2×Dic6—31no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—61no—
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—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4C22×D311yescharacteristic
312C3×C4⋊C4C22×D311yescharacteristic
313C3×C22⋊C4—61no—
314C3×C22⋊C4—61no—
315C3×C42—31no—
316C3×C42—31no—
317#217—21no—
318#217—21no—
319#217—61no—
320#217—61no—
321#217—121no—
322#214—34no—
323#214—34no—
324#214—64no—
325C4⋊Dic3—31no—
326C4⋊Dic3—31no—
327C4⋊Dic3—31no—
328C4⋊Dic3—31no—
329C4⋊Dic3—61no—
330C4⋊Dic3—61no—
331C4⋊Dic3—61no—
332C4⋊Dic3—61no—
333C4⋊Dic3—61no—
334C4⋊Dic3C22×D311yescharacteristic
335C4⋊Dic3C22×D311yescharacteristic
336C4⋊Dic3C22×D311yescharacteristic
337C4⋊Dic3C22×D311yescharacteristic
338Dic3⋊C4—21no—
339Dic3⋊C4—21no—
340Dic3⋊C4—31no—
341Dic3⋊C4—31no—
342Dic3⋊C4—31no—
343Dic3⋊C4—31no—
344Dic3⋊C4—61no—
345Dic3⋊C4—61no—
346Dic3⋊C4—61no—
347Dic3⋊C4—61no—
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—
359C4×Dic3—31no—
360C4×Dic3—31no—
361C4×Dic3—61no—
362C4×Dic3—61no—
363C4×Dic3—61no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—121no—
369C4×Dic3C22×D311yescharacteristic
370C4×Dic3C22×D311yescharacteristic
371C2×C3⋊C8—31no—
372C2×C3⋊C8—31no—
373C2×C3⋊C8—61no—
374C2×C3⋊C8C22×D311yescharacteristic
375C2×C3⋊C8C22×D311yescharacteristic
376C22×C32—22no—
377C22×C32—41no—
378C22×C32—41no—
379C22×C32C22×D411yescharacteristic
380C32×C4—41no—
381C32×C4C22×Q811yescharacteristic
382C32×C42−1+411yescharacteristic
383C3⋊Dic3—22no—
384C3⋊Dic3—21no—
385C3⋊Dic3—21no—
386C3⋊Dic3—41no—
387C3×Dic3—21no—
388C3×Dic3—21no—
389C3×Dic3—21no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C3×Dic3#13712yes—
395C2×SD16—91no—
396C4⋊Q8—31no—
397C4⋊Q8—31no—
398C4⋊Q8—91no—
399C4⋊Q8—91no—
400C4⋊Q8—181no—
401C4⋊Q8—181no—
402C4⋊Q8—181no—
403#125—91no—
404#125—91no—
405C22⋊Q8—181no—
406C22⋊Q8—181no—
407C22⋊Q8—181no—
408C4×Q8—91no—
409C4×Q8—91no—
410C4×Q8—91no—
411C4×Q8—91no—
412C4×Q8—181no—
413C4×D4—31no—
414C4×D4—31no—
415C4×D4—91no—
416C2×C4⋊C4—181no—
417#107—31no—
418#107—31no—
419#107—91no—
420#107—91no—
421#107—91no—
422#107—91no—
423#106—31no—
424#106—31no—
425#106—91no—
426C4⋊C8—31no—
427C4⋊C8—31no—
428C4⋊C8—91no—
429#103—91no—
430#103—91no—
431#103—91no—
432#102—31no—
433#102—31no—
434#102D3211yescharacteristic
435#97—91no—
436#97—91no—
437C4×C8—91no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—41no—
441C3×Q8—241no—
442C3×Q8—241no—
443C3×D4—21no—
444C3×D4—21no—
445C3×D4—22no—
446C3×D4—41no—
447C3×D4D3×Q812yes—
448C3×D4D3×Q812yes—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—31no—
453C2×C3×C4—31no—
454C2×C3×C4—31no—
455C2×C3×C4—31no—
456C2×C3×C4—41no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—122no—
462C2×C3×C4—241no—
463C2×C3×C4C23×D311yescharacteristic
464C2×C3×C4C23×D311yescharacteristic
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—31no—
470C2×Dic3—31no—
471C2×Dic3—31no—
472C2×Dic3—31no—
473C2×Dic3—42no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—81no—
481C2×Dic3—121no—
482C2×Dic3—121no—
483C2×Dic3—241no—
484C2×Dic3—241no—
485C2×Dic3—242no—
486C2×Dic3D3×D411yescharacteristic
487C2×Dic3D3×D411yescharacteristic
488C2×Dic3D3×D411yescharacteristic
489C2×Dic3D3×D411yescharacteristic
490Dic6—32no—
491Dic6—32no—
492Dic6—62no—
493Dic6—62no—
494Dic6—61no—
495Dic6—61no—
496Dic6—62no—
497Dic6—81no—
498Dic6—81no—
499Dic6—121no—
500Dic6—241no—
501Dic6—241no—
502Dic6—241no—
503Dic6—241no—
504C3×C8—21no—
505C3×C8—21no—
506C3×C8—41no—
507C3×C8—61no—
508C3×C8—61no—
509C3⋊C8—21no—
510C3⋊C8—21no—
511C3⋊C8—32no—
512C3⋊C8—32no—
513C3⋊C8—62no—
514C2×C32—42no—
515C2×C32D4×Q811yescharacteristic
516C2×C32C2×#13711yescharacteristic
517C2×C32#57611yescharacteristic
518C2×Q8—61no—
519C2×Q8—61no—
520C2×Q8—91no—
521C2×Q8—91no—
522C2×Q8—181no—
523C2×Q8—181no—
524C2×D4C2×D3211yescharacteristic
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—181no—
528SD16—94no—
529C2×C8—31no—
530C2×C8—31no—
531C2×C8—91no—
532C2×C8C2×D3211yescharacteristic
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—31no—
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⋊C4—181no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4C2×D3211yescharacteristic
553C22⋊C4—61no—
554C22⋊C4—61no—
555C22⋊C4—181no—
556C42—31no—
557C42—31no—
558C42—91no—
559C42—181no—
560C42—181no—
561C42—181no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—21no—
565C22×C3—42no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—81no—
571C22×C3—81no—
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C2×D3×D411yescharacteristic
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—32no—
577C3×C4—41no—
578C3×C4—41no—
579C3×C4—61no—
580C3×C4—61no—
581C3×C4—61no—
582C3×C4—81no—
583C3×C4—121no—
584C3×C4—121no—
585C3×C4—121no—
586C3×C4—121no—
587C3×C4C2×D3×Q811yescharacteristic
588C3×C4C2×D3×Q811yescharacteristic
589C3×C4#101011yescharacteristic
590C3×C4#101011yescharacteristic
591Dic3—21no—
592Dic3—21no—
593Dic3—21no—
594Dic3—41no—
595Dic3—41no—
596Dic3—41no—
597Dic3—41no—
598Dic3—62no—
599Dic3—62no—
600Dic3—61no—
601Dic3—61no—
602Dic3—61no—
603Dic3—61no—
604Dic3—122no—
605Dic3—121no—
606Dic3—121no—
607Dic3—121no—
608Dic3—121no—
609Dic3—241no—
610Dic3#91512yes—
611C32#338511yescharacteristic, complemented, Sylow
612C23—21no—
613Q8—92no—
614Q8—182no—
615Q8—181no—
616Q8—241no—
617Q8—241no—
618Q8—721no—
619Q8—721no—
620D4—21no—
621D4#379712yes—
622C2×C4—21no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—91no—
632C2×C4—91no—
633C2×C4—122no—
634C2×C4—181no—
635C2×C4—181no—
636C2×C4—241no—
637C2×C4—721no—
638C2×C4C22×D3211yescharacteristic
639C8—21no—
640C8—61no—
641C8—61no—
642C8—92no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—42no—
647C2×C3—42no—
648C2×C3—82no—
649C2×C3#563211yescharacteristic
650C2×C3#563211yescharacteristic
651C2×C3#575711yescharacteristic
652C2×C3C2×#91511yescharacteristic
653C2×C3#577411yescharacteristic
654C2×C3D3×#13711yescharacteristic
655C22—22no—
656C22—41no—
657C22—41no—
658C22D32×D411yescharacteristic
659C4—32no—
660C4—41no—
661C4—61no—
662C4—61no—
663C4—61no—
664C4—121no—
665C4—121no—
666C4—121no—
667C4—121no—
668C4—182no—
669C4—181no—
670C4—181no—
671C4—361no—
672C4C2×#379711yescharacteristic
673C4#6430911yescharacteristic
674C3—21no—
675C3#8096011yescharacteristic, complemented
676C3#8105611yescharacteristic, complemented
677C2—42no—
678C2#1059407211yescharacteristic
679C2#1059473211yescharacteristic
680C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×C32×D4C23
hypercenter#102D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594313C2semidirect
9. #10590903C2semidirect
10. #10590809C2semidirect
11. #10590805C2semidirect
12. #10590646C2semidirect
13. #10590434C2semidirect
14. #10590421C2semidirect
15. #10590411C2semidirect
105. #3754Q8semidirect
611. C32#3385semidirect
675. C3#80960semidirect
676. C3#81056semidirect

Maximal subgroups

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

subgroupindex
#105952722
#105943132
#105924562
C3×#47612
C3×#47592
#105914942
#105914052
#105914012
#105909032
#105908092
#105908052
#105906462
#105904342
#105904212
#105904112
#810563
#809603