Finite Group Databasebeta

← #11897654

Subgroups — #11897654

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#10595272C211yesmaximal, characteristic
2#10594312C211yesmaximal, characteristic, complemented
3#10592458C211yesmaximal, characteristic
4C3×#4761C211yesmaximal, characteristic
5C3×#4757C211yesmaximal, characteristic
6#10591446C211yesmaximal, characteristic
7Dic3×#214C211yesmaximal, characteristic
8#10591410C211yesmaximal, characteristic
9#10590892C211yesmaximal, characteristic, complemented
10#10590820C211yesmaximal, characteristic, complemented
11#10590804C211yesmaximal, characteristic, complemented
12#10590786C211yesmaximal, characteristic, complemented
13#10590546C211yesmaximal, characteristic, complemented
14#10590543C211yesmaximal, characteristic, complemented
15#10590411C211yesmaximal, characteristic, complemented
16#81056—31nomaximal
17#79759—31nomaximal
18D4×C3⋊Dic3C2211yescharacteristic
19#64097C2211yescharacteristic
20C3×D4×Dic3C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C3×#888C2211yescharacteristic
24C3×#887C2211yescharacteristic
25#63982—21no—
26C2×Dic3⋊Dic3—21no—
27#63964—21no—
28#63964—21no—
29#63918C2211yescharacteristic
30#63918C2211yescharacteristic
31C4×#627C2211yescharacteristic
32#63872C2211yescharacteristic
33#63869C2211yescharacteristic
34#63866—21no—
35#63843C2211yescharacteristic
36Dic3×Dic6C2211yescharacteristic
37#63840—21no—
38#63839—21no—
39#63837—21no—
40C32×#102C2211yescharacteristic
41#63659C2211yescharacteristic
42#63645C2211yescharacteristic
43#63641C2211yescharacteristic
44#63634C2211yescharacteristic
45C3×#832C2211yescharacteristic
46C3×#817C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×#815C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52#63576C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63555C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5722—31no—
62Q8×Dic6—31no—
63#5543—31no—
64#5539—31no—
65C3×#476—31no—
66C3×#440—31no—
67#5164—31no—
68Dic3×SD16—31no—
69#5078—31no—
70#5022—31no—
71C4×#214—31no—
72#5007—31no—
73#4876—31no—
74#4874—31no—
75#4857—31no—
76#4857—31no—
77#4856—31no—
78#4856—31no—
79#4850—31no—
80#4831—31no—
81#4799—31no—
82#4793—31no—
83#4761D311yescharacteristic
84#4759—31no—
85#4759—31no—
86#4759—31no—
87#4759—61no—
88#4757—31no—
89#4757D311yescharacteristic
90#4702—31no—
91#4701—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627—21no—
101C2×#627D411yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104#3757—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C3×#217—21no—
111C3×#217—21no—
112C3×#214Q814yescomplemented
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
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⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134Dic32—21no—
135Dic32—21no—
136#3385—91noSylow
137C2×C3×SD16—31no—
138C3×C4⋊Q8—31no—
139C3×C4×Q8—31no—
140C3×C4×D4—31no—
141C3×C4×D4—31no—
142Q8×Dic3—31no—
143Q8×Dic3—31no—
144#944—61no—
145#944—61no—
146D4×Dic3—31no—
147D4×Dic3—31no—
148D4×Dic3—61no—
149D4×Dic3C2×D311yescharacteristic
150D4×Dic3C2×D311yescharacteristic
151C2×#214C2×D311yescharacteristic
152C2×C4⋊Dic3—61no—
153#924—61no—
154#924—61no—
155C2×Dic3⋊C4—61no—
156#890—31no—
157#890—31no—
158#890—31no—
159#888—31no—
160#888—31no—
161#888—31no—
162#888—31no—
163#888—61no—
164#888—61no—
165#888—61no—
166#888—61no—
167#888C2×D311yescharacteristic
168#887—31no—
169#887—61no—
170#887C2×D311yescharacteristic
171#878—61no—
172#878—61no—
173#878—61no—
174#878—61no—
175#870—31no—
176#869—31no—
177#869—31no—
178#869—61no—
179C4×Dic6—31no—
180C4×Dic6—31no—
181C4×Dic6—31no—
182C4×Dic6—61no—
183C3×#107—31no—
184C3×#106—31no—
185C3×#106—31no—
186C3×C4⋊C8—31no—
187C3×#103—31no—
188C3×#102—21no—
189C3×#102—31no—
190C3×#102C2×D311yescharacteristic
191C3×#102C2×D311yescharacteristic
192C3×#97—31no—
193#835—31no—
194#835—31no—
195#832—31no—
196#832—31no—
197#832—61no—
198#832C2×D311yescharacteristic
199#818—31no—
200#818—31no—
201#818—31no—
202#818—31no—
203#818—61no—
204#817—31no—
205#817C2×D311yescharacteristic
206#816—31no—
207#816C2×D311yescharacteristic
208#815—31no—
209#815—31no—
210#815C2×D311yescharacteristic
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—61no—
215Dic3⋊C8C2×D311yescharacteristic
216C8×Dic3—31no—
217#810—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
228C4⋊(C3⋊C8)—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—81no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—42no—
246C2×C3×Dic3—81no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×Dic6—21no—
252C3×Dic6—81no—
253C3×Dic6C2×Q812yes—
254#627—22no—
255#627—81no—
256#627—81no—
257C32×C8—21no—
258C3⋊(C3⋊C8)—21no—
259C3×C3⋊C8—21no—
260C3×C3⋊C8C2×Q812yes—
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—91no—
271#474—91no—
272#446—91no—
273#440—31no—
274#440—91no—
275C4×SD16—91no—
276C2×C3×Q8—31no—
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—31no—
290C2×Dic6—31no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—121no—
298C2×Dic6C22×D311yescharacteristic
299C3×SD16—34no—
300C2×C3×C8—21no—
301C2×C3×C8—31no—
302C2×C3×C8—31no—
303C2×C3×C8C22×D311yescharacteristic
304C2×C3×C8C22×D311yescharacteristic
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⋊C4C22×D311yescharacteristic
312C3×C4⋊C4C22×D311yescharacteristic
313C3×C22⋊C4—61no—
314C3×C22⋊C4—61no—
315C3×C42—31no—
316C3×C42—31no—
317C3×C42—61no—
318#217—21no—
319#217—21no—
320#217—61no—
321#217—61no—
322#217—121no—
323#214Dic614yescomplemented
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—61no—
339C4⋊Dic3C22×D311yescharacteristic
340C4⋊Dic3C22×D311yescharacteristic
341C4⋊Dic3C22×D311yescharacteristic
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—61no—
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×C32—22no—
376C22×C32—41no—
377C22×C32—41no—
378C22×C32C22×D411yescharacteristic
379C32×C4—41no—
380C32×C4C22×Q811yescharacteristic
381C32×C42−1+411yescharacteristic
382C3⋊Dic3—21no—
383C3⋊Dic3—21no—
384C3⋊Dic3—41no—
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—31no—
395C4⋊Q8—31no—
396C4⋊Q8—91no—
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—31no—
414C4×D4—91no—
415C2×C4⋊C4—181no—
416#107—31no—
417#107—91no—
418#107—91no—
419#107—91no—
420#107—91no—
421#107—91no—
422#106—31no—
423#106—31no—
424#106—91no—
425C4⋊C8—31no—
426C4⋊C8—91no—
427C4⋊C8—91no—
428#103—31no—
429#103—91no—
430#103—91no—
431#102—31no—
432#102—91no—
433#102D3211yescharacteristic
434#97—31no—
435#97—91no—
436C4×C8—91no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—41no—
440C3×Q8—32no—
441C3×Q8—61no—
442C3×Q8—241no—
443C3×D4—21no—
444C3×D4—21no—
445C3×D4—22no—
446C3×D4—41no—
447C3×D4C2×Dic612yes—
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—21no—
491Dic6—62no—
492Dic6—62no—
493Dic6—81no—
494Dic6—241no—
495Dic6—241no—
496Dic6—241no—
497Dic6—241no—
498Dic6—241no—
499Dic6—241no—
500Dic6—242no—
501Dic6C2×Dic612yes—
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⋊C8C2×Dic612yes—
512C2×C32—42no—
513C2×C32D4×Q811yescharacteristic
514C2×C32C2×#13711yescharacteristic
515C2×C32#57611yescharacteristic
516C2×Q8—31no—
517C2×Q8—61no—
518C2×Q8—91no—
519C2×Q8—181no—
520C2×Q8—181no—
521C2×Q8—181no—
522C2×D4C2×D3211yescharacteristic
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—181no—
526SD16—34no—
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—91no—
537C4⋊C4—91no—
538C4⋊C4—91no—
539C4⋊C4—91no—
540C4⋊C4—91no—
541C4⋊C4—181no—
542C4⋊C4—181no—
543C4⋊C4—181no—
544C4⋊C4—181no—
545C4⋊C4—181no—
546C4⋊C4—181no—
547C4⋊C4—181no—
548C4⋊C4—181no—
549C4⋊C4—181no—
550C4⋊C4C2×D3211yescharacteristic
551C22⋊C4—61no—
552C22⋊C4—61no—
553C22⋊C4—181no—
554C42—31no—
555C42—31no—
556C42—61no—
557C42—91no—
558C42—181no—
559C42—181no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—21no—
563C22×C3—42no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—81no—
569C22×C3—81no—
570C22×C3C2×D3×D411yescharacteristic
571C22×C3C2×D3×D411yescharacteristic
572C3×C4—21no—
573C3×C4—21no—
574C3×C4—32no—
575C3×C4—41no—
576C3×C4—41no—
577C3×C4—62no—
578C3×C4—61no—
579C3×C4—61no—
580C3×C4—61no—
581C3×C4—81no—
582C3×C4—121no—
583C3×C4—121no—
584C3×C4—121no—
585C3×C4C22×Dic611yescharacteristic
586C3×C4C2×D3×Q811yescharacteristic
587C3×C4#101011yescharacteristic
588C3×C4#101011yescharacteristic
589Dic3—21no—
590Dic3—21no—
591Dic3—21no—
592Dic3—22no—
593Dic3—41no—
594Dic3—41no—
595Dic3—41no—
596Dic3—62no—
597Dic3—61no—
598Dic3—61no—
599Dic3—61no—
600Dic3—61no—
601Dic3—121no—
602Dic3—121no—
603Dic3—121no—
604Dic3—121no—
605Dic3—121no—
606Dic3—241no—
607Dic3—241no—
608Dic3#91512yes—
609C32#338511yescharacteristic, complemented, Sylow
610C23—21no—
611Q8—32no—
612Q8—61no—
613Q8—182no—
614Q8—241no—
615Q8—721no—
616Q8—721no—
617Q8—721no—
618D4—21no—
619D4D3×Dic612yes—
620C2×C4—21no—
621C2×C4—31no—
622C2×C4—31no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—91no—
630C2×C4—91no—
631C2×C4—122no—
632C2×C4—181no—
633C2×C4—181no—
634C2×C4—241no—
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—42no—
645C2×C3—42no—
646C2×C3—82no—
647C2×C3D4×Dic611yescharacteristic
648C2×C3#563211yescharacteristic
649C2×C3C2×#91511yescharacteristic
650C2×C3#577411yescharacteristic
651C2×C3#577411yescharacteristic
652C2×C3D3×#13711yescharacteristic
653C22—22no—
654C22—41no—
655C22—41no—
656C22D32×D411yescharacteristic
657C4—32no—
658C4—41no—
659C4—62no—
660C4—61no—
661C4—61no—
662C4—61no—
663C4—121no—
664C4—121no—
665C4—121no—
666C4—181no—
667C4—181no—
668C4—361no—
669C4—361no—
670C4C2×D3×Dic611yescharacteristic
671C4#6430911yescharacteristic
672C3—21no—
673C3#7975911yescharacteristic, complemented
674C3#8105611yescharacteristic, complemented
675C2—42no—
676C2#1059407111yescharacteristic
677C2#1059473511yescharacteristic
678C2D3×#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. #10594312C2semidirect
9. #10590892C2semidirect
10. #10590820C2semidirect
11. #10590804C2semidirect
12. #10590786C2semidirect
13. #10590546C2semidirect
14. #10590543C2semidirect
15. #10590411C2semidirect
112. C3×#214Q8semidirect
323. #214Dic6semidirect
609. C32#3385semidirect
673. C3#79759semidirect
674. C3#81056semidirect

Maximal subgroups

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

subgroupindex
#105952722
#105943122
#105924582
C3×#47612
C3×#47572
#105914462
Dic3×#2142
#105914102
#105908922
#105908202
#105908042
#105907862
#105905462
#105905432
#105904112
#810563
#797593