Finite Group Databasebeta

← #11897641

Subgroups — #11897641

Order 1152.

727 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593941C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592527C211yesmaximal, characteristic, complemented
4C3×#4846C211yesmaximal, characteristic
5C3×#4829C211yesmaximal, characteristic, complemented
6#10590903C211yesmaximal, characteristic, complemented
7#10590902C211yesmaximal, characteristic, complemented
8#10590821C211yesmaximal, characteristic, complemented
9#10590817C211yesmaximal, characteristic, complemented
10#10590778C211yesmaximal, characteristic
11#10590776C211yesmaximal, characteristic
12#10590743C211yesmaximal, characteristic
13#10590742C211yesmaximal, characteristic
14#10590358C211yesmaximal, characteristic
15#10590315C211yesmaximal, characteristic, complemented
16#81223—31nomaximal
17#80960—31nomaximal
18C4×#634C2211yescharacteristic
19C3×C4×D12C2211yescharacteristic
20C3×#870C2211yescharacteristic
21C3×#869C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23#63919C2211yescharacteristic
24#63919C2211yescharacteristic
25#63919C2211yescharacteristic
26#63918—21no—
27#63898C2211yescharacteristic
28#63898C2211yescharacteristic
29#63896—21no—
30#63893—21no—
31D3×Dic3⋊C4—21no—
32#63872C2211yescharacteristic
33#63851—21no—
34#63844—21no—
35#63843C2211yescharacteristic
36#63843C2211yescharacteristic
37#63839—21no—
38#63839—21no—
39C2×#3715C2211yescharacteristic
40C32×C4⋊C8C2211yescharacteristic
41#63642C2211yescharacteristic
42#63641C2211yescharacteristic
43#63641C2211yescharacteristic
44C8×C3⋊Dic3C2211yescharacteristic
45#63630C2211yescharacteristic
46C3×#821C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54#63576C2211yescharacteristic
55#63576C2211yescharacteristic
56#63576C2211yescharacteristic
57#63574C2211yescharacteristic
58#63574C2211yescharacteristic
59#63565C2211yescharacteristic
60#63562C2211yescharacteristic
61#5722—31no—
62#5690—31no—
63Q8×Dic6—31no—
64#5539—31no—
65C3×#479—31no—
66C3×#474—31no—
67#5081—31no—
68#5064—31no—
69#5026—31no—
70#5018—31no—
71#4890—31no—
72#4877—31no—
73#4876—31no—
74#4875—31no—
75#4874—31no—
76#4874—31no—
77#4870—31no—
78#4856—31no—
79#4846D311yescharacteristic
80#4829D311yescharacteristic, complemented
81#4828—31no—
82#4828—31no—
83#4828—61no—
84#4817—31no—
85#4796—31no—
86#4793—31no—
87#4788—31no—
88#4761—31no—
89#4759—31no—
90#4758—31no—
91#4757—31no—
92C2×#634D411yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#627—21no—
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C42C2311yescharacteristic
105C4⋊(C3⋊Dic3)D411yescharacteristic
106#3750D411yescharacteristic
107#3750D411yescharacteristic
108C4×C3⋊Dic3C2311yescharacteristic
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×(C2×D3)⋊C4—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3—21no—
124#3724—21no—
125#3724—21no—
126#3724—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133Dic32—21no—
134Dic32—21no—
135#3715Q814yescomplemented
136#3385—91noSylow
137C3×C4⋊Q8—31no—
138C3×#125—31no—
139C3×C4×Q8—31no—
140C3×C4×D4—31no—
141Q8×Dic3—31no—
142Q8×Dic3—31no—
143#944—61no—
144#944—61no—
145C2×#215—31no—
146D4×Dic3—31no—
147D4×Dic3—31no—
148C2×#214—31no—
149#924—61no—
150C2×Dic3⋊C4—61no—
151#897—61no—
152#896—61no—
153#896—61no—
154#893—31no—
155#893—31no—
156D3×C4⋊C4—61no—
157#890—31no—
158#890—31no—
159#888—31no—
160#888—31no—
161#888—31no—
162#888—31no—
163#888—31no—
164#888—31no—
165#888—61no—
166#888—61no—
167#888—61no—
168#887—31no—
169#887—31no—
170#887—61no—
171#878—61no—
172#878—61no—
173C4×D12C2×D311yescharacteristic
174#870C2×D311yescharacteristic
175#869—61no—
176#869C2×D311yescharacteristic
177C4×Dic6—31no—
178C4×Dic6—31no—
179C4×Dic6—61no—
180C4×Dic6—61no—
181C4×Dic6C2×D311yescharacteristic
182C3×#107—31no—
183C3×#107—31no—
184C3×#107—31no—
185C3×#106—31no—
186C3×C4⋊C8—21no—
187C3×C4⋊C8C2×D311yescharacteristic
188C3×C4⋊C8C2×D311yescharacteristic
189C3×#103—31no—
190C3×#103—31no—
191C3×#102—31no—
192C3×#102—31no—
193#835—31no—
194#832—31no—
195#821C2×D311yescharacteristic
196#821C2×D311yescharacteristic
197#818C2×D311yescharacteristic
198#818C2×D311yescharacteristic
199#818C2×D311yescharacteristic
200#817C2×D311yescharacteristic
201#816C2×D311yescharacteristic
202#816C2×D311yescharacteristic
203#815—31no—
204#815—31no—
205#815—61no—
206Dic3⋊C8—31no—
207Dic3⋊C8—31no—
208Dic3⋊C8—31no—
209Dic3⋊C8—31no—
210Dic3⋊C8—61no—
211Dic3⋊C8—61no—
212C8×Dic3—31no—
213C8×Dic3—31no—
214C8×Dic3—61no—
215#810—31no—
216#809—31no—
217#808—31no—
218#808—31no—
219#808—31no—
220#808—31no—
221#807—31no—
222#807—31no—
223#807—31no—
224#807—31no—
225#807—31no—
226#807—31no—
227#803—31no—
228#803—31no—
229#803—61no—
230C22×C3×D3—21no—
231C2×C32×C4C2×D411yescharacteristic
232C2×C32×C4C2×D411yescharacteristic
233C2×C32×C4C2411yescharacteristic
234C2×C3⋊Dic3C2×D411yescharacteristic
235C2×C3⋊Dic3C2×D411yescharacteristic
236C2×C3⋊Dic3C2×D411yescharacteristic
237C2×C3⋊Dic3C2×D411yescharacteristic
238#634—22no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C3×D12—21no—
247C3×D12C2×Q812yes—
248C3×C4×D3—81no—
249C3×Dic6—21no—
250C3×Dic6—81no—
251C3×Dic6C2×Q812yes—
252#627—81no—
253#627—81no—
254#627—81no—
255D3×Dic3—42no—
256D3×Dic3—81no—
257C32×C8—21no—
258C32×C8—21no—
259C3⋊(C3⋊C8)—21no—
260C3⋊(C3⋊C8)C2×Q812yes—
261Q82—91no—
262#554—91no—
263#501—91no—
264#501—91no—
265#500—91no—
266#479—31no—
267#479—91no—
268#477—91no—
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×D4—31no—
279C22×C3×C4—61no—
280C22×Dic3—61no—
281C22×Dic3—61no—
282C2×D12C22×D311yescharacteristic
283C2×C4×D3—21no—
284C2×C4×D3—61no—
285C2×C4×D3—61no—
286C2×Dic6—21no—
287C2×Dic6—31no—
288C2×Dic6—31no—
289C2×Dic6—61no—
290C2×Dic6—61no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6C22×D311yescharacteristic
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8C22×D311yescharacteristic
300C2×C3×C8C22×D311yescharacteristic
301C2×C3×C8C22×D311yescharacteristic
302C2×C3×C8C22×D311yescharacteristic
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
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⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C22⋊C4—61no—
314C3×C42—21no—
315C3×C42—61no—
316C3×C42C22×D311yescharacteristic
317C3×C42C22×D311yescharacteristic
318#217—61no—
319#217—61no—
320#215—34no—
321#214—34no—
322(C2×D3)⋊C4—21no—
323(C2×D3)⋊C4—61no—
324(C2×D3)⋊C4—61no—
325C4⋊Dic3—21no—
326C4⋊Dic3—31no—
327C4⋊Dic3—31no—
328C4⋊Dic3—61no—
329C4⋊Dic3—61no—
330C4⋊Dic3—61no—
331C4⋊Dic3—61no—
332C4⋊Dic3—61no—
333C4⋊Dic3C22×D311yescharacteristic
334C4⋊Dic3C22×D311yescharacteristic
335C4⋊Dic3C22×D311yescharacteristic
336C4⋊Dic3C22×D311yescharacteristic
337C4⋊Dic3C22×D311yescharacteristic
338C4⋊Dic3C22×D311yescharacteristic
339Dic3⋊C4—21no—
340Dic3⋊C4—21no—
341Dic3⋊C4—21no—
342Dic3⋊C4—31no—
343Dic3⋊C4—31no—
344Dic3⋊C4—31no—
345Dic3⋊C4—31no—
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—
358C4×Dic3—21no—
359C4×Dic3—31no—
360C4×Dic3—31no—
361C4×Dic3—31no—
362C4×Dic3—31no—
363C4×Dic3—61no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C2×C3⋊C8—31no—
370C2×C3⋊C8—31no—
371C2×C3⋊C8—31no—
372C2×C3⋊C8—31no—
373C2×C3⋊C8—61no—
374C2×C3⋊C8—61no—
375C22×C32C22×D411yescharacteristic
376C2×C3×D3—22no—
377C2×C3×D3—41no—
378C2×C3×D3—41no—
379C32×C4—21no—
380C32×C4—21no—
381C32×C4C22×Q811yescharacteristic
382C32×C42−1+411yescharacteristic
383C3⋊Dic3—21no—
384C3⋊Dic3—21no—
385C3⋊Dic3—21no—
386C3⋊Dic3#13712yes—
387C3×Dic3—22no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C2×SD16—91no—
395C4⋊Q8—31no—
396C4⋊Q8—91no—
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—31no—
413C4×D4—91no—
414C4×D4—91no—
415C2×C4⋊C4—181no—
416#107—31no—
417#107—31no—
418#107—31no—
419#107—91no—
420#107—91no—
421#107—91no—
422#106—31no—
423#106—91no—
424#106—91no—
425C4⋊C8—91no—
426C4⋊C8—91no—
427C4⋊C8D3211yescharacteristic
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×D4—32no—
443C3×D4—61no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—61no—
448C2×C3×C4—61no—
449C2×C3×C4—61no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—241no—
455C2×C3×C4D3×D411yescharacteristic
456C2×C3×C4D3×D411yescharacteristic
457C2×C3×C4D3×D411yescharacteristic
458C2×C3×C4D3×D411yescharacteristic
459C2×C3×C4C23×D311yescharacteristic
460C2×C3×C4C23×D311yescharacteristic
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—31no—
469C2×Dic3—31no—
470C2×Dic3—31no—
471C2×Dic3—31no—
472C2×Dic3—31no—
473C2×Dic3—31no—
474C2×Dic3—31no—
475C2×Dic3—31no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—122no—
481C2×Dic3—241no—
482D12—21no—
483D12D3×Q812yes—
484C4×D3—81no—
485C4×D3—122no—
486C4×D3—241no—
487Dic6—21no—
488Dic6—62no—
489Dic6—62no—
490Dic6—81no—
491Dic6—122no—
492Dic6—241no—
493Dic6—241no—
494Dic6—241no—
495Dic6—241no—
496Dic6—241no—
497Dic6—241no—
498Dic6D3×Q812yes—
499C3×C8—21no—
500C3×C8—21no—
501C3×C8—21no—
502C3×C8—21no—
503C3×C8—41no—
504C3×C8—41no—
505C3⋊C8—32no—
506C3⋊C8—32no—
507C3⋊C8—62no—
508C3⋊C8—61no—
509C3⋊C8—61no—
510C3⋊C8—121no—
511C2×C32D4×Q811yescharacteristic
512C2×C32C2×#13711yescharacteristic
513C2×C32#57611yescharacteristic
514C3×D3—42no—
515C2×Q8—31no—
516C2×Q8—61no—
517C2×Q8—91no—
518C2×Q8—181no—
519C2×Q8—181no—
520C2×Q8—181no—
521C2×D4—31no—
522C22×C4—61no—
523C22×C4—181no—
524C22×C4—181no—
525SD16—94no—
526C2×C8—91no—
527C2×C8—91no—
528C2×C8C2×D3211yescharacteristic
529C2×C8C2×D3211yescharacteristic
530C4⋊C4—31no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—31no—
534C4⋊C4—31no—
535C4⋊C4—31no—
536C4⋊C4—61no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—61no—
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—
550C22⋊C4—61no—
551C22⋊C4—181no—
552C22⋊C4—181no—
553C42—61no—
554C42—91no—
555C42—91no—
556C42—181no—
557C42—181no—
558C42C2×D3211yescharacteristic
559C22×C3—21no—
560C22×C3—62no—
561C22×C3—121no—
562C22×C3—121no—
563C22×C3C2×D3×D411yescharacteristic
564C22×C3C2×D3×D411yescharacteristic
565C2×D3—22no—
566C2×D3—41no—
567C2×D3—41no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—21no—
572C3×C4—21no—
573C3×C4—21no—
574C3×C4—41no—
575C3×C4—41no—
576C3×C4—62no—
577C3×C4—121no—
578C3×C4—121no—
579C3×C4—121no—
580C3×C4—121no—
581C3×C4—121no—
582C3×C4—121no—
583C3×C4C2×D3×Q811yescharacteristic
584C3×C4C2×D3×Q811yescharacteristic
585C3×C4#101011yescharacteristic
586C3×C4#101011yescharacteristic
587Dic3—22no—
588Dic3—32no—
589Dic3—32no—
590Dic3—41no—
591Dic3—41no—
592Dic3—41no—
593Dic3—41no—
594Dic3—41no—
595Dic3—41no—
596Dic3—62no—
597Dic3—61no—
598Dic3—61no—
599Dic3—61no—
600Dic3—61no—
601Dic3—61no—
602Dic3—61no—
603Dic3—121no—
604Dic3—121no—
605Dic3—121no—
606C32#338511yescharacteristic, complemented, Sylow
607C23—61no—
608Q8—32no—
609Q8—61no—
610Q8—182no—
611Q8—241no—
612Q8—721no—
613Q8—721no—
614Q8—721no—
615D4—32no—
616D4—61no—
617C2×C4—61no—
618C2×C4—61no—
619C2×C4—61no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—91no—
625C2×C4—91no—
626C2×C4—91no—
627C2×C4—91no—
628C2×C4—241no—
629C2×C4—362no—
630C2×C4—721no—
631C2×C4#380211yescharacteristic
632C2×C4#380211yescharacteristic
633C2×C4C22×D3211yescharacteristic
634C8—21no—
635C8—21no—
636C8—92no—
637C8—181no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—122no—
642C2×C3#563211yescharacteristic
643C2×C3#563211yescharacteristic
644C2×C3#575711yescharacteristic
645C2×C3#576911yescharacteristic
646C2×C3D3×#13711yescharacteristic
647C2×C3D3×#13711yescharacteristic
648D3—42no—
649C22—62no—
650C22—121no—
651C22—121no—
652C22C2×#380211yescharacteristic
653C4—21no—
654C4—21no—
655C4—62no—
656C4—92no—
657C4—121no—
658C4—121no—
659C4—121no—
660C4—121no—
661C4—121no—
662C4—121no—
663C4—181no—
664C4—181no—
665C4—181no—
666C4#6430911yescharacteristic
667C4D32×Q811yescharacteristic
668C3—21no—
669C3#8096011yescharacteristic, complemented
670C3#8122311yescharacteristic, complemented
671C2—122no—
672C2#1059452611yescharacteristic
673C2#1059468711yescharacteristic
674C2#1059471711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenterC4⋊C8D32
hypocenterC32#3385
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593856C2semidirect
3. #10592527C2semidirect
5. C3×#4829C2semidirect
6. #10590903C2semidirect
7. #10590902C2semidirect
8. #10590821C2semidirect
9. #10590817C2semidirect
15. #10590315C2semidirect
80. #4829D3semidirect
135. #3715Q8semidirect
606. C32#3385semidirect
669. C3#80960semidirect
670. C3#81223semidirect

Maximal subgroups

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

subgroupindex
#105939412
#105938562
#105925272
C3×#48462
C3×#48292
#105909032
#105909022
#105908212
#105908172
#105907782
#105907762
#105907432
#105907422
#105903582
#105903152
#812233
#809603