Finite Group Databasebeta

← #11895377

Subgroups — #11895377

Order 1152.

772 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594582C211yesmaximal, characteristic, complemented
2#10594485C211yesmaximal, characteristic, complemented
3#10592574C211yesmaximal, characteristic, complemented
4C3×#4891C211yesmaximal, characteristic, complemented
5C3×#4872C211yesmaximal, characteristic, complemented
6#10590863C211yesmaximal, characteristic, complemented
7#10590755C211yesmaximal, characteristic, complemented
8#10590749C211yesmaximal, characteristic
9#10590644C211yesmaximal, characteristic, complemented
10#10590552C211yesmaximal, characteristic, complemented
11#10590545C211yesmaximal, characteristic, complemented
12#10590533C211yesmaximal, characteristic, complemented
13#10590530C211yesmaximal, characteristic, complemented
14#10590460C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#81150—31nomaximal
17#79569—31nomaximal
18#64097C2211yescharacteristic
19#64096C2211yescharacteristic
20C2×C3×D24C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#890C2211yescharacteristic
25C4×#627C2211yescharacteristic
26#63915—21no—
27#63914C2211yescharacteristic
28#63905—21no—
29#63905—21no—
30C4×#625—21no—
31#63899—21no—
32#63898C2211yescharacteristic
33#63896—21no—
34Dic3×D12C2211yescharacteristic
35D3×Dic3⋊C4—21no—
36#63869C2211yescharacteristic
37#63860C2211yescharacteristic
38#63860C2211yescharacteristic
39#63857—21no—
40C2×#3716C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C32×#107C2211yescharacteristic
43#63643C2211yescharacteristic
44#63641C2211yescharacteristic
45#63637C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5690—31no—
62#5559—31no—
63#5559—31no—
64#5539—31no—
65C3×#478—31no—
66C3×C4×D8—31no—
67#5153—31no—
68#5150—31no—
69#5068—31no—
70#5016—31no—
71C4×#213—31no—
72#5009—31no—
73#4891D311yescharacteristic, complemented
74#4875—31no—
75#4875—31no—
76#4875—61no—
77#4872D311yescharacteristic, complemented
78#4871—31no—
79#4852—31no—
80#4844—31no—
81#4830—31no—
82#4787—31no—
83#4786—31no—
84#4768—31no—
85#4768—31no—
86#4760—31no—
87#4760—31no—
88#4758—31no—
89#4756—31no—
90#4697—31no—
91C8×Dic6—31no—
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×#627D411yescharacteristic
101C2×#625—21no—
102C2×#625—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110#3750—21no—
111C4×C3⋊Dic3—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C3×D24—22no—
125#3724—21no—
126#3724D411yescharacteristic
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136#3716—22no—
137#3713—22no—
138#3361—91noSylow
139C2×C3×D8—31no—
140C3×#125—31no—
141C3×C4×D4—31no—
142C3×C4×D4—31no—
143C3×C4×D4—31no—
144#940—31no—
145#940—31no—
146#936—31no—
147#936—31no—
148D4×Dic3—31no—
149D4×Dic3—31no—
150C2×#214—31no—
151C2×#213—31no—
152C2×#213—31no—
153#929—61no—
154#929—61no—
155C4×#67—61no—
156C4×#67—61no—
157#924—61no—
158C2×Dic3⋊C4—61no—
159C2×D24C2×D311yescharacteristic
160C2×#204—31no—
161#897—61no—
162#896—61no—
163#896—61no—
164#893—31no—
165#893C2×D311yescharacteristic
166#893C2×D311yescharacteristic
167#893C2×D311yescharacteristic
168D3×C4⋊C4—61no—
169#890—31no—
170#890C2×D311yescharacteristic
171#888—31no—
172#888—31no—
173#888—61no—
174#887—31no—
175#887—31no—
176#887—61no—
177#885—61no—
178#885—61no—
179#883—61no—
180#883—61no—
181#878—61no—
182#878—61no—
183#875—31no—
184#875—31no—
185C4×D12—31no—
186#870—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C3×#107—21no—
190C3×#107C2×D311yescharacteristic
191C3×#107C2×D311yescharacteristic
192C3×#106—31no—
193C3×C4⋊C8—31no—
194C3×#102—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#821—31no—
203#821—31no—
204#821C2×D311yescharacteristic
205#816—31no—
206#816—31no—
207#816—31no—
208#816—61no—
209Dic3⋊C8—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—61no—
213Dic3⋊C8C2×D311yescharacteristic
214C8×Dic3—31no—
215C8×Dic3—31no—
216C8×Dic3—31no—
217C8×Dic3C2×D311yescharacteristic
218#810—31no—
219#810—31no—
220#810—31no—
221#810—61no—
222#809—31no—
223#809C2×D311yescharacteristic
224#809C2×D311yescharacteristic
225#809C2×D311yescharacteristic
226#808C2×D311yescharacteristic
227#807—31no—
228#807—31no—
229#807—61no—
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242#634—21no—
243#634—21no—
244#634—81no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C3×D12—21no—
251C3×D12—21no—
252C3×D12—21no—
253C3×D12—21no—
254C3×D12—21no—
255C3×D12#4112yes—
256C3×C4×D3—81no—
257C3×C4×D3—81no—
258C3×C4×D3—81no—
259#627—22no—
260#625—42no—
261#625—81no—
262D3×Dic3—42no—
263D3×Dic3—81no—
264C32×C8—21no—
265C3⋊(C3⋊C8)—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268#559—91no—
269#554—91no—
270#488—91no—
271#488—91no—
272#486—91no—
273#478—31no—
274#478—91no—
275#477—91no—
276#463—91no—
277#463—91no—
278#459—91no—
279C8×Q8—91no—
280C4×SD16—91no—
281C4×D8—31no—
282C4×D8—91no—
283C2×C3×D4—31no—
284C2×C3×D4—31no—
285C2×C3×D4—31no—
286C22×C3×C4—61no—
287C22×C3×C4—61no—
288C22×C3×C4—61no—
289C2×#67—61no—
290C2×#67—61no—
291C2×#67—61no—
292C2×#67—61no—
293C22×Dic3—61no—
294C22×Dic3—61no—
295C2×D12C22×D311yescharacteristic
296C2×D12C22×D311yescharacteristic
297C2×D12C22×D311yescharacteristic
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—61no—
302C2×C4×D3—61no—
303C2×Dic6—31no—
304C2×Dic6—31no—
305C2×Dic6—31no—
306C2×Dic6—31no—
307C2×Dic6—61no—
308C2×Dic6—61no—
309C2×Dic6—61no—
310C2×Dic6—121no—
311C3×D8—62no—
312C2×C3×C8—21no—
313C2×C3×C8—31no—
314C2×C3×C8—31no—
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C22×D311yescharacteristic
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C22⋊C4—61no—
329C3×C42—31no—
330C3×C42—31no—
331#217—61no—
332#217—61no—
333#217—61no—
334#217—61no—
335#217—61no—
336#217—61no—
337#214—62no—
338#213—62no—
339#213—62no—
340(C2×D3)⋊C4—21no—
341(C2×D3)⋊C4—21no—
342(C2×D3)⋊C4—21no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349C4⋊Dic3—21no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3C22×D311yescharacteristic
357Dic3⋊C4—21no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—121no—
370Dic3⋊C4—121no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—121no—
377C4×Dic3C22×D311yescharacteristic
378C4×Dic3C22×D311yescharacteristic
379C2×C3⋊C8—31no—
380C2×C3⋊C8—31no—
381C2×C3⋊C8—61no—
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384D24—22no—
385#204—62no—
386C22×C32C22×D411yescharacteristic
387C2×C3×D3—22no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C2×C3×D3—41no—
396C32×C4—41no—
397C32×C4—41no—
398C32×C4C2×#4111yescharacteristic
399C32×C42−1+411yescharacteristic
400C3⋊Dic3—21no—
401C3⋊Dic3—41no—
402C3⋊Dic3—41no—
403C3⋊Dic3#13512yes—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—21no—
408C3×Dic3—41no—
409C2×SD16—91no—
410C2×D8—31no—
411C2×D8—91no—
412C4⋊Q8—91no—
413#127—91no—
414#125—31no—
415#125—91no—
416#124—91no—
417#124—91no—
418#124—181no—
419#123—181no—
420#123—181no—
421C22⋊Q8—181no—
422C22⋊Q8—181no—
423C22⋊Q8—181no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×D4—31no—
427C4×D4—31no—
428C4×D4—31no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—181no—
432C2×C4⋊C4—181no—
433#107—91no—
434#107D3211yescharacteristic
435#106—31no—
436C4⋊C8—31no—
437C4⋊C8—91no—
438C4⋊C8—91no—
439#103—91no—
440#103—91no—
441#103—91no—
442#102—31no—
443#102—31no—
444#102—31no—
445#102—31no—
446#102—91no—
447#102—91no—
448#102—91no—
449C4×C8—31no—
450C4×C8—91no—
451C4×C8—91no—
452C23×C3—61no—
453C23×C3—61no—
454C23×C3—61no—
455C22×D3—21no—
456C22×D3—21no—
457C22×D3—21no—
458C3×D4—32no—
459C3×D4—61no—
460C3×D4—61no—
461C3×D4—61no—
462C3×D4—61no—
463C3×D4—61no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—61no—
476C2×C3×C4—241no—
477C2×C3×C4—241no—
478C2×C3×C4—241no—
479C2×C3×C4C23×D311yescharacteristic
480C2×C3×C4C23×D311yescharacteristic
481#67—122no—
482#67—122no—
483#67—241no—
484#67—241no—
485C2×Dic3—21no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—121no—
497C2×Dic3—121no—
498C2×Dic3—122no—
499C2×Dic3—241no—
500C2×Dic3D3×D411yescharacteristic
501C2×Dic3D3×D411yescharacteristic
502C2×Dic3D3×D411yescharacteristic
503C2×Dic3D3×D411yescharacteristic
504D12—21no—
505D12—21no—
506D12—21no—
507D12—21no—
508D12—21no—
509D12#23512yes—
510C4×D3—81no—
511C4×D3—81no—
512C4×D3—81no—
513C4×D3—122no—
514C4×D3—241no—
515Dic6—62no—
516Dic6—62no—
517Dic6—62no—
518Dic6—61no—
519Dic6—61no—
520Dic6—61no—
521Dic6—61no—
522Dic6—121no—
523Dic6—241no—
524Dic6—241no—
525Dic6—242no—
526C3×C8—21no—
527C3×C8—21no—
528C3×C8—41no—
529C3×C8—61no—
530C3×C8—61no—
531C3⋊C8—21no—
532C3⋊C8—21no—
533C3⋊C8—61no—
534C3⋊C8—61no—
535C3⋊C8—121no—
536C2×C32#54811yescharacteristic
537C2×C32C2×#13511yescharacteristic
538C2×C32#57611yescharacteristic
539C3×D3—42no—
540C3×D3—81no—
541C3×D3—81no—
542C2×Q8—91no—
543C2×Q8—91no—
544C2×Q8—181no—
545C2×D4—31no—
546C2×D4—31no—
547C2×D4—31no—
548C2×D4—181no—
549C2×D4—181no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—181no—
554C22×C4—181no—
555SD16—182no—
556D8—62no—
557D8—182no—
558C2×C8—31no—
559C2×C8—31no—
560C2×C8—91no—
561C2×C8C2×D3211yescharacteristic
562C4⋊C4—31no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4C2×D3211yescharacteristic
574C4⋊C4C2×D3211yescharacteristic
575C22⋊C4—61no—
576C22⋊C4—61no—
577C22⋊C4—61no—
578C22⋊C4—181no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C22⋊C4—181no—
582C22⋊C4—181no—
583C22⋊C4—181no—
584C42—31no—
585C42—31no—
586C42—91no—
587C42—181no—
588C22×C3—21no—
589C22×C3—62no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3—121no—
593C22×C3—121no—
594C22×C3—121no—
595C22×C3—121no—
596C22×C3—121no—
597C22×C3—121no—
598C22×C3C2×D3×D411yescharacteristic
599C22×C3C2×D3×D411yescharacteristic
600C2×D3—22no—
601C2×D3—41no—
602C2×D3—41no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—41no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—41no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—61no—
616C3×C4—61no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—81no—
620C3×C4—81no—
621C3×C4—121no—
622C3×C4C2×#23511yescharacteristic
623C3×C4#100711yescharacteristic
624C3×C4D3×#4111yescharacteristic
625C3×C4#101011yescharacteristic
626Dic3—21no—
627Dic3—21no—
628Dic3—21no—
629Dic3—21no—
630Dic3—32no—
631Dic3—32no—
632Dic3—41no—
633Dic3—62no—
634Dic3—61no—
635Dic3—61no—
636Dic3—121no—
637Dic3—122no—
638Dic3—121no—
639Dic3—121no—
640Dic3—121no—
641Dic3—121no—
642Dic3—241no—
643C32#336111yescharacteristic, complemented, Sylow
644C23—61no—
645C23—61no—
646C23—61no—
647Q8—182no—
648Q8—181no—
649Q8—181no—
650Q8—721no—
651D4—32no—
652D4—61no—
653D4—61no—
654D4—61no—
655D4—61no—
656D4—61no—
657D4—362no—
658D4—721no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—31no—
665C2×C4—61no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—241no—
671C2×C4—241no—
672C2×C4—241no—
673C2×C4—362no—
674C2×C4—721no—
675C2×C4C22×D3211yescharacteristic
676C8—21no—
677C8—61no—
678C8—61no—
679C8—181no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—122no—
684C2×C3—241no—
685C2×C3—241no—
686C2×C3#555211yescharacteristic
687C2×C3#563311yescharacteristic
688C2×C3#575711yescharacteristic
689C2×C3D3×#13511yescharacteristic
690C2×C3D3×#13511yescharacteristic
691C2×C3#577411yescharacteristic
692D3—42no—
693D3—81no—
694D3—81no—
695C22—62no—
696C22—121no—
697C22—121no—
698C22—121no—
699C22—121no—
700C22—121no—
701C22—121no—
702C22—121no—
703C22—121no—
704C22D32×D411yescharacteristic
705C4—41no—
706C4—41no—
707C4—61no—
708C4—61no—
709C4—61no—
710C4—61no—
711C4—92no—
712C4—121no—
713C4—181no—
714C4—361no—
715C4—361no—
716C4D3×#23511yescharacteristic
717C4#6431511yescharacteristic
718C3—21no—
719C3#7956911yescharacteristic, complemented
720C3#8115011yescharacteristic, complemented
721C2—122no—
722C2—241no—
723C2—241no—
724C2#1059437511yescharacteristic
725C2#1059473211yescharacteristic
726C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#10590749C2
hypercenter#107D32
hypocenterC32#3361
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
1. #10594582C2semidirect
2. #10594485C2semidirect
3. #10592574C2semidirect
4. C3×#4891C2semidirect
5. C3×#4872C2semidirect
6. #10590863C2semidirect
7. #10590755C2semidirect
9. #10590644C2semidirect
10. #10590552C2semidirect
11. #10590545C2semidirect
12. #10590533C2semidirect
13. #10590530C2semidirect
14. #10590460C2semidirect
15. #10590452C2semidirect
73. #4891D3semidirect
77. #4872D3semidirect
643. C32#3361semidirect
719. C3#79569semidirect
720. C3#81150semidirect

Maximal subgroups

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

subgroupindex
#105945822
#105944852
#105925742
C3×#48912
C3×#48722
#105908632
#105907552
#105907492
#105906442
#105905522
#105905452
#105905332
#105905302
#105904602
#105904522
#811503
#795693