Finite Group Databasebeta

← #11872524

Subgroups — #11872524

Order 1152.

798 conjugacy classes of subgroups.

The subgroup lattice has 725 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595348C211yesmaximal, characteristic, complemented
2#10594359C211yesmaximal, characteristic
3#10592494C211yesmaximal, characteristic, complemented
4C3×#4817C211yesmaximal, characteristic, complemented
5C3×#4805C211yesmaximal, characteristic, complemented
6#10591655C211yesmaximal, characteristic
7#10591569C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10590969C211yesmaximal, characteristic
10#10590810C211yesmaximal, characteristic, complemented
11#10590782C211yesmaximal, characteristic, complemented
12#10590697C211yesmaximal, characteristic, complemented
13#10590479C211yesmaximal, characteristic, complemented
14#10590434C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#81416—31nomaximal
17#79786—31nomaximal
18C2×#3795C2211yescharacteristic
19#64153C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21C2×#3746C2211yescharacteristic
22#64096C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28C4×#625—21no—
29#63898C2211yescharacteristic
30#63879—21no—
31#63878—21no—
32D3×Dic3⋊C4—21no—
33#63872C2211yescharacteristic
34#63867—21no—
35#63859—21no—
36#63858—21no—
37#63857C2211yescharacteristic
38#63855C2211yescharacteristic
39#63846—21no—
40#63844C2211yescharacteristic
41#63844C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C32×#103C2211yescharacteristic
44#63641C2211yescharacteristic
45#63637C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63572C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5625—31no—
62#5583—31no—
63#5546—31no—
64#5504—31no—
65C3×#483—31no—
66C3×#440—31no—
67#5173—31no—
68#5162—31no—
69#5047—31no—
70C4×#216—31no—
71C4×#214—31no—
72#4970—31no—
73#4884—31no—
74#4877—31no—
75#4871—31no—
76#4857—31no—
77#4853—31no—
78#4852—31no—
79#4818—31no—
80#4817D311yescharacteristic, complemented
81#4805D311yescharacteristic, complemented
82#4795—31no—
83#4795—31no—
84#4795—61no—
85#4790—31no—
86#4783—31no—
87#4763—31no—
88#4733—31no—
89#4720—31no—
90#4716—31no—
91#4709—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×#625—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102#3795—22no—
103#3795—22no—
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106#3756—22no—
107#3750—21no—
108#3750—21no—
109#3750—21no—
110C4×C3⋊Dic3—21no—
111C4×C3⋊Dic3C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113#3746—22no—
114C3×#215—22no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3D411yescharacteristic
138Dic32—21no—
139Dic32—21no—
140#3716—22no—
141#3120—91noSylow
142C2×#237—31no—
143C2×#235—31no—
144C2×C3×SD16—31no—
145C3×C22⋊Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×D4—31no—
148C2×C3×C4⋊C4—31no—
149#946C2×D311yescharacteristic
150Q8×Dic3C2×D311yescharacteristic
151#944—31no—
152#944—31no—
153#944—61no—
154C2×#216—31no—
155C2×#216—31no—
156C2×#216—61no—
157C2×#215C2×D311yescharacteristic
158D4×Dic3—31no—
159C2×#214—31no—
160C4×#67—61no—
161C4×#67—61no—
162C4×#67—61no—
163#926—31no—
164#924—31no—
165C2×Dic3⋊C4—61no—
166C2×Dic12—31no—
167C2×Dic12—31no—
168C2×Dic12—61no—
169C2×#204—31no—
170#898—61no—
171#897—31no—
172#893—31no—
173#893C2×D311yescharacteristic
174#892—61no—
175D3×C4⋊C4—61no—
176D3×C4⋊C4C2×D311yescharacteristic
177#890—31no—
178#890—31no—
179#890—61no—
180#889—61no—
181#889—61no—
182#887—31no—
183#887—31no—
184#887—31no—
185#887—31no—
186#887—61no—
187#67⋊C4—61no—
188#879—61no—
189#879—61no—
190#877—61no—
191#876—61no—
192#872—31no—
193#870—61no—
194C4×Dic6—31no—
195C4×Dic6—31no—
196C3×#107—31no—
197C3×#106—31no—
198C3×#106—31no—
199C3×#103—21no—
200C3×#103—31no—
201C3×#103C2×D311yescharacteristic
202C3×#103C2×D311yescharacteristic
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×#97—31no—
206#835C2×D311yescharacteristic
207#832—31no—
208#830—31no—
209#821C2×D311yescharacteristic
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8C2×D311yescharacteristic
212#817C2×D311yescharacteristic
213#816—31no—
214#816—31no—
215#816—31no—
216#815C2×D311yescharacteristic
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—61no—
222C8×Dic3—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#809—31no—
230#808C2×D311yescharacteristic
231#807—31no—
232#807—31no—
233#807C2×D311yescharacteristic
234C4×C3⋊C8—31no—
235C22×C3×D3—21no—
236C22×C3×D3C2×D411yescharacteristic
237C32×Q8—21no—
238C32×Q8—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2411yescharacteristic
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3C2×D411yescharacteristic
245C2×C3⋊Dic3C2×D411yescharacteristic
246#634—21no—
247#634—21no—
248#634—21no—
249#634#4112yes—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12#4112yes—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—81no—
261C3×C4×D3—81no—
262#625—24no—
263D3×Dic3—24no—
264D3×Dic3—81no—
265C32×C8—21no—
266C3⋊(C3⋊C8)—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#541—91no—
270#520—91no—
271#484—91no—
272#483—31no—
273#479—91no—
274#478—91no—
275#462—91no—
276#461—91no—
277#452—91no—
278#452—91no—
279#441—91no—
280#440—31no—
281C4×Q16—91no—
282C4×SD16—91no—
283#433—91no—
284C2×C3×Q8—21no—
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×D4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—61no—
290C22×C3×C4—61no—
291C2×#67—61no—
292C2×#67—61no—
293C22×Dic3—61no—
294C22×Dic3—61no—
295#237—62no—
296#237—62no—
297#235—62no—
298#235—62no—
299C2×D12C22×D311yescharacteristic
300C2×C4×D3—21no—
301C2×C4×D3—21no—
302C2×C4×D3—61no—
303C2×C4×D3—61no—
304C2×C4×D3C22×D311yescharacteristic
305C2×Dic6—31no—
306C2×Dic6—31no—
307C2×Dic6—31no—
308C2×Dic6—31no—
309C2×Dic6—61no—
310C2×Dic6—61no—
311C3×SD16—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—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C42—31no—
329C3×C42—61no—
330#217—31no—
331#217—31no—
332#217—61no—
333#217—61no—
334#216—62no—
335#216—62no—
336#216—122no—
337#215—22no—
338#214—62no—
339(C2×D3)⋊C4—21no—
340(C2×D3)⋊C4—21no—
341(C2×D3)⋊C4—31no—
342(C2×D3)⋊C4—31no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345C4⋊Dic3—21no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3C22×D311yescharacteristic
352C4⋊Dic3C22×D311yescharacteristic
353C4⋊Dic3C22×D311yescharacteristic
354Dic3⋊C4—21no—
355Dic3⋊C4—21no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—121no—
372Dic3⋊C4—121no—
373Dic3⋊C4—121no—
374C4×Dic3—21no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—121no—
385C4×Dic3C22×D311yescharacteristic
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8C22×D311yescharacteristic
390C2×C3⋊C8C22×D311yescharacteristic
391Dic12—62no—
392Dic12—62no—
393Dic12—122no—
394#204—62no—
395C22×C32C22×D411yescharacteristic
396C2×C3×D3—22no—
397C2×C3×D3—21no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—41no—
401C2×C3×D3—41no—
402C32×C4—41no—
403C32×C4—41no—
404C32×C4C2×#4111yescharacteristic
405C32×C4C2×#4111yescharacteristic
406C3⋊Dic3—21no—
407C3⋊Dic3—22no—
408C3⋊Dic3—21no—
409C3⋊Dic3—41no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C2×#41—91no—
417C2×Q16—91no—
418C2×Q16—91no—
419C2×SD16—31no—
420C2×SD16—91no—
421C4⋊Q8—91no—
422#126—181no—
423#126—181no—
424#125—91no—
425#125—181no—
426#125—181no—
427C22⋊Q8—31no—
428C22⋊Q8—91no—
429C4×Q8—31no—
430C4×Q8—91no—
431C4×Q8—91no—
432C4×Q8—91no—
433C4×D4—31no—
434C4×D4—91no—
435C4×D4—181no—
436C4×D4—181no—
437#117—91no—
438#117—181no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—181no—
441#107—31no—
442#107—91no—
443#106—31no—
444#106—31no—
445C4⋊C8—91no—
446C4⋊C8—91no—
447#103—31no—
448#103—91no—
449#103—91no—
450#103—91no—
451#103—91no—
452#103D3211yescharacteristic
453#102—31no—
454#102—91no—
455C22⋊C8—31no—
456C22⋊C8—91no—
457#97—31no—
458C4×C8—91no—
459C23×C3—31no—
460C23×C3—61no—
461C22×D3—21no—
462C22×D3D3×D411yescharacteristic
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—21no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×D4—32no—
470C3×D4—61no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—241no—
487C2×C3×C4—241no—
488C2×C3×C4C23×D311yescharacteristic
489C2×C3×C4C23×D311yescharacteristic
490#67—64no—
491#67—64no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—64no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—121no—
507C2×Dic3—121no—
508C2×Dic3—241no—
509C2×Dic3D3×D411yescharacteristic
510C2×Dic3D3×D411yescharacteristic
511C2×Dic3D3×D411yescharacteristic
512D12—21no—
513D12#23512yes—
514C4×D3—21no—
515C4×D3—21no—
516C4×D3—64no—
517C4×D3—81no—
518C4×D3—81no—
519C4×D3—241no—
520Dic6—32no—
521Dic6—32no—
522Dic6—62no—
523Dic6—61no—
524Dic6—61no—
525Dic6—61no—
526Dic6—61no—
527Dic6—61no—
528Dic6—61no—
529Dic6—121no—
530Dic6—121no—
531Dic6—121no—
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—41no—
535C3×C8—61no—
536C3×C8—61no—
537C3⋊C8—21no—
538C3⋊C8—21no—
539C3⋊C8—61no—
540C3⋊C8—61no—
541C3⋊C8—121no—
542C2×C32#52511yescharacteristic
543C2×C32#57711yescharacteristic
544C2×C32#57811yescharacteristic
545C3×D3—41no—
546C3×D3—42no—
547#41—182no—
548#41—182no—
549C2×Q8—91no—
550C2×Q8—91no—
551C2×Q8C2×D3211yescharacteristic
552C2×D4—31no—
553C2×D4—181no—
554C22×C4—31no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—181no—
558C22×C4—181no—
559Q16—182no—
560Q16—182no—
561SD16—62no—
562SD16—182no—
563C2×C8—31no—
564C2×C8—31no—
565C2×C8—91no—
566C2×C8C2×D3211yescharacteristic
567C4⋊C4—31no—
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—91no—
574C4⋊C4—91no—
575C4⋊C4—181no—
576C4⋊C4—181no—
577C4⋊C4—181no—
578C4⋊C4—181no—
579C4⋊C4—181no—
580C4⋊C4—181no—
581C4⋊C4—181no—
582C4⋊C4—181no—
583C4⋊C4C2×D3211yescharacteristic
584C22⋊C4—61no—
585C22⋊C4—61no—
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—181no—
589C22⋊C4—181no—
590C42—31no—
591C42—61no—
592C42—91no—
593C42—181no—
594C42—181no—
595C42—181no—
596C22×C3—21no—
597C22×C3—62no—
598C22×C3—61no—
599C22×C3—61no—
600C22×C3—61no—
601C22×C3—121no—
602C22×C3—121no—
603C22×C3C2×D3×D411yescharacteristic
604C22×C3C2×D3×D411yescharacteristic
605C2×D3—21no—
606C2×D3—21no—
607C2×D3—21no—
608C2×D3—22no—
609C2×D3—41no—
610C2×D3—41no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—61no—
620C3×C4—81no—
621C3×C4—81no—
622C3×C4—121no—
623C3×C4—121no—
624C3×C4—121no—
625C3×C4C2×#23511yescharacteristic
626C3×C4D3×#4111yescharacteristic
627C3×C4D3×#4111yescharacteristic
628C3×C4D3×#4111yescharacteristic
629Dic3—21no—
630Dic3—21no—
631Dic3—21no—
632Dic3—41no—
633Dic3—41no—
634Dic3—41no—
635Dic3—62no—
636Dic3—62no—
637Dic3—61no—
638Dic3—61no—
639Dic3—61no—
640Dic3—61no—
641Dic3—62no—
642Dic3—122no—
643Dic3—121no—
644Dic3—121no—
645Dic3—121no—
646Dic3—241no—
647C32#312011yescharacteristic, complemented, Sylow
648C23—31no—
649C23—61no—
650Q8—21no—
651Q8—21no—
652Q8—92no—
653Q8—181no—
654Q8—181no—
655Q8—181no—
656D4—32no—
657D4—61no—
658D4—184no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—91no—
670C2×C4—91no—
671C2×C4—184no—
672C2×C4—181no—
673C2×C4—181no—
674C2×C4—241no—
675C2×C4—241no—
676C2×C4—721no—
677C2×C4C22×D3211yescharacteristic
678C8—21no—
679C8—61no—
680C8—61no—
681C8—181no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—122no—
686C2×C3—121no—
687C2×C3#554711yescharacteristic
688C2×C3#565611yescharacteristic
689C2×C3#576211yescharacteristic
690C2×C3#577511yescharacteristic
691C2×C3#577911yescharacteristic
692C2×C3#577911yescharacteristic
693D3—41no—
694D3—42no—
695C22—61no—
696C22—61no—
697C22—61no—
698C22—62no—
699C22—121no—
700C22—121no—
701C22D32×D411yescharacteristic
702C4—41no—
703C4—41no—
704C4—61no—
705C4—61no—
706C4—61no—
707C4—121no—
708C4—121no—
709C4—121no—
710C4—181no—
711C4—181no—
712C4—182no—
713C4—361no—
714C4D3×#23511yescharacteristic
715C4#6431211yescharacteristic
716C3—21no—
717C3#7978611yescharacteristic, complemented
718C3#8141611yescharacteristic, complemented
719C2—121no—
720C2—122no—
721C2#1059426611yescharacteristic
722C2#1059474911yescharacteristic
723C2#1059476911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3795C22
hypercenter#103D32
hypocenterC32#3120
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595348C2semidirect
3. #10592494C2semidirect
4. C3×#4817C2semidirect
5. C3×#4805C2semidirect
7. #10591569C2semidirect
8. #10591537C2semidirect
10. #10590810C2semidirect
11. #10590782C2semidirect
12. #10590697C2semidirect
13. #10590479C2semidirect
14. #10590434C2semidirect
15. #10590427C2semidirect
80. #4817D3semidirect
81. #4805D3semidirect
647. C32#3120semidirect
717. C3#79786semidirect
718. C3#81416semidirect

Maximal subgroups

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

subgroupindex
#105953482
#105943592
#105924942
C3×#48172
C3×#48052
#105916552
#105915692
#105915372
#105909692
#105908102
#105907822
#105906972
#105904792
#105904342
#105904272
#814163
#797863