Finite Group Databasebeta

← #11872515

Subgroups — #11872515

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 719 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594359C211yesmaximal, characteristic
2#10594345C211yesmaximal, characteristic, complemented
3#10592576C211yesmaximal, characteristic, complemented
4C3×#4889C211yesmaximal, characteristic, complemented
5C3×#4884C211yesmaximal, characteristic, complemented
6#10590960C211yesmaximal, characteristic
7#10590794C211yesmaximal, characteristic, complemented
8#10590748C211yesmaximal, characteristic, complemented
9#10590697C211yesmaximal, characteristic, complemented
10#10590614C211yesmaximal, characteristic
11#10590566C211yesmaximal, characteristic, complemented
12#10590516C211yesmaximal, characteristic, complemented
13#10590481C211yesmaximal, characteristic, complemented
14#10590475C211yesmaximal, characteristic, complemented
15#10590473C211yesmaximal, characteristic, complemented
16#81456—31nomaximal
17#79786—31nomaximal
18C2×#3795C2211yescharacteristic
19#64099C2211yescharacteristic
20#64096C2211yescharacteristic
21C2×C3×#204C2211yescharacteristic
22C3×#897C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×D3×C4⋊C4C2211yescharacteristic
25C3×#887C2211yescharacteristic
26C4×#625—21no—
27#63898C2211yescharacteristic
28#63879—21no—
29#63878—21no—
30D3×Dic3⋊C4—21no—
31#63873C2211yescharacteristic
32#63869—21no—
33#63861—21no—
34#63859—21no—
35#63856C2211yescharacteristic
36#63855C2211yescharacteristic
37#63847—21no—
38#63844C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40C2×#3719C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C32×#107C2211yescharacteristic
44#63643C2211yescharacteristic
45#63641C2211yescharacteristic
46#63637C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5625—31no—
62#5583—31no—
63#5546—31no—
64#5504—31no—
65C3×#484—31no—
66C3×#440—31no—
67#5173—31no—
68#5162—31no—
69#5047—31no—
70C4×#216—31no—
71C4×#214—31no—
72#4971—31no—
73#4891—31no—
74#4889D311yescharacteristic, complemented
75#4884D311yescharacteristic, complemented
76#4877—31no—
77#4877—31no—
78#4877—61no—
79#4873—31no—
80#4818—31no—
81#4805—31no—
82#4795—31no—
83#4795—31no—
84#4789—31no—
85#4788—31no—
86#4783—31no—
87#4763—31no—
88#4733—31no—
89#4720—31no—
90#4716—31no—
91#4709—31no—
92C2×#634C2311yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#625—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102#3795—22no—
103#3795—22no—
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C4⋊(C3⋊Dic3)—21no—
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×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C3×#204—22no—
125#3724—21no—
126#3724—21no—
127#3724—21no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3D411yescharacteristic
135(C2×D3)⋊Dic3D411yescharacteristic
136Dic32—21no—
137Dic32—21no—
138#3719—22no—
139#3719—22no—
140#3715—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#946—31no—
150Q8×Dic3—31no—
151#944—31no—
152#944—31no—
153C2×#216—31no—
154C2×#216—31no—
155C2×#215—31no—
156D4×Dic3—31no—
157C2×#214—31no—
158C4×#67—61no—
159C4×#67—61no—
160C4×#67—61no—
161#926—31no—
162#924—31no—
163C2×Dic3⋊C4—61no—
164C2×Dic12—31no—
165C2×Dic12—31no—
166C2×#204C2×D311yescharacteristic
167#898—61no—
168#897C2×D311yescharacteristic
169#893—31no—
170#893C2×D311yescharacteristic
171#892—61no—
172D3×C4⋊C4—61no—
173D3×C4⋊C4C2×D311yescharacteristic
174#890—31no—
175#890—31no—
176#890—61no—
177#890—61no—
178#889—61no—
179#889—61no—
180#887—31no—
181#887—31no—
182#887—31no—
183#887—61no—
184#887C2×D311yescharacteristic
185#67⋊C4—61no—
186#879—61no—
187#879—61no—
188#877—61no—
189#876—61no—
190#872—31no—
191#870—61no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic
197C3×#107C2×D311yescharacteristic
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203C3×#97—31no—
204#835—31no—
205#832—31no—
206#830—31no—
207#821—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8C2×D311yescharacteristic
210#817—31no—
211#816—31no—
212#816—31no—
213#816—61no—
214#816C2×D311yescharacteristic
215#815C2×D311yescharacteristic
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221C8×Dic3—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—61no—
226#810C2×D311yescharacteristic
227#810C2×D311yescharacteristic
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—61no—
233#807C2×D311yescharacteristic
234C4×C3⋊C8—31no—
235C22×C3×D3—21no—
236C22×C3×D3C2×D411yescharacteristic
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3C2×D411yescharacteristic
243C2×C3⋊Dic3C2×D411yescharacteristic
244#634—21no—
245#634#4112yes—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—21no—
253C3×D12#4112yes—
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×C4×D3—81no—
257C3×C4×D3—81no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6—21no—
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—31no—
272#483—91no—
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—31no—
285C2×C3×Q8—31no—
286C2×C3×D4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—61no—
289C22×C3×C4—61no—
290C2×#67—61no—
291C2×#67—61no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294#237—62no—
295#237—62no—
296#235—62no—
297#235—62no—
298C2×D12C22×D311yescharacteristic
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—61no—
302C2×C4×D3—61no—
303C2×C4×D3C22×D311yescharacteristic
304C2×Dic6—31no—
305C2×Dic6—31no—
306C2×Dic6—61no—
307C2×Dic6C22×D311yescharacteristic
308C2×Dic6C22×D311yescharacteristic
309C3×SD16—62no—
310C2×C3×C8—21no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C22×D311yescharacteristic
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C22⋊C4—61no—
326C3×C22⋊C4—61no—
327C3×C42—31no—
328C3×C42—61no—
329#217—31no—
330#217—31no—
331#217—61no—
332#217—61no—
333#216—62no—
334#216—62no—
335#215—62no—
336#214—62no—
337(C2×D3)⋊C4—21no—
338(C2×D3)⋊C4—21no—
339(C2×D3)⋊C4—31no—
340(C2×D3)⋊C4—31no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—61no—
343C4⋊Dic3—21no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—121no—
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—
373C4×Dic3—21no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—121no—
384C4×Dic3C22×D311yescharacteristic
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390Dic12—62no—
391Dic12—62no—
392#204—22no—
393C22×C32C22×D411yescharacteristic
394C2×C3×D3—22no—
395C2×C3×D3—21no—
396C2×C3×D3—21no—
397C2×C3×D3—21no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4C2×#4111yescharacteristic
403C32×C4C2×#4111yescharacteristic
404C3⋊Dic3—22no—
405C3⋊Dic3—21no—
406C3⋊Dic3—21no—
407C3⋊Dic3—41no—
408C3×Dic3—21no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C2×#41—91no—
415C2×Q16—91no—
416C2×Q16—91no—
417C2×SD16—31no—
418C2×SD16—91no—
419C4⋊Q8—91no—
420#126—181no—
421#126—181no—
422#125—91no—
423#125—181no—
424#125—181no—
425C22⋊Q8—31no—
426C22⋊Q8—91no—
427C4×Q8—31no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—91no—
431C4×D4—31no—
432C4×D4—91no—
433C4×D4—181no—
434C4×D4—181no—
435#117—91no—
436#117—181no—
437C2×C4⋊C4—31no—
438C2×C4⋊C4—181no—
439#107—31no—
440#107D3211yescharacteristic
441#106—91no—
442#106—91no—
443C4⋊C8—91no—
444C4⋊C8—91no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—91no—
449#103—91no—
450#103—91no—
451#102—31no—
452#102—91no—
453C22⋊C8—31no—
454C22⋊C8—91no—
455#97—31no—
456C4×C8—91no—
457C23×C3—31no—
458C23×C3—61no—
459C22×D3—21no—
460C22×D3D3×D411yescharacteristic
461C3×Q8—61no—
462C3×Q8—61no—
463C3×Q8—61no—
464C3×Q8—61no—
465C3×D4—32no—
466C3×D4—61no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—241no—
483C2×C3×C4—241no—
484C2×C3×C4C23×D311yescharacteristic
485C2×C3×C4C23×D311yescharacteristic
486#67—64no—
487#67—64no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—64no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—121no—
503C2×Dic3—121no—
504C2×Dic3—241no—
505C2×Dic3D3×D411yescharacteristic
506C2×Dic3D3×D411yescharacteristic
507C2×Dic3D3×D411yescharacteristic
508D12—21no—
509D12#23512yes—
510C4×D3—21no—
511C4×D3—21no—
512C4×D3—64no—
513C4×D3—81no—
514C4×D3—81no—
515C4×D3—241no—
516Dic6—21no—
517Dic6—21no—
518Dic6—21no—
519Dic6—21no—
520Dic6—32no—
521Dic6—32no—
522Dic6—62no—
523Dic6—61no—
524Dic6—61no—
525Dic6—121no—
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#52511yescharacteristic
537C2×C32#57711yescharacteristic
538C2×C32#57811yescharacteristic
539C3×D3—41no—
540C3×D3—42no—
541#41—182no—
542#41—182no—
543C2×Q8—31no—
544C2×Q8—31no—
545C2×Q8—91no—
546C2×D4—31no—
547C2×D4—181no—
548C22×C4—31no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—181no—
552C22×C4—181no—
553Q16—182no—
554Q16—182no—
555SD16—62no—
556SD16—182no—
557C2×C8—31no—
558C2×C8—31no—
559C2×C8—91no—
560C2×C8C2×D3211yescharacteristic
561C4⋊C4—31no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C4⋊C4C2×D3211yescharacteristic
577C4⋊C4C2×D3211yescharacteristic
578C22⋊C4—61no—
579C22⋊C4—61no—
580C22⋊C4—91no—
581C22⋊C4—91no—
582C22⋊C4—181no—
583C22⋊C4—181no—
584C42—31no—
585C42—61no—
586C42—91no—
587C42—181no—
588C42—181no—
589C42—181no—
590C22×C3—21no—
591C22×C3—62no—
592C22×C3—61no—
593C22×C3—61no—
594C22×C3—61no—
595C22×C3—121no—
596C22×C3—121no—
597C22×C3C2×D3×D411yescharacteristic
598C22×C3C2×D3×D411yescharacteristic
599C2×D3—21no—
600C2×D3—21no—
601C2×D3—21no—
602C2×D3—22no—
603C2×D3—41no—
604C2×D3—41no—
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—61no—
612C3×C4—61no—
613C3×C4—61no—
614C3×C4—81no—
615C3×C4—81no—
616C3×C4—121no—
617C3×C4—121no—
618C3×C4—121no—
619C3×C4C2×#23511yescharacteristic
620C3×C4D3×#4111yescharacteristic
621C3×C4D3×#4111yescharacteristic
622C3×C4D3×#4111yescharacteristic
623Dic3—21no—
624Dic3—21no—
625Dic3—21no—
626Dic3—41no—
627Dic3—41no—
628Dic3—41no—
629Dic3—62no—
630Dic3—61no—
631Dic3—61no—
632Dic3—61no—
633Dic3—61no—
634Dic3—62no—
635Dic3—122no—
636Dic3—121no—
637Dic3—121no—
638Dic3—121no—
639Dic3—121no—
640Dic3—241no—
641C32#312011yescharacteristic, complemented, Sylow
642C23—31no—
643C23—61no—
644Q8—61no—
645Q8—61no—
646Q8—61no—
647Q8—61no—
648Q8—92no—
649Q8—181no—
650D4—32no—
651D4—61no—
652D4—184no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—31no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—184no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—241no—
669C2×C4—241no—
670C2×C4—721no—
671C2×C4C22×D3211yescharacteristic
672C8—21no—
673C8—61no—
674C8—61no—
675C8—181no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—122no—
680C2×C3—121no—
681C2×C3#554711yescharacteristic
682C2×C3#565611yescharacteristic
683C2×C3#576611yescharacteristic
684C2×C3#577511yescharacteristic
685C2×C3#577511yescharacteristic
686C2×C3#577911yescharacteristic
687D3—41no—
688D3—42no—
689C22—61no—
690C22—62no—
691C22—61no—
692C22—61no—
693C22—121no—
694C22—121no—
695C22D32×D411yescharacteristic
696C4—41no—
697C4—41no—
698C4—61no—
699C4—61no—
700C4—61no—
701C4—121no—
702C4—121no—
703C4—121no—
704C4—182no—
705C4—181no—
706C4—181no—
707C4—361no—
708C4D3×#23511yescharacteristic
709C4#6431911yescharacteristic
710C3—21no—
711C3#7978611yescharacteristic, complemented
712C3#8145611yescharacteristic, complemented
713C2—121no—
714C2—122no—
715C2#1059461411yescharacteristic
716C2#1059473311yescharacteristic
717C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#3795C22
hypercenter#107D32
hypocenterC32#3120
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
2. #10594345C2semidirect
3. #10592576C2semidirect
4. C3×#4889C2semidirect
5. C3×#4884C2semidirect
7. #10590794C2semidirect
8. #10590748C2semidirect
9. #10590697C2semidirect
11. #10590566C2semidirect
12. #10590516C2semidirect
13. #10590481C2semidirect
14. #10590475C2semidirect
15. #10590473C2semidirect
74. #4889D3semidirect
75. #4884D3semidirect
641. C32#3120semidirect
711. C3#79786semidirect
712. C3#81456semidirect

Maximal subgroups

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

subgroupindex
#105943592
#105943452
#105925762
C3×#48892
C3×#48842
#105909602
#105907942
#105907482
#105906972
#105906142
#105905662
#105905162
#105904812
#105904752
#105904732
#814563
#797863