Finite Group Databasebeta

← #11872534

Subgroups — #11872534

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 723 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594345C211yesmaximal, characteristic, complemented
2#10594327C211yesmaximal, characteristic
3#10592590C211yesmaximal, characteristic, complemented
4C3×#4884C211yesmaximal, characteristic, complemented
5C3×#4873C211yesmaximal, characteristic, complemented
6#10590966C211yesmaximal, characteristic
7#10590798C211yesmaximal, characteristic, complemented
8#10590792C211yesmaximal, characteristic, complemented
9#10590696C211yesmaximal, characteristic, complemented
10#10590616C211yesmaximal, characteristic
11#10590565C211yesmaximal, characteristic, complemented
12#10590516C211yesmaximal, characteristic, complemented
13#10590494C211yesmaximal, characteristic, complemented
14#10590477C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#81456—31nomaximal
17#79748—31nomaximal
18C2×#3799C2211yescharacteristic
19#64102C2211yescharacteristic
20#64099C2211yescharacteristic
21C2×C3×Dic12C2211yescharacteristic
22C3×#897C2211yescharacteristic
23C3×D3×C4⋊C4C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C3×#887C2211yescharacteristic
26#63904—21no—
27C4×#626—21no—
28#63894C2211yescharacteristic
29#63883—21no—
30#63873C2211yescharacteristic
31#63869—21no—
32#63861—21no—
33#63859—21no—
34#63856C2211yescharacteristic
35#63855C2211yescharacteristic
36#63847—21no—
37#63843C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63836—21no—
40C2×#3718C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C32×#107C2211yescharacteristic
44#63648C2211yescharacteristic
45#63641C2211yescharacteristic
46#63636C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61#5625—31no—
62#5583—31no—
63#5574—31no—
64#5504—31no—
65C3×#484—31no—
66C3×C4×Q16—31no—
67#5187—31no—
68#5182—31no—
69#5047—31no—
70#5030—31no—
71#5026—31no—
72#4971—31no—
73#4891—31no—
74#4891—31no—
75#4891—61no—
76#4889—31no—
77#4884D311yescharacteristic, complemented
78#4877—31no—
79#4873D311yescharacteristic, complemented
80#4818—31no—
81#4818—31no—
82#4808—31no—
83#4805—31no—
84#4799—31no—
85#4795—31no—
86#4789—31no—
87#4788—31no—
88#4733—31no—
89#4720—31no—
90C4×#204—31no—
91#4690—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#626—21no—
100C2×#624—21no—
101C2×#624—21no—
102#3799—22no—
103#3799—22no—
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107#3752—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111C4×C3⋊Dic3C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C3×Dic12—22no—
125#3724—21no—
126#3724—21no—
127#3724—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132#3722—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3D411yescharacteristic
135(C2×D3)⋊Dic3D411yescharacteristic
136Dic32—21no—
137Dic32—21no—
138#3718—22no—
139#3717—22no—
140#3717—22no—
141#3120—91noSylow
142C2×#239—31no—
143C2×#235—31no—
144C2×C3×Q16—31no—
145C3×C22⋊Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C2×C3×C4⋊C4—31no—
149#946—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152#944—31no—
153#944—31no—
154C2×#216—31no—
155C2×#216—31no—
156C2×#215—31no—
157C2×#215—31no—
158C4×#67—61no—
159C4×#67—61no—
160#926—31no—
161#924—31no—
162C2×Dic12C2×D311yescharacteristic
163C2×#204—31no—
164C2×#204—31no—
165#898—61no—
166#897C2×D311yescharacteristic
167#893—31no—
168#893—31no—
169#893—31no—
170#893—61no—
171#893—61no—
172#892—61no—
173D3×C4⋊C4—61no—
174D3×C4⋊C4—61no—
175D3×C4⋊C4C2×D311yescharacteristic
176#890—31no—
177#890—31no—
178#890—61no—
179#890—61no—
180#889—61no—
181#889—61no—
182#887—31no—
183#887C2×D311yescharacteristic
184#887C2×D311yescharacteristic
185#879—61no—
186#879—61no—
187#876—61no—
188C4×D12—31no—
189C4×D12—61no—
190#872—31no—
191#872—61no—
192#870—61no—
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×#103—31no—
202C3×C22⋊C8—31no—
203C3×C4×C8—31no—
204#835—31no—
205#835—31no—
206#830—31no—
207#821—31no—
208#821—31no—
209#821—61no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8C2×D311yescharacteristic
212#817—31no—
213#816—31no—
214#816C2×D311yescharacteristic
215#815—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221C8×Dic3C2×D311yescharacteristic
222#810—31no—
223#810C2×D311yescharacteristic
224#810C2×D311yescharacteristic
225#810C2×D311yescharacteristic
226#809—31no—
227#809—31no—
228#809—61no—
229#808—31no—
230#808—31no—
231#808—31no—
232#808—61no—
233#807C2×D311yescharacteristic
234#803—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⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243C4⋊(C3⋊D3)—21no—
244C4⋊(C3⋊D3)#4112yes—
245C4×C3⋊D3—81no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×C4×D3—81no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
262#626—24no—
263#624—24no—
264#624—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—91no—
281C4×Q16—31no—
282C4×SD16—91no—
283#433—91no—
284C2×C3×Q8—31no—
285C2×C3×Q8—31no—
286C2×C3×Q8—31no—
287C22×C3×C4—31no—
288C22×C3×C4—61no—
289C2×#67—61no—
290#239—62no—
291#239—62no—
292#235—62no—
293#235—62no—
294C2×D12—31no—
295C2×D12—31no—
296C2×D12—61no—
297C2×D12—61no—
298C2×C4×D3—21no—
299C2×C4×D3—61no—
300C2×C4×D3—61no—
301C2×C4×D3—61no—
302C2×C4×D3—61no—
303C2×C4×D3—61no—
304C2×C4×D3—61no—
305C2×C4×D3—121no—
306C2×C4×D3C22×D311yescharacteristic
307C2×Dic6C22×D311yescharacteristic
308C2×Dic6C22×D311yescharacteristic
309C2×Dic6C22×D311yescharacteristic
310C3×Q16—62no—
311C2×C3×C8—21no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C22⋊C4—61no—
328C3×C42—31no—
329C3×C42—61no—
330C3×C42—61no—
331#217—31no—
332#217—31no—
333#217—61no—
334#216—62no—
335#216—62no—
336#215—62no—
337#215—62no—
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—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—121no—
347C4⋊Dic3—21no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—121no—
358C4⋊Dic3C22×D311yescharacteristic
359Dic3⋊C4—21no—
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—121no—
375C4×Dic3—21no—
376C4×Dic3—21no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3C22×D311yescharacteristic
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390Dic12—22no—
391#204—62no—
392#204—62no—
393C22×C32C22×D411yescharacteristic
394C2×C3⋊D3—22no—
395C2×C3⋊D3—41no—
396C2×C3⋊D3—41no—
397C2×C3×D3—21no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4C2×#4111yescharacteristic
403C32×C4C2×#4111yescharacteristic
404C3⋊Dic3—21no—
405C3⋊Dic3—21no—
406C3⋊Dic3—41no—
407C3×Dic3—21no—
408C3×Dic3—22no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C2×#41—91no—
415C2×Q16—31no—
416C2×Q16—91no—
417C2×SD16—91no—
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—31no—
429C4×Q8—91no—
430C4×Q8—91no—
431C4×D4—91no—
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—31no—
449#103—91no—
450#103—91no—
451#102—91no—
452#102—91no—
453C22⋊C8—31no—
454C22⋊C8—91no—
455#97—91no—
456C4×C8—31no—
457C23×C3—31no—
458C22×D3—61no—
459C22×D3—61no—
460C22×D3—121no—
461C22×D3D3×D411yescharacteristic
462C3×Q8—32no—
463C3×Q8—61no—
464C3×Q8—61no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—61no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—241no—
485C2×C3×C4C23×D311yescharacteristic
486C2×C3×C4C23×D311yescharacteristic
487#67—64no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—121no—
501C2×Dic3D3×D411yescharacteristic
502C2×Dic3D3×D411yescharacteristic
503C2×Dic3D3×D411yescharacteristic
504D12—32no—
505D12—32no—
506D12—62no—
507D12—64no—
508D12—61no—
509D12—61no—
510D12—121no—
511C4×D3—21no—
512C4×D3—21no—
513C4×D3—64no—
514C4×D3—64no—
515C4×D3—81no—
516C4×D3—241no—
517C4×D3—241no—
518C4×D3—241no—
519C4×D3—241no—
520C4×D3—242no—
521Dic6—21no—
522Dic6—21no—
523Dic6—21no—
524Dic6—21no—
525Dic6—21no—
526Dic6#23512yes—
527C3×C8—21no—
528C3×C8—21no—
529C3×C8—41no—
530C3×C8—61no—
531C3×C8—61no—
532C3⋊C8—21no—
533C3⋊C8—21no—
534C3⋊C8—61no—
535C3⋊C8—61no—
536C3⋊C8—121no—
537C2×C32#52511yescharacteristic
538C2×C32#57711yescharacteristic
539C2×C32#57811yescharacteristic
540C3⋊D3—42no—
541C3×D3—41no—
542#41—182no—
543#41—182no—
544C2×Q8—31no—
545C2×Q8—31no—
546C2×Q8—31no—
547C2×D4—91no—
548C2×D4—181no—
549C22×C4—31no—
550C22×C4—61no—
551C22×C4—181no—
552C22×C4—181no—
553C22×C4—181no—
554Q16—62no—
555Q16—182no—
556SD16—182no—
557SD16—182no—
558C2×C8—31no—
559C2×C8—31no—
560C2×C8—91no—
561C2×C8C2×D3211yescharacteristic
562C4⋊C4—31no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—91no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C4⋊C4—181no—
577C4⋊C4C2×D3211yescharacteristic
578C4⋊C4C2×D3211yescharacteristic
579C22⋊C4—61no—
580C22⋊C4—91no—
581C22⋊C4—91no—
582C22⋊C4—181no—
583C22⋊C4—181no—
584C22⋊C4—181no—
585C42—31no—
586C42—61no—
587C42—61no—
588C42—91no—
589C42—181no—
590C42—181no—
591C22×C3—21no—
592C22×C3—61no—
593C22×C3—61no—
594C22×C3—61no—
595C22×C3C2×D3×D411yescharacteristic
596C22×C3C2×D3×D411yescharacteristic
597C2×D3—21no—
598C2×D3—21no—
599C2×D3—21no—
600C2×D3—62no—
601C2×D3—62no—
602C2×D3—122no—
603C2×D3—121no—
604C2×D3—121no—
605C2×D3—121no—
606C2×D3—121no—
607C2×D3—241no—
608C2×D3—241no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—41no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—62no—
616C3×C4—61no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—81no—
620C3×C4—81no—
621C3×C4—121no—
622C3×C4—121no—
623C3×C4—121no—
624C3×C4C2×#23511yescharacteristic
625C3×C4D3×#4111yescharacteristic
626C3×C4D3×#4111yescharacteristic
627C3×C4D3×#4111yescharacteristic
628Dic3—21no—
629Dic3—21no—
630Dic3—21no—
631Dic3—22no—
632Dic3—41no—
633Dic3—41no—
634Dic3—41no—
635Dic3—61no—
636Dic3—61no—
637Dic3—61no—
638Dic3—61no—
639Dic3—121no—
640Dic3—121no—
641Dic3—121no—
642Dic3—121no—
643Dic3—241no—
644C32#312011yescharacteristic, complemented, Sylow
645C23—31no—
646C23—181no—
647Q8—32no—
648Q8—61no—
649Q8—61no—
650Q8—61no—
651Q8—61no—
652Q8—61no—
653D4—92no—
654D4—184no—
655D4—181no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—184no—
670C2×C4—181no—
671C2×C4—241no—
672C2×C4—721no—
673C2×C4—721no—
674C2×C4C22×D3211yescharacteristic
675C8—21no—
676C8—61no—
677C8—61no—
678C8—181no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—121no—
683C2×C3#554711yescharacteristic
684C2×C3#565611yescharacteristic
685C2×C3#576611yescharacteristic
686C2×C3#576611yescharacteristic
687C2×C3#577011yescharacteristic
688C2×C3#577511yescharacteristic
689D3—41no—
690D3—122no—
691D3—122no—
692D3—242no—
693C22—61no—
694C22—61no—
695C22—61no—
696C22—182no—
697C22—361no—
698C22—361no—
699C22D32×D411yescharacteristic
700C4—41no—
701C4—41no—
702C4—61no—
703C4—62no—
704C4—61no—
705C4—61no—
706C4—121no—
707C4—121no—
708C4—121no—
709C4—181no—
710C4—181no—
711C4—361no—
712C4D3×#23511yescharacteristic
713C4#6431911yescharacteristic
714C3—21no—
715C3#7974811yescharacteristic, complemented
716C3#8145611yescharacteristic, complemented
717C2—121no—
718C2—362no—
719C2#1059461411yescharacteristic
720C2#1059473611yescharacteristic
721C2#1059476511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#3799C22
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
1. #10594345C2semidirect
3. #10592590C2semidirect
4. C3×#4884C2semidirect
5. C3×#4873C2semidirect
7. #10590798C2semidirect
8. #10590792C2semidirect
9. #10590696C2semidirect
11. #10590565C2semidirect
12. #10590516C2semidirect
13. #10590494C2semidirect
14. #10590477C2semidirect
15. #10590457C2semidirect
77. #4884D3semidirect
79. #4873D3semidirect
644. C32#3120semidirect
715. C3#79748semidirect
716. C3#81456semidirect

Maximal subgroups

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

subgroupindex
#105943452
#105943272
#105925902
C3×#48842
C3×#48732
#105909662
#105907982
#105907922
#105906962
#105906162
#105905652
#105905162
#105904942
#105904772
#105904572
#814563
#797483