Finite Group Databasebeta

← #11869054

Subgroups — #11869054

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 711 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596160C211yesmaximal, characteristic
2#10593848C211yesmaximal, characteristic
3C3×#5063C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5#10590602C211yesmaximal, characteristic
6#10590601C211yesmaximal, characteristic
7#10590583C211yesmaximal, characteristic
8#10590574C211yesmaximal, characteristic
9#10590497C211yesmaximal, characteristic, complemented
10#10590496C211yesmaximal, characteristic, complemented
11#10590495C211yesmaximal, characteristic, complemented
12#10590494C211yesmaximal, characteristic, complemented
13#10590332C211yesmaximal, characteristic
14#10590301C211yesmaximal, characteristic, complemented
15#10590283C211yesmaximal, characteristic, complemented
16#81233—31nomaximal
17#81232—31nomaximal
18C2×#3797C2211yescharacteristic
19C32×#125C2211yescharacteristic
20#64106—21no—
21#64105—21no—
22#64101C2211yescharacteristic
23C4⋊C4×C3⋊D3C2211yescharacteristic
24#64099C2211yescharacteristic
25#64098—21no—
26#64097—21no—
27#64097C2211yescharacteristic
28#64081C2211yescharacteristic
29#64078C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63849C2211yescharacteristic
33#63843C2211yescharacteristic
34#63843C2211yescharacteristic
35#63837—21no—
36#63837—21no—
37#63836—21no—
38#63836—21no—
39C2×#3712C2211yescharacteristic
40C2×#3710C2211yescharacteristic
41C3×#810C2211yescharacteristic
42C3×#810C2211yescharacteristic
43C3×#810C2211yescharacteristic
44C3×#810C2211yescharacteristic
45C3×#808C2211yescharacteristic
46C3×#808C2211yescharacteristic
47C3×#807C2211yescharacteristic
48C3×#807C2211yescharacteristic
49C3×C4⋊(C3⋊C8)C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63573C2211yescharacteristic
54#63573C2211yescharacteristic
55#63572C2211yescharacteristic
56#63572C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#5689—31no—
62#5689—31no—
63#5689—61no—
64#5572—31no—
65#5572—31no—
66C3×#479—31no—
67C3×#479—31no—
68#5063D311yescharacteristic, complemented
69#5063D311yescharacteristic, complemented
70#5021—31no—
71#5020—31no—
72#4881—31no—
73#4880—31no—
74#4877—31no—
75#4875—31no—
76#4861—31no—
77#4860—31no—
78#4857—31no—
79#4854—31no—
80#4851—31no—
81#4850—31no—
82#4839—31no—
83#4839—31no—
84#4802—31no—
85#4802—31no—
86D3×#103—31no—
87D3×#103—31no—
88#4799—31no—
89#4796—31no—
90#4793—31no—
91#4791—31no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×#634—21no—
95C2×#634—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#624—21no—
100#3797—22no—
101#3797Q814yescomplemented
102C32×C4⋊C4—21no—
103C32×C4⋊C4—21no—
104C32×C4⋊C4C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C42C2311yescharacteristic
107#3752—21no—
108#3752D411yescharacteristic
109#3752D411yescharacteristic
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750—21no—
117#3750D411yescharacteristic
118#3750D411yescharacteristic
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137#3712—22no—
138#3710—22no—
139#3082—91noSylow
140C2×D3×Q8—31no—
141C2×D3×Q8—31no—
142C3×#125—21no—
143C3×#125C2×D311yescharacteristic
144C3×#125C2×D311yescharacteristic
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149C2×ΓL(1,𝔽25)—31no—
150C2×ΓL(1,𝔽25)—31no—
151C2×D3×C8—31no—
152C2×D3×C8—31no—
153#897—61no—
154#897—61no—
155#897—62no—
156#896—61no—
157#896—61no—
158#896—62no—
159#892—31no—
160#892—31no—
161#892—31no—
162#892—31no—
163#892—61no—
164#892—61no—
165#892—61no—
166D3×C4⋊C4—31no—
167D3×C4⋊C4—31no—
168D3×C4⋊C4—61no—
169#890—31no—
170#890—31no—
171#890—61no—
172#889—61no—
173#889—61no—
174#889—62no—
175#888—31no—
176#888—31no—
177#888—61no—
178#888—61no—
179#888—61no—
180#888—62no—
181#887—31no—
182#887—31no—
183#887—61no—
184#887—61no—
185#872—31no—
186#872—31no—
187#872—61no—
188#872—61no—
189#872—61no—
190#869—31no—
191#869—31no—
192#869—61no—
193C4×Dic6—61no—
194C4×Dic6—61no—
195C4×Dic6C2×D311yescharacteristic
196C4×Dic6C2×D311yescharacteristic
197C3×#107—31no—
198C3×#107—31no—
199C3×#106—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#818—31no—
212#818—31no—
213#817—31no—
214#817—31no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223#810C2×D311yescharacteristic
224#810C2×D311yescharacteristic
225#810C2×D311yescharacteristic
226#810C2×D311yescharacteristic
227#808—31no—
228#808—31no—
229#808C2×D311yescharacteristic
230#808C2×D311yescharacteristic
231#807—31no—
232#807—31no—
233#807C2×D311yescharacteristic
234#807C2×D311yescharacteristic
235C4⋊(C3⋊C8)C2×D311yescharacteristic
236C4⋊(C3⋊C8)C2×D311yescharacteristic
237C22×C3⋊D3C2×D411yescharacteristic
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2×D411yescharacteristic
242C2×C32×C4C2411yescharacteristic
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3C2×D411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4×C3⋊D3—81no—
249C4×C3⋊D3C2×Q812yes—
250C4×C3⋊D3#4112yes—
251#634—81no—
252#634—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6C2×Q812yes—
260C3×Dic6C2×Q812yes—
261#627—24no—
262#624—24no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266C3×C3⋊C8—21no—
267#544—91no—
268#519—91no—
269#479—31no—
270#479—31no—
271#479—91no—
272#479—91no—
273#477—91no—
274#477—91no—
275#475—91no—
276#475—91no—
277#428—91no—
278#427—91no—
279#424—91no—
280#419—91no—
281C2×#103—91no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284D3×Q8—34no—
285D3×Q8—34no—
286D3×Q8—62no—
287D3×Q8—62no—
288C2×C4×D3—31no—
289C2×C4×D3—31no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—62no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6—62no—
301C2×Dic6—62no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6C22×D311yescharacteristic
305C2×Dic6C22×D311yescharacteristic
306C2×C3×C8—31no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—22no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
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×C42—21no—
327C3×C42—61no—
328C3×C42—61no—
329C3×C42C22×D311yescharacteristic
330C3×C42C22×D311yescharacteristic
331(C2×D3)⋊C4—31no—
332(C2×D3)⋊C4—31no—
333(C2×D3)⋊C4—31no—
334(C2×D3)⋊C4—31no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341(C2×D3)⋊C4—62no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—62no—
353C4⋊Dic3—62no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3C22×D311yescharacteristic
357C4⋊Dic3C22×D311yescharacteristic
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
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—62no—
375Dic3⋊C4—62no—
376Dic3⋊C4—62no—
377C4×Dic3—21no—
378C4×Dic3—21no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—62no—
391C2×C3⋊C8C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394C2×C3⋊C8C22×D311yescharacteristic
395ΓL(1,𝔽25)—62no—
396ΓL(1,𝔽25)—62no—
397D3×C8—62no—
398D3×C8—62no—
399C22×C32C22×D411yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3C22⋊Q812yes—
403C32×C4—21no—
404C32×C4—21no—
405C32×C4—41no—
406C32×C4—41no—
407C32×C4C22×Q811yescharacteristic
408C32×C4C2×#4111yescharacteristic
409C3⋊Dic3—21no—
410C3⋊Dic3—21no—
411C3⋊Dic3—41no—
412C3⋊Dic3—41no—
413C3⋊Dic3C22⋊Q812yes—
414C3×Dic3—22no—
415C3×Dic3—22no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C22×Q8—91no—
419C2×M16—91no—
420C22×C8—91no—
421C4⋊Q8—91no—
422C4⋊Q8—91no—
423C4⋊Q8—181no—
424#125—91no—
425#125—181no—
426#125D3211yescharacteristic
427C22⋊Q8—181no—
428C22⋊Q8—181no—
429C4×Q8—31no—
430C4×Q8—31no—
431C4×Q8—91no—
432C4×Q8—91no—
433C4×Q8—181no—
434C4×Q8—181no—
435#117—91no—
436#117—91no—
437#117—91no—
438#117—181no—
439#117—181no—
440C2×C4⋊C4—91no—
441#107—31no—
442#107—31no—
443#107—91no—
444#107—91no—
445#106—31no—
446#106—31no—
447#106—91no—
448#106—91no—
449C4⋊C8—31no—
450C4⋊C8—31no—
451C4⋊C8—91no—
452C4⋊C8—91no—
453#103—31no—
454#103—31no—
455#103—31no—
456#103—31no—
457#103—91no—
458#103—91no—
459#103—91no—
460#103—91no—
461C22×D3—31no—
462C22×D3—31no—
463C22×D3—61no—
464C3×Q8—32no—
465C3×Q8—32no—
466C3×Q8—61no—
467C3×Q8—61no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4D3×D411yescharacteristic
482C2×C3×C4D3×D411yescharacteristic
483C2×C3×C4D3×D411yescharacteristic
484C2×C3×C4D3×D411yescharacteristic
485C2×C3×C4C23×D311yescharacteristic
486C2×C3×C4C23×D311yescharacteristic
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C4×D3—32no—
507C4×D3—32no—
508C4×D3—32no—
509C4×D3—32no—
510C4×D3—62no—
511C4×D3—62no—
512C4×D3—64no—
513C4×D3—64no—
514C4×D3—241no—
515C4×D3—241no—
516C4×D3—242no—
517Dic6—21no—
518Dic6—21no—
519Dic6—64no—
520Dic6—64no—
521Dic6—241no—
522Dic6—241no—
523Dic6—241no—
524Dic6—241no—
525Dic6—242no—
526Dic6—242no—
527Dic6D3×Q812yes—
528Dic6D3×Q812yes—
529C3×C8—61no—
530C3×C8—61no—
531C3×C8—61no—
532C3×C8—61no—
533C3⋊C8—21no—
534C3⋊C8—21no—
535C3⋊C8—21no—
536C3⋊C8—21no—
537C2×C32C2×C22⋊Q811yescharacteristic
538C2×C32#57711yescharacteristic
539C2×C32#57811yescharacteristic
540C3⋊D3—22no—
541C2×Q8—31no—
542C2×Q8—31no—
543C2×Q8—94no—
544C2×Q8—181no—
545C2×Q8—181no—
546C2×Q8—182no—
547C2×Q8—181no—
548C22×C4—91no—
549C22×C4—181no—
550C22×C4—181no—
551M16—182no—
552C2×C8—31no—
553C2×C8—31no—
554C2×C8—31no—
555C2×C8—31no—
556C2×C8—182no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—91no—
564C4⋊C4—91no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4C2×D3211yescharacteristic
575C4⋊C4C2×D3211yescharacteristic
576C22⋊C4—91no—
577C22⋊C4—91no—
578C22⋊C4—181no—
579C22⋊C4—181no—
580C42—61no—
581C42—61no—
582C42—91no—
583C42—181no—
584C42—181no—
585C42—181no—
586C42—181no—
587C42C2×D3211yescharacteristic
588C22×C3—21no—
589C22×C3C2×D3×D411yescharacteristic
590C22×C3C2×D3×D411yescharacteristic
591C2×D3—32no—
592C2×D3—32no—
593C2×D3—62no—
594C2×D3—61no—
595C2×D3—61no—
596C2×D3—61no—
597C2×D3—61no—
598C2×D3—121no—
599C2×D3—121no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—21no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—42no—
609C3×C4—42no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—41no—
613C3×C4—41no—
614C3×C4—62no—
615C3×C4—62no—
616C3×C4—121no—
617C3×C4—121no—
618C3×C4C2×D3×Q811yescharacteristic
619C3×C4C2×D3×Q811yescharacteristic
620C3×C4D3×#4111yescharacteristic
621C3×C4D3×#4111yescharacteristic
622Dic3—22no—
623Dic3—22no—
624Dic3—32no—
625Dic3—32no—
626Dic3—41no—
627Dic3—41no—
628Dic3—62no—
629Dic3—61no—
630Dic3—61no—
631Dic3—61no—
632Dic3—61no—
633Dic3—121no—
634Dic3—121no—
635Dic3—122no—
636Dic3—122no—
637Dic3—121no—
638Dic3—121no—
639Dic3—121no—
640Dic3—121no—
641C32#308211yescharacteristic, complemented, Sylow
642C23—91no—
643Q8—32no—
644Q8—32no—
645Q8—61no—
646Q8—61no—
647Q8—184no—
648Q8—721no—
649Q8—721no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—91no—
657C2×C4—92no—
658C2×C4—92no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—184no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—721no—
665C2×C4#381111yescharacteristic
666C2×C4#381111yescharacteristic
667C2×C4C22×D3211yescharacteristic
668C8—61no—
669C8—61no—
670C8—61no—
671C8—61no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3D3×C22⋊Q811yescharacteristic
676C2×C3D3×C22⋊Q811yescharacteristic
677C2×C3#577011yescharacteristic
678C2×C3#577111yescharacteristic
679C2×C3#577811yescharacteristic
680C2×C3#577911yescharacteristic
681D3—62no—
682D3—62no—
683D3—122no—
684C22—92no—
685C22—181no—
686C22—181no—
687C22C2×#381111yescharacteristic
688C4—21no—
689C4—21no—
690C4—41no—
691C4—41no—
692C4—62no—
693C4—62no—
694C4—92no—
695C4—121no—
696C4—121no—
697C4—181no—
698C4—181no—
699C4—361no—
700C4—361no—
701C4D32×Q811yescharacteristic
702C4#6431911yescharacteristic
703C3—21no—
704C3#8123211yescharacteristic, complemented
705C3#8123311yescharacteristic, complemented
706C2—182no—
707C2#1059542911yescharacteristic
708C2#1059547211yescharacteristic
709C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#125D32
hypocenterC32#3082
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
3. C3×#5063C2semidirect
4. C3×#5063C2semidirect
9. #10590497C2semidirect
10. #10590496C2semidirect
11. #10590495C2semidirect
12. #10590494C2semidirect
14. #10590301C2semidirect
15. #10590283C2semidirect
68. #5063D3semidirect
69. #5063D3semidirect
101. #3797Q8semidirect
641. C32#3082semidirect
704. C3#81232semidirect
705. C3#81233semidirect

Maximal subgroups

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

subgroupindex
#105961602
#105938482
C3×#50632
#105906022
#105906012
#105905832
#105905742
#105904972
#105904962
#105904952
#105904942
#105903322
#105903012
#105902832
#812333
#812323