Finite Group Databasebeta

← #11869057

Subgroups — #11869057

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593855C211yesmaximal, characteristic
2#10593848C211yesmaximal, characteristic
3#10592538C211yesmaximal, characteristic
4C3×#4850C211yesmaximal, characteristic, complemented
5C3×#4829C211yesmaximal, characteristic, complemented
6#10590821C211yesmaximal, characteristic, complemented
7#10590821C211yesmaximal, characteristic, complemented
8#10590817C211yesmaximal, characteristic, complemented
9#10590816C211yesmaximal, characteristic, complemented
10#10590714C211yesmaximal, characteristic
11#10590691C211yesmaximal, characteristic
12#10590688C211yesmaximal, characteristic
13#10590672C211yesmaximal, characteristic
14#10590286C211yesmaximal, characteristic, complemented
15#10590285C211yesmaximal, characteristic, complemented
16#81232—31nomaximal
17#81110—31nomaximal
18C2×#3797C2211yescharacteristic
19C2×#3743C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21#64081C2211yescharacteristic
22C3×#870C2211yescharacteristic
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63919C2211yescharacteristic
27#63900C2211yescharacteristic
28#63895—21no—
29#63888—21no—
30#63872C2211yescharacteristic
31#63849C2211yescharacteristic
32#63849C2211yescharacteristic
33#63847—21no—
34#63843C2211yescharacteristic
35#63843C2211yescharacteristic
36#63839—21no—
37#63837—21no—
38#63837—21no—
39#63836—21no—
40#63836—21no—
41C32×C4⋊C8C2211yescharacteristic
42#63641C2211yescharacteristic
43#63641C2211yescharacteristic
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C3×#818C2211yescharacteristic
46C3×#818C2211yescharacteristic
47C3×#818C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53#63576C2211yescharacteristic
54#63574C2211yescharacteristic
55#63574C2211yescharacteristic
56#63574C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61#5729—31no—
62#5689—31no—
63#5572—31no—
64#5572—31no—
65C3×#479—31no—
66C3×#477—31no—
67#5094—31no—
68#5063—31no—
69#5022—31no—
70#5020—31no—
71#4881—31no—
72#4880—31no—
73#4880—31no—
74#4877—31no—
75#4877—31no—
76#4875—31no—
77#4861—31no—
78#4854—31no—
79#4850D311yescharacteristic, complemented
80#4839—31no—
81#4839—31no—
82#4839—61no—
83#4829D311yescharacteristic, complemented
84#4802—31no—
85#4802—31no—
86D3×#103—31no—
87D3×#103—31no—
88#4796—31no—
89#4796—31no—
90#4793—31no—
91#4791—31no—
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×C3×Dic6—21no—
94C2×C3×Dic6C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×#627—21no—
97C2×#627—21no—
98C2×#624—21no—
99C2×#624—21no—
100#3797—22no—
101#3797Q814yescomplemented
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C42C2311yescharacteristic
105#3752D411yescharacteristic
106#3752D411yescharacteristic
107#3750D411yescharacteristic
108#3750D411yescharacteristic
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112#3743—22no—
113C8×C3⋊D3—22no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127#3724—21no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134#3722—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3082—91noSylow
140C2×D3×Q8—31no—
141C2×D3×Q8—31no—
142C3×C4⋊Q8—31no—
143C3×#125—31no—
144C3×C4×Q8—31no—
145C3×C4×Q8—31no—
146#946—61no—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149#944—61no—
150C2×ΓL(1,𝔽25)—31no—
151C2×ΓL(1,𝔽25)—31no—
152C2×ΓL(1,𝔽25)—61no—
153C2×D3×C8—31no—
154C2×D3×C8—31no—
155C2×D3×C8—61no—
156#897—61no—
157#896—61no—
158#896—61no—
159#892—31no—
160#892—31no—
161#892—31no—
162#892—31no—
163#892—61no—
164#892—61no—
165D3×C4⋊C4—31no—
166D3×C4⋊C4—31no—
167#890—31no—
168#890—31no—
169#889—61no—
170#889—61no—
171#888—31no—
172#888—31no—
173#888—61no—
174#887—31no—
175#887—31no—
176#887—61no—
177#887—61no—
178#872—31no—
179#872—31no—
180#872—61no—
181#872—61no—
182#872—61no—
183#870C2×D311yescharacteristic
184#869C2×D311yescharacteristic
185C4×Dic6—61no—
186C4×Dic6—61no—
187C4×Dic6C2×D311yescharacteristic
188C4×Dic6C2×D311yescharacteristic
189C3×#107—31no—
190C3×#107—31no—
191C3×#107—31no—
192C3×#106—31no—
193C3×C4⋊C8—21no—
194C3×C4⋊C8C2×D311yescharacteristic
195C3×C4⋊C8C2×D311yescharacteristic
196C3×#103—31no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#103—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#818C2×D311yescharacteristic
205#818C2×D311yescharacteristic
206#818C2×D311yescharacteristic
207#817C2×D311yescharacteristic
208#816C2×D311yescharacteristic
209#816C2×D311yescharacteristic
210#816C2×D311yescharacteristic
211#816C2×D311yescharacteristic
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—61no—
217Dic3⋊C8—61no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#808—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#807—31no—
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—61no—
233C22×C3⋊D3C2×D411yescharacteristic
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3C2×D411yescharacteristic
238C2×C3⋊Dic3C2×D411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
240C4×C3⋊D3C2×Q812yes—
241C4×C3⋊D3#4112yes—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C3×Dic6—21no—
251C3×Dic6—21no—
252C3×Dic6—81no—
253C3×Dic6C2×Q812yes—
254C3×Dic6C2×Q812yes—
255#627—24no—
256#627—81no—
257#624—24no—
258#624—81no—
259C32×C8—21no—
260C32×C8—21no—
261C3⋊(C3⋊C8)—21no—
262C3⋊(C3⋊C8)—21no—
263#544—91no—
264#519—91no—
265#479—31no—
266#479—91no—
267#479—91no—
268#479—91no—
269#477—31no—
270#477—91no—
271#475—91no—
272#475—91no—
273#428—91no—
274#427—91no—
275#424—91no—
276#419—91no—
277C2×#103—91no—
278C2×C3×Q8—31no—
279C2×C3×Q8—31no—
280C2×C3×Q8—61no—
281D3×Q8—34no—
282D3×Q8—34no—
283D3×Q8—62no—
284D3×Q8—62no—
285C2×C4×D3—31no—
286C2×C4×D3—31no—
287C2×C4×D3—61no—
288C2×C4×D3—61no—
289C2×C4×D3—61no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×Dic6—21no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6C22×D311yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8C22×D311yescharacteristic
302C2×C3×C8C22×D311yescharacteristic
303C2×C3×C8C22×D311yescharacteristic
304C2×C3×C8C22×D311yescharacteristic
305C3×C4⋊C4—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C42—21no—
317C3×C42—61no—
318C3×C42—61no—
319C3×C42C22×D311yescharacteristic
320C3×C42C22×D311yescharacteristic
321(C2×D3)⋊C4—31no—
322(C2×D3)⋊C4—31no—
323(C2×D3)⋊C4—31no—
324(C2×D3)⋊C4—31no—
325(C2×D3)⋊C4—61no—
326(C2×D3)⋊C4—61no—
327(C2×D3)⋊C4—61no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331C4⋊Dic3—21no—
332C4⋊Dic3—61no—
333C4⋊Dic3—61no—
334C4⋊Dic3—61no—
335C4⋊Dic3—61no—
336C4⋊Dic3C22×D311yescharacteristic
337C4⋊Dic3C22×D311yescharacteristic
338C4⋊Dic3C22×D311yescharacteristic
339C4⋊Dic3C22×D311yescharacteristic
340C4⋊Dic3C22×D311yescharacteristic
341C4⋊Dic3C22×D311yescharacteristic
342Dic3⋊C4—21no—
343Dic3⋊C4—21no—
344Dic3⋊C4—21no—
345Dic3⋊C4—21no—
346Dic3⋊C4—31no—
347Dic3⋊C4—31no—
348Dic3⋊C4—31no—
349Dic3⋊C4—31no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360C4×Dic3—21no—
361C4×Dic3—21no—
362C4×Dic3—31no—
363C4×Dic3—31no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C2×C3⋊C8—31no—
374C2×C3⋊C8—31no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—61no—
378C2×C3⋊C8—61no—
379ΓL(1,𝔽25)—62no—
380ΓL(1,𝔽25)—62no—
381ΓL(1,𝔽25)—122no—
382D3×C8—62no—
383D3×C8—62no—
384D3×C8—122no—
385C22×C32C22×D411yescharacteristic
386C2×C3⋊D3—21no—
387C2×C3⋊D3—21no—
388C2×C3⋊D3C22⋊Q812yes—
389C32×C4—21no—
390C32×C4—21no—
391C32×C4C22×Q811yescharacteristic
392C32×C4C2×#4111yescharacteristic
393C3⋊Dic3—21no—
394C3⋊Dic3—21no—
395C3⋊Dic3C22⋊Q812yes—
396C3×Dic3—22no—
397C3×Dic3—22no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C22×Q8—91no—
405C2×M16—91no—
406C22×C8—91no—
407C4⋊Q8—31no—
408C4⋊Q8—91no—
409C4⋊Q8—181no—
410#125—31no—
411#125—91no—
412#125—181no—
413C22⋊Q8—181no—
414C22⋊Q8—181no—
415C4×Q8—31no—
416C4×Q8—31no—
417C4×Q8—91no—
418C4×Q8—91no—
419C4×Q8—181no—
420C4×Q8—181no—
421#117—91no—
422#117—91no—
423#117—91no—
424#117—181no—
425#117—181no—
426C2×C4⋊C4—91no—
427#107—31no—
428#107—31no—
429#107—31no—
430#107—91no—
431#106—31no—
432#106—91no—
433#106—91no—
434#106—91no—
435C4⋊C8—91no—
436C4⋊C8—91no—
437C4⋊C8—91no—
438C4⋊C8D3211yescharacteristic
439#103—31no—
440#103—31no—
441#103—31no—
442#103—31no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447C22×D3—31no—
448C22×D3—31no—
449C22×D3—61no—
450C3×Q8—32no—
451C3×Q8—32no—
452C3×Q8—61no—
453C3×Q8—61no—
454C3×Q8—241no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4D3×D411yescharacteristic
467C2×C3×C4D3×D411yescharacteristic
468C2×C3×C4D3×D411yescharacteristic
469C2×C3×C4D3×D411yescharacteristic
470C2×C3×C4C23×D311yescharacteristic
471C2×C3×C4C23×D311yescharacteristic
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—31no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C4×D3—32no—
490C4×D3—32no—
491C4×D3—32no—
492C4×D3—32no—
493C4×D3—62no—
494C4×D3—62no—
495C4×D3—64no—
496C4×D3—64no—
497C4×D3—241no—
498C4×D3—241no—
499Dic6—21no—
500Dic6—21no—
501Dic6—64no—
502Dic6—64no—
503Dic6—81no—
504Dic6—241no—
505Dic6—241no—
506Dic6D3×Q812yes—
507Dic6D3×Q812yes—
508C3×C8—21no—
509C3×C8—21no—
510C3×C8—21no—
511C3×C8—21no—
512C3×C8—41no—
513C3×C8—41no—
514C3⋊C8—61no—
515C3⋊C8—61no—
516C3⋊C8—61no—
517C3⋊C8—61no—
518C3⋊C8—121no—
519C3⋊C8—121no—
520C2×C32C2×C22⋊Q811yescharacteristic
521C2×C32#57711yescharacteristic
522C2×C32#57811yescharacteristic
523C3⋊D3—22no—
524C2×Q8—31no—
525C2×Q8—31no—
526C2×Q8—61no—
527C2×Q8—94no—
528C2×Q8—181no—
529C2×Q8—181no—
530C2×Q8—182no—
531C22×C4—91no—
532C22×C4—181no—
533C22×C4—181no—
534M16—182no—
535C2×C8—91no—
536C2×C8—91no—
537C2×C8—182no—
538C2×C8C2×D3211yescharacteristic
539C2×C8C2×D3211yescharacteristic
540C4⋊C4—31no—
541C4⋊C4—31no—
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—31no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—91no—
552C4⋊C4—91no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C22⋊C4—91no—
560C22⋊C4—91no—
561C22⋊C4—181no—
562C22⋊C4—181no—
563C42—61no—
564C42—61no—
565C42—91no—
566C42—181no—
567C42—181no—
568C42—181no—
569C42—181no—
570C42C2×D3211yescharacteristic
571C22×C3—21no—
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C2×D3×D411yescharacteristic
574C2×D3—32no—
575C2×D3—32no—
576C2×D3—62no—
577C2×D3—61no—
578C2×D3—61no—
579C2×D3—61no—
580C2×D3—61no—
581C2×D3—121no—
582C2×D3—121no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—62no—
592C3×C4—62no—
593C3×C4—121no—
594C3×C4—121no—
595C3×C4—121no—
596C3×C4—121no—
597C3×C4—121no—
598C3×C4—121no—
599C3×C4C2×D3×Q811yescharacteristic
600C3×C4C2×D3×Q811yescharacteristic
601C3×C4D3×#4111yescharacteristic
602C3×C4D3×#4111yescharacteristic
603Dic3—22no—
604Dic3—22no—
605Dic3—32no—
606Dic3—32no—
607Dic3—41no—
608Dic3—41no—
609Dic3—41no—
610Dic3—41no—
611Dic3—41no—
612Dic3—41no—
613Dic3—62no—
614Dic3—61no—
615Dic3—61no—
616Dic3—61no—
617Dic3—61no—
618Dic3—121no—
619Dic3—121no—
620C32#308211yescharacteristic, complemented, Sylow
621C23—91no—
622Q8—32no—
623Q8—32no—
624Q8—61no—
625Q8—61no—
626Q8—184no—
627Q8—241no—
628Q8—721no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—91no—
638C2×C4—92no—
639C2×C4—92no—
640C2×C4—91no—
641C2×C4—91no—
642C2×C4—184no—
643C2×C4—721no—
644C2×C4#380211yescharacteristic
645C2×C4#380211yescharacteristic
646C2×C4C22×D3211yescharacteristic
647C8—21no—
648C8—21no—
649C8—181no—
650C8—181no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3D3×C22⋊Q811yescharacteristic
655C2×C3D3×C22⋊Q811yescharacteristic
656C2×C3#576611yescharacteristic
657C2×C3#577111yescharacteristic
658C2×C3#577511yescharacteristic
659C2×C3#577811yescharacteristic
660D3—62no—
661D3—62no—
662D3—122no—
663C22—92no—
664C22—181no—
665C22—181no—
666C22C2×#380211yescharacteristic
667C4—21no—
668C4—21no—
669C4—62no—
670C4—62no—
671C4—92no—
672C4—121no—
673C4—121no—
674C4—121no—
675C4—121no—
676C4—121no—
677C4—121no—
678C4—181no—
679C4—181no—
680C4#6431211yescharacteristic
681C4D32×Q811yescharacteristic
682C3—21no—
683C3#8111011yescharacteristic, complemented
684C3#8123211yescharacteristic, complemented
685C2—182no—
686C2#1059463111yescharacteristic
687C2#1059470311yescharacteristic
688C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊C8D32
hypocenterC32#3082
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4850C2semidirect
5. C3×#4829C2semidirect
6. #10590821C2semidirect
7. #10590821C2semidirect
8. #10590817C2semidirect
9. #10590816C2semidirect
14. #10590286C2semidirect
15. #10590285C2semidirect
79. #4850D3semidirect
83. #4829D3semidirect
101. #3797Q8semidirect
620. C32#3082semidirect
683. C3#81110semidirect
684. C3#81232semidirect

Maximal subgroups

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

subgroupindex
#105938552
#105938482
#105925382
C3×#48502
C3×#48292
#105908212
#105908172
#105908162
#105907142
#105906912
#105906882
#105906722
#105902862
#105902852
#812323
#811103