Finite Group Databasebeta

← #11869050

Subgroups — #11869050

Order 1152.

772 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593959C211yesmaximal, characteristic
2#10593885C211yesmaximal, characteristic
3#10592550C211yesmaximal, characteristic, complemented
4C3×#4839C211yesmaximal, characteristic
5C3×#4829C211yesmaximal, characteristic, complemented
6#10590948C211yesmaximal, characteristic
7#10590815C211yesmaximal, characteristic, complemented
8#10590809C211yesmaximal, characteristic, complemented
9#10590805C211yesmaximal, characteristic, complemented
10#10590803C211yesmaximal, characteristic, complemented
11#10590706C211yesmaximal, characteristic
12#10590683C211yesmaximal, characteristic
13D3×#816C211yesmaximal, characteristic
14#10590292C211yesmaximal, characteristic, complemented
15#10590283C211yesmaximal, characteristic, complemented
16#81233—31nomaximal
17#79101—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19#64078C2211yescharacteristic
20C4×#634C2211yescharacteristic
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23C3×#872C2211yescharacteristic
24C3×#870C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63918C2211yescharacteristic
27#63896—21no—
28#63893—21no—
29D3×C4⋊Dic3C2211yescharacteristic
30#63878—21no—
31#63877—21no—
32#63869C2211yescharacteristic
33#63845—21no—
34#63844C2211yescharacteristic
35Dic3×Dic6C2211yescharacteristic
36#63841C2211yescharacteristic
37#63841C2211yescharacteristic
38#63840—21no—
39#63838—21no—
40#63837—21no—
41C32×C4⋊C8C2211yescharacteristic
42#63644C2211yescharacteristic
43#63644C2211yescharacteristic
44#63643C2211yescharacteristic
45#63643C2211yescharacteristic
46C3×#818C2211yescharacteristic
47C3×#817C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×C4⋊(C3⋊C8)C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#5689—31no—
62#5572—31no—
63#5519—31no—
64#5516—31no—
65C3×#479—31no—
66C3×#424—31no—
67#5121—31no—
68#5120—31no—
69#5106—31no—
70C2×#816—31no—
71#5063—31no—
72#5021—31no—
73#4881—31no—
74#4875—31no—
75#4860—31no—
76#4857—31no—
77#4851—31no—
78#4851—31no—
79#4851—31no—
80#4851—61no—
81#4850—31no—
82#4850—31no—
83#4839D311yescharacteristic
84#4829—31no—
85#4829—31no—
86#4829—31no—
87#4829D311yescharacteristic, complemented
88#4802—31no—
89D3×#103—31no—
90#4799—31no—
91#4791—31no—
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×#627—21no—
97C2×#627—21no—
98C2×D3×Dic3—21no—
99C2×D3×Dic3—21no—
100D3×Dic6—22no—
101D3×Dic6Q814yescomplemented
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C42C2311yescharacteristic
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110C4×C3⋊Dic3—21no—
111C3×(C2×D3)⋊C4D411yescharacteristic
112C3×(C2×D3)⋊C4D411yescharacteristic
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4D411yescharacteristic
120C3×Dic3⋊C4D411yescharacteristic
121C3×C4×Dic3—21no—
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C3×ΓL(1,𝔽25)—22no—
126C3×D3×C8—22no—
127#3724—21no—
128#3724—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3082—91noSylow
140C2×D3×Q8—31no—
141C22×Dic6—31no—
142C2×C3×M16—31no—
143C22×C3×C8—31no—
144C3×#125—31no—
145C3×C4×Q8—31no—
146C3×#117—31no—
147Q8×Dic3—31no—
148#926—31no—
149#926—31no—
150C2×C4⋊Dic3—31no—
151C2×ΓL(1,𝔽25)C2×D311yescharacteristic
152C2×D3×C8C2×D311yescharacteristic
153#897—61no—
154#896—61no—
155#892—31no—
156#892—31no—
157#892—61no—
158D3×C4⋊C4—31no—
159#890—31no—
160#890—61no—
161#889—61no—
162#888—31no—
163#888—61no—
164#888—61no—
165#887—31no—
166#887—61no—
167#887—61no—
168#887—61no—
169#878—61no—
170#878—61no—
171#877—61no—
172#877—61no—
173#872—61no—
174#872C2×D311yescharacteristic
175#870—31no—
176#870C2×D311yescharacteristic
177#869—31no—
178#869—31no—
179#869—31no—
180#869—61no—
181C4×Dic6—31no—
182C4×Dic6—31no—
183C4×Dic6—31no—
184C4×Dic6—31no—
185C4×Dic6—61no—
186C4×Dic6—61no—
187C4×Dic6C2×D311yescharacteristic
188C3×#107—31no—
189C3×#106—31no—
190C3×C4⋊C8—21no—
191C3×C4⋊C8—31no—
192C3×C4⋊C8—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8C2×D311yescharacteristic
195C3×C4⋊C8C2×D311yescharacteristic
196C3×#103—31no—
197C3×#103—31no—
198#835—31no—
199#835—31no—
200#818—31no—
201#818—31no—
202#818—31no—
203#818C2×D311yescharacteristic
204#817—31no—
205#817—31no—
206#817—31no—
207#817—31no—
208#817—31no—
209#817—61no—
210#817—61no—
211#817C2×D311yescharacteristic
212#816—31no—
213#816—31no—
214#816—31no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—61no—
221#816—61no—
222#816C2×D311yescharacteristic
223#816C2×D311yescharacteristic
224Dic3⋊C8C2×D311yescharacteristic
225Dic3⋊C8C2×D311yescharacteristic
226#810—31no—
227#810—31no—
228#808—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233C22×C3×D3C2×D411yescharacteristic
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241#634—21no—
242#634—81no—
243#634C2×Q812yes—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×C4×D3C2×Q812yes—
252C3×C4×D3#4112yes—
253C3×Dic6—21no—
254C3×Dic6C2×Q812yes—
255#627—24no—
256#627—81no—
257D3×Dic3—24no—
258D3×Dic3—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—91no—
270#477—91no—
271#475—91no—
272#475—91no—
273#428—91no—
274#427—91no—
275#424—31no—
276#419—91no—
277C2×#103—91no—
278C2×C3×Q8—31no—
279C22×C3×C4—31no—
280C22×Dic3—61no—
281C22×Dic3—61no—
282D3×Q8—34no—
283D3×Q8—62no—
284C2×C4×D3—61no—
285C2×C4×D3—61no—
286C2×C4×D3C22×D311yescharacteristic
287C2×Dic6—31no—
288C2×Dic6—31no—
289C2×Dic6—34no—
290C2×Dic6—61no—
291C2×Dic6—62no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—121no—
299C2×Dic6C22×D311yescharacteristic
300C3×M16—62no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—31no—
304C2×C3×C8—31no—
305C2×C3×C8—62no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C2×C3×C8C22×D311yescharacteristic
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C22⋊C4—31no—
319C3×C22⋊C4—31no—
320C3×C42—21no—
321C3×C42—31no—
322C3×C42—61no—
323C3×C42C22×D311yescharacteristic
324C3×C42C22×D311yescharacteristic
325#217—61no—
326#217—61no—
327(C2×D3)⋊C4—61no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4D1211yescharacteristic
330(C2×D3)⋊C4D1211yescharacteristic
331C4⋊Dic3—31no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—121no—
347C4⋊Dic3C22×D311yescharacteristic
348C4⋊Dic3C22×D311yescharacteristic
349C4⋊Dic3C22×D311yescharacteristic
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—121no—
364Dic3⋊C4D1211yescharacteristic
365Dic3⋊C4D1211yescharacteristic
366C4×Dic3—21no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—121no—
378C4×Dic3C22×D311yescharacteristic
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381ΓL(1,𝔽25)—22no—
382D3×C8—22no—
383C22×C32C22×D411yescharacteristic
384C2×C3×D3—21no—
385C2×C3×D3—21no—
386C2×C3×D3C22⋊Q812yes—
387C32×C4—21no—
388C32×C4—21no—
389C32×C4C22×Q811yescharacteristic
390C32×C4C2×#4111yescharacteristic
391C3⋊Dic3—22no—
392C3⋊Dic3—41no—
393C3⋊Dic3—41no—
394C3⋊Dic3—41no—
395C3×Dic3—22no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3C22⋊Q812yes—
402C22×Q8—91no—
403C2×M16—31no—
404C22×C8—31no—
405C4⋊Q8—91no—
406C4⋊Q8—91no—
407C4⋊Q8—181no—
408#125—31no—
409#125—91no—
410#125—181no—
411C22⋊Q8—181no—
412C22⋊Q8—181no—
413C4×Q8—31no—
414C4×Q8—91no—
415C4×Q8—91no—
416C4×Q8—91no—
417C4×Q8—181no—
418C4×Q8—181no—
419#117—31no—
420#117—91no—
421#117—91no—
422#117—181no—
423#117—181no—
424C2×C4⋊C4—91no—
425#107—31no—
426#107—91no—
427#107—91no—
428#107—91no—
429#106—31no—
430#106—91no—
431#106—91no—
432#106—91no—
433C4⋊C8—31no—
434C4⋊C8—31no—
435C4⋊C8—31no—
436C4⋊C8D3211yescharacteristic
437#103—31no—
438#103—31no—
439#103—91no—
440#103—91no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103—91no—
445C23×C3—31no—
446C22×D3C2×D1211yescharacteristic
447C3×Q8—32no—
448C3×Q8—61no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—31no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—31no—
456C2×C3×C4—31no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4C2×D1211yescharacteristic
462C2×C3×C4C2×D1211yescharacteristic
463C2×C3×C4D3×D411yescharacteristic
464C2×C3×C4D3×D411yescharacteristic
465C2×C3×C4C23×D311yescharacteristic
466C2×C3×C4C23×D311yescharacteristic
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—64no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—121no—
481C2×Dic3—121no—
482C2×Dic3—121no—
483C2×Dic3—121no—
484C2×Dic3—241no—
485C2×Dic3C2×D1211yescharacteristic
486C2×Dic3C2×D1211yescharacteristic
487C2×Dic3C2×D1211yescharacteristic
488C4×D3—64no—
489C4×D3—241no—
490C4×D3#23712yes—
491C4×D3D3×Q812yes—
492Dic6—21no—
493Dic6—32no—
494Dic6—32no—
495Dic6—62no—
496Dic6—64no—
497Dic6—61no—
498Dic6—61no—
499Dic6—64no—
500Dic6—121no—
501Dic6—241no—
502Dic6—241no—
503Dic6—241no—
504Dic6—241no—
505Dic6—242no—
506Dic6D3×Q812yes—
507C3×C8—21no—
508C3×C8—21no—
509C3×C8—21no—
510C3×C8—21no—
511C3×C8—41no—
512C3×C8—41no—
513C3×C8—61no—
514C3×C8—61no—
515C3⋊C8—21no—
516C3⋊C8—21no—
517C2×C32C2×C22⋊Q811yescharacteristic
518C2×C32#57711yescharacteristic
519C2×C32#57811yescharacteristic
520C3×D3—22no—
521C2×Q8—31no—
522C2×Q8—94no—
523C2×Q8—91no—
524C2×Q8—181no—
525C2×Q8—181no—
526C2×Q8—182no—
527C2×Q8—181no—
528C22×C4—31no—
529C22×C4—181no—
530C22×C4—181no—
531M16—62no—
532C2×C8—31no—
533C2×C8—31no—
534C2×C8—62no—
535C2×C8C2×D3211yescharacteristic
536C2×C8C2×D3211yescharacteristic
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—31no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—91no—
546C4⋊C4—91no—
547C4⋊C4—91no—
548C4⋊C4—181no—
549C4⋊C4—181no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4—181no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C22⋊C4—31no—
557C22⋊C4—31no—
558C22⋊C4—181no—
559C22⋊C4—181no—
560C42—31no—
561C42—61no—
562C42—181no—
563C42—181no—
564C42—181no—
565C42—181no—
566C42—181no—
567C42C2×D3211yescharacteristic
568C22×C3—21no—
569C22×C3—32no—
570C22×C3—61no—
571C22×C3—61no—
572C22×C3C22×D1211yescharacteristic
573C22×C3C2×D3×D411yescharacteristic
574C2×D3—21no—
575C2×D3—21no—
576C2×D3#89712yes—
577C3×C4—22no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—32no—
585C3×C4—41no—
586C3×C4—62no—
587C3×C4—61no—
588C3×C4—61no—
589C3×C4—121no—
590C3×C4—121no—
591C3×C4—121no—
592C3×C4C2×#23711yescharacteristic
593C3×C4C2×D3×Q811yescharacteristic
594C3×C4C2×D3×Q811yescharacteristic
595C3×C4D3×#4111yescharacteristic
596Dic3—21no—
597Dic3—21no—
598Dic3—22no—
599Dic3—41no—
600Dic3—41no—
601Dic3—41no—
602Dic3—62no—
603Dic3—62no—
604Dic3—122no—
605Dic3—121no—
606Dic3—121no—
607Dic3—121no—
608Dic3—121no—
609Dic3—121no—
610Dic3—121no—
611Dic3—241no—
612Dic3—241no—
613Dic3—241no—
614Dic3#89712yes—
615C32#308211yescharacteristic, complemented, Sylow
616C23—31no—
617Q8—32no—
618Q8—61no—
619Q8—92no—
620Q8—184no—
621Q8—181no—
622Q8—721no—
623Q8—721no—
624C2×C4—31no—
625C2×C4—32no—
626C2×C4—32no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—184no—
634C2×C4—181no—
635C2×C4—181no—
636C2×C4—181no—
637C2×C4—181no—
638C2×C4—721no—
639C2×C4D3×D1211yescharacteristic
640C2×C4D3×D1211yescharacteristic
641C2×C4C22×D3211yescharacteristic
642C8—21no—
643C8—21no—
644C8—61no—
645C8—61no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—62no—
650C2×C3C2×#89711yescharacteristic
651C2×C3D3×C22⋊Q811yescharacteristic
652C2×C3#575111yescharacteristic
653C2×C3#575311yescharacteristic
654C2×C3#577011yescharacteristic
655C2×C3#577911yescharacteristic
656D3—22no—
657C22—32no—
658C22—61no—
659C22—61no—
660C22C2×D3×D1211yescharacteristic
661C4—21no—
662C4—21no—
663C4—32no—
664C4—62no—
665C4—61no—
666C4—61no—
667C4—121no—
668C4—121no—
669C4—121no—
670C4—182no—
671C4—361no—
672C4—361no—
673C4—361no—
674C4D3×#23711yescharacteristic
675C4D32×Q811yescharacteristic
676C3—21no—
677C3#7910111yescharacteristic, complemented
678C3#8123311yescharacteristic, complemented
679C2—62no—
680C2D3×#89711yescharacteristic
681C2#1059467911yescharacteristic
682C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
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
3. #10592550C2semidirect
5. C3×#4829C2semidirect
7. #10590815C2semidirect
8. #10590809C2semidirect
9. #10590805C2semidirect
10. #10590803C2semidirect
14. #10590292C2semidirect
15. #10590283C2semidirect
87. #4829D3semidirect
101. D3×Dic6Q8semidirect
615. C32#3082semidirect
677. C3#79101semidirect
678. C3#81233semidirect

Maximal subgroups

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

subgroupindex
#105939592
#105938852
#105925502
C3×#48392
C3×#48292
#105909482
#105908152
#105908092
#105908052
#105908032
#105907062
#105906832
D3×#8162
#105902922
#105902832
#812333
#791013