Finite Group Databasebeta

← #11869062

Subgroups — #11869062

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
1C3×#5572C211yesmaximal, characteristic
2#10593959C211yesmaximal, characteristic
3#10592719C211yesmaximal, characteristic, complemented
4C3×#5022C211yesmaximal, characteristic, complemented
5#10591557C211yesmaximal, characteristic
6D3×#835C211yesmaximal, characteristic
7#10591547C211yesmaximal, characteristic, complemented
8#10591546C211yesmaximal, characteristic, complemented
9#10590571C211yesmaximal, characteristic
10#10590556C211yesmaximal, characteristic, complemented
11#10590544C211yesmaximal, characteristic, complemented
12#10590437C211yesmaximal, characteristic
13#10590324C211yesmaximal, characteristic
14#10590286C211yesmaximal, characteristic, complemented
15#10590283C211yesmaximal, characteristic, complemented
16#82550—31nomaximal
17#81232—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20#64078C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×#892—21no—
23C3×#892C2211yescharacteristic
24C3×#887—21no—
25C3×#887C2211yescharacteristic
26C3×#872—21no—
27C3×#872C2211yescharacteristic
28C3×#870C2211yescharacteristic
29C3×C4×Dic6—21no—
30C3×C4×Dic6C2211yescharacteristic
31#63918C2211yescharacteristic
32#63896—21no—
33#63893—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63869C2211yescharacteristic
36#63845—21no—
37#63841C2211yescharacteristic
38#63840—21no—
39C2×#3711C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41#63662C2211yescharacteristic
42#63662C2211yescharacteristic
43#63635C2211yescharacteristic
44#63635C2211yescharacteristic
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#808C2211yescharacteristic
49C3×#807C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63576C2211yescharacteristic
52#63575C2211yescharacteristic
53#63575C2211yescharacteristic
54#63574C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61C3×#519—31no—
62#5689—31no—
63#5572D311yescharacteristic
64#5519—31no—
65C3×#479—31no—
66#5225—31no—
67C2×#835—31no—
68#5063—31no—
69#5022—31no—
70#5022—31no—
71#5022—31no—
72#5022D311yescharacteristic, complemented
73#5021—31no—
74#5021—31no—
75#5020—31no—
76#5020—31no—
77#5020—31no—
78#5020—61no—
79#4999—31no—
80#4998—31no—
81#4995—31no—
82#4880—31no—
83#4877—31no—
84#4861—31no—
85#4854—31no—
86#4850—31no—
87#4839—31no—
88#4802—31no—
89D3×#103—31no—
90#4796—31no—
91#4793—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C3×D3×Q8—22no—
95C3×D3×Q8Q814yescomplemented
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6—21no—
99C2×C3×Dic6C2311yescharacteristic
100C2×#627—21no—
101C2×D3×Dic3—21no—
102C32×C4⋊C4—21no—
103C32×C4⋊C4C2311yescharacteristic
104C32×C42—21no—
105C32×C42C2311yescharacteristic
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×(C2×D3)⋊C4—21no—
112C3×(C2×D3)⋊C4D411yescharacteristic
113C3×(C2×D3)⋊C4D411yescharacteristic
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4D411yescharacteristic
123C3×Dic3⋊C4D411yescharacteristic
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137#3711—22no—
138D3×C3⋊C8—22no—
139#3082—91noSylow
140C22×C3×Q8—31no—
141C2×D3×Q8C2×D311yescharacteristic
142C3×#125—31no—
143C3×C4×Q8—21no—
144C3×C4×Q8—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—61no—
148C3×C4×Q8—61no—
149C3×C4×Q8C2×D311yescharacteristic
150C3×C4×Q8C2×D311yescharacteristic
151C3×#117—31no—
152C3×#117—31no—
153C3×#117—61no—
154C3×#117—61no—
155Q8×Dic3C2×D311yescharacteristic
156#926—31no—
157C2×C4⋊Dic3—31no—
158C2×#208—31no—
159C22×C3⋊C8—31no—
160C2×ΓL(1,𝔽25)—31no—
161C2×D3×C8—31no—
162#897—61no—
163#896—61no—
164#892—21no—
165#892—31no—
166#892C2×D311yescharacteristic
167D3×C4⋊C4—31no—
168#890—31no—
169#890—61no—
170#889—61no—
171#888—31no—
172#888—61no—
173#888—61no—
174#887—21no—
175#887C2×D311yescharacteristic
176#878—61no—
177#878—61no—
178#872—21no—
179#872C2×D311yescharacteristic
180#870—31no—
181#870C2×D311yescharacteristic
182#869—31no—
183#869—31no—
184#869—31no—
185#869—61no—
186C4×Dic6—21no—
187C4×Dic6C2×D311yescharacteristic
188C3×#107—31no—
189C3×#106—31no—
190C3×C4⋊C8—31no—
191C3×#103—31no—
192C3×#103—31no—
193#835—31no—
194#835—31no—
195#835—31no—
196#835—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#835—61no—
202#835—61no—
203#835C2×D311yescharacteristic
204#835C2×D311yescharacteristic
205#818—31no—
206#818—31no—
207#816—31no—
208#816—31no—
209Dic3⋊C8—31no—
210Dic3⋊C8—31no—
211#810—31no—
212#810—31no—
213#808—31no—
214#808—31no—
215#808—31no—
216#808—31no—
217#808—31no—
218#808—31no—
219#808—61no—
220#808—61no—
221#808C2×D311yescharacteristic
222#807—31no—
223#807—31no—
224#807—31no—
225#807—31no—
226#807C2×D311yescharacteristic
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233C22×C3×D3C2×D411yescharacteristic
234C32×Q8—21no—
235C32×Q8C2×Q812yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2×D411yescharacteristic
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243#634—81no—
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×D3—24no—
252C3×C4×D3C2×Q812yes—
253C3×C4×D3#4112yes—
254C3×Dic6—21no—
255C3×Dic6—24no—
256C3×Dic6C2×Q812yes—
257#627—81no—
258D3×Dic3—81no—
259C3⋊(C3⋊C8)—21no—
260C3⋊(C3⋊C8)—21no—
261C3×C3⋊C8—21no—
262C3×C3⋊C8—21no—
263#544—91no—
264#519—31no—
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—91no—
276#419—91no—
277C2×#103—91no—
278C2×C3×Q8—21no—
279C2×C3×Q8—34no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×Q8—62no—
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×Q8C22×D311yescharacteristic
285C22×C3×C4—31no—
286C22×C3×C4—61no—
287C22×Dic3—61no—
288D3×Q8—22no—
289D3×Q8Dic614yescomplemented
290C2×C4×D3—21no—
291C2×C4×D3—61no—
292C2×C4×D3C22×D311yescharacteristic
293C2×Dic6—21no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—121no—
299C2×Dic6C22×D311yescharacteristic
300C2×C3×C8—31no—
301C2×C3×C8—31no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—31no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—41no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C4⋊C4C22×D311yescharacteristic
318C3×C22⋊C4—31no—
319C3×C22⋊C4—31no—
320C3×C22⋊C4—61no—
321C3×C42—21no—
322C3×C42—21no—
323C3×C42—21no—
324C3×C42—31no—
325C3×C42—41no—
326C3×C42—61no—
327C3×C42—61no—
328C3×C42—61no—
329C3×C42—61no—
330C3×C42C22×D311yescharacteristic
331C3×C42C22×D311yescharacteristic
332#217—61no—
333(C2×D3)⋊C4—21no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4#6711yescharacteristic
336(C2×D3)⋊C4#6711yescharacteristic
337C4⋊Dic3—21no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—121no—
350C4⋊Dic3C22×D311yescharacteristic
351C4⋊Dic3C22×D311yescharacteristic
352C4⋊Dic3C22×D311yescharacteristic
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
355Dic3⋊C4—21no—
356Dic3⋊C4—21no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4#6711yescharacteristic
363Dic3⋊C4#6711yescharacteristic
364C4×Dic3—21no—
365C4×Dic3—21no—
366C4×Dic3—21no—
367C4×Dic3—21no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3C22×D311yescharacteristic
371#208—62no—
372C2×C3⋊C8—31no—
373C2×C3⋊C8—31no—
374C2×C3⋊C8—31no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—61no—
377C2×C3⋊C8—61no—
378C2×C3⋊C8—62no—
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381ΓL(1,𝔽25)—62no—
382D3×C8—62no—
383C22×C32C22×D411yescharacteristic
384C2×C3×D3—21no—
385C2×C3×D3—21no—
386C2×C3×D3C22⋊Q812yes—
387C32×C4—21no—
388C32×C4—22no—
389C32×C4—21no—
390C32×C4—41no—
391C32×C4C22×Q811yescharacteristic
392C32×C4C2×#4111yescharacteristic
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—31no—
403C2×M16—91no—
404C22×C8—91no—
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—31no—
415C4×Q8—31no—
416C4×Q8—61no—
417C4×Q8—61no—
418C4×Q8D3211yescharacteristic
419#117—31no—
420#117—31no—
421#117—61no—
422#117—61no—
423#117—91no—
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—91no—
435C4⋊C8—91no—
436C4⋊C8—91no—
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×#6711yescharacteristic
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—22no—
450C3×Q8—32no—
451C3×Q8—41no—
452C3×Q8—64no—
453C3×Q8—61no—
454C3×Q8C2×Dic612yes—
455C3×Q8D3×Q812yes—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—31no—
464C2×C3×C4—32no—
465C2×C3×C4—32no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—64no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4D3×D411yescharacteristic
476C2×C3×C4D3×D411yescharacteristic
477C2×C3×C4C2×#6711yescharacteristic
478C2×C3×C4C2×#6711yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480C2×C3×C4C23×D311yescharacteristic
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—121no—
490C2×Dic3—121no—
491C2×Dic3—241no—
492C2×Dic3C2×#6711yescharacteristic
493C2×Dic3C2×#6711yescharacteristic
494C2×Dic3C2×#6711yescharacteristic
495C4×D3—24no—
496C4×D3—241no—
497C4×D3C2×Dic612yes—
498C4×D3#23512yes—
499Dic6—21no—
500Dic6—24no—
501Dic6—241no—
502Dic6—241no—
503Dic6—241no—
504Dic6—241no—
505Dic6—242no—
506Dic6C2×Dic612yes—
507C3×C8—61no—
508C3×C8—61no—
509C3⋊C8—21no—
510C3⋊C8—21no—
511C3⋊C8—61no—
512C3⋊C8—61no—
513C3⋊C8—61no—
514C3⋊C8—61no—
515C3⋊C8—121no—
516C3⋊C8—121no—
517C2×C32C2×C22⋊Q811yescharacteristic
518C2×C32#57711yescharacteristic
519C2×C32#57811yescharacteristic
520C3×D3—22no—
521C2×Q8—34no—
522C2×Q8—31no—
523C2×Q8—61no—
524C2×Q8—62no—
525C2×Q8—181no—
526C2×Q8—181no—
527C2×Q8C2×D3211yescharacteristic
528C22×C4—31no—
529C22×C4—61no—
530C22×C4—181no—
531M16—182no—
532C2×C8—31no—
533C2×C8—31no—
534C2×C8—91no—
535C2×C8—91no—
536C2×C8—182no—
537C4⋊C4—21no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—31no—
541C4⋊C4—31no—
542C4⋊C4—31no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—91no—
549C4⋊C4—91no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4—181no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4C2×D3211yescharacteristic
556C22⋊C4—31no—
557C22⋊C4—31no—
558C22⋊C4—61no—
559C22⋊C4—181no—
560C42—21no—
561C42—31no—
562C42—61no—
563C42—61no—
564C42—61no—
565C42—61no—
566C42—181no—
567C42C2×D3211yescharacteristic
568C22×C3—21no—
569C22×C3—32no—
570C22×C3—61no—
571C22×C3—61no—
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C22×#6711yescharacteristic
574C2×D3—21no—
575C2×D3—21no—
576C2×D3#92412yes—
577C3×C4—22no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—22no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—22no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—32no—
587C3×C4—41no—
588C3×C4—42no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—61no—
592C3×C4—61no—
593C3×C4—62no—
594C3×C4—81no—
595C3×C4—121no—
596C3×C4—121no—
597C3×C4—121no—
598C3×C4C22×Dic611yescharacteristic
599C3×C4C2×#23511yescharacteristic
600C3×C4C2×D3×Q811yescharacteristic
601C3×C4D3×#4111yescharacteristic
602Dic3—22no—
603Dic3—21no—
604Dic3—21no—
605Dic3—41no—
606Dic3—41no—
607Dic3—41no—
608Dic3—121no—
609Dic3—121no—
610Dic3—121no—
611Dic3—121no—
612Dic3—241no—
613Dic3—241no—
614Dic3#92412yes—
615C32#308211yescharacteristic, complemented, Sylow
616C23—31no—
617Q8—21no—
618Q8—32no—
619Q8—64no—
620Q8—61no—
621Q8—721no—
622Q8—721no—
623Q8D3×Dic612yes—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—31no—
627C2×C4—32no—
628C2×C4—32no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—64no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—181no—
637C2×C4—181no—
638C2×C4—721no—
639C2×C4D3×#6711yescharacteristic
640C2×C4D3×#6711yescharacteristic
641C2×C4C22×D3211yescharacteristic
642C8—61no—
643C8—61no—
644C8—181no—
645C8—181no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—62no—
650C2×C3D3×C22⋊Q811yescharacteristic
651C2×C3#577111yescharacteristic
652C2×C3#577811yescharacteristic
653C2×C3C2×#92411yescharacteristic
654C2×C3#583711yescharacteristic
655C2×C3#583811yescharacteristic
656D3—22no—
657C22—32no—
658C22—61no—
659C22—61no—
660C22C2×D3×#6711yescharacteristic
661C4—22no—
662C4—21no—
663C4—21no—
664C4—32no—
665C4—41no—
666C4—62no—
667C4—61no—
668C4—61no—
669C4—121no—
670C4—121no—
671C4—121no—
672C4—361no—
673C4—361no—
674C4C2×D3×Dic611yescharacteristic
675C4D3×#23511yescharacteristic
676C3—21no—
677C3#8123211yescharacteristic, complemented
678C3#8255011yescharacteristic, complemented
679C2—62no—
680C2D3×#92411yescharacteristic
681C2#1059531911yescharacteristic
682C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4×Q8D32
hypocenterC32#3082
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #10592719C2semidirect
4. C3×#5022C2semidirect
7. #10591547C2semidirect
8. #10591546C2semidirect
10. #10590556C2semidirect
11. #10590544C2semidirect
14. #10590286C2semidirect
15. #10590283C2semidirect
72. #5022D3semidirect
95. C3×D3×Q8Q8semidirect
289. D3×Q8Dic6semidirect
615. C32#3082semidirect
677. C3#81232semidirect
678. C3#82550semidirect

Maximal subgroups

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

subgroupindex
C3×#55722
#105939592
#105927192
C3×#50222
#105915572
D3×#8352
#105915472
#105915462
#105905712
#105905562
#105905442
#105904372
#105903242
#105902862
#105902832
#825503
#812323