Finite Group Databasebeta

← #11895188

Subgroups — #11895188

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595420C211yesmaximal, characteristic, complemented
2#10594376C211yesmaximal, characteristic
3#10592491C211yesmaximal, characteristic, complemented
4C3×#4792C211yesmaximal, characteristic, complemented
5C3×#4788C211yesmaximal, characteristic
6#10591569C211yesmaximal, characteristic
7#10591564C211yesmaximal, characteristic
8#10591544C211yesmaximal, characteristic, complemented
9#10590890C211yesmaximal, characteristic, complemented
10C8×#627C211yesmaximal, characteristic, complemented
11#10590744C211yesmaximal, characteristic
12#10590742C211yesmaximal, characteristic
13#10590559C211yesmaximal, characteristic
14#10590497C211yesmaximal, characteristic, complemented
15#10590487C211yesmaximal, characteristic, complemented
16#81620—31nomaximal
17#79619—31nomaximal
18C2×D3×Dic6—21no—
19#64153C2211yescharacteristic
20#64097C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×#888C2211yescharacteristic
26#63918C2211yescharacteristic
27C4×#627C2211yescharacteristic
28#63898C2211yescharacteristic
29#63896—21no—
30Dic3×D12C2211yescharacteristic
31#63887—21no—
32#63867—21no—
33#63866C2211yescharacteristic
34#63851—21no—
35#63847—21no—
36#63846—21no—
37#63844C2211yescharacteristic
38#63843C2211yescharacteristic
39#63837—21no—
40C2×#3716C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63662C2211yescharacteristic
44#63643C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63567C2211yescharacteristic
60#63566C2211yescharacteristic
61#5727—31no—
62#5721—31no—
63#5567—31no—
64D4×Dic6—31no—
65C3×#487—31no—
66C3×C4×SD16—31no—
67#5162—31no—
68#5162—31no—
69#5094—31no—
70#5083—31no—
71#5020—31no—
72#5019—31no—
73#4854—31no—
74#4854—31no—
75#4818—31no—
76#4818—31no—
77#4792—31no—
78#4792—31no—
79#4792—31no—
80#4792—61no—
81#4792D311yescharacteristic, complemented
82#4791—31no—
83#4791—31no—
84#4788—31no—
85#4788D311yescharacteristic
86#4758—31no—
87#4758—31no—
88C4×#204—31no—
89#4681—31no—
90C8×Dic6—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627D411yescharacteristic
101C2×D3×Dic3—21no—
102C2×D3×Dic3—21no—
103D3×Dic6—44no—
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108#3750—21no—
109#3750—21no—
110C4×C3⋊Dic3C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×#215—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125#3724—21no—
126#3724D411yescharacteristic
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3D411yescharacteristic
132Dic3⋊Dic3D411yescharacteristic
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135Dic32—21no—
136Dic32—21no—
137#3716—22no—
138#3715—22no—
139#3359—91noSylow
140C2×D3×Q8—61no—
141C22×Dic6—61no—
142C2×C3×SD16—31no—
143C3×C4⋊Q8—31no—
144C3×C4⋊Q8—31no—
145C3×C4×Q8—31no—
146C3×C4×D4—31no—
147#946—61no—
148Q8×Dic3—31no—
149Q8×Dic3C2×D311yescharacteristic
150#944—31no—
151#944—31no—
152#944—31no—
153#944—61no—
154#944C2×D311yescharacteristic
155C2×#215—31no—
156C2×#215C2×D311yescharacteristic
157D4×Dic3—31no—
158D4×Dic3—31no—
159C2×#214—31no—
160C2×#214—31no—
161#924—61no—
162C2×#204—31no—
163#896—61no—
164#896—61no—
165#893—31no—
166#893C2×D311yescharacteristic
167#890—61no—
168#889—61no—
169#889—61no—
170#889—61no—
171#889—61no—
172#888—31no—
173#888—31no—
174#888—31no—
175#888—61no—
176#888C2×D311yescharacteristic
177#887—31no—
178#887—31no—
179#887—61no—
180#878—61no—
181#878—61no—
182C4×D12—31no—
183#870—61no—
184#869—31no—
185#869—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—61no—
190C3×#106—31no—
191C3×#103—21no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103C2×D311yescharacteristic
196C3×#103C2×D311yescharacteristic
197C3×#102—31no—
198C3×C4×C8—31no—
199C3×C4×C8—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—61no—
204#835C2×D311yescharacteristic
205#821C2×D311yescharacteristic
206#817—31no—
207#816—31no—
208#816—31no—
209#816—31no—
210#816—31no—
211#816—61no—
212#816C2×D311yescharacteristic
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217C8×Dic3—31no—
218C8×Dic3—31no—
219C8×Dic3—61no—
220C8×Dic3C2×D311yescharacteristic
221C8×Dic3C2×D311yescharacteristic
222#810—31no—
223#810—31no—
224#810—31no—
225#810—61no—
226#810C2×D311yescharacteristic
227#808—31no—
228#808—31no—
229#808—31no—
230#808C2×D311yescharacteristic
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C2×C3⋊Dic3C2×D411yescharacteristic
243#634—21no—
244#634—21no—
245#634—42no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×D12—21no—
254C3×D12#4112yes—
255C3×C4×D3—42no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—42no—
259#627—42no—
260#627SD1614yescomplemented
261D3×Dic3—42no—
262D3×Dic3—42no—
263C32×C8—21no—
264C3⋊(C3⋊C8)—21no—
265C3×C3⋊C8—21no—
266C3×C3⋊C8—21no—
267#557—91no—
268D4×Q8—91no—
269#487—31no—
270#487—91no—
271#487—91no—
272#475—91no—
273#475—91no—
274#475—91no—
275#461—91no—
276#461—91no—
277#461—91no—
278C8×Q8—91no—
279C4×SD16—31no—
280C4×SD16—91no—
281C4×SD16—91no—
282C2×C3×Q8—21no—
283C2×C3×Q8—31no—
284C2×C3×Q8—61no—
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×D4—31no—
288C22×C3×C4—61no—
289C22×Dic3—61no—
290C22×Dic3—61no—
291D3×Q8—124no—
292C2×D12C22×D311yescharacteristic
293C2×C4×D3—21no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×Dic6—21no—
297C2×Dic6—31no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—121no—
307C2×Dic6—124no—
308C2×Dic6C22×D311yescharacteristic
309C3×SD16—62no—
310C2×C3×C8—21no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C22×D311yescharacteristic
315C3×C4⋊C4—21no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C22⋊C4—61no—
325C3×C42—31no—
326C3×C42—31no—
327C3×C42—61no—
328#217—61no—
329#217—61no—
330#215—22no—
331#215—62no—
332#214—62no—
333#214—62no—
334(C2×D3)⋊C4—21no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
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⋊Dic3C22×D311yescharacteristic
348C4⋊Dic3C22×D311yescharacteristic
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—121no—
369Dic3⋊C4—121no—
370Dic3⋊C4—121no—
371C4×Dic3—21no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3C22×D311yescharacteristic
380C4×Dic3C22×D311yescharacteristic
381C2×C3⋊C8—31no—
382C2×C3⋊C8—31no—
383C2×C3⋊C8—61no—
384C2×C3⋊C8C22×D311yescharacteristic
385C2×C3⋊C8C22×D311yescharacteristic
386#204—62no—
387C22×C32C22×D411yescharacteristic
388C2×C3×D3—22no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C32×C4—41no—
392C32×C4—41no—
393C32×C4C2×#4111yescharacteristic
394C32×C42−1+411yescharacteristic
395C3⋊Dic3—21no—
396C3⋊Dic3—41no—
397C3⋊Dic3—41no—
398C3⋊Dic3C2×SD1612yes—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3C2×SD1612yes—
405C3×Dic3C2×SD1612yes—
406C22×Q8—181no—
407C2×SD16—31no—
408C2×SD16—91no—
409C2×SD16—91no—
410C4⋊Q8—31no—
411C4⋊Q8—31no—
412C4⋊Q8—91no—
413C4⋊Q8—91no—
414C4⋊Q8—91no—
415C4⋊Q8—91no—
416#125—181no—
417#125—181no—
418#125—181no—
419C22⋊Q8—181no—
420C22⋊Q8—181no—
421C22⋊Q8—181no—
422C4×Q8—31no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—181no—
427C4×D4—31no—
428C4×D4—91no—
429C4×D4—91no—
430#106—31no—
431#106—91no—
432#106—91no—
433C4⋊C8—91no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436#103—31no—
437#103—31no—
438#103—31no—
439#103—91no—
440#103—91no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103D3211yescharacteristic
445#102—31no—
446C4×C8—31no—
447C4×C8—31no—
448C4×C8—91no—
449C23×C3—61no—
450C22×D3—21no—
451C3×Q8—21no—
452C3×Q8—21no—
453C3×Q8—21no—
454C3×Q8—21no—
455C3×Q8—41no—
456C3×Q8—41no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8—122no—
460C3×D4—32no—
461C3×D4—61no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—122no—
477C2×C3×C4C23×D311yescharacteristic
478C2×C3×C4C23×D311yescharacteristic
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—121no—
493C2×Dic3—121no—
494C2×Dic3—122no—
495C2×Dic3—122no—
496C2×Dic3D3×D411yescharacteristic
497C2×Dic3D3×D411yescharacteristic
498C2×Dic3D3×D411yescharacteristic
499C2×Dic3D3×D411yescharacteristic
500D12—21no—
501D12#23512yes—
502C4×D3—42no—
503C4×D3—122no—
504C4×D3—122no—
505Dic6—21no—
506Dic6—21no—
507Dic6—34no—
508Dic6—34no—
509Dic6—42no—
510Dic6—61no—
511Dic6—61no—
512Dic6—61no—
513Dic6—61no—
514Dic6—121no—
515Dic6—121no—
516Dic6—122no—
517Dic6—122no—
518Dic6—122no—
519Dic6—122no—
520Dic6—242no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—41no—
524C3×C8—61no—
525C3×C8—61no—
526C3⋊C8—21no—
527C3⋊C8—21no—
528C3⋊C8—61no—
529C3⋊C8—61no—
530C3⋊C8—121no—
531C2×C32#54811yescharacteristic
532C2×C32C22×SD1611yescharacteristic
533C2×C32#57811yescharacteristic
534C3×D3—42no—
535C2×Q8—31no—
536C2×Q8—61no—
537C2×Q8—91no—
538C2×Q8—91no—
539C2×Q8—181no—
540C2×Q8—181no—
541C2×Q8—364no—
542C2×Q8C2×D3211yescharacteristic
543C2×D4—31no—
544C22×C4—61no—
545C22×C4—181no—
546C22×C4—181no—
547SD16—62no—
548SD16—182no—
549SD16—182no—
550C2×C8—31no—
551C2×C8—31no—
552C2×C8—91no—
553C2×C8C2×D3211yescharacteristic
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—91no—
563C4⋊C4—91no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4C2×D3211yescharacteristic
573C22⋊C4—61no—
574C22⋊C4—181no—
575C22⋊C4—181no—
576C42—31no—
577C42—31no—
578C42—61no—
579C42—91no—
580C42—181no—
581C42—181no—
582C22×C3—21no—
583C22×C3—62no—
584C22×C3—121no—
585C22×C3—121no—
586C22×C3C2×D3×D411yescharacteristic
587C22×C3C2×D3×D411yescharacteristic
588C2×D3—22no—
589C2×D3—41no—
590C2×D3—41no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—32no—
594C3×C4—32no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—81no—
602C3×C4—81no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4—121no—
606C3×C4C2×#23511yescharacteristic
607C3×C4D3×#4111yescharacteristic
608C3×C4#101011yescharacteristic
609C3×C4#101011yescharacteristic
610Dic3—21no—
611Dic3—21no—
612Dic3—32no—
613Dic3—32no—
614Dic3—41no—
615Dic3—41no—
616Dic3—41no—
617Dic3—62no—
618Dic3—62no—
619Dic3—61no—
620Dic3—61no—
621Dic3—121no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—241no—
626Dic3—241no—
627Dic3D3×SD1612yes—
628Dic3D3×SD1612yes—
629C32#335911yescharacteristic, complemented, Sylow
630C23—61no—
631Q8—21no—
632Q8—21no—
633Q8—61no—
634Q8—61no—
635Q8—94no—
636Q8—122no—
637Q8—181no—
638Q8—181no—
639Q8—362no—
640Q8—362no—
641D4—32no—
642D4—61no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—91no—
653C2×C4—91no—
654C2×C4—122no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—362no—
658C2×C4—362no—
659C2×C4C22×D3211yescharacteristic
660C8—21no—
661C8—61no—
662C8—61no—
663C8—181no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—122no—
668C2×C3#555211yescharacteristic
669C2×C3#567711yescharacteristic
670C2×C3C2×D3×SD1611yescharacteristic
671C2×C3C2×D3×SD1611yescharacteristic
672C2×C3#576611yescharacteristic
673C2×C3#577111yescharacteristic
674D3—42no—
675C22—62no—
676C22—121no—
677C22—121no—
678C22D32×D411yescharacteristic
679C4—32no—
680C4—32no—
681C4—41no—
682C4—41no—
683C4—61no—
684C4—61no—
685C4—92no—
686C4—121no—
687C4—121no—
688C4—121no—
689C4—181no—
690C4—361no—
691C4—361no—
692C4D3×#23511yescharacteristic
693C4#6430911yescharacteristic
694C3—21no—
695C3#7961911yescharacteristic, complemented
696C3#8162011yescharacteristic, complemented
697C2—122no—
698C2#1059407311yescharacteristic
699C2D32×SD1611yescharacteristic
700C2#1059476811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenter#103D32
hypocenterC32#3359
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595420C2semidirect
3. #10592491C2semidirect
4. C3×#4792C2semidirect
8. #10591544C2semidirect
9. #10590890C2semidirect
10. C8×#627C2semidirect
14. #10590497C2semidirect
15. #10590487C2semidirect
81. #4792D3semidirect
260. #627SD16semidirect
629. C32#3359semidirect
695. C3#79619semidirect
696. C3#81620semidirect

Maximal subgroups

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

subgroupindex
#105954202
#105943762
#105924912
C3×#47922
C3×#47882
#105915692
#105915642
#105915442
#105908902
C8×#6272
#105907442
#105907422
#105905592
#105904972
#105904872
#816203
#796193