Finite Group Databasebeta

← #11895184

Subgroups — #11895184

Order 1152.

788 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595338C211yesmaximal, characteristic, complemented
2#10594376C211yesmaximal, characteristic
3#10592490C211yesmaximal, characteristic, complemented
4C3×#4818C211yesmaximal, characteristic
5C3×#4792C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591571C211yesmaximal, characteristic
8#10591564C211yesmaximal, characteristic
9#10590803C211yesmaximal, characteristic, complemented
10Dic3×#204C211yesmaximal, characteristic
11#10590748C211yesmaximal, characteristic
12#10590644C211yesmaximal, characteristic, complemented
13#10590567C211yesmaximal, characteristic, complemented
14#10590486C211yesmaximal, characteristic, complemented
15#10590475C211yesmaximal, characteristic
16#81620—31nomaximal
17#80414—31nomaximal
18C2×D3×Dic6—21no—
19Q8×C3⋊Dic3C2211yescharacteristic
20#64097C2211yescharacteristic
21C3×#944C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#888C2211yescharacteristic
27#63918C2211yescharacteristic
28C4×#627C2211yescharacteristic
29#63898C2211yescharacteristic
30#63896—21no—
31Dic3×D12C2211yescharacteristic
32#63887—21no—
33#63873C2211yescharacteristic
34#63870—21no—
35#63851—21no—
36#63845—21no—
37#63845—21no—
38Dic3×Dic6C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40#63838—21no—
41C2×#3715C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63662C2211yescharacteristic
44#63644C2211yescharacteristic
45#63641C2211yescharacteristic
46#63635C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53#63573C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5727—31no—
62#5721—31no—
63#5721—31no—
64D4×Dic6—31no—
65C3×#487—31no—
66C3×#461—31no—
67#5162—31no—
68#5162—31no—
69Dic3×SD16—31no—
70Dic3×SD16—31no—
71#5094—31no—
72#5083—31no—
73#5079—31no—
74C4×#214—31no—
75#4851—31no—
76#4830—31no—
77#4818—31no—
78#4818D311yescharacteristic
79#4792—31no—
80#4792—31no—
81#4792—31no—
82#4792D311yescharacteristic, complemented
83#4791—31no—
84#4791—31no—
85#4791—31no—
86#4791—31no—
87#4791—61no—
88#4788—31no—
89#4788—31no—
90C4×#204—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6C2311yescharacteristic
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)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110C4×C3⋊Dic3—21no—
111C4×C3⋊Dic3C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C3×#215—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C3×#204—22no—
126#3724—21no—
127#3724—21no—
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136Dic32—21no—
137Dic32—21no—
138#3715—22no—
139#3359—91noSylow
140C2×D3×Q8—61no—
141C22×Dic6—61no—
142C2×C3×SD16—31no—
143C2×C3×SD16—31no—
144C3×C4⋊Q8—31no—
145C3×C4⋊Q8—31no—
146C3×C4⋊Q8—31no—
147C3×C4×D4—31no—
148#946—61no—
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—61no—
154#944—31no—
155#944—31no—
156#944C2×D311yescharacteristic
157#944C2×D311yescharacteristic
158C2×#215—31no—
159C2×#215C2×D311yescharacteristic
160D4×Dic3—31no—
161D4×Dic3—31no—
162C2×#214—31no—
163#924—61no—
164C2×#204C2×D311yescharacteristic
165#896—61no—
166#896—61no—
167#893—31no—
168#893C2×D311yescharacteristic
169#890—61no—
170#890—61no—
171#889—61no—
172#889—61no—
173#889—61no—
174#889—61no—
175#888—31no—
176#888—31no—
177#888—31no—
178#888—61no—
179#888C2×D311yescharacteristic
180#887—61no—
181#887—61no—
182#878—61no—
183#878—61no—
184C4×D12—31no—
185#869—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C3×C4⋊C8—31no—
191C3×#103—21no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#103C2×D311yescharacteristic
197C3×#103C2×D311yescharacteristic
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#835—61no—
205#835C2×D311yescharacteristic
206#832—31no—
207#821—31no—
208#817—31no—
209#817—31no—
210#817—31no—
211#817—61no—
212#816—31no—
213#816—31no—
214#816C2×D311yescharacteristic
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—61no—
219Dic3⋊C8C2×D311yescharacteristic
220C8×Dic3—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3C2×D311yescharacteristic
224#810—31no—
225#810C2×D311yescharacteristic
226#810C2×D311yescharacteristic
227#808—31no—
228#808—31no—
229#808—31no—
230#808—61no—
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—42no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12#4112yes—
253C3×C4×D3—42no—
254C3×Dic6—21no—
255C3×Dic6—21no—
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—31no—
276#461—91no—
277#461—91no—
278C8×Q8—91no—
279C4×SD16—91no—
280C4×SD16—91no—
281C4×SD16—91no—
282C2×C3×Q8—21no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—61no—
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×Q8C22×D311yescharacteristic
288C2×C3×D4—31no—
289C22×C3×C4—61no—
290C22×Dic3—61no—
291C22×Dic3—61no—
292D3×Q8—124no—
293C2×D12C22×D311yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×Dic6—21no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—121no—
305C2×Dic6—124no—
306C2×Dic6C22×D311yescharacteristic
307C2×Dic6C22×D311yescharacteristic
308C3×SD16—62no—
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—61no—
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—
327#217—61no—
328#217—61no—
329#215—22no—
330#215—62no—
331#214—62no—
332(C2×D3)⋊C4—21no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—121no—
349C4⋊Dic3C22×D311yescharacteristic
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
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—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—121no—
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—22no—
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—31no—
409C2×SD16—91no—
410C4⋊Q8—31no—
411C4⋊Q8—31no—
412C4⋊Q8—31no—
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—91no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—181no—
427C4×D4—31no—
428C4×D4—91no—
429C4×D4—91no—
430#106—91no—
431#106—91no—
432#106—91no—
433C4⋊C8—31no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436#103—31no—
437#103—31no—
438#103—31no—
439#103—31no—
440#103—91no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103D3211yescharacteristic
445#102—91no—
446C4×C8—31no—
447C4×C8—91no—
448C4×C8—91no—
449C23×C3—61no—
450C22×D3—21no—
451C3×Q8—22no—
452C3×Q8—21no—
453C3×Q8—21no—
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—41no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×Q8—122no—
462C3×D4—32no—
463C3×D4—61no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—122no—
479C2×C3×C4C23×D311yescharacteristic
480C2×C3×C4C23×D311yescharacteristic
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—121no—
495C2×Dic3—121no—
496C2×Dic3—122no—
497C2×Dic3—122no—
498C2×Dic3D3×D411yescharacteristic
499C2×Dic3D3×D411yescharacteristic
500C2×Dic3D3×D411yescharacteristic
501C2×Dic3D3×D411yescharacteristic
502D12—21no—
503D12#23712yes—
504C4×D3—42no—
505C4×D3—122no—
506C4×D3—122no—
507Dic6—21no—
508Dic6—21no—
509Dic6—21no—
510Dic6—21no—
511Dic6—34no—
512Dic6—34no—
513Dic6—42no—
514Dic6—122no—
515Dic6—122no—
516Dic6—122no—
517Dic6—122no—
518Dic6—242no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—41no—
522C3×C8—61no—
523C3×C8—61no—
524C3⋊C8—21no—
525C3⋊C8—21no—
526C3⋊C8—61no—
527C3⋊C8—61no—
528C3⋊C8—121no—
529C2×C32#54811yescharacteristic
530C2×C32C22×SD1611yescharacteristic
531C2×C32#57811yescharacteristic
532C3×D3—42no—
533C2×Q8—31no—
534C2×Q8—31no—
535C2×Q8—61no—
536C2×Q8—91no—
537C2×Q8—181no—
538C2×Q8—181no—
539C2×Q8—364no—
540C2×Q8C2×D3211yescharacteristic
541C2×D4—31no—
542C22×C4—61no—
543C22×C4—181no—
544C22×C4—181no—
545SD16—62no—
546SD16—62no—
547SD16—182no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—91no—
551C2×C8C2×D3211yescharacteristic
552C4⋊C4—31no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—91no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C4⋊C4C2×D3211yescharacteristic
571C22⋊C4—61no—
572C22⋊C4—181no—
573C22⋊C4—181no—
574C42—31no—
575C42—31no—
576C42—91no—
577C42—181no—
578C42—181no—
579C42—181no—
580C22×C3—21no—
581C22×C3—62no—
582C22×C3—121no—
583C22×C3—121no—
584C22×C3C2×D3×D411yescharacteristic
585C22×C3C2×D3×D411yescharacteristic
586C2×D3—22no—
587C2×D3—41no—
588C2×D3—41no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—32no—
592C3×C4—32no—
593C3×C4—42no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—81no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4C2×#23711yescharacteristic
605C3×C4D3×#4111yescharacteristic
606C3×C4#101011yescharacteristic
607C3×C4#101011yescharacteristic
608Dic3—21no—
609Dic3—21no—
610Dic3—32no—
611Dic3—32no—
612Dic3—41no—
613Dic3—41no—
614Dic3—41no—
615Dic3—62no—
616Dic3—61no—
617Dic3—61no—
618Dic3—121no—
619Dic3—121no—
620Dic3—121no—
621Dic3—121no—
622Dic3—121no—
623Dic3—241no—
624Dic3—241no—
625Dic3D3×SD1612yes—
626Dic3D3×SD1612yes—
627C32#335911yescharacteristic, complemented, Sylow
628C23—61no—
629Q8—21no—
630Q8—21no—
631Q8—61no—
632Q8—61no—
633Q8—61no—
634Q8—61no—
635Q8—94no—
636Q8—122no—
637Q8—362no—
638Q8—362no—
639D4—32no—
640D4—61no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—122no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—362no—
656C2×C4—362no—
657C2×C4C22×D3211yescharacteristic
658C8—21no—
659C8—61no—
660C8—61no—
661C8—181no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—122no—
666C2×C3#559811yescharacteristic
667C2×C3#567711yescharacteristic
668C2×C3C2×D3×SD1611yescharacteristic
669C2×C3C2×D3×SD1611yescharacteristic
670C2×C3#576611yescharacteristic
671C2×C3#577911yescharacteristic
672D3—42no—
673C22—62no—
674C22—121no—
675C22—121no—
676C22D32×D411yescharacteristic
677C4—32no—
678C4—32no—
679C4—41no—
680C4—41no—
681C4—61no—
682C4—61no—
683C4—92no—
684C4—121no—
685C4—121no—
686C4—121no—
687C4—181no—
688C4—361no—
689C4—361no—
690C4#6429811yescharacteristic
691C4D3×#23711yescharacteristic
692C3—21no—
693C3#8041411yescharacteristic, complemented
694C3#8162011yescharacteristic, complemented
695C2—122no—
696C2#1059407611yescharacteristic
697C2D32×SD1611yescharacteristic
698C2#1059476611yescharacteristic
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. #10595338C2semidirect
3. #10592490C2semidirect
5. C3×#4792C2semidirect
6. #10591623C2semidirect
9. #10590803C2semidirect
12. #10590644C2semidirect
13. #10590567C2semidirect
14. #10590486C2semidirect
82. #4792D3semidirect
260. #627SD16semidirect
627. C32#3359semidirect
693. C3#80414semidirect
694. C3#81620semidirect

Maximal subgroups

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

subgroupindex
#105953382
#105943762
#105924902
C3×#48182
C3×#47922
#105916232
#105915712
#105915642
#105908032
Dic3×#2042
#105907482
#105906442
#105905672
#105904862
#105904752
#816203
#804143