Finite Group Databasebeta

← #11872528

Subgroups — #11872528

Order 1152.

804 conjugacy classes of subgroups.

The subgroup lattice has 729 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595348C211yesmaximal, characteristic, complemented
2#10594327C211yesmaximal, characteristic
3#10592517C211yesmaximal, characteristic, complemented
4C3×#4805C211yesmaximal, characteristic, complemented
5C3×#4790C211yesmaximal, characteristic, complemented
6#10591657C211yesmaximal, characteristic
7#10591580C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10590970C211yesmaximal, characteristic
10#10590820C211yesmaximal, characteristic, complemented
11#10590758C211yesmaximal, characteristic, complemented
12#10590696C211yesmaximal, characteristic, complemented
13#10590480C211yesmaximal, characteristic, complemented
14#10590435C211yesmaximal, characteristic, complemented
15#10590427C211yesmaximal, characteristic, complemented
16#81416—31nomaximal
17#79748—31nomaximal
18C2×#3799C2211yescharacteristic
19#64153C2211yescharacteristic
20C2×#3755C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28#63904—21no—
29C4×#626—21no—
30#63894C2211yescharacteristic
31#63883—21no—
32#63872C2211yescharacteristic
33#63867—21no—
34#63859—21no—
35#63858—21no—
36#63857C2211yescharacteristic
37#63855C2211yescharacteristic
38#63846—21no—
39#63844C2211yescharacteristic
40#63843C2211yescharacteristic
41#63836—21no—
42C2×#3719C2211yescharacteristic
43C32×#103C2211yescharacteristic
44#63641C2211yescharacteristic
45#63637C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63572C2211yescharacteristic
55#63567C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61#5625—31no—
62#5583—31no—
63#5574—31no—
64#5504—31no—
65C3×#483—31no—
66C3×C4×Q16—31no—
67#5187—31no—
68#5182—31no—
69#5047—31no—
70#5030—31no—
71#5026—31no—
72#4970—31no—
73#4891—31no—
74#4884—31no—
75#4871—31no—
76#4857—31no—
77#4853—31no—
78#4852—31no—
79#4818—31no—
80#4818—31no—
81#4818—61no—
82#4817—31no—
83#4808—31no—
84#4805D311yescharacteristic, complemented
85#4799—31no—
86#4795—31no—
87#4790D311yescharacteristic, complemented
88#4733—31no—
89#4720—31no—
90C4×#204—31no—
91#4690—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#626—21no—
100C2×#624—21no—
101C2×#624—21no—
102#3799—22no—
103#3799—22no—
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106#3755—22no—
107#3752—21no—
108#3750—21no—
109#3750—21no—
110C4×C3⋊Dic3C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112#3744—22no—
113C3×#216—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3D411yescharacteristic
138Dic32—21no—
139Dic32—21no—
140#3719—22no—
141#3120—91noSylow
142C2×#239—31no—
143C2×#235—31no—
144C2×C3×Q16—31no—
145C3×C22⋊Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C2×C3×C4⋊C4—31no—
149#946C2×D311yescharacteristic
150Q8×Dic3—31no—
151Q8×Dic3C2×D311yescharacteristic
152#944—31no—
153#944—31no—
154#944—61no—
155C2×#216—31no—
156C2×#216C2×D311yescharacteristic
157C2×#215—31no—
158C2×#215—31no—
159C2×#215—61no—
160C4×#67—61no—
161C4×#67—61no—
162#926—31no—
163#924—31no—
164C2×Dic12—31no—
165C2×#204—31no—
166C2×#204—31no—
167C2×#204—61no—
168#898—61no—
169#897—31no—
170#893—31no—
171#893—31no—
172#893—31no—
173#893—61no—
174#893—61no—
175#892—61no—
176D3×C4⋊C4—61no—
177D3×C4⋊C4—61no—
178D3×C4⋊C4C2×D311yescharacteristic
179#890—31no—
180#890—31no—
181#890—61no—
182#889—61no—
183#889—61no—
184#887—31no—
185#887—31no—
186#887C2×D311yescharacteristic
187#879—61no—
188#879—61no—
189#876—61no—
190C4×D12—31no—
191C4×D12—61no—
192#872—31no—
193#872—61no—
194#870—61no—
195C4×Dic6—31no—
196C3×#107—31no—
197C3×#106—31no—
198C3×#106—31no—
199C3×#103—21no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103C2×D311yescharacteristic
203C3×#103C2×D311yescharacteristic
204C3×C22⋊C8—31no—
205C3×C4×C8—31no—
206#835—31no—
207#835C2×D311yescharacteristic
208#830—31no—
209#821—31no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8C2×D311yescharacteristic
213#817C2×D311yescharacteristic
214#816—31no—
215#816C2×D311yescharacteristic
216#815—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—61no—
222C8×Dic3C2×D311yescharacteristic
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—61no—
228#809—31no—
229#809—31no—
230#808C2×D311yescharacteristic
231#807—31no—
232#807—31no—
233#807C2×D311yescharacteristic
234#803—31no—
235C22×C3⋊D3—21no—
236C22×C3×D3C2×D411yescharacteristic
237C32×Q8—21no—
238C32×Q8—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2411yescharacteristic
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C2×D411yescharacteristic
244C2×C3⋊Dic3C2×D411yescharacteristic
245C4⋊(C3⋊D3)—21no—
246C4⋊(C3⋊D3)#4112yes—
247C4×C3⋊D3—81no—
248#634—21no—
249#634—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—81no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
262#626—24no—
263#624—24no—
264#624—81no—
265C32×C8—21no—
266C3⋊(C3⋊C8)—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#541—91no—
270#520—91no—
271#484—91no—
272#483—31no—
273#479—91no—
274#478—91no—
275#462—91no—
276#461—91no—
277#452—91no—
278#452—91no—
279#441—91no—
280#440—91no—
281C4×Q16—31no—
282C4×SD16—91no—
283#433—91no—
284C2×C3×Q8—21no—
285C2×C3×Q8—31no—
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×Q8C22×D311yescharacteristic
288C22×C3×C4—31no—
289C22×C3×C4—61no—
290C2×#67—61no—
291#239—62no—
292#239—62no—
293#235—62no—
294#235—62no—
295C2×D12—31no—
296C2×D12—31no—
297C2×D12—61no—
298C2×D12—61no—
299C2×C4×D3—21no—
300C2×C4×D3—61no—
301C2×C4×D3—61no—
302C2×C4×D3—61no—
303C2×C4×D3—61no—
304C2×C4×D3—61no—
305C2×C4×D3—61no—
306C2×C4×D3—121no—
307C2×C4×D3C22×D311yescharacteristic
308C2×Dic6—31no—
309C2×Dic6—31no—
310C2×Dic6—61no—
311C2×Dic6C22×D311yescharacteristic
312C3×Q16—62no—
313C2×C3×C8—21no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C2×C3×C8C22×D311yescharacteristic
317C2×C3×C8C22×D311yescharacteristic
318C3×C4⋊C4—21no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4—61no—
325C3×C4⋊C4—61no—
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C4⋊C4C22×D311yescharacteristic
328C3×C22⋊C4—61no—
329C3×C42—31no—
330C3×C42—61no—
331C3×C42—61no—
332#217—31no—
333#217—31no—
334#217—61no—
335#216—22no—
336#216—62no—
337#215—62no—
338#215—62no—
339#215—122no—
340(C2×D3)⋊C4—21no—
341(C2×D3)⋊C4—31no—
342(C2×D3)⋊C4—31no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—121no—
349C4⋊Dic3—21no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3C22×D311yescharacteristic
357C4⋊Dic3C22×D311yescharacteristic
358C4⋊Dic3C22×D311yescharacteristic
359Dic3⋊C4—21no—
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—121no—
375Dic3⋊C4—121no—
376C4×Dic3—21no—
377C4×Dic3—21no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3C22×D311yescharacteristic
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8C22×D311yescharacteristic
390C2×C3⋊C8C22×D311yescharacteristic
391Dic12—62no—
392#204—62no—
393#204—62no—
394#204—122no—
395C22×C32C22×D411yescharacteristic
396C2×C3⋊D3—22no—
397C2×C3⋊D3—41no—
398C2×C3⋊D3—41no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—21no—
402C32×C4—41no—
403C32×C4—41no—
404C32×C4C2×#4111yescharacteristic
405C32×C4C2×#4111yescharacteristic
406C3⋊Dic3—21no—
407C3⋊Dic3—21no—
408C3⋊Dic3—41no—
409C3×Dic3—21no—
410C3×Dic3—22no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C2×#41—91no—
417C2×Q16—31no—
418C2×Q16—91no—
419C2×SD16—91no—
420C2×SD16—91no—
421C4⋊Q8—91no—
422#126—181no—
423#126—181no—
424#125—91no—
425#125—181no—
426#125—181no—
427C22⋊Q8—31no—
428C22⋊Q8—91no—
429C4×Q8—31no—
430C4×Q8—31no—
431C4×Q8—91no—
432C4×Q8—91no—
433C4×D4—91no—
434C4×D4—91no—
435C4×D4—181no—
436C4×D4—181no—
437#117—91no—
438#117—181no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—181no—
441#107—31no—
442#107—91no—
443#106—31no—
444#106—31no—
445C4⋊C8—91no—
446C4⋊C8—91no—
447#103—31no—
448#103—31no—
449#103—91no—
450#103—91no—
451#103—91no—
452#103D3211yescharacteristic
453#102—91no—
454#102—91no—
455C22⋊C8—31no—
456C22⋊C8—91no—
457#97—91no—
458C4×C8—31no—
459C23×C3—31no—
460C22×D3—61no—
461C22×D3—61no—
462C22×D3—121no—
463C22×D3D3×D411yescharacteristic
464C3×Q8—21no—
465C3×Q8—21no—
466C3×Q8—21no—
467C3×Q8—21no—
468C3×Q8—32no—
469C3×Q8—41no—
470C3×Q8—41no—
471C3×Q8—61no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—241no—
489C2×C3×C4C23×D311yescharacteristic
490C2×C3×C4C23×D311yescharacteristic
491#67—64no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—121no—
505C2×Dic3D3×D411yescharacteristic
506C2×Dic3D3×D411yescharacteristic
507C2×Dic3D3×D411yescharacteristic
508D12—32no—
509D12—32no—
510D12—62no—
511D12—64no—
512D12—61no—
513D12—61no—
514D12—121no—
515C4×D3—21no—
516C4×D3—21no—
517C4×D3—64no—
518C4×D3—64no—
519C4×D3—81no—
520C4×D3—241no—
521C4×D3—241no—
522C4×D3—241no—
523C4×D3—241no—
524C4×D3—242no—
525Dic6—21no—
526Dic6—61no—
527Dic6—61no—
528Dic6—61no—
529Dic6—61no—
530Dic6—121no—
531Dic6—121no—
532Dic6#23512yes—
533C3×C8—21no—
534C3×C8—21no—
535C3×C8—41no—
536C3×C8—61no—
537C3×C8—61no—
538C3⋊C8—21no—
539C3⋊C8—21no—
540C3⋊C8—61no—
541C3⋊C8—61no—
542C3⋊C8—121no—
543C2×C32#52511yescharacteristic
544C2×C32#57711yescharacteristic
545C2×C32#57811yescharacteristic
546C3⋊D3—42no—
547C3×D3—41no—
548#41—182no—
549#41—182no—
550C2×Q8—31no—
551C2×Q8—91no—
552C2×Q8C2×D3211yescharacteristic
553C2×D4—91no—
554C2×D4—181no—
555C22×C4—31no—
556C22×C4—61no—
557C22×C4—181no—
558C22×C4—181no—
559C22×C4—181no—
560Q16—62no—
561Q16—182no—
562SD16—182no—
563SD16—182no—
564C2×C8—31no—
565C2×C8—31no—
566C2×C8—91no—
567C2×C8C2×D3211yescharacteristic
568C4⋊C4—31no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—181no—
578C4⋊C4—181no—
579C4⋊C4—181no—
580C4⋊C4—181no—
581C4⋊C4—181no—
582C4⋊C4—181no—
583C4⋊C4—181no—
584C4⋊C4C2×D3211yescharacteristic
585C22⋊C4—61no—
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—181no—
589C22⋊C4—181no—
590C22⋊C4—181no—
591C42—31no—
592C42—61no—
593C42—61no—
594C42—91no—
595C42—181no—
596C42—181no—
597C22×C3—21no—
598C22×C3—61no—
599C22×C3—61no—
600C22×C3—61no—
601C22×C3C2×D3×D411yescharacteristic
602C22×C3C2×D3×D411yescharacteristic
603C2×D3—21no—
604C2×D3—21no—
605C2×D3—21no—
606C2×D3—62no—
607C2×D3—62no—
608C2×D3—122no—
609C2×D3—121no—
610C2×D3—121no—
611C2×D3—121no—
612C2×D3—121no—
613C2×D3—241no—
614C2×D3—241no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—62no—
622C3×C4—61no—
623C3×C4—61no—
624C3×C4—61no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—121no—
628C3×C4—121no—
629C3×C4—121no—
630C3×C4C2×#23511yescharacteristic
631C3×C4D3×#4111yescharacteristic
632C3×C4D3×#4111yescharacteristic
633C3×C4D3×#4111yescharacteristic
634Dic3—21no—
635Dic3—21no—
636Dic3—21no—
637Dic3—22no—
638Dic3—41no—
639Dic3—41no—
640Dic3—41no—
641Dic3—62no—
642Dic3—61no—
643Dic3—61no—
644Dic3—61no—
645Dic3—61no—
646Dic3—121no—
647Dic3—121no—
648Dic3—121no—
649Dic3—241no—
650C32#312011yescharacteristic, complemented, Sylow
651C23—31no—
652C23—181no—
653Q8—21no—
654Q8—21no—
655Q8—32no—
656Q8—61no—
657Q8—181no—
658Q8—181no—
659D4—92no—
660D4—184no—
661D4—181no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—91no—
674C2×C4—91no—
675C2×C4—184no—
676C2×C4—181no—
677C2×C4—241no—
678C2×C4—721no—
679C2×C4—721no—
680C2×C4C22×D3211yescharacteristic
681C8—21no—
682C8—61no—
683C8—61no—
684C8—181no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—121no—
689C2×C3#554711yescharacteristic
690C2×C3#565611yescharacteristic
691C2×C3#576211yescharacteristic
692C2×C3#576611yescharacteristic
693C2×C3#577011yescharacteristic
694C2×C3#577911yescharacteristic
695D3—41no—
696D3—122no—
697D3—122no—
698D3—242no—
699C22—61no—
700C22—61no—
701C22—61no—
702C22—182no—
703C22—361no—
704C22—361no—
705C22D32×D411yescharacteristic
706C4—41no—
707C4—41no—
708C4—61no—
709C4—61no—
710C4—61no—
711C4—62no—
712C4—121no—
713C4—121no—
714C4—121no—
715C4—181no—
716C4—181no—
717C4—361no—
718C4D3×#23511yescharacteristic
719C4#6431211yescharacteristic
720C3—21no—
721C3#7974811yescharacteristic, complemented
722C3#8141611yescharacteristic, complemented
723C2—121no—
724C2—362no—
725C2#1059426611yescharacteristic
726C2#1059475311yescharacteristic
727C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×#3799C22
hypercenter#103D32
hypocenterC32#3120
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. #10595348C2semidirect
3. #10592517C2semidirect
4. C3×#4805C2semidirect
5. C3×#4790C2semidirect
7. #10591580C2semidirect
8. #10591540C2semidirect
10. #10590820C2semidirect
11. #10590758C2semidirect
12. #10590696C2semidirect
13. #10590480C2semidirect
14. #10590435C2semidirect
15. #10590427C2semidirect
84. #4805D3semidirect
87. #4790D3semidirect
650. C32#3120semidirect
721. C3#79748semidirect
722. C3#81416semidirect

Maximal subgroups

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

subgroupindex
#105953482
#105943272
#105925172
C3×#48052
C3×#47902
#105916572
#105915802
#105915402
#105909702
#105908202
#105907582
#105906962
#105904802
#105904352
#105904272
#814163
#797483