Finite Group Databasebeta

← #11873344

Subgroups — #11873344

Order 1152.

764 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#10595354C211yesmaximal, characteristic
2#10594347C211yesmaximal, characteristic
3#10592514C211yesmaximal, characteristic
4C3×#4795C211yesmaximal, characteristic, complemented
5C3×#4789C211yesmaximal, characteristic, complemented
6#10591654C211yesmaximal, characteristic
7#10591574C211yesmaximal, characteristic, complemented
8Dic3×#216C211yesmaximal, characteristic, complemented
9#10590950C211yesmaximal, characteristic
10#10590815C211yesmaximal, characteristic, complemented
11#10590812C211yesmaximal, characteristic, complemented
12#10590647C211yesmaximal, characteristic
13#10590543C211yesmaximal, characteristic, complemented
14#10590527C211yesmaximal, characteristic
15#10590476C211yesmaximal, characteristic, complemented
16#80461—31nomaximal
17#79836—31nomaximal
18C2×#3797C2211yescharacteristic
19#64155C2211yescharacteristic
20#64101C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic
26C3×#887C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C4×#627—21no—
29#63874C2211yescharacteristic
30#63871C2211yescharacteristic
31#63869C2211yescharacteristic
32#63868—21no—
33#63867—21no—
34#63848—21no—
35#63847—21no—
36Dic3×Dic6C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63838—21no—
40#63836—21no—
41#63836—21no—
42C2×#3718C2211yescharacteristic
43C32×#103C2211yescharacteristic
44#63662C2211yescharacteristic
45#63647C2211yescharacteristic
46#63644C2211yescharacteristic
47#63634C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#815C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63575C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5731—31no—
62#5583—31no—
63#5572—31no—
64#5572—31no—
65C3×#462—31no—
66C3×#441—31no—
67#5186—31no—
68#5186—31no—
69#5186—31no—
70#5184—31no—
71#5182—31no—
72Dic3×Q16—31no—
73#5090—31no—
74C4×#216—31no—
75C4×#216—31no—
76#5022—31no—
77#4868—31no—
78#4857—31no—
79#4840—31no—
80#4829—31no—
81#4815—31no—
82#4815—31no—
83#4815—61no—
84#4814—31no—
85#4809—31no—
86#4799—31no—
87#4795D311yescharacteristic, complemented
88#4790—31no—
89#4789D311yescharacteristic, complemented
90#4716—31no—
91#4709—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C3×Dic6C2311yescharacteristic
95C2×C3×Dic6C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#624—21no—
99#3797—22no—
100#3797—22no—
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4C2311yescharacteristic
103#3752—21no—
104#3752—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C3×#216—22no—
111C3×#216—22no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3C2311yescharacteristic
114C3×Dic3⋊C4—21no—
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C3×Dic12—22no—
126#3724—21no—
127#3724D411yescharacteristic
128#3724D411yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722D411yescharacteristic
136#3722D411yescharacteristic
137Dic32—21no—
138Dic32—21no—
139Dic32—21no—
140#3718—22no—
141#3127—91noSylow
142C2×D3×Q8—31no—
143C2×D3×Q8—31no—
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C2×C3×Q16—31no—
147C3×C4⋊Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×Q8—31no—
151#946—31no—
152#946—31no—
153#946—31no—
154#946—61no—
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3C2×D311yescharacteristic
159#944C2×D311yescharacteristic
160C2×#216—31no—
161C2×#216—31no—
162C2×#216C2×D311yescharacteristic
163C2×#216C2×D311yescharacteristic
164C2×Dic12C2×D311yescharacteristic
165#898—61no—
166#898—61no—
167#898—61no—
168#897—31no—
169#892—31no—
170#892—31no—
171#892—61no—
172#892—61no—
173#892—61no—
174#890—31no—
175#889—61no—
176#889—61no—
177#889—61no—
178#887—61no—
179#887—61no—
180#887C2×D311yescharacteristic
181#887C2×D311yescharacteristic
182#876—61no—
183#872—31no—
184#872—31no—
185#872—61no—
186#872—61no—
187#870—31no—
188#870—61no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—61no—
193C4×Dic6—61no—
194C3×#106—31no—
195C3×C4⋊C8—31no—
196C3×#103—21no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#103C2×D311yescharacteristic
200C3×#103C2×D311yescharacteristic
201C3×#97—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—61no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—61no—
214#818—31no—
215#817—31no—
216#817—31no—
217#817—61no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816C2×D311yescharacteristic
222#815C2×D311yescharacteristic
223Dic3⋊C8—31no—
224Dic3⋊C8C2×D311yescharacteristic
225C8×Dic3—31no—
226#810—31no—
227#810C2×D311yescharacteristic
228#808C2×D311yescharacteristic
229#807—31no—
230#807—31no—
231#807—31no—
232#807—61no—
233C4⋊(C3⋊C8)—31no—
234C4×C3⋊C8—31no—
235C22×C3⋊D3C2×D411yescharacteristic
236C32×Q8—21no—
237C32×Q8—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3C2×D411yescharacteristic
244C4×C3⋊D3—21no—
245C4×C3⋊D3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6#4112yes—
259C3×Dic6#4112yes—
260#627—24no—
261#624—24no—
262C32×C8—21no—
263C3⋊(C3⋊C8)—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266#541—91no—
267#519—91no—
268#485—91no—
269#485—91no—
270#479—91no—
271#479—91no—
272#462—31no—
273#462—91no—
274#451—91no—
275#451—91no—
276#441—31no—
277#441—91no—
278C4×Q16—91no—
279C4×Q16—91no—
280#433—91no—
281C2×C3×Q8—21no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×Q8C22×D311yescharacteristic
287D3×Q8—62no—
288D3×Q8—62no—
289D3×Q8—62no—
290D3×Q8—62no—
291C2×C4×D3—31no—
292C2×C4×D3—31no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C3×Q16—62no—
302C3×Q16—62no—
303C3×Q16—62no—
304C2×C3×C8—21no—
305C2×C3×C8—31no—
306C2×C3×C8—31no—
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C3×C4⋊C4—21no—
310C3×C4⋊C4—31no—
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×C42—31no—
319C3×C42—31no—
320C3×C42—61no—
321C3×C42—61no—
322C3×C42—61no—
323#216—22no—
324#216—22no—
325#216—62no—
326#216—62no—
327(C2×D3)⋊C4—31no—
328(C2×D3)⋊C4—31no—
329(C2×D3)⋊C4—31no—
330(C2×D3)⋊C4—31no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—121no—
338(C2×D3)⋊C4—121no—
339C4⋊Dic3—21no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3C22×D311yescharacteristic
352Dic3⋊C4—21no—
353Dic3⋊C4—21no—
354Dic3⋊C4—21no—
355Dic3⋊C4—21no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
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—61no—
369Dic3⋊C4—121no—
370C4×Dic3—21no—
371C4×Dic3—21no—
372C4×Dic3—21no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—121no—
382C4×Dic3C22×D311yescharacteristic
383C4×Dic3C22×D311yescharacteristic
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8C22×D311yescharacteristic
388C2×C3⋊C8C22×D311yescharacteristic
389Dic12—22no—
390C22×C32C22×D411yescharacteristic
391C2×C3⋊D3—21no—
392C2×C3⋊D3—21no—
393C2×C3⋊D3—21no—
394C32×C4—41no—
395C32×C4—41no—
396C32×C4C2×#4111yescharacteristic
397C32×C4C2×#4111yescharacteristic
398C3⋊Dic3—21no—
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—21no—
404C3×Dic3—21no—
405C3×Dic3—21no—
406C3×Dic3—21no—
407C3×Dic3—41no—
408C3×Dic3—41no—
409C22×Q8—91no—
410C2×Q16—31no—
411C2×Q16—31no—
412C2×Q16—31no—
413C2×Q16—91no—
414C4⋊Q8—31no—
415#126—181no—
416#126—181no—
417#125—91no—
418#125—181no—
419#125—181no—
420C22⋊Q8—91no—
421C22⋊Q8—91no—
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—31no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—181no—
429C4×Q8—181no—
430#117—91no—
431#117—91no—
432#117—181no—
433#117—181no—
434#107—91no—
435#107—91no—
436#106—31no—
437#106—91no—
438C4⋊C8—31no—
439C4⋊C8—91no—
440#103—31no—
441#103—31no—
442#103—91no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103D3211yescharacteristic
448C22⋊C8—91no—
449C22⋊C8—91no—
450#97—31no—
451C4×C8—91no—
452C22×D3—31no—
453C22×D3—31no—
454C22×D3—61no—
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—32no—
460C3×Q8—32no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—61no—
464C3×Q8—61no—
465C3×Q8—61no—
466C3×Q8—61no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4C23×D311yescharacteristic
483C2×C3×C4C23×D311yescharacteristic
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—121no—
496C2×Dic3—121no—
497C2×Dic3D3×D411yescharacteristic
498C2×Dic3D3×D411yescharacteristic
499C2×Dic3D3×D411yescharacteristic
500C2×Dic3D3×D411yescharacteristic
501C4×D3—64no—
502C4×D3—64no—
503C4×D3—61no—
504C4×D3—61no—
505C4×D3—61no—
506C4×D3—61no—
507C4×D3—121no—
508C4×D3—121no—
509Dic6—21no—
510Dic6—21no—
511Dic6—21no—
512Dic6—21no—
513Dic6—64no—
514Dic6—64no—
515Dic6#23512yes—
516Dic6#23712yes—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—41no—
520C3×C8—61no—
521C3×C8—61no—
522C3⋊C8—21no—
523C3⋊C8—21no—
524C3⋊C8—61no—
525C3⋊C8—61no—
526C3⋊C8—121no—
527C2×C32#52511yescharacteristic
528C2×C32#57811yescharacteristic
529C2×C32#57811yescharacteristic
530C3⋊D3—41no—
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—181no—
535C2×Q8—182no—
536C2×Q8—182no—
537C2×Q8C2×D3211yescharacteristic
538C22×C4—91no—
539C22×C4—181no—
540Q16—62no—
541Q16—62no—
542Q16—62no—
543Q16—182no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8—91no—
547C2×C8C2×D3211yescharacteristic
548C4⋊C4—31no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4C2×D3211yescharacteristic
566C22⋊C4—91no—
567C22⋊C4—91no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C42—31no—
572C42—31no—
573C42—61no—
574C42—61no—
575C42—61no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42—181no—
580C22×C3—21no—
581C22×C3C2×D3×D411yescharacteristic
582C22×C3C2×D3×D411yescharacteristic
583C2×D3—61no—
584C2×D3—61no—
585C2×D3—61no—
586C2×D3—61no—
587C2×D3—61no—
588C2×D3—61no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—61no—
602C3×C4—62no—
603C3×C4—62no—
604C3×C4—81no—
605C3×C4—81no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4C2×#23511yescharacteristic
609C3×C4C2×#23711yescharacteristic
610C3×C4D3×#4111yescharacteristic
611C3×C4D3×#4111yescharacteristic
612Dic3—21no—
613Dic3—21no—
614Dic3—21no—
615Dic3—21no—
616Dic3—22no—
617Dic3—22no—
618Dic3—41no—
619Dic3—41no—
620Dic3—61no—
621Dic3—61no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—241no—
628Dic3—241no—
629C32#312711yescharacteristic, complemented, Sylow
630C23—91no—
631Q8—21no—
632Q8—21no—
633Q8—32no—
634Q8—32no—
635Q8—61no—
636Q8—61no—
637Q8—61no—
638Q8—61no—
639Q8—184no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—91no—
651C2×C4—184no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—181no—
656C2×C4C22×D3211yescharacteristic
657C8—21no—
658C8—61no—
659C8—61no—
660C8—181no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3#554711yescharacteristic
665C2×C3#560611yescharacteristic
666C2×C3#576611yescharacteristic
667C2×C3#577911yescharacteristic
668C2×C3#577911yescharacteristic
669C2×C3#577911yescharacteristic
670D3—121no—
671D3—121no—
672D3—241no—
673C22—181no—
674C22—181no—
675C22—181no—
676C22D32×D411yescharacteristic
677C4—41no—
678C4—41no—
679C4—61no—
680C4—61no—
681C4—61no—
682C4—61no—
683C4—62no—
684C4—62no—
685C4—121no—
686C4—121no—
687C4—181no—
688C4—361no—
689C4—361no—
690C4D3×#23511yescharacteristic
691C4D3×#23711yescharacteristic
692C3—21no—
693C3#7983611yescharacteristic, complemented
694C3#8046111yescharacteristic, complemented
695C2—361no—
696C2#1059428611yescharacteristic
697C2#1059475211yescharacteristic
698C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#103D32
hypocenterC32#3127
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
4. C3×#4795C2semidirect
5. C3×#4789C2semidirect
7. #10591574C2semidirect
8. Dic3×#216C2semidirect
10. #10590815C2semidirect
11. #10590812C2semidirect
13. #10590543C2semidirect
15. #10590476C2semidirect
87. #4795D3semidirect
89. #4789D3semidirect
629. C32#3127semidirect
693. C3#79836semidirect
694. C3#80461semidirect

Maximal subgroups

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

subgroupindex
#105953542
#105943472
#105925142
C3×#47952
C3×#47892
#105916542
#105915742
Dic3×#2162
#105909502
#105908152
#105908122
#105906472
#105905432
#105905272
#105904762
#804613
#798363