Finite Group Databasebeta

← #11873293

Subgroups — #11873293

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#10594824C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic
3#10592422C211yesmaximal, characteristic
4C3×#4739C211yesmaximal, characteristic
5C3×#4720C211yesmaximal, characteristic
6#10591186C211yesmaximal, characteristic
7#10591127C211yesmaximal, characteristic
8#10590815C211yesmaximal, characteristic, complemented
9#10590812C211yesmaximal, characteristic, complemented
10#10590811C211yesmaximal, characteristic, complemented
11Dic3×Dic12C211yesmaximal, characteristic, complemented
12#10590800C211yesmaximal, characteristic, complemented
13#10590800C211yesmaximal, characteristic, complemented
14#10590794C211yesmaximal, characteristic, complemented
15#10590793C211yesmaximal, characteristic, complemented
16#80177—31nomaximal
17#79396—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19#64135C2211yescharacteristic
20#64133C2211yescharacteristic
21C3×#926C2211yescharacteristic
22C3×#924C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25#63956—21no—
26#63956—21no—
27#63955—21no—
28#63955—21no—
29#63869C2211yescharacteristic
30#63866C2211yescharacteristic
31#63847—21no—
32#63846—21no—
33#63844C2211yescharacteristic
34#63843—21no—
35#63843—21no—
36Dic3×Dic6C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C32×C22⋊C8C2211yescharacteristic
44#63645C2211yescharacteristic
45#63644C2211yescharacteristic
46#63643C2211yescharacteristic
47#63643C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#815C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#5812—31no—
62#5625—31no—
63#5518—31no—
64#5516—31no—
65C3×#451—31no—
66C3×#433—31no—
67#5228—31no—
68#5184—31no—
69#5182—31no—
70#5182—31no—
71Dic3×Q16—31no—
72#5045—31no—
73#4849—31no—
74#4849—31no—
75#4829—31no—
76#4829—31no—
77#4799—31no—
78#4796—31no—
79#4790—31no—
80#4789—31no—
81#4739—31no—
82#4739D311yescharacteristic
83#4723—31no—
84#4723—31no—
85#4723—31no—
86#4723—61no—
87#4720D311yescharacteristic
88#4716—31no—
89#4716—31no—
90C4×Dic12—31no—
91C4×Dic12—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C22×C3×Dic3—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6—22no—
97C2×C3×Dic6—22no—
98C2×C3×Dic6C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103#3757—21no—
104#3757—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109C4×C3⋊Dic3—21no—
110C3×#217—21no—
111C3×#217D411yescharacteristic
112C3×#217D411yescharacteristic
113C3×C4⋊Dic3D411yescharacteristic
114C3×C4⋊Dic3D411yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×C4×Dic3C2311yescharacteristic
118C3×C4×Dic3C2311yescharacteristic
119C2×C3×C3⋊C8C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C3×Dic12—22no—
122C3×Dic12—22no—
123#3724—21no—
124#3724—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic32—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3719—22no—
140#3719—22no—
141#3127—91noSylow
142C22×C3×Q8—31no—
143C22×Dic6C2×D311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×Q16—31no—
146C3×C22⋊Q8—31no—
147C3×#117—31no—
148Q8×Dic3—31no—
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—61no—
154Q8×Dic3—61no—
155#944—31no—
156C2×#216—31no—
157C2×#216—31no—
158#926—31no—
159#926—31no—
160#926—61no—
161#926—61no—
162#926—61no—
163#926C2×D311yescharacteristic
164#924—31no—
165#924—31no—
166#924—61no—
167#924C2×D311yescharacteristic
168C2×Dic12—31no—
169C2×Dic12—31no—
170C2×Dic12C2×D311yescharacteristic
171C2×Dic12C2×D311yescharacteristic
172#890—31no—
173#890—61no—
174#889—61no—
175#889—61no—
176#889—61no—
177#887—31no—
178#887—61no—
179#887—61no—
180#879—61no—
181#879—61no—
182#879—61no—
183#879—61no—
184#877—61no—
185#877—61no—
186#870—31no—
187#869—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C3×C4⋊C8—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×C22⋊C8—21no—
199C3×C22⋊C8—31no—
200C3×C22⋊C8C2×D311yescharacteristic
201C3×C22⋊C8C2×D311yescharacteristic
202C3×#97—31no—
203C3×C4×C8—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#830C2×D311yescharacteristic
209#818—31no—
210#818—31no—
211#818—31no—
212#818—61no—
213#817—31no—
214#817—31no—
215#817—31no—
216#817—61no—
217#816—31no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#816—61no—
227#816C2×D311yescharacteristic
228#816C2×D311yescharacteristic
229#815C2×D311yescharacteristic
230Dic3⋊C8C2×D311yescharacteristic
231Dic3⋊C8C2×D311yescharacteristic
232C8×Dic3C2×D311yescharacteristic
233#808—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4C2×D411yescharacteristic
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244#634—21no—
245#634—21no—
246C2×C3×Dic3—24no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×Dic6—24no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6#4112yes—
261C3×Dic6#4112yes—
262C32×C8—21no—
263C32×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—91no—
273#462—91no—
274#451—31no—
275#451—91no—
276#441—91no—
277#441—91no—
278C4×Q16—91no—
279C4×Q16—91no—
280#433—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—31no—
284C2×C3×Q8—62no—
285C2×C3×Q8—62no—
286C2×C3×Q8—61no—
287C22×C3×C4—21no—
288C22×C3×C4—61no—
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×Dic3—21no—
292C2×Dic6—21no—
293C2×Dic6—22no—
294C2×Dic6—22no—
295C2×Dic6—31no—
296C2×Dic6—31no—
297C2×Dic6—61no—
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C3×Q16—62no—
302C3×Q16—62no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—31no—
306C2×C3×C8—31no—
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—61no—
315C3×C22⋊C4—31no—
316C3×C22⋊C4—31no—
317C3×C22⋊C4—61no—
318C3×C42—31no—
319C3×C42—31no—
320#217—21no—
321#217—61no—
322#217—61no—
323#217—61no—
324#217—61no—
325#217—121no—
326#217—121no—
327#217D1211yescharacteristic
328#217D1211yescharacteristic
329#216—62no—
330#216—62no—
331C4⋊Dic3—31no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3D1211yescharacteristic
349C4⋊Dic3D1211yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351Dic3⋊C4—21no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
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—121no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
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⋊C8C22×D311yescharacteristic
385C2×C3⋊C8C22×D311yescharacteristic
386Dic12—22no—
387Dic12—22no—
388Dic12—62no—
389Dic12—62no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32C22×D411yescharacteristic
394C32×C4—21no—
395C32×C4C2×#4111yescharacteristic
396C32×C4C2×#4111yescharacteristic
397C3⋊Dic3—41no—
398C3⋊Dic3—41no—
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—31no—
410C2×Q16—31no—
411C2×Q16—31no—
412C2×Q16—91no—
413C2×Q16—91no—
414C4⋊Q8—91no—
415#126—181no—
416#126—181no—
417#125—91no—
418#125—181no—
419#125—181no—
420C22⋊Q8—31no—
421C22⋊Q8—91no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—181no—
429C4×Q8—181no—
430#117—31no—
431#117—91no—
432#117—181no—
433#117—181no—
434#107—91no—
435#107—91no—
436#106—91no—
437#106—91no—
438C4⋊C8—31no—
439C4⋊C8—31no—
440#103—31no—
441#103—31no—
442#103—91no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448C22⋊C8—31no—
449C22⋊C8D3211yescharacteristic
450#97—31no—
451C4×C8—31no—
452C23×C3—21no—
453C23×C3C2×D1211yescharacteristic
454C23×C3D3×D411yescharacteristic
455C3×Q8—32no—
456C3×Q8—32no—
457C3×Q8—64no—
458C3×Q8—61no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×Q8—61no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—64no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4C2×D1211yescharacteristic
480C2×C3×C4D3×D411yescharacteristic
481C2×C3×C4C23×D311yescharacteristic
482C2×C3×C4C23×D311yescharacteristic
483C2×Dic3—24no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—121no—
497C2×Dic3—121no—
498C2×Dic3—121no—
499C2×Dic3—121no—
500C2×Dic3C2×D1211yescharacteristic
501C2×Dic3C2×D1211yescharacteristic
502C2×Dic3C2×D1211yescharacteristic
503C2×Dic3C2×D1211yescharacteristic
504Dic6—24no—
505Dic6—21no—
506Dic6—21no—
507Dic6—21no—
508Dic6—21no—
509Dic6—61no—
510Dic6—61no—
511Dic6—61no—
512Dic6—61no—
513Dic6—121no—
514Dic6—121no—
515Dic6#23712yes—
516Dic6#23712yes—
517C3×C8—21no—
518C3×C8—21no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—41no—
522C3×C8—41no—
523C3×C8—61no—
524C3×C8—61no—
525C3⋊C8—21no—
526C3⋊C8—21no—
527C2×C32—41no—
528C2×C32#52511yescharacteristic
529C2×C32#57811yescharacteristic
530C2×C32#57811yescharacteristic
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—31no—
534C2×Q8—62no—
535C2×Q8—62no—
536C2×Q8—61no—
537C2×Q8—91no—
538C22×C4—61no—
539C22×C4C2×D3211yescharacteristic
540Q16—62no—
541Q16—62no—
542Q16—182no—
543Q16—182no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8C2×D3211yescharacteristic
547C2×C8C2×D3211yescharacteristic
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—61no—
552C4⋊C4—91no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C22⋊C4—31no—
567C22⋊C4—31no—
568C22⋊C4—61no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C42—31no—
572C42—31no—
573C42—181no—
574C42—181no—
575C42—181no—
576C42—181no—
577C42—181no—
578C42—181no—
579C42—181no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3C22×D1211yescharacteristic
591C22×C3C2×D3×D411yescharacteristic
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—41no—
597C3×C4—61no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—61no—
601C3×C4—62no—
602C3×C4—62no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4C2×#23711yescharacteristic
606C3×C4C2×#23711yescharacteristic
607C3×C4D3×#4111yescharacteristic
608C3×C4D3×#4111yescharacteristic
609Dic3—21no—
610Dic3—21no—
611Dic3—21no—
612Dic3—21no—
613Dic3—22no—
614Dic3—22no—
615Dic3—41no—
616Dic3—41no—
617Dic3—121no—
618Dic3—121no—
619Dic3—121no—
620Dic3—121no—
621Dic3—121no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—241no—
626Dic3—241no—
627Dic3—241no—
628Dic3—241no—
629C32#312711yescharacteristic, complemented, Sylow
630C23D3×D1211yescharacteristic
631Q8—32no—
632Q8—32no—
633Q8—64no—
634Q8—61no—
635Q8—61no—
636Q8—61no—
637Q8—61no—
638Q8—181no—
639Q8—181no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—64no—
647C2×C4—61no—
648C2×C4—61no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4D3×D1211yescharacteristic
656C2×C4C22×D3211yescharacteristic
657C8—21no—
658C8—21no—
659C8—61no—
660C8—61no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—41no—
665C2×C3—41no—
666C2×C3—81no—
667C2×C3#552411yescharacteristic
668C2×C3#558611yescharacteristic
669C2×C3#575311yescharacteristic
670C2×C3#575311yescharacteristic
671C2×C3#576611yescharacteristic
672C2×C3#577911yescharacteristic
673C22—21no—
674C22—21no—
675C22—21no—
676C22C2×D3×D1211yescharacteristic
677C4—21no—
678C4—62no—
679C4—62no—
680C4—61no—
681C4—61no—
682C4—61no—
683C4—61no—
684C4—121no—
685C4—121no—
686C4—361no—
687C4—361no—
688C4—361no—
689C4—361no—
690C4D3×#23711yescharacteristic
691C4D3×#23711yescharacteristic
692C3—21no—
693C3#7939611yescharacteristic, complemented
694C3#8017711yescharacteristic, complemented
695C2—41no—
696C2#1059407811yescharacteristic
697C2#1059469111yescharacteristic
698C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22⋊C8D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
8. #10590815C2semidirect
9. #10590812C2semidirect
10. #10590811C2semidirect
11. Dic3×Dic12C2semidirect
12. #10590800C2semidirect
13. #10590800C2semidirect
14. #10590794C2semidirect
15. #10590793C2semidirect
629. C32#3127semidirect
693. C3#79396semidirect
694. C3#80177semidirect

Maximal subgroups

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

subgroupindex
#105948242
#105948182
#105924222
C3×#47392
C3×#47202
#105911862
#105911272
#105908152
#105908122
#105908112
Dic3×Dic122
#105908002
#105907942
#105907932
#801773
#793963