Finite Group Databasebeta

← #11873289

Subgroups — #11873289

Order 1152.

812 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596096C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic
3C3×#5050C211yesmaximal, characteristic
4C3×#5045C211yesmaximal, characteristic
5#10591582C211yesmaximal, characteristic, complemented
6#10591581C211yesmaximal, characteristic, complemented
7#10591580C211yesmaximal, characteristic, complemented
8#10591580C211yesmaximal, characteristic, complemented
9#10591186C211yesmaximal, characteristic
10#10591134C211yesmaximal, characteristic
11#10591062C211yesmaximal, characteristic
12#10590495C211yesmaximal, characteristic, complemented
13#10590494C211yesmaximal, characteristic, complemented
14#10590485C211yesmaximal, characteristic, complemented
15#10590482C211yesmaximal, characteristic, complemented
16#81499—31nomaximal
17#80177—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64153C2211yescharacteristic
22#64135C2211yescharacteristic
23#64133C2211yescharacteristic
24#64099—21no—
25#64099C2211yescharacteristic
26#64098—21no—
27#64096C2211yescharacteristic
28#64088—21no—
29#64088—21no—
30C2×C3×#216C2211yescharacteristic
31C2×C3×#216C2211yescharacteristic
32C3×#926C2211yescharacteristic
33#63955—21no—
34#63955—21no—
35#63843C2211yescharacteristic
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38#63843C2211yescharacteristic
39Dic3×Dic6—21no—
40Dic3×Dic6—21no—
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C3×#835C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#830C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#807C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63572C2211yescharacteristic
54#63572C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63555C2211yescharacteristic
60#63553C2211yescharacteristic
61#5812—31no—
62#5625—31no—
63#5625—31no—
64#5625—61no—
65#5516—31no—
66C3×#485—31no—
67C3×#451—31no—
68#5228—31no—
69#5184—31no—
70#5182—31no—
71#5182—31no—
72Dic3×Q16—31no—
73#5050D311yescharacteristic
74#5045D311yescharacteristic
75#4996—31no—
76#4877—31no—
77#4873—31no—
78#4857—31no—
79#4853—31no—
80#4799—31no—
81#4796—31no—
82#4795—31no—
83#4795—31no—
84#4790—31no—
85#4790—31no—
86#4789—31no—
87#4789—31no—
88#4739—31no—
89#4723—31no—
90#4720—31no—
91#4720—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C22×C3×Dic3—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6—22no—
98C2×C3×Dic6—22no—
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C32×C4⋊C4—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C22⋊C4—21no—
104#3757—21no—
105#3757D411yescharacteristic
106#3757D411yescharacteristic
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)D411yescharacteristic
110C4⋊(C3⋊Dic3)D411yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C3×#217—21no—
122C3×#216—22no—
123C3×#216—22no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4×Dic3—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—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—21no—
147C3×C22⋊Q8C2×D311yescharacteristic
148C3×C22⋊Q8C2×D311yescharacteristic
149C3×#117—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156Q8×Dic3—61no—
157Q8×Dic3—61no—
158Q8×Dic3—61no—
159#944—31no—
160#944—31no—
161#944—61no—
162C2×#216—31no—
163C2×#216—31no—
164C2×#216C2×D311yescharacteristic
165C2×#216C2×D311yescharacteristic
166#926—31no—
167#926—31no—
168#926—61no—
169#926—61no—
170#926—61no—
171#926C2×D311yescharacteristic
172#924—31no—
173#924—31no—
174#924—61no—
175C2×Dic12—31no—
176C2×Dic12—31no—
177#890—31no—
178#890—31no—
179#890—61no—
180#890—61no—
181#890—61no—
182#890—62no—
183#889—61no—
184#889—61no—
185#889—62no—
186#887—31no—
187#887—31no—
188#887—31no—
189#887—31no—
190#887—31no—
191#887—31no—
192#887—61no—
193#879—61no—
194#879—61no—
195#879—61no—
196#879—61no—
197#879—62no—
198#879—62no—
199#877—61no—
200#877—61no—
201C4×Dic6—61no—
202C4×Dic6—61no—
203C3×#107—31no—
204C3×#106—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×C22⋊C8—31no—
210C3×C22⋊C8—31no—
211#835—31no—
212#835—31no—
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#830C2×D311yescharacteristic
216#830C2×D311yescharacteristic
217#818—31no—
218#817—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#815—31no—
224#815—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231#810—31no—
232#810—31no—
233#810C2×D311yescharacteristic
234#810C2×D311yescharacteristic
235#808—31no—
236#808C2×D311yescharacteristic
237#807—31no—
238#807C2×D311yescharacteristic
239C23×C32C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254#634—21no—
255#634—21no—
256C2×C3×Dic3—24no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C3×Dic6—24no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6#4112yes—
265C3×Dic6#4112yes—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269C3×C3⋊C8—21no—
270#541—91no—
271#519—91no—
272#485—31no—
273#485—91no—
274#479—91no—
275#479—91no—
276#462—91no—
277#462—91no—
278#451—31no—
279#451—91no—
280#441—91no—
281#441—91no—
282C4×Q16—91no—
283C4×Q16—91no—
284#433—91no—
285C2×C3×Q8—21no—
286C2×C3×Q8—31no—
287C2×C3×Q8—31no—
288C2×C3×Q8—62no—
289C2×C3×Q8—62no—
290C2×C3×Q8—61no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—61no—
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×Dic3—21no—
298C2×Dic6—21no—
299C2×Dic6—22no—
300C2×Dic6—22no—
301C2×Dic6—31no—
302C2×Dic6—31no—
303C2×Dic6—61no—
304C2×Dic6C22×D311yescharacteristic
305C2×Dic6C22×D311yescharacteristic
306C3×Q16—62no—
307C3×Q16—62no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C3×C4⋊C4—22no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4C22×D311yescharacteristic
319C3×C4⋊C4C22×D311yescharacteristic
320C3×C22⋊C4—22no—
321C3×C22⋊C4—21no—
322C3×C22⋊C4—21no—
323C3×C22⋊C4—61no—
324C3×C42—61no—
325#217—21no—
326#217—31no—
327#217—31no—
328#217—31no—
329#217—31no—
330#217—61no—
331#217—61no—
332#217—62no—
333#217—61no—
334#217—61no—
335#216—22no—
336#216—22no—
337#216—62no—
338#216—62no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3—62no—
357C4⋊Dic3—62no—
358C4⋊Dic3C22×D311yescharacteristic
359C4⋊Dic3C22×D311yescharacteristic
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—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4—62no—
376Dic3⋊C4—62no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379C4×Dic3—21no—
380C4×Dic3—31no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—62no—
399C4×Dic3—62no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404Dic12—62no—
405Dic12—62no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32C22×D411yescharacteristic
410C32×C4—21no—
411C32×C4—41no—
412C32×C4—41no—
413C32×C4C2×#4111yescharacteristic
414C32×C4C2×#4111yescharacteristic
415C3⋊Dic3—21no—
416C3⋊Dic3—21no—
417C3⋊Dic3—21no—
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—22no—
422C3×Dic3—22no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×Q8—31no—
426C2×Q16—31no—
427C2×Q16—31no—
428C2×Q16—91no—
429C2×Q16—91no—
430C4⋊Q8—91no—
431#126—181no—
432#126—181no—
433#125—91no—
434#125—181no—
435#125—181no—
436C22⋊Q8—91no—
437C22⋊Q8D3211yescharacteristic
438C4×Q8—91no—
439C4×Q8—91no—
440C4×Q8—91no—
441C4×Q8—91no—
442C4×Q8—91no—
443C4×Q8—91no—
444C4×Q8—181no—
445C4×Q8—181no—
446#117—31no—
447#117—91no—
448#117—181no—
449#117—181no—
450#107—31no—
451#107—91no—
452#106—31no—
453#106—91no—
454C4⋊C8—91no—
455C4⋊C8—91no—
456#103—31no—
457#103—31no—
458#103—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464C22⋊C8—31no—
465C22⋊C8—31no—
466#97—91no—
467C4×C8—91no—
468C23×C3—21no—
469C23×C3D3×D411yescharacteristic
470C23×C3D3×D411yescharacteristic
471C3×Q8—21no—
472C3×Q8—21no—
473C3×Q8—21no—
474C3×Q8—21no—
475C3×Q8—32no—
476C3×Q8—32no—
477C3×Q8—41no—
478C3×Q8—41no—
479C3×Q8—64no—
480C3×Q8—61no—
481C3×Q8—61no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—64no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4D3×D411yescharacteristic
502C2×C3×C4D3×D411yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×Dic3—24no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—62no—
523C2×Dic3—62no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528Dic6—24no—
529Dic6—21no—
530Dic6—21no—
531Dic6—61no—
532Dic6—61no—
533Dic6—61no—
534Dic6—61no—
535Dic6—121no—
536Dic6—121no—
537Dic6#23712yes—
538Dic6#23712yes—
539C3×C8—61no—
540C3×C8—61no—
541C3×C8—61no—
542C3×C8—61no—
543C3⋊C8—21no—
544C3⋊C8—21no—
545C3⋊C8—21no—
546C3⋊C8—21no—
547C2×C32—41no—
548C2×C32#52511yescharacteristic
549C2×C32#57811yescharacteristic
550C2×C32#57811yescharacteristic
551C2×Q8—31no—
552C2×Q8—31no—
553C2×Q8—62no—
554C2×Q8—62no—
555C2×Q8—61no—
556C2×Q8—91no—
557C2×Q8C2×D3211yescharacteristic
558C22×C4—61no—
559C22×C4C2×D3211yescharacteristic
560Q16—62no—
561Q16—62no—
562Q16—182no—
563Q16—182no—
564C2×C8—31no—
565C2×C8—31no—
566C2×C8—31no—
567C2×C8—31no—
568C4⋊C4—21no—
569C4⋊C4—31no—
570C4⋊C4—31no—
571C4⋊C4—91no—
572C4⋊C4—91no—
573C4⋊C4—91no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C4⋊C4—181no—
577C4⋊C4—181no—
578C4⋊C4—181no—
579C4⋊C4—181no—
580C4⋊C4—181no—
581C4⋊C4—181no—
582C4⋊C4—181no—
583C4⋊C4—181no—
584C4⋊C4—181no—
585C4⋊C4C2×D3211yescharacteristic
586C22⋊C4—21no—
587C22⋊C4—61no—
588C22⋊C4—91no—
589C22⋊C4—91no—
590C22⋊C4—181no—
591C42—61no—
592C42—91no—
593C42—91no—
594C42—181no—
595C42—181no—
596C42—181no—
597C42—181no—
598C42—181no—
599C42—181no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3C2×D3×D411yescharacteristic
611C22×C3C2×D3×D411yescharacteristic
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—41no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—62no—
624C3×C4—62no—
625C3×C4—121no—
626C3×C4—121no—
627C3×C4C2×#23711yescharacteristic
628C3×C4C2×#23711yescharacteristic
629C3×C4D3×#4111yescharacteristic
630C3×C4D3×#4111yescharacteristic
631Dic3—22no—
632Dic3—22no—
633Dic3—41no—
634Dic3—41no—
635Dic3—61no—
636Dic3—61no—
637Dic3—61no—
638Dic3—61no—
639Dic3—61no—
640Dic3—61no—
641Dic3—61no—
642Dic3—61no—
643Dic3—121no—
644Dic3—121no—
645Dic3—121no—
646Dic3—121no—
647Dic3—122no—
648Dic3—122no—
649Dic3—121no—
650Dic3—121no—
651Dic3—121no—
652Dic3—121no—
653C32#312711yescharacteristic, complemented, Sylow
654C23#381111yescharacteristic
655Q8—21no—
656Q8—21no—
657Q8—32no—
658Q8—32no—
659Q8—64no—
660Q8—61no—
661Q8—61no—
662Q8—181no—
663Q8—181no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—64no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—91no—
674C2×C4—91no—
675C2×C4—91no—
676C2×C4—91no—
677C2×C4—181no—
678C2×C4—181no—
679C2×C4#381111yescharacteristic
680C2×C4C22×D3211yescharacteristic
681C8—61no—
682C8—61no—
683C8—61no—
684C8—61no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—41no—
689C2×C3—41no—
690C2×C3—81no—
691C2×C3#558611yescharacteristic
692C2×C3#565611yescharacteristic
693C2×C3#576611yescharacteristic
694C2×C3#577111yescharacteristic
695C2×C3#577911yescharacteristic
696C2×C3#577911yescharacteristic
697C22—21no—
698C22—21no—
699C22—21no—
700C22C2×#381111yescharacteristic
701C4—21no—
702C4—41no—
703C4—41no—
704C4—62no—
705C4—62no—
706C4—121no—
707C4—121no—
708C4—181no—
709C4—181no—
710C4—181no—
711C4—181no—
712C4—361no—
713C4—361no—
714C4D3×#23711yescharacteristic
715C4D3×#23711yescharacteristic
716C3—21no—
717C3#8017711yescharacteristic, complemented
718C3#8149911yescharacteristic, complemented
719C2—41no—
720C2#1059516011yescharacteristic
721C2#1059533711yescharacteristic
722C2#1059547211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenterC22⋊Q8D32
hypocenterC32#3127
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
5. #10591582C2semidirect
6. #10591581C2semidirect
7. #10591580C2semidirect
8. #10591580C2semidirect
12. #10590495C2semidirect
13. #10590494C2semidirect
14. #10590485C2semidirect
15. #10590482C2semidirect
653. C32#3127semidirect
717. C3#80177semidirect
718. C3#81499semidirect

Maximal subgroups

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

subgroupindex
#105960962
#105948182
C3×#50502
C3×#50452
#105915822
#105915812
#105915802
#105911862
#105911342
#105910622
#105904952
#105904942
#105904852
#105904822
#814993
#801773