Finite Group Databasebeta

← #11870828

Subgroups — #11870828

Order 1152.

816 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594385C211yesmaximal, characteristic
2D3×#887C211yesmaximal, characteristic
3#10592574C211yesmaximal, characteristic, complemented
4C3×#4884C211yesmaximal, characteristic
5C3×#4873C211yesmaximal, characteristic, complemented
6#10590949C211yesmaximal, characteristic
7#10590798C211yesmaximal, characteristic, complemented
8#10590793C211yesmaximal, characteristic, complemented
9#10590655C211yesmaximal, characteristic
10#10590604C211yesmaximal, characteristic
11#10590566C211yesmaximal, characteristic, complemented
12#10590517C211yesmaximal, characteristic
13#10590496C211yesmaximal, characteristic, complemented
14#10590481C211yesmaximal, characteristic, complemented
15#10590476C211yesmaximal, characteristic, complemented
16#81452—31nomaximal
17#79722—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19#64097C2211yescharacteristic
20#64096C2211yescharacteristic
21C2×C3×Dic12C2211yescharacteristic
22C3×#897C2211yescharacteristic
23C3×D3×C4⋊C4C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C3×#887C2211yescharacteristic
26#63896—21no—
27#63877—21no—
28D3×Dic3⋊C4—21no—
29C4×D3×Dic3—21no—
30C4×D3×Dic3C2211yescharacteristic
31#63873C2211yescharacteristic
32#63856C2211yescharacteristic
33#63847—21no—
34#63844—21no—
35#63844C2211yescharacteristic
36#63843C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38#63838—21no—
39#63837—21no—
40C2×#3719C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C32×#107C2211yescharacteristic
44#63643C2211yescharacteristic
45#63641C2211yescharacteristic
46#63637C2211yescharacteristic
47#63634C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63575C2211yescharacteristic
56#63572C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5622—31no—
62#5578—31no—
63C4×D3×Q8—31no—
64C2×#887—31no—
65C3×#484—31no—
66C3×C4×Q16—31no—
67#5186—31no—
68#5182—31no—
69#5050—31no—
70C4×#216—31no—
71C4×#216—31no—
72#4970—31no—
73#4884D311yescharacteristic
74#4875—31no—
75#4875—31no—
76#4875—31no—
77#4875—61no—
78#4873—31no—
79#4873D311yescharacteristic, complemented
80#4811—31no—
81#4809—31no—
82#4795—31no—
83#4795—31no—
84#4795—31no—
85#4793—31no—
86#4790—31no—
87#4790—31no—
88#4739—31no—
89#4718—31no—
90C4×Dic12—31no—
91#4685—31no—
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3D411yescharacteristic
102C2×D3×Dic3D411yescharacteristic
103D3×Dic6—22no—
104D3×Dic6—22no—
105C2×C32×C8C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C32×C4⋊C4C2311yescharacteristic
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110#3750—21no—
111C4×C3⋊Dic3—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C3×Dic12—22no—
126#3724—21no—
127#3724—21no—
128#3724—21no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133Dic32—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138#3719—22no—
139#3719—22no—
140#3718—22no—
141#3104—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C2×C3×Q16—31no—
145C3×C22⋊Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C2×C3×C4⋊C4—31no—
149#946—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152#944—31no—
153#944—31no—
154C2×#216—31no—
155C2×#216—31no—
156C2×#216—31no—
157C2×#216—31no—
158#924—31no—
159C2×Dic3⋊C4—61no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—61no—
162C2×Dic12—31no—
163C2×Dic12—31no—
164C2×Dic12C2×D311yescharacteristic
165#897C2×D311yescharacteristic
166#896—61no—
167D3×C4⋊C4—61no—
168D3×C4⋊C4C2×D311yescharacteristic
169#889—61no—
170#889—61no—
171#888—31no—
172#888—31no—
173#888—61no—
174#887—31no—
175#887—31no—
176#887—31no—
177#887—31no—
178#887—61no—
179#887—61no—
180#887—61no—
181#887—61no—
182#887—61no—
183#887C2×D311yescharacteristic
184#887C2×D311yescharacteristic
185#878—61no—
186#877—61no—
187#872—61no—
188C42×D3—31no—
189C42×D3—61no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—61no—
193C4×Dic6—61no—
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic
197C3×#107C2×D311yescharacteristic
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×C22⋊C8—31no—
203C3×C4×C8—31no—
204#835—31no—
205#835—31no—
206#830—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8C2×D311yescharacteristic
209#818—31no—
210#816—31no—
211#816—31no—
212#816—31no—
213#816—61no—
214#816C2×D311yescharacteristic
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—61no—
220C8×Dic3—31no—
221C8×Dic3C2×D311yescharacteristic
222#810—31no—
223#810—31no—
224#810—31no—
225#810—61no—
226#810C2×D311yescharacteristic
227#810C2×D311yescharacteristic
228#810C2×D311yescharacteristic
229#807—31no—
230#807—31no—
231#807—31no—
232#807—61no—
233#807C2×D311yescharacteristic
234C4×C3⋊C8—31no—
235C22×C3×D3C2×D411yescharacteristic
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—21no—
244#634—42no—
245#634#4112yes—
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
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×C4×D3—42no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
262#627—24no—
263D3×Dic3—24no—
264D3×Dic3—41no—
265D3×Dic3Q1614yescomplemented
266C32×C8—21no—
267C3⋊(C3⋊C8)—21no—
268C3×C3⋊C8—21no—
269C3×C3⋊C8—21no—
270#533—91no—
271C2×C4×Q8—91no—
272#484—31no—
273#484—91no—
274#477—91no—
275#477—91no—
276#462—91no—
277#462—91no—
278#451—91no—
279#451—91no—
280C4×Q16—31no—
281C4×Q16—91no—
282C4×Q16—91no—
283C4×Q16—91no—
284#431—91no—
285C2×C3×Q8—31no—
286C2×C3×Q8—31no—
287C2×C3×Q8—31no—
288C22×C3×C4—31no—
289C22×C3×C4—61no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—61no—
293D3×Q8—62no—
294D3×Q8—62no—
295C2×C4×D3—21no—
296C2×C4×D3—31no—
297C2×C4×D3—31no—
298C2×C4×D3—61no—
299C2×C4×D3C22×D311yescharacteristic
300C2×Dic6—31no—
301C2×Dic6—31no—
302C2×Dic6—61no—
303C2×Dic6—62no—
304C2×Dic6—61no—
305C2×Dic6—61no—
306C2×Dic6—62no—
307C2×Dic6—61no—
308C2×Dic6—61no—
309C2×Dic6—121no—
310C2×Dic6C22×D311yescharacteristic
311C2×Dic6C22×D311yescharacteristic
312C2×Dic6C22×D311yescharacteristic
313C3×Q16—62no—
314C2×C3×C8—21no—
315C2×C3×C8—31no—
316C2×C3×C8—31no—
317C2×C3×C8C22×D311yescharacteristic
318C2×C3×C8C22×D311yescharacteristic
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
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×C4⋊C4C22×D311yescharacteristic
329C3×C4⋊C4C22×D311yescharacteristic
330C3×C22⋊C4—61no—
331C3×C42—31no—
332C3×C42—61no—
333C3×C42—61no—
334#217—61no—
335#216—62no—
336#216—62no—
337#216—62no—
338#216—62no—
339(C2×D3)⋊C4—21no—
340(C2×D3)⋊C4—61no—
341C4⋊Dic3—21no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3C22×D311yescharacteristic
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
351Dic3⋊C4—61no—
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—121no—
366Dic3⋊C4—121no—
367C4×Dic3—21no—
368C4×Dic3—21no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—121no—
385C4×Dic3C22×D311yescharacteristic
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8C22×D311yescharacteristic
390C2×C3⋊C8C22×D311yescharacteristic
391Dic12—22no—
392Dic12—62no—
393Dic12—62no—
394C22×C32C22×D411yescharacteristic
395C2×C3×D3—21no—
396C2×C3×D3—21no—
397C2×C3×D3C2×Q1612yes—
398C32×C4—41no—
399C32×C4—41no—
400C32×C4C2×#4111yescharacteristic
401C32×C4C2×#4111yescharacteristic
402C3⋊Dic3—22no—
403C3⋊Dic3—21no—
404C3⋊Dic3—41no—
405C3⋊Dic3C2×Q1612yes—
406C3×Dic3—22no—
407C3×Dic3—21no—
408C3×Dic3—21no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C3×Dic3C2×Q1612yes—
413C22×Q8—91no—
414C2×Q16—31no—
415C2×Q16—91no—
416C2×Q16—91no—
417C2×Q16—91no—
418C4⋊Q8—91no—
419C4⋊Q8—91no—
420#125—181no—
421C22⋊Q8—31no—
422C22⋊Q8—91no—
423C22⋊Q8—181no—
424C4×Q8—31no—
425C4×Q8—31no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—181no—
431C4×Q8—181no—
432C4×Q8—181no—
433#117—181no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—181no—
436C2×C42—91no—
437C2×C42—181no—
438#107—31no—
439#107—91no—
440#107—91no—
441#107D3211yescharacteristic
442C4⋊C8—91no—
443C4⋊C8—91no—
444#103—31no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—91no—
449#103—91no—
450#103—91no—
451#103—91no—
452C22⋊C8—31no—
453C22⋊C8—91no—
454C4×C8—31no—
455C4×C8—91no—
456C23×C3—31no—
457C22×D3D3×D411yescharacteristic
458C3×Q8—32no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×Q8—61no—
462C3×Q8—61no—
463C3×Q8—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—41no—
473C2×C3×C4—41no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—122no—
481C2×C3×C4C23×D311yescharacteristic
482C2×C3×C4C23×D311yescharacteristic
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—34no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—64no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—121no—
500C2×Dic3—121no—
501C2×Dic3—121no—
502C2×Dic3D3×D411yescharacteristic
503C2×Dic3D3×D411yescharacteristic
504C2×Dic3D3×D411yescharacteristic
505C4×D3—21no—
506C4×D3—21no—
507C4×D3—34no—
508C4×D3—42no—
509C4×D3—64no—
510C4×D3—121no—
511Dic6—21no—
512Dic6—21no—
513Dic6—21no—
514Dic6—21no—
515Dic6—21no—
516Dic6—32no—
517Dic6—32no—
518Dic6—62no—
519Dic6—64no—
520Dic6—64no—
521Dic6—61no—
522Dic6—61no—
523Dic6—121no—
524Dic6—122no—
525Dic6—122no—
526Dic6—242no—
527Dic6#23512yes—
528C3×C8—21no—
529C3×C8—21no—
530C3×C8—41no—
531C3×C8—61no—
532C3×C8—61no—
533C3⋊C8—21no—
534C3⋊C8—21no—
535C3⋊C8—61no—
536C3⋊C8—61no—
537C3⋊C8—121no—
538C2×C32#52511yescharacteristic
539C2×C32C22×Q1611yescharacteristic
540C2×C32#57511yescharacteristic
541C3×D3—22no—
542C2×Q8—31no—
543C2×Q8—31no—
544C2×Q8—31no—
545C2×Q8—91no—
546C2×Q8—181no—
547C2×Q8—181no—
548C2×Q8—182no—
549C2×Q8—182no—
550C22×C4—31no—
551C22×C4—61no—
552C22×C4—91no—
553C22×C4—91no—
554C22×C4—181no—
555Q16—62no—
556Q16—182no—
557Q16—182no—
558Q16—182no—
559C2×C8—31no—
560C2×C8—31no—
561C2×C8—91no—
562C2×C8C2×D3211yescharacteristic
563C4⋊C4—31no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—91no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C4⋊C4—181no—
577C4⋊C4C2×D3211yescharacteristic
578C4⋊C4C2×D3211yescharacteristic
579C22⋊C4—61no—
580C22⋊C4—181no—
581C42—31no—
582C42—61no—
583C42—61no—
584C42—91no—
585C42—91no—
586C42—91no—
587C42—181no—
588C42—181no—
589C42—181no—
590C42—181no—
591C22×C3—21no—
592C22×C3—32no—
593C22×C3—61no—
594C22×C3—61no—
595C22×C3C2×D3×D411yescharacteristic
596C22×C3C2×D3×D411yescharacteristic
597C2×D3—21no—
598C2×D3—21no—
599C2×D3D3×Q1612yes—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—32no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—62no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—81no—
611C3×C4—81no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4—121no—
615C3×C4C2×#23511yescharacteristic
616C3×C4D3×#4111yescharacteristic
617C3×C4D3×#4111yescharacteristic
618C3×C4D3×#4111yescharacteristic
619Dic3—21no—
620Dic3—21no—
621Dic3—22no—
622Dic3—32no—
623Dic3—32no—
624Dic3—41no—
625Dic3—41no—
626Dic3—41no—
627Dic3—62no—
628Dic3—62no—
629Dic3—61no—
630Dic3—61no—
631Dic3—62no—
632Dic3—122no—
633Dic3—121no—
634Dic3—121no—
635Dic3—121no—
636Dic3—241no—
637Dic3D3×Q1612yes—
638C32#310411yescharacteristic, complemented, Sylow
639C23—31no—
640Q8—32no—
641Q8—61no—
642Q8—61no—
643Q8—61no—
644Q8—61no—
645Q8—61no—
646Q8—92no—
647Q8—184no—
648Q8—181no—
649Q8—362no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—94no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—122no—
665C2×C4—184no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—361no—
669C2×C4C22×D3211yescharacteristic
670C8—21no—
671C8—61no—
672C8—61no—
673C8—181no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—62no—
678C2×C3#554711yescharacteristic
679C2×C3#565611yescharacteristic
680C2×C3C2×D3×Q1611yescharacteristic
681C2×C3C2×D3×Q1611yescharacteristic
682C2×C3#576811yescharacteristic
683C2×C3#577311yescharacteristic
684D3—22no—
685C22—32no—
686C22—61no—
687C22—61no—
688C22D32×D411yescharacteristic
689C4—32no—
690C4—41no—
691C4—41no—
692C4—61no—
693C4—62no—
694C4—61no—
695C4—92no—
696C4—121no—
697C4—121no—
698C4—121no—
699C4—182no—
700C4—181no—
701C4—361no—
702C4D3×#23511yescharacteristic
703C4#6431911yescharacteristic
704C3—21no—
705C3#7972211yescharacteristic, complemented
706C3#8145211yescharacteristic, complemented
707C2—62no—
708C2#1059461411yescharacteristic
709C2#1059472911yescharacteristic
710C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#107D32
hypocenterC32#3104
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
3. #10592574C2semidirect
5. C3×#4873C2semidirect
7. #10590798C2semidirect
8. #10590793C2semidirect
11. #10590566C2semidirect
13. #10590496C2semidirect
14. #10590481C2semidirect
15. #10590476C2semidirect
79. #4873D3semidirect
265. D3×Dic3Q16semidirect
638. C32#3104semidirect
705. C3#79722semidirect
706. C3#81452semidirect

Maximal subgroups

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

subgroupindex
#105943852
D3×#8872
#105925742
C3×#48842
C3×#48732
#105909492
#105907982
#105907932
#105906552
#105906042
#105905662
#105905172
#105904962
#105904812
#105904762
#814523
#797223