Finite Group Databasebeta

← #11872685

Subgroups — #11872685

Order 1152.

788 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594592C211yesmaximal, characteristic
2#10594357C211yesmaximal, characteristic, complemented
3#10592574C211yesmaximal, characteristic, complemented
4C3×#4889C211yesmaximal, characteristic, complemented
5C3×#4888C211yesmaximal, characteristic, complemented
6#10590822C211yesmaximal, characteristic
7#10590796C211yesmaximal, characteristic, complemented
8#10590794C211yesmaximal, characteristic, complemented
9#10590697C211yesmaximal, characteristic, complemented
10#10590604C211yesmaximal, characteristic, complemented
11#10590538C211yesmaximal, characteristic, complemented
12#10590502C211yesmaximal, characteristic
13#10590497C211yesmaximal, characteristic, complemented
14#10590479C211yesmaximal, characteristic, complemented
15#10590476C211yesmaximal, characteristic, complemented
16#81497—31nomaximal
17#79814—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19#64097C2211yescharacteristic
20#64096C2211yescharacteristic
21C2×C3×#204C2211yescharacteristic
22C3×#897C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#887C2211yescharacteristic
26C4×#627—21no—
27#63913—21no—
28#63908C2211yescharacteristic
29#63905—21no—
30#63878—21no—
31#63877—21no—
32#63863C2211yescharacteristic
33#63858—21no—
34#63857—21no—
35#63855C2211yescharacteristic
36#63844C2211yescharacteristic
37#63843C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63837—21no—
40C2×#3719C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C32×#107C2211yescharacteristic
44#63643C2211yescharacteristic
45#63641C2211yescharacteristic
46#63637C2211yescharacteristic
47#63634C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#815C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#808C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63566C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5643—31no—
62#5572—31no—
63#5561—31no—
64#5516—31no—
65C3×#485—31no—
66C3×#440—31no—
67#5170—31no—
68#5166—31no—
69#5050—31no—
70C4×#216—31no—
71C4×#214—31no—
72#5003—31no—
73#4889D311yescharacteristic, complemented
74#4888D311yescharacteristic, complemented
75#4875—31no—
76#4875—31no—
77#4875—61no—
78#4854—31no—
79#4852—31no—
80#4809—31no—
81#4798—31no—
82#4798—31no—
83#4791—31no—
84#4790—31no—
85#4789—31no—
86#4779—31no—
87#4767—31no—
88#4738—31no—
89#4720—31no—
90#4716—31no—
91#4709—31no—
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#625—21no—
101C2×D3×Dic3—21no—
102D3×Dic6—22no—
103D3×Dic6—22no—
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109#3750—21no—
110C4×C3⋊Dic3—21no—
111C4×C3⋊Dic3C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C3×#204—22no—
125#3724—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3D411yescharacteristic
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138#3719—22no—
139#3718—22no—
140#3716—22no—
141#3121—91noSylow
142C2×D3×Q8—31no—
143C22×Dic6—31no—
144C2×C3×SD16—31no—
145C3×C22⋊Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×D4—31no—
148C3×#117—31no—
149#947—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152C2×#216—31no—
153C2×#216—31no—
154C2×#216—31no—
155#938—31no—
156#936—31no—
157C2×#214—31no—
158#930—31no—
159#929—61no—
160#926—31no—
161#924—61no—
162C2×Dic12—31no—
163C2×#204—31no—
164C2×#204C2×D311yescharacteristic
165#898—61no—
166#897—61no—
167#897C2×D311yescharacteristic
168#893C2×D311yescharacteristic
169#892—61no—
170#892C2×D311yescharacteristic
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#887C2×D311yescharacteristic
181#885—61no—
182#885—61no—
183#883—61no—
184#879—61no—
185#877—61no—
186#877—61no—
187#872—31no—
188#872—61no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C4×Dic6—61no—
192C4×Dic6—61no—
193C4×Dic6—61no—
194C3×#107—21no—
195C3×#107C2×D311yescharacteristic
196C3×#107C2×D311yescharacteristic
197C3×#106—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203C3×#97—31no—
204#835—31no—
205#832—31no—
206#830—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8C2×D311yescharacteristic
209#817—31no—
210#816—31no—
211#816—31no—
212#816—31no—
213#816—61no—
214#816C2×D311yescharacteristic
215#815C2×D311yescharacteristic
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221C8×Dic3—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#810C2×D311yescharacteristic
226#810C2×D311yescharacteristic
227#809—31no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808C2×D311yescharacteristic
231#807—31no—
232#807—31no—
233#807—61no—
234C4×C3⋊C8—31no—
235C22×C3×D3—21no—
236C22×C3×D3C2×D411yescharacteristic
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3C2×D411yescharacteristic
243C2×C3⋊Dic3C2×D411yescharacteristic
244#634—21no—
245#634—81no—
246#634#4112yes—
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×D12—21no—
254C3×D12—21no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×C4×D3—81no—
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
262#627—24no—
263#625—81no—
264D3×Dic3—24no—
265C32×C8—21no—
266C3⋊(C3⋊C8)—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#542—91no—
270#519—91no—
271#485—31no—
272#482—91no—
273#477—91no—
274#475—91no—
275#464—91no—
276#464—91no—
277#451—91no—
278#448—91no—
279#441—91no—
280#440—31no—
281C4×Q16—91no—
282C4×SD16—91no—
283#433—91no—
284C2×C3×Q8—31no—
285C2×C3×Q8—31no—
286C2×C3×D4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—61no—
289C2×#67—61no—
290C2×#67—61no—
291C22×Dic3—61no—
292D3×Q8—62no—
293D3×Q8—62no—
294C2×D12C22×D311yescharacteristic
295C2×C4×D3—21no—
296C2×C4×D3—61no—
297C2×C4×D3C22×D311yescharacteristic
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—61no—
301C2×Dic6—62no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—62no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—121no—
308C2×Dic6C22×D311yescharacteristic
309C2×Dic6C22×D311yescharacteristic
310C3×SD16—62no—
311C2×C3×C8—21no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C22⋊C4—61no—
326C3×C22⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C42—31no—
329C3×C42—61no—
330C3×C42—61no—
331#217—31no—
332#217—31no—
333#217—61no—
334#217—61no—
335#217—61no—
336#216—62no—
337#216—62no—
338#216—62no—
339#214—62no—
340(C2×D3)⋊C4—21no—
341(C2×D3)⋊C4—21no—
342(C2×D3)⋊C4—21no—
343(C2×D3)⋊C4—31no—
344(C2×D3)⋊C4—31no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348C4⋊Dic3—21no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3C22×D311yescharacteristic
357Dic3⋊C4—21no—
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—121no—
369Dic3⋊C4—121no—
370C4×Dic3—21no—
371C4×Dic3—21no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—61no—
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—121no—
384C4×Dic3C22×D311yescharacteristic
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390Dic12—62no—
391#204—22no—
392#204—62no—
393C22×C32C22×D411yescharacteristic
394C2×C3×D3—21no—
395C2×C3×D3—21no—
396C2×C3×D3—21no—
397C2×C3×D3—41no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4C2×#4111yescharacteristic
403C32×C4C2×#4111yescharacteristic
404C3⋊Dic3—21no—
405C3⋊Dic3—22no—
406C3⋊Dic3—21no—
407C3⋊Dic3—41no—
408C3×Dic3—22no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C22×Q8—91no—
415C2×Q16—91no—
416C2×Q16—91no—
417C2×SD16—31no—
418C2×SD16—91no—
419C4⋊Q8—91no—
420#126—181no—
421#124—91no—
422#124—181no—
423#123—181no—
424C22⋊Q8—31no—
425C22⋊Q8—181no—
426#121—91no—
427C4×Q8—31no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—91no—
431C4×Q8—91no—
432C4×Q8—181no—
433C4×Q8—181no—
434C4×D4—31no—
435#117—31no—
436#117—91no—
437#117—181no—
438#117—181no—
439#107—91no—
440#107D3211yescharacteristic
441#106—31no—
442#106—91no—
443C4⋊C8—91no—
444C4⋊C8—91no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—91no—
449#103—91no—
450#103—91no—
451#102—31no—
452#102—91no—
453C22⋊C8—31no—
454C22⋊C8—91no—
455#97—31no—
456C4×C8—91no—
457C23×C3—31no—
458C23×C3—61no—
459C22×D3—21no—
460C22×D3D3×D411yescharacteristic
461C3×Q8—32no—
462C3×Q8—61no—
463C3×Q8—61no—
464C3×Q8—61no—
465C3×D4—61no—
466C3×D4—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—41no—
476C2×C3×C4—41no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—241no—
483C2×C3×C4C23×D311yescharacteristic
484C2×C3×C4C23×D311yescharacteristic
485#67—241no—
486#67—241no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—64no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—121no—
502C2×Dic3—121no—
503C2×Dic3D3×D411yescharacteristic
504C2×Dic3D3×D411yescharacteristic
505C2×Dic3D3×D411yescharacteristic
506D12—21no—
507D12—21no—
508C4×D3—21no—
509C4×D3—21no—
510C4×D3—64no—
511C4×D3—81no—
512Dic6—21no—
513Dic6—21no—
514Dic6—21no—
515Dic6—32no—
516Dic6—32no—
517Dic6—62no—
518Dic6—64no—
519Dic6—64no—
520Dic6—61no—
521Dic6—61no—
522Dic6—121no—
523Dic6—241no—
524Dic6—241no—
525Dic6—242no—
526Dic6#23512yes—
527C3×C8—21no—
528C3×C8—21no—
529C3×C8—41no—
530C3×C8—61no—
531C3×C8—61no—
532C3⋊C8—21no—
533C3⋊C8—21no—
534C3⋊C8—61no—
535C3⋊C8—61no—
536C3⋊C8—121no—
537C2×C32#52511yescharacteristic
538C2×C32#57711yescharacteristic
539C2×C32#57811yescharacteristic
540C3×D3—41no—
541C3×D3—81no—
542C2×Q8—31no—
543C2×Q8—31no—
544C2×Q8—91no—
545C2×Q8—181no—
546C2×Q8—181no—
547C2×Q8—182no—
548C2×Q8—182no—
549C2×D4—31no—
550C2×D4—181no—
551C22×C4—31no—
552C22×C4—61no—
553C22×C4—181no—
554Q16—182no—
555Q16—182no—
556SD16—62no—
557SD16—182no—
558C2×C8—31no—
559C2×C8—31no—
560C2×C8—91no—
561C2×C8C2×D3211yescharacteristic
562C4⋊C4—31no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—91no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—181no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4C2×D3211yescharacteristic
574C4⋊C4C2×D3211yescharacteristic
575C22⋊C4—61no—
576C22⋊C4—61no—
577C22⋊C4—61no—
578C22⋊C4—91no—
579C22⋊C4—91no—
580C22⋊C4—181no—
581C22⋊C4—181no—
582C22⋊C4—181no—
583C42—31no—
584C42—61no—
585C42—61no—
586C42—91no—
587C42—181no—
588C42—181no—
589C42—181no—
590C42—181no—
591C22×C3—21no—
592C22×C3—61no—
593C22×C3—61no—
594C22×C3—61no—
595C22×C3—121no—
596C22×C3—121no—
597C22×C3—121no—
598C22×C3C2×D3×D411yescharacteristic
599C22×C3C2×D3×D411yescharacteristic
600C2×D3—21no—
601C2×D3—21no—
602C2×D3—21no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C3×C4—21no—
607C3×C4—21no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—62no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—61no—
616C3×C4—81no—
617C3×C4—81no—
618C3×C4—121no—
619C3×C4—121no—
620C3×C4C2×#23511yescharacteristic
621C3×C4D3×#4111yescharacteristic
622C3×C4D3×#4111yescharacteristic
623C3×C4D3×#4111yescharacteristic
624Dic3—21no—
625Dic3—21no—
626Dic3—21no—
627Dic3—22no—
628Dic3—41no—
629Dic3—41no—
630Dic3—62no—
631Dic3—62no—
632Dic3—61no—
633Dic3—61no—
634Dic3—61no—
635Dic3—61no—
636Dic3—62no—
637Dic3—122no—
638Dic3—121no—
639Dic3—121no—
640Dic3—121no—
641Dic3—241no—
642C32#312111yescharacteristic, complemented, Sylow
643C23—31no—
644C23—61no—
645Q8—32no—
646Q8—61no—
647Q8—61no—
648Q8—61no—
649Q8—92no—
650Q8—184no—
651Q8—181no—
652Q8—721no—
653D4—61no—
654D4—61no—
655D4—721no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—91no—
667C2×C4—91no—
668C2×C4—184no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4—241no—
672C2×C4C22×D3211yescharacteristic
673C8—21no—
674C8—61no—
675C8—61no—
676C8—181no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—121no—
681C2×C3—241no—
682C2×C3#554711yescharacteristic
683C2×C3#565611yescharacteristic
684C2×C3#577011yescharacteristic
685C2×C3#577511yescharacteristic
686C2×C3#577911yescharacteristic
687C2×C3#577911yescharacteristic
688D3—41no—
689D3—81no—
690C22—61no—
691C22—61no—
692C22—61no—
693C22—121no—
694C22—121no—
695C22—121no—
696C22D32×D411yescharacteristic
697C4—41no—
698C4—41no—
699C4—61no—
700C4—62no—
701C4—61no—
702C4—61no—
703C4—121no—
704C4—121no—
705C4—182no—
706C4—181no—
707C4—181no—
708C4—361no—
709C4D3×#23511yescharacteristic
710C4#6431911yescharacteristic
711C3—21no—
712C3#7981411yescharacteristic, complemented
713C3#8149711yescharacteristic, complemented
714C2—121no—
715C2—241no—
716C2#1059461411yescharacteristic
717C2#1059473611yescharacteristic
718C2#1059476911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#63908C22
hypercenter#107D32
hypocenterC32#3121
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
2. #10594357C2semidirect
3. #10592574C2semidirect
4. C3×#4889C2semidirect
5. C3×#4888C2semidirect
7. #10590796C2semidirect
8. #10590794C2semidirect
9. #10590697C2semidirect
10. #10590604C2semidirect
11. #10590538C2semidirect
13. #10590497C2semidirect
14. #10590479C2semidirect
15. #10590476C2semidirect
73. #4889D3semidirect
74. #4888D3semidirect
642. C32#3121semidirect
712. C3#79814semidirect
713. C3#81497semidirect

Maximal subgroups

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

subgroupindex
#105945922
#105943572
#105925742
C3×#48892
C3×#48882
#105908222
#105907962
#105907942
#105906972
#105906042
#105905382
#105905022
#105904972
#105904792
#105904762
#814973
#798143