Finite Group Databasebeta

← #11895598

Subgroups — #11895598

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 685 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595389C211yesmaximal, characteristic
2#10594324C211yesmaximal, characteristic, complemented
3#10592494C211yesmaximal, characteristic, complemented
4C3×#4800C211yesmaximal, characteristic
5C3×#4796C211yesmaximal, characteristic, complemented
6#10591577C211yesmaximal, characteristic
7#10591538C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10590861C211yesmaximal, characteristic
10#10590807C211yesmaximal, characteristic, complemented
11#10590778C211yesmaximal, characteristic
12#10590644C211yesmaximal, characteristic, complemented
13#10590533C211yesmaximal, characteristic
14#10590490C211yesmaximal, characteristic, complemented
15#10590460C211yesmaximal, characteristic
16#81634—31nomaximal
17#81216—31nomaximal
18#64153C2211yescharacteristic
19C2×#3756C2211yescharacteristic
20C2×#3746C2211yescharacteristic
21#64096C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#890C2211yescharacteristic
25C3×#890C2211yescharacteristic
26#63919—21no—
27#63919C2211yescharacteristic
28C4×#627C2211yescharacteristic
29#63899—21no—
30#63898C2211yescharacteristic
31#63877—21no—
32#63860C2211yescharacteristic
33#63859—21no—
34#63858—21no—
35#63847—21no—
36#63847—21no—
37#63844C2211yescharacteristic
38#63844C2211yescharacteristic
39#63844C2211yescharacteristic
40#63838—21no—
41C2×#3716C2211yescharacteristic
42C32×#103C2211yescharacteristic
43#63641C2211yescharacteristic
44#63637C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53#63576C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63562C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5685—31no—
62#5685—31no—
63#5671—31no—
64#5568—31no—
65C3×#488—31no—
66C3×#479—31no—
67#5068—31no—
68#5063—31no—
69#5054—31no—
70C4×#216—31no—
71#4890—31no—
72#4873—31no—
73#4857—31no—
74#4852—31no—
75#4845—31no—
76#4830—31no—
77#4800D311yescharacteristic
78#4798—31no—
79#4796D311yescharacteristic, complemented
80#4795—31no—
81#4795—31no—
82#4795—61no—
83#4792—31no—
84#4792—31no—
85#4790—31no—
86#4768—31no—
87#4767—31no—
88#4759—31no—
89#4758—31no—
90C4×Dic12—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×#627—21no—
97C2×#627D411yescharacteristic
98C2×D3×Dic3—21no—
99C2×C32×C8C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101#3756—22no—
102#3750—21no—
103#3750—21no—
104#3750—21no—
105C4×C3⋊Dic3—21no—
106C4×C3⋊Dic3C2311yescharacteristic
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108#3746—22no—
109C3×(C2×D3)⋊C4—21no—
110C3×(C2×D3)⋊C4—21no—
111C3×C4⋊Dic3—21no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3—21no—
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124#3724—21no—
125#3724—21no—
126#3724—21no—
127#3724—21no—
128#3724D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130Dic3⋊Dic3D411yescharacteristic
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137#3716—22no—
138#3364—91noSylow
139C3×#125—31no—
140C3×#125—31no—
141C3×#124—31no—
142C3×C4×Q8—31no—
143#947C2×D311yescharacteristic
144Q8×Dic3C2×D311yescharacteristic
145#944—31no—
146#944—31no—
147#944—61no—
148C2×#216—31no—
149C2×#216—31no—
150C2×#216—61no—
151#936—31no—
152D4×Dic3—31no—
153C2×#214—31no—
154C2×Dic12—31no—
155C2×Dic12—31no—
156C2×Dic12—61no—
157C2×#204—31no—
158#898—61no—
159#896—61no—
160#893—31no—
161#890C2×D311yescharacteristic
162#890C2×D311yescharacteristic
163#889—61no—
164#889—61no—
165#889—61no—
166#889—61no—
167#888—31no—
168#888—31no—
169#888—61no—
170#888—61no—
171#887—31no—
172#887—31no—
173#887—31no—
174#887—31no—
175#887—31no—
176#887—61no—
177#887—61no—
178#887—61no—
179#879—61no—
180#879—61no—
181#878—61no—
182#877—61no—
183#876—61no—
184#875—31no—
185#872—61no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C3×#107—31no—
192C3×#106—31no—
193C3×C4⋊C8—31no—
194C3×#103—21no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#103C2×D311yescharacteristic
198C3×#103C2×D311yescharacteristic
199C3×#102—31no—
200C3×#102—31no—
201C3×C4×C8—31no—
202#835C2×D311yescharacteristic
203#835C2×D311yescharacteristic
204#832—31no—
205#821C2×D311yescharacteristic
206#818C2×D311yescharacteristic
207#816—31no—
208#816—31no—
209#816—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—61no—
214Dic3⋊C8C2×D311yescharacteristic
215C8×Dic3—31no—
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3C2×D311yescharacteristic
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#809—31no—
226#809C2×D311yescharacteristic
227#808C2×D311yescharacteristic
228#807—31no—
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C22×C3×D3—21no—
233C32×Q8—21no—
234C32×Q8—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242#634—21no—
243#634—21no—
244#634—21no—
245#634#4112yes—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×D12—21no—
254C3×D12—21no—
255#627—22no—
256#627—42no—
257D3×Dic3—42no—
258C32×C8—21no—
259C3⋊(C3⋊C8)—21no—
260C3×C3⋊C8—21no—
261C3×C3⋊C8—21no—
262#557—91no—
263#556—91no—
264#488—31no—
265#488—91no—
266#487—91no—
267#479—31no—
268#479—91no—
269#474—91no—
270#464—91no—
271#464—91no—
272#462—91no—
273C8×Q8—91no—
274C4×Q16—91no—
275C4×Q16—91no—
276C4×SD16—91no—
277C2×C3×Q8—21no—
278C2×C3×Q8C22×D311yescharacteristic
279C2×C3×Q8C22×D311yescharacteristic
280C2×C3×D4—31no—
281C22×Dic3—61no—
282C2×D12C22×D311yescharacteristic
283C2×C4×D3—61no—
284C2×Dic6—31no—
285C2×Dic6—31no—
286C2×Dic6—31no—
287C2×Dic6—31no—
288C2×Dic6—31no—
289C2×Dic6—31no—
290C2×Dic6—61no—
291C2×Dic6—61no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×C3×C8—21no—
295C2×C3×C8—31no—
296C2×C3×C8—31no—
297C2×C3×C8C22×D311yescharacteristic
298C2×C3×C8C22×D311yescharacteristic
299C3×C4⋊C4—21no—
300C3×C4⋊C4—31no—
301C3×C4⋊C4—31no—
302C3×C4⋊C4—31no—
303C3×C4⋊C4—61no—
304C3×C4⋊C4—61no—
305C3×C4⋊C4—61no—
306C3×C4⋊C4—61no—
307C3×C4⋊C4—61no—
308C3×C4⋊C4C22×D311yescharacteristic
309C3×C4⋊C4C22×D311yescharacteristic
310C3×C22⋊C4—61no—
311C3×C22⋊C4—61no—
312C3×C42—31no—
313C3×C42—31no—
314C3×C42—61no—
315#217—61no—
316#217—61no—
317#217—61no—
318#216—62no—
319#216—62no—
320#216—122no—
321#214—62no—
322(C2×D3)⋊C4—21no—
323(C2×D3)⋊C4—21no—
324(C2×D3)⋊C4—61no—
325(C2×D3)⋊C4—61no—
326(C2×D3)⋊C4—61no—
327C4⋊Dic3—21no—
328C4⋊Dic3—21no—
329C4⋊Dic3—21no—
330C4⋊Dic3—31no—
331C4⋊Dic3—31no—
332C4⋊Dic3C22×D311yescharacteristic
333C4⋊Dic3C22×D311yescharacteristic
334C4⋊Dic3C22×D311yescharacteristic
335Dic3⋊C4—21no—
336Dic3⋊C4—21no—
337Dic3⋊C4—31no—
338Dic3⋊C4—31no—
339Dic3⋊C4—31no—
340Dic3⋊C4—31no—
341Dic3⋊C4—61no—
342Dic3⋊C4—61no—
343Dic3⋊C4—61no—
344Dic3⋊C4—61no—
345Dic3⋊C4—61no—
346Dic3⋊C4—61no—
347Dic3⋊C4—61no—
348Dic3⋊C4—61no—
349Dic3⋊C4—61no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—121no—
356Dic3⋊C4—121no—
357Dic3⋊C4—121no—
358C4×Dic3—21no—
359C4×Dic3—31no—
360C4×Dic3—31no—
361C4×Dic3—61no—
362C4×Dic3—61no—
363C4×Dic3—61no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—121no—
371C4×Dic3C22×D311yescharacteristic
372C4×Dic3C22×D311yescharacteristic
373C2×C3⋊C8—31no—
374C2×C3⋊C8—31no—
375C2×C3⋊C8—61no—
376C2×C3⋊C8C22×D311yescharacteristic
377C2×C3⋊C8C22×D311yescharacteristic
378Dic12—62no—
379Dic12—62no—
380Dic12—122no—
381#204—62no—
382C22×C32C22×D411yescharacteristic
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C32×C4—41no—
387C32×C4—41no—
388C32×C4C2×#4111yescharacteristic
389C32×C42−1+411yescharacteristic
390C3⋊Dic3—22no—
391C3⋊Dic3—21no—
392C3⋊Dic3—41no—
393C3⋊Dic3#13512yes—
394C3×Dic3—21no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C2×Q16—91no—
402C2×Q16—91no—
403C2×SD16—91no—
404C4⋊Q8—91no—
405C4⋊Q8—91no—
406C4⋊Q8—181no—
407#126—181no—
408#126—181no—
409#125—31no—
410#125—31no—
411#125—181no—
412#125—181no—
413#124—31no—
414#124—91no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—91no—
418C4×Q8—91no—
419C4×Q8—91no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—181no—
423C4×D4—91no—
424#117—181no—
425#107—31no—
426#107—91no—
427#106—31no—
428C4⋊C8—31no—
429C4⋊C8—91no—
430C4⋊C8—91no—
431#103—31no—
432#103—31no—
433#103—91no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103D3211yescharacteristic
438#102—31no—
439#102—31no—
440#102—91no—
441C4×C8—31no—
442C4×C8—91no—
443C4×C8—91no—
444C23×C3—61no—
445C22×D3—21no—
446C3×Q8—21no—
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—21no—
450C3×Q8—41no—
451C3×Q8—41no—
452C3×D4—61no—
453C3×D4—61no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—31no—
460C2×C3×C4—31no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4C23×D311yescharacteristic
469C2×C3×C4C23×D311yescharacteristic
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—31no—
474C2×Dic3—31no—
475C2×Dic3—31no—
476C2×Dic3—31no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—121no—
484C2×Dic3—121no—
485C2×Dic3—122no—
486C2×Dic3D3×D411yescharacteristic
487C2×Dic3D3×D411yescharacteristic
488C2×Dic3D3×D411yescharacteristic
489C2×Dic3D3×D411yescharacteristic
490D12—21no—
491D12—21no—
492C4×D3—122no—
493Dic6—32no—
494Dic6—32no—
495Dic6—62no—
496Dic6—62no—
497Dic6—62no—
498Dic6—61no—
499Dic6—61no—
500Dic6—61no—
501Dic6—61no—
502Dic6—61no—
503Dic6—61no—
504Dic6—121no—
505Dic6—121no—
506Dic6—121no—
507Dic6—122no—
508Dic6—122no—
509C3×C8—21no—
510C3×C8—21no—
511C3×C8—41no—
512C3×C8—61no—
513C3×C8—61no—
514C3⋊C8—21no—
515C3⋊C8—21no—
516C3⋊C8—61no—
517C3⋊C8—61no—
518C3⋊C8—121no—
519C2×C32#54811yescharacteristic
520C2×C32C2×#13511yescharacteristic
521C2×C32#57811yescharacteristic
522C3×D3—81no—
523C2×Q8—91no—
524C2×Q8—91no—
525C2×Q8—91no—
526C2×Q8—181no—
527C2×Q8C2×D3211yescharacteristic
528C2×D4—31no—
529C22×C4—181no—
530Q16—182no—
531Q16—182no—
532SD16—182no—
533C2×C8—31no—
534C2×C8—31no—
535C2×C8—91no—
536C2×C8C2×D3211yescharacteristic
537C4⋊C4—31no—
538C4⋊C4—31no—
539C4⋊C4—31no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—91no—
546C4⋊C4—91no—
547C4⋊C4—91no—
548C4⋊C4—181no—
549C4⋊C4—181no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4—181no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4C2×D3211yescharacteristic
556C22⋊C4—61no—
557C22⋊C4—61no—
558C22⋊C4—181no—
559C22⋊C4—181no—
560C22⋊C4—181no—
561C42—31no—
562C42—31no—
563C42—61no—
564C42—91no—
565C42—181no—
566C42—181no—
567C42—181no—
568C42—181no—
569C22×C3—21no—
570C22×C3—121no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3C2×D3×D411yescharacteristic
574C22×C3C2×D3×D411yescharacteristic
575C2×D3—41no—
576C2×D3—41no—
577C2×D3—41no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—61no—
585C3×C4—61no—
586C3×C4—61no—
587C3×C4—61no—
588C3×C4—81no—
589C3×C4—81no—
590C3×C4—121no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4#100711yescharacteristic
594C3×C4D3×#4111yescharacteristic
595C3×C4D3×#4111yescharacteristic
596C3×C4#101011yescharacteristic
597Dic3—21no—
598Dic3—21no—
599Dic3—21no—
600Dic3—21no—
601Dic3—32no—
602Dic3—32no—
603Dic3—41no—
604Dic3—41no—
605Dic3—41no—
606Dic3—62no—
607Dic3—62no—
608Dic3—62no—
609Dic3—61no—
610Dic3—61no—
611Dic3—122no—
612Dic3—121no—
613Dic3—121no—
614Dic3—121no—
615Dic3—241no—
616C32#336411yescharacteristic, complemented, Sylow
617C23—61no—
618Q8—21no—
619Q8—21no—
620Q8—92no—
621Q8—182no—
622Q8—181no—
623Q8—181no—
624Q8—181no—
625Q8—362no—
626D4—61no—
627D4—61no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—31no—
631C2×C4—31no—
632C2×C4—31no—
633C2×C4—31no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—91no—
638C2×C4—91no—
639C2×C4—181no—
640C2×C4—181no—
641C2×C4—362no—
642C2×C4C22×D3211yescharacteristic
643C8—21no—
644C8—61no—
645C8—61no—
646C8—181no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—241no—
651C2×C3#563311yescharacteristic
652C2×C3#567711yescharacteristic
653C2×C3D3×#13511yescharacteristic
654C2×C3D3×#13511yescharacteristic
655C2×C3#577111yescharacteristic
656C2×C3#577911yescharacteristic
657D3—81no—
658C22—121no—
659C22—121no—
660C22—121no—
661C22D32×D411yescharacteristic
662C4—41no—
663C4—41no—
664C4—61no—
665C4—61no—
666C4—61no—
667C4—61no—
668C4—92no—
669C4—121no—
670C4—121no—
671C4—121no—
672C4—182no—
673C4—181no—
674C4—361no—
675C4#6429711yescharacteristic
676C4#6431211yescharacteristic
677C3—21no—
678C3#8121611yescharacteristic, complemented
679C3#8163411yescharacteristic, complemented
680C2—241no—
681C2#1059407511yescharacteristic
682C2#1059475611yescharacteristic
683C2#1059476411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenter#103D32
hypocenterC32#3364
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
2. #10594324C2semidirect
3. #10592494C2semidirect
5. C3×#4796C2semidirect
7. #10591538C2semidirect
8. #10591537C2semidirect
10. #10590807C2semidirect
12. #10590644C2semidirect
14. #10590490C2semidirect
79. #4796D3semidirect
616. C32#3364semidirect
678. C3#81216semidirect
679. C3#81634semidirect

Maximal subgroups

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

subgroupindex
#105953892
#105943242
#105924942
C3×#48002
C3×#47962
#105915772
#105915382
#105915372
#105908612
#105908072
#105907782
#105906442
#105905332
#105904902
#105904602
#816343
#812163