Finite Group Databasebeta

← #11896092

Subgroups — #11896092

Order 1152.

730 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594350C211yesmaximal, characteristic
2#10594312C211yesmaximal, characteristic, complemented
3#10592569C211yesmaximal, characteristic
4C3×#4854C211yesmaximal, characteristic, complemented
5C3×#4853C211yesmaximal, characteristic, complemented
6#10590893C211yesmaximal, characteristic
7#10590801C211yesmaximal, characteristic
8#10590798C211yesmaximal, characteristic, complemented
9#10590789C211yesmaximal, characteristic, complemented
10#10590567C211yesmaximal, characteristic, complemented
11#10590556C211yesmaximal, characteristic, complemented
12#10590536C211yesmaximal, characteristic
13#10590535C211yesmaximal, characteristic
14#10590483C211yesmaximal, characteristic
15#10590477C211yesmaximal, characteristic, complemented
16#81004—31nomaximal
17#79815—31nomaximal
18#64102C2211yescharacteristic
19#64097C2211yescharacteristic
20C2×C3×Dic12C2211yescharacteristic
21C3×#888C2211yescharacteristic
22C3×#887C2211yescharacteristic
23C3×#887C2211yescharacteristic
24C3×#887C2211yescharacteristic
25#63918C2211yescharacteristic
26C4×#627C2211yescharacteristic
27#63874—21no—
28#63873C2211yescharacteristic
29#63868—21no—
30#63868—21no—
31#63866—21no—
32#63865—21no—
33#63864C2211yescharacteristic
34#63864C2211yescharacteristic
35#63843C2211yescharacteristic
36Dic3×Dic6C2211yescharacteristic
37#63840—21no—
38#63839—21no—
39#63837—21no—
40C2×#3718C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C32×#106C2211yescharacteristic
43#63648C2211yescharacteristic
44#63641C2211yescharacteristic
45#63636C2211yescharacteristic
46#63635C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×#815C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59#63554C2211yescharacteristic
60#63553C2211yescharacteristic
61#5722—31no—
62#5568—31no—
63#5568—31no—
64Q8×Dic6—31no—
65C3×#475—31no—
66C3×#441—31no—
67#5185—31no—
68#5182—31no—
69#5089—31no—
70#5030—31no—
71#5028—31no—
72#5020—31no—
73#4870—31no—
74#4870—31no—
75#4870—61no—
76#4854—31no—
77#4854D311yescharacteristic, complemented
78#4853D311yescharacteristic, complemented
79#4852—31no—
80#4845—31no—
81#4828—31no—
82#4798—31no—
83#4795—31no—
84#4794—31no—
85#4794—31no—
86#4792—31no—
87#4792—31no—
88#4789—31no—
89#4788—31no—
90#4714—31no—
91#4701—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×#634—21no—
95C2×C3×Dic6—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627D411yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C32×C4⋊C4C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104#3752—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107C4×C3⋊Dic3C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C3×C4⋊Dic3C2311yescharacteristic
110C3×Dic3⋊C4—21no—
111C3×Dic3⋊C4—21no—
112C3×Dic3⋊C4—21no—
113C3×Dic3⋊C4—21no—
114C3×C4×Dic3—21no—
115C3×C4×Dic3—21no—
116C3×C4×Dic3—21no—
117C3×C4×Dic3C2311yescharacteristic
118C3×C4×Dic3C2311yescharacteristic
119C2×C3×C3⋊C8C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C3×Dic12—22no—
122#3724—21no—
123#3724—21no—
124#3724D411yescharacteristic
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130#3722—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134Dic32—21no—
135Dic32—21no—
136#3718—22no—
137#3717—22no—
138#3369—91noSylow
139C2×C3×Q16—31no—
140C3×C4⋊Q8—31no—
141C3×C4×Q8—31no—
142C3×C4×Q8—31no—
143C3×C4×Q8—31no—
144#947—31no—
145#947—31no—
146Q8×Dic3—31no—
147Q8×Dic3—31no—
148#944—31no—
149#944—31no—
150#944—61no—
151#944—61no—
152C2×#216—31no—
153C2×#216—31no—
154C2×#215—31no—
155C2×Dic12C2×D311yescharacteristic
156C2×#204—31no—
157#898—61no—
158#898—61no—
159#896—61no—
160#896—61no—
161#893—31no—
162#893—31no—
163#893—61no—
164#888—31no—
165#888—31no—
166#888—31no—
167#888—61no—
168#888—61no—
169#888—61no—
170#888—61no—
171#888C2×D311yescharacteristic
172#887—31no—
173#887—61no—
174#887C2×D311yescharacteristic
175#887C2×D311yescharacteristic
176#887C2×D311yescharacteristic
177#876—61no—
178#876—61no—
179#875—31no—
180#875—31no—
181#872—61no—
182#872—61no—
183#869—31no—
184#869—61no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×#106—21no—
190C3×#106—31no—
191C3×#106C2×D311yescharacteristic
192C3×#106C2×D311yescharacteristic
193C3×C4⋊C8—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#97—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#821—31no—
203#821—31no—
204#821—31no—
205#821—61no—
206#816—31no—
207#816—31no—
208#816C2×D311yescharacteristic
209#815—31no—
210#815C2×D311yescharacteristic
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—61no—
215Dic3⋊C8C2×D311yescharacteristic
216C8×Dic3—31no—
217C8×Dic3—31no—
218#810—31no—
219#810C2×D311yescharacteristic
220#810C2×D311yescharacteristic
221#810C2×D311yescharacteristic
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#808—31no—
227#808—31no—
228#808—61no—
229#808C2×D311yescharacteristic
230C4⋊(C3⋊C8)—31no—
231#803—31no—
232C22×C3⋊D3—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4C2411yescharacteristic
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3C2×D411yescharacteristic
238C2×C3⋊Dic3C2×D411yescharacteristic
239C4⋊(C3⋊D3)—21no—
240C4⋊(C3⋊D3)—21no—
241C4×C3⋊D3—42no—
242#634—81no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×Dic6—21no—
252C3×Dic6—21no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—81no—
257C3×Dic6#4112yes—
258#627—22no—
259#627—81no—
260C32×C8—21no—
261C3⋊(C3⋊C8)—21no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264Q82—91no—
265#556—91no—
266#489—91no—
267#489—91no—
268#487—91no—
269#476—91no—
270#475—31no—
271#475—91no—
272#464—91no—
273#464—91no—
274#462—91no—
275#446—91no—
276#441—31no—
277#441—91no—
278C4×SD16—91no—
279C2×C3×Q8—31no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—61no—
283C2×D12—31no—
284C2×D12—31no—
285C2×D12—61no—
286C2×C4×D3—61no—
287C2×C4×D3—61no—
288C2×C4×D3—121no—
289C2×Dic6—21no—
290C2×Dic6—31no—
291C2×Dic6—31no—
292C2×Dic6—61no—
293C2×Dic6—61no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—121no—
297C2×Dic6C22×D311yescharacteristic
298C2×Dic6C22×D311yescharacteristic
299C2×Dic6C22×D311yescharacteristic
300C3×Q16—62no—
301C2×C3×C8—21no—
302C2×C3×C8—31no—
303C2×C3×C8—31no—
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—61no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4C22×D311yescharacteristic
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C4⋊C4C22×D311yescharacteristic
317C3×C42—31no—
318C3×C42—31no—
319C3×C42—61no—
320C3×C42—61no—
321C3×C42—61no—
322#216—62no—
323#216—62no—
324#215—62no—
325(C2×D3)⋊C4—61no—
326(C2×D3)⋊C4—61no—
327(C2×D3)⋊C4—61no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—121no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3C22×D311yescharacteristic
345Dic3⋊C4—21no—
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—21no—
349Dic3⋊C4—31no—
350Dic3⋊C4—31no—
351Dic3⋊C4—31no—
352Dic3⋊C4—31no—
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—121no—
363C4×Dic3—21no—
364C4×Dic3—21no—
365C4×Dic3—21no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3C22×D311yescharacteristic
374C4×Dic3C22×D311yescharacteristic
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—61no—
378C2×C3⋊C8C22×D311yescharacteristic
379C2×C3⋊C8C22×D311yescharacteristic
380Dic12—22no—
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—21no—
391C3⋊Dic3—41no—
392C3⋊Dic3#13712yes—
393C3×Dic3—22no—
394C3×Dic3—21no—
395C3×Dic3—21no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C2×Q16—31no—
402C2×Q16—91no—
403C2×SD16—91no—
404C4⋊Q8—31no—
405C4⋊Q8—91no—
406C4⋊Q8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409C4⋊Q8—181no—
410C4⋊Q8—181no—
411#126—181no—
412#126—181no—
413#124—91no—
414#124—91no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—31no—
419C4×Q8—91no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—181no—
423C4×D4—91no—
424#117—181no—
425#106—31no—
426#106—91no—
427#106D3211yescharacteristic
428C4⋊C8—31no—
429C4⋊C8—91no—
430C4⋊C8—91no—
431#103—31no—
432#103—31no—
433#103—31no—
434#103—31no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—91no—
439#102—91no—
440#102—91no—
441#97—31no—
442#97—91no—
443C4×C8—91no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—121no—
447C3×Q8—32no—
448C3×Q8—61no—
449C3×Q8—61no—
450C3×Q8—61no—
451C3×Q8—61no—
452C3×Q8—61no—
453C3×Q8—241no—
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×C4—61no—
469C2×C3×C4C23×D311yescharacteristic
470C2×C3×C4C23×D311yescharacteristic
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—31no—
476C2×Dic3—31no—
477C2×Dic3—31no—
478C2×Dic3—31no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—121no—
484C2×Dic3D3×D411yescharacteristic
485C2×Dic3D3×D411yescharacteristic
486C2×Dic3D3×D411yescharacteristic
487C2×Dic3D3×D411yescharacteristic
488D12—62no—
489D12—61no—
490D12—61no—
491D12—61no—
492D12—61no—
493D12—121no—
494C4×D3—122no—
495C4×D3—122no—
496C4×D3—242no—
497Dic6—21no—
498Dic6—21no—
499Dic6—21no—
500Dic6—21no—
501Dic6—21no—
502Dic6—62no—
503Dic6—62no—
504Dic6—81no—
505Dic6—241no—
506Dic6—241no—
507Dic6—241no—
508Dic6—241no—
509Dic6—242no—
510Dic6#23512yes—
511C3×C8—21no—
512C3×C8—21no—
513C3×C8—41no—
514C3×C8—61no—
515C3×C8—61no—
516C3⋊C8—21no—
517C3⋊C8—21no—
518C3⋊C8—61no—
519C3⋊C8—61no—
520C3⋊C8—121no—
521C2×C32#54811yescharacteristic
522C2×C32C2×#13711yescharacteristic
523C2×C32#57711yescharacteristic
524C3⋊D3—81no—
525C2×Q8—31no—
526C2×Q8—31no—
527C2×Q8—31no—
528C2×Q8—61no—
529C2×Q8—91no—
530C2×Q8—181no—
531C2×Q8—181no—
532C2×D4—91no—
533C22×C4—181no—
534Q16—62no—
535Q16—182no—
536SD16—182no—
537C2×C8—31no—
538C2×C8—31no—
539C2×C8—91no—
540C2×C8C2×D3211yescharacteristic
541C4⋊C4—31no—
542C4⋊C4—61no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—91no—
547C4⋊C4—91no—
548C4⋊C4—91no—
549C4⋊C4—91no—
550C4⋊C4—181no—
551C4⋊C4—181no—
552C4⋊C4—181no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4C2×D3211yescharacteristic
557C4⋊C4C2×D3211yescharacteristic
558C22⋊C4—181no—
559C22⋊C4—181no—
560C22⋊C4—181no—
561C22⋊C4—181no—
562C22⋊C4—181no—
563C42—31no—
564C42—31no—
565C42—61no—
566C42—61no—
567C42—61no—
568C42—91no—
569C42—181no—
570C42—181no—
571C22×C3—21no—
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C2×D3×D411yescharacteristic
574C2×D3—122no—
575C2×D3—121no—
576C2×D3—121no—
577C2×D3—121no—
578C2×D3—121no—
579C2×D3—121no—
580C2×D3—121no—
581C2×D3—241no—
582C2×D3—241no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—41no—
586C3×C4—41no—
587C3×C4—41no—
588C3×C4—41no—
589C3×C4—62no—
590C3×C4—61no—
591C3×C4—61no—
592C3×C4—61no—
593C3×C4—61no—
594C3×C4—81no—
595C3×C4—81no—
596C3×C4—121no—
597C3×C4—121no—
598C3×C4—121no—
599C3×C4C2×#23511yescharacteristic
600C3×C4#100711yescharacteristic
601C3×C4D3×#4111yescharacteristic
602C3×C4#101011yescharacteristic
603Dic3—21no—
604Dic3—21no—
605Dic3—21no—
606Dic3—21no—
607Dic3—22no—
608Dic3—32no—
609Dic3—32no—
610Dic3—41no—
611Dic3—41no—
612Dic3—41no—
613Dic3—62no—
614Dic3—61no—
615Dic3—61no—
616Dic3—121no—
617Dic3—121no—
618Dic3—121no—
619Dic3—241no—
620C32#336911yescharacteristic, complemented, Sylow
621C23—181no—
622Q8—32no—
623Q8—61no—
624Q8—61no—
625Q8—61no—
626Q8—61no—
627Q8—61no—
628Q8—182no—
629Q8—241no—
630Q8—721no—
631Q8—721no—
632D4—181no—
633D4—181no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—31no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—31no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—91no—
645C2×C4—91no—
646C2×C4—181no—
647C2×C4—362no—
648C2×C4C22×D3211yescharacteristic
649C8—21no—
650C8—61no—
651C8—61no—
652C8—181no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3#555211yescharacteristic
657C2×C3#563311yescharacteristic
658C2×C3#576211yescharacteristic
659C2×C3D3×#13711yescharacteristic
660C2×C3D3×#13711yescharacteristic
661C2×C3#577811yescharacteristic
662D3—242no—
663D3—241no—
664D3—241no—
665C22—361no—
666C22—361no—
667C22—361no—
668C22D32×D411yescharacteristic
669C4—41no—
670C4—41no—
671C4—62no—
672C4—61no—
673C4—61no—
674C4—61no—
675C4—61no—
676C4—92no—
677C4—121no—
678C4—121no—
679C4—121no—
680C4—181no—
681C4—361no—
682C4D3×#23511yescharacteristic
683C4#6431511yescharacteristic
684C3—21no—
685C3#7981511yescharacteristic, complemented
686C3#8100411yescharacteristic, complemented
687C2—721no—
688C2#1059437511yescharacteristic
689C2#1059474211yescharacteristic
690C2#1059475111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenter#106D32
hypocenterC32#3369
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594312C2semidirect
4. C3×#4854C2semidirect
5. C3×#4853C2semidirect
8. #10590798C2semidirect
9. #10590789C2semidirect
10. #10590567C2semidirect
11. #10590556C2semidirect
15. #10590477C2semidirect
77. #4854D3semidirect
78. #4853D3semidirect
620. C32#3369semidirect
685. C3#79815semidirect
686. C3#81004semidirect

Maximal subgroups

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

subgroupindex
#105943502
#105943122
#105925692
C3×#48542
C3×#48532
#105908932
#105908012
#105907982
#105907892
#105905672
#105905562
#105905362
#105905352
#105904832
#105904772
#810043
#798153