Finite Group Databasebeta

← #11869059

Subgroups — #11869059

Order 1152.

772 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595347C211yesmaximal, characteristic
2#10594344C211yesmaximal, characteristic
3#10592490C211yesmaximal, characteristic, complemented
4C3×D3×#103C211yesmaximal, characteristic
5C3×#4799C211yesmaximal, characteristic, complemented
6#10591615C211yesmaximal, characteristic, complemented
7#10591557C211yesmaximal, characteristic
8#10591546C211yesmaximal, characteristic, complemented
9#10590820C211yesmaximal, characteristic, complemented
10#10590803C211yesmaximal, characteristic, complemented
11#10590706C211yesmaximal, characteristic
12#10590694C211yesmaximal, characteristic
13#10590580C211yesmaximal, characteristic
14#10590496C211yesmaximal, characteristic, complemented
15#10590491C211yesmaximal, characteristic, complemented
16#81233—31nomaximal
17#78779—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20#64097C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23C3×D3×C4⋊C4C2211yescharacteristic
24C3×#890C2211yescharacteristic
25#63918C2211yescharacteristic
26#63872C2211yescharacteristic
27#63857—21no—
28#63855—21no—
29#63855C2211yescharacteristic
30#63851—21no—
31#63846—21no—
32#63843—21no—
33#63843C2211yescharacteristic
34Dic3×Dic6—21no—
35Dic3×Dic6C2211yescharacteristic
36#63841—21no—
37#63841C2211yescharacteristic
38#63841C2211yescharacteristic
39#63840—21no—
40C2×#3711C2211yescharacteristic
41C32×#103C2211yescharacteristic
42#63662C2211yescharacteristic
43#63644C2211yescharacteristic
44#63641C2211yescharacteristic
45#63635C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63575C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63572C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63566C2211yescharacteristic
60#63565C2211yescharacteristic
61#5812—31no—
62#5689—31no—
63#5572—31no—
64#5500—31no—
65C3×#479—31no—
66C2×C3×#103—31no—
67#5225—31no—
68#5106—31no—
69#5102—31no—
70#5063—31no—
71#5021—31no—
72#4964—31no—
73#4881—31no—
74#4875—31no—
75#4860—31no—
76#4857—31no—
77#4851—31no—
78#4839—31no—
79#4802—31no—
80D3×#103D311yescharacteristic
81#4799—31no—
82#4799—31no—
83#4799D311yescharacteristic, complemented
84#4796—31no—
85#4796—31no—
86#4793—31no—
87#4793—31no—
88#4791—31no—
89#4791—31no—
90#4791—31no—
91#4791—61no—
92C2×C32×Q8C2311yescharacteristic
93C2×#634—21no—
94C3×D3×Q8—22no—
95C3×D3×Q8Q814yescomplemented
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6—21no—
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C4⋊(C3⋊Dic3)—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×C4⋊Dic3—21no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C3×D3×C8—22no—
123Dic3⋊Dic3—21no—
124Dic3⋊Dic3—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3D411yescharacteristic
133(C2×D3)⋊Dic3D411yescharacteristic
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138#3711—22no—
139#3082—91noSylow
140C22×C3×Q8—31no—
141C2×D3×Q8C2×D311yescharacteristic
142C22×C3×C8—31no—
143C3×#125—31no—
144C3×C4×Q8—31no—
145C2×C3×C4⋊C4—31no—
146Q8×Dic3—31no—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149Q8×Dic3—31no—
150Q8×Dic3—61no—
151Q8×Dic3—61no—
152Q8×Dic3—61no—
153Q8×Dic3C2×D311yescharacteristic
154#926—31no—
155#926—31no—
156#926—31no—
157#926—61no—
158#926—61no—
159#924—61no—
160#924—61no—
161C2×#208—31no—
162C2×ΓL(1,𝔽25)—31no—
163C2×D3×C8C2×D311yescharacteristic
164#897—61no—
165#896—61no—
166#892—31no—
167#892—31no—
168#892—61no—
169D3×C4⋊C4C2×D311yescharacteristic
170#890—31no—
171#890—31no—
172#890—61no—
173#890C2×D311yescharacteristic
174#889—61no—
175#888—31no—
176#888—31no—
177#888—31no—
178#888—61no—
179#888—61no—
180#888—61no—
181#887—31no—
182#887—61no—
183#872—31no—
184#872—61no—
185#869—31no—
186C4×Dic6—31no—
187C4×Dic6—61no—
188C3×#107—31no—
189C3×#106—31no—
190C3×C4⋊C8—31no—
191C3×#103—21no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#103C2×D311yescharacteristic
197C3×#103C2×D311yescharacteristic
198#835—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—61no—
203#835C2×D311yescharacteristic
204#835C2×D311yescharacteristic
205#818—31no—
206#818—31no—
207#817—31no—
208#817—31no—
209#817—31no—
210#817—61no—
211#817C2×D311yescharacteristic
212#816—31no—
213#816C2×D311yescharacteristic
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—61no—
220Dic3⋊C8C2×D311yescharacteristic
221#810—31no—
222#810C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231#807C2×D311yescharacteristic
232C4⋊(C3⋊C8)—31no—
233C22×C3×D3C2×D411yescharacteristic
234C32×Q8—21no—
235C32×Q8C2×Q812yes—
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—81no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×C4×D3—24no—
252C3×C4×D3—81no—
253C3×C4×D3C2×Q812yes—
254C3×C4×D3#4112yes—
255C3×Dic6—21no—
256C3×Dic6—24no—
257C3×Dic6C2×Q812yes—
258#627—81no—
259C32×C8—21no—
260C3⋊(C3⋊C8)—21no—
261C3×C3⋊C8—21no—
262C3×C3⋊C8—21no—
263#544—91no—
264#519—91no—
265#479—31no—
266#479—91no—
267#479—91no—
268#479—91no—
269#477—91no—
270#477—91no—
271#475—91no—
272#475—91no—
273#428—91no—
274#427—91no—
275#424—91no—
276#419—91no—
277C2×#103—31no—
278C2×C3×Q8—21no—
279C2×C3×Q8—34no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×Q8—62no—
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×Q8C22×D311yescharacteristic
285C22×C3×C4—31no—
286C22×C3×C4—61no—
287C22×C3×C4—61no—
288D3×Q8—22no—
289D3×Q8Dic614yescomplemented
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×C4×D3C22×D311yescharacteristic
293C2×Dic6—21no—
294C2×Dic6—61no—
295C2×Dic6—61no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—121no—
299C2×Dic6C22×D311yescharacteristic
300C2×C3×C8—21no—
301C2×C3×C8—31no—
302C2×C3×C8—31no—
303C2×C3×C8—62no—
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C3×C4⋊C4—21no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C42—31no—
317C3×C42—61no—
318#217—31no—
319#217—31no—
320#217—61no—
321#217—61no—
322(C2×D3)⋊C4—31no—
323(C2×D3)⋊C4—31no—
324(C2×D3)⋊C4—61no—
325(C2×D3)⋊C4—61no—
326C4⋊Dic3—21no—
327C4⋊Dic3—21no—
328C4⋊Dic3—31no—
329C4⋊Dic3—31no—
330C4⋊Dic3—31no—
331C4⋊Dic3—31no—
332C4⋊Dic3—31no—
333C4⋊Dic3—31no—
334C4⋊Dic3—61no—
335C4⋊Dic3—61no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—121no—
344C4⋊Dic3C22×D311yescharacteristic
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347Dic3⋊C4—21no—
348Dic3⋊C4—21no—
349Dic3⋊C4—31no—
350Dic3⋊C4—31no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—121no—
359C4×Dic3—21no—
360C4×Dic3—31no—
361C4×Dic3—31no—
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—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—121no—
374C4×Dic3C22×D311yescharacteristic
375#208—62no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381ΓL(1,𝔽25)—62no—
382D3×C8—22no—
383C22×C32C22×D411yescharacteristic
384C2×C3×D3—21no—
385C2×C3×D3—21no—
386C2×C3×D3C22⋊Q812yes—
387C32×C4—22no—
388C32×C4—41no—
389C32×C4C22×Q811yescharacteristic
390C32×C4C2×#4111yescharacteristic
391C3⋊Dic3—21no—
392C3⋊Dic3—21no—
393C3⋊Dic3—41no—
394C3⋊Dic3—41no—
395C3×Dic3—22no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3C22⋊Q812yes—
402C22×Q8—31no—
403C2×M16—91no—
404C22×C8—31no—
405C4⋊Q8—91no—
406C4⋊Q8—91no—
407C4⋊Q8—181no—
408#125—31no—
409#125—91no—
410#125—181no—
411C22⋊Q8—181no—
412C22⋊Q8—181no—
413C4×Q8—31no—
414C4×Q8—91no—
415C4×Q8—91no—
416C4×Q8—91no—
417C4×Q8—181no—
418C4×Q8—181no—
419#117—91no—
420#117—91no—
421#117—91no—
422#117—181no—
423#117—181no—
424C2×C4⋊C4—31no—
425#107—31no—
426#107—91no—
427#107—91no—
428#107—91no—
429#106—31no—
430#106—91no—
431#106—91no—
432#106—91no—
433C4⋊C8—31no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436C4⋊C8—91no—
437#103—31no—
438#103—31no—
439#103—31no—
440#103—31no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103D3211yescharacteristic
445C23×C3—31no—
446C22×D3D3×D411yescharacteristic
447C3×Q8—21no—
448C3×Q8—21no—
449C3×Q8—22no—
450C3×Q8—32no—
451C3×Q8—41no—
452C3×Q8—64no—
453C3×Q8—61no—
454C3×Q8C2×Dic612yes—
455C3×Q8D3×Q812yes—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—31no—
462C2×C3×C4—32no—
463C2×C3×C4—32no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—64no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—241no—
474C2×C3×C4C23×D311yescharacteristic
475C2×C3×C4C23×D311yescharacteristic
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—31no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—121no—
491C2×Dic3—121no—
492C2×Dic3D3×D411yescharacteristic
493C2×Dic3D3×D411yescharacteristic
494C2×Dic3D3×D411yescharacteristic
495C4×D3—24no—
496C4×D3—81no—
497C4×D3C2×Dic612yes—
498C4×D3#23712yes—
499Dic6—21no—
500Dic6—24no—
501Dic6—241no—
502Dic6—241no—
503Dic6—241no—
504Dic6—241no—
505Dic6—242no—
506Dic6C2×Dic612yes—
507C3×C8—21no—
508C3×C8—21no—
509C3×C8—41no—
510C3×C8—61no—
511C3×C8—61no—
512C3⋊C8—21no—
513C3⋊C8—21no—
514C3⋊C8—61no—
515C3⋊C8—61no—
516C3⋊C8—121no—
517C2×C32C2×C22⋊Q811yescharacteristic
518C2×C32#57711yescharacteristic
519C2×C32#57811yescharacteristic
520C3×D3—22no—
521C2×Q8—34no—
522C2×Q8—31no—
523C2×Q8—61no—
524C2×Q8—62no—
525C2×Q8—181no—
526C2×Q8—181no—
527C2×Q8C2×D3211yescharacteristic
528C22×C4—31no—
529C22×C4—61no—
530C22×C4—61no—
531M16—182no—
532C2×C8—31no—
533C2×C8—31no—
534C2×C8—62no—
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—91no—
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—91no—
557C22⋊C4—91no—
558C22⋊C4—181no—
559C22⋊C4—181no—
560C42—31no—
561C42—61no—
562C42—91no—
563C42—181no—
564C42—181no—
565C42—181no—
566C42—181no—
567C42—181no—
568C22×C3—21no—
569C22×C3—32no—
570C22×C3—61no—
571C22×C3—61no—
572C22×C3C2×D3×D411yescharacteristic
573C22×C3C2×D3×D411yescharacteristic
574C2×D3—21no—
575C2×D3—21no—
576C2×D3#87812yes—
577C3×C4—22no—
578C3×C4—22no—
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—32no—
582C3×C4—42no—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—61no—
586C3×C4—61no—
587C3×C4—62no—
588C3×C4—81no—
589C3×C4—121no—
590C3×C4—121no—
591C3×C4—121no—
592C3×C4C22×Dic611yescharacteristic
593C3×C4C2×#23711yescharacteristic
594C3×C4C2×D3×Q811yescharacteristic
595C3×C4D3×#4111yescharacteristic
596Dic3—22no—
597Dic3—21no—
598Dic3—21no—
599Dic3—41no—
600Dic3—41no—
601Dic3—41no—
602Dic3—62no—
603Dic3—61no—
604Dic3—61no—
605Dic3—61no—
606Dic3—61no—
607Dic3—121no—
608Dic3—121no—
609Dic3—121no—
610Dic3—121no—
611Dic3—121no—
612Dic3—241no—
613Dic3—241no—
614Dic3#87812yes—
615C32#308211yescharacteristic, complemented, Sylow
616C23—31no—
617Q8—21no—
618Q8—32no—
619Q8—64no—
620Q8—61no—
621Q8—721no—
622Q8—721no—
623Q8D3×Dic612yes—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—31no—
627C2×C4—32no—
628C2×C4—32no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—64no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—91no—
637C2×C4—91no—
638C2×C4—181no—
639C2×C4—181no—
640C2×C4—241no—
641C2×C4C22×D3211yescharacteristic
642C8—21no—
643C8—61no—
644C8—61no—
645C8—181no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—62no—
650C2×C3C2×#87811yescharacteristic
651C2×C3D3×C22⋊Q811yescharacteristic
652C2×C3#576211yescharacteristic
653C2×C3#576611yescharacteristic
654C2×C3#577011yescharacteristic
655C2×C3#577911yescharacteristic
656D3—22no—
657C22—32no—
658C22—61no—
659C22—61no—
660C22D32×D411yescharacteristic
661C4—22no—
662C4—32no—
663C4—41no—
664C4—62no—
665C4—61no—
666C4—61no—
667C4—121no—
668C4—121no—
669C4—121no—
670C4—181no—
671C4—181no—
672C4—361no—
673C4—361no—
674C4C2×D3×Dic611yescharacteristic
675C4D3×#23711yescharacteristic
676C3—21no—
677C3#7877911yescharacteristic, complemented
678C3#8123311yescharacteristic, complemented
679C2—62no—
680C2D3×#87811yescharacteristic
681C2#1059475311yescharacteristic
682C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#103D32
hypocenterC32#3082
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
3. #10592490C2semidirect
5. C3×#4799C2semidirect
6. #10591615C2semidirect
8. #10591546C2semidirect
9. #10590820C2semidirect
10. #10590803C2semidirect
14. #10590496C2semidirect
15. #10590491C2semidirect
83. #4799D3semidirect
95. C3×D3×Q8Q8semidirect
289. D3×Q8Dic6semidirect
615. C32#3082semidirect
677. C3#78779semidirect
678. C3#81233semidirect

Maximal subgroups

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

subgroupindex
#105953472
#105943442
#105924902
C3×D3×#1032
C3×#47992
#105916152
#105915572
#105915462
#105908202
#105908032
#105907062
#105906942
#105905802
#105904962
#105904912
#812333
#787793