Finite Group Databasebeta

← #11869060

Subgroups — #11869060

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595339C211yesmaximal, characteristic
2#10594325C211yesmaximal, characteristic
3C3⋊D3×#103C211yesmaximal, characteristic
4C3×#4799C211yesmaximal, characteristic, complemented
5C3×#4791C211yesmaximal, characteristic, complemented
6#10591562C211yesmaximal, characteristic
7#10591546C211yesmaximal, characteristic, complemented
8#10591545C211yesmaximal, characteristic, complemented
9#10590809C211yesmaximal, characteristic, complemented
10#10590802C211yesmaximal, characteristic, complemented
11#10590712C211yesmaximal, characteristic
12#10590701C211yesmaximal, characteristic
13#10590583C211yesmaximal, characteristic
14#10590490C211yesmaximal, characteristic, complemented
15#10590488C211yesmaximal, characteristic, complemented
16#81233—31nomaximal
17#81013—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C8×C3⋊D3C2211yescharacteristic
20C4⋊C4×C3⋊D3C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×#890C2211yescharacteristic
24C3×#888C2211yescharacteristic
25#63918C2211yescharacteristic
26#63874—21no—
27#63874C2211yescharacteristic
28#63871—21no—
29#63869C2211yescharacteristic
30#63865—21no—
31#63849—21no—
32#63849C2211yescharacteristic
33#63849C2211yescharacteristic
34#63847—21no—
35#63844—21no—
36#63844—21no—
37#63844C2211yescharacteristic
38#63844C2211yescharacteristic
39#63839—21no—
40C2×#3712C2211yescharacteristic
41C32×#103C2211yescharacteristic
42#63662C2211yescharacteristic
43#63643C2211yescharacteristic
44#63637C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#817C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63576C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63567C2211yescharacteristic
60#63567C2211yescharacteristic
61#5729—31no—
62#5689—31no—
63#5572—31no—
64#5572—31no—
65C3×#479—31no—
66C3×#475—31no—
67#5091—31no—
68#5063—31no—
69#5022—31no—
70#5021—31no—
71#4881—31no—
72#4875—31no—
73#4861—31no—
74#4860—31no—
75#4860—31no—
76#4857—31no—
77#4857—31no—
78#4854—31no—
79#4851—31no—
80#4839—31no—
81#4839—31no—
82#4829—31no—
83#4802—31no—
84#4802—31no—
85D3×#103—31no—
86D3×#103—31no—
87D3×#103—61no—
88#4799—31no—
89#4799D311yescharacteristic, complemented
90#4793—31no—
91#4791D311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93Q8×C3⋊D3—22no—
94Q8×C3⋊D3Q814yescomplemented
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C2×#634C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×#627—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C4⋊(C3⋊Dic3)C2311yescharacteristic
105#3750—21no—
106C2×C3⋊(C3⋊C8)C2311yescharacteristic
107C8×C3⋊D3—22no—
108C3×C4⋊Dic3—21no—
109C3×C4⋊Dic3—21no—
110C3×C4⋊Dic3—21no—
111C3×C4⋊Dic3C2311yescharacteristic
112C3×C4⋊Dic3C2311yescharacteristic
113C3×C4⋊Dic3C2311yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123#3724—21no—
124#3724—21no—
125#3724—21no—
126#3724D411yescharacteristic
127#3724D411yescharacteristic
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130#3722—21no—
131#3722—21no—
132#3722D411yescharacteristic
133#3722D411yescharacteristic
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138#3712—22no—
139#3082—91noSylow
140C2×D3×Q8—31no—
141C2×D3×Q8—31no—
142C2×D3×Q8—61no—
143C3×C4⋊Q8—31no—
144C3×#125—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147#946—61no—
148Q8×Dic3C2×D311yescharacteristic
149Q8×Dic3C2×D311yescharacteristic
150#944—61no—
151C2×ΓL(1,𝔽25)—31no—
152C2×ΓL(1,𝔽25)—31no—
153C2×D3×C8—31no—
154C2×D3×C8—31no—
155C2×D3×C8—61no—
156#897—61no—
157#896—61no—
158#896—61no—
159#892—31no—
160#892—31no—
161#892—31no—
162#892—31no—
163#892—61no—
164#892—61no—
165D3×C4⋊C4—31no—
166D3×C4⋊C4—31no—
167D3×C4⋊C4—61no—
168#890—31no—
169#890C2×D311yescharacteristic
170#889—61no—
171#889—61no—
172#888—31no—
173#888—61no—
174#888C2×D311yescharacteristic
175#887—31no—
176#887—31no—
177#887—61no—
178#887—61no—
179#872—31no—
180#872—31no—
181#872—61no—
182#872—61no—
183#870—31no—
184#869—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—61no—
188C4×Dic6—61no—
189C3×#107—31no—
190C3×#106—31no—
191C3×#106—31no—
192C3×#106—31no—
193C3×C4⋊C8—31no—
194C3×C4⋊C8—31no—
195C3×#103—21no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#103C2×D311yescharacteristic
199C3×#103C2×D311yescharacteristic
200#835—31no—
201#835—31no—
202#835—61no—
203#835C2×D311yescharacteristic
204#835C2×D311yescharacteristic
205#818—31no—
206#817—31no—
207#817C2×D311yescharacteristic
208#817C2×D311yescharacteristic
209#816—31no—
210#816—31no—
211#816—31no—
212#816—31no—
213#816—61no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8C2×D311yescharacteristic
217Dic3⋊C8C2×D311yescharacteristic
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—61no—
223#808—31no—
224#808C2×D311yescharacteristic
225#807—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807C2×D311yescharacteristic
231C4⋊(C3⋊C8)—31no—
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
242C4×C3⋊D3—24no—
243C4×C3⋊D3—81no—
244C4×C3⋊D3C2×Q812yes—
245C4×C3⋊D3#4112yes—
246#634—21no—
247#634—24no—
248#634C2×Q812yes—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×Dic6—81no—
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—31no—
272#475—91no—
273#428—91no—
274#427—91no—
275#424—91no—
276#419—91no—
277C2×#103—91no—
278C2×C3×Q8—21no—
279C2×C3×Q8—61no—
280C2×C3×Q8C22×D311yescharacteristic
281C2×C3×Q8C22×D311yescharacteristic
282D3×Q8—34no—
283D3×Q8—34no—
284D3×Q8—64no—
285D3×Q8—62no—
286D3×Q8—62no—
287D3×Q8—122no—
288C2×C4×D3—31no—
289C2×C4×D3—31no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—121no—
296C2×C4×D3—121no—
297C2×Dic6—21no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—61no—
305C2×Dic6—121no—
306C2×C3×C8—21no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C3×C4⋊C4—21no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C42—31no—
324C3×C42—31no—
325C3×C42—61no—
326C3×C42—61no—
327(C2×D3)⋊C4—31no—
328(C2×D3)⋊C4—31no—
329(C2×D3)⋊C4—31no—
330(C2×D3)⋊C4—31no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337C4⋊Dic3—21no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3C22×D311yescharacteristic
344C4⋊Dic3C22×D311yescharacteristic
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
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—61no—
363Dic3⋊C4—121no—
364C4×Dic3—21no—
365C4×Dic3—21no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381ΓL(1,𝔽25)—62no—
382ΓL(1,𝔽25)—62no—
383D3×C8—62no—
384D3×C8—62no—
385D3×C8—122no—
386C22×C32C22×D411yescharacteristic
387C2×C3⋊D3—21no—
388C2×C3⋊D3—21no—
389C2×C3⋊D3C22⋊Q812yes—
390C32×C4—22no—
391C32×C4—41no—
392C32×C4C22×Q811yescharacteristic
393C32×C4C2×#4111yescharacteristic
394C3⋊Dic3—22no—
395C3⋊Dic3—41no—
396C3⋊Dic3C22⋊Q812yes—
397C3×Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C22×Q8—91no—
406C2×M16—91no—
407C22×C8—91no—
408C4⋊Q8—31no—
409C4⋊Q8—91no—
410C4⋊Q8—181no—
411#125—31no—
412#125—91no—
413#125—181no—
414C22⋊Q8—181no—
415C22⋊Q8—181no—
416C4×Q8—31no—
417C4×Q8—31no—
418C4×Q8—91no—
419C4×Q8—91no—
420C4×Q8—181no—
421C4×Q8—181no—
422#117—91no—
423#117—91no—
424#117—91no—
425#117—181no—
426#117—181no—
427C2×C4⋊C4—91no—
428#107—31no—
429#107—91no—
430#107—91no—
431#107—91no—
432#106—31no—
433#106—31no—
434#106—31no—
435#106—91no—
436C4⋊C8—31no—
437C4⋊C8—31no—
438C4⋊C8—91no—
439C4⋊C8—91no—
440#103—31no—
441#103—31no—
442#103—91no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103D3211yescharacteristic
448C22×D3—31no—
449C22×D3—31no—
450C22×D3—61no—
451C3×Q8—21no—
452C3×Q8—21no—
453C3×Q8—22no—
454C3×Q8—41no—
455C3×Q8—241no—
456C3×Q8D3×Q812yes—
457C3×Q8D3×Q812yes—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—31no—
480C2×Dic3—31no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—121no—
487C2×Dic3—121no—
488C2×Dic3D3×D411yescharacteristic
489C2×Dic3D3×D411yescharacteristic
490C2×Dic3D3×D411yescharacteristic
491C2×Dic3D3×D411yescharacteristic
492C4×D3—32no—
493C4×D3—32no—
494C4×D3—32no—
495C4×D3—32no—
496C4×D3—62no—
497C4×D3—62no—
498C4×D3—64no—
499C4×D3—64no—
500C4×D3—124no—
501C4×D3—241no—
502C4×D3—241no—
503C4×D3—242no—
504Dic6—32no—
505Dic6—32no—
506Dic6—62no—
507Dic6—64no—
508Dic6—64no—
509Dic6—61no—
510Dic6—61no—
511Dic6—81no—
512Dic6—124no—
513Dic6—121no—
514Dic6—241no—
515Dic6—241no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—41no—
519C3×C8—61no—
520C3×C8—61no—
521C3⋊C8—21no—
522C3⋊C8—21no—
523C3⋊C8—61no—
524C3⋊C8—61no—
525C3⋊C8—121no—
526C2×C32C2×C22⋊Q811yescharacteristic
527C2×C32#57711yescharacteristic
528C2×C32#57811yescharacteristic
529C3⋊D3—22no—
530C2×Q8—61no—
531C2×Q8—94no—
532C2×Q8—91no—
533C2×Q8—181no—
534C2×Q8—181no—
535C2×Q8—182no—
536C2×Q8C2×D3211yescharacteristic
537C22×C4—91no—
538C22×C4—181no—
539C22×C4—181no—
540M16—182no—
541C2×C8—31no—
542C2×C8—31no—
543C2×C8—91no—
544C2×C8—182no—
545C2×C8C2×D3211yescharacteristic
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4C2×D3211yescharacteristic
565C22⋊C4—91no—
566C22⋊C4—91no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C42—31no—
570C42—31no—
571C42—61no—
572C42—61no—
573C42—181no—
574C42—181no—
575C42—181no—
576C42—181no—
577C22×C3—21no—
578C22×C3C2×D3×D411yescharacteristic
579C22×C3C2×D3×D411yescharacteristic
580C2×D3—32no—
581C2×D3—32no—
582C2×D3—62no—
583C2×D3—62no—
584C2×D3—62no—
585C2×D3—61no—
586C2×D3—61no—
587C2×D3—61no—
588C2×D3—61no—
589C3×C4—22no—
590C3×C4—22no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—42no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—61no—
597C3×C4—61no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—81no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4C2×D3×Q811yescharacteristic
606C3×C4C2×D3×Q811yescharacteristic
607C3×C4D3×#4111yescharacteristic
608C3×C4D3×#4111yescharacteristic
609Dic3—21no—
610Dic3—21no—
611Dic3—21no—
612Dic3—21no—
613Dic3—32no—
614Dic3—32no—
615Dic3—41no—
616Dic3—41no—
617Dic3—41no—
618Dic3—41no—
619Dic3—62no—
620Dic3—62no—
621Dic3—62no—
622Dic3—122no—
623Dic3—121no—
624Dic3—121no—
625Dic3—241no—
626C32#308211yescharacteristic, complemented, Sylow
627C23—91no—
628Q8—21no—
629Q8—92no—
630Q8—184no—
631Q8—181no—
632Q8—241no—
633Q8—721no—
634Q8#379712yes—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—31no—
640C2×C4—31no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—91no—
646C2×C4—92no—
647C2×C4—92no—
648C2×C4—184no—
649C2×C4—181no—
650C2×C4—181no—
651C2×C4—721no—
652C2×C4C22×D3211yescharacteristic
653C8—21no—
654C8—61no—
655C8—61no—
656C8—181no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3D3×C22⋊Q811yescharacteristic
661C2×C3D3×C22⋊Q811yescharacteristic
662C2×C3#576211yescharacteristic
663C2×C3#577011yescharacteristic
664C2×C3#577911yescharacteristic
665C2×C3#577911yescharacteristic
666D3—64no—
667D3—62no—
668D3—62no—
669C22—92no—
670C22—181no—
671C22—181no—
672C22D32×D411yescharacteristic
673C4—22no—
674C4—41no—
675C4—61no—
676C4—61no—
677C4—61no—
678C4—61no—
679C4—92no—
680C4—121no—
681C4—121no—
682C4—121no—
683C4—121no—
684C4—182no—
685C4—361no—
686C4C2×#379711yescharacteristic
687C4#6431211yescharacteristic
688C3—21no—
689C3#8101311yescharacteristic, complemented
690C3#8123311yescharacteristic, complemented
691C2—182no—
692C2#1059406711yescharacteristic
693C2#1059475311yescharacteristic
694C2#1059476911yescharacteristic
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
4. C3×#4799C2semidirect
5. C3×#4791C2semidirect
7. #10591546C2semidirect
8. #10591545C2semidirect
9. #10590809C2semidirect
10. #10590802C2semidirect
14. #10590490C2semidirect
15. #10590488C2semidirect
89. #4799D3semidirect
91. #4791D3semidirect
94. Q8×C3⋊D3Q8semidirect
626. C32#3082semidirect
689. C3#81013semidirect
690. C3#81233semidirect

Maximal subgroups

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

subgroupindex
#105953392
#105943252
C3⋊D3×#1032
C3×#47992
C3×#47912
#105915622
#105915462
#105915452
#105908092
#105908022
#105907122
#105907012
#105905832
#105904902
#105904882
#812333
#810133