Finite Group Databasebeta

← #11876929

Subgroups — #11876929

Order 1152.

857 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596151C211yesmaximal, characteristic, complemented
2#10593943C211yesmaximal, characteristic, complemented
3C3×#5059C211yesmaximal, characteristic, complemented
4C3×#5056C211yesmaximal, characteristic, complemented
5#10591600C211yesmaximal, characteristic, complemented
6#10591590C211yesmaximal, characteristic, complemented
7#10591582C211yesmaximal, characteristic, complemented
8#10591572C211yesmaximal, characteristic, complemented
9#10591464C211yesmaximal, characteristic, complemented
10#10591454C211yesmaximal, characteristic
11#10591446C211yesmaximal, characteristic, complemented
12#10591436C211yesmaximal, characteristic, complemented
13C4×#3712C211yesmaximal, characteristic, complemented
14#10590304C211yesmaximal, characteristic, complemented
15#10590274C211yesmaximal, characteristic, complemented
16#81812—31nomaximal
17#81631—31nomaximal
18C32×#124C2211yescharacteristic
19#64155C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64147C2211yescharacteristic
22D4×C3⋊Dic3C2211yescharacteristic
23#64092—21no—
24#64090—21no—
25#64088—21no—
26#64086—21no—
27C42×C3⋊D3C2211yescharacteristic
28#64079C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×#875C2211yescharacteristic
34C3×#870C2211yescharacteristic
35#63916C2211yescharacteristic
36#63898C2211yescharacteristic
37#63881—21no—
38#63878—21no—
39#63871C2211yescharacteristic
40#63862—21no—
41#63853—21no—
42#63843C2211yescharacteristic
43C2×#3712C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×C4×C3⋊C8C2211yescharacteristic
50C3×C4×C3⋊C8C2211yescharacteristic
51#63575C2211yescharacteristic
52#63575C2211yescharacteristic
53#63573C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63555C2211yescharacteristic
60#63555C2211yescharacteristic
61#5691—31no—
62#5680—31no—
63#5680—31no—
64#5680—31no—
65#5680—61no—
66C3×#495—31no—
67C3×#488—31no—
68#5189—31no—
69#5184—31no—
70#5174—31no—
71#5174—31no—
72#5164—31no—
73#5164—31no—
74#5159—31no—
75#5152—31no—
76#5065—31no—
77#5059D311yescharacteristic, complemented
78#5056—31no—
79#5056D311yescharacteristic, complemented
80#4817—31no—
81#4816—31no—
82#4812—31no—
83#4789—31no—
84#4785—31no—
85#4782—31no—
86#4780—31no—
87#4757—31no—
88#4697—31no—
89C4×ΓL(1,𝔽25)—31no—
90C4×ΓL(1,𝔽25)—31no—
91#4683—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C22×C3⋊Dic3—21no—
96C2×C4×C3⋊D3D411yescharacteristic
97C2×C4×C3⋊D3D411yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×D3×Dic3—21no—
103C32×C22⋊C4—21no—
104C32×C22⋊C4—21no—
105C32×C42C2311yescharacteristic
106#3757—21no—
107#3757—21no—
108#3752—21no—
109C4⋊(C3⋊Dic3)—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3D411yescharacteristic
117C4×C3⋊Dic3D411yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C3×#216—22no—
120C3×#215—22no—
121C3×#214—22no—
122C3×#213—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3712—22no—
140#3712—22no—
141#3183—91noSylow
142C2×C3×Q16—31no—
143C2×C3×SD16—31no—
144C2×C3×SD16—31no—
145C2×C3×D8—31no—
146C3×#125—31no—
147C3×#124—21no—
148C3×#124—31no—
149C3×#124C2×D311yescharacteristic
150C3×#124C2×D311yescharacteristic
151#946—31no—
152#946—31no—
153#946—31no—
154#946—61no—
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—61no—
159C2×#216C2×D311yescharacteristic
160C2×#215C2×D311yescharacteristic
161#938—31no—
162#938—31no—
163#938—31no—
164#938—61no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—61no—
169C2×#214C2×D311yescharacteristic
170C2×#213C2×D311yescharacteristic
171C2×ΓL(1,𝔽25)—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×ΓL(1,𝔽25)—31no—
175#898—61no—
176#897—31no—
177#895—31no—
178#894—61no—
179#893—31no—
180#893—61no—
181#892—61no—
182#887—31no—
183#883—61no—
184#883—61no—
185#883—61no—
186#883—62no—
187#67⋊C4—61no—
188#67⋊C4—61no—
189#67⋊C4—61no—
190#67⋊C4—62no—
191#879—61no—
192#879—61no—
193#879—61no—
194#879—62no—
195#877—61no—
196#877—61no—
197#877—61no—
198#877—62no—
199#875C2×D311yescharacteristic
200C42×D3—31no—
201C42×D3—31no—
202C42×D3—61no—
203#870—31no—
204#870—31no—
205#870—61no—
206#870C2×D311yescharacteristic
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×C4×C8—31no—
212C3×C4×C8—31no—
213#835—31no—
214#835—31no—
215#835C2×D311yescharacteristic
216#835C2×D311yescharacteristic
217#832—31no—
218#832—31no—
219#832C2×D311yescharacteristic
220#832C2×D311yescharacteristic
221#821—31no—
222#821—31no—
223#818—31no—
224#818—31no—
225#817—31no—
226#817—31no—
227#816—31no—
228#816—31no—
229#815—31no—
230#815—31no—
231#815—31no—
232#815—31no—
233#808—31no—
234#808—31no—
235#807—31no—
236#807—31no—
237C4×C3⋊C8C2×D311yescharacteristic
238C4×C3⋊C8C2×D311yescharacteristic
239C23×C32—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—42no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—41no—
260C4×C3⋊D3—41no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#626—42no—
269D3×Dic3—42no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8#4112yes—
273C3×C3⋊C8#4112yes—
274#529—91no—
275#529—91no—
276#499—91no—
277#495—31no—
278#488—31no—
279#488—91no—
280#470—91no—
281#469—91no—
282#468—91no—
283#468—91no—
284#442—91no—
285#441—91no—
286#440—91no—
287#440—91no—
288C4×M16—91no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4C22×D311yescharacteristic
296C2×C3×D4C22×D311yescharacteristic
297C2×#67—61no—
298C2×#67—61no—
299C2×#67—61no—
300C2×#67—62no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—62no—
305C2×D12—61no—
306C2×D12C22×D311yescharacteristic
307C2×C4×D3—31no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3—31no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×Dic6C22×D311yescharacteristic
318C3×Q16—62no—
319C3×SD16—62no—
320C3×SD16—62no—
321C3×D8—62no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C22⋊C4—22no—
331C3×C22⋊C4—22no—
332C3×C22⋊C4—21no—
333C3×C22⋊C4—21no—
334C3×C22⋊C4—21no—
335C3×C22⋊C4—21no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C42—21no—
339C3×C42C22×D311yescharacteristic
340C3×C42C22×D311yescharacteristic
341#217—61no—
342#217—61no—
343#217—61no—
344#217—61no—
345#217—61no—
346#217—61no—
347#217—62no—
348#217—62no—
349#216—22no—
350#215—22no—
351#214—22no—
352#213—22no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—62no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—62no—
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—62no—
382Dic3⋊C4—62no—
383Dic3⋊C4—62no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—62no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406ΓL(1,𝔽25)—62no—
407ΓL(1,𝔽25)—62no—
408ΓL(1,𝔽25)—62no—
409ΓL(1,𝔽25)—62no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32C22×D411yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3⋊Dic3—21no—
426C3⋊Dic3—21no—
427C3⋊Dic3—21no—
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C2×Q16—31no—
434C2×SD16—31no—
435C2×SD16—31no—
436C2×D8—31no—
437C2×M16—91no—
438C2×M16—91no—
439#126—181no—
440#126—181no—
441#125—31no—
442#125—91no—
443#124—31no—
444#124D3211yescharacteristic
445#123—181no—
446#123—181no—
447C22⋊Q8—91no—
448C22⋊Q8—91no—
449#121—91no—
450#121—91no—
451C4×Q8—91no—
452C4×Q8—91no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—181no—
456C4×D4—181no—
457#117—181no—
458#117—181no—
459C2×C42—91no—
460#107—91no—
461#107—91no—
462#106—91no—
463#106—91no—
464#103—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#102—31no—
469#102—31no—
470#102—91no—
471#102—91no—
472#97—91no—
473#97—91no—
474C4×C8—31no—
475C4×C8—31no—
476C23×C3—22no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3—31no—
482C22×D3—31no—
483C22×D3—61no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—61no—
499C3×D4—61no—
500C2×C3×C4—22no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—122no—
516#67—124no—
517#67—122no—
518#67—122no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—62no—
532C2×Dic3—62no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—122no—
538C2×Dic3—124no—
539C2×Dic3—122no—
540C2×Dic3—122no—
541D12—21no—
542D12—21no—
543D12—122no—
544C4×D3—61no—
545C4×D3—61no—
546C4×D3—61no—
547C4×D3—61no—
548C4×D3—121no—
549C4×D3—121no—
550C4×D3—121no—
551C4×D3—121no—
552C4×D3—121no—
553C4×D3—121no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557Dic6—21no—
558Dic6—21no—
559C3×C8—32no—
560C3×C8—32no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C3⋊C8#23712yes—
566C3⋊C8#23712yes—
567C2×C32—81no—
568C2×C32#53211yescharacteristic
569C2×C32#57511yescharacteristic
570C2×C32#57511yescharacteristic
571C3⋊D3—41no—
572C3×D3—81no—
573C2×Q8—31no—
574C2×Q8C2×D3211yescharacteristic
575C2×D4—31no—
576C2×D4—181no—
577C2×D4—181no—
578C2×D4C2×D3211yescharacteristic
579C22×C4—91no—
580C22×C4—91no—
581C22×C4—91no—
582C22×C4—181no—
583C22×C4—181no—
584Q16—62no—
585SD16—62no—
586SD16—62no—
587D8—62no—
588M16—182no—
589M16—182no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—91no—
617C42—91no—
618C42—91no—
619C42—181no—
620C42—181no—
621C42C2×D3211yescharacteristic
622C22×C3—21no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C2×D3×D411yescharacteristic
636C22×C3C2×D3×D411yescharacteristic
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—62no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—61no—
647C2×D3—121no—
648C2×D3—121no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—42no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4C2×#23711yescharacteristic
664C3×C4C2×#23711yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—62no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—121no—
678Dic3—121no—
679Dic3—122no—
680Dic3—122no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685C32#318311yescharacteristic, complemented, Sylow
686C23—21no—
687C23—61no—
688C23—91no—
689Q8—21no—
690Q8—21no—
691Q8—61no—
692Q8—61no—
693D4—21no—
694D4—21no—
695D4—61no—
696D4—61no—
697D4—362no—
698D4—362no—
699C2×C4—21no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—91no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—361no—
711C2×C4—361no—
712C2×C4—362no—
713C2×C4—362no—
714C2×C4#381111yescharacteristic
715C2×C4#381111yescharacteristic
716C2×C4C22×D3211yescharacteristic
717C8—32no—
718C8—32no—
719C8—61no—
720C8—61no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—82no—
725C2×C3—81no—
726C2×C3—81no—
727C2×C3—241no—
728C2×C3#566811yescharacteristic
729C2×C3#571611yescharacteristic
730C2×C3#576811yescharacteristic
731C2×C3#576811yescharacteristic
732C2×C3#576811yescharacteristic
733C2×C3#576811yescharacteristic
734D3—81no—
735D3—122no—
736D3—121no—
737D3—121no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—181no—
745C22—181no—
746C22—181no—
747C22C2×#381111yescharacteristic
748C4—21no—
749C4—21no—
750C4—41no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—181no—
755C4—181no—
756C4—181no—
757C4—361no—
758C4—361no—
759C4D3×#23711yescharacteristic
760C4D3×#23711yescharacteristic
761C3—21no—
762C3#8163111yescharacteristic, complemented
763C3#8181211yescharacteristic, complemented
764C2—81no—
765C2—241no—
766C2—361no—
767C2#1059516711yescharacteristic
768C2#1059546011yescharacteristic
769C2#1059546011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radical#10591454C2
hypercenter#124D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #10596151C2semidirect
2. #10593943C2semidirect
3. C3×#5059C2semidirect
4. C3×#5056C2semidirect
5. #10591600C2semidirect
6. #10591590C2semidirect
7. #10591582C2semidirect
8. #10591572C2semidirect
9. #10591464C2semidirect
11. #10591446C2semidirect
12. #10591436C2semidirect
13. C4×#3712C2semidirect
14. #10590304C2semidirect
15. #10590274C2semidirect
77. #5059D3semidirect
79. #5056D3semidirect
685. C32#3183semidirect
762. C3#81631semidirect
763. C3#81812semidirect

Maximal subgroups

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

subgroupindex
#105961512
#105939432
C3×#50592
C3×#50562
#105916002
#105915902
#105915822
#105915722
#105914642
#105914542
#105914462
#105914362
C4×#37122
#105903042
#105902742
#818123
#816313