Finite Group Databasebeta

← #11860617

Subgroups — #11860617

Order 1152.

994 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63800C211yesmaximal, characteristic
2#10593887C211yesmaximal, characteristic
3#10593885C211yesmaximal, characteristic, complemented
4#10592415C211yesmaximal, characteristic, complemented
5C3×#4710C211yesmaximal, characteristic, complemented
6C3×#4708C211yesmaximal, characteristic, complemented
7#10590954C211yesmaximal, characteristic
8#10590807C211yesmaximal, characteristic, complemented
9#10590794C211yesmaximal, characteristic, complemented
10Dic3×#204C211yesmaximal, characteristic, complemented
11#10590747C211yesmaximal, characteristic, complemented
12#10590683C211yesmaximal, characteristic, complemented
13D3×#816C211yesmaximal, characteristic, complemented
14C4×#3719C211yesmaximal, characteristic, complemented
15C4×#3716C211yesmaximal, characteristic, complemented
16#79776—31nomaximal
17#78571—31nomaximal
18C2×#3795C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×#3746C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×#872C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29#63902—21no—
30Dic3×D12C2211yescharacteristic
31D3×C4⋊Dic3C2211yescharacteristic
32#63879—21no—
33#63878—21no—
34#63878—21no—
35#63877—21no—
36D3×Dic3⋊C4—21no—
37#63844C2211yescharacteristic
38#63844C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40#63841C2211yescharacteristic
41#63838—21no—
42#63837—21no—
43C2×#3719C2211yescharacteristic
44C2×#3716C2211yescharacteristic
45#63800C418yescomplemented
46C32×#97C2211yescharacteristic
47#63644C2211yescharacteristic
48#63643C2211yescharacteristic
49#63643C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×C4×C3⋊C8C2211yescharacteristic
56#63575C2211yescharacteristic
57#63573C2211yescharacteristic
58#63567C2211yescharacteristic
59#63567C2211yescharacteristic
60#63566C2211yescharacteristic
61#63563C2211yescharacteristic
62C2×#915—31no—
63C2×#909—31no—
64#5572—31no—
65#5546—31no—
66#5523—31no—
67#5516—31no—
68C3×#440—31no—
69C3×#405—31no—
70Dic3×SD16—31no—
71#5121—31no—
72#5113—31no—
73C2×#816—31no—
74C4×#216—31no—
75C4×#214—31no—
76#4881—31no—
77#4873—31no—
78D3×#103—31no—
79#4789—31no—
80#4772—31no—
81#4757—31no—
82#4716—31no—
83#4716—31no—
84#4716—31no—
85#4716—61no—
86#4710—31no—
87#4710D311yescharacteristic, complemented
88#4708D311yescharacteristic, complemented
89C4×Dic12—31no—
90C4×Dic12—31no—
91C4×#204—31no—
92C4×#204—31no—
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#625—21no—
101C2×D3×Dic3—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105#3795—22no—
106#3795C2×C414yes—
107D3×Dic6—22no—
108D3×Dic6C2×C414yescomplemented
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C42C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3—21no—
118#3746C2×C414yescomplemented
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4D411yescharacteristic
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204C2×C414yescomplemented
132C3×ΓL(1,𝔽25)C2×C414yescomplemented
133C3×D3×C8—22no—
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143Dic32—21no—
144#3719C2×C414yescomplemented
145#3716C2×C414yescomplemented
146#2947—91noSylow
147C2×D3×Q8—31no—
148C2×#237—31no—
149C2×#235—31no—
150C22×Dic6—31no—
151C2×C3×SD16—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156C3×#117—31no—
157Q8×Dic3—31no—
158C2×#216—31no—
159D4×Dic3—31no—
160C2×#214—31no—
161C4×#67—61no—
162#926—31no—
163C2×C4⋊Dic3—31no—
164C2×Dic3⋊C4—61no—
165#915—38no—
166#909—38no—
167C2×Dic12—31no—
168C2×Dic12—31no—
169C2×Dic12—31no—
170C2×Dic12—61no—
171C2×#204—31no—
172C2×#204C2×D311yescharacteristic
173C2×ΓL(1,𝔽25)C2×D311yescharacteristic
174C2×D3×C8C2×D311yescharacteristic
175#892—31no—
176#892—61no—
177#892—61no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—61no—
180#887—31no—
181#887—31no—
182#887—61no—
183#887—61no—
184#887—61no—
185#67⋊C4—61no—
186#67⋊C4—61no—
187#67⋊C4—61no—
188#877—61no—
189#877—61no—
190#877—61no—
191C4×D12—31no—
192C4×D12C2×D311yescharacteristic
193#872—61no—
194#872C2×D311yescharacteristic
195C4×Dic6—31no—
196C4×Dic6—31no—
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—31no—
201C4×Dic6—31no—
202C4×Dic6—61no—
203C4×Dic6—61no—
204C4×Dic6—61no—
205C4×Dic6C2×D311yescharacteristic
206C3×#107—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×#97—21no—
210C3×#97—31no—
211C3×#97C2×D311yescharacteristic
212C3×#97C2×D311yescharacteristic
213C3×C4×C8—31no—
214C3×C4×C8—31no—
215#835—31no—
216#832—31no—
217#821—31no—
218#821C2×D311yescharacteristic
219#818—31no—
220#818C2×D311yescharacteristic
221#817—31no—
222#817—31no—
223#817—31no—
224#817—61no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#816—61no—
233#816—61no—
234#816C2×D311yescharacteristic
235#815C2×D311yescharacteristic
236C8×Dic3C2×D311yescharacteristic
237#810—31no—
238#810—31no—
239#808—31no—
240#807—31no—
241C4×C3⋊C8C2×D311yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251#634—21no—
252#634—21no—
253#634C22×C412yes—
254#634C22×C412yes—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12C22×C412yes—
263C3×C4×D3—81no—
264C3×C4×D3C22×C412yes—
265C3×C4×D3#4112yes—
266C3×Dic6—21no—
267C3×Dic6C22×C412yes—
268#627—24no—
269#625—24no—
270D3×Dic3—24no—
271D3×Dic3—24no—
272D3×Dic3—81no—
273D3×Dic3—81no—
274C32×C8—21no—
275C32×C8C22×C412yes—
276C3×C3⋊C8—21no—
277C3×C3⋊C8C22×C412yes—
278C2×#137—91no—
279#520—91no—
280#519—91no—
281#441—91no—
282#441—91no—
283#440—31no—
284#440—91no—
285C4×Q16—91no—
286C4×Q16—91no—
287C4×SD16—91no—
288C4×SD16—91no—
289#428—91no—
290#416—91no—
291C2×#103—91no—
292#405—31no—
293C2×C3×Q8—31no—
294C2×C3×D4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—61no—
297C2×#67—61no—
298C2×#67—61no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303D3×Q8—34no—
304D3×Q8—62no—
305#237—34no—
306#237—62no—
307#235—34no—
308#235—62no—
309C2×D12C22×D311yescharacteristic
310C2×C4×D3—21no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3C22×D311yescharacteristic
316C2×Dic6—31no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—34no—
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×Dic6—62no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6C22×D311yescharacteristic
327C3×SD16—34no—
328C3×M16—34no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8—62no—
334C2×C3×C8C22×D311yescharacteristic
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—61no—
346C3×C42—21no—
347C3×C42—31no—
348C3×C42—61no—
349C3×C42C22×D311yescharacteristic
350C3×C42C22×D311yescharacteristic
351#217—61no—
352#217—61no—
353#216—34no—
354#214—34no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4D1211yescharacteristic
359(C2×D3)⋊C4D1211yescharacteristic
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3C22×D311yescharacteristic
369C4⋊Dic3C22×D311yescharacteristic
370Dic3⋊C4—21no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—121no—
382Dic3⋊C4—121no—
383Dic3⋊C4D1211yescharacteristic
384Dic3⋊C4D1211yescharacteristic
385C4×Dic3—21no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—121no—
399C4×Dic3—121no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—34no—
404Dic12—34no—
405Dic12—34no—
406Dic12—64no—
407#204—34no—
408#204C4×D314yescomplemented
409ΓL(1,𝔽25)C4×D314yescomplemented
410D3×C8—22no—
411C22×C32C22×D411yescharacteristic
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—22no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3C4×D412yes—
418C32×C4—21no—
419C32×C4—21no—
420C32×C4C23×C411yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3⋊Dic3—22no—
423C3⋊Dic3—22no—
424C3⋊Dic3—41no—
425C3⋊Dic3—41no—
426C3×Dic3—22no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3C4×D412yes—
432C2×#41—91no—
433C22×Q8—91no—
434#137—98no—
435C2×Q16—91no—
436C2×Q16—91no—
437C2×SD16—31no—
438C2×SD16—91no—
439C2×M16—31no—
440C22×C8—31no—
441C4×Q8—31no—
442C4×Q8—91no—
443C4×Q8—91no—
444C4×Q8—91no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—181no—
448C4×Q8—181no—
449C4×D4—31no—
450C4×D4—91no—
451C4×D4—181no—
452C4×D4—181no—
453#117—31no—
454#117—91no—
455#117—181no—
456#117—181no—
457#117—181no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—181no—
460#107—31no—
461#107—91no—
462#106—91no—
463#106—91no—
464#103—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—91no—
472#97—31no—
473#97D3211yescharacteristic
474C4×C8—31no—
475C4×C8—31no—
476C23×C3—31no—
477C23×C3—61no—
478C22×D3—21no—
479C22×D3C2×D1211yescharacteristic
480C3×Q8—32no—
481C3×Q8—61no—
482C3×D4—32no—
483C3×D4—61no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—241no—
496C2×C3×C4C2×D1211yescharacteristic
497C2×C3×C4C2×D1211yescharacteristic
498C2×C3×C4D3×D411yescharacteristic
499C2×C3×C4D3×D411yescharacteristic
500C2×C3×C4C23×D311yescharacteristic
501C2×C3×C4C23×D311yescharacteristic
502#67—64no—
503#67—64no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—64no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—64no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—121no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—241no—
522C2×Dic3—241no—
523C2×Dic3C2×D1211yescharacteristic
524C2×Dic3C2×D1211yescharacteristic
525C2×Dic3C2×D1211yescharacteristic
526D12—21no—
527D12C2×C4×D312yes—
528C4×D3—64no—
529C4×D3—64no—
530C4×D3—81no—
531C4×D3—241no—
532C4×D3—241no—
533C4×D3C2×C4×D312yes—
534C4×D3#23512yes—
535Dic6—21no—
536Dic6—32no—
537Dic6—32no—
538Dic6—32no—
539Dic6—32no—
540Dic6—62no—
541Dic6—62no—
542Dic6—64no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—64no—
548Dic6—121no—
549Dic6—121no—
550Dic6C2×C4×D312yes—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—22no—
554C3×C8—32no—
555C3×C8—41no—
556C3×C8—61no—
557C3×C8C2×C4×D312yes—
558C3×C8C2×C4×D312yes—
559C3⋊C8—21no—
560C3⋊C8C2×C4×D312yes—
561C2×C32C2×C4×D411yescharacteristic
562C2×C32#57711yescharacteristic
563C2×C32#57811yescharacteristic
564C3×D3—22no—
565C3×D3—42no—
566#41—94no—
567#41—182no—
568C2×Q8—31no—
569C2×Q8—94no—
570C2×Q8—91no—
571C2×Q8—91no—
572C2×Q8—181no—
573C2×Q8—182no—
574C2×D4—31no—
575C2×D4—181no—
576C22×C4—31no—
577C22×C4—61no—
578C22×C4—181no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—181no—
582Q16—94no—
583Q16—94no—
584SD16—34no—
585SD16—94no—
586M16—34no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—62no—
590C2×C8C2×D3211yescharacteristic
591C2×C8C2×D3211yescharacteristic
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4—61no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—31no—
611C42—61no—
612C42—181no—
613C42—181no—
614C42—181no—
615C42—181no—
616C42—181no—
617C42—181no—
618C42C2×D3211yescharacteristic
619C22×C3—21no—
620C22×C3—32no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—62no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3C22×D1211yescharacteristic
627C22×C3C2×D3×D411yescharacteristic
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—22no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3C4×D1212yes—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—32no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—62no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4C22×C4×D311yescharacteristic
649C3×C4C22×C4×D311yescharacteristic
650C3×C4C2×#23511yescharacteristic
651C3×C4D3×#4111yescharacteristic
652Dic3—21no—
653Dic3—21no—
654Dic3—22no—
655Dic3—41no—
656Dic3—41no—
657Dic3—62no—
658Dic3—62no—
659Dic3—62no—
660Dic3—62no—
661Dic3—122no—
662Dic3—122no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—241no—
668Dic3—241no—
669Dic3C4×D1212yes—
670C32#294711yescharacteristic, complemented, Sylow
671C23—31no—
672C23—61no—
673Q8—32no—
674Q8—61no—
675Q8—92no—
676Q8—92no—
677Q8—184no—
678Q8—181no—
679Q8—181no—
680D4—32no—
681D4—61no—
682D4—184no—
683C2×C4—31no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—184no—
692C2×C4—184no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—181no—
696C2×C4—181no—
697C2×C4—241no—
698C2×C4—721no—
699C2×C4—721no—
700C2×C4D3×D1211yescharacteristic
701C2×C4D3×D1211yescharacteristic
702C2×C4C22×D3211yescharacteristic
703C8—21no—
704C8—32no—
705C8—61no—
706C8C4×D3212yes—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—62no—
711C2×C3—122no—
712C2×C3C2×C4×D1211yescharacteristic
713C2×C3C4×D3×D411yescharacteristic
714C2×C3#575111yescharacteristic
715C2×C3#575311yescharacteristic
716C2×C3#577511yescharacteristic
717C2×C3#577911yescharacteristic
718D3—22no—
719D3—42no—
720C22—32no—
721C22—61no—
722C22—61no—
723C22—62no—
724C22—121no—
725C22—121no—
726C22C2×D3×D1211yescharacteristic
727C4—21no—
728C4—21no—
729C4—32no—
730C4—61no—
731C4—61no—
732C4—62no—
733C4—121no—
734C4—121no—
735C4—182no—
736C4—182no—
737C4—361no—
738C4—361no—
739C4C2×C4×D3211yescharacteristic
740C4D3×#23511yescharacteristic
741C3—21no—
742C3#7857111yescharacteristic, complemented
743C3#7977611yescharacteristic, complemented
744C2—62no—
745C2—122no—
746C2C4×D3×D1211yescharacteristic
747C2#1059471311yescharacteristic
748C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#3795C22
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
3. #10593885C2semidirect
4. #10592415C2semidirect
5. C3×#4710C2semidirect
6. C3×#4708C2semidirect
8. #10590807C2semidirect
9. #10590794C2semidirect
10. Dic3×#204C2semidirect
11. #10590747C2semidirect
12. #10590683C2semidirect
13. D3×#816C2semidirect
14. C4×#3719C2semidirect
15. C4×#3716C2semidirect
45. #63800C4semidirect
87. #4710D3semidirect
88. #4708D3semidirect
108. D3×Dic6C2×C4semidirect
118. #3746C2×C4semidirect
131. C3×#204C2×C4semidirect
132. C3×ΓL(1,𝔽25)C2×C4semidirect
144. #3719C2×C4semidirect
145. #3716C2×C4semidirect
408. #204C4×D3semidirect
409. ΓL(1,𝔽25)C4×D3semidirect
670. C32#2947semidirect
742. C3#78571semidirect
743. C3#79776semidirect

Maximal subgroups

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

subgroupindex
C2×#638002
#105938872
#105938852
#105924152
C3×#47102
C3×#47082
#105909542
#105908072
#105907942
Dic3×#2042
#105907472
#105906832
D3×#8162
C4×#37192
C4×#37162
#797763
#785713