Finite Group Databasebeta

← #11860619

Subgroups — #11860619

Order 1152.

1000 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63801C211yesmaximal, characteristic
2#10593890C211yesmaximal, characteristic
3#10593885C211yesmaximal, characteristic, complemented
4#10592409C211yesmaximal, characteristic, complemented
5C3×#4716C211yesmaximal, characteristic, complemented
6C3×#4708C211yesmaximal, characteristic, complemented
7Dic3×Dic12C211yesmaximal, characteristic, complemented
8#10590795C211yesmaximal, characteristic, complemented
9#10590794C211yesmaximal, characteristic, complemented
10#10590758C211yesmaximal, characteristic, complemented
11#10590690C211yesmaximal, characteristic
12#10590681C211yesmaximal, characteristic, complemented
13D3×#816C211yesmaximal, characteristic, complemented
14C4×#3719C211yesmaximal, characteristic, complemented
15C4×#3717C211yesmaximal, characteristic, complemented
16#79830—31nomaximal
17#78571—31nomaximal
18C2×#3799C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×#872C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29#63894C2211yescharacteristic
30D3×C4⋊Dic3C2211yescharacteristic
31#63883—21no—
32#63881—21no—
33#63880—21no—
34#63878—21no—
35#63877—21no—
36#63844C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63841C2211yescharacteristic
40#63838—21no—
41#63837—21no—
42#63836—21no—
43C2×#3719C2211yescharacteristic
44C2×#3717C2211yescharacteristic
45#63801C418yescomplemented
46C32×#97C2211yescharacteristic
47#63648C2211yescharacteristic
48#63645C2211yescharacteristic
49#63643C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×C4×C3⋊C8C2211yescharacteristic
56#63575C2211yescharacteristic
57#63573C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#63564C2211yescharacteristic
62C2×#918—31no—
63C2×#909—31no—
64#5574—31no—
65#5572—31no—
66#5523—31no—
67#5516—31no—
68C3×#441—31no—
69C3×#405—31no—
70Dic3×Q16—31no—
71#5121—31no—
72#5113—31no—
73C2×#816—31no—
74C4×#216—31no—
75C4×#215—31no—
76#4861—31no—
77#4852—31no—
78#4817—31no—
79#4804—31no—
80D3×#103—31no—
81#4789—31no—
82#4716—31no—
83#4716D311yescharacteristic, complemented
84#4710—31no—
85#4710—31no—
86#4710—31no—
87#4710—61no—
88#4708D311yescharacteristic, complemented
89C4×Dic12—31no—
90C4×Dic12—31no—
91C4×#204—31no—
92C4×#204—31no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#626—21no—
101C2×#624—21no—
102C2×#624—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105#3799—22no—
106#3799C2×C414yes—
107D3×Dic6—22no—
108D3×Dic6C2×C414yescomplemented
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C42C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117#3744C2×C414yescomplemented
118C3×(C2×D3)⋊C4D411yescharacteristic
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4D411yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×Dic12C2×C414yescomplemented
132C3×ΓL(1,𝔽25)C2×C414yescomplemented
133C3×D3×C8—22no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143Dic32—21no—
144#3719C2×C414yescomplemented
145#3717C2×C414yescomplemented
146#2947—91noSylow
147C2×#239—31no—
148C2×D3×Q8—31no—
149C2×#235—31no—
150C22×Dic6—31no—
151C2×C3×Q16—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×#117—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159C2×#216—31no—
160C2×#215—31no—
161#926—31no—
162C2×C4⋊Dic3—31no—
163#918—38no—
164#909—38no—
165C2×Dic12—31no—
166C2×Dic12C2×D311yescharacteristic
167C2×#204—31no—
168C2×#204—31no—
169C2×#204—31no—
170C2×#204—61no—
171C2×ΓL(1,𝔽25)C2×D311yescharacteristic
172C2×D3×C8C2×D311yescharacteristic
173#893—31no—
174#893—61no—
175#892—31no—
176#892—61no—
177#892—61no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—61no—
180D3×C4⋊C4—61no—
181#887—31no—
182#887—61no—
183#887—61no—
184#887—61no—
185#67⋊C4—61no—
186#67⋊C4—61no—
187#877—61no—
188#877—61no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12—61no—
194#872—61no—
195#872—61no—
196#872C2×D311yescharacteristic
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—31no—
201C4×Dic6—31no—
202C4×Dic6—61no—
203C4×Dic6—61no—
204C4×Dic6C2×D311yescharacteristic
205C4×Dic6C2×D311yescharacteristic
206C3×#106—31no—
207C3×#103—31no—
208C3×#103—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#835—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#818—31no—
222#818—31no—
223#818—31no—
224#818—61no—
225#817—31no—
226#817C2×D311yescharacteristic
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#816—61no—
233#816C2×D311yescharacteristic
234#816C2×D311yescharacteristic
235#815C2×D311yescharacteristic
236C8×Dic3C2×D311yescharacteristic
237#810—31no—
238#809—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—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)C22×C412yes—
252C4×C3⋊D3—81no—
253#634—21no—
254#634C22×C412yes—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3C22×C412yes—
263C3×C4×D3#4112yes—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6C22×C412yes—
267C3×Dic6C22×C412yes—
268#627—24no—
269#626—24no—
270#624—24no—
271#624—81no—
272D3×Dic3—24no—
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—31no—
282#441—91no—
283#440—91no—
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×Q8—31no—
295C22×C3×C4—31no—
296C2×#67—61no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299#239—34no—
300#239—62no—
301D3×Q8—34no—
302D3×Q8—62no—
303#235—34no—
304#235—62no—
305C2×D12—31no—
306C2×D12—31no—
307C2×D12—61no—
308C2×D12—61no—
309C2×C4×D3—61no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—121no—
318C2×C4×D3C22×D311yescharacteristic
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—34no—
322C2×Dic6—61no—
323C2×Dic6—62no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6C22×D311yescharacteristic
327C2×Dic6C22×D311yescharacteristic
328C3×Q16—34no—
329C3×M16—34no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—62no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C42—21no—
348C3×C42—31no—
349C3×C42—61no—
350C3×C42—61no—
351C3×C42C22×D311yescharacteristic
352C3×C42C22×D311yescharacteristic
353#217—61no—
354#216—34no—
355#215—34no—
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—121no—
362(C2×D3)⋊C4D1211yescharacteristic
363(C2×D3)⋊C4D1211yescharacteristic
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
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
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385Dic3⋊C4D1211yescharacteristic
386Dic3⋊C4D1211yescharacteristic
387C4×Dic3—21no—
388C4×Dic3—21no—
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—61no—
399C4×Dic3—121no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—34no—
404Dic12C4×D314yescomplemented
405#204—34no—
406#204—34no—
407#204—34no—
408#204—64no—
409ΓL(1,𝔽25)C4×D314yescomplemented
410D3×C8—22no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—22no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3C4×D412yes—
418C32×C4—21no—
419C32×C4—21no—
420C32×C4C23×C411yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3⋊Dic3—22no—
423C3⋊Dic3—41no—
424C3⋊Dic3—41no—
425C3×Dic3—22no—
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—31no—
436C2×Q16—91no—
437C2×SD16—91no—
438C2×SD16—91no—
439C2×M16—31no—
440C22×C8—31no—
441C4×Q8—31no—
442C4×Q8—31no—
443C4×Q8—91no—
444C4×Q8—91no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—181no—
448C4×Q8—181no—
449C4×D4—91no—
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—91no—
461#107—91no—
462#106—31no—
463#106—91no—
464#103—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—91no—
471#102—91no—
472#97—31no—
473#97D3211yescharacteristic
474C4×C8—31no—
475C4×C8—31no—
476C23×C3—31no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—121no—
480C22×D3C2×D1211yescharacteristic
481C3×Q8—32no—
482C3×Q8—32no—
483C3×Q8—61no—
484C3×Q8—61no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4C2×D1211yescharacteristic
498C2×C3×C4C2×D1211yescharacteristic
499C2×C3×C4D3×D411yescharacteristic
500C2×C3×C4D3×D411yescharacteristic
501C2×C3×C4C23×D311yescharacteristic
502C2×C3×C4C23×D311yescharacteristic
503#67—64no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—64no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—121no—
516C2×Dic3—121no—
517C2×Dic3—121no—
518C2×Dic3—241no—
519C2×Dic3C2×D1211yescharacteristic
520C2×Dic3C2×D1211yescharacteristic
521C2×Dic3C2×D1211yescharacteristic
522D12—32no—
523D12—32no—
524D12—62no—
525D12—64no—
526D12—61no—
527D12—61no—
528D12—121no—
529C4×D3—64no—
530C4×D3—64no—
531C4×D3—64no—
532C4×D3—241no—
533C4×D3—241no—
534C4×D3—241no—
535C4×D3—241no—
536C4×D3—241no—
537C4×D3—242no—
538C4×D3C2×C4×D312yes—
539C4×D3#23512yes—
540Dic6—21no—
541Dic6—21no—
542Dic6—32no—
543Dic6—32no—
544Dic6—62no—
545Dic6—64no—
546Dic6—61no—
547Dic6—61no—
548Dic6—64no—
549Dic6—121no—
550Dic6C2×C4×D312yes—
551Dic6C2×C4×D312yes—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—22no—
555C3×C8—32no—
556C3×C8—41no—
557C3×C8—61no—
558C3×C8C2×C4×D312yes—
559C3×C8C2×C4×D312yes—
560C3⋊C8—21no—
561C3⋊C8C2×C4×D312yes—
562C2×C32C2×C4×D411yescharacteristic
563C2×C32#57711yescharacteristic
564C2×C32#57811yescharacteristic
565C3⋊D3—42no—
566C3×D3—22no—
567#41—94no—
568#41—182no—
569C2×Q8—31no—
570C2×Q8—31no—
571C2×Q8—94no—
572C2×Q8—91no—
573C2×Q8—181no—
574C2×Q8—182no—
575C2×D4—91no—
576C2×D4—181no—
577C22×C4—31no—
578C22×C4—181no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—181no—
582C22×C4—181no—
583Q16—34no—
584Q16—94no—
585SD16—94no—
586SD16—94no—
587M16—34no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—62no—
591C2×C8C2×D3211yescharacteristic
592C2×C8C2×D3211yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C42—31no—
612C42—61no—
613C42—61no—
614C42—181no—
615C42—181no—
616C42—181no—
617C42—181no—
618C42—181no—
619C42C2×D3211yescharacteristic
620C22×C3—21no—
621C22×C3—32no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3C22×D1211yescharacteristic
625C22×C3C2×D3×D411yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—62no—
629C2×D3—62no—
630C2×D3—122no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—241no—
636C2×D3—241no—
637C2×D3C4×D1212yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—32no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—62no—
648C3×C4—62no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C22×C4×D311yescharacteristic
654C3×C4C22×C4×D311yescharacteristic
655C3×C4C2×#23511yescharacteristic
656C3×C4D3×#4111yescharacteristic
657Dic3—21no—
658Dic3—21no—
659Dic3—22no—
660Dic3—22no—
661Dic3—41no—
662Dic3—41no—
663Dic3—62no—
664Dic3—62no—
665Dic3—122no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—241no—
671Dic3—241no—
672Dic3C4×D1212yes—
673C32#294711yescharacteristic, complemented, Sylow
674C23—31no—
675C23—181no—
676Q8—32no—
677Q8—32no—
678Q8—61no—
679Q8—61no—
680Q8—92no—
681Q8—184no—
682Q8—181no—
683D4—92no—
684D4—184no—
685D4—181no—
686C2×C4—31no—
687C2×C4—32no—
688C2×C4—32no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—184no—
696C2×C4—184no—
697C2×C4—181no—
698C2×C4—181no—
699C2×C4—181no—
700C2×C4—721no—
701C2×C4—721no—
702C2×C4—721no—
703C2×C4D3×D1211yescharacteristic
704C2×C4D3×D1211yescharacteristic
705C2×C4C22×D3211yescharacteristic
706C8—21no—
707C8—32no—
708C8—61no—
709C8C4×D3212yes—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—62no—
714C2×C3C2×C4×D1211yescharacteristic
715C2×C3C4×D3×D411yescharacteristic
716C2×C3#575111yescharacteristic
717C2×C3#575311yescharacteristic
718C2×C3#577811yescharacteristic
719C2×C3#577911yescharacteristic
720D3—22no—
721D3—122no—
722D3—122no—
723D3—242no—
724C22—32no—
725C22—61no—
726C22—61no—
727C22—182no—
728C22—361no—
729C22—361no—
730C22C2×D3×D1211yescharacteristic
731C4—21no—
732C4—21no—
733C4—32no—
734C4—61no—
735C4—61no—
736C4—62no—
737C4—62no—
738C4—121no—
739C4—121no—
740C4—182no—
741C4—361no—
742C4—361no—
743C4C2×C4×D3211yescharacteristic
744C4D3×#23511yescharacteristic
745C3—21no—
746C3#7857111yescharacteristic, complemented
747C3#7983011yescharacteristic, complemented
748C2—62no—
749C2—362no—
750C2C4×D3×D1211yescharacteristic
751C2#1059471511yescharacteristic
752C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#3799C22
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. #10592409C2semidirect
5. C3×#4716C2semidirect
6. C3×#4708C2semidirect
7. Dic3×Dic12C2semidirect
8. #10590795C2semidirect
9. #10590794C2semidirect
10. #10590758C2semidirect
12. #10590681C2semidirect
13. D3×#816C2semidirect
14. C4×#3719C2semidirect
15. C4×#3717C2semidirect
45. #63801C4semidirect
83. #4716D3semidirect
88. #4708D3semidirect
108. D3×Dic6C2×C4semidirect
117. #3744C2×C4semidirect
131. C3×Dic12C2×C4semidirect
132. C3×ΓL(1,𝔽25)C2×C4semidirect
144. #3719C2×C4semidirect
145. #3717C2×C4semidirect
404. Dic12C4×D3semidirect
409. ΓL(1,𝔽25)C4×D3semidirect
673. C32#2947semidirect
746. C3#78571semidirect
747. C3#79830semidirect

Maximal subgroups

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

subgroupindex
C2×#638012
#105938902
#105938852
#105924092
C3×#47162
C3×#47082
Dic3×Dic122
#105907952
#105907942
#105907582
#105906902
#105906812
D3×#8162
C4×#37192
C4×#37172
#798303
#785713