Finite Group Databasebeta

← #11858561

Subgroups — #11858561

Order 1152.

1011 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63804C211yesmaximal, characteristic
2#10594511C211yesmaximal, characteristic
3#10594510C211yesmaximal, characteristic
4#10592580C211yesmaximal, characteristic, complemented
5C3×#4881C211yesmaximal, characteristic, complemented
6C3×#4880C211yesmaximal, characteristic, complemented
7#10590688C211yesmaximal, characteristic, complemented
8#10590683C211yesmaximal, characteristic, complemented
9D3×#817C211yesmaximal, characteristic, complemented
10#10590575C211yesmaximal, characteristic, complemented
11#10590574C211yesmaximal, characteristic, complemented
12#10590572C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14#10590437C211yesmaximal, characteristic, complemented
15#10590436C211yesmaximal, characteristic, complemented
16#79209—31nomaximal
17#79178—31nomaximal
18C2×#3798C2211yescharacteristic
19C2×#3743C2211yescharacteristic
20#64101C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28C4×#627—21no—
29C4×#626—21no—
30#63902—21no—
31#63900C2211yescharacteristic
32D3×C4⋊Dic3C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63881—21no—
36#63880—21no—
37#63880—21no—
38#63879—21no—
39#63849C2211yescharacteristic
40#63841C2211yescharacteristic
41#63837—21no—
42C2×#3711C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63804C418yescomplemented
46C32×#107C2211yescharacteristic
47#63644C2211yescharacteristic
48#63635C2211yescharacteristic
49#63634C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×#808C2211yescharacteristic
54C3×#808C2211yescharacteristic
55C3×#807C2211yescharacteristic
56#63576C2211yescharacteristic
57#63575C2211yescharacteristic
58#63574C2211yescharacteristic
59#63573C2211yescharacteristic
60#63573C2211yescharacteristic
61#63573C2211yescharacteristic
62C2×#907—31no—
63C2×#901—31no—
64#5523—31no—
65#5523—31no—
66#5523—31no—
67#5504—31no—
68C3×#428—31no—
69C3×#427—31no—
70#5121—31no—
71C2×#817—31no—
72#4998—31no—
73#4995—31no—
74#4995—31no—
75C2×#808—31no—
76#4881—31no—
77#4881—31no—
78#4881—31no—
79#4881—31no—
80#4881—31no—
81#4881—61no—
82#4881D311yescharacteristic, complemented
83#4880—31no—
84#4880D311yescharacteristic, complemented
85#4861—31no—
86#4861—31no—
87#4860—31no—
88#4860—31no—
89D3×#106—31no—
90D3×#106—31no—
91D3×#106—31no—
92D3×#106—31no—
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3C2311yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×#627D411yescharacteristic
99C2×#626D411yescharacteristic
100C2×#626D411yescharacteristic
101C2×#625D411yescharacteristic
102C2×#624—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106#3798C2×C414yes—
107#3798Q814yes—
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C4×C3⋊Dic3—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117#3743C2×C414yescomplemented
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×ΓL(1,𝔽25)C2×C414yescomplemented
132C3×D3×C8C2×C414yescomplemented
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3711C2×C414yescomplemented
142#3710C2×C414yescomplemented
143D3×C3⋊C8C2×C414yescomplemented
144#2912—91noSylow
145C2×#235—31no—
146C2×#235—31no—
147C2×C3×M16—31no—
148C22×C3×C8—31no—
149C3×#117—31no—
150C3×#117—31no—
151C3×#117—31no—
152C2×C3×C4⋊C4—31no—
153C4×#67—61no—
154C4×#67—61no—
155#926—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×#208—31no—
160C22×C3⋊C8—31no—
161#907—38no—
162#901—38no—
163C2×ΓL(1,𝔽25)—31no—
164C2×ΓL(1,𝔽25)—31no—
165C2×ΓL(1,𝔽25)—31no—
166C2×ΓL(1,𝔽25)—61no—
167C2×ΓL(1,𝔽25)C2×D311yescharacteristic
168C2×D3×C8—31no—
169C2×D3×C8—31no—
170C2×D3×C8—31no—
171C2×D3×C8C2×D311yescharacteristic
172#893—61no—
173#892—31no—
174#892—31no—
175#892—31no—
176#892—31no—
177#892—31no—
178#892—61no—
179#892C2×D311yescharacteristic
180#892C2×D311yescharacteristic
181#892C2×D311yescharacteristic
182D3×C4⋊C4—31no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190D3×C4⋊C4C2×D311yescharacteristic
191#887—61no—
192#67⋊C4—61no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195#67⋊C4—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198C4×D12—61no—
199C4×D12—61no—
200C4×D12—61no—
201C4×Dic6—61no—
202C4×Dic6—61no—
203C4×Dic6—61no—
204C3×#107—21no—
205C3×#107—31no—
206C3×#107—31no—
207C3×#107C2×D311yescharacteristic
208C3×#107C2×D311yescharacteristic
209C3×#106—31no—
210C3×#106—31no—
211C3×#106—31no—
212C3×#106—31no—
213#818—31no—
214#818C2×D311yescharacteristic
215#817—31no—
216#817—31no—
217#817—31no—
218#817—31no—
219#817—31no—
220#817—61no—
221#817C2×D311yescharacteristic
222#808—31no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—61no—
230#808C2×D311yescharacteristic
231#808C2×D311yescharacteristic
232#808C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238#807—61no—
239#807C2×D311yescharacteristic
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C4×C3⋊D3—81no—
250C4×C3⋊D3C22×C412yes—
251C4×C3⋊D3C2×Q812yes—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×C4×D3—81no—
259C3×C4×D3C22×C412yes—
260C3×C4×D3C22×C412yes—
261C3×C4×D3C2×Q812yes—
262C3×C4×D3C2×Q812yes—
263#627C4⋊C414yes—
264#626C4⋊C414yes—
265#626C4⋊C414yes—
266#625C4⋊C414yes—
267#624—81no—
268D3×Dic3—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C32×C8C22×C412yes—
272C3⋊(C3⋊C8)C22×C412yes—
273C3×C3⋊C8C22×C412yes—
274C3×C3⋊C8C22×C412yes—
275C2×#131—91no—
276#520—91no—
277#520—91no—
278#428—31no—
279#428—91no—
280#428—91no—
281#428—91no—
282#428—91no—
283#428—91no—
284#427—31no—
285#427—91no—
286#427—91no—
287C2×#106—91no—
288C2×#106—91no—
289C2×#106—91no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—61no—
293C2×#67—31no—
294C2×#67—31no—
295C2×#67—31no—
296C2×#67—31no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300#235—34no—
301#235—34no—
302#235—34no—
303#235—34no—
304C2×D12—31no—
305C2×D12—31no—
306C2×C4×D3—21no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
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×C4×D3C22×D311yescharacteristic
320C2×Dic6—31no—
321C2×Dic6—31no—
322C3×M16—34no—
323C2×C3×C8—21no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C2×C3×C8—34no—
327C2×C3×C8C22×D311yescharacteristic
328C2×C3×C8C22×D311yescharacteristic
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C42—61no—
344C3×C42—61no—
345C3×C42—61no—
346#217—61no—
347(C2×D3)⋊C4—21no—
348(C2×D3)⋊C4—21no—
349(C2×D3)⋊C4—21no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—121no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—31no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3C22×D311yescharacteristic
366C4⋊Dic3C22×D311yescharacteristic
367C4⋊Dic3C22×D311yescharacteristic
368C4⋊Dic3C22×D311yescharacteristic
369Dic3⋊C4—21no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—121no—
378C4×Dic3—21no—
379C4×Dic3—21no—
380C4×Dic3—21no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—121no—
388#208—34no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—34no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8C22×D311yescharacteristic
394C2×C3⋊C8C22×D311yescharacteristic
395ΓL(1,𝔽25)—34no—
396ΓL(1,𝔽25)—34no—
397ΓL(1,𝔽25)—34no—
398ΓL(1,𝔽25)—64no—
399ΓL(1,𝔽25)C4×D314yescomplemented
400D3×C8—34no—
401D3×C8—34no—
402D3×C8—34no—
403D3×C8C4×D314yescomplemented
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—21no—
406C2×C3⋊D3—21no—
407C2×C3⋊D3C2×C4⋊C412yes—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3C2×C4⋊C412yes—
413C2×C3×D3C2×C4⋊C412yes—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C23×C411yescharacteristic
417C32×C4C22×Q811yescharacteristic
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3⋊Dic3C2×C4⋊C412yes—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3C2×C4⋊C412yes—
426C3×Dic3C2×C4⋊C412yes—
427C2×#41—91no—
428#131—98no—
429C2×M16—31no—
430C2×M16—91no—
431C2×M16—91no—
432C22×C8—31no—
433C22×C8—91no—
434C22×C8—91no—
435C4×Q8—181no—
436C4×Q8—181no—
437C4×D4—181no—
438C4×D4—181no—
439C4×D4—181no—
440C4×D4—181no—
441C4×D4—181no—
442C4×D4—181no—
443#117—31no—
444#117—31no—
445#117—31no—
446#117—91no—
447#117—91no—
448#117—91no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—91no—
451C2×C4⋊C4—91no—
452C2×C4⋊C4—91no—
453C2×C4⋊C4—91no—
454C2×C4⋊C4—91no—
455#107—31no—
456#107—31no—
457#107—91no—
458#107—91no—
459#107—91no—
460#107D3211yescharacteristic
461#106—31no—
462#106—31no—
463#106—31no—
464#106—31no—
465#106—91no—
466#106—91no—
467#106—91no—
468#106—91no—
469#106—91no—
470#106—91no—
471C23×C3—31no—
472C23×C3—31no—
473C22×D3—31no—
474C22×D3—31no—
475C22×D3—61no—
476C22×D3D3×D411yescharacteristic
477C22×D3D3×D411yescharacteristic
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—241no—
496C2×C3×C4C23×D311yescharacteristic
497C2×C3×C4C23×D311yescharacteristic
498#67—34no—
499#67—34no—
500#67—34no—
501#67—34no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—31no—
507C2×Dic3—31no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—121no—
514C2×Dic3—121no—
515C2×Dic3—241no—
516C2×Dic3—241no—
517C2×Dic3—241no—
518C2×Dic3D3×D411yescharacteristic
519C2×Dic3D3×D411yescharacteristic
520D12—34no—
521D12—34no—
522C4×D3—32no—
523C4×D3—32no—
524C4×D3—32no—
525C4×D3—32no—
526C4×D3—62no—
527C4×D3—62no—
528C4×D3—81no—
529C4×D3—241no—
530C4×D3—241no—
531C4×D3—241no—
532C4×D3—241no—
533C4×D3—241no—
534C4×D3—241no—
535C4×D3—241no—
536C4×D3—242no—
537C4×D3C2×C4×D312yes—
538C4×D3C2×C4×D312yes—
539C4×D3D3×Q812yes—
540C4×D3D3×Q812yes—
541Dic6—34no—
542Dic6—34no—
543C3×C8—22no—
544C3×C8—32no—
545C3×C8—32no—
546C3×C8C2×C4×D312yes—
547C3×C8C2×C4×D312yes—
548C3⋊C8—32no—
549C3⋊C8—32no—
550C3⋊C8—62no—
551C3⋊C8C2×C4×D312yes—
552C3⋊C8C2×C4×D312yes—
553C2×C32C22×C4⋊C411yescharacteristic
554C2×C32#57711yescharacteristic
555C2×C32#57711yescharacteristic
556C3⋊D3—22no—
557C3×D3—22no—
558C3×D3—22no—
559#41—94no—
560#41—94no—
561C2×Q8—91no—
562C2×D4—91no—
563C2×D4—91no—
564C2×D4—91no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—61no—
568C22×C4—91no—
569C22×C4—181no—
570C22×C4—181no—
571C22×C4—181no—
572C22×C4—181no—
573C22×C4—181no—
574M16—34no—
575M16—94no—
576M16—94no—
577C2×C8—31no—
578C2×C8—31no—
579C2×C8—34no—
580C2×C8—94no—
581C2×C8—94no—
582C2×C8—91no—
583C2×C8C2×D3211yescharacteristic
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—31no—
588C4⋊C4—61no—
589C4⋊C4—91no—
590C4⋊C4—91no—
591C4⋊C4—181no—
592C4⋊C4—181no—
593C4⋊C4—181no—
594C4⋊C4—181no—
595C4⋊C4—181no—
596C4⋊C4C2×D3211yescharacteristic
597C4⋊C4C2×D3211yescharacteristic
598C22⋊C4—61no—
599C22⋊C4—61no—
600C22⋊C4—61no—
601C22⋊C4—181no—
602C22⋊C4—181no—
603C22⋊C4—181no—
604C42—61no—
605C42—61no—
606C42—61no—
607C42—181no—
608C42—181no—
609C42—181no—
610C22×C3—21no—
611C22×C3—32no—
612C22×C3—32no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3C2×D3×D411yescharacteristic
618C22×C3C2×D3×D411yescharacteristic
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—32no—
624C2×D3—32no—
625C2×D3—62no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3D3×C4⋊C412yes—
633C2×D3D3×C4⋊C412yes—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—32no—
637C3×C4—32no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—81no—
643C3×C4—81no—
644C3×C4—121no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4C22×C4×D311yescharacteristic
649C3×C4C22×C4×D311yescharacteristic
650C3×C4C2×D3×Q811yescharacteristic
651C3×C4C2×D3×Q811yescharacteristic
652Dic3—32no—
653Dic3—32no—
654Dic3—41no—
655Dic3—41no—
656Dic3—41no—
657Dic3—41no—
658Dic3—62no—
659Dic3—121no—
660Dic3—121no—
661Dic3—121no—
662Dic3—121no—
663Dic3—241no—
664Dic3—241no—
665Dic3D3×C4⋊C412yes—
666Dic3D3×C4⋊C412yes—
667C32#291211yescharacteristic, complemented, Sylow
668C23—31no—
669C23—31no—
670C23—91no—
671Q8—94no—
672D4—94no—
673D4—94no—
674D4—94no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—32no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—91no—
688C2×C4—92no—
689C2×C4—92no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—241no—
693C2×C4—721no—
694C2×C4—721no—
695C2×C4—721no—
696C2×C4—721no—
697C2×C4—721no—
698C2×C4C22×D3211yescharacteristic
699C8—32no—
700C8—32no—
701C8—92no—
702C8C4×D3212yes—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—62no—
707C2×C3—62no—
708C2×C3C2×D3×C4⋊C411yescharacteristic
709C2×C3C2×D3×C4⋊C411yescharacteristic
710C2×C3#577011yescharacteristic
711C2×C3#577011yescharacteristic
712C2×C3#577511yescharacteristic
713C2×C3#577811yescharacteristic
714D3—22no—
715D3—22no—
716D3—62no—
717D3—62no—
718D3—122no—
719C22—32no—
720C22—32no—
721C22—61no—
722C22—61no—
723C22—61no—
724C22—61no—
725C22—92no—
726C22—181no—
727C22—181no—
728C22D32×D411yescharacteristic
729C4—32no—
730C4—32no—
731C4—41no—
732C4—41no—
733C4—92no—
734C4—121no—
735C4—121no—
736C4—121no—
737C4—121no—
738C4—361no—
739C4—361no—
740C4C2×C4×D3211yescharacteristic
741C4D32×Q811yescharacteristic
742C3—21no—
743C3#7917811yescharacteristic, complemented
744C3#7920911yescharacteristic, complemented
745C2—62no—
746C2—62no—
747C2—182no—
748C2D32×C4⋊C411yescharacteristic
749C2#1059473611yescharacteristic
750C2#1059477011yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#3798C22
cosocleC2×C32×C4C24
hypercenter#107D32
hypocenterC32#2912
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
4. #10592580C2semidirect
5. C3×#4881C2semidirect
6. C3×#4880C2semidirect
7. #10590688C2semidirect
8. #10590683C2semidirect
9. D3×#817C2semidirect
10. #10590575C2semidirect
11. #10590574C2semidirect
12. #10590572C2semidirect
13. D3×#808C2semidirect
14. #10590437C2semidirect
15. #10590436C2semidirect
45. #63804C4semidirect
82. #4881D3semidirect
84. #4880D3semidirect
117. #3743C2×C4semidirect
131. C3×ΓL(1,𝔽25)C2×C4semidirect
132. C3×D3×C8C2×C4semidirect
141. #3711C2×C4semidirect
142. #3710C2×C4semidirect
143. D3×C3⋊C8C2×C4semidirect
399. ΓL(1,𝔽25)C4×D3semidirect
403. D3×C8C4×D3semidirect
667. C32#2912semidirect
743. C3#79178semidirect
744. C3#79209semidirect

Maximal subgroups

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

subgroupindex
C2×#638042
#105945112
#105945102
#105925802
C3×#48812
C3×#48802
#105906882
#105906832
D3×#8172
#105905752
#105905742
#105905722
D3×#8082
#105904372
#105904362
#792093
#791783