Finite Group Databasebeta

← #11860950

Subgroups — #11860950

Order 1152.

1029 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63806C211yesmaximal, characteristic
2#10593890C211yesmaximal, characteristic, complemented
3#10593887C211yesmaximal, characteristic, complemented
4C4×#3744C211yesmaximal, characteristic, complemented
5C3×C4×#204C211yesmaximal, characteristic, complemented
6C3×#4689C211yesmaximal, characteristic, complemented
7#10590794C211yesmaximal, characteristic, complemented
8#10590758C211yesmaximal, characteristic, complemented
9Dic3×#204C211yesmaximal, characteristic, complemented
10#10590746C211yesmaximal, characteristic, complemented
11D3×#817C211yesmaximal, characteristic, complemented
12#10590671C211yesmaximal, characteristic, complemented
13#10590670C211yesmaximal, characteristic, complemented
14#10590383C211yesmaximal, characteristic, complemented
15#10590346C211yesmaximal, characteristic, complemented
16#79650—31nomaximal
17#78574—31nomaximal
18C2×#3799C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×#3744C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
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—
30#63894C2211yescharacteristic
31Dic3×D12C2211yescharacteristic
32D3×C4⋊Dic3C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63883—21no—
35#63881—21no—
36#63880—21no—
37#63879—21no—
38#63878—21no—
39D3×Dic3⋊C4—21no—
40#63844C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42#63836—21no—
43C2×#3719C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45#63806C418yescomplemented
46C32×C4×C8C2211yescharacteristic
47#63648C2211yescharacteristic
48#63644C2211yescharacteristic
49#63643C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×#803C2211yescharacteristic
56#63573C2211yescharacteristic
57#63573C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63564C2211yescharacteristic
61#63563C2211yescharacteristic
62C2×#916—31no—
63C2×#904—31no—
64#5574—31no—
65#5546—31no—
66#5523—31no—
67#5523—31no—
68C3×C4×SD16—31no—
69C3×#405—31no—
70Dic3×SD16—31no—
71#5133—31no—
72#5133—31no—
73C2×#817—31no—
74#5030—31no—
75#5014—31no—
76D3×#106—31no—
77#4852—31no—
78#4803—31no—
79#4789—31no—
80#4785—31no—
81#4771—31no—
82#4716—31no—
83#4716—31no—
84#4711—31no—
85#4711—31no—
86C4×#204—31no—
87C4×#204—31no—
88C4×#204—31no—
89C4×#204—31no—
90C4×#204—61no—
91C4×#204D311yescharacteristic, complemented
92#4689D311yescharacteristic, complemented
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×#626—21no—
101C2×#625—21no—
102C2×#624—21no—
103C2×#624—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3799—22no—
109#3799C2×C414yescomplemented
110#3795—22no—
111#3795C2×C414yescomplemented
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C42C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3—21no—
120#3744C2×C414yescomplemented
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×#204C2×C414yescomplemented
134C3×ΓL(1,𝔽25)—22no—
135C3×D3×C8C2×C414yescomplemented
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143Dic32—21no—
144#3719C2×C414yescomplemented
145#3714C2×C414yescomplemented
146#2952—91noSylow
147C2×#239—31no—
148C2×#237—31no—
149C2×#235—31no—
150C2×#235—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×#213—31no—
161C4×#67—61no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—31no—
164C2×Dic3⋊C4—61no—
165#916—38no—
166C2×Dic12—31no—
167#904—38no—
168C2×D24—31no—
169C2×#204—31no—
170C2×#204—31no—
171C2×#204—61no—
172C2×#204C2×D311yescharacteristic
173C2×ΓL(1,𝔽25)C2×D311yescharacteristic
174C2×D3×C8C2×D311yescharacteristic
175#893—31no—
176#893—61no—
177#892—61no—
178#892—61no—
179D3×C4⋊C4—31no—
180D3×C4⋊C4—31no—
181D3×C4⋊C4—61no—
182D3×C4⋊C4—61no—
183D3×C4⋊C4—61no—
184#887—31no—
185#67⋊C4—61no—
186#67⋊C4—61no—
187#67⋊C4—61no—
188#67⋊C4—61no—
189#67⋊C4—61no—
190#877—61no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—61no—
196C4×D12—61no—
197C4×D12C2×D311yescharacteristic
198#872—61no—
199#872C2×D311yescharacteristic
200C4×Dic6—31no—
201C4×Dic6—31no—
202C4×Dic6—31no—
203C4×Dic6—31no—
204C4×Dic6—61no—
205C4×Dic6C2×D311yescharacteristic
206C3×#106—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×#97—31no—
210C3×#97—31no—
211C3×C4×C8—21no—
212C3×C4×C8—31no—
213C3×C4×C8C2×D311yescharacteristic
214C3×C4×C8C2×D311yescharacteristic
215#835—31no—
216#832—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—61no—
222#821C2×D311yescharacteristic
223#817—31no—
224#817—31no—
225#817—31no—
226#817—31no—
227#817—61no—
228#817C2×D311yescharacteristic
229#816—31no—
230#816—31no—
231#816—31no—
232#816—31no—
233#816—61no—
234#816C2×D311yescharacteristic
235#815C2×D311yescharacteristic
236C8×Dic3C2×D311yescharacteristic
237#810—31no—
238#809—31no—
239#808—31no—
240#808—31no—
241#803C2×D311yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)C22×C412yes—
253C4×C3⋊D3—81no—
254#634—21no—
255#634C22×C412yes—
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×D12—21no—
263C3×D12C22×C412yes—
264C3×C4×D3—81no—
265C3×C4×D3C22×C412yes—
266C3×C4×D3#4112yes—
267C3×Dic6—21no—
268C3×Dic6C22×C412yes—
269#626—24no—
270#625—24no—
271#624—24no—
272#624—81no—
273D3×Dic3—24no—
274D3×Dic3—81no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C32×C8C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282#520—91no—
283#520—91no—
284#442—91no—
285#442—91no—
286#441—91no—
287#441—91no—
288C4×SD16—31no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292C2×#106—91no—
293#417—91no—
294#417—91no—
295#405—31no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—61no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307#239—34no—
308#239—62no—
309#237—34no—
310#237—62no—
311#235—34no—
312#235—34no—
313#235—62no—
314#235—62no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12C22×D311yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—34no—
338C3×M16—62no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—34no—
343C2×C3×C8—31no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—61no—
356C3×C42—21no—
357C3×C42—31no—
358C3×C42—61no—
359C3×C42C22×D311yescharacteristic
360C3×C42C22×D311yescharacteristic
361#217—61no—
362#216—34no—
363#213—34no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—121no—
371(C2×D3)⋊C4D1211yescharacteristic
372(C2×D3)⋊C4D1211yescharacteristic
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—121no—
393Dic3⋊C4D1211yescharacteristic
394Dic3⋊C4D1211yescharacteristic
395C4×Dic3—21no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—121no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12—34no—
407D24—34no—
408#204—34no—
409#204—34no—
410#204—64no—
411#204C4×D314yescomplemented
412ΓL(1,𝔽25)—22no—
413D3×C8C4×D314yescomplemented
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—22no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424C32×C4—21no—
425C32×C4—21no—
426C32×C4C23×C411yescharacteristic
427C32×C4C2×#4111yescharacteristic
428C3⋊Dic3—22no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3C4×D412yes—
437C2×#41—91no—
438C2×#41—91no—
439#135—98no—
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×D8—91no—
444C2×M16—31no—
445C22×C8—31no—
446C4×Q8—31no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×D4—31no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—91no—
454C4×D4—181no—
455C4×D4—181no—
456C4×D4—181no—
457C4×D4—181no—
458#117—31no—
459#117—181no—
460#117—181no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—181no—
464C2×C4⋊C4—181no—
465#106—31no—
466#106—91no—
467#106—91no—
468#106—91no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#97—31no—
478#97—31no—
479C4×C8—31no—
480C4×C8D3211yescharacteristic
481C23×C3—31no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3C2×D1211yescharacteristic
488C3×Q8—32no—
489C3×Q8—61no—
490C3×D4—32no—
491C3×D4—61no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—32no—
497C2×C3×C4—32no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—241no—
504C2×C3×C4C2×D1211yescharacteristic
505C2×C3×C4C2×D1211yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—64no—
511#67—64no—
512#67—64no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—64no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—241no—
527C2×Dic3—241no—
528C2×Dic3—241no—
529C2×Dic3C2×D1211yescharacteristic
530C2×Dic3C2×D1211yescharacteristic
531C2×Dic3C2×D1211yescharacteristic
532D12—21no—
533D12—32no—
534D12—32no—
535D12—62no—
536D12—64no—
537D12—61no—
538D12—61no—
539D12—121no—
540D12C2×C4×D312yes—
541C4×D3—64no—
542C4×D3—64no—
543C4×D3—64no—
544C4×D3—81no—
545C4×D3—241no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—241no—
551C4×D3—241no—
552C4×D3—242no—
553C4×D3C2×C4×D312yes—
554C4×D3#23512yes—
555Dic6—21no—
556Dic6—32no—
557Dic6—32no—
558Dic6—62no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562Dic6C2×C4×D312yes—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—22no—
566C3×C8—32no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8C2×C4×D312yes—
570C3×C8C2×C4×D312yes—
571C3⋊C8—21no—
572C3⋊C8C2×C4×D312yes—
573C2×C32C2×C4×D411yescharacteristic
574C2×C32#57711yescharacteristic
575C2×C32#57711yescharacteristic
576C3⋊D3—42no—
577C3×D3—22no—
578C3×D3—42no—
579#41—94no—
580#41—94no—
581#41—182no—
582#41—182no—
583C2×Q8—31no—
584C2×Q8—91no—
585C2×D4—31no—
586C2×D4—91no—
587C2×D4—181no—
588C2×D4—181no—
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—181no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598Q16—94no—
599SD16—34no—
600SD16—94no—
601D8—94no—
602M16—62no—
603C2×C8—31no—
604C2×C8—34no—
605C2×C8—31no—
606C2×C8C2×D3211yescharacteristic
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—31no—
627C42—61no—
628C42—181no—
629C42—181no—
630C42—181no—
631C42C2×D3211yescharacteristic
632C22×C3—21no—
633C22×C3—32no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—62no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3C22×D1211yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—122no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—241no—
654C2×D3—241no—
655C2×D3C4×D1212yes—
656C3×C4—22no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—32no—
664C3×C4—41no—
665C3×C4—62no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C22×C4×D311yescharacteristic
671C3×C4C22×C4×D311yescharacteristic
672C3×C4C2×#23511yescharacteristic
673C3×C4D3×#4111yescharacteristic
674Dic3—21no—
675Dic3—21no—
676Dic3—22no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—62no—
681Dic3—122no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—241no—
687Dic3—241no—
688Dic3C4×D1212yes—
689C32#295211yescharacteristic, complemented, Sylow
690C23—31no—
691C23—61no—
692C23—181no—
693Q8—32no—
694Q8—61no—
695Q8—92no—
696Q8—181no—
697D4—32no—
698D4—61no—
699D4—92no—
700D4—184no—
701D4—184no—
702D4—181no—
703C2×C4—31no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—184no—
712C2×C4—184no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—241no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4—721no—
722C2×C4D3×D1211yescharacteristic
723C2×C4D3×D1211yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—21no—
726C8—32no—
727C8—61no—
728C8C4×D3212yes—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—62no—
733C2×C3—122no—
734C2×C3C2×C4×D1211yescharacteristic
735C2×C3C4×D3×D411yescharacteristic
736C2×C3#575111yescharacteristic
737C2×C3#575111yescharacteristic
738C2×C3#576211yescharacteristic
739C2×C3#577011yescharacteristic
740D3—22no—
741D3—42no—
742D3—122no—
743D3—122no—
744D3—242no—
745C22—32no—
746C22—61no—
747C22—61no—
748C22—62no—
749C22—121no—
750C22—121no—
751C22—182no—
752C22—361no—
753C22—361no—
754C22C2×D3×D1211yescharacteristic
755C4—21no—
756C4—21no—
757C4—32no—
758C4—61no—
759C4—61no—
760C4—62no—
761C4—121no—
762C4—121no—
763C4—182no—
764C4—361no—
765C4—361no—
766C4C2×C4×D3211yescharacteristic
767C4D3×#23511yescharacteristic
768C3—21no—
769C3#7857411yescharacteristic, complemented
770C3#7965011yescharacteristic, complemented
771C2—62no—
772C2—122no—
773C2—362no—
774C2C4×D3×D1211yescharacteristic
775C2#1059467711yescharacteristic
776C2#1059467911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#63806C2
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593890C2semidirect
3. #10593887C2semidirect
4. C4×#3744C2semidirect
5. C3×C4×#204C2semidirect
6. C3×#4689C2semidirect
7. #10590794C2semidirect
8. #10590758C2semidirect
9. Dic3×#204C2semidirect
10. #10590746C2semidirect
11. D3×#817C2semidirect
12. #10590671C2semidirect
13. #10590670C2semidirect
14. #10590383C2semidirect
15. #10590346C2semidirect
45. #63806C4semidirect
91. C4×#204D3semidirect
92. #4689D3semidirect
109. #3799C2×C4semidirect
111. #3795C2×C4semidirect
120. #3744C2×C4semidirect
133. C3×#204C2×C4semidirect
135. C3×D3×C8C2×C4semidirect
144. #3719C2×C4semidirect
145. #3714C2×C4semidirect
411. #204C4×D3semidirect
413. D3×C8C4×D3semidirect
689. C32#2952semidirect
769. C3#78574semidirect
770. C3#79650semidirect

Maximal subgroups

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

subgroupindex
C2×#638062
#105938902
#105938872
C4×#37442
C3×C4×#2042
C3×#46892
#105907942
#105907582
Dic3×#2042
#105907462
D3×#8172
#105906712
#105906702
#105903832
#105903462
#796503
#785743