Finite Group Databasebeta

← #11866259

Subgroups — #11866259

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63798C211yesmaximal, characteristic
2C2×#63796C211yesmaximal, characteristic, complemented
3#10593996C211yesmaximal, characteristic, complemented
4#10593908C211yesmaximal, characteristic, complemented
5#10592538C211yesmaximal, characteristic, complemented
6C3×#4844C211yesmaximal, characteristic, complemented
7C3×#4841C211yesmaximal, characteristic, complemented
8#10590956C211yesmaximal, characteristic, complemented
9#10590751C211yesmaximal, characteristic, complemented
10#10590750C211yesmaximal, characteristic, complemented
11#10590748C211yesmaximal, characteristic, complemented
12#10590748C211yesmaximal, characteristic, complemented
13#10590691C211yesmaximal, characteristic, complemented
14#10590363C211yesmaximal, characteristic, complemented
15#10590348C211yesmaximal, characteristic, complemented
16#80537—31nomaximal
17#80430—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3797C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×#3743C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic
23#64081C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C3×#875C2211yescharacteristic, complemented
29C3×C4×D12C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×#869C2211yescharacteristic, complemented
32D3×(C2×D3)⋊C4—21no—
33D3×(C2×D3)⋊C4—21no—
34#63899—21no—
35#63899—21no—
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic
38#63879—21no—
39#63879—21no—
40#63873C2211yescharacteristic, complemented
41#63863C2211yescharacteristic, complemented
42#63854—21no—
43#63854—21no—
44#63849C2211yescharacteristic
45C2×#3715C2211yescharacteristic
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic
48C2×#3713C2211yescharacteristic
49#63798—24no—
50#63796—24no—
51C32×C4⋊C8C2211yescharacteristic, complemented
52#63641C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×D3×SD16—31no—
65C2×D3×SD16—31no—
66C2×#911—31no—
67#5724—31no—
68#5675—31no—
69#5545—31no—
70#5545—31no—
71C3×#463—31no—
72C3×#461—31no—
73#5165—31no—
74#5162—31no—
75#5162—31no—
76#5153—31no—
77#5083—31no—
78#5057—31no—
79#5019—31no—
80#5016—31no—
81#4844D311yescharacteristic, complemented
82#4841D311yescharacteristic, complemented
83#4839—31no—
84#4839—31no—
85#4839—61no—
86#4819—31no—
87#4818—31no—
88#4818—31no—
89#4804—31no—
90#4802—31no—
91#4802—31no—
92#4787—31no—
93#4772—31no—
94C22×D32—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3802—22no—
112#3802D414yes—
113#3797—22no—
114#3797—22no—
115#3796—22no—
116#3796—22no—
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C32×C42C2311yescharacteristic
120#3752D411yescharacteristic
121#3752D411yescharacteristic
122#3750D411yescharacteristic
123#3750D411yescharacteristic
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3743—22no—
128C8×C3⋊D3—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×D24—22no—
138C3×#204—22no—
139C3×#204—22no—
140C3×#204—22no—
141#3724—21no—
142#3724—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3715—22no—
150#3715—22no—
151#3715—22no—
152#3713—22no—
153#3042—91noSylow
154C2×#239—31no—
155C2×D3×Q8—31no—
156C2×D3×Q8—31no—
157C2×#237—31no—
158C2×D3×D4—31no—
159C2×D3×D4—31no—
160C2×C3×SD16—31no—
161C2×C3×SD16—31no—
162C2×C3×SD16—31no—
163C2×C3×D8—31no—
164C3×C4⋊Q8—31no—
165C3×#124—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168#947—31no—
169#944—31no—
170#944—31no—
171C2×#215—31no—
172C2×#215—31no—
173C2×#215—31no—
174#936—31no—
175D4×Dic3—31no—
176D4×Dic3—31no—
177C2×#214—31no—
178C2×#214—31no—
179C2×#214—31no—
180C2×#213—31no—
181C2×#213—31no—
182C4×#67—61no—
183C4×#67—61no—
184C2×(C2×D3)⋊C4—61no—
185C2×(C2×D3)⋊C4—61no—
186#914—64no—
187D3×SD16—64no—
188D3×SD16—64no—
189#911—64no—
190C2×D24C2×D311yescharacteristic
191C2×#204C2×D311yescharacteristic
192C2×#204C2×D311yescharacteristic
193C2×#204C2×D311yescharacteristic
194C2×ΓL(1,𝔽25)—31no—
195C2×ΓL(1,𝔽25)—31no—
196C2×ΓL(1,𝔽25)—61no—
197C2×D3×C8—31no—
198C2×D3×C8—31no—
199C2×D3×C8—61no—
200#896—61no—
201#896—61no—
202#894—61no—
203#894—61no—
204#893—31no—
205#893—31no—
206#892—31no—
207#892—31no—
208#883—61no—
209#883—61no—
210#67⋊C4—61no—
211#67⋊C4—61no—
212D3×C22⋊C4—61no—
213D3×C22⋊C4—61no—
214#878—61no—
215#878—61no—
216#875C2×D311yescharacteristic, complemented
217C4×D12C2×D311yescharacteristic
218C4×D12C2×D311yescharacteristic
219#872—31no—
220#872—31no—
221#872—61no—
222#869C2×D311yescharacteristic, complemented
223C3×C4⋊C8—21no—
224C3×C4⋊C8C2×D311yescharacteristic, complemented
225C3×C4⋊C8C2×D311yescharacteristic, complemented
226C3×#103—31no—
227C3×#103—31no—
228C3×#103—31no—
229C3×#102—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#832—31no—
234#821C2×D311yescharacteristic, complemented
235#816C2×D311yescharacteristic, complemented
236#816C2×D311yescharacteristic, complemented
237#816C2×D311yescharacteristic, complemented
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—31no—
242Dic3⋊C8—61no—
243Dic3⋊C8—61no—
244#810—31no—
245#810—31no—
246#810—31no—
247#809—31no—
248C4⋊(C3⋊C8)—31no—
249C4⋊(C3⋊C8)—31no—
250C4⋊(C3⋊C8)—61no—
251C22×C3⋊D3C2×D411yescharacteristic
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C2×D32—24no—
256C2×D32—81no—
257C2×D32—81no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C4×C3⋊D3C2×D412yes—
265C4×C3⋊D3#4112yes—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×D12C2×D412yes—
276C3×D12C2×D412yes—
277C3×C4×D3—81no—
278C3×C4×D3—81no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6—21no—
285#627—42no—
286#626—42no—
287#625—24no—
288#624—42no—
289D3×Dic3—42no—
290D3×Dic3—81no—
291D3×Dic3—81no—
292C32×C8—21no—
293C32×C8—21no—
294C3⋊(C3⋊C8)—21no—
295C3⋊(C3⋊C8)—21no—
296C2×AGL(1,ℤ/8)—91no—
297C22×SD16—91no—
298#536—91no—
299#518—91no—
300#463—31no—
301#463—91no—
302#463—91no—
303#463—91no—
304#461—31no—
305#461—91no—
306#461—91no—
307#461—91no—
308#424—91no—
309#419—91no—
310#416—91no—
311C23×D3—61no—
312C23×D3—61no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C22×Dic3—61no—
325C22×Dic3—61no—
326C22×Dic3—61no—
327#239—62no—
328#239—62no—
329D3×Q8—62no—
330D3×Q8—62no—
331D3×Q8—62no—
332D3×Q8—62no—
333#237—62no—
334#237—62no—
335D3×D4—34no—
336D3×D4—34no—
337D3×D4—62no—
338D3×D4—62no—
339C2×D12—61no—
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—21no—
344C2×C4×D3—21no—
345C2×C4×D3—31no—
346C2×C4×D3—31no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3—61no—
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×Dic6—61no—
354C2×Dic6—61no—
355C2×Dic6C22×D311yescharacteristic
356C2×Dic6C22×D311yescharacteristic
357C2×Dic6C22×D311yescharacteristic
358C3×SD16—62no—
359C3×SD16—62no—
360C3×SD16—62no—
361C3×D8—62no—
362C2×C3×C8—21no—
363C2×C3×C8—21no—
364C2×C3×C8C22×D311yescharacteristic
365C2×C3×C8C22×D311yescharacteristic
366C2×C3×C8C22×D311yescharacteristic
367C2×C3×C8C22×D311yescharacteristic
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C42—21no—
377C3×C42C22×D311yescharacteristic
378C3×C42C22×D311yescharacteristic
379#217—61no—
380#217—61no—
381#217—61no—
382#217—61no—
383#215—62no—
384#215—62no—
385#215—62no—
386#214—62no—
387#214—62no—
388#214—62no—
389#213—62no—
390#213—62no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—21no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—31no—
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—31no—
398(C2×D3)⋊C4—31no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—61no—
405(C2×D3)⋊C4—61no—
406(C2×D3)⋊C4—61no—
407C4⋊Dic3—21no—
408C4⋊Dic3—21no—
409C4⋊Dic3C22×D311yescharacteristic
410C4⋊Dic3C22×D311yescharacteristic
411Dic3⋊C4—31no—
412Dic3⋊C4—31no—
413Dic3⋊C4—31no—
414Dic3⋊C4—31no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C2×C3⋊C8—31no—
427C2×C3⋊C8—31no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—61no—
431C2×C3⋊C8—61no—
432D24—22no—
433#204—22no—
434#204—22no—
435#204—22no—
436ΓL(1,𝔽25)—62no—
437ΓL(1,𝔽25)—62no—
438ΓL(1,𝔽25)—122no—
439D3×C8—62no—
440D3×C8—62no—
441D3×C8—122no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—21no—
444C2×C3⋊D3—21no—
445C2×C3⋊D3#12112yes—
446C2×C3×D3—22no—
447C2×C3×D3—22no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455D32—84no—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4C22×D411yescharacteristic
459C32×C4C2×#4111yescharacteristic
460C3⋊Dic3—21no—
461C3⋊Dic3—21no—
462C3⋊Dic3#12112yes—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3—41no—
468C2×#41—91no—
469C22×Q8—91no—
470C22×D4—91no—
471AGL(1,ℤ/8)—184no—
472C2×SD16—31no—
473C2×SD16—31no—
474C2×SD16—31no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—184no—
479C2×D8—31no—
480C2×D8—91no—
481C2×M16—91no—
482C22×C8—91no—
483C4⋊Q8—31no—
484C4⋊Q8—91no—
485#124—31no—
486#124—91no—
487#123—181no—
488#123—181no—
489C22⋊Q8—181no—
490C22⋊Q8—181no—
491C4×D4—31no—
492C4×D4—31no—
493C4×D4—91no—
494C4×D4—91no—
495C4×D4—181no—
496C4×D4—181no—
497#117—91no—
498#117—91no—
499C2×C22⋊C4—181no—
500C2×C22⋊C4—181no—
501C4⋊C8—91no—
502C4⋊C8—91no—
503C4⋊C8—91no—
504C4⋊C8D3211yescharacteristic, complemented
505#103—31no—
506#103—31no—
507#103—31no—
508#103—91no—
509#103—91no—
510#103—91no—
511#102—31no—
512#102—91no—
513C23×C3—61no—
514C23×C3—61no—
515C23×C3—61no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3—31no—
520C22×D3—31no—
521C22×D3—61no—
522C22×D3—64no—
523C22×D3—64no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3—241no—
528C3×Q8—61no—
529C3×Q8—61no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×Q8—61no—
534C3×D4—32no—
535C3×D4—32no—
536C3×D4—61no—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—61no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—241no—
549C2×C3×C4—241no—
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4D3×D411yescharacteristic
553C2×C3×C4D3×D411yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—64no—
557#67—64no—
558#67—122no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—31no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—122no—
574C2×Dic3—241no—
575C2×Dic3—241no—
576D12—21no—
577D12—21no—
578D12—21no—
579D12—21no—
580D12—122no—
581D12D3×D412yes—
582D12D3×D412yes—
583C4×D3—32no—
584C4×D3—32no—
585C4×D3—32no—
586C4×D3—32no—
587C4×D3—62no—
588C4×D3—62no—
589C4×D3—81no—
590C4×D3—81no—
591C4×D3—122no—
592C4×D3—122no—
593C4×D3—122no—
594C4×D3—241no—
595C4×D3—241no—
596Dic6—21no—
597Dic6—21no—
598Dic6—21no—
599Dic6—21no—
600Dic6—21no—
601Dic6—21no—
602Dic6—122no—
603Dic6—122no—
604C3×C8—21no—
605C3×C8—21no—
606C3×C8—21no—
607C3×C8—21no—
608C3×C8—41no—
609C3×C8—41no—
610C3⋊C8—61no—
611C3⋊C8—61no—
612C3⋊C8—61no—
613C3⋊C8—61no—
614C3⋊C8—121no—
615C3⋊C8—121no—
616C2×C32C2×#12111yescharacteristic
617C2×C32#57711yescharacteristic
618C2×C32#57711yescharacteristic
619C3⋊D3—22no—
620C3×D3—42no—
621C3×D3—42no—
622C3×D3—81no—
623C24—181no—
624#41—182no—
625#41—182no—
626C2×Q8—31no—
627C2×Q8—31no—
628C2×Q8—31no—
629C2×Q8—181no—
630C2×Q8—182no—
631C2×Q8—182no—
632C2×D4—31no—
633C2×D4—31no—
634C2×D4—31no—
635C2×D4—94no—
636C2×D4—181no—
637C2×D4—182no—
638C2×D4—181no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—91no—
642C22×C4—181no—
643C22×C4—181no—
644C22×C4—181no—
645C22×C4—181no—
646SD16—62no—
647SD16—62no—
648SD16—62no—
649SD16—182no—
650SD16—182no—
651SD16—182no—
652D8—62no—
653D8—182no—
654M16—182no—
655C2×C8—91no—
656C2×C8—91no—
657C2×C8—182no—
658C2×C8C2×D3211yescharacteristic
659C2×C8C2×D3211yescharacteristic
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—91no—
673C22⋊C4—91no—
674C22⋊C4—181no—
675C22⋊C4—181no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C42—91no—
680C42—181no—
681C42C2×D3211yescharacteristic
682C22×C3—21no—
683C22×C3—62no—
684C22×C3—62no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3C2×D3×D411yescharacteristic
693C22×C3C2×D3×D411yescharacteristic
694C2×D3—22no—
695C2×D3—22no—
696C2×D3—32no—
697C2×D3—32no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—62no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—244no—
713C2×D3—244no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727C3×C4C2×D3×D411yescharacteristic
728C3×C4C2×D3×D411yescharacteristic
729C3×C4D3×#4111yescharacteristic
730C3×C4D3×#4111yescharacteristic
731Dic3—32no—
732Dic3—32no—
733Dic3—41no—
734Dic3—41no—
735Dic3—41no—
736Dic3—41no—
737Dic3—41no—
738Dic3—62no—
739Dic3—61no—
740Dic3—61no—
741Dic3—61no—
742Dic3—61no—
743Dic3—121no—
744Dic3—121no—
745C32#304211yescharacteristic, complemented, Sylow
746C23—61no—
747C23—61no—
748C23—61no—
749C23—91no—
750C23—184no—
751C23—721no—
752C23—721no—
753Q8—61no—
754Q8—61no—
755Q8—61no—
756Q8—61no—
757Q8—61no—
758Q8—61no—
759Q8—362no—
760D4—32no—
761D4—32no—
762D4—61no—
763D4—61no—
764D4—61no—
765D4—61no—
766D4—184no—
767D4—362no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—91no—
774C2×C4—92no—
775C2×C4—92no—
776C2×C4—91no—
777C2×C4—91no—
778C2×C4—241no—
779C2×C4—241no—
780C2×C4—362no—
781C2×C4—362no—
782C2×C4—721no—
783C2×C4—721no—
784C2×C4#380211yescharacteristic
785C2×C4#380211yescharacteristic
786C2×C4C22×D3211yescharacteristic
787C8—21no—
788C8—21no—
789C8—181no—
790C8—181no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—122no—
795C2×C3—122no—
796C2×C3—241no—
797C2×C3D3×#12111yescharacteristic
798C2×C3D3×#12111yescharacteristic
799C2×C3#576211yescharacteristic
800C2×C3#577011yescharacteristic
801C2×C3#577511yescharacteristic
802C2×C3#577811yescharacteristic
803D3—42no—
804D3—42no—
805D3—62no—
806D3—62no—
807D3—81no—
808D3—122no—
809C22—62no—
810C22—62no—
811C22—92no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—181no—
820C22—181no—
821C22—724no—
822C22C2×#380211yescharacteristic
823C4—21no—
824C4—21no—
825C4—92no—
826C4—121no—
827C4—121no—
828C4—121no—
829C4—121no—
830C4—121no—
831C4—181no—
832C4—181no—
833C4D32×D411yescharacteristic
834C4#6431911yescharacteristic
835C3—21no—
836C3#8043011yescharacteristic, complemented
837C3#8053711yescharacteristic, complemented
838C2—122no—
839C2—122no—
840C2—182no—
841C2—241no—
842C2#1059461211yescharacteristic
843C2#1059468611yescharacteristic
844C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#63798C2
hypercenterC4⋊C8D32
hypocenterC32#3042
LCSG ▷ C2×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. C2×#63796C2semidirect
3. #10593996C2semidirect
4. #10593908C2semidirect
5. #10592538C2semidirect
6. C3×#4844C2semidirect
7. C3×#4841C2semidirect
8. #10590956C2semidirect
9. #10590751C2semidirect
10. #10590750C2semidirect
11. #10590748C2semidirect
12. #10590748C2semidirect
13. #10590691C2semidirect
14. #10590363C2semidirect
15. #10590348C2semidirect
28. C3×#875C22semidirect
31. C3×#869C22semidirect
40. #63873C22semidirect
41. #63863C22semidirect
51. C32×C4⋊C8C22semidirect
52. #63641C22semidirect
53. #63641C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#821C22semidirect
56. C3×#816C22semidirect
57. C3×#816C22semidirect
58. C3×#816C22semidirect
59. #63565C22semidirect
60. #63565C22semidirect
61. #63565C22semidirect
62. #63562C22semidirect
81. #4844D3semidirect
82. #4841D3semidirect
216. #875C2×D3semidirect
222. #869C2×D3semidirect
224. C3×C4⋊C8C2×D3semidirect
225. C3×C4⋊C8C2×D3semidirect
234. #821C2×D3semidirect
235. #816C2×D3semidirect
236. #816C2×D3semidirect
237. #816C2×D3semidirect
504. C4⋊C8D32semidirect
745. C32#3042semidirect
836. C3#80430semidirect
837. C3#80537semidirect

Maximal subgroups

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

subgroupindex
C2×#637982
C2×#637962
#105939962
#105939082
#105925382
C3×#48442
C3×#48412
#105909562
#105907512
#105907502
#105907482
#105906912
#105903632
#105903482
#805373
#804303