Finite Group Databasebeta

← #11861691

Subgroups — #11861691

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594839C211yesmaximal, characteristic
2C8×#638C211yesmaximal, characteristic, complemented
3C3×C8×#67C211yesmaximal, characteristic, complemented
4C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
5#10591157C211yesmaximal, characteristic, complemented
6#10591155C211yesmaximal, characteristic, complemented
7#10591063C211yesmaximal, characteristic, complemented
8#10590785C211yesmaximal, characteristic, complemented
9C8×#627C211yesmaximal, characteristic, complemented
10#10590730C211yesmaximal, characteristic, complemented
11C8×#626C211yesmaximal, characteristic, complemented
12#10590700C211yesmaximal, characteristic, complemented
13#10590696C211yesmaximal, characteristic, complemented
14#10590692C211yesmaximal, characteristic, complemented
15#10590648C211yesmaximal, characteristic, complemented
16#79400—31nomaximal
17#78448—31nomaximal
18C22×C32×C8C2211yescharacteristic
19C4×#638C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C3×C4×#67C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25#63978C411yescharacteristic
26#63966C411yescharacteristic
27#63964C411yescharacteristic
28#63961C411yescharacteristic
29C4×#627C2211yescharacteristic
30C4×#626C2211yescharacteristic
31#63874C2211yescharacteristic
32#63868C411yescharacteristic
33#63867C411yescharacteristic
34#63859C411yescharacteristic
35#63855C2211yescharacteristic
36#63852C411yescharacteristic
37C2×#3712C2211yescharacteristic
38C2×#3711C2211yescharacteristic
39#63657C2211yescharacteristic
40#63647C2211yescharacteristic
41#63641C2211yescharacteristic
42C8×C3⋊Dic3C2211yescharacteristic
43C3×#830C2211yescharacteristic
44C3×(C2×D3)⋊C8C2211yescharacteristic
45C3×Dic3⋊C8C2211yescharacteristic
46C3×C8×Dic3C2211yescharacteristic
47C3×C8×Dic3C2211yescharacteristic
48C3×C8×Dic3C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51#63572C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63557C2211yescharacteristic
56(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
57#63555C2211yescharacteristic
58#63554C2211yescharacteristic
59#63554C2211yescharacteristic
60#63554C2211yescharacteristic
61#5538—31no—
62#5479—31no—
63C3×C8×D4—31no—
64C2×C3×C4×C8—31no—
65#5111—31no—
66#5111—31no—
67C8×#67—31no—
68C8×#67—31no—
69C8×#67—31no—
70C8×#67—61no—
71C8×#67D311yescharacteristic, complemented
72#5101—31no—
73C2×C8×Dic3D311yescharacteristic, complemented
74#5011—31no—
75#4926—31no—
76#4840—31no—
77#4828—31no—
78#4730—31no—
79#4729—31no—
80#4720—31no—
81#4719—31no—
82#4690—31no—
83#4690—31no—
84#4689—31no—
85#4689—31no—
86#4689—31no—
87#4688—31no—
88C8×D12—31no—
89#4679—31no—
90C8×Dic6—31no—
91C8×Dic6—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638C2×C411yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×#67C2×C411yescharacteristic
96C22×C3×Dic3C2×C411yescharacteristic
97C22×C3×Dic3C2×C411yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×#627C2×C411yescharacteristic
100C2×#626C2×C411yescharacteristic
101C2×C32×C8—22no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104#3757C2×C411yescharacteristic
105#3752C2×C411yescharacteristic
106#3750C2×C411yescharacteristic
107C4×C3⋊Dic3C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C8×C3⋊D3—22no—
111C3×#217C2×C411yescharacteristic
112C3×(C2×D3)⋊C4C2×C411yescharacteristic
113C3×Dic3⋊C4C2×C411yescharacteristic
114C3×C4×Dic3C2×C411yescharacteristic
115C3×C4×Dic3C2×C411yescharacteristic
116C3×C4×Dic3C2311yescharacteristic
117C3×C4×Dic3C2311yescharacteristic
118C3×C4×Dic3C2311yescharacteristic
119C2×C3×C3⋊C8—22no—
120C2×C3×C3⋊C8C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C3×D3×C8—22no—
125#3724C2×C411yescharacteristic
126#3724C2×C411yescharacteristic
127#3724C2×C411yescharacteristic
128Dic3⋊Dic3C2×C411yescharacteristic
129Dic3⋊Dic3C2×C411yescharacteristic
130Dic3⋊Dic3C2×C411yescharacteristic
131Dic3⋊Dic3C2×C411yescharacteristic
132Dic3⋊Dic3C2×C411yescharacteristic
133#3722C2×C411yescharacteristic
134#3722C2×C411yescharacteristic
135#3722C2×C411yescharacteristic
136(C2×D3)⋊Dic3C2×C411yescharacteristic
137(C2×D3)⋊Dic3C2×C411yescharacteristic
138(C2×D3)⋊Dic3C2×C411yescharacteristic
139#3712—22no—
140#3711—22no—
141#2966—91noSylow
142C22×C3×C8—21no—
143C22×C3×C8—31no—
144C22×C3×C8—31no—
145C22×C3×C8C2×D311yescharacteristic
146C22×C3×C8C2×D311yescharacteristic
147C3×C4×D4—31no—
148C2×C3×C42—31no—
149#939—31no—
150#935—31no—
151#930—31no—
152#929—31no—
153#929—31no—
154C4×#67—31no—
155C4×#67—31no—
156C4×#67—31no—
157C4×#67—61no—
158C4×#67C2×D311yescharacteristic
159#926—31no—
160#924—31no—
161C2×C4×Dic3C2×D311yescharacteristic
162C2×#208—31no—
163C22×C3⋊C8C2×D311yescharacteristic
164C2×ΓL(1,𝔽25)—31no—
165C2×ΓL(1,𝔽25)—31no—
166C2×ΓL(1,𝔽25)—31no—
167C2×D3×C8—31no—
168C2×D3×C8—31no—
169C2×D3×C8—61no—
170C2×D3×C8C2×D311yescharacteristic
171#898—31no—
172#889—31no—
173#886—31no—
174#885—31no—
175#879—31no—
176#878—31no—
177#876—31no—
178#876—31no—
179#875—31no—
180C4×D12—31no—
181#872—31no—
182#872—31no—
183#872—31no—
184#870—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C3×C4⋊C8—31no—
188C3×C22⋊C8—31no—
189C3×C22⋊C8—31no—
190C3×C4×C8—31no—
191C3×C4×C8—31no—
192C3×C4×C8—31no—
193C3×C4×C8—31no—
194C3×C4×C8—31no—
195#830—31no—
196#830—31no—
197#830—31no—
198#830—61no—
199#830C2×D311yescharacteristic
200(C2×D3)⋊C8—31no—
201(C2×D3)⋊C8—31no—
202(C2×D3)⋊C8—31no—
203(C2×D3)⋊C8—31no—
204(C2×D3)⋊C8—31no—
205(C2×D3)⋊C8—61no—
206(C2×D3)⋊C8C2×D311yescharacteristic
207#815—31no—
208#815—31no—
209#815—31no—
210#815—31no—
211#815—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—61no—
220Dic3⋊C8C2×D311yescharacteristic
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—61no—
224C8×Dic3C2×D311yescharacteristic
225C8×Dic3C2×D311yescharacteristic
226C8×Dic3C2×D311yescharacteristic
227C8×Dic3C2×D311yescharacteristic
228C8×Dic3C2×D311yescharacteristic
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232#803—31no—
233#803—31no—
234#803—31no—
235C23×C32C22×C411yescharacteristic
236C22×C3⋊D3C22×C411yescharacteristic
237C22×C3×D3C22×C411yescharacteristic
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C22×C411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242#638—22no—
243C2×C3⋊Dic3C22×C411yescharacteristic
244C2×C3⋊Dic3C22×C411yescharacteristic
245C2×C3⋊Dic3C22×C411yescharacteristic
246C4×C3⋊D3—21no—
247C4×C3⋊D3—21no—
248C3×#67—22no—
249C2×C3×Dic3—22no—
250C2×C3×Dic3—22no—
251C2×C3×Dic3C22×C411yescharacteristic
252C2×C3×Dic3C22×C411yescharacteristic
253C2×C3×Dic3C22×C411yescharacteristic
254C2×C3×Dic3C22×C411yescharacteristic
255C2×C3×Dic3C22×C411yescharacteristic
256C2×C3×Dic3C22×C411yescharacteristic
257C2×C3×Dic3C22×C411yescharacteristic
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260#627—22no—
261#626—22no—
262C32×C8—21no—
263C32×C8#4112yes—
264C3⋊(C3⋊C8)—21no—
265C3⋊(C3⋊C8)—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269C3×C3⋊C8#4112yes—
270#529—91no—
271#446—91no—
272C8×Q8—91no—
273#436—91no—
274#435—91no—
275#435—91no—
276C8×D4—31no—
277C8×D4—91no—
278C8×D4—91no—
279#433—91no—
280#433—91no—
281#432—91no—
282#405—91no—
283#405—91no—
284C2×C4×C8—31no—
285C2×C3×D4—31no—
286C22×C3×C4—21no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C2×#67—31no—
293C2×#67—31no—
294C2×#67—31no—
295C2×#67—61no—
296C2×#67C4×D311yescharacteristic
297C22×Dic3C4×D311yescharacteristic
298C22×Dic3C4×D311yescharacteristic
299C2×D12—31no—
300C2×C4×D3—31no—
301C2×C4×D3—31no—
302C2×C4×D3—61no—
303C2×C4×D3C22×D311yescharacteristic
304C2×Dic6—31no—
305C2×Dic6—31no—
306C2×C3×C8—22no—
307C2×C3×C8—22no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8—42no—
315C2×C3×C8—62no—
316C2×C3×C8—62no—
317C2×C3×C8C22×D311yescharacteristic
318C2×C3×C8C22×D311yescharacteristic
319C2×C3×C8C22×D311yescharacteristic
320C2×C3×C8C22×D311yescharacteristic
321C3×C4⋊C4—31no—
322C3×C22⋊C4—31no—
323C3×C22⋊C4—31no—
324C3×C42—31no—
325C3×C42—31no—
326C3×C42—31no—
327C3×C42—31no—
328C3×C42—31no—
329#217—31no—
330#217—31no—
331#217—31no—
332#217—31no—
333#217—31no—
334#217—61no—
335#217C4×D311yescharacteristic
336(C2×D3)⋊C4—31no—
337(C2×D3)⋊C4—31no—
338(C2×D3)⋊C4—31no—
339(C2×D3)⋊C4—31no—
340(C2×D3)⋊C4—31no—
341(C2×D3)⋊C4—31no—
342(C2×D3)⋊C4—31no—
343(C2×D3)⋊C4—31no—
344(C2×D3)⋊C4—31no—
345(C2×D3)⋊C4—31no—
346(C2×D3)⋊C4—31no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4C4×D311yescharacteristic
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—31no—
365Dic3⋊C4—31no—
366Dic3⋊C4—31no—
367Dic3⋊C4—61no—
368Dic3⋊C4C4×D311yescharacteristic
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—61no—
372C4×Dic3C4×D311yescharacteristic
373C4×Dic3C4×D311yescharacteristic
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C4×Dic3C22×D311yescharacteristic
377#208—62no—
378C2×C3⋊C8—22no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—31no—
381C2×C3⋊C8—31no—
382C2×C3⋊C8—31no—
383C2×C3⋊C8—61no—
384C2×C3⋊C8—61no—
385C2×C3⋊C8C22×D311yescharacteristic
386C2×C3⋊C8C22×D311yescharacteristic
387C2×C3⋊C8C22×D311yescharacteristic
388C2×C3⋊C8C22×D311yescharacteristic
389ΓL(1,𝔽25)—62no—
390ΓL(1,𝔽25)—62no—
391ΓL(1,𝔽25)—62no—
392D3×C8—22no—
393D3×C8—62no—
394D3×C8—62no—
395D3×C8—122no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32#13112yes—
399C22×C32C23×C411yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C32×C4—21no—
407C32×C4C2×#4111yescharacteristic
408C32×C4C2×#4111yescharacteristic
409C3⋊Dic3—21no—
410C3⋊Dic3—21no—
411C3⋊Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3#13112yes—
419C2×M16—91no—
420C2×M16—91no—
421C22×C8—31no—
422C22×C8—31no—
423C22×C8—91no—
424C22×C8D3211yescharacteristic
425#126—91no—
426#126—91no—
427#125—91no—
428#124—91no—
429#123—91no—
430#123—91no—
431C22⋊Q8—91no—
432#121—91no—
433C4×Q8—91no—
434C4×D4—31no—
435C4×D4—91no—
436C4×D4—91no—
437#117—91no—
438#117—91no—
439C2×C42—31no—
440C4⋊C8—31no—
441C4⋊C8—91no—
442C4⋊C8—91no—
443C4⋊C8—91no—
444C4⋊C8—91no—
445C4⋊C8—91no—
446C22⋊C8—31no—
447C22⋊C8—31no—
448C22⋊C8—91no—
449C22⋊C8—91no—
450C22⋊C8—91no—
451C22⋊C8—91no—
452#97—91no—
453#97—91no—
454#97—91no—
455#97—91no—
456C4×C8—31no—
457C4×C8—31no—
458C4×C8—31no—
459C4×C8—31no—
460C4×C8—31no—
461C4×C8—91no—
462C23×C3—21no—
463C23×C3—31no—
464C23×C3C2×C4×D311yescharacteristic
465C23×C3C2×C4×D311yescharacteristic
466C22×D3—31no—
467C22×D3—31no—
468C22×D3—61no—
469C22×D3C2×C4×D311yescharacteristic
470C3×D4—62no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—62no—
487C2×C3×C4—62no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4C2×C4×D311yescharacteristic
491C2×C3×C4C2×C4×D311yescharacteristic
492C2×C3×C4C23×D311yescharacteristic
493C2×C3×C4C23×D311yescharacteristic
494#67—22no—
495#67—64no—
496#67—62no—
497#67—62no—
498#67—62no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—31no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3C2×C4×D311yescharacteristic
511C2×Dic3C2×C4×D311yescharacteristic
512C2×Dic3C2×C4×D311yescharacteristic
513C2×Dic3C2×C4×D311yescharacteristic
514C2×Dic3C2×C4×D311yescharacteristic
515C2×Dic3C2×C4×D311yescharacteristic
516C2×Dic3C2×C4×D311yescharacteristic
517D12—62no—
518C4×D3—21no—
519C4×D3—21no—
520C4×D3—61no—
521C4×D3—61no—
522C4×D3—61no—
523C4×D3—61no—
524C4×D3—121no—
525C4×D3—121no—
526Dic6—62no—
527Dic6—62no—
528C3×C8—21no—
529C3×C8—21no—
530C3×C8—22no—
531C3×C8—32no—
532C3×C8—41no—
533C3×C8—61no—
534C3×C8—61no—
535C3×C8—61no—
536C3×C8#23512yes—
537C3×C8#23712yes—
538C3⋊C8—21no—
539C3⋊C8—21no—
540C3⋊C8—21no—
541C3⋊C8—61no—
542C3⋊C8—61no—
543C3⋊C8—61no—
544C3⋊C8—61no—
545C3⋊C8—121no—
546C3⋊C8—121no—
547C3⋊C8#23512yes—
548C2×C32—22no—
549C2×C32C4×#4111yescharacteristic
550C2×C32C2×#13111yescharacteristic
551C2×C32C2×#13111yescharacteristic
552C3⋊D3—41no—
553C3×D3—41no—
554C2×Q8—91no—
555C2×D4—31no—
556C2×D4—91no—
557C2×D4—91no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—91no—
562C22×C4C2×D3211yescharacteristic
563M16—182no—
564M16—182no—
565C2×C8—22no—
566C2×C8—31no—
567C2×C8—31no—
568C2×C8—31no—
569C2×C8—31no—
570C2×C8—62no—
571C2×C8—62no—
572C2×C8—91no—
573C2×C8—91no—
574C2×C8—182no—
575C2×C8C2×D3211yescharacteristic
576C2×C8C2×D3211yescharacteristic
577C4⋊C4—31no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C4⋊C4—91no—
585C4⋊C4—91no—
586C4⋊C4—91no—
587C22⋊C4—31no—
588C22⋊C4—31no—
589C22⋊C4—91no—
590C22⋊C4—91no—
591C22⋊C4—91no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4—91no—
596C22⋊C4—91no—
597C42—31no—
598C42—31no—
599C42—31no—
600C42—31no—
601C42—31no—
602C42—91no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—22no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3#90112yes—
615C22×C3#90112yes—
616C22×C3C22×C4×D311yescharacteristic
617C22×C3C22×C4×D311yescharacteristic
618C2×D3—21no—
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—62no—
622C2×D3—61no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—121no—
629C2×D3—121no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—32no—
635C3×C4—41no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4C2×#23511yescharacteristic
643C3×C4C2×#23511yescharacteristic
644C3×C4C2×#23711yescharacteristic
645C3×C4D3×#4111yescharacteristic
646Dic3—21no—
647Dic3—21no—
648Dic3—21no—
649Dic3—21no—
650Dic3—21no—
651Dic3—21no—
652Dic3—62no—
653Dic3—61no—
654Dic3—61no—
655Dic3—61no—
656Dic3—61no—
657Dic3—61no—
658Dic3—61no—
659Dic3—121no—
660Dic3—121no—
661Dic3#90112yes—
662C32#296611yescharacteristic, complemented, Sylow
663C23—31no—
664C23—91no—
665C23C4×D3211yescharacteristic
666Q8—182no—
667D4—62no—
668D4—182no—
669D4—182no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—31no—
673C2×C4—31no—
674C2×C4—31no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—181no—
687C2×C4—181no—
688C2×C4C4×D3211yescharacteristic
689C2×C4C22×D3211yescharacteristic
690C8—21no—
691C8—32no—
692C8—61no—
693C8—61no—
694C8—61no—
695C8—181no—
696C8—181no—
697C8#380412yes—
698C2×C3—22no—
699C2×C3—22no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—42no—
704C2×C3—121no—
705C2×C3C4×#23511yescharacteristic
706C2×C3C4×#23711yescharacteristic
707C2×C3C2×#90111yescharacteristic
708C2×C3C2×#90111yescharacteristic
709C2×C3C2×#90111yescharacteristic
710C2×C3D3×#13111yescharacteristic
711D3—41no—
712D3—122no—
713D3—121no—
714D3—121no—
715C22—21no—
716C22—21no—
717C22—61no—
718C22—61no—
719C22—61no—
720C22—181no—
721C22—181no—
722C22—181no—
723C22#6380312yes—
724C22C2×C4×D3211yescharacteristic
725C4—21no—
726C4—32no—
727C4—61no—
728C4—61no—
729C4—61no—
730C4—61no—
731C4—61no—
732C4—61no—
733C4—181no—
734C4—181no—
735C4—181no—
736C4D3×#23511yescharacteristic
737C4C2×#380411yescharacteristic
738C3—21no—
739C3#7844811yescharacteristic, complemented
740C3#7940011yescharacteristic, complemented
741C2—22no—
742C2—121no—
743C2—361no—
744C2D3×#90111yescharacteristic
745C2C2×#6380311yescharacteristic
746C2C4×#380411yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
prime radical#63978C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2966
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C8×#638C2semidirect
3. C3×C8×#67C2semidirect
4. C2×C3×C8×Dic3C2semidirect
5. #10591157C2semidirect
6. #10591155C2semidirect
7. #10591063C2semidirect
8. #10590785C2semidirect
9. C8×#627C2semidirect
10. #10590730C2semidirect
11. C8×#626C2semidirect
12. #10590700C2semidirect
13. #10590696C2semidirect
14. #10590692C2semidirect
15. #10590648C2semidirect
71. C8×#67D3semidirect
73. C2×C8×Dic3D3semidirect
662. C32#2966semidirect
739. C3#78448semidirect
740. C3#79400semidirect

Maximal subgroups

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

subgroupindex
#105948392
C8×#6382
C3×C8×#672
C2×C3×C8×Dic32
#105911572
#105911552
#105910632
#105907852
C8×#6272
#105907302
C8×#6262
#105907002
#105906962
#105906922
#105906482
#794003
#784483