Finite Group Databasebeta

← #11861695

Subgroups — #11861695

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593910C211yesmaximal, characteristic
2C8×#634C211yesmaximal, characteristic, complemented
3C3×#4689C211yesmaximal, characteristic, complemented
4C3×C8×D12C211yesmaximal, characteristic, complemented
5#10590735C211yesmaximal, characteristic, complemented
6#10590724C211yesmaximal, characteristic, complemented
7C8×#625C211yesmaximal, characteristic, complemented
8C8×#625C211yesmaximal, characteristic, complemented
9#10590697C211yesmaximal, characteristic, complemented
10#10590692C211yesmaximal, characteristic, complemented
11#10590660C211yesmaximal, characteristic, complemented
12D3×C8×Dic3C211yesmaximal, characteristic, complemented
13#10590326C211yesmaximal, characteristic, complemented
14#10590255C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#79400—31nomaximal
17#78556—31nomaximal
18C4×#634C2211yescharacteristic
19C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
20C2×C3×D3×C8C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×#872C2211yescharacteristic
25#63913C411yescharacteristic
26C4×#625C2211yescharacteristic
27C4×#625C2211yescharacteristic
28#63896C411yescharacteristic
29#63891C411yescharacteristic
30#63885C411yescharacteristic
31#63884C411yescharacteristic
32C4×D3×Dic3C2211yescharacteristic
33#63861C411yescharacteristic
34#63858C411yescharacteristic
35#63855C2211yescharacteristic
36#63847C411yescharacteristic
37C2×#3711C2211yescharacteristic
38C2×D3×C3⋊C8C2211yescharacteristic
39C32×C4×C8C2211yescharacteristic
40#63641C2211yescharacteristic
41#63641C2211yescharacteristic
42C8×C3⋊Dic3C2211yescharacteristic
43C8×C3⋊Dic3C2211yescharacteristic
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C3×(C2×D3)⋊C8C2211yescharacteristic
46C3×(C2×D3)⋊C8C2211yescharacteristic
47C3×#815C2211yescharacteristic
48C3×C8×Dic3C2211yescharacteristic
49C3×C4⋊(C3⋊C8)C2211yescharacteristic
50C3×#803C2211yescharacteristic
51#63572C2211yescharacteristic
52#63572C2211yescharacteristic
53(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
54(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
55(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
56(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
57#63555C2211yescharacteristic
58#63554C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5538—31no—
62#5528—31no—
63C3×C8×D4—31no—
64C3×#405—31no—
65#5128—31no—
66#5127—31no—
67C8×#67—31no—
68C8×#67—31no—
69C8×#67—31no—
70C8×#67—31no—
71#5101—31no—
72C2×C8×Dic3—31no—
73#5011—31no—
74#5000—31no—
75#4840—31no—
76#4828—31no—
77#4730—31no—
78#4729—31no—
79#4720—31no—
80#4719—31no—
81#4709—31no—
82#4706—31no—
83#4705—31no—
84#4701—31no—
85#4689—31no—
86#4689D311yescharacteristic, complemented
87C8×D12D311yescharacteristic, complemented
88C4×D3×C8—31no—
89C8×Dic6—31no—
90C8×Dic6—31no—
91C8×Dic6—61no—
92C2×#634C2×C411yescharacteristic
93C2×C3×D12C2×C411yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×#625C2×C411yescharacteristic
98C2×#625C2×C411yescharacteristic
99C2×D3×Dic3C2×C411yescharacteristic
100C2×D3×Dic3C2×C411yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C42C2311yescharacteristic
104C4⋊(C3⋊Dic3)C2×C411yescharacteristic
105#3750C2×C411yescharacteristic
106#3750C2×C411yescharacteristic
107C4×C3⋊Dic3C2311yescharacteristic
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×(C2×D3)⋊C4C2×C411yescharacteristic
112C3×(C2×D3)⋊C4C2×C411yescharacteristic
113C3×(C2×D3)⋊C4C2×C411yescharacteristic
114C3×(C2×D3)⋊C4C2×C411yescharacteristic
115C3×C4⋊Dic3C2×C411yescharacteristic
116C3×Dic3⋊C4C2×C411yescharacteristic
117C3×Dic3⋊C4C2×C411yescharacteristic
118C3×C4×Dic3C2311yescharacteristic
119C2×C3×C3⋊C8C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×ΓL(1,𝔽25)—22no—
124C3×D3×C8—22no—
125C3×D3×C8—22no—
126C3×D3×C8—22no—
127#3724C2×C411yescharacteristic
128#3724C2×C411yescharacteristic
129Dic3⋊Dic3C2×C411yescharacteristic
130Dic3⋊Dic3C2×C411yescharacteristic
131(C2×D3)⋊Dic3C2×C411yescharacteristic
132(C2×D3)⋊Dic3C2×C411yescharacteristic
133(C2×D3)⋊Dic3C2×C411yescharacteristic
134(C2×D3)⋊Dic3C2×C411yescharacteristic
135(C2×D3)⋊Dic3C2×C411yescharacteristic
136(C2×D3)⋊Dic3C2×C411yescharacteristic
137Dic32C2×C411yescharacteristic
138Dic32C2×C411yescharacteristic
139#3711—22no—
140D3×C3⋊C8—22no—
141#2966—91noSylow
142C2×C3×M16—31no—
143C22×C3×C8—31no—
144C22×C3×C8—31no—
145C22×C3×C8—31no—
146C3×C4×D4—31no—
147C3×#117—31no—
148#939—31no—
149#935—31no—
150C4×#67—31no—
151C4×#67—31no—
152C4×#67—31no—
153C4×#67—31no—
154#926—31no—
155C2×C4×Dic3—31no—
156C2×#208—31no—
157C22×C3⋊C8—31no—
158C2×ΓL(1,𝔽25)—31no—
159C2×ΓL(1,𝔽25)C2×D311yescharacteristic
160C2×D3×C8—31no—
161C2×D3×C8C2×D311yescharacteristic
162C2×D3×C8C2×D311yescharacteristic
163C2×D3×C8C2×D311yescharacteristic
164#898—31no—
165#898—31no—
166#896—31no—
167#894—31no—
168#889—31no—
169#889—31no—
170#886—31no—
171#885—31no—
172#885—31no—
173#884—31no—
174#883—31no—
175#879—31no—
176#879—31no—
177#878—31no—
178C4×D12C2×D311yescharacteristic
179#872—31no—
180#872C2×D311yescharacteristic
181C42×D3—31no—
182C4×Dic6—31no—
183C4×Dic6—31no—
184C4×Dic6—61no—
185C3×C4⋊C8—31no—
186C3×C22⋊C8—31no—
187C3×C22⋊C8—31no—
188C3×#97—31no—
189C3×#97—31no—
190C3×C4×C8—21no—
191C3×C4×C8—31no—
192C3×C4×C8C2×D311yescharacteristic
193C3×C4×C8C2×D311yescharacteristic
194#830—31no—
195#830—31no—
196#830—31no—
197#830—31no—
198(C2×D3)⋊C8—31no—
199(C2×D3)⋊C8—31no—
200(C2×D3)⋊C8—31no—
201(C2×D3)⋊C8—31no—
202(C2×D3)⋊C8C2×D311yescharacteristic
203(C2×D3)⋊C8C2×D311yescharacteristic
204#815—31no—
205#815—31no—
206#815—31no—
207#815C2×D311yescharacteristic
208Dic3⋊C8—31no—
209Dic3⋊C8—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—61no—
217Dic3⋊C8—61no—
218C8×Dic3—31no—
219C8×Dic3—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—31no—
225C8×Dic3—61no—
226C8×Dic3—61no—
227C8×Dic3C2×D311yescharacteristic
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—61no—
231C4⋊(C3⋊C8)C2×D311yescharacteristic
232#803—31no—
233#803C2×D311yescharacteristic
234C4×C3⋊C8—31no—
235C22×C3×D3C22×C411yescharacteristic
236C22×C3×D3C22×C411yescharacteristic
237C22×C3×D3C22×C411yescharacteristic
238C2×C32×C4C22×C411yescharacteristic
239C2×C32×C4C22×C411yescharacteristic
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3C22×C411yescharacteristic
242C2×C3⋊Dic3C22×C411yescharacteristic
243C2×C3⋊Dic3C22×C411yescharacteristic
244C2×C3⋊Dic3C22×C411yescharacteristic
245#634—22no—
246C2×C3×Dic3C22×C411yescharacteristic
247C2×C3×Dic3C22×C411yescharacteristic
248C2×C3×Dic3C22×C411yescharacteristic
249C2×C3×Dic3C22×C411yescharacteristic
250C2×C3×Dic3C22×C411yescharacteristic
251C3×D12—22no—
252C3×C4×D3—21no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258#625—22no—
259#625—22no—
260D3×Dic3—22no—
261D3×Dic3—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—31no—
283#405—91no—
284C2×C4×C8—91no—
285C2×C3×D4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C2×#67—31no—
290C2×#67—31no—
291C2×#67—31no—
292C2×#67—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C2×D12C4×D311yescharacteristic
296C2×C4×D3—31no—
297C2×C4×D3—31no—
298C2×C4×D3C22×D311yescharacteristic
299C2×C4×D3C22×D311yescharacteristic
300C2×C4×D3C22×D311yescharacteristic
301C2×Dic6—31no—
302C2×Dic6—31no—
303C2×Dic6—61no—
304C3×M16—62no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8—62no—
312C2×C3×C8—62no—
313C2×C3×C8—62no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C22×D311yescharacteristic
317C2×C3×C8C22×D311yescharacteristic
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—31no—
321C3×C22⋊C4—31no—
322C3×C22⋊C4—31no—
323C3×C22⋊C4—31no—
324C3×C22⋊C4—31no—
325C3×C42—21no—
326C3×C42—31no—
327C3×C42C22×D311yescharacteristic
328C3×C42C22×D311yescharacteristic
329#217—31no—
330#217—31no—
331#217—31no—
332#217—31no—
333#217—31no—
334#217—31no—
335(C2×D3)⋊C4—31no—
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)⋊C4C4×D311yescharacteristic
342(C2×D3)⋊C4C4×D311yescharacteristic
343(C2×D3)⋊C4C4×D311yescharacteristic
344(C2×D3)⋊C4C4×D311yescharacteristic
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—61no—
350C4⋊Dic3C4×D311yescharacteristic
351Dic3⋊C4—31no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4C4×D311yescharacteristic
364Dic3⋊C4C4×D311yescharacteristic
365C4×Dic3—31no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3C22×D311yescharacteristic
376#208—62no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—31no—
381C2×C3⋊C8—61no—
382C2×C3⋊C8—61no—
383C2×C3⋊C8—62no—
384C2×C3⋊C8C22×D311yescharacteristic
385C2×C3⋊C8C22×D311yescharacteristic
386C2×C3⋊C8C22×D311yescharacteristic
387C2×C3⋊C8C22×D311yescharacteristic
388ΓL(1,𝔽25)—22no—
389ΓL(1,𝔽25)—62no—
390D3×C8—22no—
391D3×C8—22no—
392D3×C8—22no—
393D3×C8—62no—
394C22×C32C23×C411yescharacteristic
395C2×C3×D3—21no—
396C2×C3×D3—21no—
397C2×C3×D3—21no—
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3#13112yes—
404C32×C4—21no—
405C32×C4—21no—
406C32×C4C2×#4111yescharacteristic
407C32×C4C2×#4111yescharacteristic
408C3⋊Dic3—21no—
409C3⋊Dic3—21no—
410C3⋊Dic3—21no—
411C3⋊Dic3#13112yes—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C2×M16—31no—
418C2×M16—91no—
419C22×C8—31no—
420C22×C8—31no—
421C22×C8—31no—
422C22×C8—91no—
423#126—91no—
424#126—91no—
425#125—91no—
426#124—91no—
427#123—91no—
428#123—91no—
429C22⋊Q8—91no—
430#121—91no—
431C4×Q8—91no—
432C4×D4—31no—
433C4×D4—91no—
434C4×D4—91no—
435#117—31no—
436#117—91no—
437C2×C42—91no—
438C4⋊C8—31no—
439C4⋊C8—91no—
440C4⋊C8—91no—
441C4⋊C8—91no—
442C4⋊C8—91no—
443C4⋊C8—91no—
444C22⋊C8—31no—
445C22⋊C8—31no—
446C22⋊C8—91no—
447C22⋊C8—91no—
448C22⋊C8—91no—
449C22⋊C8—91no—
450#97—31no—
451#97—31no—
452#97—91no—
453#97—91no—
454C4×C8—31no—
455C4×C8—91no—
456C4×C8—91no—
457C4×C8—91no—
458C4×C8—91no—
459C4×C8D3211yescharacteristic
460C23×C3—31no—
461C23×C3—31no—
462C23×C3—31no—
463C22×D3C2×C4×D311yescharacteristic
464C22×D3C2×C4×D311yescharacteristic
465C22×D3C2×C4×D311yescharacteristic
466C3×D4—62no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4C2×C4×D311yescharacteristic
482C2×C3×C4C2×C4×D311yescharacteristic
483C2×C3×C4C2×C4×D311yescharacteristic
484C2×C3×C4C2×C4×D311yescharacteristic
485C2×C3×C4C23×D311yescharacteristic
486C2×C3×C4C23×D311yescharacteristic
487#67—62no—
488#67—62no—
489#67—62no—
490#67—62no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—62no—
504C2×Dic3—62no—
505C2×Dic3C2×C4×D311yescharacteristic
506C2×Dic3C2×C4×D311yescharacteristic
507C2×Dic3C2×C4×D311yescharacteristic
508C2×Dic3C2×C4×D311yescharacteristic
509C2×Dic3C2×C4×D311yescharacteristic
510D12—22no—
511C4×D3—21no—
512C4×D3—21no—
513C4×D3—21no—
514C4×D3—21no—
515C4×D3—21no—
516C4×D3—21no—
517C4×D3—62no—
518C4×D3—62no—
519Dic6—62no—
520Dic6—62no—
521Dic6—64no—
522C3×C8—21no—
523C3×C8—21no—
524C3×C8—22no—
525C3×C8—32no—
526C3×C8—41no—
527C3×C8—61no—
528C3×C8—61no—
529C3×C8—61no—
530C3×C8#23512yes—
531C3×C8#23712yes—
532C3⋊C8—21no—
533C3⋊C8—21no—
534C3⋊C8—21no—
535C3⋊C8—61no—
536C3⋊C8—61no—
537C3⋊C8—61no—
538C3⋊C8—61no—
539C3⋊C8—121no—
540C3⋊C8—121no—
541C3⋊C8#23512yes—
542C2×C32C4×#4111yescharacteristic
543C2×C32C2×#13111yescharacteristic
544C2×C32C2×#13111yescharacteristic
545C3×D3—22no—
546C3×D3—41no—
547C3×D3—41no—
548C2×Q8—91no—
549C2×D4—31no—
550C2×D4—91no—
551C2×D4—91no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—91no—
556C22×C4—91no—
557M16—62no—
558M16—182no—
559C2×C8—31no—
560C2×C8—31no—
561C2×C8—31no—
562C2×C8—31no—
563C2×C8—62no—
564C2×C8—62no—
565C2×C8—62no—
566C2×C8—91no—
567C2×C8—91no—
568C2×C8—182no—
569C2×C8C2×D3211yescharacteristic
570C2×C8C2×D3211yescharacteristic
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4—31no—
574C4⋊C4—91no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—91no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C22⋊C4—31no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—31no—
585C22⋊C4—91no—
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—91no—
589C22⋊C4—91no—
590C22⋊C4—91no—
591C42—31no—
592C42—91no—
593C42—91no—
594C42—91no—
595C42—91no—
596C42C2×D3211yescharacteristic
597C22×C3—21no—
598C22×C3—32no—
599C22×C3—61no—
600C22×C3—61no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—61no—
604C22×C3—61no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3C22×C4×D311yescharacteristic
608C22×C3C22×C4×D311yescharacteristic
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—21no—
612C2×D3—21no—
613C2×D3—21no—
614C2×D3—21no—
615C2×D3—21no—
616C2×D3—21no—
617C2×D3#90112yes—
618C3×C4—22no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—41no—
626C3×C4—61no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—61no—
630C3×C4—61no—
631C3×C4C2×#23511yescharacteristic
632C3×C4C2×#23511yescharacteristic
633C3×C4C2×#23711yescharacteristic
634C3×C4D3×#4111yescharacteristic
635Dic3—21no—
636Dic3—21no—
637Dic3—21no—
638Dic3—21no—
639Dic3—21no—
640Dic3—32no—
641Dic3—32no—
642Dic3—62no—
643Dic3—62no—
644Dic3—61no—
645Dic3—61no—
646Dic3—61no—
647Dic3—61no—
648Dic3—61no—
649Dic3—61no—
650Dic3—121no—
651Dic3—121no—
652C32#296611yescharacteristic, complemented, Sylow
653C23—31no—
654C23—31no—
655C23—31no—
656Q8—182no—
657D4—62no—
658D4—182no—
659D4—182no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—31no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—91no—
672C2×C4—91no—
673C2×C4—91no—
674C2×C4—91no—
675C2×C4—182no—
676C2×C4—182no—
677C2×C4C4×D3211yescharacteristic
678C2×C4C4×D3211yescharacteristic
679C2×C4C22×D3211yescharacteristic
680C8—21no—
681C8—32no—
682C8—61no—
683C8—61no—
684C8—61no—
685C8—181no—
686C8—181no—
687C8#379512yes—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—62no—
692C2×C3—121no—
693C2×C3—121no—
694C2×C3C4×#23511yescharacteristic
695C2×C3C4×#23711yescharacteristic
696C2×C3C2×#90111yescharacteristic
697C2×C3D3×#13111yescharacteristic
698C2×C3D3×#13111yescharacteristic
699C2×C3D3×#13111yescharacteristic
700D3—22no—
701D3—41no—
702D3—41no—
703C22—32no—
704C22—61no—
705C22—61no—
706C22—61no—
707C22—61no—
708C22—61no—
709C22—61no—
710C22—61no—
711C22—61no—
712C22C2×C4×D3211yescharacteristic
713C4—21no—
714C4—21no—
715C4—61no—
716C4—61no—
717C4—61no—
718C4—61no—
719C4—61no—
720C4—92no—
721C4—181no—
722C4—181no—
723C4—181no—
724C4C2×#379511yescharacteristic
725C4D3×#23511yescharacteristic
726C3—21no—
727C3#7855611yescharacteristic, complemented
728C3#7940011yescharacteristic, complemented
729C2—62no—
730C2—121no—
731C2—121no—
732C2C4×#379511yescharacteristic
733C2D3×#90111yescharacteristic
734C2#1059466911yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
prime radical#63885C4
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2966
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C8×#634C2semidirect
3. C3×#4689C2semidirect
4. C3×C8×D12C2semidirect
5. #10590735C2semidirect
6. #10590724C2semidirect
7. C8×#625C2semidirect
8. C8×#625C2semidirect
9. #10590697C2semidirect
10. #10590692C2semidirect
11. #10590660C2semidirect
12. D3×C8×Dic3C2semidirect
13. #10590326C2semidirect
14. #10590255C2semidirect
15. #10590253C2semidirect
86. #4689D3semidirect
87. C8×D12D3semidirect
652. C32#2966semidirect
727. C3#78556semidirect
728. C3#79400semidirect

Maximal subgroups

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

subgroupindex
#105939102
C8×#6342
C3×#46892
C3×C8×D122
#105907352
#105907242
C8×#6252
#105906972
#105906922
#105906602
D3×C8×Dic32
#105903262
#105902552
#105902532
#794003
#785563