Finite Group Databasebeta

← #11861694

Subgroups — #11861694

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593911C211yesmaximal, characteristic
2#10592388C211yesmaximal, characteristic, complemented
3C3×C8×D12C211yesmaximal, characteristic, complemented
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5#10590907C211yesmaximal, characteristic, complemented
6#10590732C211yesmaximal, characteristic, complemented
7C8×#626C211yesmaximal, characteristic, complemented
8C8×#626C211yesmaximal, characteristic, complemented
9#10590699C211yesmaximal, characteristic, complemented
10#10590692C211yesmaximal, characteristic, complemented
11#10590661C211yesmaximal, characteristic, complemented
12D3×C8×Dic3C211yesmaximal, characteristic, complemented
13#10590330C211yesmaximal, characteristic, complemented
14#10590257C211yesmaximal, characteristic, complemented
15#10590252C211yesmaximal, characteristic, complemented
16#79903—31nomaximal
17#79400—31nomaximal
18C2×#3743C2211yescharacteristic
19C2×C8×C3⋊D3C2211yescharacteristic
20#64081C2211yescharacteristic
21C2×C3×D3×C8C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23C3×C4×D12C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63907C411yescharacteristic
26C4×#626C2211yescharacteristic
27C4×#626C2211yescharacteristic
28#63890C411yescharacteristic
29#63887C411yescharacteristic
30#63886C411yescharacteristic
31#63884C411yescharacteristic
32C4×D3×Dic3C2211yescharacteristic
33#63858C411yescharacteristic
34#63855C2211yescharacteristic
35#63848C411yescharacteristic
36#63846C411yescharacteristic
37C2×#3711C2211yescharacteristic
38C2×D3×C3⋊C8C2211yescharacteristic
39C32×C4×C8C2211yescharacteristic
40#63642C2211yescharacteristic
41C8×C3⋊Dic3C2211yescharacteristic
42#63630C2211yescharacteristic
43C3×(C2×D3)⋊C8C2211yescharacteristic
44C3×(C2×D3)⋊C8C2211yescharacteristic
45C3×Dic3⋊C8C2211yescharacteristic
46C3×Dic3⋊C8C2211yescharacteristic
47C3×C8×Dic3C2211yescharacteristic
48C3×C8×Dic3C2211yescharacteristic
49C3×C4⋊(C3⋊C8)C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63557C2211yescharacteristic
54#63557C2211yescharacteristic
55(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
56(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
57#63555C2211yescharacteristic
58#63554C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5580—31no—
62#5538—31no—
63C3×C8×Q8—31no—
64C3×C8×D4—31no—
65C8×#67—31no—
66C8×#67—31no—
67#5101—31no—
68C2×C8×Dic3—31no—
69#5024—31no—
70#5011—31no—
71#4840—31no—
72#4840—31no—
73#4840—31no—
74#4838—31no—
75#4836—31no—
76#4836—31no—
77#4835—31no—
78#4828—31no—
79#4730—31no—
80#4729—31no—
81#4720—31no—
82#4719—31no—
83#4689—31no—
84#4689—31no—
85#4689—31no—
86#4689—61no—
87C8×D12—31no—
88C8×D12—31no—
89C8×D12D311yescharacteristic, complemented
90C4×D3×C8—31no—
91C8×Dic6D311yescharacteristic, complemented
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×C3×D12C2×C411yescharacteristic
94C2×C3×C4×D3C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6C2×C411yescharacteristic
97C2×#626C2×C411yescharacteristic
98C2×#626C2×C411yescharacteristic
99C2×D3×Dic3C2×C411yescharacteristic
100C2×D3×Dic3C2×C411yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C42C2311yescharacteristic
104#3752C2×C411yescharacteristic
105#3752C2×C411yescharacteristic
106#3750C2×C411yescharacteristic
107#3750C2×C411yescharacteristic
108C4×C3⋊Dic3C2311yescharacteristic
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111#3743—22no—
112C8×C3⋊D3—22no—
113C3×(C2×D3)⋊C4C2×C411yescharacteristic
114C3×(C2×D3)⋊C4C2×C411yescharacteristic
115C3×C4⋊Dic3C2×C411yescharacteristic
116C3×C4⋊Dic3C2×C411yescharacteristic
117C3×Dic3⋊C4C2×C411yescharacteristic
118C3×Dic3⋊C4C2×C411yescharacteristic
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C3×D3×C8—22no—
126C3×D3×C8—22no—
127Dic3⋊Dic3C2×C411yescharacteristic
128Dic3⋊Dic3C2×C411yescharacteristic
129Dic3⋊Dic3C2×C411yescharacteristic
130Dic3⋊Dic3C2×C411yescharacteristic
131#3722C2×C411yescharacteristic
132#3722C2×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
142C22×C3×C8—31no—
143C22×C3×C8—31no—
144C3×C4×Q8—31no—
145C3×C4×D4—31no—
146#947—31no—
147#946—31no—
148#939—31no—
149#935—31no—
150C4×#67—31no—
151C4×#67—31no—
152#926—31no—
153C2×C4×Dic3—31no—
154C2×#208—31no—
155C22×C3⋊C8—31no—
156C2×ΓL(1,𝔽25)—31no—
157C2×ΓL(1,𝔽25)—31no—
158C2×ΓL(1,𝔽25)—31no—
159C2×ΓL(1,𝔽25)—61no—
160C2×D3×C8—31no—
161C2×D3×C8—31no—
162C2×D3×C8—31no—
163C2×D3×C8—61no—
164C2×D3×C8C2×D311yescharacteristic
165C2×D3×C8C2×D311yescharacteristic
166#898—31no—
167#898—31no—
168#898—31no—
169#895—31no—
170#894—31no—
171#894—31no—
172#890—31no—
173#889—31no—
174#886—31no—
175#885—31no—
176#879—31no—
177#878—31no—
178C4×D12—31no—
179C4×D12—31no—
180C4×D12C2×D311yescharacteristic
181#872—31no—
182#872—31no—
183#872—31no—
184#872—61no—
185C42×D3—31no—
186C4×Dic6C2×D311yescharacteristic
187C3×C4⋊C8—31no—
188C3×C4⋊C8—31no—
189C3×C4⋊C8—31no—
190C3×C4⋊C8—31no—
191C3×C22⋊C8—31no—
192C3×C22⋊C8—31no—
193C3×C4×C8—21no—
194C3×C4×C8—31no—
195C3×C4×C8—31no—
196C3×C4×C8C2×D311yescharacteristic
197C3×C4×C8C2×D311yescharacteristic
198#830—31no—
199#830—31no—
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—31no—
206(C2×D3)⋊C8C2×D311yescharacteristic
207(C2×D3)⋊C8C2×D311yescharacteristic
208#815—31no—
209#815—31no—
210#815—31no—
211#815—31no—
212#815—31no—
213#815—61no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8C2×D311yescharacteristic
217Dic3⋊C8C2×D311yescharacteristic
218C8×Dic3—31no—
219C8×Dic3—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—61no—
224C8×Dic3C2×D311yescharacteristic
225C8×Dic3C2×D311yescharacteristic
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)C2×D311yescharacteristic
229C4⋊(C3⋊C8)C2×D311yescharacteristic
230#803—31no—
231#803—31no—
232#803—31no—
233#803—61no—
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
244C4×C3⋊D3—21no—
245C4×C3⋊D3—21no—
246C2×C3×Dic3C22×C411yescharacteristic
247C2×C3×Dic3C22×C411yescharacteristic
248C2×C3×Dic3C22×C411yescharacteristic
249C2×C3×Dic3C22×C411yescharacteristic
250C2×C3×Dic3C22×C411yescharacteristic
251C2×C3×Dic3C22×C411yescharacteristic
252C3×D12—22no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×Dic6—22no—
258#626—22no—
259#626—22no—
260D3×Dic3—22no—
261D3×Dic3—22no—
262C32×C8—21no—
263C32×C8#4112yes—
264C3⋊(C3⋊C8)—21no—
265C3⋊(C3⋊C8)#4112yes—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269C3×C3⋊C8—21no—
270#529—91no—
271#446—91no—
272C8×Q8—31no—
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—91no—
285C2×C3×Q8—31no—
286C2×C3×D4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C2×#67—31no—
290C2×#67—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C2×D12—31no—
294C2×D12—31no—
295C2×D12C4×D311yescharacteristic
296C2×C4×D3—31no—
297C2×C4×D3—31no—
298C2×C4×D3—31no—
299C2×C4×D3—31no—
300C2×C4×D3—61no—
301C2×C4×D3C22×D311yescharacteristic
302C2×C4×D3C22×D311yescharacteristic
303C2×Dic6C4×D311yescharacteristic
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—31no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C2×C3×C8—62no—
311C2×C3×C8—62no—
312C2×C3×C8C22×D311yescharacteristic
313C2×C3×C8C22×D311yescharacteristic
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316C3×C4⋊C4—31no—
317C3×C4⋊C4—31no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C22⋊C4—31no—
321C3×C22⋊C4—31no—
322C3×C42—21no—
323C3×C42—31no—
324C3×C42—31no—
325C3×C42C22×D311yescharacteristic
326C3×C42C22×D311yescharacteristic
327#217—31no—
328#217—31no—
329#217—31no—
330#217—31no—
331(C2×D3)⋊C4—31no—
332(C2×D3)⋊C4—31no—
333(C2×D3)⋊C4—31no—
334(C2×D3)⋊C4—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)⋊C4—31no—
342(C2×D3)⋊C4—31no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4C4×D311yescharacteristic
346(C2×D3)⋊C4C4×D311yescharacteristic
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3C4×D311yescharacteristic
352C4⋊Dic3C4×D311yescharacteristic
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—61no—
372C4×Dic3C22×D311yescharacteristic
373C4×Dic3C22×D311yescharacteristic
374#208—62no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8—62no—
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384C2×C3⋊C8C22×D311yescharacteristic
385C2×C3⋊C8C22×D311yescharacteristic
386ΓL(1,𝔽25)—62no—
387ΓL(1,𝔽25)—62no—
388ΓL(1,𝔽25)—62no—
389ΓL(1,𝔽25)—64no—
390D3×C8—22no—
391D3×C8—22no—
392D3×C8—62no—
393D3×C8—64no—
394D3×C8—62no—
395D3×C8—62no—
396C22×C32C23×C411yescharacteristic
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—21no—
404C2×C3×D3—21no—
405C2×C3×D3#13112yes—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4C2×#4111yescharacteristic
409C32×C4C2×#4111yescharacteristic
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×C8—91no—
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—31no—
434C4×D4—31no—
435C4×D4—91no—
436C4×D4—91no—
437#117—91no—
438#117—91no—
439C2×C42—91no—
440C4⋊C8—31no—
441C4⋊C8—31no—
442C4⋊C8—31no—
443C4⋊C8—31no—
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—91no—
459C4×C8—91no—
460C4×C8—91no—
461C4×C8D3211yescharacteristic
462C23×C3—31no—
463C23×C3—31no—
464C22×D3—31no—
465C22×D3—31no—
466C22×D3—61no—
467C22×D3C2×C4×D311yescharacteristic
468C22×D3C2×C4×D311yescharacteristic
469C3×Q8—62no—
470C3×D4—62no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4C2×C4×D311yescharacteristic
485C2×C3×C4C2×C4×D311yescharacteristic
486C2×C3×C4C2×C4×D311yescharacteristic
487C2×C3×C4C2×C4×D311yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489C2×C3×C4C23×D311yescharacteristic
490#67—62no—
491#67—62no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3C2×C4×D311yescharacteristic
504C2×Dic3C2×C4×D311yescharacteristic
505C2×Dic3C2×C4×D311yescharacteristic
506C2×Dic3C2×C4×D311yescharacteristic
507C2×Dic3C2×C4×D311yescharacteristic
508C2×Dic3C2×C4×D311yescharacteristic
509D12—22no—
510D12—62no—
511D12—62no—
512C4×D3—21no—
513C4×D3—21no—
514C4×D3—21no—
515C4×D3—21no—
516C4×D3—62no—
517C4×D3—62no—
518C4×D3—62no—
519C4×D3—62no—
520C4×D3—61no—
521C4×D3—61no—
522C4×D3—61no—
523C4×D3—61no—
524Dic6—22no—
525C3×C8—22no—
526C3×C8—21no—
527C3×C8—21no—
528C3×C8—22no—
529C3×C8—61no—
530C3×C8—61no—
531C3×C8—61no—
532C3×C8—61no—
533C3×C8#23712yes—
534C3×C8#23912yes—
535C3⋊C8—21no—
536C3⋊C8—21no—
537C3⋊C8—21no—
538C3⋊C8—21no—
539C3⋊C8—32no—
540C3⋊C8—32no—
541C3⋊C8—62no—
542C3⋊C8—62no—
543C3⋊C8—61no—
544C3⋊C8—61no—
545C2×C32C4×#4111yescharacteristic
546C2×C32C2×#13111yescharacteristic
547C2×C32C2×#13111yescharacteristic
548C3⋊D3—41no—
549C3×D3—22no—
550C3×D3—41no—
551C2×Q8—31no—
552C2×D4—31no—
553C2×D4—91no—
554C2×D4—91no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—91no—
560M16—182no—
561M16—182no—
562C2×C8—31no—
563C2×C8—31no—
564C2×C8—31no—
565C2×C8—31no—
566C2×C8—62no—
567C2×C8—62no—
568C2×C8—91no—
569C2×C8—91no—
570C2×C8—182no—
571C2×C8—182no—
572C2×C8C2×D3211yescharacteristic
573C2×C8C2×D3211yescharacteristic
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—31no—
577C4⋊C4—31no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—91no—
581C4⋊C4—91no—
582C4⋊C4—91no—
583C4⋊C4—91no—
584C22⋊C4—31no—
585C22⋊C4—31no—
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—91no—
589C22⋊C4—91no—
590C22⋊C4—91no—
591C22⋊C4—91no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C42—31no—
595C42—31no—
596C42—91no—
597C42—91no—
598C42—91no—
599C42C2×D3211yescharacteristic
600C22×C3—21no—
601C22×C3—32no—
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—62no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—61no—
618C2×D3—61no—
619C2×D3—61no—
620C2×D3—61no—
621C2×D3—121no—
622C2×D3—121no—
623C2×D3#90112yes—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—32no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—61no—
634C3×C4—61no—
635C3×C4—61no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4C2×#23711yescharacteristic
639C3×C4C2×#23911yescharacteristic
640C3×C4D3×#4111yescharacteristic
641C3×C4D3×#4111yescharacteristic
642Dic3—21no—
643Dic3—21no—
644Dic3—21no—
645Dic3—21no—
646Dic3—21no—
647Dic3—62no—
648Dic3—61no—
649Dic3—61no—
650Dic3—61no—
651Dic3—61no—
652Dic3—61no—
653Dic3—61no—
654Dic3—121no—
655Dic3—121no—
656Dic3#90112yes—
657C32#296611yescharacteristic, complemented, Sylow
658C23—31no—
659C23—31no—
660C23—91no—
661Q8—62no—
662D4—62no—
663D4—182no—
664D4—182no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—91no—
676C2×C4—91no—
677C2×C4—91no—
678C2×C4—182no—
679C2×C4—182no—
680C2×C4—181no—
681C2×C4—181no—
682C2×C4C4×D3211yescharacteristic
683C2×C4C4×D3211yescharacteristic
684C2×C4C22×D3211yescharacteristic
685C8—21no—
686C8—61no—
687C8—61no—
688C8—61no—
689C8—61no—
690C8—92no—
691C8—181no—
692C8#379612yes—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—62no—
697C2×C3—121no—
698C2×C3C4×#23711yescharacteristic
699C2×C3C4×#23911yescharacteristic
700C2×C3C2×#90111yescharacteristic
701C2×C3C2×#90111yescharacteristic
702C2×C3D3×#13111yescharacteristic
703C2×C3D3×#13111yescharacteristic
704D3—22no—
705D3—41no—
706D3—122no—
707D3—121no—
708D3—121no—
709C22—32no—
710C22—61no—
711C22—61no—
712C22—61no—
713C22—61no—
714C22—61no—
715C22—181no—
716C22—181no—
717C22—181no—
718C22C2×C4×D3211yescharacteristic
719C4—21no—
720C4—21no—
721C4—32no—
722C4—61no—
723C4—61no—
724C4—61no—
725C4—61no—
726C4—61no—
727C4—181no—
728C4—181no—
729C4—181no—
730C4C2×#379611yescharacteristic
731C4#6430611yescharacteristic
732C3—21no—
733C3#7940011yescharacteristic, complemented
734C3#7990311yescharacteristic, complemented
735C2—62no—
736C2—121no—
737C2—361no—
738C2C4×#379611yescharacteristic
739C2D3×#90111yescharacteristic
740C2D3×#90111yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
prime radical#63886C4
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. #10592388C2semidirect
3. C3×C8×D12C2semidirect
4. C3×C8×Dic6C2semidirect
5. #10590907C2semidirect
6. #10590732C2semidirect
7. C8×#626C2semidirect
8. C8×#626C2semidirect
9. #10590699C2semidirect
10. #10590692C2semidirect
11. #10590661C2semidirect
12. D3×C8×Dic3C2semidirect
13. #10590330C2semidirect
14. #10590257C2semidirect
15. #10590252C2semidirect
89. C8×D12D3semidirect
91. C8×Dic6D3semidirect
657. C32#2966semidirect
733. C3#79400semidirect
734. C3#79903semidirect

Maximal subgroups

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

subgroupindex
#105939112
#105923882
C3×C8×D122
C3×C8×Dic62
#105909072
#105907322
C8×#6262
#105906992
#105906922
#105906612
D3×C8×Dic32
#105903302
#105902572
#105902522
#799033
#794003