Finite Group Databasebeta

← #11861693

Subgroups — #11861693

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#10593934C211yesmaximal, characteristic
2C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C3×#4689C211yesmaximal, characteristic, complemented
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5#10590738C211yesmaximal, characteristic, complemented
6#10590731C211yesmaximal, characteristic, complemented
7C8×#626C211yesmaximal, characteristic, complemented
8C8×#626C211yesmaximal, characteristic, complemented
9#10590700C211yesmaximal, characteristic, complemented
10#10590665C211yesmaximal, characteristic, complemented
11C8×#624C211yesmaximal, characteristic, complemented
12#10590647C211yesmaximal, characteristic, complemented
13#10590328C211yesmaximal, characteristic, complemented
14#10590253C211yesmaximal, characteristic, complemented
15#10590251C211yesmaximal, characteristic, complemented
16#79903—31nomaximal
17#78556—31nomaximal
18C2×C8×C3⋊D3C2211yescharacteristic
19C2×C8×C3⋊D3C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
22C2×C3×D3×C8C2211yescharacteristic
23C3×#872C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63910C411yescharacteristic
26#63907C411yescharacteristic
27C4×#626C2211yescharacteristic
28C4×#626C2211yescharacteristic
29#63897C411yescharacteristic
30#63888C411yescharacteristic
31C4×#624C2211yescharacteristic
32#63874C2211yescharacteristic
33#63861C411yescharacteristic
34#63854C411yescharacteristic
35#63848C411yescharacteristic
36#63845C411yescharacteristic
37C2×#3712C2211yescharacteristic
38C2×#3710C2211yescharacteristic
39C32×C4×C8C2211yescharacteristic
40#63647C2211yescharacteristic
41#63647C2211yescharacteristic
42C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
43C3×#815C2211yescharacteristic
44C3×Dic3⋊C8C2211yescharacteristic
45C3×Dic3⋊C8C2211yescharacteristic
46C3×C8×Dic3C2211yescharacteristic
47C3×C8×Dic3C2211yescharacteristic
48C3×C8×Dic3C2211yescharacteristic
49C3×C4⋊(C3⋊C8)C2211yescharacteristic
50C3×#803C2211yescharacteristic
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#63554C2211yescharacteristic
58#63554C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5580—31no—
62#5528—31no—
63C3×C8×Q8—31no—
64C3×#405—31no—
65#5128—31no—
66#5127—31no—
67C8×#67—31no—
68C8×#67—31no—
69#5024—31no—
70#5000—31no—
71#4840—31no—
72#4840—31no—
73#4838—31no—
74#4836—31no—
75#4836—31no—
76#4835—31no—
77#4709—31no—
78#4706—31no—
79#4705—31no—
80#4701—31no—
81#4689—31no—
82#4689—31no—
83#4689D311yescharacteristic, complemented
84C8×D12—31no—
85C8×D12—31no—
86C8×D12—31no—
87C8×D12—31no—
88C8×D12—61no—
89C4×D3×C8—31no—
90C4×D3×C8—31no—
91C8×Dic6D311yescharacteristic, complemented
92C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6C2×C411yescharacteristic
97C2×#626C2×C411yescharacteristic
98C2×#626C2×C411yescharacteristic
99C2×#624C2×C411yescharacteristic
100C2×#624C2×C411yescharacteristic
101C2×C32×C8C2311yescharacteristic
102C2×C32×C8C2311yescharacteristic
103C32×C42C2311yescharacteristic
104#3752C2×C411yescharacteristic
105#3752C2×C411yescharacteristic
106C4⋊(C3⋊Dic3)C2×C411yescharacteristic
107C2×C3⋊(C3⋊C8)C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C8×C3⋊D3—22no—
110C8×C3⋊D3—22no—
111C3×(C2×D3)⋊C4C2×C411yescharacteristic
112C3×(C2×D3)⋊C4C2×C411yescharacteristic
113C3×C4⋊Dic3C2×C411yescharacteristic
114C3×Dic3⋊C4C2×C411yescharacteristic
115C3×Dic3⋊C4C2×C411yescharacteristic
116C3×Dic3⋊C4C2×C411yescharacteristic
117C3×Dic3⋊C4C2×C411yescharacteristic
118C3×C4×Dic3C2311yescharacteristic
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C3×ΓL(1,𝔽25)—22no—
126C3×D3×C8—22no—
127#3724C2×C411yescharacteristic
128#3724C2×C411yescharacteristic
129Dic3⋊Dic3C2×C411yescharacteristic
130Dic3⋊Dic3C2×C411yescharacteristic
131#3722C2×C411yescharacteristic
132#3722C2×C411yescharacteristic
133#3722C2×C411yescharacteristic
134#3722C2×C411yescharacteristic
135(C2×D3)⋊Dic3C2×C411yescharacteristic
136(C2×D3)⋊Dic3C2×C411yescharacteristic
137Dic32C2×C411yescharacteristic
138Dic32C2×C411yescharacteristic
139#3712—22no—
140#3710—22no—
141#2966—91noSylow
142C2×C3×M16—31no—
143C22×C3×C8—31no—
144C3×C4×Q8—31no—
145C3×#117—31no—
146#947—31no—
147#946—31no—
148C4×#67—31no—
149C4×#67—31no—
150C2×ΓL(1,𝔽25)—31no—
151C2×ΓL(1,𝔽25)—31no—
152C2×ΓL(1,𝔽25)C2×D311yescharacteristic
153C2×D3×C8—31no—
154C2×D3×C8—31no—
155C2×D3×C8—31no—
156C2×D3×C8—31no—
157C2×D3×C8—31no—
158C2×D3×C8—31no—
159C2×D3×C8—61no—
160C2×D3×C8—61no—
161C2×D3×C8C2×D311yescharacteristic
162#898—31no—
163#898—31no—
164#898—31no—
165#896—31no—
166#895—31no—
167#894—31no—
168#894—31no—
169#894—31no—
170#890—31no—
171#889—31no—
172#885—31no—
173#884—31no—
174#883—31no—
175#879—31no—
176C4×D12—31no—
177C4×D12—31no—
178C4×D12—31no—
179C4×D12—31no—
180C4×D12—61no—
181#872—31no—
182#872—31no—
183#872C2×D311yescharacteristic
184C42×D3—31no—
185C42×D3—31no—
186C4×Dic6C2×D311yescharacteristic
187C3×C4⋊C8—31no—
188C3×C4⋊C8—31no—
189C3×C4⋊C8—31no—
190C3×#97—31no—
191C3×#97—31no—
192C3×C4×C8—21no—
193C3×C4×C8—31no—
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)⋊C8—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—61no—
211(C2×D3)⋊C8—61no—
212#815—31no—
213#815—31no—
214#815C2×D311yescharacteristic
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8C2×D311yescharacteristic
218Dic3⋊C8C2×D311yescharacteristic
219C8×Dic3—31no—
220C8×Dic3—31no—
221C8×Dic3C2×D311yescharacteristic
222C8×Dic3C2×D311yescharacteristic
223C8×Dic3C2×D311yescharacteristic
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—61no—
229C4⋊(C3⋊C8)C2×D311yescharacteristic
230#803—31no—
231#803—31no—
232#803C2×D311yescharacteristic
233C4×C3⋊C8—31no—
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
243C4⋊(C3⋊D3)—22no—
244C4×C3⋊D3—21no—
245C4×C3⋊D3—21no—
246C4×C3⋊D3—21no—
247C4×C3⋊D3—21no—
248C2×C3×Dic3C22×C411yescharacteristic
249C2×C3×Dic3C22×C411yescharacteristic
250C2×C3×Dic3C22×C411yescharacteristic
251C2×C3×Dic3C22×C411yescharacteristic
252C2×C3×Dic3C22×C411yescharacteristic
253C2×C3×Dic3C22×C411yescharacteristic
254C2×C3×Dic3C22×C411yescharacteristic
255C3×C4×D3—21no—
256C3×C4×D3—21no—
257C3×Dic6—22no—
258#626—22no—
259#626—22no—
260#624—22no—
261#624—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—31no—
273#436—91no—
274#435—91no—
275#435—91no—
276C8×D4—91no—
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×Q8—31no—
286C22×C3×C4—31no—
287C2×#67—31no—
288C2×#67—31no—
289C2×D12—31no—
290C2×D12—31no—
291C2×D12—31no—
292C2×D12—31no—
293C2×D12—61no—
294C2×C4×D3—31no—
295C2×C4×D3—31no—
296C2×C4×D3—31no—
297C2×C4×D3—31no—
298C2×C4×D3—31no—
299C2×C4×D3—31no—
300C2×C4×D3—31no—
301C2×C4×D3—31no—
302C2×C4×D3—61no—
303C2×C4×D3—61no—
304C2×C4×D3C22×D311yescharacteristic
305C2×Dic6C4×D311yescharacteristic
306C3×M16—62no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
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×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C22⋊C4—31no—
324C3×C22⋊C4—31no—
325C3×C42—21no—
326C3×C42—31no—
327C3×C42—31no—
328C3×C42—31no—
329C3×C42C22×D311yescharacteristic
330C3×C42C22×D311yescharacteristic
331#217—31no—
332#217—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—31no—
344(C2×D3)⋊C4—31no—
345(C2×D3)⋊C4—31no—
346(C2×D3)⋊C4—31no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4C4×D311yescharacteristic
350(C2×D3)⋊C4C4×D311yescharacteristic
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—61no—
356C4⋊Dic3C4×D311yescharacteristic
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4C4×D311yescharacteristic
364Dic3⋊C4C4×D311yescharacteristic
365Dic3⋊C4C4×D311yescharacteristic
366Dic3⋊C4C4×D311yescharacteristic
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3C22×D311yescharacteristic
372C4×Dic3C22×D311yescharacteristic
373C4×Dic3C22×D311yescharacteristic
374C2×C3⋊C8—31no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384ΓL(1,𝔽25)—22no—
385ΓL(1,𝔽25)—62no—
386ΓL(1,𝔽25)—62no—
387D3×C8—22no—
388D3×C8—62no—
389D3×C8—62no—
390D3×C8—62no—
391D3×C8—62no—
392D3×C8—62no—
393D3×C8—62no—
394D3×C8—122no—
395D3×C8—122no—
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#13112yes—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
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—31no—
420C2×M16—91no—
421C22×C8—31no—
422C22×C8—91no—
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—91no—
435C4×D4—91no—
436C4×D4—91no—
437#117—31no—
438#117—91no—
439C2×C42—91no—
440C4⋊C8—31no—
441C4⋊C8—31no—
442C4⋊C8—31no—
443C4⋊C8—91no—
444C4⋊C8—91no—
445C4⋊C8—91no—
446C22⋊C8—91no—
447C22⋊C8—91no—
448C22⋊C8—91no—
449C22⋊C8—91no—
450C22⋊C8—91no—
451C22⋊C8—91no—
452#97—31no—
453#97—31no—
454#97—91no—
455#97—91no—
456C4×C8—31no—
457C4×C8—31no—
458C4×C8—31no—
459C4×C8—91no—
460C4×C8—91no—
461C4×C8D3211yescharacteristic
462C23×C3—31no—
463C22×D3—31no—
464C22×D3—31no—
465C22×D3—31no—
466C22×D3—31no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3C2×C4×D311yescharacteristic
470C3×Q8—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—31no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4C2×C4×D311yescharacteristic
484C2×C3×C4C2×C4×D311yescharacteristic
485C2×C3×C4C2×C4×D311yescharacteristic
486C2×C3×C4C2×C4×D311yescharacteristic
487C2×C3×C4C23×D311yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489#67—62no—
490#67—62no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3C2×C4×D311yescharacteristic
498C2×Dic3C2×C4×D311yescharacteristic
499C2×Dic3C2×C4×D311yescharacteristic
500C2×Dic3C2×C4×D311yescharacteristic
501C2×Dic3C2×C4×D311yescharacteristic
502C2×Dic3C2×C4×D311yescharacteristic
503C2×Dic3C2×C4×D311yescharacteristic
504D12—62no—
505D12—62no—
506D12—64no—
507D12—62no—
508D12—62no—
509C4×D3—21no—
510C4×D3—21no—
511C4×D3—62no—
512C4×D3—62no—
513C4×D3—62no—
514C4×D3—61no—
515C4×D3—61no—
516C4×D3—61no—
517C4×D3—61no—
518C4×D3—61no—
519C4×D3—61no—
520C4×D3—61no—
521C4×D3—61no—
522C4×D3—62no—
523C4×D3—121no—
524C4×D3—121no—
525C4×D3—121no—
526C4×D3—121no—
527Dic6—22no—
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#23912yes—
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×C32C4×#4111yescharacteristic
549C2×C32C2×#13111yescharacteristic
550C2×C32C2×#13111yescharacteristic
551C3⋊D3—22no—
552C3⋊D3—41no—
553C3×D3—41no—
554C2×Q8—31no—
555C2×D4—91no—
556C2×D4—91no—
557C2×D4—91no—
558C22×C4—31no—
559C22×C4—91no—
560C22×C4—91no—
561C22×C4—91no—
562C22×C4—91no—
563M16—62no—
564M16—182no—
565C2×C8—31no—
566C2×C8—31no—
567C2×C8—31no—
568C2×C8—31no—
569C2×C8—62no—
570C2×C8—91no—
571C2×C8—91no—
572C2×C8—182no—
573C2×C8—182no—
574C2×C8—182no—
575C2×C8C2×D3211yescharacteristic
576C2×C8C2×D3211yescharacteristic
577C4⋊C4—31no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—31no—
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—91no—
601C42—91no—
602C42C2×D3211yescharacteristic
603C22×C3—21no—
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—32no—
613C2×D3—32no—
614C2×D3—62no—
615C2×D3—61no—
616C2×D3—61no—
617C2×D3—61no—
618C2×D3—61no—
619C2×D3—62no—
620C2×D3—61no—
621C2×D3—61no—
622C2×D3—61no—
623C2×D3—61no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—121no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—121no—
630C3×C4—22no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—32no—
638C3×C4—41no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4C2×#23511yescharacteristic
646C3×C4C2×#23511yescharacteristic
647C3×C4C2×#23911yescharacteristic
648C3×C4D3×#4111yescharacteristic
649Dic3—21no—
650Dic3—21no—
651Dic3—21no—
652Dic3—21no—
653Dic3—21no—
654Dic3—21no—
655Dic3—61no—
656Dic3—61no—
657Dic3—61no—
658Dic3—61no—
659Dic3—121no—
660Dic3—121no—
661Dic3#90112yes—
662C32#296611yescharacteristic, complemented, Sylow
663C23—31no—
664C23—91no—
665C23—91no—
666Q8—62no—
667D4—182no—
668D4—182no—
669D4—182no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—31no—
673C2×C4—31no—
674C2×C4—31no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—91no—
680C2×C4—91no—
681C2×C4—182no—
682C2×C4—182no—
683C2×C4—181no—
684C2×C4—181no—
685C2×C4—181no—
686C2×C4—181no—
687C2×C4C4×D3211yescharacteristic
688C2×C4C4×D3211yescharacteristic
689C2×C4C22×D3211yescharacteristic
690C8—21no—
691C8—32no—
692C8—61no—
693C8—61no—
694C8—61no—
695C8—181no—
696C8—181no—
697C8#379912yes—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—121no—
702C2×C3C4×#23511yescharacteristic
703C2×C3C4×#23911yescharacteristic
704C2×C3C2×#90111yescharacteristic
705C2×C3D3×#13111yescharacteristic
706C2×C3D3×#13111yescharacteristic
707C2×C3D3×#13111yescharacteristic
708D3—41no—
709D3—62no—
710D3—62no—
711D3—122no—
712D3—122no—
713D3—121no—
714D3—121no—
715C22—61no—
716C22—61no—
717C22—61no—
718C22—92no—
719C22—181no—
720C22—181no—
721C22—181no—
722C22—181no—
723C22—181no—
724C22C2×C4×D3211yescharacteristic
725C4—21no—
726C4—21no—
727C4—32no—
728C4—61no—
729C4—61no—
730C4—61no—
731C4—61no—
732C4—61no—
733C4—61no—
734C4—181no—
735C4—181no—
736C4C2×#379911yescharacteristic
737C4D3×#23511yescharacteristic
738C3—21no—
739C3#7855611yescharacteristic, complemented
740C3#7990311yescharacteristic, complemented
741C2—121no—
742C2—182no—
743C2—361no—
744C2C4×#379911yescharacteristic
745C2D3×#90111yescharacteristic
746C2#1059466911yescharacteristic
subgroupG/H
centerC2×C8C2×D32
commutator, socleC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
prime radical#63910C4
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×C4⋊(C3⋊D3)C2semidirect
3. C3×#4689C2semidirect
4. C3×C8×Dic6C2semidirect
5. #10590738C2semidirect
6. #10590731C2semidirect
7. C8×#626C2semidirect
8. C8×#626C2semidirect
9. #10590700C2semidirect
10. #10590665C2semidirect
11. C8×#624C2semidirect
12. #10590647C2semidirect
13. #10590328C2semidirect
14. #10590253C2semidirect
15. #10590251C2semidirect
83. #4689D3semidirect
91. C8×Dic6D3semidirect
662. C32#2966semidirect
739. C3#78556semidirect
740. C3#79903semidirect

Maximal subgroups

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

subgroupindex
#105939342
C8×C4⋊(C3⋊D3)2
C3×#46892
C3×C8×Dic62
#105907382
#105907312
C8×#6262
#105907002
#105906652
C8×#6242
#105906472
#105903282
#105902532
#105902512
#799033
#785563