Finite Group Databasebeta

← #11859139

Subgroups — #11859139

Order 1152.

832 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593965C211yesmaximal, characteristic
2#10592539C211yesmaximal, characteristic, complemented
3C3×#4840C211yesmaximal, characteristic, complemented
4C3×#4837C211yesmaximal, characteristic, complemented
5#10590955C211yesmaximal, characteristic
6#10590955C211yesmaximal, characteristic
7#10590909C211yesmaximal, characteristic, complemented
8#10590908C211yesmaximal, characteristic, complemented
9#10590665C211yesmaximal, characteristic, complemented
10#10590661C211yesmaximal, characteristic, complemented
11#10590656C211yesmaximal, characteristic, complemented
12#10590643C211yesmaximal, characteristic, complemented
13D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
14#10590257C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#79375—31nomaximal
17#79040—31nomaximal
18C2×#3798C2211yescharacteristic
19#64081C2211yescharacteristic
20C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
22C3×#872C2211yescharacteristic
23C3×C42×D3C2211yescharacteristic
24#63904C411yescharacteristic
25#63904C411yescharacteristic
26C4×#624C2211yescharacteristic
27#63880C411yescharacteristic
28#63880C411yescharacteristic
29#63879C411yescharacteristic
30#63879C411yescharacteristic
31C4×D3×Dic3C2211yescharacteristic
32#63855C2211yescharacteristic
33#63837C411yescharacteristic
34#63837C411yescharacteristic
35C2×D3×C3⋊C8C2211yescharacteristic
36C2×D3×C3⋊C8C2211yescharacteristic
37C32×C4⋊C8C2211yescharacteristic
38#63647C2211yescharacteristic
39#63647C2211yescharacteristic
40#63642C2211yescharacteristic
41C8×C3⋊Dic3C2211yescharacteristic
42C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
43C3×(C2×D3)⋊C8C2211yescharacteristic
44C3×(C2×D3)⋊C8C2211yescharacteristic
45C3×#815C2211yescharacteristic
46C3×Dic3⋊C8C2211yescharacteristic
47C3×Dic3⋊C8C2211yescharacteristic
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#5522—31no—
62C4×#235—31no—
63C3×#433—31no—
64C3×#423—31no—
65#5129—31no—
66#5129—31no—
67#5122—31no—
68#5122—31no—
69#5000—31no—
70C2×C4⋊(C3⋊C8)—31no—
71#4840—31no—
72#4840—31no—
73#4840—31no—
74#4840—31no—
75#4840—31no—
76#4840—61no—
77#4840D311yescharacteristic, complemented
78#4837D311yescharacteristic, complemented
79#4835—31no—
80#4835—31no—
81#4833—31no—
82#4833—31no—
83D3×C4⋊C8—31no—
84#4727—31no—
85#4727—31no—
86#4719—31no—
87#4718—31no—
88#4708—31no—
89#4705—31no—
90#4689—31no—
91#4685—31no—
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×C3×C4×D3C2×C411yescharacteristic
94C2×C3×C4×D3C2×C411yescharacteristic
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×C4×D3C2311yescharacteristic
97C2×#627C2×C411yescharacteristic
98C2×#626C2×C411yescharacteristic
99C2×#626C2×C411yescharacteristic
100C2×#625C2×C411yescharacteristic
101C2×#624C2×C411yescharacteristic
102C2×#624C2×C411yescharacteristic
103C2×D3×Dic3C2×C411yescharacteristic
104C2×D3×Dic3C2×C411yescharacteristic
105#3798—22no—
106#3798—22no—
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C42C2311yescharacteristic
110#3752C2×C411yescharacteristic
111#3752C2×C411yescharacteristic
112#3750C2×C411yescharacteristic
113#3750C2×C411yescharacteristic
114C4×C3⋊Dic3C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×(C2×D3)⋊C4C2×C411yescharacteristic
118C3×(C2×D3)⋊C4C2×C411yescharacteristic
119C3×Dic3⋊C4C2×C411yescharacteristic
120C3×Dic3⋊C4C2×C411yescharacteristic
121C3×C4×Dic3C2×C411yescharacteristic
122C3×C4×Dic3C2×C411yescharacteristic
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×ΓL(1,𝔽25)—22no—
130C3×ΓL(1,𝔽25)—22no—
131Dic3⋊Dic3C2×C411yescharacteristic
132Dic3⋊Dic3C2×C411yescharacteristic
133(C2×D3)⋊Dic3C2×C411yescharacteristic
134(C2×D3)⋊Dic3C2×C411yescharacteristic
135Dic32C2×C411yescharacteristic
136Dic32C2×C411yescharacteristic
137Dic32C2×C411yescharacteristic
138Dic32C2×C411yescharacteristic
139D3×C3⋊C8—22no—
140D3×C3⋊C8—22no—
141#2925—91noSylow
142C2×#235—31no—
143C2×#235—31no—
144C2×C3×M16—31no—
145C2×C3×M16—31no—
146C3×#117—31no—
147C2×C3×C42—31no—
148C4×#67—31no—
149C4×#67—31no—
150C4×#67—31no—
151C4×#67—31no—
152#926—31no—
153C2×C4×Dic3—31no—
154C22×C3⋊C8—31no—
155C22×C3⋊C8—31no—
156C2×ΓL(1,𝔽25)C2×D311yescharacteristic
157C2×ΓL(1,𝔽25)C2×D311yescharacteristic
158C2×D3×C8—31no—
159C2×D3×C8—31no—
160#893—31no—
161#893—31no—
162#887—31no—
163#887—31no—
164#67⋊C4—31no—
165#67⋊C4—31no—
166#67⋊C4—31no—
167#67⋊C4—31no—
168C4×D12—31no—
169C4×D12—31no—
170#872—31no—
171#872—31no—
172#872—31no—
173#872—61no—
174#872C2×D311yescharacteristic
175C42×D3—31no—
176C42×D3—31no—
177C42×D3—31no—
178C42×D3C2×D311yescharacteristic
179C4×Dic6—31no—
180C4×Dic6—31no—
181C3×C4⋊C8—21no—
182C3×C4⋊C8—31no—
183C3×C4⋊C8—31no—
184C3×C4⋊C8—31no—
185C3×C4⋊C8—31no—
186C3×C4⋊C8C2×D311yescharacteristic
187C3×C4⋊C8C2×D311yescharacteristic
188C3×C22⋊C8—31no—
189C3×C22⋊C8—31no—
190C3×#97—31no—
191C3×C4×C8—31no—
192#830—31no—
193#830—31no—
194(C2×D3)⋊C8—31no—
195(C2×D3)⋊C8—31no—
196(C2×D3)⋊C8—31no—
197(C2×D3)⋊C8—31no—
198(C2×D3)⋊C8—31no—
199(C2×D3)⋊C8—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—61no—
205(C2×D3)⋊C8—61no—
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—
214#815C2×D311yescharacteristic
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8C2×D311yescharacteristic
218Dic3⋊C8C2×D311yescharacteristic
219C8×Dic3—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—61no—
225C8×Dic3C2×D311yescharacteristic
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—61no—
231C4⋊(C3⋊C8)C2×D311yescharacteristic
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233#803—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
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×C4×D3—21no—
253C3×C4×D3—21no—
254C3×C4×D3—22no—
255C3×C4×D3—41no—
256C3×C4×D3#4112yes—
257C3×C4×D3#4112yes—
258#627—22no—
259#626—22no—
260#626—22no—
261#625—22no—
262#624—22no—
263#624—41no—
264D3×Dic3—22no—
265D3×Dic3—41no—
266C32×C8—21no—
267C32×C8—21no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C4×#41—91no—
275#433—31no—
276#433—91no—
277#433—91no—
278#433—91no—
279#432—91no—
280#432—91no—
281#431—91no—
282#431—91no—
283#423—31no—
284C2×C4⋊C8—91no—
285#408—91no—
286#408—91no—
287#405—91no—
288#405—91no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C2×#67—31no—
294C2×#67—31no—
295C2×#67—31no—
296C2×#67—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299#235—62no—
300#235—62no—
301#235—62no—
302#235—62no—
303C2×D12—31no—
304C2×D12—31no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3—31no—
313C2×C4×D3—61no—
314C2×C4×D3C4×D311yescharacteristic
315C2×C4×D3C4×D311yescharacteristic
316C2×C4×D3C22×D311yescharacteristic
317C2×C4×D3C22×D311yescharacteristic
318C2×Dic6—31no—
319C2×Dic6—31no—
320C3×M16—62no—
321C3×M16—62no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C2×C3×C8C22×D311yescharacteristic
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C22⋊C4—31no—
335C3×C22⋊C4—31no—
336C3×C42—21no—
337C3×C42—31no—
338C3×C42—31no—
339C3×C42—31no—
340C3×C42—31no—
341C3×C42C22×D311yescharacteristic
342C3×C42C22×D311yescharacteristic
343#217—31no—
344#217—31no—
345(C2×D3)⋊C4—31no—
346(C2×D3)⋊C4—31no—
347(C2×D3)⋊C4—31no—
348(C2×D3)⋊C4—31no—
349(C2×D3)⋊C4—31no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4C4×D311yescharacteristic
354(C2×D3)⋊C4C4×D311yescharacteristic
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4C4×D311yescharacteristic
366Dic3⋊C4C4×D311yescharacteristic
367C4×Dic3—31no—
368C4×Dic3—31no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—61no—
378C4×Dic3C4×D311yescharacteristic
379C4×Dic3C4×D311yescharacteristic
380C4×Dic3C22×D311yescharacteristic
381C4×Dic3C22×D311yescharacteristic
382C2×C3⋊C8—31no—
383C2×C3⋊C8—31no—
384C2×C3⋊C8—31no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—61no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8—62no—
389C2×C3⋊C8—62no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392C2×C3⋊C8C22×D311yescharacteristic
393C2×C3⋊C8C22×D311yescharacteristic
394ΓL(1,𝔽25)—22no—
395ΓL(1,𝔽25)—22no—
396D3×C8—62no—
397D3×C8—62no—
398C22×C32C23×C411yescharacteristic
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—21no—
406C2×C3×D3—21no—
407C2×C3×D3#11712yes—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4C2×#4111yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3⋊Dic3—21no—
413C3⋊Dic3—21no—
414C3⋊Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3#11712yes—
420C3×Dic3#13112yes—
421C2×#41—91no—
422C2×M16—31no—
423C2×M16—31no—
424C22×C8—91no—
425C22×C8—91no—
426C4×Q8—91no—
427C4×Q8—91no—
428C4×D4—91no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—91no—
432C4×D4—91no—
433C4×D4—91no—
434#117—31no—
435#117—91no—
436#117—91no—
437C2×C42—31no—
438C2×C42—91no—
439C2×C42—91no—
440C4⋊C8—31no—
441C4⋊C8—31no—
442C4⋊C8—31no—
443C4⋊C8—31no—
444C4⋊C8—91no—
445C4⋊C8—91no—
446C4⋊C8—91no—
447C4⋊C8D3211yescharacteristic
448C22⋊C8—31no—
449C22⋊C8—31no—
450C22⋊C8—91no—
451C22⋊C8—91no—
452C22⋊C8—91no—
453C22⋊C8—91no—
454C22⋊C8—91no—
455C22⋊C8—91no—
456#97—31no—
457#97—91no—
458#97—91no—
459#97—91no—
460C4×C8—31no—
461C4×C8—91no—
462C4×C8—91no—
463C4×C8—91no—
464C23×C3—31no—
465C23×C3—31no—
466C22×D3—31no—
467C22×D3—31no—
468C22×D3—61no—
469C22×D3C2×C4×D311yescharacteristic
470C22×D3C2×C4×D311yescharacteristic
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—32no—
477C2×C3×C4—32no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—31no—
481C2×C3×C4—31no—
482C2×C3×C4—62no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—121no—
486C2×C3×C4C2×C4×D311yescharacteristic
487C2×C3×C4C2×C4×D311yescharacteristic
488C2×C3×C4C2×C4×D311yescharacteristic
489C2×C3×C4C2×C4×D311yescharacteristic
490C2×C3×C4C23×D311yescharacteristic
491C2×C3×C4C23×D311yescharacteristic
492#67—62no—
493#67—62no—
494#67—62no—
495#67—62no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—62no—
506C2×Dic3—121no—
507C2×Dic3C2×C4×D311yescharacteristic
508C2×Dic3C2×C4×D311yescharacteristic
509C2×Dic3C2×C4×D311yescharacteristic
510C2×Dic3C2×C4×D311yescharacteristic
511C2×Dic3C2×C4×D311yescharacteristic
512C2×Dic3C2×C4×D311yescharacteristic
513D12—62no—
514D12—62no—
515C4×D3—21no—
516C4×D3—21no—
517C4×D3—22no—
518C4×D3—41no—
519C4×D3—62no—
520C4×D3—62no—
521C4×D3—61no—
522C4×D3—61no—
523C4×D3—61no—
524C4×D3—61no—
525C4×D3—62no—
526C4×D3—121no—
527C4×D3—121no—
528C4×D3—121no—
529C4×D3—121no—
530C4×D3—121no—
531C4×D3#23712yes—
532C4×D3#23912yes—
533Dic6—62no—
534Dic6—62no—
535C3×C8—21no—
536C3×C8—21no—
537C3×C8—21no—
538C3×C8—21no—
539C3×C8—41no—
540C3×C8—41no—
541C3×C8—61no—
542C3×C8—61no—
543C3×C8—61no—
544C3×C8—61no—
545C3⋊C8—21no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C3⋊C8—21no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—121no—
554C3⋊C8—121no—
555C2×C32C2×#11711yescharacteristic
556C2×C32C2×#13111yescharacteristic
557C2×C32#56811yescharacteristic
558C3⋊D3—41no—
559C3×D3—22no—
560C3×D3—41no—
561#41—182no—
562#41—182no—
563C2×Q8—91no—
564C2×D4—91no—
565C2×D4—91no—
566C2×D4—91no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—91no—
572C22×C4—91no—
573C22×C4—91no—
574C22×C4—91no—
575C22×C4—91no—
576M16—62no—
577M16—62no—
578C2×C8—31no—
579C2×C8—31no—
580C2×C8—31no—
581C2×C8—31no—
582C2×C8—91no—
583C2×C8—91no—
584C2×C8—182no—
585C2×C8—182no—
586C2×C8C2×D3211yescharacteristic
587C2×C8C2×D3211yescharacteristic
588C4⋊C4—31no—
589C4⋊C4—31no—
590C4⋊C4—91no—
591C4⋊C4—91no—
592C4⋊C4—91no—
593C4⋊C4—91no—
594C22⋊C4—31no—
595C22⋊C4—31no—
596C22⋊C4—91no—
597C22⋊C4—91no—
598C22⋊C4—91no—
599C22⋊C4—91no—
600C42—31no—
601C42—31no—
602C42—31no—
603C42—31no—
604C42—91no—
605C42—91no—
606C42—91no—
607C42—91no—
608C42—91no—
609C42C2×D3211yescharacteristic
610C22×C3—21no—
611C22×C3—32no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3C22×C4×D311yescharacteristic
618C22×C3C22×C4×D311yescharacteristic
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—121no—
633C2×D3#89212yes—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—32no—
641C3×C4—32no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4C2×#23711yescharacteristic
649C3×C4C2×#23911yescharacteristic
650C3×C4D3×#4111yescharacteristic
651C3×C4D3×#4111yescharacteristic
652Dic3—21no—
653Dic3—21no—
654Dic3—21no—
655Dic3—21no—
656Dic3—61no—
657Dic3—61no—
658Dic3—61no—
659Dic3—61no—
660Dic3—61no—
661Dic3—61no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3#89212yes—
666Dic3#90712yes—
667C32#292511yescharacteristic, complemented, Sylow
668C23—31no—
669C23—31no—
670C23—91no—
671Q8—182no—
672D4—182no—
673D4—182no—
674D4—182no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—32no—
678C2×C4—32no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—62no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—91no—
687C2×C4—91no—
688C2×C4—91no—
689C2×C4—121no—
690C2×C4—182no—
691C2×C4—182no—
692C2×C4—181no—
693C2×C4—181no—
694C2×C4—361no—
695C2×C4—361no—
696C2×C4C4×D3211yescharacteristic
697C2×C4C4×D3211yescharacteristic
698C2×C4C22×D3211yescharacteristic
699C8—21no—
700C8—21no—
701C8—61no—
702C8—61no—
703C8—61no—
704C8—61no—
705C8—181no—
706C8—181no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—62no—
711C2×C3—121no—
712C2×C3C2×#89211yescharacteristic
713C2×C3D3×#11711yescharacteristic
714C2×C3C2×#90711yescharacteristic
715C2×C3#574511yescharacteristic
716C2×C3D3×#13111yescharacteristic
717C2×C3#575011yescharacteristic
718D3—22no—
719D3—41no—
720D3—121no—
721D3—121no—
722D3—241no—
723C22—32no—
724C22—61no—
725C22—61no—
726C22—61no—
727C22—61no—
728C22—61no—
729C22—181no—
730C22—181no—
731C22—181no—
732C22C2×C4×D3211yescharacteristic
733C4—21no—
734C4—21no—
735C4—32no—
736C4—32no—
737C4—61no—
738C4—61no—
739C4—61no—
740C4—61no—
741C4—181no—
742C4—181no—
743C4—181no—
744C4D3×#23711yescharacteristic
745C4D3×#23911yescharacteristic
746C3—21no—
747C3#7904011yescharacteristic, complemented
748C3#7937511yescharacteristic, complemented
749C2—62no—
750C2—121no—
751C2—361no—
752C2D3×#89211yescharacteristic
753C2#1059466811yescharacteristic
754C2D3×#90711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4⋊C8C22
prime radicalC2×#3798C22
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592539C2semidirect
3. C3×#4840C2semidirect
4. C3×#4837C2semidirect
7. #10590909C2semidirect
8. #10590908C2semidirect
9. #10590665C2semidirect
10. #10590661C2semidirect
11. #10590656C2semidirect
12. #10590643C2semidirect
13. D3×C4⋊(C3⋊C8)C2semidirect
14. #10590257C2semidirect
15. #10590253C2semidirect
77. #4840D3semidirect
78. #4837D3semidirect
667. C32#2925semidirect
747. C3#79040semidirect
748. C3#79375semidirect

Maximal subgroups

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

subgroupindex
#105939652
#105925392
C3×#48402
C3×#48372
#105909552
#105909092
#105909082
#105906652
#105906612
#105906562
#105906432
D3×C4⋊(C3⋊C8)2
#105902572
#105902532
#793753
#790403