Finite Group Databasebeta

← C2×C83×#3524 #35290616

Subgroups — C2×C83×#3524 #35290616

Order 21248.

7226 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3524C2132yesmaximal, direct product factor
2C2×#559×C83C213yesmaximal, complemented
3C2×#557×C83C211yesmaximal, characteristic, complemented
4C2×#555×C83C213yesmaximal, complemented
5C2×#553×C83C213yesmaximal, complemented
6C2×#552×C83C213yesmaximal, complemented
7C2×#550×C83C211yesmaximal, characteristic, complemented
8C2×#548×C83C211yesmaximal, characteristic, complemented
9C2×#548×C83C211yesmaximal, characteristic, complemented
10C2×#542×C83C213yesmaximal, complemented
11C2×#540×C83C213yesmaximal, complemented
12C2×#529×C83C213yesmaximal, complemented
13C2×#529×C83C213yesmaximal, complemented
14C2×#520×C83C211yesmaximal, characteristic, complemented
15C2×#519×C83C211yesmaximal, characteristic, complemented
16C2×C4×#41×C83C211yesmaximal, characteristic, complemented
17C22×#41×C83C2211yescharacteristic
18C22×#41×C83C2211yescharacteristic
19C23×Q8×C83C2211yescharacteristic
20#559×C83C22148yescomplemented
21#557×C83C22116yescomplemented
22#555×C83C22148yescomplemented
23#553×C83C22148yescomplemented
24#552×C83C22148yescomplemented
25#550×C83C22116yescomplemented
26#548×C83C22116yescomplemented
27#548×C83C22116yescomplemented
28#542×C83C22148yescomplemented
29#540×C83C22148yescomplemented
30C2×C4⋊Q8×C83C2213yes—
31C2×#127×C83C2213yes—
32#529×C83C22148yescomplemented
33#529×C83C22148yescomplemented
34C2×#126×C83C2211yescharacteristic
35C2×#126×C83C2213yes—
36C2×#126×C83C2216yes—
37C2×#125×C83C2213yes—
38C2×#125×C83C2213yes—
39C2×#125×C83C2213yes—
40C2×#124×C83C2213yes—
41C2×#124×C83C2213yes—
42C2×#124×C83C2213yes—
43C2×#124×C83C2216yes—
44C2×#123×C83C2216yes—
45C2×#123×C83C2213yes—
46C2×#123×C83C2213yes—
47C2×#123×C83C2216yes—
48C2×C22⋊Q8×C83C2213yes—
49C2×C22⋊Q8×C83C2213yes—
50C2×C22⋊Q8×C83C2213yes—
51C2×#121×C83C2213yes—
52C2×#121×C83C2213yes—
53C2×#121×C83C2213yes—
54C2×#121×C83C2213yes—
55C2×#121×C83C2216yes—
56C2×#121×C83C2213yes—
57#520×C83C22116yescomplemented
58#519×C83C22116yescomplemented
59C4×#41×C83C22116yescomplemented
60C2×C4×Q8×C83C2211yescharacteristic
61C2×C4×Q8×C83C2211yescharacteristic
62C2×C4×Q8×C83C2213yes—
63C2×C4×Q8×C83C2211yescharacteristic
64C2×C4×Q8×C83C2213yes—
65C2×C4×Q8×C83C2211yescharacteristic
66C2×C4×Q8×C83C2213yes—
67C2×C4×D4×C83C2213yes—
68C2×C4×D4×C83C2213yes—
69C2×C4×D4×C83C2213yes—
70C2×C4×D4×C83C2213yes—
71C2×C4×D4×C83C2213yes—
72C2×C4×D4×C83C2213yes—
73C2×C4×D4×C83C2213yes—
74C2×C4×D4×C83C2216yes—
75C2×#117×C83C2213yes—
76C2×#117×C83C2213yes—
77C2×#117×C83C2213yes—
78C2×#117×C83C2213yes—
79C2×#117×C83C2216yes—
80C22×C4⋊C4×C83C2213yes—
81C22×C42×C83C2213yes—
82C2×#41×C83—28no—
83C2×#41×C83—28no—
84C2×#41×C83C2318yes—
85C2×#41×C83C2318yes—
86C22×Q8×C83—28no—
87C22×Q8×C83C2313yes—
88C22×Q8×C83C2318yes—
89C22×Q8×C83C2313yes—
90C22×Q8×C83C2311yescharacteristic
91C22×D4×C83C2313yes—
92C22×D4×C83C2313yes—
93C22×D4×C83C2313yes—
94C22×D4×C83C2313yes—
95C22×D4×C83C2316yes—
96C22×D4×C83C2313yes—
97C23×C4×C83C2313yes—
98C23×C4×C83C2313yes—
99C23×C4×C83C2313yes—
100C23×C4×C83C2313yes—
101C23×C4×C83C2313yes—
102C23×C4×C83C2316yes—
103C4⋊Q8×C83C23124yes—
104#127×C83C23124yes—
105#126×C83C2318yes—
106#126×C83C23124yes—
107#126×C83C23148yes—
108#125×C83C23124yes—
109#125×C83C23124yes—
110#125×C83C23124yes—
111#124×C83C23124yes—
112#124×C83C23124yes—
113#124×C83C23124yes—
114#124×C83C23148yes—
115#123×C83C23148yes—
116#123×C83C23124yes—
117#123×C83C23124yes—
118#123×C83C23148yes—
119C22⋊Q8×C83C23124yes—
120C22⋊Q8×C83C23124yes—
121C22⋊Q8×C83C23124yes—
122#121×C83C23124yes—
123#121×C83C23124yes—
124#121×C83C23124yes—
125#121×C83C23124yes—
126#121×C83C23148yes—
127#121×C83C23124yes—
128C4×Q8×C83C2318yes—
129C4×Q8×C83C2318yes—
130C4×Q8×C83C23124yes—
131C4×Q8×C83C2318yes—
132C4×Q8×C83C23124yes—
133C4×Q8×C83C2318yes—
134C4×Q8×C83C23124yes—
135C4×D4×C83C23124yes—
136C4×D4×C83C23124yes—
137C4×D4×C83C23124yes—
138C4×D4×C83C23124yes—
139C4×D4×C83C23124yes—
140C4×D4×C83C23124yes—
141C4×D4×C83C23124yes—
142C4×D4×C83C23148yes—
143#117×C83C23124yes—
144#117×C83C23124yes—
145#117×C83C23124yes—
146#117×C83C23124yes—
147#117×C83C23148yes—
148C2×C4⋊C4×C83C2313yes—
149C2×C4⋊C4×C83C2313yes—
150C2×C4⋊C4×C83C2313yes—
151C2×C4⋊C4×C83C23124yes—
152C2×C4⋊C4×C83C2311yescharacteristic
153C2×C4⋊C4×C83C2313yes—
154C2×C4⋊C4×C83C2313yes—
155C2×C4⋊C4×C83C2313yes—
156C2×C4⋊C4×C83C2313yes—
157C2×C4⋊C4×C83C2313yes—
158C2×C4⋊C4×C83C2316yes—
159C2×C4⋊C4×C83C2311yescharacteristic
160C2×C4⋊C4×C83C2313yes—
161C2×C4⋊C4×C83C2313yes—
162C2×C4⋊C4×C83C2311yescharacteristic
163C2×C4⋊C4×C83C2313yes—
164C2×C22⋊C4×C83C2311yescharacteristic
165C2×C22⋊C4×C83C2313yes—
166C2×C22⋊C4×C83C2313yes—
167C2×C22⋊C4×C83C2313yes—
168C2×C22⋊C4×C83C2316yes—
169C2×C22⋊C4×C83C2313yes—
170C2×C22⋊C4×C83C2316yes—
171C2×C22⋊C4×C83C2311yescharacteristic
172C2×C22⋊C4×C83C2313yes—
173C2×C22⋊C4×C83C2311yescharacteristic
174C2×C22⋊C4×C83C2313yes—
175C2×C22⋊C4×C83C2316yes—
176C2×C22⋊C4×C83C2313yes—
177C2×C42×C83C2311yescharacteristic
178C2×C42×C83C2313yes—
179C2×C42×C83C2313yes—
180C2×C42×C83C2313yes—
181C2×C42×C83C23124yes—
182C2×C42×C83C2316yes—
183C2×C42×C83C2313yes—
184C2×C42×C83C2313yes—
185C24×C83C2411yescharacteristic
186C24×C83C2413yes—
187C24×C83C2413yes—
188#41×C83—232no—
189#41×C83—232no—
190C2×Q8×C83—232no—
191C2×Q8×C83—212no—
192C2×Q8×C83—46no—
193C2×Q8×C83#4118yes—
194C2×Q8×C83C24112yes—
195C2×Q8×C83C24112yes—
196C2×Q8×C83C2414yes—
197C2×D4×C83—212no—
198C2×D4×C83—212no—
199C2×D4×C83—46no—
200C2×D4×C83—46no—
201C2×D4×C83—46no—
202C2×D4×C83—412no—
203C2×D4×C83C24112yes—
204C2×D4×C83C24112yes—
205C2×D4×C83C24112yes—
206C2×D4×C83C24112yes—
207C2×D4×C83C24124yes—
208C2×D4×C83C24112yes—
209C22×C4×C83—212no—
210C22×C4×C83—212no—
211C22×C4×C83—212no—
212C22×C4×C83—46no—
213C22×C4×C83—412no—
214C22×C4×C83—46no—
215C22×C4×C83C24112yes—
216C22×C4×C83C24112yes—
217C22×C4×C83C24112yes—
218C22×C4×C83C2411yescharacteristic
219C22×C4×C83C2411yescharacteristic
220C22×C4×C83C2411yescharacteristic
221C22×C4×C83C2413yes—
222C22×C4×C83C2411yescharacteristic
223C22×C4×C83C2413yes—
224C22×C4×C83C2411yescharacteristic
225C22×C4×C83C2413yes—
226C22×C4×C83C2413yes—
227C22×C4×C83C2413yes—
228C22×C4×C83C2411yescharacteristic
229C22×C4×C83C24112yes—
230C22×C4×C83C24112yes—
231C22×C4×C83C24124yes—
232C22×C4×C83C2413yes—
233C4⋊C4×C83C24112yes—
234C4⋊C4×C83C24112yes—
235C4⋊C4×C83C24112yes—
236C4⋊C4×C83C2414yes—
237C4⋊C4×C83C24112yes—
238C4⋊C4×C83C24112yes—
239C4⋊C4×C83C24112yes—
240C4⋊C4×C83C24112yes—
241C4⋊C4×C83C24112yes—
242C4⋊C4×C83C24124yes—
243C4⋊C4×C83C2414yes—
244C4⋊C4×C83C24112yes—
245C4⋊C4×C83C24112yes—
246C4⋊C4×C83C2414yes—
247C4⋊C4×C83C24112yes—
248C22⋊C4×C83C2414yes—
249C22⋊C4×C83C24112yes—
250C22⋊C4×C83C24112yes—
251C22⋊C4×C83C24112yes—
252C22⋊C4×C83C24124yes—
253C22⋊C4×C83C24112yes—
254C22⋊C4×C83C24124yes—
255C22⋊C4×C83C2414yes—
256C22⋊C4×C83C24112yes—
257C22⋊C4×C83C2414yes—
258C22⋊C4×C83C24112yes—
259C22⋊C4×C83C24124yes—
260C22⋊C4×C83C24112yes—
261C42×C83C2414yes—
262C42×C83C24112yes—
263C42×C83C24112yes—
264C42×C83C24112yes—
265C42×C83C24124yes—
266C42×C83C24112yes—
267C42×C83C24112yes—
268C23×C83—22no—
269C23×C83—26no—
270C23×C83—26no—
271C23×C83—26no—
272C23×C83—26no—
273C23×C83—26no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—26no—
277C23×C83C2512yes—
278C23×C83C2516yes—
279C23×C83C2516yes—
280C23×C83C2511yescharacteristic
281Q8×C83—224no—
282Q8×C83—412no—
283Q8×C83C2×#41116yes—
284D4×C83—224no—
285D4×C83—224no—
286D4×C83—412no—
287D4×C83—412no—
288D4×C83—412no—
289D4×C83—424no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—26no—
293C2×C4×C83—22no—
294C2×C4×C83—26no—
295C2×C4×C83—22no—
296C2×C4×C83—26no—
297C2×C4×C83—26no—
298C2×C4×C83—22no—
299C2×C4×C83—26no—
300C2×C4×C83—22no—
301C2×C4×C83—224no—
302C2×C4×C83—224no—
303C2×C4×C83—224no—
304C2×C4×C83—412no—
305C2×C4×C83—424no—
306C2×C4×C83—412no—
307C2×C4×C83C2×#41112yes—
308C2×C4×C83C2512yes—
309C2×C4×C83C2512yes—
310C2×C4×C83C2512yes—
311C2×C4×C83C2516yes—
312C2×C4×C83C2512yes—
313C2×C4×C83C2516yes—
314C2×C4×C83C2512yes—
315C2×C4×C83C2516yes—
316C2×C4×C83C2516yes—
317C2×C4×C83C2516yes—
318C2×C4×C83C2512yes—
319C2×C4×C83C2516yes—
320C22×C83—22no—
321C22×C83—26no—
322C22×C83—26no—
323C22×C83—26no—
324C22×C83—26no—
325C22×C83—26no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83—26no—
329C22×C83—44no—
330C22×C83—412no—
331C22×C83—412no—
332C22×C83C22×#4112yes—
333C22×C83#58512yes—
334C22×C83#58512yes—
335C22×C83C2611yescharacteristic
336C4×C83—22no—
337C4×C83—22no—
338C4×C83—26no—
339C4×C83—22no—
340C4×C83—26no—
341C4×C83—22no—
342C4×C83—26no—
343C4×C83—26no—
344C4×C83—22no—
345C4×C83—26no—
346C4×C83—22no—
347C4×C83C22×#41112yes—
348C2×#3524C8311yesmaximal, characteristic, direct product factor, Sylow
349C2×C83—42no—
350C2×C83—46no—
351C2×C83—46no—
352C2×C83#352414yesdirect product factor
353C2×C83C23×#4111yescharacteristic
354C2×C83C2×#58511yescharacteristic
355C2×C83C2×#58511yescharacteristic
356#3524C2×C83132yesdirect product factor
357C2×#559C2×C8313yescomplemented
358C2×#557C2×C8311yescharacteristic, complemented
359C2×#555C2×C8313yescomplemented
360C2×#553C2×C8313yescomplemented
361C2×#552C2×C8313yescomplemented
362C2×#550C2×C8311yescharacteristic, complemented
363C2×#548C2×C8311yescharacteristic, complemented
364C2×#548C2×C8311yescharacteristic, complemented
365C2×#542C2×C8313yescomplemented
366C2×#540C2×C8313yescomplemented
367C2×#529C2×C8313yescomplemented
368C2×#529C2×C8313yescomplemented
369C2×#520C2×C8311yescharacteristic, complemented
370C2×#519C2×C8311yescharacteristic, complemented
371C2×C4×#41C2×C8311yescharacteristic, complemented
372C83C2×#352411yescharacteristic, direct product factor, Sylow
373C22×#41C22×C8311yescharacteristic
374C22×#41C22×C8311yescharacteristic
375C23×Q8C22×C8311yescharacteristic
376#559C22×C83148yescomplemented
377#557C22×C83116yescomplemented
378#555C22×C83148yescomplemented
379#553C22×C83148yescomplemented
380#552C22×C83148yescomplemented
381#550C22×C83116yescomplemented
382#548C22×C83116yescomplemented
383#548C22×C83116yescomplemented
384#542C22×C83148yescomplemented
385#540C22×C83148yescomplemented
386C2×C4⋊Q8C22×C8313yes—
387C2×#127C22×C8313yes—
388#529C22×C83148yescomplemented
389#529C22×C83148yescomplemented
390C2×#126C22×C8311yescharacteristic
391C2×#126C22×C8313yes—
392C2×#126C22×C8316yes—
393C2×#125C22×C8313yes—
394C2×#125C22×C8313yes—
395C2×#125C22×C8313yes—
396C2×#124C22×C8313yes—
397C2×#124C22×C8313yes—
398C2×#124C22×C8313yes—
399C2×#124C22×C8316yes—
400C2×#123C22×C8316yes—
401C2×#123C22×C8313yes—
402C2×#123C22×C8313yes—
403C2×#123C22×C8316yes—
404C2×C22⋊Q8C22×C8313yes—
405C2×C22⋊Q8C22×C8313yes—
406C2×C22⋊Q8C22×C8313yes—
407C2×#121C22×C8313yes—
408C2×#121C22×C8313yes—
409C2×#121C22×C8313yes—
410C2×#121C22×C8313yes—
411C2×#121C22×C8316yes—
412C2×#121C22×C8313yes—
413#520C22×C83116yescomplemented
414#519C22×C83116yescomplemented
415C4×#41C22×C83116yescomplemented
416C2×C4×Q8C22×C8311yescharacteristic
417C2×C4×Q8C22×C8311yescharacteristic
418C2×C4×Q8C22×C8313yes—
419C2×C4×Q8C22×C8311yescharacteristic
420C2×C4×Q8C22×C8313yes—
421C2×C4×Q8C22×C8311yescharacteristic
422C2×C4×Q8C22×C8313yes—
423C2×C4×D4C22×C8313yes—
424C2×C4×D4C22×C8313yes—
425C2×C4×D4C22×C8313yes—
426C2×C4×D4C22×C8313yes—
427C2×C4×D4C22×C8313yes—
428C2×C4×D4C22×C8313yes—
429C2×C4×D4C22×C8313yes—
430C2×C4×D4C22×C8316yes—
431C2×#117C22×C8313yes—
432C2×#117C22×C8313yes—
433C2×#117C22×C8313yes—
434C2×#117C22×C8313yes—
435C2×#117C22×C8316yes—
436C22×C4⋊C4C22×C8313yes—
437C22×C42C22×C8313yes—
438C2×#41—28no—
439C2×#41—28no—
440C2×#41C23×C8318yes—
441C2×#41C23×C8318yes—
442C22×Q8—28no—
443C22×Q8C23×C8313yes—
444C22×Q8C23×C8318yes—
445C22×Q8C23×C8313yes—
446C22×Q8C23×C8311yescharacteristic
447C22×D4C23×C8313yes—
448C22×D4C23×C8313yes—
449C22×D4C23×C8313yes—
450C22×D4C23×C8313yes—
451C22×D4C23×C8316yes—
452C22×D4C23×C8313yes—
453C23×C4C23×C8313yes—
454C23×C4C23×C8313yes—
455C23×C4C23×C8313yes—
456C23×C4C23×C8316yes—
457C23×C4C23×C8313yes—
458C23×C4C23×C8313yes—
459C4⋊Q8C23×C83124yes—
460#127C23×C83124yes—
461#126C23×C8318yes—
462#126C23×C83124yes—
463#126C23×C83148yes—
464#125C23×C83124yes—
465#125C23×C83124yes—
466#125C23×C83124yes—
467#124C23×C83124yes—
468#124C23×C83124yes—
469#124C23×C83124yes—
470#124C23×C83148yes—
471#123C23×C83148yes—
472#123C23×C83124yes—
473#123C23×C83124yes—
474#123C23×C83148yes—
475C22⋊Q8C23×C83124yes—
476C22⋊Q8C23×C83124yes—
477C22⋊Q8C23×C83124yes—
478#121C23×C83124yes—
479#121C23×C83124yes—
480#121C23×C83124yes—
481#121C23×C83124yes—
482#121C23×C83148yes—
483#121C23×C83124yes—
484C4×Q8C23×C8318yes—
485C4×Q8C23×C8318yes—
486C4×Q8C23×C83124yes—
487C4×Q8C23×C8318yes—
488C4×Q8C23×C83124yes—
489C4×Q8C23×C8318yes—
490C4×Q8C23×C83124yes—
491C4×D4C23×C83124yes—
492C4×D4C23×C83124yes—
493C4×D4C23×C83124yes—
494C4×D4C23×C83124yes—
495C4×D4C23×C83124yes—
496C4×D4C23×C83124yes—
497C4×D4C23×C83124yes—
498C4×D4C23×C83148yes—
499#117C23×C83124yes—
500#117C23×C83124yes—
501#117C23×C83124yes—
502#117C23×C83124yes—
503#117C23×C83148yes—
504C2×C4⋊C4C23×C8313yes—
505C2×C4⋊C4C23×C8313yes—
506C2×C4⋊C4C23×C8313yes—
507C2×C4⋊C4C23×C83124yes—
508C2×C4⋊C4C23×C8311yescharacteristic
509C2×C4⋊C4C23×C8313yes—
510C2×C4⋊C4C23×C8313yes—
511C2×C4⋊C4C23×C8313yes—
512C2×C4⋊C4C23×C8313yes—
513C2×C4⋊C4C23×C8313yes—
514C2×C4⋊C4C23×C8316yes—
515C2×C4⋊C4C23×C8311yescharacteristic
516C2×C4⋊C4C23×C8313yes—
517C2×C4⋊C4C23×C8313yes—
518C2×C4⋊C4C23×C8311yescharacteristic
519C2×C4⋊C4C23×C8313yes—
520C2×C22⋊C4C23×C8311yescharacteristic
521C2×C22⋊C4C23×C8313yes—
522C2×C22⋊C4C23×C8313yes—
523C2×C22⋊C4C23×C8313yes—
524C2×C22⋊C4C23×C8316yes—
525C2×C22⋊C4C23×C8313yes—
526C2×C22⋊C4C23×C8316yes—
527C2×C22⋊C4C23×C8311yescharacteristic
528C2×C22⋊C4C23×C8313yes—
529C2×C22⋊C4C23×C8311yescharacteristic
530C2×C22⋊C4C23×C8313yes—
531C2×C22⋊C4C23×C8316yes—
532C2×C22⋊C4C23×C8313yes—
533C2×C42C23×C8313yes—
534C2×C42C23×C8313yes—
535C2×C42C23×C8316yes—
536C2×C42C23×C8313yes—
537C2×C42C23×C8313yes—
538C2×C42C23×C8313yes—
539C2×C42C23×C83124yes—
540C2×C42C23×C8311yescharacteristic
541C24C24×C8311yescharacteristic
542C24C24×C8313yes—
543C24C24×C8313yes—
544#41—232no—
545#41—232no—
546C2×Q8—232no—
547C2×Q8—212no—
548C2×Q8—46no—
549C2×Q8#41×C8318yes—
550C2×Q8C24×C83112yes—
551C2×Q8C24×C83112yes—
552C2×Q8C24×C8314yes—
553C2×D4—212no—
554C2×D4—212no—
555C2×D4—46no—
556C2×D4—46no—
557C2×D4—46no—
558C2×D4—412no—
559C2×D4C24×C83112yes—
560C2×D4C24×C83112yes—
561C2×D4C24×C83112yes—
562C2×D4C24×C83112yes—
563C2×D4C24×C83124yes—
564C2×D4C24×C83112yes—
565C22×C4—212no—
566C22×C4—212no—
567C22×C4—212no—
568C22×C4—46no—
569C22×C4—412no—
570C22×C4—46no—
571C22×C4C24×C8311yescharacteristic
572C22×C4C24×C8313yes—
573C22×C4C24×C8311yescharacteristic
574C22×C4C24×C8311yescharacteristic
575C22×C4C24×C8311yescharacteristic
576C22×C4C24×C8313yes—
577C22×C4C24×C8311yescharacteristic
578C22×C4C24×C8313yes—
579C22×C4C24×C8313yes—
580C22×C4C24×C83112yes—
581C22×C4C24×C8313yes—
582C22×C4C24×C8311yescharacteristic
583C22×C4C24×C83112yes—
584C22×C4C24×C83112yes—
585C22×C4C24×C83112yes—
586C22×C4C24×C83112yes—
587C22×C4C24×C83124yes—
588C22×C4C24×C8313yes—
589C4⋊C4C24×C83112yes—
590C4⋊C4C24×C83112yes—
591C4⋊C4C24×C83112yes—
592C4⋊C4C24×C8314yes—
593C4⋊C4C24×C83112yes—
594C4⋊C4C24×C83112yes—
595C4⋊C4C24×C83112yes—
596C4⋊C4C24×C83112yes—
597C4⋊C4C24×C83112yes—
598C4⋊C4C24×C83124yes—
599C4⋊C4C24×C8314yes—
600C4⋊C4C24×C83112yes—
601C4⋊C4C24×C83112yes—
602C4⋊C4C24×C8314yes—
603C4⋊C4C24×C83112yes—
604C22⋊C4C24×C8314yes—
605C22⋊C4C24×C83112yes—
606C22⋊C4C24×C83112yes—
607C22⋊C4C24×C83112yes—
608C22⋊C4C24×C83124yes—
609C22⋊C4C24×C83112yes—
610C22⋊C4C24×C83124yes—
611C22⋊C4C24×C8314yes—
612C22⋊C4C24×C83112yes—
613C22⋊C4C24×C8314yes—
614C22⋊C4C24×C83112yes—
615C22⋊C4C24×C83124yes—
616C22⋊C4C24×C83112yes—
617C42C24×C8314yes—
618C42C24×C83112yes—
619C42C24×C83112yes—
620C42C24×C83112yes—
621C42C24×C83124yes—
622C42C24×C83112yes—
623C42C24×C83112yes—
624C23—22no—
625C23—26no—
626C23—26no—
627C23—26no—
628C23—26no—
629C23—26no—
630C23—22no—
631C23—22no—
632C23—26no—
633C23C25×C8312yes—
634C23C25×C8316yes—
635C23C25×C8316yes—
636C23C25×C8311yescharacteristic
637Q8—224no—
638Q8—412no—
639Q8C2×#41×C83116yes—
640D4—224no—
641D4—224no—
642D4—412no—
643D4—412no—
644D4—412no—
645D4—424no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—26no—
649C2×C4—22no—
650C2×C4—26no—
651C2×C4—22no—
652C2×C4—26no—
653C2×C4—26no—
654C2×C4—22no—
655C2×C4—26no—
656C2×C4—22no—
657C2×C4—224no—
658C2×C4—224no—
659C2×C4—224no—
660C2×C4—412no—
661C2×C4—424no—
662C2×C4—412no—
663C2×C4C2×#41×C83112yes—
664C2×C4C25×C8312yes—
665C2×C4C25×C8312yes—
666C2×C4C25×C8312yes—
667C2×C4C25×C8316yes—
668C2×C4C25×C8312yes—
669C2×C4C25×C8316yes—
670C2×C4C25×C8312yes—
671C2×C4C25×C8316yes—
672C2×C4C25×C8316yes—
673C2×C4C25×C8316yes—
674C2×C4C25×C8312yes—
675C2×C4C25×C8316yes—
676C22—22no—
677C22—26no—
678C22—26no—
679C22—26no—
680C22—26no—
681C22—26no—
682C22—22no—
683C22—22no—
684C22—26no—
685C22—44no—
686C22—412no—
687C22—412no—
688C22C22×#41×C8312yes—
689C22#585×C8312yes—
690C22#585×C8312yes—
691C22C26×C8311yescharacteristic
692C4—22no—
693C4—22no—
694C4—26no—
695C4—22no—
696C4—26no—
697C4—22no—
698C4—26no—
699C4—26no—
700C4—22no—
701C4—26no—
702C4—22no—
703C4C22×#41×C83112yes—
704C2—42no—
705C2—46no—
706C2—46no—
707C2C83×#352414yesdirect product factor
708C2C23×#41×C8311yescharacteristic
709C2C2×#585×C8311yescharacteristic
710C2C2×#585×C8311yescharacteristic
subgroupG/H
center, socleC23×C83C25
commutator, Frattini, cosocleC22C26×C83
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C83×#3524C2direct (N × H)
2. C2×#559×C83C2semidirect
3. C2×#557×C83C2semidirect
4. C2×#555×C83C2semidirect
5. C2×#553×C83C2semidirect
6. C2×#552×C83C2semidirect
7. C2×#550×C83C2semidirect
8. C2×#548×C83C2semidirect
9. C2×#548×C83C2semidirect
10. C2×#542×C83C2semidirect
11. C2×#540×C83C2semidirect
12. C2×#529×C83C2semidirect
13. C2×#529×C83C2semidirect
14. C2×#520×C83C2semidirect
15. C2×#519×C83C2semidirect
16. C2×C4×#41×C83C2semidirect
20. #559×C83C22semidirect
21. #557×C83C22semidirect
22. #555×C83C22semidirect
23. #553×C83C22semidirect
24. #552×C83C22semidirect
25. #550×C83C22semidirect
26. #548×C83C22semidirect
27. #548×C83C22semidirect
28. #542×C83C22semidirect
29. #540×C83C22semidirect
32. #529×C83C22semidirect
33. #529×C83C22semidirect
57. #520×C83C22semidirect
58. #519×C83C22semidirect
59. C4×#41×C83C22semidirect
348. C2×#3524C83direct (N × H)
352. C2×C83#3524direct (N × H)
356. #3524C2×C83direct (N × H)
357. C2×#559C2×C83semidirect
358. C2×#557C2×C83semidirect
359. C2×#555C2×C83semidirect
360. C2×#553C2×C83semidirect
361. C2×#552C2×C83semidirect
362. C2×#550C2×C83semidirect
363. C2×#548C2×C83semidirect
364. C2×#548C2×C83semidirect
365. C2×#542C2×C83semidirect
366. C2×#540C2×C83semidirect
367. C2×#529C2×C83semidirect
368. C2×#529C2×C83semidirect
369. C2×#520C2×C83semidirect
370. C2×#519C2×C83semidirect
371. C2×C4×#41C2×C83semidirect
372. C83C2×#3524direct (N × H)
376. #559C22×C83semidirect
377. #557C22×C83semidirect
378. #555C22×C83semidirect
379. #553C22×C83semidirect
380. #552C22×C83semidirect
381. #550C22×C83semidirect
382. #548C22×C83semidirect
383. #548C22×C83semidirect
384. #542C22×C83semidirect
385. #540C22×C83semidirect
388. #529C22×C83semidirect
389. #529C22×C83semidirect
413. #520C22×C83semidirect
414. #519C22×C83semidirect
415. C4×#41C22×C83semidirect
707. C2C83×#3524direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#35242
C2×#559×C832
C2×#557×C832
C2×#555×C832
C2×#553×C832
C2×#552×C832
C2×#550×C832
C2×#548×C832
C2×#542×C832
C2×#540×C832
C2×#529×C832
C2×#520×C832
C2×#519×C832
C2×C4×#41×C832
C2×#352483