Finite Group Databasebeta

← #35326261

Subgroups — #35326261

Order 21248.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127623C211yesmaximal, characteristic
2C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
4C2×#19127552C211yesmaximal, characteristic, complemented
5C2×#19127548C211yesmaximal, characteristic
6C2×#19127548C211yesmaximal, characteristic
7C2×#19127548C211yesmaximal, characteristic
8#24905724C211yesmaximal, characteristic, complemented
9#24905717C211yesmaximal, characteristic, complemented
10#24905715C211yesmaximal, characteristic, complemented
11#24905709C211yesmaximal, characteristic
12#24905707C211yesmaximal, characteristic
13#24905705C211yesmaximal, characteristic
14#95×Dic83C211yesmaximal, characteristic, complemented
15C83×#1441C211yesmaximal, characteristic, complemented
16C23×C4×D83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×Dic83⋊C4C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×(C2×D83)⋊C4C2211yescharacteristic
22C22×(C2×D83)⋊C4C2211yescharacteristic
23C22×(C2×D83)⋊C4C2211yescharacteristic
24C22×(C2×D83)⋊C4C2211yescharacteristic
25C22×(C2×D83)⋊C4C2211yescharacteristic
26C22×(C2×D83)⋊C4C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28C22×C4×Dic83C2211yescharacteristic
29C22×C4×Dic83C2211yescharacteristic
30C22×C4×Dic83C2211yescharacteristic
31C22×C4×Dic83C2211yescharacteristic
32C22×C4×Dic83C2211yescharacteristic
33#19127623C418yescomplemented
34C4⋊C4×Dic83—24no—
35C4⋊C4×Dic83—24no—
36#19127552—24no—
37#19127548—24no—
38#19127548—24no—
39#19127548—24no—
40C2×C83⋊#95C2211yescharacteristic
41C2×C83⋊#95C2211yescharacteristic
42C2×C83⋊#95C2211yescharacteristic
43C2×C83⋊#95C2211yescharacteristic
44C2×C83⋊#95C2211yescharacteristic
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
47C2×C83⋊#95C2211yescharacteristic
48C2×C83⋊#95C2211yescharacteristic
49C2×C83⋊#95C2211yescharacteristic
50C2×C83⋊#95C2211yescharacteristic
51C22×C4⋊C4×C83C2211yescharacteristic
52C22×C4⋊C4×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C2×#95×C83C2211yescharacteristic
57C2×#95×C83C2211yescharacteristic
58C24×D83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2311yescharacteristic
64C23×Dic83C2311yescharacteristic
65C23×Dic83C2311yescharacteristic
66C22×C4×D83—22no—
67C22×C4×D83—22no—
68C22×C4×D83—22no—
69C22×C4×D83—22no—
70C22×C4×D83—22no—
71C22×C4×D83—22no—
72C22×C4×D83Q814yes—
73C2×C4⋊Dic83—22no—
74C2×C4⋊Dic83—22no—
75C2×C4⋊Dic83—22no—
76C2×C4⋊Dic83—22no—
77C2×C4⋊Dic83—22no—
78C2×C4⋊Dic83C2×C414yescomplemented
79C2×Dic83⋊C4—22no—
80C2×Dic83⋊C4—22no—
81C2×Dic83⋊C4—22no—
82C2×Dic83⋊C4—22no—
83C2×Dic83⋊C4—22no—
84C2×Dic83⋊C4C2×C414yescomplemented
85C2×(C2×D83)⋊C4—22no—
86C2×(C2×D83)⋊C4—22no—
87C2×(C2×D83)⋊C4—22no—
88C2×(C2×D83)⋊C4—22no—
89C2×(C2×D83)⋊C4—22no—
90C2×(C2×D83)⋊C4—22no—
91C2×(C2×D83)⋊C4—22no—
92C2×(C2×D83)⋊C4—22no—
93C2×(C2×D83)⋊C4—22no—
94C2×(C2×D83)⋊C4—22no—
95C2×(C2×D83)⋊C4—22no—
96C2×(C2×D83)⋊C4—22no—
97C2×(C2×D83)⋊C4—22no—
98C2×(C2×D83)⋊C4—22no—
99C2×(C2×D83)⋊C4—22no—
100C2×(C2×D83)⋊C4C2×C414yes—
101C2×(C2×D83)⋊C4C2×C414yes—
102C2×(C2×D83)⋊C4C2×C414yes—
103C2×C4×Dic83—22no—
104C2×C4×Dic83—22no—
105C2×C4×Dic83—22no—
106C2×C4×Dic83—22no—
107C2×C4×Dic83—22no—
108C2×C4×Dic83—22no—
109C2×C4×Dic83—22no—
110C2×C4×Dic83—22no—
111C2×C4×Dic83—22no—
112C2×C4×Dic83—22no—
113C2×C4×Dic83—22no—
114C2×C4×Dic83—22no—
115C2×C4×Dic83—22no—
116C2×C4×Dic83—22no—
117C2×C4×Dic83—22no—
118C2×C4×Dic83D414yes—
119C2×C4×Dic83D414yes—
120C2×C4×Dic83D414yes—
121C83⋊#95—22no—
122C83⋊#95—22no—
123C83⋊#95—22no—
124C83⋊#95—22no—
125C83⋊#95—22no—
126C83⋊#95—22no—
127C83⋊#95—22no—
128C83⋊#95—22no—
129C83⋊#95—22no—
130C83⋊#95—22no—
131C83⋊#95C2×C414yescomplemented
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139C2×C4⋊C4×C83—22no—
140C2×C4⋊C4×C83—22no—
141C2×C4⋊C4×C83—22no—
142C2×C4⋊C4×C83—22no—
143C2×C4⋊C4×C83—22no—
144C2×C4⋊C4×C83C2×C414yescomplemented
145#95×C83—22no—
146#95×C83—22no—
147#95×C83—22no—
148#95×C83—22no—
149#95×C83—22no—
150C23×D83—21no—
151C23×D83—21no—
152C23×D83—21no—
153C23×D83—21no—
154C23×D83—21no—
155C23×D83—21no—
156C23×D83—21no—
157C23×D83—21no—
158C23×D83—21no—
159C23×D83—21no—
160C23×D83—21no—
161C23×D83—21no—
162C23×D83C22×C412yes—
163C23×D83C2×Q812yes—
164C23×D83#4112yes—
165C22×Dic83—21no—
166C22×Dic83—21no—
167C22×Dic83—21no—
168C22×Dic83—21no—
169C22×Dic83—21no—
170C22×Dic83—21no—
171C22×Dic83—21no—
172C22×Dic83—21no—
173C22×Dic83—21no—
174C22×Dic83—21no—
175C22×Dic83—21no—
176C22×Dic83—21no—
177C22×Dic83—21no—
178C22×Dic83—21no—
179C22×Dic83—21no—
180C22×Dic83—21no—
181C22×Dic83—21no—
182C22×Dic83—21no—
183C22×Dic83—21no—
184C22×Dic83—21no—
185C22×Dic83—21no—
186C22×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—21no—
189C22×Dic83—21no—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—21no—
198C22×Dic83—21no—
199C22×Dic83C22×C412yes—
200C22×Dic83C22×C412yes—
201C22×Dic83C22×C412yes—
202C22×Dic83C2×D412yes—
203C22×Dic83C2×D412yes—
204C22×Dic83C2×D412yes—
205C22×Dic83C2×D412yes—
206C22×Dic83C2×D412yes—
207C22×Dic83C2×D412yes—
208C22×Dic83C2×Q812yes—
209C22×Dic83#4112yes—
210C22×Dic83#4112yes—
211C22×Dic83#4112yes—
212C22×Dic83#4112yes—
213C22×Dic83#4112yes—
214C2×C4×D83—28no—
215C2×C4×D83—28no—
216C2×C4×D83—28no—
217C2×C4×D83—44no—
218C2×C4×D83—44no—
219C2×C4×D83—44no—
220C2×C4×D83—44no—
221C4⋊Dic83—28no—
222C4⋊Dic83—28no—
223Dic83⋊C4—28no—
224Dic83⋊C4—28no—
225(C2×D83)⋊C4—28no—
226(C2×D83)⋊C4—28no—
227(C2×D83)⋊C4—28no—
228(C2×D83)⋊C4—28no—
229(C2×D83)⋊C4—28no—
230(C2×D83)⋊C4—28no—
231C4×Dic83—28no—
232C4×Dic83—28no—
233C4×Dic83—28no—
234C4×Dic83—44no—
235C4×Dic83—44no—
236C4×Dic83—44no—
237C24×C83C2411yescharacteristic
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83—21no—
251C22×C4×C83—21no—
252C22×C4×C83—21no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—21no—
259C22×C4×C83—21no—
260C22×C4×C83—21no—
261C22×C4×C83—21no—
262C22×C4×C83—21no—
263C22×C4×C83—21no—
264C22×C4×C83—21no—
265C22×C4×C83—21no—
266C22×C4×C83—21no—
267C22×C4×C83—21no—
268C22×C4×C83—21no—
269C22×C4×C83—21no—
270C22×C4×C83—21no—
271C22×C4×C83—21no—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83—21no—
275C22×C4×C83—21no—
276C22×C4×C83C22×C412yes—
277C22×C4×C83C22×C412yes—
278C22×C4×C83C22×C412yes—
279C22×C4×C83C2×D412yes—
280C22×C4×C83C2×D412yes—
281C22×C4×C83C2×D412yes—
282C22×C4×C83C2×Q812yes—
283C22×C4×C83#4112yes—
284C22×C4×C83#4112yes—
285C22×C4×C83#4112yes—
286C22×C4×C83#4112yes—
287C4⋊C4×C83—28no—
288C4⋊C4×C83—28no—
289C23×C83C23×C411yescharacteristic
290C23×C83C22×D411yescharacteristic
291C23×C83C22×D411yescharacteristic
292C23×C83C22×D411yescharacteristic
293C23×C83C22×Q811yescharacteristic
294C23×C83C2×#4111yescharacteristic
295C23×C83C2×#4111yescharacteristic
296C23×C83C2×#4111yescharacteristic
297C23×C83C2×#4111yescharacteristic
298C23×C83C2×#4111yescharacteristic
299C23×C83C2×#4111yescharacteristic
300C23×C83C2×#4111yescharacteristic
301C23×C83C2×#4111yescharacteristic
302C23×C83C2×#4111yescharacteristic
303C23×C83C2×#4111yescharacteristic
304C22×D83—22no—
305C22×D83—22no—
306C22×D83—22no—
307C22×D83—22no—
308C22×D83—22no—
309C22×D83—22no—
310C22×D83—22no—
311C22×D83—22no—
312C22×D83—22no—
313C22×D83—22no—
314C22×D83—22no—
315C22×D83—22no—
316C22×D83—22no—
317C22×D83—22no—
318C22×D83—22no—
319C22×D83—22no—
320C22×D83—22no—
321C22×D83—22no—
322C22×D83—41no—
323C22×D83—41no—
324C22×D83—41no—
325C22×D83—41no—
326C22×D83—41no—
327C22×D83—41no—
328C22×D83—41no—
329C22×D83—41no—
330C22×D83—41no—
331C22×D83—41no—
332C22×D83—41no—
333C22×D83—41no—
334C22×D83—41no—
335C22×D83—41no—
336C22×D83—41no—
337C22×D83—41no—
338C22×D83C4×Q814yes—
339C2×C4×C83—22no—
340C2×C4×C83—22no—
341C2×C4×C83—22no—
342C2×C4×C83—22no—
343C2×C4×C83—22no—
344C2×C4×C83—22no—
345C2×C4×C83—22no—
346C2×C4×C83—22no—
347C2×C4×C83—22no—
348C2×C4×C83—22no—
349C2×C4×C83—22no—
350C2×C4×C83—22no—
351C2×C4×C83—22no—
352C2×C4×C83—22no—
353C2×C4×C83—22no—
354C2×C4×C83—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—22no—
358C2×C4×C83—22no—
359C2×C4×C83—22no—
360C2×C4×C83—22no—
361C2×C4×C83—22no—
362C2×C4×C83—22no—
363C2×C4×C83—22no—
364C2×C4×C83—22no—
365C2×C4×C83—22no—
366C2×C4×C83—41no—
367C2×C4×C83—41no—
368C2×C4×C83—41no—
369C2×C4×C83—41no—
370C2×C4×C83—41no—
371C2×C4×C83—41no—
372C2×C4×C83—41no—
373C2×C4×C83—41no—
374C2×C4×C83—41no—
375C2×C4×C83—41no—
376C2×C4×C83—41no—
377C2×C4×C83—41no—
378C2×C4×C83—41no—
379C2×C4×C83—41no—
380C2×C4×C83—41no—
381C2×C4×C83—41no—
382C2×C4×C83—41no—
383C2×C4×C83—41no—
384C2×C4×C83—41no—
385C2×C4×C83—41no—
386C2×C4×C83C4×D414yes—
387C2×C4×C83C4×D414yes—
388C2×Dic83—22no—
389C2×Dic83—22no—
390C2×Dic83—22no—
391C2×Dic83—22no—
392C2×Dic83—22no—
393C2×Dic83—22no—
394C2×Dic83—22no—
395C2×Dic83—22no—
396C2×Dic83—22no—
397C2×Dic83—22no—
398C2×Dic83—22no—
399C2×Dic83—22no—
400C2×Dic83—22no—
401C2×Dic83—22no—
402C2×Dic83—22no—
403C2×Dic83—22no—
404C2×Dic83—22no—
405C2×Dic83—22no—
406C2×Dic83—22no—
407C2×Dic83—22no—
408C2×Dic83—22no—
409C2×Dic83—41no—
410C2×Dic83—41no—
411C2×Dic83—41no—
412C2×Dic83—41no—
413C2×Dic83—41no—
414C2×Dic83—41no—
415C2×Dic83—41no—
416C2×Dic83—41no—
417C2×Dic83—41no—
418C2×Dic83—41no—
419C2×Dic83—41no—
420C2×Dic83—41no—
421C2×Dic83—41no—
422C2×Dic83—41no—
423C2×Dic83—41no—
424C2×Dic83—41no—
425C2×Dic83—41no—
426C2×Dic83—41no—
427C2×Dic83—41no—
428C2×Dic83—41no—
429C2×Dic83C4×D414yes—
430C2×Dic83#12114yes—
431C2×Dic83#12114yes—
432C2×Dic83#12114yes—
433C2×Dic83C22⋊Q814yes—
434C2×Dic83C22⋊Q814yes—
435C2×Dic83C22⋊Q814yes—
436C2×Dic83#12614yes—
437C4×D83—416no—
438C22×C83C2×C4×D411yescharacteristic
439C22×C83C2×C4×D411yescharacteristic
440C22×C83C2×C4×D411yescharacteristic
441C22×C83C2×C4×Q811yescharacteristic
442C22×C83C4×#4111yescharacteristic
443C22×C83C4×#4111yescharacteristic
444C22×C83C4×#4111yescharacteristic
445C22×C83C2×#12111yescharacteristic
446C22×C83C2×#12111yescharacteristic
447C22×C83C2×#12111yescharacteristic
448C22×C83C2×C22⋊Q811yescharacteristic
449C22×C83C2×C22⋊Q811yescharacteristic
450C22×C83C2×C22⋊Q811yescharacteristic
451C22×C83#52511yescharacteristic
452C22×C83#52511yescharacteristic
453C22×C83#52511yescharacteristic
454C22×C83#52511yescharacteristic
455C22×C83#52511yescharacteristic
456C22×C83#52511yescharacteristic
457C22×C83C2×#12611yescharacteristic
458C22×C83#52911yescharacteristic
459C22×C83#52911yescharacteristic
460C22×C83#52911yescharacteristic
461C22×C83#52911yescharacteristic
462C22×C83#52911yescharacteristic
463C22×C83#52911yescharacteristic
464C22×C83#52911yescharacteristic
465C22×C83#52911yescharacteristic
466C22×C83#52911yescharacteristic
467C22×C83#53211yescharacteristic
468C22×C83#53211yescharacteristic
469C22×C83#53211yescharacteristic
470C22×C83#53311yescharacteristic
471C22×C83#53311yescharacteristic
472C22×C83#53311yescharacteristic
473C2×D83—24no—
474C2×D83—24no—
475C2×D83—24no—
476C2×D83—42no—
477C2×D83—42no—
478C2×D83—42no—
479C2×D83—42no—
480C2×D83—42no—
481C2×D83—42no—
482C2×D83—42no—
483C2×D83—42no—
484C2×D83—42no—
485C2×D83—42no—
486C2×D83—42no—
487C2×D83—42no—
488C4×C83—24no—
489C4×C83—24no—
490C4×C83—42no—
491C4×C83—42no—
492C4×C83—42no—
493C4×C83—42no—
494C4×C83—42no—
495Dic83—24no—
496Dic83—42no—
497Dic83—42no—
498Dic83—42no—
499Dic83—42no—
500Dic83—42no—
501Dic83#39618yescomplemented
502C4×#396—831nomaximal, Sylow
503C2×C83C4×#12111yescharacteristic
504C2×C83C4×#12111yescharacteristic
505C2×C83C4×#12111yescharacteristic
506C2×C83C4×C22⋊Q811yescharacteristic
507C2×C83C4×C22⋊Q811yescharacteristic
508C2×C83C4×C22⋊Q811yescharacteristic
509C2×C83C4×#12611yescharacteristic
510C2×C83C2×#39611yescharacteristic
511C2×C83#239211yescharacteristic
512C2×C83#239211yescharacteristic
513C2×C83#239211yescharacteristic
514C2×C83#239611yescharacteristic
515C2×C83#239611yescharacteristic
516C2×C83#239611yescharacteristic
517C2×C83#240111yescharacteristic
518D83—44no—
519C2×#396—831no—
520C2×C4×C4⋊C4—831no—
521C2×C4×C4⋊C4—831no—
522C2×C4×C4⋊C4—831no—
523C2×C4×C22⋊C4—831no—
524C2×C4×C22⋊C4—831no—
525C2×C4×C22⋊C4—831no—
526#1443—831no—
527#1441—831no—
528#1441—831no—
529#1441D8311yescharacteristic, complemented
530#1439—831no—
531#1439—831no—
532#1439—831no—
533C4×#95—831no—
534C83C4×#39611yescharacteristic, complemented, Sylow
535C24×C4—831no—
536C22×C4⋊C4—831no—
537C22×C4⋊C4—831no—
538C22×C4⋊C4—831no—
539C22×C4⋊C4—831no—
540C22×C4⋊C4C2×D8311yescharacteristic
541C22×C4⋊C4C2×D8311yescharacteristic
542C22×C22⋊C4—831no—
543C22×C22⋊C4—831no—
544C22×C22⋊C4—831no—
545C22×C22⋊C4—831no—
546C22×C22⋊C4—831no—
547C22×C22⋊C4—831no—
548C22×C42—831no—
549C22×C42—831no—
550C22×C42—831no—
551C22×C42—831no—
552C22×C42—831no—
553C22×C42—831no—
554#396—838no—
555C4×C4⋊C4—1664no—
556C4×C4⋊C4—1664no—
557C4×C4⋊C4—1664no—
558C4×C22⋊C4—1664no—
559C4×C22⋊C4—1664no—
560C4×C22⋊C4—1664no—
561C2×#95—831no—
562C2×#95—831no—
563C2×#95—831no—
564C2×#95—831no—
565C2×#95—831no—
566C2×#95—831no—
567C2×#95—831no—
568C2×#95—831no—
569C2×#95—831no—
570C2×#95—831no—
571C2×#95—831no—
572C2×#95C2×D8311yescharacteristic
573C2×#95C2×D8311yescharacteristic
574C2×#95C2×D8311yescharacteristic
575C2×#95C2×D8311yescharacteristic
576C2×#95C2×D8311yescharacteristic
577C25—831no—
578C23×C4—831no—
579C23×C4—831no—
580C23×C4—831no—
581C23×C4—831no—
582C23×C4—831no—
583C23×C4—831no—
584C23×C4—831no—
585C23×C4—834no—
586C23×C4—1662no—
587C23×C4—1662no—
588C23×C4—1662no—
589C23×C4—1662no—
590C23×C4—1662no—
591C23×C4—1662no—
592C23×C4C22×D8311yescharacteristic
593C23×C4C22×D8311yescharacteristic
594C23×C4C22×D8311yescharacteristic
595C23×C4C22×D8311yescharacteristic
596C23×C4C22×D8311yescharacteristic
597C23×C4C22×D8311yescharacteristic
598C23×C4C22×D8311yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—834no—
605C2×C4⋊C4—834no—
606C2×C4⋊C4—1662no—
607C2×C4⋊C4—1662no—
608C2×C4⋊C4—1662no—
609C2×C4⋊C4—1662no—
610C2×C4⋊C4—1662no—
611C2×C4⋊C4—1662no—
612C2×C4⋊C4—1662no—
613C2×C4⋊C4—1662no—
614C2×C4⋊C4—1662no—
615C2×C4⋊C4—1662no—
616C2×C4⋊C4C4×D8314yescomplemented
617C2×C22⋊C4—834no—
618C2×C22⋊C4—834no—
619C2×C22⋊C4—834no—
620C2×C22⋊C4—1662no—
621C2×C22⋊C4—1662no—
622C2×C22⋊C4—1662no—
623C2×C22⋊C4—1662no—
624C2×C22⋊C4—1662no—
625C2×C22⋊C4—1662no—
626C2×C22⋊C4—1662no—
627C2×C22⋊C4—1662no—
628C2×C22⋊C4—1662no—
629C2×C22⋊C4—1662no—
630C2×C22⋊C4—1662no—
631C2×C22⋊C4—1662no—
632C2×C22⋊C4—1662no—
633C2×C22⋊C4—1662no—
634C2×C22⋊C4—1662no—
635C2×C42—834no—
636C2×C42—834no—
637C2×C42—834no—
638C2×C42—1662no—
639C2×C42—1662no—
640C2×C42—1662no—
641C2×C42—1662no—
642C2×C42—1662no—
643C2×C42—1662no—
644C2×C42—1662no—
645C2×C42—1662no—
646C2×C42—1662no—
647C2×C42—1662no—
648C2×C42—1662no—
649C2×C42—1662no—
650C2×C42—1662no—
651C2×C42—1662no—
652C2×C42—1662no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—834no—
659#95—1662no—
660#95—1662no—
661#95—1662no—
662#95—1662no—
663#95—1662no—
664#95—1662no—
665#95—1662no—
666#95—1662no—
667#95—1662no—
668#95—1662no—
669C24—832no—
670C24—832no—
671C24—832no—
672C24—1661no—
673C24—1661no—
674C24—1661no—
675C24—1661no—
676C24—1661no—
677C24—1661no—
678C24—1661no—
679C24—1661no—
680C24—1661no—
681C24—1661no—
682C24—1661no—
683C24—1661no—
684C24C23×D8311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—3324no—
724C22×C4—3324no—
725C22×C4—3324no—
726C22×C4—3324no—
727C22×C4—832no—
728C22×C4—832no—
729C22×C4—832no—
730C22×C4—832no—
731C22×C4—832no—
732C22×C4—832no—
733C22×C4—832no—
734C22×C4—832no—
735C22×C4—832no—
736C22×C4—832no—
737C22×C4—832no—
738C22×C4—832no—
739C22×C4—832no—
740C22×C4—832no—
741C22×C4—832no—
742C22×C4—1668no—
743C22×C4—1668no—
744C22×C4—1668no—
745C22×C4—1661no—
746C22×C4—1661no—
747C22×C4—1661no—
748C22×C4—1661no—
749C22×C4—1661no—
750C22×C4—1661no—
751C22×C4—1661no—
752C22×C4—1661no—
753C22×C4—1661no—
754C22×C4—1661no—
755C22×C4—1661no—
756C22×C4—1661no—
757C22×C4—1661no—
758C22×C4—1661no—
759C22×C4—1661no—
760C22×C4—1661no—
761C22×C4—1661no—
762C22×C4—1661no—
763C22×C4—1661no—
764C22×C4—1661no—
765C22×C4—1661no—
766C22×C4—1661no—
767C22×C4—1661no—
768C22×C4—1661no—
769C22×C4—1661no—
770C22×C4—1661no—
771C22×C4—1661no—
772C22×C4—1661no—
773C22×C4—1661no—
774C22×C4—1661no—
775C22×C4—1661no—
776C22×C4—1661no—
777C22×C4—1661no—
778C22×C4—1661no—
779C22×C4C2×C4×D8312yes—
780C22×C4C2×C4×D8312yes—
781C22×C4C2×C4×D8312yes—
782C22×C4D4×D8312yes—
783C22×C4D4×D8312yes—
784C22×C4D4×D8312yes—
785C22×C4Q8×D8312yes—
786C22×C4#1305058912yes—
787C22×C4#1305058912yes—
788C22×C4#1305059112yes—
789C22×C4#1305059112yes—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—1668no—
793C4⋊C4—1668no—
794C4⋊C4—1668no—
795C4⋊C4—1668no—
796C22⋊C4—1668no—
797C22⋊C4—1668no—
798C22⋊C4—1668no—
799C22⋊C4—1668no—
800C22⋊C4—1668no—
801C22⋊C4—1668no—
802C42—3324no—
803C42—3324no—
804C42—3324no—
805C42—1668no—
806C42—1668no—
807C42—1668no—
808C23—3321no—
809C23—3321no—
810C23—3321no—
811C23—3321no—
812C23—3321no—
813C23—3321no—
814C23—3321no—
815C23—3321no—
816C23—3321no—
817C23—3321no—
818C23—3321no—
819C23—3321no—
820C23—3321no—
821C23—3321no—
822C23—3321no—
823C23—3321no—
824C23—834no—
825C23—1662no—
826C23—1662no—
827C23—1662no—
828C23—1662no—
829C23—1662no—
830C23—1662no—
831C23—1662no—
832C23—1662no—
833C23—1662no—
834C23—1662no—
835C23—1662no—
836C23—1662no—
837C23—1662no—
838C23—1662no—
839C23—1662no—
840C23—1662no—
841C23—1662no—
842C23—1662no—
843C23C22×C4×D8311yescharacteristic
844C23C2×D4×D8311yescharacteristic
845C23C2×D4×D8311yescharacteristic
846C23C2×D4×D8311yescharacteristic
847C23C2×Q8×D8311yescharacteristic
848C23#41×D8311yescharacteristic
849C23#41×D8311yescharacteristic
850C23#41×D8311yescharacteristic
851C23#41×D8311yescharacteristic
852C23#41×D8311yescharacteristic
853C23#41×D8311yescharacteristic
854C23C2×#1305058911yescharacteristic
855C23C2×#1305058911yescharacteristic
856C23C2×#1305059111yescharacteristic
857C23C2×#1305059111yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—33216no—
906C2×C4—3321no—
907C2×C4—3321no—
908C2×C4—3321no—
909C2×C4—3321no—
910C2×C4—3321no—
911C2×C4—3321no—
912C2×C4—3321no—
913C2×C4—3321no—
914C2×C4—3321no—
915C2×C4—3321no—
916C2×C4—3321no—
917C2×C4—3321no—
918C2×C4—3321no—
919C2×C4—3321no—
920C2×C4—3321no—
921C2×C4—3321no—
922C2×C4—3321no—
923C2×C4—3321no—
924C2×C4—3321no—
925C2×C4—3321no—
926C2×C4—834no—
927C2×C4—834no—
928C2×C4—834no—
929C2×C4—834no—
930C2×C4—834no—
931C2×C4—834no—
932C2×C4—834no—
933C2×C4—834no—
934C2×C4—1662no—
935C2×C4—1662no—
936C2×C4—1662no—
937C2×C4—1662no—
938C2×C4—1662no—
939C2×C4—1662no—
940C2×C4—1662no—
941C2×C4—1662no—
942C2×C4—1662no—
943C2×C4—1662no—
944C2×C4—1662no—
945C2×C4—1662no—
946C2×C4—1662no—
947C2×C4—1662no—
948C2×C4—1662no—
949C2×C4—1662no—
950C2×C4—1662no—
951C2×C4—1662no—
952C2×C4—1662no—
953C2×C4—1662no—
954C2×C4—1662no—
955C2×C4(C22⋊D83)⋊C414yes—
956C2×C4#1458175414yes—
957C22—3322no—
958C22—3322no—
959C22—3322no—
960C22—3322no—
961C22—3322no—
962C22—3322no—
963C22—3322no—
964C22—3322no—
965C22—3322no—
966C22—3322no—
967C22—3322no—
968C22—3322no—
969C22—1664no—
970C22—1664no—
971C22—1664no—
972C22C4×D4×D8311yescharacteristic
973C22C2×(C22⋊D83)⋊C411yescharacteristic
974C22C2×#1458175411yescharacteristic
975C22C4×Q8×D8311yescharacteristic
976C22C4×#1305058911yescharacteristic
977C22#1912816911yescharacteristic
978C22C4×#1305059111yescharacteristic
979C22#121×D8311yescharacteristic
980C22#121×D8311yescharacteristic
981C22#121×D8311yescharacteristic
982C22C22⋊Q8×D8311yescharacteristic
983C22C22⋊Q8×D8311yescharacteristic
984C22C22⋊Q8×D8311yescharacteristic
985C22#1912820711yescharacteristic
986C22#1912820911yescharacteristic
987C22#1912821111yescharacteristic
988C22#1912821411yescharacteristic
989C22#1912821411yescharacteristic
990C22#1912821411yescharacteristic
991C22#126×D8311yescharacteristic
992C22#1912822811yescharacteristic
993C22#1912822811yescharacteristic
994C22#1912823011yescharacteristic
995C22#1912823411yescharacteristic
996C22#1912823611yescharacteristic
997C22#1912823611yescharacteristic
998C22#1912823611yescharacteristic
999C22#1912823711yescharacteristic
1000C22#1912823711yescharacteristic
1001C22#1912824611yescharacteristic
1002C22#1912824611yescharacteristic
1003C22#1912825211yescharacteristic
1004C22#1912825611yescharacteristic
1005C22#1912825611yescharacteristic
1006C22#1912825711yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—3322no—
1015C4—3322no—
1016C4—3322no—
1017C4—3322no—
1018C4—3322no—
1019C4—838no—
1020C4—1664no—
1021C2—3324no—
1022C2#2490996911yescharacteristic
1023C2#2490997111yescharacteristic
1024C2#2490997311yescharacteristic
1025C2#2490999311yescharacteristic
1026C2#2490999711yescharacteristic
1027C2#2491000111yescharacteristic
1028C2#2491001311yescharacteristic
1029C2#396×D8311yescharacteristic
1030C2#2491070411yescharacteristic
1031C2#2491070611yescharacteristic
1032C2#2491070811yescharacteristic
1033C2#2491073411yescharacteristic
1034C2#2491074011yescharacteristic
1035C2#2491074011yescharacteristic
1036C2#2491076211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×#1441C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenter#1441D83
hypocenterC83C4×#396
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic83C2semidirect
3. C2×C4⋊C4×Dic83C2semidirect
4. C2×#19127552C2semidirect
8. #24905724C2semidirect
9. #24905717C2semidirect
10. #24905715C2semidirect
14. #95×Dic83C2semidirect
15. C83×#1441C2semidirect
33. #19127623C4semidirect
78. C2×C4⋊Dic83C2×C4semidirect
84. C2×Dic83⋊C4C2×C4semidirect
131. C83⋊#95C2×C4semidirect
144. C2×C4⋊C4×C83C2×C4semidirect
501. Dic83#396semidirect
529. #1441D83semidirect
534. C83C4×#396semidirect
616. C2×C4⋊C4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191276232
C2×C4⋊C4×Dic832
C2×#191275522
C2×#191275482
#249057242
#249057172
#249057152
#249057092
#249057072
#249057052
#95×Dic832
C83×#14412
C4×#39683