Finite Group Databasebeta

← #35325834

Subgroups — #35325834

Order 21248.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127558C211yesmaximal, characteristic
2C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
3C2×#19127548C211yesmaximal, characteristic
4C2×#19127548C211yesmaximal, characteristic
5C2×#95×D83C211yesmaximal, characteristic
6#24905697C211yesmaximal, characteristic, complemented
7#24905697C211yesmaximal, characteristic, complemented
8#24905695C211yesmaximal, characteristic, complemented
9#24905689C211yesmaximal, characteristic, complemented
10#24905687C211yesmaximal, characteristic, complemented
11(C2×D83)⋊#95C211yesmaximal, characteristic
12(C2×D83)⋊#95C211yesmaximal, characteristic
13C4×C83⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic83C211yesmaximal, characteristic, complemented
15C83×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D83C2211yescharacteristic
17C23×C4×D83C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×(C2×D83)⋊C4C2211yescharacteristic
21C22×(C2×D83)⋊C4C2211yescharacteristic
22C22×(C2×D83)⋊C4C2211yescharacteristic
23C22×(C2×D83)⋊C4C2211yescharacteristic
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26C22×C4×Dic83C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28C22×C4×Dic83C2211yescharacteristic
29#19127558C418yescomplemented
30C4×(C2×D83)⋊C4—24no—
31#19127548—24no—
32#19127548C418yescomplemented
33C2×C83⋊#95C2211yescharacteristic
34C2×C83⋊#95C2211yescharacteristic
35C2×C83⋊#95C2211yescharacteristic
36C2×C83⋊#95C2211yescharacteristic
37C2×C83⋊#95C2211yescharacteristic
38C2×C83⋊#95C2211yescharacteristic
39C2×C83⋊#95C2211yescharacteristic
40C2×C83⋊#95C2211yescharacteristic
41C2×C83⋊#95C2211yescharacteristic
42C2×C83⋊#95C2211yescharacteristic
43C2×C83⋊#95C2211yescharacteristic
44C2×C83⋊#95C2211yescharacteristic
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
47C2×C83⋊#95C2211yescharacteristic
48#95×D83C418yescomplemented
49C22×C4⋊C4×C83C2211yescharacteristic
50C22×C42×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C24×D83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2311yescharacteristic
64C22×C4×D83—22no—
65C22×C4×D83—22no—
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×D83—41no—
73C22×C4×D83—41no—
74C22×C4×D83—41no—
75C22×C4×D83—41no—
76C22×C4×D83—41no—
77C22×C4×D83—41no—
78C22×C4×D83—41no—
79C22×C4×D83—41no—
80C22×C4×D83C2×C414yes—
81C22×C4×D83C2×C414yes—
82C22×C4×D83C2×C414yes—
83C22×C4×D83C2×C414yes—
84C22×C4×D83C2×C414yes—
85C2×C4⋊Dic83—41no—
86C2×C4⋊Dic83—41no—
87C2×C4⋊Dic83C2×C414yescomplemented
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)⋊C4C2×C414yes—
95C2×(C2×D83)⋊C4C2×C414yes—
96C2×(C2×D83)⋊C4C2×C414yes—
97C2×(C2×D83)⋊C4C2×C414yes—
98C2×(C2×D83)⋊C4D414yes—
99C2×(C2×D83)⋊C4Q814yes—
100C2×C4×Dic83—22no—
101C2×C4×Dic83—22no—
102C2×C4×Dic83—22no—
103C2×C4×Dic83—22no—
104C2×C4×Dic83—22no—
105C2×C4×Dic83—22no—
106C2×C4×Dic83—41no—
107C2×C4×Dic83—41no—
108C2×C4×Dic83—41no—
109C2×C4×Dic83—41no—
110C2×C4×Dic83—41no—
111C2×C4×Dic83—41no—
112C2×C4×Dic83—41no—
113C2×C4×Dic83C2×C414yescomplemented
114C2×C4×Dic83C2×C414yescomplemented
115C83⋊#95—22no—
116C83⋊#95—22no—
117C83⋊#95—22no—
118C83⋊#95—22no—
119C83⋊#95—22no—
120C83⋊#95—22no—
121C83⋊#95—41no—
122C83⋊#95—41no—
123C83⋊#95—41no—
124C83⋊#95C2×C414yes—
125C83⋊#95C2×C414yes—
126C83⋊#95C2×C414yes—
127C83⋊#95C2×C414yescomplemented
128C83⋊#95C2×C414yescomplemented
129C83⋊#95C2×C414yescomplemented
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C2×C4⋊C4×C83—41no—
138C2×C4⋊C4×C83—41no—
139C2×C4⋊C4×C83C2×C414yescomplemented
140C2×C42×C83—22no—
141C2×C42×C83—22no—
142C2×C42×C83—41no—
143#95×C83—22no—
144#95×C83—22no—
145#95×C83—41no—
146#95×C83C2×C414yes—
147#95×C83C2×C414yescomplemented
148C23×D83—21no—
149C23×D83—21no—
150C23×D83—21no—
151C23×D83—21no—
152C23×D83—21no—
153C23×D83—21no—
154C23×D83—21no—
155C23×D83—21no—
156C23×D83C22×C412yes—
157C23×D83C22×C412yes—
158C23×D83C22×C412yes—
159C23×D83C2×D412yes—
160C23×D83C2×Q812yes—
161C23×D83#4112yes—
162C23×D83#4112yes—
163C22×Dic83—21no—
164C22×Dic83—21no—
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×Dic83C22×C412yes—
203C22×Dic83C22×C412yes—
204C22×Dic83C22×C412yes—
205C22×Dic83C22×C412yes—
206C22×Dic83C22×C412yes—
207C22×Dic83C22×C412yes—
208C22×Dic83C2×D412yes—
209C22×Dic83C2×Q812yes—
210C22×Dic83#4112yes—
211C22×Dic83#4112yes—
212C2×C4×D83—28no—
213C2×C4×D83—28no—
214C2×C4×D83—28no—
215C2×C4×D83—28no—
216C2×C4×D83—44no—
217C2×C4×D83—44no—
218C2×C4×D83—44no—
219C2×C4×D83—44no—
220C2×C4×D83—44no—
221C2×C4×D83—44no—
222C2×C4×D83—44no—
223C2×C4×D83—44no—
224C2×C4×D83—44no—
225C2×C4×D83—44no—
226C2×C4×D83—44no—
227C2×C4×D83—44no—
228C2×C4×D83—44no—
229C2×C4×D83—44no—
230C2×C4×D83—44no—
231C2×C4×D83—44no—
232C2×C4×D83C42116yescomplemented
233C4⋊Dic83—44no—
234(C2×D83)⋊C4—28no—
235(C2×D83)⋊C4—28no—
236(C2×D83)⋊C4—28no—
237(C2×D83)⋊C4C4⋊C4116yescomplemented
238C4×Dic83—44no—
239C4×Dic83—44no—
240C4×Dic83—44no—
241C4×Dic83—44no—
242C4×Dic83—44no—
243C24×C83C2411yescharacteristic
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×C83—21no—
277C22×C4×C83—21no—
278C22×C4×C83—21no—
279C22×C4×C83—21no—
280C22×C4×C83C22×C412yes—
281C22×C4×C83C22×C412yes—
282C22×C4×C83C22×C412yes—
283C22×C4×C83C22×C412yes—
284C22×C4×C83C22×C412yes—
285C22×C4×C83C22×C412yes—
286C22×C4×C83C22×C412yes—
287C22×C4×C83C22×C412yes—
288C22×C4×C83C22×C412yes—
289C22×C4×C83C2×D412yes—
290C22×C4×C83C2×Q812yes—
291C22×C4×C83#4112yes—
292C22×C4×C83#4112yes—
293C4⋊C4×C83—44no—
294C42×C83—44no—
295C23×C83C23×C411yescharacteristic
296C23×C83C23×C411yescharacteristic
297C23×C83C23×C411yescharacteristic
298C23×C83C22×D411yescharacteristic
299C23×C83C22×Q811yescharacteristic
300C23×C83C2×#4111yescharacteristic
301C23×C83C2×#4111yescharacteristic
302C23×C83C2×#4111yescharacteristic
303C23×C83C2×#4111yescharacteristic
304C23×C83C2×#4111yescharacteristic
305C23×C83C2×#4111yescharacteristic
306C23×C83H(5,𝔽2)11yescharacteristic
307C23×C83H(5,𝔽2)11yescharacteristic
308C23×C83H(5,𝔽2)11yescharacteristic
309C23×C83H(5,𝔽2)11yescharacteristic
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—22no—
323C22×D83—22no—
324C22×D83—22no—
325C22×D83—22no—
326C22×D83—22no—
327C22×D83—22no—
328C22×D83—22no—
329C22×D83—22no—
330C22×D83—22no—
331C22×D83—22no—
332C22×D83—22no—
333C22×D83—22no—
334C22×D83—22no—
335C22×D83—22no—
336C22×D83—22no—
337C22×D83—22no—
338C22×D83C2×C4214yes—
339C22×D83C2×C4⋊C414yes—
340C22×D83#11714yes—
341C22×D83C4×D414yes—
342C22×D83C4×D414yes—
343C22×D83C4×Q814yes—
344C22×D83C4×Q814yes—
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—22no—
367C2×C4×C83—22no—
368C2×C4×C83—22no—
369C2×C4×C83—22no—
370C2×C4×C83—22no—
371C2×C4×C83—22no—
372C2×C4×C83—22no—
373C2×C4×C83—22no—
374C2×C4×C83—22no—
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×C83—41no—
387C2×C4×C83—41no—
388C2×C4×C83—41no—
389C2×C4×C83—41no—
390C2×C4×C83—41no—
391C2×C4×C83C2×C4214yes—
392C2×C4×C83C2×C4⋊C414yes—
393C2×C4×C83#11714yes—
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—22no—
410C2×Dic83—22no—
411C2×Dic83—22no—
412C2×Dic83—22no—
413C2×Dic83—22no—
414C2×Dic83—22no—
415C2×Dic83—22no—
416C2×Dic83—22no—
417C2×Dic83—22no—
418C2×Dic83—22no—
419C2×Dic83—22no—
420C2×Dic83—22no—
421C2×Dic83—22no—
422C2×Dic83—22no—
423C2×Dic83—22no—
424C2×Dic83—41no—
425C2×Dic83—41no—
426C2×Dic83—41no—
427C2×Dic83—41no—
428C2×Dic83—41no—
429C2×Dic83—41no—
430C2×Dic83—41no—
431C2×Dic83—41no—
432C2×Dic83—41no—
433C2×Dic83—41no—
434C2×Dic83—41no—
435C2×Dic83—41no—
436C2×Dic83—41no—
437C2×Dic83—41no—
438C2×Dic83—41no—
439C2×Dic83—41no—
440C2×Dic83C2×C4214yes—
441C2×Dic83C2×C4⋊C414yes—
442C2×Dic83#11714yes—
443C4×D83—416no—
444C4×D83—416no—
445C4×D83—416no—
446C22×C83C22×C4211yescharacteristic
447C22×C83C22×C4⋊C411yescharacteristic
448C22×C83C2×#11711yescharacteristic
449C22×C83C2×#11711yescharacteristic
450C22×C83C2×#11711yescharacteristic
451C22×C83C2×C4×D411yescharacteristic
452C22×C83C2×C4×D411yescharacteristic
453C22×C83C2×C4×Q811yescharacteristic
454C22×C83C2×C4×Q811yescharacteristic
455C22×C83C4×#4111yescharacteristic
456C22×C83C4×#4111yescharacteristic
457C22×C83C4×#4111yescharacteristic
458C22×C83C4×#4111yescharacteristic
459C22×C83#51811yescharacteristic
460C22×C83#51811yescharacteristic
461C22×C83#51811yescharacteristic
462C22×C83#51811yescharacteristic
463C22×C83#51811yescharacteristic
464C22×C83#51811yescharacteristic
465C22×C83#54611yescharacteristic
466C22×C83#54611yescharacteristic
467C22×C83#54611yescharacteristic
468C22×C83#54611yescharacteristic
469C22×C83#55111yescharacteristic
470C22×C83#55111yescharacteristic
471C22×C83#55111yescharacteristic
472C22×C83#55111yescharacteristic
473C22×C83#55311yescharacteristic
474C22×C83#55311yescharacteristic
475C22×C83#55311yescharacteristic
476C22×C83#55311yescharacteristic
477C22×C83#55411yescharacteristic
478C22×C83#55411yescharacteristic
479C22×C83#55411yescharacteristic
480C22×C83#55411yescharacteristic
481C2×D83—24no—
482C2×D83—24no—
483C2×D83—24no—
484C2×D83—24no—
485C2×D83—24no—
486C2×D83—24no—
487C2×D83—24no—
488C2×D83—24no—
489C2×D83—24no—
490C2×D83—24no—
491C2×D83—24no—
492C2×D83—24no—
493C2×D83—24no—
494C2×D83—24no—
495C2×D83C4×C4⋊C418yes—
496C4×C83—24no—
497C4×C83—24no—
498C4×C83—24no—
499C4×C83—42no—
500C4×C83—42no—
501C4×C83—42no—
502C4×C83—42no—
503Dic83—24no—
504Dic83—24no—
505Dic83—24no—
506Dic83—42no—
507Dic83—42no—
508Dic83—42no—
509Dic83—42no—
510#13802—831nomaximal, Sylow
511C2×C83C2×C4×C4⋊C411yescharacteristic
512C2×C83C4×#11711yescharacteristic
513C2×C83#227311yescharacteristic
514C2×C83#234211yescharacteristic
515C2×C83#234211yescharacteristic
516C2×C83#234511yescharacteristic
517C2×C83#234511yescharacteristic
518C2×C83#234911yescharacteristic
519C2×C83#234911yescharacteristic
520C2×C83#235311yescharacteristic
521C2×C83#235311yescharacteristic
522C2×C83#236411yescharacteristic
523C2×C83#236411yescharacteristic
524C2×C83#236811yescharacteristic
525C2×C83#236811yescharacteristic
526D83—28no—
527C2×#380—831no—
528C2×C4×C22⋊C4—831no—
529C2×C4×C22⋊C4—831no—
530C2×C4×C22⋊C4—831no—
531C22×#95—831no—
532#1436—831no—
533#1436—831no—
534#1436—831no—
535#1436D8311yescharacteristic, complemented
536#1434—831no—
537#1434—831no—
538C22⋊#95—831no—
539C22⋊#95—831no—
540C4×#95—831no—
541C4×#95—831no—
542C83#1380211yescharacteristic, complemented, Sylow
543C24×C4—831no—
544C24×C4—831no—
545C24×C4—831no—
546C22×C4⋊C4—831no—
547C22×C4⋊C4C2×D8311yescharacteristic
548C22×C22⋊C4—831no—
549C22×C22⋊C4—831no—
550C22×C22⋊C4—831no—
551C22×C22⋊C4—831no—
552C22×C42—831no—
553C22×C42—831no—
554C22×C42—831no—
555C22×C42—831no—
556C22×C42—831no—
557C22×C42C2×D8311yescharacteristic
558#380—838no—
559C4×C22⋊C4—838no—
560C4×C22⋊C4—1664no—
561C4×C22⋊C4—1664no—
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—838no—
572C2×#95—831no—
573C2×#95—831no—
574C2×#95—831no—
575C2×#95—831no—
576C2×#95—831no—
577C2×#95—831no—
578C2×#95C2×D8311yescharacteristic
579C2×#95C2×D8311yescharacteristic
580C2×#95C2×D8311yescharacteristic
581C2×#95C2×D8311yescharacteristic
582C2×#95C2×D8311yescharacteristic
583C25—831no—
584C23×C4—3321no—
585C23×C4—3321no—
586C23×C4—3321no—
587C23×C4—3321no—
588C23×C4—3321no—
589C23×C4—3321no—
590C23×C4—3321no—
591C23×C4—3321no—
592C23×C4—834no—
593C23×C4—834no—
594C23×C4—834no—
595C23×C4—834no—
596C23×C4—834no—
597C23×C4—831no—
598C23×C4—831no—
599C23×C4—831no—
600C23×C4—831no—
601C23×C4—831no—
602C23×C4—831no—
603C23×C4—831no—
604C23×C4—1662no—
605C23×C4—1662no—
606C23×C4—1662no—
607C23×C4—1662no—
608C23×C4—1662no—
609C23×C4—1662no—
610C23×C4—1662no—
611C23×C4—1662no—
612C23×C4C22×D8311yescharacteristic
613C23×C4C22×D8311yescharacteristic
614C23×C4C22×D8311yescharacteristic
615C23×C4C22×D8311yescharacteristic
616C23×C4C22×D8311yescharacteristic
617C23×C4C22×D8311yescharacteristic
618C23×C4C22×D8311yescharacteristic
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—3321no—
622C2×C4⋊C4—3321no—
623C2×C4⋊C4—834no—
624C2×C4⋊C4C4×D8314yescomplemented
625C2×C22⋊C4—834no—
626C2×C22⋊C4—834no—
627C2×C22⋊C4—834no—
628C2×C22⋊C4—834no—
629C2×C22⋊C4—834no—
630C2×C22⋊C4—834no—
631C2×C22⋊C4—1662no—
632C2×C22⋊C4—1662no—
633C2×C22⋊C4—1662no—
634C2×C22⋊C4—1662no—
635C2×C22⋊C4—1662no—
636C2×C22⋊C4—1662no—
637C2×C42—22no—
638C2×C42—22no—
639C2×C42—41no—
640C2×C42—3321no—
641C2×C42—3321no—
642C2×C42—3321no—
643C2×C42—3321no—
644C2×C42—3321no—
645C2×C42—3321no—
646C2×C42—3321no—
647C2×C42—834no—
648C2×C42—834no—
649C2×C42—1662no—
650C2×C42—1662no—
651C2×C42—1662no—
652C2×C42—1662no—
653C2×C42—1662no—
654C2×C42—1662no—
655#95—22no—
656#95—22no—
657#95—41no—
658#95—3321no—
659#95—3321no—
660#95—3321no—
661#95—834no—
662#95—834no—
663#95—834no—
664#95—834no—
665#95—834no—
666#95—834no—
667#95—1662no—
668#95—1662no—
669#95—1662no—
670#95—1662no—
671#95—1662no—
672#95—1662no—
673#95C4×D8314yes—
674#95C4×D8314yescomplemented
675C24—832no—
676C24—832no—
677C24—832no—
678C24—832no—
679C24—832no—
680C24—832no—
681C24—832no—
682C24—1661no—
683C24—1661no—
684C24—1661no—
685C24—1661no—
686C24—1661no—
687C24—1661no—
688C24—1661no—
689C24—1661no—
690C24C23×D8311yescharacteristic
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—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—3324no—
728C22×C4—3324no—
729C22×C4—3324no—
730C22×C4—3324no—
731C22×C4—3324no—
732C22×C4—3324no—
733C22×C4—3324no—
734C22×C4—3324no—
735C22×C4—3324no—
736C22×C4—3324no—
737C22×C4—3324no—
738C22×C4—3324no—
739C22×C4—3324no—
740C22×C4—3324no—
741C22×C4—3324no—
742C22×C4—3324no—
743C22×C4—8316no—
744C22×C4—832no—
745C22×C4—832no—
746C22×C4—832no—
747C22×C4—832no—
748C22×C4—832no—
749C22×C4—832no—
750C22×C4—832no—
751C22×C4—832no—
752C22×C4—832no—
753C22×C4—832no—
754C22×C4—832no—
755C22×C4—832no—
756C22×C4—832no—
757C22×C4—1668no—
758C22×C4—1668no—
759C22×C4—1668no—
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×C4—1661no—
780C22×C4—1661no—
781C22×C4—1661no—
782C22×C4—1661no—
783C22×C4—1661no—
784C22×C4—1668no—
785C22×C4—1661no—
786C22×C4—1661no—
787C22×C4—1661no—
788C22×C4—1661no—
789C22×C4—1661no—
790C22×C4—1661no—
791C22×C4—1661no—
792C22×C4—1661no—
793C22×C4—1661no—
794C22×C4—1661no—
795C22×C4—1661no—
796C22×C4—1661no—
797C22×C4C2×C4×D8312yes—
798C22×C4C2×C4×D8312yes—
799C22×C4C2×C4×D8312yes—
800C22×C4C2×C4×D8312yes—
801C22×C4C2×C4×D8312yes—
802C22×C4C2×C4×D8312yes—
803C22×C4C2×C4×D8312yes—
804C22×C4C2×C4×D8312yes—
805C22×C4C2×C4×D8312yes—
806C22×C4D4×D8312yes—
807C22×C4Q8×D8312yes—
808C22×C4#1305058912yes—
809C22×C4#1305059112yes—
810C4⋊C4—44no—
811C4⋊C4—3324no—
812C22⋊C4—8316no—
813C22⋊C4—1668no—
814C22⋊C4—1668no—
815C22⋊C4—1668no—
816C42—44no—
817C42—3324no—
818C42—3324no—
819C42—3324no—
820C42—3324no—
821C42—3324no—
822C23—834no—
823C23—834no—
824C23—834no—
825C23—834no—
826C23—834no—
827C23—834no—
828C23—834no—
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—
843C23—1662no—
844C23—1662no—
845C23—1662no—
846C23—1662no—
847C23—1662no—
848C23—1662no—
849C23—1662no—
850C23—1662no—
851C23—1662no—
852C23—1662no—
853C23—1662no—
854C23—1662no—
855C23—1662no—
856C23—1662no—
857C23C22×C4×D8311yescharacteristic
858C23C22×C4×D8311yescharacteristic
859C23C22×C4×D8311yescharacteristic
860C23C2×D4×D8311yescharacteristic
861C23C2×Q8×D8311yescharacteristic
862C23#41×D8311yescharacteristic
863C23#41×D8311yescharacteristic
864C23#41×D8311yescharacteristic
865C23#41×D8311yescharacteristic
866C23C2×#1305058911yescharacteristic
867C23C2×#1305059111yescharacteristic
868C23#1458183711yescharacteristic
869C23#1458183711yescharacteristic
870C23#1458183811yescharacteristic
871C23#1458183811yescharacteristic
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—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—33216no—
919C2×C4—33216no—
920C2×C4—33216no—
921C2×C4—3321no—
922C2×C4—3321no—
923C2×C4—3321no—
924C2×C4—3321no—
925C2×C4—3321no—
926C2×C4—3321no—
927C2×C4—3321no—
928C2×C4—3321no—
929C2×C4—3321no—
930C2×C4—3321no—
931C2×C4—3321no—
932C2×C4—3321no—
933C2×C4—3321no—
934C2×C4—3321no—
935C2×C4—3321no—
936C2×C4—3321no—
937C2×C4—834no—
938C2×C4—834no—
939C2×C4—834no—
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—1662no—
956C2×C4—1662no—
957C2×C4—1662no—
958C2×C4—1662no—
959C2×C4—1662no—
960C2×C4—1662no—
961C2×C4—1662no—
962C2×C4—1662no—
963C2×C4—1662no—
964C2×C4—1662no—
965C2×C4—1662no—
966C2×C4—1662no—
967C2×C4—1662no—
968C2×C4—1662no—
969C2×C4—1662no—
970C2×C4C42×D8314yes—
971C2×C4C4⋊C4×D8314yes—
972C2×C4#1458175014yes—
973C22—838no—
974C22—1664no—
975C22—1664no—
976C22—1664no—
977C22—1664no—
978C22—1664no—
979C22—1664no—
980C22—1664no—
981C22—1664no—
982C22—1664no—
983C22—1664no—
984C22—1664no—
985C22—1664no—
986C22—1664no—
987C22—1664no—
988C22C2×C42×D8311yescharacteristic
989C22C2×C4⋊C4×D8311yescharacteristic
990C22#117×D8311yescharacteristic
991C22#117×D8311yescharacteristic
992C22C2×#1458175011yescharacteristic
993C22C4×D4×D8311yescharacteristic
994C22C4×D4×D8311yescharacteristic
995C22C4×Q8×D8311yescharacteristic
996C22C4×Q8×D8311yescharacteristic
997C22C4×#1305058911yescharacteristic
998C22C4×#1305058911yescharacteristic
999C22C4×#1305059111yescharacteristic
1000C22C4×#1305059111yescharacteristic
1001C22#1912817311yescharacteristic
1002C22#1912817311yescharacteristic
1003C22#1912817311yescharacteristic
1004C22#1912817311yescharacteristic
1005C22#1912817411yescharacteristic
1006C22#1912817511yescharacteristic
1007C22#1912833811yescharacteristic
1008C22#1912834211yescharacteristic
1009C22#1912834311yescharacteristic
1010C22#1912834811yescharacteristic
1011C22#1912837411yescharacteristic
1012C22#1912837611yescharacteristic
1013C22#1912837811yescharacteristic
1014C22#1912838111yescharacteristic
1015C22#1912839611yescharacteristic
1016C22#1912839811yescharacteristic
1017C22#1912840211yescharacteristic
1018C22#1912840411yescharacteristic
1019C22#1912840511yescharacteristic
1020C22#1912840711yescharacteristic
1021C22#1912840911yescharacteristic
1022C22#1912841211yescharacteristic
1023C4—24no—
1024C4—24no—
1025C4—24no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—3322no—
1031C4—3322no—
1032C4—3322no—
1033C4—3322no—
1034C4—1664no—
1035C4—1664no—
1036C4—1664no—
1037C2—1668no—
1038C2C4×C4⋊C4×D8311yescharacteristic
1039C2C4×#1458175011yescharacteristic
1040C2#2490981511yescharacteristic
1041C2#2491030711yescharacteristic
1042C2#2491031011yescharacteristic
1043C2#2491033711yescharacteristic
1044C2#2491033911yescharacteristic
1045C2#2491036911yescharacteristic
1046C2#2491037211yescharacteristic
1047C2#2491039811yescharacteristic
1048C2#2491040211yescharacteristic
1049C2#2491050911yescharacteristic
1050C2#2491051211yescharacteristic
1051C2#2491054211yescharacteristic
1052C2#2491054511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC83×#1436C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenter#1436D83
hypocenterC83#13802
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
6. #24905697C2semidirect
7. #24905697C2semidirect
8. #24905695C2semidirect
9. #24905689C2semidirect
10. #24905687C2semidirect
13. C4×C83⋊#95C2semidirect
14. #95×Dic83C2semidirect
15. C83×#1436C2semidirect
29. #19127558C4semidirect
32. #19127548C4semidirect
48. #95×D83C4semidirect
87. C2×C4⋊Dic83C2×C4semidirect
113. C2×C4×Dic83C2×C4semidirect
114. C2×C4×Dic83C2×C4semidirect
127. C83⋊#95C2×C4semidirect
128. C83⋊#95C2×C4semidirect
129. C83⋊#95C2×C4semidirect
139. C2×C4⋊C4×C83C2×C4semidirect
147. #95×C83C2×C4semidirect
232. C2×C4×D83C42semidirect
237. (C2×D83)⋊C4C4⋊C4semidirect
535. #1436D83semidirect
542. C83#13802semidirect
624. C2×C4⋊C4C4×D83semidirect
674. #95C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191275582
C2×C4×(C2×D83)⋊C42
C2×#191275482
C2×#95×D832
#249056972
#249056952
#249056892
#249056872
(C2×D83)⋊#952
C4×C83⋊#952
#95×Dic832
C83×#14362
#1380283