Finite Group Databasebeta

← #35420470

Subgroups — #35420470

Order 21248.

1202 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128231C211yesmaximal, characteristic
2C2×D4×C83⋊C8C211yesmaximal, characteristic, complemented
3#24908403C211yesmaximal, characteristic, complemented
4#24908398C211yesmaximal, characteristic, complemented
5#24907760C211yesmaximal, characteristic, complemented
6#24907755C211yesmaximal, characteristic, complemented
7#24907753C211yesmaximal, characteristic, complemented
8#24907753C211yesmaximal, characteristic, complemented
9#24907532C211yesmaximal, characteristic, complemented
10#24907529C211yesmaximal, characteristic, complemented
11#24907444C211yesmaximal, characteristic, complemented
12#24907232C211yesmaximal, characteristic, complemented
13#24907161C211yesmaximal, characteristic, complemented
14C2×#19127455C211yesmaximal, characteristic, complemented
15C2×#435×C83C211yesmaximal, characteristic, complemented
16C23×C83⋊C8C2211yescharacteristic
17C23×C83⋊C8C2211yescharacteristic
18#19128231—24no—
19#19128231—24no—
20C2×#14581787C411yescharacteristic
21C2×#14581785C411yescharacteristic
22C2×#14581782C411yescharacteristic
23C2×#14581778C411yescharacteristic
24C2×#14581776C411yescharacteristic
25C2×#14581773C411yescharacteristic
26C2×#14581769C411yescharacteristic
27C2×#14581764C411yescharacteristic
28C2×C4×Dic166C2211yescharacteristic
29C2×C4×C22⋊D83C2211yescharacteristic
30C2×C4×C22⋊D83C2211yescharacteristic
31C2×#14581751C2211yescharacteristic
32C2×#14581749C2211yescharacteristic
33C22×C4×Dic83C2211yescharacteristic
34D4×C83⋊C8—24no—
35C2×C4⋊(C83⋊C8)C2211yescharacteristic
36C2×C22⋊(C83⋊C8)C2211yescharacteristic
37C2×C22⋊(C83⋊C8)C2211yescharacteristic
38C2×(C2×D83)⋊C8C2211yescharacteristic
39C2×(C2×D83)⋊C8C2211yescharacteristic
40C2×(C2×D83)⋊C8C2211yescharacteristic
41C2×(C2×D83)⋊C8C2211yescharacteristic
42C2×C4×C83⋊C8C2211yescharacteristic
43#19127455C2211yescharacteristic
44#19127455C2211yescharacteristic
45#19127455C2211yescharacteristic
46#19127455C2211yescharacteristic
47#19127455C2211yescharacteristic
48#19127455C2211yescharacteristic
49#19127455C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54#19127455C2211yescharacteristic
55C22×M16×C83C2211yescharacteristic
56C23×C8×C83C2211yescharacteristic
57C2×C4×D4×C83C2211yescharacteristic
58#435×C83—24no—
59C2×C4⋊C8×C83C2211yescharacteristic
60C2×C22⋊C8×C83C2211yescharacteristic
61C2×C22⋊C8×C83C2211yescharacteristic
62C2×#97×C83C2211yescharacteristic
63C22×Dic166C2×C411yescharacteristic
64C22×C22⋊D83C2×C411yescharacteristic
65C22×C22⋊D83C2×C411yescharacteristic
66C23×Dic83C2×C411yescharacteristic
67C23×Dic83C2×C411yescharacteristic
68C22×C4×D83C2311yescharacteristic
69C22×C83⋊C8—22no—
70C22×C83⋊C8—22no—
71C22×C83⋊C8—22no—
72C22×C83⋊C8—22no—
73C22×C83⋊C8—41no—
74C22×C83⋊C8—41no—
75C22×C83⋊C8C2311yescharacteristic
76C22×C83⋊C8C2311yescharacteristic
77C22×C83⋊C8C2311yescharacteristic
78C22×C83⋊C8C2311yescharacteristic
79#14581787—24no—
80#14581785—24no—
81#14581782—24no—
82#14581778—24no—
83#14581776—24no—
84#14581773—24no—
85#14581769—24no—
86#14581764—24no—
87C4×Dic166—22no—
88C4×Dic166—22no—
89C4×C22⋊D83—22no—
90C4×C22⋊D83—22no—
91C4×C22⋊D83—22no—
92C4×C22⋊D83—22no—
93#14581751—22no—
94#14581751—22no—
95#14581749—22no—
96#14581749—22no—
97C2×C4⋊Dic83C2×C411yescharacteristic
98C2×C4⋊Dic83C2×C411yescharacteristic
99C2×C4⋊Dic83C2×C411yescharacteristic
100C2×Dic83⋊C4C2×C411yescharacteristic
101C2×Dic83⋊C4C2×C411yescharacteristic
102C2×Dic83⋊C4C2×C411yescharacteristic
103C2×Dic83⋊C4C2×C411yescharacteristic
104C2×Dic83⋊C4C2×C411yescharacteristic
105C2×Dic83⋊C4C2×C411yescharacteristic
106C2×C22⋊Dic83C2×C411yescharacteristic
107C2×C22⋊Dic83C2×C411yescharacteristic
108C2×C22⋊Dic83C2×C411yescharacteristic
109C2×C22⋊Dic83C2×C411yescharacteristic
110C2×(C2×D83)⋊C4C2×C411yescharacteristic
111C2×(C2×D83)⋊C4C2×C411yescharacteristic
112C2×(C2×D83)⋊C4C2×C411yescharacteristic
113C2×(C2×D83)⋊C4C2×C411yescharacteristic
114C2×C4×Dic83—22no—
115C2×C4×Dic83—22no—
116C2×C4×Dic83C2×C411yescharacteristic
117C2×C4×Dic83C2×C411yescharacteristic
118C2×C4×Dic83C2311yescharacteristic
119C2×C4×Dic83C2311yescharacteristic
120C2×C4×Dic83C2311yescharacteristic
121C4⋊(C83⋊C8)—22no—
122C22⋊(C83⋊C8)—22no—
123C22⋊(C83⋊C8)—22no—
124(C2×D83)⋊C8—22no—
125(C2×D83)⋊C8—22no—
126(C2×D83)⋊C8—41no—
127(C2×D83)⋊C8—41no—
128C4×C83⋊C8—22no—
129C22×D4×C83C2×C411yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C2×M16×C83—22no—
133C2×M16×C83—22no—
134C2×M16×C83—41no—
135C22×C8×C83—22no—
136C22×C8×C83—22no—
137C22×C8×C83—41no—
138C22×C8×C83C2311yescharacteristic
139C22×C8×C83C2311yescharacteristic
140C22×C8×C83C2311yescharacteristic
141C22×C8×C83C2311yescharacteristic
142C4×D4×C83D414yes—
143C4×D4×C83D414yes—
144C2×C4⋊C4×C83C2×C411yescharacteristic
145C2×C22⋊C4×C83C2×C411yescharacteristic
146C2×C22⋊C4×C83C2×C411yescharacteristic
147C2×C42×C83C2311yescharacteristic
148C4⋊C8×C83—22no—
149C22⋊C8×C83—22no—
150C22⋊C8×C83—22no—
151#97×C83—22no—
152C23×D83C22×C411yescharacteristic
153C2×Dic166—22no—
154C2×Dic166—22no—
155C2×Dic166—41no—
156C2×C22⋊D83—22no—
157C2×C22⋊D83—22no—
158C2×C22⋊D83—22no—
159C2×C22⋊D83—22no—
160C2×C22⋊D83—22no—
161C2×C22⋊D83—41no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—22no—
166C22×Dic83—22no—
167C22×Dic83—41no—
168C22×Dic83C22×C411yescharacteristic
169C22×Dic83C22×C411yescharacteristic
170C22×Dic83C22×C411yescharacteristic
171C22×Dic83C22×C411yescharacteristic
172C22×Dic83C22×C411yescharacteristic
173C22×Dic83C22×C411yescharacteristic
174C22×Dic83C22×C411yescharacteristic
175C2×C4×D83—21no—
176C2×C4×D83—21no—
177C2×C4×D83—21no—
178C2×C4×D83—21no—
179C2×C4×D83—21no—
180C2×C4×D83—21no—
181C2×C83⋊C8—21no—
182C2×C83⋊C8—21no—
183C2×C83⋊C8—21no—
184C2×C83⋊C8—21no—
185C2×C83⋊C8—21no—
186C2×C83⋊C8—21no—
187C2×C83⋊C8—21no—
188C2×C83⋊C8—21no—
189C2×C83⋊C8—21no—
190C2×C83⋊C8—21no—
191C2×C83⋊C8—21no—
192C2×C83⋊C8—44no—
193C2×C83⋊C8—44no—
194C2×C83⋊C8#4112yes—
195C4⋊Dic83—22no—
196C4⋊Dic83—22no—
197C4⋊Dic83—22no—
198Dic83⋊C4—22no—
199Dic83⋊C4—22no—
200Dic83⋊C4—22no—
201Dic83⋊C4—22no—
202Dic83⋊C4—22no—
203Dic83⋊C4—22no—
204C22⋊Dic83—22no—
205C22⋊Dic83—22no—
206C22⋊Dic83—22no—
207C22⋊Dic83—22no—
208(C2×D83)⋊C4—22no—
209(C2×D83)⋊C4—22no—
210(C2×D83)⋊C4—22no—
211(C2×D83)⋊C4—22no—
212C4×Dic83—22no—
213C4×Dic83—22no—
214C4×Dic83—21no—
215C4×Dic83—21no—
216C4×Dic83—21no—
217C4×Dic83—21no—
218C4×Dic83—21no—
219C4×Dic83—21no—
220C24×C83C22×C411yescharacteristic
221C24×C83C22×C411yescharacteristic
222C2×D4×C83—22no—
223C2×D4×C83—22no—
224C2×D4×C83C22⋊C414yes—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—21no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83C22×C411yescharacteristic
234C22×C4×C83C22×C411yescharacteristic
235C22×C4×C83C22×C411yescharacteristic
236C22×C4×C83C22×C411yescharacteristic
237C22×C4×C83C2×D412yes—
238C22×C4×C83C2×D412yes—
239C22×C4×C83C2×D412yes—
240C22×C4×C83C2×D412yes—
241C22×C4×C83C2411yescharacteristic
242M16×C83—44no—
243C2×C8×C83—21no—
244C2×C8×C83—21no—
245C2×C8×C83—21no—
246C2×C8×C83—21no—
247C2×C8×C83—21no—
248C2×C8×C83—21no—
249C2×C8×C83—21no—
250C2×C8×C83—21no—
251C2×C8×C83—21no—
252C2×C8×C83—21no—
253C2×C8×C83—21no—
254C2×C8×C83—44no—
255C2×C8×C83#4112yes—
256C4⋊C4×C83C22⋊C414yes—
257C22⋊C4×C83C22⋊C414yes—
258C22⋊C4×C83C22⋊C414yes—
259C42×C83C2×D412yes—
260C42×C83C2×D412yes—
261C23×C83—21no—
262C23×C83—21no—
263C23×C83—21no—
264C23×C83—21no—
265C23×C83—21no—
266C23×C83—21no—
267C23×C83—21no—
268C23×C83—21no—
269C23×C83—21no—
270C23×C83—21no—
271C23×C83C2×C22⋊C412yes—
272C23×C83C2×C22⋊C412yes—
273C23×C83#13112yes—
274C23×C83#13112yes—
275C23×C83C23×C411yescharacteristic
276C22×D83—21no—
277C22×D83—21no—
278C22×D83—21no—
279C22×D83—21no—
280C22×D83—21no—
281C22×D83—21no—
282C22×D83—21no—
283D4×C83—28no—
284C2×C4×C83—21no—
285C2×C4×C83—21no—
286C2×C4×C83—21no—
287C2×C4×C83—21no—
288C2×C4×C83—21no—
289C2×C4×C83—21no—
290C2×C4×C83—21no—
291C2×C4×C83—21no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83C2×C22⋊C412yes—
301C2×C4×C83C2×C22⋊C412yes—
302C2×C4×C83C2×C22⋊C412yes—
303C2×C4×C83C2×C22⋊C412yes—
304C2×C4×C83C22×D411yescharacteristic
305C2×C4×C83C22×D411yescharacteristic
306C2×C4×C83C2×#4111yescharacteristic
307C2×C4×C83C2×#4111yescharacteristic
308C2×C4×C83H(5,𝔽2)11yescharacteristic
309C2×C4×C832−1+411yescharacteristic
310C22⋊D83—44no—
311C22⋊D83—44no—
312C2×Dic83—21no—
313C2×Dic83—21no—
314C2×Dic83—21no—
315C2×Dic83—21no—
316C2×Dic83—21no—
317C2×Dic83—21no—
318C2×Dic83—21no—
319C2×Dic83—21no—
320C2×Dic83—21no—
321C2×Dic83—21no—
322C2×Dic83—21no—
323C2×Dic83—21no—
324C2×Dic83—21no—
325C2×Dic83—21no—
326C2×Dic83—21no—
327C2×Dic83—21no—
328C2×Dic83—21no—
329C2×Dic83—21no—
330C2×Dic83—21no—
331C2×Dic83—21no—
332C2×Dic83—44no—
333C2×Dic83—44no—
334C2×Dic83#13112yes—
335C4×D83—41no—
336C4×D83—41no—
337C4×D83—41no—
338C4×D83—41no—
339Dic166—44no—
340C8×C83—22no—
341C8×C83—41no—
342C8×C83—41no—
343C8×C83—41no—
344C83⋊C8—22no—
345C83⋊C8—41no—
346C83⋊C8—41no—
347C83⋊C8—41no—
348C22×C83—22no—
349C22×C83—22no—
350C22×C83—22no—
351C22×C83—22no—
352C22×C83—22no—
353C22×C83—22no—
354C22×C83—22no—
355C22×C83—22no—
356C22×C83—22no—
357C22×C83—41no—
358C22×C83—41no—
359C22×C83—41no—
360C22×C83—41no—
361C22×C83#40814yes—
362C22×C83C22×C22⋊C411yescharacteristic
363C22×C83C4×#4111yescharacteristic
364C22×C83#52011yescharacteristic
365C22×C83C2×#13111yescharacteristic
366C22×C83C2×#13111yescharacteristic
367C22×C83C2×#13111yescharacteristic
368C22×C83#56811yescharacteristic
369C2×D83—41no—
370C2×D83—41no—
371C2×D83—41no—
372C2×D83—41no—
373C2×D83—41no—
374C2×D83—41no—
375C2×D83—41no—
376C4×C83—22no—
377C4×C83—22no—
378C4×C83—22no—
379C4×C83—22no—
380C4×C83#54611yescharacteristic
381C4×C83#54611yescharacteristic
382C4×C83#54711yescharacteristic
383C4×C83#54711yescharacteristic
384Dic83—22no—
385Dic83—41no—
386Dic83—41no—
387Dic83—41no—
388Dic83—41no—
389Dic83—41no—
390Dic83—41no—
391#22470—831nomaximal, Sylow
392C2×C83—24no—
393C2×C83—42no—
394C2×C83#233911yescharacteristic
395C2×C83C2×#40811yescharacteristic
396C2×C83#288011yescharacteristic
397C2×C83#296611yescharacteristic
398C2×C83#296811yescharacteristic
399C2×C83#299211yescharacteristic
400C2×C83#299411yescharacteristic
401D83—81no—
402C2×#529—831no—
403C2×#435D8311yescharacteristic, complemented
404C2×C8×D4—831no—
405#1985—831no—
406#1984—831no—
407#1870—831no—
408#1869—831no—
409#1869—831no—
410#1869—831no—
411#1818—831no—
412#1817—831no—
413#1798—831no—
414#1750—831no—
415#1729—831no—
416C2×#336—831no—
417C83#2247011yescharacteristic, complemented, Sylow
418C22×M16C2×D8311yescharacteristic
419C23×C8—831no—
420C23×C8—831no—
421C23×C8C2×D8311yescharacteristic
422#529—1664no—
423#529—1664no—
424C2×#126—831no—
425C2×#126—831no—
426C2×#125—831no—
427C2×#124—831no—
428C2×#123—831no—
429C2×#123—831no—
430C2×C22⋊Q8—831no—
431C2×#121—831no—
432C2×C4×Q8—831no—
433C2×C4×D4—831no—
434C2×C4×D4—831no—
435C2×C4×D4C2×D8311yescharacteristic
436C2×#117—831no—
437C2×#117—831no—
438C22×C42—831no—
439#435—24no—
440C8×D4—1664no—
441C2×C4⋊C8—831no—
442C2×C4⋊C8C2×D8311yescharacteristic
443C2×C22⋊C8—831no—
444C2×C22⋊C8—831no—
445C2×C22⋊C8—831no—
446C2×C22⋊C8—831no—
447C2×C22⋊C8—831no—
448C2×C22⋊C8—831no—
449C2×C22⋊C8C2×D8311yescharacteristic
450C2×C22⋊C8C2×D8311yescharacteristic
451C2×#97C2×D8311yescharacteristic
452C2×C4×C8—831no—
453#336—831no—
454#336—831no—
455#336—831no—
456#336—831no—
457#336—831no—
458#336—831no—
459#336—831no—
460#336—831no—
461#336—831no—
462#336—831no—
463#336—831no—
464#336—831no—
465C22×Q8—831no—
466C22×D4—831no—
467C22×D4—831no—
468C22×D4C4×D8311yescharacteristic
469C23×C4—831no—
470C23×C4—831no—
471C23×C4—831no—
472C23×C4C22×D8311yescharacteristic
473C23×C4C22×D8311yescharacteristic
474C2×M16—22no—
475C2×M16—22no—
476C2×M16—41no—
477C22×C8—22no—
478C22×C8—22no—
479C22×C8—41no—
480C22×C8—3321no—
481C22×C8—3321no—
482C22×C8—831no—
483C22×C8—831no—
484C22×C8—831no—
485C22×C8—831no—
486C22×C8—1662no—
487C22×C8—1662no—
488C22×C8—1662no—
489C22×C8—1662no—
490C22×C8C22×D8311yescharacteristic
491C22×C8C22×D8311yescharacteristic
492C22×C8C22×D8311yescharacteristic
493C22×C8C22×D8311yescharacteristic
494#126—1664no—
495#126—1664no—
496#125—1664no—
497#124—1664no—
498#123—1664no—
499#123—1664no—
500C22⋊Q8—1664no—
501#121—1664no—
502C4×Q8—1662no—
503C4×Q8—1662no—
504C4×D4—1662no—
505C4×D4—1662no—
506C4×D4—1662no—
507C4×D4—1662no—
508C4×D4D33214yes—
509C4×D4C22⋊D8314yes—
510#117—1662no—
511#117—1662no—
512#117—1662no—
513#117—1662no—
514C2×C4⋊C4—831no—
515C2×C4⋊C4—831no—
516C2×C4⋊C4—831no—
517C2×C4⋊C4—831no—
518C2×C4⋊C4—831no—
519C2×C4⋊C4—831no—
520C2×C4⋊C4—831no—
521C2×C4⋊C4—831no—
522C2×C4⋊C4—831no—
523C2×C4⋊C4C4×D8311yescharacteristic
524C2×C22⋊C4—831no—
525C2×C22⋊C4—831no—
526C2×C22⋊C4—831no—
527C2×C22⋊C4—831no—
528C2×C22⋊C4—831no—
529C2×C22⋊C4—831no—
530C2×C22⋊C4—831no—
531C2×C22⋊C4—831no—
532C2×C22⋊C4C4×D8311yescharacteristic
533C2×C22⋊C4C4×D8311yescharacteristic
534C2×C42—831no—
535C2×C42—831no—
536C2×C42—831no—
537C2×C42—831no—
538C2×C42—831no—
539C2×C42—1662no—
540C2×C42—1662no—
541C2×C42C22×D8311yescharacteristic
542C4⋊C8—22no—
543C4⋊C8—1662no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—3321no—
547C22⋊C8—3321no—
548C22⋊C8—1662no—
549C22⋊C8—1662no—
550C22⋊C8—1662no—
551C22⋊C8—1662no—
552#97—22no—
553C4×C8—1662no—
554C24—831no—
555C24C2×C4×D8311yescharacteristic
556C24C2×C4×D8311yescharacteristic
557C2×Q8—3321no—
558C2×Q8—1662no—
559C2×Q8—1662no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—3321no—
563C2×D4—1662no—
564C2×D4—1662no—
565C2×D4—1662no—
566C2×D4—1662no—
567C2×D4—1662no—
568C2×D4(C2×D83)⋊C414yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—3321no—
578C22×C4—831no—
579C22×C4—831no—
580C22×C4—831no—
581C22×C4—831no—
582C22×C4—831no—
583C22×C4—831no—
584C22×C4—831no—
585C22×C4—1662no—
586C22×C4—1662no—
587C22×C4—1662no—
588C22×C4—1662no—
589C22×C4—1662no—
590C22×C4—1661no—
591C22×C4—1661no—
592C22×C4—1661no—
593C22×C4—1661no—
594C22×C4—1661no—
595C22×C4—1661no—
596C22×C4C2×C4×D8311yescharacteristic
597C22×C4C2×C4×D8311yescharacteristic
598C22×C4C2×C4×D8311yescharacteristic
599C22×C4C2×C4×D8311yescharacteristic
600C22×C4C2×C22⋊D8312yes—
601C22×C4C2×C22⋊D8312yes—
602C22×C4C2×D33212yes—
603C22×C4C2×D33212yes—
604C22×C4C23×D8311yescharacteristic
605M16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—44no—
618C2×C8—3324no—
619C2×C8—3324no—
620C2×C8—832no—
621C2×C8—1661no—
622C2×C8—1661no—
623C2×C8—1661no—
624C2×C8—1661no—
625C2×C8—1661no—
626C2×C8—1661no—
627C2×C8—1661no—
628C2×C8—1661no—
629C2×C8—1661no—
630C2×C8—1661no—
631C2×C8—1661no—
632C2×C8#1305058912yes—
633C4⋊C4—1662no—
634C4⋊C4—1662no—
635C4⋊C4—1662no—
636C4⋊C4—1662no—
637C4⋊C4—1662no—
638C4⋊C4—1662no—
639C4⋊C4—1662no—
640C4⋊C4—1662no—
641C4⋊C4—1662no—
642C4⋊C4(C2×D83)⋊C414yes—
643C22⋊C4—1662no—
644C22⋊C4—1662no—
645C22⋊C4—1662no—
646C22⋊C4—1662no—
647C22⋊C4—1662no—
648C22⋊C4—1662no—
649C22⋊C4—1662no—
650C22⋊C4—1662no—
651C22⋊C4(C2×D83)⋊C414yes—
652C22⋊C4(C2×D83)⋊C414yes—
653C42—1661no—
654C42—1661no—
655C42—1661no—
656C42—1661no—
657C42—1661no—
658C42—1661no—
659C42—1662no—
660C42—1662no—
661C42C2×C22⋊D8312yes—
662C42C2×D33212yes—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—1661no—
674C23—1661no—
675C23—1661no—
676C23—1661no—
677C23—1661no—
678C23—1661no—
679C23—1661no—
680C23C2×(C2×D83)⋊C412yes—
681C23C2×(C2×D83)⋊C412yes—
682C23#1458180012yes—
683C23#1458180012yes—
684C23C22×C4×D8311yescharacteristic
685Q8—3324no—
686D4—28no—
687D4—3324no—
688D4—3324no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—3324no—
706C2×C4—3324no—
707C2×C4—3321no—
708C2×C4—3321no—
709C2×C4—3321no—
710C2×C4—3321no—
711C2×C4—832no—
712C2×C4—1661no—
713C2×C4—1661no—
714C2×C4—1661no—
715C2×C4—1661no—
716C2×C4—1661no—
717C2×C4—1661no—
718C2×C4—1661no—
719C2×C4—1661no—
720C2×C4—1661no—
721C2×C4—1661no—
722C2×C4—1661no—
723C2×C4—1661no—
724C2×C4—1661no—
725C2×C4—1661no—
726C2×C4—1661no—
727C2×C4—1661no—
728C2×C4—1661no—
729C2×C4—1661no—
730C2×C4—1661no—
731C2×C4—1661no—
732C2×C4C2×(C2×D83)⋊C412yes—
733C2×C4C2×(C2×D83)⋊C412yes—
734C2×C4C2×(C2×D83)⋊C412yes—
735C2×C4C2×(C2×D83)⋊C412yes—
736C2×C4C22×C22⋊D8311yescharacteristic
737C2×C4C22×D33211yescharacteristic
738C2×C4#41×D8311yescharacteristic
739C2×C4C2×#1305058911yescharacteristic
740C2×C4#1458183711yescharacteristic
741C2×C4#1458183911yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—3321no—
747C8—3321no—
748C8—3321no—
749C8—1662no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—3321no—
764C22—3321no—
765C22—3321no—
766C22—3321no—
767C22—3321no—
768C22—3321no—
769C22—3321no—
770C22#1912766914yes—
771C22C22×(C2×D83)⋊C411yescharacteristic
772C22C4×#1305058911yescharacteristic
773C22#1912818011yescharacteristic
774C22#131×D8311yescharacteristic
775C22C2×#1458180011yescharacteristic
776C22C2×#1458180011yescharacteristic
777C22#1912846611yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—3321no—
783C4—3321no—
784C4—3321no—
785C4—3321no—
786C4—3321no—
787C4—3321no—
788C4—1662no—
789C4#1912834511yescharacteristic
790C4#1912834611yescharacteristic
791C4#1912835011yescharacteristic
792C4#1912835511yescharacteristic
793C2—24no—
794C2—42no—
795C2—6641no—
796C2#2491028811yescharacteristic
797C2C2×#1912766911yescharacteristic
798C2#2491591011yescharacteristic
799C2#2491643311yescharacteristic
800C2#2491645811yescharacteristic
801C2#2491660311yescharacteristic
802C2#2491661611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC2×#435×C83C2
prime radicalC2×#14581764C4
cosocleC22×C4×C83C24
hypercenterC2×#435D83
hypocenterC83#22470
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×D4×C83⋊C8C2semidirect
3. #24908403C2semidirect
4. #24908398C2semidirect
5. #24907760C2semidirect
6. #24907755C2semidirect
7. #24907753C2semidirect
8. #24907753C2semidirect
9. #24907532C2semidirect
10. #24907529C2semidirect
11. #24907444C2semidirect
12. #24907232C2semidirect
13. #24907161C2semidirect
14. C2×#19127455C2semidirect
15. C2×#435×C83C2semidirect
403. C2×#435D83semidirect
417. C83#22470semidirect

Maximal subgroups

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

subgroupindex
C2×#191282312
C2×D4×C83⋊C82
#249084032
#249083982
#249077602
#249077552
#249077532
#249075322
#249075292
#249074442
#249072322
#249071612
C2×#191274552
C2×#435×C832
#2247083