Finite Group Databasebeta

← #35409413

Subgroups — #35409413

Order 21248.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128235C211yesmaximal, characteristic
2C2×#19127760C211yesmaximal, characteristic, complemented
3C2×#19127655C211yesmaximal, characteristic, complemented
4#24908401C211yesmaximal, characteristic, complemented
5#24908397C211yesmaximal, characteristic, complemented
6#24908259C211yesmaximal, characteristic, complemented
7#24908255C211yesmaximal, characteristic, complemented
8#24907759C211yesmaximal, characteristic, complemented
9#24907757C211yesmaximal, characteristic, complemented
10#24907754C211yesmaximal, characteristic, complemented
11#24907752C211yesmaximal, characteristic, complemented
12#24907230C211yesmaximal, characteristic, complemented
13#24907230C211yesmaximal, characteristic, complemented
14#24907225C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C83C211yesmaximal, characteristic, complemented
16C22×#13050573C2211yescharacteristic
17C22×C8×D83C2211yescharacteristic
18#19128235—24no—
19#19128235—24no—
20C2×#14581786C411yescharacteristic
21C2×#14581786C411yescharacteristic
22C2×#14581784C411yescharacteristic
23C2×#14581780C411yescharacteristic
24C2×#14581775C411yescharacteristic
25C2×#14581775C411yescharacteristic
26C2×#14581771C411yescharacteristic
27C2×#14581766C411yescharacteristic
28C2×C4×Dic166C2211yescharacteristic
29C2×C4×D332C2211yescharacteristic
30C2×C4×C22⋊D83C2211yescharacteristic
31C2×C4×C22⋊D83C2211yescharacteristic
32C2×#14581749C2211yescharacteristic
33C2×#14581749C2211yescharacteristic
34#19127760—24no—
35C2×Dic83⋊C8C2211yescharacteristic
36C2×Dic83⋊C8C2211yescharacteristic
37C2×C22⋊(C83⋊C8)C2211yescharacteristic
38C2×C22⋊(C83⋊C8)C2211yescharacteristic
39C2×(C2×D83)⋊C8C2211yescharacteristic
40C2×(C2×D83)⋊C8C2211yescharacteristic
41C2×(C2×D83)⋊C8C2211yescharacteristic
42C2×(C2×D83)⋊C8C2211yescharacteristic
43C2×(C2×D83)⋊C8C2211yescharacteristic
44C2×(C2×D83)⋊C8C2211yescharacteristic
45#19127655—24no—
46C2×#14581703C2211yescharacteristic
47C2×#14581703C2211yescharacteristic
48C2×#14581702C2211yescharacteristic
49C2×C8×Dic83C2211yescharacteristic
50#19127456C2211yescharacteristic
51#19127456C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54#19127455C2211yescharacteristic
55#19127455C2211yescharacteristic
56C22×C42×C83C2211yescharacteristic
57C2×C22⋊C8×C83C2211yescharacteristic
58C2×C22⋊C8×C83C2211yescharacteristic
59C2×C4×C8×C83C2211yescharacteristic
60C2×C4×C8×C83C2211yescharacteristic
61#336×C83C2211yescharacteristic
62#336×C83C2211yescharacteristic
63C22×Dic166C2×C411yescharacteristic
64C22×D332C2×C411yescharacteristic
65C22×C22⋊D83C2×C411yescharacteristic
66C22×C22⋊D83C2×C411yescharacteristic
67C22×C4×D83C2311yescharacteristic
68C22×C4×D83C2311yescharacteristic
69C2×#13050573—22no—
70C2×#13050573—22no—
71C2×#13050573—22no—
72C22×C83⋊C8C2311yescharacteristic
73C22×C83⋊C8C2311yescharacteristic
74C22×C83⋊C8C2311yescharacteristic
75C22×C83⋊C8C2311yescharacteristic
76C2×C8×D83—22no—
77C2×C8×D83—22no—
78C2×C8×D83—22no—
79#14581786—24no—
80#14581786—24no—
81#14581784—24no—
82#14581780—24no—
83#14581775—24no—
84#14581775—24no—
85#14581771—24no—
86#14581766—24no—
87C4×Dic166—22no—
88C4×Dic166—22no—
89C4×D332—22no—
90C4×D332—22no—
91C4×C22⋊D83—22no—
92C4×C22⋊D83—22no—
93C4×C22⋊D83—22no—
94C4×C22⋊D83—22no—
95#14581749—22no—
96#14581749—22no—
97#14581749D414yes—
98#14581749D414yes—
99C2×C4⋊Dic83C2×C411yescharacteristic
100C2×C4⋊Dic83C2×C411yescharacteristic
101C2×Dic83⋊C4C2×C411yescharacteristic
102C2×Dic83⋊C4C2×C411yescharacteristic
103C2×Dic83⋊C4C2×C411yescharacteristic
104C2×Dic83⋊C4C2×C411yescharacteristic
105C2×Dic83⋊C4C2×C411yescharacteristic
106C2×Dic83⋊C4C2×C411yescharacteristic
107C2×Dic83⋊C4C2×C411yescharacteristic
108C2×Dic83⋊C4C2×C411yescharacteristic
109C2×C22⋊Dic83C2×C411yescharacteristic
110C2×C22⋊Dic83C2×C411yescharacteristic
111C2×(C2×D83)⋊C4C2×C411yescharacteristic
112C2×(C2×D83)⋊C4C2×C411yescharacteristic
113C2×(C2×D83)⋊C4C2×C411yescharacteristic
114C2×(C2×D83)⋊C4C2×C411yescharacteristic
115C2×(C2×D83)⋊C4C2×C411yescharacteristic
116C2×(C2×D83)⋊C4C2×C411yescharacteristic
117C2×(C2×D83)⋊C4C2×C411yescharacteristic
118C2×(C2×D83)⋊C4C2×C411yescharacteristic
119C2×C4×Dic83C2311yescharacteristic
120C2×C4×Dic83C2311yescharacteristic
121Dic83⋊C8—22no—
122Dic83⋊C8—22no—
123C22⋊(C83⋊C8)—22no—
124C22⋊(C83⋊C8)—22no—
125(C2×D83)⋊C8—22no—
126(C2×D83)⋊C8—22no—
127(C2×D83)⋊C8—22no—
128(C2×D83)⋊C8—22no—
129(C2×D83)⋊C8—22no—
130(C2×D83)⋊C8—22no—
131#14581703—22no—
132#14581703—22no—
133#14581702—22no—
134C8×Dic83—22no—
135C23×C4×C83C2×C411yescharacteristic
136C23×C4×C83C2×C411yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C22×C8×C83C2311yescharacteristic
139C22×C8×C83C2311yescharacteristic
140C22×C8×C83C2311yescharacteristic
141C22×C8×C83C2311yescharacteristic
142C2×C42×C83—22no—
143C2×C42×C83—22no—
144C2×C42×C83C2×C411yescharacteristic
145C2×C42×C83C2×C411yescharacteristic
146C2×C42×C83C2311yescharacteristic
147C2×C42×C83C2311yescharacteristic
148C22⋊C8×C83—22no—
149C22⋊C8×C83—22no—
150C4×C8×C83—22no—
151C4×C8×C83—22no—
152C23×D83C22×C411yescharacteristic
153C23×D83C22×C411yescharacteristic
154C2×Dic166—22no—
155C2×Dic166—22no—
156C2×Dic166—41no—
157C2×D332—22no—
158C2×D332—22no—
159C2×D332—41no—
160C2×C22⋊D83—22no—
161C2×C22⋊D83—22no—
162C2×C22⋊D83—22no—
163C2×C22⋊D83—22no—
164C2×C22⋊D83—41no—
165C2×C22⋊D83—41no—
166C22×Dic83C22×C411yescharacteristic
167C22×Dic83C22×C411yescharacteristic
168C22×Dic83C22×C411yescharacteristic
169C22×Dic83C22×C411yescharacteristic
170C22×Dic83C22×C411yescharacteristic
171C22×Dic83C22×C411yescharacteristic
172C2×C4×D83—21no—
173C2×C4×D83—21no—
174C2×C4×D83—21no—
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×C4×D83—21no—
182C2×C4×D83C2×D412yes—
183C2×C4×D83C2×D412yes—
184#13050573—28no—
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—21no—
193C2×C83⋊C8—21no—
194C2×C83⋊C8—21no—
195C2×C83⋊C8#4112yes—
196C2×C83⋊C8#4112yes—
197C8×D83—28no—
198C4⋊Dic83—22no—
199C4⋊Dic83—22no—
200Dic83⋊C4—22no—
201Dic83⋊C4—22no—
202Dic83⋊C4—22no—
203Dic83⋊C4—22no—
204Dic83⋊C4—22no—
205Dic83⋊C4—22no—
206Dic83⋊C4C22⋊C414yes—
207Dic83⋊C4C22⋊C414yes—
208C22⋊Dic83—22no—
209C22⋊Dic83—22no—
210(C2×D83)⋊C4—22no—
211(C2×D83)⋊C4—22no—
212(C2×D83)⋊C4—22no—
213(C2×D83)⋊C4—22no—
214(C2×D83)⋊C4—22no—
215(C2×D83)⋊C4—22no—
216(C2×D83)⋊C4C22⋊C414yes—
217(C2×D83)⋊C4C22⋊C414yes—
218C4×Dic83—21no—
219C4×Dic83—21no—
220C4×Dic83C2×D412yes—
221C4×Dic83C2×D412yes—
222C24×C83C22×C411yescharacteristic
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—22no—
226C22×C4×C83—22no—
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×C83—41no—
234C22×C4×C83—41no—
235C22×C4×C83C22×C411yescharacteristic
236C22×C4×C83C22×C411yescharacteristic
237C22×C4×C83C22×C411yescharacteristic
238C22×C4×C83C22×C411yescharacteristic
239C22×C4×C83C22×C411yescharacteristic
240C22×C4×C83C2411yescharacteristic
241C2×C8×C83—21no—
242C2×C8×C83—21no—
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#4112yes—
252C2×C8×C83#4112yes—
253C42×C83—22no—
254C42×C83—22no—
255C42×C83—21no—
256C42×C83—21no—
257C42×C83C2×D412yes—
258C42×C83C2×D412yes—
259C23×C83—21no—
260C23×C83—21no—
261C23×C83—21no—
262C23×C83—21no—
263C23×C83—21no—
264C23×C83—21no—
265C23×C83#13112yes—
266C23×C83C23×C411yescharacteristic
267C22×D83—21no—
268C22×D83—21no—
269C22×D83—21no—
270C22×D83—21no—
271C22×D83—21no—
272C22×D83—21no—
273C22×D83—21no—
274C22×D83—21no—
275C22×D83—21no—
276C22×D83—21no—
277C22×D83—21no—
278C22×D83—21no—
279C22×D83—21no—
280C22×D83C2×C22⋊C412yes—
281C2×C4×C83—21no—
282C2×C4×C83—21no—
283C2×C4×C83—21no—
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—21no—
293C2×C4×C83—44no—
294C2×C4×C83—44no—
295C2×C4×C83—41no—
296C2×C4×C83—41no—
297C2×C4×C83—41no—
298C2×C4×C83—41no—
299C2×C4×C83C2×C22⋊C412yes—
300C2×C4×C83C2×C22⋊C412yes—
301C2×C4×C83#13112yes—
302C2×C4×C83C22×D411yescharacteristic
303C2×C4×C83C22×D411yescharacteristic
304C2×C4×C83C2×#4111yescharacteristic
305C2×C4×C83C2×#4111yescharacteristic
306C2×C4×C83C2×#4111yescharacteristic
307C2×C4×C83C2×#4111yescharacteristic
308C22⋊D83—44no—
309C22⋊D83—44no—
310C2×Dic83—21no—
311C2×Dic83—21no—
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×Dic83C2×C22⋊C412yes—
326C2×Dic83C2×C22⋊C412yes—
327C2×Dic83C2×C22⋊C412yes—
328D332—44no—
329C4×D83—22no—
330C4×D83—22no—
331C4×D83—22no—
332C4×D83—22no—
333C4×D83—41no—
334C4×D83—41no—
335C4×D83—41no—
336C4×D83—41no—
337Dic166—44no—
338C8×C83—22no—
339C8×C83—22no—
340C8×C83—41no—
341C8×C83—41no—
342C83⋊C8—22no—
343C83⋊C8—22no—
344C83⋊C8—41no—
345C83⋊C8—41no—
346C22×C83—22no—
347C22×C83—22no—
348C22×C83—22no—
349C22×C83—41no—
350C22×C83—41no—
351C22×C83—41no—
352C22×C83—41no—
353C22×C83C22×C22⋊C411yescharacteristic
354C22×C83C4×#4111yescharacteristic
355C22×C83C4×#4111yescharacteristic
356C22×C83C2×#13111yescharacteristic
357C22×C83C2×#13111yescharacteristic
358C22×C83#56811yescharacteristic
359C22×C83#56811yescharacteristic
360C2×D83—22no—
361C2×D83—22no—
362C2×D83—22no—
363C2×D83—41no—
364C2×D83—41no—
365C2×D83—41no—
366C2×D83—41no—
367C2×D83—41no—
368C2×D83—41no—
369C2×D83—41no—
370C2×D83—41no—
371C2×D83—41no—
372C2×D83—41no—
373C2×D83—41no—
374C4×C83—22no—
375C4×C83—22no—
376C4×C83—22no—
377C4×C83—41no—
378C4×C83—41no—
379C4×C83#52511yescharacteristic
380C4×C83#52511yescharacteristic
381C4×C83#53211yescharacteristic
382C4×C83#53211yescharacteristic
383Dic83—22no—
384Dic83—22no—
385Dic83—22no—
386Dic83—41no—
387Dic83—41no—
388Dic83—41no—
389#21381—831nomaximal, Sylow
390C2×C83—42no—
391C2×C83#229711yescharacteristic
392C2×C83#288011yescharacteristic
393C2×C83#288011yescharacteristic
394C2×C83#296611yescharacteristic
395C2×C83#296711yescharacteristic
396C2×C83#296811yescharacteristic
397C2×C83#296911yescharacteristic
398D83—42no—
399D83—81no—
400C2×#529—831no—
401C2×#433—831no—
402C2×#405—831no—
403#1985—831no—
404#1984—831no—
405#1955—831no—
406#1954—831no—
407#1870—831no—
408#1870—831no—
409#1869—831no—
410#1869—831no—
411#1750—831no—
412#1750—831no—
413#1749—831no—
414C4×C22⋊C8D8311yescharacteristic, complemented
415C83#2138111yescharacteristic, complemented, Sylow
416C22×M16—831no—
417C23×C8—831no—
418#529—1664no—
419#529—1664no—
420C2×#126—831no—
421C2×#126—831no—
422C2×#125—831no—
423C2×#124—831no—
424C2×#123—831no—
425C2×#123—831no—
426C2×C22⋊Q8—831no—
427C2×#121—831no—
428C2×C4×Q8—831no—
429C2×C4×D4—831no—
430C2×C4×D4—831no—
431C2×C4×D4—831no—
432C2×#117—831no—
433C2×#117—831no—
434C22×C42C2×D8311yescharacteristic
435#433—1664no—
436C2×C4⋊C8—831no—
437C2×C4⋊C8—831no—
438C2×C22⋊C8—831no—
439C2×C22⋊C8—831no—
440C2×C22⋊C8—831no—
441C2×C22⋊C8—831no—
442C2×C22⋊C8—831no—
443C2×C22⋊C8—831no—
444C2×C22⋊C8—831no—
445C2×C22⋊C8—831no—
446C2×C22⋊C8C2×D8311yescharacteristic
447C2×C22⋊C8C2×D8311yescharacteristic
448#405—1664no—
449C2×#97—831no—
450C2×#97—831no—
451C2×#97—831no—
452C2×C4×C8—831no—
453C2×C4×C8C2×D8311yescharacteristic
454C2×C4×C8C2×D8311yescharacteristic
455#336—831no—
456#336—831no—
457#336—831no—
458#336—831no—
459#336—831no—
460#336—831no—
461#336C2×D8311yescharacteristic
462#336C2×D8311yescharacteristic
463C22×Q8—831no—
464C22×D4—831no—
465C22×D4—831no—
466C22×D4—831no—
467C23×C4—831no—
468C23×C4—831no—
469C23×C4C4×D8311yescharacteristic
470C23×C4C4×D8311yescharacteristic
471C23×C4C22×D8311yescharacteristic
472C2×M16—1662no—
473C2×M16—1662no—
474C2×M16—1662no—
475C22×C8—831no—
476C22×C8—831no—
477C22×C8—831no—
478C22×C8—831no—
479C22×C8—1662no—
480C22×C8—1662no—
481C22×C8—1662no—
482C22×C8C22×D8311yescharacteristic
483C22×C8C22×D8311yescharacteristic
484C22×C8C22×D8311yescharacteristic
485C22×C8C22×D8311yescharacteristic
486#126—1664no—
487#126—1664no—
488#125—1664no—
489#124—1664no—
490#123—1664no—
491#123—1664no—
492C22⋊Q8—1664no—
493#121—1664no—
494C4×Q8—1662no—
495C4×Q8—1662no—
496C4×D4—1662no—
497C4×D4—1662no—
498C4×D4—1662no—
499C4×D4—1662no—
500C4×D4—1662no—
501C4×D4—1662no—
502#117—834no—
503#117—834no—
504#117—1662no—
505#117—1662no—
506C2×C4⋊C4—831no—
507C2×C4⋊C4—831no—
508C2×C4⋊C4—831no—
509C2×C4⋊C4—831no—
510C2×C4⋊C4—831no—
511C2×C4⋊C4—831no—
512C2×C4⋊C4—831no—
513C2×C4⋊C4—831no—
514C2×C4⋊C4—831no—
515C2×C4⋊C4—831no—
516C2×C22⋊C4—831no—
517C2×C22⋊C4—831no—
518C2×C22⋊C4—831no—
519C2×C22⋊C4—831no—
520C2×C22⋊C4—831no—
521C2×C22⋊C4—831no—
522C2×C22⋊C4—831no—
523C2×C22⋊C4—831no—
524C2×C22⋊C4—831no—
525C2×C22⋊C4—831no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—831no—
529C2×C42—831no—
530C2×C42C4×D8311yescharacteristic
531C2×C42C4×D8311yescharacteristic
532C2×C42C22×D8311yescharacteristic
533C2×C42C22×D8311yescharacteristic
534C4⋊C8—1662no—
535C4⋊C8—1662no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—1662no—
539C22⋊C8—1662no—
540C22⋊C8—1662no—
541C22⋊C8—1662no—
542C22⋊C8—1662no—
543C22⋊C8—1662no—
544C22⋊C8—1662no—
545C22⋊C8—1662no—
546#97—1662no—
547#97—1662no—
548#97—1662no—
549C4×C8—22no—
550C4×C8—22no—
551C4×C8—1662no—
552C24—831no—
553C24—831no—
554C24C2×C4×D8311yescharacteristic
555C2×Q8—3321no—
556C2×Q8—1662no—
557C2×Q8—1662no—
558C2×D4—3321no—
559C2×D4—3321no—
560C2×D4—3321no—
561C2×D4—1662no—
562C2×D4—1662no—
563C2×D4—1662no—
564C2×D4—1662no—
565C2×D4—1662no—
566C2×D4—1662no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—831no—
580C22×C4—831no—
581C22×C4—831no—
582C22×C4—832no—
583C22×C4—832no—
584C22×C4—831no—
585C22×C4—831no—
586C22×C4—831no—
587C22×C4—1661no—
588C22×C4—1661no—
589C22×C4—1661no—
590C22×C4—1661no—
591C22×C4—1661no—
592C22×C4—1661no—
593C22×C4—1661no—
594C22×C4—1661no—
595C22×C4—1661no—
596C22×C4—1661no—
597C22×C4C2×C4×D8311yescharacteristic
598C22×C4C2×C4×D8311yescharacteristic
599C22×C4C2×C4×D8311yescharacteristic
600C22×C4C2×C4×D8311yescharacteristic
601C22×C4C2×C4×D8311yescharacteristic
602C22×C4C23×D8311yescharacteristic
603M16—1668no—
604C2×C8—21no—
605C2×C8—21no—
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—832no—
615C2×C8—832no—
616C2×C8—1668no—
617C2×C8—1661no—
618C2×C8—1661no—
619C2×C8—1661no—
620C2×C8—1661no—
621C2×C8—1661no—
622C2×C8—1661no—
623C2×C8—1661no—
624C2×C8—1661no—
625C2×C8—1661no—
626C2×C8—1661no—
627C2×C8#1305059012yes—
628C2×C8#1305059012yes—
629C4⋊C4—834no—
630C4⋊C4—834no—
631C4⋊C4—1662no—
632C4⋊C4—1662no—
633C4⋊C4—1662no—
634C4⋊C4—1662no—
635C4⋊C4—1662no—
636C4⋊C4—1662no—
637C4⋊C4—1662no—
638C4⋊C4—1662no—
639C22⋊C4—834no—
640C22⋊C4—834no—
641C22⋊C4—1662no—
642C22⋊C4—1662no—
643C22⋊C4—1662no—
644C22⋊C4—1662no—
645C22⋊C4—1662no—
646C22⋊C4—1662no—
647C22⋊C4—1662no—
648C22⋊C4—1662no—
649C42—21no—
650C42—21no—
651C42—22no—
652C42—22no—
653C42—832no—
654C42—832no—
655C42—1661no—
656C42—1661no—
657C42D4×D8312yes—
658C42D4×D8312yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—832no—
666C23—1661no—
667C23—1661no—
668C23—1661no—
669C23—1661no—
670C23—1661no—
671C23—1661no—
672C23—1661no—
673C23—1661no—
674C23—1661no—
675C23—1661no—
676C23—1661no—
677C23—1661no—
678C23—1661no—
679C23#1458179812yes—
680C23C22×C4×D8311yescharacteristic
681Q8—3324no—
682D4—3324no—
683D4—3324no—
684D4—3324no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
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—44no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—3321no—
704C2×C4—3321no—
705C2×C4—3321no—
706C2×C4—3321no—
707C2×C4—832no—
708C2×C4—832no—
709C2×C4—832no—
710C2×C4—1661no—
711C2×C4—1661no—
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—1662no—
726C2×C4—1662no—
727C2×C4—1662no—
728C2×C4—1662no—
729C2×C4C22⋊C4×D8312yes—
730C2×C4C22⋊C4×D8312yes—
731C2×C4#1458179812yes—
732C2×C4C2×D4×D8311yescharacteristic
733C2×C4C2×D4×D8311yescharacteristic
734C2×C4#41×D8311yescharacteristic
735C2×C4#41×D8311yescharacteristic
736C2×C4C2×#1305059011yescharacteristic
737C2×C4C2×#1305059011yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C8—3321no—
743C8—3321no—
744C8—1662no—
745C8—1662no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—3321no—
754C22—3321no—
755C22—3321no—
756C22—3321no—
757C22—3321no—
758C22—3321no—
759C22—3321no—
760C22—3321no—
761C22—3321no—
762C22—3321no—
763C22—3321no—
764C22—1662no—
765C22—1662no—
766C22—1662no—
767C22C2×C22⋊C4×D8311yescharacteristic
768C22#1912816911yescharacteristic
769C22C4×#1305059011yescharacteristic
770C22C2×#1458179811yescharacteristic
771C22C2×#1458179811yescharacteristic
772C22#1912846711yescharacteristic
773C22#1912846711yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—41no—
779C4—3321no—
780C4—3321no—
781C4—3321no—
782C4—1662no—
783C4—1662no—
784C4—1662no—
785C4#1912821011yescharacteristic
786C4#1912821011yescharacteristic
787C4#1912824811yescharacteristic
788C4#1912824811yescharacteristic
789C2—42no—
790C2—3322no—
791C2—6641no—
792C2#2490994911yescharacteristic
793C2#2491590911yescharacteristic
794C2#2491590911yescharacteristic
795C2#2491643811yescharacteristic
796C2#2491644811yescharacteristic
797C2#2491645211yescharacteristic
798C2#2491646111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC4×C22⋊C8×C83C2
prime radicalC2×#14581766C4
cosocleC22×C4×C83C24
hypercenterC4×C22⋊C8D83
hypocenterC83#21381
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#19127760C2semidirect
3. C2×#19127655C2semidirect
4. #24908401C2semidirect
5. #24908397C2semidirect
6. #24908259C2semidirect
7. #24908255C2semidirect
8. #24907759C2semidirect
9. #24907757C2semidirect
10. #24907754C2semidirect
11. #24907752C2semidirect
12. #24907230C2semidirect
13. #24907230C2semidirect
14. #24907225C2semidirect
15. C4×C22⋊C8×C83C2semidirect
414. C4×C22⋊C8D83semidirect
415. C83#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#191282352
C2×#191277602
C2×#191276552
#249084012
#249083972
#249082592
#249082552
#249077592
#249077572
#249077542
#249077522
#249072302
#249072252
C4×C22⋊C8×C832
#2138183