Finite Group Databasebeta

← #35409415

Subgroups — #35409415

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×#19128229C211yesmaximal, characteristic
2C2×#19127657C211yesmaximal, characteristic, complemented
3#24908402C211yesmaximal, characteristic, complemented
4#24908398C211yesmaximal, characteristic, complemented
5#24908260C211yesmaximal, characteristic, complemented
6#24908256C211yesmaximal, characteristic, complemented
7#24907758C211yesmaximal, characteristic, complemented
8#24907758C211yesmaximal, characteristic, complemented
9#24907753C211yesmaximal, characteristic, complemented
10#24907753C211yesmaximal, characteristic, complemented
11#24907232C211yesmaximal, characteristic, complemented
12#24907230C211yesmaximal, characteristic, complemented
13#24907226C211yesmaximal, characteristic, complemented
14C4×(C2×D83)⋊C8C211yesmaximal, characteristic, complemented
15C2×#433×C83C211yesmaximal, characteristic, complemented
16C22×#13050574C2211yescharacteristic
17C23×C83⋊C8C2211yescharacteristic
18#19128229—24no—
19#19128229—24no—
20C2×#14581787C411yescharacteristic
21C2×#14581785C411yescharacteristic
22C2×#14581782C411yescharacteristic
23C2×#14581778C411yescharacteristic
24C2×#14581777C411yescharacteristic
25C2×#14581774C411yescharacteristic
26C2×#14581770C411yescharacteristic
27C2×#14581765C411yescharacteristic
28C2×C4×Dic166C2211yescharacteristic
29C2×C4×D332C2211yescharacteristic
30C2×C4×C22⋊D83C2211yescharacteristic
31C2×C4×C22⋊D83C2211yescharacteristic
32C2×#14581749C2211yescharacteristic
33C2×C42×D83C2211yescharacteristic
34C2×(C2×D83)⋊C8C2211yescharacteristic
35C2×(C2×D83)⋊C8C2211yescharacteristic
36C2×(C2×D83)⋊C8C2211yescharacteristic
37C2×(C2×D83)⋊C8C2211yescharacteristic
38C2×(C2×D83)⋊C8C2211yescharacteristic
39C2×(C2×D83)⋊C8C2211yescharacteristic
40C2×(C2×D83)⋊C8C2211yescharacteristic
41C2×(C2×D83)⋊C8C2211yescharacteristic
42#19127657—24no—
43C2×#14581703C2211yescharacteristic
44C2×#14581703C2211yescharacteristic
45C2×C4×C83⋊C8C2211yescharacteristic
46C2×C4×C83⋊C8C2211yescharacteristic
47#19127455C2211yescharacteristic
48#19127455C2211yescharacteristic
49#19127455C2211yescharacteristic
50#19127455C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54#19127455C2211yescharacteristic
55C2×#117×C83C2211yescharacteristic
56#433×C83—24no—
57C2×C4⋊C8×C83C2211yescharacteristic
58C2×C4⋊C8×C83C2211yescharacteristic
59C2×C22⋊C8×C83C2211yescharacteristic
60C2×C22⋊C8×C83C2211yescharacteristic
61C2×#97×C83C2211yescharacteristic
62C2×C4×C8×C83C2211yescharacteristic
63C22×Dic166C2×C411yescharacteristic
64C22×D332C2×C411yescharacteristic
65C22×C22⋊D83C2×C411yescharacteristic
66C22×C22⋊D83C2×C411yescharacteristic
67C22×C4×D83C2×C411yescharacteristic
68C22×C4×D83C2×C411yescharacteristic
69C22×C4×D83C2311yescharacteristic
70C22×C4×D83C2311yescharacteristic
71C2×#13050574—22no—
72C2×#13050574—22no—
73C2×#13050574—22no—
74C22×C83⋊C8—22no—
75C22×C83⋊C8—22no—
76C22×C83⋊C8—22no—
77C22×C83⋊C8C2311yescharacteristic
78C22×C83⋊C8C2311yescharacteristic
79C22×C83⋊C8C2311yescharacteristic
80C22×C83⋊C8C2311yescharacteristic
81#14581787—24no—
82#14581785—24no—
83#14581782—24no—
84#14581778—24no—
85#14581777—24no—
86#14581774—24no—
87#14581770—24no—
88#14581765—24no—
89C4×Dic166—22no—
90C4×Dic166—22no—
91C4×D332—22no—
92C4×D332—22no—
93C4×C22⋊D83—22no—
94C4×C22⋊D83—22no—
95C4×C22⋊D83—22no—
96C4×C22⋊D83—22no—
97#14581749—22no—
98#14581749—22no—
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×C22⋊Dic83C2×C411yescharacteristic
108C2×C22⋊Dic83C2×C411yescharacteristic
109C2×(C2×D83)⋊C4C2×C411yescharacteristic
110C2×(C2×D83)⋊C4C2×C411yescharacteristic
111C2×(C2×D83)⋊C4C2×C411yescharacteristic
112C2×(C2×D83)⋊C4C2×C411yescharacteristic
113C2×(C2×D83)⋊C4C2×C411yescharacteristic
114C2×(C2×D83)⋊C4C2×C411yescharacteristic
115C2×C4×Dic83C2×C411yescharacteristic
116C2×C4×Dic83C2×C411yescharacteristic
117C2×C4×Dic83C2311yescharacteristic
118C2×C4×Dic83C2311yescharacteristic
119C42×D83—22no—
120C42×D83—22no—
121(C2×D83)⋊C8—22no—
122(C2×D83)⋊C8—22no—
123(C2×D83)⋊C8—22no—
124(C2×D83)⋊C8—22no—
125(C2×D83)⋊C8—22no—
126(C2×D83)⋊C8—22no—
127(C2×D83)⋊C8—22no—
128(C2×D83)⋊C8—22no—
129#14581703—22no—
130#14581703—22no—
131C4×C83⋊C8—22no—
132C4×C83⋊C8—22no—
133C23×C4×C83C2311yescharacteristic
134C22×C8×C83C2311yescharacteristic
135C22×C8×C83C2311yescharacteristic
136C22×C8×C83C2311yescharacteristic
137C22×C8×C83C2311yescharacteristic
138#117×C83D414yes—
139#117×C83D414yes—
140C2×C4⋊C4×C83C2×C411yescharacteristic
141C2×C4⋊C4×C83C2×C411yescharacteristic
142C2×C22⋊C4×C83C2×C411yescharacteristic
143C2×C22⋊C4×C83C2×C411yescharacteristic
144C2×C42×C83C2311yescharacteristic
145C2×C42×C83C2311yescharacteristic
146C4⋊C8×C83—22no—
147C4⋊C8×C83—22no—
148C22⋊C8×C83—22no—
149C22⋊C8×C83—22no—
150#97×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—22no—
173C2×C4×D83—22no—
174C2×C4×D83—22no—
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×D83—21no—
183C2×C4×D83—21no—
184C2×C4×D83—21no—
185C2×C4×D83—21no—
186C2×C4×D83—21no—
187C2×C4×D83—22no—
188C2×C4×D83—41no—
189C2×C4×D83—41no—
190#13050574—28no—
191C2×C83⋊C8—28no—
192C2×C83⋊C8—21no—
193C2×C83⋊C8—21no—
194C2×C83⋊C8—21no—
195C2×C83⋊C8—21no—
196C2×C83⋊C8—21no—
197C2×C83⋊C8—21no—
198C2×C83⋊C8—21no—
199C2×C83⋊C8—21no—
200C2×C83⋊C8#4112yes—
201C2×C83⋊C8#4112yes—
202C2×C83⋊C8#4112yes—
203C2×C83⋊C8#4112yes—
204C4⋊Dic83—22no—
205C4⋊Dic83—22no—
206Dic83⋊C4—22no—
207Dic83⋊C4—22no—
208Dic83⋊C4—22no—
209Dic83⋊C4—22no—
210Dic83⋊C4—22no—
211Dic83⋊C4—22no—
212C22⋊Dic83—22no—
213C22⋊Dic83—22no—
214(C2×D83)⋊C4—22no—
215(C2×D83)⋊C4—22no—
216(C2×D83)⋊C4—22no—
217(C2×D83)⋊C4—22no—
218(C2×D83)⋊C4—22no—
219(C2×D83)⋊C4—22no—
220C4×Dic83—22no—
221C4×Dic83—22no—
222C4×Dic83—21no—
223C4×Dic83—21no—
224C4×Dic83—21no—
225C4×Dic83—21no—
226C24×C83C22×C411yescharacteristic
227C22×C4×C83—21no—
228C22×C4×C83—21no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83C22×C411yescharacteristic
232C22×C4×C83C22×C411yescharacteristic
233C22×C4×C83C22×C411yescharacteristic
234C22×C4×C83C22×C411yescharacteristic
235C22×C4×C83C22×C411yescharacteristic
236C22×C4×C83C2×D412yes—
237C22×C4×C83C2×D412yes—
238C22×C4×C83C2411yescharacteristic
239C2×C8×C83—21no—
240C2×C8×C83—21no—
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—
251C4⋊C4×C83C22⋊C414yes—
252C4⋊C4×C83C22⋊C414yes—
253C22⋊C4×C83C22⋊C414yes—
254C22⋊C4×C83C22⋊C414yes—
255C42×C83C2×D412yes—
256C42×C83C2×D412yes—
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×C83C2×C22⋊C412yes—
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×D83#13112yes—
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—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83C2×C22⋊C412yes—
296C2×C4×C83C2×C22⋊C412yes—
297C2×C4×C83C2×C22⋊C412yes—
298C2×C4×C83C2×C22⋊C412yes—
299C2×C4×C83C2×C22⋊C412yes—
300C2×C4×C83C22×D411yescharacteristic
301C2×C4×C83C22×D411yescharacteristic
302C2×C4×C83C2×#4111yescharacteristic
303C2×C4×C83C2×#4111yescharacteristic
304C2×C4×C83C2×#4111yescharacteristic
305C2×C4×C83C2×#4111yescharacteristic
306C22⋊D83—44no—
307C22⋊D83—44no—
308C2×Dic83—21no—
309C2×Dic83—21no—
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×Dic83#13112yes—
326D332—44no—
327C4×D83—44no—
328C4×D83—44no—
329C4×D83—41no—
330C4×D83—41no—
331C4×D83—41no—
332C4×D83—41no—
333C4×D83—41no—
334C4×D83—41no—
335C4×D83—41no—
336C4×D83—41no—
337Dic166—44no—
338C8×C83—41no—
339C8×C83—41no—
340C8×C83—41no—
341C8×C83—41no—
342C83⋊C8—22no—
343C83⋊C8—22no—
344C83⋊C8—22no—
345C83⋊C8—22no—
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—22no—
378C4×C83—22no—
379C4×C83#52511yescharacteristic
380C4×C83#52511yescharacteristic
381C4×C83#53211yescharacteristic
382C4×C83#53211yescharacteristic
383Dic83—22no—
384Dic83—41no—
385Dic83—41no—
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×#433D8311yescharacteristic, complemented
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⋊C8—831no—
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×#117C2×D8311yescharacteristic
434C22×C42—831no—
435#433—24no—
436C2×C4⋊C8C2×D8311yescharacteristic
437C2×C4⋊C8C2×D8311yescharacteristic
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×#97C2×D8311yescharacteristic
452C2×C4×C8—831no—
453C2×C4×C8—831no—
454C2×C4×C8C2×D8311yescharacteristic
455#336—831no—
456#336—831no—
457#336—831no—
458#336—831no—
459#336—831no—
460#336—831no—
461#336—831no—
462#336—831no—
463C22×Q8—831no—
464C22×D4—831no—
465C22×D4—831no—
466C22×D4—831no—
467C23×C4—831no—
468C23×C4—831no—
469C23×C4—831no—
470C23×C4—831no—
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—1662no—
503#117—1662no—
504#117D33214yes—
505#117C22⋊D8314yes—
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⋊C4C4×D8311yescharacteristic
515C2×C4⋊C4C4×D8311yescharacteristic
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⋊C4C4×D8311yescharacteristic
525C2×C22⋊C4C4×D8311yescharacteristic
526C2×C42—831no—
527C2×C42—831no—
528C2×C42—831no—
529C2×C42—831no—
530C2×C42—1662no—
531C2×C42—1662no—
532C2×C42C22×D8311yescharacteristic
533C2×C42C22×D8311yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
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—22no—
547#97—1662no—
548#97—1662no—
549C4×C8—22no—
550C4×C8—1662no—
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—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—3321no—
572C22×C4—3321no—
573C22×C4—831no—
574C22×C4—831no—
575C22×C4—831no—
576C22×C4—831no—
577C22×C4—831no—
578C22×C4—831no—
579C22×C4—1662no—
580C22×C4—1662no—
581C22×C4—1661no—
582C22×C4—1661no—
583C22×C4—1661no—
584C22×C4—1661no—
585C22×C4—1661no—
586C22×C4—1661no—
587C22×C4—1661no—
588C22×C4—1661no—
589C22×C4—1661no—
590C22×C4—1661no—
591C22×C4—1661no—
592C22×C4—1661no—
593C22×C4—1662no—
594C22×C4—1662no—
595C22×C4C2×C4×D8311yescharacteristic
596C22×C4C2×C4×D8311yescharacteristic
597C22×C4C2×C4×D8311yescharacteristic
598C22×C4C2×C4×D8311yescharacteristic
599C22×C4C2×C4×D8311yescharacteristic
600C22×C4C2×C22⋊D8312yes—
601C22×C4C2×D33212yes—
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—21no—
615C2×C8—21no—
616C2×C8—832no—
617C2×C8—832no—
618C2×C8—832no—
619C2×C8—832no—
620C2×C8—1668no—
621C2×C8—1661no—
622C2×C8—1661no—
623C2×C8—1661no—
624C2×C8—1661no—
625C2×C8—1661no—
626C2×C8—1661no—
627C2×C8—1661no—
628C2×C8—1661no—
629C4⋊C4—1662no—
630C4⋊C4—1662no—
631C4⋊C4—1662no—
632C4⋊C4—1662no—
633C4⋊C4—1662no—
634C4⋊C4—1662no—
635C4⋊C4—1662no—
636C4⋊C4—1662no—
637C4⋊C4(C2×D83)⋊C414yes—
638C4⋊C4(C2×D83)⋊C414yes—
639C22⋊C4—1662no—
640C22⋊C4—1662no—
641C22⋊C4—1662no—
642C22⋊C4—1662no—
643C22⋊C4—1662no—
644C22⋊C4—1662no—
645C22⋊C4—1662no—
646C22⋊C4—1662no—
647C22⋊C4(C2×D83)⋊C414yes—
648C22⋊C4(C2×D83)⋊C414yes—
649C42—1661no—
650C42—1661no—
651C42—1661no—
652C42—1661no—
653C42—1662no—
654C42—1662no—
655C42C2×C22⋊D8312yes—
656C42C2×C22⋊D8312yes—
657C42C2×D33212yes—
658C42C2×D33212yes—
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—
679C23C2×(C2×D83)⋊C412yes—
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—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—3324no—
700C2×C4—3324no—
701C2×C4—3321no—
702C2×C4—3321no—
703C2×C4—3321no—
704C2×C4—3321no—
705C2×C4—3321no—
706C2×C4—3321no—
707C2×C4—3321no—
708C2×C4—3321no—
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—1661no—
726C2×C4—1661no—
727C2×C4C2×(C2×D83)⋊C412yes—
728C2×C4C2×(C2×D83)⋊C412yes—
729C2×C4C2×(C2×D83)⋊C412yes—
730C2×C4C2×(C2×D83)⋊C412yes—
731C2×C4C2×(C2×D83)⋊C412yes—
732C2×C4C22×C22⋊D8311yescharacteristic
733C2×C4C22×D33211yescharacteristic
734C2×C4#41×D8311yescharacteristic
735C2×C4#41×D8311yescharacteristic
736C2×C4#41×D8311yescharacteristic
737C2×C4#41×D8311yescharacteristic
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
742C8—1662no—
743C8—1662no—
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—
767C22C22×(C2×D83)⋊C411yescharacteristic
768C22#1912816911yescharacteristic
769C22#1912816911yescharacteristic
770C22#131×D8311yescharacteristic
771C22#131×D8311yescharacteristic
772C22#1912846611yescharacteristic
773C22#1912846611yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—3321no—
780C4—3321no—
781C4—3321no—
782C4—3321no—
783C4—3321no—
784C4—1662no—
785C4#1912821311yescharacteristic
786C4#1912821311yescharacteristic
787C4#1912824711yescharacteristic
788C4#1912824711yescharacteristic
789C2—42no—
790C2—3322no—
791C2—6641no—
792C2#2490995111yescharacteristic
793C2#2491591011yescharacteristic
794C2#2491591011yescharacteristic
795C2#2491643611yescharacteristic
796C2#2491644611yescharacteristic
797C2#2491645511yescharacteristic
798C2#2491646511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC2×#433×C83C2
prime radicalC2×#14581765C4
cosocleC22×C4×C83C24
hypercenterC2×#433D83
hypocenterC83#21381
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. C2×#19127657C2semidirect
3. #24908402C2semidirect
4. #24908398C2semidirect
5. #24908260C2semidirect
6. #24908256C2semidirect
7. #24907758C2semidirect
8. #24907758C2semidirect
9. #24907753C2semidirect
10. #24907753C2semidirect
11. #24907232C2semidirect
12. #24907230C2semidirect
13. #24907226C2semidirect
14. C4×(C2×D83)⋊C8C2semidirect
15. C2×#433×C83C2semidirect
401. C2×#433D83semidirect
415. C83#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#191282292
C2×#191276572
#249084022
#249083982
#249082602
#249082562
#249077582
#249077532
#249072322
#249072302
#249072262
C4×(C2×D83)⋊C82
C2×#433×C832
#2138183