Finite Group Databasebeta

← #35420496

Subgroups — #35420496

Order 21248.

1162 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×#19127773C211yesmaximal, characteristic, complemented
3#24908402C211yesmaximal, characteristic, complemented
4#24908399C211yesmaximal, characteristic, complemented
5#24907760C211yesmaximal, characteristic, complemented
6#24907760C211yesmaximal, characteristic, complemented
7#24907758C211yesmaximal, characteristic, complemented
8#24907753C211yesmaximal, characteristic, complemented
9#24907532C211yesmaximal, characteristic, complemented
10#24907529C211yesmaximal, characteristic, complemented
11#24907444C211yesmaximal, characteristic, complemented
12#24907230C211yesmaximal, characteristic, complemented
13#24907161C211yesmaximal, characteristic, complemented
14#24907156C211yesmaximal, characteristic, complemented
15C2×#436×C83C211yesmaximal, characteristic, complemented
16C22×#13050574C2211yescharacteristic
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
34#19127773—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×#14581703C2211yescharacteristic
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
56C22×M16×C83C2211yescharacteristic
57C2×C4×D4×C83C2211yescharacteristic
58#436×C83—24no—
59C2×C4⋊C8×C83C2211yescharacteristic
60C2×C22⋊C8×C83C2211yescharacteristic
61C2×C22⋊C8×C83C2211yescharacteristic
62C2×C4×C8×C83C2211yescharacteristic
63C22×Dic166C2×C411yescharacteristic
64C22×C22⋊D83C2×C411yescharacteristic
65C22×C22⋊D83C2×C411yescharacteristic
66C23×Dic83C2×C411yescharacteristic
67C23×Dic83C2×C411yescharacteristic
68C22×C4×D83C2311yescharacteristic
69C2×#13050574—22no—
70C2×#13050574—22no—
71C2×#13050574—41no—
72C22×C83⋊C8—22no—
73C22×C83⋊C8—22no—
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—
128#14581703—22no—
129C22×D4×C83C2×C411yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C2×M16×C83—22no—
133C2×M16×C83—22no—
134C2×M16×C83—22no—
135C2×M16×C83—22no—
136C2×M16×C83—41no—
137C2×M16×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—
151C4×C8×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—41no—
160C2×C22⋊D83—41no—
161C2×C22⋊D83—41no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—41no—
166C22×Dic83—41no—
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—
181#13050574—44no—
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—21no—
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—41no—
223C2×D4×C83—41no—
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—
243M16×C83—44no—
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—21no—
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×C83—21no—
272C23×C83—21no—
273C23×C83C2×C22⋊C412yes—
274C23×C83C2×C22⋊C412yes—
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—44no—
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—41no—
355C22×C83—41no—
356C22×C83—41no—
357C22×C83—41no—
358C22×C83—41no—
359C22×C83—41no—
360C22×C83—41no—
361C22×C83—41no—
362C22×C83C22×C22⋊C411yescharacteristic
363C22×C83C4×#4111yescharacteristic
364C22×C83#52011yescharacteristic
365C22×C83C2×#13111yescharacteristic
366C22×C83#56811yescharacteristic
367C22×C83#56811yescharacteristic
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#22472—831nomaximal, Sylow
392C2×C83—42no—
393C2×C83—42no—
394C2×C83#233911yescharacteristic
395C2×C83#287911yescharacteristic
396C2×C83#288011yescharacteristic
397C2×C83#296711yescharacteristic
398C2×C83#296911yescharacteristic
399C2×C83#299311yescharacteristic
400C2×C83#299511yescharacteristic
401D83—81no—
402C2×#529—831no—
403C2×#436D8311yescharacteristic, complemented
404C2×#435—831no—
405#1985—831no—
406#1984—831no—
407#1870—831no—
408#1870—831no—
409#1870—831no—
410#1869—831no—
411#1818—831no—
412#1817—831no—
413#1798—831no—
414#1750—831no—
415#1729—831no—
416#1728—831no—
417C83#2247211yescharacteristic, complemented, Sylow
418C22×M16—831no—
419C22×M16C2×D8311yescharacteristic
420C22×M16C2×D8311yescharacteristic
421C23×C8—831no—
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#436—24no—
440#435—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×#97—831no—
452C2×C4×C8C2×D8311yescharacteristic
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—22no—
477C2×M16—22no—
478C2×M16—41no—
479C2×M16—41no—
480C2×M16—3321no—
481C2×M16—1662no—
482C2×M16—1662no—
483C22×C8—3321no—
484C22×C8—831no—
485C22×C8—831no—
486C22×C8—831no—
487C22×C8—831no—
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—1662no—
553C4×C8—22no—
554C24—831no—
555C24C2×C4×D8311yescharacteristic
556C24C2×C4×D8311yescharacteristic
557C2×Q8—3321no—
558C2×Q8—1662no—
559C2×Q8—1662no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—3321no—
563C2×D4—3321no—
564C2×D4—3321no—
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—3321no—
579C22×C4—3321no—
580C22×C4—831no—
581C22×C4—831no—
582C22×C4—831no—
583C22×C4—831no—
584C22×C4—831no—
585C22×C4—831no—
586C22×C4—831no—
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—
606M16—44no—
607M16—3324no—
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—21no—
618C2×C8—21no—
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—21no—
674C23—21no—
675C23—1661no—
676C23—1661no—
677C23—1661no—
678C23—1661no—
679C23—1661no—
680C23—1661no—
681C23—1661no—
682C23C2×(C2×D83)⋊C412yes—
683C23C2×(C2×D83)⋊C412yes—
684C23C22×C4×D8311yescharacteristic
685Q8—3324no—
686D4—44no—
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—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—3321no—
765C22—3321no—
766C22—3321no—
767C22—3321no—
768C22—3321no—
769C22—3321no—
770C22—3321no—
771C22C22×(C2×D83)⋊C411yescharacteristic
772C22C4×#1305058911yescharacteristic
773C22#1912818011yescharacteristic
774C22#131×D8311yescharacteristic
775C22#1912846611yescharacteristic
776C22#1912846711yescharacteristic
777C22#1912846711yescharacteristic
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—42no—
794C2—42no—
795C2—6641no—
796C2#2491028811yescharacteristic
797C2#2491590711yescharacteristic
798C2#2491591011yescharacteristic
799C2#2491644911yescharacteristic
800C2#2491646211yescharacteristic
801C2#2491660911yescharacteristic
802C2#2491662711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC2×#436×C83C2
prime radicalC2×#14581764C4
cosocleC22×C4×C83C24
hypercenterC2×#436D83
hypocenterC83#22472
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. C2×#19127773C2semidirect
3. #24908402C2semidirect
4. #24908399C2semidirect
5. #24907760C2semidirect
6. #24907760C2semidirect
7. #24907758C2semidirect
8. #24907753C2semidirect
9. #24907532C2semidirect
10. #24907529C2semidirect
11. #24907444C2semidirect
12. #24907230C2semidirect
13. #24907161C2semidirect
14. #24907156C2semidirect
15. C2×#436×C83C2semidirect
403. C2×#436D83semidirect
417. C83#22472semidirect

Maximal subgroups

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

subgroupindex
C2×#191282312
C2×#191277732
#249084022
#249083992
#249077602
#249077582
#249077532
#249075322
#249075292
#249074442
#249072302
#249071612
#249071562
C2×#436×C832
#2247283