Finite Group Databasebeta

← #35409412

Subgroups — #35409412

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×#19128231C211yesmaximal, characteristic
2C2×#19127759C211yesmaximal, characteristic, complemented
3C2×#19127656C211yesmaximal, characteristic, complemented
4#24908401C211yesmaximal, characteristic, complemented
5#24908397C211yesmaximal, characteristic, complemented
6#24908259C211yesmaximal, characteristic, complemented
7#24908255C211yesmaximal, characteristic, complemented
8#24907761C211yesmaximal, characteristic, complemented
9#24907758C211yesmaximal, characteristic, complemented
10#24907755C211yesmaximal, characteristic, complemented
11#24907228C211yesmaximal, characteristic, complemented
12#24907228C211yesmaximal, characteristic, complemented
13#24907227C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic83C211yesmaximal, characteristic, complemented
15C83×#1869C211yesmaximal, characteristic, complemented
16C22×#13050574C2211yescharacteristic
17#19128231—24no—
18#19128231—24no—
19C2×#14581787C411yescharacteristic
20C2×#14581785C411yescharacteristic
21C2×#14581782C411yescharacteristic
22C2×#14581778C411yescharacteristic
23C2×#14581776C411yescharacteristic
24C2×#14581773C411yescharacteristic
25C2×#14581769C411yescharacteristic
26C2×#14581764C411yescharacteristic
27C2×C4×Dic166C2211yescharacteristic
28C2×C4×C22⋊D83C2211yescharacteristic
29C2×C4×C22⋊D83C2211yescharacteristic
30C2×#14581751C2211yescharacteristic
31C2×#14581749C2211yescharacteristic
32C22×C4×Dic83C2211yescharacteristic
33#19127759—24no—
34C2×Dic83⋊C8C2211yescharacteristic
35C2×Dic83⋊C8C2211yescharacteristic
36C2×C22⋊(C83⋊C8)C2211yescharacteristic
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
43#19127656—24no—
44C2×#14581702C2211yescharacteristic
45C2×#14581702C2211yescharacteristic
46C2×#14581702C2211yescharacteristic
47C2×C8×Dic83C2211yescharacteristic
48C2×C8×Dic83C2211yescharacteristic
49C2×C8×Dic83C2211yescharacteristic
50#19127456C2211yescharacteristic
51#19127456C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54#19127455C2211yescharacteristic
55#19127455C2211yescharacteristic
56C23×C8×C83C2211yescharacteristic
57C2×C4×D4×C83C2211yescharacteristic
58C2×C22⋊C8×C83C2211yescharacteristic
59C2×C22⋊C8×C83C2211yescharacteristic
60C2×C22⋊C8×C83C2211yescharacteristic
61#336×C83C2211yescharacteristic
62#336×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—22no—
72C22×C83⋊C8C2311yescharacteristic
73C22×C83⋊C8C2311yescharacteristic
74C22×C83⋊C8C2311yescharacteristic
75C22×C83⋊C8C2311yescharacteristic
76#14581787—24no—
77#14581785—24no—
78#14581782—24no—
79#14581778—24no—
80#14581776—24no—
81#14581773—24no—
82#14581769—24no—
83#14581764—24no—
84C4×Dic166—22no—
85C4×Dic166—22no—
86C4×C22⋊D83—22no—
87C4×C22⋊D83—22no—
88C4×C22⋊D83—22no—
89C4×C22⋊D83—22no—
90#14581751D414yes—
91#14581751D414yes—
92#14581749—22no—
93#14581749—22no—
94C2×C4⋊Dic83C2×C411yescharacteristic
95C2×C4⋊Dic83C2×C411yescharacteristic
96C2×C4⋊Dic83C2×C411yescharacteristic
97C2×Dic83⋊C4C2×C411yescharacteristic
98C2×Dic83⋊C4C2×C411yescharacteristic
99C2×Dic83⋊C4C2×C411yescharacteristic
100C2×Dic83⋊C4C2×C411yescharacteristic
101C2×Dic83⋊C4C2×C411yescharacteristic
102C2×Dic83⋊C4C2×C411yescharacteristic
103C2×C22⋊Dic83C2×C411yescharacteristic
104C2×C22⋊Dic83C2×C411yescharacteristic
105C2×C22⋊Dic83C2×C411yescharacteristic
106C2×C22⋊Dic83C2×C411yescharacteristic
107C2×(C2×D83)⋊C4C2×C411yescharacteristic
108C2×(C2×D83)⋊C4C2×C411yescharacteristic
109C2×(C2×D83)⋊C4C2×C411yescharacteristic
110C2×(C2×D83)⋊C4C2×C411yescharacteristic
111C2×C4×Dic83—22no—
112C2×C4×Dic83—22no—
113C2×C4×Dic83C2×C411yescharacteristic
114C2×C4×Dic83C2×C411yescharacteristic
115C2×C4×Dic83C2311yescharacteristic
116C2×C4×Dic83C2311yescharacteristic
117C2×C4×Dic83C2311yescharacteristic
118Dic83⋊C8—22no—
119Dic83⋊C8—22no—
120C22⋊(C83⋊C8)—22no—
121C22⋊(C83⋊C8)—22no—
122C22⋊(C83⋊C8)—22no—
123(C2×D83)⋊C8—22no—
124(C2×D83)⋊C8—22no—
125(C2×D83)⋊C8—22no—
126(C2×D83)⋊C8—22no—
127#14581702—22no—
128#14581702—22no—
129#14581702—22no—
130C8×Dic83—22no—
131C8×Dic83—22no—
132C8×Dic83—22no—
133C22×D4×C83C2×C411yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C22×C8×C83—22no—
137C22×C8×C83—22no—
138C22×C8×C83—22no—
139C22×C8×C83C2311yescharacteristic
140C22×C8×C83C2311yescharacteristic
141C22×C8×C83C2311yescharacteristic
142C22×C8×C83C2311yescharacteristic
143C4×D4×C83—22no—
144C4×D4×C83—22no—
145C2×C4⋊C4×C83C2×C411yescharacteristic
146C2×C22⋊C4×C83C2×C411yescharacteristic
147C2×C22⋊C4×C83C2×C411yescharacteristic
148C2×C42×C83C2311yescharacteristic
149C22⋊C8×C83—22no—
150C22⋊C8×C83—22no—
151C22⋊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—22no—
160C2×C22⋊D83—41no—
161C2×C22⋊D83—41no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—22no—
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—28no—
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#4112yes—
193C2×C83⋊C8#4112yes—
194C4⋊Dic83—22no—
195C4⋊Dic83C22⋊C414yes—
196C4⋊Dic83C22⋊C414yes—
197Dic83⋊C4—22no—
198Dic83⋊C4—22no—
199Dic83⋊C4—22no—
200Dic83⋊C4—22no—
201Dic83⋊C4—22no—
202Dic83⋊C4—22no—
203C22⋊Dic83—22no—
204C22⋊Dic83—22no—
205C22⋊Dic83C22⋊C414yes—
206C22⋊Dic83C22⋊C414yes—
207(C2×D83)⋊C4—22no—
208(C2×D83)⋊C4—22no—
209(C2×D83)⋊C4—22no—
210(C2×D83)⋊C4—22no—
211C4×Dic83—21no—
212C4×Dic83—21no—
213C4×Dic83—22no—
214C4×Dic83—22no—
215C4×Dic83C2×D412yes—
216C4×Dic83C2×D412yes—
217C4×Dic83C2×D412yes—
218C4×Dic83C2×D412yes—
219C24×C83C22×C411yescharacteristic
220C24×C83C22×C411yescharacteristic
221C2×D4×C83—22no—
222C2×D4×C83—22no—
223C2×D4×C83—41no—
224C22×C4×C83—21no—
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×C83—21no—
234C22×C4×C83C22×C411yescharacteristic
235C22×C4×C83C22×C411yescharacteristic
236C22×C4×C83C22×C411yescharacteristic
237C22×C4×C83C22×C411yescharacteristic
238C22×C4×C83C2×D412yes—
239C22×C4×C83C2×D412yes—
240C22×C4×C83C2411yescharacteristic
241C2×C8×C83—28no—
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—21no—
252C2×C8×C83#4112yes—
253C2×C8×C83#4112yes—
254C4⋊C4×C83—22no—
255C22⋊C4×C83—22no—
256C22⋊C4×C83—22no—
257C42×C83—21no—
258C42×C83—21no—
259C23×C83—21no—
260C23×C83—21no—
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×C83#13112yes—
273C23×C83C23×C411yescharacteristic
274C22×D83—21no—
275C22×D83—21no—
276C22×D83—21no—
277C22×D83—21no—
278C22×D83—21no—
279C22×D83—21no—
280C22×D83—21no—
281D4×C83—44no—
282C2×C4×C83—21no—
283C2×C4×C83—21no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—21no—
289C2×C4×C83—21no—
290C2×C4×C83—21no—
291C2×C4×C83—21no—
292C2×C4×C83—21no—
293C2×C4×C83—21no—
294C2×C4×C83—21no—
295C2×C4×C83—21no—
296C2×C4×C83—21no—
297C2×C4×C83—41no—
298C2×C4×C83—41no—
299C2×C4×C83—41no—
300C2×C4×C83—41no—
301C2×C4×C83C2×C22⋊C412yes—
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×Dic83—21no—
326C2×Dic83—44no—
327C2×Dic83—44no—
328C2×Dic83C2×C22⋊C412yes—
329C2×Dic83C2×C22⋊C412yes—
330C2×Dic83C2×C22⋊C412yes—
331C2×Dic83C2×C22⋊C412yes—
332C2×Dic83#13112yes—
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—22no—
350C22×C83—22no—
351C22×C83—22no—
352C22×C83—41no—
353C22×C83—41no—
354C22×C83—41no—
355C22×C83—41no—
356C22×C83—41no—
357C22×C83—41no—
358C22×C83—41no—
359C22×C83—41no—
360C22×C83C22×C22⋊C411yescharacteristic
361C22×C83C4×#4111yescharacteristic
362C22×C83C4×#4111yescharacteristic
363C22×C83C2×#13111yescharacteristic
364C22×C83C2×#13111yescharacteristic
365C22×C83#56811yescharacteristic
366C22×C83#56811yescharacteristic
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—41no—
376C4×C83—41no—
377C4×C83—41no—
378C4×C83#52511yescharacteristic
379C4×C83#52511yescharacteristic
380C4×C83#53211yescharacteristic
381C4×C83#53211yescharacteristic
382Dic83—22no—
383Dic83—22no—
384Dic83—22no—
385Dic83—22no—
386Dic83—22no—
387Dic83—41no—
388Dic83—41no—
389#21381—831nomaximal, Sylow
390C2×C83—42no—
391C2×C83—42no—
392C2×C83#229711yescharacteristic
393C2×C83#288011yescharacteristic
394C2×C83#288011yescharacteristic
395C2×C83#296611yescharacteristic
396C2×C83#296711yescharacteristic
397C2×C83#296811yescharacteristic
398C2×C83#296911yescharacteristic
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#1869D8311yescharacteristic, complemented
411#1750—831no—
412#1750—831no—
413#1749—831no—
414C4×C22⋊C8—831no—
415C83#2138111yescharacteristic, complemented, Sylow
416C22×M16—831no—
417C23×C8C2×D8311yescharacteristic
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×D4C2×D8311yescharacteristic
432C2×#117—831no—
433C2×#117—831no—
434C22×C42—831no—
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⋊C8C2×D8311yescharacteristic
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×C8—831no—
454C2×C4×C8—831no—
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×D4C4×D8311yescharacteristic
467C23×C4—831no—
468C23×C4—831no—
469C23×C4—831no—
470C23×C4C22×D8311yescharacteristic
471C23×C4C22×D8311yescharacteristic
472C2×M16—1662no—
473C2×M16—1662no—
474C2×M16—1662no—
475C22×C8—22no—
476C22×C8—22no—
477C22×C8—22no—
478C22×C8—831no—
479C22×C8—831no—
480C22×C8—831no—
481C22×C8—831no—
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—22no—
497C4×D4—22no—
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⋊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—831no—
531C2×C42—1662no—
532C2×C42—1662no—
533C2×C42C22×D8311yescharacteristic
534C4⋊C8—1662no—
535C4⋊C8—1662no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
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—1662no—
550C4×C8—1662no—
551C4×C8—1662no—
552C24—831no—
553C24C2×C4×D8311yescharacteristic
554C24C2×C4×D8311yescharacteristic
555C2×Q8—3321no—
556C2×Q8—1662no—
557C2×Q8—1662no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—41no—
561C2×D4—3321no—
562C2×D4—3321no—
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—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—3321no—
578C22×C4—3321no—
579C22×C4—831no—
580C22×C4—831no—
581C22×C4—831no—
582C22×C4—831no—
583C22×C4—831no—
584C22×C4—831no—
585C22×C4—831no—
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×C4D4×D8312yes—
601C22×C4D4×D8312yes—
602C22×C4C23×D8311yescharacteristic
603M16—1668no—
604C2×C8—28no—
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—832no—
616C2×C8—832no—
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#1305058912yes—
628C2×C8#1305058912yes—
629C4⋊C4—22no—
630C4⋊C4—834no—
631C4⋊C4—834no—
632C4⋊C4—1662no—
633C4⋊C4—1662no—
634C4⋊C4—1662no—
635C4⋊C4—1662no—
636C4⋊C4—1662no—
637C4⋊C4—1662no—
638C4⋊C4—1662no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—834no—
642C22⋊C4—834no—
643C22⋊C4—1662no—
644C22⋊C4—1662no—
645C22⋊C4—1662no—
646C22⋊C4—1662no—
647C22⋊C4—1662no—
648C22⋊C4—1662no—
649C42—21no—
650C42—21no—
651C42—832no—
652C42—832no—
653C42—832no—
654C42—832no—
655C42—1662no—
656C42—1662no—
657C42—1661no—
658C42—1661no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—1661no—
672C23—1661no—
673C23—1661no—
674C23—1661no—
675C23—1661no—
676C23—1661no—
677C23—1661no—
678C23C22⋊C4×D8312yes—
679C23#1458179812yes—
680C23C22×C4×D8311yescharacteristic
681Q8—3324no—
682D4—44no—
683D4—3324no—
684D4—3324no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—3324no—
705C2×C4—3321no—
706C2×C4—3321no—
707C2×C4—3321no—
708C2×C4—3321no—
709C2×C4—3324no—
710C2×C4—832no—
711C2×C4—832no—
712C2×C4—832no—
713C2×C4—832no—
714C2×C4—832no—
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×C4C22⋊C4×D8312yes—
732C2×C4C2×D4×D8311yescharacteristic
733C2×C4C2×D4×D8311yescharacteristic
734C2×C4#41×D8311yescharacteristic
735C2×C4#41×D8311yescharacteristic
736C2×C4C2×#1305058911yescharacteristic
737C2×C4C2×#1305058911yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C8—3321no—
743C8—3321no—
744C8—1662no—
745C8—1662no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—3321no—
761C22—3321no—
762C22—3321no—
763C22—3321no—
764C22—3321no—
765C22—3321no—
766C22—3321no—
767C22C2×C22⋊C4×D8311yescharacteristic
768C22C4×#1305058911yescharacteristic
769C22C4×#1305058911yescharacteristic
770C22#131×D8311yescharacteristic
771C22C2×#1458179811yescharacteristic
772C22#1912846611yescharacteristic
773C22#1912846711yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—3321no—
779C4—3321no—
780C4—1662no—
781C4—1662no—
782C4—1662no—
783C4—1662no—
784C4—1662no—
785C4#1912820711yescharacteristic
786C4#1912820911yescharacteristic
787C4#1912824611yescharacteristic
788C4#1912824611yescharacteristic
789C2—42no—
790C2—42no—
791C2—6641no—
792C2#2490994811yescharacteristic
793C2#2491590911yescharacteristic
794C2#2491591111yescharacteristic
795C2#2491643111yescharacteristic
796C2#2491644211yescharacteristic
797C2#2491645111yescharacteristic
798C2#2491646011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1869C2
prime radicalC2×#14581764C4
cosocleC22×C4×C83C24
hypercenter#1869D83
hypocenterC83#21381
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C2×#19127759C2semidirect
3. C2×#19127656C2semidirect
4. #24908401C2semidirect
5. #24908397C2semidirect
6. #24908259C2semidirect
7. #24908255C2semidirect
8. #24907761C2semidirect
9. #24907758C2semidirect
10. #24907755C2semidirect
11. #24907228C2semidirect
12. #24907228C2semidirect
13. #24907227C2semidirect
14. C22⋊C8×Dic83C2semidirect
15. C83×#1869C2semidirect
410. #1869D83semidirect
415. C83#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#191282312
C2×#191277592
C2×#191276562
#249084012
#249083972
#249082592
#249082552
#249077612
#249077582
#249077552
#249072282
#249072272
C22⋊C8×Dic832
C83×#18692
#2138183