Finite Group Databasebeta

← #35410567

Subgroups — #35410567

Order 21248.

1044 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127780C211yesmaximal, characteristic, complemented
2C2×#19127774C211yesmaximal, characteristic, complemented
3C2×#19127774C211yesmaximal, characteristic, complemented
4C2×#19127658C211yesmaximal, characteristic, complemented
5#24910703C211yesmaximal, characteristic
6#24908256C211yesmaximal, characteristic, complemented
7#24908182C211yesmaximal, characteristic, complemented
8#24908077C211yesmaximal, characteristic, complemented
9#24908077C211yesmaximal, characteristic, complemented
10#24907754C211yesmaximal, characteristic, complemented
11#24907754C211yesmaximal, characteristic, complemented
12#24907444C211yesmaximal, characteristic, complemented
13#24907248C211yesmaximal, characteristic, complemented
14C8×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
15C83×#1771C211yesmaximal, characteristic, complemented
16C22×#13050573C2211yescharacteristic
17C22×#13050573C2211yescharacteristic
18C22×C8×D83C2211yescharacteristic
19C22×C8×D83C2211yescharacteristic
20C2×C4×D332C2211yescharacteristic
21C2×C4×D332C2211yescharacteristic
22C2×C4×D332C2211yescharacteristic
23C2×#14581749C2211yescharacteristic
24#19127780—24no—
25#19127774—24no—
26#19127774—24no—
27C2×C4⋊(C83⋊C8)C2211yescharacteristic
28C2×C4⋊(C83⋊C8)C2211yescharacteristic
29C2×C4⋊(C83⋊C8)C2211yescharacteristic
30C2×(C2×D83)⋊C8C2211yescharacteristic
31C2×(C2×D83)⋊C8C2211yescharacteristic
32C2×(C2×D83)⋊C8C2211yescharacteristic
33C2×(C2×D83)⋊C8C2211yescharacteristic
34C2×(C2×D83)⋊C8C2211yescharacteristic
35C2×(C2×D83)⋊C8C2211yescharacteristic
36C2×(C2×D83)⋊C8C2211yescharacteristic
37C2×(C2×D83)⋊C8C2211yescharacteristic
38#19127658—24no—
39C2×#14581702C2211yescharacteristic
40C2×C4×C83⋊C8C2211yescharacteristic
41C2×C8×Dic83C2211yescharacteristic
42#19127633C411yescharacteristic
43#19127628C411yescharacteristic
44#19127623C411yescharacteristic
45#19127623C411yescharacteristic
46#19127619C411yescharacteristic
47#19127618C411yescharacteristic
48#19127618C411yescharacteristic
49#19127611C411yescharacteristic
50C4×(C2×D83)⋊C4C2211yescharacteristic
51C4×(C2×D83)⋊C4C2211yescharacteristic
52#19127456C2211yescharacteristic
53#19127456C2211yescharacteristic
54#19127455C2211yescharacteristic
55#19127455C2211yescharacteristic
56C2×C4⋊C8×C83C2211yescharacteristic
57C2×#97×C83C2211yescharacteristic
58C2×#97×C83C2211yescharacteristic
59C2×C4×C8×C83C2211yescharacteristic
60C4×C4⋊C4×C83C2211yescharacteristic
61#336×C83C2211yescharacteristic
62#336×C83C2211yescharacteristic
63C22×D332C2×C411yescharacteristic
64C22×D332C2×C411yescharacteristic
65C22×D332C2×C411yescharacteristic
66C22×C4×D83C2311yescharacteristic
67C22×C4×D83C2311yescharacteristic
68C22×C4×D83C2311yescharacteristic
69C2×#13050573—22no—
70C2×#13050573—22no—
71C2×#13050573—22no—
72C2×#13050573—22no—
73C2×#13050573—22no—
74C2×#13050573D414yescomplemented
75C22×C83⋊C8C2311yescharacteristic
76C22×C83⋊C8C2311yescharacteristic
77C22×C83⋊C8C2311yescharacteristic
78C22×C83⋊C8C2311yescharacteristic
79C2×C8×D83—22no—
80C2×C8×D83—22no—
81C2×C8×D83—22no—
82C2×C8×D83—22no—
83C2×C8×D83—22no—
84C2×C8×D83—22no—
85C4×D332—22no—
86C4×D332—22no—
87C4×D332—22no—
88C4×D332—22no—
89C4×D332—22no—
90C4×D332—22no—
91#14581749—22no—
92#14581749—22no—
93C2×C4⋊Dic83C2×C411yescharacteristic
94C2×C4⋊Dic83C2×C411yescharacteristic
95C2×C4⋊Dic83C2×C411yescharacteristic
96C2×Dic83⋊C4C2×C411yescharacteristic
97C2×Dic83⋊C4C2×C411yescharacteristic
98C2×(C2×D83)⋊C4C2×C411yescharacteristic
99C2×(C2×D83)⋊C4C2×C411yescharacteristic
100C2×(C2×D83)⋊C4C2×C411yescharacteristic
101C2×(C2×D83)⋊C4C2×C411yescharacteristic
102C2×(C2×D83)⋊C4C2×C411yescharacteristic
103C2×(C2×D83)⋊C4C2×C411yescharacteristic
104C2×(C2×D83)⋊C4C2×C411yescharacteristic
105C2×(C2×D83)⋊C4C2×C411yescharacteristic
106C2×(C2×D83)⋊C4C2×C411yescharacteristic
107C2×(C2×D83)⋊C4C2×C411yescharacteristic
108C2×(C2×D83)⋊C4C2×C411yescharacteristic
109C2×(C2×D83)⋊C4C2×C411yescharacteristic
110C2×C4×Dic83C2311yescharacteristic
111C4⋊(C83⋊C8)—22no—
112C4⋊(C83⋊C8)—22no—
113C4⋊(C83⋊C8)—22no—
114(C2×D83)⋊C8—22no—
115(C2×D83)⋊C8—22no—
116(C2×D83)⋊C8—22no—
117(C2×D83)⋊C8—22no—
118(C2×D83)⋊C8—22no—
119(C2×D83)⋊C8—22no—
120(C2×D83)⋊C8—22no—
121(C2×D83)⋊C8—22no—
122#14581702—22no—
123C4×C83⋊C8—22no—
124C8×Dic83—22no—
125C83⋊#95C2×C411yescharacteristic
126C83⋊#95C2×C411yescharacteristic
127C83⋊#95C2×C411yescharacteristic
128C83⋊#95C2×C411yescharacteristic
129C22×C8×C83C2311yescharacteristic
130C22×C8×C83C2311yescharacteristic
131C22×C8×C83C2311yescharacteristic
132C22×C8×C83C2311yescharacteristic
133C2×C4⋊C4×C83C2×C411yescharacteristic
134C2×C4⋊C4×C83C2×C411yescharacteristic
135C2×C42×C83C2311yescharacteristic
136C2×C42×C83C2311yescharacteristic
137C2×C42×C83C2311yescharacteristic
138C4⋊C8×C83—22no—
139#97×C83—22no—
140#97×C83D414yescomplemented
141C4×C8×C83—22no—
142#95×C83C2×C411yescharacteristic
143#95×C83C2×C411yescharacteristic
144C23×D83C22×C411yescharacteristic
145C23×D83C22×C411yescharacteristic
146C23×D83C22×C411yescharacteristic
147C2×D332—22no—
148C2×D332—22no—
149C2×D332—22no—
150C2×D332—22no—
151C2×D332—22no—
152C2×D332—22no—
153C2×D332—41no—
154C2×D332—41no—
155C2×D332—41no—
156C22×Dic83C22×C411yescharacteristic
157C22×Dic83C22×C411yescharacteristic
158C22×Dic83C22×C411yescharacteristic
159C22×Dic83C22×C411yescharacteristic
160C22×Dic83C22×C411yescharacteristic
161C2×C4×D83—21no—
162C2×C4×D83—21no—
163C2×C4×D83—21no—
164C2×C4×D83—21no—
165C2×C4×D83—21no—
166C2×C4×D83—21no—
167C2×C4×D83—21no—
168C2×C4×D83—21no—
169C2×C4×D83—21no—
170C2×C4×D83—21no—
171C2×C4×D83—21no—
172C2×C4×D83—21no—
173C2×C4×D83—21no—
174C2×C4×D83—21no—
175C2×C4×D83—21no—
176C2×C4×D83—21no—
177C2×C4×D83C2×D412yes—
178C2×C4×D83#4112yes—
179#13050573—28no—
180#13050573—44no—
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⋊C8C2×D412yes—
192C2×C83⋊C8#4112yes—
193C8×D83—28no—
194C8×D83—44no—
195C4⋊Dic83—22no—
196C4⋊Dic83—22no—
197C4⋊Dic83—22no—
198Dic83⋊C4—22no—
199Dic83⋊C4—22no—
200(C2×D83)⋊C4—22no—
201(C2×D83)⋊C4—22no—
202(C2×D83)⋊C4—22no—
203(C2×D83)⋊C4—22no—
204(C2×D83)⋊C4—22no—
205(C2×D83)⋊C4—22no—
206(C2×D83)⋊C4—22no—
207(C2×D83)⋊C4—22no—
208(C2×D83)⋊C4—22no—
209(C2×D83)⋊C4—22no—
210(C2×D83)⋊C4—41no—
211(C2×D83)⋊C4—41no—
212C4×Dic83—21no—
213C4×Dic83—21no—
214C22×C4×C83C22×C411yescharacteristic
215C22×C4×C83C22×C411yescharacteristic
216C22×C4×C83C22×C411yescharacteristic
217C22×C4×C83C22×C411yescharacteristic
218C22×C4×C83C22×C411yescharacteristic
219C22×C4×C83C22×C411yescharacteristic
220C22×C4×C83C2411yescharacteristic
221C2×C8×C83—21no—
222C2×C8×C83—21no—
223C2×C8×C83—21no—
224C2×C8×C83—21no—
225C2×C8×C83—21no—
226C2×C8×C83—21no—
227C2×C8×C83—21no—
228C2×C8×C83—21no—
229C2×C8×C83C2×D412yes—
230C2×C8×C83C2×D412yes—
231C2×C8×C83C2×D412yes—
232C2×C8×C83#4112yes—
233C4⋊C4×C83—22no—
234C4⋊C4×C83—41no—
235C42×C83—21no—
236C42×C83—21no—
237C42×C83—21no—
238C42×C83—21no—
239C42×C83C2×D412yes—
240C42×C83#4112yes—
241C23×C83C23×C411yescharacteristic
242C22×D83—21no—
243C22×D83—21no—
244C22×D83—21no—
245C22×D83—21no—
246C22×D83—21no—
247C22×D83—21no—
248C22×D83—21no—
249C22×D83—21no—
250C22×D83—21no—
251C22×D83—21no—
252C22×D83—21no—
253C22×D83—21no—
254C22×D83—21no—
255C22×D83—21no—
256C22×D83—21no—
257C22×D83—21no—
258C22×D83—21no—
259C22×D83—21no—
260C22×D83—21no—
261C22×D83C4×D412yes—
262C22×D83#13112yes—
263C2×C4×C83—21no—
264C2×C4×C83—21no—
265C2×C4×C83—21no—
266C2×C4×C83—21no—
267C2×C4×C83—21no—
268C2×C4×C83—21no—
269C2×C4×C83—21no—
270C2×C4×C83—21no—
271C2×C4×C83—21no—
272C2×C4×C83—21no—
273C2×C4×C83—21no—
274C2×C4×C83—21no—
275C2×C4×C83—21no—
276C2×C4×C83—21no—
277C2×C4×C83—21no—
278C2×C4×C83C4×D412yes—
279C2×C4×C83C4×D412yes—
280C2×C4×C83#13112yes—
281C2×C4×C83C22×D411yescharacteristic
282C2×C4×C83C22×D411yescharacteristic
283C2×C4×C83C2×#4111yescharacteristic
284C2×C4×C83C2×#4111yescharacteristic
285C2×C4×C83C2×#4111yescharacteristic
286C2×C4×C83C2×#4111yescharacteristic
287C2×Dic83—21no—
288C2×Dic83—21no—
289C2×Dic83—21no—
290C2×Dic83—21no—
291C2×Dic83—21no—
292C2×Dic83—21no—
293C2×Dic83—21no—
294C2×Dic83—21no—
295C2×Dic83—21no—
296C2×Dic83—21no—
297C2×Dic83—21no—
298C2×Dic83—21no—
299C2×Dic83—21no—
300C2×Dic83—21no—
301C2×Dic83C4×D412yes—
302D332—44no—
303D332—44no—
304D332—44no—
305C4×D83—22no—
306C4×D83—22no—
307C4×D83—22no—
308C4×D83—22no—
309C4×D83—41no—
310C4×D83—41no—
311C4×D83—41no—
312C4×D83—41no—
313C4×D83—41no—
314C4×D83—41no—
315C4×D83—41no—
316C4×D83—41no—
317C8×C83—22no—
318C8×C83—41no—
319C8×C83—41no—
320C8×C83#12114yes—
321C83⋊C8—22no—
322C83⋊C8—22no—
323C83⋊C8—41no—
324C83⋊C8—41no—
325C22×C83C2×C4×D411yescharacteristic
326C22×C83C2×C4×D411yescharacteristic
327C22×C83C4×#4111yescharacteristic
328C22×C83C2×#13111yescharacteristic
329C22×C83C2×#13111yescharacteristic
330C22×C83#56811yescharacteristic
331C22×C83#56811yescharacteristic
332C2×D83—22no—
333C2×D83—22no—
334C2×D83—22no—
335C2×D83—22no—
336C2×D83—22no—
337C2×D83—22no—
338C2×D83—41no—
339C2×D83—41no—
340C2×D83—41no—
341C2×D83—41no—
342C2×D83—41no—
343C2×D83—41no—
344C2×D83—41no—
345C2×D83—41no—
346C2×D83—41no—
347C2×D83—41no—
348C2×D83—41no—
349C2×D83—41no—
350C2×D83—41no—
351C2×D83—41no—
352C2×D83—41no—
353C4×C83—22no—
354C4×C83—22no—
355C4×C83—22no—
356C4×C83—41no—
357C4×C83—41no—
358C4×C83—41no—
359C4×C83C2×#12111yescharacteristic
360C4×C83#52511yescharacteristic
361C4×C83#52911yescharacteristic
362C4×C83#53211yescharacteristic
363Dic83—22no—
364Dic83—41no—
365Dic83—41no—
366Dic83—41no—
367Dic83—41no—
368#21496—831nomaximal, Sylow
369C2×C83C4×#12111yescharacteristic
370C2×C83#293311yescharacteristic
371C2×C83#293311yescharacteristic
372C2×C83#293311yescharacteristic
373C2×C83#293511yescharacteristic
374C2×C83#296611yescharacteristic
375C2×C83#296711yescharacteristic
376D83—42no—
377D83—42no—
378D83—81no—
379C2×#436—831no—
380C2×#435—831no—
381C2×#435—831no—
382C2×#405—831no—
383#2392—831no—
384#1954—831no—
385#1939—831no—
386#1924—831no—
387#1924—831no—
388#1869—831no—
389#1869—831no—
390#1798—831no—
391#1771D8311yescharacteristic, complemented
392#1753—831no—
393C8×C22⋊C4—831no—
394C83#2149611yescharacteristic, complemented, Sylow
395C22×M16—831no—
396C22×M16—831no—
397C23×C8—831no—
398C23×C8—831no—
399C2×C4×D4—831no—
400C2×C4×D4—831no—
401C2×C4×D4—831no—
402C2×#117—831no—
403#436—1664no—
404#435—1664no—
405#435—1664no—
406C2×C4⋊C8—831no—
407C2×C4⋊C8—831no—
408C2×C4⋊C8—831no—
409C2×C4⋊C8C2×D8311yescharacteristic
410C2×C22⋊C8—831no—
411C2×C22⋊C8—831no—
412C2×C22⋊C8—831no—
413C2×C22⋊C8—831no—
414C2×C22⋊C8—831no—
415C2×C22⋊C8—831no—
416C2×C22⋊C8—831no—
417C2×C22⋊C8—831no—
418#405—1664no—
419C2×#97—831no—
420C2×#97C2×D8311yescharacteristic
421C2×#97C2×D8311yescharacteristic
422C2×C4×C8—831no—
423C2×C4×C8—831no—
424C2×C4×C8C2×D8311yescharacteristic
425#398—831no—
426#397—831no—
427#396—831no—
428#396—831no—
429#394—831no—
430#394—831no—
431#394—831no—
432#392—831no—
433C4×C4⋊C4C2×D8311yescharacteristic
434C4×C22⋊C4—831no—
435C4×C22⋊C4—831no—
436#336—831no—
437#336—831no—
438#336—831no—
439#336—831no—
440#336C2×D8311yescharacteristic
441#336C2×D8311yescharacteristic
442C22×D4—831no—
443C22×D4—831no—
444C22×D4—831no—
445C23×C4—831no—
446C23×C4—831no—
447C23×C4—831no—
448C2×M16—834no—
449C2×M16—1662no—
450C2×M16—1662no—
451C2×M16—1662no—
452C2×M16—1662no—
453C2×M16—1662no—
454C22×C8—831no—
455C22×C8—831no—
456C22×C8—831no—
457C22×C8—831no—
458C22×C8—1662no—
459C22×C8—1662no—
460C22×C8—1662no—
461C22×C8—1662no—
462C22×C8—1662no—
463C22×C8—1662no—
464C22×C8C22×D8311yescharacteristic
465C22×C8C22×D8311yescharacteristic
466C22×C8C22×D8311yescharacteristic
467C22×C8C22×D8311yescharacteristic
468C4×D4—1662no—
469C4×D4—1662no—
470C4×D4—1662no—
471C4×D4—1662no—
472C4×D4—1662no—
473C4×D4—1662no—
474#117—1662no—
475#117—1662no—
476C2×C4⋊C4—831no—
477C2×C4⋊C4—831no—
478C2×C4⋊C4—831no—
479C2×C4⋊C4—831no—
480C2×C4⋊C4—831no—
481C2×C4⋊C4C4×D8311yescharacteristic
482C2×C4⋊C4C4×D8311yescharacteristic
483C2×C22⋊C4—831no—
484C2×C22⋊C4—831no—
485C2×C22⋊C4—831no—
486C2×C22⋊C4—831no—
487C2×C22⋊C4—831no—
488C2×C22⋊C4—831no—
489C2×C22⋊C4—831no—
490C2×C22⋊C4—831no—
491C2×C22⋊C4—831no—
492C2×C22⋊C4—831no—
493C2×C22⋊C4—831no—
494C2×C22⋊C4—831no—
495C2×C42—831no—
496C2×C42C22×D8311yescharacteristic
497C2×C42C22×D8311yescharacteristic
498C2×C42C22×D8311yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—1662no—
501C4⋊C8—1662no—
502C4⋊C8—1662no—
503C22⋊C8—1662no—
504C22⋊C8—1662no—
505C22⋊C8—1662no—
506C22⋊C8—1662no—
507C22⋊C8—1662no—
508C22⋊C8—1662no—
509C22⋊C8—1662no—
510C22⋊C8—1662no—
511#97—22no—
512#97—1662no—
513#97D33214yescomplemented
514C4×C8—22no—
515C4×C8—1662no—
516C4×C8—1662no—
517#95—831no—
518#95—831no—
519#95—831no—
520#95—831no—
521#95C4×D8311yescharacteristic
522#95C4×D8311yescharacteristic
523C24—831no—
524C24—831no—
525C24—831no—
526C2×D4—3321no—
527C2×D4—3321no—
528C2×D4—3321no—
529C2×D4—1662no—
530C2×D4—1662no—
531C2×D4—1662no—
532C2×D4—1662no—
533C2×D4—1662no—
534C2×D4—1662no—
535C22×C4—831no—
536C22×C4—832no—
537C22×C4—832no—
538C22×C4—831no—
539C22×C4—831no—
540C22×C4—831no—
541C22×C4—831no—
542C22×C4—1661no—
543C22×C4—1661no—
544C22×C4—1661no—
545C22×C4—1661no—
546C22×C4—1661no—
547C22×C4—1661no—
548C22×C4—1661no—
549C22×C4—1661no—
550C22×C4—1661no—
551C22×C4—1661no—
552C22×C4—1661no—
553C22×C4—1661no—
554C22×C4—1661no—
555C22×C4—1661no—
556C22×C4—1661no—
557C22×C4—1661no—
558C22×C4C2×C4×D8311yescharacteristic
559C22×C4C2×C4×D8311yescharacteristic
560C22×C4C2×C4×D8311yescharacteristic
561C22×C4C2×C4×D8311yescharacteristic
562C22×C4C2×C4×D8311yescharacteristic
563C22×C4C2×C4×D8311yescharacteristic
564C22×C4C23×D8311yescharacteristic
565M16—3324no—
566M16—1668no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—3324no—
576C2×C8—832no—
577C2×C8—832no—
578C2×C8—1668no—
579C2×C8—1661no—
580C2×C8—1661no—
581C2×C8—1661no—
582C2×C8—1661no—
583C2×C8—1661no—
584C2×C8—1661no—
585C2×C8—1661no—
586C2×C8—1661no—
587C2×C8—1661no—
588C2×C8—1661no—
589C2×C8D4×D8312yes—
590C2×C8C2×D33212yes—
591C2×C8C2×D33212yes—
592C2×C8#1305059112yes—
593C4⋊C4—22no—
594C4⋊C4—41no—
595C4⋊C4—1662no—
596C4⋊C4—1662no—
597C4⋊C4—1662no—
598C4⋊C4—1662no—
599C4⋊C4—1662no—
600C22⋊C4—3321no—
601C22⋊C4—3321no—
602C22⋊C4—1662no—
603C22⋊C4—1662no—
604C22⋊C4—1662no—
605C22⋊C4—1662no—
606C22⋊C4—1662no—
607C22⋊C4—1662no—
608C22⋊C4—1662no—
609C22⋊C4—1662no—
610C22⋊C4—1662no—
611C22⋊C4—1662no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—1661no—
617C42—1661no—
618C42C2×D33212yes—
619C42#1305059012yes—
620C23—832no—
621C23—832no—
622C23—1661no—
623C23—1661no—
624C23—1661no—
625C23—1661no—
626C23—1661no—
627C23—1661no—
628C23—1661no—
629C23—1661no—
630C23—1661no—
631C23—1661no—
632C23—1661no—
633C23—1661no—
634C23—1661no—
635C23—1661no—
636C23—1661no—
637C23—1661no—
638C23—1661no—
639C23—1661no—
640C23—1661no—
641C23C22×C4×D8311yescharacteristic
642D4—3324no—
643D4—3324no—
644D4—3324no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—3321no—
661C2×C4—3321no—
662C2×C4—3321no—
663C2×C4—3321no—
664C2×C4—3321no—
665C2×C4—3321no—
666C2×C4—3321no—
667C2×C4—3321no—
668C2×C4—832no—
669C2×C4—1661no—
670C2×C4—1661no—
671C2×C4—1661no—
672C2×C4—1661no—
673C2×C4—1661no—
674C2×C4—1661no—
675C2×C4—1661no—
676C2×C4—1661no—
677C2×C4—1661no—
678C2×C4—1661no—
679C2×C4—1661no—
680C2×C4—1661no—
681C2×C4—1661no—
682C2×C4—1661no—
683C2×C4—1662no—
684C2×C4—1662no—
685C2×C4—1662no—
686C2×C4—1662no—
687C2×C4C4×D33212yes—
688C2×C4C4×D33212yes—
689C2×C4#1458180012yes—
690C2×C4C2×D4×D8311yescharacteristic
691C2×C4C22×D33211yescharacteristic
692C2×C4#41×D8311yescharacteristic
693C2×C4#41×D8311yescharacteristic
694C2×C4C2×#1305059011yescharacteristic
695C2×C4C2×#1305059111yescharacteristic
696C8—22no—
697C8—41no—
698C8—41no—
699C8—3321no—
700C8—3321no—
701C8—1662no—
702C8—1662no—
703C8#1458176714yes—
704C22—3321no—
705C22—3321no—
706C22—3321no—
707C22—3321no—
708C22—3321no—
709C22—3321no—
710C22—3321no—
711C22—3321no—
712C22—3321no—
713C22—3321no—
714C22—3321no—
715C22—3321no—
716C22—3321no—
717C22—3321no—
718C22—3321no—
719C22—1662no—
720C22—1662no—
721C22—1662no—
722C22—1662no—
723C22—1662no—
724C22—1662no—
725C22C4×D4×D8311yescharacteristic
726C22C2×C4×D33211yescharacteristic
727C22C4×#1305059111yescharacteristic
728C22#131×D8311yescharacteristic
729C22C2×#1458180011yescharacteristic
730C22#1912846611yescharacteristic
731C22#1912846711yescharacteristic
732C4—22no—
733C4—22no—
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—3321no—
739C4—3321no—
740C4—3321no—
741C4—3321no—
742C4—1662no—
743C4C2×#1458176711yescharacteristic
744C4#1912821311yescharacteristic
745C4#1912823811yescharacteristic
746C4#1912824811yescharacteristic
747C2—3322no—
748C2—3322no—
749C2—6641no—
750C2C4×#1458176711yescharacteristic
751C2#2491618611yescharacteristic
752C2#2491618911yescharacteristic
753C2#2491619111yescharacteristic
754C2#2491620911yescharacteristic
755C2#2491643711yescharacteristic
756C2#2491644711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1771C2
prime radical#19127611C4
cosocleC22×C4×C83C24
hypercenter#1771D83
hypocenterC83#21496
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
1. C2×#19127780C2semidirect
2. C2×#19127774C2semidirect
3. C2×#19127774C2semidirect
4. C2×#19127658C2semidirect
6. #24908256C2semidirect
7. #24908182C2semidirect
8. #24908077C2semidirect
9. #24908077C2semidirect
10. #24907754C2semidirect
11. #24907754C2semidirect
12. #24907444C2semidirect
13. #24907248C2semidirect
14. C8×(C2×D83)⋊C4C2semidirect
15. C83×#1771C2semidirect
74. C2×#13050573D4semidirect
140. #97×C83D4semidirect
391. #1771D83semidirect
394. C83#21496semidirect
513. #97D332semidirect

Maximal subgroups

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

subgroupindex
C2×#191277802
C2×#191277742
C2×#191276582
#249107032
#249082562
#249081822
#249080772
#249077542
#249074442
#249072482
C8×(C2×D83)⋊C42
C83×#17712
#2149683