Finite Group Databasebeta

← #35410560

Subgroups — #35410560

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×#19127778C211yesmaximal, characteristic, complemented
2C2×#19127771C211yesmaximal, characteristic, complemented
3C2×#19127771C211yesmaximal, characteristic, complemented
4C2×#19127655C211yesmaximal, characteristic, complemented
5#24910703C211yesmaximal, characteristic
6#24908257C211yesmaximal, characteristic, complemented
7#24908075C211yesmaximal, characteristic, complemented
8#24908075C211yesmaximal, characteristic, complemented
9#24907754C211yesmaximal, characteristic, complemented
10#24907754C211yesmaximal, characteristic, complemented
11#24907444C211yesmaximal, characteristic, complemented
12#24907338C211yesmaximal, characteristic, complemented
13#24907245C211yesmaximal, characteristic, complemented
14#24907233C211yesmaximal, characteristic, complemented
15C83×#1939C211yesmaximal, characteristic, complemented
16C22×#13050573C2211yescharacteristic
17C22×#13050573C2211yescharacteristic
18C22×C8×D83C2211yescharacteristic
19C22×C8×D83C2211yescharacteristic
20C2×C4×D332C2211yescharacteristic
21C2×C4×D332C2211yescharacteristic
22C2×C4×D332C2211yescharacteristic
23C2×#14581749C2211yescharacteristic
24#19127778—24no—
25#19127771—24no—
26#19127771—24no—
27C2×C4⋊(C83⋊C8)C2211yescharacteristic
28C2×(C2×D83)⋊C8C2211yescharacteristic
29C2×(C2×D83)⋊C8C2211yescharacteristic
30C2×(C2×D83)⋊C8C2211yescharacteristic
31C2×(C2×D83)⋊C8C2211yescharacteristic
32C2×(C2×D83)⋊C8C2211yescharacteristic
33C2×(C2×D83)⋊C8C2211yescharacteristic
34C2×(C2×D83)⋊C8C2211yescharacteristic
35C2×(C2×D83)⋊C8C2211yescharacteristic
36#19127655—24no—
37C2×#14581703C2211yescharacteristic
38C2×#14581703C2211yescharacteristic
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×C4⋊C8×C83C2211yescharacteristic
58C2×C4⋊C8×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—
112(C2×D83)⋊C8—22no—
113(C2×D83)⋊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#14581703—22no—
121#14581703D414yescomplemented
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—
139C4⋊C8×C83—22no—
140C4⋊C8×C83—22no—
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⋊C8C2×D412yes—
190C2×C83⋊C8C2×D412yes—
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×C83—21no—
230C2×C8×C83—21no—
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—22no—
319C8×C83—41no—
320C8×C83—41no—
321C83⋊C8—22no—
322C83⋊C8—41no—
323C83⋊C8—41no—
324C83⋊C8#12114yes—
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#1939D8311yescharacteristic, complemented
386#1924—831no—
387#1924—831no—
388#1869—831no—
389#1869—831no—
390#1798—831no—
391#1771—831no—
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⋊C8C2×D8311yescharacteristic
408C2×C4⋊C8C2×D8311yescharacteristic
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×#97—831no—
421C2×#97—831no—
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—22no—
501C4⋊C8—22no—
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—834no—
512#97—1662no—
513#97—1662no—
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—21no—
576C2×C8—21no—
577C2×C8—3324no—
578C2×C8—832no—
579C2×C8—832no—
580C2×C8—832no—
581C2×C8—832no—
582C2×C8—1668no—
583C2×C8—1661no—
584C2×C8—1661no—
585C2×C8—1661no—
586C2×C8—1661no—
587C2×C8—1661no—
588C2×C8—1661no—
589C2×C8—1661no—
590C2×C8—1661no—
591C2×C8D4×D8312yes—
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—
618C42D4×D8312yes—
619C42#1305059112yes—
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×C4#1458175412yes—
688C2×C4#1458175412yes—
689C2×C4#1458179812yes—
690C2×C4C2×D4×D8311yescharacteristic
691C2×C4C2×D4×D8311yescharacteristic
692C2×C4#41×D8311yescharacteristic
693C2×C4#41×D8311yescharacteristic
694C2×C4C2×#1305059111yescharacteristic
695C2×C4C2×#1305059111yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—3321no—
701C8—3321no—
702C8—834no—
703C8—1662no—
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×#1458175411yescharacteristic
727C22C4×#1305059111yescharacteristic
728C22#131×D8311yescharacteristic
729C22C2×#1458179811yescharacteristic
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—
743C4#121×D8311yescharacteristic
744C4#1912821411yescharacteristic
745C4#1912823611yescharacteristic
746C4#1912825211yescharacteristic
747C2—3322no—
748C2—3322no—
749C2—6641no—
750C2#2490997111yescharacteristic
751C2#2491618311yescharacteristic
752C2#2491618711yescharacteristic
753C2#2491619211yescharacteristic
754C2#2491620611yescharacteristic
755C2#2491644011yescharacteristic
756C2#2491644711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1939C2
prime radical#19127611C4
cosocleC22×C4×C83C24
hypercenter#1939D83
hypocenterC83#21496
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. C2×#19127778C2semidirect
2. C2×#19127771C2semidirect
3. C2×#19127771C2semidirect
4. C2×#19127655C2semidirect
6. #24908257C2semidirect
7. #24908075C2semidirect
8. #24908075C2semidirect
9. #24907754C2semidirect
10. #24907754C2semidirect
11. #24907444C2semidirect
12. #24907338C2semidirect
13. #24907245C2semidirect
14. #24907233C2semidirect
15. C83×#1939C2semidirect
74. C2×#13050573D4semidirect
121. #14581703D4semidirect
385. #1939D83semidirect
394. C83#21496semidirect

Maximal subgroups

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

subgroupindex
C2×#191277782
C2×#191277712
C2×#191276552
#249107032
#249082572
#249080752
#249077542
#249074442
#249073382
#249072452
#249072332
C83×#19392
#2149683