Finite Group Databasebeta

← #35410571

Subgroups — #35410571

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×#19127777C211yesmaximal, characteristic, complemented
2C2×#19127774C211yesmaximal, characteristic, complemented
3C2×#19127770C211yesmaximal, characteristic, complemented
4C2×#19127655C211yesmaximal, characteristic, complemented
5#24910707C211yesmaximal, characteristic
6#24908255C211yesmaximal, characteristic, complemented
7#24908180C211yesmaximal, characteristic, complemented
8#24908078C211yesmaximal, characteristic, complemented
9#24908074C211yesmaximal, characteristic, complemented
10#24907754C211yesmaximal, characteristic, complemented
11#24907752C211yesmaximal, characteristic, complemented
12#24907446C211yesmaximal, characteristic, complemented
13#24907339C211yesmaximal, characteristic, complemented
14C8×(C2×D83)⋊C4C211yesmaximal, characteristic, complemented
15C83×#1753C211yesmaximal, characteristic, complemented
16C22×#13050573C2211yescharacteristic
17C22×C8×D83C2211yescharacteristic
18C22×C8×D83C2211yescharacteristic
19C2×C4×D332C2211yescharacteristic
20C2×C4×C22⋊D83C2211yescharacteristic
21C2×C4×C22⋊D83C2211yescharacteristic
22C2×#14581749C2211yescharacteristic
23#19127777—24no—
24#19127774—24no—
25#19127770—24no—
26C2×C4⋊(C83⋊C8)C2211yescharacteristic
27C2×Dic83⋊C8C2211yescharacteristic
28C2×Dic83⋊C8C2211yescharacteristic
29C2×Dic83⋊C8C2211yescharacteristic
30C2×C22⋊(C83⋊C8)C2211yescharacteristic
31C2×C22⋊(C83⋊C8)C2211yescharacteristic
32C2×(C2×D83)⋊C8C2211yescharacteristic
33C2×(C2×D83)⋊C8C2211yescharacteristic
34C2×(C2×D83)⋊C8C2211yescharacteristic
35C2×(C2×D83)⋊C8C2211yescharacteristic
36C2×(C2×D83)⋊C8C2211yescharacteristic
37#19127655—24no—
38C2×#14581703C2211yescharacteristic
39C2×#14581702C2211yescharacteristic
40C2×C8×Dic83C2211yescharacteristic
41C2×C8×Dic83C2211yescharacteristic
42#19127635C411yescharacteristic
43#19127630C411yescharacteristic
44#19127625C411yescharacteristic
45#19127624C411yescharacteristic
46#19127619C411yescharacteristic
47#19127616C411yescharacteristic
48#19127616C411yescharacteristic
49#19127610C411yescharacteristic
50C4×Dic83⋊C4C2211yescharacteristic
51C4×(C2×D83)⋊C4C2211yescharacteristic
52#19127456C2211yescharacteristic
53#19127456C2211yescharacteristic
54#19127455C2211yescharacteristic
55#19127455C2211yescharacteristic
56C22×M16×C83C2211yescharacteristic
57C2×C22⋊C8×C83C2211yescharacteristic
58C2×#97×C83C2211yescharacteristic
59C2×C4×C8×C83C2211yescharacteristic
60C4×C22⋊C4×C83C2211yescharacteristic
61#336×C83C2211yescharacteristic
62#336×C83C2211yescharacteristic
63C22×D332C2×C411yescharacteristic
64C22×C22⋊D83C2×C411yescharacteristic
65C22×C22⋊D83C2×C411yescharacteristic
66C22×C4×D83C2311yescharacteristic
67C22×C4×D83C2311yescharacteristic
68C2×#13050573—22no—
69C2×#13050573—22no—
70C2×#13050573D414yescomplemented
71C22×C83⋊C8C2311yescharacteristic
72C22×C83⋊C8C2311yescharacteristic
73C22×C83⋊C8C2311yescharacteristic
74C22×C83⋊C8C2311yescharacteristic
75C2×C8×D83—22no—
76C2×C8×D83—22no—
77C2×C8×D83—22no—
78C2×C8×D83—22no—
79C2×C8×D83—22no—
80C2×C8×D83—22no—
81C4×D332—22no—
82C4×D332—22no—
83C4×C22⋊D83—22no—
84C4×C22⋊D83—22no—
85C4×C22⋊D83—22no—
86C4×C22⋊D83—22no—
87#14581749—22no—
88#14581749—22no—
89C2×C4⋊Dic83C2×C411yescharacteristic
90C2×Dic83⋊C4C2×C411yescharacteristic
91C2×Dic83⋊C4C2×C411yescharacteristic
92C2×Dic83⋊C4C2×C411yescharacteristic
93C2×Dic83⋊C4C2×C411yescharacteristic
94C2×Dic83⋊C4C2×C411yescharacteristic
95C2×Dic83⋊C4C2×C411yescharacteristic
96C2×C22⋊Dic83C2×C411yescharacteristic
97C2×C22⋊Dic83C2×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×C4×Dic83C2311yescharacteristic
107C2×C4×Dic83C2311yescharacteristic
108C4⋊(C83⋊C8)—22no—
109Dic83⋊C8—22no—
110Dic83⋊C8—22no—
111Dic83⋊C8—22no—
112C22⋊(C83⋊C8)—22no—
113C22⋊(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#14581703—22no—
120#14581702D414yescomplemented
121C8×Dic83—22no—
122C8×Dic83—22no—
123C83⋊#95C2×C411yescharacteristic
124C83⋊#95C2×C411yescharacteristic
125C83⋊#95C2×C411yescharacteristic
126C83⋊#95C2×C411yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C2×M16×C83—22no—
129C2×M16×C83—22no—
130C2×M16×C83—22no—
131C22×C8×C83C2311yescharacteristic
132C22×C8×C83C2311yescharacteristic
133C22×C8×C83C2311yescharacteristic
134C22×C8×C83C2311yescharacteristic
135C2×C22⋊C4×C83C2×C411yescharacteristic
136C2×C22⋊C4×C83C2×C411yescharacteristic
137C2×C42×C83C2311yescharacteristic
138C2×C42×C83C2311yescharacteristic
139C22⋊C8×C83—22no—
140#97×C83—22no—
141C4×C8×C83—22no—
142#95×C83C2×C411yescharacteristic
143#95×C83C2×C411yescharacteristic
144C23×D83C22×C411yescharacteristic
145C23×D83C22×C411yescharacteristic
146C2×D332—22no—
147C2×D332—22no—
148C2×D332—41no—
149C2×C22⋊D83—22no—
150C2×C22⋊D83—22no—
151C2×C22⋊D83—22no—
152C2×C22⋊D83—22no—
153C2×C22⋊D83—41no—
154C2×C22⋊D83—41no—
155C22×Dic83C22×C411yescharacteristic
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×D83C2×D412yes—
172C2×C4×D83#4112yes—
173#13050573—28no—
174C2×C83⋊C8—21no—
175C2×C83⋊C8—21no—
176C2×C83⋊C8—21no—
177C2×C83⋊C8—21no—
178C2×C83⋊C8—21no—
179C2×C83⋊C8—21no—
180C2×C83⋊C8—21no—
181C2×C83⋊C8—21no—
182C2×C83⋊C8—21no—
183C2×C83⋊C8—21no—
184C2×C83⋊C8C2×D412yes—
185C2×C83⋊C8C2×D412yes—
186C8×D83—28no—
187C8×D83—44no—
188C4⋊Dic83—22no—
189Dic83⋊C4—22no—
190Dic83⋊C4—22no—
191Dic83⋊C4—22no—
192Dic83⋊C4—22no—
193Dic83⋊C4—22no—
194Dic83⋊C4—41no—
195C22⋊Dic83—22no—
196C22⋊Dic83—22no—
197(C2×D83)⋊C4—22no—
198(C2×D83)⋊C4—22no—
199(C2×D83)⋊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—
205C4×Dic83—21no—
206C4×Dic83—21no—
207C4×Dic83C2×D412yes—
208C4×Dic83#4112yes—
209C24×C83C22×C411yescharacteristic
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—21no—
216C22×C4×C83C22×C411yescharacteristic
217C22×C4×C83C22×C411yescharacteristic
218C22×C4×C83C22×C411yescharacteristic
219C22×C4×C83C22×C411yescharacteristic
220C22×C4×C83C22×C411yescharacteristic
221C22×C4×C83C2411yescharacteristic
222M16×C83—44no—
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×C83C2×D412yes—
233C2×C8×C83#4112yes—
234C2×C8×C83#4112yes—
235C22⋊C4×C83—41no—
236C22⋊C4×C83—41no—
237C42×C83—21no—
238C42×C83—21no—
239C42×C83—21no—
240C42×C83—21no—
241C23×C83—21no—
242C23×C83—21no—
243C23×C83—21no—
244C23×C83—21no—
245C23×C83—21no—
246C23×C83—21no—
247C23×C83—21no—
248C23×C83C23×C411yescharacteristic
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×C83—41no—
279C2×C4×C83—41no—
280C2×C4×C83—41no—
281C2×C4×C83—41no—
282C2×C4×C83C22×D411yescharacteristic
283C2×C4×C83C22×D411yescharacteristic
284C2×C4×C83C2×#4111yescharacteristic
285C2×C4×C83C2×#4111yescharacteristic
286C2×C4×C83C2×#4111yescharacteristic
287C2×C4×C83C2×#4111yescharacteristic
288C22⋊D83—44no—
289C22⋊D83—44no—
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×Dic83—21no—
302C2×Dic83—21no—
303C2×Dic83—21no—
304C2×Dic83C4×D412yes—
305C2×Dic83C4×D412yes—
306C2×Dic83C4×D412yes—
307C2×Dic83#13112yes—
308D332—44no—
309C4×D83—22no—
310C4×D83—22no—
311C4×D83—22no—
312C4×D83—22no—
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×C83—41no—
326C22×C83—41no—
327C22×C83—41no—
328C22×C83—41no—
329C22×C83—41no—
330C22×C83—41no—
331C22×C83—41no—
332C22×C83C2×C4×D411yescharacteristic
333C22×C83C2×C4×D411yescharacteristic
334C22×C83C4×#4111yescharacteristic
335C22×C83C2×#13111yescharacteristic
336C22×C83C2×#13111yescharacteristic
337C22×C83#56811yescharacteristic
338C22×C83#56811yescharacteristic
339C2×D83—22no—
340C2×D83—22no—
341C2×D83—22no—
342C2×D83—22no—
343C2×D83—22no—
344C2×D83—22no—
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—41no—
354C4×C83—41no—
355C4×C83—41no—
356C4×C83—41no—
357C4×C83—41no—
358C4×C83C2×#12111yescharacteristic
359C4×C83#52511yescharacteristic
360C4×C83#52911yescharacteristic
361C4×C83#53211yescharacteristic
362Dic83—22no—
363Dic83—22no—
364Dic83—22no—
365Dic83—22no—
366Dic83—41no—
367Dic83—41no—
368#21496—831nomaximal, Sylow
369C2×C83—81no—
370C2×C83C4×#12111yescharacteristic
371C2×C83#293311yescharacteristic
372C2×C83#293311yescharacteristic
373C2×C83#293311yescharacteristic
374C2×C83#293511yescharacteristic
375C2×C83#296611yescharacteristic
376C2×C83#296711yescharacteristic
377D83—42no—
378D83—42no—
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#1771—831no—
392#1753D8311yescharacteristic, complemented
393C8×C22⋊C4—831no—
394C83#2149611yescharacteristic, complemented, Sylow
395C22×M16—831no—
396C22×M16C2×D8311yescharacteristic
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⋊C8—831no—
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⋊C8C2×D8311yescharacteristic
418#405—1664no—
419C2×#97—831no—
420C2×#97—831no—
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⋊C4—831no—
434C4×C22⋊C4—831no—
435C4×C22⋊C4C2×D8311yescharacteristic
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×C4C22×D8311yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—834no—
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⋊C4—831no—
482C2×C4⋊C4—831no—
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⋊C4C4×D8311yescharacteristic
494C2×C22⋊C4C4×D8311yescharacteristic
495C2×C42—831no—
496C2×C42—831no—
497C2×C42C22×D8311yescharacteristic
498C2×C42C22×D8311yescharacteristic
499C4⋊C8—1662no—
500C4⋊C8—1662no—
501C4⋊C8—1662no—
502C4⋊C8—1662no—
503C22⋊C8—22no—
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—834no—
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—
525C24C2×C4×D8311yescharacteristic
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—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—831no—
542C22×C4—831no—
543C22×C4—831no—
544C22×C4—831no—
545C22×C4—832no—
546C22×C4—832no—
547C22×C4—831no—
548C22×C4—831no—
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×C4—1661no—
559C22×C4C2×C4×D8311yescharacteristic
560C22×C4C2×C4×D8311yescharacteristic
561C22×C4C2×C4×D8311yescharacteristic
562C22×C4C2×C4×D8311yescharacteristic
563C22×C4C2×C4×D8311yescharacteristic
564C22×C4C23×D8311yescharacteristic
565M16—44no—
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×C8D4×D8312yes—
591C2×C8#1305059012yes—
592C2×C8#1305059012yes—
593C4⋊C4—3321no—
594C4⋊C4—1662no—
595C4⋊C4—1662no—
596C4⋊C4—1662no—
597C4⋊C4—1662no—
598C4⋊C4—1662no—
599C4⋊C4—1662no—
600C22⋊C4—41no—
601C22⋊C4—41no—
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—832no—
617C42—832no—
618C42—1661no—
619C42—1661no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—832no—
628C23—832no—
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—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—3321no—
665C2×C4—3321no—
666C2×C4—3321no—
667C2×C4—3321no—
668C2×C4—832no—
669C2×C4—832no—
670C2×C4—832no—
671C2×C4—832no—
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—1661no—
684C2×C4—1661no—
685C2×C4—1661no—
686C2×C4—1662no—
687C2×C4—1662no—
688C2×C4—1662no—
689C2×C4—1662no—
690C2×C4C2×D4×D8311yescharacteristic
691C2×C4C2×D4×D8311yescharacteristic
692C2×C4#41×D8311yescharacteristic
693C2×C4#41×D8311yescharacteristic
694C2×C4C2×#1305059011yescharacteristic
695C2×C4C2×#1305059011yescharacteristic
696C8—22no—
697C8—41no—
698C8—41no—
699C8—3321no—
700C8—3321no—
701C8—1662no—
702C8—1662no—
703C8#1458176514yes—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
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
726C22C4×D4×D8311yescharacteristic
727C22C4×#1305059011yescharacteristic
728C22#131×D8311yescharacteristic
729C22#131×D8311yescharacteristic
730C22#1912846711yescharacteristic
731C22#1912846711yescharacteristic
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—3321no—
738C4—3321no—
739C4—1662no—
740C4—1662no—
741C4—1662no—
742C4—1662no—
743C4C2×#1458176511yescharacteristic
744C4#1912821011yescharacteristic
745C4#1912822911yescharacteristic
746C4#1912824811yescharacteristic
747C2—81no—
748C2—3322no—
749C2—3322no—
750C2C4×#1458176511yescharacteristic
751C2#2491618611yescharacteristic
752C2#2491619211yescharacteristic
753C2#2491619211yescharacteristic
754C2#2491620411yescharacteristic
755C2#2491643411yescharacteristic
756C2#2491644811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1753C2
prime radical#19127610C4
cosocleC22×C4×C83C24
hypercenter#1753D83
hypocenterC83#21496
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#19127777C2semidirect
2. C2×#19127774C2semidirect
3. C2×#19127770C2semidirect
4. C2×#19127655C2semidirect
6. #24908255C2semidirect
7. #24908180C2semidirect
8. #24908078C2semidirect
9. #24908074C2semidirect
10. #24907754C2semidirect
11. #24907752C2semidirect
12. #24907446C2semidirect
13. #24907339C2semidirect
14. C8×(C2×D83)⋊C4C2semidirect
15. C83×#1753C2semidirect
70. C2×#13050573D4semidirect
120. #14581702D4semidirect
392. #1753D83semidirect
394. C83#21496semidirect

Maximal subgroups

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

subgroupindex
C2×#191277772
C2×#191277742
C2×#191277702
C2×#191276552
#249107072
#249082552
#249081802
#249080782
#249080742
#249077542
#249077522
#249074462
#249073392
C8×(C2×D83)⋊C42
C83×#17532
#2149683