Finite Group Databasebeta

← #35410572

Subgroups — #35410572

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×#19127769C211yesmaximal, characteristic, complemented
3C2×#19127769C211yesmaximal, characteristic, complemented
4C2×#19127658C211yesmaximal, characteristic, complemented
5#24910707C211yesmaximal, characteristic
6#24908255C211yesmaximal, characteristic, complemented
7#24908178C211yesmaximal, characteristic, complemented
8#24908076C211yesmaximal, characteristic, complemented
9#24907754C211yesmaximal, characteristic, complemented
10#24907752C211yesmaximal, characteristic, complemented
11#24907446C211yesmaximal, characteristic, complemented
12#24907334C211yesmaximal, characteristic, complemented
13#24907243C211yesmaximal, characteristic, complemented
14C22⋊C4×C83⋊C8C211yesmaximal, characteristic, complemented
15C83×#1924C211yesmaximal, characteristic, complemented
16C22×#13050573C2211yescharacteristic
17C22×#13050573C2211yescharacteristic
18C23×C83⋊C8C2211yescharacteristic
19C22×C8×D83C2211yescharacteristic
20C2×C4×D332C2211yescharacteristic
21C2×C4×C22⋊D83C2211yescharacteristic
22C2×C4×C22⋊D83C2211yescharacteristic
23C2×#14581749C2211yescharacteristic
24#19127778—24no—
25#19127769—24no—
26#19127769—24no—
27C2×Dic83⋊C8C2211yescharacteristic
28C2×Dic83⋊C8C2211yescharacteristic
29C2×Dic83⋊C8C2211yescharacteristic
30C2×C22⋊(C83⋊C8)C2211yescharacteristic
31C2×(C2×D83)⋊C8C2211yescharacteristic
32C2×(C2×D83)⋊C8C2211yescharacteristic
33C2×(C2×D83)⋊C8C2211yescharacteristic
34C2×(C2×D83)⋊C8C2211yescharacteristic
35C2×(C2×D83)⋊C8C2211yescharacteristic
36#19127658—24no—
37C2×#14581702C2211yescharacteristic
38C2×#14581702C2211yescharacteristic
39C2×C4×C83⋊C8C2211yescharacteristic
40C2×C4×C83⋊C8C2211yescharacteristic
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
56C2×C4⋊C8×C83C2211yescharacteristic
57C2×C22⋊C8×C83C2211yescharacteristic
58C2×C22⋊C8×C83C2211yescharacteristic
59C2×#97×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×#13050573—22no—
71C2×#13050573—22no—
72C2×#13050573—22no—
73C2×#13050573D414yescomplemented
74C22×C83⋊C8—22no—
75C22×C83⋊C8—22no—
76C22×C83⋊C8—22no—
77C22×C83⋊C8C2311yescharacteristic
78C22×C83⋊C8C2311yescharacteristic
79C22×C83⋊C8C2311yescharacteristic
80C22×C83⋊C8C2311yescharacteristic
81C2×C8×D83—22no—
82C2×C8×D83—22no—
83C2×C8×D83—22no—
84C4×D332—22no—
85C4×D332—22no—
86C4×C22⋊D83—22no—
87C4×C22⋊D83—22no—
88C4×C22⋊D83—22no—
89C4×C22⋊D83—22no—
90#14581749—22no—
91#14581749—22no—
92C2×C4⋊Dic83C2×C411yescharacteristic
93C2×Dic83⋊C4C2×C411yescharacteristic
94C2×Dic83⋊C4C2×C411yescharacteristic
95C2×Dic83⋊C4C2×C411yescharacteristic
96C2×Dic83⋊C4C2×C411yescharacteristic
97C2×Dic83⋊C4C2×C411yescharacteristic
98C2×Dic83⋊C4C2×C411yescharacteristic
99C2×C22⋊Dic83C2×C411yescharacteristic
100C2×C22⋊Dic83C2×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×C4×Dic83C2311yescharacteristic
110C2×C4×Dic83C2311yescharacteristic
111Dic83⋊C8—22no—
112Dic83⋊C8—22no—
113Dic83⋊C8—22no—
114C22⋊(C83⋊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#14581702—22no—
121#14581702D414yescomplemented
122C4×C83⋊C8—22no—
123C4×C83⋊C8—22no—
124C8×Dic83—22no—
125C83⋊#95C2×C411yescharacteristic
126C83⋊#95C2×C411yescharacteristic
127C83⋊#95C2×C411yescharacteristic
128C83⋊#95C2×C411yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C22×C8×C83C2311yescharacteristic
131C22×C8×C83C2311yescharacteristic
132C22×C8×C83C2311yescharacteristic
133C22×C8×C83C2311yescharacteristic
134C2×C22⋊C4×C83C2×C411yescharacteristic
135C2×C22⋊C4×C83C2×C411yescharacteristic
136C2×C42×C83C2311yescharacteristic
137C2×C42×C83C2311yescharacteristic
138C4⋊C8×C83—22no—
139C22⋊C8×C83—22no—
140C22⋊C8×C83—22no—
141#97×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—
174#13050573—44no—
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—44no—
184C2×C83⋊C8C2×D412yes—
185C2×C83⋊C8C2×D412yes—
186C2×C83⋊C8#4112yes—
187C2×C83⋊C8#4112yes—
188C8×D83—28no—
189C4⋊Dic83—22no—
190Dic83⋊C4—22no—
191Dic83⋊C4—22no—
192Dic83⋊C4—22no—
193Dic83⋊C4—22no—
194Dic83⋊C4—22no—
195Dic83⋊C4—41no—
196C22⋊Dic83—22no—
197C22⋊Dic83—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—41no—
205(C2×D83)⋊C4—41no—
206C4×Dic83—21no—
207C4×Dic83—21no—
208C4×Dic83C2×D412yes—
209C4×Dic83#4112yes—
210C24×C83C22×C411yescharacteristic
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—21no—
216C22×C4×C83—21no—
217C22×C4×C83C22×C411yescharacteristic
218C22×C4×C83C22×C411yescharacteristic
219C22×C4×C83C22×C411yescharacteristic
220C22×C4×C83C22×C411yescharacteristic
221C22×C4×C83C22×C411yescharacteristic
222C22×C4×C83C2411yescharacteristic
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×C83—21no—
232C2×C8×C83—21no—
233C2×C8×C83C2×D412yes—
234C2×C8×C83C2×D412yes—
235C22⋊C4×C83—22no—
236C22⋊C4×C83—22no—
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#13112yes—
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×D83—21no—
262C22×D83C4×D412yes—
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—41no—
278C2×C4×C83—41no—
279C2×C4×C83—41no—
280C2×C4×C83—41no—
281C2×C4×C83#13112yes—
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×Dic83—21no—
305C2×Dic83C4×D412yes—
306C2×Dic83C4×D412yes—
307C2×Dic83C4×D412yes—
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—22no—
319C8×C83—41no—
320C8×C83—41no—
321C83⋊C8—22no—
322C83⋊C8—41no—
323C83⋊C8—41no—
324C83⋊C8#12114yes—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—22no—
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—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—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—41no—
366Dic83—41no—
367Dic83—41no—
368#21496—831nomaximal, Sylow
369C2×C83—42no—
370C2×C83C4×#12111yescharacteristic
371C2×C83#293311yescharacteristic
372C2×C83#293311yescharacteristic
373C2×C83#293311yescharacteristic
374C2×C83#293511yescharacteristic
375C2×C83#296611yescharacteristic
376C2×C83#296711yescharacteristic
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#1924D8311yescharacteristic, complemented
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⋊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⋊C8C2×D8311yescharacteristic
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×C8—831no—
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—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⋊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—22no—
500C4⋊C8—1662no—
501C4⋊C8—1662no—
502C4⋊C8—1662no—
503C22⋊C8—22no—
504C22⋊C8—22no—
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—1662no—
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—832no—
545C22×C4—832no—
546C22×C4—831no—
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—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×C8D4×D8312yes—
593C4⋊C4—3321no—
594C4⋊C4—1662no—
595C4⋊C4—1662no—
596C4⋊C4—1662no—
597C4⋊C4—1662no—
598C4⋊C4—1662no—
599C4⋊C4—1662no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—3321no—
603C22⋊C4—3321no—
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—832no—
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#1458180012yes—
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—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—3321no—
664C2×C4—3321no—
665C2×C4—3321no—
666C2×C4—3321no—
667C2×C4—832no—
668C2×C4—832no—
669C2×C4—832no—
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—1661no—
684C2×C4—1661no—
685C2×C4—1662no—
686C2×C4—1662no—
687C2×C4—1662no—
688C2×C4—1662no—
689C2×C4#1458180012yes—
690C2×C4C2×D4×D8311yescharacteristic
691C2×C4C2×D4×D8311yescharacteristic
692C2×C4#41×D8311yescharacteristic
693C2×C4#41×D8311yescharacteristic
694C2×C4#41×D8311yescharacteristic
695C2×C4#41×D8311yescharacteristic
696C8—22no—
697C8—22no—
698C8—41no—
699C8—41no—
700C8—3321no—
701C8—3321no—
702C8—834no—
703C8—1662no—
704C22—22no—
705C22—22no—
706C22—22no—
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—3321no—
720C22—3321no—
721C22—3321no—
722C22—1662no—
723C22—1662no—
724C22—1662no—
725C22C4×D4×D8311yescharacteristic
726C22C4×D4×D8311yescharacteristic
727C22#1912816911yescharacteristic
728C22C2×#1458180011yescharacteristic
729C22C2×#1458180011yescharacteristic
730C22#1912846611yescharacteristic
731C22#1912846611yescharacteristic
732C4—22no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—3321no—
738C4—3321no—
739C4—3321no—
740C4—1662no—
741C4—1662no—
742C4—1662no—
743C4#121×D8311yescharacteristic
744C4#1912820911yescharacteristic
745C4#1912823411yescharacteristic
746C4#1912825011yescharacteristic
747C2—42no—
748C2—3322no—
749C2—6641no—
750C2#2490997511yescharacteristic
751C2#2491618911yescharacteristic
752C2#2491618911yescharacteristic
753C2#2491618911yescharacteristic
754C2#2491620811yescharacteristic
755C2#2491643211yescharacteristic
756C2#2491644611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1924C2
prime radical#19127610C4
cosocleC22×C4×C83C24
hypercenter#1924D83
hypocenterC83#21496
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#19127778C2semidirect
2. C2×#19127769C2semidirect
3. C2×#19127769C2semidirect
4. C2×#19127658C2semidirect
6. #24908255C2semidirect
7. #24908178C2semidirect
8. #24908076C2semidirect
9. #24907754C2semidirect
10. #24907752C2semidirect
11. #24907446C2semidirect
12. #24907334C2semidirect
13. #24907243C2semidirect
14. C22⋊C4×C83⋊C8C2semidirect
15. C83×#1924C2semidirect
73. C2×#13050573D4semidirect
121. #14581702D4semidirect
387. #1924D83semidirect
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×#191277692
C2×#191276582
#249107072
#249082552
#249081782
#249080762
#249077542
#249077522
#249074462
#249073342
#249072432
C22⋊C4×C83⋊C82
C83×#19242
#2149683