Finite Group Databasebeta

← #35420694

Subgroups — #35420694

Order 21248.

1194 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128391C211yesmaximal, characteristic
2D4×C4⋊Dic83C211yesmaximal, characteristic
3#24908432C211yesmaximal, characteristic, complemented
4#24908418C211yesmaximal, characteristic, complemented
5#24907896C211yesmaximal, characteristic, complemented
6#24907886C211yesmaximal, characteristic, complemented
7#24907768C211yesmaximal, characteristic, complemented
8#24907768C211yesmaximal, characteristic, complemented
9#24907559C211yesmaximal, characteristic, complemented
10#24907550C211yesmaximal, characteristic, complemented
11#24907469C211yesmaximal, characteristic, complemented
12#24907294C211yesmaximal, characteristic, complemented
13#24907183C211yesmaximal, characteristic, complemented
14C2×#19127464C211yesmaximal, characteristic, complemented
15C2×#435×C83C211yesmaximal, characteristic
16#19128391—24no—
17#19128391C418yescomplemented
18C2×#14581785—21no—
19C2×#14581784C2211yescharacteristic
20C2×#14581782—21no—
21C2×#14581773—21no—
22C2×#14581771C2211yescharacteristic
23C2×#14581771C2211yescharacteristic
24C2×C4×Dic166C2211yescharacteristic
25C2×D4×Dic83—21no—
26C2×#14581751C2211yescharacteristic
27C2×#14581748—21no—
28C22×C4⋊Dic83C2211yescharacteristic
29C22×C4⋊Dic83C2211yescharacteristic
30C22×C4⋊Dic83C2211yescharacteristic
31C2×#14581717C2211yescharacteristic
32C2×#14581717C2211yescharacteristic
33C2×#14581717C2211yescharacteristic
34C2×#14581717C2211yescharacteristic
35#19127600—21no—
36#19127576—21no—
37#19127576—21no—
38#19127571C2211yescharacteristic
39#19127561C2211yescharacteristic
40#19127561C2211yescharacteristic
41C4×C4⋊Dic83C2211yescharacteristic
42#19127464C2211yescharacteristic
43#19127464C2211yescharacteristic
44#19127464C2211yescharacteristic
45#19127464C2211yescharacteristic
46#19127464C2211yescharacteristic
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127464C2211yescharacteristic
50#19127464C2211yescharacteristic
51#19127464C2211yescharacteristic
52#19127464C2211yescharacteristic
53#19127464C2211yescharacteristic
54C22×M16×C83C2211yescharacteristic
55C23×C8×C83C2211yescharacteristic
56C2×C4×D4×C83C2211yescharacteristic
57#435×C83—24no—
58C2×C4⋊C8×C83C2211yescharacteristic
59C2×C22⋊C8×C83C2211yescharacteristic
60C2×C22⋊C8×C83C2211yescharacteristic
61C2×#97×C83C2211yescharacteristic
62C22×Dic166C2311yescharacteristic
63C23×Dic83—21no—
64C23×Dic83—21no—
65C23×Dic83—21no—
66#14581785—28no—
67#14581784—22no—
68#14581784C2×C414yescomplemented
69#14581782—28no—
70#14581773—28no—
71#14581771—22no—
72#14581771—22no—
73#14581771C2×C414yescomplemented
74#14581771C2×C414yescomplemented
75C4×Dic166—22no—
76C4×Dic166C2×C414yescomplemented
77D4×Dic83—44no—
78#14581751—22no—
79#14581751C2×C414yescomplemented
80#14581748—28no—
81C2×C4⋊Dic83—22no—
82C2×C4⋊Dic83—22no—
83C2×C4⋊Dic83—22no—
84C2×C4⋊Dic83—21no—
85C2×C4⋊Dic83—21no—
86C2×C4⋊Dic83—21no—
87C2×C4⋊Dic83—21no—
88C2×C4⋊Dic83—21no—
89C2×C4⋊Dic83—41no—
90C2×C4⋊Dic83—41no—
91C2×C4⋊Dic83C2×C414yescomplemented
92C2×C4⋊Dic83C2311yescharacteristic
93C2×C4⋊Dic83C2311yescharacteristic
94C2×C4⋊Dic83C2311yescharacteristic
95C2×C4⋊Dic83C2311yescharacteristic
96C2×C4⋊Dic83C2311yescharacteristic
97C2×C4⋊Dic83C2311yescharacteristic
98C2×C4⋊Dic83C2311yescharacteristic
99C2×Dic83⋊C4—21no—
100C2×Dic83⋊C4—21no—
101C2×Dic83⋊C4—21no—
102C2×Dic83⋊C4—21no—
103C2×Dic83⋊C4—21no—
104C2×C22⋊Dic83—21no—
105C2×C22⋊Dic83—21no—
106C2×C22⋊Dic83—21no—
107C2×C22⋊Dic83—21no—
108C2×C22⋊Dic83—21no—
109C2×C4×Dic83—21no—
110C2×C4×Dic83—21no—
111C2×C4×Dic83—21no—
112#14581717—22no—
113#14581717—22no—
114#14581717—41no—
115#14581717—41no—
116C83⋊#95—21no—
117C83⋊#95—21no—
118C83⋊#95—21no—
119C22×D4×C83D411yescharacteristic
120C23×C4×C83C2311yescharacteristic
121C23×C4×C83C2311yescharacteristic
122C2×M16×C83—22no—
123C2×M16×C83—22no—
124C2×M16×C83—41no—
125C22×C8×C83—22no—
126C22×C8×C83—22no—
127C22×C8×C83—41no—
128C22×C8×C83C2311yescharacteristic
129C22×C8×C83C2311yescharacteristic
130C22×C8×C83C2311yescharacteristic
131C22×C8×C83C2311yescharacteristic
132C4×D4×C83C2×C414yes—
133C4×D4×C83D414yes—
134C2×C4⋊C4×C83D411yescharacteristic
135C2×C22⋊C4×C83D411yescharacteristic
136C2×C22⋊C4×C83D411yescharacteristic
137C2×C42×C83C2311yescharacteristic
138C4⋊C8×C83—22no—
139C22⋊C8×C83—22no—
140C22⋊C8×C83—22no—
141#97×C83—22no—
142C2×Dic166—21no—
143C2×Dic166—21no—
144C2×Dic166—21no—
145C2×Dic166—21no—
146C2×Dic166—21no—
147C2×Dic166C22×C412yes—
148C22×Dic83—24no—
149C22×Dic83—21no—
150C22×Dic83—21no—
151C22×Dic83—21no—
152C22×Dic83—21no—
153C22×Dic83—21no—
154C22×Dic83—21no—
155C22×Dic83—21no—
156C22×Dic83—21no—
157C22×Dic83—42no—
158C22×Dic83—42no—
159C22×Dic83—42no—
160C22×Dic83—42no—
161C22×Dic83—42no—
162C22×Dic83—42no—
163C22×Dic83—81no—
164C22×Dic83—81no—
165C4⋊Dic83—24no—
166C4⋊Dic83—21no—
167C4⋊Dic83—21no—
168C4⋊Dic83—21no—
169C4⋊Dic83—21no—
170C4⋊Dic83—21no—
171C4⋊Dic83—21no—
172C4⋊Dic83—21no—
173C4⋊Dic83—21no—
174C4⋊Dic83—21no—
175C4⋊Dic83—21no—
176C4⋊Dic83—42no—
177C4⋊Dic83—42no—
178C4⋊Dic83—42no—
179C4⋊Dic83—81no—
180C4⋊Dic83C22×C412yes—
181C4⋊Dic83C22×C412yes—
182C4⋊Dic83C22×C412yes—
183C4⋊Dic83#4112yes—
184Dic83⋊C4—24no—
185Dic83⋊C4—24no—
186Dic83⋊C4—24no—
187Dic83⋊C4—24no—
188Dic83⋊C4—24no—
189C22⋊Dic83—24no—
190C22⋊Dic83—24no—
191C22⋊Dic83—24no—
192C22⋊Dic83—42no—
193C22⋊Dic83—42no—
194C4×Dic83—24no—
195C4×Dic83—24no—
196C4×Dic83—42no—
197C24×C83C2×D411yescharacteristic
198C24×C83C2×D411yescharacteristic
199C2×D4×C83—22no—
200C2×D4×C83—22no—
201C2×D4×C83C22⋊C414yes—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83C22×C412yes—
211C22×C4×C83C22×C412yes—
212C22×C4×C83C2×D412yes—
213C22×C4×C83C2×D412yes—
214C22×C4×C83C2×D411yescharacteristic
215C22×C4×C83C2×D411yescharacteristic
216C22×C4×C83C2×D411yescharacteristic
217C22×C4×C83C2×D411yescharacteristic
218C22×C4×C83C2411yescharacteristic
219M16×C83—44no—
220C2×C8×C83—21no—
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×C83—44no—
232C2×C8×C83#4112yes—
233C4⋊C4×C83C22⋊C414yes—
234C22⋊C4×C83C22⋊C414yes—
235C22⋊C4×C83C22⋊C414yes—
236C42×C83C22×C412yes—
237C42×C83C2×D412yes—
238C23×C83—21no—
239C23×C83—21no—
240C23×C83—21no—
241C23×C83—21no—
242C23×C83—21no—
243C23×C83—21no—
244C23×C83—21no—
245C23×C83—21no—
246C23×C83—21no—
247C23×C83—21no—
248C23×C83C2×C22⋊C412yes—
249C23×C83C2×C22⋊C412yes—
250C23×C83AGL(1,ℤ/8)12yes—
251C23×C83#13712yes—
252C23×C83C22×D411yescharacteristic
253D4×C83—28no—
254C2×C4×C83—21no—
255C2×C4×C83—21no—
256C2×C4×C83—21no—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—21no—
260C2×C4×C83—21no—
261C2×C4×C83—21no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83—22no—
266C2×C4×C83—22no—
267C2×C4×C83—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83C2×C22⋊C412yes—
271C2×C4×C83C2×C22⋊C412yes—
272C2×C4×C83C2×C22⋊C412yes—
273C2×C4×C83C2×C22⋊C412yes—
274C2×C4×C83C23×C411yescharacteristic
275C2×C4×C83C22×D411yescharacteristic
276C2×C4×C83C2×#4111yescharacteristic
277C2×C4×C83C2×#4111yescharacteristic
278C2×C4×C83H(5,𝔽2)11yescharacteristic
279C2×C4×C832−1+411yescharacteristic
280C2×Dic83—22no—
281C2×Dic83—22no—
282C2×Dic83—22no—
283C2×Dic83—22no—
284C2×Dic83—22no—
285C2×Dic83—41no—
286C2×Dic83—41no—
287C2×Dic83—41no—
288C2×Dic83—41no—
289C2×Dic83—41no—
290C2×Dic83—41no—
291C2×Dic83—41no—
292C2×Dic83—41no—
293C2×Dic83—41no—
294C2×Dic83—41no—
295C2×Dic83—48no—
296C2×Dic83—41no—
297C2×Dic83—41no—
298C2×Dic83—41no—
299C2×Dic83—41no—
300C2×Dic83—41no—
301C2×Dic83—41no—
302C2×Dic83—41no—
303C2×Dic83—41no—
304C2×Dic83—41no—
305C2×Dic83—84no—
306C2×Dic83—84no—
307Dic166—22no—
308Dic166—22no—
309Dic166—41no—
310Dic166—41no—
311C8×C83—22no—
312C8×C83—41no—
313C8×C83—41no—
314C8×C83—41no—
315C22×C83—22no—
316C22×C83—22no—
317C22×C83—22no—
318C22×C83—22no—
319C22×C83—22no—
320C22×C83—22no—
321C22×C83—22no—
322C22×C83—22no—
323C22×C83—22no—
324C22×C83—41no—
325C22×C83—41no—
326C22×C83—41no—
327C22×C83—41no—
328C22×C83#41714yes—
329C22×C83C22×C22⋊C411yescharacteristic
330C22×C83#54611yescharacteristic
331C22×C83#54711yescharacteristic
332C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C83C2×#13711yescharacteristic
334C22×C83#57711yescharacteristic
335C22×C83#57811yescharacteristic
336C4×C83—22no—
337C4×C83—22no—
338C4×C83—22no—
339C4×C83—22no—
340C4×C83C4×#4111yescharacteristic
341C4×C83#52011yescharacteristic
342C4×C83#54611yescharacteristic
343C4×C83#54711yescharacteristic
344Dic83—42no—
345Dic83—42no—
346Dic83—42no—
347Dic83—42no—
348Dic83—42no—
349Dic83—81no—
350Dic83—81no—
351Dic83—81no—
352#22491—831nomaximal, Sylow
353C2×C83—24no—
354C2×C83—42no—
355C2×C83#233911yescharacteristic
356C2×C83C2×#41711yescharacteristic
357C2×C83#289811yescharacteristic
358C2×C83#331011yescharacteristic
359C2×C83#331211yescharacteristic
360C2×C83#334311yescharacteristic
361C2×C83#334411yescharacteristic
362C2×#552—831no—
363C2×#435D8311yescharacteristic
364D4×C4⋊C4—831no—
365#1992—831no—
366#1989—831no—
367#1894—831no—
368#1892—831no—
369#1872—831no—
370#1872—831no—
371#1825—831no—
372#1823—831no—
373#1803—831no—
374#1763—831no—
375#1736—831no—
376C2×#340—831no—
377C83#2249111yescharacteristic, complemented, Sylow
378C22×M16C2×D8311yescharacteristic
379C23×C8C2×D8311yescharacteristic
380#552—838no—
381#552—1664no—
382C2×#126—1661no—
383C2×#125—831no—
384C2×#125—1661no—
385C2×#123—1661no—
386C2×C22⋊Q8—831no—
387C2×C22⋊Q8—831no—
388C2×C4×Q8—831no—
389C2×C4×D4—1661no—
390C2×C4×D4C2×D8311yescharacteristic
391C2×#117—831no—
392C2×#117—1661no—
393C22×C4⋊C4—831no—
394C22×C4⋊C4—831no—
395C22×C4⋊C4—831no—
396#435—24no—
397C2×C4⋊C8C2×D8311yescharacteristic
398C2×#103—831no—
399C2×#103—831no—
400C2×#103—831no—
401C2×#103—831no—
402C2×C22⋊C8C2×D8311yescharacteristic
403C2×C22⋊C8C2×D8311yescharacteristic
404C2×#97C2×D8311yescharacteristic
405#389—1661no—
406#385—1661no—
407#385—1661no—
408#384—831no—
409#380—831no—
410#380—831no—
411C4×C4⋊C4—831no—
412#340—831no—
413#340—831no—
414#340—831no—
415#340—831no—
416#340—831no—
417#340—831no—
418#340—831no—
419#340—831no—
420#340—831no—
421#340—831no—
422#340—831no—
423#340—831no—
424C22×Q8—831no—
425C22×D4D33211yescharacteristic
426C23×C4—1661no—
427C23×C4—1661no—
428C23×C4—1661no—
429C23×C4C22×D8311yescharacteristic
430C23×C4C22×D8311yescharacteristic
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—41no—
434C22×C8—22no—
435C22×C8—22no—
436C22×C8—41no—
437C22×C8C22×D8311yescharacteristic
438C22×C8C22×D8311yescharacteristic
439C22×C8C22×D8311yescharacteristic
440C22×C8C22×D8311yescharacteristic
441#126—1668no—
442#125—834no—
443#125—1668no—
444#125—1662no—
445#123—1668no—
446C22⋊Q8—834no—
447C22⋊Q8—834no—
448C22⋊Q8—1662no—
449C22⋊Q8—1662no—
450C4×Q8—834no—
451C4×Q8—1662no—
452C4×D4—3324no—
453C4×D4C4×D8314yes—
454C4×D4C22⋊D8314yes—
455#117—834no—
456#117—1662no—
457#117—1668no—
458C2×C4⋊C4—3321no—
459C2×C4⋊C4—3321no—
460C2×C4⋊C4—834no—
461C2×C4⋊C4—831no—
462C2×C4⋊C4—831no—
463C2×C4⋊C4—831no—
464C2×C4⋊C4—831no—
465C2×C4⋊C4—831no—
466C2×C4⋊C4—831no—
467C2×C4⋊C4—831no—
468C2×C4⋊C4—1661no—
469C2×C4⋊C4—1661no—
470C2×C4⋊C4—1661no—
471C2×C4⋊C4—1662no—
472C2×C4⋊C4—1662no—
473C2×C4⋊C4—1661no—
474C2×C4⋊C4—1662no—
475C2×C4⋊C4—1661no—
476C2×C4⋊C4—1661no—
477C2×C4⋊C4—1661no—
478C2×C4⋊C4—1661no—
479C2×C4⋊C4—1661no—
480C2×C4⋊C4—1661no—
481C2×C4⋊C4D33211yescharacteristic
482C2×C22⋊C4—1661no—
483C2×C22⋊C4—1661no—
484C2×C22⋊C4—1661no—
485C2×C22⋊C4—1661no—
486C2×C22⋊C4—1661no—
487C2×C22⋊C4D33211yescharacteristic
488C2×C22⋊C4D33211yescharacteristic
489C2×C42—1661no—
490C2×C42—1661no—
491C2×C42—1661no—
492C2×C42C22×D8311yescharacteristic
493C4⋊C8—22no—
494#103—3321no—
495#103—3321no—
496#103—1662no—
497#103—1662no—
498C22⋊C8—22no—
499C22⋊C8—22no—
500#97—22no—
501#95—1661no—
502#95—1661no—
503#95—1661no—
504C24C2×D33211yescharacteristic
505C24C2×D33211yescharacteristic
506C2×Q8—832no—
507C2×Q8—1661no—
508C2×Q8—1661no—
509C2×Q8—1661no—
510C2×Q8—1661no—
511C2×Q8—1661no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4(C2×D83)⋊C414yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—3322no—
524C22×C4—3322no—
525C22×C4—3322no—
526C22×C4—3322no—
527C22×C4—3322no—
528C22×C4—3322no—
529C22×C4—6641no—
530C22×C4—6641no—
531C22×C4—1661no—
532C22×C4—1661no—
533C22×C4—1661no—
534C22×C4—1661no—
535C22×C4—1661no—
536C22×C4—1661no—
537C22×C4—1661no—
538C22×C4—1661no—
539C22×C4—1664no—
540C22×C4C2×C4×D8312yes—
541C22×C4C2×C4×D8312yes—
542C22×C4C2×C22⋊D8312yes—
543C22×C4C2×C22⋊D8312yes—
544C22×C4C2×D33211yescharacteristic
545C22×C4C2×D33211yescharacteristic
546C22×C4C2×D33211yescharacteristic
547C22×C4C2×D33211yescharacteristic
548C22×C4C23×D8311yescharacteristic
549M16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—44no—
562C2×C8#1305058912yes—
563C4⋊C4—3322no—
564C4⋊C4—3322no—
565C4⋊C4—3322no—
566C4⋊C4—832no—
567C4⋊C4—832no—
568C4⋊C4—832no—
569C4⋊C4—832no—
570C4⋊C4—6641no—
571C4⋊C4—1661no—
572C4⋊C4—1661no—
573C4⋊C4—1661no—
574C4⋊C4—1661no—
575C4⋊C4—1661no—
576C4⋊C4—1661no—
577C4⋊C4—1661no—
578C4⋊C4—1661no—
579C4⋊C4—1661no—
580C4⋊C4—1661no—
581C4⋊C4—1664no—
582C4⋊C4—1664no—
583C4⋊C4—1664no—
584C4⋊C4—1664no—
585C4⋊C4—1664no—
586C4⋊C4—1664no—
587C4⋊C4(C2×D83)⋊C414yes—
588C22⋊C4—3322no—
589C22⋊C4—3322no—
590C22⋊C4—1664no—
591C22⋊C4—1664no—
592C22⋊C4—1664no—
593C22⋊C4(C2×D83)⋊C414yes—
594C22⋊C4(C2×D83)⋊C414yes—
595C42—3322no—
596C42—1664no—
597C42—1664no—
598C42C2×C4×D8312yes—
599C42C2×C22⋊D8312yes—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23C2×(C2×D83)⋊C412yes—
611C23C2×(C2×D83)⋊C412yes—
612C23#1458182012yes—
613C23#1458182512yes—
614C23C22×D33211yescharacteristic
615Q8—3321no—
616Q8—3321no—
617Q8—1662no—
618Q8—1662no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—3321no—
637C2×C4—3321no—
638C2×C4—3328no—
639C2×C4—3321no—
640C2×C4—3321no—
641C2×C4—3321no—
642C2×C4—3321no—
643C2×C4—3321no—
644C2×C4—3321no—
645C2×C4—3321no—
646C2×C4—3321no—
647C2×C4—3321no—
648C2×C4—3321no—
649C2×C4—3321no—
650C2×C4—3321no—
651C2×C4—3321no—
652C2×C4—3321no—
653C2×C4—3321no—
654C2×C4—3321no—
655C2×C4—3321no—
656C2×C4—6644no—
657C2×C4—6644no—
658C2×C4—1662no—
659C2×C4—1662no—
660C2×C4—1662no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4C2×(C2×D83)⋊C412yes—
664C2×C4C2×(C2×D83)⋊C412yes—
665C2×C4C2×(C2×D83)⋊C412yes—
666C2×C4C2×(C2×D83)⋊C412yes—
667C2×C4C22×C4×D8311yescharacteristic
668C2×C4C22×C22⋊D8311yescharacteristic
669C2×C4#41×D8311yescharacteristic
670C2×C4C2×#1305058911yescharacteristic
671C2×C4#1458183711yescharacteristic
672C2×C4#1458183911yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1912770314yes—
691C22C22×(C2×D83)⋊C411yescharacteristic
692C22#1912834611yescharacteristic
693C22#1912835511yescharacteristic
694C22C2×#1458182011yescharacteristic
695C22C2×#1458182511yescharacteristic
696C22#1912851311yescharacteristic
697C22#1912851811yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—3322no—
703C4—3322no—
704C4—3322no—
705C4—3322no—
706C4—3322no—
707C4—6641no—
708C4—6641no—
709C4—6641no—
710C4C4×#1305058911yescharacteristic
711C4#1912818011yescharacteristic
712C4#1912834511yescharacteristic
713C4#1912835011yescharacteristic
714C2—24no—
715C2—42no—
716C2#2491028811yescharacteristic
717C2C2×#1912770311yescharacteristic
718C2#2491599711yescharacteristic
719C2#2491948611yescharacteristic
720C2#2491951611yescharacteristic
721C2#2491990511yescharacteristic
722C2#2491992011yescharacteristic
subgroupG/H
centerC23C22×D332
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC2×#435×C83C2
socleC23×C83C22×D4
prime radicalC22×D4×C83D4
cosocleC22×C4×C83C24
hypercenterC2×#435D83
hypocenterC83#22491
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #24908432C2semidirect
4. #24908418C2semidirect
5. #24907896C2semidirect
6. #24907886C2semidirect
7. #24907768C2semidirect
8. #24907768C2semidirect
9. #24907559C2semidirect
10. #24907550C2semidirect
11. #24907469C2semidirect
12. #24907294C2semidirect
13. #24907183C2semidirect
14. C2×#19127464C2semidirect
17. #19128391C4semidirect
68. #14581784C2×C4semidirect
73. #14581771C2×C4semidirect
74. #14581771C2×C4semidirect
76. C4×Dic166C2×C4semidirect
79. #14581751C2×C4semidirect
91. C2×C4⋊Dic83C2×C4semidirect
377. C83#22491semidirect

Maximal subgroups

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

subgroupindex
C2×#191283912
D4×C4⋊Dic832
#249084322
#249084182
#249078962
#249078862
#249077682
#249075592
#249075502
#249074692
#249072942
#249071832
C2×#191274642
C2×#435×C832
#2249183