Finite Group Databasebeta

← #35420640

Subgroups — #35420640

Order 21248.

1258 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128406C211yesmaximal, characteristic
2C2×C8×C22⋊D83C211yesmaximal, characteristic
3C4⋊C4×C22⋊D83C211yesmaximal, characteristic
4#24908422C211yesmaximal, characteristic, complemented
5#24908409C211yesmaximal, characteristic, complemented
6#24907886C211yesmaximal, characteristic, complemented
7#24907885C211yesmaximal, characteristic, complemented
8#24907770C211yesmaximal, characteristic, complemented
9#24907769C211yesmaximal, characteristic, complemented
10#24907553C211yesmaximal, characteristic, complemented
11#24907552C211yesmaximal, characteristic, complemented
12#24907467C211yesmaximal, characteristic, complemented
13#24907282C211yesmaximal, characteristic, complemented
14#340×D83C211yesmaximal, characteristic, complemented
15C2×#340×C83C211yesmaximal, characteristic, complemented
16C22×C8×D83C2211yescharacteristic
17#19128406—24no—
18#19128406C418yescomplemented
19C2×#14581791C2211yescharacteristic
20C2×#14581782—21no—
21C2×#14581772C2211yescharacteristic
22C2×#14581771—21no—
23C2×#14581771C2211yescharacteristic
24C2×#14581770—21no—
25C2×#14581757C2211yescharacteristic
26C2×C4×C22⋊D83—21no—
27C2×C4×C22⋊D83—21no—
28C2×C4×C22⋊D83C2211yescharacteristic
29C2×C4⋊C4×D83C2211yescharacteristic
30C2×C4⋊C4×D83C2211yescharacteristic
31C8×C22⋊D83—24no—
32C2×Dic83⋊C8C2211yescharacteristic
33C2×#14581717C2211yescharacteristic
34C2×#14581717C2211yescharacteristic
35C2×#14581715C2211yescharacteristic
36C2×#14581715C2211yescharacteristic
37C2×C22⋊(C83⋊C8)C2211yescharacteristic
38C2×(C2×D83)⋊C8C2211yescharacteristic
39C2×C8×Dic83C2211yescharacteristic
40#19127596—21no—
41#19127574—21no—
42#19127572—21no—
43#19127570C2211yescharacteristic
44#19127561C2211yescharacteristic
45#19127558C2211yescharacteristic
46C4⋊C4×Dic83C2211yescharacteristic
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51#19127463C2211yescharacteristic
52#19127463C2211yescharacteristic
53#19127463C2211yescharacteristic
54#19127463C2211yescharacteristic
55C23×C8×C83C2211yescharacteristic
56C22×C4⋊C4×C83C2211yescharacteristic
57C22×C4⋊C4×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic
60#340×C83C2211yescharacteristic
61#340×C83C2211yescharacteristic
62C22×Dic166—21no—
63C22×Dic166C2311yescharacteristic
64C22×C22⋊D83D411yescharacteristic
65C22×C4×D83—21no—
66C22×C4×D83—21no—
67C22×C4×D83C2311yescharacteristic
68C22×C83⋊C8C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C2×C8×D83—22no—
71C2×C8×D83—22no—
72C2×C8×D83—41no—
73#14581791—22no—
74#14581791C2×C414yescomplemented
75#14581782—28no—
76#14581772—22no—
77#14581772C2×C414yescomplemented
78#14581771—28no—
79#14581771—22no—
80#14581771C2×C414yescomplemented
81#14581770—28no—
82#14581757—22no—
83#14581757C2×C414yescomplemented
84C4×C22⋊D83—28no—
85C4×C22⋊D83—44no—
86C4×C22⋊D83C2×C414yes—
87C4×C22⋊D83D414yes—
88C2×C4⋊Dic83—21no—
89C2×C4⋊Dic83C2311yescharacteristic
90C2×C4⋊Dic83C2311yescharacteristic
91C2×C4⋊Dic83C2311yescharacteristic
92C2×Dic83⋊C4—21no—
93C2×Dic83⋊C4—21no—
94C2×Dic83⋊C4—21no—
95C2×Dic83⋊C4—21no—
96C2×Dic83⋊C4—21no—
97C2×Dic83⋊C4—21no—
98C2×Dic83⋊C4—21no—
99C2×Dic83⋊C4D411yescharacteristic
100C4⋊C4×D83—22no—
101C4⋊C4×D83—22no—
102C4⋊C4×D83—41no—
103C4⋊C4×D83C2×C414yescomplemented
104C2×C22⋊Dic83—21no—
105C2×C22⋊Dic83—21no—
106C2×C22⋊Dic83D411yescharacteristic
107C2×(C2×D83)⋊C4—21no—
108C2×(C2×D83)⋊C4—21no—
109C2×(C2×D83)⋊C4D411yescharacteristic
110C2×C4×Dic83—21no—
111C2×C4×Dic83—21no—
112C2×C4×Dic83C2311yescharacteristic
113Dic83⋊C8—22no—
114#14581717—22no—
115#14581717—41no—
116#14581715—22no—
117#14581715—41no—
118C22⋊(C83⋊C8)—22no—
119(C2×D83)⋊C8—22no—
120C8×Dic83—22no—
121C83⋊#95—21no—
122C83⋊#95—21no—
123C83⋊#95—21no—
124C23×C4×C83—21no—
125C23×C4×C83—21no—
126C23×C4×C83C2311yescharacteristic
127C22×C8×C83—22no—
128C22×C8×C83—22no—
129C22×C8×C83—41no—
130C22×C8×C83C2311yescharacteristic
131C22×C8×C83C2311yescharacteristic
132C2×C4⋊C4×C83—22no—
133C2×C4⋊C4×C83—21no—
134C2×C4⋊C4×C83—22no—
135C2×C4⋊C4×C83—21no—
136C2×C4⋊C4×C83—41no—
137C2×C4⋊C4×C83C2×C414yescomplemented
138C2×C4⋊C4×C83C2311yescharacteristic
139C2×C4⋊C4×C83C2311yescharacteristic
140C2×C4⋊C4×C83C2311yescharacteristic
141C2×C4⋊C4×C83C2311yescharacteristic
142C23×D83C2×D411yescharacteristic
143C2×Dic166—21no—
144C2×Dic166—21no—
145C2×Dic166—21no—
146C2×Dic166—21no—
147C2×Dic166—21no—
148C2×Dic166—24no—
149C2×Dic166—81no—
150C2×Dic166—81no—
151C2×Dic166C22×C412yes—
152C2×C22⋊D83C22⋊C414yes—
153C2×C22⋊D83SD1614yes—
154C2×C22⋊D83Q1614yes—
155C22×Dic83—21no—
156C22×Dic83—21no—
157C22×Dic83—21no—
158C22×Dic83—21no—
159C22×Dic83C2×D411yescharacteristic
160C22×Dic83C2×D411yescharacteristic
161C22×Dic83C2×D411yescharacteristic
162C2×C4×D83—21no—
163C2×C4×D83—21no—
164C2×C4×D83—21no—
165C2×C4×D83—21no—
166C2×C4×D83—24no—
167C2×C4×D83—42no—
168C2×C4×D83—42no—
169C2×C4×D83—81no—
170C2×C4×D83—81no—
171C2×C4×D83—81no—
172C2×C4×D83C22×C412yes—
173C2×C4×D83C2×D412yes—
174C2×C83⋊C8—21no—
175C2×C83⋊C8—21no—
176C2×C83⋊C8—21no—
177C2×C83⋊C8—21no—
178C2×C83⋊C8—21no—
179C2×C83⋊C8—21no—
180C8×D83—44no—
181C4⋊Dic83—21no—
182C4⋊Dic83—24no—
183C4⋊Dic83—21no—
184C4⋊Dic83—21no—
185C4⋊Dic83—21no—
186C4⋊Dic83—21no—
187C4⋊Dic83C22×C412yes—
188Dic83⋊C4—24no—
189Dic83⋊C4—24no—
190Dic83⋊C4—24no—
191Dic83⋊C4—24no—
192Dic83⋊C4—42no—
193Dic83⋊C4—42no—
194Dic83⋊C4—81no—
195Dic83⋊C4C22⋊C414yes—
196C22⋊Dic83—24no—
197C22⋊Dic83—42no—
198C22⋊Dic83C22⋊C414yes—
199(C2×D83)⋊C4—24no—
200(C2×D83)⋊C4—42no—
201(C2×D83)⋊C4C22⋊C414yes—
202C4×Dic83—24no—
203C4×Dic83—42no—
204C4×Dic83C22×C412yes—
205C4×Dic83C2×D412yes—
206C24×C83C2×D411yescharacteristic
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—24no—
215C22×C4×C83—21no—
216C22×C4×C83—42no—
217C22×C4×C83—42no—
218C22×C4×C83—81no—
219C22×C4×C83—81no—
220C22×C4×C83—81no—
221C22×C4×C83C22×C412yes—
222C22×C4×C83C2×D411yescharacteristic
223C22×C4×C83C2×D412yes—
224C22×C4×C83C2411yescharacteristic
225C2×C8×C83—21no—
226C2×C8×C83—21no—
227C2×C8×C83—21no—
228C2×C8×C83—21no—
229C2×C8×C83—21no—
230C2×C8×C83—44no—
231C2×C8×C83#4112yes—
232C4⋊C4×C83—24no—
233C4⋊C4×C83—21no—
234C4⋊C4×C83—21no—
235C4⋊C4×C83—21no—
236C4⋊C4×C83—21no—
237C4⋊C4×C83—21no—
238C4⋊C4×C83—42no—
239C4⋊C4×C83C22×C412yes—
240C4⋊C4×C83C22×C412yes—
241C4⋊C4×C83#4112yes—
242C23×C83—21no—
243C23×C83—21no—
244C23×C83—21no—
245C23×C83—21no—
246C23×C83C2×C22⋊C412yes—
247C23×C83C2×SD1612yes—
248C23×C83C2×Q1612yes—
249C23×C83C22×D411yescharacteristic
250C22×D83—21no—
251C22×D83—21no—
252C22×D83—21no—
253C22×D83—21no—
254C22×D83C2×C22⋊C412yes—
255C22×D83C2×SD1612yes—
256C22×D83C2×Q1612yes—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—22no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83—22no—
266C2×C4×C83—41no—
267C2×C4×C83—41no—
268C2×C4×C83—41no—
269C2×C4×C83—41no—
270C2×C4×C83—41no—
271C2×C4×C83—41no—
272C2×C4×C83—41no—
273C2×C4×C83—41no—
274C2×C4×C83—41no—
275C2×C4×C83—84no—
276C2×C4×C83—84no—
277C2×C4×C83C2×C22⋊C412yes—
278C2×C4×C83C23×C411yescharacteristic
279C2×C4×C83C22×D411yescharacteristic
280C2×C4×C83C2×#4111yescharacteristic
281C2×C4×C83C2×#4111yescharacteristic
282C2×C4×C83H(5,𝔽2)11yescharacteristic
283C2×C4×C832−1+411yescharacteristic
284C22⋊D83#103116yescomplemented
285C2×Dic83—21no—
286C2×Dic83—21no—
287C2×Dic83—21no—
288C2×Dic83—21no—
289C2×Dic83—22no—
290C2×Dic83—22no—
291C2×Dic83—41no—
292C2×Dic83—41no—
293C2×Dic83—41no—
294C2×Dic83—41no—
295C2×Dic83—41no—
296C2×Dic83—41no—
297C2×Dic83—41no—
298C2×Dic83—41no—
299C2×Dic83—41no—
300C2×Dic83—41no—
301C2×Dic83C2×C22⋊C412yes—
302C2×Dic83C2×C22⋊C412yes—
303C2×Dic83C2×C22⋊C412yes—
304C2×Dic83C2×SD1612yes—
305C2×Dic83C2×Q1612yes—
306C4×D83—22no—
307C4×D83—22no—
308C4×D83—22no—
309C4×D83—22no—
310C4×D83—84no—
311C4×D83—84no—
312Dic166—22no—
313Dic166—22no—
314Dic166—41no—
315Dic166—41no—
316Dic166—84no—
317C8×C83—22no—
318C8×C83—41no—
319C83⋊C8—41no—
320C83⋊C8—41no—
321C22×C83—22no—
322C22×C83—22no—
323C22×C83—22no—
324C22×C83—22no—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83C2×#10314yes—
328C22×C83C22×C22⋊C411yescharacteristic
329C22×C83#54611yescharacteristic
330C22×C83#54711yescharacteristic
331C22×C83C22×SD1611yescharacteristic
332C22×C83C22×Q1611yescharacteristic
333C22×C83#57611yescharacteristic
334C22×C83#57711yescharacteristic
335C2×D83—22no—
336C2×D83—22no—
337C2×D83—22no—
338C2×D83—22no—
339C2×D83—22no—
340C2×D83—22no—
341C2×D83C2×#10314yes—
342C4×C83—22no—
343C4×C83—42no—
344C4×C83—42no—
345C4×C83—42no—
346C4×C83—81no—
347C4×C83C4×#4111yescharacteristic
348C4×C83#52011yescharacteristic
349C4×C83#54611yescharacteristic
350C4×C83#54711yescharacteristic
351Dic83—22no—
352Dic83—22no—
353Dic83—42no—
354Dic83—42no—
355Dic83—81no—
356Dic83—81no—
357Dic83C2×#10314yes—
358#22487—831nomaximal, Sylow
359C2×C83—24no—
360C2×C83#233911yescharacteristic
361C2×C83C22×#10311yescharacteristic
362C2×C83#289711yescharacteristic
363C2×C83#329511yescharacteristic
364C2×C83#329911yescharacteristic
365C2×C83#333511yescharacteristic
366C2×C83#333811yescharacteristic
367D83—24no—
368C2×#554—831no—
369C2×C8×D4—831no—
370D4×C4⋊C4—831no—
371#1990—831no—
372#1987—831no—
373#1892—831no—
374#1892—831no—
375#1872—831no—
376#1872—831no—
377#1824—831no—
378#1824—831no—
379#1803—831no—
380C4×#103—831no—
381C2×#340—831no—
382C2×#340D8311yescharacteristic, complemented
383C83#2248711yescharacteristic, complemented, Sylow
384C23×C8—831no—
385C23×C8C2×D8311yescharacteristic
386#554—838no—
387#554—1664no—
388C2×C4⋊Q8—831no—
389C2×#125—1661no—
390C2×C22⋊Q8—831no—
391C2×C22⋊Q8—831no—
392C2×C22⋊Q8—1661no—
393C2×C22⋊Q8—1661no—
394C2×C4×Q8—831no—
395C2×C4×D4—831no—
396C2×C4×D4—1661no—
397C2×C4×D4—1661no—
398C22×C4⋊C4—831no—
399C22×C4⋊C4—831no—
400C22×C4⋊C4C2×D8311yescharacteristic
401C22×C4⋊C4C2×D8311yescharacteristic
402C8×D4—1664no—
403C2×C4⋊C8—831no—
404C2×#103—831no—
405C2×#103—831no—
406C2×#103—831no—
407C2×#103—831no—
408C2×C22⋊C8—831no—
409C2×C22⋊C8—831no—
410C2×C4×C8—831no—
411#389—1661no—
412#385—1661no—
413#385—1661no—
414#384—831no—
415#380—831no—
416#380—831no—
417C4×C4⋊C4—831no—
418#340—831no—
419#340—831no—
420#340—831no—
421#340—831no—
422#340—831no—
423#340—831no—
424#340—831no—
425#340—831no—
426#340C2×D8311yescharacteristic
427#340C2×D8311yescharacteristic
428#340C2×D8311yescharacteristic
429#340C2×D8311yescharacteristic
430C22×Q8—831no—
431C22×Q8—1661no—
432C22×D4—831no—
433C23×C4—21no—
434C23×C4—21no—
435C23×C4—831no—
436C23×C4—1661no—
437C23×C4—1661no—
438C23×C4C22×D8311yescharacteristic
439C22×C8—22no—
440C22×C8—22no—
441C22×C8—41no—
442C22×C8—3321no—
443C22×C8—831no—
444C22×C8—831no—
445C22×C8—1662no—
446C22×C8—1662no—
447C22×C8C22×D8311yescharacteristic
448C22×C8C22×D8311yescharacteristic
449C4⋊Q8—834no—
450C4⋊Q8—1662no—
451#125—1668no—
452C22⋊Q8—834no—
453C22⋊Q8—834no—
454C22⋊Q8—1668no—
455C22⋊Q8—1668no—
456C22⋊Q8—1662no—
457C22⋊Q8—1662no—
458C4×Q8—834no—
459C4×Q8—1662no—
460C4×D4—3324no—
461C4×D4—834no—
462C4×D4—834no—
463C4×D4—1668no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—3321no—
470C2×C4⋊C4—831no—
471C2×C4⋊C4—831no—
472C2×C4⋊C4—834no—
473C2×C4⋊C4—831no—
474C2×C4⋊C4—831no—
475C2×C4⋊C4—1662no—
476C2×C4⋊C4—1661no—
477C2×C4⋊C4—1661no—
478C2×C4⋊C4—1662no—
479C2×C4⋊C4—1661no—
480C2×C4⋊C4—1661no—
481C2×C4⋊C4—1661no—
482C2×C4⋊C4—1661no—
483C2×C4⋊C4—1661no—
484C2×C4⋊C4—1661no—
485C2×C4⋊C4C4×D8314yescomplemented
486C2×C4⋊C4C22×D8311yescharacteristic
487C2×C4⋊C4C22×D8311yescharacteristic
488C2×C4⋊C4C22×D8311yescharacteristic
489C2×C4⋊C4C22×D8311yescharacteristic
490C2×C22⋊C4—831no—
491C2×C22⋊C4—831no—
492C2×C22⋊C4—1661no—
493C2×C22⋊C4—1661no—
494C2×C22⋊C4—1661no—
495C2×C22⋊C4—1661no—
496C2×C42—831no—
497C2×C42—1661no—
498C2×C42—1661no—
499C4⋊C8—1662no—
500#103—3321no—
501#103—3321no—
502#103—1662no—
503#103—1662no—
504C22⋊C8—1662no—
505C22⋊C8—1662no—
506C4×C8—1662no—
507#95—1661no—
508#95—1661no—
509#95—1661no—
510C24—831no—
511C24D4×D8311yescharacteristic
512C2×Q8—832no—
513C2×Q8—6641no—
514C2×Q8—6641no—
515C2×Q8—1664no—
516C2×Q8—1661no—
517C2×Q8—1661no—
518C2×Q8—1661no—
519C2×Q8—1661no—
520C2×Q8—1661no—
521C2×D4—834no—
522C2×D4—834no—
523C2×D4—834no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—81no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—3322no—
539C22×C4—3322no—
540C22×C4—831no—
541C22×C4—831no—
542C22×C4—831no—
543C22×C4—832no—
544C22×C4—832no—
545C22×C4—6641no—
546C22×C4—6641no—
547C22×C4—6641no—
548C22×C4—1664no—
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×C4C2×C4×D8312yes—
558C22×C4D4×D8312yes—
559C22×C4D4×D8311yescharacteristic
560C22×C4C23×D8311yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—44no—
567C2×C8—3324no—
568C2×C8—1661no—
569C2×C8—1661no—
570C2×C8—1661no—
571C2×C8—1661no—
572C2×C8—1661no—
573C2×C8—1661no—
574C2×C8#1305059012yes—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—24no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—42no—
582C4⋊C4—3322no—
583C4⋊C4—3322no—
584C4⋊C4—834no—
585C4⋊C4—832no—
586C4⋊C4—6641no—
587C4⋊C4—1664no—
588C4⋊C4—1664no—
589C4⋊C4—1664no—
590C4⋊C4—1664no—
591C4⋊C4—1661no—
592C4⋊C4—1661no—
593C4⋊C4—1661no—
594C4⋊C4—1661no—
595C4⋊C4—1661no—
596C4⋊C4—1664no—
597C4⋊C4C2×C4×D8312yes—
598C4⋊C4C2×C4×D8312yes—
599C4⋊C4#1305059012yes—
600C22⋊C4—3322no—
601C22⋊C4—3322no—
602C22⋊C4—834no—
603C22⋊C4—834no—
604C22⋊C4—1664no—
605C22⋊C4—1664no—
606C42—3322no—
607C42—832no—
608C42—832no—
609C42—1664no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—832no—
615C23—832no—
616C23—832no—
617C23—1661no—
618C23—1661no—
619C23—1661no—
620C23—1661no—
621C23C22⋊C4×D8312yes—
622C23SD16×D8312yes—
623C23Q16×D8312yes—
624C23C2×D4×D8311yescharacteristic
625Q8—3321no—
626Q8—3321no—
627Q8—6644no—
628Q8—1662no—
629Q8—1662no—
630D4—8316no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—84no—
650C2×C4—84no—
651C2×C4—3321no—
652C2×C4—3321no—
653C2×C4—3321no—
654C2×C4—3321no—
655C2×C4—3321no—
656C2×C4—3321no—
657C2×C4—3321no—
658C2×C4—3321no—
659C2×C4—3321no—
660C2×C4—3321no—
661C2×C4—832no—
662C2×C4—832no—
663C2×C4—832no—
664C2×C4—832no—
665C2×C4—832no—
666C2×C4—6644no—
667C2×C4—6644no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4—1661no—
671C2×C4—1661no—
672C2×C4—1661no—
673C2×C4—1661no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4—1662no—
677C2×C4—1662no—
678C2×C4C22⋊C4×D8312yes—
679C2×C4C22×C4×D8311yescharacteristic
680C2×C4C2×D4×D8311yescharacteristic
681C2×C4C2×#1305059011yescharacteristic
682C2×C4C2×#1305059011yescharacteristic
683C2×C4#1458183711yescharacteristic
684C2×C4#1458184011yescharacteristic
685C8—22no—
686C8—41no—
687C8—3321no—
688C8—3321no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—834no—
696C22—1662no—
697C22—1662no—
698C22—1662no—
699C22—1662no—
700C22—1662no—
701C22—1662no—
702C22#103×D8314yes—
703C22C2×C22⋊C4×D8311yescharacteristic
704C22#1912834111yescharacteristic
705C22#1912835211yescharacteristic
706C22C2×SD16×D8311yescharacteristic
707C22C2×Q16×D8311yescharacteristic
708C22#1912850211yescharacteristic
709C22#1912850711yescharacteristic
710C4—22no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—81no—
715C4—3322no—
716C4—3322no—
717C4—834no—
718C4—6641no—
719C4—6641no—
720C4—1662no—
721C4—1662no—
722C4C4×#1305059011yescharacteristic
723C4#1912818211yescharacteristic
724C4#1912834111yescharacteristic
725C4#1912835211yescharacteristic
726C2—24no—
727C2—1664no—
728C2#2491029011yescharacteristic
729C2C2×#103×D8311yescharacteristic
730C2#2491598411yescharacteristic
731C2#2491928311yescharacteristic
732C2#2491933511yescharacteristic
733C2#2491981611yescharacteristic
734C2#2491985311yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC2×#340×C83C2
socleC23×C83C22×D4
prime radicalC22×C22⋊D83D4
cosocleC22×C4×C83C24
hypercenterC2×#340D83
hypocenterC83#22487
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #24908422C2semidirect
5. #24908409C2semidirect
6. #24907886C2semidirect
7. #24907885C2semidirect
8. #24907770C2semidirect
9. #24907769C2semidirect
10. #24907553C2semidirect
11. #24907552C2semidirect
12. #24907467C2semidirect
13. #24907282C2semidirect
14. #340×D83C2semidirect
15. C2×#340×C83C2semidirect
18. #19128406C4semidirect
74. #14581791C2×C4semidirect
77. #14581772C2×C4semidirect
80. #14581771C2×C4semidirect
83. #14581757C2×C4semidirect
103. C4⋊C4×D83C2×C4semidirect
137. C2×C4⋊C4×C83C2×C4semidirect
284. C22⋊D83#103semidirect
382. C2×#340D83semidirect
383. C83#22487semidirect
485. C2×C4⋊C4C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191284062
C2×C8×C22⋊D832
C4⋊C4×C22⋊D832
#249084222
#249084092
#249078862
#249078852
#249077702
#249077692
#249075532
#249075522
#249074672
#249072822
#340×D832
C2×#340×C832
#2248783