Finite Group Databasebeta

← C2×#24917328 #36272000

Subgroups — C2×#24917328 #36272000

Order 21248.

2094 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128331C211yesmaximal, characteristic, complemented
2C2×#19128183C211yesmaximal, characteristic
3#24917328C2116yesmaximal, direct product factor
4C2×#19128006C211yesmaximal, characteristic, complemented
5C2×#19127986C211yesmaximal, characteristic, complemented
6C2×#19127984C211yesmaximal, characteristic, complemented
7C2×#19128004C211yesmaximal, characteristic, complemented
8C2×#19127998C211yesmaximal, characteristic, complemented
9C2×#19127992C211yesmaximal, characteristic, complemented
10C2×#19127990C211yesmaximal, characteristic, complemented
11C2×#19127742C211yesmaximal, characteristic, complemented
12C2×#106×D83C211yesmaximal, characteristic, complemented
13C2×#19127726C211yesmaximal, characteristic, complemented
14C2×#19127701C211yesmaximal, characteristic
15C2×#19127696C211yesmaximal, characteristic
16C2×#479×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C22×#13050573C2211yescharacteristic
19C22×C8×D83C2211yescharacteristic
20#19128331—24no—
21#19128331C2218yescomplemented
22C2×#14581792C2211yescharacteristic
23C2×#14581791—21no—
24C2×#14581791C2211yescharacteristic
25C2×#14581783C2211yescharacteristic
26C2×#14581782—21no—
27C2×#14581772—21no—
28C2×#14581770—21no—
29#19128183—24no—
30#19128183C2218yes—
31C2×Q8×Dic83C2211yescharacteristic
32C2×C4×D332—21no—
33C2×C4×D332C2211yescharacteristic
34C2×#14581754—21no—
35C2×#14581754C2211yescharacteristic
36C2×#14581750C2211yescharacteristic
37C2×#14581749—21no—
38C2×#14581749C2211yescharacteristic
39C2×C4⋊C4×D83—21no—
40C2×C4⋊C4×D83C2211yescharacteristic
41C2×C4⋊C4×D83C2211yescharacteristic
42#19128006C2218yescomplemented
43#19128004C2218yescomplemented
44#19127998C2218yescomplemented
45#19127992C2218yescomplemented
46#19127990C2218yescomplemented
47#19127986C2218yescomplemented
48#19127984C2218yescomplemented
49#19127742C2218yescomplemented
50C2×#14581725C2211yescharacteristic
51C2×#14581724C2211yescharacteristic
52C2×#14581724C2211yescharacteristic
53C2×#14581723C2211yescharacteristic
54C2×#14581723C2211yescharacteristic
55C2×#14581723C2211yescharacteristic
56#106×D83C2218yescomplemented
57#19127726C2218yescomplemented
58C2×C4⋊(C83⋊C8)C2211yescharacteristic
59C2×Dic83⋊C8C2211yescharacteristic
60C2×Dic83⋊C8C2211yescharacteristic
61#19127701C2218yes—
62#19127696C2218yes—
63C2×#14581716C2211yescharacteristic
64C2×#14581716C2211yescharacteristic
65C2×#14581714C2211yescharacteristic
66C2×#14581714C2211yescharacteristic
67C2×#14581712C2211yescharacteristic
68C2×#14581712C2211yescharacteristic
69C2×#125×C83C2211yescharacteristic
70C2×C4×Q8×C83C2211yescharacteristic
71#479×C83C2218yescomplemented
72C2×#107×C83C2211yescharacteristic
73C2×#106×C83C2211yescharacteristic
74C2×C4⋊C8×C83C2211yescharacteristic
75C2×#103×C83C2211yescharacteristic
76C2×#103×C83C2211yescharacteristic
77C2×#13050591—22no—
78C2×#13050591—24no—
79C2×#13050591Q818yescomplemented
80C2×#13050591C2314yes—
81C22×Dic166—21no—
82C22×Dic166—21no—
83C22×D332—21no—
84C22×D332C2311yescharacteristic
85C22×C4×D83—21no—
86C22×C4×D83—21no—
87C22×C4×D83—21no—
88C22×C4×D83—21no—
89C22×C4×D83—21no—
90C22×C4×D83C2311yescharacteristic
91C2×#13050573—24no—
92C2×#13050573C2314yes—
93C22×C83⋊C8C2311yescharacteristic
94C22×C83⋊C8C2311yescharacteristic
95C2×C8×D83—24no—
96C2×C8×D83C2314yes—
97#14581792—22no—
98#14581792C2314yes—
99#14581791—28no—
100#14581791—22no—
101#14581791C2314yes—
102#14581783—22no—
103#14581783C2314yes—
104#14581782—28no—
105#14581772—28no—
106#14581770—28no—
107Q8×Dic83—22no—
108Q8×Dic83C2314yes—
109C4×D332—28no—
110C4×D332—22no—
111C4×D332C2314yes—
112#14581754—28no—
113#14581754—22no—
114#14581754C2314yes—
115#14581750—22no—
116#14581750C2314yes—
117#14581749—28no—
118#14581749D414yes—
119#14581749C2314yes—
120C2×C4⋊Dic83—21no—
121C2×C4⋊Dic83—21no—
122C2×C4⋊Dic83—21no—
123C2×C4⋊Dic83C2311yescharacteristic
124C2×C4⋊Dic83C2311yescharacteristic
125C2×C4⋊Dic83C2311yescharacteristic
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4D411yescharacteristic
131C2×Dic83⋊C4D411yescharacteristic
132C4⋊C4×D83—22no—
133C4⋊C4×D83—22no—
134C4⋊C4×D83—28no—
135C4⋊C4×D83C2314yes—
136C4⋊C4×D83C2314yes—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4—21no—
139C2×(C2×D83)⋊C4—21no—
140C2×(C2×D83)⋊C4D411yescharacteristic
141C2×(C2×D83)⋊C4D411yescharacteristic
142C2×C4×Dic83—21no—
143C2×C4×Dic83—21no—
144C2×C4×Dic83C2311yescharacteristic
145#14581725C2314yes—
146#14581724C2314yes—
147#14581724C2314yes—
148#14581723C2314yes—
149#14581723C2314yes—
150#14581723C2314yes—
151C4⋊(C83⋊C8)C2314yes—
152Dic83⋊C8C2314yes—
153Dic83⋊C8C2314yes—
154#14581716C2314yes—
155#14581716C2314yes—
156#14581714C2314yes—
157#14581714C2314yes—
158#14581712C2314yes—
159#14581712C2314yes—
160C22×Q8×C83C2311yescharacteristic
161C22×C8×C83C2311yescharacteristic
162C22×C8×C83C2311yescharacteristic
163#125×C83—22no—
164#125×C83C2314yes—
165C4×Q8×C83—22no—
166C4×Q8×C83C2314yes—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C42×C83—21no—
174C2×C42×C83C2311yescharacteristic
175#107×C83C2314yes—
176#106×C83C2314yes—
177C4⋊C8×C83C2314yes—
178#103×C83C2314yes—
179#103×C83C2314yes—
180C23×D83—21no—
181C23×D83C2×D411yescharacteristic
182#13050591—216no—
183#13050591—28no—
184#13050591C2×Q8116yescomplemented
185C2×Dic166—24no—
186C2×Dic166—24no—
187C2×Dic166—82no—
188C2×Dic166—82no—
189C2×D332—28no—
190C2×D332—24no—
191C2×D332—21no—
192C2×D332—22no—
193C2×D332C2×Q814yes—
194C2×D332C2412yes—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—21no—
198C22×Dic83C2×D411yescharacteristic
199C22×Dic83C2×D411yescharacteristic
200C22×Dic83C2×D411yescharacteristic
201C2×C4×D83—28no—
202C2×C4×D83—24no—
203C2×C4×D83—24no—
204C2×C4×D83—24no—
205C2×C4×D83—24no—
206C2×C4×D83—24no—
207C2×C4×D83—82no—
208C2×C4×D83—82no—
209C2×C4×D83—82no—
210C2×C4×D83—82no—
211C2×C4×D83C2×D412yes—
212C2×C4×D83C2×Q814yes—
213C2×C4×D83#4114yes—
214C2×C4×D83C2412yes—
215#13050573—28no—
216C2×C83⋊C8—22no—
217C2×C83⋊C8—22no—
218C2×C83⋊C8C2412yes—
219C2×C83⋊C8C2412yes—
220C8×D83—28no—
221C4⋊Dic83—24no—
222C4⋊Dic83—21no—
223C4⋊Dic83—21no—
224C4⋊Dic83—21no—
225C4⋊Dic83—24no—
226C4⋊Dic83—24no—
227C4⋊Dic83C2412yes—
228C4⋊Dic83C2412yes—
229C4⋊Dic83C2412yes—
230Dic83⋊C4—24no—
231Dic83⋊C4—24no—
232Dic83⋊C4—24no—
233Dic83⋊C4—24no—
234Dic83⋊C4C2×D414yes—
235Dic83⋊C4C2×D414yes—
236(C2×D83)⋊C4—24no—
237(C2×D83)⋊C4—24no—
238(C2×D83)⋊C4—24no—
239(C2×D83)⋊C4C2×D414yes—
240(C2×D83)⋊C4C2×D414yes—
241C4×Dic83—24no—
242C4×Dic83—24no—
243C4×Dic83C2×D412yes—
244C4×Dic83C2412yes—
245C2×Q8×C83—21no—
246C2×Q8×C83—22no—
247C2×Q8×C83C2×Q814yes—
248C2×Q8×C83C2412yes—
249C22×C4×C83—21no—
250C22×C4×C83—21no—
251C22×C4×C83—21no—
252C22×C4×C83—21no—
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2×D411yescharacteristic
255C22×C4×C83C2411yescharacteristic
256C2×C8×C83—22no—
257C2×C8×C83—22no—
258C2×C8×C83C2412yes—
259C2×C8×C83C2412yes—
260C4⋊C4×C83—24no—
261C4⋊C4×C83—24no—
262C4⋊C4×C83—21no—
263C4⋊C4×C83—21no—
264C4⋊C4×C83—24no—
265C4⋊C4×C83—21no—
266C4⋊C4×C83C2412yes—
267C4⋊C4×C83C2412yes—
268C4⋊C4×C83C2412yes—
269C42×C83—24no—
270C42×C83C2×D412yes—
271C42×C83C2412yes—
272C23×C83C22×D411yescharacteristic
273C22×D83—22no—
274C22×D83—22no—
275C22×D83—24no—
276C22×D83—22no—
277C22×D83—42no—
278C22×D83—42no—
279C22×D83C22⋊Q814yes—
280C22×D83C22×D412yes—
281Q8×C83—24no—
282Q8×C83—22no—
283Q8×C83C22×Q814yes—
284C2×C4×C83—24no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—42no—
292C2×C4×C83—42no—
293C2×C4×C83—42no—
294C2×C4×C83C22×D412yes—
295C2×C4×C83C22×D412yes—
296C2×C4×C83C22×D411yescharacteristic
297C2×C4×C83C22×Q812yes—
298C2×C4×C83C2×#4112yes—
299C2×C4×C83C2511yescharacteristic
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—42no—
306C2×Dic83—42no—
307C2×Dic83—42no—
308C2×Dic83C22⋊Q814yes—
309C2×Dic83C22×D412yes—
310C2×Dic83C22×D412yes—
311C2×Dic83C22×D412yes—
312D332—216no—
313D332—24no—
314D332—22no—
315D332C22×Q814yes—
316C4×D83—216no—
317C4×D83—84no—
318C4×D83—84no—
319C4×D83—84no—
320C4×D83—84no—
321C4×D83C22⋊Q818yes—
322C4×D83C22×Q814yes—
323C4×D83C2×#4114yes—
324Dic166—84no—
325Dic166—84no—
326C8×C83—22no—
327C8×C83—22no—
328C83⋊C8—22no—
329C83⋊C8—22no—
330C22×C83C2×C22⋊Q812yes—
331C22×C83#57712yes—
332C22×C83#57712yes—
333C22×C83C23×D411yescharacteristic
334C2×D83—28no—
335C2×D83—22no—
336C2×D83—22no—
337C2×D83—24no—
338C2×D83—48no—
339C2×D83—42no—
340C2×D83—42no—
341C2×D83C2×C22⋊Q814yes—
342C4×C83—24no—
343C4×C83—22no—
344C4×C83—22no—
345C4×C83—42no—
346C4×C83—42no—
347C4×C83—42no—
348C4×C83C2×C22⋊Q812yes—
349C4×C83C23×Q811yescharacteristic
350C4×C83C22×#4111yescharacteristic
351Dic83—22no—
352Dic83—22no—
353Dic83—42no—
354Dic83—42no—
355Dic83—42no—
356Dic83C2×C22⋊Q814yes—
357C2×#3084—831nomaximal, Sylow
358C2×C83#308414yescomplemented
359C2×C83C22×C22⋊Q811yescharacteristic
360C2×C83C2×#57711yescharacteristic
361C2×C83C2×#57711yescharacteristic
362D83—24no—
363D83—44no—
364C2×#544—831no—
365C2×#520—831no—
366#3084—8316no—
367C2×#479—831no—
368C2×#479D8311yescharacteristic, complemented
369C2×#475—831no—
370C2×#475—831no—
371C2×#478—831no—
372C2×#478—831no—
373C2×#476—831no—
374C2×#476—831no—
375C2×#428—831no—
376C22×#106—831no—
377C2×#424—831no—
378C2×#417—831no—
379C2×#416—831no—
380C83C2×#308411yescharacteristic, complemented, Sylow
381C22×#41—831no—
382C22×M16—831no—
383C23×C8—831no—
384#544—838no—
385#544—1664no—
386C2×C4⋊Q8—831no—
387C2×C4⋊Q8—831no—
388C2×C4⋊Q8—1661no—
389C2×#125—831no—
390C2×#125—1661no—
391C2×#125C2×D8311yescharacteristic
392C2×C22⋊Q8—1661no—
393C2×C22⋊Q8—1661no—
394#520—838no—
395#520—1664no—
396C2×C4×Q8—831no—
397C2×C4×Q8C2×D8311yescharacteristic
398C2×C4×D4—831no—
399C2×C4×D4—831no—
400C2×C4×D4—1661no—
401C2×C4×D4—1661no—
402C2×#117—831no—
403C2×#117—831no—
404C2×#117—1661no—
405C22×C4⋊C4—831no—
406C22×C4⋊C4—831no—
407C22×C4⋊C4—1661no—
408#479—838no—
409#479C2×D8318yescomplemented
410#478—838no—
411#478—838no—
412#476—838no—
413#476—838no—
414#475—838no—
415#475—838no—
416#428—838no—
417C2×#107—831no—
418C2×#107C2×D8311yescharacteristic
419C2×#106—831no—
420C2×#106—831no—
421C2×#106—831no—
422C2×#106—831no—
423C2×#106—831no—
424C2×#106—838no—
425C2×#106C2×D8311yescharacteristic
426#424—838no—
427C2×C4⋊C8—831no—
428C2×C4⋊C8—831no—
429C2×C4⋊C8—831no—
430C2×C4⋊C8C2×D8311yescharacteristic
431#417—838no—
432#416—838no—
433C2×#103—831no—
434C2×#103—831no—
435C2×#103C2×D8311yescharacteristic
436C2×#103C2×D8311yescharacteristic
437C2×#102—831no—
438C2×#102—831no—
439C2×#102—831no—
440C2×#102—831no—
441C2×#41—838no—
442C2×#41—834no—
443C2×#41—1662no—
444C2×#41—1664no—
445C22×Q8—1661no—
446C22×Q8—1661no—
447C22×Q8C22×D8311yescharacteristic
448C22×D4—831no—
449C22×D4—1661no—
450C23×C4—831no—
451C23×C4—1661no—
452C23×C4—1661no—
453C23×C4—1661no—
454C23×C4—1661no—
455C23×C4—1661no—
456C2×M16—834no—
457C2×M16—1664no—
458C22×C8—831no—
459C22×C8—831no—
460C22×C8—834no—
461C22×C8—1664no—
462C22×C8C22×D8311yescharacteristic
463C22×C8C22×D8311yescharacteristic
464C4⋊Q8—834no—
465C4⋊Q8—834no—
466C4⋊Q8—1662no—
467C4⋊Q8—1668no—
468C4⋊Q8—1662no—
469#125—22no—
470#125—834no—
471#125—1662no—
472#125—1668no—
473#125C22×D8314yes—
474C22⋊Q8—1668no—
475C22⋊Q8—1668no—
476C4×Q8—22no—
477C4×Q8—834no—
478C4×Q8—1662no—
479C4×Q8C22×D8314yes—
480C4×D4—834no—
481C4×D4—834no—
482C4×D4—1668no—
483C4×D4—1662no—
484C4×D4—1668no—
485C4×D4—1662no—
486#117—834no—
487#117—834no—
488#117—834no—
489#117—1668no—
490#117—1662no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—831no—
495C2×C4⋊C4—831no—
496C2×C4⋊C4—831no—
497C2×C4⋊C4—831no—
498C2×C4⋊C4—831no—
499C2×C4⋊C4—834no—
500C2×C4⋊C4—834no—
501C2×C4⋊C4—1668no—
502C2×C4⋊C4—1662no—
503C2×C4⋊C4—1662no—
504C2×C4⋊C4—1661no—
505C2×C4⋊C4—1661no—
506C2×C4⋊C4—1661no—
507C2×C4⋊C4—1661no—
508C2×C4⋊C4—1661no—
509C2×C4⋊C4—1661no—
510C2×C4⋊C4—1661no—
511C2×C4⋊C4C22×D8311yescharacteristic
512C2×C4⋊C4C22×D8311yescharacteristic
513C2×C4⋊C4C22×D8311yescharacteristic
514C2×C22⋊C4—831no—
515C2×C22⋊C4—831no—
516C2×C22⋊C4—1661no—
517C2×C22⋊C4—1661no—
518C2×C22⋊C4—1661no—
519C2×C42—21no—
520C2×C42—831no—
521C2×C42—1661no—
522C2×C42—1661no—
523C2×C42C22×D8311yescharacteristic
524#107—834no—
525#107C22×D8314yes—
526#106—834no—
527#106—834no—
528#106—834no—
529#106—834no—
530#106—834no—
531#106C22×D8314yes—
532C4⋊C8—834no—
533C4⋊C8—834no—
534C4⋊C8—834no—
535C4⋊C8C22×D8314yes—
536#103—834no—
537#103—834no—
538#103C22×D8314yes—
539#103C22×D8314yes—
540#102—834no—
541#102—834no—
542#102—834no—
543#102—834no—
544C24—831no—
545C24—1661no—
546#41—8316no—
547#41—16616no—
548#41—1668no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—6642no—
552C2×Q8—6642no—
553C2×Q8—1664no—
554C2×Q8—1664no—
555C2×Q8Q8×D8314yes—
556C2×Q8C23×D8312yes—
557C2×D4—834no—
558C2×D4—832no—
559C2×D4—1664no—
560C2×D4—1668no—
561C2×D4—1661no—
562C2×D4—1662no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—831no—
568C22×C4—832no—
569C22×C4—834no—
570C22×C4—834no—
571C22×C4—832no—
572C22×C4—831no—
573C22×C4—831no—
574C22×C4—6642no—
575C22×C4—6642no—
576C22×C4—6642no—
577C22×C4—6642no—
578C22×C4—1664no—
579C22×C4—1664no—
580C22×C4—1668no—
581C22×C4—1664no—
582C22×C4—1664no—
583C22×C4—1661no—
584C22×C4—1661no—
585C22×C4—1661no—
586C22×C4—1664no—
587C22×C4D4×D8311yescharacteristic
588C22×C4D4×D8311yescharacteristic
589C22×C4C23×D8311yescharacteristic
590M16—1668no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—832no—
594C2×C8—832no—
595C2×C8—1668no—
596C2×C8—1662no—
597C2×C8—1662no—
598C2×C8C23×D8312yes—
599C2×C8C23×D8312yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—834no—
607C4⋊C4—834no—
608C4⋊C4—832no—
609C4⋊C4—832no—
610C4⋊C4—832no—
611C4⋊C4—1664no—
612C4⋊C4—1664no—
613C4⋊C4—1664no—
614C4⋊C4—1664no—
615C4⋊C4—1664no—
616C4⋊C4—1664no—
617C4⋊C4—1661no—
618C4⋊C4—1661no—
619C4⋊C4—1661no—
620C4⋊C4—1664no—
621C4⋊C4C23×D8312yes—
622C4⋊C4C23×D8312yes—
623C4⋊C4C23×D8312yes—
624C22⋊C4—834no—
625C22⋊C4—834no—
626C22⋊C4—1664no—
627C22⋊C4—1664no—
628C22⋊C4—1664no—
629C42—24no—
630C42—832no—
631C42—832no—
632C42—1664no—
633C42—1664no—
634C42D4×D8312yes—
635C42C23×D8312yes—
636C23—3322no—
637C23—3322no—
638C23—834no—
639C23—832no—
640C23—1664no—
641C23—1662no—
642C23—1662no—
643C23—1662no—
644C23C2×D4×D8311yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8—6644no—
648Q8—6644no—
649Q8C2×Q8×D8314yes—
650D4—834no—
651D4—16616no—
652D4—1664no—
653D4—1662no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—3322no—
665C2×C4—3322no—
666C2×C4—3322no—
667C2×C4—834no—
668C2×C4—832no—
669C2×C4—838no—
670C2×C4—834no—
671C2×C4—834no—
672C2×C4—832no—
673C2×C4—832no—
674C2×C4—6644no—
675C2×C4—6644no—
676C2×C4—6644no—
677C2×C4—6644no—
678C2×C4—16616no—
679C2×C4—1662no—
680C2×C4—1662no—
681C2×C4—1662no—
682C2×C4—1662no—
683C2×C4—1662no—
684C2×C4C2×D4×D8312yes—
685C2×C4C2×D4×D8312yes—
686C2×C4C2×D4×D8311yescharacteristic
687C2×C4C2×Q8×D8312yes—
688C2×C4#41×D8312yes—
689C2×C4C24×D8311yescharacteristic
690C8—22no—
691C8—22no—
692C8—1662no—
693C8—1662no—
694C22—3328no—
695C22—3322no—
696C22—3322no—
697C22—834no—
698C22—1664no—
699C22—1668no—
700C22—1662no—
701C22—1662no—
702C22C22⋊Q8×D8312yes—
703C22#1912850812yes—
704C22#1912851012yes—
705C22C22×D4×D8311yescharacteristic
706C4—22no—
707C4—22no—
708C4—24no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—3322no—
713C4—3322no—
714C4—3322no—
715C4—834no—
716C4—1662no—
717C4—1662no—
718C4C22⋊Q8×D8312yes—
719C4C22×Q8×D8311yescharacteristic
720C4C2×#41×D8311yescharacteristic
721C2—3324no—
722C2—1664no—
723C2#2491732814yesdirect product factor
724C2C2×C22⋊Q8×D8311yescharacteristic
725C2C2×#1912850811yescharacteristic
726C2C2×#1912851011yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#479×C83C2
socleC23×C83C22×D4
prime radicalC22×#13050591C22
hypercenterC2×#479D83
hypocenterC83C2×#3084
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#19128331C2semidirect
3. #24917328C2direct (N × H)
4. C2×#19128006C2semidirect
5. C2×#19127986C2semidirect
6. C2×#19127984C2semidirect
7. C2×#19128004C2semidirect
8. C2×#19127998C2semidirect
9. C2×#19127992C2semidirect
10. C2×#19127990C2semidirect
11. C2×#19127742C2semidirect
12. C2×#106×D83C2semidirect
13. C2×#19127726C2semidirect
16. C2×#479×C83C2semidirect
21. #19128331C22semidirect
42. #19128006C22semidirect
43. #19128004C22semidirect
44. #19127998C22semidirect
45. #19127992C22semidirect
46. #19127990C22semidirect
47. #19127986C22semidirect
48. #19127984C22semidirect
49. #19127742C22semidirect
56. #106×D83C22semidirect
57. #19127726C22semidirect
71. #479×C83C22semidirect
79. C2×#13050591Q8semidirect
184. #13050591C2×Q8semidirect
358. C2×C83#3084semidirect
368. C2×#479D83semidirect
380. C83C2×#3084semidirect
409. #479C2×D83semidirect
723. C2#24917328direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283312
C2×#191281832
#249173282
C2×#191280062
C2×#191279862
C2×#191279842
C2×#191280042
C2×#191279982
C2×#191279922
C2×#191279902
C2×#191277422
C2×#106×D832
C2×#191277262
C2×#191277012
C2×#191276962
C2×#479×C832
C2×#308483