Finite Group Databasebeta

← C2×#24918245 #36274957

Subgroups — C2×#24918245 #36274957

Order 21248.

2374 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128214C211yesmaximal, characteristic
2C2×C22⋊Q8×D83C211yesmaximal, characteristic, complemented
3#24918245C2116yesmaximal, direct product factor
4C2×#19128044C211yesmaximal, characteristic, complemented
5C2×#19128040C211yesmaximal, characteristic, complemented
6C2×#19128030C211yesmaximal, characteristic, complemented
7C2×#19128016C211yesmaximal, characteristic, complemented
8C2×#19127940C211yesmaximal, characteristic, complemented
9C2×#19127932C211yesmaximal, characteristic, complemented
10C2×#19127930C211yesmaximal, characteristic, complemented
11C2×#19127866C211yesmaximal, characteristic, complemented
12C2×#19127862C211yesmaximal, characteristic, complemented
13C2×#19127855C211yesmaximal, characteristic, complemented
14C2×#19127841C211yesmaximal, characteristic, complemented
15C22×(C2×D83)⋊C8C211yesmaximal, characteristic, complemented
16C2×#467×C83C211yesmaximal, characteristic, complemented
17C22×#13050591C2211yescharacteristic
18C22×Q8×D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C22×#13050580C2211yescharacteristic, complemented
21C22×#13050579C2211yescharacteristic, complemented
22C22×#13050577C2211yescharacteristic, complemented
23C23×C83⋊C8C2211yescharacteristic
24#19128214—24no—
25#19128214C2218yes—
26C2×#14581777—21no—
27C2×#14581772C2211yescharacteristic
28C2×#14581771C2211yescharacteristic
29C2×#14581770—21no—
30C2×#14581769—21no—
31C2×#14581768C2211yescharacteristic
32C2×#14581768C2211yescharacteristic
33C22⋊Q8×D83—24no—
34C22⋊Q8×D83C2218yescomplemented
35C2×#14581767C2211yescharacteristic
36C2×#14581766C2211yescharacteristic
37C2×#14581762—21no—
38C2×#14581754—21no—
39C2×(C22⋊D83)⋊C4—21no—
40C2×#14581750C2211yescharacteristic
41C2×C4⋊C4×D83—21no—
42C2×C4⋊C4×D83C2211yescharacteristic
43C2×C22⋊C4×D83—21no—
44#19128044C2218yescomplemented
45#19128040C2218yescomplemented
46#19128030C2218yescomplemented
47#19128016C2218yescomplemented
48#19127940C2218yescomplemented
49#19127932C2218yescomplemented
50#19127930C2218yescomplemented
51#19127866C2218yescomplemented
52#19127862C2218yescomplemented
53#19127855C2218yescomplemented
54#19127841C2218yescomplemented
55C2×#14581725C2211yescharacteristic, complemented
56C2×#14581724C2211yescharacteristic, complemented
57C2×#14581723C2211yescharacteristic, complemented
58C2×#14581717C2211yescharacteristic, complemented
59C2×#14581716C2211yescharacteristic, complemented
60C2×#14581716C2211yescharacteristic, complemented
61C2×#14581715C2211yescharacteristic, complemented
62C2×#14581714C2211yescharacteristic, complemented
63C2×#14581712C2211yescharacteristic, complemented
64C2×(C2×D83)⋊C8C2211yescharacteristic
65C2×(C2×D83)⋊C8C2211yescharacteristic
66C2×(C2×D83)⋊C8C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×(C2×D83)⋊C8C2218yescomplemented
69C22×Q16×C83C2211yescharacteristic, complemented
70C23×C8×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×C22⋊Q8×C83C2211yescharacteristic
73#467×C83C2218yescomplemented
74C2×#107×C83C2211yescharacteristic, complemented
75C2×#103×C83C2211yescharacteristic, complemented
76C2×#103×C83C2211yescharacteristic, complemented
77C24×D83D411yescharacteristic
78C2×#13050591—22no—
79C2×#13050591—42no—
80C2×#13050591—42no—
81C2×#13050591C2314yes—
82C22×Dic166—21no—
83C22×Dic166C2311yescharacteristic
84C2×Q8×D83—22no—
85C2×Q8×D83—42no—
86C2×Q8×D83—42no—
87C2×Q8×D83C2314yes—
88C22×D332—21no—
89C22×D332—21no—
90C22×D332C2311yescharacteristic
91C22×C22⋊D83—21no—
92C23×Dic83D411yescharacteristic
93C22×C4×D83—21no—
94C22×C4×D83—21no—
95C22×C4×D83—21no—
96C22×C4×D83—42no—
97C22×C4×D83—42no—
98C22×C4×D83D411yescharacteristic
99C22×C4×D83D414yes—
100C22×C4×D83D411yescharacteristic
101C22×C4×D83C2311yescharacteristic
102C22×C4×D83C2311yescharacteristic
103C22×C4×D83C2314yes—
104C2×#13050580—42no—
105C2×#13050580C2314yescomplemented
106C2×#13050579—42no—
107C2×#13050579C2314yescomplemented
108C2×#13050577—42no—
109C2×#13050577C2314yescomplemented
110C22×C83⋊C8—42no—
111C22×C83⋊C8C2311yescharacteristic
112C22×C83⋊C8C2311yescharacteristic
113C22×C83⋊C8C2314yes—
114#14581777—28no—
115#14581772—22no—
116#14581772C2314yes—
117#14581771—22no—
118#14581771C2314yes—
119#14581770—28no—
120#14581769—28no—
121#14581768—22no—
122#14581768—22no—
123#14581768C2314yes—
124#14581768C2314yes—
125#14581767—22no—
126#14581767C2314yes—
127#14581766—22no—
128#14581766C2314yes—
129#14581762—28no—
130#14581754—28no—
131(C22⋊D83)⋊C4—28no—
132#14581750—22no—
133#14581750C2314yes—
134C2×C4⋊Dic83—21no—
135C2×C4⋊Dic83C2311yescharacteristic
136C2×C4⋊Dic83C2311yescharacteristic
137C2×Dic83⋊C4—21no—
138C2×Dic83⋊C4—21no—
139C2×Dic83⋊C4—21no—
140C2×Dic83⋊C4—21no—
141C4⋊C4×D83—28no—
142C4⋊C4×D83—22no—
143C4⋊C4×D83C2314yes—
144C2×C22⋊Dic83—21no—
145C2×(C2×D83)⋊C4—21no—
146C2×(C2×D83)⋊C4—21no—
147C2×(C2×D83)⋊C4—21no—
148C2×(C2×D83)⋊C4—21no—
149C2×(C2×D83)⋊C4—21no—
150C2×(C2×D83)⋊C4—21no—
151C22⋊C4×D83—28no—
152C2×C4×Dic83—21no—
153#14581725C2314yescomplemented
154#14581724C2314yescomplemented
155#14581723C2314yescomplemented
156#14581717C2314yescomplemented
157#14581716C2314yescomplemented
158#14581716C2314yescomplemented
159#14581715C2314yescomplemented
160#14581714C2314yescomplemented
161#14581712C2314yescomplemented
162(C2×D83)⋊C8C2314yes—
163(C2×D83)⋊C8C2314yes—
164(C2×D83)⋊C8C2314yes—
165(C2×D83)⋊C8C2314yes—
166C22×Q8×C83C2311yescharacteristic
167C22×Q8×C83C2311yescharacteristic
168C23×C4×C83C2311yescharacteristic
169C2×Q16×C83—42no—
170C2×Q16×C83C2314yescomplemented
171C22×C8×C83—42no—
172C22×C8×C83C2311yescharacteristic
173C22×C8×C83C2311yescharacteristic
174C22×C8×C83C2314yes—
175C22⋊Q8×C83—22no—
176C22⋊Q8×C83—22no—
177C22⋊Q8×C83C2314yes—
178C22⋊Q8×C83C2314yes—
179C2×C4⋊C4×C83—21no—
180C2×C4⋊C4×C83—21no—
181C2×C4⋊C4×C83C2311yescharacteristic
182C2×C4⋊C4×C83C2311yescharacteristic
183C2×C22⋊C4×C83—21no—
184C2×C22⋊C4×C83—21no—
185#107×C83C2314yescomplemented
186#103×C83C2314yescomplemented
187#103×C83C2314yescomplemented
188C23×D83—24no—
189C23×D83—24no—
190C23×D83—21no—
191C23×D83—42no—
192C23×D83C2×D411yescharacteristic
193C23×D83C2×D414yes—
194C23×D83C2×D411yescharacteristic
195#13050591—44no—
196#13050591—44no—
197#13050591—48no—
198C2×Dic166—22no—
199C2×Dic166—22no—
200C2×Dic166—21no—
201C2×Dic166—24no—
202C2×Dic166—44no—
203C2×Dic166C2412yes—
204Q8×D83—44no—
205Q8×D83—44no—
206Q8×D83—48no—
207C2×D332—22no—
208C2×D332—22no—
209C2×D332—24no—
210C2×D332—24no—
211C2×D332—21no—
212C2×D332—44no—
213C2×D332—44no—
214C2×D332C2412yes—
215C2×C22⋊D83—24no—
216C2×C22⋊D83—44no—
217C22×Dic83—21no—
218C22×Dic83—21no—
219C22×Dic83—21no—
220C22×Dic83—42no—
221C22×Dic83C2×D411yescharacteristic
222C22×Dic83C2×D411yescharacteristic
223C22×Dic83C2×D414yes—
224C2×C4×D83—22no—
225C2×C4×D83—22no—
226C2×C4×D83—22no—
227C2×C4×D83—22no—
228C2×C4×D83—24no—
229C2×C4×D83—24no—
230C2×C4×D83—24no—
231C2×C4×D83—48no—
232C2×C4×D83—44no—
233C2×C4×D83—44no—
234C2×C4×D83—42no—
235C2×C4×D83—42no—
236C2×C4×D83—44no—
237C2×C4×D83—44no—
238C2×C4×D83—44no—
239C2×C4×D83C2×D412yes—
240C2×C4×D83C2×D412yes—
241C2×C4×D83C2×D414yes—
242C2×C4×D83C2×D414yes—
243C2×C4×D83C2412yes—
244C2×C4×D83C2412yes—
245#13050580—44no—
246#13050579—44no—
247#13050577—44no—
248C2×C83⋊C8—22no—
249C2×C83⋊C8—22no—
250C2×C83⋊C8—44no—
251C2×C83⋊C8C2412yes—
252C2×C83⋊C8C2412yes—
253C4⋊Dic83—21no—
254C4⋊Dic83—21no—
255C4⋊Dic83—24no—
256C4⋊Dic83C2412yes—
257C4⋊Dic83C2412yes—
258Dic83⋊C4—24no—
259Dic83⋊C4—24no—
260Dic83⋊C4—24no—
261Dic83⋊C4—24no—
262C22⋊Dic83—24no—
263(C2×D83)⋊C4—24no—
264(C2×D83)⋊C4—24no—
265(C2×D83)⋊C4—24no—
266(C2×D83)⋊C4—24no—
267(C2×D83)⋊C4—24no—
268(C2×D83)⋊C4—24no—
269C4×Dic83—24no—
270C24×C83C2×D411yescharacteristic
271C2×Q8×C83—21no—
272C2×Q8×C83—21no—
273C2×Q8×C83—22no—
274C2×Q8×C83—22no—
275C2×Q8×C83—22no—
276C2×Q8×C83—22no—
277C2×Q8×C83C2412yes—
278C2×Q8×C83C2412yes—
279C22×C4×C83—22no—
280C22×C4×C83—22no—
281C22×C4×C83—21no—
282C22×C4×C83—21no—
283C22×C4×C83—21no—
284C22×C4×C83—21no—
285C22×C4×C83C2×D412yes—
286C22×C4×C83C2×D411yescharacteristic
287C22×C4×C83C2412yes—
288C22×C4×C83C2411yescharacteristic
289Q16×C83—44no—
290C2×C8×C83—22no—
291C2×C8×C83—22no—
292C2×C8×C83—44no—
293C2×C8×C83C2412yes—
294C2×C8×C83C2412yes—
295C4⋊C4×C83—21no—
296C4⋊C4×C83—24no—
297C4⋊C4×C83—21no—
298C4⋊C4×C83—24no—
299C4⋊C4×C83C2412yes—
300C4⋊C4×C83C2412yes—
301C22⋊C4×C83—24no—
302C22⋊C4×C83—24no—
303C23×C83—22no—
304C23×C83—22no—
305C23×C83#13714yes—
306C23×C83C22×D412yes—
307C23×C83C22×D411yescharacteristic
308C22×D83—22no—
309C22×D83—22no—
310C22×D83—22no—
311C22×D83—22no—
312C22×D83—28no—
313C22×D83—22no—
314C22×D83—28no—
315C22×D83—22no—
316C22×D83—44no—
317C22×D83—416no—
318C22×D83—42no—
319C22×D83—42no—
320C22×D83—42no—
321C22×D83#13514yes—
322C22×D83C22×D412yes—
323C22×D83C22×D412yes—
324Q8×C83—22no—
325Q8×C83—22no—
326Q8×C83—22no—
327Q8×C83—22no—
328Q8×C83—42no—
329Q8×C83—42no—
330C2×C4×C83—22no—
331C2×C4×C83—24no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—22no—
335C2×C4×C83—22no—
336C2×C4×C83—22no—
337C2×C4×C83—22no—
338C2×C4×C83—42no—
339C2×C4×C83—42no—
340C2×C4×C83—42no—
341C2×C4×C83—42no—
342C2×C4×C83C22×D412yes—
343C2×C4×C83C22×D411yescharacteristic
344C2×C4×C83H(5,𝔽2)12yes—
345C2×C4×C83H(5,𝔽2)12yes—
346C2×C4×C83C2511yescharacteristic
347C22⋊D83—48no—
348C2×Dic83—22no—
349C2×Dic83—22no—
350C2×Dic83—22no—
351C2×Dic83—22no—
352C2×Dic83—22no—
353C2×Dic83—44no—
354C2×Dic83—42no—
355C2×Dic83—42no—
356C2×Dic83—42no—
357C2×Dic83C22×D412yes—
358C2×Dic83C22×D412yes—
359D332—22no—
360D332—22no—
361D332—48no—
362D332—48no—
363D332—42no—
364C4×D83—24no—
365C4×D83—24no—
366C4×D83—22no—
367C4×D83—22no—
368C4×D83—22no—
369C4×D83—22no—
370C4×D83—44no—
371C4×D83—44no—
372C4×D83—48no—
373C4×D83—48no—
374C4×D83—48no—
375Dic166—22no—
376Dic166—22no—
377Dic166—48no—
378Dic166—42no—
379C8×C83—22no—
380C8×C83—22no—
381C83⋊C8—22no—
382C83⋊C8—22no—
383C22×C83—22no—
384C22×C83—28no—
385C22×C83—22no—
386C22×C83#53412yes—
387C22×C83C2×#13512yes—
388C22×C83C2×#13714yes—
389C22×C83C2×#13712yes—
390C22×C83C23×D411yescharacteristic
391C2×D83—22no—
392C2×D83—28no—
393C2×D83—22no—
394C2×D83—22no—
395C2×D83—22no—
396C2×D83—22no—
397C2×D83—416no—
398C2×D83—44no—
399C2×D83—42no—
400C2×D83—42no—
401C2×D83—42no—
402C2×D83—84no—
403C2×D83C2×#13514yes—
404C4×C83—22no—
405C4×C83—42no—
406C4×C83—42no—
407C4×C83—42no—
408C4×C83—42no—
409C4×C83#53412yes—
410C4×C83C2×H(5,𝔽2)11yescharacteristic
411C4×C83C2×H(5,𝔽2)11yescharacteristic
412Dic83—22no—
413Dic83—22no—
414Dic83—42no—
415Dic83—42no—
416Dic83—42no—
417C2×#3190—831nomaximal, Sylow
418C2×C83—24no—
419C2×C83#319014yescomplemented
420C2×C83C2×#53411yescharacteristic
421C2×C83C22×#13511yescharacteristic
422C2×C83C22×#13711yescharacteristic
423D83—24no—
424D83—42no—
425D83—82no—
426C2×#525—831no—
427C22×C22⋊Q8—831no—
428#3190—8316no—
429C2×#485—831no—
430C2×#485—831no—
431C2×#483—831no—
432C2×#480—831no—
433C2×#467—831no—
434C2×#467D8311yescharacteristic, complemented
435C2×#465—831no—
436C2×#465—831no—
437C2×#452—831no—
438C2×#452—831no—
439C2×#451—831no—
440C2×#448—831no—
441C22×C22⋊C8—831no—
442C83C2×#319011yescharacteristic, complemented, Sylow
443C22×#41—831no—
444C23×Q8—831no—
445C24×C4—831no—
446C22×Q16—831no—
447C22×Q16C2×D8311yescharacteristic, complemented
448C22×SD16—831no—
449C22×SD16—831no—
450C23×C8—831no—
451C23×C8C2×D8311yescharacteristic
452#525—838no—
453#525—1664no—
454C2×#123—1661no—
455C2×C22⋊Q8—831no—
456C2×C22⋊Q8—831no—
457C2×C22⋊Q8—831no—
458C2×C22⋊Q8—838no—
459C2×C22⋊Q8—831no—
460C2×C22⋊Q8—1661no—
461C2×C22⋊Q8—1661no—
462C2×C22⋊Q8—1664no—
463C2×C22⋊Q8C2×D8311yescharacteristic
464C2×C22⋊Q8C2×D8311yescharacteristic
465C2×#121—831no—
466C2×#121—831no—
467C2×#120—1661no—
468C2×C4×D4—1661no—
469C2×C4×D4—1661no—
470C2×#117—831no—
471C22×C4⋊C4—831no—
472C22×C4⋊C4—1661no—
473C22×C22⋊C4—1661no—
474#485—838no—
475#485—838no—
476#483—838no—
477#480—838no—
478#467—838no—
479#467C2×D8318yescomplemented
480#465—838no—
481#465—838no—
482#452—838no—
483#452—838no—
484#451—838no—
485#448—838no—
486C2×#107—831no—
487C2×#107C2×D8311yescharacteristic, complemented
488C2×#106—831no—
489C2×#106—831no—
490C2×#103—831no—
491C2×#103—831no—
492C2×#103—831no—
493C2×#103—831no—
494C2×#103C2×D8311yescharacteristic, complemented
495C2×#103C2×D8311yescharacteristic, complemented
496C2×#102—831no—
497C2×#102—831no—
498C2×C22⋊C8—831no—
499C2×C22⋊C8—831no—
500C2×C22⋊C8—831no—
501C2×C22⋊C8—831no—
502C2×C22⋊C8—838no—
503C25—831no—
504C2×#41—3322no—
505C2×#41—3322no—
506C2×#41—834no—
507C2×#41—1662no—
508C22×Q8—3322no—
509C22×Q8—3322no—
510C22×Q8—834no—
511C22×Q8—831no—
512C22×Q8—1661no—
513C22×Q8—1662no—
514C22×Q8C22×D8311yescharacteristic
515C22×Q8C22×D8311yescharacteristic
516C22×D4—831no—
517C22×D4—1661no—
518C22×D4—1661no—
519C22×D4—1661no—
520C23×C4—3322no—
521C23×C4—3322no—
522C23×C4—831no—
523C23×C4—831no—
524C23×C4—831no—
525C23×C4—834no—
526C23×C4—834no—
527C23×C4—831no—
528C23×C4—831no—
529C23×C4—1661no—
530C23×C4—1661no—
531C23×C4—1661no—
532C23×C4C22×D8311yescharacteristic
533C2×Q16—42no—
534C2×Q16—3322no—
535C2×Q16—834no—
536C2×Q16C22×D8314yescomplemented
537C2×SD16—3322no—
538C2×SD16—3322no—
539C2×SD16—834no—
540C2×SD16—834no—
541C22×C8—42no—
542C22×C8—3322no—
543C22×C8—834no—
544C22×C8—831no—
545C22×C8—831no—
546C22×C8C22×D8311yescharacteristic
547C22×C8C22×D8311yescharacteristic
548C22×C8C22×D8314yes—
549#123—1668no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—834no—
553C22⋊Q8—834no—
554C22⋊Q8—834no—
555C22⋊Q8—834no—
556C22⋊Q8—1668no—
557C22⋊Q8—1668no—
558C22⋊Q8—1662no—
559C22⋊Q8—1662no—
560C22⋊Q8—1662no—
561C22⋊Q8—1662no—
562C22⋊Q8C22×D8314yes—
563C22⋊Q8C22×D8314yes—
564#121—834no—
565#121—834no—
566#121—1662no—
567#121—1662no—
568#120—1668no—
569C4×D4—1668no—
570C4×D4—1668no—
571#117—834no—
572#117—1662no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—831no—
576C2×C4⋊C4—831no—
577C2×C4⋊C4—834no—
578C2×C4⋊C4—1662no—
579C2×C4⋊C4—1668no—
580C2×C4⋊C4—1661no—
581C2×C4⋊C4—1661no—
582C2×C4⋊C4—1661no—
583C2×C4⋊C4—1661no—
584C2×C4⋊C4—1661no—
585C2×C4⋊C4C22×D8311yescharacteristic
586C2×C4⋊C4C22×D8311yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—1668no—
590C2×C22⋊C4—1661no—
591C2×C22⋊C4—1661no—
592C2×C22⋊C4—1661no—
593C2×C22⋊C4—1661no—
594C2×C22⋊C4—1661no—
595C2×C22⋊C4—1661no—
596C2×C22⋊C4—1661no—
597C2×C42—1661no—
598#107—834no—
599#107C22×D8314yescomplemented
600#106—834no—
601#106—834no—
602#103—834no—
603#103—834no—
604#103—834no—
605#103—834no—
606#103C22×D8314yescomplemented
607#103C22×D8314yescomplemented
608#102—834no—
609#102—834no—
610C22⋊C8—834no—
611C22⋊C8—834no—
612C22⋊C8—834no—
613C22⋊C8—834no—
614C24—3322no—
615C24—834no—
616C24—831no—
617C24—831no—
618C24—1664no—
619C24—1661no—
620C24—1664no—
621C24D4×D8311yescharacteristic
622#41—3328no—
623#41—3324no—
624#41—3324no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—3324no—
632C2×Q8—3324no—
633C2×Q8—3324no—
634C2×Q8—3328no—
635C2×Q8—832no—
636C2×Q8—1664no—
637C2×Q8—1662no—
638C2×Q8—1662no—
639C2×Q8—1661no—
640C2×Q8C23×D8312yes—
641C2×Q8C23×D8312yes—
642C2×D4—3324no—
643C2×D4—3324no—
644C2×D4—3324no—
645C2×D4—832no—
646C2×D4—1664no—
647C2×D4—1664no—
648C2×D4—1664no—
649C2×D4—1661no—
650C2×D4—1662no—
651C2×D4—1662no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—3322no—
659C22×C4—3322no—
660C22×C4—3328no—
661C22×C4—3324no—
662C22×C4—3324no—
663C22×C4—3324no—
664C22×C4—3324no—
665C22×C4—3324no—
666C22×C4—3322no—
667C22×C4—834no—
668C22×C4—834no—
669C22×C4—834no—
670C22×C4—831no—
671C22×C4—831no—
672C22×C4—832no—
673C22×C4—832no—
674C22×C4—832no—
675C22×C4—832no—
676C22×C4—1664no—
677C22×C4—1664no—
678C22×C4—1664no—
679C22×C4—1661no—
680C22×C4—1661no—
681C22×C4—1661no—
682C22×C4—1662no—
683C22×C4—1662no—
684C22×C4—1662no—
685C22×C4—1662no—
686C22×C4D4×D8312yes—
687C22×C4D4×D8311yescharacteristic
688C22×C4C23×D8312yes—
689C22×C4C23×D8311yescharacteristic
690Q16—44no—
691Q16—3324no—
692SD16—3324no—
693SD16—3324no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—44no—
697C2×C8—3324no—
698C2×C8—832no—
699C2×C8—832no—
700C2×C8—1662no—
701C2×C8—1662no—
702C2×C8C23×D8312yes—
703C2×C8C23×D8312yes—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—832no—
709C4⋊C4—832no—
710C4⋊C4—1664no—
711C4⋊C4—1664no—
712C4⋊C4—1664no—
713C4⋊C4—1664no—
714C4⋊C4—1661no—
715C4⋊C4—1661no—
716C4⋊C4—1664no—
717C4⋊C4C23×D8312yes—
718C4⋊C4C23×D8312yes—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—1664no—
722C22⋊C4—1664no—
723C22⋊C4—1664no—
724C22⋊C4—1664no—
725C22⋊C4—1664no—
726C22⋊C4—1664no—
727C22⋊C4—1664no—
728C42—1664no—
729C23—22no—
730C23—22no—
731C23—33216no—
732C23—3324no—
733C23—3322no—
734C23—3322no—
735C23—3322no—
736C23—834no—
737C23—832no—
738C23—832no—
739C23—1668no—
740C23—1662no—
741C23—1662no—
742C23—1668no—
743C23—1662no—
744C23—1662no—
745C23—1662no—
746C23—1662no—
747C23#1458182414yes—
748C23C2×D4×D8312yes—
749C23C2×D4×D8311yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—42no—
755Q8—42no—
756Q8—3328no—
757Q8—3322no—
758Q8—1662no—
759Q8—1662no—
760D4—3328no—
761D4—3328no—
762D4—3328no—
763D4—3322no—
764D4—1662no—
765D4—1662no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—3324no—
779C2×C4—3324no—
780C2×C4—3328no—
781C2×C4—3328no—
782C2×C4—3328no—
783C2×C4—3322no—
784C2×C4—3322no—
785C2×C4—3322no—
786C2×C4—3324no—
787C2×C4—832no—
788C2×C4—832no—
789C2×C4—1662no—
790C2×C4—1662no—
791C2×C4—1662no—
792C2×C4—1662no—
793C2×C4—1662no—
794C2×C4—1664no—
795C2×C4—1664no—
796C2×C4—1662no—
797C2×C4—1662no—
798C2×C4—1662no—
799C2×C4—1662no—
800C2×C4C2×D4×D8312yes—
801C2×C4C2×D4×D8311yescharacteristic
802C2×C4#1458183712yes—
803C2×C4#1458183812yes—
804C2×C4C24×D8311yescharacteristic
805C8—22no—
806C8—22no—
807C8—1662no—
808C8—1662no—
809C22—22no—
810C22—22no—
811C22—28no—
812C22—33216no—
813C22—3324no—
814C22—3322no—
815C22—3322no—
816C22—3322no—
817C22—834no—
818C22—6644no—
819C22—1662no—
820C22—1662no—
821C22—1662no—
822C22—1662no—
823C22—1662no—
824C22—1668no—
825C22#1912825912yes—
826C22#135×D8312yes—
827C22C2×#1458182414yes—
828C22C2×#1458182412yes—
829C22C22×D4×D8311yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—3322no—
836C4—3322no—
837C4—3322no—
838C4—1662no—
839C4—1662no—
840C4#1912825912yes—
841C4C2×#1458183711yescharacteristic
842C4C2×#1458183811yescharacteristic
843C2—24no—
844C2—3322no—
845C2—6642no—
846C2—1664no—
847C2#2491824514yesdirect product factor
848C2C2×#1912825911yescharacteristic
849C2C2×#135×D8311yescharacteristic
850C2C22×#1458182411yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#467×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128214C2
hypercenterC2×#467D83
hypocenterC83C2×#3190
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×D83C2semidirect
3. #24918245C2direct (N × H)
4. C2×#19128044C2semidirect
5. C2×#19128040C2semidirect
6. C2×#19128030C2semidirect
7. C2×#19128016C2semidirect
8. C2×#19127940C2semidirect
9. C2×#19127932C2semidirect
10. C2×#19127930C2semidirect
11. C2×#19127866C2semidirect
12. C2×#19127862C2semidirect
13. C2×#19127855C2semidirect
14. C2×#19127841C2semidirect
15. C22×(C2×D83)⋊C8C2semidirect
16. C2×#467×C83C2semidirect
20. C22×#13050580C22semidirect
21. C22×#13050579C22semidirect
22. C22×#13050577C22semidirect
34. C22⋊Q8×D83C22semidirect
44. #19128044C22semidirect
45. #19128040C22semidirect
46. #19128030C22semidirect
47. #19128016C22semidirect
48. #19127940C22semidirect
49. #19127932C22semidirect
50. #19127930C22semidirect
51. #19127866C22semidirect
52. #19127862C22semidirect
53. #19127855C22semidirect
54. #19127841C22semidirect
55. C2×#14581725C22semidirect
56. C2×#14581724C22semidirect
57. C2×#14581723C22semidirect
58. C2×#14581717C22semidirect
59. C2×#14581716C22semidirect
60. C2×#14581716C22semidirect
61. C2×#14581715C22semidirect
62. C2×#14581714C22semidirect
63. C2×#14581712C22semidirect
68. C2×(C2×D83)⋊C8C22semidirect
69. C22×Q16×C83C22semidirect
73. #467×C83C22semidirect
74. C2×#107×C83C22semidirect
75. C2×#103×C83C22semidirect
76. C2×#103×C83C22semidirect
105. C2×#13050580C23semidirect
107. C2×#13050579C23semidirect
109. C2×#13050577C23semidirect
153. #14581725C23semidirect
154. #14581724C23semidirect
155. #14581723C23semidirect
156. #14581717C23semidirect
157. #14581716C23semidirect
158. #14581716C23semidirect
159. #14581715C23semidirect
160. #14581714C23semidirect
161. #14581712C23semidirect
170. C2×Q16×C83C23semidirect
185. #107×C83C23semidirect
186. #103×C83C23semidirect
187. #103×C83C23semidirect
419. C2×C83#3190semidirect
434. C2×#467D83semidirect
442. C83C2×#3190semidirect
447. C22×Q16C2×D83semidirect
479. #467C2×D83semidirect
487. C2×#107C2×D83semidirect
494. C2×#103C2×D83semidirect
495. C2×#103C2×D83semidirect
536. C2×Q16C22×D83semidirect
599. #107C22×D83semidirect
606. #103C22×D83semidirect
607. #103C22×D83semidirect
847. C2#24918245direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282142
C2×C22⋊Q8×D832
#249182452
C2×#191280442
C2×#191280402
C2×#191280302
C2×#191280162
C2×#191279402
C2×#191279322
C2×#191279302
C2×#191278662
C2×#191278622
C2×#191278552
C2×#191278412
C22×(C2×D83)⋊C82
C2×#467×C832
C2×#319083