Finite Group Databasebeta

← C2×#24921546 #36312609

Subgroups — C2×#24921546 #36312609

Order 21248.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921546C2132yesmaximal, direct product factor
2C2×#19128436C211yesmaximal, characteristic, complemented
3C2×#19128433C212yesmaximal, complemented
4C2×Q8×Dic166C211yesmaximal, characteristic, complemented
5C2×#19128408C211yesmaximal, characteristic, complemented
6C2×#19128407C212yesmaximal, complemented
7C2×#19128372C211yesmaximal, characteristic, complemented
8C2×#19128360C212yesmaximal, complemented
9C2×#19128355C212yesmaximal, complemented
10C2×#19128349C214yesmaximal, complemented
11C2×#19128322C212yesmaximal, complemented
12C2×#19128317C214yesmaximal, complemented
13C2×#19128251C211yesmaximal, characteristic, complemented
14C2×#19128246C212yesmaximal, complemented
15C2×#19128237C212yesmaximal, complemented
16C2×#19128181C212yesmaximal, complemented
17C22×C4×Dic166C211yesmaximal, characteristic, complemented
18C2×#529×C83C211yesmaximal, characteristic, complemented
19C22×#13050590C2212yes—
20C22×#13050590C2212yes—
21C22×#13050589C2214yes—
22C23×Dic166C2211yescharacteristic
23#19128436C22116yescomplemented
24#19128433C22132yescomplemented
25Q8×Dic166C22116yescomplemented
26#19128408C22116yescomplemented
27#19128407C22132yescomplemented
28#19128372C22116yescomplemented
29#19128360C22132yescomplemented
30#19128355C22132yescomplemented
31#19128349C22164yescomplemented
32#19128322C22132yescomplemented
33#19128317C22164yescomplemented
34#19128251C22116yescomplemented
35#19128246C22132yescomplemented
36C2×#14581792C2212yes—
37C2×#14581792C2211yescharacteristic
38C2×#14581791C2214yes—
39C2×#14581791C2212yes—
40C2×#14581789C2211yescharacteristic
41C2×#14581788C2212yes—
42#19128237C22132yescomplemented
43C2×#14581787C2214yes—
44C2×#14581783C2212yes—
45C2×#14581781C2212yes—
46C2×#14581780C2212yes—
47C2×#14581780C2212yes—
48C2×#14581778C2214yes—
49C2×#14581778C2214yes—
50C2×#14581777C2214yes—
51C2×#14581776C2214yes—
52C2×#14581776C2214yes—
53C2×#14581774C2214yes—
54C2×#14581772C2214yes—
55C2×#14581771C2212yes—
56C2×#14581770C2214yes—
57C2×#14581770C2214yes—
58C2×#14581769C2214yes—
59C2×#14581766C2212yes—
60C2×#14581766C2212yes—
61C2×#14581766C2212yes—
62C2×#14581765C2214yes—
63C2×#14581764C2214yes—
64#19128181C22132yescomplemented
65C2×Q8×Dic83C2212yes—
66C2×C4×Dic166C2212yes—
67C2×C4×Dic166C2211yescharacteristic
68C2×C4×Dic166C2211yescharacteristic
69C2×C4×Dic166C2211yescharacteristic
70C2×C4×Dic166C2212yes—
71C2×C4×Dic166C2211yescharacteristic
72C2×C4×Dic166C2212yes—
73C2×C4×Dic166C22116yescomplemented
74C2×C4×D332C2212yes—
75C2×C4×D332C2212yes—
76C2×C4×D332C2212yes—
77C2×D4×Dic83C2212yes—
78C2×#14581754C2212yes—
79C2×#14581754C2212yes—
80C2×(C22⋊D83)⋊C4C2214yes—
81C2×(C22⋊D83)⋊C4C2214yes—
82C2×(C22⋊D83)⋊C4C2214yes—
83C2×#14581750C2214yes—
84C22×C4⋊Dic83C2211yescharacteristic
85C22×C4⋊Dic83C2212yes—
86C22×Dic83⋊C4C2212yes—
87C2×C4⋊C4×D83C2214yes—
88C22×C4×Dic83C2212yes—
89#529×C83C22116yescomplemented
90C2×#126×C83C2212yes—
91C2×#125×C83C2211yescharacteristic
92C2×#124×C83C2211yescharacteristic
93C2×#123×C83C2212yes—
94C2×C22⋊Q8×C83C2211yescharacteristic
95C2×#121×C83C2211yescharacteristic
96C2×C4×Q8×C83C2211yescharacteristic
97C2×C4×D4×C83C2212yes—
98C2×C4×D4×C83C2211yescharacteristic
99C2×#117×C83C2212yes—
100C22×C42×C83C2211yescharacteristic
101C2×#13050590—216no—
102C2×#13050590—48no—
103C2×#13050590C23116yes—
104C2×#13050590C23116yes—
105C2×#13050589—416no—
106C2×#13050589C23132yes—
107C22×Dic166—28no—
108C22×Dic166C2318yes—
109C22×Dic166C2312yes—
110C22×Dic166C2311yescharacteristic
111C22×Dic166C2312yes—
112C22×Dic166C2314yes—
113C22×Dic166C2311yescharacteristic
114C22×D332C2312yes—
115C22×D332C2312yes—
116C22×D332C2312yes—
117C22×C22⋊D83C2314yes—
118C22×C22⋊D83C2314yes—
119C22×C22⋊D83C2314yes—
120C23×Dic83C2312yes—
121C23×Dic83C2312yes—
122C23×Dic83C2314yes—
123C22×C4×D83C2314yes—
124C22×C4×D83C2314yes—
125C22×C4×D83C2314yes—
126#14581792C23116yes—
127#14581792C2318yes—
128#14581791C23132yes—
129#14581791C23116yes—
130#14581789C2318yes—
131#14581788C23116yes—
132#14581787C23132yes—
133#14581783C23116yes—
134#14581781C23116yes—
135#14581780C23116yes—
136#14581780C23116yes—
137#14581778C23132yes—
138#14581778C23132yes—
139#14581777C23132yes—
140#14581776C23132yes—
141#14581776C23132yes—
142#14581774C23132yes—
143#14581772C23132yes—
144#14581771C23116yes—
145#14581770C23132yes—
146#14581770C23132yes—
147#14581769C23132yes—
148#14581766C23116yes—
149#14581766C23116yes—
150#14581766C23116yes—
151#14581765C23132yes—
152#14581764C23132yes—
153Q8×Dic83C23116yes—
154C4×Dic166C2318yes—
155C4×Dic166C23116yes—
156C4×Dic166C2318yes—
157C4×Dic166C23116yes—
158C4×Dic166C2318yes—
159C4×Dic166C2318yes—
160C4×Dic166C23116yes—
161C4×D332C23116yes—
162C4×D332C23116yes—
163C4×D332C23116yes—
164D4×Dic83C23116yes—
165#14581754C23116yes—
166#14581754C23116yes—
167(C22⋊D83)⋊C4C23132yes—
168(C22⋊D83)⋊C4C23132yes—
169(C22⋊D83)⋊C4C23132yes—
170#14581750C23132yes—
171C2×C4⋊Dic83C2318yes—
172C2×C4⋊Dic83C23116yes—
173C2×C4⋊Dic83C2314yes—
174C2×C4⋊Dic83C2311yescharacteristic
175C2×C4⋊Dic83C2312yes—
176C2×C4⋊Dic83C2311yescharacteristic
177C2×C4⋊Dic83C2312yes—
178C2×C4⋊Dic83C2312yes—
179C2×C4⋊Dic83C2314yes—
180C2×Dic83⋊C4C23116yes—
181C2×Dic83⋊C4C2312yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2314yes—
187C4⋊C4×D83C23132yes—
188C2×C22⋊Dic83C2314yes—
189C2×(C2×D83)⋊C4C2314yes—
190C2×(C2×D83)⋊C4C2314yes—
191C2×(C2×D83)⋊C4C2314yes—
192C2×(C2×D83)⋊C4C2314yes—
193C2×(C2×D83)⋊C4C2314yes—
194C2×(C2×D83)⋊C4C2314yes—
195C2×C4×Dic83C2312yes—
196C2×C4×Dic83C2312yes—
197C2×C4×Dic83C2312yes—
198C2×C4×Dic83C2312yes—
199C2×C4×Dic83C23116yes—
200C2×C4×Dic83C2314yes—
201C22×Q8×C83C2311yescharacteristic
202C22×D4×C83C2312yes—
203C22×D4×C83C2311yescharacteristic
204C23×C4×C83C2311yescharacteristic
205C23×C4×C83C2311yescharacteristic
206C23×C4×C83C2311yescharacteristic
207C23×C4×C83C2312yes—
208#126×C83C23116yes—
209#125×C83C2318yes—
210#124×C83C2318yes—
211#123×C83C23116yes—
212C22⋊Q8×C83C2318yes—
213#121×C83C2318yes—
214C4×Q8×C83C2318yes—
215C4×D4×C83C23116yes—
216C4×D4×C83C2318yes—
217#117×C83C23116yes—
218C2×C4⋊C4×C83C2312yes—
219C2×C4⋊C4×C83C2312yes—
220C2×C4⋊C4×C83C2311yescharacteristic
221C2×C4⋊C4×C83C2312yes—
222C2×C4⋊C4×C83C2311yescharacteristic
223C2×C4⋊C4×C83C2312yes—
224C2×C22⋊C4×C83C2312yes—
225C2×C22⋊C4×C83C2312yes—
226C2×C22⋊C4×C83C2312yes—
227C2×C22⋊C4×C83C2312yes—
228C2×C22⋊C4×C83C2312yes—
229C2×C42×C83C2311yescharacteristic
230C2×C42×C83C2311yescharacteristic
231C2×C42×C83C2311yescharacteristic
232C2×C42×C83C2311yescharacteristic
233C2×C42×C83C2318yes—
234C2×C42×C83C2312yes—
235C23×D83C2414yes—
236#13050590—264no—
237#13050590—432no—
238#13050589—464no—
239C2×Dic166—24no—
240C2×Dic166—28no—
241C2×Dic166—232no—
242C2×Dic166—48no—
243C2×Dic166—44no—
244C2×Dic166#4118yescomplemented
245C2×Dic166C2418yes—
246C2×Dic166C2414yes—
247C2×Dic166C2418yes—
248C2×Dic166C24116yes—
249C2×Dic166C2414yes—
250C2×D332—28no—
251C2×D332—28no—
252C2×D332—44no—
253C2×D332C2418yes—
254C2×D332C2418yes—
255C2×D332C2418yes—
256C2×C22⋊D83—216no—
257C2×C22⋊D83—216no—
258C2×C22⋊D83—48no—
259C2×C22⋊D83C24116yes—
260C2×C22⋊D83C24116yes—
261C2×C22⋊D83C24116yes—
262C22×Dic83—28no—
263C22×Dic83—28no—
264C22×Dic83—48no—
265C22×Dic83C2418yes—
266C22×Dic83C2418yes—
267C22×Dic83C2412yes—
268C22×Dic83C2414yes—
269C22×Dic83C2412yes—
270C22×Dic83C2412yes—
271C22×Dic83C24116yes—
272C22×Dic83C2412yes—
273C2×C4×D83—216no—
274C2×C4×D83—48no—
275C2×C4×D83—48no—
276C2×C4×D83C24116yes—
277C2×C4×D83C24116yes—
278C2×C4×D83C24116yes—
279C4⋊Dic83C2414yes—
280C4⋊Dic83C2418yes—
281C4⋊Dic83C2418yes—
282C4⋊Dic83C24116yes—
283C4⋊Dic83C2418yes—
284C4⋊Dic83C24116yes—
285C4⋊Dic83C2414yes—
286Dic83⋊C4C24116yes—
287Dic83⋊C4C2418yes—
288Dic83⋊C4C2418yes—
289Dic83⋊C4C24116yes—
290Dic83⋊C4C2418yes—
291Dic83⋊C4C2418yes—
292C22⋊Dic83C24116yes—
293(C2×D83)⋊C4C24116yes—
294(C2×D83)⋊C4C24116yes—
295(C2×D83)⋊C4C24116yes—
296(C2×D83)⋊C4C24116yes—
297(C2×D83)⋊C4C24116yes—
298(C2×D83)⋊C4C24116yes—
299C4×Dic83C2418yes—
300C4×Dic83C24116yes—
301C4×Dic83C2418yes—
302C4×Dic83C2418yes—
303C4×Dic83C2418yes—
304C24×C83C2412yes—
305C24×C83C2411yescharacteristic
306C2×Q8×C83—24no—
307C2×Q8×C83C2414yes—
308C2×D4×C83—28no—
309C2×D4×C83—24no—
310C2×D4×C83C2418yes—
311C2×D4×C83C2414yes—
312C22×C4×C83—24no—
313C22×C4×C83—24no—
314C22×C4×C83—28no—
315C22×C4×C83—24no—
316C22×C4×C83C2414yes—
317C22×C4×C83C2414yes—
318C22×C4×C83C2418yes—
319C22×C4×C83C2411yescharacteristic
320C22×C4×C83C2412yes—
321C22×C4×C83C2412yes—
322C22×C4×C83C2411yescharacteristic
323C22×C4×C83C2411yescharacteristic
324C22×C4×C83C2414yes—
325C22×C4×C83C2411yescharacteristic
326C22×C4×C83C2412yes—
327C22×C4×C83C2411yescharacteristic
328C22×C4×C83C2411yescharacteristic
329C4⋊C4×C83C2418yes—
330C4⋊C4×C83C2418yes—
331C4⋊C4×C83C2418yes—
332C4⋊C4×C83C2414yes—
333C4⋊C4×C83C2418yes—
334C4⋊C4×C83C2414yes—
335C22⋊C4×C83C2418yes—
336C22⋊C4×C83C2418yes—
337C22⋊C4×C83C2418yes—
338C22⋊C4×C83C2418yes—
339C22⋊C4×C83C2418yes—
340C42×C83C2414yes—
341C42×C83C2418yes—
342C42×C83C2414yes—
343C42×C83C2414yes—
344C42×C83C2414yes—
345C23×C83—22no—
346C23×C83—22no—
347C23×C83—24no—
348C23×C83—24no—
349C23×C83—24no—
350C23×C83H(5,𝔽2)14yes—
351C23×C83C2514yes—
352C23×C83C2512yes—
353C23×C83C2511yescharacteristic
354C22×D83—28no—
355C22×D83—28no—
356C22×D83—28no—
357C22×D83C2518yes—
358Q8×C83—28no—
359D4×C83—216no—
360D4×C83—28no—
361C2×C4×C83—24no—
362C2×C4×C83—22no—
363C2×C4×C83—22no—
364C2×C4×C83—22no—
365C2×C4×C83—28no—
366C2×C4×C83—24no—
367C2×C4×C83—22no—
368C2×C4×C83—24no—
369C2×C4×C83—28no—
370C2×C4×C83—216no—
371C2×C4×C83—28no—
372C2×C4×C83C2×#4114yes—
373C2×C4×C832−1+414yes—
374C2×C4×C83C2512yes—
375C2×C4×C83C2512yes—
376C2×C4×C83C2512yes—
377C2×C4×C83C2512yes—
378C2×C4×C83C2514yes—
379C2×C4×C83C2514yes—
380C2×C4×C83C2514yes—
381C2×C4×C83C2512yes—
382C2×C4×C83C2512yes—
383C22⋊D83—232no—
384C22⋊D83—232no—
385C22⋊D83—416no—
386C2×Dic83—24no—
387C2×Dic83—24no—
388C2×Dic83—28no—
389C2×Dic83—24no—
390C2×Dic83—216no—
391C2×Dic83—216no—
392C2×Dic83—416no—
393C2×Dic83C2×#4118yes—
394C2×Dic83C2514yes—
395C2×Dic83C2514yes—
396C2×Dic83C2514yes—
397C2×Dic83C2518yes—
398C2×Dic83C2514yes—
399D332—216no—
400D332—216no—
401D332—48no—
402C4×D83—232no—
403C4×D83—416no—
404C4×D83—416no—
405Dic166—28no—
406Dic166—216no—
407Dic166—416no—
408Dic166—48no—
409Dic166C2×#41116yescomplemented
410C22×C83—22no—
411C22×C83—22no—
412C22×C83—28no—
413C22×C83—24no—
414C22×C83—24no—
415C22×C83—24no—
416C22×C83—48no—
417C22×C83C22×#4112yes—
418C22×C83C2×H(5,𝔽2)14yes—
419C22×C83C2×H(5,𝔽2)12yes—
420C22×C83C2×2−1+412yes—
421C22×C83C2611yescharacteristic
422C2×D83—28no—
423C2×D83—28no—
424C2×D83—28no—
425C2×D83—416no—
426C4×C83—22no—
427C4×C83—24no—
428C4×C83—24no—
429C4×C83—22no—
430C4×C83—22no—
431C4×C83—22no—
432C4×C83—24no—
433C4×C83C22×#4114yes—
434C4×C83C2×2−1+414yes—
435Dic83—24no—
436Dic83—28no—
437Dic83—24no—
438Dic83—24no—
439Dic83C22×#4118yes—
440C2×#3522—831nomaximal, Sylow
441C2×C83—24no—
442C2×C83—44no—
443C2×C83#352214yescomplemented
444C2×C83C23×#4111yescharacteristic
445C2×C83C22×H(5,𝔽2)11yescharacteristic
446C2×C83C22×2−1+411yescharacteristic
447D83—48no—
448#3522—8332no—
449C2×#559—832no—
450C2×#559—831no—
451C2×Q82—831no—
452C2×#554—832no—
453C2×#554—831no—
454C2×#550—831no—
455C2×#548—832no—
456C2×#547—834no—
457C2×#547—832no—
458C2×#542—834no—
459C2×#542—832no—
460C2×#532—831no—
461C2×#532—832no—
462C2×#529—832no—
463C2×#529D8311yescharacteristic, complemented
464C2×#520—832no—
465C22×C4×Q8—831no—
466C83C2×#352211yescharacteristic, complemented, Sylow
467C22×#41—834no—
468C22×#41—832no—
469C22×#41—832no—
470C23×Q8—831no—
471#559—8332no—
472#559—8316no—
473Q82—8316no—
474#554—8332no—
475#554—8316no—
476#550—8316no—
477#548—8332no—
478#547—8364no—
479#547—8332no—
480#542—8364no—
481#542—8332no—
482#532—8332no—
483#532—8316no—
484C2×C4⋊Q8—832no—
485C2×C4⋊Q8—834no—
486C2×C4⋊Q8—831no—
487C2×C4⋊Q8—832no—
488C2×#127—832no—
489C2×#127—831no—
490#529—8332no—
491#529C2×D83116yescomplemented
492C2×#126—834no—
493C2×#126C2×D8312yes—
494C2×#125—832no—
495C2×#125C2×D8311yescharacteristic
496C2×#124—832no—
497C2×#124—834no—
498C2×#124—834no—
499C2×#124—832no—
500C2×#124—832no—
501C2×#124C2×D8311yescharacteristic
502C2×#123—834no—
503C2×#123—834no—
504C2×#123—834no—
505C2×#123—834no—
506C2×#123C2×D8312yes—
507C2×C22⋊Q8—832no—
508C2×C22⋊Q8—834no—
509C2×C22⋊Q8—834no—
510C2×C22⋊Q8—834no—
511C2×C22⋊Q8—834no—
512C2×C22⋊Q8C2×D8311yescharacteristic
513C2×#121—834no—
514C2×#121—832no—
515C2×#121—832no—
516C2×#121—832no—
517C2×#121—834no—
518C2×#121C2×D8311yescharacteristic
519#520—8332no—
520C2×C4×Q8—832no—
521C2×C4×Q8—831no—
522C2×C4×Q8—832no—
523C2×C4×Q8—831no—
524C2×C4×Q8—831no—
525C2×C4×Q8—831no—
526C2×C4×Q8—832no—
527C2×C4×Q8—8316no—
528C2×C4×Q8—832no—
529C2×C4×Q8C2×D8311yescharacteristic
530C2×C4×D4—832no—
531C2×C4×D4—832no—
532C2×C4×D4—832no—
533C2×C4×D4—834no—
534C2×C4×D4—834no—
535C2×C4×D4—834no—
536C2×C4×D4—832no—
537C2×C4×D4—832no—
538C2×C4×D4—832no—
539C2×C4×D4C2×D8312yes—
540C2×C4×D4C2×D8311yescharacteristic
541C2×#117—834no—
542C2×#117C2×D8312yes—
543C22×C4⋊C4—832no—
544C22×C4⋊C4—831no—
545C22×C4⋊C4—832no—
546C22×C4⋊C4—834no—
547C22×C42—832no—
548C22×C42C2×D8311yescharacteristic
549C2×#41—3328no—
550C2×#41—33216no—
551C2×#41—8332no—
552C2×#41—8316no—
553C2×#41—8316no—
554C2×#41—16616no—
555C22×Q8—834no—
556C22×Q8—832no—
557C22×Q8—831no—
558C22×Q8—832no—
559C22×Q8—831no—
560C22×Q8—838no—
561C22×Q8—1668no—
562C22×Q8C22×D8311yescharacteristic
563C22×D4—834no—
564C22×D4—834no—
565C22×D4—834no—
566C22×D4—832no—
567C22×D4—832no—
568C22×D4—832no—
569C22×D4C22×D8311yescharacteristic
570C22×D4C22×D8312yes—
571C23×C4—834no—
572C23×C4—834no—
573C23×C4—834no—
574C23×C4—832no—
575C23×C4—832no—
576C23×C4—834no—
577C23×C4C22×D8311yescharacteristic
578C23×C4C22×D8312yes—
579C23×C4C22×D8311yescharacteristic
580C23×C4C22×D8311yescharacteristic
581C4⋊Q8—8316no—
582C4⋊Q8—8332no—
583C4⋊Q8—838no—
584C4⋊Q8—8316no—
585#127—8316no—
586#127—838no—
587#126—8332no—
588#126C22×D83116yes—
589#125—8316no—
590#125C22×D8318yes—
591#124—8316no—
592#124—8332no—
593#124—8332no—
594#124—8316no—
595#124—8316no—
596#124C22×D8318yes—
597#123—8332no—
598#123—8332no—
599#123—8332no—
600#123—8332no—
601#123C22×D83116yes—
602C22⋊Q8—8316no—
603C22⋊Q8—8332no—
604C22⋊Q8—8332no—
605C22⋊Q8—8332no—
606C22⋊Q8—8332no—
607C22⋊Q8C22×D8318yes—
608#121—8332no—
609#121—8316no—
610#121—8316no—
611#121—8316no—
612#121—8332no—
613#121C22×D8318yes—
614C4×Q8—8316no—
615C4×Q8—838no—
616C4×Q8—8316no—
617C4×Q8—838no—
618C4×Q8—838no—
619C4×Q8—838no—
620C4×Q8—8316no—
621C4×Q8—8316no—
622C4×Q8C22×D8318yes—
623C4×D4—8316no—
624C4×D4—8316no—
625C4×D4—8316no—
626C4×D4—8332no—
627C4×D4—8332no—
628C4×D4—8332no—
629C4×D4—8316no—
630C4×D4—8316no—
631C4×D4—8316no—
632C4×D4C22×D83116yes—
633C4×D4C22×D8318yes—
634#117—8332no—
635#117C22×D83116yes—
636C2×C4⋊C4—832no—
637C2×C4⋊C4—831no—
638C2×C4⋊C4—834no—
639C2×C4⋊C4—834no—
640C2×C4⋊C4—832no—
641C2×C4⋊C4—832no—
642C2×C4⋊C4—831no—
643C2×C4⋊C4—832no—
644C2×C4⋊C4—832no—
645C2×C4⋊C4—832no—
646C2×C4⋊C4—8316no—
647C2×C4⋊C4—838no—
648C2×C4⋊C4—8316no—
649C2×C4⋊C4—832no—
650C2×C4⋊C4—834no—
651C2×C4⋊C4—834no—
652C2×C4⋊C4—8332no—
653C2×C4⋊C4C22×D8312yes—
654C2×C4⋊C4C22×D8312yes—
655C2×C4⋊C4C22×D8311yescharacteristic
656C2×C4⋊C4C22×D8311yescharacteristic
657C2×C4⋊C4C22×D8312yes—
658C2×C4⋊C4C22×D8312yes—
659C2×C22⋊C4—834no—
660C2×C22⋊C4—834no—
661C2×C22⋊C4—834no—
662C2×C22⋊C4—834no—
663C2×C22⋊C4—834no—
664C2×C22⋊C4—834no—
665C2×C22⋊C4—834no—
666C2×C22⋊C4C22×D8312yes—
667C2×C22⋊C4C22×D8312yes—
668C2×C22⋊C4C22×D8312yes—
669C2×C22⋊C4C22×D8312yes—
670C2×C22⋊C4C22×D8312yes—
671C2×C42—832no—
672C2×C42—834no—
673C2×C42—832no—
674C2×C42—832no—
675C2×C42—832no—
676C2×C42—8316no—
677C2×C42C22×D8311yescharacteristic
678C2×C42C22×D8312yes—
679C2×C42C22×D8311yescharacteristic
680C2×C42C22×D8311yescharacteristic
681C2×C42C22×D8311yescharacteristic
682C2×C42C22×D8318yes—
683C24—834no—
684C24C23×D8312yes—
685C24C23×D8311yescharacteristic
686#41—33232no—
687#41—33264no—
688#41—16664no—
689C2×Q8—24no—
690C2×Q8—3324no—
691C2×Q8—3328no—
692C2×Q8—838no—
693C2×Q8—8316no—
694C2×Q8—838no—
695C2×Q8—834no—
696C2×Q8—838no—
697C2×Q8—834no—
698C2×Q8—1668no—
699C2×Q8—16632no—
700C2×Q8—1664no—
701C2×Q8C23×D8314yes—
702C2×D4—28no—
703C2×D4—24no—
704C2×D4—3324no—
705C2×D4—3328no—
706C2×D4—8316no—
707C2×D4—8316no—
708C2×D4—8316no—
709C2×D4—838no—
710C2×D4—838no—
711C2×D4—838no—
712C2×D4—16616no—
713C2×D4—16616no—
714C2×D4—1668no—
715C2×D4—1668no—
716C2×D4C23×D8314yes—
717C2×D4C23×D8318yes—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—28no—
721C22×C4—24no—
722C22×C4—3328no—
723C22×C4—3328no—
724C22×C4—3328no—
725C22×C4—8316no—
726C22×C4—8316no—
727C22×C4—8316no—
728C22×C4—832no—
729C22×C4—838no—
730C22×C4—838no—
731C22×C4—832no—
732C22×C4—832no—
733C22×C4—832no—
734C22×C4—834no—
735C22×C4—8316no—
736C22×C4—16616no—
737C22×C4—1668no—
738C22×C4—1668no—
739C22×C4C23×D8314yes—
740C22×C4C23×D8314yes—
741C22×C4C23×D8314yes—
742C22×C4C23×D8318yes—
743C22×C4C23×D8311yescharacteristic
744C22×C4C23×D8312yes—
745C22×C4C23×D8311yescharacteristic
746C22×C4C23×D8311yescharacteristic
747C22×C4C23×D8311yescharacteristic
748C22×C4C23×D8312yes—
749C22×C4C23×D8312yes—
750C22×C4C23×D8311yescharacteristic
751C22×C4C23×D8311yescharacteristic
752C4⋊C4—838no—
753C4⋊C4—834no—
754C4⋊C4—8316no—
755C4⋊C4—8316no—
756C4⋊C4—838no—
757C4⋊C4—838no—
758C4⋊C4—834no—
759C4⋊C4—838no—
760C4⋊C4—838no—
761C4⋊C4—838no—
762C4⋊C4—838no—
763C4⋊C4—8316no—
764C4⋊C4—8316no—
765C4⋊C4C23×D8318yes—
766C4⋊C4C23×D8318yes—
767C4⋊C4C23×D8314yes—
768C4⋊C4C23×D8314yes—
769C4⋊C4C23×D8318yes—
770C4⋊C4C23×D8318yes—
771C22⋊C4—8316no—
772C22⋊C4—8316no—
773C22⋊C4—8316no—
774C22⋊C4—8316no—
775C22⋊C4—8316no—
776C22⋊C4—8316no—
777C22⋊C4—8316no—
778C22⋊C4C23×D8318yes—
779C22⋊C4C23×D8318yes—
780C22⋊C4C23×D8318yes—
781C22⋊C4C23×D8318yes—
782C22⋊C4C23×D8318yes—
783C42—838no—
784C42—838no—
785C42—838no—
786C42—838no—
787C42—8316no—
788C42C23×D8314yes—
789C42C23×D8314yes—
790C42C23×D8314yes—
791C42C23×D8314yes—
792C42C23×D8318yes—
793C23—22no—
794C23—22no—
795C23—24no—
796C23—24no—
797C23—24no—
798C23—838no—
799C23—1668no—
800C23—1668no—
801C23—1668no—
802C23#1458183814yes—
803C23C24×D8314yes—
804C23C24×D8312yes—
805C23C24×D8311yescharacteristic
806Q8—28no—
807Q8—3328no—
808Q8—33216no—
809Q8—8316no—
810Q8—16616no—
811Q8—1668no—
812D4—216no—
813D4—28no—
814D4—3328no—
815D4—33216no—
816D4—16632no—
817D4—16632no—
818D4—16616no—
819D4—16616no—
820C2×C4—24no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—28no—
825C2×C4—24no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—28no—
829C2×C4—216no—
830C2×C4—28no—
831C2×C4—33216no—
832C2×C4—33216no—
833C2×C4—33216no—
834C2×C4—838no—
835C2×C4—834no—
836C2×C4—834no—
837C2×C4—834no—
838C2×C4—834no—
839C2×C4—838no—
840C2×C4—16632no—
841C2×C4—16616no—
842C2×C4—1664no—
843C2×C4—1664no—
844C2×C4—1668no—
845C2×C4—1664no—
846C2×C4—16616no—
847C2×C4#41×D8314yes—
848C2×C4#1458183914yes—
849C2×C4C24×D8312yes—
850C2×C4C24×D8314yes—
851C2×C4C24×D8312yes—
852C2×C4C24×D8312yes—
853C2×C4C24×D8312yes—
854C2×C4C24×D8314yes—
855C2×C4C24×D8314yes—
856C2×C4C24×D8312yes—
857C2×C4C24×D8312yes—
858C22—22no—
859C22—22no—
860C22—28no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—48no—
865C22—33216no—
866C22—1668no—
867C22—1668no—
868C22—1668no—
869C22C2×#41×D8312yes—
870C22C2×#1458183814yes—
871C22C2×#1458183812yes—
872C22C2×#1458183912yes—
873C22C25×D8311yescharacteristic
874C4—24no—
875C4—22no—
876C4—22no—
877C4—22no—
878C4—24no—
879C4—22no—
880C4—24no—
881C4—838no—
882C4—1664no—
883C4—1664no—
884C4—1668no—
885C4—1664no—
886C4C2×#41×D8314yes—
887C4C2×#1458183914yes—
888C2—24no—
889C2—44no—
890C2—3328no—
891C2#2492154614yesdirect product factor
892C2C22×#41×D8311yescharacteristic
893C2C22×#1458183811yescharacteristic
894C2C22×#1458183911yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#529×C83C2
socleC23×C83C25
hypercenterC2×#529D83
hypocenterC83C2×#3522
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #24921546C2direct (N × H)
2. C2×#19128436C2semidirect
3. C2×#19128433C2semidirect
4. C2×Q8×Dic166C2semidirect
5. C2×#19128408C2semidirect
6. C2×#19128407C2semidirect
7. C2×#19128372C2semidirect
8. C2×#19128360C2semidirect
9. C2×#19128355C2semidirect
10. C2×#19128349C2semidirect
11. C2×#19128322C2semidirect
12. C2×#19128317C2semidirect
13. C2×#19128251C2semidirect
14. C2×#19128246C2semidirect
15. C2×#19128237C2semidirect
16. C2×#19128181C2semidirect
17. C22×C4×Dic166C2semidirect
18. C2×#529×C83C2semidirect
23. #19128436C22semidirect
24. #19128433C22semidirect
25. Q8×Dic166C22semidirect
26. #19128408C22semidirect
27. #19128407C22semidirect
28. #19128372C22semidirect
29. #19128360C22semidirect
30. #19128355C22semidirect
31. #19128349C22semidirect
32. #19128322C22semidirect
33. #19128317C22semidirect
34. #19128251C22semidirect
35. #19128246C22semidirect
42. #19128237C22semidirect
64. #19128181C22semidirect
73. C2×C4×Dic166C22semidirect
89. #529×C83C22semidirect
244. C2×Dic166#41semidirect
409. Dic166C2×#41semidirect
443. C2×C83#3522semidirect
463. C2×#529D83semidirect
466. C83C2×#3522semidirect
491. #529C2×D83semidirect
891. C2#24921546direct (N × H)

Maximal subgroups

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

subgroupindex
#249215462
C2×#191284362
C2×#191284332
C2×Q8×Dic1662
C2×#191284082
C2×#191284072
C2×#191283722
C2×#191283602
C2×#191283552
C2×#191283492
C2×#191283222
C2×#191283172
C2×#191282512
C2×#191282462
C2×#191282372
C2×#191281812
C22×C4×Dic1662
C2×#529×C832
C2×#352283