Finite Group Databasebeta

← C2×#24921540 #36312607

Subgroups — C2×#24921540 #36312607

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#24921540C2132yesmaximal, direct product factor
2C2×#19128437C211yesmaximal, characteristic, complemented
3C2×#19128434C212yesmaximal, complemented
4C2×#19128431C211yesmaximal, characteristic, complemented
5C2×#19128412C211yesmaximal, characteristic, complemented
6C2×#19128410C212yesmaximal, complemented
7C2×#19128371C211yesmaximal, characteristic, complemented
8C2×#19128357C212yesmaximal, complemented
9C2×#19128351C212yesmaximal, complemented
10C2×#19128350C214yesmaximal, complemented
11C2×#19128316C212yesmaximal, complemented
12C2×#19128315C214yesmaximal, complemented
13C2×#19128246C212yesmaximal, complemented
14C2×#19128235C211yesmaximal, characteristic, complemented
15C2×#19128232C212yesmaximal, complemented
16C2×#19128180C212yesmaximal, complemented
17C22×C4×Dic166C211yesmaximal, characteristic, complemented
18C2×#532×C83C211yesmaximal, characteristic, complemented
19C22×#13050589C2212yes—
20C22×#13050589C2214yes—
21C23×Dic166C2211yescharacteristic
22#19128437C22116yescomplemented
23#19128434C22132yescomplemented
24#19128431C22116yescomplemented
25#19128412C22116yescomplemented
26#19128410C22132yescomplemented
27#19128371C22116yescomplemented
28#19128357C22132yescomplemented
29#19128351C22132yescomplemented
30#19128350C22164yescomplemented
31#19128316C22132yescomplemented
32#19128315C22164yescomplemented
33#19128246C22132yescomplemented
34C2×#14581791C2212yes—
35C2×#14581791C2212yes—
36C2×#14581790C2214yes—
37C2×#14581788C2212yes—
38#19128235C22116yescomplemented
39#19128232C22132yescomplemented
40C2×#14581786C2212yes—
41C2×#14581785C2214yes—
42C2×#14581784C2211yescharacteristic
43C2×#14581783C2212yes—
44C2×#14581780C2211yescharacteristic
45C2×#14581779C2212yes—
46C2×#14581779C2212yes—
47C2×#14581778C2214yes—
48C2×#14581778C2214yes—
49C2×#14581775C2214yes—
50C2×#14581775C2212yes—
51C2×#14581774C2214yes—
52C2×#14581773C2214yes—
53C2×#14581773C2214yes—
54C2×#14581772C2212yes—
55C2×#14581771C2214yes—
56C2×#14581771C2211yescharacteristic
57C2×#14581769C2214yes—
58C2×#14581769C2214yes—
59C2×#14581768C2214yes—
60C2×#14581766C2211yescharacteristic
61C2×#14581764C2214yes—
62C2×#14581764C2214yes—
63C2×#14581763C2212yes—
64#19128180C22132yescomplemented
65C2×C4×Dic166C2212yes—
66C2×C4×Dic166C2211yescharacteristic
67C2×C4×Dic166C2211yescharacteristic
68C2×C4×Dic166C2211yescharacteristic
69C2×C4×Dic166C2212yes—
70C2×C4×Dic166C2211yescharacteristic
71C2×C4×Dic166C2211yescharacteristic
72C2×C4×Dic166C22116yescomplemented
73C2×#14581757C2212yes—
74C2×#14581757C2212yes—
75C2×C4×D332C2211yescharacteristic
76C2×D4×Dic83C2212yes—
77C2×D4×Dic83C2214yes—
78C2×D4×Dic83C2212yes—
79C2×D4×Dic83C2212yes—
80C2×#14581754C2212yes—
81C2×C4×C22⋊D83C2214yes—
82C2×C4×C22⋊D83C2212yes—
83C2×(C22⋊D83)⋊C4C2214yes—
84C2×#14581749C2212yes—
85C2×#14581748C2214yes—
86C22×C4⋊Dic83C2211yescharacteristic
87C22×Dic83⋊C4C2212yes—
88C22×Dic83⋊C4C2214yes—
89C2×C4⋊C4×D83C2212yes—
90C22×C4×Dic83C2212yes—
91C22×#41×C83C2212yes—
92#532×C83C22116yescomplemented
93C2×C4⋊Q8×C83C2211yescharacteristic
94C2×#127×C83C2211yescharacteristic
95C2×#124×C83C2212yes—
96C2×#121×C83C2212yes—
97C2×#121×C83C2212yes—
98C2×C4×D4×C83C2212yes—
99C2×C4×D4×C83C2212yes—
100C22×C42×C83C2211yescharacteristic
101C2×#13050589—216no—
102C2×#13050589—416no—
103C2×#13050589C23116yes—
104C2×#13050589C23132yes—
105C22×Dic166—28no—
106C22×Dic166C2318yes—
107C22×Dic166C2311yescharacteristic
108C22×Dic166C2312yes—
109C22×Dic166C2311yescharacteristic
110C22×Dic166C2314yes—
111C22×Dic166C2311yescharacteristic
112C22×D332C2311yescharacteristic
113C22×C22⋊D83C2314yes—
114C22×C22⋊D83C2312yes—
115C22×C22⋊D83C2314yes—
116C23×Dic83C2312yes—
117C23×Dic83C2312yes—
118C23×Dic83C2314yes—
119C23×Dic83C2314yes—
120C22×C4×D83C2312yes—
121C22×C4×D83C2314yes—
122#14581791C23116yes—
123#14581791C23116yes—
124#14581790C23132yes—
125#14581788C23116yes—
126#14581786C23116yes—
127#14581785C23132yes—
128#14581784C2318yes—
129#14581783C23116yes—
130#14581780C2318yes—
131#14581779C23116yes—
132#14581779C23116yes—
133#14581778C23132yes—
134#14581778C23132yes—
135#14581775C23116yes—
136#14581775C23132yes—
137#14581774C23132yes—
138#14581773C23132yes—
139#14581773C23132yes—
140#14581772C23116yes—
141#14581771C23132yes—
142#14581771C2318yes—
143#14581769C23132yes—
144#14581769C23132yes—
145#14581768C23132yes—
146#14581766C2318yes—
147#14581764C23132yes—
148#14581764C23132yes—
149#14581763C23116yes—
150C4×Dic166C2318yes—
151C4×Dic166C23116yes—
152C4×Dic166C2318yes—
153C4×Dic166C2318yes—
154C4×Dic166C23116yes—
155C4×Dic166C2318yes—
156C4×Dic166C2318yes—
157#14581757C23116yes—
158#14581757C23116yes—
159C4×D332C2318yes—
160D4×Dic83C23132yes—
161D4×Dic83C23116yes—
162D4×Dic83C23116yes—
163D4×Dic83C23116yes—
164#14581754C23116yes—
165C4×C22⋊D83C23132yes—
166C4×C22⋊D83C23116yes—
167(C22⋊D83)⋊C4C23132yes—
168#14581749C23116yes—
169#14581748C23132yes—
170C2×C4⋊Dic83C2318yes—
171C2×C4⋊Dic83C2311yescharacteristic
172C2×C4⋊Dic83C2311yescharacteristic
173C2×C4⋊Dic83C2312yes—
174C2×C4⋊Dic83C2311yescharacteristic
175C2×C4⋊Dic83C2311yescharacteristic
176C2×C4⋊Dic83C2314yes—
177C2×Dic83⋊C4C23116yes—
178C2×Dic83⋊C4C23132yes—
179C2×Dic83⋊C4C2314yes—
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2312yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2312yes—
187C2×Dic83⋊C4C2312yes—
188C2×Dic83⋊C4C2314yes—
189C2×Dic83⋊C4C2312yes—
190C4⋊C4×D83C23116yes—
191C2×C22⋊Dic83C2314yes—
192C2×C22⋊Dic83C2312yes—
193C2×C22⋊Dic83C2314yes—
194C2×C22⋊Dic83C2314yes—
195C2×C22⋊Dic83C2314yes—
196C2×(C2×D83)⋊C4C2312yes—
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2312yes—
199C2×(C2×D83)⋊C4C2314yes—
200C2×(C2×D83)⋊C4C2312yes—
201C2×C4×Dic83C2312yes—
202C2×C4×Dic83C2312yes—
203C2×C4×Dic83C2312yes—
204C2×C4×Dic83C2312yes—
205C2×C4×Dic83C23116yes—
206C2×C4×Dic83C2314yes—
207C2×C4×Dic83C2312yes—
208C2×#41×C83—48no—
209C2×#41×C83C23116yes—
210C22×Q8×C83C2312yes—
211C22×D4×C83C2312yes—
212C22×D4×C83C2312yes—
213C22×D4×C83C2314yes—
214C22×D4×C83C2312yes—
215C23×C4×C83C2311yescharacteristic
216C23×C4×C83C2311yescharacteristic
217C23×C4×C83C2311yescharacteristic
218C23×C4×C83C2314yes—
219C4⋊Q8×C83C2318yes—
220#127×C83C2318yes—
221#124×C83C23116yes—
222#121×C83C23116yes—
223#121×C83C23116yes—
224C4×D4×C83C23116yes—
225C4×D4×C83C23116yes—
226C2×C4⋊C4×C83C2312yes—
227C2×C4⋊C4×C83C2312yes—
228C2×C22⋊C4×C83C2314yes—
229C2×C22⋊C4×C83C2314yes—
230C2×C42×C83C2311yescharacteristic
231C2×C42×C83C2311yescharacteristic
232C2×C42×C83C2311yescharacteristic
233C2×C42×C83C2311yescharacteristic
234C2×C42×C83C2318yes—
235C23×D83C2412yes—
236#13050589—264no—
237#13050589—464no—
238C2×Dic166—24no—
239C2×Dic166—24no—
240C2×Dic166—28no—
241C2×Dic166—232no—
242C2×Dic166—48no—
243C2×Dic166#4118yescomplemented
244C2×Dic166C2418yes—
245C2×Dic166C2414yes—
246C2×Dic166C2414yes—
247C2×Dic166C24116yes—
248C2×Dic166C2414yes—
249C2×D332—24no—
250C2×D332C2414yes—
251C2×C22⋊D83—28no—
252C2×C22⋊D83—216no—
253C2×C22⋊D83—48no—
254C2×C22⋊D83C2418yes—
255C2×C22⋊D83C24116yes—
256C2×C22⋊D83C24116yes—
257C22×Dic83—28no—
258C22×Dic83—28no—
259C22×Dic83—216no—
260C22×Dic83—48no—
261C22×Dic83C2418yes—
262C22×Dic83C24116yes—
263C22×Dic83C2418yes—
264C22×Dic83C2412yes—
265C22×Dic83C2412yes—
266C22×Dic83C2412yes—
267C22×Dic83C2412yes—
268C22×Dic83C2412yes—
269C22×Dic83C2412yes—
270C22×Dic83C24116yes—
271C22×Dic83C2412yes—
272C2×C4×D83—28no—
273C2×C4×D83—48no—
274C2×C4×D83C2418yes—
275C2×C4×D83C24116yes—
276C4⋊Dic83C2414yes—
277C4⋊Dic83C2414yes—
278C4⋊Dic83C24116yes—
279C4⋊Dic83C2418yes—
280C4⋊Dic83C2414yes—
281C4⋊Dic83C2414yes—
282Dic83⋊C4C2418yes—
283Dic83⋊C4C24116yes—
284Dic83⋊C4C2418yes—
285Dic83⋊C4C24116yes—
286Dic83⋊C4C2418yes—
287Dic83⋊C4C2418yes—
288Dic83⋊C4C2418yes—
289Dic83⋊C4C2418yes—
290Dic83⋊C4C2418yes—
291Dic83⋊C4C24116yes—
292Dic83⋊C4C2418yes—
293C22⋊Dic83C24116yes—
294C22⋊Dic83C24116yes—
295C22⋊Dic83C2418yes—
296C22⋊Dic83C24116yes—
297C22⋊Dic83C24116yes—
298(C2×D83)⋊C4C2418yes—
299(C2×D83)⋊C4C24116yes—
300(C2×D83)⋊C4C2418yes—
301(C2×D83)⋊C4C2418yes—
302(C2×D83)⋊C4C2418yes—
303C4×Dic83C2418yes—
304C4×Dic83C24116yes—
305C4×Dic83C2418yes—
306C4×Dic83C2418yes—
307C4×Dic83C2418yes—
308C4×Dic83C2418yes—
309C24×C83C2414yes—
310C24×C83C2411yescharacteristic
311#41×C83—432no—
312C2×Q8×C83—44no—
313C2×Q8×C83C2418yes—
314C2×D4×C83—216no—
315C2×D4×C83—28no—
316C2×D4×C83—28no—
317C2×D4×C83—44no—
318C2×D4×C83C2418yes—
319C2×D4×C83C24116yes—
320C2×D4×C83C2418yes—
321C2×D4×C83C2418yes—
322C22×C4×C83—24no—
323C22×C4×C83—24no—
324C22×C4×C83—24no—
325C22×C4×C83—48no—
326C22×C4×C83C2414yes—
327C22×C4×C83C2414yes—
328C22×C4×C83C2414yes—
329C22×C4×C83C2411yescharacteristic
330C22×C4×C83C2414yes—
331C22×C4×C83C2411yescharacteristic
332C22×C4×C83C2411yescharacteristic
333C22×C4×C83C2411yescharacteristic
334C22×C4×C83C24116yes—
335C22×C4×C83C2411yescharacteristic
336C22×C4×C83C2411yescharacteristic
337C4⋊C4×C83C2418yes—
338C4⋊C4×C83C2418yes—
339C22⋊C4×C83C24116yes—
340C22⋊C4×C83C24116yes—
341C42×C83C2414yes—
342C42×C83C2414yes—
343C42×C83C2414yes—
344C42×C83C2414yes—
345C23×C83—22no—
346C23×C83—22no—
347C23×C83—28no—
348C23×C83—28no—
349C23×C83—28no—
350C23×C83H(5,𝔽2)14yes—
351C23×C83C2518yes—
352C23×C83C2512yes—
353C23×C83C2511yescharacteristic
354C22×D83—24no—
355C22×D83—24no—
356C22×D83—24no—
357C22×D83C2514yes—
358Q8×C83—48no—
359D4×C83—232no—
360D4×C83—216no—
361D4×C83—216no—
362D4×C83—48no—
363C2×C4×C83—22no—
364C2×C4×C83—22no—
365C2×C4×C83—22no—
366C2×C4×C83—28no—
367C2×C4×C83—28no—
368C2×C4×C83—22no—
369C2×C4×C83—28no—
370C2×C4×C83—28no—
371C2×C4×C83—416no—
372C2×C4×C83C2×#4114yes—
373C2×C4×C832−1+414yes—
374C2×C4×C83C2512yes—
375C2×C4×C83C2512yes—
376C2×C4×C83C2512yes—
377C2×C4×C83C2512yes—
378C2×C4×C83C2518yes—
379C2×C4×C83C2512yes—
380C2×C4×C83C2512yes—
381C22⋊D83—216no—
382C22⋊D83—232no—
383C22⋊D83—416no—
384C2×Dic83—24no—
385C2×Dic83—24no—
386C2×Dic83—24no—
387C2×Dic83—24no—
388C2×Dic83—216no—
389C2×Dic83—24no—
390C2×Dic83—24no—
391C2×Dic83—216no—
392C2×Dic83—232no—
393C2×Dic83—416no—
394C2×Dic83C2×#4118yes—
395C2×Dic83C2514yes—
396C2×Dic83C2514yes—
397C2×Dic83C2514yes—
398C2×Dic83C2514yes—
399C2×Dic83C2514yes—
400C2×Dic83C2514yes—
401C2×Dic83C2514yes—
402D332—28no—
403C4×D83—216no—
404C4×D83—416no—
405Dic166—28no—
406Dic166—28no—
407Dic166—216no—
408Dic166—416no—
409Dic166C2×#41116yescomplemented
410C22×C83—22no—
411C22×C83—22no—
412C22×C83—28no—
413C22×C83—28no—
414C22×C83—28no—
415C22×C83—28no—
416C22×C83—416no—
417C22×C83C22×#4112yes—
418C22×C83C2×H(5,𝔽2)14yes—
419C22×C83C2×H(5,𝔽2)12yes—
420C22×C83C2×2−1+412yes—
421C22×C83C2611yescharacteristic
422C2×D83—24no—
423C2×D83—24no—
424C2×D83—24no—
425C2×D83—48no—
426C4×C83—22no—
427C4×C83—28no—
428C4×C83—22no—
429C4×C83—22no—
430C4×C83—22no—
431C4×C83C22×#4114yes—
432C4×C83C2×2−1+414yes—
433Dic83—24no—
434Dic83—24no—
435Dic83—24no—
436Dic83—24no—
437Dic83—24no—
438Dic83—24no—
439Dic83C22×#4118yes—
440C2×#3522—831nomaximal, Sylow
441C2×C83—24no—
442C2×C83—48no—
443C2×C83#352214yescomplemented
444C2×C83C23×#4111yescharacteristic
445C2×C83C22×H(5,𝔽2)11yescharacteristic
446C2×C83C22×2−1+411yescharacteristic
447D83—44no—
448#3522—8332no—
449C2×#559—831no—
450C2×#559—832no—
451C2×Q82—831no—
452C2×#554—831no—
453C2×#554—832no—
454C2×#550—831no—
455C2×#548—832no—
456C2×#547—834no—
457C2×#547—832no—
458C2×#542—834no—
459C2×#542—832no—
460C2×#532—832no—
461C2×#532D8311yescharacteristic, complemented
462C2×#529—831no—
463C2×#529—832no—
464C2×#520—832no—
465C22×C4×Q8—831no—
466C83C2×#352211yescharacteristic, complemented, Sylow
467C22×#41—834no—
468C22×#41—832no—
469C22×#41C2×D8312yes—
470C23×Q8—831no—
471#559—8316no—
472#559—8332no—
473Q82—8316no—
474#554—8316no—
475#554—8332no—
476#550—8316no—
477#548—8332no—
478#547—8364no—
479#547—8332no—
480#542—8364no—
481#542—8332no—
482#532—8332no—
483#532C2×D83116yescomplemented
484C2×C4⋊Q8—834no—
485C2×C4⋊Q8—832no—
486C2×C4⋊Q8—832no—
487C2×C4⋊Q8C2×D8311yescharacteristic
488C2×#127—832no—
489C2×#127C2×D8311yescharacteristic
490#529—8332no—
491#529—8316no—
492C2×#126—834no—
493C2×#126—832no—
494C2×#125—832no—
495C2×#125—831no—
496C2×#124—832no—
497C2×#124—832no—
498C2×#124—834no—
499C2×#124—834no—
500C2×#124—831no—
501C2×#124C2×D8312yes—
502C2×#123—834no—
503C2×#123—834no—
504C2×#123—832no—
505C2×#123—834no—
506C2×#123—834no—
507C2×C22⋊Q8—834no—
508C2×C22⋊Q8—831no—
509C2×C22⋊Q8—834no—
510C2×C22⋊Q8—832no—
511C2×C22⋊Q8—834no—
512C2×C22⋊Q8—834no—
513C2×#121—834no—
514C2×#121—832no—
515C2×#121—834no—
516C2×#121—831no—
517C2×#121C2×D8312yes—
518C2×#121C2×D8312yes—
519#520—8332no—
520C2×C4×Q8—832no—
521C2×C4×Q8—832no—
522C2×C4×Q8—831no—
523C2×C4×Q8—832no—
524C2×C4×Q8—831no—
525C2×C4×Q8—831no—
526C2×C4×Q8—831no—
527C2×C4×Q8—832no—
528C2×C4×Q8—8316no—
529C2×C4×Q8—831no—
530C2×C4×D4—832no—
531C2×C4×D4—834no—
532C2×C4×D4—832no—
533C2×C4×D4—832no—
534C2×C4×D4—834no—
535C2×C4×D4—832no—
536C2×C4×D4—832no—
537C2×C4×D4—834no—
538C2×C4×D4—831no—
539C2×C4×D4C2×D8312yes—
540C2×C4×D4C2×D8312yes—
541C2×#117—834no—
542C2×#117—832no—
543C22×C4⋊C4—832no—
544C22×C4⋊C4—834no—
545C22×C4⋊C4—831no—
546C22×C4⋊C4—832no—
547C22×C42—832no—
548C22×C42C2×D8311yescharacteristic
549C2×#41—48no—
550C2×#41—33216no—
551C2×#41—8332no—
552C2×#41—8316no—
553C2×#41—16616no—
554C2×#41C22×D83116yes—
555C22×Q8—834no—
556C22×Q8—831no—
557C22×Q8—831no—
558C22×Q8—832no—
559C22×Q8—831no—
560C22×Q8—838no—
561C22×Q8—1668no—
562C22×Q8C22×D8312yes—
563C22×D4—834no—
564C22×D4—834no—
565C22×D4—832no—
566C22×D4—831no—
567C22×D4C22×D8312yes—
568C22×D4C22×D8312yes—
569C22×D4C22×D8314yes—
570C22×D4C22×D8312yes—
571C23×C4—834no—
572C23×C4—834no—
573C23×C4—832no—
574C23×C4—834no—
575C23×C4—832no—
576C23×C4—832no—
577C23×C4C22×D8311yescharacteristic
578C23×C4C22×D8311yescharacteristic
579C23×C4C22×D8311yescharacteristic
580C23×C4C22×D8314yes—
581C4⋊Q8—8332no—
582C4⋊Q8—8316no—
583C4⋊Q8—8316no—
584C4⋊Q8C22×D8318yes—
585#127—8316no—
586#127C22×D8318yes—
587#126—8332no—
588#126—8316no—
589#125—8316no—
590#125—838no—
591#124—8316no—
592#124—8316no—
593#124—8332no—
594#124—8332no—
595#124—838no—
596#124C22×D83116yes—
597#123—8332no—
598#123—8332no—
599#123—8316no—
600#123—8332no—
601#123—8332no—
602C22⋊Q8—8332no—
603C22⋊Q8—838no—
604C22⋊Q8—8332no—
605C22⋊Q8—8316no—
606C22⋊Q8—8332no—
607C22⋊Q8—8332no—
608#121—8316no—
609#121—8332no—
610#121—8332no—
611#121—838no—
612#121C22×D83116yes—
613#121C22×D83116yes—
614C4×Q8—8316no—
615C4×Q8—8316no—
616C4×Q8—838no—
617C4×Q8—8316no—
618C4×Q8—838no—
619C4×Q8—838no—
620C4×Q8—838no—
621C4×Q8—8316no—
622C4×Q8—838no—
623C4×D4—8316no—
624C4×D4—8332no—
625C4×D4—8316no—
626C4×D4—8316no—
627C4×D4—8332no—
628C4×D4—8316no—
629C4×D4—8316no—
630C4×D4—8332no—
631C4×D4—838no—
632C4×D4C22×D83116yes—
633C4×D4C22×D83116yes—
634#117—8332no—
635#117—8316no—
636C2×C4⋊C4—832no—
637C2×C4⋊C4—831no—
638C2×C4⋊C4—834no—
639C2×C4⋊C4—832no—
640C2×C4⋊C4—834no—
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—8332no—
649C2×C4⋊C4—832no—
650C2×C4⋊C4—831no—
651C2×C4⋊C4—831no—
652C2×C4⋊C4—832no—
653C2×C4⋊C4—834no—
654C2×C4⋊C4—834no—
655C2×C4⋊C4—832no—
656C2×C4⋊C4—8316no—
657C2×C4⋊C4C22×D8312yes—
658C2×C4⋊C4C22×D8312yes—
659C2×C22⋊C4—834no—
660C2×C22⋊C4—832no—
661C2×C22⋊C4—834no—
662C2×C22⋊C4—834no—
663C2×C22⋊C4—834no—
664C2×C22⋊C4—832no—
665C2×C22⋊C4—832no—
666C2×C22⋊C4—832no—
667C2×C22⋊C4—834no—
668C2×C22⋊C4—832no—
669C2×C22⋊C4C22×D8314yes—
670C2×C22⋊C4C22×D8314yes—
671C2×C42—832no—
672C2×C42—834no—
673C2×C42—832no—
674C2×C42—832no—
675C2×C42—832no—
676C2×C42—832no—
677C2×C42—8316no—
678C2×C42C22×D8311yescharacteristic
679C2×C42C22×D8311yescharacteristic
680C2×C42C22×D8311yescharacteristic
681C2×C42C22×D8311yescharacteristic
682C2×C42C22×D8318yes—
683C24—832no—
684C24C23×D8314yes—
685C24C23×D8311yescharacteristic
686#41—432no—
687#41—33264no—
688#41—16664no—
689C2×Q8—44no—
690C2×Q8—3328no—
691C2×Q8—838no—
692C2×Q8—8316no—
693C2×Q8—834no—
694C2×Q8—834no—
695C2×Q8—838no—
696C2×Q8—834no—
697C2×Q8—1668no—
698C2×Q8—16632no—
699C2×Q8—1664no—
700C2×Q8—1664no—
701C2×Q8C23×D8318yes—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—44no—
706C2×D4—3328no—
707C2×D4—8316no—
708C2×D4—8316no—
709C2×D4—838no—
710C2×D4—834no—
711C2×D4—16616no—
712C2×D4—1668no—
713C2×D4—1664no—
714C2×D4C23×D8318yes—
715C2×D4C23×D8318yes—
716C2×D4C23×D83116yes—
717C2×D4C23×D8318yes—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—48no—
722C22×C4—3328no—
723C22×C4—3328no—
724C22×C4—8316no—
725C22×C4—8316no—
726C22×C4—832no—
727C22×C4—838no—
728C22×C4—838no—
729C22×C4—8316no—
730C22×C4—832no—
731C22×C4—832no—
732C22×C4—832no—
733C22×C4—832no—
734C22×C4—832no—
735C22×C4—832no—
736C22×C4—838no—
737C22×C4—1668no—
738C22×C4—16616no—
739C22×C4—1668no—
740C22×C4—1668no—
741C22×C4C23×D8314yes—
742C22×C4C23×D8314yes—
743C22×C4C23×D8314yes—
744C22×C4C23×D8311yescharacteristic
745C22×C4C23×D8314yes—
746C22×C4C23×D8311yescharacteristic
747C22×C4C23×D8311yescharacteristic
748C22×C4C23×D8311yescharacteristic
749C22×C4C23×D83116yes—
750C22×C4C23×D8311yescharacteristic
751C22×C4C23×D8311yescharacteristic
752C4⋊C4—838no—
753C4⋊C4—834no—
754C4⋊C4—8316no—
755C4⋊C4—838no—
756C4⋊C4—8316no—
757C4⋊C4—838no—
758C4⋊C4—834no—
759C4⋊C4—838no—
760C4⋊C4—838no—
761C4⋊C4—838no—
762C4⋊C4—838no—
763C4⋊C4—834no—
764C4⋊C4—834no—
765C4⋊C4—838no—
766C4⋊C4—8316no—
767C4⋊C4—8316no—
768C4⋊C4—838no—
769C4⋊C4C23×D8318yes—
770C4⋊C4C23×D8318yes—
771C22⋊C4—8316no—
772C22⋊C4—838no—
773C22⋊C4—8316no—
774C22⋊C4—8316no—
775C22⋊C4—8316no—
776C22⋊C4—838no—
777C22⋊C4—838no—
778C22⋊C4—838no—
779C22⋊C4—8316no—
780C22⋊C4—838no—
781C22⋊C4C23×D83116yes—
782C22⋊C4C23×D83116yes—
783C42—838no—
784C42—838no—
785C42—838no—
786C42—838no—
787C42—8316no—
788C42—838no—
789C42C23×D8314yes—
790C42C23×D8314yes—
791C42C23×D8314yes—
792C42C23×D8314yes—
793C23—22no—
794C23—22no—
795C23—28no—
796C23—28no—
797C23—28no—
798C23—834no—
799C23—1664no—
800C23—1664no—
801C23—1664no—
802C23#1458183714yes—
803C23C24×D8318yes—
804C23C24×D8312yes—
805C23C24×D8311yescharacteristic
806Q8—48no—
807Q8—33216no—
808Q8—8316no—
809Q8—16616no—
810Q8—1668no—
811Q8—1668no—
812D4—232no—
813D4—216no—
814D4—216no—
815D4—48no—
816D4—33216no—
817D4—16632no—
818D4—16616no—
819D4—1668no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—28no—
824C2×C4—28no—
825C2×C4—22no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—416no—
829C2×C4—33216no—
830C2×C4—33216no—
831C2×C4—838no—
832C2×C4—834no—
833C2×C4—834no—
834C2×C4—834no—
835C2×C4—834no—
836C2×C4—834no—
837C2×C4—834no—
838C2×C4—834no—
839C2×C4—16616no—
840C2×C4—16632no—
841C2×C4—1664no—
842C2×C4—1664no—
843C2×C4—1664no—
844C2×C4—1664no—
845C2×C4—1664no—
846C2×C4—16616no—
847C2×C4—1664no—
848C2×C4—16616no—
849C2×C4#41×D8314yes—
850C2×C4#1458183914yes—
851C2×C4C24×D8312yes—
852C2×C4C24×D8318yes—
853C2×C4C24×D8312yes—
854C2×C4C24×D8312yes—
855C2×C4C24×D8312yes—
856C2×C4C24×D8312yes—
857C2×C4C24×D8312yes—
858C22—22no—
859C22—22no—
860C22—28no—
861C22—28no—
862C22—28no—
863C22—28no—
864C22—416no—
865C22—3328no—
866C22—1664no—
867C22—1664no—
868C22—1664no—
869C22C2×#41×D8312yes—
870C22C2×#1458183714yes—
871C22C2×#1458183712yes—
872C22C2×#1458183912yes—
873C22C25×D8311yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—28no—
878C4—22no—
879C4—838no—
880C4—1664no—
881C4—1664no—
882C4—1664no—
883C4—1664no—
884C4—1664no—
885C4—1664no—
886C4C2×#41×D8314yes—
887C4C2×#1458183914yes—
888C2—24no—
889C2—48no—
890C2—3324no—
891C2#2492154014yesdirect product factor
892C2C22×#41×D8311yescharacteristic
893C2C22×#1458183711yescharacteristic
894C2C22×#1458183911yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#532×C83C2
socleC23×C83C25
hypercenterC2×#532D83
hypocenterC83C2×#3522
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #24921540C2direct (N × H)
2. C2×#19128437C2semidirect
3. C2×#19128434C2semidirect
4. C2×#19128431C2semidirect
5. C2×#19128412C2semidirect
6. C2×#19128410C2semidirect
7. C2×#19128371C2semidirect
8. C2×#19128357C2semidirect
9. C2×#19128351C2semidirect
10. C2×#19128350C2semidirect
11. C2×#19128316C2semidirect
12. C2×#19128315C2semidirect
13. C2×#19128246C2semidirect
14. C2×#19128235C2semidirect
15. C2×#19128232C2semidirect
16. C2×#19128180C2semidirect
17. C22×C4×Dic166C2semidirect
18. C2×#532×C83C2semidirect
22. #19128437C22semidirect
23. #19128434C22semidirect
24. #19128431C22semidirect
25. #19128412C22semidirect
26. #19128410C22semidirect
27. #19128371C22semidirect
28. #19128357C22semidirect
29. #19128351C22semidirect
30. #19128350C22semidirect
31. #19128316C22semidirect
32. #19128315C22semidirect
33. #19128246C22semidirect
38. #19128235C22semidirect
39. #19128232C22semidirect
64. #19128180C22semidirect
72. C2×C4×Dic166C22semidirect
92. #532×C83C22semidirect
243. C2×Dic166#41semidirect
409. Dic166C2×#41semidirect
443. C2×C83#3522semidirect
461. C2×#532D83semidirect
466. C83C2×#3522semidirect
483. #532C2×D83semidirect
891. C2#24921540direct (N × H)

Maximal subgroups

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

subgroupindex
#249215402
C2×#191284372
C2×#191284342
C2×#191284312
C2×#191284122
C2×#191284102
C2×#191283712
C2×#191283572
C2×#191283512
C2×#191283502
C2×#191283162
C2×#191283152
C2×#191282462
C2×#191282352
C2×#191282322
C2×#191281802
C22×C4×Dic1662
C2×#532×C832
C2×#352283