Finite Group Databasebeta

← C2×#24921166 #36312340

Subgroups — C2×#24921166 #36312340

Order 21248.

7910 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921166C2132yesmaximal, direct product factor
2C2×#19128411C212yesmaximal, complemented
3C2×#19128406C212yesmaximal, complemented
4C2×#19128401C212yesmaximal, complemented
5C2×#19128395C212yesmaximal, complemented
6C2×#19128392C212yesmaximal, complemented
7C2×#19128390C212yesmaximal, complemented
8C2×#19128356C212yesmaximal, complemented
9C2×#19128352C212yesmaximal, complemented
10C2×#19128329C211yesmaximal, characteristic, complemented
11C2×#19128293C214yesmaximal, complemented
12C2×#19128279C211yesmaximal, characteristic, complemented
13C2×#19128213C211yesmaximal, characteristic, complemented
14C2×#19128210C214yesmaximal, complemented
15C2×#19128208C211yesmaximal, characteristic, complemented
16C2×#19128182C211yesmaximal, characteristic, complemented
17C22×C4⋊C4×D83C211yesmaximal, characteristic, complemented
18C2×#520×C83C211yesmaximal, characteristic, complemented
19C22×#13050590C2211yescharacteristic
20C22×#13050590C2214yes—
21C23×C4×D83C2211yescharacteristic
22C23×C4×D83C2212yes—
23#19128411C22132yescomplemented
24#19128406C22132yescomplemented
25#19128401C22132yescomplemented
26#19128395C22132yescomplemented
27#19128392C22132yescomplemented
28#19128390C22132yescomplemented
29#19128356C22132yescomplemented
30#19128352C22132yescomplemented
31#19128329C22116yescomplemented
32#19128293C22164yescomplemented
33#19128279C22116yescomplemented
34C2×#14581792C2212yescomplemented
35C2×#14581791C2212yescomplemented
36C2×#14581786C2214yescomplemented
37C2×#14581785C2214yescomplemented
38C2×#14581784C2212yescomplemented
39C2×#14581784C2214yescomplemented
40C2×#14581783C2212yescomplemented
41C2×#14581782C2214yescomplemented
42#19128213C22116yescomplemented
43#19128210C22164yescomplemented
44#19128208C22116yescomplemented
45C2×#14581777C2214yes—
46C2×#14581776C2212yes—
47C2×#14581775C2214yescomplemented
48C2×#14581774C2214yes—
49C2×#14581774C2214yescomplemented
50C2×#14581773C2212yes—
51C2×#14581772C2211yescharacteristic
52C2×#14581772C2211yescharacteristic
53C2×#14581771C2214yescomplemented
54C2×#14581771C2212yescomplemented
55C2×#14581770C2214yes—
56C2×#14581770C2214yescomplemented
57C2×#14581769C2214yes—
58C2×#14581768C2211yescharacteristic
59C2×#14581768C2211yescharacteristic
60C2×#14581768C2212yescomplemented
61C2×#14581767C2211yescharacteristic
62C2×#14581767C2211yescharacteristic
63C2×#14581766C2212yescomplemented
64C2×#14581765C2214yes—
65C2×#14581764C2214yes—
66C2×#14581763C2211yescharacteristic
67C2×#14581763C2211yescharacteristic
68C2×#14581763C2212yescomplemented
69C2×#14581762C2212yes—
70C2×#14581760C2212yes—
71#19128182C22116yescomplemented
72C2×#14581757C2212yescomplemented
73C2×C4×D332C2212yes—
74C2×C4×D332C2214yes—
75C2×C4×D332C2212yes—
76C2×#14581754C2212yescomplemented
77C2×C4×C22⋊D83C2214yes—
78C2×C4×C22⋊D83C2212yes—
79C2×C4×C22⋊D83C2212yes—
80C2×C4×C22⋊D83C2214yes—
81C2×#14581751C2211yescharacteristic
82C2×#14581750C2212yescomplemented
83C2×#14581749C2214yes—
84C22×C4⋊Dic83C2211yescharacteristic
85C22×Dic83⋊C4C2212yes—
86C2×C4⋊C4×D83C2212yes—
87C2×C4⋊C4×D83C2212yes—
88C2×C4⋊C4×D83C2212yes—
89C2×C4⋊C4×D83C2212yes—
90C2×C4⋊C4×D83C22116yescomplemented
91C2×C4⋊C4×D83C2212yescomplemented
92C22×#41×C83C2211yescharacteristic
93#520×C83C22116yescomplemented
94C2×C4×Q8×C83C2212yescomplemented
95C2×C4×D4×C83C2214yes—
96C2×C4×D4×C83C2212yescomplemented
97C2×#117×C83C2211yescharacteristic
98C2×#117×C83C2212yescomplemented
99C22×C4⋊C4×C83C2211yescharacteristic
100C22×C4⋊C4×C83C2212yescomplemented
101C24×D83C2311yescharacteristic
102C2×#13050590—28no—
103C2×#13050590—416no—
104C2×#13050590C2318yes—
105C2×#13050590C23132yes—
106C22×Dic166C2311yescharacteristic
107C22×Dic166C2314yes—
108C22×D332C2311yescharacteristic
109C22×D332C2312yes—
110C22×D332C2312yes—
111C22×C22⋊D83C2312yes—
112C22×C22⋊D83C2312yes—
113C22×C22⋊D83C2312yes—
114C22×C22⋊D83C2314yes—
115C23×Dic83C2311yescharacteristic
116C23×Dic83C2312yes—
117C22×C4×D83—28no—
118C22×C4×D83—48no—
119C22×C4×D83C2314yes—
120C22×C4×D83C2311yescharacteristic
121C22×C4×D83C2311yescharacteristic
122C22×C4×D83C2311yescharacteristic
123C22×C4×D83C2311yescharacteristic
124C22×C4×D83C2318yes—
125C22×C4×D83C2312yes—
126C22×C4×D83C2314yes—
127C22×C4×D83C23116yes—
128C22×C4×D83C2314yes—
129#14581792C23116yescomplemented
130#14581791C23116yescomplemented
131#14581786C23132yescomplemented
132#14581785C23132yescomplemented
133#14581784C23116yescomplemented
134#14581784C23132yescomplemented
135#14581783C23116yescomplemented
136#14581782C23132yescomplemented
137#14581777C23132yes—
138#14581776C23116yes—
139#14581775C23132yescomplemented
140#14581774C23132yes—
141#14581774C23132yescomplemented
142#14581773C23116yes—
143#14581772C2318yes—
144#14581772C2318yes—
145#14581771C23132yescomplemented
146#14581771C23116yescomplemented
147#14581770C23132yes—
148#14581770C23132yescomplemented
149#14581769C23132yes—
150#14581768C2318yes—
151#14581768C2318yes—
152#14581768C23116yescomplemented
153#14581767C2318yes—
154#14581767C2318yes—
155#14581766C23116yescomplemented
156#14581765C23132yes—
157#14581764C23132yes—
158#14581763C2318yes—
159#14581763C2318yes—
160#14581763C23116yescomplemented
161#14581762C23116yes—
162#14581760C23116yes—
163#14581757C23116yescomplemented
164C4×D332C23116yes—
165C4×D332C23132yes—
166C4×D332C23116yes—
167#14581754C23116yescomplemented
168C4×C22⋊D83C23116yes—
169C4×C22⋊D83C23116yes—
170C4×C22⋊D83C23132yes—
171C4×C22⋊D83C23132yes—
172#14581751C2318yes—
173#14581750C23116yescomplemented
174#14581749C23132yes—
175C2×C4⋊Dic83C2318yes—
176C2×C4⋊Dic83C2312yes—
177C2×C4⋊Dic83C2312yes—
178C2×C4⋊Dic83C2311yescharacteristic
179C2×C4⋊Dic83C2311yescharacteristic
180C2×C4⋊Dic83C2314yes—
181C2×C4⋊Dic83C2312yes—
182C2×C4⋊Dic83C2312yes—
183C2×Dic83⋊C4C2314yes—
184C2×Dic83⋊C4C2314yes—
185C2×Dic83⋊C4C23116yes—
186C2×Dic83⋊C4C2314yes—
187C2×Dic83⋊C4C2314yes—
188C2×Dic83⋊C4C2314yes—
189C2×Dic83⋊C4C2312yes—
190C2×Dic83⋊C4C2312yes—
191C2×Dic83⋊C4C2314yes—
192C4⋊C4×D83C23116yes—
193C4⋊C4×D83C23116yes—
194C4⋊C4×D83C23116yes—
195C4⋊C4×D83C23116yes—
196C4⋊C4×D83C23116yescomplemented
197C2×C22⋊Dic83C2312yes—
198C2×C22⋊Dic83C2312yes—
199C2×C22⋊Dic83C2312yes—
200C2×C22⋊Dic83C2314yes—
201C2×(C2×D83)⋊C4C2312yes—
202C2×(C2×D83)⋊C4C2312yes—
203C2×(C2×D83)⋊C4C2314yes—
204C2×(C2×D83)⋊C4C2312yes—
205C2×(C2×D83)⋊C4C2312yes—
206C2×(C2×D83)⋊C4C2314yes—
207C2×(C2×D83)⋊C4C2312yes—
208C2×(C2×D83)⋊C4C2312yes—
209C2×C4×Dic83C2314yes—
210C2×C4×Dic83C2312yes—
211C2×#41×C83—28no—
212C2×#41×C83C2318yes—
213C22×Q8×C83C2311yescharacteristic
214C22×D4×C83C2312yes—
215C22×D4×C83C2311yescharacteristic
216C23×C4×C83C2312yes—
217C23×C4×C83C2312yes—
218C23×C4×C83C2314yes—
219C23×C4×C83C2311yescharacteristic
220C4×Q8×C83C23116yescomplemented
221C4×D4×C83C23132yes—
222C4×D4×C83C23116yescomplemented
223#117×C83C2318yes—
224#117×C83C23116yescomplemented
225C2×C4⋊C4×C83C2312yes—
226C2×C4⋊C4×C83C2312yes—
227C2×C4⋊C4×C83C2318yes—
228C2×C4⋊C4×C83C2311yescharacteristic
229C2×C4⋊C4×C83C2314yes—
230C2×C4⋊C4×C83C2311yescharacteristic
231C2×C4⋊C4×C83C23116yescomplemented
232C2×C22⋊C4×C83C2312yes—
233C2×C22⋊C4×C83C2314yes—
234C2×C42×C83C2312yes—
235C2×C42×C83C2314yes—
236C23×D83—24no—
237C23×D83—24no—
238C23×D83—24no—
239C23×D83C2414yes—
240C23×D83C2412yes—
241C23×D83C2411yescharacteristic
242C23×D83C2411yescharacteristic
243#13050590—232no—
244#13050590—464no—
245C2×Dic166—24no—
246C2×Dic166—48no—
247C2×Dic166C2414yes—
248C2×Dic166C24116yes—
249C2×D332—28no—
250C2×D332—28no—
251C2×D332—24no—
252C2×D332C2418yes—
253C2×D332C2418yes—
254C2×D332C2414yes—
255C2×C22⋊D83—28no—
256C2×C22⋊D83—28no—
257C2×C22⋊D83—28no—
258C2×C22⋊D83—48no—
259C2×C22⋊D83C2418yes—
260C2×C22⋊D83C2418yes—
261C2×C22⋊D83C2418yes—
262C2×C22⋊D83C24116yes—
263C22×Dic83—24no—
264C22×Dic83—44no—
265C22×Dic83C2414yes—
266C22×Dic83C2414yes—
267C22×Dic83C2411yescharacteristic
268C22×Dic83C2411yescharacteristic
269C22×Dic83C2412yes—
270C22×Dic83C2412yes—
271C22×Dic83C2412yes—
272C22×Dic83C2418yes—
273C2×C4×D83—216no—
274C2×C4×D83—24no—
275C2×C4×D83—24no—
276C2×C4×D83—24no—
277C2×C4×D83—24no—
278C2×C4×D83—28no—
279C2×C4×D83—232no—
280C2×C4×D83—432no—
281C2×C4×D83—48no—
282C2×C4×D83—48no—
283C2×C4×D83C2414yes—
284C2×C4×D83C2414yes—
285C2×C4×D83C2418yes—
286C2×C4×D83C2414yes—
287C2×C4×D83C2414yes—
288C2×C4×D83C24116yes—
289C2×C4×D83C24116yes—
290C2×C4×D83C24116yes—
291C4⋊Dic83C2414yes—
292C4⋊Dic83C2414yes—
293C4⋊Dic83C2418yes—
294C4⋊Dic83C2418yes—
295C4⋊Dic83C24116yes—
296C4⋊Dic83C2418yes—
297C4⋊Dic83C2418yes—
298Dic83⋊C4C24116yes—
299Dic83⋊C4C24116yes—
300Dic83⋊C4C2418yes—
301Dic83⋊C4C2418yes—
302Dic83⋊C4C24116yes—
303Dic83⋊C4C24116yes—
304Dic83⋊C4C24116yes—
305Dic83⋊C4C24116yes—
306C22⋊Dic83C2418yes—
307C22⋊Dic83C2418yes—
308C22⋊Dic83C2418yes—
309C22⋊Dic83C24116yes—
310(C2×D83)⋊C4C2418yes—
311(C2×D83)⋊C4C2418yes—
312(C2×D83)⋊C4C2418yes—
313(C2×D83)⋊C4C2418yes—
314(C2×D83)⋊C4C24116yes—
315(C2×D83)⋊C4C24116yes—
316(C2×D83)⋊C4C2418yes—
317(C2×D83)⋊C4C2418yes—
318C4×Dic83C24116yes—
319C4×Dic83C2418yes—
320C24×C83C2412yes—
321C24×C83C2411yescharacteristic
322#41×C83—232no—
323C2×Q8×C83—24no—
324C2×Q8×C83C2414yes—
325C2×D4×C83—28no—
326C2×D4×C83—24no—
327C2×D4×C83C2418yes—
328C2×D4×C83C2414yes—
329C22×C4×C83—28no—
330C22×C4×C83—44no—
331C22×C4×C83—48no—
332C22×C4×C83#4118yescomplemented
333C22×C4×C83C2418yes—
334C22×C4×C83C2414yes—
335C22×C4×C83C2412yes—
336C22×C4×C83C2412yes—
337C22×C4×C83C2412yes—
338C22×C4×C83C24116yes—
339C22×C4×C83C2418yes—
340C22×C4×C83C2411yescharacteristic
341C22×C4×C83C2411yescharacteristic
342C22×C4×C83C2414yes—
343C4⋊C4×C83C2414yes—
344C4⋊C4×C83C2414yes—
345C4⋊C4×C83C24116yes—
346C4⋊C4×C83C2418yes—
347C4⋊C4×C83C2418yes—
348C22⋊C4×C83C2418yes—
349C22⋊C4×C83C24116yes—
350C42×C83C24116yes—
351C42×C83C2418yes—
352C23×C83—22no—
353C23×C83—22no—
354C23×C83—24no—
355C23×C83—24no—
356C23×C83—24no—
357C23×C83C2×#4114yes—
358C23×C83C2514yes—
359C23×C83C2512yes—
360C23×C83C2511yescharacteristic
361C22×D83—232no—
362C22×D83—28no—
363C22×D83—22no—
364C22×D83—22no—
365C22×D83—22no—
366C22×D83—22no—
367C22×D83—28no—
368C22×D83—28no—
369C22×D83—24no—
370C22×D83—24no—
371C22×D83—24no—
372C22×D83H(5,𝔽2)14yes—
373C22×D832−1+414yes—
374C22×D83C2514yes—
375C22×D83C2512yes—
376C22×D83C2512yes—
377Q8×C83—28no—
378D4×C83—216no—
379D4×C83—28no—
380C2×C4×C83—24no—
381C2×C4×C83—28no—
382C2×C4×C83—24no—
383C2×C4×C83—24no—
384C2×C4×C83—216no—
385C2×C4×C83—48no—
386C2×C4×C83—416no—
387C2×C4×C83C2×#4114yes—
388C2×C4×C83C2×#4114yes—
389C2×C4×C83C2×#41116yescomplemented
390C2×C4×C83C2514yes—
391C2×C4×C83C2514yes—
392C2×C4×C83C2518yes—
393C2×C4×C83C2514yes—
394C2×C4×C83C2512yes—
395C2×C4×C83C2512yes—
396C22⋊D83—216no—
397C22⋊D83—216no—
398C22⋊D83—216no—
399C22⋊D83—416no—
400C2×Dic83—28no—
401C2×Dic83—22no—
402C2×Dic83—22no—
403C2×Dic83—24no—
404C2×Dic83—28no—
405C2×Dic83—24no—
406C2×Dic83—24no—
407C2×Dic83—48no—
408C2×Dic83C2514yes—
409C2×Dic83C2514yes—
410C2×Dic83C2514yes—
411C2×Dic83C2512yes—
412C2×Dic83C2512yes—
413C2×Dic83C2518yes—
414D332—216no—
415D332—216no—
416D332—28no—
417C4×D83—232no—
418C4×D83—28no—
419C4×D83—28no—
420C4×D83—28no—
421C4×D83—28no—
422C4×D83—216no—
423C4×D83—416no—
424C4×D83—416no—
425Dic166—28no—
426Dic166—416no—
427C22×C83—22no—
428C22×C83—22no—
429C22×C83—28no—
430C22×C83—24no—
431C22×C83—24no—
432C22×C83—24no—
433C22×C83—48no—
434C22×C83C22×#4114yes—
435C22×C83C22×#4112yes—
436C22×C83C2×H(5,𝔽2)12yes—
437C22×C83C2×2−1+412yes—
438C22×C83C2611yescharacteristic
439C2×D83—232no—
440C2×D83—22no—
441C2×D83—22no—
442C2×D83—22no—
443C2×D83—22no—
444C2×D83—28no—
445C2×D83—28no—
446C2×D83—24no—
447C2×D83—24no—
448C2×D83—24no—
449C2×D83—48no—
450C2×D83C2×H(5,𝔽2)14yes—
451C2×D83C2×2−1+414yes—
452C4×C83—24no—
453C4×C83—24no—
454C4×C83—28no—
455C4×C83—24no—
456C4×C83C22×#4114yes—
457C4×C83C22×#4114yes—
458Dic83—24no—
459Dic83—22no—
460Dic83—22no—
461Dic83—24no—
462Dic83—28no—
463Dic83—24no—
464C2×#3492—831nomaximal, Sylow
465C2×C83—24no—
466C2×C83—44no—
467C2×C83#349214yescomplemented
468C2×C83C23×#4111yescharacteristic
469C2×C83C22×H(5,𝔽2)11yescharacteristic
470C2×C83C22×2−1+411yescharacteristic
471D83—24no—
472D83—24no—
473D83—44no—
474#3492—8332no—
475C2×#554—832no—
476C2×#554—832no—
477C2×#553—832no—
478C2×#553—832no—
479C2×#552—832no—
480C2×#552—832no—
481C2×#547—832no—
482C2×#547—832no—
483C2×#544—831no—
484C2×#539—834no—
485C2×#537—831no—
486C2×#525—831no—
487C2×#525—834no—
488C2×#525—831no—
489C2×#520—831no—
490C2×#520D8311yescharacteristic, complemented
491C23×C4⋊C4—831no—
492C83C2×#349211yescharacteristic, complemented, Sylow
493C22×#41—834no—
494C22×#41—831no—
495C22×#41C2×D8311yescharacteristic
496C24×C4—832no—
497C24×C4—831no—
498#554—8332no—
499#554—8332no—
500#553—8332no—
501#553—8332no—
502#552—8332no—
503#552—8332no—
504#547—8332no—
505#547—8332no—
506#544—8316no—
507#539—8364no—
508#537—8316no—
509C2×C4⋊Q8—832no—
510C2×C4⋊Q8—832no—
511C2×#126—834no—
512C2×#126—834no—
513C2×#125—834no—
514C2×#125—832no—
515C2×#125—834no—
516C2×#125—832no—
517#525—8316no—
518#525—8364no—
519#525—8316no—
520C2×#123—832no—
521C2×#123—834no—
522C2×#123—834no—
523C2×#123—832no—
524C2×#123—834no—
525C2×#123—834no—
526C2×C22⋊Q8—831no—
527C2×C22⋊Q8—831no—
528C2×C22⋊Q8—832no—
529C2×C22⋊Q8—832no—
530C2×C22⋊Q8—834no—
531C2×C22⋊Q8—834no—
532C2×C22⋊Q8—831no—
533C2×C22⋊Q8—831no—
534C2×C22⋊Q8—834no—
535C2×C22⋊Q8—834no—
536C2×#121—834no—
537C2×#121—831no—
538C2×#121—831no—
539C2×#121—832no—
540C2×#121—832no—
541C2×#121—831no—
542C2×#121—831no—
543C2×#121—834no—
544C2×#120—832no—
545C2×#120—832no—
546#520—8316no—
547#520C2×D83116yescomplemented
548C2×C4×Q8—832no—
549C2×C4×Q8C2×D8312yescomplemented
550C2×C4×D4—834no—
551C2×C4×D4—832no—
552C2×C4×D4—834no—
553C2×C4×D4—832no—
554C2×C4×D4—832no—
555C2×C4×D4—832no—
556C2×C4×D4—834no—
557C2×C4×D4—832no—
558C2×C4×D4C2×D8314yes—
559C2×C4×D4C2×D8312yescomplemented
560C2×#117—831no—
561C2×#117—832no—
562C2×#117—834no—
563C2×#117C2×D8311yescharacteristic
564C2×#117C2×D8312yescomplemented
565C22×C4⋊C4—832no—
566C22×C4⋊C4—831no—
567C22×C4⋊C4—832no—
568C22×C4⋊C4—832no—
569C22×C4⋊C4—832no—
570C22×C4⋊C4—832no—
571C22×C4⋊C4—8316no—
572C22×C4⋊C4—832no—
573C22×C4⋊C4C2×D8311yescharacteristic
574C22×C4⋊C4C2×D8312yescomplemented
575C25—831no—
576C2×#41—28no—
577C2×#41—33216no—
578C2×#41—8332no—
579C2×#41—838no—
580C2×#41—1668no—
581C2×#41C22×D8318yes—
582C22×Q8—834no—
583C22×Q8—831no—
584C22×Q8C22×D8311yescharacteristic
585C22×D4—834no—
586C22×D4—832no—
587C22×D4—832no—
588C22×D4—832no—
589C22×D4—832no—
590C22×D4—831no—
591C22×D4—832no—
592C22×D4C22×D8312yes—
593C22×D4C22×D8311yescharacteristic
594C23×C4—3328no—
595C23×C4—832no—
596C23×C4—834no—
597C23×C4—8316no—
598C23×C4—834no—
599C23×C4—831no—
600C23×C4—834no—
601C23×C4—831no—
602C23×C4—831no—
603C23×C4—831no—
604C23×C4—831no—
605C23×C4—838no—
606C23×C4—832no—
607C23×C4—1668no—
608C23×C4C22×D8312yes—
609C23×C4C22×D8312yes—
610C23×C4C22×D8314yes—
611C23×C4C22×D8311yescharacteristic
612C4⋊Q8—8316no—
613C4⋊Q8—8316no—
614#126—8332no—
615#126—8332no—
616#125—8332no—
617#125—8316no—
618#125—8332no—
619#125—8316no—
620#123—8316no—
621#123—8332no—
622#123—8332no—
623#123—8332no—
624#123—8316no—
625#123—8332no—
626C22⋊Q8—838no—
627C22⋊Q8—838no—
628C22⋊Q8—8316no—
629C22⋊Q8—8316no—
630C22⋊Q8—8332no—
631C22⋊Q8—8332no—
632C22⋊Q8—8332no—
633C22⋊Q8—838no—
634C22⋊Q8—838no—
635C22⋊Q8—8332no—
636#121—838no—
637#121—838no—
638#121—8316no—
639#121—8332no—
640#121—8316no—
641#121—838no—
642#121—838no—
643#121—8332no—
644#120—8316no—
645#120—8316no—
646C4×Q8—8316no—
647C4×Q8C22×D83116yescomplemented
648C4×D4—8332no—
649C4×D4—8316no—
650C4×D4—8332no—
651C4×D4—8316no—
652C4×D4—8316no—
653C4×D4—8316no—
654C4×D4—8332no—
655C4×D4—8316no—
656C4×D4C22×D83132yes—
657C4×D4C22×D83116yescomplemented
658#117—838no—
659#117—8316no—
660#117—8332no—
661#117C22×D8318yes—
662#117C22×D83116yescomplemented
663C2×C4⋊C4—832no—
664C2×C4⋊C4—832no—
665C2×C4⋊C4—834no—
666C2×C4⋊C4—834no—
667C2×C4⋊C4—838no—
668C2×C4⋊C4—8316no—
669C2×C4⋊C4—831no—
670C2×C4⋊C4—834no—
671C2×C4⋊C4—831no—
672C2×C4⋊C4—834no—
673C2×C4⋊C4—834no—
674C2×C4⋊C4—832no—
675C2×C4⋊C4—832no—
676C2×C4⋊C4—834no—
677C2×C4⋊C4—834no—
678C2×C4⋊C4—832no—
679C2×C4⋊C4—832no—
680C2×C4⋊C4—8316no—
681C2×C4⋊C4—8316no—
682C2×C4⋊C4—8316no—
683C2×C4⋊C4—8316no—
684C2×C4⋊C4—8316no—
685C2×C4⋊C4C22×D8312yes—
686C2×C4⋊C4C22×D8312yes—
687C2×C4⋊C4C22×D8318yes—
688C2×C4⋊C4C22×D8311yescharacteristic
689C2×C4⋊C4C22×D8314yes—
690C2×C4⋊C4C22×D8311yescharacteristic
691C2×C4⋊C4C22×D83116yescomplemented
692C2×C22⋊C4—832no—
693C2×C22⋊C4—834no—
694C2×C22⋊C4—832no—
695C2×C22⋊C4—832no—
696C2×C22⋊C4—832no—
697C2×C22⋊C4—832no—
698C2×C22⋊C4—834no—
699C2×C22⋊C4—832no—
700C2×C22⋊C4—832no—
701C2×C22⋊C4—834no—
702C2×C22⋊C4—832no—
703C2×C22⋊C4—832no—
704C2×C22⋊C4C22×D8312yes—
705C2×C22⋊C4C22×D8314yes—
706C2×C42—834no—
707C2×C42—832no—
708C2×C42C22×D8314yes—
709C2×C42C22×D8312yes—
710C24—831no—
711C24—831no—
712C24—834no—
713C24—832no—
714C24—1664no—
715C24—1664no—
716C24—1664no—
717C24C23×D8312yes—
718C24C23×D8311yescharacteristic
719#41—232no—
720#41—33264no—
721#41—16632no—
722C2×Q8—24no—
723C2×Q8—3328no—
724C2×Q8—8316no—
725C2×Q8—834no—
726C2×Q8—1664no—
727C2×Q8C23×D8314yes—
728C2×D4—28no—
729C2×D4—24no—
730C2×D4—3328no—
731C2×D4—8316no—
732C2×D4—838no—
733C2×D4—838no—
734C2×D4—838no—
735C2×D4—838no—
736C2×D4—834no—
737C2×D4—838no—
738C2×D4—1668no—
739C2×D4—1668no—
740C2×D4—1668no—
741C2×D4—1668no—
742C2×D4—1668no—
743C2×D4—1664no—
744C2×D4C23×D8318yes—
745C2×D4C23×D8314yes—
746C22×C4—28no—
747C22×C4—44no—
748C22×C4—48no—
749C22×C4—3328no—
750C22×C4—3328no—
751C22×C4—33232no—
752C22×C4—3324no—
753C22×C4—838no—
754C22×C4—8316no—
755C22×C4—8316no—
756C22×C4—834no—
757C22×C4—832no—
758C22×C4—832no—
759C22×C4—832no—
760C22×C4—831no—
761C22×C4—831no—
762C22×C4—834no—
763C22×C4—8316no—
764C22×C4—834no—
765C22×C4—834no—
766C22×C4—834no—
767C22×C4—834no—
768C22×C4—838no—
769C22×C4—16616no—
770C22×C4—1664no—
771C22×C4—1664no—
772C22×C4—1664no—
773C22×C4—1664no—
774C22×C4—1664no—
775C22×C4—1668no—
776C22×C4—16632no—
777C22×C4#1305059018yescomplemented
778C22×C4C23×D8318yes—
779C22×C4C23×D8314yes—
780C22×C4C23×D8312yes—
781C22×C4C23×D8312yes—
782C22×C4C23×D8312yes—
783C22×C4C23×D8318yes—
784C22×C4C23×D83116yes—
785C22×C4C23×D8311yescharacteristic
786C22×C4C23×D8311yescharacteristic
787C22×C4C23×D8314yes—
788C4⋊C4—838no—
789C4⋊C4—838no—
790C4⋊C4—8316no—
791C4⋊C4—8316no—
792C4⋊C4—834no—
793C4⋊C4—8316no—
794C4⋊C4—834no—
795C4⋊C4—8316no—
796C4⋊C4—8316no—
797C4⋊C4—838no—
798C4⋊C4—838no—
799C4⋊C4—8316no—
800C4⋊C4—8316no—
801C4⋊C4—838no—
802C4⋊C4—838no—
803C4⋊C4C23×D8318yes—
804C4⋊C4C23×D8318yes—
805C4⋊C4C23×D8314yes—
806C4⋊C4C23×D83116yes—
807C4⋊C4C23×D8314yes—
808C22⋊C4—838no—
809C22⋊C4—8316no—
810C22⋊C4—838no—
811C22⋊C4—838no—
812C22⋊C4—838no—
813C22⋊C4—838no—
814C22⋊C4—8316no—
815C22⋊C4—838no—
816C22⋊C4—838no—
817C22⋊C4—8316no—
818C22⋊C4—838no—
819C22⋊C4—838no—
820C22⋊C4C23×D8318yes—
821C22⋊C4C23×D83116yes—
822C42—8316no—
823C42—838no—
824C42C23×D83116yes—
825C42C23×D8318yes—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—834no—
832C23—834no—
833C23—832no—
834C23—832no—
835C23—834no—
836C23—1668no—
837C23—1668no—
838C23—16632no—
839C23—1664no—
840C23—1664no—
841C23—1664no—
842C23—1668no—
843C23—1662no—
844C23—1662no—
845C23—1662no—
846C23—1662no—
847C23C2×#1305059014yes—
848C23C24×D8314yes—
849C23C24×D8312yes—
850C23C24×D8311yescharacteristic
851Q8—28no—
852Q8—33216no—
853Q8—1668no—
854D4—216no—
855D4—28no—
856D4—33216no—
857D4—16616no—
858D4—16616no—
859D4—16616no—
860D4—16616no—
861D4—16616no—
862D4—1668no—
863C2×C4—24no—
864C2×C4—28no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—216no—
868C2×C4—48no—
869C2×C4—416no—
870C2×C4—33216no—
871C2×C4—33216no—
872C2×C4—3328no—
873C2×C4—834no—
874C2×C4—834no—
875C2×C4—834no—
876C2×C4—832no—
877C2×C4—832no—
878C2×C4—838no—
879C2×C4—16632no—
880C2×C4—1668no—
881C2×C4—1662no—
882C2×C4—1662no—
883C2×C4—1664no—
884C2×C4—1668no—
885C2×C4—1664no—
886C2×C4—1664no—
887C2×C4—1668no—
888C2×C4—1668no—
889C2×C4—1668no—
890C2×C4—1668no—
891C2×C4—16616no—
892C2×C4C2×#1305059014yes—
893C2×C4C2×#1305059014yes—
894C2×C4C2×#13050590116yescomplemented
895C2×C4C24×D8318yes—
896C2×C4C24×D8314yes—
897C2×C4C24×D8314yes—
898C2×C4C24×D8314yes—
899C2×C4C24×D8312yes—
900C2×C4C24×D8312yes—
901C22—28no—
902C22—22no—
903C22—22no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—48no—
908C22—3328no—
909C22—834no—
910C22—834no—
911C22—16632no—
912C22—1664no—
913C22—1664no—
914C22—1664no—
915C22—1668no—
916C22—1668no—
917C22—1662no—
918C22—1662no—
919C22—1662no—
920C22—1662no—
921C22C22×#1305059014yes—
922C22C22×#1305059012yes—
923C22H(5,𝔽2)×D8312yes—
924C222−1+4×D8312yes—
925C22C25×D8311yescharacteristic
926C4—24no—
927C4—28no—
928C4—24no—
929C4—24no—
930C4—1662no—
931C4—1662no—
932C4—1664no—
933C4—1668no—
934C4—1664no—
935C4—1664no—
936C4C22×#1305059014yes—
937C4C22×#1305059014yes—
938C2—24no—
939C2—44no—
940C2—3324no—
941C2—1664no—
942C2—1664no—
943C2#2492116614yesdirect product factor
944C2C23×#1305059011yescharacteristic
945C2C2×H(5,𝔽2)×D8311yescharacteristic
946C2C2×2−1+4×D8311yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#520×C83C2
socleC23×C83C25
hypercenterC2×#520D83
hypocenterC83C2×#3492
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #24921166C2direct (N × H)
2. C2×#19128411C2semidirect
3. C2×#19128406C2semidirect
4. C2×#19128401C2semidirect
5. C2×#19128395C2semidirect
6. C2×#19128392C2semidirect
7. C2×#19128390C2semidirect
8. C2×#19128356C2semidirect
9. C2×#19128352C2semidirect
10. C2×#19128329C2semidirect
11. C2×#19128293C2semidirect
12. C2×#19128279C2semidirect
13. C2×#19128213C2semidirect
14. C2×#19128210C2semidirect
15. C2×#19128208C2semidirect
16. C2×#19128182C2semidirect
17. C22×C4⋊C4×D83C2semidirect
18. C2×#520×C83C2semidirect
23. #19128411C22semidirect
24. #19128406C22semidirect
25. #19128401C22semidirect
26. #19128395C22semidirect
27. #19128392C22semidirect
28. #19128390C22semidirect
29. #19128356C22semidirect
30. #19128352C22semidirect
31. #19128329C22semidirect
32. #19128293C22semidirect
33. #19128279C22semidirect
34. C2×#14581792C22semidirect
35. C2×#14581791C22semidirect
36. C2×#14581786C22semidirect
37. C2×#14581785C22semidirect
38. C2×#14581784C22semidirect
39. C2×#14581784C22semidirect
40. C2×#14581783C22semidirect
41. C2×#14581782C22semidirect
42. #19128213C22semidirect
43. #19128210C22semidirect
44. #19128208C22semidirect
47. C2×#14581775C22semidirect
49. C2×#14581774C22semidirect
53. C2×#14581771C22semidirect
54. C2×#14581771C22semidirect
56. C2×#14581770C22semidirect
60. C2×#14581768C22semidirect
63. C2×#14581766C22semidirect
68. C2×#14581763C22semidirect
71. #19128182C22semidirect
72. C2×#14581757C22semidirect
76. C2×#14581754C22semidirect
82. C2×#14581750C22semidirect
90. C2×C4⋊C4×D83C22semidirect
91. C2×C4⋊C4×D83C22semidirect
93. #520×C83C22semidirect
94. C2×C4×Q8×C83C22semidirect
96. C2×C4×D4×C83C22semidirect
98. C2×#117×C83C22semidirect
100. C22×C4⋊C4×C83C22semidirect
129. #14581792C23semidirect
130. #14581791C23semidirect
131. #14581786C23semidirect
132. #14581785C23semidirect
133. #14581784C23semidirect
134. #14581784C23semidirect
135. #14581783C23semidirect
136. #14581782C23semidirect
139. #14581775C23semidirect
141. #14581774C23semidirect
145. #14581771C23semidirect
146. #14581771C23semidirect
148. #14581770C23semidirect
152. #14581768C23semidirect
155. #14581766C23semidirect
160. #14581763C23semidirect
163. #14581757C23semidirect
167. #14581754C23semidirect
173. #14581750C23semidirect
196. C4⋊C4×D83C23semidirect
220. C4×Q8×C83C23semidirect
222. C4×D4×C83C23semidirect
224. #117×C83C23semidirect
231. C2×C4⋊C4×C83C23semidirect
332. C22×C4×C83#41semidirect
389. C2×C4×C83C2×#41semidirect
467. C2×C83#3492semidirect
490. C2×#520D83semidirect
492. C83C2×#3492semidirect
547. #520C2×D83semidirect
549. C2×C4×Q8C2×D83semidirect
559. C2×C4×D4C2×D83semidirect
564. C2×#117C2×D83semidirect
574. C22×C4⋊C4C2×D83semidirect
647. C4×Q8C22×D83semidirect
657. C4×D4C22×D83semidirect
662. #117C22×D83semidirect
691. C2×C4⋊C4C22×D83semidirect
777. C22×C4#13050590semidirect
894. C2×C4C2×#13050590semidirect
943. C2#24921166direct (N × H)

Maximal subgroups

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

subgroupindex
#249211662
C2×#191284112
C2×#191284062
C2×#191284012
C2×#191283952
C2×#191283922
C2×#191283902
C2×#191283562
C2×#191283522
C2×#191283292
C2×#191282932
C2×#191282792
C2×#191282132
C2×#191282102
C2×#191282082
C2×#191281822
C22×C4⋊C4×D832
C2×#520×C832
C2×#349283