Finite Group Databasebeta

← C2×#24921442 #36312512

Subgroups — C2×#24921442 #36312512

Order 21248.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921442C2132yesmaximal, direct product factor
2C2×#19128430C211yesmaximal, characteristic, complemented
3C2×#19128412C211yesmaximal, characteristic, complemented
4C2×#19128399C212yesmaximal, complemented
5C2×#19128393C212yesmaximal, complemented
6C2×#19128393C214yesmaximal, complemented
7C2×#19128389C212yesmaximal, complemented
8C2×#19128355C211yesmaximal, characteristic, complemented
9C2×#19128355C212yesmaximal, complemented
10C2×#19128314C212yesmaximal, complemented
11C2×#19128300C214yesmaximal, complemented
12C2×#19128256C211yesmaximal, characteristic, complemented
13C2×#19128238C211yesmaximal, characteristic, complemented
14C2×#19128237C212yesmaximal, complemented
15C22×#14581783C212yesmaximal, complemented
16C2×#19128180C212yesmaximal, complemented
17C2×C4×#13050589C211yesmaximal, characteristic, complemented
18C2×#554×C83C211yesmaximal, characteristic, complemented
19C22×#13050589C2211yescharacteristic
20C22×#13050589C2212yes—
21#19128430C22116yescomplemented
22#19128412C22116yescomplemented
23#19128399C22132yescomplemented
24#19128393C22132yescomplemented
25#19128393C22164yescomplemented
26#19128389C22132yescomplemented
27#19128355C22116yescomplemented
28#19128355C22132yescomplemented
29#19128314C22132yescomplemented
30#19128300C22164yescomplemented
31#19128256C22116yescomplemented
32C2×#14581792C2212yes—
33C2×#14581792C2211yescharacteristic
34#19128238C22116yescomplemented
35#19128237C22132yescomplemented
36C2×#14581787C2214yes—
37C2×#14581787C2214yes—
38C2×#14581787C2214yes—
39C2×#14581787C2212yes—
40C2×#14581783C2214yes—
41C2×#14581783C2214yes—
42C2×#14581783C2211yescharacteristic
43C2×#14581783C2214yes—
44C2×#14581783C2212yes—
45C2×#14581783C2212yes—
46C2×#14581783C2212yes—
47C2×#14581783C2214yes—
48C2×#14581783C22132yescomplemented
49C2×#14581781C2211yescharacteristic
50C2×#14581777C2214yes—
51C2×#14581777C2212yes—
52C2×#14581776C2214yes—
53C2×#14581776C2214yes—
54C2×#14581776C2214yes—
55C2×#14581772C2212yes—
56C2×#14581772C2212yes—
57C2×#14581772C2212yes—
58C2×#14581768C2211yescharacteristic
59C2×#14581768C2214yes—
60C2×#14581768C2212yes—
61C2×#14581767C2211yescharacteristic
62C2×#14581766C2212yes—
63C2×#14581766C2214yes—
64#19128180C22132yescomplemented
65C4×#13050589C22116yescomplemented
66C2×Q8×Dic83C2212yes—
67C2×Q8×Dic83C2212yes—
68C2×C4×Dic166C2211yescharacteristic
69C2×C4×Dic166C2212yes—
70C2×#14581757C2211yescharacteristic
71C2×#14581757C2212yes—
72C2×C4×D332C2212yes—
73C2×C4×D332C2211yescharacteristic
74C2×D4×Dic83C2211yescharacteristic
75C2×#14581754C2212yes—
76C2×C4×C22⋊D83C2212yes—
77C2×C4×C22⋊D83C2214yes—
78C2×(C22⋊D83)⋊C4C2212yes—
79C2×(C22⋊D83)⋊C4C2214yes—
80C2×#14581750C2211yescharacteristic
81C2×#14581750C2214yes—
82C2×#14581750C2212yes—
83C2×#14581749C2212yes—
84C2×#14581748C2212yes—
85C2×#14581748C2214yes—
86C22×C4⋊Dic83C2214yes—
87C22×C4⋊Dic83C2212yes—
88C22×Dic83⋊C4C2214yes—
89C2×C4⋊C4×D83C2212yes—
90C22×C4×Dic83C2212yes—
91C2×C42×D83C2211yescharacteristic
92#554×C83C22116yescomplemented
93C2×C4⋊Q8×C83C2211yescharacteristic
94C2×#125×C83C2212yes—
95C2×C22⋊Q8×C83C2212yes—
96C2×C22⋊Q8×C83C2214yes—
97C2×C4×Q8×C83C2211yescharacteristic
98C2×C4×D4×C83C2211yescharacteristic
99C2×C4×D4×C83C2212yes—
100C22×C4⋊C4×C83C2212yes—
101C2×#13050589—28no—
102C2×#13050589—216no—
103C2×#13050589C2318yes—
104C2×#13050589C23116yes—
105C22×Dic166C2311yescharacteristic
106C22×Dic166C2312yes—
107C22×D332C2311yescharacteristic
108C22×D332C2312yes—
109C22×C22⋊D83C2312yes—
110C22×C22⋊D83C2314yes—
111C23×Dic83C2312yes—
112C23×Dic83C2314yes—
113C23×Dic83C2312yes—
114C22×C4×D83C2311yescharacteristic
115C22×C4×D83C2311yescharacteristic
116C22×C4×D83C2312yes—
117C22×C4×D83C2311yescharacteristic
118C22×C4×D83C2314yes—
119#14581792C2318yes—
120#14581792C23116yes—
121#14581787C23132yes—
122#14581787C23116yes—
123#14581787C23132yes—
124#14581787C23132yes—
125#14581783C23132yes—
126#14581783C23132yes—
127#14581783C23116yes—
128#14581783C23132yes—
129#14581783C23116yes—
130#14581783C2318yes—
131#14581783C23116yes—
132#14581783C23132yes—
133#14581781C2318yes—
134#14581777C23132yes—
135#14581777C23116yes—
136#14581776C23132yes—
137#14581776C23132yes—
138#14581776C23132yes—
139#14581772C23116yes—
140#14581772C23116yes—
141#14581772C23116yes—
142#14581768C2318yes—
143#14581768C23132yes—
144#14581768C23116yes—
145#14581767C2318yes—
146#14581766C23116yes—
147#14581766C23132yes—
148Q8×Dic83C23116yes—
149Q8×Dic83C23116yes—
150C4×Dic166C23116yes—
151C4×Dic166C2318yes—
152#14581757C2318yes—
153#14581757C23116yes—
154C4×D332C23116yes—
155C4×D332C2318yes—
156D4×Dic83C2318yes—
157#14581754C23116yes—
158C4×C22⋊D83C23116yes—
159C4×C22⋊D83C23132yes—
160(C22⋊D83)⋊C4C23116yes—
161(C22⋊D83)⋊C4C23132yes—
162#14581750C2318yes—
163#14581750C23132yes—
164#14581750C23116yes—
165#14581749C23116yes—
166#14581748C23116yes—
167#14581748C23132yes—
168C2×C4⋊Dic83C23116yes—
169C2×C4⋊Dic83C23132yes—
170C2×C4⋊Dic83C2311yescharacteristic
171C2×C4⋊Dic83C2311yescharacteristic
172C2×C4⋊Dic83C2312yes—
173C2×C4⋊Dic83C2312yes—
174C2×C4⋊Dic83C2314yes—
175C2×C4⋊Dic83C2314yes—
176C2×C4⋊Dic83C2314yes—
177C2×C4⋊Dic83C2314yes—
178C2×C4⋊Dic83C2312yes—
179C2×C4⋊Dic83C2314yes—
180C2×Dic83⋊C4C2314yes—
181C2×Dic83⋊C4C2312yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2314yes—
184C2×Dic83⋊C4C23132yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2312yes—
187C2×Dic83⋊C4C2312yes—
188C4⋊C4×D83C23116yes—
189C2×C22⋊Dic83C2312yes—
190C2×(C2×D83)⋊C4C2312yes—
191C2×(C2×D83)⋊C4C2312yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2312yes—
194C2×(C2×D83)⋊C4C2314yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2312yes—
199C2×C4×Dic83C2311yescharacteristic
200C2×C4×Dic83C2311yescharacteristic
201C2×C4×Dic83C2311yescharacteristic
202C2×C4×Dic83C2312yes—
203C2×C4×Dic83C2312yes—
204C2×C4×Dic83C2312yes—
205C2×C4×Dic83C23116yes—
206C2×C4×Dic83C2314yes—
207C2×C4×Dic83C2314yes—
208C42×D83C2318yes—
209C22×Q8×C83C2311yescharacteristic
210C22×Q8×C83C2312yes—
211C22×D4×C83C2311yescharacteristic
212C23×C4×C83C2312yes—
213C23×C4×C83C2314yes—
214C4⋊Q8×C83C2318yes—
215#125×C83C23116yes—
216C22⋊Q8×C83C23116yes—
217C22⋊Q8×C83C23132yes—
218C4×Q8×C83C2318yes—
219C4×D4×C83C2318yes—
220C4×D4×C83C23116yes—
221C2×C4⋊C4×C83C2311yescharacteristic
222C2×C4⋊C4×C83C2314yes—
223C2×C4⋊C4×C83C2312yes—
224C2×C4⋊C4×C83C23116yes—
225C2×C4⋊C4×C83C2311yescharacteristic
226C2×C4⋊C4×C83C2312yes—
227C2×C4⋊C4×C83C2312yes—
228C2×C4⋊C4×C83C2314yes—
229C2×C22⋊C4×C83C2312yes—
230C2×C22⋊C4×C83C2314yes—
231C2×C42×C83C2312yes—
232C2×C42×C83C2311yescharacteristic
233C23×D83C2411yescharacteristic
234C23×D83C2412yes—
235#13050589—232no—
236#13050589—264no—
237C2×Dic166—24no—
238C2×Dic166—28no—
239C2×Dic166C2418yes—
240C2×Dic166C2414yes—
241C2×D332—24no—
242C2×D332—44no—
243C2×D332C2414yes—
244C2×D332C2418yes—
245C2×C22⋊D83—28no—
246C2×C22⋊D83—216no—
247C2×C22⋊D83C24116yes—
248C2×C22⋊D83C2418yes—
249C22×Dic83—28no—
250C22×Dic83—216no—
251C22×Dic83—44no—
252C22×Dic83C2418yes—
253C22×Dic83C24116yes—
254C22×Dic83C2412yes—
255C22×Dic83C2411yescharacteristic
256C22×Dic83C2411yescharacteristic
257C22×Dic83C2412yes—
258C22×Dic83C2411yescharacteristic
259C22×Dic83C2412yes—
260C22×Dic83C2414yes—
261C22×Dic83C2418yes—
262C2×C4×D83—24no—
263C2×C4×D83—28no—
264C2×C4×D83—24no—
265C2×C4×D83—48no—
266C2×C4×D83—42no—
267C2×C4×D83C2414yes—
268C2×C4×D83C2414yes—
269C2×C4×D83C2418yes—
270C2×C4×D83C2414yes—
271C2×C4×D83C24116yes—
272C4⋊Dic83C24116yes—
273C4⋊Dic83C2418yes—
274C4⋊Dic83C24116yes—
275C4⋊Dic83C2418yes—
276C4⋊Dic83C2414yes—
277C4⋊Dic83C24116yes—
278C4⋊Dic83C24116yes—
279C4⋊Dic83C24116yes—
280C4⋊Dic83C2418yes—
281C4⋊Dic83C2414yes—
282Dic83⋊C4C2418yes—
283Dic83⋊C4C24116yes—
284Dic83⋊C4C24116yes—
285Dic83⋊C4C2418yes—
286Dic83⋊C4C2418yes—
287Dic83⋊C4C24116yes—
288Dic83⋊C4C2418yes—
289C22⋊Dic83C2418yes—
290(C2×D83)⋊C4C24116yes—
291(C2×D83)⋊C4C24116yes—
292(C2×D83)⋊C4C24116yes—
293(C2×D83)⋊C4C2418yes—
294(C2×D83)⋊C4C2418yes—
295(C2×D83)⋊C4C2418yes—
296(C2×D83)⋊C4C2418yes—
297(C2×D83)⋊C4C2418yes—
298(C2×D83)⋊C4C2418yes—
299C4×Dic83C2414yes—
300C4×Dic83C2418yes—
301C4×Dic83C2418yes—
302C4×Dic83C2418yes—
303C4×Dic83C24116yes—
304C4×Dic83C24116yes—
305C4×Dic83C2414yes—
306C4×Dic83C2414yes—
307C24×C83C2412yes—
308C2×Q8×C83—24no—
309C2×Q8×C83—44no—
310C2×Q8×C83C2414yes—
311C2×Q8×C83C2418yes—
312C2×D4×C83#4118yes—
313C2×D4×C83C2414yes—
314C22×C4×C83—28no—
315C22×C4×C83—48no—
316C22×C4×C83C2418yes—
317C22×C4×C83C2411yescharacteristic
318C22×C4×C83C2414yes—
319C22×C4×C83C2412yes—
320C22×C4×C83C2412yes—
321C22×C4×C83C2412yes—
322C22×C4×C83C24116yes—
323C22×C4×C83C2411yescharacteristic
324C22×C4×C83C2411yescharacteristic
325C4⋊C4×C83C2414yes—
326C4⋊C4×C83C2414yes—
327C4⋊C4×C83C2418yes—
328C4⋊C4×C83C24116yes—
329C4⋊C4×C83C2418yes—
330C4⋊C4×C83C2418yes—
331C4⋊C4×C83C24116yes—
332C22⋊C4×C83C24116yes—
333C22⋊C4×C83C2418yes—
334C42×C83C2418yes—
335C42×C83C2414yes—
336C23×C83—24no—
337C23×C83—24no—
338C23×C83C2×#4118yes—
339C23×C83C2514yes—
340C23×C83C2511yescharacteristic
341C22×D83—22no—
342C22×D83—24no—
343C22×D83—22no—
344C22×D83—24no—
345C22×D83—24no—
346C22×D83—22no—
347C22×D83C2512yes—
348C22×D83C2514yes—
349Q8×C83—28no—
350Q8×C83—48no—
351D4×C83C2×#41116yes—
352C2×C4×C83—24no—
353C2×C4×C83—24no—
354C2×C4×C83—24no—
355C2×C4×C83—28no—
356C2×C4×C83—22no—
357C2×C4×C83—216no—
358C2×C4×C83—416no—
359C2×C4×C83C2×#4114yes—
360C2×C4×C832−1+414yes—
361C2×C4×C83C2514yes—
362C2×C4×C83C2512yes—
363C2×C4×C83C2514yes—
364C2×C4×C83C2514yes—
365C2×C4×C83C2518yes—
366C2×C4×C83C2512yes—
367C2×C4×C83C2512yes—
368C22⋊D83—232no—
369C22⋊D83—216no—
370C2×Dic83—22no—
371C2×Dic83—24no—
372C2×Dic83—24no—
373C2×Dic83—28no—
374C2×Dic83—216no—
375C2×Dic83—232no—
376C2×Dic83—22no—
377C2×Dic83—24no—
378C2×Dic83—22no—
379C2×Dic83—48no—
380C2×Dic83C2512yes—
381C2×Dic83C2512yes—
382C2×Dic83C2512yes—
383C2×Dic83C2514yes—
384C2×Dic83C2514yes—
385C2×Dic83C2518yes—
386C2×Dic83C2514yes—
387D332—28no—
388D332—48no—
389C4×D83—28no—
390C4×D83—216no—
391C4×D83—28no—
392C4×D83—416no—
393C4×D83—44no—
394Dic166—216no—
395Dic166—28no—
396C22×C83—24no—
397C22×C83—24no—
398C22×C83—216no—
399C22×C83C22×#4118yes—
400C22×C83C22×#4112yes—
401C22×C83C2×2−1+412yes—
402C22×C83#58512yes—
403C22×C83C2611yescharacteristic
404C2×D83—22no—
405C2×D83—24no—
406C2×D83—22no—
407C2×D83—24no—
408C2×D83—24no—
409C2×D83—22no—
410C2×D83—44no—
411C2×D83—48no—
412C4×C83—24no—
413C4×C83—24no—
414C4×C83—28no—
415C4×C83—22no—
416C4×C83—24no—
417C4×C83C22×#4114yes—
418C4×C83C2×2−1+414yes—
419Dic83—24no—
420Dic83—28no—
421Dic83—22no—
422Dic83—24no—
423Dic83—22no—
424Dic83—24no—
425Dic83—22no—
426C2×#3515—831nomaximal, Sylow
427C2×C83—28no—
428C2×C83#351514yescomplemented
429C2×C83C23×#4111yescharacteristic
430C2×C83C22×2−1+411yescharacteristic
431C2×C83C2×#58511yescharacteristic
432D83—42no—
433D83—44no—
434#3515—8332no—
435C2×#557—831no—
436C2×#554—831no—
437C2×#554D8311yescharacteristic, complemented
438C2×#553—832no—
439C2×#552—832no—
440C2×#552—834no—
441C2×#552—832no—
442C2×#547—832no—
443C2×#547—831no—
444C2×#541—832no—
445C2×#539—834no—
446C2×#533—831no—
447C2×#529—832no—
448C2×#529—831no—
449C22×#125—832no—
450C2×#520—832no—
451C2×C4×#41—831no—
452C83C2×#351511yescharacteristic, complemented, Sylow
453C22×#41—831no—
454C22×#41—832no—
455#557—8316no—
456#554—8316no—
457#554C2×D83116yescomplemented
458#553—8332no—
459#552—8332no—
460#552—8364no—
461#552—8332no—
462#547—8332no—
463#547—8316no—
464#541—8332no—
465#539—8364no—
466#533—8316no—
467C2×C4⋊Q8—831no—
468C2×C4⋊Q8—832no—
469C2×C4⋊Q8C2×D8311yescharacteristic
470#529—8332no—
471#529—8316no—
472C2×#126—834no—
473C2×#126—832no—
474C2×#126—834no—
475C2×#126—834no—
476C2×#125—831no—
477C2×#125—832no—
478C2×#125—834no—
479C2×#125—834no—
480C2×#125—832no—
481C2×#125—832no—
482C2×#125—8332no—
483C2×#125—834no—
484C2×#125—834no—
485C2×#125C2×D8312yes—
486C2×#124—831no—
487C2×#123—832no—
488C2×#123—834no—
489C2×#123—834no—
490C2×#123—834no—
491C2×#123—834no—
492C2×C22⋊Q8—831no—
493C2×C22⋊Q8—832no—
494C2×C22⋊Q8—834no—
495C2×C22⋊Q8—832no—
496C2×C22⋊Q8—832no—
497C2×C22⋊Q8—832no—
498C2×C22⋊Q8C2×D8312yes—
499C2×C22⋊Q8C2×D8314yes—
500C2×#121—832no—
501C2×#121—834no—
502C2×#121—831no—
503#520—8332no—
504C4×#41—8316no—
505C2×C4×Q8—832no—
506C2×C4×Q8—832no—
507C2×C4×Q8—831no—
508C2×C4×Q8—832no—
509C2×C4×Q8—831no—
510C2×C4×Q8—832no—
511C2×C4×Q8C2×D8311yescharacteristic
512C2×C4×D4—831no—
513C2×C4×D4—832no—
514C2×C4×D4—834no—
515C2×C4×D4—832no—
516C2×C4×D4—832no—
517C2×C4×D4—834no—
518C2×C4×D4—832no—
519C2×C4×D4—831no—
520C2×C4×D4C2×D8311yescharacteristic
521C2×C4×D4C2×D8312yes—
522C2×#117—831no—
523C2×#117—834no—
524C2×#117—832no—
525C2×#117—832no—
526C2×#117—834no—
527C2×#117—832no—
528C22×C4⋊C4—834no—
529C22×C4⋊C4—832no—
530C22×C4⋊C4—834no—
531C22×C4⋊C4—832no—
532C22×C4⋊C4C2×D8312yes—
533C22×C42—832no—
534C22×C42—831no—
535C2×#41—838no—
536C2×#41—8316no—
537C2×#41—1668no—
538C2×#41—16616no—
539C22×Q8—831no—
540C22×Q8—832no—
541C22×Q8C22×D8311yescharacteristic
542C22×Q8C22×D8312yes—
543C22×D4—832no—
544C22×D4—834no—
545C22×D4—832no—
546C22×D4—831no—
547C22×D4C22×D8311yescharacteristic
548C23×C4—832no—
549C23×C4—834no—
550C23×C4—831no—
551C23×C4—834no—
552C23×C4—832no—
553C23×C4—832no—
554C23×C4—831no—
555C23×C4—831no—
556C23×C4C22×D8312yes—
557C23×C4C22×D8314yes—
558C4⋊Q8—838no—
559C4⋊Q8—8316no—
560C4⋊Q8C22×D8318yes—
561#126—8332no—
562#126—8316no—
563#126—8332no—
564#126—8332no—
565#125—838no—
566#125—8316no—
567#125—8332no—
568#125—8332no—
569#125—8316no—
570#125—8316no—
571#125—8332no—
572#125—8332no—
573#125C22×D83116yes—
574#124—838no—
575#123—8316no—
576#123—8332no—
577#123—8332no—
578#123—8332no—
579#123—8332no—
580C22⋊Q8—838no—
581C22⋊Q8—8316no—
582C22⋊Q8—8332no—
583C22⋊Q8—8316no—
584C22⋊Q8—8316no—
585C22⋊Q8—8316no—
586C22⋊Q8C22×D83116yes—
587C22⋊Q8C22×D83132yes—
588#121—8316no—
589#121—8332no—
590#121—838no—
591C4×Q8—8316no—
592C4×Q8—8316no—
593C4×Q8—838no—
594C4×Q8—8316no—
595C4×Q8—838no—
596C4×Q8—8316no—
597C4×Q8C22×D8318yes—
598C4×D4—838no—
599C4×D4—8316no—
600C4×D4—8332no—
601C4×D4—8316no—
602C4×D4—8316no—
603C4×D4—8332no—
604C4×D4—8316no—
605C4×D4—838no—
606C4×D4C22×D8318yes—
607C4×D4C22×D83116yes—
608#117—838no—
609#117—8332no—
610#117—8316no—
611#117—8316no—
612#117—8332no—
613#117—8316no—
614C2×C4⋊C4—831no—
615C2×C4⋊C4—834no—
616C2×C4⋊C4—832no—
617C2×C4⋊C4—831no—
618C2×C4⋊C4—832no—
619C2×C4⋊C4—832no—
620C2×C4⋊C4—834no—
621C2×C4⋊C4—834no—
622C2×C4⋊C4—834no—
623C2×C4⋊C4—8332no—
624C2×C4⋊C4—834no—
625C2×C4⋊C4—834no—
626C2×C4⋊C4—834no—
627C2×C4⋊C4—8316no—
628C2×C4⋊C4—8332no—
629C2×C4⋊C4—832no—
630C2×C4⋊C4—832no—
631C2×C4⋊C4—832no—
632C2×C4⋊C4—832no—
633C2×C4⋊C4—834no—
634C2×C4⋊C4—8316no—
635C2×C4⋊C4C22×D8312yes—
636C2×C4⋊C4C22×D8311yescharacteristic
637C2×C4⋊C4C22×D8312yes—
638C2×C4⋊C4C22×D8314yes—
639C2×C4⋊C4C22×D83116yes—
640C2×C4⋊C4C22×D8311yescharacteristic
641C2×C4⋊C4C22×D8314yes—
642C2×C4⋊C4C22×D8312yes—
643C2×C22⋊C4—832no—
644C2×C22⋊C4—832no—
645C2×C22⋊C4—832no—
646C2×C22⋊C4—832no—
647C2×C22⋊C4—832no—
648C2×C22⋊C4—834no—
649C2×C22⋊C4—834no—
650C2×C22⋊C4—834no—
651C2×C22⋊C4—832no—
652C2×C22⋊C4—832no—
653C2×C22⋊C4C22×D8314yes—
654C2×C22⋊C4C22×D8312yes—
655C2×C42—832no—
656C2×C42—831no—
657C2×C42—834no—
658C2×C42—834no—
659C2×C42—831no—
660C2×C42—832no—
661C2×C42—832no—
662C2×C42—8316no—
663C2×C42—831no—
664C2×C42—838no—
665C2×C42C22×D8312yes—
666C2×C42C22×D8311yescharacteristic
667C24—831no—
668C24—832no—
669C24C23×D8312yes—
670#41—16632no—
671#41—16664no—
672C2×Q8—24no—
673C2×Q8—44no—
674C2×Q8—834no—
675C2×Q8—838no—
676C2×Q8—1664no—
677C2×Q8—1668no—
678C2×Q8C23×D8314yes—
679C2×Q8C23×D8318yes—
680C2×D4—3324no—
681C2×D4—838no—
682C2×D4—8316no—
683C2×D4—838no—
684C2×D4—834no—
685C2×D4—1668no—
686C2×D4—16616no—
687C2×D4—1664no—
688C2×D4#1305059118yes—
689C2×D4C23×D8314yes—
690C22×C4—28no—
691C22×C4—48no—
692C22×C4—3328no—
693C22×C4—3322no—
694C22×C4—3324no—
695C22×C4—838no—
696C22×C4—834no—
697C22×C4—8316no—
698C22×C4—838no—
699C22×C4—8316no—
700C22×C4—831no—
701C22×C4—831no—
702C22×C4—832no—
703C22×C4—831no—
704C22×C4—834no—
705C22×C4—832no—
706C22×C4—832no—
707C22×C4—834no—
708C22×C4—834no—
709C22×C4—838no—
710C22×C4—16616no—
711C22×C4—1668no—
712C22×C4—1668no—
713C22×C4—1664no—
714C22×C4—1664no—
715C22×C4C23×D8318yes—
716C22×C4C23×D8312yes—
717C22×C4C23×D8312yes—
718C22×C4C23×D8311yescharacteristic
719C22×C4C23×D8314yes—
720C22×C4C23×D8312yes—
721C22×C4C23×D83116yes—
722C22×C4C23×D8311yescharacteristic
723C22×C4C23×D8311yescharacteristic
724C4⋊C4—834no—
725C4⋊C4—8316no—
726C4⋊C4—838no—
727C4⋊C4—834no—
728C4⋊C4—838no—
729C4⋊C4—838no—
730C4⋊C4—8316no—
731C4⋊C4—8316no—
732C4⋊C4—8316no—
733C4⋊C4—8316no—
734C4⋊C4—8316no—
735C4⋊C4—8316no—
736C4⋊C4—838no—
737C4⋊C4—838no—
738C4⋊C4—838no—
739C4⋊C4—838no—
740C4⋊C4—8316no—
741C4⋊C4C23×D8318yes—
742C4⋊C4C23×D8314yes—
743C4⋊C4C23×D8318yes—
744C4⋊C4C23×D83116yes—
745C4⋊C4C23×D8314yes—
746C4⋊C4C23×D83116yes—
747C4⋊C4C23×D8318yes—
748C22⋊C4—838no—
749C22⋊C4—838no—
750C22⋊C4—838no—
751C22⋊C4—838no—
752C22⋊C4—838no—
753C22⋊C4—8316no—
754C22⋊C4—8316no—
755C22⋊C4—8316no—
756C22⋊C4—838no—
757C22⋊C4—838no—
758C22⋊C4C23×D83116yes—
759C22⋊C4C23×D8318yes—
760C42—834no—
761C42—838no—
762C42—834no—
763C42—834no—
764C42—838no—
765C42—838no—
766C42—8316no—
767C42—8316no—
768C42C23×D8314yes—
769C42C23×D8318yes—
770C23—24no—
771C23—24no—
772C23—832no—
773C23—834no—
774C23—1662no—
775C23—1664no—
776C23—1662no—
777C23—1664no—
778C23—1664no—
779C23—1662no—
780C23C2×#1305059118yes—
781C23C24×D8314yes—
782C23C24×D8311yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—1668no—
786Q8—16616no—
787D4—3328no—
788D4—16616no—
789D4—16632no—
790D4—1668no—
791D4C2×#13050591116yes—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—216no—
798C2×C4—416no—
799C2×C4—33216no—
800C2×C4—3324no—
801C2×C4—3328no—
802C2×C4—832no—
803C2×C4—832no—
804C2×C4—832no—
805C2×C4—834no—
806C2×C4—834no—
807C2×C4—838no—
808C2×C4—834no—
809C2×C4—1662no—
810C2×C4—1664no—
811C2×C4—1668no—
812C2×C4—1664no—
813C2×C4—16616no—
814C2×C4—16632no—
815C2×C4—1662no—
816C2×C4—1664no—
817C2×C4—1662no—
818C2×C4—1668no—
819C2×C4—16616no—
820C2×C4—1668no—
821C2×C4C2×#1305059114yes—
822C2×C4#1458183914yes—
823C2×C4C24×D8314yes—
824C2×C4C24×D8314yes—
825C2×C4C24×D8312yes—
826C2×C4C24×D8318yes—
827C2×C4C24×D8314yes—
828C2×C4C24×D8312yes—
829C2×C4C24×D8312yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—3324no—
834C22—3328no—
835C22—1662no—
836C22—1664no—
837C22—1662no—
838C22—1664no—
839C22—1664no—
840C22—1662no—
841C22C22×#1305059118yes—
842C22C22×#1305059112yes—
843C22C2×#1458183912yes—
844C22#1912853612yes—
845C22C25×D8311yescharacteristic
846C4—24no—
847C4—24no—
848C4—24no—
849C4—28no—
850C4—22no—
851C4—1662no—
852C4—1664no—
853C4—1664no—
854C4—1668no—
855C4—1662no—
856C4—1664no—
857C4—1662no—
858C4C22×#1305059114yes—
859C4C2×#1458183914yes—
860C2—28no—
861C2—3322no—
862C2—3324no—
863C2#2492144214yesdirect product factor
864C2C23×#1305059111yescharacteristic
865C2C22×#1458183911yescharacteristic
866C2C2×#1912853611yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#554×C83C2
socleC23×C83C25
hypercenterC2×#554D83
hypocenterC83C2×#3515
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #24921442C2direct (N × H)
2. C2×#19128430C2semidirect
3. C2×#19128412C2semidirect
4. C2×#19128399C2semidirect
5. C2×#19128393C2semidirect
6. C2×#19128393C2semidirect
7. C2×#19128389C2semidirect
8. C2×#19128355C2semidirect
9. C2×#19128355C2semidirect
10. C2×#19128314C2semidirect
11. C2×#19128300C2semidirect
12. C2×#19128256C2semidirect
13. C2×#19128238C2semidirect
14. C2×#19128237C2semidirect
15. C22×#14581783C2semidirect
16. C2×#19128180C2semidirect
17. C2×C4×#13050589C2semidirect
18. C2×#554×C83C2semidirect
21. #19128430C22semidirect
22. #19128412C22semidirect
23. #19128399C22semidirect
24. #19128393C22semidirect
25. #19128393C22semidirect
26. #19128389C22semidirect
27. #19128355C22semidirect
28. #19128355C22semidirect
29. #19128314C22semidirect
30. #19128300C22semidirect
31. #19128256C22semidirect
34. #19128238C22semidirect
35. #19128237C22semidirect
48. C2×#14581783C22semidirect
64. #19128180C22semidirect
65. C4×#13050589C22semidirect
92. #554×C83C22semidirect
428. C2×C83#3515semidirect
437. C2×#554D83semidirect
452. C83C2×#3515semidirect
457. #554C2×D83semidirect
863. C2#24921442direct (N × H)

Maximal subgroups

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

subgroupindex
#249214422
C2×#191284302
C2×#191284122
C2×#191283992
C2×#191283932
C2×#191283892
C2×#191283552
C2×#191283142
C2×#191283002
C2×#191282562
C2×#191282382
C2×#191282372
C22×#145817832
C2×#191281802
C2×C4×#130505892
C2×#554×C832
C2×#351583