Finite Group Databasebeta

← C2×#24922077 #36311806

Subgroups — C2×#24922077 #36311806

Order 21248.

6598 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24922077C2132yesmaximal, direct product factor
2C2×#19128452C212yesmaximal, complemented
3C2×#19128452C212yesmaximal, complemented
4C2×#19128422C212yesmaximal, complemented
5C2×#19128405C212yesmaximal, complemented
6C2×#19128393C212yesmaximal, complemented
7C2×#19128385C212yesmaximal, complemented
8C2×#19128377C212yesmaximal, complemented
9C2×#19128377C212yesmaximal, complemented
10C2×#19128330C211yesmaximal, characteristic, complemented
11C2×#19128321C212yesmaximal, complemented
12C2×#19128311C212yesmaximal, complemented
13C2×#19128311C212yesmaximal, complemented
14C2×#19128300C211yesmaximal, characteristic, complemented
15C2×#19128297C212yesmaximal, complemented
16C2×#19128289C211yesmaximal, characteristic
17C2×#19128253C211yesmaximal, characteristic, complemented
18C2×#19128237C211yesmaximal, characteristic, complemented
19C22×#14581785C211yesmaximal, characteristic, complemented
20C2×#543×C83C211yesmaximal, characteristic, complemented
21#19128452C22132yescomplemented
22#19128452C22132yescomplemented
23#19128422C22132yescomplemented
24#19128405C22132yescomplemented
25#19128393C22132yescomplemented
26#19128385C22132yescomplemented
27#19128377C22132yescomplemented
28#19128377C22132yescomplemented
29#19128330C22116yescomplemented
30#19128321C22132yescomplemented
31#19128311C22132yescomplemented
32#19128311C22132yescomplemented
33#19128300C22116yescomplemented
34#19128297C22132yescomplemented
35#19128289C22116yes—
36#19128253C22116yescomplemented
37C2×#14581791C2212yescomplemented
38C2×#14581791C2211yescharacteristic, complemented
39C2×#14581790C2212yescomplemented
40C2×#14581790C2212yescomplemented
41C2×#14581790C2211yescharacteristic, complemented
42#19128237C22116yescomplemented
43C2×#14581787C2212yescomplemented
44C2×#14581787C2212yescomplemented
45C2×#14581787C2212yescomplemented
46C2×#14581787C2212yescomplemented
47C2×#14581785C2212yes—
48C2×#14581785C2212yes—
49C2×#14581785C2212yes—
50C2×#14581785C2212yes—
51C2×#14581785C2212yes—
52C2×#14581785C2212yes—
53C2×#14581785C2212yes—
54C2×#14581785C2212yes—
55C2×#14581785C2212yes—
56C2×#14581785C22116yescomplemented
57C2×#14581783C2212yescomplemented
58C2×#14581783C2212yescomplemented
59C2×#14581783C2212yescomplemented
60C2×#14581783C2211yescharacteristic, complemented
61C2×#14581783C2212yescomplemented
62C2×#14581782C2212yescomplemented
63C2×#14581782C2212yescomplemented
64C2×#14581782C2212yescomplemented
65C2×#14581782C2212yescomplemented
66C2×#14581782C2212yescomplemented
67C2×#14581781C2211yescharacteristic, complemented
68C2×#14581778C2212yes—
69C2×#14581778C2212yes—
70C2×#14581778C2212yes—
71C2×#14581777C2212yescomplemented
72C2×#14581776C2212yes—
73C2×#14581776C2212yes—
74C2×#14581775C2212yes—
75C2×#14581775C2212yes—
76C2×#14581774C2212yes—
77C2×#14581774C2212yes—
78C2×#14581774C2212yes—
79C2×#14581771C2211yescharacteristic
80C2×#14581771C2212yes—
81C2×#14581771C2212yes—
82C2×#14581770C2212yescomplemented
83C2×#14581770C2212yescomplemented
84C2×#14581769C2212yes—
85C2×#14581769C2212yes—
86C2×#14581768C2212yescomplemented
87C2×#14581768C2212yescomplemented
88C2×#14581768C2212yescomplemented
89C2×#14581766C2211yescharacteristic
90C2×#14581765C2212yes—
91C2×#14581761C2212yes—
92C2×Q8×Dic83C2211yescharacteristic, complemented
93C2×Q8×Dic83C2212yescomplemented
94C2×Q8×Dic83C2211yescharacteristic, complemented
95C2×#14581757C2212yescomplemented
96C2×#14581757C2212yescomplemented
97C2×#14581757C2211yescharacteristic, complemented
98C2×#14581754C2211yescharacteristic, complemented
99C2×C4×C22⋊D83C2212yes—
100C2×C4×C22⋊D83C2212yes—
101C2×C4×C22⋊D83C2212yes—
102C2×(C22⋊D83)⋊C4C2212yes—
103C2×(C22⋊D83)⋊C4C2212yes—
104C2×#14581751C2212yes—
105C2×#14581751C2212yes—
106C2×#14581750C2212yescomplemented
107C2×#14581750C2212yescomplemented
108C2×#14581748C2212yes—
109C2×#14581748C2212yes—
110C22×C4⋊Dic83C2211yescharacteristic
111C22×Dic83⋊C4C2211yescharacteristic
112C22×Dic83⋊C4C2211yescharacteristic
113C2×C4⋊C4×D83C2212yescomplemented
114C22×C22⋊Dic83C2211yescharacteristic
115C22×C22⋊Dic83C2211yescharacteristic
116C22×C4×Dic83C2211yescharacteristic
117#543×C83C22116yescomplemented
118C2×C22⋊Q8×C83C2212yes—
119C2×C22⋊Q8×C83C2211yescharacteristic
120C2×C22⋊Q8×C83C2212yes—
121C2×C22⋊Q8×C83C2212yes—
122C2×C22⋊Q8×C83C2211yescharacteristic
123C2×C22⋊Q8×C83C2212yes—
124C2×C22⋊Q8×C83C2212yes—
125C22×C22⋊C4×C83C2212yes—
126C22×C22⋊C4×C83C2211yescharacteristic
127C22×Dic166C2312yes—
128C22×Dic166C2312yes—
129C22×Dic166C2311yescharacteristic
130C22×D332C2311yescharacteristic
131C22×C22⋊D83C2312yes—
132C22×C22⋊D83C2312yes—
133C22×C22⋊D83C2312yes—
134C23×Dic83C2311yescharacteristic
135C23×Dic83C2311yescharacteristic
136C23×Dic83C2311yescharacteristic
137C23×Dic83C2311yescharacteristic
138C22×C4×D83C2312yes—
139C22×C4×D83C2312yes—
140C22×C4×D83C2312yes—
141#14581791C23116yescomplemented
142#14581791C2318yescomplemented
143#14581790C23116yescomplemented
144#14581790C23116yescomplemented
145#14581790C2318yescomplemented
146#14581787C23116yescomplemented
147#14581787C23116yescomplemented
148#14581787C23116yescomplemented
149#14581787C23116yescomplemented
150#14581785C23116yes—
151#14581785C23116yes—
152#14581785C23116yes—
153#14581785C23116yes—
154#14581785C23116yes—
155#14581785C23116yes—
156#14581785C23116yes—
157#14581785C23116yes—
158#14581785C23116yes—
159#14581783C23116yescomplemented
160#14581783C23116yescomplemented
161#14581783C23116yescomplemented
162#14581783C2318yescomplemented
163#14581783C23116yescomplemented
164#14581782C23116yescomplemented
165#14581782C23116yescomplemented
166#14581782C23116yescomplemented
167#14581782C23116yescomplemented
168#14581782C23116yescomplemented
169#14581781C2318yescomplemented
170#14581778C23116yes—
171#14581778C23116yes—
172#14581778C23116yes—
173#14581777C23116yescomplemented
174#14581776C23116yes—
175#14581776C23116yes—
176#14581775C23116yes—
177#14581775C23116yes—
178#14581774C23116yes—
179#14581774C23116yes—
180#14581774C23116yes—
181#14581771C2318yes—
182#14581771C23116yes—
183#14581771C23116yes—
184#14581770C23116yescomplemented
185#14581770C23116yescomplemented
186#14581769C23116yes—
187#14581769C23116yes—
188#14581768C23116yescomplemented
189#14581768C23116yescomplemented
190#14581768C23116yescomplemented
191#14581766C2318yes—
192#14581765C23116yes—
193#14581761C23116yes—
194Q8×Dic83C2318yescomplemented
195Q8×Dic83C23116yescomplemented
196Q8×Dic83C2318yescomplemented
197#14581757C23116yescomplemented
198#14581757C23116yescomplemented
199#14581757C2318yescomplemented
200#14581754C2318yescomplemented
201C4×C22⋊D83C23116yes—
202C4×C22⋊D83C23116yes—
203C4×C22⋊D83C23116yes—
204(C22⋊D83)⋊C4C23116yes—
205(C22⋊D83)⋊C4C23116yes—
206#14581751C23116yes—
207#14581751C23116yes—
208#14581750C23116yescomplemented
209#14581750C23116yescomplemented
210#14581748C23116yes—
211#14581748C23116yes—
212C2×C4⋊Dic83C2318yes—
213C2×C4⋊Dic83C2312yes—
214C2×C4⋊Dic83C2312yes—
215C2×C4⋊Dic83C2312yes—
216C2×C4⋊Dic83C2312yes—
217C2×C4⋊Dic83C2312yes—
218C2×C4⋊Dic83C2312yes—
219C2×C4⋊Dic83C2311yescharacteristic
220C2×C4⋊Dic83C2311yescharacteristic
221C2×C4⋊Dic83C2312yes—
222C2×C4⋊Dic83C2312yes—
223C2×Dic83⋊C4C2318yes—
224C2×Dic83⋊C4C2318yes—
225C2×Dic83⋊C4C2312yes—
226C2×Dic83⋊C4C2312yes—
227C2×Dic83⋊C4C2312yes—
228C2×Dic83⋊C4C2312yes—
229C2×Dic83⋊C4C2312yes—
230C2×Dic83⋊C4C2312yes—
231C2×Dic83⋊C4C2312yes—
232C2×Dic83⋊C4C2312yes—
233C2×Dic83⋊C4C2312yes—
234C2×Dic83⋊C4C2312yes—
235C2×Dic83⋊C4C2312yes—
236C2×Dic83⋊C4C2312yes—
237C2×Dic83⋊C4C2312yes—
238C2×Dic83⋊C4C2312yes—
239C2×Dic83⋊C4C2312yes—
240C2×Dic83⋊C4C2312yes—
241C4⋊C4×D83C23116yescomplemented
242C2×C22⋊Dic83C2318yes—
243C2×C22⋊Dic83C2318yes—
244C2×C22⋊Dic83C2312yes—
245C2×C22⋊Dic83C2312yes—
246C2×C22⋊Dic83C2312yes—
247C2×C22⋊Dic83C2312yes—
248C2×C22⋊Dic83C2312yes—
249C2×C22⋊Dic83C2312yes—
250C2×C22⋊Dic83C2312yes—
251C2×(C2×D83)⋊C4C2312yes—
252C2×(C2×D83)⋊C4C2312yes—
253C2×(C2×D83)⋊C4C2312yes—
254C2×(C2×D83)⋊C4C2312yes—
255C2×(C2×D83)⋊C4C2312yes—
256C2×(C2×D83)⋊C4C2312yes—
257C2×(C2×D83)⋊C4C2312yes—
258C2×(C2×D83)⋊C4C2312yes—
259C2×C4×Dic83C2311yescharacteristic
260C2×C4×Dic83C2311yescharacteristic
261C2×C4×Dic83C2311yescharacteristic
262C2×C4×Dic83C2311yescharacteristic
263C2×C4×Dic83C2318yes—
264C2×C4×Dic83C2312yes—
265C2×C4×Dic83C2312yes—
266C2×C4×Dic83C2312yes—
267C2×C4×Dic83C2312yes—
268C2×C4×Dic83C2312yes—
269C2×C4×Dic83C2312yes—
270C2×C4×Dic83C2312yes—
271C25×C83C2311yescharacteristic
272C22×Q8×C83C2311yescharacteristic
273C22×Q8×C83C2312yes—
274C22×Q8×C83C2311yescharacteristic
275C23×C4×C83C2311yescharacteristic
276C23×C4×C83C2311yescharacteristic
277C23×C4×C83C2312yes—
278C23×C4×C83C2312yes—
279C22⋊Q8×C83C23116yes—
280C22⋊Q8×C83C2318yes—
281C22⋊Q8×C83C23116yes—
282C22⋊Q8×C83C23116yes—
283C22⋊Q8×C83C23116yes—
284C22⋊Q8×C83C2318yes—
285C22⋊Q8×C83C23116yes—
286C2×C4⋊C4×C83C2312yes—
287C2×C4⋊C4×C83C2312yes—
288C2×C4⋊C4×C83C2312yes—
289C2×C4⋊C4×C83C2311yescharacteristic
290C2×C4⋊C4×C83C2312yes—
291C2×C4⋊C4×C83C2312yes—
292C2×C4⋊C4×C83C2311yescharacteristic
293C2×C22⋊C4×C83C23116yes—
294C2×C22⋊C4×C83C2312yes—
295C2×C22⋊C4×C83C2312yes—
296C2×C22⋊C4×C83C2312yes—
297C2×C22⋊C4×C83C2312yes—
298C2×C22⋊C4×C83C2312yes—
299C2×C22⋊C4×C83C2312yes—
300C2×C22⋊C4×C83C2318yes—
301C23×D83C2412yes—
302C2×Dic166—44no—
303C2×Dic166—44no—
304C2×Dic166—42no—
305C2×Dic166C2418yes—
306C2×Dic166C2418yes—
307C2×Dic166C2414yes—
308C2×D332—42no—
309C2×D332C2414yes—
310C2×C22⋊D83—28no—
311C2×C22⋊D83—44no—
312C2×C22⋊D83—44no—
313C2×C22⋊D83C2418yes—
314C2×C22⋊D83C2418yes—
315C2×C22⋊D83C2418yes—
316C22×Dic83—24no—
317C22×Dic83—24no—
318C22×Dic83—42no—
319C22×Dic83—42no—
320C22×Dic83C2414yes—
321C22×Dic83C2414yes—
322C22×Dic83C2411yescharacteristic
323C22×Dic83C2412yes—
324C22×Dic83C2412yes—
325C22×Dic83C2411yescharacteristic
326C22×Dic83C2411yescharacteristic
327C22×Dic83C2411yescharacteristic
328C22×Dic83C2412yes—
329C22×Dic83C2412yes—
330C22×Dic83C2412yes—
331C22×Dic83C2414yes—
332C22×Dic83C2414yes—
333C2×C4×D83—44no—
334C2×C4×D83—44no—
335C2×C4×D83—44no—
336C2×C4×D83C2418yes—
337C2×C4×D83C2418yes—
338C2×C4×D83C2418yes—
339C4⋊Dic83C2414yes—
340C4⋊Dic83C2418yes—
341C4⋊Dic83C2418yes—
342C4⋊Dic83C2418yes—
343C4⋊Dic83C2418yes—
344C4⋊Dic83C2414yes—
345C4⋊Dic83C2418yes—
346C4⋊Dic83C2418yes—
347C4⋊Dic83C2418yes—
348C4⋊Dic83C2418yes—
349Dic83⋊C4C2418yes—
350Dic83⋊C4C2418yes—
351Dic83⋊C4C2418yes—
352Dic83⋊C4C2418yes—
353Dic83⋊C4C2418yes—
354Dic83⋊C4C2418yes—
355Dic83⋊C4C2418yes—
356Dic83⋊C4C2418yes—
357Dic83⋊C4C2418yes—
358Dic83⋊C4C2418yes—
359Dic83⋊C4C2418yes—
360Dic83⋊C4C2418yes—
361Dic83⋊C4C2418yes—
362Dic83⋊C4C2418yes—
363Dic83⋊C4C2418yes—
364Dic83⋊C4C2418yes—
365C22⋊Dic83C2418yes—
366C22⋊Dic83C2418yes—
367C22⋊Dic83C2418yes—
368C22⋊Dic83C2418yes—
369C22⋊Dic83C2418yes—
370C22⋊Dic83C2418yes—
371C22⋊Dic83C2418yes—
372(C2×D83)⋊C4C2418yes—
373(C2×D83)⋊C4C2418yes—
374(C2×D83)⋊C4C2418yes—
375(C2×D83)⋊C4C2418yes—
376(C2×D83)⋊C4C2418yes—
377(C2×D83)⋊C4C2418yes—
378(C2×D83)⋊C4C2418yes—
379(C2×D83)⋊C4C2418yes—
380C4×Dic83C2418yes—
381C4×Dic83C2418yes—
382C4×Dic83C2418yes—
383C4×Dic83C2414yes—
384C4×Dic83C2414yes—
385C4×Dic83C2418yes—
386C4×Dic83C2418yes—
387C4×Dic83C2418yes—
388C4×Dic83C2418yes—
389C4×Dic83C2414yes—
390C4×Dic83C2414yes—
391C24×C83—24no—
392C24×C83—42no—
393C24×C83—42no—
394C24×C83C2412yes—
395C24×C83C2411yescharacteristic
396C24×C83C2414yes—
397C2×Q8×C83—42no—
398C2×Q8×C83—44no—
399C2×Q8×C83—42no—
400C2×Q8×C83C2414yes—
401C2×Q8×C83C2418yes—
402C2×Q8×C83C2414yes—
403C22×C4×C83—42no—
404C22×C4×C83—44no—
405C22×C4×C83—44no—
406C22×C4×C83—42no—
407C22×C4×C83C2412yes—
408C22×C4×C83C2412yes—
409C22×C4×C83C2412yes—
410C22×C4×C83C2411yescharacteristic
411C22×C4×C83C2412yes—
412C22×C4×C83C2412yes—
413C22×C4×C83C2411yescharacteristic
414C22×C4×C83C2414yes—
415C22×C4×C83C2418yes—
416C22×C4×C83C2418yes—
417C22×C4×C83C2414yes—
418C4⋊C4×C83C2418yes—
419C4⋊C4×C83C2418yes—
420C4⋊C4×C83C2418yes—
421C4⋊C4×C83C2414yes—
422C4⋊C4×C83C2418yes—
423C4⋊C4×C83C2418yes—
424C4⋊C4×C83C2414yes—
425C22⋊C4×C83C2418yes—
426C22⋊C4×C83C2418yes—
427C22⋊C4×C83C2418yes—
428C22⋊C4×C83C2418yes—
429C22⋊C4×C83C2418yes—
430C22⋊C4×C83C2418yes—
431C23×C83—22no—
432C23×C83—22no—
433C23×C83—24no—
434C23×C83—24no—
435C23×C83—24no—
436C23×C83—28no—
437C23×C83—44no—
438C23×C83—44no—
439C23×C83—88no—
440C23×C832−1+414yes—
441C23×C83C2514yes—
442C23×C83C2512yes—
443C23×C83C2511yescharacteristic
444C22×D83—24no—
445C22×D83—24no—
446C22×D83—24no—
447C22×D83C2514yes—
448Q8×C83—44no—
449Q8×C83—44no—
450Q8×C83—48no—
451C2×C4×C83—24no—
452C2×C4×C83—24no—
453C2×C4×C83—24no—
454C2×C4×C83—22no—
455C2×C4×C83—24no—
456C2×C4×C83—24no—
457C2×C4×C83—22no—
458C2×C4×C83—48no—
459C2×C4×C83—48no—
460C2×C4×C83—44no—
461C2×C4×C83—44no—
462C2×C4×C83C2514yes—
463C2×C4×C83C2514yes—
464C2×C4×C83C2512yes—
465C2×C4×C83C2512yes—
466C2×C4×C83C2514yes—
467C2×C4×C83C2514yes—
468C2×C4×C83C2514yes—
469C22⋊D83—216no—
470C22⋊D83—48no—
471C22⋊D83—48no—
472C2×Dic83—28no—
473C2×Dic83—28no—
474C2×Dic83—22no—
475C2×Dic83—22no—
476C2×Dic83—24no—
477C2×Dic83—24no—
478C2×Dic83—22no—
479C2×Dic83—24no—
480C2×Dic83—24no—
481C2×Dic83—22no—
482C2×Dic83—24no—
483C2×Dic83—44no—
484C2×Dic83—44no—
485C2×Dic83C2512yes—
486C2×Dic83C2512yes—
487C2×Dic83C2514yes—
488C2×Dic83C2514yes—
489C2×Dic83C2512yes—
490C2×Dic83C2514yes—
491C2×Dic83C2512yes—
492C2×Dic83C2514yes—
493C2×Dic83C2514yes—
494D332—44no—
495C4×D83—48no—
496C4×D83—48no—
497C4×D83—48no—
498Dic166—48no—
499Dic166—44no—
500Dic166—48no—
501C22×C83—22no—
502C22×C83—22no—
503C22×C83—28no—
504C22×C83—24no—
505C22×C83—24no—
506C22×C83—24no—
507C22×C83—48no—
508C22×C83—88no—
509C22×C83C2×2−1+414yes—
510C22×C83C2×2−1+412yes—
511C22×C83#58512yes—
512C22×C83#58512yes—
513C22×C83C2611yescharacteristic
514C2×D83—24no—
515C2×D83—24no—
516C2×D83—24no—
517C2×D83—48no—
518C4×C83—24no—
519C4×C83—22no—
520C4×C83—24no—
521C4×C83—24no—
522C4×C83—24no—
523C4×C83—24no—
524C4×C83—22no—
525Dic83—22no—
526Dic83—22no—
527Dic83—24no—
528Dic83—24no—
529Dic83—22no—
530Dic83—24no—
531Dic83—24no—
532Dic83—24no—
533Dic83—22no—
534C2×#3564—831nomaximal, Sylow
535C2×C83—24no—
536C2×C83—44no—
537C2×C83#356414yescomplemented
538C2×C83C22×2−1+411yescharacteristic
539C2×C83C2×#58511yescharacteristic
540C2×C83C2×#58511yescharacteristic
541D83—44no—
542#3564—8332no—
543C2×#563—832no—
544C2×#563—832no—
545C2×#556—832no—
546C2×#554—832no—
547C2×#552—832no—
548C2×#552—832no—
549C2×#551—832no—
550C2×#551—832no—
551C2×#544—831no—
552C2×#543D8311yescharacteristic, complemented
553C2×#542—832no—
554C2×#541—832no—
555C2×#541—832no—
556C2×#539—832no—
557C2×#539—831no—
558C2×#538—831no—
559C2×#533—831no—
560C2×#529—831no—
561C22×#126—831no—
562C83C2×#356411yescharacteristic, complemented, Sylow
563#563—8332no—
564#563—8332no—
565#556—8332no—
566#554—8332no—
567#552—8332no—
568#552—8332no—
569#551—8332no—
570#551—8332no—
571#544—8316no—
572#543C2×D83116yescomplemented
573#542—8332no—
574#541—8332no—
575#541—8332no—
576#539—8332no—
577#539—8316no—
578#538—8316no—
579#533—8316no—
580C2×C4⋊Q8—831no—
581C2×C4⋊Q8—832no—
582C2×C4⋊Q8—832no—
583C2×C4⋊Q8—831no—
584C2×C4⋊Q8—832no—
585#529—8316no—
586C2×#126—832no—
587C2×#126—832no—
588C2×#126—832no—
589C2×#126—832no—
590C2×#126—832no—
591C2×#126—832no—
592C2×#126—832no—
593C2×#126—832no—
594C2×#126—8316no—
595C2×#126—832no—
596C2×#126—832no—
597C2×#126—832no—
598C2×#126—832no—
599C2×#126—832no—
600C2×#125—831no—
601C2×#125—832no—
602C2×#125—832no—
603C2×#125—832no—
604C2×#125—832no—
605C2×#125—832no—
606C2×#125—832no—
607C2×#125—832no—
608C2×#125—832no—
609C2×#125—832no—
610C2×#124—831no—
611C2×#124—832no—
612C2×#124—832no—
613C2×#124—832no—
614C2×#123—832no—
615C2×#123—832no—
616C2×#123—832no—
617C2×#123—832no—
618C2×#123—832no—
619C2×#123—832no—
620C2×#123—832no—
621C2×#123—832no—
622C2×C22⋊Q8—832no—
623C2×C22⋊Q8—832no—
624C2×C22⋊Q8—832no—
625C2×C22⋊Q8—831no—
626C2×C22⋊Q8—832no—
627C2×C22⋊Q8—832no—
628C2×C22⋊Q8—832no—
629C2×C22⋊Q8—832no—
630C2×C22⋊Q8—832no—
631C2×C22⋊Q8—832no—
632C2×C22⋊Q8C2×D8311yescharacteristic
633C2×C22⋊Q8C2×D8311yescharacteristic
634C2×C22⋊Q8C2×D8312yes—
635C2×C22⋊Q8C2×D8312yes—
636C2×C22⋊Q8C2×D8312yes—
637C2×C22⋊Q8C2×D8312yes—
638C2×C22⋊Q8C2×D8312yes—
639C2×#121—831no—
640C2×#121—832no—
641C2×#120—832no—
642C2×C4×Q8—831no—
643C2×C4×Q8—831no—
644C2×C4×Q8—832no—
645C2×C4×Q8—832no—
646C2×C4×Q8—831no—
647C2×C4×Q8—832no—
648C2×C4×D4—832no—
649C2×C4×D4—832no—
650C2×C4×D4—832no—
651C2×C4×D4—831no—
652C2×C4×D4—832no—
653C2×C4×D4—832no—
654C2×#117—832no—
655C2×#117—832no—
656C2×#117—832no—
657C2×#117—832no—
658C2×#117—832no—
659C2×#117—832no—
660C22×C4⋊C4—831no—
661C22×C4⋊C4—831no—
662C22×C4⋊C4—831no—
663C22×C4⋊C4—832no—
664C22×C22⋊C4—831no—
665C22×C22⋊C4—831no—
666C22×C22⋊C4C2×D8311yescharacteristic
667C22×C22⋊C4C2×D8312yes—
668C22×C42—831no—
669C25C22×D8311yescharacteristic
670C22×Q8—832no—
671C22×Q8—832no—
672C22×Q8—831no—
673C22×Q8C22×D8311yescharacteristic
674C22×Q8C22×D8312yes—
675C22×Q8C22×D8311yescharacteristic
676C22×D4—832no—
677C22×D4—832no—
678C22×D4—832no—
679C22×D4—831no—
680C23×C4—831no—
681C23×C4—831no—
682C23×C4—832no—
683C23×C4—832no—
684C23×C4—832no—
685C23×C4—831no—
686C23×C4—831no—
687C23×C4C22×D8311yescharacteristic
688C23×C4C22×D8311yescharacteristic
689C23×C4C22×D8312yes—
690C23×C4C22×D8312yes—
691C4⋊Q8—838no—
692C4⋊Q8—8316no—
693C4⋊Q8—8316no—
694C4⋊Q8—838no—
695C4⋊Q8—8316no—
696#126—8316no—
697#126—8316no—
698#126—8316no—
699#126—8316no—
700#126—8316no—
701#126—8316no—
702#126—8316no—
703#126—8316no—
704#126—8316no—
705#126—8316no—
706#126—8316no—
707#126—8316no—
708#126—8316no—
709#125—838no—
710#125—8316no—
711#125—8316no—
712#125—8316no—
713#125—8316no—
714#125—8316no—
715#125—8316no—
716#125—8316no—
717#125—8316no—
718#125—8316no—
719#124—838no—
720#124—8316no—
721#124—8316no—
722#124—8316no—
723#123—8316no—
724#123—8316no—
725#123—8316no—
726#123—8316no—
727#123—8316no—
728#123—8316no—
729#123—8316no—
730#123—8316no—
731C22⋊Q8—8316no—
732C22⋊Q8—8316no—
733C22⋊Q8—8316no—
734C22⋊Q8—838no—
735C22⋊Q8—8316no—
736C22⋊Q8—8316no—
737C22⋊Q8—8316no—
738C22⋊Q8—8316no—
739C22⋊Q8—8316no—
740C22⋊Q8—8316no—
741C22⋊Q8C22×D8318yes—
742C22⋊Q8C22×D8318yes—
743C22⋊Q8C22×D83116yes—
744C22⋊Q8C22×D83116yes—
745C22⋊Q8C22×D83116yes—
746C22⋊Q8C22×D83116yes—
747C22⋊Q8C22×D83116yes—
748#121—838no—
749#121—8316no—
750#120—8316no—
751C4×Q8—838no—
752C4×Q8—838no—
753C4×Q8—8316no—
754C4×Q8—8316no—
755C4×Q8—838no—
756C4×Q8—8316no—
757C4×D4—8316no—
758C4×D4—8316no—
759C4×D4—8316no—
760C4×D4—838no—
761C4×D4—8316no—
762C4×D4—8316no—
763#117—8316no—
764#117—8316no—
765#117—8316no—
766#117—8316no—
767#117—8316no—
768#117—8316no—
769C2×C4⋊C4—832no—
770C2×C4⋊C4—832no—
771C2×C4⋊C4—832no—
772C2×C4⋊C4—832no—
773C2×C4⋊C4—832no—
774C2×C4⋊C4—832no—
775C2×C4⋊C4—832no—
776C2×C4⋊C4—832no—
777C2×C4⋊C4—838no—
778C2×C4⋊C4—838no—
779C2×C4⋊C4—838no—
780C2×C4⋊C4—832no—
781C2×C4⋊C4—832no—
782C2×C4⋊C4—832no—
783C2×C4⋊C4—832no—
784C2×C4⋊C4—832no—
785C2×C4⋊C4—832no—
786C2×C4⋊C4—832no—
787C2×C4⋊C4—832no—
788C2×C4⋊C4—832no—
789C2×C4⋊C4—832no—
790C2×C4⋊C4—832no—
791C2×C4⋊C4—832no—
792C2×C4⋊C4—832no—
793C2×C4⋊C4—831no—
794C2×C4⋊C4—832no—
795C2×C4⋊C4—831no—
796C2×C4⋊C4—832no—
797C2×C4⋊C4—832no—
798C2×C4⋊C4—8316no—
799C2×C4⋊C4C22×D8312yes—
800C2×C4⋊C4C22×D8312yes—
801C2×C4⋊C4C22×D8312yes—
802C2×C4⋊C4C22×D8311yescharacteristic
803C2×C4⋊C4C22×D8312yes—
804C2×C4⋊C4C22×D8312yes—
805C2×C4⋊C4C22×D8311yescharacteristic
806C2×C22⋊C4—832no—
807C2×C22⋊C4—832no—
808C2×C22⋊C4—832no—
809C2×C22⋊C4—832no—
810C2×C22⋊C4—838no—
811C2×C22⋊C4—838no—
812C2×C22⋊C4—832no—
813C2×C22⋊C4—832no—
814C2×C22⋊C4—832no—
815C2×C22⋊C4—832no—
816C2×C22⋊C4—832no—
817C2×C22⋊C4—832no—
818C2×C22⋊C4—832no—
819C2×C22⋊C4—832no—
820C2×C22⋊C4—832no—
821C2×C22⋊C4—832no—
822C2×C22⋊C4—832no—
823C2×C22⋊C4C22×D8312yes—
824C2×C22⋊C4C22×D8312yes—
825C2×C22⋊C4C22×D8312yes—
826C2×C22⋊C4C22×D8312yes—
827C2×C22⋊C4C22×D8312yes—
828C2×C22⋊C4C22×D8312yes—
829C2×C22⋊C4C22×D8318yes—
830C2×C22⋊C4C22×D83116yes—
831C2×C42—832no—
832C2×C42—832no—
833C2×C42—832no—
834C2×C42—832no—
835C2×C42—831no—
836C2×C42—832no—
837C2×C42—832no—
838C2×C42—832no—
839C2×C42—831no—
840C2×C42—831no—
841C2×C42—831no—
842C2×C42—838no—
843C24—24no—
844C24—42no—
845C24—42no—
846C24—832no—
847C24C23×D8312yes—
848C24C23×D8311yescharacteristic
849C24C23×D8314yes—
850C2×Q8—42no—
851C2×Q8—44no—
852C2×Q8—42no—
853C2×Q8—3324no—
854C2×Q8—3324no—
855C2×Q8—3322no—
856C2×Q8—838no—
857C2×Q8—838no—
858C2×Q8—834no—
859C2×Q8C23×D8314yes—
860C2×Q8C23×D8318yes—
861C2×Q8C23×D8314yes—
862C2×D4—3322no—
863C2×D4—3324no—
864C2×D4—3324no—
865C2×D4—838no—
866C2×D4—838no—
867C2×D4—838no—
868C2×D4—834no—
869C2×D4—1668no—
870C22×C4—42no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—42no—
874C22×C4—3324no—
875C22×C4—3324no—
876C22×C4—3324no—
877C22×C4—3322no—
878C22×C4—3322no—
879C22×C4—834no—
880C22×C4—834no—
881C22×C4—838no—
882C22×C4—838no—
883C22×C4—838no—
884C22×C4—834no—
885C22×C4—834no—
886C22×C4—831no—
887C22×C4—831no—
888C22×C4—832no—
889C22×C4—832no—
890C22×C4—832no—
891C22×C4—831no—
892C22×C4—831no—
893C22×C4—832no—
894C22×C4—832no—
895C22×C4—1664no—
896C22×C4—1664no—
897C22×C4C23×D8312yes—
898C22×C4C23×D8312yes—
899C22×C4C23×D8311yescharacteristic
900C22×C4C23×D8311yescharacteristic
901C22×C4C23×D8312yes—
902C22×C4C23×D8312yes—
903C22×C4C23×D8312yes—
904C22×C4C23×D8314yes—
905C22×C4C23×D8314yes—
906C22×C4C23×D8318yes—
907C22×C4C23×D8318yes—
908C4⋊C4—838no—
909C4⋊C4—838no—
910C4⋊C4—838no—
911C4⋊C4—838no—
912C4⋊C4—838no—
913C4⋊C4—838no—
914C4⋊C4—838no—
915C4⋊C4—838no—
916C4⋊C4—838no—
917C4⋊C4—838no—
918C4⋊C4—838no—
919C4⋊C4—838no—
920C4⋊C4—838no—
921C4⋊C4—838no—
922C4⋊C4—838no—
923C4⋊C4—838no—
924C4⋊C4—838no—
925C4⋊C4—838no—
926C4⋊C4—838no—
927C4⋊C4—838no—
928C4⋊C4—838no—
929C4⋊C4—834no—
930C4⋊C4—838no—
931C4⋊C4—834no—
932C4⋊C4—838no—
933C4⋊C4—838no—
934C4⋊C4C23×D8318yes—
935C4⋊C4C23×D8318yes—
936C4⋊C4C23×D8318yes—
937C4⋊C4C23×D8314yes—
938C4⋊C4C23×D8318yes—
939C4⋊C4C23×D8318yes—
940C4⋊C4C23×D8314yes—
941C22⋊C4—838no—
942C22⋊C4—838no—
943C22⋊C4—838no—
944C22⋊C4—838no—
945C22⋊C4—838no—
946C22⋊C4—838no—
947C22⋊C4—838no—
948C22⋊C4—838no—
949C22⋊C4—838no—
950C22⋊C4—838no—
951C22⋊C4—838no—
952C22⋊C4—838no—
953C22⋊C4—838no—
954C22⋊C4—838no—
955C22⋊C4—838no—
956C22⋊C4C23×D8318yes—
957C22⋊C4C23×D8318yes—
958C22⋊C4C23×D8318yes—
959C22⋊C4C23×D8318yes—
960C22⋊C4C23×D8318yes—
961C22⋊C4C23×D8318yes—
962C42—834no—
963C42—834no—
964C42—834no—
965C42—834no—
966C42—838no—
967C42—838no—
968C42—838no—
969C42—838no—
970C42—838no—
971C42—838no—
972C42—838no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—28no—
979C23—44no—
980C23—44no—
981C23—88no—
982C23—834no—
983C23—1664no—
984C23—1664no—
985C23—1664no—
986C23#1458184014yes—
987C23C24×D8314yes—
988C23C24×D8312yes—
989C23C24×D8311yescharacteristic
990Q8—44no—
991Q8—48no—
992Q8—44no—
993Q8—3328no—
994Q8—3328no—
995Q8—3324no—
996D4—3324no—
997D4—3328no—
998D4—3328no—
999D4—16616no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—22no—
1007C2×C4—44no—
1008C2×C4—48no—
1009C2×C4—48no—
1010C2×C4—44no—
1011C2×C4—3328no—
1012C2×C4—3328no—
1013C2×C4—3328no—
1014C2×C4—3324no—
1015C2×C4—3324no—
1016C2×C4—832no—
1017C2×C4—832no—
1018C2×C4—834no—
1019C2×C4—834no—
1020C2×C4—832no—
1021C2×C4—834no—
1022C2×C4—832no—
1023C2×C4—834no—
1024C2×C4—834no—
1025C2×C4—1668no—
1026C2×C4—1668no—
1027C2×C4—1662no—
1028C2×C4—1664no—
1029C2×C4—1662no—
1030C2×C4—1664no—
1031C2×C4—1662no—
1032C2×C4—1664no—
1033C2×C4—1664no—
1034C2×C4—1662no—
1035C2×C4—1664no—
1036C2×C4C24×D8312yes—
1037C2×C4C24×D8314yes—
1038C2×C4C24×D8314yes—
1039C2×C4C24×D8312yes—
1040C2×C4C24×D8314yes—
1041C2×C4C24×D8314yes—
1042C2×C4C24×D8314yes—
1043C22—22no—
1044C22—22no—
1045C22—28no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—48no—
1050C22—88no—
1051C22—3328no—
1052C22—1664no—
1053C22—1664no—
1054C22—1664no—
1055C22C2×#1458184014yes—
1056C22C2×#1458184012yes—
1057C22#1912853612yes—
1058C22#1912853612yes—
1059C22C25×D8311yescharacteristic
1060C4—24no—
1061C4—24no—
1062C4—24no—
1063C4—22no—
1064C4—24no—
1065C4—24no—
1066C4—22no—
1067C4—1662no—
1068C4—1662no—
1069C4—1664no—
1070C4—1664no—
1071C4—1662no—
1072C4—1664no—
1073C4—1664no—
1074C4—1662no—
1075C4—1664no—
1076C2—24no—
1077C2—44no—
1078C2—3324no—
1079C2#2492207714yesdirect product factor
1080C2C22×#1458184011yescharacteristic
1081C2C2×#1912853611yescharacteristic
1082C2C2×#1912853611yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#543×C83C2
socleC23×C83C25
prime radicalC2×#19128289C2
hypercenterC2×#543D83
hypocenterC83C2×#3564
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. #24922077C2direct (N × H)
2. C2×#19128452C2semidirect
3. C2×#19128452C2semidirect
4. C2×#19128422C2semidirect
5. C2×#19128405C2semidirect
6. C2×#19128393C2semidirect
7. C2×#19128385C2semidirect
8. C2×#19128377C2semidirect
9. C2×#19128377C2semidirect
10. C2×#19128330C2semidirect
11. C2×#19128321C2semidirect
12. C2×#19128311C2semidirect
13. C2×#19128311C2semidirect
14. C2×#19128300C2semidirect
15. C2×#19128297C2semidirect
17. C2×#19128253C2semidirect
18. C2×#19128237C2semidirect
19. C22×#14581785C2semidirect
20. C2×#543×C83C2semidirect
21. #19128452C22semidirect
22. #19128452C22semidirect
23. #19128422C22semidirect
24. #19128405C22semidirect
25. #19128393C22semidirect
26. #19128385C22semidirect
27. #19128377C22semidirect
28. #19128377C22semidirect
29. #19128330C22semidirect
30. #19128321C22semidirect
31. #19128311C22semidirect
32. #19128311C22semidirect
33. #19128300C22semidirect
34. #19128297C22semidirect
36. #19128253C22semidirect
37. C2×#14581791C22semidirect
38. C2×#14581791C22semidirect
39. C2×#14581790C22semidirect
40. C2×#14581790C22semidirect
41. C2×#14581790C22semidirect
42. #19128237C22semidirect
43. C2×#14581787C22semidirect
44. C2×#14581787C22semidirect
45. C2×#14581787C22semidirect
46. C2×#14581787C22semidirect
56. C2×#14581785C22semidirect
57. C2×#14581783C22semidirect
58. C2×#14581783C22semidirect
59. C2×#14581783C22semidirect
60. C2×#14581783C22semidirect
61. C2×#14581783C22semidirect
62. C2×#14581782C22semidirect
63. C2×#14581782C22semidirect
64. C2×#14581782C22semidirect
65. C2×#14581782C22semidirect
66. C2×#14581782C22semidirect
67. C2×#14581781C22semidirect
71. C2×#14581777C22semidirect
82. C2×#14581770C22semidirect
83. C2×#14581770C22semidirect
86. C2×#14581768C22semidirect
87. C2×#14581768C22semidirect
88. C2×#14581768C22semidirect
92. C2×Q8×Dic83C22semidirect
93. C2×Q8×Dic83C22semidirect
94. C2×Q8×Dic83C22semidirect
95. C2×#14581757C22semidirect
96. C2×#14581757C22semidirect
97. C2×#14581757C22semidirect
98. C2×#14581754C22semidirect
106. C2×#14581750C22semidirect
107. C2×#14581750C22semidirect
113. C2×C4⋊C4×D83C22semidirect
117. #543×C83C22semidirect
141. #14581791C23semidirect
142. #14581791C23semidirect
143. #14581790C23semidirect
144. #14581790C23semidirect
145. #14581790C23semidirect
146. #14581787C23semidirect
147. #14581787C23semidirect
148. #14581787C23semidirect
149. #14581787C23semidirect
159. #14581783C23semidirect
160. #14581783C23semidirect
161. #14581783C23semidirect
162. #14581783C23semidirect
163. #14581783C23semidirect
164. #14581782C23semidirect
165. #14581782C23semidirect
166. #14581782C23semidirect
167. #14581782C23semidirect
168. #14581782C23semidirect
169. #14581781C23semidirect
173. #14581777C23semidirect
184. #14581770C23semidirect
185. #14581770C23semidirect
188. #14581768C23semidirect
189. #14581768C23semidirect
190. #14581768C23semidirect
194. Q8×Dic83C23semidirect
195. Q8×Dic83C23semidirect
196. Q8×Dic83C23semidirect
197. #14581757C23semidirect
198. #14581757C23semidirect
199. #14581757C23semidirect
200. #14581754C23semidirect
208. #14581750C23semidirect
209. #14581750C23semidirect
241. C4⋊C4×D83C23semidirect
537. C2×C83#3564semidirect
552. C2×#543D83semidirect
562. C83C2×#3564semidirect
572. #543C2×D83semidirect
1079. C2#24922077direct (N × H)

Maximal subgroups

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

subgroupindex
#249220772
C2×#191284522
C2×#191284222
C2×#191284052
C2×#191283932
C2×#191283852
C2×#191283772
C2×#191283302
C2×#191283212
C2×#191283112
C2×#191283002
C2×#191282972
C2×#191282892
C2×#191282532
C2×#191282372
C22×#145817852
C2×#543×C832
C2×#356483