Finite Group Databasebeta

← C2×#20258002 #27123680

Subgroups — C2×#20258002 #27123680

Order 12032.

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#20258002C2132yesmaximal, direct product factor
2C2×#15689874C212yesmaximal, complemented
3C2×#15689874C212yesmaximal, complemented
4C2×#15689844C212yesmaximal, complemented
5C2×#15689827C212yesmaximal, complemented
6C2×#15689815C212yesmaximal, complemented
7C2×#15689807C212yesmaximal, complemented
8C2×#15689799C212yesmaximal, complemented
9C2×#15689799C212yesmaximal, complemented
10C2×#15689752C211yesmaximal, characteristic, complemented
11C2×#15689743C212yesmaximal, complemented
12C2×#15689733C212yesmaximal, complemented
13C2×#15689733C212yesmaximal, complemented
14C2×#15689722C211yesmaximal, characteristic, complemented
15C2×#15689719C212yesmaximal, complemented
16C2×#15689711C211yesmaximal, characteristic
17C2×#15689675C211yesmaximal, characteristic, complemented
18C2×#15689659C211yesmaximal, characteristic, complemented
19C22×#13094017C211yesmaximal, characteristic, complemented
20C2×C47×#543C211yesmaximal, characteristic, complemented
21#15689874C22132yescomplemented
22#15689874C22132yescomplemented
23#15689844C22132yescomplemented
24#15689827C22132yescomplemented
25#15689815C22132yescomplemented
26#15689807C22132yescomplemented
27#15689799C22132yescomplemented
28#15689799C22132yescomplemented
29#15689752C22116yescomplemented
30#15689743C22132yescomplemented
31#15689733C22132yescomplemented
32#15689733C22132yescomplemented
33#15689722C22116yescomplemented
34#15689719C22132yescomplemented
35#15689711C22116yes—
36#15689675C22116yescomplemented
37C2×#13094023C2212yescomplemented
38C2×#13094023C2211yescharacteristic, complemented
39C2×#13094022C2212yescomplemented
40C2×#13094022C2212yescomplemented
41C2×#13094022C2211yescharacteristic, complemented
42#15689659C22116yescomplemented
43C2×#13094019C2212yescomplemented
44C2×#13094019C2212yescomplemented
45C2×#13094019C2212yescomplemented
46C2×#13094019C2212yescomplemented
47C2×#13094017C2212yes—
48C2×#13094017C2212yes—
49C2×#13094017C2212yes—
50C2×#13094017C2212yes—
51C2×#13094017C2212yes—
52C2×#13094017C2212yes—
53C2×#13094017C2212yes—
54C2×#13094017C2212yes—
55C2×#13094017C2212yes—
56C2×#13094017C22116yescomplemented
57C2×#13094015C2212yescomplemented
58C2×#13094015C2212yescomplemented
59C2×#13094015C2212yescomplemented
60C2×#13094015C2211yescharacteristic, complemented
61C2×#13094015C2212yescomplemented
62C2×#13094014C2212yescomplemented
63C2×#13094014C2212yescomplemented
64C2×#13094014C2212yescomplemented
65C2×#13094014C2212yescomplemented
66C2×#13094014C2212yescomplemented
67C2×#13094013C2211yescharacteristic, complemented
68C2×#13094010C2212yes—
69C2×#13094010C2212yes—
70C2×#13094010C2212yes—
71C2×#13094009C2212yescomplemented
72C2×#13094008C2212yes—
73C2×#13094008C2212yes—
74C2×#13094007C2212yes—
75C2×#13094007C2212yes—
76C2×#13094006C2212yes—
77C2×#13094006C2212yes—
78C2×#13094006C2212yes—
79C2×#13094003C2211yescharacteristic
80C2×#13094003C2212yes—
81C2×#13094003C2212yes—
82C2×#13094002C2212yescomplemented
83C2×#13094002C2212yescomplemented
84C2×#13094001C2212yes—
85C2×#13094001C2212yes—
86C2×#13094000C2212yescomplemented
87C2×#13094000C2212yescomplemented
88C2×#13094000C2212yescomplemented
89C2×#13093998C2211yescharacteristic
90C2×#13093997C2212yes—
91C2×#13093993C2212yes—
92C2×Q8×Dic47C2211yescharacteristic, complemented
93C2×Q8×Dic47C2212yescomplemented
94C2×Q8×Dic47C2211yescharacteristic, complemented
95C2×#13093989C2212yescomplemented
96C2×#13093989C2211yescharacteristic, complemented
97C2×#13093989C2212yescomplemented
98C2×#13093986C2211yescharacteristic, complemented
99C2×C4×C22⋊D47C2212yes—
100C2×C4×C22⋊D47C2212yes—
101C2×C4×C22⋊D47C2212yes—
102C2×(C22⋊D47)⋊C4C2212yes—
103C2×(C22⋊D47)⋊C4C2212yes—
104C2×#13093983C2212yes—
105C2×#13093983C2212yes—
106C2×#13093982C2212yescomplemented
107C2×#13093982C2212yescomplemented
108C2×#13093980C2212yes—
109C2×#13093980C2212yes—
110C22×C4⋊Dic47C2211yescharacteristic
111C22×Dic47⋊C4C2211yescharacteristic
112C22×Dic47⋊C4C2211yescharacteristic
113C2×C4⋊C4×D47C2212yescomplemented
114C22×C22⋊Dic47C2211yescharacteristic
115C22×C22⋊Dic47C2211yescharacteristic
116C22×C4×Dic47C2211yescharacteristic
117C47×#543C22116yescomplemented
118C2×C22⋊Q8×C47C2211yescharacteristic
119C2×C22⋊Q8×C47C2212yes—
120C2×C22⋊Q8×C47C2212yes—
121C2×C22⋊Q8×C47C2211yescharacteristic
122C2×C22⋊Q8×C47C2212yes—
123C2×C22⋊Q8×C47C2212yes—
124C2×C22⋊Q8×C47C2212yes—
125C22×C22⋊C4×C47C2212yes—
126C22×C22⋊C4×C47C2211yescharacteristic
127C22×Dic94C2312yes—
128C22×Dic94C2312yes—
129C22×Dic94C2311yescharacteristic
130C22×D188C2311yescharacteristic
131C22×C22⋊D47C2312yes—
132C22×C22⋊D47C2312yes—
133C22×C22⋊D47C2312yes—
134C23×Dic47C2311yescharacteristic
135C23×Dic47C2311yescharacteristic
136C23×Dic47C2311yescharacteristic
137C23×Dic47C2311yescharacteristic
138C22×C4×D47C2312yes—
139C22×C4×D47C2312yes—
140C22×C4×D47C2312yes—
141#13094023C23116yescomplemented
142#13094023C2318yescomplemented
143#13094022C23116yescomplemented
144#13094022C23116yescomplemented
145#13094022C2318yescomplemented
146#13094019C23116yescomplemented
147#13094019C23116yescomplemented
148#13094019C23116yescomplemented
149#13094019C23116yescomplemented
150#13094017C23116yes—
151#13094017C23116yes—
152#13094017C23116yes—
153#13094017C23116yes—
154#13094017C23116yes—
155#13094017C23116yes—
156#13094017C23116yes—
157#13094017C23116yes—
158#13094017C23116yes—
159#13094015C2318yescomplemented
160#13094015C23116yescomplemented
161#13094015C23116yescomplemented
162#13094015C23116yescomplemented
163#13094015C23116yescomplemented
164#13094014C23116yescomplemented
165#13094014C23116yescomplemented
166#13094014C23116yescomplemented
167#13094014C23116yescomplemented
168#13094014C23116yescomplemented
169#13094013C2318yescomplemented
170#13094010C23116yes—
171#13094010C23116yes—
172#13094010C23116yes—
173#13094009C23116yescomplemented
174#13094008C23116yes—
175#13094008C23116yes—
176#13094007C23116yes—
177#13094007C23116yes—
178#13094006C23116yes—
179#13094006C23116yes—
180#13094006C23116yes—
181#13094003C23116yes—
182#13094003C23116yes—
183#13094003C2318yes—
184#13094002C23116yescomplemented
185#13094002C23116yescomplemented
186#13094001C23116yes—
187#13094001C23116yes—
188#13094000C23116yescomplemented
189#13094000C23116yescomplemented
190#13094000C23116yescomplemented
191#13093998C2318yes—
192#13093997C23116yes—
193#13093993C23116yes—
194Q8×Dic47C2318yescomplemented
195Q8×Dic47C23116yescomplemented
196Q8×Dic47C2318yescomplemented
197#13093989C23116yescomplemented
198#13093989C23116yescomplemented
199#13093989C2318yescomplemented
200#13093986C2318yescomplemented
201C4×C22⋊D47C23116yes—
202C4×C22⋊D47C23116yes—
203C4×C22⋊D47C23116yes—
204(C22⋊D47)⋊C4C23116yes—
205(C22⋊D47)⋊C4C23116yes—
206#13093983C23116yes—
207#13093983C23116yes—
208#13093982C23116yescomplemented
209#13093982C23116yescomplemented
210#13093980C23116yes—
211#13093980C23116yes—
212C2×C4⋊Dic47C2318yes—
213C2×C4⋊Dic47C2312yes—
214C2×C4⋊Dic47C2312yes—
215C2×C4⋊Dic47C2312yes—
216C2×C4⋊Dic47C2312yes—
217C2×C4⋊Dic47C2312yes—
218C2×C4⋊Dic47C2312yes—
219C2×C4⋊Dic47C2311yescharacteristic
220C2×C4⋊Dic47C2311yescharacteristic
221C2×C4⋊Dic47C2312yes—
222C2×C4⋊Dic47C2312yes—
223C2×Dic47⋊C4C2318yes—
224C2×Dic47⋊C4C2318yes—
225C2×Dic47⋊C4C2312yes—
226C2×Dic47⋊C4C2312yes—
227C2×Dic47⋊C4C2312yes—
228C2×Dic47⋊C4C2312yes—
229C2×Dic47⋊C4C2312yes—
230C2×Dic47⋊C4C2312yes—
231C2×Dic47⋊C4C2312yes—
232C2×Dic47⋊C4C2312yes—
233C2×Dic47⋊C4C2312yes—
234C2×Dic47⋊C4C2312yes—
235C2×Dic47⋊C4C2312yes—
236C2×Dic47⋊C4C2312yes—
237C2×Dic47⋊C4C2312yes—
238C2×Dic47⋊C4C2312yes—
239C2×Dic47⋊C4C2312yes—
240C2×Dic47⋊C4C2312yes—
241C4⋊C4×D47C23116yescomplemented
242C2×C22⋊Dic47C2318yes—
243C2×C22⋊Dic47C2318yes—
244C2×C22⋊Dic47C2312yes—
245C2×C22⋊Dic47C2312yes—
246C2×C22⋊Dic47C2312yes—
247C2×C22⋊Dic47C2312yes—
248C2×C22⋊Dic47C2312yes—
249C2×C22⋊Dic47C2312yes—
250C2×C22⋊Dic47C2312yes—
251C2×(C2×D47)⋊C4C2312yes—
252C2×(C2×D47)⋊C4C2312yes—
253C2×(C2×D47)⋊C4C2312yes—
254C2×(C2×D47)⋊C4C2312yes—
255C2×(C2×D47)⋊C4C2312yes—
256C2×(C2×D47)⋊C4C2312yes—
257C2×(C2×D47)⋊C4C2312yes—
258C2×(C2×D47)⋊C4C2312yes—
259C2×C4×Dic47C2311yescharacteristic
260C2×C4×Dic47C2311yescharacteristic
261C2×C4×Dic47C2311yescharacteristic
262C2×C4×Dic47C2311yescharacteristic
263C2×C4×Dic47C2318yes—
264C2×C4×Dic47C2312yes—
265C2×C4×Dic47C2312yes—
266C2×C4×Dic47C2312yes—
267C2×C4×Dic47C2312yes—
268C2×C4×Dic47C2312yes—
269C2×C4×Dic47C2312yes—
270C2×C4×Dic47C2312yes—
271C25×C47C2311yescharacteristic
272C22×Q8×C47C2311yescharacteristic
273C22×Q8×C47C2312yes—
274C22×Q8×C47C2311yescharacteristic
275C23×C4×C47C2311yescharacteristic
276C23×C4×C47C2311yescharacteristic
277C23×C4×C47C2312yes—
278C23×C4×C47C2312yes—
279C22⋊Q8×C47C23116yes—
280C22⋊Q8×C47C23116yes—
281C22⋊Q8×C47C2318yes—
282C22⋊Q8×C47C23116yes—
283C22⋊Q8×C47C23116yes—
284C22⋊Q8×C47C23116yes—
285C22⋊Q8×C47C2318yes—
286C2×C4⋊C4×C47C2312yes—
287C2×C4⋊C4×C47C2312yes—
288C2×C4⋊C4×C47C2312yes—
289C2×C4⋊C4×C47C2311yescharacteristic
290C2×C4⋊C4×C47C2312yes—
291C2×C4⋊C4×C47C2312yes—
292C2×C4⋊C4×C47C2311yescharacteristic
293C2×C22⋊C4×C47C23116yes—
294C2×C22⋊C4×C47C2312yes—
295C2×C22⋊C4×C47C2312yes—
296C2×C22⋊C4×C47C2312yes—
297C2×C22⋊C4×C47C2312yes—
298C2×C22⋊C4×C47C2312yes—
299C2×C22⋊C4×C47C2312yes—
300C2×C22⋊C4×C47C2318yes—
301C24×C47—24no—
302C24×C47—42no—
303C24×C47—42no—
304C24×C47C2412yes—
305C24×C47C2411yescharacteristic
306C24×C47C2414yes—
307C23×D47C2412yes—
308C2×Q8×C47—42no—
309C2×Q8×C47—42no—
310C2×Q8×C47—44no—
311C2×Q8×C47C2418yes—
312C2×Q8×C47C2414yes—
313C2×Q8×C47C2414yes—
314C22×C4×C47—44no—
315C22×C4×C47—44no—
316C22×C4×C47—42no—
317C22×C4×C47—42no—
318C22×C4×C47C2412yes—
319C22×C4×C47C2412yes—
320C22×C4×C47C2411yescharacteristic
321C22×C4×C47C2411yescharacteristic
322C22×C4×C47C2412yes—
323C22×C4×C47C2412yes—
324C22×C4×C47C2412yes—
325C22×C4×C47C2414yes—
326C22×C4×C47C2414yes—
327C22×C4×C47C2418yes—
328C22×C4×C47C2418yes—
329C2×C22⋊D47—28no—
330C2×C22⋊D47—44no—
331C2×C22⋊D47—44no—
332C2×C22⋊D47C2418yes—
333C2×C22⋊D47C2418yes—
334C2×C22⋊D47C2418yes—
335C22×Dic47—24no—
336C22×Dic47—24no—
337C22×Dic47—42no—
338C22×Dic47—42no—
339C22×Dic47C2411yescharacteristic
340C22×Dic47C2411yescharacteristic
341C22×Dic47C2412yes—
342C22×Dic47C2412yes—
343C22×Dic47C2411yescharacteristic
344C22×Dic47C2411yescharacteristic
345C22×Dic47C2412yes—
346C22×Dic47C2412yes—
347C22×Dic47C2414yes—
348C22×Dic47C2412yes—
349C22×Dic47C2414yes—
350C22×Dic47C2414yes—
351C22×Dic47C2414yes—
352C2×D188—42no—
353C2×D188C2414yes—
354C2×C4×D47—44no—
355C2×C4×D47—44no—
356C2×C4×D47—44no—
357C2×C4×D47C2418yes—
358C2×C4×D47C2418yes—
359C2×C4×D47C2418yes—
360C2×Dic94—44no—
361C2×Dic94—42no—
362C2×Dic94—44no—
363C2×Dic94C2418yes—
364C2×Dic94C2418yes—
365C2×Dic94C2414yes—
366C4⋊C4×C47C2418yes—
367C4⋊C4×C47C2418yes—
368C4⋊C4×C47C2418yes—
369C4⋊C4×C47C2414yes—
370C4⋊C4×C47C2418yes—
371C4⋊C4×C47C2418yes—
372C4⋊C4×C47C2414yes—
373C22⋊C4×C47C2418yes—
374C22⋊C4×C47C2418yes—
375C22⋊C4×C47C2418yes—
376C22⋊C4×C47C2418yes—
377C22⋊C4×C47C2418yes—
378C22⋊C4×C47C2418yes—
379C22⋊Dic47C2418yes—
380C22⋊Dic47C2418yes—
381C22⋊Dic47C2418yes—
382C22⋊Dic47C2418yes—
383C22⋊Dic47C2418yes—
384C22⋊Dic47C2418yes—
385C22⋊Dic47C2418yes—
386(C2×D47)⋊C4C2418yes—
387(C2×D47)⋊C4C2418yes—
388(C2×D47)⋊C4C2418yes—
389(C2×D47)⋊C4C2418yes—
390(C2×D47)⋊C4C2418yes—
391(C2×D47)⋊C4C2418yes—
392(C2×D47)⋊C4C2418yes—
393(C2×D47)⋊C4C2418yes—
394C4⋊Dic47C2418yes—
395C4⋊Dic47C2418yes—
396C4⋊Dic47C2418yes—
397C4⋊Dic47C2418yes—
398C4⋊Dic47C2418yes—
399C4⋊Dic47C2418yes—
400C4⋊Dic47C2414yes—
401C4⋊Dic47C2414yes—
402C4⋊Dic47C2418yes—
403C4⋊Dic47C2418yes—
404Dic47⋊C4C2418yes—
405Dic47⋊C4C2418yes—
406Dic47⋊C4C2418yes—
407Dic47⋊C4C2418yes—
408Dic47⋊C4C2418yes—
409Dic47⋊C4C2418yes—
410Dic47⋊C4C2418yes—
411Dic47⋊C4C2418yes—
412Dic47⋊C4C2418yes—
413Dic47⋊C4C2418yes—
414Dic47⋊C4C2418yes—
415Dic47⋊C4C2418yes—
416Dic47⋊C4C2418yes—
417Dic47⋊C4C2418yes—
418Dic47⋊C4C2418yes—
419Dic47⋊C4C2418yes—
420C4×Dic47C2414yes—
421C4×Dic47C2414yes—
422C4×Dic47C2414yes—
423C4×Dic47C2414yes—
424C4×Dic47C2418yes—
425C4×Dic47C2418yes—
426C4×Dic47C2418yes—
427C4×Dic47C2418yes—
428C4×Dic47C2418yes—
429C4×Dic47C2418yes—
430C4×Dic47C2418yes—
431C23×C47—22no—
432C23×C47—22no—
433C23×C47—24no—
434C23×C47—24no—
435C23×C47—24no—
436C23×C47—28no—
437C23×C47—44no—
438C23×C47—44no—
439C23×C47—88no—
440C23×C472−1+414yes—
441C23×C47C2514yes—
442C23×C47C2512yes—
443C23×C47C2511yescharacteristic
444C22×D47—24no—
445C22×D47—24no—
446C22×D47—24no—
447C22×D47C2514yes—
448Q8×C47—44no—
449Q8×C47—48no—
450Q8×C47—44no—
451C2×C4×C47—24no—
452C2×C4×C47—22no—
453C2×C4×C47—24no—
454C2×C4×C47—24no—
455C2×C4×C47—24no—
456C2×C4×C47—24no—
457C2×C4×C47—22no—
458C2×C4×C47—48no—
459C2×C4×C47—48no—
460C2×C4×C47—44no—
461C2×C4×C47—44no—
462C2×C4×C47C2512yes—
463C2×C4×C47C2512yes—
464C2×C4×C47C2514yes—
465C2×C4×C47C2514yes—
466C2×C4×C47C2514yes—
467C2×C4×C47C2514yes—
468C2×C4×C47C2514yes—
469C22⋊D47—216no—
470C22⋊D47—48no—
471C22⋊D47—48no—
472C2×Dic47—28no—
473C2×Dic47—28no—
474C2×Dic47—22no—
475C2×Dic47—22no—
476C2×Dic47—24no—
477C2×Dic47—24no—
478C2×Dic47—22no—
479C2×Dic47—24no—
480C2×Dic47—24no—
481C2×Dic47—24no—
482C2×Dic47—22no—
483C2×Dic47—44no—
484C2×Dic47—44no—
485C2×Dic47C2512yes—
486C2×Dic47C2512yes—
487C2×Dic47C2514yes—
488C2×Dic47C2514yes—
489C2×Dic47C2514yes—
490C2×Dic47C2512yes—
491C2×Dic47C2512yes—
492C2×Dic47C2514yes—
493C2×Dic47C2514yes—
494D188—44no—
495C4×D47—48no—
496C4×D47—48no—
497C4×D47—48no—
498Dic94—48no—
499Dic94—44no—
500Dic94—48no—
501C2×#3564—471nomaximal, Sylow
502C22×C47—22no—
503C22×C47—22no—
504C22×C47—28no—
505C22×C47—24no—
506C22×C47—24no—
507C22×C47—24no—
508C22×C47—48no—
509C22×C47—88no—
510C22×C47C2×2−1+414yes—
511C22×C47C2×2−1+412yes—
512C22×C47#58512yes—
513C22×C47#58512yes—
514C22×C47C2611yescharacteristic
515C2×D47—24no—
516C2×D47—24no—
517C2×D47—24no—
518C2×D47—48no—
519C4×C47—24no—
520C4×C47—22no—
521C4×C47—24no—
522C4×C47—24no—
523C4×C47—24no—
524C4×C47—24no—
525C4×C47—22no—
526Dic47—22no—
527Dic47—22no—
528Dic47—24no—
529Dic47—24no—
530Dic47—22no—
531Dic47—24no—
532Dic47—24no—
533Dic47—24no—
534Dic47—22no—
535#3564—4732no—
536C2×#563—472no—
537C2×#563—472no—
538C2×#556—472no—
539C2×#554—472no—
540C2×#552—472no—
541C2×#552—472no—
542C2×#551—472no—
543C2×#551—472no—
544C2×#544—471no—
545C2×#543D4711yescharacteristic, complemented
546C2×#542—472no—
547C2×#541—472no—
548C2×#541—472no—
549C2×#539—472no—
550C2×#539—471no—
551C2×#538—471no—
552C2×#533—471no—
553C2×#529—471no—
554C22×#126—471no—
555C2×C47—24no—
556C2×C47—44no—
557C2×C47#356414yescomplemented
558C2×C47C22×2−1+411yescharacteristic
559C2×C47C2×#58511yescharacteristic
560C2×C47C2×#58511yescharacteristic
561D47—44no—
562#563—4732no—
563#563—4732no—
564#556—4732no—
565#554—4732no—
566#552—4732no—
567#552—4732no—
568#551—4732no—
569#551—4732no—
570#544—4716no—
571#543C2×D47116yescomplemented
572#542—4732no—
573#541—4732no—
574#541—4732no—
575#539—4732no—
576#539—4716no—
577#538—4716no—
578#533—4716no—
579C2×C4⋊Q8—471no—
580C2×C4⋊Q8—472no—
581C2×C4⋊Q8—472no—
582C2×C4⋊Q8—471no—
583C2×C4⋊Q8—472no—
584#529—4716no—
585C2×#126—472no—
586C2×#126—472no—
587C2×#126—472no—
588C2×#126—472no—
589C2×#126—472no—
590C2×#126—472no—
591C2×#126—472no—
592C2×#126—472no—
593C2×#126—4716no—
594C2×#126—472no—
595C2×#126—472no—
596C2×#126—472no—
597C2×#126—472no—
598C2×#126—472no—
599C2×#125—471no—
600C2×#125—472no—
601C2×#125—472no—
602C2×#125—472no—
603C2×#125—472no—
604C2×#125—472no—
605C2×#125—472no—
606C2×#125—472no—
607C2×#125—472no—
608C2×#125—472no—
609C2×#124—471no—
610C2×#124—472no—
611C2×#124—472no—
612C2×#124—472no—
613C2×#123—472no—
614C2×#123—472no—
615C2×#123—472no—
616C2×#123—472no—
617C2×#123—472no—
618C2×#123—472no—
619C2×#123—472no—
620C2×#123—472no—
621C2×C22⋊Q8—472no—
622C2×C22⋊Q8—472no—
623C2×C22⋊Q8—472no—
624C2×C22⋊Q8—471no—
625C2×C22⋊Q8—472no—
626C2×C22⋊Q8—472no—
627C2×C22⋊Q8—472no—
628C2×C22⋊Q8—472no—
629C2×C22⋊Q8—472no—
630C2×C22⋊Q8—472no—
631C2×C22⋊Q8C2×D4711yescharacteristic
632C2×C22⋊Q8C2×D4711yescharacteristic
633C2×C22⋊Q8C2×D4712yes—
634C2×C22⋊Q8C2×D4712yes—
635C2×C22⋊Q8C2×D4712yes—
636C2×C22⋊Q8C2×D4712yes—
637C2×C22⋊Q8C2×D4712yes—
638C2×#121—471no—
639C2×#121—472no—
640C2×#120—472no—
641C2×C4×Q8—471no—
642C2×C4×Q8—471no—
643C2×C4×Q8—472no—
644C2×C4×Q8—472no—
645C2×C4×Q8—471no—
646C2×C4×Q8—472no—
647C2×C4×D4—472no—
648C2×C4×D4—472no—
649C2×C4×D4—472no—
650C2×C4×D4—471no—
651C2×C4×D4—472no—
652C2×C4×D4—472no—
653C2×#117—472no—
654C2×#117—472no—
655C2×#117—472no—
656C2×#117—472no—
657C2×#117—472no—
658C2×#117—472no—
659C22×C4⋊C4—471no—
660C22×C4⋊C4—471no—
661C22×C4⋊C4—471no—
662C22×C4⋊C4—472no—
663C22×C22⋊C4—471no—
664C22×C22⋊C4—471no—
665C22×C22⋊C4C2×D4711yescharacteristic
666C22×C22⋊C4C2×D4712yes—
667C22×C42—471no—
668C47C2×#356411yescharacteristic, complemented, Sylow
669C25C22×D4711yescharacteristic
670C22×Q8—472no—
671C22×Q8—472no—
672C22×Q8—471no—
673C22×Q8C22×D4711yescharacteristic
674C22×Q8C22×D4712yes—
675C22×Q8C22×D4711yescharacteristic
676C22×D4—472no—
677C22×D4—472no—
678C22×D4—472no—
679C22×D4—471no—
680C23×C4—471no—
681C23×C4—471no—
682C23×C4—471no—
683C23×C4—471no—
684C23×C4—472no—
685C23×C4—472no—
686C23×C4—472no—
687C23×C4C22×D4711yescharacteristic
688C23×C4C22×D4711yescharacteristic
689C23×C4C22×D4712yes—
690C23×C4C22×D4712yes—
691C4⋊Q8—478no—
692C4⋊Q8—4716no—
693C4⋊Q8—4716no—
694C4⋊Q8—478no—
695C4⋊Q8—4716no—
696#126—4716no—
697#126—4716no—
698#126—4716no—
699#126—4716no—
700#126—4716no—
701#126—4716no—
702#126—4716no—
703#126—4716no—
704#126—4716no—
705#126—4716no—
706#126—4716no—
707#126—4716no—
708#126—4716no—
709#125—478no—
710#125—4716no—
711#125—4716no—
712#125—4716no—
713#125—4716no—
714#125—4716no—
715#125—4716no—
716#125—4716no—
717#125—4716no—
718#125—4716no—
719#124—478no—
720#124—4716no—
721#124—4716no—
722#124—4716no—
723#123—4716no—
724#123—4716no—
725#123—4716no—
726#123—4716no—
727#123—4716no—
728#123—4716no—
729#123—4716no—
730#123—4716no—
731C22⋊Q8—4716no—
732C22⋊Q8—4716no—
733C22⋊Q8—4716no—
734C22⋊Q8—478no—
735C22⋊Q8—4716no—
736C22⋊Q8—4716no—
737C22⋊Q8—4716no—
738C22⋊Q8—4716no—
739C22⋊Q8—4716no—
740C22⋊Q8—4716no—
741C22⋊Q8C22×D4718yes—
742C22⋊Q8C22×D4718yes—
743C22⋊Q8C22×D47116yes—
744C22⋊Q8C22×D47116yes—
745C22⋊Q8C22×D47116yes—
746C22⋊Q8C22×D47116yes—
747C22⋊Q8C22×D47116yes—
748#121—478no—
749#121—4716no—
750#120—4716no—
751C4×Q8—478no—
752C4×Q8—478no—
753C4×Q8—4716no—
754C4×Q8—4716no—
755C4×Q8—478no—
756C4×Q8—4716no—
757C4×D4—4716no—
758C4×D4—4716no—
759C4×D4—4716no—
760C4×D4—478no—
761C4×D4—4716no—
762C4×D4—4716no—
763#117—4716no—
764#117—4716no—
765#117—4716no—
766#117—4716no—
767#117—4716no—
768#117—4716no—
769C2×C4⋊C4—472no—
770C2×C4⋊C4—472no—
771C2×C4⋊C4—472no—
772C2×C4⋊C4—472no—
773C2×C4⋊C4—472no—
774C2×C4⋊C4—472no—
775C2×C4⋊C4—472no—
776C2×C4⋊C4—472no—
777C2×C4⋊C4—478no—
778C2×C4⋊C4—478no—
779C2×C4⋊C4—478no—
780C2×C4⋊C4—472no—
781C2×C4⋊C4—472no—
782C2×C4⋊C4—472no—
783C2×C4⋊C4—472no—
784C2×C4⋊C4—472no—
785C2×C4⋊C4—472no—
786C2×C4⋊C4—472no—
787C2×C4⋊C4—472no—
788C2×C4⋊C4—472no—
789C2×C4⋊C4—472no—
790C2×C4⋊C4—472no—
791C2×C4⋊C4—472no—
792C2×C4⋊C4—472no—
793C2×C4⋊C4—471no—
794C2×C4⋊C4—472no—
795C2×C4⋊C4—471no—
796C2×C4⋊C4—472no—
797C2×C4⋊C4—472no—
798C2×C4⋊C4—4716no—
799C2×C4⋊C4C22×D4712yes—
800C2×C4⋊C4C22×D4712yes—
801C2×C4⋊C4C22×D4712yes—
802C2×C4⋊C4C22×D4711yescharacteristic
803C2×C4⋊C4C22×D4712yes—
804C2×C4⋊C4C22×D4712yes—
805C2×C4⋊C4C22×D4711yescharacteristic
806C2×C22⋊C4—472no—
807C2×C22⋊C4—472no—
808C2×C22⋊C4—472no—
809C2×C22⋊C4—472no—
810C2×C22⋊C4—478no—
811C2×C22⋊C4—478no—
812C2×C22⋊C4—472no—
813C2×C22⋊C4—472no—
814C2×C22⋊C4—472no—
815C2×C22⋊C4—472no—
816C2×C22⋊C4—472no—
817C2×C22⋊C4—472no—
818C2×C22⋊C4—472no—
819C2×C22⋊C4—472no—
820C2×C22⋊C4—472no—
821C2×C22⋊C4—472no—
822C2×C22⋊C4—472no—
823C2×C22⋊C4C22×D4712yes—
824C2×C22⋊C4C22×D4712yes—
825C2×C22⋊C4C22×D4712yes—
826C2×C22⋊C4C22×D4712yes—
827C2×C22⋊C4C22×D4712yes—
828C2×C22⋊C4C22×D4712yes—
829C2×C22⋊C4C22×D4718yes—
830C2×C22⋊C4C22×D47116yes—
831C2×C42—472no—
832C2×C42—472no—
833C2×C42—472no—
834C2×C42—472no—
835C2×C42—471no—
836C2×C42—472no—
837C2×C42—472no—
838C2×C42—472no—
839C2×C42—471no—
840C2×C42—471no—
841C2×C42—471no—
842C2×C42—478no—
843C24—24no—
844C24—42no—
845C24—42no—
846C24—472no—
847C24C23×D4712yes—
848C24C23×D4711yescharacteristic
849C24C23×D4714yes—
850C2×Q8—42no—
851C2×Q8—44no—
852C2×Q8—42no—
853C2×Q8—478no—
854C2×Q8—478no—
855C2×Q8—474no—
856C2×Q8—1884no—
857C2×Q8—1884no—
858C2×Q8—1882no—
859C2×Q8C23×D4714yes—
860C2×Q8C23×D4718yes—
861C2×Q8C23×D4714yes—
862C2×D4—478no—
863C2×D4—478no—
864C2×D4—478no—
865C2×D4—474no—
866C2×D4—948no—
867C2×D4—1882no—
868C2×D4—1884no—
869C2×D4—1884no—
870C22×C4—42no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—42no—
874C22×C4—474no—
875C22×C4—474no—
876C22×C4—471no—
877C22×C4—471no—
878C22×C4—472no—
879C22×C4—472no—
880C22×C4—472no—
881C22×C4—471no—
882C22×C4—471no—
883C22×C4—472no—
884C22×C4—472no—
885C22×C4—474no—
886C22×C4—474no—
887C22×C4—478no—
888C22×C4—478no—
889C22×C4—478no—
890C22×C4—944no—
891C22×C4—944no—
892C22×C4—1884no—
893C22×C4—1884no—
894C22×C4—1884no—
895C22×C4—1882no—
896C22×C4—1882no—
897C22×C4C23×D4712yes—
898C22×C4C23×D4712yes—
899C22×C4C23×D4711yescharacteristic
900C22×C4C23×D4711yescharacteristic
901C22×C4C23×D4712yes—
902C22×C4C23×D4712yes—
903C22×C4C23×D4712yes—
904C22×C4C23×D4714yes—
905C22×C4C23×D4714yes—
906C22×C4C23×D4718yes—
907C22×C4C23×D4718yes—
908C4⋊C4—478no—
909C4⋊C4—478no—
910C4⋊C4—478no—
911C4⋊C4—478no—
912C4⋊C4—478no—
913C4⋊C4—478no—
914C4⋊C4—478no—
915C4⋊C4—478no—
916C4⋊C4—478no—
917C4⋊C4—478no—
918C4⋊C4—478no—
919C4⋊C4—478no—
920C4⋊C4—478no—
921C4⋊C4—478no—
922C4⋊C4—478no—
923C4⋊C4—478no—
924C4⋊C4—478no—
925C4⋊C4—478no—
926C4⋊C4—478no—
927C4⋊C4—478no—
928C4⋊C4—478no—
929C4⋊C4—478no—
930C4⋊C4—474no—
931C4⋊C4—474no—
932C4⋊C4—478no—
933C4⋊C4—478no—
934C4⋊C4C23×D4718yes—
935C4⋊C4C23×D4718yes—
936C4⋊C4C23×D4718yes—
937C4⋊C4C23×D4714yes—
938C4⋊C4C23×D4718yes—
939C4⋊C4C23×D4718yes—
940C4⋊C4C23×D4714yes—
941C22⋊C4—478no—
942C22⋊C4—478no—
943C22⋊C4—478no—
944C22⋊C4—478no—
945C22⋊C4—478no—
946C22⋊C4—478no—
947C22⋊C4—478no—
948C22⋊C4—478no—
949C22⋊C4—478no—
950C22⋊C4—478no—
951C22⋊C4—478no—
952C22⋊C4—478no—
953C22⋊C4—478no—
954C22⋊C4—478no—
955C22⋊C4—478no—
956C22⋊C4C23×D4718yes—
957C22⋊C4C23×D4718yes—
958C22⋊C4C23×D4718yes—
959C22⋊C4C23×D4718yes—
960C22⋊C4C23×D4718yes—
961C22⋊C4C23×D4718yes—
962C42—474no—
963C42—474no—
964C42—474no—
965C42—474no—
966C42—478no—
967C42—478no—
968C42—478no—
969C42—478no—
970C42—478no—
971C42—478no—
972C42—478no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—28no—
979C23—44no—
980C23—44no—
981C23—88no—
982C23—474no—
983C23—944no—
984C23—944no—
985C23—944no—
986C23#1309407214yes—
987C23C24×D4714yes—
988C23C24×D4712yes—
989C23C24×D4711yescharacteristic
990Q8—44no—
991Q8—48no—
992Q8—44no—
993Q8—1888no—
994Q8—1888no—
995Q8—1884no—
996D4—9416no—
997D4—1884no—
998D4—1888no—
999D4—1888no—
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—472no—
1012C2×C4—472no—
1013C2×C4—474no—
1014C2×C4—474no—
1015C2×C4—472no—
1016C2×C4—474no—
1017C2×C4—472no—
1018C2×C4—474no—
1019C2×C4—474no—
1020C2×C4—948no—
1021C2×C4—948no—
1022C2×C4—942no—
1023C2×C4—944no—
1024C2×C4—942no—
1025C2×C4—944no—
1026C2×C4—942no—
1027C2×C4—944no—
1028C2×C4—944no—
1029C2×C4—942no—
1030C2×C4—944no—
1031C2×C4—1888no—
1032C2×C4—1888no—
1033C2×C4—1888no—
1034C2×C4—1884no—
1035C2×C4—1884no—
1036C2×C4C24×D4712yes—
1037C2×C4C24×D4714yes—
1038C2×C4C24×D4714yes—
1039C2×C4C24×D4712yes—
1040C2×C4C24×D4714yes—
1041C2×C4C24×D4714yes—
1042C2×C4C24×D4714yes—
1043C22—22no—
1044C22—22no—
1045C22—28no—
1046C22—24no—
1047C22—24no—
1048C22—24no—
1049C22—48no—
1050C22—88no—
1051C22—944no—
1052C22—944no—
1053C22—944no—
1054C22—1888no—
1055C22C2×#1309407214yes—
1056C22C2×#1309407212yes—
1057C22#1568995812yes—
1058C22#1568995812yes—
1059C22C25×D4711yescharacteristic
1060C4—24no—
1061C4—24no—
1062C4—24no—
1063C4—22no—
1064C4—24no—
1065C4—24no—
1066C4—22no—
1067C4—942no—
1068C4—942no—
1069C4—944no—
1070C4—944no—
1071C4—942no—
1072C4—944no—
1073C4—944no—
1074C4—942no—
1075C4—944no—
1076C2—24no—
1077C2—44no—
1078C2—1884no—
1079C2#2025800214yesdirect product factor
1080C2C22×#1309407211yescharacteristic
1081C2C2×#1568995811yescharacteristic
1082C2C2×#1568995811yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#543C2
socleC23×C47C25
prime radicalC2×#15689711C2
hypercenterC2×#543D47
hypocenterC47C2×#3564
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. #20258002C2direct (N × H)
2. C2×#15689874C2semidirect
3. C2×#15689874C2semidirect
4. C2×#15689844C2semidirect
5. C2×#15689827C2semidirect
6. C2×#15689815C2semidirect
7. C2×#15689807C2semidirect
8. C2×#15689799C2semidirect
9. C2×#15689799C2semidirect
10. C2×#15689752C2semidirect
11. C2×#15689743C2semidirect
12. C2×#15689733C2semidirect
13. C2×#15689733C2semidirect
14. C2×#15689722C2semidirect
15. C2×#15689719C2semidirect
17. C2×#15689675C2semidirect
18. C2×#15689659C2semidirect
19. C22×#13094017C2semidirect
20. C2×C47×#543C2semidirect
21. #15689874C22semidirect
22. #15689874C22semidirect
23. #15689844C22semidirect
24. #15689827C22semidirect
25. #15689815C22semidirect
26. #15689807C22semidirect
27. #15689799C22semidirect
28. #15689799C22semidirect
29. #15689752C22semidirect
30. #15689743C22semidirect
31. #15689733C22semidirect
32. #15689733C22semidirect
33. #15689722C22semidirect
34. #15689719C22semidirect
36. #15689675C22semidirect
37. C2×#13094023C22semidirect
38. C2×#13094023C22semidirect
39. C2×#13094022C22semidirect
40. C2×#13094022C22semidirect
41. C2×#13094022C22semidirect
42. #15689659C22semidirect
43. C2×#13094019C22semidirect
44. C2×#13094019C22semidirect
45. C2×#13094019C22semidirect
46. C2×#13094019C22semidirect
56. C2×#13094017C22semidirect
57. C2×#13094015C22semidirect
58. C2×#13094015C22semidirect
59. C2×#13094015C22semidirect
60. C2×#13094015C22semidirect
61. C2×#13094015C22semidirect
62. C2×#13094014C22semidirect
63. C2×#13094014C22semidirect
64. C2×#13094014C22semidirect
65. C2×#13094014C22semidirect
66. C2×#13094014C22semidirect
67. C2×#13094013C22semidirect
71. C2×#13094009C22semidirect
82. C2×#13094002C22semidirect
83. C2×#13094002C22semidirect
86. C2×#13094000C22semidirect
87. C2×#13094000C22semidirect
88. C2×#13094000C22semidirect
92. C2×Q8×Dic47C22semidirect
93. C2×Q8×Dic47C22semidirect
94. C2×Q8×Dic47C22semidirect
95. C2×#13093989C22semidirect
96. C2×#13093989C22semidirect
97. C2×#13093989C22semidirect
98. C2×#13093986C22semidirect
106. C2×#13093982C22semidirect
107. C2×#13093982C22semidirect
113. C2×C4⋊C4×D47C22semidirect
117. C47×#543C22semidirect
141. #13094023C23semidirect
142. #13094023C23semidirect
143. #13094022C23semidirect
144. #13094022C23semidirect
145. #13094022C23semidirect
146. #13094019C23semidirect
147. #13094019C23semidirect
148. #13094019C23semidirect
149. #13094019C23semidirect
159. #13094015C23semidirect
160. #13094015C23semidirect
161. #13094015C23semidirect
162. #13094015C23semidirect
163. #13094015C23semidirect
164. #13094014C23semidirect
165. #13094014C23semidirect
166. #13094014C23semidirect
167. #13094014C23semidirect
168. #13094014C23semidirect
169. #13094013C23semidirect
173. #13094009C23semidirect
184. #13094002C23semidirect
185. #13094002C23semidirect
188. #13094000C23semidirect
189. #13094000C23semidirect
190. #13094000C23semidirect
194. Q8×Dic47C23semidirect
195. Q8×Dic47C23semidirect
196. Q8×Dic47C23semidirect
197. #13093989C23semidirect
198. #13093989C23semidirect
199. #13093989C23semidirect
200. #13093986C23semidirect
208. #13093982C23semidirect
209. #13093982C23semidirect
241. C4⋊C4×D47C23semidirect
545. C2×#543D47semidirect
557. C2×C47#3564semidirect
571. #543C2×D47semidirect
668. C47C2×#3564semidirect
1079. C2#20258002direct (N × H)

Maximal subgroups

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

subgroupindex
#202580022
C2×#156898742
C2×#156898442
C2×#156898272
C2×#156898152
C2×#156898072
C2×#156897992
C2×#156897522
C2×#156897432
C2×#156897332
C2×#156897222
C2×#156897192
C2×#156897112
C2×#156896752
C2×#156896592
C22×#130940172
C2×C47×#5432
C2×#356447