Finite Group Databasebeta

← C2×#20257204 #27124604

Subgroups — C2×#20257204 #27124604

Order 12032.

7478 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257204C2132yesmaximal, direct product factor
2C2×#15689853C212yesmaximal, complemented
3C2×#15689848C212yesmaximal, complemented
4C2×#15689834C212yesmaximal, complemented
5C2×#15689828C214yesmaximal, complemented
6C2×#15689788C212yesmaximal, complemented
7C2×Q8×C22⋊D47C214yesmaximal, complemented
8C2×#15689754C212yesmaximal, complemented
9C2×#15689750C214yesmaximal, complemented
10C2×#15689680C211yesmaximal, characteristic, complemented
11C2×#15689678C212yesmaximal, complemented
12C2×C4⋊Q8×D47C212yesmaximal, complemented
13C2×#15689604C212yesmaximal
14C2×C4×#10625350C211yesmaximal, characteristic
15C22×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C22×Q8×D47C2214yes—
18#15689853C22132yescomplemented
19#15689848C22132yescomplemented
20#15689834C22132yescomplemented
21#15689828C22164yescomplemented
22#15689788C22132yescomplemented
23Q8×C22⋊D47C22164yescomplemented
24#15689754C22132yescomplemented
25#15689750C22164yescomplemented
26#15689680C22116yescomplemented
27#15689678C22132yescomplemented
28C2×#13094024C2211yescharacteristic
29C2×#13094024C2211yescharacteristic
30C2×#13094023C2214yes—
31C2×#13094023C2214yes—
32C2×#13094023C2214yes—
33C2×#13094022C2218yes—
34C2×#13094022C2214yes—
35C4⋊Q8×D47C22132yescomplemented
36C2×#13094016C2212yes—
37C2×#13094015C2214yes—
38C2×#13094015C2214yes—
39C2×#13094014C2218yes—
40C2×#13094004C2214yes—
41C2×#13094003C2218yes—
42C2×#13094003C2212yes—
43C2×#13094003C2212yes—
44C2×#13094002C2218yes—
45C2×#13094000C2218yes—
46C2×#13094000C2214yes—
47#15689604C22132yes—
48C4×#10625350C22116yes—
49C2×Q8×Dic47C2214yes—
50C2×C4×Dic94C2211yescharacteristic
51C2×C4×Dic94C2211yescharacteristic
52C2×C4×Dic94C2212yes—
53C2×C4×Dic94C2212yes—
54C2×#13093989C2214yes—
55C2×#13093989C2214yes—
56C2×C4×D188C2211yescharacteristic
57C2×C4×D188C2211yescharacteristic
58C2×#13093986C2214yes—
59C2×C4×C22⋊D47C2212yes—
60C2×C4×C22⋊D47C2212yes—
61C2×C4×C22⋊D47C2218yes—
62C2×#13093983C2211yescharacteristic
63C2×#13093983C2212yes—
64C2×#13093982C2214yes—
65C2×#13093981C2212yes—
66C2×C4⋊C4×D47C2214yes—
67C2×C4⋊C4×D47C2214yes—
68C2×C42×D47C2212yes—
69C23×Q8×C47C2212yes—
70C2×C4⋊Q8×C47C2212yes—
71C2×C4⋊Q8×C47C2212yes—
72C2×C4⋊Q8×C47C2212yes—
73C2×C4⋊Q8×C47C2212yes—
74C2×C4⋊Q8×C47C22116yescomplemented
75C22×C4⋊C4×C47C2212yes—
76C22×C4⋊C4×C47C2212yes—
77C22×C42×C47C2211yescharacteristic
78C2×#10625350Q8116yescomplemented
79C2×#10625350C2318yes—
80C22×Dic94C2312yes—
81C22×Dic94C2312yes—
82C22×Dic94C2318yes—
83C22×Dic94C2311yescharacteristic
84C2×Q8×D47—416no—
85C2×Q8×D47C23132yes—
86C22×D188C2311yescharacteristic
87C22×C22⋊D47C2312yes—
88C22×C4×D47C2312yes—
89C22×C4×D47C2312yes—
90C22×C4×D47C2318yes—
91C22×C4×D47C2312yes—
92#13094024C2318yes—
93#13094024C2318yes—
94#13094023C23132yes—
95#13094023C23132yes—
96#13094023C23132yes—
97#13094022C23164yes—
98#13094022C23132yes—
99#13094016C23116yes—
100#13094015C23132yes—
101#13094015C23132yes—
102#13094014C23164yes—
103#13094004C23132yes—
104#13094003C23164yes—
105#13094003C23116yes—
106#13094003C23116yes—
107#13094002C23164yes—
108#13094000C23164yes—
109#13094000C23132yes—
110Q8×Dic47C23132yes—
111C4×Dic94C23116yes—
112C4×Dic94C23116yes—
113C4×Dic94C2318yes—
114C4×Dic94C2318yes—
115#13093989C23132yes—
116#13093989C23132yes—
117C4×D188C2318yes—
118C4×D188C2318yes—
119#13093986C23132yes—
120C4×C22⋊D47C23116yes—
121C4×C22⋊D47C23164yes—
122C4×C22⋊D47C23116yes—
123#13093983C2318yes—
124#13093983C23116yes—
125#13093982C23132yes—
126#13093981C23116yes—
127C2×C4⋊Dic47C2312yes—
128C2×C4⋊Dic47C2312yes—
129C2×C4⋊Dic47C2312yes—
130C2×C4⋊Dic47C2311yescharacteristic
131C2×C4⋊Dic47C2311yescharacteristic
132C2×C4⋊Dic47C2312yes—
133C2×C4⋊Dic47C2318yes—
134C2×Dic47⋊C4C2318yes—
135C2×Dic47⋊C4C2318yes—
136C2×Dic47⋊C4C2312yes—
137C2×Dic47⋊C4C2312yes—
138C2×Dic47⋊C4C2318yes—
139C2×Dic47⋊C4C2314yes—
140C2×Dic47⋊C4C2314yes—
141C4⋊C4×D47C23132yes—
142C4⋊C4×D47C23132yes—
143C2×C22⋊Dic47C2314yes—
144C2×C22⋊Dic47C2312yes—
145C2×(C2×D47)⋊C4C2312yes—
146C2×(C2×D47)⋊C4C2312yes—
147C2×(C2×D47)⋊C4C2318yes—
148C2×C4×Dic47C2312yes—
149C2×C4×Dic47C2312yes—
150C2×C4×Dic47C2312yes—
151C2×C4×Dic47C2318yes—
152C2×C4×Dic47C2314yes—
153C42×D47C23116yes—
154C22×Q8×C47—48no—
155C22×Q8×C47C2314yes—
156C22×Q8×C47C23116yes—
157C22×Q8×C47C2314yes—
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2314yes—
161C23×C4×C47C2311yescharacteristic
162C4⋊Q8×C47C23116yes—
163C4⋊Q8×C47C23116yes—
164C4⋊Q8×C47C23116yes—
165C4⋊Q8×C47C23116yes—
166C2×C4⋊C4×C47C23116yes—
167C2×C4⋊C4×C47C2314yes—
168C2×C4⋊C4×C47C2314yes—
169C2×C4⋊C4×C47C2314yes—
170C2×C4⋊C4×C47C2314yes—
171C2×C4⋊C4×C47C23116yes—
172C2×C42×C47C2311yescharacteristic
173C2×C42×C47C2311yescharacteristic
174C2×C42×C47C2311yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C2×C42×C47C2318yes—
177C24×C47C2411yescharacteristic
178C23×D47C2412yes—
179C2×Q8×C47—216no—
180C2×Q8×C47—48no—
181C2×Q8×C47—432no—
182C2×Q8×C47C24116yes—
183C2×Q8×C47C24116yes—
184C22×C4×C47—24no—
185C22×C4×C47—24no—
186C22×C4×C47—48no—
187C22×C4×C47C2×Q818yescomplemented
188C22×C4×C47C2411yescharacteristic
189C22×C4×C47C2414yes—
190C22×C4×C47C2411yescharacteristic
191C22×C4×C47C2414yes—
192C22×C4×C47C2418yes—
193C22×C4×C47C24116yes—
194C22×C4×C47C2411yescharacteristic
195C22×C4×C47C2411yescharacteristic
196C22×C4×C47C2414yes—
197C22×C4×C47C2411yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C2×C22⋊D47C2×Q8116yescomplemented
200C2×C22⋊D47C2418yes—
201C22×Dic47C2414yes—
202C22×Dic47C2412yes—
203C22×Dic47C2412yes—
204C22×Dic47C2414yes—
205C22×Dic47C2412yes—
206Q8×D47—464no—
207#10625350C2×Q8164yescomplemented
208C2×D188C2×Q818yescomplemented
209C2×D188C2414yes—
210C2×C4×D47—28no—
211C2×C4×D47—28no—
212C2×C4×D47—416no—
213C2×C4×D47C2×Q8116yescomplemented
214C2×C4×D47C2418yes—
215C2×C4×D47C2418yes—
216C2×C4×D47C24132yes—
217C2×C4×D47C2418yes—
218C2×Dic94—28no—
219C2×Dic94—28no—
220C2×Dic94—416no—
221C2×Dic94C2×Q818yescomplemented
222C2×Dic94C2418yes—
223C2×Dic94C2418yes—
224C2×Dic94C24132yes—
225C2×Dic94C2414yes—
226C4⋊C4×C47C24116yes—
227C4⋊C4×C47C24116yes—
228C4⋊C4×C47C24116yes—
229C4⋊C4×C47C24116yes—
230C42×C47C2414yes—
231C42×C47C2414yes—
232C42×C47C2414yes—
233C42×C47C2414yes—
234C22⋊Dic47C24116yes—
235C22⋊Dic47C2418yes—
236(C2×D47)⋊C4C2418yes—
237(C2×D47)⋊C4C2418yes—
238(C2×D47)⋊C4C24132yes—
239C4⋊Dic47C2418yes—
240C4⋊Dic47C2418yes—
241C4⋊Dic47C2418yes—
242C4⋊Dic47C2414yes—
243C4⋊Dic47C2414yes—
244C4⋊Dic47C2418yes—
245C4⋊Dic47C24132yes—
246Dic47⋊C4C24132yes—
247Dic47⋊C4C24132yes—
248Dic47⋊C4C2418yes—
249Dic47⋊C4C2418yes—
250Dic47⋊C4C24132yes—
251Dic47⋊C4C24116yes—
252Dic47⋊C4C24116yes—
253C4×Dic47C2418yes—
254C4×Dic47C2418yes—
255C4×Dic47C2418yes—
256C4×Dic47C24132yes—
257C4×Dic47C24116yes—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47C22×Q814yes—
261C23×C47C2512yes—
262C23×C47C2511yescharacteristic
263C22×D47—24no—
264C22×D47—24no—
265C22×D47C22×Q818yes—
266C22×D47C2514yes—
267Q8×C47—232no—
268Q8×C47—416no—
269C2×C4×C47—216no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—28no—
273C2×C4×C47—28no—
274C2×C4×C47—416no—
275C2×C4×C47C22×Q814yes—
276C2×C4×C47C22×Q814yes—
277C2×C4×C47C22×Q8116yescomplemented
278C2×C4×C47H(5,𝔽2)14yes—
279C2×C4×C472−1+414yes—
280C2×C4×C47C25116yes—
281C2×C4×C47C2512yes—
282C2×C4×C47C2512yes—
283C2×C4×C47C2512yes—
284C2×C4×C47C2512yes—
285C2×C4×C47C2512yes—
286C2×C4×C47C2512yes—
287C22⋊D47C22×Q8132yescomplemented
288C2×Dic47—28no—
289C2×Dic47—24no—
290C2×Dic47—28no—
291C2×Dic47—24no—
292C2×Dic47C22×Q818yes—
293C2×Dic47C2518yes—
294C2×Dic47C2514yes—
295C2×Dic47C2514yes—
296C2×Dic47C2518yes—
297C2×Dic47C2514yes—
298D188C22×Q8116yescomplemented
299C4×D47—216no—
300C4×D47—216no—
301C4×D47—432no—
302C4×D47C22×Q8132yescomplemented
303Dic94—216no—
304Dic94—216no—
305Dic94—432no—
306Dic94C22×Q8116yescomplemented
307C2×#3503—471nomaximal, Sylow
308C22×C47—22no—
309C22×C47—22no—
310C22×C47—28no—
311C22×C47C23×Q814yes—
312C22×C47C23×Q812yes—
313C22×C47C2×H(5,𝔽2)12yes—
314C22×C47C2×2−1+412yes—
315C22×C47C2611yescharacteristic
316C2×D47—24no—
317C2×D47—24no—
318C2×D47—216no—
319C2×D47C23×Q818yes—
320C4×C47—216no—
321C4×C47—22no—
322C4×C47—22no—
323C4×C47C23×Q814yes—
324C4×C47C23×Q814yes—
325C4×C47C2×H(5,𝔽2)14yes—
326C4×C47C2×2−1+414yes—
327Dic47—28no—
328Dic47—24no—
329Dic47—28no—
330Dic47—24no—
331Dic47C23×Q818yes—
332#3503—4732no—
333C2×Q82—472no—
334C2×#557—472no—
335C2×#554—472no—
336C2×#554—474no—
337C2×D4×Q8—474no—
338C2×D4×Q8—472no—
339C2×#544—474no—
340C2×#544—472no—
341C2×#533—471no—
342C2×#533—472no—
343C22×C4⋊Q8—472no—
344C22×C4⋊Q8D4711yescharacteristic, complemented
345C2×#520—472no—
346C2×C4×#41—471no—
347C2×C47—24no—
348C2×C47#350314yescomplemented
349C2×C47C24×Q811yescharacteristic
350C2×C47C22×H(5,𝔽2)11yescharacteristic
351C2×C47C22×2−1+411yescharacteristic
352D47—28no—
353C22×#41—471no—
354C23×Q8—474no—
355C23×Q8C2×D4712yes—
356Q82—4732no—
357#557—4732no—
358#554—4732no—
359#554—4764no—
360D4×Q8—4764no—
361D4×Q8—4732no—
362#544—4764no—
363#544—4732no—
364#533—4732no—
365#533—4716no—
366C2×C4⋊Q8—474no—
367C2×C4⋊Q8—478no—
368C2×C4⋊Q8—4732no—
369C2×C4⋊Q8—474no—
370C2×C4⋊Q8—474no—
371C2×C4⋊Q8—474no—
372C2×C4⋊Q8—471no—
373C2×C4⋊Q8—471no—
374C2×C4⋊Q8C2×D4712yes—
375C2×C4⋊Q8C2×D4712yes—
376C2×C4⋊Q8C2×D4712yes—
377C2×C4⋊Q8C2×D4712yes—
378C2×C4⋊Q8C2×D47116yescomplemented
379C2×#125—474no—
380C2×#125—478no—
381C2×#125—474no—
382C2×#125—472no—
383C2×C22⋊Q8—474no—
384C2×C22⋊Q8—478no—
385C2×C22⋊Q8—472no—
386C2×C22⋊Q8—472no—
387C2×C22⋊Q8—478no—
388C2×C22⋊Q8—474no—
389C2×C22⋊Q8—478no—
390#520—4732no—
391C4×#41—4716no—
392C2×C4×Q8—474no—
393C2×C4×Q8—474no—
394C2×C4×Q8—474no—
395C2×C4×Q8—471no—
396C2×C4×Q8—471no—
397C2×C4×Q8—472no—
398C2×C4×Q8—472no—
399C2×C4×D4—472no—
400C2×C4×D4—472no—
401C2×C4×D4—478no—
402C2×C4×D4—474no—
403C2×C4×D4—471no—
404C2×C4×D4—471no—
405C2×#117—471no—
406C2×#117—472no—
407C2×#117—474no—
408C2×#117—472no—
409C22×C4⋊C4—474no—
410C22×C4⋊C4—474no—
411C22×C4⋊C4C2×D4712yes—
412C22×C4⋊C4C2×D4712yes—
413C22×C42—472no—
414C22×C42C2×D4711yescharacteristic
415C47C2×#350311yescharacteristic, complemented, Sylow
416C2×#41—4716no—
417C2×#41—478no—
418C22×Q8—48no—
419C22×Q8—4732no—
420C22×Q8—471no—
421C22×Q8—472no—
422C22×Q8—472no—
423C22×Q8—478no—
424C22×Q8—18816no—
425C22×Q8C22×D4714yes—
426C22×Q8C22×D4714yes—
427C22×Q8C22×D47116yes—
428C22×D4—472no—
429C22×D4—471no—
430C23×C4—472no—
431C23×C4—472no—
432C23×C4—472no—
433C23×C4—478no—
434C23×C4C22×D4711yescharacteristic
435C23×C4C22×D4711yescharacteristic
436C23×C4C22×D4714yes—
437C23×C4C22×D4711yescharacteristic
438C4⋊Q8—4732no—
439C4⋊Q8—4764no—
440C4⋊Q8—4732no—
441C4⋊Q8—4732no—
442C4⋊Q8—4732no—
443C4⋊Q8—478no—
444C4⋊Q8—478no—
445C4⋊Q8C22×D47116yes—
446C4⋊Q8C22×D47116yes—
447C4⋊Q8C22×D47116yes—
448C4⋊Q8C22×D47116yes—
449#125—4732no—
450#125—4764no—
451#125—4732no—
452#125—4716no—
453C22⋊Q8—4732no—
454C22⋊Q8—4764no—
455C22⋊Q8—4716no—
456C22⋊Q8—4716no—
457C22⋊Q8—4764no—
458C22⋊Q8—4732no—
459C22⋊Q8—4764no—
460C4×Q8—4732no—
461C4×Q8—4732no—
462C4×Q8—4732no—
463C4×Q8—478no—
464C4×Q8—478no—
465C4×Q8—4716no—
466C4×Q8—4716no—
467C4×D4—4716no—
468C4×D4—4716no—
469C4×D4—4764no—
470C4×D4—4732no—
471C4×D4—478no—
472C4×D4—478no—
473#117—478no—
474#117—4716no—
475#117—4732no—
476#117—4716no—
477C2×C4⋊C4—472no—
478C2×C4⋊C4—472no—
479C2×C4⋊C4—478no—
480C2×C4⋊C4—478no—
481C2×C4⋊C4—472no—
482C2×C4⋊C4—472no—
483C2×C4⋊C4—471no—
484C2×C4⋊C4—472no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—472no—
487C2×C4⋊C4—474no—
488C2×C4⋊C4—478no—
489C2×C4⋊C4—478no—
490C2×C4⋊C4—474no—
491C2×C4⋊C4—4732no—
492C2×C4⋊C4—4732no—
493C2×C4⋊C4C22×D4714yes—
494C2×C4⋊C4C22×D4714yes—
495C2×C4⋊C4C22×D4714yes—
496C2×C4⋊C4C22×D47116yes—
497C2×C4⋊C4C22×D4714yes—
498C2×C4⋊C4C22×D47116yes—
499C2×C22⋊C4—474no—
500C2×C22⋊C4—472no—
501C2×C22⋊C4—478no—
502C2×C22⋊C4—472no—
503C2×C22⋊C4—472no—
504C2×C42—472no—
505C2×C42—478no—
506C2×C42—474no—
507C2×C42—472no—
508C2×C42—472no—
509C2×C42—4716no—
510C2×C42C22×D4711yescharacteristic
511C2×C42C22×D4711yescharacteristic
512C2×C42C22×D4711yescharacteristic
513C2×C42C22×D4718yes—
514C2×C42C22×D4711yescharacteristic
515C24—472no—
516C24C23×D4711yescharacteristic
517#41—4764no—
518C2×Q8—216no—
519C2×Q8—48no—
520C2×Q8—432no—
521C2×Q8—478no—
522C2×Q8—474no—
523C2×Q8—478no—
524C2×Q8—478no—
525C2×Q8—4732no—
526C2×Q8—948no—
527C2×Q8—948no—
528C2×Q8—18816no—
529C2×Q8—18864no—
530C2×Q8C23×D47116yes—
531C2×Q8C23×D47116yes—
532C2×D4—4716no—
533C2×D4—478no—
534C2×D4—478no—
535C2×D4—474no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—48no—
539C22×C4—472no—
540C22×C4—4716no—
541C22×C4—478no—
542C22×C4—474no—
543C22×C4—472no—
544C22×C4—472no—
545C22×C4—474no—
546C22×C4—478no—
547C22×C4—478no—
548C22×C4—4732no—
549C22×C4—948no—
550C22×C4—948no—
551C22×C4—18816no—
552C22×C4Q8×D4718yescomplemented
553C22×C4C23×D4714yes—
554C22×C4C23×D4714yes—
555C22×C4C23×D4718yes—
556C22×C4C23×D4711yescharacteristic
557C22×C4C23×D4711yescharacteristic
558C22×C4C23×D47116yes—
559C22×C4C23×D4711yescharacteristic
560C22×C4C23×D4711yescharacteristic
561C22×C4C23×D4714yes—
562C22×C4C23×D4711yescharacteristic
563C22×C4C23×D4711yescharacteristic
564C4⋊C4—4732no—
565C4⋊C4—4732no—
566C4⋊C4—478no—
567C4⋊C4—478no—
568C4⋊C4—4716no—
569C4⋊C4—4732no—
570C4⋊C4—4716no—
571C4⋊C4—478no—
572C4⋊C4—478no—
573C4⋊C4—478no—
574C4⋊C4—474no—
575C4⋊C4—474no—
576C4⋊C4—478no—
577C4⋊C4—4732no—
578C4⋊C4C23×D47116yes—
579C4⋊C4C23×D47116yes—
580C4⋊C4C23×D47116yes—
581C4⋊C4C23×D47116yes—
582C22⋊C4—4716no—
583C22⋊C4—478no—
584C22⋊C4—4732no—
585C22⋊C4—478no—
586C22⋊C4—478no—
587C42—478no—
588C42—478no—
589C42—478no—
590C42—4732no—
591C42—4716no—
592C42C23×D4714yes—
593C42C23×D4714yes—
594C42C23×D4714yes—
595C42C23×D4714yes—
596C23—22no—
597C23—22no—
598C23—478no—
599C23—474no—
600C23—944no—
601C23—944no—
602C23C2×Q8×D4714yes—
603C23C24×D4712yes—
604C23C24×D4711yescharacteristic
605Q8—232no—
606Q8—416no—
607Q8—4716no—
608Q8—9416no—
609Q8—9416no—
610Q8—18832no—
611D4—4732no—
612D4—4716no—
613C2×C4—22no—
614C2×C4—216no—
615C2×C4—22no—
616C2×C4—28no—
617C2×C4—28no—
618C2×C4—416no—
619C2×C4—478no—
620C2×C4—474no—
621C2×C4—4732no—
622C2×C4—478no—
623C2×C4—474no—
624C2×C4—474no—
625C2×C4—478no—
626C2×C4—944no—
627C2×C4—948no—
628C2×C4—944no—
629C2×C4—948no—
630C2×C4—9416no—
631C2×C4—9416no—
632C2×C4—18832no—
633C2×C4C2×Q8×D4714yes—
634C2×C4C2×Q8×D4714yes—
635C2×C4C2×Q8×D47116yescomplemented
636C2×C4#1309406914yes—
637C2×C4#1309407214yes—
638C2×C4C24×D47116yes—
639C2×C4C24×D4712yes—
640C2×C4C24×D4712yes—
641C2×C4C24×D4712yes—
642C2×C4C24×D4712yes—
643C2×C4C24×D4712yes—
644C2×C4C24×D4712yes—
645C22—22no—
646C22—22no—
647C22—28no—
648C22—478no—
649C22—944no—
650C22—944no—
651C22—9416no—
652C22C22×Q8×D4714yes—
653C22C22×Q8×D4712yes—
654C22C2×#1309406912yes—
655C22C2×#1309407212yes—
656C22C25×D4711yescharacteristic
657C4—22no—
658C4—216no—
659C4—22no—
660C4—478no—
661C4—944no—
662C4—948no—
663C4—944no—
664C4—948no—
665C4C22×Q8×D4714yes—
666C4C22×Q8×D4714yes—
667C4C2×#1309406914yes—
668C4C2×#1309407214yes—
669C2—24no—
670C2—948no—
671C2#2025720414yesdirect product factor
672C2C23×Q8×D4711yescharacteristic
673C2C22×#1309406911yescharacteristic
674C2C22×#1309407211yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC22×C4⋊Q8×C47C2
socleC23×C47C25
prime radicalC22×#10625350C22
hypercenterC22×C4⋊Q8D47
hypocenterC47C2×#3503
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #20257204C2direct (N × H)
2. C2×#15689853C2semidirect
3. C2×#15689848C2semidirect
4. C2×#15689834C2semidirect
5. C2×#15689828C2semidirect
6. C2×#15689788C2semidirect
7. C2×Q8×C22⋊D47C2semidirect
8. C2×#15689754C2semidirect
9. C2×#15689750C2semidirect
10. C2×#15689680C2semidirect
11. C2×#15689678C2semidirect
12. C2×C4⋊Q8×D47C2semidirect
15. C22×C4⋊Q8×C47C2semidirect
18. #15689853C22semidirect
19. #15689848C22semidirect
20. #15689834C22semidirect
21. #15689828C22semidirect
22. #15689788C22semidirect
23. Q8×C22⋊D47C22semidirect
24. #15689754C22semidirect
25. #15689750C22semidirect
26. #15689680C22semidirect
27. #15689678C22semidirect
35. C4⋊Q8×D47C22semidirect
74. C2×C4⋊Q8×C47C22semidirect
78. C2×#10625350Q8semidirect
187. C22×C4×C47C2×Q8semidirect
199. C2×C22⋊D47C2×Q8semidirect
207. #10625350C2×Q8semidirect
208. C2×D188C2×Q8semidirect
213. C2×C4×D47C2×Q8semidirect
221. C2×Dic94C2×Q8semidirect
277. C2×C4×C47C22×Q8semidirect
287. C22⋊D47C22×Q8semidirect
298. D188C22×Q8semidirect
302. C4×D47C22×Q8semidirect
306. Dic94C22×Q8semidirect
344. C22×C4⋊Q8D47semidirect
348. C2×C47#3503semidirect
378. C2×C4⋊Q8C2×D47semidirect
415. C47C2×#3503semidirect
552. C22×C4Q8×D47semidirect
635. C2×C4C2×Q8×D47semidirect
671. C2#20257204direct (N × H)

Maximal subgroups

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

subgroupindex
#202572042
C2×#156898532
C2×#156898482
C2×#156898342
C2×#156898282
C2×#156897882
C2×Q8×C22⋊D472
C2×#156897542
C2×#156897502
C2×#156896802
C2×#156896782
C2×C4⋊Q8×D472
C2×#156896042
C2×C4×#106253502
C22×C4⋊Q8×C472
C2×#350347