Finite Group Databasebeta

← C2×#20252480 #27081231

Subgroups — C2×#20252480 #27081231

Order 12032.

1750 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689676C211yesmaximal, characteristic
2#20252480C2116yesmaximal, direct product factor
3C2×#15689253C211yesmaximal, characteristic, complemented
4C2×#15689252C211yesmaximal, characteristic, complemented
5C2×#15689252C211yesmaximal, characteristic, complemented
6C2×#15689251C211yesmaximal, characteristic, complemented
7C2×#15689251C211yesmaximal, characteristic, complemented
8C2×#15689250C211yesmaximal, characteristic, complemented
9C2×C8×Dic94C211yesmaximal, characteristic, complemented
10C2×#15689247C211yesmaximal, characteristic, complemented
11C2×#15689184C211yesmaximal, characteristic
12C2×#15689181C211yesmaximal, characteristic
13C2×#15689181C211yesmaximal, characteristic
14C2×#15689177C211yesmaximal, characteristic
15C2×#15689173C211yesmaximal, characteristic
16C2×C47×#433C211yesmaximal, characteristic
17#15689676C418yes—
18#15689676C2218yes—
19C2×#13094023C411yescharacteristic
20C2×#13094023C411yescharacteristic
21C2×#13094015C411yescharacteristic
22C2×#13094015C411yescharacteristic
23C2×#13094001C411yescharacteristic
24C2×#13094001C411yescharacteristic
25C2×#13094001C411yescharacteristic
26C2×#13094001C411yescharacteristic
27C2×C4×Dic94C2211yescharacteristic
28C2×C4×Dic94C2211yescharacteristic
29C2×C4×Dic94C2211yescharacteristic
30C2×C4×Dic94C2211yescharacteristic
31C2×#13093983C2211yescharacteristic
32C22×C4×Dic47C2211yescharacteristic
33#15689253C2218yescomplemented
34#15689252C2218yescomplemented
35#15689252C2218yescomplemented
36#15689251C2218yescomplemented
37#15689251C2218yescomplemented
38#15689250C2218yescomplemented
39C8×Dic94C2218yescomplemented
40#15689247C2218yescomplemented
41#15689184C2218yes—
42#15689181C2218yes—
43#15689181C2218yes—
44#15689177C2218yes—
45#15689173C2218yes—
46C2×C4⋊(C47⋊C8)C2211yescharacteristic
47C2×C4⋊(C47⋊C8)C2211yescharacteristic
48C2×Dic47⋊C8C2211yescharacteristic
49C2×Dic47⋊C8C2211yescharacteristic
50C2×Dic47⋊C8C2211yescharacteristic
51C2×Dic47⋊C8C2211yescharacteristic
52C2×Dic47⋊C8C2211yescharacteristic
53C2×Dic47⋊C8C2211yescharacteristic
54C2×Dic47⋊C8C2211yescharacteristic
55C2×Dic47⋊C8C2211yescharacteristic
56C2×C22⋊(C47⋊C8)C2211yescharacteristic
57C2×C22⋊(C47⋊C8)C2211yescharacteristic
58C2×#13093935C2211yescharacteristic
59C2×#13093934C2211yescharacteristic
60C2×#13093934C2211yescharacteristic
61C2×#13093934C2211yescharacteristic
62C2×#13093934C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C2×C8×Dic47C2211yescharacteristic
65C2×C8×Dic47C2211yescharacteristic
66C2×C8×Dic47C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×#117×C47C2211yescharacteristic
69C47×#433C2218yes—
70C2×C4⋊C8×C47C2211yescharacteristic
71C2×C4⋊C8×C47C2211yescharacteristic
72C2×C22⋊C8×C47C2211yescharacteristic
73C2×C22⋊C8×C47C2211yescharacteristic
74C2×#97×C47C2211yescharacteristic
75C2×C4×C8×C47C2211yescharacteristic
76C22×Dic94C2×C411yescharacteristic
77C22×Dic94C2×C411yescharacteristic
78C22×Dic94C2×C411yescharacteristic
79C22×Dic94C2×C411yescharacteristic
80C23×Dic47C2×C411yescharacteristic
81C23×Dic47C2×C411yescharacteristic
82C22×C47⋊C8C2311yescharacteristic
83C22×C47⋊C8C2311yescharacteristic
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86#13094023C2×C418yes—
87#13094023C2×C418yes—
88#13094015C2×C418yes—
89#13094015C2×C418yes—
90#13094001C2×C418yes—
91#13094001C2×C418yes—
92#13094001C2×C418yes—
93#13094001C2×C418yes—
94C4×Dic94C2×C414yes—
95C4×Dic94C2×C414yes—
96C4×Dic94C2×C414yes—
97C4×Dic94C2×C414yes—
98C4×Dic94C2314yes—
99C4×Dic94C2314yes—
100C4×Dic94C2314yes—
101C4×Dic94C2314yes—
102#13093983C2×C414yes—
103#13093983C2314yes—
104C2×C4⋊Dic47C2×C411yescharacteristic
105C2×C4⋊Dic47C2×C411yescharacteristic
106C2×C4⋊Dic47C2×C411yescharacteristic
107C2×C4⋊Dic47C2×C411yescharacteristic
108C2×C4⋊Dic47C2×C411yescharacteristic
109C2×C4⋊Dic47C2×C411yescharacteristic
110C2×Dic47⋊C4C2×C411yescharacteristic
111C2×Dic47⋊C4C2×C411yescharacteristic
112C2×Dic47⋊C4C2×C411yescharacteristic
113C2×Dic47⋊C4C2×C411yescharacteristic
114C2×Dic47⋊C4C2×C411yescharacteristic
115C2×Dic47⋊C4C2×C411yescharacteristic
116C2×Dic47⋊C4C2×C411yescharacteristic
117C2×Dic47⋊C4C2×C411yescharacteristic
118C2×C22⋊Dic47C2×C411yescharacteristic
119C2×C22⋊Dic47C2×C411yescharacteristic
120C2×C4×Dic47C2×C411yescharacteristic
121C2×C4×Dic47C2×C411yescharacteristic
122C2×C4×Dic47C2×C414yes—
123C2×C4×Dic47C2311yescharacteristic
124C2×C4×Dic47C2311yescharacteristic
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2311yescharacteristic
127C2×C4×Dic47C2311yescharacteristic
128C4⋊(C47⋊C8)C2314yes—
129C4⋊(C47⋊C8)C2314yes—
130Dic47⋊C8C2314yes—
131Dic47⋊C8C2314yes—
132Dic47⋊C8C2314yes—
133Dic47⋊C8C2314yes—
134Dic47⋊C8C2314yes—
135Dic47⋊C8C2314yes—
136Dic47⋊C8C2314yes—
137Dic47⋊C8C2314yes—
138C22⋊(C47⋊C8)C2314yes—
139C22⋊(C47⋊C8)C2314yes—
140#13093935C2314yes—
141#13093934C2314yes—
142#13093934C2314yes—
143#13093934C2314yes—
144#13093934C2314yes—
145C4×C47⋊C8C2314yes—
146C8×Dic47C2314yes—
147C8×Dic47C2314yes—
148C8×Dic47C2314yes—
149C8×Dic47C2314yes—
150C23×C4×C47C2311yescharacteristic
151C22×C8×C47C2311yescharacteristic
152C22×C8×C47C2311yescharacteristic
153C22×C8×C47C2311yescharacteristic
154C22×C8×C47C2311yescharacteristic
155#117×C47C2×C414yes—
156#117×C47C2314yes—
157C2×C4⋊C4×C47C2×C411yescharacteristic
158C2×C4⋊C4×C47C2×C411yescharacteristic
159C2×C22⋊C4×C47C2×C411yescharacteristic
160C2×C22⋊C4×C47C2×C411yescharacteristic
161C2×C42×C47C2311yescharacteristic
162C2×C42×C47C2311yescharacteristic
163C4⋊C8×C47C2314yes—
164C4⋊C8×C47C2314yes—
165C22⋊C8×C47C2314yes—
166C22⋊C8×C47C2314yes—
167#97×C47C2314yes—
168C4×C8×C47C2314yes—
169C24×C47C22×C411yescharacteristic
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47C22×C411yescharacteristic
173C22×C4×C47C22×C411yescharacteristic
174C22×C4×C47C22×C411yescharacteristic
175C22×C4×C47C22×C411yescharacteristic
176C22×C4×C47C22×C411yescharacteristic
177C22×C4×C47C22×C412yes—
178C22×C4×C47C2412yes—
179C22×C4×C47C2411yescharacteristic
180C22×Dic47—24no—
181C22×Dic47—42no—
182C22×Dic47C22×C411yescharacteristic
183C22×Dic47C22×C411yescharacteristic
184C22×Dic47C22×C411yescharacteristic
185C22×Dic47C22×C414yes—
186C22×Dic47C22×C411yescharacteristic
187C22×Dic47C22×C411yescharacteristic
188C22×Dic47C22×C411yescharacteristic
189C22×Dic47C22×C411yescharacteristic
190C22×Dic47C22×C414yes—
191C22×Dic47C22×C411yescharacteristic
192C2×Dic94—24no—
193C2×Dic94—24no—
194C2×Dic94—42no—
195C2×Dic94—42no—
196C2×Dic94C22×C414yes—
197C2×Dic94C22×C414yes—
198C2×Dic94C22×C414yes—
199C2×Dic94C22×C414yes—
200C2×C8×C47—22no—
201C2×C8×C47—22no—
202C2×C8×C47—22no—
203C2×C8×C47—22no—
204C2×C8×C47C2412yes—
205C2×C8×C47C2412yes—
206C2×C8×C47C2412yes—
207C2×C8×C47C2412yes—
208C4⋊C4×C47C22×C414yes—
209C4⋊C4×C47C22×C414yes—
210C22⋊C4×C47C22×C414yes—
211C22⋊C4×C47C22×C414yes—
212C42×C47C22×C412yes—
213C42×C47C22×C412yes—
214C42×C47C2412yes—
215C42×C47C2412yes—
216C22⋊Dic47C22×C414yes—
217C22⋊Dic47C22×C414yes—
218C4⋊Dic47C22×C414yes—
219C4⋊Dic47C22×C414yes—
220C4⋊Dic47C22×C414yes—
221C4⋊Dic47C22×C414yes—
222C4⋊Dic47C22×C414yes—
223C4⋊Dic47C22×C414yes—
224Dic47⋊C4C22×C414yes—
225Dic47⋊C4C22×C414yes—
226Dic47⋊C4C22×C414yes—
227Dic47⋊C4C22×C414yes—
228Dic47⋊C4C22×C414yes—
229Dic47⋊C4C22×C414yes—
230Dic47⋊C4C22×C414yes—
231Dic47⋊C4C22×C414yes—
232C4×Dic47C22×C412yes—
233C4×Dic47C22×C412yes—
234C4×Dic47C22×C414yes—
235C4×Dic47C22×C414yes—
236C4×Dic47C22×C412yes—
237C4×Dic47C22×C412yes—
238C4×Dic47C2412yes—
239C4×Dic47C2412yes—
240C4×Dic47C2412yes—
241C4×Dic47C2412yes—
242C2×C47⋊C8—22no—
243C2×C47⋊C8—22no—
244C2×C47⋊C8—22no—
245C2×C47⋊C8—22no—
246C2×C47⋊C8C2412yes—
247C2×C47⋊C8C2412yes—
248C2×C47⋊C8C2412yes—
249C2×C47⋊C8C2412yes—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47C23×C412yes—
254C23×C47C23×C411yescharacteristic
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—24no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47C23×C412yes—
264C2×C4×C47C23×C412yes—
265C2×C4×C47C23×C412yes—
266C2×C4×C47C23×C412yes—
267C2×C4×C47C23×C412yes—
268C2×C4×C47C23×C411yescharacteristic
269C2×C4×C472−1+412yes—
270C2×C4×C472−1+412yes—
271C2×C4×C47C2511yescharacteristic
272C2×Dic47—22no—
273C2×Dic47—22no—
274C2×Dic47—22no—
275C2×Dic47—22no—
276C2×Dic47—22no—
277C2×Dic47—22no—
278C2×Dic47—22no—
279C2×Dic47—28no—
280C2×Dic47—44no—
281C2×Dic47#13114yes—
282C2×Dic47C23×C412yes—
283C2×Dic47C23×C412yes—
284C2×Dic47C23×C412yes—
285C2×Dic47C23×C412yes—
286C2×Dic47C23×C412yes—
287C2×Dic47C23×C412yes—
288C2×Dic47C23×C412yes—
289C2×Dic47C23×C412yes—
290Dic94—28no—
291Dic94—28no—
292Dic94—44no—
293Dic94—44no—
294C8×C47—22no—
295C8×C47—22no—
296C8×C47—22no—
297C8×C47—22no—
298C47⋊C8—22no—
299C47⋊C8—22no—
300C47⋊C8—22no—
301C47⋊C8—22no—
302C2×#2985—471nomaximal, Sylow
303C22×C47—22no—
304C22×C47—22no—
305C22×C47—22no—
306C22×C47—44no—
307C22×C47#51912yes—
308C22×C47C2×#13112yes—
309C22×C47#56812yes—
310C22×C47C24×C411yescharacteristic
311C4×C47—22no—
312C4×C47—22no—
313C4×C47—22no—
314C4×C47—22no—
315C4×C47—22no—
316C4×C47#51912yes—
317C4×C47C2×2−1+411yescharacteristic
318C4×C47C2×2−1+411yescharacteristic
319Dic47—22no—
320Dic47—22no—
321Dic47—22no—
322Dic47—22no—
323Dic47—22no—
324Dic47—22no—
325Dic47—22no—
326Dic47C2×#13114yes—
327C2×#533—471no—
328#2985—4716no—
329C2×#446—471no—
330C2×#446—471no—
331C2×#446—471no—
332C2×#446—471no—
333C2×#446—471no—
334C2×#446—471no—
335C2×C8×Q8—471no—
336C2×C8×Q8—471no—
337C2×#433—471no—
338C2×#433—471no—
339C2×#433—471no—
340C2×#433D4711yescharacteristic
341C2×#432—471no—
342C2×#431—471no—
343C2×C47—42no—
344C2×C47#298514yescomplemented
345C2×C47C2×#51911yescharacteristic
346C2×C47C22×#13111yescharacteristic
347C2×C47C2×#56811yescharacteristic
348#533—478no—
349#533—478no—
350C2×C4⋊Q8—471no—
351C2×C4⋊Q8—471no—
352C2×#125—471no—
353C2×#125—471no—
354C2×C22⋊Q8—471no—
355C2×C22⋊Q8—471no—
356C2×C22⋊Q8—471no—
357C2×C22⋊Q8—471no—
358C2×C4×Q8—471no—
359C2×C4×Q8—471no—
360C2×C4×Q8—471no—
361C2×C4×Q8—471no—
362C2×#117—471no—
363C2×#117C2×D4711yescharacteristic
364C22×C42—471no—
365#446—478no—
366#446—478no—
367#446—478no—
368#446—478no—
369#446—478no—
370#446—478no—
371C8×Q8—478no—
372C8×Q8—478no—
373#433—478no—
374#433—478no—
375#433—478no—
376#433C2×D4718yes—
377#432—478no—
378#431—478no—
379C2×C4⋊C8—471no—
380C2×C4⋊C8—471no—
381C2×C4⋊C8—471no—
382C2×C4⋊C8—471no—
383C2×C4⋊C8—471no—
384C2×C4⋊C8—471no—
385C2×C4⋊C8—471no—
386C2×C4⋊C8—471no—
387C2×C4⋊C8—471no—
388C2×C4⋊C8—471no—
389C2×C4⋊C8C2×D4711yescharacteristic
390C2×C4⋊C8C2×D4711yescharacteristic
391C2×C22⋊C8—471no—
392C2×C22⋊C8—471no—
393C2×C22⋊C8C2×D4711yescharacteristic
394C2×C22⋊C8C2×D4711yescharacteristic
395C2×#97—471no—
396C2×#97—471no—
397C2×#97—471no—
398C2×#97—471no—
399C2×#97—471no—
400C2×#97C2×D4711yescharacteristic
401C2×C4×C8—471no—
402C2×C4×C8—471no—
403C2×C4×C8—471no—
404C2×C4×C8—471no—
405C2×C4×C8—471no—
406C2×C4×C8C2×D4711yescharacteristic
407C47C2×#298511yescharacteristic, complemented, Sylow
408C22×Q8—471no—
409C22×Q8—471no—
410C22×Q8—471no—
411C22×Q8—471no—
412C23×C4—471no—
413C23×C4—471no—
414C23×C4C22×D4711yescharacteristic
415C22×C8—471no—
416C22×C8—471no—
417C22×C8—471no—
418C22×C8—471no—
419C22×C8C22×D4711yescharacteristic
420C22×C8C22×D4711yescharacteristic
421C22×C8C22×D4711yescharacteristic
422C22×C8C22×D4711yescharacteristic
423C4⋊Q8—478no—
424C4⋊Q8—478no—
425#125—478no—
426#125—478no—
427C22⋊Q8—478no—
428C22⋊Q8—478no—
429C22⋊Q8—478no—
430C22⋊Q8—478no—
431C4×Q8—474no—
432C4×Q8—474no—
433C4×Q8—474no—
434C4×Q8—474no—
435C4×Q8—474no—
436C4×Q8—474no—
437C4×Q8—474no—
438C4×Q8—474no—
439#117—474no—
440#117—474no—
441#117C4×D4714yes—
442#117C22×D4714yes—
443C2×C4⋊C4—471no—
444C2×C4⋊C4—471no—
445C2×C4⋊C4—471no—
446C2×C4⋊C4—471no—
447C2×C4⋊C4—471no—
448C2×C4⋊C4—471no—
449C2×C4⋊C4—471no—
450C2×C4⋊C4—471no—
451C2×C4⋊C4—471no—
452C2×C4⋊C4—471no—
453C2×C4⋊C4—471no—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—471no—
456C2×C4⋊C4—471no—
457C2×C4⋊C4C4×D4711yescharacteristic
458C2×C4⋊C4C4×D4711yescharacteristic
459C2×C22⋊C4—471no—
460C2×C22⋊C4—471no—
461C2×C22⋊C4C4×D4711yescharacteristic
462C2×C22⋊C4C4×D4711yescharacteristic
463C2×C42—471no—
464C2×C42—471no—
465C2×C42—474no—
466C2×C42—474no—
467C2×C42—471no—
468C2×C42—471no—
469C2×C42—471no—
470C2×C42—471no—
471C2×C42C22×D4711yescharacteristic
472C2×C42C22×D4711yescharacteristic
473C4⋊C8—474no—
474C4⋊C8—474no—
475C4⋊C8—474no—
476C4⋊C8—474no—
477C4⋊C8—474no—
478C4⋊C8—474no—
479C4⋊C8—474no—
480C4⋊C8—474no—
481C4⋊C8—474no—
482C4⋊C8—474no—
483C4⋊C8C22×D4714yes—
484C4⋊C8C22×D4714yes—
485C22⋊C8—474no—
486C22⋊C8—474no—
487C22⋊C8C22×D4714yes—
488C22⋊C8C22×D4714yes—
489#97—474no—
490#97—474no—
491#97—474no—
492#97—474no—
493#97—474no—
494#97C22×D4714yes—
495C4×C8—474no—
496C4×C8—474no—
497C4×C8—474no—
498C4×C8—474no—
499C4×C8—474no—
500C4×C8C22×D4714yes—
501C24C2×C4×D4711yescharacteristic
502C2×Q8—474no—
503C2×Q8—474no—
504C2×Q8—474no—
505C2×Q8—474no—
506C2×Q8—944no—
507C2×Q8—944no—
508C2×Q8—1882no—
509C2×Q8—1882no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—471no—
513C22×C4—471no—
514C22×C4—471no—
515C22×C4—471no—
516C22×C4—474no—
517C22×C4—471no—
518C22×C4—471no—
519C22×C4—471no—
520C22×C4—471no—
521C22×C4—474no—
522C22×C4—944no—
523C22×C4—1882no—
524C22×C4C2×C4×D4711yescharacteristic
525C22×C4C2×C4×D4712yes—
526C22×C4C2×C4×D4711yescharacteristic
527C22×C4C2×C4×D4711yescharacteristic
528C22×C4C2×C4×D4711yescharacteristic
529C22×C4C2×C4×D4711yescharacteristic
530C22×C4C23×D4712yes—
531C22×C4C23×D4711yescharacteristic
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—472no—
537C2×C8—472no—
538C2×C8—472no—
539C2×C8—472no—
540C2×C8—942no—
541C2×C8—942no—
542C2×C8—942no—
543C2×C8—942no—
544C2×C8C23×D4712yes—
545C2×C8C23×D4712yes—
546C2×C8C23×D4712yes—
547C2×C8C23×D4712yes—
548C4⋊C4—474no—
549C4⋊C4—474no—
550C4⋊C4—474no—
551C4⋊C4—474no—
552C4⋊C4—474no—
553C4⋊C4—474no—
554C4⋊C4—474no—
555C4⋊C4—474no—
556C4⋊C4—474no—
557C4⋊C4—474no—
558C4⋊C4—474no—
559C4⋊C4—474no—
560C4⋊C4—474no—
561C4⋊C4—474no—
562C4⋊C4C2×C4×D4714yes—
563C4⋊C4C2×C4×D4714yes—
564C22⋊C4—474no—
565C22⋊C4—474no—
566C22⋊C4C2×C4×D4714yes—
567C22⋊C4C2×C4×D4714yes—
568C42—472no—
569C42—472no—
570C42—474no—
571C42—474no—
572C42—472no—
573C42—472no—
574C42—472no—
575C42—472no—
576C42—472no—
577C42—472no—
578C42C2×C4×D4712yes—
579C42C2×C4×D4712yes—
580C42C23×D4712yes—
581C42C23×D4712yes—
582C23—22no—
583C23—22no—
584C23—22no—
585C23C22×C4×D4712yes—
586C23C22×C4×D4711yescharacteristic
587Q8—948no—
588Q8—948no—
589Q8—1884no—
590Q8—1884no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—474no—
600C2×C4—472no—
601C2×C4—472no—
602C2×C4—472no—
603C2×C4—472no—
604C2×C4—472no—
605C2×C4—472no—
606C2×C4—472no—
607C2×C4—472no—
608C2×C4—948no—
609C2×C4—942no—
610C2×C4—942no—
611C2×C4—942no—
612C2×C4—942no—
613C2×C4—942no—
614C2×C4—942no—
615C2×C4—942no—
616C2×C4—1884no—
617C2×C4C22×C4×D4712yes—
618C2×C4C22×C4×D4712yes—
619C2×C4C22×C4×D4712yes—
620C2×C4C22×C4×D4712yes—
621C2×C4C22×C4×D4712yes—
622C2×C4C22×C4×D4711yescharacteristic
623C2×C4#1309407112yes—
624C2×C4#1309407112yes—
625C2×C4C24×D4711yescharacteristic
626C8—22no—
627C8—22no—
628C8—22no—
629C8—22no—
630C8—942no—
631C8—942no—
632C8—942no—
633C8—942no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—44no—
638C22#1568960012yes—
639C22#131×D4712yes—
640C22#1568988812yes—
641C22C23×C4×D4711yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—474no—
648C4—942no—
649C4—942no—
650C4—942no—
651C4—942no—
652C4—942no—
653C4—942no—
654C4—942no—
655C4#1568960012yes—
656C4C2×#1309407111yescharacteristic
657C4C2×#1309407111yescharacteristic
658C2—42no—
659C2#2025248014yesdirect product factor
660C2C2×#1568960011yescharacteristic
661C2C2×#131×D4711yescharacteristic
662C2C2×#1568988811yescharacteristic
subgroupG/H
centerC22×C4C23×D47
commutatorC22×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#433C2
socleC23×C47C23×C4
prime radicalC24×C47C22×C4
cosocleC2×C4×C47C25
hypercenterC2×#433D47
hypocenterC47C2×#2985
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #20252480C2direct (N × H)
3. C2×#15689253C2semidirect
4. C2×#15689252C2semidirect
5. C2×#15689252C2semidirect
6. C2×#15689251C2semidirect
7. C2×#15689251C2semidirect
8. C2×#15689250C2semidirect
9. C2×C8×Dic94C2semidirect
10. C2×#15689247C2semidirect
33. #15689253C22semidirect
34. #15689252C22semidirect
35. #15689252C22semidirect
36. #15689251C22semidirect
37. #15689251C22semidirect
38. #15689250C22semidirect
39. C8×Dic94C22semidirect
40. #15689247C22semidirect
344. C2×C47#2985semidirect
407. C47C2×#2985semidirect
659. C2#20252480direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896762
#202524802
C2×#156892532
C2×#156892522
C2×#156892512
C2×#156892502
C2×C8×Dic942
C2×#156892472
C2×#156891842
C2×#156891812
C2×#156891772
C2×#156891732
C2×C47×#4332
C2×#298547