Finite Group Databasebeta

← C2×#20254671 #27088499

Subgroups — C2×#20254671 #27088499

Order 12032.

1742 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689744C211yesmaximal, characteristic
2#20254671C2116yesmaximal, direct product factor
3C2×#15689533C211yesmaximal, characteristic, complemented
4C2×#15689526C211yesmaximal, characteristic, complemented
5C2×#15689485C211yesmaximal, characteristic, complemented
6C2×#15689480C211yesmaximal, characteristic, complemented
7C2×#15689458C211yesmaximal, characteristic, complemented
8C2×#15689464C211yesmaximal, characteristic, complemented
9C2×#15689447C211yesmaximal, characteristic
10C2×#15689436C211yesmaximal, characteristic
11C2×#15689427C211yesmaximal, characteristic, complemented
12C2×#15689415C211yesmaximal, characteristic, complemented
13C2×#15689420C211yesmaximal, characteristic, complemented
14C2×#15689400C211yesmaximal, characteristic, complemented
15C2×#15689184C211yesmaximal, characteristic, complemented
16C2×C47×#544C211yesmaximal, characteristic, complemented
17#15689744—24no—
18#15689744C2218yes—
19C2×#13094024C2211yescharacteristic
20C2×#13094019—21no—
21C2×#13094012C2211yescharacteristic
22C2×#13094010—21no—
23C2×#13094006—21no—
24C2×#13094003C2211yescharacteristic
25C2×#13094002—21no—
26C2×#13093998C2211yescharacteristic
27C2×C4×Dic94C2211yescharacteristic
28C2×C4×D188C2211yescharacteristic
29#15689533C2218yescomplemented
30#15689526C2218yescomplemented
31#15689485C2218yescomplemented
32#15689480C2218yescomplemented
33#15689464C2218yescomplemented
34#15689458C2218yescomplemented
35#15689447C2218yes—
36#15689436C2218yes—
37#15689427C2218yescomplemented
38#15689420C2218yescomplemented
39#15689415C2218yescomplemented
40#15689400C2218yescomplemented
41#15689184C2218yescomplemented
42C2×#13093957C2211yescharacteristic
43C2×#13093957C2211yescharacteristic
44C2×#13093957C2211yescharacteristic
45C2×#13093957C2211yescharacteristic
46C2×#13093957C2211yescharacteristic
47C2×#13093957C2211yescharacteristic
48C2×#13093955C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×C4⋊(C47⋊C8)C2211yescharacteristic
51C2×C4⋊(C47⋊C8)C2211yescharacteristic
52C2×#13093947C2211yescharacteristic
53C2×#13093947C2211yescharacteristic
54C2×#13093947C2211yescharacteristic
55C2×#13093947C2211yescharacteristic
56C2×#13093944C2211yescharacteristic
57C2×#13093944C2211yescharacteristic
58C2×#13093944C2211yescharacteristic
59C2×#13093944C2211yescharacteristic
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#544—24no—
65C47×#544C2218yescomplemented
66C2×C4⋊Q8×C47—21no—
67C2×C4⋊Q8×C47C2211yescharacteristic
68C2×C4⋊Q8×C47C2211yescharacteristic
69C2×#125×C47—21no—
70C2×#125×C47C2211yescharacteristic
71C2×#125×C47C2211yescharacteristic
72C2×C22⋊Q8×C47—21no—
73C2×C22⋊Q8×C47—21no—
74C2×#117×C47C2211yescharacteristic
75C2×#117×C47C2211yescharacteristic
76C22×C4⋊C4×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C4×D47—21no—
82C22×C47⋊C8C2311yescharacteristic
83C22×C47⋊C8C2311yescharacteristic
84C22×C47⋊C8C2311yescharacteristic
85C22×C47⋊C8C2311yescharacteristic
86#13094024—22no—
87#13094024C2314yes—
88#13094019—28no—
89#13094012—22no—
90#13094012C2314yes—
91#13094010—28no—
92#13094006—28no—
93#13094003—22no—
94#13094003C2314yes—
95#13094002—28no—
96#13093998—22no—
97#13093998C2314yes—
98C4×Dic94—22no—
99C4×Dic94C2314yes—
100C4×D188—22no—
101C4×D188C2314yes—
102C2×C4⋊Dic47—21no—
103C2×C4⋊Dic47C2311yescharacteristic
104C2×C4⋊Dic47C2311yescharacteristic
105C2×Dic47⋊C4—21no—
106C2×Dic47⋊C4—21no—
107C2×C22⋊Dic47—21no—
108C2×(C2×D47)⋊C4—21no—
109C2×(C2×D47)⋊C4—21no—
110C2×(C2×D47)⋊C4—21no—
111C2×(C2×D47)⋊C4—21no—
112C2×C4×Dic47—21no—
113#13093957C2314yes—
114#13093957C2314yes—
115#13093957C2314yes—
116#13093957C2314yes—
117#13093957C2314yes—
118#13093957C2314yes—
119#13093955C2314yes—
120#13093955C2314yes—
121C4⋊(C47⋊C8)C2314yes—
122C4⋊(C47⋊C8)C2314yes—
123#13093947C2314yes—
124#13093947C2314yes—
125#13093947C2314yes—
126#13093947C2314yes—
127#13093944C2314yes—
128#13093944C2314yes—
129#13093944C2314yes—
130#13093944C2314yes—
131C22⋊(C47⋊C8)C2314yes—
132C22⋊(C47⋊C8)C2314yes—
133#13093935C2314yes—
134C4×C47⋊C8C2314yes—
135C22×Q8×C47—21no—
136C22×Q8×C47—21no—
137C23×C4×C47—21no—
138C23×C4×C47C2311yescharacteristic
139C4⋊Q8×C47—28no—
140C4⋊Q8×C47—22no—
141C4⋊Q8×C47—22no—
142C4⋊Q8×C47C2314yes—
143C4⋊Q8×C47C2314yes—
144#125×C47—28no—
145#125×C47—22no—
146#125×C47—22no—
147#125×C47C2314yes—
148#125×C47C2314yes—
149C22⋊Q8×C47—28no—
150C22⋊Q8×C47—28no—
151#117×C47—22no—
152#117×C47D414yes—
153#117×C47C2314yes—
154#117×C47C2314yes—
155C2×C4⋊C4×C47—21no—
156C2×C4⋊C4×C47—22no—
157C2×C4⋊C4×C47—21no—
158C2×C4⋊C4×C47—21no—
159C2×C4⋊C4×C47—21no—
160C2×C4⋊C4×C47—21no—
161C2×C4⋊C4×C47—21no—
162C2×C4⋊C4×C47—21no—
163C2×C4⋊C4×C47D411yescharacteristic
164C2×C4⋊C4×C47D411yescharacteristic
165C2×C4⋊C4×C47C2311yescharacteristic
166C2×C4⋊C4×C47C2311yescharacteristic
167C2×C4⋊C4×C47C2314yes—
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C22⋊C4×C47—21no—
171C2×C22⋊C4×C47D411yescharacteristic
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C42×C47—21no—
174C2×C42×C47C2311yescharacteristic
175C2×C42×C47C2311yescharacteristic
176C24×C47C2×D411yescharacteristic
177C23×D47—21no—
178C2×Q8×C47—24no—
179C2×Q8×C47—24no—
180C2×Q8×C47—82no—
181C2×Q8×C47—82no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—24no—
189C22×C4×C47—82no—
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2411yescharacteristic
198C2×C22⋊D47—24no—
199C2×C22⋊D47—82no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C2×D188—22no—
204C2×D188—22no—
205C2×D188—21no—
206C2×D188C2412yes—
207C2×C4×D47—24no—
208C2×C4×D47—82no—
209C2×Dic94—22no—
210C2×Dic94—22no—
211C2×Dic94—21no—
212C2×Dic94—24no—
213C2×Dic94—82no—
214C2×Dic94C2412yes—
215C4⋊C4×C47—24no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—24no—
219C4⋊C4×C47—24no—
220C4⋊C4×C47—24no—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—24no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47C2×D414yes—
227C4⋊C4×C47C2×D414yes—
228C4⋊C4×C47C2412yes—
229C4⋊C4×C47C2412yes—
230C4⋊C4×C47C2412yes—
231C4⋊C4×C47C2412yes—
232C22⋊C4×C47—24no—
233C22⋊C4×C47C2×D414yes—
234C22⋊C4×C47C2×D414yes—
235C42×C47—24no—
236C42×C47C2×D412yes—
237C42×C47C2×D412yes—
238C42×C47C2412yes—
239C42×C47C2412yes—
240C22⋊Dic47—24no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244(C2×D47)⋊C4—24no—
245C4⋊Dic47—24no—
246C4⋊Dic47—21no—
247C4⋊Dic47—21no—
248C4⋊Dic47C2412yes—
249C4⋊Dic47C2412yes—
250Dic47⋊C4—24no—
251Dic47⋊C4—24no—
252C4×Dic47—24no—
253C2×C47⋊C8—22no—
254C2×C47⋊C8—22no—
255C2×C47⋊C8—22no—
256C2×C47⋊C8—22no—
257C2×C47⋊C8C2412yes—
258C2×C47⋊C8C2412yes—
259C2×C47⋊C8C2412yes—
260C2×C47⋊C8C2412yes—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47C22×D412yes—
265C23×C47C22×D411yescharacteristic
266C22×D47—22no—
267C22×D47—42no—
268C22×D47—42no—
269C22×D47—42no—
270Q8×C47—84no—
271Q8×C47—84no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—24no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—84no—
289C2×C4×C47C22×D412yes—
290C2×C4×C47C22×D412yes—
291C2×C4×C47C22×D412yes—
292C2×C4×C47C22×D412yes—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D411yescharacteristic
295C2×C4×C472−1+412yes—
296C2×C4×C472−1+412yes—
297C2×C4×C47C2511yescharacteristic
298C22⋊D47—84no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305D188—22no—
306D188—22no—
307D188—42no—
308C4×D47—84no—
309Dic94—22no—
310Dic94—22no—
311Dic94—42no—
312Dic94—84no—
313C47⋊C8—22no—
314C47⋊C8—22no—
315C47⋊C8—22no—
316C47⋊C8—22no—
317C2×#3243—471nomaximal, Sylow
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47—44no—
322C22×C47#53612yes—
323C22×C47#57612yes—
324C22×C47#57812yes—
325C22×C47C23×D411yescharacteristic
326C2×D47—42no—
327C2×D47—42no—
328C2×D47—42no—
329C2×D47—84no—
330C4×C47—22no—
331C4×C47—22no—
332C4×C47—22no—
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—42no—
336C4×C47—42no—
337C4×C47—42no—
338C4×C47—42no—
339C4×C47#53612yes—
340C4×C47C2×2−1+411yescharacteristic
341C4×C47C2×2−1+411yescharacteristic
342Dic47—42no—
343Dic47—42no—
344Dic47—42no—
345C2×#544D4711yescharacteristic, complemented
346C2×#542—471no—
347#3243—4716no—
348C2×#501—471no—
349C2×#500—471no—
350C2×#489—471no—
351C2×#488—471no—
352C2×#484—471no—
353C2×#485—471no—
354C2×#482—471no—
355C2×#480—471no—
356C2×#479—471no—
357C2×#477—471no—
358C2×#478—471no—
359C2×#474—471no—
360C2×#433—471no—
361C2×C47—42no—
362C2×C47#324314yescomplemented
363C2×C47C2×#53611yescharacteristic
364C2×C47C2×#57611yescharacteristic
365C2×C47C2×#57811yescharacteristic
366D47—82no—
367#544—24no—
368#544C2×D4718yescomplemented
369#542—478no—
370#542—944no—
371C2×C4⋊Q8—21no—
372C2×C4⋊Q8—471no—
373C2×C4⋊Q8C2×D4711yescharacteristic
374C2×C4⋊Q8C2×D4711yescharacteristic
375C2×#126—941no—
376C2×#125—21no—
377C2×#125C2×D4711yescharacteristic
378C2×#125C2×D4711yescharacteristic
379C2×#124—471no—
380C2×#124—941no—
381C2×#123—941no—
382C2×C22⋊Q8—21no—
383C2×C22⋊Q8—21no—
384C2×C22⋊Q8—471no—
385C2×C22⋊Q8—941no—
386C2×#121—471no—
387C2×C4×Q8—471no—
388C2×C4×D4—471no—
389C2×#117C2×D4711yescharacteristic
390C2×#117C2×D4711yescharacteristic
391C22×C4⋊C4C2×D4711yescharacteristic
392#501—478no—
393#500—478no—
394#489—478no—
395#488—478no—
396#485—478no—
397#484—478no—
398#482—478no—
399#480—478no—
400#479—478no—
401#478—478no—
402#477—478no—
403#474—478no—
404#433—478no—
405C2×#107—471no—
406C2×#107—471no—
407C2×#107—471no—
408C2×#107—471no—
409C2×#107—471no—
410C2×#107—471no—
411C2×#106—471no—
412C2×#106—471no—
413C2×C4⋊C8—471no—
414C2×C4⋊C8—471no—
415C2×#103—471no—
416C2×#103—471no—
417C2×#103—471no—
418C2×#103—471no—
419C2×#102—471no—
420C2×#102—471no—
421C2×#102—471no—
422C2×#102—471no—
423C2×C22⋊C8—471no—
424C2×C22⋊C8—471no—
425C2×#97—471no—
426C2×C4×C8—471no—
427C47C2×#324311yescharacteristic, complemented, Sylow
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—471no—
431C22×Q8—941no—
432C22×D4—471no—
433C22×D4—941no—
434C23×C4—21no—
435C23×C4—941no—
436C23×C4C22×D4711yescharacteristic
437C22×C8—471no—
438C22×C8—471no—
439C22×C8—471no—
440C22×C8—471no—
441C4⋊Q8—28no—
442C4⋊Q8—22no—
443C4⋊Q8—22no—
444C4⋊Q8—474no—
445C4⋊Q8—942no—
446C4⋊Q8C22×D4714yes—
447C4⋊Q8C22×D4714yes—
448#126—948no—
449#125—28no—
450#125—22no—
451#125—22no—
452#125C22×D4714yes—
453#125C22×D4714yes—
454#124—474no—
455#124—948no—
456#124—942no—
457#123—948no—
458C22⋊Q8—28no—
459C22⋊Q8—28no—
460C22⋊Q8—474no—
461C22⋊Q8—942no—
462C22⋊Q8—948no—
463#121—474no—
464#121—942no—
465C4×Q8—474no—
466C4×Q8—942no—
467C4×D4—474no—
468C4×D4—942no—
469#117—22no—
470#117C22⋊D4714yes—
471#117C22×D4714yes—
472#117C22×D4714yes—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—471no—
482C2×C4⋊C4—471no—
483C2×C4⋊C4—941no—
484C2×C4⋊C4—941no—
485C2×C4⋊C4—941no—
486C2×C4⋊C4C22⋊D4711yescharacteristic
487C2×C4⋊C4C22⋊D4711yescharacteristic
488C2×C4⋊C4C22×D4711yescharacteristic
489C2×C4⋊C4C22×D4711yescharacteristic
490C2×C4⋊C4C22×D4714yes—
491C2×C4⋊C4C22×D4711yescharacteristic
492C2×C4⋊C4C22×D4711yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—941no—
495C2×C22⋊C4—941no—
496C2×C22⋊C4—941no—
497C2×C22⋊C4—941no—
498C2×C22⋊C4—941no—
499C2×C22⋊C4C22⋊D4711yescharacteristic
500C2×C22⋊C4C22⋊D4711yescharacteristic
501C2×C42—21no—
502C2×C42—941no—
503C2×C42C22×D4711yescharacteristic
504C2×C42C22×D4711yescharacteristic
505#107—474no—
506#107—474no—
507#107—474no—
508#107—474no—
509#107—474no—
510#107—474no—
511#106—474no—
512#106—474no—
513C4⋊C8—474no—
514C4⋊C8—474no—
515#103—474no—
516#103—474no—
517#103—474no—
518#103—474no—
519#102—474no—
520#102—474no—
521#102—474no—
522#102—474no—
523C22⋊C8—474no—
524C22⋊C8—474no—
525#97—474no—
526C4×C8—474no—
527C24—941no—
528C24C2×C22⋊D4711yescharacteristic
529C2×Q8—24no—
530C2×Q8—24no—
531C2×Q8—82no—
532C2×Q8—82no—
533C2×Q8—472no—
534C2×Q8—944no—
535C2×Q8—941no—
536C2×Q8—942no—
537C2×Q8—942no—
538C2×Q8—3762no—
539C2×D4—472no—
540C2×D4—944no—
541C2×D4—941no—
542C2×D4—942no—
543C2×D4—942no—
544C2×D4—3762no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—24no—
552C22×C4—82no—
553C22×C4—941no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—944no—
557C22×C4—3762no—
558C22×C4C2×C22⋊D4712yes—
559C22×C4C2×C22⋊D4711yescharacteristic
560C22×C4C2×C22⋊D4711yescharacteristic
561C22×C4C2×C22⋊D4711yescharacteristic
562C22×C4C2×C22⋊D4711yescharacteristic
563C22×C4C2×C22⋊D4711yescharacteristic
564C22×C4C23×D4712yes—
565C22×C4C23×D4711yescharacteristic
566C2×C8—472no—
567C2×C8—472no—
568C2×C8—472no—
569C2×C8—472no—
570C2×C8—942no—
571C2×C8—942no—
572C2×C8—942no—
573C2×C8—942no—
574C4⋊C4—24no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—472no—
586C4⋊C4—472no—
587C4⋊C4—944no—
588C4⋊C4—944no—
589C4⋊C4—941no—
590C4⋊C4—941no—
591C4⋊C4—944no—
592C4⋊C4C2×C22⋊D4714yes—
593C4⋊C4C2×C22⋊D4714yes—
594C4⋊C4C23×D4712yes—
595C4⋊C4C23×D4712yes—
596C4⋊C4C23×D4712yes—
597C4⋊C4C23×D4712yes—
598C22⋊C4—24no—
599C22⋊C4—944no—
600C22⋊C4—944no—
601C22⋊C4—944no—
602C22⋊C4—944no—
603C22⋊C4—944no—
604C22⋊C4C2×C22⋊D4714yes—
605C22⋊C4C2×C22⋊D4714yes—
606C42—24no—
607C42—944no—
608C42C2×C22⋊D4712yes—
609C42C2×C22⋊D4712yes—
610C42C23×D4712yes—
611C42C23×D4712yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—942no—
616C23—1882no—
617C23—1882no—
618C23—1882no—
619C23C22×C22⋊D4712yes—
620C23C22×C22⋊D4711yescharacteristic
621Q8—84no—
622Q8—84no—
623Q8—942no—
624Q8—942no—
625Q8—3764no—
626Q8—1882no—
627D4—942no—
628D4—942no—
629D4—3764no—
630D4—1882no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—84no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—3764no—
652C2×C4—1882no—
653C2×C4—1882no—
654C2×C4—1882no—
655C2×C4C22×C22⋊D4712yes—
656C2×C4C22×C22⋊D4712yes—
657C2×C4C22×C22⋊D4712yes—
658C2×C4C22×C22⋊D4712yes—
659C2×C4C22×C22⋊D4712yes—
660C2×C4C22×C22⋊D4711yescharacteristic
661C2×C4#1309407212yes—
662C2×C4#1309407212yes—
663C2×C4C24×D4711yescharacteristic
664C8—942no—
665C8—942no—
666C8—942no—
667C8—942no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—3764no—
673C22—1882no—
674C22—1882no—
675C22—1882no—
676C22#1568969712yes—
677C22#1568992612yes—
678C22#1568993812yes—
679C22C23×C22⋊D4711yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—42no—
689C4—1882no—
690C4—1882no—
691C4—1882no—
692C4#1568969712yes—
693C4C2×#1309407211yescharacteristic
694C4C2×#1309407211yescharacteristic
695C2—42no—
696C2—3762no—
697C2#2025467114yesdirect product factor
698C2C2×#1568969711yescharacteristic
699C2C2×#1568992611yescharacteristic
700C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#544C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenterC2×#544D47
hypocenterC47C2×#3243
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #20254671C2direct (N × H)
3. C2×#15689533C2semidirect
4. C2×#15689526C2semidirect
5. C2×#15689485C2semidirect
6. C2×#15689480C2semidirect
7. C2×#15689458C2semidirect
8. C2×#15689464C2semidirect
11. C2×#15689427C2semidirect
12. C2×#15689415C2semidirect
13. C2×#15689420C2semidirect
14. C2×#15689400C2semidirect
15. C2×#15689184C2semidirect
16. C2×C47×#544C2semidirect
29. #15689533C22semidirect
30. #15689526C22semidirect
31. #15689485C22semidirect
32. #15689480C22semidirect
33. #15689464C22semidirect
34. #15689458C22semidirect
37. #15689427C22semidirect
38. #15689420C22semidirect
39. #15689415C22semidirect
40. #15689400C22semidirect
41. #15689184C22semidirect
65. C47×#544C22semidirect
345. C2×#544D47semidirect
362. C2×C47#3243semidirect
368. #544C2×D47semidirect
427. C47C2×#3243semidirect
697. C2#20254671direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897442
#202546712
C2×#156895332
C2×#156895262
C2×#156894852
C2×#156894802
C2×#156894582
C2×#156894642
C2×#156894472
C2×#156894362
C2×#156894272
C2×#156894152
C2×#156894202
C2×#156894002
C2×#156891842
C2×C47×#5442
C2×#324347