Finite Group Databasebeta

← C2×#20254656 #27088483

Subgroups — C2×#20254656 #27088483

Order 12032.

1678 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689735C211yesmaximal, characteristic
2#20254656C2116yesmaximal, direct product factor
3C2×#15689529C211yesmaximal, characteristic, complemented
4C2×#15689522C211yesmaximal, characteristic, complemented
5C2×#15689493C211yesmaximal, characteristic, complemented
6C2×#15689475C211yesmaximal, characteristic, complemented
7C2×#15689458C211yesmaximal, characteristic
8C2×#15689464C211yesmaximal, characteristic
9C2×#15689464C211yesmaximal, characteristic
10C2×#15689453C211yesmaximal, characteristic
11C2×#15689427C211yesmaximal, characteristic, complemented
12C2×#15689427C211yesmaximal, characteristic, complemented
13C2×#15689415C211yesmaximal, characteristic, complemented
14C2×#15689405C211yesmaximal, characteristic, complemented
15C2×#15689184C211yesmaximal, characteristic
16C2×C47×#544C211yesmaximal, characteristic
17#15689735—24no—
18#15689735C2218yes—
19C2×#13094024C2211yescharacteristic
20C2×#13094017—21no—
21C2×#13094017—21no—
22C2×#13094016C2211yescharacteristic
23C2×#13094014—21no—
24C2×#13094014—21no—
25C2×#13094003C2211yescharacteristic
26C2×#13094003C2211yescharacteristic
27C2×C4×Dic94C2211yescharacteristic
28C2×C4×Dic94C2211yescharacteristic
29#15689529C2218yescomplemented
30#15689522C2218yescomplemented
31#15689493C2218yescomplemented
32#15689475C2218yescomplemented
33#15689464C2218yes—
34#15689464C2218yes—
35#15689458C2218yes—
36#15689453C2218yes—
37#15689427C2218yescomplemented
38#15689427C2218yescomplemented
39#15689415C2218yescomplemented
40#15689405C2218yescomplemented
41#15689184C2218yes—
42C2×#13093957C2211yescharacteristic
43C2×#13093957C2211yescharacteristic
44C2×#13093957C2211yescharacteristic
45C2×#13093957C2211yescharacteristic
46C2×#13093955C2211yescharacteristic
47C2×#13093955C2211yescharacteristic
48C2×#13093955C2211yescharacteristic
49C2×#13093955C2211yescharacteristic
50C2×C4⋊(C47⋊C8)C2211yescharacteristic
51C2×C4⋊(C47⋊C8)C2211yescharacteristic
52C2×#13093947C2211yescharacteristic
53C2×#13093947C2211yescharacteristic
54C2×#13093947C2211yescharacteristic
55C2×#13093947C2211yescharacteristic
56C2×#13093947C2211yescharacteristic
57C2×#13093947C2211yescharacteristic
58C2×#13093947C2211yescharacteristic
59C2×#13093947C2211yescharacteristic
60C2×C22⋊(C47⋊C8)C2211yescharacteristic
61C2×C22⋊(C47⋊C8)C2211yescharacteristic
62C2×#13093935C2211yescharacteristic
63C2×C4×C47⋊C8C2211yescharacteristic
64C47×#544—24no—
65C47×#544C2218yes—
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×Dic94C2311yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×C47⋊C8C2311yescharacteristic
80C22×C47⋊C8C2311yescharacteristic
81C22×C47⋊C8C2311yescharacteristic
82C22×C47⋊C8C2311yescharacteristic
83#13094024—22no—
84#13094024C2314yes—
85#13094017—28no—
86#13094017—28no—
87#13094016—22no—
88#13094016C2314yes—
89#13094014—28no—
90#13094014—28no—
91#13094003—22no—
92#13094003—22no—
93#13094003C2314yes—
94#13094003C2314yes—
95C4×Dic94—22no—
96C4×Dic94—22no—
97C4×Dic94C2314yes—
98C4×Dic94C2314yes—
99C2×C4⋊Dic47—21no—
100C2×C4⋊Dic47—21no—
101C2×C4⋊Dic47C2311yescharacteristic
102C2×C4⋊Dic47C2311yescharacteristic
103C2×Dic47⋊C4—21no—
104C2×Dic47⋊C4—21no—
105C2×Dic47⋊C4—21no—
106C2×Dic47⋊C4—21no—
107C2×Dic47⋊C4—21no—
108C2×Dic47⋊C4—21no—
109C2×C22⋊Dic47—21no—
110C2×C22⋊Dic47—21no—
111C2×C4×Dic47—21no—
112C2×C4×Dic47—21no—
113#13093957C2314yes—
114#13093957C2314yes—
115#13093957C2314yes—
116#13093957C2314yes—
117#13093955C2314yes—
118#13093955C2314yes—
119#13093955C2314yes—
120#13093955C2314yes—
121C4⋊(C47⋊C8)C2314yes—
122C4⋊(C47⋊C8)C2314yes—
123#13093947C2314yes—
124#13093947C2314yes—
125#13093947C2314yes—
126#13093947C2314yes—
127#13093947C2314yes—
128#13093947C2314yes—
129#13093947C2314yes—
130#13093947C2314yes—
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
177C2×Q8×C47—24no—
178C2×Q8×C47—24no—
179C2×Q8×C47—82no—
180C2×Q8×C47—82no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—24no—
188C22×C4×C47—82no—
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2411yescharacteristic
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C2×Dic94—22no—
202C2×Dic94—22no—
203C2×Dic94—22no—
204C2×Dic94—22no—
205C2×Dic94—21no—
206C2×Dic94—21no—
207C2×Dic94C2412yes—
208C2×Dic94C2412yes—
209C4⋊C4×C47—24no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—24no—
213C4⋊C4×C47—24no—
214C4⋊C4×C47—24no—
215C4⋊C4×C47—24no—
216C4⋊C4×C47—24no—
217C4⋊C4×C47—24no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47C2×D414yes—
221C4⋊C4×C47C2×D414yes—
222C4⋊C4×C47C2412yes—
223C4⋊C4×C47C2412yes—
224C4⋊C4×C47C2412yes—
225C4⋊C4×C47C2412yes—
226C22⋊C4×C47—24no—
227C22⋊C4×C47C2×D414yes—
228C22⋊C4×C47C2×D414yes—
229C42×C47—24no—
230C42×C47C2×D412yes—
231C42×C47C2×D412yes—
232C42×C47C2412yes—
233C42×C47C2412yes—
234C22⋊Dic47—24no—
235C22⋊Dic47—24no—
236C4⋊Dic47—24no—
237C4⋊Dic47—24no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47C2412yes—
241C4⋊Dic47C2412yes—
242Dic47⋊C4—24no—
243Dic47⋊C4—24no—
244Dic47⋊C4—24no—
245Dic47⋊C4—24no—
246Dic47⋊C4—24no—
247Dic47⋊C4—24no—
248C4×Dic47—24no—
249C4×Dic47—24no—
250C2×C47⋊C8—22no—
251C2×C47⋊C8—22no—
252C2×C47⋊C8—22no—
253C2×C47⋊C8—22no—
254C2×C47⋊C8C2412yes—
255C2×C47⋊C8C2412yes—
256C2×C47⋊C8C2412yes—
257C2×C47⋊C8C2412yes—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47C22×D412yes—
262C23×C47C22×D411yescharacteristic
263Q8×C47—84no—
264Q8×C47—84no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—24no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—42no—
278C2×C4×C47—42no—
279C2×C4×C47—42no—
280C2×C4×C47—42no—
281C2×C4×C47—84no—
282C2×C4×C47C22×D412yes—
283C2×C4×C47C22×D412yes—
284C2×C4×C47C22×D412yes—
285C2×C4×C47C22×D412yes—
286C2×C4×C47C22×D412yes—
287C2×C4×C47C22×D411yescharacteristic
288C2×C4×C472−1+412yes—
289C2×C4×C472−1+412yes—
290C2×C4×C47C2511yescharacteristic
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—42no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47—42no—
299Dic94—22no—
300Dic94—22no—
301Dic94—22no—
302Dic94—22no—
303Dic94—42no—
304Dic94—42no—
305C47⋊C8—22no—
306C47⋊C8—22no—
307C47⋊C8—22no—
308C47⋊C8—22no—
309C2×#3242—471nomaximal, Sylow
310C22×C47—22no—
311C22×C47—22no—
312C22×C47—22no—
313C22×C47—44no—
314C22×C47#53612yes—
315C22×C47#57712yes—
316C22×C47#57812yes—
317C22×C47C23×D411yescharacteristic
318C4×C47—22no—
319C4×C47—22no—
320C4×C47—22no—
321C4×C47—22no—
322C4×C47—22no—
323C4×C47—42no—
324C4×C47—42no—
325C4×C47—42no—
326C4×C47—42no—
327C4×C47#53612yes—
328C4×C47C2×2−1+411yescharacteristic
329C4×C47C2×2−1+411yescharacteristic
330Dic47—42no—
331Dic47—42no—
332Dic47—42no—
333Dic47—42no—
334C2×#544D4711yescharacteristic
335C2×#541—471no—
336#3242—4716no—
337C2×#501—471no—
338C2×#499—471no—
339C2×#491—471no—
340C2×#487—471no—
341C2×#484—471no—
342C2×#485—471no—
343C2×#485—471no—
344C2×#483—471no—
345C2×#479—471no—
346C2×#479—471no—
347C2×#477—471no—
348C2×#475—471no—
349C2×#433—471no—
350C2×C47—42no—
351C2×C47#324214yescomplemented
352C2×C47C2×#53611yescharacteristic
353C2×C47C2×#57711yescharacteristic
354C2×C47C2×#57811yescharacteristic
355#544—24no—
356#544C2×D4718yes—
357#541—478no—
358#541—944no—
359C2×C4⋊Q8—21no—
360C2×C4⋊Q8—471no—
361C2×C4⋊Q8C2×D4711yescharacteristic
362C2×C4⋊Q8C2×D4711yescharacteristic
363C2×#126—941no—
364C2×#126—941no—
365C2×#125—21no—
366C2×#125—471no—
367C2×#125—941no—
368C2×#125—941no—
369C2×#125C2×D4711yescharacteristic
370C2×#125C2×D4711yescharacteristic
371C2×C22⋊Q8—21no—
372C2×C22⋊Q8—21no—
373C2×C22⋊Q8—471no—
374C2×C22⋊Q8—471no—
375C2×C4×Q8—471no—
376C2×C4×Q8—471no—
377C2×#117C2×D4711yescharacteristic
378C2×#117C2×D4711yescharacteristic
379C22×C4⋊C4C2×D4711yescharacteristic
380#501—478no—
381#499—478no—
382#491—478no—
383#487—478no—
384#485—478no—
385#485—478no—
386#484—478no—
387#483—478no—
388#479—478no—
389#479—478no—
390#477—478no—
391#475—478no—
392#433—478no—
393C2×#107—471no—
394C2×#107—471no—
395C2×#107—471no—
396C2×#107—471no—
397C2×#106—471no—
398C2×#106—471no—
399C2×#106—471no—
400C2×#106—471no—
401C2×C4⋊C8—471no—
402C2×C4⋊C8—471no—
403C2×#103—471no—
404C2×#103—471no—
405C2×#103—471no—
406C2×#103—471no—
407C2×#103—471no—
408C2×#103—471no—
409C2×#103—471no—
410C2×#103—471no—
411C2×C22⋊C8—471no—
412C2×C22⋊C8—471no—
413C2×#97—471no—
414C2×C4×C8—471no—
415C47C2×#324211yescharacteristic, complemented, Sylow
416C22×Q8—21no—
417C22×Q8—21no—
418C22×Q8—471no—
419C22×Q8—471no—
420C23×C4—21no—
421C23×C4C22×D4711yescharacteristic
422C22×C8—471no—
423C22×C8—471no—
424C22×C8—471no—
425C22×C8—471no—
426C4⋊Q8—28no—
427C4⋊Q8—22no—
428C4⋊Q8—22no—
429C4⋊Q8—474no—
430C4⋊Q8—942no—
431C4⋊Q8C22×D4714yes—
432C4⋊Q8C22×D4714yes—
433#126—948no—
434#126—948no—
435#125—28no—
436#125—22no—
437#125—22no—
438#125—474no—
439#125—948no—
440#125—948no—
441#125—942no—
442#125C22×D4714yes—
443#125C22×D4714yes—
444C22⋊Q8—28no—
445C22⋊Q8—28no—
446C22⋊Q8—474no—
447C22⋊Q8—474no—
448C22⋊Q8—942no—
449C22⋊Q8—942no—
450C4×Q8—474no—
451C4×Q8—474no—
452C4×Q8—942no—
453C4×Q8—942no—
454#117—22no—
455#117C22⋊D4714yes—
456#117C22×D4714yes—
457#117C22×D4714yes—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—471no—
467C2×C4⋊C4—471no—
468C2×C4⋊C4—941no—
469C2×C4⋊C4—941no—
470C2×C4⋊C4—941no—
471C2×C4⋊C4—941no—
472C2×C4⋊C4—941no—
473C2×C4⋊C4—941no—
474C2×C4⋊C4—941no—
475C2×C4⋊C4—941no—
476C2×C4⋊C4C22⋊D4711yescharacteristic
477C2×C4⋊C4C22⋊D4711yescharacteristic
478C2×C4⋊C4C22×D4711yescharacteristic
479C2×C4⋊C4C22×D4711yescharacteristic
480C2×C4⋊C4C22×D4714yes—
481C2×C4⋊C4C22×D4711yescharacteristic
482C2×C4⋊C4C22×D4711yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—941no—
485C2×C22⋊C4—941no—
486C2×C22⋊C4C22⋊D4711yescharacteristic
487C2×C22⋊C4C22⋊D4711yescharacteristic
488C2×C42—21no—
489C2×C42—941no—
490C2×C42—941no—
491C2×C42C22×D4711yescharacteristic
492C2×C42C22×D4711yescharacteristic
493#107—474no—
494#107—474no—
495#107—474no—
496#107—474no—
497#106—474no—
498#106—474no—
499#106—474no—
500#106—474no—
501C4⋊C8—474no—
502C4⋊C8—474no—
503#103—474no—
504#103—474no—
505#103—474no—
506#103—474no—
507#103—474no—
508#103—474no—
509#103—474no—
510#103—474no—
511C22⋊C8—474no—
512C22⋊C8—474no—
513#97—474no—
514C4×C8—474no—
515C24C2×C22⋊D4711yescharacteristic
516C2×Q8—24no—
517C2×Q8—24no—
518C2×Q8—82no—
519C2×Q8—82no—
520C2×Q8—472no—
521C2×Q8—472no—
522C2×Q8—941no—
523C2×Q8—941no—
524C2×Q8—942no—
525C2×Q8—942no—
526C2×Q8—942no—
527C2×Q8—942no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—82no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4C2×C22⋊D4712yes—
541C22×C4C2×C22⋊D4711yescharacteristic
542C22×C4C2×C22⋊D4711yescharacteristic
543C22×C4C2×C22⋊D4711yescharacteristic
544C22×C4C2×C22⋊D4711yescharacteristic
545C22×C4C2×C22⋊D4711yescharacteristic
546C22×C4C23×D4712yes—
547C22×C4C23×D4711yescharacteristic
548C2×C8—472no—
549C2×C8—472no—
550C2×C8—472no—
551C2×C8—472no—
552C2×C8—942no—
553C2×C8—942no—
554C2×C8—942no—
555C2×C8—942no—
556C4⋊C4—24no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—24no—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—472no—
568C4⋊C4—472no—
569C4⋊C4—944no—
570C4⋊C4—944no—
571C4⋊C4—944no—
572C4⋊C4—944no—
573C4⋊C4—944no—
574C4⋊C4—944no—
575C4⋊C4—941no—
576C4⋊C4—941no—
577C4⋊C4—944no—
578C4⋊C4—944no—
579C4⋊C4C2×C22⋊D4714yes—
580C4⋊C4C2×C22⋊D4714yes—
581C4⋊C4C23×D4712yes—
582C4⋊C4C23×D4712yes—
583C4⋊C4C23×D4712yes—
584C4⋊C4C23×D4712yes—
585C22⋊C4—24no—
586C22⋊C4—944no—
587C22⋊C4—944no—
588C22⋊C4C2×C22⋊D4714yes—
589C22⋊C4C2×C22⋊D4714yes—
590C42—24no—
591C42—944no—
592C42—944no—
593C42C2×C22⋊D4712yes—
594C42C2×C22⋊D4712yes—
595C42C23×D4712yes—
596C42C23×D4712yes—
597C23—22no—
598C23—22no—
599C23—22no—
600C23C22×C22⋊D4712yes—
601C23C22×C22⋊D4711yescharacteristic
602Q8—84no—
603Q8—84no—
604Q8—942no—
605Q8—942no—
606Q8—942no—
607Q8—942no—
608Q8—1882no—
609Q8—1882no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—84no—
627C2×C4—942no—
628C2×C4—942no—
629C2×C4—942no—
630C2×C4—942no—
631C2×C4—1882no—
632C2×C4—1882no—
633C2×C4—1882no—
634C2×C4—1882no—
635C2×C4C22×C22⋊D4712yes—
636C2×C4C22×C22⋊D4712yes—
637C2×C4C22×C22⋊D4712yes—
638C2×C4C22×C22⋊D4712yes—
639C2×C4C22×C22⋊D4712yes—
640C2×C4C22×C22⋊D4711yescharacteristic
641C2×C4#1309407212yes—
642C2×C4#1309407212yes—
643C2×C4C24×D4711yescharacteristic
644C8—942no—
645C8—942no—
646C8—942no—
647C8—942no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—44no—
652C22#1568969712yes—
653C22#1568993412yes—
654C22#1568993812yes—
655C22C23×C22⋊D4711yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—22no—
660C4—22no—
661C4—42no—
662C4—42no—
663C4—42no—
664C4—42no—
665C4—1882no—
666C4—1882no—
667C4—1882no—
668C4—1882no—
669C4#1568969712yes—
670C4C2×#1309407211yescharacteristic
671C4C2×#1309407211yescharacteristic
672C2—42no—
673C2#2025465614yesdirect product factor
674C2C2×#1568969711yescharacteristic
675C2C2×#1568993411yescharacteristic
676C2C2×#1568993811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#544C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenterC2×#544D47
hypocenterC47C2×#3242
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. #20254656C2direct (N × H)
3. C2×#15689529C2semidirect
4. C2×#15689522C2semidirect
5. C2×#15689493C2semidirect
6. C2×#15689475C2semidirect
11. C2×#15689427C2semidirect
12. C2×#15689427C2semidirect
13. C2×#15689415C2semidirect
14. C2×#15689405C2semidirect
29. #15689529C22semidirect
30. #15689522C22semidirect
31. #15689493C22semidirect
32. #15689475C22semidirect
37. #15689427C22semidirect
38. #15689427C22semidirect
39. #15689415C22semidirect
40. #15689405C22semidirect
351. C2×C47#3242semidirect
415. C47C2×#3242semidirect
673. C2#20254656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897352
#202546562
C2×#156895292
C2×#156895222
C2×#156894932
C2×#156894752
C2×#156894582
C2×#156894642
C2×#156894532
C2×#156894272
C2×#156894152
C2×#156894052
C2×#156891842
C2×C47×#5442
C2×#324247