Finite Group Databasebeta

← C2×#20255956 #27094965

Subgroups — C2×#20255956 #27094965

Order 12032.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689815C211yesmaximal, characteristic
2C2×#15689812C211yesmaximal, characteristic
3#20255956C2116yesmaximal, direct product factor
4C2×#15689524C211yesmaximal, characteristic, complemented
5C2×#15689459C211yesmaximal, characteristic, complemented
6C2×#15689457C211yesmaximal, characteristic, complemented
7C2×#15689466C211yesmaximal, characteristic, complemented
8C2×#15689433C211yesmaximal, characteristic, complemented
9C2×#15689432C211yesmaximal, characteristic, complemented
10C2×#15689380C211yesmaximal, characteristic, complemented
11C2×#15689379C211yesmaximal, characteristic, complemented
12C2×#15689215C211yesmaximal, characteristic, complemented
13C2×#15689198C211yesmaximal, characteristic
14C2×#15689166C211yesmaximal, characteristic, complemented
15C2×#15689162C211yesmaximal, characteristic, complemented
16C2×C47×#485C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625329C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20#15689815—24no—
21#15689815C2218yes—
22#15689812—24no—
23#15689812C2218yes—
24C2×#13094019—21no—
25C2×#13094017—21no—
26C2×#13094016—21no—
27C2×#13094015—21no—
28C2×#13094015C2211yescharacteristic
29C2×#13094015C2211yescharacteristic
30C2×#13094008—21no—
31C2×#13094006—21no—
32C2×#13094004C2211yescharacteristic
33C2×#13094003C2211yescharacteristic
34C2×#13094000C2211yescharacteristic
35C2×Q8×Dic47C2211yescharacteristic
36C2×#13093989C2211yescharacteristic
37C2×C4×C22⋊D47C2211yescharacteristic
38C2×#13093982C2211yescharacteristic
39C2×#13093981—21no—
40C2×#13093980—21no—
41C22×C4⋊Dic47C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689524C2218yescomplemented
44#15689466C2218yescomplemented
45#15689459C2218yescomplemented
46#15689457C2218yescomplemented
47#15689433C2218yescomplemented
48#15689432C2218yescomplemented
49#15689380C2218yescomplemented
50#15689379C2218yescomplemented
51#15689215C2218yescomplemented
52#15689198C2218yes—
53#15689166C2218yescomplemented
54#15689162C2218yescomplemented
55C2×#13093958C2211yescharacteristic
56C2×#13093958C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093957C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×#13093955C2211yescharacteristic
62C2×Dic47⋊C8C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093947C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×C22⋊Q8×C47C2211yescharacteristic
70C2×#117×C47C2211yescharacteristic
71C47×#485C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×C22⋊C8×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×C22⋊D47D411yescharacteristic
79C23×Dic47—21no—
80C22×C4×D47—21no—
81C22×C4×D47C2311yescharacteristic
82C2×#10625337—24no—
83C2×#10625337C2314yes—
84C2×#10625329—24no—
85C2×#10625329C2314yes—
86C2×#10625324—24no—
87C2×#10625324C2314yes—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90#13094019—28no—
91#13094017—28no—
92#13094016—28no—
93#13094015—28no—
94#13094015—22no—
95#13094015—22no—
96#13094015C2314yes—
97#13094015C2314yes—
98#13094008—28no—
99#13094006—28no—
100#13094004—22no—
101#13094004C2314yes—
102#13094003—22no—
103#13094003C2314yes—
104#13094000—22no—
105#13094000C2314yes—
106Q8×Dic47—22no—
107Q8×Dic47C2314yes—
108#13093989—22no—
109#13093989C2314yes—
110C4×C22⋊D47D414yes—
111C4×C22⋊D47C2314yes—
112#13093982—22no—
113#13093982C2314yes—
114#13093981—28no—
115#13093980—28no—
116C2×C4⋊Dic47—22no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47C2314yes—
123C2×C4⋊Dic47C2311yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4D411yescharacteristic
133C4⋊C4×D47—22no—
134C4⋊C4×D47C2314yes—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47D411yescharacteristic
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4D411yescharacteristic
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145#13093958C2314yes—
146#13093958C2314yes—
147#13093957C2314yes—
148#13093957C2314yes—
149#13093955C2314yes—
150#13093955C2314yes—
151#13093955C2314yes—
152Dic47⋊C8C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093948C2314yes—
156#13093947C2314yes—
157(C2×D47)⋊C8C2314yes—
158C8×Dic47C2314yes—
159C22×Q8×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163C22⋊Q8×C47—22no—
164C22⋊Q8×C47C2314yes—
165#117×C47—22no—
166#117×C47C2314yes—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C22⋊C4×C47—21no—
172C2×C22⋊C4×C47—21no—
173C2×C42×C47—21no—
174#107×C47C2314yes—
175#106×C47C2314yes—
176#103×C47C2314yes—
177#103×C47C2314yes—
178C22⋊C8×C47C2314yes—
179C24×C47C2×D411yescharacteristic
180C23×D47C2×D411yescharacteristic
181C2×Q8×C47—21no—
182C2×Q8×C47—22no—
183C2×Q8×C47—22no—
184C2×Q8×C47C2412yes—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2411yescharacteristic
195C2×C22⋊D47—42no—
196C2×C22⋊D47C2×D414yes—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—24no—
202C22×Dic47—44no—
203C22×Dic47C2×D411yescharacteristic
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C2×C4×D47—22no—
207C2×C4×D47—22no—
208C2×C4×D47—24no—
209C2×C4×D47—44no—
210C2×C4×D47C2×D412yes—
211C2×C4×D47C2412yes—
212C2×Dic94—22no—
213C2×Dic94—22no—
214C2×Dic94—21no—
215C2×Dic94C2412yes—
216C2×C8×C47—22no—
217C2×C8×C47—22no—
218C2×C8×C47C2412yes—
219C2×C8×C47C2412yes—
220C4⋊C4×C47—24no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47C2412yes—
225C4⋊C4×C47C2412yes—
226C4⋊C4×C47C2412yes—
227C22⋊C4×C47—24no—
228C22⋊C4×C47—24no—
229C42×C47—24no—
230C22⋊Dic47—24no—
231C22⋊Dic47C2×D414yes—
232#10625337—28no—
233(C2×D47)⋊C4—24no—
234(C2×D47)⋊C4—24no—
235(C2×D47)⋊C4—24no—
236(C2×D47)⋊C4C2×D414yes—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—24no—
241C4⋊Dic47—24no—
242C4⋊Dic47—24no—
243C4⋊Dic47—24no—
244C4⋊Dic47—24no—
245C4⋊Dic47C2412yes—
246C4⋊Dic47C2412yes—
247C4⋊Dic47C2412yes—
248Dic47⋊C4—24no—
249Dic47⋊C4—24no—
250Dic47⋊C4—24no—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4C2×D414yes—
255C4×Dic47—24no—
256C4×Dic47—24no—
257C4×Dic47—24no—
258C4×Dic47C2×D412yes—
259C4×Dic47C2412yes—
260#10625329—28no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8#4114yes—
263C2×C47⋊C8C2412yes—
264C2×C47⋊C8C2412yes—
265#10625324—28no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47C22×D412yes—
270C23×C47C22×D411yescharacteristic
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47C22×D412yes—
275Q8×C47—22no—
276Q8×C47—22no—
277Q8×C47—42no—
278C2×C4×C47—22no—
279C2×C4×C47—24no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47C22×D412yes—
291C2×C4×C47C22×D411yescharacteristic
292C2×C4×C47C2×#4112yes—
293C2×C4×C472−1+412yes—
294C2×C4×C47C2511yescharacteristic
295C22⋊D47—44no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—48no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47C22×D412yes—
309C2×Dic47C22×D412yes—
310C2×Dic47C22×D412yes—
311C4×D47—24no—
312C4×D47—22no—
313C4×D47—22no—
314C4×D47—48no—
315Dic94—22no—
316Dic94—22no—
317Dic94—42no—
318C8×C47—22no—
319C8×C47—22no—
320C47⋊C8—22no—
321C47⋊C8C2×#4114yes—
322C2×#3352—471nomaximal, Sylow
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—44no—
327C22×C47#54712yes—
328C22×C47#57512yes—
329C22×C47#57812yes—
330C22×C47C23×D411yescharacteristic
331C2×D47—22no—
332C2×D47—22no—
333C2×D47—22no—
334C2×D47—44no—
335C4×C47—22no—
336C4×C47—42no—
337C4×C47—42no—
338C4×C47—42no—
339C4×C47—42no—
340C4×C47#54712yes—
341C4×C47C22×#4111yescharacteristic
342C4×C47C2×2−1+411yescharacteristic
343Dic47—22no—
344Dic47—22no—
345Dic47—22no—
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349Dic47—42no—
350C2×#552—471no—
351C2×#552—471no—
352#3352—4716no—
353C2×#499—471no—
354C2×#484—471no—
355C2×#484—471no—
356C2×#485—471no—
357C2×#485D4711yescharacteristic, complemented
358C2×#479—471no—
359C2×#479—471no—
360C2×#470—471no—
361C2×#470—471no—
362C2×C4×Q16—471no—
363C2×#436—471no—
364C2×#428—471no—
365C2×#428—471no—
366C2×C47—42no—
367C2×C47#335214yescomplemented
368C2×C47C2×#54711yescharacteristic
369C2×C47C2×#57511yescharacteristic
370C2×C47C2×#57811yescharacteristic
371D47—42no—
372C22×Q16—471no—
373C22×M16—471no—
374C22×M16—471no—
375#552—478no—
376#552—478no—
377#552—944no—
378#552—944no—
379C2×#126—941no—
380C2×#126—941no—
381C2×#125—471no—
382C2×#125—471no—
383C2×#125—941no—
384C2×#125—941no—
385C2×#123—941no—
386C2×#123—941no—
387C2×C22⋊Q8—471no—
388C2×C22⋊Q8—471no—
389C2×C22⋊Q8—471no—
390C2×C22⋊Q8C2×D4711yescharacteristic
391C2×C4×Q8—471no—
392C2×C4×Q8—471no—
393C2×C4×D4—471no—
394C2×#117—471no—
395C2×#117—941no—
396C2×#117—941no—
397C2×#117C2×D4711yescharacteristic
398C22×C4⋊C4—471no—
399C22×C4⋊C4—471no—
400#499—478no—
401#485—478no—
402#485C2×D4718yescomplemented
403#484—478no—
404#484—478no—
405#479—478no—
406#479—478no—
407#470—478no—
408#470—478no—
409C4×Q16—478no—
410#436—478no—
411#428—478no—
412#428—478no—
413C2×#107—471no—
414C2×#107—471no—
415C2×#107—471no—
416C2×#107—471no—
417C2×#107C2×D4711yescharacteristic
418C2×#106—471no—
419C2×#106—471no—
420C2×#106—471no—
421C2×#106C2×D4711yescharacteristic
422C2×C4⋊C8—471no—
423C2×#103—471no—
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103C2×D4711yescharacteristic
428C2×#103C2×D4711yescharacteristic
429C2×C22⋊C8—471no—
430C2×C22⋊C8C2×D4711yescharacteristic
431C2×C4×C8—471no—
432C47C2×#335211yescharacteristic, complemented, Sylow
433C22×Q8—471no—
434C22×Q8C22×D4711yescharacteristic
435C22×D4—471no—
436C23×C4—471no—
437C23×C4—941no—
438C23×C4—941no—
439C23×C4C22×D4711yescharacteristic
440C2×Q16—474no—
441C2×Q16—944no—
442C2×M16—474no—
443C2×M16—474no—
444C2×M16—944no—
445C2×M16—944no—
446C22×C8—471no—
447C22×C8—471no—
448C22×C8C22×D4711yescharacteristic
449C22×C8C22×D4711yescharacteristic
450#126—948no—
451#126—948no—
452#125—474no—
453#125—474no—
454#125—948no—
455#125—942no—
456#125—942no—
457#125—948no—
458#123—948no—
459#123—948no—
460C22⋊Q8—22no—
461C22⋊Q8—474no—
462C22⋊Q8—474no—
463C22⋊Q8—474no—
464C22⋊Q8—942no—
465C22⋊Q8—942no—
466C22⋊Q8—942no—
467C22⋊Q8C22×D4714yes—
468C4×Q8—474no—
469C4×Q8—474no—
470C4×Q8—942no—
471C4×Q8—942no—
472C4×D4—474no—
473C4×D4—474no—
474#117—22no—
475#117—474no—
476#117—948no—
477#117—948no—
478#117—942no—
479#117C22×D4714yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—471no—
482C2×C4⋊C4—471no—
483C2×C4⋊C4—471no—
484C2×C4⋊C4—471no—
485C2×C4⋊C4—474no—
486C2×C4⋊C4—474no—
487C2×C4⋊C4—942no—
488C2×C4⋊C4—941no—
489C2×C4⋊C4—941no—
490C2×C4⋊C4—941no—
491C2×C4⋊C4—941no—
492C2×C4⋊C4—941no—
493C2×C4⋊C4—941no—
494C2×C4⋊C4—941no—
495C2×C4⋊C4—941no—
496C2×C4⋊C4—941no—
497C2×C4⋊C4—941no—
498C2×C4⋊C4—942no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4C22×D4711yescharacteristic
501C2×C4⋊C4C22×D4711yescharacteristic
502C2×C4⋊C4C22×D4711yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—471no—
506C2×C22⋊C4—471no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C22⋊C4—941no—
511C2×C42—21no—
512C2×C42—471no—
513C2×C42—941no—
514C2×C42—941no—
515C2×C42—941no—
516#107—474no—
517#107—474no—
518#107—474no—
519#107—474no—
520#107C22×D4714yes—
521#106—474no—
522#106—474no—
523#106—474no—
524#106C22×D4714yes—
525C4⋊C8—474no—
526#103—474no—
527#103—474no—
528#103—474no—
529#103—474no—
530#103C22×D4714yes—
531#103C22×D4714yes—
532C22⋊C8—474no—
533C22⋊C8C22×D4714yes—
534C4×C8—474no—
535C24—471no—
536C24D4×D4711yescharacteristic
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—472no—
541C2×Q8—941no—
542C2×Q8—942no—
543C2×Q8—942no—
544C2×Q8C23×D4712yes—
545C2×D4—474no—
546C2×D4—1882no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—471no—
554C22×C4—471no—
555C22×C4—471no—
556C22×C4—472no—
557C22×C4—472no—
558C22×C4—944no—
559C22×C4—942no—
560C22×C4—942no—
561C22×C4—944no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—1884no—
567C22×C4—1884no—
568C22×C4D4×D4712yes—
569C22×C4D4×D4711yescharacteristic
570C22×C4C23×D4712yes—
571C22×C4C23×D4711yescharacteristic
572Q16—948no—
573M16—948no—
574M16—948no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—474no—
578C2×C8—472no—
579C2×C8—472no—
580C2×C8—942no—
581C2×C8C23×D4712yes—
582C2×C8C23×D4712yes—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—474no—
588C4⋊C4—472no—
589C4⋊C4—472no—
590C4⋊C4—472no—
591C4⋊C4—944no—
592C4⋊C4—944no—
593C4⋊C4—944no—
594C4⋊C4—944no—
595C4⋊C4—944no—
596C4⋊C4—944no—
597C4⋊C4—944no—
598C4⋊C4—944no—
599C4⋊C4—944no—
600C4⋊C4—944no—
601C4⋊C4—941no—
602C4⋊C4—941no—
603C4⋊C4—941no—
604C4⋊C4—944no—
605C4⋊C4C23×D4712yes—
606C4⋊C4C23×D4712yes—
607C4⋊C4C23×D4712yes—
608C22⋊C4—24no—
609C22⋊C4—24no—
610C22⋊C4—474no—
611C22⋊C4—474no—
612C22⋊C4—944no—
613C22⋊C4—944no—
614C22⋊C4—944no—
615C22⋊C4—944no—
616C42—24no—
617C42—472no—
618C42—472no—
619C42—944no—
620C42—944no—
621C42—944no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—472no—
626C23—942no—
627C23—942no—
628C23—942no—
629C23C2×D4×D4712yes—
630C23C2×D4×D4711yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—942no—
635Q8—942no—
636Q8—1882no—
637D4—1884no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—472no—
651C2×C4—472no—
652C2×C4—472no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—944no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—1888no—
664C2×C4—1888no—
665C2×C4—1882no—
666C2×C4—1882no—
667C2×C4—1882no—
668C2×C4—1882no—
669C2×C4C2×D4×D4712yes—
670C2×C4C2×D4×D4711yescharacteristic
671C2×C4#41×D4712yes—
672C2×C4#1309407112yes—
673C2×C4C24×D4711yescharacteristic
674C8—22no—
675C8—22no—
676C8—474no—
677C8—942no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—942no—
683C22—942no—
684C22—942no—
685C22—1884no—
686C22#1568977112yes—
687C22#1568992212yes—
688C22#1568993712yes—
689C22C22×D4×D4711yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—942no—
696C4—942no—
697C4—942no—
698C4—1882no—
699C4—1882no—
700C4—1882no—
701C4—1882no—
702C4#1568977112yes—
703C4C2×#41×D4711yescharacteristic
704C4C2×#1309407111yescharacteristic
705C2—42no—
706C2—1882no—
707C2#2025595614yesdirect product factor
708C2C2×#1568977111yescharacteristic
709C2C2×#1568992211yescharacteristic
710C2C2×#1568993711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#485C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
hypercenterC2×#485D47
hypocenterC47C2×#3352
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #20255956C2direct (N × H)
4. C2×#15689524C2semidirect
5. C2×#15689459C2semidirect
6. C2×#15689457C2semidirect
7. C2×#15689466C2semidirect
8. C2×#15689433C2semidirect
9. C2×#15689432C2semidirect
10. C2×#15689380C2semidirect
11. C2×#15689379C2semidirect
12. C2×#15689215C2semidirect
14. C2×#15689166C2semidirect
15. C2×#15689162C2semidirect
16. C2×C47×#485C2semidirect
43. #15689524C22semidirect
44. #15689466C22semidirect
45. #15689459C22semidirect
46. #15689457C22semidirect
47. #15689433C22semidirect
48. #15689432C22semidirect
49. #15689380C22semidirect
50. #15689379C22semidirect
51. #15689215C22semidirect
53. #15689166C22semidirect
54. #15689162C22semidirect
71. C47×#485C22semidirect
357. C2×#485D47semidirect
367. C2×C47#3352semidirect
402. #485C2×D47semidirect
432. C47C2×#3352semidirect
707. C2#20255956direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898152
C2×#156898122
#202559562
C2×#156895242
C2×#156894592
C2×#156894572
C2×#156894662
C2×#156894332
C2×#156894322
C2×#156893802
C2×#156893792
C2×#156892152
C2×#156891982
C2×#156891662
C2×#156891622
C2×C47×#4852
C2×#335247