Finite Group Databasebeta

← C2×#20255917 #27094904

Subgroups — C2×#20255917 #27094904

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×#15689847C211yesmaximal, characteristic
2C2×#15689811C211yesmaximal, characteristic
3#20255917C2116yesmaximal, direct product factor
4C2×#15689460C211yesmaximal, characteristic, complemented
5C2×#15689467C211yesmaximal, characteristic, complemented
6C2×#15689467C211yesmaximal, characteristic, complemented
7C2×#15689466C211yesmaximal, characteristic, complemented
8C2×#15689427C211yesmaximal, characteristic, complemented
9C2×#15689415C211yesmaximal, characteristic, complemented
10C2×#15689382C211yesmaximal, characteristic, complemented
11C2×#15689365C211yesmaximal, characteristic, complemented
12C2×#15689231C211yesmaximal, characteristic, complemented
13C2×#15689196C211yesmaximal, characteristic
14C2×#15689164C211yesmaximal, characteristic, complemented
15C2×#15689158C211yesmaximal, characteristic, complemented
16C2×C47×#501C211yesmaximal, characteristic, complemented
17C22×Dic188C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20#15689847—24no—
21#15689847C2218yes—
22#15689811—24no—
23#15689811C2218yes—
24C2×#13094019—21no—
25C2×#13094019—21no—
26C2×#13094019—21no—
27C2×#13094015—21no—
28C2×#13094013—21no—
29C2×#13094009—21no—
30C2×#13094004C2211yescharacteristic
31C2×#13094004C2211yescharacteristic
32C2×#13094004C2211yescharacteristic
33C2×#13094004C2211yescharacteristic
34C2×Q8×Dic47—21no—
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×Dic94C2211yescharacteristic
37C2×C4×D188C2211yescharacteristic
38C2×#13093982—21no—
39C2×#13093982C2211yescharacteristic
40C2×#13093982C2211yescharacteristic
41C2×#13093982C2211yescharacteristic
42C2×C4⋊C4×D47C2211yescharacteristic
43#15689467C2218yescomplemented
44#15689467C2218yescomplemented
45#15689466C2218yescomplemented
46#15689460C2218yescomplemented
47#15689427C2218yescomplemented
48#15689415C2218yescomplemented
49#15689382C2218yescomplemented
50#15689365C2218yescomplemented
51#15689231C2218yescomplemented
52#15689196C2218yes—
53#15689164C2218yescomplemented
54#15689158C2218yescomplemented
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×C4⋊(C47⋊C8)C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093949C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093947C2211yescharacteristic
66C2×#13093947C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×(C2×D47)⋊C8C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×#125×C47C2211yescharacteristic
71C47×#501C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×#106×C47C2211yescharacteristic
75C2×#106×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94C2311yescharacteristic
78C22×Dic94C2311yescharacteristic
79C22×D188D411yescharacteristic
80C22×C4×D47—21no—
81C22×C4×D47C2311yescharacteristic
82C22×C4×D47C2311yescharacteristic
83C2×Dic188—24no—
84C2×Dic188C2314yes—
85C2×#10625324—24no—
86C2×#10625324C2314yes—
87C22×C47⋊C8C2311yescharacteristic
88C22×C47⋊C8C2311yescharacteristic
89C2×C8×D47—24no—
90C2×C8×D47C2314yes—
91#13094019—28no—
92#13094019—28no—
93#13094019—28no—
94#13094015—28no—
95#13094013—28no—
96#13094009—28no—
97#13094004—22no—
98#13094004—22no—
99#13094004—22no—
100#13094004—22no—
101#13094004C2314yes—
102#13094004C2314yes—
103#13094004C2314yes—
104#13094004C2314yes—
105Q8×Dic47—28no—
106C4×Dic94—22no—
107C4×Dic94—22no—
108C4×Dic94C2314yes—
109C4×Dic94C2314yes—
110C4×D188D414yes—
111C4×D188C2314yes—
112#13093982—22no—
113#13093982—22no—
114#13093982—22no—
115#13093982—28no—
116#13093982C2314yes—
117#13093982C2314yes—
118#13093982C2314yes—
119C2×C4⋊Dic47—21no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47D411yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C4⋊C4×D47—22no—
130C4⋊C4×D47C2314yes—
131C2×(C2×D47)⋊C4—21no—
132C2×(C2×D47)⋊C4—21no—
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4D411yescharacteristic
139C2×(C2×D47)⋊C4D411yescharacteristic
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47—21no—
145#13093957C2314yes—
146#13093957C2314yes—
147#13093957C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
150C4⋊(C47⋊C8)C2314yes—
151#13093949C2314yes—
152#13093949C2314yes—
153#13093947C2314yes—
154#13093947C2314yes—
155#13093947C2314yes—
156#13093947C2314yes—
157(C2×D47)⋊C8C2314yes—
158(C2×D47)⋊C8C2314yes—
159C22×Q8×C47—21no—
160C22×C8×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162C4⋊Q8×C47—22no—
163C4⋊Q8×C47C2314yes—
164#125×C47—22no—
165#125×C47C2314yes—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C42×C47C2311yescharacteristic
174#107×C47C2314yes—
175#107×C47C2314yes—
176#106×C47C2314yes—
177#106×C47C2314yes—
178#97×C47C2314yes—
179C23×D47C2×D411yescharacteristic
180C23×D47C2×D411yescharacteristic
181C2×Q8×C47—24no—
182C2×Q8×C47—44no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2411yescharacteristic
190C22×Dic47—21no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47C2×D411yescharacteristic
195C22×Dic47C2×D411yescharacteristic
196C2×D188—42no—
197C2×D188C2×D414yes—
198C2×C4×D47—22no—
199C2×C4×D47—22no—
200C2×C4×D47—22no—
201C2×C4×D47—22no—
202C2×C4×D47—24no—
203C2×C4×D47—44no—
204C2×C4×D47C2×D412yes—
205C2×C4×D47C2×D412yes—
206C2×C4×D47C2412yes—
207C2×C4×D47C2412yes—
208C2×Dic94—22no—
209C2×Dic94—22no—
210C2×Dic94—22no—
211C2×Dic94—22no—
212C2×Dic94—21no—
213C2×Dic94—21no—
214C2×Dic94C2412yes—
215C2×Dic94C2412yes—
216C2×C8×C47—22no—
217C2×C8×C47#4114yes—
218C2×C8×C47C2412yes—
219C2×C8×C47C2412yes—
220C4⋊C4×C47—24no—
221C4⋊C4×C47—24no—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47C2412yes—
228C4⋊C4×C47C2412yes—
229C4⋊C4×C47C2412yes—
230C4⋊C4×C47C2412yes—
231C42×C47C2×D412yes—
232C42×C47C2412yes—
233(C2×D47)⋊C4—24no—
234(C2×D47)⋊C4—24no—
235(C2×D47)⋊C4—24no—
236(C2×D47)⋊C4—24no—
237(C2×D47)⋊C4—24no—
238(C2×D47)⋊C4—24no—
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4C2×D414yes—
241(C2×D47)⋊C4C2×D414yes—
242C4⋊Dic47—21no—
243C4⋊Dic47—21no—
244C4⋊Dic47—24no—
245C4⋊Dic47—24no—
246C4⋊Dic47—24no—
247C4⋊Dic47—24no—
248C4⋊Dic47C2×D414yes—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254C4×Dic47—24no—
255C4×Dic47—24no—
256C4×Dic47—24no—
257C4×Dic47—24no—
258C4×Dic47—24no—
259C2×C47⋊C8—22no—
260C2×C47⋊C8—22no—
261C2×C47⋊C8C2412yes—
262C2×C47⋊C8C2412yes—
263Dic188—28no—
264#10625324—28no—
265C8×D47—28no—
266C23×C47C22×D411yescharacteristic
267C22×D47—22no—
268C22×D47—22no—
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—22no—
273C22×D47C22×D412yes—
274C22×D47C22×D412yes—
275Q8×C47—48no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—42no—
285C2×C4×C47—42no—
286C2×C4×C47C22×D412yes—
287C2×C4×C47C22×D412yes—
288C2×C4×C47C22×D411yescharacteristic
289C2×C4×C47C2×#4112yes—
290C2×C4×C472−1+412yes—
291C2×C4×C47C2511yescharacteristic
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—42no—
299C2×Dic47—42no—
300C2×Dic47—42no—
301C2×Dic47—42no—
302C2×Dic47C22×D412yes—
303C2×Dic47C22×D412yes—
304D188—44no—
305C4×D47—24no—
306C4×D47—24no—
307C4×D47—22no—
308C4×D47—22no—
309C4×D47—22no—
310C4×D47—22no—
311C4×D47—48no—
312Dic94—22no—
313Dic94—22no—
314Dic94—22no—
315Dic94—22no—
316Dic94—42no—
317Dic94—42no—
318C8×C47—22no—
319C8×C47C2×#4114yes—
320C47⋊C8—22no—
321C47⋊C8—22no—
322C2×#3349—471nomaximal, Sylow
323C22×C47#54712yes—
324C22×C47#57512yes—
325C22×C47#57812yes—
326C22×C47C23×D411yescharacteristic
327C2×D47—22no—
328C2×D47—22no—
329C2×D47—22no—
330C2×D47—22no—
331C2×D47—22no—
332C2×D47—22no—
333C2×D47—44no—
334C2×D47—44no—
335C4×C47—22no—
336C4×C47—22no—
337C4×C47—42no—
338C4×C47—42no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47#54712yes—
342C4×C47C22×#4111yescharacteristic
343C4×C47C2×2−1+411yescharacteristic
344Dic47—22no—
345Dic47—22no—
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349Dic47—42no—
350C2×#556—471no—
351C2×#552—471no—
352#3349—4716no—
353C2×#501D4711yescharacteristic, complemented
354C2×#484—471no—
355C2×#485—471no—
356C2×#485—471no—
357C2×#485—471no—
358C2×#479—471no—
359C2×#477—471no—
360C2×#470—471no—
361C2×#467—471no—
362C2×#441—471no—
363C2×#435—471no—
364C2×#428—471no—
365C2×#427—471no—
366C2×C47#334914yescomplemented
367C2×C47C2×#54711yescharacteristic
368C2×C47C2×#57511yescharacteristic
369C2×C47C2×#57811yescharacteristic
370D47—42no—
371D47—42no—
372C22×Q16—471no—
373C22×M16—471no—
374C23×C8—471no—
375#556—478no—
376#556—944no—
377#552—478no—
378#552—944no—
379C2×C4⋊Q8C2×D4711yescharacteristic
380C2×#126—941no—
381C2×#126—941no—
382C2×#126—941no—
383C2×#125—941no—
384C2×#125C2×D4711yescharacteristic
385C2×#124—941no—
386C2×#123—941no—
387C2×C22⋊Q8—471no—
388C2×C22⋊Q8—471no—
389C2×C22⋊Q8—471no—
390C2×C22⋊Q8—471no—
391C2×C4×Q8—471no—
392C2×C4×Q8—471no—
393C2×C4×Q8—941no—
394C2×C4×D4—471no—
395C2×#117—471no—
396C2×#117—471no—
397C2×#117—471no—
398C2×#117—941no—
399C22×C4⋊C4—471no—
400#501C2×D4718yescomplemented
401#485—478no—
402#485—478no—
403#485—478no—
404#484—478no—
405#479—478no—
406#477—478no—
407#470—478no—
408#467—478no—
409#441—478no—
410#435—478no—
411#428—478no—
412#427—478no—
413C2×#107—471no—
414C2×#107—471no—
415C2×#107—471no—
416C2×#107C2×D4711yescharacteristic
417C2×#107C2×D4711yescharacteristic
418C2×#106—471no—
419C2×#106—471no—
420C2×#106C2×D4711yescharacteristic
421C2×#106C2×D4711yescharacteristic
422C2×C4⋊C8—471no—
423C2×#103—471no—
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×C22⋊C8—471no—
430C2×C22⋊C8—471no—
431C2×#97C2×D4711yescharacteristic
432C47C2×#334911yescharacteristic, complemented, Sylow
433C22×Q8—21no—
434C22×Q8—471no—
435C22×Q8—471no—
436C22×D4—471no—
437C23×C4—471no—
438C23×C4—471no—
439C23×C4—941no—
440C2×Q16—474no—
441C2×Q16—944no—
442C2×M16—474no—
443C2×M16—944no—
444C22×C8—471no—
445C22×C8—471no—
446C22×C8—474no—
447C22×C8—944no—
448C22×C8C22×D4711yescharacteristic
449C22×C8C22×D4711yescharacteristic
450C4⋊Q8—22no—
451C4⋊Q8C22×D4714yes—
452#126—948no—
453#126—948no—
454#126—948no—
455#125—22no—
456#125—948no—
457#125C22×D4714yes—
458#124—948no—
459#123—948no—
460C22⋊Q8—474no—
461C22⋊Q8—474no—
462C22⋊Q8—474no—
463C22⋊Q8—474no—
464C22⋊Q8—942no—
465C22⋊Q8—942no—
466C22⋊Q8—942no—
467C22⋊Q8—942no—
468C4×Q8—474no—
469C4×Q8—474no—
470C4×Q8—948no—
471C4×Q8—942no—
472C4×Q8—942no—
473C4×D4—474no—
474C4×D4—474no—
475#117—474no—
476#117—474no—
477#117—474no—
478#117—948no—
479#117—942no—
480#117—942no—
481#117—942no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—474no—
489C2×C4⋊C4—942no—
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⋊C4C22×D4711yescharacteristic
498C2×C4⋊C4C22×D4711yescharacteristic
499C2×C4⋊C4C22×D4711yescharacteristic
500C2×C4⋊C4C22×D4711yescharacteristic
501C2×C22⋊C4—471no—
502C2×C22⋊C4—471no—
503C2×C22⋊C4—941no—
504C2×C22⋊C4—941no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—941no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C42—941no—
511C2×C42—941no—
512C2×C42—941no—
513C2×C42—941no—
514C2×C42—941no—
515C2×C42C22×D4711yescharacteristic
516#107—474no—
517#107—474no—
518#107—474no—
519#107C22×D4714yes—
520#107C22×D4714yes—
521#106—474no—
522#106—474no—
523#106C22×D4714yes—
524#106C22×D4714yes—
525C4⋊C8—474no—
526#103—474no—
527#103—474no—
528#103—474no—
529#103—474no—
530#103—474no—
531#103—474no—
532C22⋊C8—474no—
533C22⋊C8—474no—
534#97C22×D4714yes—
535C24—471no—
536C24—471no—
537C2×Q8—24no—
538C2×Q8—44no—
539C2×Q8—472no—
540C2×Q8—472no—
541C2×Q8—941no—
542C2×Q8—941no—
543C2×Q8—942no—
544C2×Q8—942no—
545C2×Q8—942no—
546C2×Q8—942no—
547C2×D4—474no—
548C2×D4—1882no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—471no—
554C22×C4—471no—
555C22×C4—472no—
556C22×C4—472no—
557C22×C4—472no—
558C22×C4—472no—
559C22×C4—944no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—1884no—
569C22×C4D4×D4711yescharacteristic
570C22×C4D4×D4711yescharacteristic
571C22×C4C23×D4711yescharacteristic
572Q16—948no—
573M16—948no—
574C2×C8—22no—
575C2×C8—472no—
576C2×C8—472no—
577C2×C8—942no—
578C2×C8—942no—
579C2×C8—948no—
580C2×C8#1062535414yes—
581C2×C8C23×D4712yes—
582C2×C8C23×D4712yes—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—474no—
591C4⋊C4—472no—
592C4⋊C4—472no—
593C4⋊C4—944no—
594C4⋊C4—944no—
595C4⋊C4—944no—
596C4⋊C4—944no—
597C4⋊C4—944no—
598C4⋊C4—944no—
599C4⋊C4—944no—
600C4⋊C4—941no—
601C4⋊C4—941no—
602C4⋊C4C23×D4712yes—
603C4⋊C4C23×D4712yes—
604C4⋊C4C23×D4712yes—
605C4⋊C4C23×D4712yes—
606C22⋊C4—474no—
607C22⋊C4—474no—
608C22⋊C4—944no—
609C22⋊C4—944no—
610C22⋊C4—944no—
611C22⋊C4—944no—
612C22⋊C4—944no—
613C22⋊C4—944no—
614C22⋊C4—944no—
615C42—944no—
616C42—944no—
617C42—944no—
618C42—944no—
619C42—944no—
620C42D4×D4712yes—
621C42C23×D4712yes—
622C23—472no—
623C23—472no—
624C23—942no—
625C23—942no—
626C23—942no—
627C23—942no—
628C23—942no—
629C23—942no—
630C23C2×D4×D4711yescharacteristic
631Q8—48no—
632Q8—942no—
633Q8—942no—
634Q8—942no—
635Q8—942no—
636Q8—1882no—
637Q8—1882no—
638D4—1884no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—472no—
650C2×C4—472no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—944no—
654C2×C4—944no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—1888no—
664C2×C4—1882no—
665C2×C4—1882no—
666C2×C4—1882no—
667C2×C4—1882no—
668C2×C4C2×D4×D4712yes—
669C2×C4C2×D4×D4712yes—
670C2×C4C2×D4×D4711yescharacteristic
671C2×C4C2×#1062535412yes—
672C2×C4#1309407212yes—
673C2×C4C24×D4711yescharacteristic
674C8—22no—
675C8—942no—
676C8—942no—
677C8C2×#1062535414yes—
678C22—942no—
679C22—942no—
680C22—942no—
681C22—942no—
682C22—942no—
683C22—942no—
684C22—1884no—
685C22—1884no—
686C22#1568977612yes—
687C22#1568991912yes—
688C22#1568993912yes—
689C22C22×D4×D4711yescharacteristic
690C4—22no—
691C4—22no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—942no—
697C4—942no—
698C4—1882no—
699C4—1882no—
700C4—1882no—
701C4—1882no—
702C4#1568977612yes—
703C4C22×#1062535411yescharacteristic
704C4C2×#1309407211yescharacteristic
705C2—1882no—
706C2—1882no—
707C2#2025591714yesdirect product factor
708C2C2×#1568977611yescharacteristic
709C2C2×#1568991911yescharacteristic
710C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#501C2
socleC23×C47C22×D4
prime radicalC22×D188D4
hypercenterC2×#501D47
hypocenterC47C2×#3349
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. #20255917C2direct (N × H)
4. C2×#15689460C2semidirect
5. C2×#15689467C2semidirect
6. C2×#15689467C2semidirect
7. C2×#15689466C2semidirect
8. C2×#15689427C2semidirect
9. C2×#15689415C2semidirect
10. C2×#15689382C2semidirect
11. C2×#15689365C2semidirect
12. C2×#15689231C2semidirect
14. C2×#15689164C2semidirect
15. C2×#15689158C2semidirect
16. C2×C47×#501C2semidirect
43. #15689467C22semidirect
44. #15689467C22semidirect
45. #15689466C22semidirect
46. #15689460C22semidirect
47. #15689427C22semidirect
48. #15689415C22semidirect
49. #15689382C22semidirect
50. #15689365C22semidirect
51. #15689231C22semidirect
53. #15689164C22semidirect
54. #15689158C22semidirect
71. C47×#501C22semidirect
353. C2×#501D47semidirect
366. C2×C47#3349semidirect
400. #501C2×D47semidirect
432. C47C2×#3349semidirect
707. C2#20255917direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898472
C2×#156898112
#202559172
C2×#156894602
C2×#156894672
C2×#156894662
C2×#156894272
C2×#156894152
C2×#156893822
C2×#156893652
C2×#156892312
C2×#156891962
C2×#156891642
C2×#156891582
C2×C47×#5012
C2×#334947