Finite Group Databasebeta

← C2×#20256312 #27096782

Subgroups — C2×#20256312 #27096782

Order 12032.

2006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689849C211yesmaximal, characteristic, complemented
2C2×#15689788C211yesmaximal, characteristic
3#20256312C2116yesmaximal, direct product factor
4C2×#15689531C211yesmaximal, characteristic, complemented
5C2×#15689529C211yesmaximal, characteristic, complemented
6C2×#15689527C211yesmaximal, characteristic, complemented
7C2×#15689416C211yesmaximal, characteristic, complemented
8C2×#15689406C211yesmaximal, characteristic, complemented
9C2×#15689426C211yesmaximal, characteristic
10C2×#15689424C211yesmaximal, characteristic
11C2×#15689402C211yesmaximal, characteristic
12C2×#15689252C211yesmaximal, characteristic, complemented
13C2×#15689226C211yesmaximal, characteristic
14C2×#15689221C211yesmaximal, characteristic
15C2×#15689208C211yesmaximal, characteristic
16C2×C47×#477C211yesmaximal, characteristic, complemented
17C22×Q8×D47—21no—
18C22×#10625336C2211yescharacteristic
19#15689849—24no—
20#15689849C2218yescomplemented
21#15689788—24no—
22#15689788C2218yes—
23C2×#13094023—21no—
24C2×#13094023C2211yescharacteristic
25C2×#13094023C2211yescharacteristic
26C2×#13094023C2211yescharacteristic
27C2×#13094016—21no—
28C2×#13094016C2211yescharacteristic
29C2×#13094015—21no—
30C2×#13094015C2211yescharacteristic
31C2×#13094002—21no—
32C2×#13094002—21no—
33C2×#13094000—21no—
34C2×Q8×Dic47C2211yescharacteristic
35C2×Q8×Dic47C2211yescharacteristic
36C2×C4×Dic94—21no—
37C2×C4×Dic94C2211yescharacteristic
38C2×C4×D188C2211yescharacteristic
39C2×#13093986C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41#15689531C2218yescomplemented
42#15689529C2218yescomplemented
43#15689527C2218yescomplemented
44#15689426C2218yes—
45#15689424C2218yes—
46#15689416C2218yescomplemented
47#15689406C2218yescomplemented
48#15689402C2218yes—
49#15689252C2218yescomplemented
50#15689226C2218yes—
51#15689221C2218yes—
52#15689208C2218yes—
53C2×#13093958C2211yescharacteristic
54C2×#13093957C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093956C2211yescharacteristic
58C2×#13093955C2211yescharacteristic
59C2×#13093955C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093946C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×#13093935C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×C4⋊Q8×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C47×#477C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#107×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94—21no—
80C22×Dic94D411yescharacteristic
81C2×Q8×D47—28no—
82C2×Q8×D47—48no—
83C22×D188C2311yescharacteristic
84C22×C4×D47—21no—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C2×#10625336Q818yescomplemented
88C2×#10625336C2314yes—
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2311yescharacteristic
91#13094023—28no—
92#13094023—22no—
93#13094023—22no—
94#13094023—22no—
95#13094023C2314yes—
96#13094023C2314yes—
97#13094023C2314yes—
98#13094016—22no—
99#13094016—28no—
100#13094016C2314yes—
101#13094015—28no—
102#13094015—22no—
103#13094015C2314yes—
104#13094002—28no—
105#13094002—28no—
106#13094000—28no—
107Q8×Dic47—22no—
108Q8×Dic47—22no—
109Q8×Dic47C2314yes—
110Q8×Dic47C2314yes—
111C4×Dic94—28no—
112C4×Dic94D414yes—
113C4×Dic94C2314yes—
114C4×D188—22no—
115C4×D188C2314yes—
116#13093986—22no—
117#13093986—22no—
118#13093986C2314yes—
119#13093986C2314yes—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47D411yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4—21no—
133C2×Dic47⋊C4D411yescharacteristic
134C2×Dic47⋊C4D411yescharacteristic
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47C2311yescharacteristic
141C2×C4×Dic47C2311yescharacteristic
142#13093958C2314yes—
143#13093957C2314yes—
144#13093957C2314yes—
145#13093957C2314yes—
146#13093956C2314yes—
147#13093955C2314yes—
148#13093955C2314yes—
149Dic47⋊C8C2314yes—
150Dic47⋊C8C2314yes—
151#13093948C2314yes—
152#13093946C2314yes—
153#13093946C2314yes—
154#13093944C2314yes—
155#13093935C2314yes—
156#13093934C2314yes—
157C8×Dic47C2314yes—
158C22×Q8×C47—21no—
159C22×Q8×C47C2311yescharacteristic
160C22×C8×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162C4⋊Q8×C47—22no—
163C4⋊Q8×C47C2314yes—
164C4×Q8×C47—22no—
165C4×Q8×C47C2314yes—
166C2×C4⋊C4×C47—21no—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47C2311yescharacteristic
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C42×C47—21no—
172C2×C42×C47C2311yescharacteristic
173#107×C47C2314yes—
174#107×C47C2314yes—
175C4⋊C8×C47C2314yes—
176#103×C47C2314yes—
177#103×C47C2314yes—
178C23×D47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47—24no—
181C2×Q8×C47—22no—
182C2×Q8×C47—44no—
183C2×Q8×C47C2×Q814yescomplemented
184C2×Q8×C47C2412yes—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2411yescharacteristic
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47C2×D411yescharacteristic
196C22×Dic47C2×D411yescharacteristic
197C22×Dic47C2×D411yescharacteristic
198C22×Dic47C2×D411yescharacteristic
199Q8×D47—432no—
200C2×D188—21no—
201C2×D188—22no—
202C2×D188C2×Q814yes—
203C2×D188C2412yes—
204C2×C4×D47—24no—
205C2×C4×D47—24no—
206C2×C4×D47—24no—
207C2×C4×D47—44no—
208C2×C4×D47—44no—
209C2×C4×D47—44no—
210C2×Dic94—24no—
211C2×Dic94—24no—
212C2×Dic94—24no—
213C2×Dic94—24no—
214C2×Dic94—44no—
215C2×Dic94—44no—
216C2×Dic94—44no—
217C2×Dic94C2×D414yes—
218C2×C8×C47—22no—
219C2×C8×C47—22no—
220C2×C8×C47C2412yes—
221C2×C8×C47C2412yes—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—24no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47—21no—
227C4⋊C4×C47C2412yes—
228C4⋊C4×C47C2412yes—
229C4⋊C4×C47C2412yes—
230C42×C47—24no—
231C42×C47C2×D412yes—
232C42×C47C2412yes—
233#10625336C2×Q8116yescomplemented
234(C2×D47)⋊C4—24no—
235(C2×D47)⋊C4—24no—
236(C2×D47)⋊C4—24no—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—24no—
241C4⋊Dic47—24no—
242C4⋊Dic47—24no—
243C4⋊Dic47C2×D414yes—
244C4⋊Dic47C2412yes—
245C4⋊Dic47C2412yes—
246C4⋊Dic47C2412yes—
247Dic47⋊C4—24no—
248Dic47⋊C4—24no—
249Dic47⋊C4—24no—
250Dic47⋊C4—24no—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4C2×D414yes—
254Dic47⋊C4C2×D414yes—
255C4×Dic47—24no—
256C4×Dic47—24no—
257C4×Dic47C2×D412yes—
258C4×Dic47C2×D412yes—
259C4×Dic47C2412yes—
260C4×Dic47C2412yes—
261C2×C47⋊C8—22no—
262C2×C47⋊C8C2×Q814yescomplemented
263C2×C47⋊C8C2412yes—
264C2×C47⋊C8C2412yes—
265C23×C47C22×D411yescharacteristic
266C22×D47—24no—
267C22×D47—22no—
268C22×D47—42no—
269C22×D47—42no—
270Q8×C47—24no—
271Q8×C47—22no—
272Q8×C47—48no—
273Q8×C47C22×Q814yescomplemented
274C2×C4×C47—24no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—22no—
281C2×C4×C47—42no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47C22×D412yes—
285C2×C4×C47C22×D412yes—
286C2×C4×C47C22×D411yescharacteristic
287C2×C4×C47C22×Q812yes—
288C2×C4×C472−1+412yes—
289C2×C4×C47C2511yescharacteristic
290C2×Dic47—22no—
291C2×Dic47—22no—
292C2×Dic47—22no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47—42no—
299C2×Dic47AGL(1,ℤ/8)14yes—
300C2×Dic47C22×D412yes—
301C2×Dic47C22×D412yes—
302C2×Dic47C22×D412yes—
303C2×Dic47C22×D412yes—
304D188—24no—
305D188—22no—
306D188C22×Q814yes—
307C4×D47—48no—
308C4×D47—48no—
309C4×D47—48no—
310Dic94—28no—
311Dic94—48no—
312Dic94—48no—
313Dic94—48no—
314C8×C47—22no—
315C8×C47—22no—
316C47⋊C8—22no—
317C47⋊C8C22×Q814yescomplemented
318C2×#3386—471nomaximal, Sylow
319C22×C47D4×Q812yes—
320C22×C47C2×AGL(1,ℤ/8)12yes—
321C22×C47#57812yes—
322C22×C47C23×D411yescharacteristic
323C2×D47—24no—
324C2×D47—48no—
325C2×D47—42no—
326C2×D47—42no—
327C4×C47—24no—
328C4×C47—22no—
329C4×C47—22no—
330C4×C47—42no—
331C4×C47—42no—
332C4×C47—42no—
333C4×C47D4×Q812yes—
334C4×C47C23×Q811yescharacteristic
335C4×C47C2×2−1+411yescharacteristic
336Dic47—22no—
337Dic47—22no—
338Dic47—22no—
339Dic47—42no—
340Dic47—42no—
341Dic47—42no—
342Dic47C2×AGL(1,ℤ/8)14yes—
343C2×#557—471no—
344C2×D4×Q8—471no—
345#3386—4716no—
346C2×#501—471no—
347C2×#501—471no—
348C2×#500—471no—
349C2×#477—471no—
350C2×#477D4711yescharacteristic, complemented
351C2×#475—471no—
352C2×#478—471no—
353C2×#478—471no—
354C2×#474—471no—
355C2×#446—471no—
356C2×#440—471no—
357C2×#440—471no—
358C2×C4×SD16—471no—
359C2×C47#338614yescomplemented
360C2×C47C2×D4×Q811yescharacteristic
361C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
362C2×C47C2×#57811yescharacteristic
363D47—44no—
364C23×Q8—941no—
365C22×SD16—471no—
366#557—478no—
367#557—944no—
368D4×Q8—478no—
369D4×Q8—944no—
370C2×C4⋊Q8—471no—
371C2×C4⋊Q8—471no—
372C2×C4⋊Q8—471no—
373C2×C4⋊Q8—941no—
374C2×C4⋊Q8C2×D4711yescharacteristic
375C2×#125—471no—
376C2×#125—471no—
377C2×#125—941no—
378C2×#125—941no—
379C2×C22⋊Q8—941no—
380C2×C22⋊Q8—941no—
381C2×C22⋊Q8—941no—
382C2×C4×Q8—471no—
383C2×C4×Q8—471no—
384C2×C4×Q8—471no—
385C2×C4×Q8—941no—
386C2×C4×Q8C2×D4711yescharacteristic
387C2×C4×D4—471no—
388C2×C4×D4—471no—
389C2×C4×D4—471no—
390#501—478no—
391#501—478no—
392#500—478no—
393#478—478no—
394#478—478no—
395#477—478no—
396#477C2×D4718yescomplemented
397#475—478no—
398#474—478no—
399#446—478no—
400#440—478no—
401#440—478no—
402C4×SD16—478no—
403C2×#107—471no—
404C2×#107—471no—
405C2×#107—471no—
406C2×#107—471no—
407C2×#107C2×D4711yescharacteristic
408C2×#107C2×D4711yescharacteristic
409C2×#106—471no—
410C2×#106—471no—
411C2×#106—471no—
412C2×C4⋊C8—471no—
413C2×C4⋊C8—471no—
414C2×C4⋊C8C2×D4711yescharacteristic
415C2×#103—471no—
416C2×#103C2×D4711yescharacteristic
417C2×#103C2×D4711yescharacteristic
418C2×#102—471no—
419C2×#102—471no—
420C2×#102—471no—
421C2×#97—471no—
422C2×#97—471no—
423C2×C4×C8—471no—
424C47C2×#338611yescharacteristic, complemented, Sylow
425C22×Q8—21no—
426C22×Q8—471no—
427C22×Q8—941no—
428C22×Q8—941no—
429C22×Q8—941no—
430C22×Q8—948no—
431C22×Q8—1888no—
432C22×Q8C22×D4711yescharacteristic
433C22×D4—471no—
434C23×C4—941no—
435C23×C4—941no—
436C23×C4—941no—
437C2×SD16—478no—
438C2×SD16—474no—
439C22×C8—471no—
440C22×C8—471no—
441C22×C8C22×D4711yescharacteristic
442C22×C8C22×D4711yescharacteristic
443C4⋊Q8—22no—
444C4⋊Q8—474no—
445C4⋊Q8—474no—
446C4⋊Q8—474no—
447C4⋊Q8—942no—
448C4⋊Q8—942no—
449C4⋊Q8—942no—
450C4⋊Q8—948no—
451C4⋊Q8C22×D4714yes—
452#125—474no—
453#125—474no—
454#125—948no—
455#125—942no—
456#125—948no—
457#125—942no—
458C22⋊Q8—948no—
459C22⋊Q8—948no—
460C22⋊Q8—948no—
461C4×Q8—22no—
462C4×Q8—474no—
463C4×Q8—474no—
464C4×Q8—474no—
465C4×Q8—474no—
466C4×Q8—948no—
467C4×Q8—942no—
468C4×Q8—942no—
469C4×Q8C22×D4714yes—
470C4×D4—474no—
471C4×D4—474no—
472C4×D4—474no—
473C4×D4—942no—
474C4×D4—942no—
475C4×D4—942no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—471no—
479C2×C4⋊C4—471no—
480C2×C4⋊C4—471no—
481C2×C4⋊C4—471no—
482C2×C4⋊C4—471no—
483C2×C4⋊C4—471no—
484C2×C4⋊C4—941no—
485C2×C4⋊C4—941no—
486C2×C4⋊C4—941no—
487C2×C4⋊C4—941no—
488C2×C4⋊C4—941no—
489C2×C4⋊C4—941no—
490C2×C4⋊C4—941no—
491C2×C4⋊C4—941no—
492C2×C4⋊C4—941no—
493C2×C4⋊C4C22×D4711yescharacteristic
494C2×C4⋊C4C22×D4711yescharacteristic
495C2×C4⋊C4C22×D4711yescharacteristic
496C2×C22⋊C4—941no—
497C2×C22⋊C4—941no—
498C2×C22⋊C4—941no—
499C2×C42—21no—
500C2×C42—471no—
501C2×C42—471no—
502C2×C42—941no—
503C2×C42—941no—
504C2×C42C22×D4711yescharacteristic
505#107—474no—
506#107—474no—
507#107—474no—
508#107—474no—
509#107C22×D4714yes—
510#107C22×D4714yes—
511#106—474no—
512#106—474no—
513#106—474no—
514C4⋊C8—474no—
515C4⋊C8—474no—
516C4⋊C8C22×D4714yes—
517#103—474no—
518#103C22×D4714yes—
519#103C22×D4714yes—
520#102—474no—
521#102—474no—
522#102—474no—
523#97—474no—
524#97—474no—
525C4×C8—474no—
526C24—941no—
527C2×Q8—21no—
528C2×Q8—24no—
529C2×Q8—22no—
530C2×Q8—44no—
531C2×Q8—474no—
532C2×Q8—944no—
533C2×Q8—944no—
534C2×Q8—944no—
535C2×Q8—944no—
536C2×Q8—1884no—
537C2×Q8—1884no—
538C2×Q8—1884no—
539C2×Q8—18832no—
540C2×Q8Q8×D4714yescomplemented
541C2×Q8C23×D4712yes—
542C2×D4—474no—
543C2×D4—472no—
544C2×D4—941no—
545C2×D4—942no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—471no—
551C22×C4—471no—
552C22×C4—471no—
553C22×C4—471no—
554C22×C4—944no—
555C22×C4—944no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4—941no—
559C22×C4—944no—
560C22×C4—1884no—
561C22×C4—1884no—
562C22×C4—1884no—
563C22×C4D4×D4711yescharacteristic
564C22×C4D4×D4711yescharacteristic
565C22×C4C23×D4711yescharacteristic
566SD16—4716no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—474no—
570C2×C8—472no—
571C2×C8—472no—
572C2×C8—942no—
573C2×C8C23×D4712yes—
574C2×C8C23×D4712yes—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—474no—
581C4⋊C4—474no—
582C4⋊C4—474no—
583C4⋊C4—472no—
584C4⋊C4—472no—
585C4⋊C4—472no—
586C4⋊C4—944no—
587C4⋊C4—944no—
588C4⋊C4—944no—
589C4⋊C4—944no—
590C4⋊C4—944no—
591C4⋊C4—944no—
592C4⋊C4—944no—
593C4⋊C4—944no—
594C4⋊C4—944no—
595C4⋊C4—941no—
596C4⋊C4—941no—
597C4⋊C4—941no—
598C4⋊C4C23×D4712yes—
599C4⋊C4C23×D4712yes—
600C4⋊C4C23×D4712yes—
601C22⋊C4—944no—
602C22⋊C4—944no—
603C22⋊C4—944no—
604C42—24no—
605C42—472no—
606C42—472no—
607C42—472no—
608C42—472no—
609C42—944no—
610C42—944no—
611C42D4×D4712yes—
612C42C23×D4712yes—
613C23—944no—
614C23—942no—
615C23—1882no—
616C23—1882no—
617C23C2×D4×D4711yescharacteristic
618Q8—24no—
619Q8—22no—
620Q8—48no—
621Q8—948no—
622Q8—1888no—
623Q8—1888no—
624Q8—1888no—
625Q8C2×Q8×D4714yescomplemented
626D4—474no—
627D4—944no—
628D4—942no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—474no—
640C2×C4—472no—
641C2×C4—472no—
642C2×C4—472no—
643C2×C4—472no—
644C2×C4—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—942no—
648C2×C4—942no—
649C2×C4—942no—
650C2×C4—1888no—
651C2×C4—1888no—
652C2×C4—1888no—
653C2×C4—1882no—
654C2×C4—1882no—
655C2×C4—1882no—
656C2×C4C2×D4×D4712yes—
657C2×C4C2×D4×D4712yes—
658C2×C4C2×D4×D4711yescharacteristic
659C2×C4C2×Q8×D4712yes—
660C2×C4#1309407112yes—
661C2×C4C24×D4711yescharacteristic
662C8—22no—
663C8—22no—
664C8—474no—
665C8—942no—
666C22—944no—
667C22—1888no—
668C22—1882no—
669C22—1882no—
670C22#1568978612yes—
671C22AGL(1,ℤ/8)×D4712yes—
672C22#1568993612yes—
673C22C22×D4×D4711yescharacteristic
674C4—22no—
675C4—24no—
676C4—22no—
677C4—42no—
678C4—42no—
679C4—42no—
680C4—474no—
681C4—942no—
682C4—942no—
683C4—942no—
684C4—1882no—
685C4—1882no—
686C4—1882no—
687C4#1568978612yes—
688C4C22×Q8×D4711yescharacteristic
689C4C2×#1309407111yescharacteristic
690C2—1884no—
691C2#2025631214yesdirect product factor
692C2C2×#1568978611yescharacteristic
693C2C2×AGL(1,ℤ/8)×D4711yescharacteristic
694C2C2×#1568993611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#477C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenterC2×#477D47
hypocenterC47C2×#3386
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#15689849C2semidirect
3. #20256312C2direct (N × H)
4. C2×#15689531C2semidirect
5. C2×#15689529C2semidirect
6. C2×#15689527C2semidirect
7. C2×#15689416C2semidirect
8. C2×#15689406C2semidirect
12. C2×#15689252C2semidirect
16. C2×C47×#477C2semidirect
20. #15689849C22semidirect
41. #15689531C22semidirect
42. #15689529C22semidirect
43. #15689527C22semidirect
46. #15689416C22semidirect
47. #15689406C22semidirect
49. #15689252C22semidirect
71. C47×#477C22semidirect
87. C2×#10625336Q8semidirect
183. C2×Q8×C47C2×Q8semidirect
233. #10625336C2×Q8semidirect
262. C2×C47⋊C8C2×Q8semidirect
273. Q8×C47C22×Q8semidirect
317. C47⋊C8C22×Q8semidirect
350. C2×#477D47semidirect
359. C2×C47#3386semidirect
396. #477C2×D47semidirect
424. C47C2×#3386semidirect
540. C2×Q8Q8×D47semidirect
625. Q8C2×Q8×D47semidirect
691. C2#20256312direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898492
C2×#156897882
#202563122
C2×#156895312
C2×#156895292
C2×#156895272
C2×#156894162
C2×#156894062
C2×#156894262
C2×#156894242
C2×#156894022
C2×#156892522
C2×#156892262
C2×#156892212
C2×#156892082
C2×C47×#4772
C2×#338647