Finite Group Databasebeta

← C2×#20253227 #27083846

Subgroups — C2×#20253227 #27083846

Order 12032.

2018 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689753C211yesmaximal, characteristic
2C2×#15689599C211yesmaximal, characteristic
3#20253227C2116yesmaximal, direct product factor
4C2×#15689433C211yesmaximal, characteristic, complemented
5C2×#15689428C211yesmaximal, characteristic, complemented
6C2×#15689427C211yesmaximal, characteristic, complemented
7C2×#15689418C211yesmaximal, characteristic, complemented
8C2×#15689417C211yesmaximal, characteristic, complemented
9C2×#15689409C211yesmaximal, characteristic, complemented
10C2×#15689406C211yesmaximal, characteristic, complemented
11C2×#15689164C211yesmaximal, characteristic
12C2×#15689158C211yesmaximal, characteristic
13C2×#15689148C211yesmaximal, characteristic
14C2×#15689130C211yesmaximal, characteristic
15C2×#103×D47C211yesmaximal, characteristic
16C2×C47×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×C8×D47C2211yescharacteristic
20#15689753—24no—
21#15689753C2218yes—
22C2×#13094024C2211yescharacteristic
23C2×#13094023—21no—
24C2×#13094023C2211yescharacteristic
25C2×#13094015C2211yescharacteristic
26C2×#13094014—21no—
27C2×#13094004—21no—
28C2×#13094002—21no—
29#15689599—24no—
30#15689599C2218yes—
31C2×Q8×Dic47C2211yescharacteristic
32C2×C4×Dic94—21no—
33C2×C4×Dic94C2211yescharacteristic
34C2×#13093989—21no—
35C2×#13093989C2211yescharacteristic
36C2×#13093982—21no—
37C2×#13093982C2211yescharacteristic
38C2×#13093982C2211yescharacteristic
39C2×#13093981—21no—
40C2×#13093981C2211yescharacteristic
41C2×C4⋊C4×D47C2211yescharacteristic
42#15689433C2218yescomplemented
43#15689428C2218yescomplemented
44#15689427C2218yescomplemented
45#15689418C2218yescomplemented
46#15689417C2218yescomplemented
47#15689409C2218yescomplemented
48#15689406C2218yescomplemented
49#15689164C2218yes—
50#15689158C2218yes—
51C2×#13093957C2211yescharacteristic
52C2×#13093957C2211yescharacteristic
53C2×#13093957C2211yescharacteristic
54C2×#13093956C2211yescharacteristic
55C2×#13093956C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57#15689148C2218yes—
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61#15689130C2218yes—
62C2×#13093949C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093947C2211yescharacteristic
67C2×#13093947C2211yescharacteristic
68#103×D47C2218yes—
69C2×#125×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C47×#479C2218yescomplemented
72C2×#107×C47C2211yescharacteristic
73C2×#106×C47C2211yescharacteristic
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94—21no—
79C22×Dic94—21no—
80C22×Dic94C2311yescharacteristic
81C2×Q8×D47—22no—
82C2×Q8×D47—24no—
83C2×Q8×D47Q818yescomplemented
84C2×Q8×D47C2314yes—
85C22×C4×D47—21no—
86C22×C4×D47—21no—
87C22×C4×D47C2311yescharacteristic
88C2×#10625324—24no—
89C2×#10625324C2314yes—
90C22×C47⋊C8C2311yescharacteristic
91C22×C47⋊C8C2311yescharacteristic
92C2×C8×D47—24no—
93C2×C8×D47C2314yes—
94#13094024—22no—
95#13094024C2314yes—
96#13094023—28no—
97#13094023—22no—
98#13094023C2314yes—
99#13094015—22no—
100#13094015C2314yes—
101#13094014—28no—
102#13094004—28no—
103#13094002—28no—
104Q8×Dic47—22no—
105Q8×Dic47C2314yes—
106C4×Dic94—22no—
107C4×Dic94—28no—
108C4×Dic94C2314yes—
109#13093989—28no—
110#13093989—22no—
111#13093989C2314yes—
112#13093982—22no—
113#13093982—22no—
114#13093982—28no—
115#13093982C2314yes—
116#13093982C2314yes—
117#13093981—28no—
118#13093981D414yes—
119#13093981C2314yes—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
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⋊C4D411yescharacteristic
132C2×Dic47⋊C4D411yescharacteristic
133C4⋊C4×D47—22no—
134C4⋊C4×D47C2314yes—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4D411yescharacteristic
138C2×(C2×D47)⋊C4D411yescharacteristic
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145#13093957C2314yes—
146#13093957C2314yes—
147#13093957C2314yes—
148#13093956C2314yes—
149#13093956C2314yes—
150#13093955C2314yes—
151C4⋊(C47⋊C8)C2314yes—
152Dic47⋊C8C2314yes—
153Dic47⋊C8C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093948C2314yes—
157#13093948C2314yes—
158#13093947C2314yes—
159#13093947C2314yes—
160C22×Q8×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163#125×C47—22no—
164#125×C47C2314yes—
165C4×Q8×C47—22no—
166C4×Q8×C47C2314yes—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C42×C47—21no—
174C2×C42×C47C2311yescharacteristic
175#107×C47C2314yes—
176#106×C47C2314yes—
177C4⋊C8×C47C2314yes—
178#103×C47C2314yes—
179#103×C47C2314yes—
180C23×D47C2×D411yescharacteristic
181C2×Q8×C47—21no—
182C2×Q8×C47—22no—
183C2×Q8×C47C2×Q814yes—
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×Dic47—21no—
196C22×Dic47C2×D411yescharacteristic
197C22×Dic47C2×D411yescharacteristic
198C22×Dic47C2×D411yescharacteristic
199Q8×D47—216no—
200Q8×D47—28no—
201Q8×D47C2×Q8116yescomplemented
202C2×C4×D47—28no—
203C2×C4×D47—24no—
204C2×C4×D47—24no—
205C2×C4×D47—82no—
206C2×C4×D47C2×D412yes—
207C2×C4×D47C2×Q814yes—
208C2×C4×D47#4114yes—
209C2×C4×D47C2412yes—
210C2×Dic94—21no—
211C2×Dic94—22no—
212C2×Dic94—28no—
213C2×Dic94—24no—
214C2×Dic94—24no—
215C2×Dic94—24no—
216C2×Dic94—82no—
217C2×Dic94—82no—
218C2×Dic94C2×Q814yes—
219C2×Dic94C2412yes—
220C2×C8×C47—22no—
221C2×C8×C47—22no—
222C2×C8×C47C2412yes—
223C2×C8×C47C2412yes—
224C4⋊C4×C47—24no—
225C4⋊C4×C47—24no—
226C4⋊C4×C47—24no—
227C4⋊C4×C47—21no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47C2412yes—
231C4⋊C4×C47C2412yes—
232C4⋊C4×C47C2412yes—
233C42×C47—24no—
234C42×C47C2×D412yes—
235C42×C47C2412yes—
236(C2×D47)⋊C4—24no—
237(C2×D47)⋊C4—24no—
238(C2×D47)⋊C4C2×D414yes—
239(C2×D47)⋊C4C2×D414yes—
240C4⋊Dic47—21no—
241C4⋊Dic47—24no—
242C4⋊Dic47—21no—
243C4⋊Dic47—21no—
244C4⋊Dic47—24no—
245C4⋊Dic47—24no—
246C4⋊Dic47C2412yes—
247C4⋊Dic47C2412yes—
248C4⋊Dic47C2412yes—
249Dic47⋊C4—24no—
250Dic47⋊C4—24no—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4C2×D414yes—
255Dic47⋊C4C2×D414yes—
256C4×Dic47—24no—
257C4×Dic47—24no—
258C4×Dic47—24no—
259C4×Dic47—24no—
260C4×Dic47—24no—
261C4×Dic47C2×D412yes—
262C4×Dic47C2412yes—
263C2×C47⋊C8—22no—
264C2×C47⋊C8—22no—
265C2×C47⋊C8C2412yes—
266C2×C47⋊C8C2412yes—
267#10625324—28no—
268C8×D47—28no—
269C23×C47C22×D411yescharacteristic
270C22×D47—22no—
271C22×D47—22no—
272C22×D47C22⋊Q814yes—
273C22×D47C22×D412yes—
274Q8×C47—24no—
275Q8×C47—22no—
276Q8×C47C22×Q814yes—
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×C47C22×D412yes—
288C2×C4×C47C22×D412yes—
289C2×C4×C47C22×D411yescharacteristic
290C2×C4×C47C22×Q812yes—
291C2×C4×C47C2×#4112yes—
292C2×C4×C47C2511yescharacteristic
293C2×Dic47—24no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—42no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47C22⋊Q814yes—
304C2×Dic47C22×D412yes—
305C2×Dic47C22×D412yes—
306C2×Dic47C22×D412yes—
307C4×D47—216no—
308C4×D47—84no—
309C4×D47C22⋊Q818yes—
310C4×D47C22×Q814yes—
311C4×D47C2×#4114yes—
312Dic94—24no—
313Dic94—22no—
314Dic94—216no—
315Dic94—84no—
316Dic94—84no—
317Dic94C22×Q814yes—
318C8×C47—22no—
319C8×C47—22no—
320C47⋊C8—22no—
321C47⋊C8—22no—
322C2×#3082—471nomaximal, Sylow
323C22×C47C2×C22⋊Q812yes—
324C22×C47#57712yes—
325C22×C47#57812yes—
326C22×C47C23×D411yescharacteristic
327C2×D47—28no—
328C2×D47—22no—
329C2×D47—22no—
330C2×D47C2×C22⋊Q814yes—
331C4×C47—24no—
332C4×C47—22no—
333C4×C47—22no—
334C4×C47—42no—
335C4×C47—42no—
336C4×C47—42no—
337C4×C47C2×C22⋊Q812yes—
338C4×C47C23×Q811yescharacteristic
339C4×C47C22×#4111yescharacteristic
340Dic47—24no—
341Dic47—22no—
342Dic47—22no—
343Dic47—42no—
344Dic47—42no—
345Dic47—42no—
346Dic47C2×C22⋊Q814yes—
347C2×#544—471no—
348C2×#519—471no—
349#3082—4716no—
350C2×#479—471no—
351C2×#479—471no—
352C2×#479—471no—
353C2×#479D4711yescharacteristic, complemented
354C2×#477—471no—
355C2×#477—471no—
356C2×#475—471no—
357C2×#475—471no—
358C2×#428—471no—
359C2×#427—471no—
360C2×#424—471no—
361C2×#419—471no—
362C22×#103—471no—
363C2×C47#308214yescomplemented
364C2×C47C22×C22⋊Q811yescharacteristic
365C2×C47C2×#57711yescharacteristic
366C2×C47C2×#57811yescharacteristic
367D47—24no—
368C23×Q8—471no—
369C22×M16—471no—
370C23×C8—471no—
371#544—478no—
372#544—944no—
373C2×C4⋊Q8—471no—
374C2×C4⋊Q8—471no—
375C2×C4⋊Q8—941no—
376C2×#125—471no—
377C2×#125—941no—
378C2×#125C2×D4711yescharacteristic
379C2×C22⋊Q8—941no—
380C2×C22⋊Q8—941no—
381#519—478no—
382#519—944no—
383C2×C4×Q8—471no—
384C2×C4×Q8—471no—
385C2×C4×Q8—471no—
386C2×C4×Q8—941no—
387C2×C4×Q8—941no—
388C2×C4×Q8C2×D4711yescharacteristic
389C2×#117—471no—
390C2×#117—471no—
391C2×#117—471no—
392C2×#117—941no—
393C2×#117—941no—
394C22×C4⋊C4—471no—
395#479—478no—
396#479—478no—
397#479—478no—
398#479C2×D4718yescomplemented
399#477—478no—
400#477—478no—
401#475—478no—
402#475—478no—
403#428—478no—
404#427—478no—
405C2×#107—471no—
406C2×#107—471no—
407C2×#107—471no—
408C2×#107C2×D4711yescharacteristic
409C2×#106—471no—
410C2×#106—471no—
411C2×#106—471no—
412C2×#106C2×D4711yescharacteristic
413#424—478no—
414C2×C4⋊C8—471no—
415C2×C4⋊C8—471no—
416C2×C4⋊C8—471no—
417C2×C4⋊C8C2×D4711yescharacteristic
418#419—478no—
419C2×#103—471no—
420C2×#103—471no—
421C2×#103—471no—
422C2×#103—471no—
423C2×#103—471no—
424C2×#103—471no—
425C2×#103—478no—
426C2×#103C2×D4711yescharacteristic
427C2×#103C2×D4711yescharacteristic
428C47C2×#308211yescharacteristic, complemented, Sylow
429C22×Q8—478no—
430C22×Q8—474no—
431C22×Q8—471no—
432C22×Q8—941no—
433C22×Q8—941no—
434C22×Q8—942no—
435C22×Q8—944no—
436C22×Q8—941no—
437C22×Q8C22×D4711yescharacteristic
438C23×C4—471no—
439C23×C4—941no—
440C23×C4—941no—
441C2×M16—474no—
442C2×M16—944no—
443C22×C8—471no—
444C22×C8—471no—
445C22×C8—474no—
446C22×C8—944no—
447C22×C8C22×D4711yescharacteristic
448C22×C8C22×D4711yescharacteristic
449C4⋊Q8—474no—
450C4⋊Q8—474no—
451C4⋊Q8—942no—
452C4⋊Q8—948no—
453C4⋊Q8—942no—
454#125—22no—
455#125—474no—
456#125—942no—
457#125—948no—
458#125C22×D4714yes—
459C22⋊Q8—948no—
460C22⋊Q8—948no—
461C4×Q8—22no—
462C4×Q8—474no—
463C4×Q8—474no—
464C4×Q8—474no—
465C4×Q8—948no—
466C4×Q8—942no—
467C4×Q8—942no—
468C4×Q8—948no—
469C4×Q8—942no—
470C4×Q8C22×D4714yes—
471#117—474no—
472#117—474no—
473#117—474no—
474#117—474no—
475#117—948no—
476#117—948no—
477#117—942no—
478#117—942no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—471no—
483C2×C4⋊C4—471no—
484C2×C4⋊C4—471no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—474no—
488C2×C4⋊C4—942no—
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⋊C4C22×D4711yescharacteristic
498C2×C4⋊C4C22×D4711yescharacteristic
499C2×C4⋊C4C22×D4711yescharacteristic
500C2×C22⋊C4—471no—
501C2×C22⋊C4—471no—
502C2×C22⋊C4—941no—
503C2×C22⋊C4—941no—
504C2×C42—21no—
505C2×C42—471no—
506C2×C42—941no—
507C2×C42—941no—
508C2×C42—941no—
509C2×C42—941no—
510C2×C42—941no—
511C2×C42C22×D4711yescharacteristic
512#107—474no—
513#107—474no—
514#107—474no—
515#107C22×D4714yes—
516#106—474no—
517#106—474no—
518#106—474no—
519#106C22×D4714yes—
520C4⋊C8—474no—
521C4⋊C8—474no—
522C4⋊C8—474no—
523C4⋊C8C22×D4714yes—
524#103—474no—
525#103—474no—
526#103—474no—
527#103—474no—
528#103—474no—
529#103—474no—
530#103C22×D4714yes—
531#103C22×D4714yes—
532C24—471no—
533C2×Q8—21no—
534C2×Q8—22no—
535C2×Q8—4716no—
536C2×Q8—474no—
537C2×Q8—472no—
538C2×Q8—944no—
539C2×Q8—948no—
540C2×Q8—944no—
541C2×Q8—9416no—
542C2×Q8—948no—
543C2×Q8—941no—
544C2×Q8—944no—
545C2×Q8—942no—
546C2×Q8—3762no—
547C2×Q8—3762no—
548C2×Q8Q8×D4714yes—
549C2×Q8C23×D4712yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—471no—
555C22×C4—472no—
556C22×C4—474no—
557C22×C4—474no—
558C22×C4—472no—
559C22×C4—471no—
560C22×C4—471no—
561C22×C4—944no—
562C22×C4—948no—
563C22×C4—944no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—941no—
568C22×C4—3762no—
569C22×C4D4×D4711yescharacteristic
570C22×C4D4×D4711yescharacteristic
571C22×C4C23×D4711yescharacteristic
572M16—948no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—472no—
576C2×C8—472no—
577C2×C8—948no—
578C2×C8—942no—
579C2×C8—942no—
580C2×C8C23×D4712yes—
581C2×C8C23×D4712yes—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—474no—
589C4⋊C4—474no—
590C4⋊C4—472no—
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⋊C4—941no—
603C4⋊C4—944no—
604C4⋊C4C23×D4712yes—
605C4⋊C4C23×D4712yes—
606C4⋊C4C23×D4712yes—
607C22⋊C4—474no—
608C22⋊C4—474no—
609C22⋊C4—944no—
610C22⋊C4—944no—
611C42—24no—
612C42—472no—
613C42—472no—
614C42—944no—
615C42—944no—
616C42—944no—
617C42—944no—
618C42—944no—
619C42D4×D4712yes—
620C42C23×D4712yes—
621C23—474no—
622C23—472no—
623C23—942no—
624C23—942no—
625C23C2×D4×D4711yescharacteristic
626Q8—24no—
627Q8—22no—
628Q8—474no—
629Q8—9416no—
630Q8—944no—
631Q8—942no—
632Q8—3764no—
633Q8—3764no—
634Q8C2×Q8×D4714yes—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—474no—
646C2×C4—472no—
647C2×C4—478no—
648C2×C4—474no—
649C2×C4—474no—
650C2×C4—472no—
651C2×C4—472no—
652C2×C4—9416no—
653C2×C4—944no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—942no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—3764no—
661C2×C4—1882no—
662C2×C4—1882no—
663C2×C4—1882no—
664C2×C4C2×D4×D4712yes—
665C2×C4C2×D4×D4712yes—
666C2×C4C2×D4×D4711yescharacteristic
667C2×C4C2×Q8×D4712yes—
668C2×C4#41×D4712yes—
669C2×C4C24×D4711yescharacteristic
670C8—22no—
671C8—22no—
672C8—942no—
673C8—942no—
674C22—474no—
675C22—948no—
676C22—942no—
677C22—942no—
678C22C22⋊Q8×D4712yes—
679C22#1568993012yes—
680C22#1568993912yes—
681C22C22×D4×D4711yescharacteristic
682C4—22no—
683C4—24no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—474no—
689C4—942no—
690C4—944no—
691C4—942no—
692C4—1882no—
693C4—1882no—
694C4—1882no—
695C4C22⋊Q8×D4712yes—
696C4C22×Q8×D4711yescharacteristic
697C4C2×#41×D4711yescharacteristic
698C2—944no—
699C2#2025322714yesdirect product factor
700C2C2×C22⋊Q8×D4711yescharacteristic
701C2C2×#1568993011yescharacteristic
702C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#479C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenterC2×#479D47
hypocenterC47C2×#3082
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #20253227C2direct (N × H)
4. C2×#15689433C2semidirect
5. C2×#15689428C2semidirect
6. C2×#15689427C2semidirect
7. C2×#15689418C2semidirect
8. C2×#15689417C2semidirect
9. C2×#15689409C2semidirect
10. C2×#15689406C2semidirect
16. C2×C47×#479C2semidirect
42. #15689433C22semidirect
43. #15689428C22semidirect
44. #15689427C22semidirect
45. #15689418C22semidirect
46. #15689417C22semidirect
47. #15689409C22semidirect
48. #15689406C22semidirect
71. C47×#479C22semidirect
83. C2×Q8×D47Q8semidirect
201. Q8×D47C2×Q8semidirect
353. C2×#479D47semidirect
363. C2×C47#3082semidirect
398. #479C2×D47semidirect
428. C47C2×#3082semidirect
699. C2#20253227direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897532
C2×#156895992
#202532272
C2×#156894332
C2×#156894282
C2×#156894272
C2×#156894182
C2×#156894172
C2×#156894092
C2×#156894062
C2×#156891642
C2×#156891582
C2×#156891482
C2×#156891302
C2×#103×D472
C2×C47×#4792
C2×#308247