Finite Group Databasebeta

← C2×#20253191 #27083796

Subgroups — C2×#20253191 #27083796

Order 12032.

2098 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×#15689679C211yesmaximal, characteristic
2C2×C4×Q8×D47C211yesmaximal, characteristic
3#20253191C2116yesmaximal, direct product factor
4C2×#15689431C211yesmaximal, characteristic, complemented
5C2×#15689430C211yesmaximal, characteristic, complemented
6C2×#15689427C211yesmaximal, characteristic, complemented
7C2×#15689417C211yesmaximal, characteristic, complemented
8C2×#15689416C211yesmaximal, characteristic, complemented
9C2×#15689407C211yesmaximal, characteristic, complemented
10C2×#15689406C211yesmaximal, characteristic, complemented
11C2×#15689164C211yesmaximal, characteristic
12C2×#15689162C211yesmaximal, characteristic
13C2×#15689145C211yesmaximal, characteristic
14C2×#15689130C211yesmaximal, characteristic
15C2×#15689130C211yesmaximal, characteristic
16C2×C47×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D47C2211yescharacteristic
18C22×#10625324C2211yescharacteristic
19C22×#10625324C2211yescharacteristic
20#15689679—24no—
21#15689679C2218yes—
22C2×#13094023C2211yescharacteristic
23C2×#13094023C2211yescharacteristic
24C2×#13094016C2211yescharacteristic
25C2×#13094002—21no—
26C2×#13094002—21no—
27C2×Q8×Dic47C2211yescharacteristic
28C2×C4×Dic94—21no—
29C2×C4×Dic94C2211yescharacteristic
30C2×#13093989—21no—
31C2×#13093989—21no—
32C2×#13093989—21no—
33C2×#13093989C2211yescharacteristic
34C4×Q8×D47—24no—
35C4×Q8×D47C2218yes—
36C2×#13093982C2211yescharacteristic
37C2×#13093982C2211yescharacteristic
38C2×C4⋊C4×D47—21no—
39C2×C4⋊C4×D47C2211yescharacteristic
40C2×C42×D47—21no—
41C2×C42×D47C2211yescharacteristic
42#15689431C2218yescomplemented
43#15689430C2218yescomplemented
44#15689427C2218yescomplemented
45#15689417C2218yescomplemented
46#15689416C2218yescomplemented
47#15689407C2218yescomplemented
48#15689406C2218yescomplemented
49#15689164C2218yes—
50#15689162C2218yes—
51C2×#13093958C2211yescharacteristic
52C2×#13093957C2211yescharacteristic
53C2×#13093957C2211yescharacteristic
54C2×#13093956C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×#13093955C2211yescharacteristic
57#15689145C2218yes—
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61#15689130C2218yes—
62#15689130C2218yes—
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×#13093948C2211yescharacteristic
67C2×#13093947C2211yescharacteristic
68C2×#13093947C2211yescharacteristic
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×D47D411yescharacteristic
88C22×C4×D47D411yescharacteristic
89C22×C4×D47C2311yescharacteristic
90C2×#10625324—24no—
91C2×#10625324—24no—
92C2×#10625324C2314yes—
93C2×#10625324C2314yes—
94C22×C47⋊C8C2311yescharacteristic
95C22×C47⋊C8C2311yescharacteristic
96#13094023—22no—
97#13094023—22no—
98#13094023C2314yes—
99#13094023C2314yes—
100#13094016—22no—
101#13094016C2314yes—
102#13094002—28no—
103#13094002—28no—
104Q8×Dic47—22no—
105Q8×Dic47C2314yes—
106C4×Dic94—22no—
107C4×Dic94—28no—
108C4×Dic94C2314yes—
109#13093989—22no—
110#13093989—28no—
111#13093989—28no—
112#13093989—28no—
113#13093989C2314yes—
114#13093982—22no—
115#13093982—22no—
116#13093982C2314yes—
117#13093982C2314yes—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47C2311yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×Dic47⋊C4—21no—
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C4⋊C4×D47—28no—
130C4⋊C4×D47—22no—
131C4⋊C4×D47C2314yes—
132C2×(C2×D47)⋊C4—21no—
133C2×(C2×D47)⋊C4—21no—
134C2×C4×Dic47—21no—
135C2×C4×Dic47—21no—
136C2×C4×Dic47—21no—
137C2×C4×Dic47—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47D411yescharacteristic
140C2×C4×Dic47D411yescharacteristic
141C2×C4×Dic47C2311yescharacteristic
142C42×D47—28no—
143C42×D47D414yes—
144C42×D47C2314yes—
145#13093958C2314yes—
146#13093957C2314yes—
147#13093957C2314yes—
148#13093956C2314yes—
149#13093955C2314yes—
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—24no—
206C2×C4×D47—42no—
207C2×C4×D47—44no—
208C2×C4×D47C2×D414yes—
209C2×C4×D47C2×D414yes—
210C2×C4×D47C2×D412yes—
211C2×C4×D47C2×Q814yes—
212C2×C4×D47#4114yes—
213C2×C4×D47C2412yes—
214C2×Dic94—21no—
215C2×Dic94—22no—
216C2×Dic94—28no—
217C2×Dic94—24no—
218C2×Dic94—24no—
219C2×Dic94—24no—
220C2×Dic94—44no—
221C2×Dic94—44no—
222C2×Dic94C2×Q814yes—
223C2×Dic94C2412yes—
224C2×C8×C47—22no—
225C2×C8×C47—22no—
226C2×C8×C47C2412yes—
227C2×C8×C47C2412yes—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—24no—
231C4⋊C4×C47—21no—
232C4⋊C4×C47—21no—
233C4⋊C4×C47—21no—
234C4⋊C4×C47C2412yes—
235C4⋊C4×C47C2412yes—
236C4⋊C4×C47C2412yes—
237C42×C47—24no—
238C42×C47C2×D412yes—
239C42×C47C2412yes—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242C4⋊Dic47—21no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
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⋊C4—24no—
255Dic47⋊C4—24no—
256C4×Dic47—24no—
257C4×Dic47—24no—
258C4×Dic47—24no—
259C4×Dic47—24no—
260C4×Dic47—24no—
261C4×Dic47C2×D412yes—
262C4×Dic47C2×D414yes—
263C4×Dic47C2×D414yes—
264C4×Dic47C2412yes—
265C2×C47⋊C8—22no—
266C2×C47⋊C8—22no—
267C2×C47⋊C8C2412yes—
268C2×C47⋊C8C2412yes—
269#10625324—28no—
270#10625324—28no—
271C23×C47C22×D411yescharacteristic
272C22×D47—22no—
273C22×D47—22no—
274C22×D47C22⋊Q814yes—
275C22×D47C22×D412yes—
276Q8×C47—24no—
277Q8×C47—22no—
278Q8×C47C22×Q814yes—
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×C47C22×D412yes—
290C2×C4×C47C22×D412yes—
291C2×C4×C47C22×D411yescharacteristic
292C2×C4×C47C22×Q812yes—
293C2×C4×C47C2×#4112yes—
294C2×C4×C47C2511yescharacteristic
295C2×Dic47—24no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47C22⋊Q814yes—
305C2×Dic47#13714yes—
306C2×Dic47C22×D412yes—
307C2×Dic47C22×D412yes—
308C2×Dic47C22×D412yes—
309C4×D47—216no—
310C4×D47—28no—
311C4×D47—44no—
312C4×D47—48no—
313C4×D47C22⋊Q818yes—
314C4×D47C22×Q814yes—
315C4×D47C2×#4114yes—
316Dic94—24no—
317Dic94—22no—
318Dic94—216no—
319Dic94—48no—
320Dic94—48no—
321Dic94C22×Q814yes—
322C8×C47—22no—
323C8×C47—22no—
324C47⋊C8—22no—
325C47⋊C8—22no—
326C2×#3078—471nomaximal, Sylow
327C22×C47C2×C22⋊Q812yes—
328C22×C47C2×#13712yes—
329C22×C47#57512yes—
330C22×C47C23×D411yescharacteristic
331C2×D47—28no—
332C2×D47—22no—
333C2×D47—22no—
334C2×D47C2×C22⋊Q814yes—
335C4×C47—24no—
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—42no—
339C4×C47—42no—
340C4×C47—42no—
341C4×C47C2×C22⋊Q812yes—
342C4×C47C23×Q811yescharacteristic
343C4×C47C22×#4111yescharacteristic
344Dic47—24no—
345Dic47—22no—
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349Dic47C2×C22⋊Q814yes—
350Dic47C2×#13714yes—
351C2×#533—471no—
352C22×C4×Q8—471no—
353#3078—4716no—
354C2×#479—471no—
355C2×#479—471no—
356C2×#479—471no—
357C2×#479D4711yescharacteristic, complemented
358C2×#477—471no—
359C2×#477—471no—
360C2×#475—471no—
361C2×#475—471no—
362C2×#428—471no—
363C2×#428—471no—
364C2×#423—471no—
365C2×#419—471no—
366C2×#419—471no—
367C2×C47#307814yescomplemented
368C2×C47C22×C22⋊Q811yescharacteristic
369C2×C47C22×#13711yescharacteristic
370C2×C47C2×#57511yescharacteristic
371D47—24no—
372C23×Q8—471no—
373C22×M16—471no—
374C22×M16—471no—
375#533—478no—
376#533—944no—
377C2×C4⋊Q8—471no—
378C2×C4⋊Q8—471no—
379C2×#125—471no—
380C2×#125C2×D4711yescharacteristic
381C2×C22⋊Q8—941no—
382C2×C22⋊Q8—941no—
383C2×C4×Q8—471no—
384C2×C4×Q8—478no—
385C2×C4×Q8—471no—
386C2×C4×Q8—471no—
387C2×C4×Q8—941no—
388C2×C4×Q8—941no—
389C2×C4×Q8—941no—
390C2×C4×Q8—941no—
391C2×C4×Q8—944no—
392C2×C4×Q8C2×D4711yescharacteristic
393C2×#117—471no—
394C2×#117—471no—
395C22×C4⋊C4—471no—
396C22×C4⋊C4—941no—
397C22×C42—471no—
398C22×C42—941no—
399#479—478no—
400#479—478no—
401#479—478no—
402#479C2×D4718yescomplemented
403#477—478no—
404#477—478no—
405#475—478no—
406#475—478no—
407#428—478no—
408#428—478no—
409C2×#107—471no—
410C2×#107—471no—
411C2×#107—471no—
412C2×#107C2×D4711yescharacteristic
413C2×#106—471no—
414C2×#106—471no—
415C2×#106—471no—
416C2×#106C2×D4711yescharacteristic
417#423—478no—
418C2×C4⋊C8—471no—
419C2×C4⋊C8—471no—
420C2×C4⋊C8—471no—
421C2×C4⋊C8C2×D4711yescharacteristic
422#419—478no—
423#419—478no—
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103—471no—
430C2×#103C2×D4711yescharacteristic
431C2×#103C2×D4711yescharacteristic
432C47C2×#307811yescharacteristic, complemented, Sylow
433C22×Q8—478no—
434C22×Q8—474no—
435C22×Q8—471no—
436C22×Q8—941no—
437C22×Q8—941no—
438C22×Q8—941no—
439C22×Q8—942no—
440C22×Q8—944no—
441C22×Q8C22×D4711yescharacteristic
442C23×C4—471no—
443C23×C4—471no—
444C23×C4—471no—
445C23×C4—941no—
446C23×C4—941no—
447C2×M16—474no—
448C2×M16—474no—
449C2×M16—944no—
450C2×M16—944no—
451C22×C8—471no—
452C22×C8—471no—
453C22×C8C22×D4711yescharacteristic
454C22×C8C22×D4711yescharacteristic
455C4⋊Q8—474no—
456C4⋊Q8—474no—
457C4⋊Q8—942no—
458C4⋊Q8—942no—
459#125—22no—
460#125—474no—
461#125—942no—
462#125C22×D4714yes—
463C22⋊Q8—948no—
464C22⋊Q8—948no—
465C4×Q8—22no—
466C4×Q8—474no—
467C4×Q8—474no—
468C4×Q8—474no—
469C4×Q8—948no—
470C4×Q8—948no—
471C4×Q8—942no—
472C4×Q8—948no—
473C4×Q8—948no—
474C4×Q8—942no—
475C4×Q8—942no—
476C4×Q8C22×D4714yes—
477#117—474no—
478#117—474no—
479#117—942no—
480#117—942no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—471no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—474no—
488C2×C4⋊C4—942no—
489C2×C4⋊C4—948no—
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⋊C4C22×D4711yescharacteristic
499C2×C4⋊C4C22×D4711yescharacteristic
500C2×C4⋊C4C22×D4711yescharacteristic
501C2×C22⋊C4—941no—
502C2×C22⋊C4—941no—
503C2×C42—21no—
504C2×C42—471no—
505C2×C42—471no—
506C2×C42—471no—
507C2×C42—474no—
508C2×C42—474no—
509C2×C42—948no—
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#106—474no—
521#106—474no—
522#106—474no—
523#106C22×D4714yes—
524C4⋊C8—474no—
525C4⋊C8—474no—
526C4⋊C8—474no—
527C4⋊C8C22×D4714yes—
528#103—474no—
529#103—474no—
530#103—474no—
531#103—474no—
532#103—474no—
533#103—474no—
534#103C22×D4714yes—
535#103C22×D4714yes—
536C24—471no—
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—4716no—
540C2×Q8—474no—
541C2×Q8—472no—
542C2×Q8—944no—
543C2×Q8—948no—
544C2×Q8—944no—
545C2×Q8—944no—
546C2×Q8—9416no—
547C2×Q8—948no—
548C2×Q8—941no—
549C2×Q8—942no—
550C2×Q8—1884no—
551C2×Q8—1884no—
552C2×Q8Q8×D4714yes—
553C2×Q8C23×D4712yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—471no—
559C22×C4—471no—
560C22×C4—472no—
561C22×C4—474no—
562C22×C4—474no—
563C22×C4—472no—
564C22×C4—471no—
565C22×C4—474no—
566C22×C4—474no—
567C22×C4—944no—
568C22×C4—944no—
569C22×C4—948no—
570C22×C4—944no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—1882no—
576C22×C4—1884no—
577C22×C4D4×D4711yescharacteristic
578C22×C4D4×D4711yescharacteristic
579C22×C4C23×D4711yescharacteristic
580M16—948no—
581M16—948no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—472no—
585C2×C8—472no—
586C2×C8—942no—
587C2×C8—942no—
588C2×C8C23×D4712yes—
589C2×C8C23×D4712yes—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—472no—
597C4⋊C4—472no—
598C4⋊C4—472no—
599C4⋊C4—944no—
600C4⋊C4—944no—
601C4⋊C4—944no—
602C4⋊C4—944no—
603C4⋊C4—944no—
604C4⋊C4—944no—
605C4⋊C4—944no—
606C4⋊C4—944no—
607C4⋊C4—941no—
608C4⋊C4—941no—
609C4⋊C4—941no—
610C4⋊C4C23×D4712yes—
611C4⋊C4C23×D4712yes—
612C4⋊C4C23×D4712yes—
613C22⋊C4—944no—
614C22⋊C4—944no—
615C42—24no—
616C42—474no—
617C42—474no—
618C42—472no—
619C42—472no—
620C42—944no—
621C42—944no—
622C42—944no—
623C42—944no—
624C42—944no—
625C42D4×D4712yes—
626C42C23×D4712yes—
627C23—474no—
628C23—472no—
629C23—942no—
630C23—942no—
631C23C2×D4×D4711yescharacteristic
632Q8—24no—
633Q8—22no—
634Q8—474no—
635Q8—9416no—
636Q8—944no—
637Q8—942no—
638Q8—1888no—
639Q8—1888no—
640Q8C2×Q8×D4714yes—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—474no—
652C2×C4—474no—
653C2×C4—472no—
654C2×C4—472no—
655C2×C4—478no—
656C2×C4—474no—
657C2×C4—474no—
658C2×C4—472no—
659C2×C4—948no—
660C2×C4—9416no—
661C2×C4—944no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—942no—
665C2×C4—942no—
666C2×C4—942no—
667C2×C4—1884no—
668C2×C4—1888no—
669C2×C4—1882no—
670C2×C4—1882no—
671C2×C4—1882no—
672C2×C4C2×D4×D4712yes—
673C2×C4C2×D4×D4712yes—
674C2×C4C2×D4×D4711yescharacteristic
675C2×C4C2×Q8×D4712yes—
676C2×C4#41×D4712yes—
677C2×C4C24×D4711yescharacteristic
678C8—22no—
679C8—22no—
680C8—942no—
681C8—942no—
682C22—474no—
683C22—948no—
684C22—942no—
685C22—942no—
686C22C22⋊Q8×D4712yes—
687C22#137×D4712yes—
688C22#1568992012yes—
689C22C22×D4×D4711yescharacteristic
690C4—22no—
691C4—22no—
692C4—24no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—474no—
697C4—474no—
698C4—942no—
699C4—944no—
700C4—1882no—
701C4—1882no—
702C4—1882no—
703C4C22⋊Q8×D4712yes—
704C4C22×Q8×D4711yescharacteristic
705C4C2×#41×D4711yescharacteristic
706C2—944no—
707C2#2025319114yesdirect product factor
708C2C2×C22⋊Q8×D4711yescharacteristic
709C2C2×#137×D4711yescharacteristic
710C2C2×#1568992011yescharacteristic
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×#3078
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. #20253191C2direct (N × H)
4. C2×#15689431C2semidirect
5. C2×#15689430C2semidirect
6. C2×#15689427C2semidirect
7. C2×#15689417C2semidirect
8. C2×#15689416C2semidirect
9. C2×#15689407C2semidirect
10. C2×#15689406C2semidirect
16. C2×C47×#479C2semidirect
42. #15689431C22semidirect
43. #15689430C22semidirect
44. #15689427C22semidirect
45. #15689417C22semidirect
46. #15689416C22semidirect
47. #15689407C22semidirect
48. #15689406C22semidirect
71. C47×#479C22semidirect
83. C2×Q8×D47Q8semidirect
201. Q8×D47C2×Q8semidirect
357. C2×#479D47semidirect
367. C2×C47#3078semidirect
402. #479C2×D47semidirect
432. C47C2×#3078semidirect
707. C2#20253191direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896792
C2×C4×Q8×D472
#202531912
C2×#156894312
C2×#156894302
C2×#156894272
C2×#156894172
C2×#156894162
C2×#156894072
C2×#156894062
C2×#156891642
C2×#156891622
C2×#156891452
C2×#156891302
C2×C47×#4792
C2×#307847