Finite Group Databasebeta

← #26216208

Subgroups — #26216208

Order 12032.

1866 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2#20245771C211yesmaximal, characteristic, complemented
3#20243460C212yesmaximal, complemented
4#20243373C214yesmaximal, complemented
5#20243302C212yesmaximal
6C4×#13093938C214yesmaximal, complemented
7C47×#2280C211yesmaximal, characteristic, complemented
8C23×C22⋊D47C2211yescharacteristic
9C23×C4×D47C411yescharacteristic, complemented
10C2×C4×C22⋊D47—21no—
11C2×C4×C22⋊D47—21no—
12C2×C4×C22⋊D47—21no—
13C2×C4×C22⋊D47—21no—
14C2×C4×C22⋊D47—21no—
15C2×C4×C22⋊D47—21no—
16C2×C4×C22⋊D47—21no—
17C2×C4×C22⋊D47—21no—
18C2×C4×C22⋊D47C412yescomplemented
19C2×C4×C22⋊D47C412yescomplemented
20C2×C4×C22⋊D47C2212yes—
21C2×C4×C22⋊D47C2212yes—
22C2×#13093983—21no—
23C22×Dic47⋊C4C411yescharacteristic, complemented
24C22×C22⋊Dic47C2211yescharacteristic
25C22×(C2×D47)⋊C4C411yescharacteristic, complemented
26C22×C4×Dic47C411yescharacteristic, complemented
27C2×#13093938C2218yes—
28#15688986—21no—
29#15688983—21no—
30#15688983C2212yescomplemented
31#15688979C2212yes—
32C4×C22⋊Dic47—21no—
33C4×C22⋊Dic47C2212yescomplemented
34#15688889C2218yescomplemented
35C24×C4×C47C2211yescharacteristic
36C2×#117×C47—21no—
37C47×#381—21no—
38C47×#380—21no—
39C47×#380C2212yescomplemented
40C47×#379C2212yes—
41C4×C22⋊C4×C47—21no—
42C4×C22⋊C4×C47C2212yescomplemented
43C24×D47C2×C411yescharacteristic
44C22×C22⋊D47—21no—
45C22×C22⋊D47—21no—
46C22×C22⋊D47—21no—
47C22×C22⋊D47—21no—
48C22×C22⋊D47—28no—
49C22×C22⋊D47C2×C412yes—
50C22×C22⋊D47C2312yes—
51C23×Dic47C2×C411yescharacteristic
52C23×Dic47C2×C411yescharacteristic
53C23×Dic47C2×C411yescharacteristic
54C22×C4×D47—21no—
55C22×C4×D47—21no—
56C22×C4×D47—21no—
57C22×C4×D47—21no—
58C22×C4×D47—44no—
59C22×C4×D47C2×C412yes—
60C22×C4×D47C2×C412yes—
61C4×C22⋊D47—22no—
62C4×C22⋊D47—22no—
63C4×C22⋊D47—22no—
64C4×C22⋊D47—22no—
65C4×C22⋊D47—22no—
66C4×C22⋊D47—22no—
67C4×C22⋊D47—22no—
68C4×C22⋊D47—22no—
69C4×C22⋊D47—22no—
70C4×C22⋊D47—22no—
71C4×C22⋊D47—22no—
72C4×C22⋊D47—22no—
73C4×C22⋊D47—22no—
74C4×C22⋊D47—22no—
75C4×C22⋊D47—22no—
76C4×C22⋊D47—22no—
77#13093983—44no—
78C2×C4⋊Dic47—22no—
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×Dic47⋊C4—21no—
83C2×Dic47⋊C4C2×C412yes—
84C2×Dic47⋊C4C2×C412yes—
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47—21no—
87C2×C22⋊Dic47—21no—
88C2×C22⋊Dic47—21no—
89C2×C22⋊Dic47—22no—
90C2×C22⋊Dic47—22no—
91C2×C22⋊Dic47C2×C412yes—
92C2×C22⋊Dic47C2314yes—
93C2×C22⋊Dic47C2312yes—
94C2×(C2×D47)⋊C4—21no—
95C2×(C2×D47)⋊C4—21no—
96C2×(C2×D47)⋊C4—21no—
97C2×(C2×D47)⋊C4—21no—
98C2×(C2×D47)⋊C4C2×C412yes—
99C2×(C2×D47)⋊C4C2×C412yes—
100C2×C4×Dic47—21no—
101C2×C4×Dic47—21no—
102C2×C4×Dic47—21no—
103C2×C4×Dic47—21no—
104C2×C4×Dic47—22no—
105C2×C4×Dic47C2×C412yes—
106C2×C4×Dic47C2×C412yes—
107#13093938—216no—
108C47⋊#95—22no—
109C47⋊#95—22no—
110C25×C47C2311yescharacteristic
111C23×C4×C47—44no—
112C23×C4×C47C2×C411yescharacteristic
113C23×C4×C47C2×C411yescharacteristic
114C23×C4×C47C2×C411yescharacteristic
115C23×C4×C47C2×C411yescharacteristic
116C23×C4×C47D411yescharacteristic
117C23×C4×C47D411yescharacteristic
118C23×C4×C47D411yescharacteristic
119C23×C4×C47D411yescharacteristic
120C23×C4×C47D411yescharacteristic
121C23×C4×C47D411yescharacteristic
122C23×C4×C47D411yescharacteristic
123C23×C4×C47D411yescharacteristic
124C23×C4×C47C2311yescharacteristic
125C23×C4×C47C2311yescharacteristic
126#117×C47—44no—
127C2×C4⋊C4×C47—22no—
128C2×C22⋊C4×C47—22no—
129C2×C22⋊C4×C47—22no—
130C2×C22⋊C4×C47C2314yes—
131C2×C42×C47—22no—
132#95×C47—22no—
133#95×C47—22no—
134C24×C47—24no—
135C24×C47—42no—
136C24×C47—42no—
137C24×C47C22×C411yescharacteristic
138C24×C47C22×C411yescharacteristic
139C24×C47C2×D411yescharacteristic
140C24×C47C2×D411yescharacteristic
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C24×C47C2411yescharacteristic
144C23×D47—21no—
145C23×D47—21no—
146C23×D47—24no—
147C23×D47—42no—
148C23×D47—42no—
149C23×D47C22×C412yes—
150C22×C4×C47—24no—
151C22×C4×C47—24no—
152C22×C4×C47—24no—
153C22×C4×C47—24no—
154C22×C4×C47—42no—
155C22×C4×C47—42no—
156C22×C4×C47—42no—
157C22×C4×C47—42no—
158C22×C4×C47—42no—
159C22×C4×C47—42no—
160C22×C4×C47—42no—
161C22×C4×C47—42no—
162C22×C4×C47—42no—
163C22×C4×C47—42no—
164C22×C4×C47—42no—
165C22×C4×C47C22⋊C411yescharacteristic
166C22×C4×C47C22⋊C411yescharacteristic
167C22×C4×C47C22⋊C411yescharacteristic
168C22×C4×C47C22⋊C411yescharacteristic
169C22×C4×C47C22⋊C411yescharacteristic
170C22×C4×C47C22⋊C411yescharacteristic
171C22×C4×C47C22⋊C411yescharacteristic
172C22×C4×C47C22⋊C411yescharacteristic
173C22×C4×C47C22⋊C411yescharacteristic
174C22×C4×C47C22⋊C411yescharacteristic
175C22×C4×C47C22⋊C411yescharacteristic
176C22×C4×C47C22⋊C411yescharacteristic
177C22×C4×C47C22⋊C411yescharacteristic
178C22×C4×C47C22⋊C411yescharacteristic
179C22×C4×C47C22⋊C411yescharacteristic
180C22×C4×C47C22⋊C411yescharacteristic
181C22×C4×C47C22×C411yescharacteristic
182C22×C4×C47C22×C411yescharacteristic
183C22×C4×C47C22×C411yescharacteristic
184C22×C4×C47C22×C411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C2×C22⋊D47—28no—
194C2×C22⋊D47—28no—
195C2×C22⋊D47—28no—
196C2×C22⋊D47—28no—
197C2×C22⋊D47—22no—
198C2×C22⋊D47—22no—
199C2×C22⋊D47—22no—
200C2×C22⋊D47—22no—
201C2×C22⋊D47—24no—
202C2×C22⋊D47—24no—
203C2×C22⋊D47—24no—
204C2×C22⋊D47#4118yes—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—24no—
208C22×Dic47—21no—
209C22×Dic47—21no—
210C22×Dic47—21no—
211C22×Dic47—21no—
212C22×Dic47—24no—
213C22×Dic47—42no—
214C22×Dic47—42no—
215C22×Dic47C22×C412yes—
216C22×Dic47C22×C412yes—
217C22×Dic47C22×C412yes—
218C2×C4×D47—22no—
219C2×C4×D47—22no—
220C2×C4×D47—22no—
221C2×C4×D47—22no—
222C2×C4×D47—44no—
223C2×C4×D47—44no—
224C2×C4×D47—44no—
225C2×C4×D47—44no—
226C2×C4×D47—44no—
227C2×C4×D47—44no—
228C4⋊C4×C47—44no—
229C22⋊C4×C47—28no—
230C22⋊C4×C47—44no—
231C22⋊C4×C47—44no—
232C42×C47—44no—
233C22⋊Dic47—22no—
234C22⋊Dic47—22no—
235C22⋊Dic47—22no—
236C22⋊Dic47—22no—
237C22⋊Dic47—28no—
238C22⋊Dic47—44no—
239C22⋊Dic47—44no—
240(C2×D47)⋊C4—22no—
241(C2×D47)⋊C4—22no—
242(C2×D47)⋊C4—22no—
243(C2×D47)⋊C4—22no—
244C4⋊Dic47—44no—
245Dic47⋊C4—22no—
246Dic47⋊C4—22no—
247Dic47⋊C4—22no—
248Dic47⋊C4—22no—
249C4×Dic47—22no—
250C4×Dic47—22no—
251C4×Dic47—22no—
252C4×Dic47—22no—
253C4×Dic47—44no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—416no—
275C23×C47C2×C22⋊C411yescharacteristic
276C23×C47C2×C22⋊C411yescharacteristic
277C23×C47C2×C22⋊C411yescharacteristic
278C23×C47C2×C22⋊C411yescharacteristic
279C23×C47C23×C411yescharacteristic
280C23×C47C22×D411yescharacteristic
281C23×C47C22×D411yescharacteristic
282C23×C47C2×#4114yes—
283C22×D47—24no—
284C22×D47—24no—
285C22×D47—22no—
286C22×D47—22no—
287C22×D47—42no—
288C22×D47—416no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47#11714yescomplemented
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—41no—
320C2×C4×C47—41no—
321C2×C4×C47—41no—
322C2×C4×C47—44no—
323C2×C4×C47—44no—
324C2×C4×C47—44no—
325C2×C4×C47#9914yescomplemented
326C2×C4×C47C2×C22⋊C411yescharacteristic
327C2×C4×C47C2×C22⋊C411yescharacteristic
328C2×C4×C47C2×C22⋊C411yescharacteristic
329C2×C4×C47C2×C22⋊C411yescharacteristic
330C2×C4×C47C2×C22⋊C411yescharacteristic
331C2×C4×C47C2×C22⋊C411yescharacteristic
332C2×C4×C47C2×C22⋊C411yescharacteristic
333C2×C4×C47C2×C22⋊C411yescharacteristic
334C22⋊D47—28no—
335C22⋊D47—28no—
336C22⋊D47—28no—
337C22⋊D47—28no—
338C2×Dic47—24no—
339C2×Dic47—24no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—42no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—44no—
351C2×Dic47—44no—
352C2×Dic47—44no—
353C2×Dic47#11714yescomplemented
354C4×D47—44no—
355C4×D47—44no—
356C4×D47—44no—
357C4×D47—44no—
358#20722—471nomaximal, Sylow
359C22×C47—28no—
360C22×C47—21no—
361C22×C47—21no—
362C22×C47—21no—
363C22×C47—21no—
364C22×C47—21no—
365C22×C47—21no—
366C22×C47—21no—
367C22×C47—21no—
368C22×C47—21no—
369C22×C47—21no—
370C22×C47—21no—
371C22×C47—21no—
372C22×C47—21no—
373C22×C47—21no—
374C22×C47—21no—
375C22×C47—21no—
376C22×C47—44no—
377C22×C47—44no—
378C22×C47—44no—
379C22×C47—44no—
380C22×C47—44no—
381C22×C47—44no—
382C22×C47C2×#9912yes—
383C22×C47#41012yes—
384C22×C47C22×C22⋊C411yescharacteristic
385C22×C47C2×#11712yes—
386C22×C47#52512yes—
387C22×C47#52512yes—
388C2×D47—24no—
389C2×D47—44no—
390C2×D47—48no—
391C2×D47—48no—
392C2×D47—42no—
393C2×D47—42no—
394C2×D47—44no—
395C4×C47—21no—
396C4×C47—21no—
397C4×C47—21no—
398C4×C47—21no—
399C4×C47—21no—
400C4×C47—21no—
401C4×C47—84no—
402C4×C47C2×#9912yes—
403C4×C47C2×#9912yes—
404Dic47—24no—
405Dic47—42no—
406Dic47—42no—
407Dic47—84no—
408C22×C4×D4—471no—
409#2280—471no—
410#2280D4711yescharacteristic, complemented
411#1819—472no—
412#1799—474no—
413#1781—472no—
414C4×#99—474no—
415C2×C47—22no—
416C2×C47—22no—
417C2×C47—22no—
418C2×C47—22no—
419C2×C47—22no—
420C2×C47—41no—
421C2×C47—41no—
422C2×C47#228011yescharacteristic
423C2×C47C22×#9911yescharacteristic
424C2×C47C2×#41011yescharacteristic
425D47—44no—
426C23×D4—471no—
427C24×C4—471no—
428C24×C4C2×D4711yescharacteristic
429C2×C4×D4—472no—
430C2×C4×D4—472no—
431C2×C4×D4—472no—
432C2×C4×D4—472no—
433C2×C4×D4—941no—
434C2×C4×D4—941no—
435C2×C4×D4—941no—
436C2×C4×D4—941no—
437C2×C4×D4—941no—
438C2×C4×D4—941no—
439C2×C4×D4—941no—
440C2×C4×D4—941no—
441C2×#117—21no—
442C2×#117—941no—
443C22×C4⋊C4—471no—
444C22×C22⋊C4—471no—
445C22×C22⋊C4—471no—
446C22×C42—471no—
447C2×#99—478no—
448#381—21no—
449#381—941no—
450#380—21no—
451#380—472no—
452#380—941no—
453#380C2×D4712yescomplemented
454#379—472no—
455#379C2×D4712yes—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—472no—
458C4×C22⋊C4—941no—
459C4×C22⋊C4C2×D4712yescomplemented
460#342—478no—
461C47#2072211yescharacteristic, complemented, Sylow
462C25—471no—
463C25C22×D4711yescharacteristic
464C22×D4—472no—
465C22×D4—472no—
466C22×D4—948no—
467C22×D4—941no—
468C22×D4—941no—
469C22×D4—941no—
470C22×D4—941no—
471C23×C4—44no—
472C23×C4—471no—
473C23×C4—471no—
474C23×C4—471no—
475C23×C4—472no—
476C23×C4—472no—
477C23×C4—941no—
478C23×C4—941no—
479C23×C4—941no—
480C23×C4—941no—
481C23×C4—1884no—
482C23×C4C4×D4711yescharacteristic
483C23×C4C4×D4711yescharacteristic
484C23×C4C4×D4711yescharacteristic
485C23×C4C4×D4711yescharacteristic
486C23×C4D18811yescharacteristic
487C23×C4D18811yescharacteristic
488C23×C4D18811yescharacteristic
489C23×C4D18811yescharacteristic
490C23×C4C22⋊D4711yescharacteristic
491C23×C4C22⋊D4711yescharacteristic
492C23×C4C22⋊D4711yescharacteristic
493C23×C4C22⋊D4711yescharacteristic
494C23×C4C22×D4711yescharacteristic
495C23×C4C22×D4711yescharacteristic
496C4×D4—942no—
497C4×D4—942no—
498C4×D4—942no—
499C4×D4—942no—
500C4×D4—942no—
501C4×D4—942no—
502C4×D4—942no—
503C4×D4—942no—
504C4×D4—942no—
505C4×D4—942no—
506C4×D4—942no—
507C4×D4—942no—
508C4×D4—942no—
509C4×D4—942no—
510C4×D4—942no—
511C4×D4—942no—
512#117—44no—
513#117—1884no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—472no—
516C2×C4⋊C4—472no—
517C2×C4⋊C4—941no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—942no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—472no—
525C2×C22⋊C4—472no—
526C2×C22⋊C4—472no—
527C2×C22⋊C4—472no—
528C2×C22⋊C4—474no—
529C2×C22⋊C4—941no—
530C2×C22⋊C4—941no—
531C2×C22⋊C4—941no—
532C2×C22⋊C4—941no—
533C2×C22⋊C4—941no—
534C2×C22⋊C4—941no—
535C2×C22⋊C4—941no—
536C2×C22⋊C4—941no—
537C2×C22⋊C4—942no—
538C2×C22⋊C4—942no—
539C2×C22⋊C4C22×D4714yes—
540C2×C42—22no—
541C2×C42—472no—
542C2×C42—472no—
543C2×C42—941no—
544C2×C42—941no—
545C2×C42—941no—
546C2×C42—941no—
547C2×C42—942no—
548#99—9416no—
549#95—22no—
550#95—22no—
551#95—942no—
552#95—942no—
553C24—24no—
554C24—42no—
555C24—42no—
556C24—472no—
557C24—944no—
558C24—941no—
559C24—941no—
560C24—1882no—
561C24—1882no—
562C24C2×C4×D4711yescharacteristic
563C24C2×C4×D4711yescharacteristic
564C24C2×D18811yescharacteristic
565C24C2×D18811yescharacteristic
566C24C2×C22⋊D4711yescharacteristic
567C24C2×C22⋊D4711yescharacteristic
568C24C23×D4711yescharacteristic
569C2×D4—478no—
570C2×D4—944no—
571C2×D4—944no—
572C2×D4—948no—
573C2×D4—948no—
574C2×D4—948no—
575C2×D4—948no—
576C2×D4—942no—
577C2×D4—942no—
578C2×D4—942no—
579C2×D4—942no—
580C2×D4—944no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—472no—
597C22×C4—472no—
598C22×C4—472no—
599C22×C4—944no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—941no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—944no—
611C22×C4—1884no—
612C22×C4—1884no—
613C22×C4—1884no—
614C22×C4—1884no—
615C22×C4—1884no—
616C22×C4—1884no—
617C22×C4—1882no—
618C22×C4—1882no—
619C22×C4(C2×D47)⋊C411yescharacteristic
620C22×C4(C2×D47)⋊C411yescharacteristic
621C22×C4(C2×D47)⋊C411yescharacteristic
622C22×C4(C2×D47)⋊C411yescharacteristic
623C22×C4(C2×D47)⋊C411yescharacteristic
624C22×C4(C2×D47)⋊C411yescharacteristic
625C22×C4(C2×D47)⋊C411yescharacteristic
626C22×C4(C2×D47)⋊C411yescharacteristic
627C22×C4(C2×D47)⋊C411yescharacteristic
628C22×C4(C2×D47)⋊C411yescharacteristic
629C22×C4(C2×D47)⋊C411yescharacteristic
630C22×C4(C2×D47)⋊C411yescharacteristic
631C22×C4(C2×D47)⋊C411yescharacteristic
632C22×C4(C2×D47)⋊C411yescharacteristic
633C22×C4(C2×D47)⋊C411yescharacteristic
634C22×C4(C2×D47)⋊C411yescharacteristic
635C22×C4C2×C4×D4711yescharacteristic
636C22×C4C2×C4×D4711yescharacteristic
637C22×C4C2×C4×D4711yescharacteristic
638C22×C4C2×C4×D4711yescharacteristic
639C22×C4C2×D18811yescharacteristic
640C22×C4C2×D18811yescharacteristic
641C22×C4C2×D18811yescharacteristic
642C22×C4C2×D18811yescharacteristic
643C22×C4C2×C22⋊D4711yescharacteristic
644C22×C4C2×C22⋊D4711yescharacteristic
645C22×C4C2×C22⋊D4711yescharacteristic
646C22×C4C2×C22⋊D4711yescharacteristic
647C4⋊C4—44no—
648C4⋊C4—942no—
649C4⋊C4—942no—
650C4⋊C4—942no—
651C4⋊C4—942no—
652C4⋊C4—1884no—
653C22⋊C4—28no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—942no—
657C22⋊C4—942no—
658C22⋊C4—942no—
659C22⋊C4—942no—
660C22⋊C4—942no—
661C22⋊C4—942no—
662C22⋊C4—942no—
663C22⋊C4—942no—
664C22⋊C4—948no—
665C22⋊C4—1884no—
666C22⋊C4—1884no—
667C42—44no—
668C42—942no—
669C42—942no—
670C42—942no—
671C42—942no—
672C42—1884no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—416no—
694C23—474no—
695C23—944no—
696C23—944no—
697C23—942no—
698C23—942no—
699C23—1882no—
700C23—1882no—
701C23—1882no—
702C23—18816no—
703C23—1882no—
704C23—1882no—
705C23—1882no—
706C23C2×(C2×D47)⋊C411yescharacteristic
707C23C2×(C2×D47)⋊C411yescharacteristic
708C23C2×(C2×D47)⋊C411yescharacteristic
709C23C2×(C2×D47)⋊C411yescharacteristic
710C23C22×C4×D4711yescharacteristic
711C23C22×C22⋊D4711yescharacteristic
712C23C22×D18811yescharacteristic
713C23#41×D4714yes—
714D4—948no—
715D4—948no—
716D4—948no—
717D4—948no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—474no—
749C2×C4—944no—
750C2×C4—944no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—1884no—
756C2×C4—1884no—
757C2×C4—1884no—
758C2×C4—1884no—
759C2×C4—1884no—
760C2×C4—1882no—
761C2×C4—1882no—
762C2×C4—1882no—
763C2×C4—1882no—
764C2×C4—1884no—
765C2×C4—1884no—
766C2×C4—1882no—
767C2×C4—1882no—
768C2×C4#1309393814yescomplemented
769C2×C4C2×(C2×D47)⋊C411yescharacteristic
770C2×C4C2×(C2×D47)⋊C411yescharacteristic
771C2×C4C2×(C2×D47)⋊C411yescharacteristic
772C2×C4C2×(C2×D47)⋊C411yescharacteristic
773C2×C4C2×(C2×D47)⋊C411yescharacteristic
774C2×C4C2×(C2×D47)⋊C411yescharacteristic
775C2×C4C2×(C2×D47)⋊C411yescharacteristic
776C2×C4C2×(C2×D47)⋊C411yescharacteristic
777C22—28no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—944no—
801C22—1884no—
802C22—1884no—
803C22—1888no—
804C22—1888no—
805C22—1882no—
806C22—1882no—
807C22C2×#1309393812yes—
808C22#1568909612yes—
809C22C22×(C2×D47)⋊C411yescharacteristic
810C22#117×D4712yes—
811C22#1568963012yes—
812C22#1568963512yes—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—21no—
817C4—21no—
818C4—21no—
819C4—84no—
820C4—944no—
821C4—3764no—
822C4—1882no—
823C4—1882no—
824C4C2×#1309393812yes—
825C4C2×#1309393812yes—
826C2—22no—
827C2—22no—
828C2—22no—
829C2—22no—
830C2—22no—
831C2—41no—
832C2—41no—
833C2—1884no—
834C2#2024576711yescharacteristic
835C2C22×#1309393811yescharacteristic
836C2C2×#1568909611yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#2280C2
socleC22×C47C22×C22⋊C4
prime radicalC23×C22⋊D47C22
cosocleC24×C47C24
hypercenter#2280D47
hypocenterC47#20722
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. #20245771C2semidirect
3. #20243460C2semidirect
4. #20243373C2semidirect
6. C4×#13093938C2semidirect
7. C47×#2280C2semidirect
9. C23×C4×D47C4semidirect
18. C2×C4×C22⋊D47C4semidirect
19. C2×C4×C22⋊D47C4semidirect
23. C22×Dic47⋊C4C4semidirect
25. C22×(C2×D47)⋊C4C4semidirect
26. C22×C4×Dic47C4semidirect
30. #15688983C22semidirect
33. C4×C22⋊Dic47C22semidirect
34. #15688889C22semidirect
39. C47×#380C22semidirect
42. C4×C22⋊C4×C47C22semidirect
294. C22×D47#117semidirect
325. C2×C4×C47#99semidirect
353. C2×Dic47#117semidirect
410. #2280D47semidirect
453. #380C2×D47semidirect
459. C4×C22⋊C4C2×D47semidirect
461. C47#20722semidirect
768. C2×C4#13093938semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
#202457712
#202434602
#202433732
#202433022
C4×#130939382
C47×#22802
#2072247