Finite Group Databasebeta

← #26183768

Subgroups — #26183768

Order 12032.

1510 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689087C211yesmaximal, characteristic, complemented
2C2×#15688983C211yesmaximal, characteristic, complemented
3#20241960C212yesmaximal, complemented
4#20241956C212yesmaximal, complemented
5#20241931C214yesmaximal, complemented
6#20241892C214yesmaximal, complemented
7C2×C47×#525C211yesmaximal, characteristic
8C22×#10625329—21no—
9C22×C4⋊Dic47—21no—
10C22×C22⋊Dic47—21no—
11#15689087—21no—
12#15689087—21no—
13#15689087C2212yescomplemented
14#15689087C2212yescomplemented
15C2×C22⋊(C47⋊C8)—21no—
16C2×C22⋊(C47⋊C8)C2212yes—
17#15688983—21no—
18#15688983—21no—
19#15688983C2212yes—
20#15688983C2212yescomplemented
21C2×C47⋊#95C2212yescomplemented
22#15688860C2218yescomplemented
23#15688857C2218yescomplemented
24C22×#41×C47C411yescharacteristic, complemented
25C24×C4×C47C2211yescharacteristic
26C47×#525—21no—
27C47×#525—21no—
28C47×#525—21no—
29C47×#525—21no—
30C47×#525C412yescomplemented
31C47×#525C412yescomplemented
32C47×#525C2212yes—
33C47×#525C2212yes—
34C2×#123×C47—21no—
35C2×C22⋊Q8×C47C411yescharacteristic, complemented
36C2×C22⋊Q8×C47C2211yescharacteristic
37C2×#121×C47C411yescharacteristic, complemented
38C2×#121×C47C2211yescharacteristic
39C2×#120×C47—21no—
40C2×C4×D4×C47—21no—
41C2×C4×D4×C47—21no—
42C2×#117×C47C411yescharacteristic, complemented
43C23×Dic47—22no—
44C2×#10625329—22no—
45C2×#10625329—22no—
46C2×#10625329—44no—
47C22×C47⋊C8—22no—
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—44no—
51C2×C22⋊Dic47—22no—
52C2×C22⋊Dic47—22no—
53C2×C22⋊Dic47—44no—
54C22⋊(C47⋊C8)—22no—
55C22⋊(C47⋊C8)—22no—
56C22⋊(C47⋊C8)—22no—
57C22⋊(C47⋊C8)C2314yes—
58C47⋊#95—22no—
59C47⋊#95C2314yes—
60C25×C47D411yescharacteristic
61C2×#41×C47—21no—
62C2×#41×C47—21no—
63C2×#41×C47—44no—
64C2×#41×C47C2×C412yes—
65C2×#41×C47C2×C412yescomplemented
66C22×Q8×C47C2×C411yescharacteristic, complemented
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47C2×C411yescharacteristic, complemented
71C23×C4×C47—21no—
72C23×C4×C47—44no—
73C23×C4×C47C2×C411yescharacteristic
74C23×C4×C47C2×C411yescharacteristic
75C23×C4×C47C2×C411yescharacteristic
76C23×C4×C47C2×C411yescharacteristic
77C23×C4×C47D411yescharacteristic
78C23×C4×C47D411yescharacteristic
79C23×C4×C47D411yescharacteristic
80C23×C4×C47D411yescharacteristic
81C23×C4×C47D411yescharacteristic
82C23×C4×C47D411yescharacteristic
83C23×C4×C47D411yescharacteristic
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87#123×C47—22no—
88#123×C47—22no—
89#123×C47—22no—
90#123×C47—22no—
91C22⋊Q8×C47—21no—
92C22⋊Q8×C47—21no—
93C22⋊Q8×C47—21no—
94C22⋊Q8×C47—21no—
95C22⋊Q8×C47C2×C412yes—
96C22⋊Q8×C47C2×C412yescomplemented
97C22⋊Q8×C47C2×C412yescomplemented
98C22⋊Q8×C47C2312yes—
99#121×C47—21no—
100#121×C47—21no—
101#121×C47—21no—
102#121×C47—21no—
103#121×C47C2×C412yes—
104#121×C47C2×C412yescomplemented
105#121×C47C2×C412yescomplemented
106#121×C47C2312yes—
107#120×C47—22no—
108#120×C47—22no—
109#120×C47—22no—
110#120×C47—22no—
111C4×D4×C47—22no—
112C4×D4×C47—22no—
113C4×D4×C47—22no—
114C4×D4×C47—22no—
115C4×D4×C47—22no—
116C4×D4×C47—22no—
117C4×D4×C47—22no—
118C4×D4×C47—22no—
119#117×C47—21no—
120#117×C47—21no—
121#117×C47C2×C412yes—
122#117×C47C2×C412yescomplemented
123C2×C4⋊C4×C47—21no—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
126C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C42×C47—21no—
133C24×C47—22no—
134C24×C47—22no—
135C24×C47—21no—
136C24×C47—42no—
137C24×C47—42no—
138C24×C47C22⋊C411yescharacteristic
139C24×C47C22⋊C411yescharacteristic
140C24×C47C22⋊C411yescharacteristic
141C24×C47C22⋊C411yescharacteristic
142C24×C47C2×D411yescharacteristic
143C24×C47C2×D411yescharacteristic
144C24×C47C2×D411yescharacteristic
145#41×C47—44no—
146#41×C47—44no—
147#41×C47—44no—
148#41×C47—44no—
149C2×Q8×C47—21no—
150C2×Q8×C47—42no—
151C2×Q8×C47C22×C412yes—
152C2×D4×C47—22no—
153C2×D4×C47—22no—
154C2×D4×C47—22no—
155C2×D4×C47—22no—
156C2×D4×C47—22no—
157C2×D4×C47—22no—
158C2×D4×C47—21no—
159C2×D4×C47—42no—
160C2×D4×C47—44no—
161C2×D4×C47—44no—
162C2×D4×C47—42no—
163C2×D4×C47—42no—
164C2×D4×C47C22×C412yes—
165C22×C4×C47—24no—
166C22×C4×C47—24no—
167C22×C4×C47—24no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—42no—
174C22×C4×C47—42no—
175C22×C4×C47—42no—
176C22×C4×C47—42no—
177C22×C4×C47—42no—
178C22×C4×C47—42no—
179C22×C4×C47—42no—
180C22×C4×C47—42no—
181C22×C4×C47—42no—
182C22×C4×C47—42no—
183C22×C4×C47—42no—
184C22×C4×C47—44no—
185C22×C4×C47C22⋊C411yescharacteristic
186C22×C4×C47C22⋊C411yescharacteristic
187C22×C4×C47C22⋊C411yescharacteristic
188C22×C4×C47C22⋊C411yescharacteristic
189C22×C4×C47C22⋊C411yescharacteristic
190C22×C4×C47C22⋊C411yescharacteristic
191C22×C4×C47C22⋊C411yescharacteristic
192C22×C4×C47C22⋊C411yescharacteristic
193C22×C4×C47C22⋊C411yescharacteristic
194C22×C4×C47C22⋊C411yescharacteristic
195C22×C4×C47C22⋊C411yescharacteristic
196C22×C4×C47C22⋊C411yescharacteristic
197C22×C4×C47C22×C411yescharacteristic
198C22×C4×C47C22×C411yescharacteristic
199C22×C4×C47C22×C411yescharacteristic
200C22×C4×C47C22×C411yescharacteristic
201C22×C4×C47C22×C411yescharacteristic
202C22×C4×C47C22×C411yescharacteristic
203C22×C4×C47C2×D411yescharacteristic
204C22×C4×C47C2×D411yescharacteristic
205C22×C4×C47C2×D411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2411yescharacteristic
213C22×Dic47—24no—
214C22×Dic47—44no—
215C22×Dic47—44no—
216C22×Dic47—44no—
217C4⋊C4×C47—22no—
218C4⋊C4×C47—22no—
219C4⋊C4×C47—22no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—22no—
223C4⋊C4×C47C22×C412yes—
224C4⋊C4×C47C22×C412yes—
225C22⋊C4×C47—22no—
226C22⋊C4×C47—22no—
227C22⋊C4×C47—22no—
228C22⋊C4×C47—22no—
229C22⋊C4×C47—22no—
230C22⋊C4×C47—22no—
231C22⋊C4×C47—22no—
232C22⋊C4×C47—22no—
233C22⋊C4×C47—22no—
234C22⋊C4×C47—22no—
235C42×C47—22no—
236C42×C47—22no—
237C22⋊Dic47—44no—
238C22⋊Dic47—44no—
239C4⋊Dic47—44no—
240C4⋊Dic47—44no—
241#10625329—44no—
242#10625329—44no—
243C2×C47⋊C8—24no—
244C2×C47⋊C8—44no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—22no—
248C23×C47—22no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47—41no—
266C23×C47—41no—
267C23×C47—41no—
268C23×C47—48no—
269C23×C47—48no—
270C23×C47—42no—
271C23×C47—42no—
272C23×C47—42no—
273C23×C47C2×C22⋊C411yescharacteristic
274C23×C47C2×C22⋊C411yescharacteristic
275C23×C47C2×C22⋊C411yescharacteristic
276C23×C47C2×C22⋊C411yescharacteristic
277C23×C47C2×C22⋊C411yescharacteristic
278C23×C47C2×C22⋊C411yescharacteristic
279C23×C47AGL(1,ℤ/8)12yes—
280C23×C47#13712yes—
281C23×C47C22×D411yescharacteristic
282Q8×C47—42no—
283Q8×C47—42no—
284D4×C47—42no—
285D4×C47—44no—
286D4×C47—44no—
287D4×C47—42no—
288D4×C47—42no—
289D4×C47—44no—
290D4×C47—44no—
291D4×C47—44no—
292D4×C47—42no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
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—22no—
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—41no—
323C2×C4×C47—44no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47—44no—
328C2×C4×C47#9914yes—
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
334C2×C4×C47C2×C22⋊C411yescharacteristic
335C2×C4×C47C23×C411yescharacteristic
336C2×C4×C47C22×D411yescharacteristic
337C2×Dic47—44no—
338C2×Dic47—44no—
339C2×Dic47—44no—
340C2×Dic47—88no—
341C47⋊C8—44no—
342#17592—471nomaximal, Sylow
343C22×C47—24no—
344C22×C47—24no—
345C22×C47—21no—
346C22×C47—21no—
347C22×C47—21no—
348C22×C47—21no—
349C22×C47—21no—
350C22×C47—21no—
351C22×C47—21no—
352C22×C47—21no—
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—21no—
357C22×C47—21no—
358C22×C47—21no—
359C22×C47—21no—
360C22×C47—21no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—44no—
364C22×C47—44no—
365C22×C47—44no—
366C22×C47—44no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—42no—
370C22×C47—42no—
371C22×C47—42no—
372C22×C47—84no—
373C22×C47C2×#9912yes—
374C22×C47#41712yes—
375C22×C47#41712yes—
376C22×C47#42112yes—
377C22×C47C22×C22⋊C411yescharacteristic
378C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
379C22×C47C2×#13711yescharacteristic
380C4×C47—21no—
381C4×C47—21no—
382C4×C47—21no—
383C4×C47—21no—
384C4×C47—21no—
385C4×C47—21no—
386C4×C47—42no—
387C4×C47—42no—
388C4×C47—42no—
389C4×C47C2×#9912yes—
390C4×C47C2×#9912yes—
391Dic47—84no—
392C2×#525D4711yescharacteristic
393C2×#407—471no—
394C2×#380—471no—
395#1520—472no—
396#1519—472no—
397#1513—474no—
398#1504—474no—
399C2×C47—21no—
400C2×C47—21no—
401C2×C47—22no—
402C2×C47—22no—
403C2×C47—22no—
404C2×C47—22no—
405C2×C47—41no—
406C2×C47—41no—
407C2×C47—82no—
408C2×C47C22×#9911yescharacteristic
409C2×C47C2×#41711yescharacteristic
410C2×C47C2×#42111yescharacteristic
411C22×#41Dic4711yescharacteristic, complemented
412C24×C4C2×D4711yescharacteristic
413C22×M16—941no—
414#525—21no—
415#525—21no—
416#525—21no—
417#525—21no—
418#525Dic4712yescomplemented
419#525Dic4712yescomplemented
420#525C2×D4712yes—
421#525C2×D4712yes—
422C2×#123—21no—
423C2×C22⋊Q8Dic4711yescharacteristic, complemented
424C2×C22⋊Q8C2×D4711yescharacteristic
425C2×#121Dic4711yescharacteristic, complemented
426C2×#121C2×D4711yescharacteristic
427C2×#120—21no—
428C2×C4×D4—21no—
429C2×C4×D4—21no—
430C2×#117Dic4711yescharacteristic, complemented
431C22×C4⋊C4—941no—
432C22×C22⋊C4—941no—
433#407—472no—
434#407—472no—
435#407—941no—
436#407—941no—
437C2×C22⋊C8—472no—
438C2×C22⋊C8—941no—
439#380—472no—
440#380—472no—
441#380—941no—
442#380—941no—
443C2×#95—472no—
444#328—478no—
445#327—478no—
446C47#1759211yescharacteristic, complemented, Sylow
447C25C22⋊D4711yescharacteristic
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—44no—
451C2×#41C2×Dic4712yes—
452C2×#41C2×Dic4712yescomplemented
453C22×Q8C2×Dic4711yescharacteristic, complemented
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4C2×Dic4711yescharacteristic, complemented
458C23×C4—21no—
459C23×C4—44no—
460C23×C4—942no—
461C23×C4C2×Dic4711yescharacteristic
462C23×C4C2×Dic4711yescharacteristic
463C23×C4C2×Dic4711yescharacteristic
464C23×C4C2×Dic4711yescharacteristic
465C23×C4C22⋊D4711yescharacteristic
466C23×C4C22⋊D4711yescharacteristic
467C23×C4C22⋊D4711yescharacteristic
468C23×C4C22⋊D4711yescharacteristic
469C23×C4C22⋊D4711yescharacteristic
470C23×C4C22⋊D4711yescharacteristic
471C23×C4C22⋊D4711yescharacteristic
472C23×C4C22×D4711yescharacteristic
473C23×C4C22×D4711yescharacteristic
474C23×C4C22×D4711yescharacteristic
475C2×M16—942no—
476C2×M16—942no—
477C2×M16—1884no—
478C22×C8—942no—
479#123—22no—
480#123—22no—
481#123—22no—
482#123—22no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8C2×Dic4712yes—
488C22⋊Q8C2×Dic4712yescomplemented
489C22⋊Q8C2×Dic4712yescomplemented
490C22⋊Q8C22×D4712yes—
491#121—21no—
492#121—21no—
493#121—21no—
494#121—21no—
495#121C2×Dic4712yes—
496#121C2×Dic4712yescomplemented
497#121C2×Dic4712yescomplemented
498#121C22×D4712yes—
499#120—22no—
500#120—22no—
501#120—22no—
502#120—22no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511#117—21no—
512#117—21no—
513#117C2×Dic4712yes—
514#117C2×Dic4712yescomplemented
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—942no—
518C2×C4⋊C4—942no—
519C2×C4⋊C4—1884no—
520C2×C4⋊C4C2×Dic4711yescharacteristic, complemented
521C2×C4⋊C4C2×Dic4711yescharacteristic, complemented
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—942no—
528C2×C22⋊C4—942no—
529C2×C22⋊C4—1884no—
530C2×C42—21no—
531C22⋊C8—474no—
532C22⋊C8—942no—
533C22⋊C8—942no—
534C22⋊C8—942no—
535#95—474no—
536#95—942no—
537C24—22no—
538C24—22no—
539C24—21no—
540C24—42no—
541C24—42no—
542C24C22⋊Dic4711yescharacteristic
543C24C22⋊Dic4711yescharacteristic
544C24C22⋊Dic4711yescharacteristic
545C24C22⋊Dic4711yescharacteristic
546C24C2×C22⋊D4711yescharacteristic
547C24C2×C22⋊D4711yescharacteristic
548C24C2×C22⋊D4711yescharacteristic
549#41—44no—
550#41—44no—
551#41—44no—
552#41—44no—
553C2×Q8—21no—
554C2×Q8—42no—
555C2×Q8C22×Dic4712yes—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—42no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4C22×Dic4712yes—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—44no—
589C22×C4—944no—
590C22×C4—1884no—
591C22×C4—1884no—
592C22×C4—1884no—
593C22×C4C22⋊Dic4711yescharacteristic
594C22×C4C22⋊Dic4711yescharacteristic
595C22×C4C22⋊Dic4711yescharacteristic
596C22×C4C22⋊Dic4711yescharacteristic
597C22×C4C22⋊Dic4711yescharacteristic
598C22×C4C22⋊Dic4711yescharacteristic
599C22×C4C22⋊Dic4711yescharacteristic
600C22×C4C22⋊Dic4711yescharacteristic
601C22×C4C22⋊Dic4711yescharacteristic
602C22×C4C22⋊Dic4711yescharacteristic
603C22×C4C22⋊Dic4711yescharacteristic
604C22×C4C22⋊Dic4711yescharacteristic
605C22×C4C22×Dic4711yescharacteristic
606C22×C4C22×Dic4711yescharacteristic
607C22×C4C22×Dic4711yescharacteristic
608C22×C4C22×Dic4711yescharacteristic
609C22×C4C22×Dic4711yescharacteristic
610C22×C4C22×Dic4711yescharacteristic
611C22×C4C2×C22⋊D4711yescharacteristic
612C22×C4C2×C22⋊D4711yescharacteristic
613C22×C4C2×C22⋊D4711yescharacteristic
614C22×C4C2×C22⋊D4711yescharacteristic
615C22×C4C2×C22⋊D4711yescharacteristic
616C22×C4C2×C22⋊D4711yescharacteristic
617C22×C4C2×C22⋊D4711yescharacteristic
618C22×C4C2×C22⋊D4711yescharacteristic
619C22×C4C2×C22⋊D4711yescharacteristic
620C22×C4C23×D4711yescharacteristic
621M16—1884no—
622M16—1884no—
623C2×C8—944no—
624C2×C8—1884no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—22no—
631C4⋊C4—1884no—
632C4⋊C4—1884no—
633C4⋊C4C22×Dic4712yes—
634C4⋊C4C22×Dic4712yes—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—1884no—
646C22⋊C4—1884no—
647C42—22no—
648C42—22no—
649C23—22no—
650C23—22no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—48no—
673C23—48no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23C2×C22⋊Dic4711yescharacteristic
678C23C2×C22⋊Dic4711yescharacteristic
679C23C2×C22⋊Dic4711yescharacteristic
680C23C2×C22⋊Dic4711yescharacteristic
681C23C2×C22⋊Dic4711yescharacteristic
682C23C2×C22⋊Dic4711yescharacteristic
683C23#1309404912yes—
684C23#1309405412yes—
685C23C22×C22⋊D4711yescharacteristic
686Q8—42no—
687Q8—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—44no—
693D4—44no—
694D4—42no—
695D4—42no—
696D4—42no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—3768no—
733C2×C4—1884no—
734C2×C4—1884no—
735C2×C4—1884no—
736C2×C4#1309393914yes—
737C2×C4C2×C22⋊Dic4711yescharacteristic
738C2×C4C2×C22⋊Dic4711yescharacteristic
739C2×C4C2×C22⋊Dic4711yescharacteristic
740C2×C4C2×C22⋊Dic4711yescharacteristic
741C2×C4C2×C22⋊Dic4711yescharacteristic
742C2×C4C2×C22⋊Dic4711yescharacteristic
743C2×C4C23×Dic4711yescharacteristic
744C2×C4C22×C22⋊D4711yescharacteristic
745C8—1884no—
746C22—24no—
747C22—24no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—84no—
776C22C2×#1309393912yes—
777C22#1568912412yes—
778C22#1568912412yes—
779C22#1568914012yes—
780C22C22×C22⋊Dic4711yescharacteristic
781C22C2×#1309404911yescharacteristic
782C22C2×#1309405411yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—3764no—
793C4C2×#1309393912yes—
794C4C2×#1309393912yes—
795C2—21no—
796C2—22no—
797C2—22no—
798C2—21no—
799C2—22no—
800C2—22no—
801C2—41no—
802C2—41no—
803C2—82no—
804C2C22×#1309393911yescharacteristic
805C2C2×#1568912411yescharacteristic
806C2C2×#1568914011yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#525C2
socleC22×C47C22×C22⋊C4
cosocleC22×C4×C47C24
hypercenterC2×#525D47
hypocenterC47#17592
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#15689087C2semidirect
2. C2×#15688983C2semidirect
3. #20241960C2semidirect
4. #20241956C2semidirect
5. #20241931C2semidirect
6. #20241892C2semidirect
13. #15689087C22semidirect
14. #15689087C22semidirect
20. #15688983C22semidirect
21. C2×C47⋊#95C22semidirect
22. #15688860C22semidirect
23. #15688857C22semidirect
24. C22×#41×C47C4semidirect
30. C47×#525C4semidirect
31. C47×#525C4semidirect
35. C2×C22⋊Q8×C47C4semidirect
37. C2×#121×C47C4semidirect
42. C2×#117×C47C4semidirect
65. C2×#41×C47C2×C4semidirect
66. C22×Q8×C47C2×C4semidirect
70. C22×D4×C47C2×C4semidirect
96. C22⋊Q8×C47C2×C4semidirect
97. C22⋊Q8×C47C2×C4semidirect
104. #121×C47C2×C4semidirect
105. #121×C47C2×C4semidirect
122. #117×C47C2×C4semidirect
125. C2×C4⋊C4×C47C2×C4semidirect
126. C2×C4⋊C4×C47C2×C4semidirect
411. C22×#41Dic47semidirect
418. #525Dic47semidirect
419. #525Dic47semidirect
423. C2×C22⋊Q8Dic47semidirect
425. C2×#121Dic47semidirect
430. C2×#117Dic47semidirect
446. C47#17592semidirect
452. C2×#41C2×Dic47semidirect
453. C22×Q8C2×Dic47semidirect
457. C22×D4C2×Dic47semidirect
488. C22⋊Q8C2×Dic47semidirect
489. C22⋊Q8C2×Dic47semidirect
496. #121C2×Dic47semidirect
497. #121C2×Dic47semidirect
514. #117C2×Dic47semidirect
520. C2×C4⋊C4C2×Dic47semidirect
521. C2×C4⋊C4C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890872
C2×#156889832
#202419602
#202419562
#202419312
#202418922
C2×C47×#5252
#1759247