Finite Group Databasebeta

← #26183557

Subgroups — #26183557

Order 12032.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689087C211yesmaximal, characteristic, complemented
2#20245771C211yesmaximal, characteristic, complemented
3#20241931C214yesmaximal, complemented
4#20241921C212yesmaximal, complemented
5#20241917C212yesmaximal, complemented
6#20241879C214yesmaximal, complemented
7C2×C47×#525C211yesmaximal, characteristic
8C22×#10625329—21no—
9C2×#13093983—21no—
10#15689087—21no—
11#15689087—21no—
12#15689087C2212yes—
13#15689087C2212yescomplemented
14C2×C22⋊(C47⋊C8)—21no—
15C2×C22⋊(C47⋊C8)C2212yescomplemented
16#15688986C2212yes—
17#15688983—21no—
18#15688983C2212yescomplemented
19#15688979—21no—
20C4×C22⋊Dic47—21no—
21C4×C22⋊Dic47C2212yescomplemented
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
43C2×#10625329—22no—
44C2×#10625329—22no—
45C2×#10625329—44no—
46C22×C47⋊C8—22no—
47#13093983—44no—
48C2×C4⋊Dic47—22no—
49C2×C22⋊Dic47—22no—
50C2×C22⋊Dic47—22no—
51C2×C22⋊Dic47—22no—
52C2×C4×Dic47—22no—
53C22⋊(C47⋊C8)—22no—
54C22⋊(C47⋊C8)—22no—
55C22⋊(C47⋊C8)—22no—
56C22⋊(C47⋊C8)C2314yes—
57C47⋊#95—22no—
58C47⋊#95C2314yes—
59C25×C47D411yescharacteristic
60C2×#41×C47—21no—
61C2×#41×C47—21no—
62C2×#41×C47—44no—
63C2×#41×C47C2×C412yes—
64C2×#41×C47C2×C412yes—
65C22×Q8×C47C2×C411yescharacteristic
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47C2×C411yescharacteristic
70C23×C4×C47—21no—
71C23×C4×C47—44no—
72C23×C4×C47C2×C411yescharacteristic
73C23×C4×C47C2×C411yescharacteristic
74C23×C4×C47C2×C411yescharacteristic
75C23×C4×C47C2×C411yescharacteristic
76C23×C4×C47D411yescharacteristic
77C23×C4×C47D411yescharacteristic
78C23×C4×C47D411yescharacteristic
79C23×C4×C47D411yescharacteristic
80C23×C4×C47D411yescharacteristic
81C23×C4×C47D411yescharacteristic
82C23×C4×C47D411yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86#123×C47—22no—
87#123×C47—22no—
88#123×C47—22no—
89#123×C47—22no—
90C22⋊Q8×C47—21no—
91C22⋊Q8×C47—21no—
92C22⋊Q8×C47—21no—
93C22⋊Q8×C47—21no—
94C22⋊Q8×C47C2×C412yes—
95C22⋊Q8×C47C2×C412yes—
96C22⋊Q8×C47C2×C412yes—
97C22⋊Q8×C47C2312yes—
98#121×C47—21no—
99#121×C47—21no—
100#121×C47—21no—
101#121×C47—21no—
102#121×C47C2×C412yes—
103#121×C47C2×C412yes—
104#121×C47C2×C412yes—
105#121×C47C2312yes—
106#120×C47—22no—
107#120×C47—22no—
108#120×C47—22no—
109#120×C47—22no—
110C4×D4×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—
118#117×C47—21no—
119#117×C47—21no—
120#117×C47C2×C412yes—
121#117×C47C2×C412yes—
122C2×C4⋊C4×C47—21no—
123C2×C4⋊C4×C47—21no—
124C2×C4⋊C4×C47C2×C411yescharacteristic
125C2×C4⋊C4×C47C2×C411yescharacteristic
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47—21no—
131C2×C42×C47—21no—
132C24×C47—21no—
133C24×C47—42no—
134C24×C47—42no—
135C24×C47—42no—
136C24×C47C22⋊C411yescharacteristic
137C24×C47C22⋊C411yescharacteristic
138C24×C47C22⋊C411yescharacteristic
139C24×C47C22⋊C411yescharacteristic
140C24×C47C2×D411yescharacteristic
141C24×C47C2×D411yescharacteristic
142C24×C47C2×D411yescharacteristic
143#41×C47—44no—
144#41×C47—44no—
145#41×C47—44no—
146#41×C47—44no—
147C2×Q8×C47—21no—
148C2×Q8×C47—42no—
149C2×Q8×C47C22×C412yes—
150C2×D4×C47—22no—
151C2×D4×C47—22no—
152C2×D4×C47—22no—
153C2×D4×C47—22no—
154C2×D4×C47—22no—
155C2×D4×C47—22no—
156C2×D4×C47—21no—
157C2×D4×C47—42no—
158C2×D4×C47—44no—
159C2×D4×C47—44no—
160C2×D4×C47—44no—
161C2×D4×C47C22×C412yes—
162C22×C4×C47—24no—
163C22×C4×C47—24no—
164C22×C4×C47—24no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—42no—
171C22×C4×C47—42no—
172C22×C4×C47—42no—
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—44no—
182C22×C4×C47C22⋊C411yescharacteristic
183C22×C4×C47C22⋊C411yescharacteristic
184C22×C4×C47C22⋊C411yescharacteristic
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×C47C2×D411yescharacteristic
201C22×C4×C47C2×D411yescharacteristic
202C22×C4×C47C2×D411yescharacteristic
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×C47C2411yescharacteristic
210C22×Dic47—24no—
211C4⋊C4×C47—22no—
212C4⋊C4×C47—22no—
213C4⋊C4×C47—22no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—22no—
217C4⋊C4×C47C22×C412yes—
218C4⋊C4×C47C22×C412yes—
219C22⋊C4×C47—22no—
220C22⋊C4×C47—22no—
221C22⋊C4×C47—22no—
222C22⋊C4×C47—22no—
223C22⋊C4×C47—22no—
224C22⋊C4×C47—22no—
225C22⋊C4×C47—22no—
226C22⋊C4×C47—22no—
227C22⋊C4×C47—22no—
228C22⋊C4×C47—22no—
229C42×C47—22no—
230C42×C47—22no—
231C22⋊Dic47—44no—
232C22⋊Dic47—44no—
233C22⋊Dic47—44no—
234C4⋊Dic47—44no—
235C4×Dic47—44no—
236#10625329—44no—
237#10625329—44no—
238C2×C47⋊C8—24no—
239C2×C47⋊C8—44no—
240C23×C47—22no—
241C23×C47—22no—
242C23×C47—22no—
243C23×C47—22no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—22no—
247C23×C47—22no—
248C23×C47—22no—
249C23×C47—22no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—41no—
255C23×C47—41no—
256C23×C47—41no—
257C23×C47—41no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—42no—
263C23×C47—42no—
264C23×C47—416no—
265C23×C47—42no—
266C23×C47C2×C22⋊C411yescharacteristic
267C23×C47C2×C22⋊C411yescharacteristic
268C23×C47C2×C22⋊C411yescharacteristic
269C23×C47C2×C22⋊C411yescharacteristic
270C23×C47C2×C22⋊C411yescharacteristic
271C23×C47C2×C22⋊C411yescharacteristic
272C23×C47C22×D411yescharacteristic
273Q8×C47—42no—
274Q8×C47—42no—
275D4×C47—42no—
276D4×C47—42no—
277D4×C47—44no—
278D4×C47—44no—
279D4×C47—44no—
280D4×C47—44no—
281D4×C47—44no—
282D4×C47—44no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
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—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—42no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—44no—
317C2×C4×C47—44no—
318C2×C4×C47#9914yes—
319C2×C4×C47C2×C22⋊C411yescharacteristic
320C2×C4×C47C2×C22⋊C411yescharacteristic
321C2×C4×C47C2×C22⋊C411yescharacteristic
322C2×C4×C47C2×C22⋊C411yescharacteristic
323C2×C4×C47C2×C22⋊C411yescharacteristic
324C2×C4×C47C2×C22⋊C411yescharacteristic
325C2×C4×C47C23×C411yescharacteristic
326C2×C4×C47C22×D411yescharacteristic
327C2×Dic47—44no—
328C2×Dic47—44no—
329C2×Dic47—44no—
330C47⋊C8—44no—
331#17559—471nomaximal, Sylow
332C22×C47—21no—
333C22×C47—21no—
334C22×C47—21no—
335C22×C47—21no—
336C22×C47—21no—
337C22×C47—21no—
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—21no—
341C22×C47—21no—
342C22×C47—21no—
343C22×C47—21no—
344C22×C47—21no—
345C22×C47—21no—
346C22×C47—21no—
347C22×C47—21no—
348C22×C47—21no—
349C22×C47—21no—
350C22×C47—44no—
351C22×C47—44no—
352C22×C47—44no—
353C22×C47—44no—
354C22×C47—44no—
355C22×C47—44no—
356C22×C47—44no—
357C22×C47—42no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—84no—
361C22×C47C2×#9912yes—
362C22×C47#42112yes—
363C22×C47C22×C22⋊C411yescharacteristic
364C22×C47#57512yes—
365C4×C47—21no—
366C4×C47—21no—
367C4×C47—21no—
368C4×C47—21no—
369C4×C47—21no—
370C4×C47—21no—
371C4×C47—42no—
372C4×C47—42no—
373C4×C47—42no—
374C4×C47C2×#9912yes—
375C4×C47C2×#9912yes—
376Dic47—84no—
377C2×#525D4711yescharacteristic
378C2×#407—471no—
379#2280—471no—
380#1513—474no—
381#1511—472no—
382#1510—472no—
383#1501—474no—
384C2×C47—22no—
385C2×C47—22no—
386C2×C47—22no—
387C2×C47—41no—
388C2×C47—41no—
389C2×C47—41no—
390C2×C47—41no—
391C2×C47—82no—
392C2×C47C22×#9911yescharacteristic
393C2×C47#289611yescharacteristic
394C2×C47C2×#42111yescharacteristic
395C22×#41Dic4711yescharacteristic, complemented
396C24×C4C2×D4711yescharacteristic
397C22×M16—941no—
398#525—21no—
399#525—21no—
400#525—21no—
401#525—21no—
402#525Dic4712yescomplemented
403#525Dic4712yescomplemented
404#525C2×D4712yes—
405#525C2×D4712yes—
406C2×#123—21no—
407C2×C22⋊Q8Dic4711yescharacteristic, complemented
408C2×C22⋊Q8C2×D4711yescharacteristic
409C2×#121Dic4711yescharacteristic, complemented
410C2×#121C2×D4711yescharacteristic
411C2×#120—21no—
412C2×C4×D4—21no—
413C2×C4×D4—21no—
414C2×#117—941no—
415C2×#117Dic4711yescharacteristic, complemented
416#407—472no—
417#407—472no—
418#407—941no—
419#407—941no—
420C2×C22⋊C8—472no—
421C2×C22⋊C8—941no—
422#381—472no—
423#380—472no—
424#380—941no—
425#379—941no—
426C4×C22⋊C4—472no—
427C4×C22⋊C4—941no—
428#328—478no—
429#327—478no—
430C47#1755911yescharacteristic, complemented, Sylow
431C25C22⋊D4711yescharacteristic
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—44no—
435C2×#41C2×Dic4712yes—
436C2×#41C2×Dic4712yes—
437C22×Q8C2×Dic4711yescharacteristic
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C2×Dic4711yescharacteristic
442C23×C4—21no—
443C23×C4—44no—
444C23×C4C2×Dic4711yescharacteristic
445C23×C4C2×Dic4711yescharacteristic
446C23×C4C2×Dic4711yescharacteristic
447C23×C4C2×Dic4711yescharacteristic
448C23×C4C22⋊D4711yescharacteristic
449C23×C4C22⋊D4711yescharacteristic
450C23×C4C22⋊D4711yescharacteristic
451C23×C4C22⋊D4711yescharacteristic
452C23×C4C22⋊D4711yescharacteristic
453C23×C4C22⋊D4711yescharacteristic
454C23×C4C22⋊D4711yescharacteristic
455C23×C4C22×D4711yescharacteristic
456C23×C4C22×D4711yescharacteristic
457C23×C4C22×D4711yescharacteristic
458C2×M16—942no—
459C2×M16—942no—
460C2×M16—1884no—
461C22×C8—942no—
462#123—22no—
463#123—22no—
464#123—22no—
465#123—22no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8—21no—
470C22⋊Q8C2×Dic4712yes—
471C22⋊Q8C2×Dic4712yes—
472C22⋊Q8C2×Dic4712yes—
473C22⋊Q8C22×D4712yes—
474#121—21no—
475#121—21no—
476#121—21no—
477#121—21no—
478#121C2×Dic4712yes—
479#121C2×Dic4712yes—
480#121C2×Dic4712yes—
481#121C22×D4712yes—
482#120—22no—
483#120—22no—
484#120—22no—
485#120—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494#117—21no—
495#117—21no—
496#117—1884no—
497#117C2×Dic4712yes—
498#117C2×Dic4712yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—942no—
502C2×C4⋊C4C2×Dic4711yescharacteristic
503C2×C4⋊C4C2×Dic4711yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—942no—
510C2×C22⋊C4—942no—
511C2×C22⋊C4—942no—
512C2×C42—21no—
513C2×C42—942no—
514C22⋊C8—474no—
515C22⋊C8—942no—
516C22⋊C8—942no—
517C22⋊C8—942no—
518#95—474no—
519#95—942no—
520C24—21no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24C22⋊Dic4711yescharacteristic
525C24C22⋊Dic4711yescharacteristic
526C24C22⋊Dic4711yescharacteristic
527C24C22⋊Dic4711yescharacteristic
528C24C2×C22⋊D4711yescharacteristic
529C24C2×C22⋊D4711yescharacteristic
530C24C2×C22⋊D4711yescharacteristic
531#41—44no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—42no—
537C2×Q8C22×Dic4712yes—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4C22×Dic4712yes—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—44no—
570C22×C4—944no—
571C22×C4C22⋊Dic4711yescharacteristic
572C22×C4C22⋊Dic4711yescharacteristic
573C22×C4C22⋊Dic4711yescharacteristic
574C22×C4C22⋊Dic4711yescharacteristic
575C22×C4C22⋊Dic4711yescharacteristic
576C22×C4C22⋊Dic4711yescharacteristic
577C22×C4C22⋊Dic4711yescharacteristic
578C22×C4C22⋊Dic4711yescharacteristic
579C22×C4C22⋊Dic4711yescharacteristic
580C22×C4C22⋊Dic4711yescharacteristic
581C22×C4C22⋊Dic4711yescharacteristic
582C22×C4C22⋊Dic4711yescharacteristic
583C22×C4C22×Dic4711yescharacteristic
584C22×C4C22×Dic4711yescharacteristic
585C22×C4C22×Dic4711yescharacteristic
586C22×C4C22×Dic4711yescharacteristic
587C22×C4C22×Dic4711yescharacteristic
588C22×C4C22×Dic4711yescharacteristic
589C22×C4C2×C22⋊D4711yescharacteristic
590C22×C4C2×C22⋊D4711yescharacteristic
591C22×C4C2×C22⋊D4711yescharacteristic
592C22×C4C2×C22⋊D4711yescharacteristic
593C22×C4C2×C22⋊D4711yescharacteristic
594C22×C4C2×C22⋊D4711yescharacteristic
595C22×C4C2×C22⋊D4711yescharacteristic
596C22×C4C2×C22⋊D4711yescharacteristic
597C22×C4C2×C22⋊D4711yescharacteristic
598C22×C4C23×D4711yescharacteristic
599M16—1884no—
600M16—1884no—
601C2×C8—944no—
602C2×C8—1884no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—22no—
609C4⋊C4—1884no—
610C4⋊C4C22×Dic4712yes—
611C4⋊C4C22×Dic4712yes—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—1884no—
623C22⋊C4—1884no—
624C22⋊C4—1884no—
625C42—22no—
626C42—22no—
627C42—1884no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—42no—
651C23—42no—
652C23—416no—
653C23—42no—
654C23C2×C22⋊Dic4711yescharacteristic
655C23C2×C22⋊Dic4711yescharacteristic
656C23C2×C22⋊Dic4711yescharacteristic
657C23C2×C22⋊Dic4711yescharacteristic
658C23C2×C22⋊Dic4711yescharacteristic
659C23C2×C22⋊Dic4711yescharacteristic
660C23C22×C22⋊D4711yescharacteristic
661Q8—42no—
662Q8—42no—
663D4—42no—
664D4—42no—
665D4—44no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—44no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—1884no—
707C2×C4—1884no—
708C2×C4—1884no—
709C2×C4#1309393914yes—
710C2×C4C2×C22⋊Dic4711yescharacteristic
711C2×C4C2×C22⋊Dic4711yescharacteristic
712C2×C4C2×C22⋊Dic4711yescharacteristic
713C2×C4C2×C22⋊Dic4711yescharacteristic
714C2×C4C2×C22⋊Dic4711yescharacteristic
715C2×C4C2×C22⋊Dic4711yescharacteristic
716C2×C4C23×Dic4711yescharacteristic
717C2×C4C22×C22⋊D4711yescharacteristic
718C8—1884no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22C2×#1309393912yes—
749C22#1568914012yes—
750C22C22×C22⋊Dic4711yescharacteristic
751C22#1568992112yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—3764no—
762C4C2×#1309393912yes—
763C4C2×#1309393912yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—82no—
772C2C22×#1309393911yescharacteristic
773C2#2025190711yescharacteristic
774C2C2×#1568914011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊Dic47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#525C2
socleC22×C47C22×C22⋊C4
cosocleC22×C4×C47C24
hypercenterC2×#525D47
hypocenterC47#17559
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#15689087C2semidirect
2. #20245771C2semidirect
3. #20241931C2semidirect
4. #20241921C2semidirect
5. #20241917C2semidirect
6. #20241879C2semidirect
13. #15689087C22semidirect
15. C2×C22⋊(C47⋊C8)C22semidirect
18. #15688983C22semidirect
21. C4×C22⋊Dic47C22semidirect
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
395. C22×#41Dic47semidirect
402. #525Dic47semidirect
403. #525Dic47semidirect
407. C2×C22⋊Q8Dic47semidirect
409. C2×#121Dic47semidirect
415. C2×#117Dic47semidirect
430. C47#17559semidirect

Maximal subgroups

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

subgroupindex
C2×#156890872
#202457712
#202419312
#202419212
#202419172
#202418792
C2×C47×#5252
#1755947