Finite Group Databasebeta

← #26376256

Subgroups — #26376256

Order 12032.

2516 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689830C211yesmaximal, characteristic
2#20246483C212yesmaximal, complemented
3#20246477C211yesmaximal, characteristic, complemented
4#20246469C214yesmaximal, complemented
5#20246393C212yesmaximal, complemented
6#20246347C211yesmaximal, characteristic, complemented
7#20246293C212yesmaximal
8#20246267C212yesmaximal, complemented
9#20245955C211yesmaximal, characteristic, complemented
10#20245947C212yesmaximal, complemented
11#20245920C214yesmaximal, complemented
12#20245916C212yesmaximal, complemented
13C4×#13093989C211yesmaximal, characteristic, complemented
14C4×D4×Dic47C212yesmaximal
15C4×D4×Dic47C211yesmaximal, characteristic
16C2×C4⋊C4×Dic47C212yesmaximal, complemented
17D4×C4⋊C4×C47C211yesmaximal, characteristic
18#15689830C4116yescomplemented
19C2×#13094024C2211yescharacteristic
20C2×#13094015C2212yes—
21C2×#13094003C2212yes—
22C2×#13094001C2214yes—
23C2×C4×Dic94C2211yescharacteristic
24C2×#13093989C2211yescharacteristic
25C2×#13093989C2211yescharacteristic
26C2×#13093989C2212yes—
27C2×D4×Dic47C2211yescharacteristic
28C2×D4×Dic47C2212yes—
29C2×D4×Dic47C2211yescharacteristic
30C22×C4⋊Dic47C2212yes—
31C22×C4×Dic47C2212yes—
32C22×C4×Dic47C2214yes—
33#15689028C2212yes—
34#15689028C2212yes—
35#15689027C2214yes—
36#15689021C2212yes—
37#15689019C2212yes—
38#15689019C2212yes—
39#15689019C2212yes—
40#15689018C2214yes—
41#15689008C2214yes—
42#15689008C2214yes—
43#15689005C2214yes—
44#15689004C2214yes—
45#15689004C2214yes—
46#15688996C2214yes—
47#15688995C2214yes—
48#15688988C2212yes—
49#15688981C2214yes—
50C4⋊C4×Dic47C2212yes—
51C4⋊C4×Dic47C2212yes—
52C4⋊C4×Dic47C2212yes—
53C4⋊C4×Dic47C2212yes—
54C4⋊C4×Dic47C2214yes—
55C4⋊C4×Dic47C2211yescharacteristic
56C4⋊C4×Dic47C2212yes—
57C4⋊C4×Dic47C2214yes—
58C4⋊C4×Dic47C2211yescharacteristic
59C4⋊C4×Dic47C2211yescharacteristic
60C4⋊C4×Dic47C2211yescharacteristic
61C4×Dic47⋊C4C2212yes—
62C4×C4⋊Dic47C2211yescharacteristic
63C4×C4⋊Dic47C2212yes—
64#15688974C2214yes—
65#15688974C2212yes—
66#15688974C2212yes—
67C22⋊C4×Dic47C2214yes—
68C22⋊C4×Dic47C2212yes—
69C22⋊C4×Dic47C2212yes—
70C22⋊C4×Dic47C2214yes—
71C4×C22⋊Dic47C2214yes—
72C4×C22⋊Dic47C2212yes—
73C2×C47⋊#95C2214yes—
74C42×Dic47C2212yes—
75C42×Dic47C2211yescharacteristic
76C2×C4×D4×C47C2212yes—
77C2×C4×D4×C47C2211yescharacteristic
78C22×C4⋊C4×C47C2212yes—
79C47×#389C2212yes—
80C47×#385C2214yes—
81C47×#384C2211yescharacteristic
82C47×#380C2212yes—
83C4×C4⋊C4×C47C2211yescharacteristic
84C22×Dic94C2311yescharacteristic
85C22×Dic94C2312yes—
86C23×Dic47C2312yes—
87C23×Dic47C2312yes—
88C23×Dic47C2314yes—
89#13094024C2×C418yescomplemented
90#13094015C2×C4116yescomplemented
91#13094003C2×C4116yescomplemented
92#13094001C2×C4132yescomplemented
93C4×Dic94C2×C418yescomplemented
94#13093989—24no—
95#13093989—24no—
96#13093989—44no—
97D4×Dic47—24no—
98D4×Dic47C2×C4116yes—
99D4×Dic47Q818yescomplemented
100C2×C4⋊Dic47C2×C4116yescomplemented
101C2×C4⋊Dic47C2311yescharacteristic
102C2×C4⋊Dic47C2312yes—
103C2×C4⋊Dic47C2311yescharacteristic
104C2×C4⋊Dic47C2314yes—
105C2×C4⋊Dic47C2312yes—
106C2×C4⋊Dic47C2311yescharacteristic
107C2×Dic47⋊C4C2312yes—
108C2×Dic47⋊C4C2312yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2312yes—
112C2×Dic47⋊C4C2314yes—
113C2×C22⋊Dic47C2312yes—
114C2×C22⋊Dic47C2314yes—
115C2×C22⋊Dic47C2312yes—
116C2×C4×Dic47—28no—
117C2×C4×Dic47—48no—
118C2×C4×Dic47C2312yes—
119C2×C4×Dic47C2311yescharacteristic
120C2×C4×Dic47C2312yes—
121C2×C4×Dic47C2311yescharacteristic
122C2×C4×Dic47C2312yes—
123C2×C4×Dic47C2311yescharacteristic
124C2×C4×Dic47C2312yes—
125C2×C4×Dic47C2312yes—
126C2×C4×Dic47C2314yes—
127C2×C4×Dic47C2312yes—
128C2×C4×Dic47C2311yescharacteristic
129C2×C4×Dic47C2312yes—
130C2×C4×Dic47C2314yes—
131C2×C4×Dic47C2314yes—
132C2×C4×Dic47C2312yes—
133C2×C4×Dic47C2311yescharacteristic
134C2×C4×Dic47C2311yescharacteristic
135C47⋊#95C2312yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C47⋊#95C2312yes—
140C47⋊#95C2314yes—
141C47⋊#95C2314yes—
142C47⋊#95C2312yes—
143C47⋊#95C2312yes—
144C47⋊#95C2314yes—
145C47⋊#95C2312yes—
146C47⋊#95C2314yes—
147C22×D4×C47C2311yescharacteristic
148C23×C4×C47C2314yes—
149C23×C4×C47C2312yes—
150C4×D4×C47—28no—
151C4×D4×C47C2×C418yes—
152C2×C4⋊C4×C47—28no—
153C2×C4⋊C4×C47C2312yes—
154C2×C4⋊C4×C47C2314yes—
155C2×C4⋊C4×C47C2312yes—
156C2×C4⋊C4×C47C2311yescharacteristic
157C2×C4⋊C4×C47C2312yes—
158C2×C4⋊C4×C47C2311yescharacteristic
159C2×C4⋊C4×C47C2311yescharacteristic
160C2×C22⋊C4×C47C2314yes—
161C2×C22⋊C4×C47C2312yes—
162C2×C42×C47C2312yes—
163C2×C42×C47C2311yescharacteristic
164#95×C47C2312yes—
165#95×C47C2314yes—
166C24×C47C2412yes—
167C2×D4×C47C22×C414yes—
168C2×D4×C47C2×Q814yes—
169C2×D4×C47#4114yes—
170C22×C4×C47—24no—
171C22×C4×C47—24no—
172C22×C4×C47—28no—
173C22×C4×C47—28no—
174C22×C4×C47—44no—
175C22×C4×C47C22×C418yes—
176C22×C4×C47C2412yes—
177C22×C4×C47C2414yes—
178C22×C4×C47C2411yescharacteristic
179C22×C4×C47C2412yes—
180C22×C4×C47C2412yes—
181C22×C4×C47C2411yescharacteristic
182C22×C4×C47C2411yescharacteristic
183C22×Dic47—24no—
184C22×Dic47—24no—
185C22×Dic47—24no—
186C22×Dic47—24no—
187C22×Dic47—44no—
188C22×Dic47—44no—
189C22×Dic47—42no—
190C22×Dic47C22×C4116yes—
191C22×Dic47C2×Q818yes—
192C22×Dic47C2412yes—
193C22×Dic47C2411yescharacteristic
194C22×Dic47C2412yes—
195C22×Dic47C2412yes—
196C22×Dic47C2414yes—
197C22×Dic47C2411yescharacteristic
198C22×Dic47C2412yes—
199C22×Dic47C2411yescharacteristic
200C22×Dic47C2411yescharacteristic
201C2×Dic94—22no—
202C2×Dic94—22no—
203C2×Dic94—42no—
204C2×Dic94—42no—
205C2×Dic94C22×C414yes—
206C2×Dic94C22×C418yes—
207C4⋊C4×C47—28no—
208C4⋊C4×C47—24no—
209C4⋊C4×C47—24no—
210C4⋊C4×C47—22no—
211C4⋊C4×C47—42no—
212C4⋊C4×C47C22×C414yes—
213C4⋊C4×C47#4114yes—
214C22⋊C4×C47—28no—
215C22⋊C4×C47C22×C418yes—
216C42×C47—24no—
217C42×C47C22×C414yes—
218C22⋊Dic47—24no—
219C22⋊Dic47C22×C4116yes—
220C22⋊Dic47C2×Q818yes—
221C4⋊Dic47—22no—
222C4⋊Dic47C22×C414yes—
223C4⋊Dic47C22×C4116yes—
224C4⋊Dic47C22×C418yes—
225C4⋊Dic47C22×C418yes—
226C4⋊Dic47C2×Q814yes—
227Dic47⋊C4—24no—
228Dic47⋊C4—24no—
229Dic47⋊C4—44no—
230Dic47⋊C4—44no—
231Dic47⋊C4C22×C418yes—
232Dic47⋊C4C22×C4116yes—
233C4×Dic47—24no—
234C4×Dic47—22no—
235C4×Dic47—24no—
236C4×Dic47—22no—
237C4×Dic47—24no—
238C4×Dic47—24no—
239C4×Dic47—24no—
240C4×Dic47—24no—
241C4×Dic47—28no—
242C4×Dic47—22no—
243C4×Dic47—44no—
244C4×Dic47—44no—
245C4×Dic47—41no—
246C4×Dic47—42no—
247C4×Dic47C22×C418yes—
248C4×Dic47C2×Q814yes—
249C4×Dic47#4114yes—
250C23×C47—22no—
251C23×C47—22no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47C23×C414yes—
255C23×C47C22×Q814yes—
256C23×C47C2×#4114yes—
257C23×C47C2511yescharacteristic
258D4×C47C4×Q8116yescomplemented
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—216no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—24no—
269C2×C4×C47—24no—
270C2×C4×C47—24no—
271C2×C4×C47—22no—
272C2×C4×C47—416no—
273C2×C4×C47C23×C414yes—
274C2×C4×C47C23×C412yes—
275C2×C4×C47C23×C412yes—
276C2×C4×C47C23×C412yes—
277C2×C4×C47C22×Q812yes—
278C2×C4×C47C2×#4112yes—
279C2×C4×C47C2×#4114yes—
280C2×C4×C47C2×#4112yes—
281C2×C4×C47C2×#4112yes—
282C2×Dic47—21no—
283C2×Dic47—22no—
284C2×Dic47—22no—
285C2×Dic47—22no—
286C2×Dic47—21no—
287C2×Dic47—22no—
288C2×Dic47—24no—
289C2×Dic47—22no—
290C2×Dic47—21no—
291C2×Dic47—22no—
292C2×Dic47—21no—
293C2×Dic47—24no—
294C2×Dic47—216no—
295C2×Dic47—22no—
296C2×Dic47—21no—
297C2×Dic47—21no—
298C2×Dic47—22no—
299C2×Dic47—21no—
300C2×Dic47—22no—
301C2×Dic47—416no—
302C2×Dic47—48no—
303C2×Dic47C23×C414yes—
304C2×Dic47C23×C414yes—
305C2×Dic47C23×C418yes—
306C2×Dic47C22×Q812yes—
307C2×Dic47C22×Q814yes—
308C2×Dic47C22×Q812yes—
309C2×Dic47C2×#4112yes—
310C2×Dic47C2×#4112yes—
311C2×Dic47H(5,𝔽2)12yes—
312Dic94—28no—
313Dic94—48no—
314C4×#554—471nomaximal, Sylow
315C22×C47—24no—
316C22×C47—24no—
317C22×C47—24no—
318C22×C47—24no—
319C22×C47—24no—
320C22×C47—24no—
321C22×C47C2×C4×Q818yes—
322C22×C47C24×C411yescharacteristic
323C22×C47C23×Q811yescharacteristic
324C22×C47C22×#4111yescharacteristic
325C22×C47C22×#4111yescharacteristic
326C22×C47C22×#4111yescharacteristic
327C22×C47C2×H(5,𝔽2)11yescharacteristic
328C22×C47#58511yescharacteristic
329C4×C47—24no—
330C4×C47—22no—
331C4×C47—24no—
332C4×C47—42no—
333C4×C47—44no—
334C4×C47C2×C4×Q814yes—
335C4×C47C4×#4114yes—
336Dic47—24no—
337Dic47—28no—
338Dic47—24no—
339Dic47—24no—
340Dic47—22no—
341Dic47—22no—
342Dic47—42no—
343Dic47—41no—
344Dic47#55414yescomplemented
345C2×#554—471no—
346#2370—472no—
347#2369—471no—
348#2368—474no—
349#2360—472no—
350#2355—471no—
351#2349—472no—
352D4×C4⋊C4D4711yescharacteristic
353#2345—472no—
354C4×C4⋊Q8—471no—
355C4×#125—472no—
356C4×C22⋊Q8—474no—
357C4×C22⋊Q8—472no—
358C42×Q8—471no—
359C42×D4—472no—
360C42×D4—471no—
361C2×C4×C4⋊C4—472no—
362C2×C47—28no—
363C2×C47C22×C4×Q811yescharacteristic
364C2×C47C2×C4×#4111yescharacteristic
365C2×C47C4×H(5,𝔽2)11yescharacteristic
366C2×C47C2×#55411yescharacteristic
367C2×C47#347511yescharacteristic
368C2×C47Q8×#4111yescharacteristic
369C2×C47#348111yescharacteristic
370#554—4716no—
371C2×C4⋊Q8—471no—
372C2×#125—472no—
373C2×C22⋊Q8—472no—
374C2×C22⋊Q8—474no—
375C2×C4×Q8—471no—
376C2×C4×Q8—471no—
377C2×C4×Q8—472no—
378C2×C4×Q8—471no—
379C2×C4×D4—472no—
380C2×C4×D4—471no—
381C2×C4×D4—471no—
382C2×C4×D4C2×D4712yes—
383C2×C4×D4C2×D4711yescharacteristic
384C22×C4⋊C4—472no—
385C22×C4⋊C4C2×D4712yes—
386C22×C42—472no—
387C22×C42—474no—
388#391—472no—
389#391—472no—
390#391—474no—
391#389—472no—
392#389—472no—
393#389—472no—
394#389—474no—
395#389—472no—
396#389C2×D4712yes—
397#387—474no—
398#387—474no—
399#387—474no—
400#387—474no—
401#387—474no—
402#385—474no—
403#385—474no—
404#385C2×D4714yes—
405#384C2×D4711yescharacteristic
406#382—472no—
407#380—474no—
408#380C2×D4712yes—
409C4×C4⋊C4—471no—
410C4×C4⋊C4—472no—
411C4×C4⋊C4—474no—
412C4×C4⋊C4—472no—
413C4×C4⋊C4—471no—
414C4×C4⋊C4—472no—
415C4×C4⋊C4—472no—
416C4×C4⋊C4—472no—
417C4×C4⋊C4—474no—
418C4×C4⋊C4—471no—
419C4×C4⋊C4—471no—
420C4×C4⋊C4—471no—
421C4×C4⋊C4—472no—
422C4×C4⋊C4—472no—
423C4×C4⋊C4—474no—
424C4×C4⋊C4—472no—
425C4×C4⋊C4—472no—
426C4×C4⋊C4C2×D4711yescharacteristic
427C4×C22⋊C4—472no—
428C4×C22⋊C4—474no—
429C4×C22⋊C4—474no—
430C4×C22⋊C4—472no—
431C4×C22⋊C4—472no—
432C4×C22⋊C4—474no—
433C2×#95—474no—
434C43—472no—
435C43—471no—
436C47C4×#55411yescharacteristic, complemented, Sylow
437C22×Q8—471no—
438C22×Q8—472no—
439C22×D4C22×D4711yescharacteristic
440C23×C4—472no—
441C23×C4—474no—
442C23×C4—472no—
443C23×C4C22×D4714yes—
444C23×C4C22×D4712yes—
445C4⋊Q8—478no—
446#125—4716no—
447C22⋊Q8—4716no—
448C22⋊Q8—4732no—
449C4×Q8—478no—
450C4×Q8—944no—
451C4×Q8—944no—
452C4×Q8—1884no—
453C4×D4—28no—
454C4×D4—4716no—
455C4×D4—478no—
456C4×D4—944no—
457C4×D4C4×D4718yes—
458C2×C4⋊C4—28no—
459C2×C4⋊C4—4716no—
460C2×C4⋊C4—471no—
461C2×C4⋊C4—474no—
462C2×C4⋊C4—472no—
463C2×C4⋊C4—472no—
464C2×C4⋊C4—471no—
465C2×C4⋊C4—472no—
466C2×C4⋊C4—474no—
467C2×C4⋊C4—471no—
468C2×C4⋊C4—472no—
469C2×C4⋊C4—472no—
470C2×C4⋊C4—474no—
471C2×C4⋊C4—474no—
472C2×C4⋊C4C22×D4712yes—
473C2×C4⋊C4C22×D4714yes—
474C2×C4⋊C4C22×D4712yes—
475C2×C4⋊C4C22×D4711yescharacteristic
476C2×C4⋊C4C22×D4712yes—
477C2×C4⋊C4C22×D4711yescharacteristic
478C2×C4⋊C4C22×D4711yescharacteristic
479C2×C22⋊C4—474no—
480C2×C22⋊C4—472no—
481C2×C22⋊C4—472no—
482C2×C22⋊C4C22×D4714yes—
483C2×C22⋊C4C22×D4712yes—
484C2×C42—472no—
485C2×C42—471no—
486C2×C42—471no—
487C2×C42—471no—
488C2×C42—471no—
489C2×C42—472no—
490C2×C42—472no—
491C2×C42—471no—
492C2×C42—474no—
493C2×C42—472no—
494C2×C42—472no—
495C2×C42—472no—
496C2×C42—472no—
497C2×C42—472no—
498C2×C42—471no—
499C2×C42—474no—
500C2×C42—474no—
501C2×C42—948no—
502C2×C42—1888no—
503C2×C42C22×D4712yes—
504C2×C42C22×D4711yescharacteristic
505#95—472no—
506#95—474no—
507#95—474no—
508#95—474no—
509#95—472no—
510#95—472no—
511#95—474no—
512#95—474no—
513#95—474no—
514#95—472no—
515#95—472no—
516#95—474no—
517#95C22×D4712yes—
518#95C22×D4714yes—
519C24C23×D4712yes—
520C2×Q8—474no—
521C2×Q8—478no—
522C2×Q8—942no—
523C2×Q8—942no—
524C2×Q8—1882no—
525C2×Q8—1882no—
526C2×D4C2×C4×D4714yes—
527C2×D4#1062535214yes—
528C2×D4Q8×D4714yes—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—44no—
534C22×C4—471no—
535C22×C4—478no—
536C22×C4—471no—
537C22×C4—472no—
538C22×C4—471no—
539C22×C4—472no—
540C22×C4—472no—
541C22×C4—474no—
542C22×C4—4716no—
543C22×C4—472no—
544C22×C4—471no—
545C22×C4—944no—
546C22×C4—944no—
547C22×C4—944no—
548C22×C4—944no—
549C22×C4—1884no—
550C22×C4—1884no—
551C22×C4—1882no—
552C22×C4C2×C4×D4718yes—
553C22×C4C23×D4714yes—
554C22×C4C23×D4712yes—
555C22×C4C23×D4711yescharacteristic
556C22×C4C23×D4712yes—
557C22×C4C23×D4712yes—
558C22×C4C23×D4711yescharacteristic
559C22×C4C23×D4711yescharacteristic
560C4⋊C4—22no—
561C4⋊C4—28no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—42no—
565C4⋊C4—478no—
566C4⋊C4—4716no—
567C4⋊C4—474no—
568C4⋊C4—4716no—
569C4⋊C4—478no—
570C4⋊C4—478no—
571C4⋊C4—474no—
572C4⋊C4—944no—
573C4⋊C4—944no—
574C4⋊C4—942no—
575C4⋊C4—1884no—
576C4⋊C4—1884no—
577C4⋊C4C2×C4×D4714yes—
578C4⋊C4#1062535214yes—
579C22⋊C4—28no—
580C22⋊C4—4716no—
581C22⋊C4—478no—
582C22⋊C4—944no—
583C22⋊C4C2×C4×D4718yes—
584C42—24no—
585C42—478no—
586C42—474no—
587C42—474no—
588C42—944no—
589C42—944no—
590C42—944no—
591C42—948no—
592C42—944no—
593C42—942no—
594C42—944no—
595C42—942no—
596C42—944no—
597C42—942no—
598C42—1881no—
599C42—1882no—
600C42—1884no—
601C42—1884no—
602C42C2×C4×D4714yes—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23C22×C4×D4714yes—
608C23C2×Q8×D4714yes—
609C23C2×#1062535214yes—
610C23C24×D4711yescharacteristic
611Q8—948no—
612Q8—1888no—
613D4#13093989116yescomplemented
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—216no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—416no—
628C2×C4—472no—
629C2×C4—472no—
630C2×C4—472no—
631C2×C4—474no—
632C2×C4—474no—
633C2×C4—478no—
634C2×C4—472no—
635C2×C4—474no—
636C2×C4—472no—
637C2×C4—9416no—
638C2×C4—942no—
639C2×C4—942no—
640C2×C4—941no—
641C2×C4—942no—
642C2×C4—941no—
643C2×C4—942no—
644C2×C4—944no—
645C2×C4—942no—
646C2×C4—941no—
647C2×C4—942no—
648C2×C4—941no—
649C2×C4—944no—
650C2×C4—942no—
651C2×C4—941no—
652C2×C4—941no—
653C2×C4—942no—
654C2×C4—941no—
655C2×C4—942no—
656C2×C4—18816no—
657C2×C4—1888no—
658C2×C4C22×C4×D4712yes—
659C2×C4C22×C4×D4714yes—
660C2×C4C22×C4×D4712yes—
661C2×C4C22×C4×D4712yes—
662C2×C4C2×Q8×D4712yes—
663C2×C4#41×D4712yes—
664C2×C4C2×#1062535214yes—
665C2×C4C2×#1062535212yes—
666C2×C4C2×#1062535212yes—
667C22—24no—
668C22—24no—
669C22—24no—
670C22—24no—
671C22—24no—
672C22—24no—
673C22C2×#1309398918yes—
674C22C23×C4×D4711yescharacteristic
675C22C22×Q8×D4711yescharacteristic
676C22C2×#41×D4711yescharacteristic
677C22C22×#1062535211yescharacteristic
678C22C22×#1062535211yescharacteristic
679C22H(5,𝔽2)×D4711yescharacteristic
680C22#1568996011yescharacteristic
681C4—24no—
682C4—22no—
683C4—24no—
684C4—42no—
685C4—44no—
686C4—474no—
687C4—944no—
688C4—944no—
689C4—948no—
690C4—944no—
691C4—942no—
692C4—942no—
693C4—1882no—
694C4—1881no—
695C4C2×#1309398914yes—
696C4C4×#1062535214yes—
697C2—28no—
698C2C22×#1309398911yescharacteristic
699C2C2×C4×#1062535211yescharacteristic
700C2#2025659411yescharacteristic
701C2#554×D4711yescharacteristic
702C2#2025695111yescharacteristic
703C2Q8×#1062535211yescharacteristic
704C2#2025698911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingD4×C4⋊C4×C47C2
socle, cosocleC23×C47C25
prime radicalC22×D4×C47C23
hypercenterD4×C4⋊C4D47
hypocenterC47C4×#554
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20246483C2semidirect
3. #20246477C2semidirect
4. #20246469C2semidirect
5. #20246393C2semidirect
6. #20246347C2semidirect
8. #20246267C2semidirect
9. #20245955C2semidirect
10. #20245947C2semidirect
11. #20245920C2semidirect
12. #20245916C2semidirect
13. C4×#13093989C2semidirect
16. C2×C4⋊C4×Dic47C2semidirect
18. #15689830C4semidirect
89. #13094024C2×C4semidirect
90. #13094015C2×C4semidirect
91. #13094003C2×C4semidirect
92. #13094001C2×C4semidirect
93. C4×Dic94C2×C4semidirect
99. D4×Dic47Q8semidirect
100. C2×C4⋊Dic47C2×C4semidirect
258. D4×C47C4×Q8semidirect
344. Dic47#554semidirect
436. C47C4×#554semidirect
613. D4#13093989semidirect

Maximal subgroups

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

subgroupindex
C2×#156898302
#202464832
#202464772
#202464692
#202463932
#202463472
#202462932
#202462672
#202459552
#202459472
#202459202
#202459162
C4×#130939892
C4×D4×Dic472
C2×C4⋊C4×Dic472
D4×C4⋊C4×C472
C4×#55447