Finite Group Databasebeta

← #26139664

Subgroups — #26139664

Order 12032.

1810 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
1C22×C4×Dic94C211yesmaximal, characteristic
2C2×#15689029C211yesmaximal, characteristic
3C2×#15689029C211yesmaximal, characteristic
4C2×#15689021C211yesmaximal, characteristic
5#20241651C212yesmaximal
6#20241646C212yesmaximal
7#20241620C212yesmaximal
8#20241619C212yesmaximal
9#20241618C211yesmaximal, characteristic
10#20241618C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C2×C4×Dic94—24no—
14C2×C4×Dic94—24no—
15C2×C4×Dic94—24no—
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×Dic47⋊C4C2212yes—
20C22×Dic47⋊C4C2212yes—
21C22×C4×Dic47C2212yes—
22#15689029—24no—
23#15689029C418yescomplemented
24#15689021—24no—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C22×C4⋊C4×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C4×C4⋊C4×C47—24no—
40C2×#95×C47C2211yescharacteristic
41C2×#95×C47C2211yescharacteristic
42C22×Dic94—22no—
43C22×Dic94—22no—
44C22×Dic94—22no—
45C22×Dic94—22no—
46C22×Dic94C2×C414yes—
47C22×Dic94D414yes—
48C22×Dic94Q814yes—
49C23×Dic47C2312yes—
50C23×Dic47C2312yes—
51C23×Dic47C2312yes—
52C23×Dic47C2312yes—
53C4×Dic94—232no—
54C2×C4⋊Dic47—22no—
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47—22no—
58C2×C4⋊Dic47—22no—
59C2×C4⋊Dic47—22no—
60C2×C4⋊Dic47—22no—
61C2×C4⋊Dic47C2×C414yes—
62C2×C4⋊Dic47D414yes—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4—24no—
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4—24no—
68C2×Dic47⋊C4—42no—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—24no—
72C47⋊#95—24no—
73C47⋊#95—24no—
74C47⋊#95—24no—
75C47⋊#95—24no—
76C47⋊#95—24no—
77C47⋊#95—42no—
78C47⋊#95—42no—
79C47⋊#95C2×C418yes—
80C47⋊#95C2×C418yes—
81C23×C4×C47C2311yescharacteristic
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2311yescharacteristic
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C2×C4⋊C4×C47—22no—
89C2×C4⋊C4×C47—22no—
90C2×C4⋊C4×C47—22no—
91C2×C4⋊C4×C47—22no—
92C2×C4⋊C4×C47—22no—
93C2×C4⋊C4×C47Q814yescomplemented
94C2×C42×C47—22no—
95C2×C42×C47—22no—
96C2×C42×C47—22no—
97C2×C42×C47—22no—
98C2×C42×C47—22no—
99C2×C42×C47—22no—
100C2×C42×C47—22no—
101C2×C42×C47C2×C414yes—
102C2×C42×C47D414yes—
103#95×C47—22no—
104#95×C47—22no—
105C24×C47C2411yescharacteristic
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47—21no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47C22×C412yes—
139C22×C4×C47C22×C412yes—
140C22×C4×C47C22×C412yes—
141C22×C4×C47C2×D412yes—
142C22×C4×C47C2×D412yes—
143C22×C4×C47C2×D412yes—
144C22×C4×C47C2×D412yes—
145C22×C4×C47C2×D412yes—
146C22×C4×C47C2×Q812yes—
147C22×C4×C47C2×Q812yes—
148C22×C4×C47C2×Q812yes—
149C22×C4×C47C2×Q812yes—
150C22×C4×C47#4112yes—
151C22×C4×C47#4112yes—
152C22×C4×C47#4112yes—
153C22×C4×C47#4112yes—
154C22×C4×C47#4112yes—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47C22×C414yes—
179C22×Dic47C22×C414yes—
180C22×Dic47C2×D414yes—
181C22×Dic47C2×D414yes—
182C22×Dic47C2×Q814yes—
183C2×Dic94—28no—
184C2×Dic94—28no—
185C2×Dic94—28no—
186C2×Dic94—28no—
187C2×Dic94—28no—
188C2×Dic94—28no—
189C2×Dic94C4⋊C4116yescomplemented
190C4⋊C4×C47—28no—
191C4⋊C4×C47—28no—
192C42×C47—28no—
193C42×C47—28no—
194C42×C47—44no—
195C4⋊Dic47—28no—
196C4⋊Dic47—28no—
197C4⋊Dic47—44no—
198Dic47⋊C4—216no—
199Dic47⋊C4—48no—
200C4×Dic47—216no—
201C23×C47C23×C411yescharacteristic
202C23×C47C22×D411yescharacteristic
203C23×C47C22×D411yescharacteristic
204C23×C47C22×D411yescharacteristic
205C23×C47C22×Q811yescharacteristic
206C23×C47C22×Q811yescharacteristic
207C23×C47C2×#4111yescharacteristic
208C23×C47C2×#4111yescharacteristic
209C23×C47C2×#4111yescharacteristic
210C23×C47C2×#4111yescharacteristic
211C23×C47C2×#4111yescharacteristic
212C23×C47H(5,𝔽2)11yescharacteristic
213C23×C472−1+411yescharacteristic
214C23×C472−1+411yescharacteristic
215C23×C472−1+411yescharacteristic
216C2×C4×C47—22no—
217C2×C4×C47—22no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—22no—
238C2×C4×C47—22no—
239C2×C4×C47—22no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47C2×C4⋊C414yes—
257C2×C4×C47C4×D414yes—
258C2×C4×C47C4×D414yes—
259C2×C4×C47C4×Q814yescomplemented
260C2×C4×C47#12014yes—
261C2×C4×C47C22⋊Q814yes—
262C2×C4×C47C22⋊Q814yes—
263C2×C4×C47C22⋊Q814yes—
264C2×C4×C47#12314yes—
265C2×Dic47—24no—
266C2×Dic47—24no—
267C2×Dic47—24no—
268C2×Dic47—24no—
269C2×Dic47—24no—
270C2×Dic47—24no—
271C2×Dic47—24no—
272C2×Dic47—24no—
273C2×Dic47—24no—
274C2×Dic47—24no—
275C2×Dic47—24no—
276C2×Dic47—24no—
277C2×Dic47—42no—
278C2×Dic47—42no—
279C2×Dic47—42no—
280C2×Dic47—42no—
281C2×Dic47—42no—
282C2×Dic47—42no—
283C2×Dic47—42no—
284C2×Dic47—42no—
285C2×Dic47—42no—
286C2×Dic47—42no—
287C2×Dic47—42no—
288C2×Dic47—42no—
289C2×Dic47—42no—
290C2×Dic47—42no—
291C2×Dic47—42no—
292C2×Dic47C2×C4⋊C418yes—
293Dic94—232no—
294#14017—471nomaximal, Sylow
295C22×C47C22×C4⋊C411yescharacteristic
296C22×C47C2×C4×D411yescharacteristic
297C22×C47C2×C4×D411yescharacteristic
298C22×C47C2×C4×Q811yescharacteristic
299C22×C47C4×#4111yescharacteristic
300C22×C47#51911yescharacteristic
301C22×C47#52011yescharacteristic
302C22×C47C2×#12011yescharacteristic
303C22×C47C2×C22⋊Q811yescharacteristic
304C22×C47C2×C22⋊Q811yescharacteristic
305C22×C47C2×C22⋊Q811yescharacteristic
306C22×C47C2×#12311yescharacteristic
307C22×C47#52511yescharacteristic
308C22×C47#52911yescharacteristic
309C22×C47#53311yescharacteristic
310C22×C47#53611yescharacteristic
311C22×C47#53711yescharacteristic
312C22×C47#54111yescharacteristic
313C22×C47#54211yescharacteristic
314C22×C47#54611yescharacteristic
315C22×C47#54711yescharacteristic
316C22×C47#54811yescharacteristic
317C22×C47#54811yescharacteristic
318C22×C47#54811yescharacteristic
319C22×C47D4×Q811yescharacteristic
320C22×C47D4×Q811yescharacteristic
321C22×C47#55011yescharacteristic
322C22×C47#55611yescharacteristic
323C22×C47#55611yescharacteristic
324C22×C47#55711yescharacteristic
325C22×C47#55711yescharacteristic
326C22×C47#55711yescharacteristic
327C22×C47#55711yescharacteristic
328C22×C47Q8211yescharacteristic
329C22×C47#55911yescharacteristic
330C4×C47—24no—
331C4×C47—24no—
332C4×C47—42no—
333C4×C47—42no—
334C4×C47—42no—
335C4×C47—42no—
336C4×C47#38518yes—
337Dic47—28no—
338Dic47—44no—
339Dic47—44no—
340Dic47—82no—
341C22×C4×Q8—471no—
342C2×#391—471no—
343C2×#391—471no—
344C2×#389—471no—
345C2×C4×C4⋊C4D4711yescharacteristic
346#1444—472no—
347#1442—472no—
348#1436—472no—
349#1436—472no—
350C4⋊#95—471no—
351C4⋊#95—471no—
352C2×C47C2×#38511yescharacteristic
353C2×C47C4×C22⋊Q811yescharacteristic
354C2×C47#232311yescharacteristic
355C2×C47Q8×C4⋊C411yescharacteristic
356C2×C47#235111yescharacteristic
357C2×C47#236511yescharacteristic
358C2×C47#236711yescharacteristic
359C2×C47#240711yescharacteristic
360C2×C47#240911yescharacteristic
361C2×C47#244611yescharacteristic
362C2×C47#244811yescharacteristic
363C2×C47#245111yescharacteristic
364C2×C47#245311yescharacteristic
365C2×C47#258111yescharacteristic
366C2×C47#258211yescharacteristic
367C23×Q8—471no—
368C2×C4×Q8—944no—
369C2×C4×Q8—944no—
370C2×C4×Q8—944no—
371C22×C4⋊C4—471no—
372C22×C4⋊C4—471no—
373C22×C4⋊C4—472no—
374C22×C4⋊C4—471no—
375C22×C4⋊C4—472no—
376C22×C4⋊C4C2×D4711yescharacteristic
377C22×C4⋊C4C2×D4711yescharacteristic
378C22×C42—472no—
379C22×C42C2×D4711yescharacteristic
380C22×C42C2×D4711yescharacteristic
381C22×C42C2×D4711yescharacteristic
382#391—478no—
383#391—944no—
384#389—944no—
385C4×C4⋊C4—24no—
386C2×#95—472no—
387C2×#95—472no—
388C2×#95—472no—
389C2×#95—472no—
390C2×#95—472no—
391C2×#95—472no—
392C2×#95—472no—
393C2×#95—472no—
394C2×#95—472no—
395C2×#95C2×D4711yescharacteristic
396C2×#95C2×D4711yescharacteristic
397C47#1401711yescharacteristic, complemented, Sylow
398C22×Q8—474no—
399C22×Q8—474no—
400C22×Q8—474no—
401C22×Q8—942no—
402C22×Q8—942no—
403C22×Q8—942no—
404C22×Q8—942no—
405C23×C4—472no—
406C23×C4—472no—
407C23×C4—472no—
408C23×C4—472no—
409C23×C4C22×D4711yescharacteristic
410C23×C4C22×D4711yescharacteristic
411C23×C4C22×D4711yescharacteristic
412C23×C4C22×D4711yescharacteristic
413C23×C4C22×D4711yescharacteristic
414C23×C4C22×D4711yescharacteristic
415C23×C4C22×D4711yescharacteristic
416C4×Q8—9432no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—474no—
423C2×C4⋊C4—474no—
424C2×C4⋊C4—944no—
425C2×C4⋊C4—944no—
426C2×C4⋊C4—942no—
427C2×C4⋊C4—942no—
428C2×C4⋊C4—942no—
429C2×C4⋊C4—944no—
430C2×C4⋊C4—942no—
431C2×C4⋊C4—944no—
432C2×C4⋊C4—944no—
433C2×C4⋊C4—942no—
434C2×C4⋊C4—942no—
435C2×C4⋊C4—942no—
436C2×C4⋊C4—1882no—
437C2×C4⋊C4Dic9414yescomplemented
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—944no—
446C2×C42—944no—
447C2×C42—944no—
448C2×C42C4×D4714yes—
449C2×C42C22⋊D4714yes—
450#95—22no—
451#95—22no—
452#95—478no—
453#95—478no—
454#95—944no—
455#95—944no—
456#95—944no—
457#95—944no—
458#95—944no—
459#95—1882no—
460#95—1882no—
461C24C23×D4711yescharacteristic
462C2×Q8—4716no—
463C2×Q8—948no—
464C2×Q8—948no—
465C2×Q8—948no—
466C2×Q8—948no—
467C2×Q8—948no—
468C2×Q8—948no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—474no—
502C22×C4—474no—
503C22×C4—474no—
504C22×C4—474no—
505C22×C4—474no—
506C22×C4—942no—
507C22×C4—942no—
508C22×C4—942no—
509C22×C4—942no—
510C22×C4—942no—
511C22×C4—942no—
512C22×C4—942no—
513C22×C4—942no—
514C22×C4—942no—
515C22×C4—942no—
516C22×C4—942no—
517C22×C4—942no—
518C22×C4—942no—
519C22×C4—942no—
520C22×C4—942no—
521C22×C4—942no—
522C22×C4—942no—
523C22×C4—942no—
524C22×C4—942no—
525C22×C4—942no—
526C22×C4—942no—
527C22×C4—942no—
528C22×C4—942no—
529C22×C4C2×Dic9412yes—
530C22×C4C2×Dic9412yes—
531C22×C4C2×Dic9412yes—
532C22×C4C2×C4×D4712yes—
533C22×C4C2×C4×D4712yes—
534C22×C4C2×C4×D4712yes—
535C22×C4#1062535012yes—
536C22×C4#1062535012yes—
537C22×C4#1062535012yes—
538C22×C4#1062535012yes—
539C22×C4D4×D4712yes—
540C22×C4D4×D4712yes—
541C22×C4Q8×D4712yes—
542C22×C4#1062535412yes—
543C22×C4C2×C22⋊D4712yes—
544C22×C4C2×C22⋊D4712yes—
545C22×C4C2×C22⋊D4712yes—
546C4⋊C4—28no—
547C4⋊C4—28no—
548C4⋊C4—9416no—
549C4⋊C4—948no—
550C4⋊C4—948no—
551C4⋊C4—1888no—
552C4⋊C4—1884no—
553C42—28no—
554C42—28no—
555C42—44no—
556C42—9416no—
557C23C22×C4×D4711yescharacteristic
558C23C2×D4×D4711yescharacteristic
559C23C2×D4×D4711yescharacteristic
560C23C22×C22⋊D4711yescharacteristic
561C23C2×Q8×D4711yescharacteristic
562C23C22×Dic9411yescharacteristic
563C23C2×#1062535011yescharacteristic
564C23C2×#1062535011yescharacteristic
565C23C2×#1062535011yescharacteristic
566C23C2×#1062535011yescharacteristic
567C23C2×#1062535411yescharacteristic
568C23#1309407011yescharacteristic
569C23#1309407111yescharacteristic
570C23#1309407111yescharacteristic
571C23#1309407111yescharacteristic
572Q8—9432no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—478no—
614C2×C4—944no—
615C2×C4—944no—
616C2×C4—944no—
617C2×C4—944no—
618C2×C4—944no—
619C2×C4—944no—
620C2×C4—944no—
621C2×C4—944no—
622C2×C4—944no—
623C2×C4—944no—
624C2×C4—944no—
625C2×C4—944no—
626C2×C4—1882no—
627C2×C4—1882no—
628C2×C4—1882no—
629C2×C4—1882no—
630C2×C4—1882no—
631C2×C4—1882no—
632C2×C4—1882no—
633C2×C4—1882no—
634C2×C4—1882no—
635C2×C4—1882no—
636C2×C4—1882no—
637C2×C4—1882no—
638C2×C4—1882no—
639C2×C4—1882no—
640C2×C4—1882no—
641C2×C4C4⋊C4×D4714yes—
642C2×C4C4×C22⋊D4714yes—
643C2×C4#1309398614yes—
644C2×C4C4×Dic9414yescomplemented
645C2×C4#1309399214yes—
646C2×C4#1309400014yes—
647C2×C4#1309400214yes—
648C2×C4#1309400314yes—
649C2×C4#1309400914yes—
650C22C2×C4⋊C4×D4711yescharacteristic
651C22C2×C4×C22⋊D4711yescharacteristic
652C22C2×#1309398611yescharacteristic
653C22C2×C4×Dic9411yescharacteristic
654C22C4×#1062535011yescharacteristic
655C22#1568960011yescharacteristic
656C22#1568960311yescharacteristic
657C22C2×#1309399211yescharacteristic
658C22C2×#1309400011yescharacteristic
659C22C2×#1309400211yescharacteristic
660C22C2×#1309400311yescharacteristic
661C22C2×#1309400911yescharacteristic
662C22#1568963411yescharacteristic
663C22#1568965711yescharacteristic
664C22#1568968011yescharacteristic
665C22#1568969411yescharacteristic
666C22#1568970111yescharacteristic
667C22#1568973511yescharacteristic
668C22#1568974411yescharacteristic
669C22#1568976911yescharacteristic
670C22#1568977811yescharacteristic
671C22#1568978211yescharacteristic
672C22#1568978211yescharacteristic
673C22#1568978211yescharacteristic
674C22D4×Dic9411yescharacteristic
675C22D4×Dic9411yescharacteristic
676C22#1568979411yescharacteristic
677C22#1568984611yescharacteristic
678C22#1568984611yescharacteristic
679C22#1568985111yescharacteristic
680C22#1568985111yescharacteristic
681C22#1568985111yescharacteristic
682C22#1568985211yescharacteristic
683C22Q8×Dic9411yescharacteristic
684C22#1568985811yescharacteristic
685C4—24no—
686C4—24no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—948no—
692C4—3762no—
693C4—1884no—
694C4—1884no—
695C4#1568899418yes—
696C2C2×#1568899411yescharacteristic
697C2C4×#1309400311yescharacteristic
698C2#2024607011yescharacteristic
699C2C4⋊C4×Dic9411yescharacteristic
700C2#2024630811yescharacteristic
701C2#2024644411yescharacteristic
702C2#2024645711yescharacteristic
703C2#2024673311yescharacteristic
704C2#2024675311yescharacteristic
705C2#2024716411yescharacteristic
706C2#2024718611yescharacteristic
707C2#2024722711yescharacteristic
708C2#2024724911yescharacteristic
709C2#2024875411yescharacteristic
710C2#2024875811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C4⋊C4×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×C4×C4⋊C4D47
hypocenterC47#14017
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
23. #15689029C4semidirect
93. C2×C4⋊C4×C47Q8semidirect
189. C2×Dic94C4⋊C4semidirect
259. C2×C4×C47C4×Q8semidirect
397. C47#14017semidirect
437. C2×C4⋊C4Dic94semidirect
644. C2×C4C4×Dic94semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic942
C2×#156890292
C2×#156890212
#202416512
#202416462
#202416202
#202416192
#202416182
C2×C4×C4⋊C4×C472
#1401747