Finite Group Databasebeta

← #26137819

Subgroups — #26137819

Order 12032.

1970 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
1C22×#13093989C211yesmaximal, characteristic
2C2×#15689029C211yesmaximal, characteristic
3C2×#15689028C211yesmaximal, characteristic
4C2×C4⋊C4×Dic47C211yesmaximal, characteristic
5#20241623C212yesmaximal
6#20241621C212yesmaximal
7#20241617C211yesmaximal, characteristic
8#20241612C212yesmaximal
9C4×C47⋊#95C211yesmaximal, characteristic
10C4×C47⋊#95C212yesmaximal
11C2×C4×C4⋊C4×C47C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C2×#13093989—24no—
14C2×#13093989—24no—
15C2×#13093989C418yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×Dic47⋊C4C2212yes—
18C22×C4×Dic47C2212yes—
19C22×C4×Dic47C2212yes—
20C22×C4×Dic47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22#15689029C418yescomplemented
23#15689028C418yescomplemented
24C4⋊C4×Dic47—24no—
25C2×C47⋊#95C2211yescharacteristic
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C42×C47C2212yes—
39C22×C42×C47C2211yescharacteristic
40C4×C4⋊C4×C47—24no—
41C2×#95×C47C2212yes—
42C22×Dic94—22no—
43C22×Dic94—22no—
44C22×Dic94—22no—
45C22×Dic94—22no—
46C22×Dic94C2×C414yes—
47C22×Dic94C2×C414yes—
48C22×Dic94C2×C414yes—
49C23×Dic47C2311yescharacteristic
50C23×Dic47C2312yes—
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2312yes—
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2311yescharacteristic
55#13093989—232no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47—22no—
58C2×C4⋊Dic47C2×C414yes—
59C2×Dic47⋊C4—24no—
60C2×Dic47⋊C4—24no—
61C2×Dic47⋊C4C2×C418yes—
62C2×C4×Dic47—22no—
63C2×C4×Dic47—24no—
64C2×C4×Dic47—24no—
65C2×C4×Dic47—22no—
66C2×C4×Dic47—22no—
67C2×C4×Dic47—22no—
68C2×C4×Dic47—24no—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—42no—
71C2×C4×Dic47C2×C414yes—
72C2×C4×Dic47C2×C414yes—
73C2×C4×Dic47C2×C418yes—
74C47⋊#95—24no—
75C47⋊#95—22no—
76C47⋊#95—22no—
77C47⋊#95—24no—
78C47⋊#95—22no—
79C47⋊#95—42no—
80C47⋊#95C2×C418yes—
81C47⋊#95C2×C418yes—
82C47⋊#95C2×C418yes—
83C47⋊#95C2×C418yes—
84C47⋊#95Q814yescomplemented
85C23×C4×C47C2312yes—
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2312yes—
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C2×C4⋊C4×C47—22no—
91C2×C4⋊C4×C47—22no—
92C2×C4⋊C4×C47C2×C414yes—
93C2×C4⋊C4×C47C2×C414yes—
94C2×C4⋊C4×C47D414yes—
95C2×C4⋊C4×C47D414yes—
96C2×C42×C47—22no—
97C2×C42×C47—22no—
98C2×C42×C47—24no—
99C2×C42×C47—24no—
100C2×C42×C47—42no—
101C2×C42×C47C2×C414yes—
102#95×C47—24no—
103C24×C47C2411yescharacteristic
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—21no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—21no—
112C22×C4×C47—22no—
113C22×C4×C47—21no—
114C22×C4×C47—21no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—22no—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C22×C414yes—
126C22×C4×C47C22×C414yes—
127C22×C4×C47C22×C412yes—
128C22×C4×C47C22×C412yes—
129C22×C4×C47C22×C412yes—
130C22×C4×C47C22×C412yes—
131C22×C4×C47C2×D414yes—
132C22×C4×C47C2×D414yes—
133C22×C4×C47C2×D412yes—
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×Q812yes—
136C22×C4×C47#4112yes—
137C22×C4×C47#4112yes—
138C22×C4×C47#4112yes—
139C22×Dic47—21no—
140C22×Dic47—21no—
141C22×Dic47—21no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—21no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47—22no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—21no—
159C22×Dic47—22no—
160C22×Dic47—21no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—21no—
164C22×Dic47—22no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C22×Dic47—21no—
168C22×Dic47—22no—
169C22×Dic47C22×C412yes—
170C22×Dic47C22×C414yes—
171C22×Dic47C22×C412yes—
172C22×Dic47C22×C414yes—
173C22×Dic47C22×C414yes—
174C22×Dic47C22×C414yes—
175C22×Dic47C22×C412yes—
176C22×Dic47C22×C412yes—
177C22×Dic47C2×Q812yes—
178C22×Dic47C2×Q812yes—
179C22×Dic47#4112yes—
180C22×Dic47#4112yes—
181C2×Dic94—28no—
182C2×Dic94—28no—
183C2×Dic94—28no—
184C2×Dic94—28no—
185C2×Dic94—28no—
186C2×Dic94—28no—
187C2×Dic94C42116yescomplemented
188C4⋊C4×C47—28no—
189C4⋊C4×C47C22⋊C4116yes—
190C42×C47—28no—
191C42×C47—48no—
192C4⋊Dic47—28no—
193Dic47⋊C4—216no—
194C4×Dic47—216no—
195C4×Dic47—28no—
196C4×Dic47—28no—
197C4×Dic47—48no—
198C23×C47C23×C411yescharacteristic
199C23×C47C23×C411yescharacteristic
200C23×C47C23×C411yescharacteristic
201C23×C47C22×D411yescharacteristic
202C23×C47C22×D411yescharacteristic
203C23×C47C22×Q811yescharacteristic
204C23×C47C2×#4111yescharacteristic
205C23×C47C2×#4111yescharacteristic
206C23×C47C2×#4111yescharacteristic
207C23×C47C2×#4111yescharacteristic
208C23×C47C2×#4111yescharacteristic
209C23×C47H(5,𝔽2)11yescharacteristic
210C23×C472−1+411yescharacteristic
211C23×C472−1+411yescharacteristic
212C23×C472−1+411yescharacteristic
213C2×C4×C47—22no—
214C2×C4×C47—24no—
215C2×C4×C47—24no—
216C2×C4×C47—22no—
217C2×C4×C47—24no—
218C2×C4×C47—22no—
219C2×C4×C47—24no—
220C2×C4×C47—24no—
221C2×C4×C47—24no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—24no—
227C2×C4×C47—24no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—24no—
231C2×C4×C47—42no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—42no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—42no—
238C2×C4×C47—42no—
239C2×C4×C47C2×C4214yes—
240C2×C4×C47C2×C22⋊C418yes—
241C2×C4×C47C2×C22⋊C414yes—
242C2×C4×C47#11714yes—
243C2×C4×C47C4×D414yes—
244C2×C4×C47C4×D414yes—
245C2×C4×C47C4×D414yes—
246C2×C4×C47C4×D414yes—
247C2×C4×C47C4×Q814yescomplemented
248C2×Dic47—22no—
249C2×Dic47—24no—
250C2×Dic47—24no—
251C2×Dic47—22no—
252C2×Dic47—24no—
253C2×Dic47—24no—
254C2×Dic47—24no—
255C2×Dic47—24no—
256C2×Dic47—22no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—22no—
262C2×Dic47—22no—
263C2×Dic47—22no—
264C2×Dic47—22no—
265C2×Dic47—22no—
266C2×Dic47—22no—
267C2×Dic47—22no—
268C2×Dic47—24no—
269C2×Dic47—22no—
270C2×Dic47—22no—
271C2×Dic47—24no—
272C2×Dic47—22no—
273C2×Dic47—22no—
274C2×Dic47—24no—
275C2×Dic47—42no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—41no—
280C2×Dic47—41no—
281C2×Dic47—41no—
282C2×Dic47—42no—
283C2×Dic47—41no—
284C2×Dic47—41no—
285C2×Dic47—42no—
286C2×Dic47—42no—
287C2×Dic47C2×C4218yes—
288C2×Dic47C4×Q814yes—
289C2×Dic47C4×Q814yescomplemented
290Dic94—232no—
291#13817—471nomaximal, Sylow
292C22×C47C22×C4211yescharacteristic
293C22×C47C22×C22⋊C411yescharacteristic
294C22×C47C2×#11711yescharacteristic
295C22×C47C2×C4×D411yescharacteristic
296C22×C47C2×C4×D411yescharacteristic
297C22×C47C2×C4×D411yescharacteristic
298C22×C47C2×C4×D411yescharacteristic
299C22×C47C2×C4×Q811yescharacteristic
300C22×C47C2×C4×Q811yescharacteristic
301C22×C47C2×C4×Q811yescharacteristic
302C22×C47C4×#4111yescharacteristic
303C22×C47C4×#4111yescharacteristic
304C22×C47C4×#4111yescharacteristic
305C22×C47#51911yescharacteristic
306C22×C47#51911yescharacteristic
307C22×C47#51911yescharacteristic
308C22×C47#52011yescharacteristic
309C22×C47#52011yescharacteristic
310C22×C47#52011yescharacteristic
311C22×C47#54611yescharacteristic
312C22×C47#54611yescharacteristic
313C22×C47#54711yescharacteristic
314C22×C47#54711yescharacteristic
315C22×C47#54811yescharacteristic
316C22×C47#54811yescharacteristic
317C22×C47D4×Q811yescharacteristic
318C22×C47D4×Q811yescharacteristic
319C22×C47#55211yescharacteristic
320C22×C47#55211yescharacteristic
321C22×C47#55411yescharacteristic
322C22×C47#55611yescharacteristic
323C22×C47#55611yescharacteristic
324C22×C47#55611yescharacteristic
325C22×C47#55711yescharacteristic
326C22×C47#55911yescharacteristic
327C4×C47—28no—
328C4×C47—24no—
329C4×C47—42no—
330C4×C47—44no—
331C4×C47C4×C22⋊C418yes—
332Dic47—24no—
333Dic47—24no—
334Dic47—28no—
335Dic47—42no—
336Dic47—42no—
337Dic47—44no—
338C22×C4×Q8—471no—
339C2×#391—471no—
340C2×#391—471no—
341C2×C4×C4⋊C4—471no—
342C2×C4×C4⋊C4D4711yescharacteristic
343#1436—472no—
344#1436—472no—
345C4⋊#95—471no—
346#1434—472no—
347C4×#95—472no—
348C4×#95—471no—
349C2×C47C2×C4×C22⋊C411yescharacteristic
350C2×C47C42×Q811yescharacteristic
351C2×C47#227611yescharacteristic
352C2×C47#233911yescharacteristic
353C2×C47Q8×C22⋊C411yescharacteristic
354C2×C47#235511yescharacteristic
355C2×C47#235611yescharacteristic
356C2×C47#236011yescharacteristic
357C2×C47#236011yescharacteristic
358C2×C47#236211yescharacteristic
359C2×C47#236211yescharacteristic
360C2×C47#236511yescharacteristic
361C2×C47#236511yescharacteristic
362C2×C47#236711yescharacteristic
363C2×C47#236711yescharacteristic
364C23×Q8—471no—
365C2×C4×Q8—478no—
366C2×C4×Q8—944no—
367C2×C4×Q8—944no—
368C22×C4⋊C4—472no—
369C22×C4⋊C4—471no—
370C22×C4⋊C4C2×D4711yescharacteristic
371C22×C4⋊C4C2×D4711yescharacteristic
372C22×C42—472no—
373C22×C42—471no—
374C22×C42—471no—
375C22×C42—472no—
376C22×C42C2×D4712yes—
377C22×C42C2×D4711yescharacteristic
378#391—478no—
379#391—478no—
380C4×C4⋊C4—24no—
381C4×C4⋊C4—944no—
382C2×#95—471no—
383C2×#95—472no—
384C2×#95—472no—
385C2×#95—472no—
386C2×#95—472no—
387C2×#95—471no—
388C2×#95—472no—
389C2×#95—471no—
390C2×#95—471no—
391C2×#95—472no—
392C2×#95—472no—
393C2×#95C2×D4712yes—
394C47#1381711yescharacteristic, complemented, Sylow
395C22×Q8—474no—
396C22×Q8—474no—
397C22×Q8—474no—
398C22×Q8—942no—
399C22×Q8—942no—
400C22×Q8—942no—
401C22×Q8—942no—
402C23×C4—472no—
403C23×C4—471no—
404C23×C4—471no—
405C23×C4—471no—
406C23×C4—472no—
407C23×C4—471no—
408C23×C4C22×D4712yes—
409C23×C4C22×D4711yescharacteristic
410C23×C4C22×D4712yes—
411C23×C4C22×D4711yescharacteristic
412C23×C4C22×D4711yescharacteristic
413C4×Q8—9432no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—478no—
417C2×C4⋊C4—474no—
418C2×C4⋊C4—944no—
419C2×C4⋊C4—942no—
420C2×C4⋊C4—942no—
421C2×C4⋊C4—944no—
422C2×C4⋊C4C4×D4714yes—
423C2×C4⋊C4C4×D4714yes—
424C2×C4⋊C4D18814yes—
425C2×C4⋊C4C22⋊D4714yes—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—24no—
429C2×C42—24no—
430C2×C42—42no—
431C2×C42—478no—
432C2×C42—474no—
433C2×C42—474no—
434C2×C42—944no—
435C2×C42—942no—
436C2×C42—942no—
437C2×C42—942no—
438C2×C42—944no—
439C2×C42—942no—
440C2×C42—944no—
441C2×C42—944no—
442C2×C42—1882no—
443C2×C42C4×D4714yes—
444#95—24no—
445#95—478no—
446#95—478no—
447#95—478no—
448#95—478no—
449#95—474no—
450#95—942no—
451#95—944no—
452#95—942no—
453#95—944no—
454#95—942no—
455#95—1882no—
456C24C23×D4711yescharacteristic
457C2×Q8—4716no—
458C2×Q8—948no—
459C2×Q8—948no—
460C2×Q8—948no—
461C2×Q8—948no—
462C2×Q8—948no—
463C2×Q8—948no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—472no—
485C22×C4—474no—
486C22×C4—474no—
487C22×C4—472no—
488C22×C4—474no—
489C22×C4—472no—
490C22×C4—472no—
491C22×C4—472no—
492C22×C4—472no—
493C22×C4—472no—
494C22×C4—474no—
495C22×C4—472no—
496C22×C4—941no—
497C22×C4—942no—
498C22×C4—941no—
499C22×C4—941no—
500C22×C4—942no—
501C22×C4—941no—
502C22×C4—942no—
503C22×C4—942no—
504C22×C4—941no—
505C22×C4—941no—
506C22×C4—941no—
507C22×C4—941no—
508C22×C4—941no—
509C22×C4—941no—
510C22×C4—942no—
511C22×C4—941no—
512C22×C4—941no—
513C22×C4—941no—
514C22×C4—942no—
515C22×C4—942no—
516C22×C4—941no—
517C22×C4—941no—
518C22×C4—941no—
519C22×C4—942no—
520C22×C4—941no—
521C22×C4—942no—
522C22×C4—941no—
523C22×C4—941no—
524C22×C4—941no—
525C22×C4—942no—
526C22×C4C2×C4×D4712yes—
527C22×C4C2×C4×D4714yes—
528C22×C4C2×C4×D4714yes—
529C22×C4C2×C4×D4712yes—
530C22×C4C2×C4×D4712yes—
531C22×C4C2×C4×D4712yes—
532C22×C4C2×C4×D4712yes—
533C22×C4C2×D18814yes—
534C22×C4C2×D18812yes—
535C22×C4#1062535012yes—
536C22×C4#1062535012yes—
537C22×C4#1062535212yes—
538C22×C4Q8×D4712yes—
539C22×C4C2×C22⋊D4714yes—
540C22×C4C2×C22⋊D4712yes—
541C4⋊C4—28no—
542C4⋊C4—9416no—
543C4⋊C4—948no—
544C4⋊C4(C2×D47)⋊C4116yes—
545C42—28no—
546C42—48no—
547C42—9416no—
548C42—948no—
549C42—948no—
550C42—1888no—
551C23C22×C4×D4711yescharacteristic
552C23C22×C4×D4711yescharacteristic
553C23C22×C4×D4711yescharacteristic
554C23C22×C22⋊D4711yescharacteristic
555C23C22×D18811yescharacteristic
556C23C2×Q8×D4711yescharacteristic
557C23#41×D4711yescharacteristic
558C23#41×D4711yescharacteristic
559C23C2×#1062535211yescharacteristic
560C23C2×#1062535011yescharacteristic
561C23C2×#1062535011yescharacteristic
562C23#1309406911yescharacteristic
563C23#1309407111yescharacteristic
564C23#1309407111yescharacteristic
565C23#1309407211yescharacteristic
566Q8—9432no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—478no—
594C2×C4—474no—
595C2×C4—474no—
596C2×C4—942no—
597C2×C4—942no—
598C2×C4—942no—
599C2×C4—942no—
600C2×C4—942no—
601C2×C4—942no—
602C2×C4—942no—
603C2×C4—942no—
604C2×C4—944no—
605C2×C4—942no—
606C2×C4—944no—
607C2×C4—944no—
608C2×C4—944no—
609C2×C4—942no—
610C2×C4—944no—
611C2×C4—944no—
612C2×C4—942no—
613C2×C4—942no—
614C2×C4—942no—
615C2×C4—942no—
616C2×C4—944no—
617C2×C4—942no—
618C2×C4—942no—
619C2×C4—944no—
620C2×C4—942no—
621C2×C4—942no—
622C2×C4—944no—
623C2×C4—1881no—
624C2×C4—1882no—
625C2×C4—1881no—
626C2×C4—1881no—
627C2×C4—1881no—
628C2×C4—1881no—
629C2×C4—1881no—
630C2×C4—1882no—
631C2×C4—1881no—
632C2×C4—1881no—
633C2×C4—1882no—
634C2×C4—1882no—
635C2×C4C42×D4714yes—
636C2×C4C2×(C2×D47)⋊C418yes—
637C2×C4C2×(C2×D47)⋊C414yes—
638C2×C4#1309398114yes—
639C2×C4C4×C22⋊D4714yes—
640C2×C4C4×C22⋊D4714yes—
641C2×C4C4×D18814yes—
642C2×C4C4×D18814yes—
643C2×C4#1309398914yescomplemented
644C22C2×C42×D4711yescharacteristic
645C22C22×(C2×D47)⋊C411yescharacteristic
646C22C2×#1309398111yescharacteristic
647C22C2×C4×C22⋊D4711yescharacteristic
648C22C2×C4×C22⋊D4711yescharacteristic
649C22C2×C4×D18811yescharacteristic
650C22C2×C4×D18811yescharacteristic
651C22C4×Q8×D4711yescharacteristic
652C22C4×Q8×D4711yescharacteristic
653C22C2×#1309398911yescharacteristic
654C22C4×#1062535211yescharacteristic
655C22C4×#1062535211yescharacteristic
656C22#1568959111yescharacteristic
657C22#1568959911yescharacteristic
658C22#1568959911yescharacteristic
659C22#1568960011yescharacteristic
660C22#1568960211yescharacteristic
661C22#1568960211yescharacteristic
662C22#1568960411yescharacteristic
663C22#1568976711yescharacteristic
664C22#1568976811yescharacteristic
665C22#1568977211yescharacteristic
666C22#1568977711yescharacteristic
667C22#1568978011yescharacteristic
668C22#1568978511yescharacteristic
669C22Q8×C22⋊D4711yescharacteristic
670C22Q8×D18811yescharacteristic
671C22#1568980811yescharacteristic
672C22#1568981211yescharacteristic
673C22#1568982811yescharacteristic
674C22#1568984111yescharacteristic
675C22#1568984311yescharacteristic
676C22#1568984511yescharacteristic
677C22#1568985111yescharacteristic
678C22#1568985611yescharacteristic
679C4—24no—
680C4—28no—
681C4—42no—
682C4—44no—
683C4—944no—
684C4—944no—
685C4—948no—
686C4—1882no—
687C4—1884no—
688C4—1882no—
689C4C4×(C2×D47)⋊C418yes—
690C2C2×C4×(C2×D47)⋊C411yescharacteristic
691C2C4×#1309398911yescharacteristic
692C2#2024575211yescharacteristic
693C2#2024621311yescharacteristic
694C2Q8×(C2×D47)⋊C411yescharacteristic
695C2#2024634111yescharacteristic
696C2#2024634911yescharacteristic
697C2#2024639311yescharacteristic
698C2#2024639511yescharacteristic
699C2#2024641511yescharacteristic
700C2#2024641711yescharacteristic
701C2#2024644211yescharacteristic
702C2#2024644611yescharacteristic
703C2#2024645911yescharacteristic
704C2#2024646111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC2×C4×C4⋊C4×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC2×C4×C4⋊C4D47
hypocenterC47#13817
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
15. C2×#13093989C4semidirect
22. #15689029C4semidirect
23. #15689028C4semidirect
84. C47⋊#95Q8semidirect
187. C2×Dic94C42semidirect
247. C2×C4×C47C4×Q8semidirect
289. C2×Dic47C4×Q8semidirect
394. C47#13817semidirect
643. C2×C4#13093989semidirect

Maximal subgroups

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

subgroupindex
C22×#130939892
C2×#156890292
C2×#156890282
C2×C4⋊C4×Dic472
#202416232
#202416212
#202416172
#202416122
C4×C47⋊#952
C2×C4×C4⋊C4×C472
#1381747