Finite Group Databasebeta

← #26231571

Subgroups — #26231571

Order 12032.

1908 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C2×#15689199C212yesmaximal, complemented
3C2×#15689085C211yesmaximal, characteristic, complemented
4#20244180C212yesmaximal, complemented
5#20243685C212yesmaximal, complemented
6#20243682C212yesmaximal, complemented
7#20243366C211yesmaximal, characteristic, complemented
8#20243298C211yesmaximal, characteristic, complemented
9#20243297C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic47C211yesmaximal, characteristic, complemented
11C2×C47×#407C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C411yescharacteristic
13C23×C4×D47C2211yescharacteristic
14C22×#10625324C2212yescomplemented
15C2×C4×C22⋊D47—28no—
16C2×C4×C22⋊D47C411yescharacteristic
17C2×C4×C22⋊D47C411yescharacteristic
18C2×C4×C22⋊D47C411yescharacteristic
19C2×C4×C22⋊D47C411yescharacteristic
20C2×C4×C22⋊D47C2211yescharacteristic
21C2×C4×C22⋊D47C2211yescharacteristic
22C2×C4×C22⋊D47C2211yescharacteristic
23C2×C4×C22⋊D47C2211yescharacteristic
24C22×Dic47⋊C4C411yescharacteristic
25C22×C22⋊Dic47C411yescharacteristic
26C22×(C2×D47)⋊C4C411yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28#15689199—28no—
29C2×Dic47⋊C8C2212yescomplemented
30#15689085—24no—
31C2×C22⋊(C47⋊C8)C2211yescharacteristic
32C2×C22⋊(C47⋊C8)C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2212yescomplemented
34C2×C22⋊(C47⋊C8)C2212yescomplemented
35C2×(C2×D47)⋊C8C2212yescomplemented
36C2×(C2×D47)⋊C8C2212yescomplemented
37C2×(C2×D47)⋊C8C2212yescomplemented
38C2×C8×Dic47C2212yescomplemented
39#15688877C2212yescomplemented
40#15688877C2212yescomplemented
41C24×C4×C47C2211yescharacteristic
42C22×M16×C47C2212yescomplemented
43C47×#407—24no—
44C2×C22⋊C8×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2211yescharacteristic
46C2×C22⋊C8×C47C2212yescomplemented
47C24×D47C2×C411yescharacteristic
48C22×C22⋊D47—24no—
49C22×C22⋊D47—24no—
50C22×C22⋊D47—24no—
51C22×C22⋊D47C2×C411yescharacteristic
52C22×C22⋊D47C2×C411yescharacteristic
53C22×C22⋊D47C2×C411yescharacteristic
54C22×C22⋊D47C2×C411yescharacteristic
55C23×Dic47C2×C411yescharacteristic
56C23×Dic47C2×C411yescharacteristic
57C23×Dic47C2×C411yescharacteristic
58C22×C4×D47—22no—
59C22×C4×D47—22no—
60C22×C4×D47—24no—
61C22×C4×D47—42no—
62C22×C4×D47C2×C411yescharacteristic
63C22×C4×D47C2×C411yescharacteristic
64C22×C4×D47C2311yescharacteristic
65C22×C4×D47C2311yescharacteristic
66C2×#10625324—24no—
67C2×#10625324—24no—
68C2×#10625324—42no—
69C22×C47⋊C8C2312yes—
70C22×C47⋊C8C2312yes—
71C4×C22⋊D47—24no—
72C4×C22⋊D47—24no—
73C4×C22⋊D47—24no—
74C4×C22⋊D47—24no—
75C4×C22⋊D47—24no—
76C4×C22⋊D47—24no—
77C4×C22⋊D47—24no—
78C4×C22⋊D47D418yes—
79C2×Dic47⋊C4—24no—
80C2×Dic47⋊C4C2×C411yescharacteristic
81C2×Dic47⋊C4C2×C411yescharacteristic
82C2×Dic47⋊C4C2×C411yescharacteristic
83C2×Dic47⋊C4C2×C411yescharacteristic
84C2×C22⋊Dic47—24no—
85C2×C22⋊Dic47C2×C411yescharacteristic
86C2×C22⋊Dic47C2×C411yescharacteristic
87C2×C22⋊Dic47C2×C411yescharacteristic
88C2×C22⋊Dic47C2×C411yescharacteristic
89C2×(C2×D47)⋊C4—24no—
90C2×(C2×D47)⋊C4C2×C411yescharacteristic
91C2×(C2×D47)⋊C4C2×C411yescharacteristic
92C2×(C2×D47)⋊C4C2×C411yescharacteristic
93C2×(C2×D47)⋊C4C2×C411yescharacteristic
94C2×C4×Dic47—24no—
95C2×C4×Dic47C2×C411yescharacteristic
96C2×C4×Dic47C2×C411yescharacteristic
97C2×C4×Dic47C2311yescharacteristic
98C2×C4×Dic47C2311yescharacteristic
99Dic47⋊C8—24no—
100C22⋊(C47⋊C8)—22no—
101C22⋊(C47⋊C8)—24no—
102C22⋊(C47⋊C8)—22no—
103C22⋊(C47⋊C8)—42no—
104(C2×D47)⋊C8—24no—
105(C2×D47)⋊C8—24no—
106(C2×D47)⋊C8—42no—
107C8×Dic47—24no—
108C25×C47C2×C411yescharacteristic
109C23×C4×C47—24no—
110C23×C4×C47—22no—
111C23×C4×C47—22no—
112C23×C4×C47—42no—
113C23×C4×C47C2×C411yescharacteristic
114C23×C4×C47C2×C411yescharacteristic
115C23×C4×C47C2×C411yescharacteristic
116C23×C4×C47C2311yescharacteristic
117C23×C4×C47C2311yescharacteristic
118C23×C4×C47C2311yescharacteristic
119C2×M16×C47—24no—
120C2×M16×C47—24no—
121C2×M16×C47—42no—
122C22×C8×C47C2312yes—
123C22×C8×C47C2312yes—
124C22⋊C8×C47—22no—
125C22⋊C8×C47—24no—
126C22⋊C8×C47D414yescomplemented
127C24×C47—22no—
128C24×C47—22no—
129C24×C47—22no—
130C24×C47—22no—
131C24×C47—22no—
132C24×C47—41no—
133C24×C47—41no—
134C24×C47C22×C411yescharacteristic
135C24×C47C22×C411yescharacteristic
136C24×C47C22×C411yescharacteristic
137C23×D47—22no—
138C23×D47—22no—
139C23×D47—22no—
140C23×D47—22no—
141C23×D47—22no—
142C23×D47—41no—
143C23×D47—41no—
144C23×D47C22×C411yescharacteristic
145C23×D47C22×C411yescharacteristic
146C22×C4×C47—21no—
147C22×C4×C47—22no—
148C22×C4×C47—21no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—22no—
161C22×C4×C47—41no—
162C22×C4×C47—41no—
163C22×C4×C47—41no—
164C22×C4×C47—48no—
165C22×C4×C47—48no—
166C22×C4×C47C22×C411yescharacteristic
167C22×C4×C47C22×C411yescharacteristic
168C22×C4×C47C22×C411yescharacteristic
169C22×C4×C47C2×D414yes—
170C22×C4×C47C2×D412yes—
171C22×C4×C47#4112yes—
172C22×C4×C47C2411yescharacteristic
173C2×C22⋊D47—232no—
174C2×C22⋊D47—22no—
175C2×C22⋊D47—22no—
176C2×C22⋊D47—22no—
177C2×C22⋊D47—22no—
178C2×C22⋊D47—22no—
179C2×C22⋊D47—22no—
180C2×C22⋊D47—22no—
181C2×C22⋊D47—22no—
182C2×C22⋊D47—22no—
183C2×C22⋊D47—22no—
184C2×C22⋊D47C22⋊C414yes—
185C2×C22⋊D47M1614yescomplemented
186C22×Dic47—22no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—41no—
193C22×Dic47—41no—
194C22×Dic47M1614yescomplemented
195C22×Dic47C22×C411yescharacteristic
196C22×Dic47C22×C411yescharacteristic
197C22×Dic47C22×C411yescharacteristic
198C22×Dic47C22×C411yescharacteristic
199C22×Dic47C22×C411yescharacteristic
200C22×Dic47C22×C411yescharacteristic
201C2×C4×D47—21no—
202C2×C4×D47—21no—
203C2×C4×D47—22no—
204C2×C4×D47—22no—
205C2×C4×D47—22no—
206C2×C4×D47—22no—
207C2×C4×D47—21no—
208C2×C4×D47—22no—
209C2×C4×D47—21no—
210C2×C4×D47—22no—
211C2×C4×D47—22no—
212C2×C4×D47—48no—
213C2×C4×D47—48no—
214C2×C4×D47—41no—
215C2×C4×D47—41no—
216C2×C4×D47C2×D414yes—
217M16×C47—48no—
218C2×C8×C47—22no—
219C2×C8×C47—22no—
220C2×C8×C47—22no—
221C2×C8×C47—22no—
222C2×C8×C47—22no—
223C2×C8×C47C2×D414yescomplemented
224C22⋊Dic47—22no—
225C22⋊Dic47—22no—
226C22⋊Dic47—22no—
227C22⋊Dic47C22⋊C414yes—
228(C2×D47)⋊C4—22no—
229(C2×D47)⋊C4—22no—
230(C2×D47)⋊C4—22no—
231(C2×D47)⋊C4C22⋊C414yes—
232Dic47⋊C4—22no—
233Dic47⋊C4—22no—
234Dic47⋊C4—22no—
235Dic47⋊C4C22⋊C414yes—
236C4×Dic47—22no—
237C4×Dic47—22no—
238C4×Dic47—22no—
239C4×Dic47C2×D414yes—
240C2×C47⋊C8—22no—
241C2×C47⋊C8—22no—
242C2×C47⋊C8—22no—
243C2×C47⋊C8—22no—
244C2×C47⋊C8—22no—
245C2×C47⋊C8—22no—
246#10625324—48no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—28no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—21no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—21no—
262C23×C47—21no—
263C23×C47—21no—
264C23×C47—44no—
265C23×C47—44no—
266C23×C47—44no—
267C23×C47—44no—
268C23×C47—44no—
269C23×C47—44no—
270C23×C47C2×C22⋊C412yes—
271C23×C47C4×D412yes—
272C23×C47C2×M1612yes—
273C23×C47C2×M1612yes—
274C23×C47#13112yes—
275C23×C47C23×C411yescharacteristic
276C22×D47—28no—
277C22×D47—21no—
278C22×D47—21no—
279C22×D47—21no—
280C22×D47—21no—
281C22×D47—21no—
282C22×D47—21no—
283C22×D47—21no—
284C22×D47—21no—
285C22×D47—21no—
286C22×D47—21no—
287C22×D47—21no—
288C22×D47—21no—
289C22×D47—44no—
290C22×D47—44no—
291C22×D47—44no—
292C22×D47—44no—
293C22×D47—44no—
294C22×D47—44no—
295C22×D47C2×C22⋊C412yes—
296C22×D47C2×M1612yes—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—24no—
302C2×C4×C47—24no—
303C2×C4×C47—24no—
304C2×C4×C47—24no—
305C2×C4×C47—21no—
306C2×C4×C47—21no—
307C2×C4×C47—21no—
308C2×C4×C47—44no—
309C2×C4×C47—44no—
310C2×C4×C47—44no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47C2×C22⋊C412yes—
314C2×C4×C47C4×D412yes—
315C2×C4×C47C22×D412yes—
316C2×C4×C47C22×D411yescharacteristic
317C2×C4×C47C2×#4111yescharacteristic
318C2×C4×C47H(5,𝔽2)12yes—
319C22⋊D47—28no—
320C22⋊D47—28no—
321C22⋊D47—28no—
322C22⋊D47—28no—
323C2×Dic47—21no—
324C2×Dic47—21no—
325C2×Dic47—21no—
326C2×Dic47—21no—
327C2×Dic47—21no—
328C2×Dic47—21no—
329C2×Dic47—28no—
330C2×Dic47—21no—
331C2×Dic47—21no—
332C2×Dic47—21no—
333C2×Dic47—21no—
334C2×Dic47—21no—
335C2×Dic47—21no—
336C2×Dic47—44no—
337C2×Dic47—44no—
338C2×Dic47C2×C22⋊C412yes—
339C2×Dic47C2×C22⋊C412yes—
340C2×Dic47C2×C22⋊C412yes—
341C2×Dic47C2×M1612yes—
342C2×Dic47C2×M1612yes—
343C2×Dic47C2×M1612yes—
344C4×D47—24no—
345C4×D47—24no—
346C4×D47—44no—
347C4×D47—44no—
348C4×D47—42no—
349C4×D47—42no—
350C8×C47—24no—
351C8×C47—42no—
352C47⋊C8—42no—
353C47⋊C8—42no—
354#22401—471nomaximal, Sylow
355C22×C47—22no—
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—22no—
360C22×C47—22no—
361C22×C47—22no—
362C22×C47—22no—
363C22×C47—22no—
364C22×C47—22no—
365C22×C47—22no—
366C22×C47—22no—
367C22×C47—416no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47#43614yescomplemented
377C22×C47C22×C22⋊C411yescharacteristic
378C22×C47C2×C4×D411yescharacteristic
379C22×C47#51811yescharacteristic
380C22×C47C22×M1611yescharacteristic
381C22×C47C22×M1611yescharacteristic
382C22×C47C2×#13111yescharacteristic
383C22×C47#56811yescharacteristic
384C2×D47—22no—
385C2×D47—22no—
386C2×D47—22no—
387C2×D47—22no—
388C2×D47—22no—
389C2×D47—22no—
390C2×D47—416no—
391C2×D47—41no—
392C2×D47—41no—
393C2×D47—41no—
394C2×D47—41no—
395C2×D47—41no—
396C2×D47—41no—
397C2×D47—41no—
398C2×D47—41no—
399C4×C47—22no—
400C4×C47—22no—
401C4×C47—41no—
402C4×C47D4212yes—
403C4×C47#54612yes—
404Dic47—22no—
405Dic47—22no—
406Dic47—22no—
407Dic47—41no—
408Dic47—41no—
409Dic47#40714yescomplemented
410C22×C4×D4—471no—
411C2×#436—472no—
412C2×#407—471no—
413C2×#407D4711yescharacteristic, complemented
414#1954—472no—
415#1870—472no—
416#1870—472no—
417#1797—471no—
418#1779—471no—
419#1779—471no—
420C4×C22⋊C8—471no—
421C2×C47—24no—
422C2×C47—42no—
423C2×C47—42no—
424C2×C47D4×C22⋊C411yescharacteristic
425C2×C47C2×#40711yescharacteristic
426C2×C47#288011yescharacteristic
427C2×C47C2×#43611yescharacteristic
428C2×C47D4×M1611yescharacteristic
429C2×C47#297411yescharacteristic
430C2×C47#297511yescharacteristic
431D47—42no—
432D47—42no—
433C23×D4—471no—
434C24×C4—471no—
435C24×C4C2×D4711yescharacteristic
436C22×M16—472no—
437C22×M16C2×D4712yescomplemented
438C2×C4×D4—471no—
439C2×C4×D4—471no—
440C2×C4×D4—471no—
441C2×C4×D4—471no—
442C2×C4×D4—471no—
443C2×C4×D4—471no—
444C2×C4×D4—471no—
445C2×C4×D4—471no—
446C2×C4×D4—948no—
447C22×C4⋊C4—471no—
448C22×C22⋊C4—471no—
449C22×C22⋊C4—471no—
450C22×C42—471no—
451#436—948no—
452C2×C4⋊C8—472no—
453#407—24no—
454#407—944no—
455C2×C22⋊C8—471no—
456C2×C22⋊C8—472no—
457C2×C22⋊C8—471no—
458C2×C22⋊C8—472no—
459C2×C22⋊C8—472no—
460C2×C22⋊C8—472no—
461C2×C22⋊C8—472no—
462C2×C22⋊C8C2×D4711yescharacteristic
463C2×C22⋊C8C2×D4711yescharacteristic
464C2×C22⋊C8C2×D4712yescomplemented
465C2×C4×C8—472no—
466#336—472no—
467#336—472no—
468C47#2240111yescharacteristic, complemented, Sylow
469C25—471no—
470C25C4×D4711yescharacteristic
471C22×D4—471no—
472C22×D4—471no—
473C22×D4—471no—
474C22×D4—471no—
475C22×D4—944no—
476C22×D4—944no—
477C22×D4—944no—
478C23×C4—22no—
479C23×C4—24no—
480C23×C4—22no—
481C23×C4—42no—
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—471no—
486C23×C4—471no—
487C23×C4—471no—
488C23×C4—471no—
489C23×C4—944no—
490C23×C4—942no—
491C23×C4—942no—
492C23×C4—1882no—
493C23×C4C4×D4711yescharacteristic
494C23×C4C4×D4711yescharacteristic
495C23×C4C4×D4711yescharacteristic
496C23×C4C22×D4711yescharacteristic
497C23×C4C22×D4711yescharacteristic
498C23×C4C22×D4711yescharacteristic
499C2×M16—24no—
500C2×M16—24no—
501C2×M16—42no—
502C2×M16—944no—
503C2×M16—944no—
504C2×M16—1882no—
505C22×C8—472no—
506C22×C8—472no—
507C22×C8C22×D4712yes—
508C22×C8C22×D4712yes—
509C4×D4—478no—
510C4×D4—944no—
511C4×D4—944no—
512C4×D4—944no—
513C4×D4—944no—
514C4×D4—944no—
515C4×D4—944no—
516C4×D4—944no—
517C2×C4⋊C4—471no—
518C2×C4⋊C4—471no—
519C2×C4⋊C4—471no—
520C2×C4⋊C4—471no—
521C2×C4⋊C4—944no—
522C2×C22⋊C4—471no—
523C2×C22⋊C4—471no—
524C2×C22⋊C4—471no—
525C2×C22⋊C4—471no—
526C2×C22⋊C4—471no—
527C2×C22⋊C4—471no—
528C2×C22⋊C4—471no—
529C2×C22⋊C4—471no—
530C2×C22⋊C4—944no—
531C2×C22⋊C4—944no—
532C2×C42—471no—
533C2×C42—471no—
534C2×C42—471no—
535C2×C42—471no—
536C2×C42—944no—
537C4⋊C8—944no—
538C22⋊C8—22no—
539C22⋊C8—24no—
540C22⋊C8—944no—
541C22⋊C8—942no—
542C22⋊C8—944no—
543C22⋊C8—942no—
544C22⋊C8—944no—
545C22⋊C8—1882no—
546C22⋊C8—1882no—
547C22⋊C8C22⋊D4714yescomplemented
548C4×C8—944no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—41no—
555C24—41no—
556C24—471no—
557C24—471no—
558C24—942no—
559C24—942no—
560C24—942no—
561C24—942no—
562C24—942no—
563C24—1881no—
564C24—1881no—
565C24C2×C4×D4711yescharacteristic
566C24C2×C4×D4711yescharacteristic
567C24C2×C4×D4711yescharacteristic
568C2×D4—474no—
569C2×D4—474no—
570C2×D4—942no—
571C2×D4—942no—
572C2×D4—942no—
573C2×D4—942no—
574C2×D4—942no—
575C2×D4—942no—
576C2×D4—942no—
577C2×D4—942no—
578C2×D4—9432no—
579C2×D4—942no—
580C2×D4—942no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—471no—
602C22×C4—474no—
603C22×C4—471no—
604C22×C4—471no—
605C22×C4—471no—
606C22×C4—474no—
607C22×C4—471no—
608C22×C4—471no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—941no—
616C22×C4—941no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—942no—
623C22×C4—941no—
624C22×C4—941no—
625C22×C4—942no—
626C22×C4—1881no—
627C22×C4—1881no—
628C22×C4—1888no—
629C22×C4—1888no—
630C22×C4—1881no—
631C22×C4—1881no—
632C22×C4C2×C4×D4711yescharacteristic
633C22×C4C2×C4×D4711yescharacteristic
634C22×C4C2×C4×D4711yescharacteristic
635C22×C4#1062535012yes—
636C22×C4D4×D4714yes—
637C22×C4C2×C22⋊D4712yes—
638C22×C4C23×D4711yescharacteristic
639M16—48no—
640M16—1888no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—942no—
647C2×C8—942no—
648C2×C8—942no—
649C2×C8—942no—
650C2×C8—942no—
651C2×C8—942no—
652C2×C8C2×C22⋊D4714yescomplemented
653C4⋊C4—474no—
654C4⋊C4—942no—
655C4⋊C4—942no—
656C4⋊C4—942no—
657C22⋊C4—474no—
658C22⋊C4—474no—
659C22⋊C4—942no—
660C22⋊C4—942no—
661C22⋊C4—942no—
662C22⋊C4—942no—
663C22⋊C4—942no—
664C22⋊C4—942no—
665C42—474no—
666C42—942no—
667C42—942no—
668C42—942no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—28no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—472no—
693C23—472no—
694C23—948no—
695C23—941no—
696C23—941no—
697C23—941no—
698C23—941no—
699C23—941no—
700C23—941no—
701C23—941no—
702C23—941no—
703C23—941no—
704C23—941no—
705C23—941no—
706C23—941no—
707C23—1884no—
708C23—1884no—
709C23—1884no—
710C23—1884no—
711C23—1884no—
712C23—1884no—
713C23C22⋊C4×D4712yes—
714C23C4×C22⋊D4712yes—
715C23M16×D4712yes—
716C23M16×D4712yes—
717C23#1309403212yes—
718C23C22×C4×D4711yescharacteristic
719D4—948no—
720D4—948no—
721D4—948no—
722D4—948no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—472no—
740C2×C4—472no—
741C2×C4—472no—
742C2×C4—472no—
743C2×C4—472no—
744C2×C4—472no—
745C2×C4—948no—
746C2×C4—941no—
747C2×C4—941no—
748C2×C4—941no—
749C2×C4—941no—
750C2×C4—941no—
751C2×C4—941no—
752C2×C4—944no—
753C2×C4—944no—
754C2×C4—941no—
755C2×C4—941no—
756C2×C4—941no—
757C2×C4—941no—
758C2×C4—941no—
759C2×C4—941no—
760C2×C4—1884no—
761C2×C4—1884no—
762C2×C4—1884no—
763C2×C4—1884no—
764C2×C4—1882no—
765C2×C4—1882no—
766C2×C4C22⋊C4×D4712yes—
767C2×C4C4×C22⋊D4712yes—
768C2×C4C2×D4×D4712yes—
769C2×C4C22×C22⋊D4711yescharacteristic
770C2×C4C2×#1062535011yescharacteristic
771C2×C4#1309406912yes—
772C8—24no—
773C8—42no—
774C8—1882no—
775C8—1882no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—416no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—942no—
798C22—942no—
799C22—942no—
800C22—942no—
801C22—942no—
802C22—942no—
803C22—18816no—
804C22—1881no—
805C22—1881no—
806C22—1881no—
807C22—1881no—
808C22—1881no—
809C22—1881no—
810C22—1881no—
811C22—1881no—
812C22#1568919914yescomplemented
813C22C2×C22⋊C4×D4711yescharacteristic
814C22C2×C4×C22⋊D4711yescharacteristic
815C22#1568959611yescharacteristic
816C22C2×M16×D4711yescharacteristic
817C22C2×M16×D4711yescharacteristic
818C22C2×#1309403211yescharacteristic
819C22#1568988911yescharacteristic
820C4—22no—
821C4—22no—
822C4—41no—
823C4—474no—
824C4—942no—
825C4—942no—
826C4—942no—
827C4—1881no—
828C4—1881no—
829C4D4×C22⋊D4712yes—
830C4#1568976312yes—
831C2—24no—
832C2—42no—
833C2—42no—
834C2—1882no—
835C2—1882no—
836C2C22⋊C4×C22⋊D4711yescharacteristic
837C2#407×D4711yescharacteristic
838C2#2025183811yescharacteristic
839C2C2×#1568919911yescharacteristic
840C2M16×C22⋊D4711yescharacteristic
841C2#2025242411yescharacteristic
842C2#2025242711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C47×#407C2
prime radicalC23×C22⋊D47C4
cosocleC22×C4×C47C24
hypercenterC2×#407D47
hypocenterC47#22401
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#15689199C2semidirect
3. C2×#15689085C2semidirect
4. #20244180C2semidirect
5. #20243685C2semidirect
6. #20243682C2semidirect
7. #20243366C2semidirect
8. #20243298C2semidirect
9. #20243297C2semidirect
10. C22⋊C8×Dic47C2semidirect
11. C2×C47×#407C2semidirect
14. C22×#10625324C22semidirect
29. C2×Dic47⋊C8C22semidirect
33. C2×C22⋊(C47⋊C8)C22semidirect
34. C2×C22⋊(C47⋊C8)C22semidirect
35. C2×(C2×D47)⋊C8C22semidirect
36. C2×(C2×D47)⋊C8C22semidirect
37. C2×(C2×D47)⋊C8C22semidirect
38. C2×C8×Dic47C22semidirect
39. #15688877C22semidirect
40. #15688877C22semidirect
42. C22×M16×C47C22semidirect
46. C2×C22⋊C8×C47C22semidirect
126. C22⋊C8×C47D4semidirect
185. C2×C22⋊D47M16semidirect
194. C22×Dic47M16semidirect
223. C2×C8×C47C2×D4semidirect
376. C22×C47#436semidirect
409. Dic47#407semidirect
413. C2×#407D47semidirect
437. C22×M16C2×D47semidirect
464. C2×C22⋊C8C2×D47semidirect
468. C47#22401semidirect
547. C22⋊C8C22⋊D47semidirect
652. C2×C8C2×C22⋊D47semidirect
812. C22#15689199semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C2×#156891992
C2×#156890852
#202441802
#202436852
#202436822
#202433662
#202432982
#202432972
C22⋊C8×Dic472
C2×C47×#4072
#2240147