Finite Group Databasebeta

← #26223373

Subgroups — #26223373

Order 12032.

872 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689201C211yesmaximal, characteristic
2C2×#15689079C211yesmaximal, characteristic, complemented
3#20244003C211yesmaximal, characteristic, complemented
4#20243996C211yesmaximal, characteristic, complemented
5#20243954C211yesmaximal, characteristic, complemented
6#20243947C211yesmaximal, characteristic, complemented
7#20243681C211yesmaximal, characteristic
8#20243568C211yesmaximal, characteristic, complemented
9#20243459C211yesmaximal, characteristic, complemented
10#20243263C211yesmaximal, characteristic, complemented
11C4⋊C4×C47⋊C8C211yesmaximal, characteristic, complemented
12#20243172C211yesmaximal, characteristic, complemented
13#20243172C211yesmaximal, characteristic, complemented
14#20243172C211yesmaximal, characteristic, complemented
15C47×#2395C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C22×#10625329C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19#15689201—24no—
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×C22⋊(C47⋊C8)C2211yescharacteristic
24C2×C22⋊(C47⋊C8)C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28#15689079—24no—
29C2×#13093935C2211yescharacteristic
30C2×#13093935C2211yescharacteristic
31C2×#13093935C2211yescharacteristic
32C2×C4×C47⋊C8C2211yescharacteristic
33C2×C4×C47⋊C8C2211yescharacteristic
34C2×C4×C47⋊C8C2211yescharacteristic
35C2×C4×C47⋊C8C2211yescharacteristic
36#15688878C2211yescharacteristic
37#15688878C2211yescharacteristic
38#15688878C2211yescharacteristic
39#15688878C2211yescharacteristic
40#15688878C2211yescharacteristic
41#15688878C2211yescharacteristic
42#15688878C2211yescharacteristic
43#15688878C2211yescharacteristic
44#15688878C2211yescharacteristic
45#15688878C2211yescharacteristic
46C2×C4×D4×C47C2211yescharacteristic
47C2×#117×C47C2211yescharacteristic
48C47×#400C411yescharacteristic
49C47×#399C411yescharacteristic
50C47×#398C411yescharacteristic
51C47×#397C411yescharacteristic
52C47×#397C411yescharacteristic
53C47×#397C411yescharacteristic
54C47×#394C411yescharacteristic
55C47×#394C411yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C4×C22⋊C4×C47C2211yescharacteristic
60C4×C22⋊C4×C47C2211yescharacteristic
61C2×#10625329—22no—
62C2×#10625329—22no—
63C2×#10625329—22no—
64C2×#10625329—22no—
65C2×#10625329—22no—
66C2×#10625329D414yes—
67C22×C47⋊C8—22no—
68C22×C47⋊C8—22no—
69C22×C47⋊C8—22no—
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C4⋊(C47⋊C8)—22no—
79C4⋊(C47⋊C8)—22no—
80C4⋊(C47⋊C8)—22no—
81C22⋊(C47⋊C8)—22no—
82C22⋊(C47⋊C8)—22no—
83C22⋊(C47⋊C8)—22no—
84C22⋊(C47⋊C8)—22no—
85C22⋊(C47⋊C8)—22no—
86#13093935—22no—
87#13093935—22no—
88#13093935—22no—
89C4×C47⋊C8—22no—
90C4×C47⋊C8—22no—
91C4×C47⋊C8—22no—
92C4×C47⋊C8—22no—
93C22×D4×C47C2×C411yescharacteristic
94C23×C4×C47C2311yescharacteristic
95C23×C4×C47C2311yescharacteristic
96C4×D4×C47—22no—
97C4×D4×C47—22no—
98#117×C47—22no—
99#117×C47—22no—
100C2×C4⋊C4×C47C2×C411yescharacteristic
101C2×C4⋊C4×C47C2×C411yescharacteristic
102C2×C4⋊C4×C47C2×C411yescharacteristic
103C2×C4⋊C4×C47C2×C411yescharacteristic
104C2×C4⋊C4×C47C2×C411yescharacteristic
105C2×C4⋊C4×C47C2×C411yescharacteristic
106C2×C4⋊C4×C47C2×C411yescharacteristic
107C2×C22⋊C4×C47C2×C411yescharacteristic
108C2×C22⋊C4×C47C2×C411yescharacteristic
109C2×C22⋊C4×C47C2×C411yescharacteristic
110C2×C22⋊C4×C47C2×C411yescharacteristic
111C2×C22⋊C4×C47C2×C411yescharacteristic
112C2×C22⋊C4×C47C2×C411yescharacteristic
113C2×C22⋊C4×C47C2×C411yescharacteristic
114C2×C22⋊C4×C47C2×C411yescharacteristic
115C2×C22⋊C4×C47C2×C411yescharacteristic
116C2×C22⋊C4×C47C2×C411yescharacteristic
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121C2×C42×C47C2311yescharacteristic
122#95×C47C2×C411yescharacteristic
123#95×C47C2×C411yescharacteristic
124#95×C47C2×C411yescharacteristic
125#95×C47C2×C411yescharacteristic
126#95×C47C2×C411yescharacteristic
127#95×C47C2×C411yescharacteristic
128#95×C47C2×C411yescharacteristic
129#95×C47C2×C411yescharacteristic
130#95×C47C2×C411yescharacteristic
131#95×C47C2×C411yescharacteristic
132C24×C47C22×C411yescharacteristic
133C24×C47C22×C411yescharacteristic
134C2×D4×C47—22no—
135C2×D4×C47—22no—
136C2×D4×C47—41no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C22×C411yescharacteristic
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C22×C411yescharacteristic
151C22×C4×C47C22×C411yescharacteristic
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C22×C411yescharacteristic
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C22×C411yescharacteristic
156C22×C4×C47C22×C411yescharacteristic
157C22×C4×C47C22×C411yescharacteristic
158C22×C4×C47C22×C411yescharacteristic
159C22×C4×C47C2×D412yes—
160C22×C4×C47#4112yes—
161C22×C4×C47C2411yescharacteristic
162C4⋊C4×C47—22no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—22no—
167C4⋊C4×C47—22no—
168C4⋊C4×C47—41no—
169C22⋊C4×C47—22no—
170C22⋊C4×C47—22no—
171C22⋊C4×C47—22no—
172C22⋊C4×C47—22no—
173C22⋊C4×C47—22no—
174C22⋊C4×C47—22no—
175C22⋊C4×C47—41no—
176C22⋊C4×C47—41no—
177C22⋊C4×C47—41no—
178C22⋊C4×C47—41no—
179C42×C47—21no—
180C42×C47—21no—
181C42×C47—21no—
182C42×C47—21no—
183C42×C47—21no—
184C42×C47—21no—
185C42×C47—21no—
186C42×C47—21no—
187C42×C47—21no—
188C42×C47—21no—
189#10625329—28no—
190#10625329—44no—
191C2×C47⋊C8—28no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—21no—
209C2×C47⋊C8—21no—
210C2×C47⋊C8C2×D412yes—
211C2×C47⋊C8C2×D412yes—
212C2×C47⋊C8#4112yes—
213C2×C47⋊C8#4112yes—
214C2×C47⋊C8#4112yes—
215C2×C47⋊C8#4112yes—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47—21no—
220C23×C47—21no—
221C23×C47—21no—
222C23×C47—21no—
223C23×C47—21no—
224C23×C47—21no—
225C23×C47—21no—
226C23×C47—21no—
227C23×C47—21no—
228C23×C47—21no—
229C23×C47C4×D412yes—
230C23×C47C23×C411yescharacteristic
231D4×C47—44no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—22no—
239C2×C4×C47—22no—
240C2×C4×C47—22no—
241C2×C4×C47—22no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—21no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47C4×D412yes—
274C2×C4×C47#13112yes—
275C2×C4×C47#13112yes—
276C2×C4×C47C22×D411yescharacteristic
277C2×C4×C47C2×#4111yescharacteristic
278C2×C4×C47C2×#4111yescharacteristic
279C2×C4×C47C2×#4111yescharacteristic
280C2×C4×C47C2×#4111yescharacteristic
281C2×C4×C47C2×#4111yescharacteristic
282C47⋊C8—22no—
283C47⋊C8—22no—
284C47⋊C8—22no—
285C47⋊C8—41no—
286C47⋊C8—41no—
287C47⋊C8—41no—
288C47⋊C8—41no—
289C47⋊C8#12314yes—
290#21571—471nomaximal, Sylow
291C22×C47—22no—
292C22×C47—22no—
293C22×C47—22no—
294C22×C47—41no—
295C22×C47—41no—
296C22×C47—41no—
297C22×C47—41no—
298C22×C47—41no—
299C22×C47—41no—
300C22×C47—41no—
301C22×C47—41no—
302C22×C47—41no—
303C22×C47—41no—
304C22×C47—41no—
305C22×C47C2×C4×D411yescharacteristic
306C22×C47C4×#4111yescharacteristic
307C22×C47C4×#4111yescharacteristic
308C22×C47C2×#13111yescharacteristic
309C22×C47C2×#13111yescharacteristic
310C22×C47#56811yescharacteristic
311C22×C47#56811yescharacteristic
312C4×C47—22no—
313C4×C47—22no—
314C4×C47—22no—
315C4×C47—41no—
316C4×C47—41no—
317C4×C47—41no—
318C4×C47—41no—
319C4×C47—41no—
320C4×C47—41no—
321C4×C47—41no—
322C4×C47—41no—
323C4×C47—41no—
324C4×C47C2×#12311yescharacteristic
325C4×C47#52511yescharacteristic
326C4×C47#52911yescharacteristic
327C4×C47#52911yescharacteristic
328C2×#436—471no—
329C2×#405—471no—
330#2395D4711yescharacteristic
331#1924—471no—
332#1923—471no—
333#1917—471no—
334#1916—471no—
335#1869—471no—
336#1850—471no—
337#1818—471no—
338#1771—471no—
339C8×C4⋊C4—471no—
340#1753—471no—
341#1753—471no—
342#1753—471no—
343C2×C47—42no—
344C2×C47—81no—
345C2×C47C4×#12311yescharacteristic
346C2×C47#293311yescharacteristic
347C2×C47#293511yescharacteristic
348C2×C47#296611yescharacteristic
349C2×C47#296711yescharacteristic
350C2×C47#296911yescharacteristic
351C2×C47#296911yescharacteristic
352C22×M16—471no—
353C22×M16—471no—
354C23×C8—471no—
355C2×C4×D4C2×D4711yescharacteristic
356C2×#117C2×D4711yescharacteristic
357#436—944no—
358C2×C4⋊C8—471no—
359C2×C4⋊C8—471no—
360C2×C4⋊C8—471no—
361C2×C22⋊C8—471no—
362C2×C22⋊C8—471no—
363C2×C22⋊C8—471no—
364C2×C22⋊C8—471no—
365C2×C22⋊C8—471no—
366#405—944no—
367C2×#97—471no—
368C2×#97—471no—
369C2×#97—471no—
370C2×C4×C8—471no—
371C2×C4×C8—471no—
372C2×C4×C8—471no—
373C2×C4×C8—471no—
374#400Dic4711yescharacteristic
375#399Dic4711yescharacteristic
376#398Dic4711yescharacteristic
377#397Dic4711yescharacteristic
378#397Dic4711yescharacteristic
379#397Dic4711yescharacteristic
380#394Dic4711yescharacteristic
381#394Dic4711yescharacteristic
382C4×C4⋊C4C2×D4711yescharacteristic
383C4×C4⋊C4C2×D4711yescharacteristic
384C4×C22⋊C4C2×D4711yescharacteristic
385C4×C22⋊C4C2×D4711yescharacteristic
386C4×C22⋊C4C2×D4711yescharacteristic
387#336—471no—
388#336—471no—
389#336—471no—
390#336—471no—
391#336—471no—
392#336—471no—
393#336—471no—
394#336—471no—
395#336—471no—
396#336—471no—
397C47#2157111yescharacteristic, complemented, Sylow
398C22×D4C2×Dic4711yescharacteristic
399C23×C4C22×D4711yescharacteristic
400C23×C4C22×D4711yescharacteristic
401C2×M16—474no—
402C2×M16—942no—
403C2×M16—942no—
404C2×M16—942no—
405C2×M16—942no—
406C2×M16—942no—
407C22×C8—471no—
408C22×C8—471no—
409C22×C8—471no—
410C22×C8—471no—
411C22×C8—471no—
412C22×C8—471no—
413C22×C8—471no—
414C22×C8—471no—
415C22×C8—942no—
416C22×C8—942no—
417C22×C8—942no—
418C4×D4—22no—
419C4×D4—22no—
420#117—22no—
421#117—22no—
422C2×C4⋊C4C2×Dic4711yescharacteristic
423C2×C4⋊C4C2×Dic4711yescharacteristic
424C2×C4⋊C4C2×Dic4711yescharacteristic
425C2×C4⋊C4C2×Dic4711yescharacteristic
426C2×C4⋊C4C2×Dic4711yescharacteristic
427C2×C4⋊C4C2×Dic4711yescharacteristic
428C2×C4⋊C4C2×Dic4711yescharacteristic
429C2×C22⋊C4C2×Dic4711yescharacteristic
430C2×C22⋊C4C2×Dic4711yescharacteristic
431C2×C22⋊C4C2×Dic4711yescharacteristic
432C2×C22⋊C4C2×Dic4711yescharacteristic
433C2×C22⋊C4C2×Dic4711yescharacteristic
434C2×C22⋊C4C2×Dic4711yescharacteristic
435C2×C22⋊C4C2×Dic4711yescharacteristic
436C2×C22⋊C4C2×Dic4711yescharacteristic
437C2×C22⋊C4C2×Dic4711yescharacteristic
438C2×C22⋊C4C2×Dic4711yescharacteristic
439C2×C42C22×D4711yescharacteristic
440C2×C42C22×D4711yescharacteristic
441C2×C42C22×D4711yescharacteristic
442C2×C42C22×D4711yescharacteristic
443C2×C42C22×D4711yescharacteristic
444C4⋊C8—942no—
445C4⋊C8—942no—
446C4⋊C8—942no—
447C22⋊C8—942no—
448C22⋊C8—942no—
449C22⋊C8—942no—
450C22⋊C8—942no—
451C22⋊C8—942no—
452#97—942no—
453#97—942no—
454#97—942no—
455C4×C8—942no—
456C4×C8—942no—
457C4×C8—942no—
458C4×C8—942no—
459#95C2×Dic4711yescharacteristic
460#95C2×Dic4711yescharacteristic
461#95C2×Dic4711yescharacteristic
462#95C2×Dic4711yescharacteristic
463#95C2×Dic4711yescharacteristic
464#95C2×Dic4711yescharacteristic
465#95C2×Dic4711yescharacteristic
466#95C2×Dic4711yescharacteristic
467#95C2×Dic4711yescharacteristic
468#95C2×Dic4711yescharacteristic
469C24C22×Dic4711yescharacteristic
470C24C22×Dic4711yescharacteristic
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—41no—
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×C4D4×D4712yes—
485C22×C4#1062535212yes—
486C22×C4C22×Dic4711yescharacteristic
487C22×C4C22×Dic4711yescharacteristic
488C22×C4C22×Dic4711yescharacteristic
489C22×C4C22×Dic4711yescharacteristic
490C22×C4C22×Dic4711yescharacteristic
491C22×C4C22×Dic4711yescharacteristic
492C22×C4C22×Dic4711yescharacteristic
493C22×C4C22×Dic4711yescharacteristic
494C22×C4C22×Dic4711yescharacteristic
495C22×C4C22×Dic4711yescharacteristic
496C22×C4C22×Dic4711yescharacteristic
497C22×C4C22×Dic4711yescharacteristic
498C22×C4C23×D4711yescharacteristic
499M16—948no—
500M16—1884no—
501C2×C8—472no—
502C2×C8—472no—
503C2×C8—472no—
504C2×C8—472no—
505C2×C8—472no—
506C2×C8—472no—
507C2×C8—948no—
508C2×C8—941no—
509C2×C8—941no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—941no—
515C2×C8—941no—
516C2×C8—941no—
517C2×C8—941no—
518C2×C8—941no—
519C2×C8—941no—
520C2×C8—941no—
521C2×C8—941no—
522C2×C8—941no—
523C2×C8—941no—
524C2×C8—941no—
525C2×C8—941no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—41no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23D4×Dic4712yes—
567C23C23×Dic4711yescharacteristic
568D4—44no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4D4×Dic4712yes—
611C2×C4#1309403112yes—
612C2×C4#1309403112yes—
613C2×C4C2×D4×D4711yescharacteristic
614C2×C4#41×D4711yescharacteristic
615C2×C4#41×D4711yescharacteristic
616C2×C4#41×D4711yescharacteristic
617C2×C4#41×D4711yescharacteristic
618C2×C4C2×#1062535211yescharacteristic
619C8—474no—
620C8—942no—
621C8—942no—
622C8—942no—
623C8—1881no—
624C8—1881no—
625C8—1881no—
626C8—1881no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×D4×Dic4711yescharacteristic
642C22#41×Dic4711yescharacteristic
643C22#41×Dic4711yescharacteristic
644C22C2×#1309403111yescharacteristic
645C22C2×#1309403111yescharacteristic
646C22#1568989011yescharacteristic
647C22#1568989011yescharacteristic
648C4—22no—
649C4—22no—
650C4—22no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4#123×D4711yescharacteristic
661C4#1568963111yescharacteristic
662C4#1568965011yescharacteristic
663C4#1568965011yescharacteristic
664C2—42no—
665C2—81no—
666C2#123×Dic4711yescharacteristic
667C2#2025211511yescharacteristic
668C2#2025213211yescharacteristic
669C2#2025236411yescharacteristic
670C2#2025237511yescharacteristic
671C2#2025239311yescharacteristic
672C2#2025239311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#2395C2
prime radicalC22×D4×C47C2×C4
cosocleC22×C4×C47C24
hypercenter#2395D47
hypocenterC47#21571
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
2. C2×#15689079C2semidirect
3. #20244003C2semidirect
4. #20243996C2semidirect
5. #20243954C2semidirect
6. #20243947C2semidirect
8. #20243568C2semidirect
9. #20243459C2semidirect
10. #20243263C2semidirect
11. C4⋊C4×C47⋊C8C2semidirect
12. #20243172C2semidirect
13. #20243172C2semidirect
14. #20243172C2semidirect
397. C47#21571semidirect

Maximal subgroups

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

subgroupindex
C2×#156892012
C2×#156890792
#202440032
#202439962
#202439542
#202439472
#202436812
#202435682
#202434592
#202432632
C4⋊C4×C47⋊C82
#202431722
C47×#23952
#2157147