Finite Group Databasebeta

← #37582757

Subgroups — #37582757

Order 24448.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133266C211yesmaximal, characteristic, complemented
2#27133138C211yesmaximal, characteristic, complemented
3#27132988C211yesmaximal, characteristic, complemented
4#27132984C211yesmaximal, characteristic, complemented
5#27132965C211yesmaximal, characteristic, complemented
6#27132961C211yesmaximal, characteristic, complemented
7#27132856C211yesmaximal, characteristic, complemented
8#27132856C211yesmaximal, characteristic, complemented
9#27132797C211yesmaximal, characteristic, complemented
10#27132775C211yesmaximal, characteristic, complemented
11#27132772C211yesmaximal, characteristic, complemented
12D8×Dic191C211yesmaximal, characteristic, complemented
13#27132743C211yesmaximal, characteristic, complemented
14#27132721C211yesmaximal, characteristic, complemented
15#447×C191C211yesmaximal, characteristic, complemented
16C2×#15690272C2211yescharacteristic
17C2×#15690272C2211yescharacteristic
18#20259318C2211yescharacteristic, complemented
19#20259313C2211yescharacteristic, complemented
20#20259306—21no—
21#20259304—21no—
22#20259296C2211yescharacteristic
23#20259294—21no—
24#20259293—21no—
25D4×Dic191—21no—
26D4×Dic191—21no—
27D4×Dic191C2211yescharacteristic
28D4×Dic191C2211yescharacteristic
29D4×Dic191C2211yescharacteristic
30D4×Dic191C2211yescharacteristic
31D4×Dic191C2211yescharacteristic, complemented
32#20259284C2211yescharacteristic, complemented
33#20259281C2211yescharacteristic
34#20259281C2211yescharacteristic
35C2×C22⋊Dic191—21no—
36C2×C22⋊Dic191—21no—
37#20259256C2211yescharacteristic, complemented
38#20259255C2211yescharacteristic, complemented
39#20259254C2211yescharacteristic, complemented
40#20259253C2211yescharacteristic, complemented
41Dic191⋊C8C2211yescharacteristic, complemented
42Dic191⋊C8C2211yescharacteristic, complemented
43#20259244C2211yescharacteristic, complemented
44#20259244C2211yescharacteristic, complemented
45#20259243C2211yescharacteristic
46#20259243C2211yescharacteristic
47#20259243C2211yescharacteristic, complemented
48#20259243C2211yescharacteristic, complemented
49C22⋊(C191⋊C8)C2211yescharacteristic
50#20259232C2211yescharacteristic, complemented
51C8×Dic191C2211yescharacteristic, complemented
52C22×D4×C191C2211yescharacteristic
53C2×D8×C191C2211yescharacteristic
54C2×D8×C191C2211yescharacteristic
55#121×C191C2211yescharacteristic
56#102×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59C2×D764C2311yescharacteristic
60C2×C22⋊D191—21no—
61C2×C22⋊D191—21no—
62C2×C22⋊D191—21no—
63C22×Dic191—21no—
64C22×Dic191—21no—
65C22×Dic191—21no—
66C22×Dic191—21no—
67C22×Dic191—21no—
68C2×C4×D191—21no—
69#15690272—22no—
70#15690272—22no—
71C2×C191⋊C8C2311yescharacteristic
72C2×C191⋊C8C2311yescharacteristic
73C4⋊Dic191—21no—
74C4⋊Dic191D411yescharacteristic
75C4⋊Dic191D411yescharacteristic
76C4⋊Dic191C2311yescharacteristic
77C4⋊Dic191C2311yescharacteristic
78C4⋊Dic191C2311yescharacteristic
79Dic191⋊C4—21no—
80C22⋊Dic191—21no—
81C22⋊Dic191—21no—
82C22⋊Dic191—21no—
83C22⋊Dic191—21no—
84C22⋊Dic191—21no—
85C22⋊Dic191—21no—
86C22⋊Dic191D411yescharacteristic
87C22⋊Dic191D411yescharacteristic
88(C2×D191)⋊C4—21no—
89(C2×D191)⋊C4—21no—
90C4×Dic191—21no—
91C4×Dic191C2311yescharacteristic
92C4×Dic191C2311yescharacteristic
93C24×C191—21no—
94C2×D4×C191—22no—
95C2×D4×C191—22no—
96C2×D4×C191—21no—
97C2×D4×C191—21no—
98C2×D4×C191C2311yescharacteristic
99C2×D4×C191C2311yescharacteristic
100C2×D4×C191C2311yescharacteristic
101C22×C4×C191C2311yescharacteristic
102D8×C191—22no—
103D8×C191—22no—
104C2×C8×C191C2311yescharacteristic
105C2×C8×C191C2311yescharacteristic
106C4⋊C4×C191C2311yescharacteristic
107C22⋊C4×C191—21no—
108C22×D191—21no—
109D764—21no—
110D764—21no—
111C22⋊D191—81no—
112C22⋊D191—81no—
113C22⋊D191—81no—
114C2×Dic191—21no—
115C2×Dic191—21no—
116C2×Dic191—21no—
117C2×Dic191—81no—
118C2×Dic191—81no—
119C2×Dic191—81no—
120C2×Dic191—81no—
121C2×Dic191—81no—
122C2×Dic191C2×D411yescharacteristic
123C2×Dic191C2×D411yescharacteristic
124C2×Dic191C2×D411yescharacteristic
125C2×Dic191C2×D411yescharacteristic
126C4×D191—81no—
127C191⋊C8—21no—
128C191⋊C8—21no—
129C23×C191—24no—
130C23×C191—21no—
131C23×C191—21no—
132C23×C191—21no—
133C23×C191—81no—
134C23×C191—81no—
135C23×C191C2×D411yescharacteristic
136D4×C191—24no—
137D4×C191—21no—
138D4×C191—21no—
139D4×C191—21no—
140D4×C191—21no—
141D4×C191—81no—
142D4×C191#4112yes—
143D4×C191#4112yes—
144C2×C4×C191—21no—
145C2×C4×C191—21no—
146C2×C4×C191—21no—
147C2×C4×C191C2×D411yescharacteristic
148C2×C4×C191C2411yescharacteristic
149C8×C191—21no—
150C8×C191—21no—
151C22×C191—21no—
152C22×C191—22no—
153C22×C191—22no—
154C22×C191—21no—
155C22×C191—21no—
156C22×C191—41no—
157C22×C191—41no—
158C22×C191—41no—
159C22×C191—41no—
160C22×C191—41no—
161C22×C191—41no—
162C22×C191—41no—
163C22×C191—84no—
164C22×C191C22×D411yescharacteristic
165C2×D191—41no—
166C2×D191—41no—
167C2×D191—41no—
168C4×C191—21no—
169C4×C191—41no—
170C4×C191C2×#4111yescharacteristic
171C4×C191C2×#4111yescharacteristic
172Dic191—21no—
173Dic191—21no—
174Dic191—21no—
175Dic191—21no—
176Dic191—41no—
177Dic191—41no—
178Dic191—41no—
179C2×C191—41no—
180C2×C191—42no—
181C2×C191—42no—
182C2×C191—81no—
183C2×C191#52511yescharacteristic
184C2×C191#57611yescharacteristic
185C2×C191#57611yescharacteristic
186D191—81no—
187C191#312211yescharacteristic, complemented, Sylow
188#3122—1911nomaximal, Sylow
189#540—1911no—
190#518—1911no—
191#482—1911no—
192#482—1911no—
193#478—1911no—
194#478—1911no—
195#459—1911no—
196#459—1911no—
197#447—1911no—
198#447D19111yescharacteristic, complemented
199#442—1911no—
200#442—1911no—
201C4×D8—1911no—
202C4×D8—1911no—
203#433—1911no—
204C22×D4C2×D19111yescharacteristic
205C2×D8—1911no—
206C2×D8—1911no—
207C2×D8C2×D19111yescharacteristic
208C2×D8C2×D19111yescharacteristic
209#127—1911no—
210#125—1911no—
211#123—3821no—
212#123—3821no—
213#121—3821no—
214#121—3821no—
215#121—1911no—
216#121C2×D19111yescharacteristic
217C4×D4—3821no—
218C4×D4—3821no—
219C4×D4—1911no—
220C4×D4—1911no—
221C4×D4—1911no—
222C4×D4—1911no—
223C4×D4—1911no—
224C4×D4—1911no—
225#117—1911no—
226#117—1911no—
227C2×C22⋊C4—3821no—
228C2×C22⋊C4—3821no—
229#107—1911no—
230#107—1911no—
231#106—1911no—
232#106—1911no—
233C4⋊C8—1911no—
234C4⋊C8—1911no—
235#102—1911no—
236#102—1911no—
237#102—1911no—
238#102—1911no—
239#102—1911no—
240#102—1911no—
241#102C2×D19111yescharacteristic
242#102C2×D19111yescharacteristic
243C22⋊C8—1911no—
244C22⋊C8C2×D19111yescharacteristic
245#97—1911no—
246C4×C8—1911no—
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—3821no—
253C2×D4—3821no—
254C2×D4—3821no—
255C2×D4—1911no—
256C2×D4C22×D19111yescharacteristic
257C2×D4C22×D19111yescharacteristic
258C2×D4C22×D19111yescharacteristic
259C22×C4—3821no—
260C22×C4—3821no—
261C22×C4—3821no—
262C22×C4—3821no—
263C22×C4—3821no—
264C22×C4—3821no—
265C22×C4C22×D19111yescharacteristic
266D8—22no—
267D8—22no—
268D8—3822no—
269D8—3822no—
270C2×C8—1911no—
271C2×C8—1911no—
272C2×C8C22×D19111yescharacteristic
273C2×C8C22×D19111yescharacteristic
274C4⋊C4—3821no—
275C4⋊C4—3821no—
276C4⋊C4—1911no—
277C4⋊C4—1911no—
278C4⋊C4—1911no—
279C4⋊C4—1911no—
280C4⋊C4—1911no—
281C4⋊C4C22×D19111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—3821no—
284C22⋊C4—3821no—
285C22⋊C4—3821no—
286C22⋊C4—3821no—
287C22⋊C4—3821no—
288C22⋊C4—3821no—
289C22⋊C4—3821no—
290C22⋊C4—3821no—
291C22⋊C4—1911no—
292C22⋊C4—1911no—
293C42—3821no—
294C42—1911no—
295C42—1911no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—3821no—
303C23D4×D19111yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—3821no—
311D4—3821no—
312D4—15281no—
313D4—15281no—
314D4—15281no—
315D4#1569028612yes—
316D4#1569028612yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—3821no—
321C2×C4—3821no—
322C2×C4—3821no—
323C2×C4—1911no—
324C2×C4—1911no—
325C2×C4—1911no—
326C2×C4—1911no—
327C2×C4—15281no—
328C2×C4—15281no—
329C2×C4—15281no—
330C2×C4—15281no—
331C2×C4—15281no—
332C2×C4—15281no—
333C2×C4D4×D19111yescharacteristic
334C2×C4C23×D19111yescharacteristic
335C8—21no—
336C8—21no—
337C8—3821no—
338C8—3821no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—22no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—7641no—
353C22—7641no—
354C22—7641no—
355C22C2×D4×D19111yescharacteristic
356C4—21no—
357C4—41no—
358C4—3821no—
359C4—3821no—
360C4—3821no—
361C4—3821no—
362C4—7641no—
363C4—7641no—
364C4—7641no—
365C4C2×#1569028611yescharacteristic
366C4C2×#1569028611yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—15281no—
372C2#2713316911yescharacteristic
373C2#2713346411yescharacteristic
374C2#2713346711yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#447×C191C2
socleC22×C191C22×D4
hypercenter#447D191
hypocenterC191#3122
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #27133266C2semidirect
2. #27133138C2semidirect
3. #27132988C2semidirect
4. #27132984C2semidirect
5. #27132965C2semidirect
6. #27132961C2semidirect
7. #27132856C2semidirect
8. #27132856C2semidirect
9. #27132797C2semidirect
10. #27132775C2semidirect
11. #27132772C2semidirect
12. D8×Dic191C2semidirect
13. #27132743C2semidirect
14. #27132721C2semidirect
15. #447×C191C2semidirect
18. #20259318C22semidirect
19. #20259313C22semidirect
31. D4×Dic191C22semidirect
32. #20259284C22semidirect
37. #20259256C22semidirect
38. #20259255C22semidirect
39. #20259254C22semidirect
40. #20259253C22semidirect
41. Dic191⋊C8C22semidirect
42. Dic191⋊C8C22semidirect
43. #20259244C22semidirect
44. #20259244C22semidirect
47. #20259243C22semidirect
48. #20259243C22semidirect
50. #20259232C22semidirect
51. C8×Dic191C22semidirect
187. C191#3122semidirect
198. #447D191semidirect

Maximal subgroups

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

subgroupindex
#271332662
#271331382
#271329882
#271329842
#271329652
#271329612
#271328562
#271327972
#271327752
#271327722
D8×Dic1912
#271327432
#271327212
#447×C1912
#3122191