Finite Group Databasebeta

← #37582905

Subgroups — #37582905

Order 24448.

400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133218C211yesmaximal, characteristic, complemented
2#124×D191C211yesmaximal, characteristic
3#27133025C211yesmaximal, characteristic, complemented
4#27133023C211yesmaximal, characteristic, complemented
5#27133022C211yesmaximal, characteristic, complemented
6#27133019C212yesmaximal, complemented
7#27133016C212yesmaximal, complemented
8#27132670C212yesmaximal, complemented
9#27132666C212yesmaximal
10#27132615C211yesmaximal, characteristic, complemented
11#489×C191C211yesmaximal, characteristic, complemented
12C2×Q8×D191C2211yescharacteristic
13C2×D4×D191C2211yescharacteristic
14C2×#15690270C2212yes—
15#20259322C2211yescharacteristic, complemented
16#20259313C2212yescomplemented
17#20259311C2211yescharacteristic
18#20259310C2211yescharacteristic
19#20259309C2211yescharacteristic
20#20259308—21no—
21#20259308—21no—
22#20259302—21no—
23#20259298—21no—
24Q8×Dic191—21no—
25#20259287—21no—
26#20259280C2212yes—
27C22⋊C4×D191—21no—
28C22⋊C4×D191—21no—
29C42×D191C2211yescharacteristic
30#20259247C2212yescomplemented
31#20259246C2212yescomplemented
32#20259245C2212yescomplemented
33#20259244C2212yes—
34#20259243C2212yes—
35#20259242C2212yes—
36#20259233C2211yescharacteristic, complemented
37C8×Dic191C2212yescomplemented
38C4⋊Q8×C191C2211yescharacteristic, complemented
39#124×C191C2211yescharacteristic
40#103×C191C2212yescomplemented
41#102×C191C2212yes—
42#97×C191C2211yescharacteristic, complemented
43C23×D191—21no—
44C2×Dic382—21no—
45C2×Dic382—21no—
46C2×Dic382C2311yescharacteristic
47Q8×D191—24no—
48C2×D764C2311yescharacteristic
49C2×C22⋊D191—21no—
50D4×D191—24no—
51C2×C4×D191—21no—
52C2×C4×D191D411yescharacteristic
53C2×C4×D191D411yescharacteristic
54C2×C4×D191C2311yescharacteristic
55#15690270—24no—
56C2×C191⋊C8C2312yes—
57C4⋊Dic191—22no—
58C4⋊Dic191—21no—
59C4⋊Dic191C2312yes—
60Dic191⋊C4—22no—
61C22⋊Dic191—21no—
62C22⋊Dic191—21no—
63(C2×D191)⋊C4—22no—
64(C2×D191)⋊C4—21no—
65(C2×D191)⋊C4—21no—
66(C2×D191)⋊C4—21no—
67(C2×D191)⋊C4—21no—
68C4×Dic191—22no—
69C4×Dic191D411yescharacteristic
70C4×Dic191D411yescharacteristic
71C4×Dic191C2311yescharacteristic
72C2×Q8×C191—21no—
73C2×Q8×C191C2311yescharacteristic
74C2×D4×C191C2311yescharacteristic
75C2×C8×C191C2312yes—
76C4⋊C4×C191—21no—
77C4⋊C4×C191C2312yes—
78C22⋊C4×C191—21no—
79C22⋊C4×C191—21no—
80C42×C191C2311yescharacteristic
81C22×D191—21no—
82C22×D191—42no—
83C22×D191—42no—
84C22×D191—42no—
85C22×D191C2×D411yescharacteristic
86Dic382—22no—
87Dic382—42no—
88Dic382—42no—
89D764—22no—
90C22⋊D191—42no—
91C2×Dic191—22no—
92C2×Dic191—21no—
93C2×Dic191C2×D411yescharacteristic
94C2×Dic191C2×D411yescharacteristic
95C2×Dic191C2×D411yescharacteristic
96C4×D191—41no—
97C4×D191—41no—
98C4×D191—42no—
99C4×D191#4114yes—
100C191⋊C8—22no—
101C23×C191—21no—
102Q8×C191—22no—
103Q8×C191—42no—
104D4×C191—22no—
105C2×C4×C191—21no—
106C2×C4×C191—22no—
107C2×C4×C191C2×D411yescharacteristic
108C2×C4×C191C2×D411yescharacteristic
109C2×C4×C191C2411yescharacteristic
110C8×C191—22no—
111C22×C191—41no—
112C22×C191—41no—
113C22×C191—41no—
114C22×C191C22×D411yescharacteristic
115C2×D191—21no—
116C2×D191—21no—
117C2×D191—41no—
118C2×D191—41no—
119C2×D191—41no—
120C2×D191—84no—
121C2×D191#12412yes—
122C4×C191—21no—
123C4×C191—21no—
124C4×C191—41no—
125C4×C191—42no—
126C4×C191C2×#4112yes—
127Dic191—21no—
128Dic191—21no—
129Dic191—41no—
130Dic191—42no—
131Dic191#12412yes—
132C2×C191—81no—
133C2×C191C2×#12411yescharacteristic
134C2×C191#57511yescharacteristic
135C2×C191#57511yescharacteristic
136D191—22no—
137D191—81no—
138C191#314011yescharacteristic, complemented, Sylow
139#3140—1911nomaximal, Sylow
140#533—1911no—
141C2×#124—1911no—
142#489—1911no—
143#489—1911no—
144#489—1911no—
145#489D19111yescharacteristic, complemented
146#488—1912no—
147#488—1912no—
148#419—1912no—
149#418—1912no—
150C4×M16—1911no—
151C22×Q8—1911no—
152C22×D4—1911no—
153C2×M16—1912no—
154C4⋊Q8—1911no—
155C4⋊Q8C2×D19111yescharacteristic, complemented
156#125—1912no—
157#124—3821no—
158#124—3821no—
159#124—1911no—
160#124—1911no—
161#124—1911no—
162#124C2×D19111yescharacteristic
163C22⋊Q8—3821no—
164C22⋊Q8—3821no—
165C4×Q8—3821no—
166C4×Q8—3821no—
167#117—1912no—
168C2×C22⋊C4—3821no—
169C2×C22⋊C4—3821no—
170C2×C42—1911no—
171#103—1912no—
172#103—1912no—
173#103—1912no—
174#103C2×D19112yescomplemented
175#102—1912no—
176#102—1912no—
177#102—1912no—
178#102C2×D19112yes—
179#97—1911no—
180#97C2×D19111yescharacteristic, complemented
181C4×C8—1912no—
182C24—3821no—
183C2×Q8—21no—
184C2×Q8—3821no—
185C2×Q8—3821no—
186C2×Q8—3824no—
187C2×Q8—1911no—
188C2×Q8C22×D19111yescharacteristic
189C2×D4—3824no—
190C2×D4—3821no—
191C2×D4—1911no—
192C2×D4C22×D19111yescharacteristic
193C22×C4—3821no—
194C22×C4—1911no—
195C22×C4—1911no—
196C22×C4—1911no—
197M16—3824no—
198C2×C8—1912no—
199C2×C8C22×D19112yes—
200C4⋊C4—21no—
201C4⋊C4—3822no—
202C4⋊C4—3822no—
203C4⋊C4—3821no—
204C4⋊C4—1912no—
205C4⋊C4C22×D19112yes—
206C22⋊C4—21no—
207C22⋊C4—21no—
208C22⋊C4—3822no—
209C22⋊C4—3821no—
210C22⋊C4—3821no—
211C22⋊C4—3821no—
212C22⋊C4—3821no—
213C22⋊C4—3821no—
214C22⋊C4—3821no—
215C42—3822no—
216C42—1911no—
217C42—1911no—
218C42—1911no—
219C42C22×D19111yescharacteristic
220C23—21no—
221C23—3821no—
222C23—1911no—
223C23—7642no—
224C23—7642no—
225C23—7642no—
226Q8—22no—
227Q8—42no—
228Q8—3822no—
229Q8—7642no—
230Q8—7642no—
231D4—22no—
232D4—3822no—
233D4—7642no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—3822no—
237C2×C4—3821no—
238C2×C4—1911no—
239C2×C4—1911no—
240C2×C4—1911no—
241C2×C4—1914no—
242C2×C4—7641no—
243C2×C4—7641no—
244C2×C4—7642no—
245C2×C4D4×D19111yescharacteristic
246C2×C4D4×D19111yescharacteristic
247C2×C4C23×D19111yescharacteristic
248C8—22no—
249C8—3822no—
250C22—41no—
251C22—41no—
252C22—41no—
253C22—3821no—
254C22—3821no—
255C22—1912no—
256C22—15284no—
257C22—7641no—
258C22—7641no—
259C22—7641no—
260C22C2×D4×D19111yescharacteristic
261C4—21no—
262C4—21no—
263C4—42no—
264C4—41no—
265C4—3821no—
266C4—3821no—
267C4—1912no—
268C4—7642no—
269C4—7641no—
270C4#41×D19112yes—
271C2—81no—
272C2—3822no—
273C2—15281no—
274C2#124×D19111yescharacteristic
275C2#2713345911yescharacteristic
276C2#2713346211yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#489×C191C2
socleC22×C191C22×D4
prime radicalC2×D4×D191C22
hypercenter#489D191
hypocenterC191#3140
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #27133218C2semidirect
3. #27133025C2semidirect
4. #27133023C2semidirect
5. #27133022C2semidirect
6. #27133019C2semidirect
7. #27133016C2semidirect
8. #27132670C2semidirect
10. #27132615C2semidirect
11. #489×C191C2semidirect
15. #20259322C22semidirect
16. #20259313C22semidirect
30. #20259247C22semidirect
31. #20259246C22semidirect
32. #20259245C22semidirect
36. #20259233C22semidirect
37. C8×Dic191C22semidirect
38. C4⋊Q8×C191C22semidirect
40. #103×C191C22semidirect
42. #97×C191C22semidirect
138. C191#3140semidirect
145. #489D191semidirect
155. C4⋊Q8C2×D191semidirect
174. #103C2×D191semidirect
180. #97C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271332182
#124×D1912
#271330252
#271330232
#271330222
#271330192
#271330162
#271326702
#271326662
#271326152
#489×C1912
#3140191