Finite Group Databasebeta

← #37583165

Subgroups — #37583165

Order 24448.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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#27133266C212yesmaximal, complemented
2#27133063C211yesmaximal, characteristic, complemented
3#27133038C211yesmaximal, characteristic, complemented
4#27133026C212yesmaximal, complemented
5#27132916C211yesmaximal, characteristic, complemented
6#27132897C212yesmaximal, complemented
7#27132775C211yesmaximal, characteristic, complemented
8#27132774C211yesmaximal, characteristic, complemented
9#27132743C212yesmaximal, complemented
10#27132621C211yesmaximal, characteristic, complemented
11#469×C191C211yesmaximal, characteristic, complemented
12C2×D1528C2211yescharacteristic
13C2×#15690272C2212yes—
14C22×C191⋊C8C2211yescharacteristic
15#20259318C2212yes—
16#20259313C2212yes—
17#20259306—22no—
18#20259304—22no—
19#20259296C2212yes—
20#20259294—22no—
21#20259293—22no—
22D4×Dic191C2212yes—
23#20259284C2212yes—
24#20259281C2211yescharacteristic
25#20259255C2212yes—
26#20259254C2211yescharacteristic
27#20259244C2212yes—
28#20259243C2212yes—
29#20259242C2212yes—
30#20259232C2211yescharacteristic
31#20259232C2211yescharacteristic
32C8×Dic191C2211yescharacteristic
33C8×Dic191C2211yescharacteristic
34C2×D8×C191C2211yescharacteristic
35C2×M16×C191C2211yescharacteristic
36#121×C191C2212yes—
37#106×C191C2211yescharacteristic
38#102×C191C2212yes—
39C2×D764C2312yes—
40C2×C22⋊D191—22no—
41C2×C22⋊D191—22no—
42C2×C22⋊D191—22no—
43C22×Dic191—22no—
44C2×C4×D191—22no—
45D1528—22no—
46#15690272—24no—
47C2×C191⋊C8—22no—
48C2×C191⋊C8C2311yescharacteristic
49C2×C191⋊C8C2311yescharacteristic
50C4⋊Dic191—22no—
51C4⋊Dic191D412yes—
52C4⋊Dic191C2312yes—
53Dic191⋊C4—22no—
54C22⋊Dic191—22no—
55C22⋊Dic191D412yes—
56(C2×D191)⋊C4—22no—
57(C2×D191)⋊C4—22no—
58C4×Dic191C2311yescharacteristic
59C4×Dic191C2311yescharacteristic
60C2×D4×C191—22no—
61C2×D4×C191C2312yes—
62C22×C4×C191C2311yescharacteristic
63D8×C191—22no—
64M16×C191—22no—
65C2×C8×C191C2311yescharacteristic
66C2×C8×C191C2311yescharacteristic
67C4⋊C4×C191C2312yes—
68C22⋊C4×C191—22no—
69C22×D191—22no—
70D764—22no—
71D764—22no—
72C22⋊D191—82no—
73C22⋊D191—82no—
74C22⋊D191—82no—
75C2×Dic191—22no—
76C2×Dic191—82no—
77C2×Dic191C2×D412yes—
78C2×Dic191C2×D412yes—
79C4×D191—82no—
80C191⋊C8—21no—
81C191⋊C8#4112yes—
82C23×C191—22no—
83C23×C191C2×D411yescharacteristic
84D4×C191—22no—
85D4×C191—22no—
86D4×C191—82no—
87C2×C4×C191—21no—
88C2×C4×C191—21no—
89C2×C4×C191—22no—
90C2×C4×C191C2×D411yescharacteristic
91C2×C4×C191C2411yescharacteristic
92C8×C191—21no—
93C8×C191#4112yes—
94C22×C191—21no—
95C22×C191—22no—
96C22×C191—42no—
97C22×C191—42no—
98C22×C191—42no—
99C22×C191C22×D411yescharacteristic
100C2×D191—42no—
101C2×D191—42no—
102C2×D191—42no—
103C4×C191—21no—
104C4×C191—42no—
105C4×C191C2×#4111yescharacteristic
106C4×C191C2×#4111yescharacteristic
107Dic191—22no—
108Dic191—22no—
109Dic191—42no—
110C2×C191—41no—
111C2×C191—82no—
112C2×C191#53211yescharacteristic
113C2×C191#57612yes—
114D191—82no—
115C191#317611yescharacteristic, complemented, Sylow
116#3176—1911nomaximal, Sylow
117#540—1912no—
118#499—1911no—
119#493—1911no—
120#490—1912no—
121#469—1911no—
122#469D19111yescharacteristic, complemented
123#466—1912no—
124#442—1911no—
125#442—1911no—
126C4×D8—1912no—
127#405—1911no—
128C2×D8—1912no—
129C2×D8—1911no—
130C2×D8C2×D19111yescharacteristic
131C2×M16C2×D19111yescharacteristic
132C22×C8—1911no—
133#127—1912no—
134#125—1912no—
135#123—3822no—
136#123—3822no—
137#121—3822no—
138#121—3822no—
139#121—1912no—
140#121C2×D19112yes—
141C4×D4—1912no—
142C4×D4—1912no—
143#117—1911no—
144#107—1912no—
145#106—1911no—
146#106C2×D19111yescharacteristic
147#102—1912no—
148#102—1912no—
149#102—1912no—
150#102C2×D19112yes—
151#97—1911no—
152#97—1911no—
153C4×C8—1911no—
154C4×C8—1911no—
155C2×D4—22no—
156C2×D4—3822no—
157C2×D4—3822no—
158C2×D4—3822no—
159C2×D4—1912no—
160C2×D4C22×D19112yes—
161C22×C4—3822no—
162C22×C4—3822no—
163C22×C4C22×D19111yescharacteristic
164D8—22no—
165D8—3824no—
166D8—3822no—
167M16—22no—
168C2×C8—3822no—
169C2×C8—1911no—
170C2×C8—1911no—
171C2×C8C22×D19111yescharacteristic
172C2×C8C22×D19111yescharacteristic
173C4⋊C4—3822no—
174C4⋊C4—3822no—
175C4⋊C4—1912no—
176C4⋊C4—1912no—
177C4⋊C4C22×D19112yes—
178C22⋊C4—22no—
179C22⋊C4—3822no—
180C22⋊C4—3822no—
181C22⋊C4—3822no—
182C22⋊C4—1912no—
183C42—1911no—
184C42—1911no—
185C23—22no—
186C23—3822no—
187C23D4×D19111yescharacteristic
188D4—22no—
189D4—22no—
190D4—82no—
191D4—3822no—
192D4—3822no—
193D4—15282no—
194D4—15282no—
195D4—15282no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—3822no—
200C2×C4—1912no—
201C2×C4—1912no—
202C2×C4—15282no—
203C2×C4—15282no—
204C2×C4D4×D19111yescharacteristic
205C2×C4C23×D19111yescharacteristic
206C8—21no—
207C8—3821no—
208C8—1912no—
209C8#1569028612yes—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—7642no—
216C22—7642no—
217C22—7642no—
218C22C2×D4×D19111yescharacteristic
219C4—21no—
220C4—42no—
221C4—3822no—
222C4—3822no—
223C4—7642no—
224C4#41×D19111yescharacteristic
225C4C2×#1569028611yescharacteristic
226C2—41no—
227C2—82no—
228C2—15282no—
229C2#2713320811yescharacteristic
230C2#2713346712yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#469×C191C2
socleC22×C191C22×D4
hypercenter#469D191
hypocenterC191#3176
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #27133266C2semidirect
2. #27133063C2semidirect
3. #27133038C2semidirect
4. #27133026C2semidirect
5. #27132916C2semidirect
6. #27132897C2semidirect
7. #27132775C2semidirect
8. #27132774C2semidirect
9. #27132743C2semidirect
10. #27132621C2semidirect
11. #469×C191C2semidirect
115. C191#3176semidirect
122. #469D191semidirect

Maximal subgroups

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

subgroupindex
#271332662
#271330632
#271330382
#271330262
#271329162
#271328972
#271327752
#271327742
#271327432
#271326212
#469×C1912
#3176191