Finite Group Databasebeta

← #37573647

Subgroups — #37573647

Order 24448.

638 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 75 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#27133225C211yesmaximal, characteristic, complemented
2C2×#20259292C212yesmaximal, complemented
3C2×#20259236C212yesmaximal, complemented
4#27132518C211yesmaximal, characteristic, complemented
5#342×C191C211yesmaximal, characteristic, complemented
6C24×D191C2211yescharacteristic
7C22×D764—22no—
8C22×C22⋊D191C2212yes—
9#20259306—22no—
10#20259296—22no—
11#20259292—22no—
12#20259292—24no—
13#20259292—24no—
14C2×C22⋊Dic191C2211yescharacteristic
15C2×(C2×D191)⋊C4—22no—
16C2×(C2×D191)⋊C4—22no—
17#20259236—24no—
18C2×C22⋊C4×C191C2211yescharacteristic
19C2×C22⋊C4×C191C2212yes—
20C23×D191—22no—
21C23×D191—21no—
22C23×D191—22no—
23C23×D191—21no—
24C23×D191—44no—
25C23×D191D412yescomplemented
26C23×D191D412yescomplemented
27C2×D764—28no—
28C2×D764—22no—
29C2×D764—48no—
30C2×C22⋊D191—22no—
31C2×C22⋊D191—22no—
32C2×C22⋊D191—22no—
33C2×C22⋊D191—22no—
34C2×C22⋊D191—22no—
35C2×C22⋊D191—22no—
36C22×Dic191—21no—
37C22×Dic191D412yescomplemented
38C4⋊Dic191—22no—
39C22⋊Dic191—22no—
40(C2×D191)⋊C4—28no—
41(C2×D191)⋊C4—24no—
42(C2×D191)⋊C4—44no—
43C24×C191C2311yescharacteristic
44C22×C4×C191—22no—
45C22×C4×C191D412yescomplemented
46C22⋊C4×C191—22no—
47C22⋊C4×C191—22no—
48C22⋊C4×C191D414yescomplemented
49C22×D191—24no—
50C22×D191—28no—
51C22×D191—24no—
52C22×D191—22no—
53C22×D191—22no—
54C22×D191—22no—
55C22×D191—22no—
56C22×D191—44no—
57C22×D191—48no—
58C22×D191—44no—
59C22×D191—42no—
60C22×D191—44no—
61C22×D191—41no—
62C22×D191—42no—
63C22×D191—41no—
64C22×D191—44no—
65D764—416no—
66D764—82no—
67C22⋊D191—42no—
68C22⋊D191—42no—
69C22⋊D191—42no—
70C22⋊D191—42no—
71C2×Dic191—22no—
72C2×Dic191—22no—
73C2×Dic191—22no—
74C2×Dic191—42no—
75C2×Dic191—41no—
76C23×C191—42no—
77C23×C191C2×D412yes—
78C23×C191C2×D411yescharacteristic
79C23×C191C2×D411yescharacteristic
80C23×C191C2×D412yes—
81C23×C191#4111yescharacteristic
82C2×C4×C191—22no—
83C2×C4×C191—24no—
84C2×C4×C191—44no—
85C2×C4×C191—42no—
86C22×C191—22no—
87C22×C191—24no—
88C22×C191—41no—
89C22×C191—42no—
90C22×C191—41no—
91C22×C191#12012yes—
92C22×C191#12011yescharacteristic
93C22×C191#12112yes—
94C22×C191#12111yescharacteristic
95C22×C191#12711yescharacteristic
96C2×D191—28no—
97C2×D191—24no—
98C2×D191—44no—
99C2×D191—44no—
100C2×D191—42no—
101C2×D191—48no—
102C2×D191—42no—
103C2×D191—44no—
104C2×D191—44no—
105C2×D191—42no—
106C2×D191—44no—
107C2×D191—82no—
108C4×C191—44no—
109C4×C191—42no—
110Dic191—42no—
111Dic191—81no—
112C2×C191—21no—
113C2×C191—22no—
114C2×C191—21no—
115C2×C191—22no—
116C2×C191#39211yescharacteristic
117C2×C191B(4,𝔽2)12yes—
118D191—44no—
119D191—82no—
120C191#202111yescharacteristic, complemented, Sylow
121#2021—1911nomaximal, Sylow
122#534—1911no—
123C2×#120—1912no—
124C2×#99—1912no—
125#379—1911no—
126#342D19111yescharacteristic, complemented
127C25—1911no—
128C22×D4—3822no—
129C22×D4—1912no—
130#123—3822no—
131#121—3822no—
132#120—3824no—
133#120—3822no—
134#120—3824no—
135C2×C22⋊C4—3822no—
136C2×C22⋊C4—3822no—
137C2×C22⋊C4—1911no—
138C2×C22⋊C4C2×D19111yescharacteristic
139C2×C22⋊C4C2×D19112yes—
140#99—3824no—
141C24—3822no—
142C24—3821no—
143C24—3822no—
144C24—3821no—
145C24—1912no—
146C24—1912no—
147C24—7644no—
148C24C22×D19111yescharacteristic
149C2×D4—3822no—
150C2×D4—3828no—
151C2×D4—3822no—
152C2×D4—3822no—
153C2×D4—3822no—
154C2×D4—3822no—
155C2×D4—3822no—
156C2×D4—3822no—
157C2×D4—7648no—
158C22×C4—22no—
159C22×C4—3821no—
160C22×C4—1912no—
161C22×C4D76412yescomplemented
162C4⋊C4—3822no—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—3828no—
166C22⋊C4—3824no—
167C22⋊C4—3822no—
168C22⋊C4—7644no—
169C22⋊C4D76414yescomplemented
170C23—42no—
171C23—3824no—
172C23—3828no—
173C23—3824no—
174C23—3822no—
175C23—3822no—
176C23—3822no—
177C23—3822no—
178C23—7644no—
179C23—7642no—
180C23—7644no—
181C23—7644no—
182C23—7648no—
183C23—7644no—
184C23—7641no—
185C23—7642no—
186C23—7641no—
187C23D4×D19112yes—
188C23D4×D19111yescharacteristic
189C23C2×D76411yescharacteristic
190C23C2×D76412yes—
191C23#1569028811yescharacteristic
192D4—15282no—
193D4—76416no—
194D4—7642no—
195D4—7642no—
196D4—7642no—
197D4—7642no—
198C2×C4—24no—
199C2×C4—22no—
200C2×C4—44no—
201C2×C4—42no—
202C2×C4—3822no—
203C2×C4—3822no—
204C2×C4—3822no—
205C2×C4—7642no—
206C2×C4—7641no—
207C22—22no—
208C22—24no—
209C22—41no—
210C22—42no—
211C22—41no—
212C22—3828no—
213C22—3824no—
214C22—15282no—
215C22—7644no—
216C22—7644no—
217C22—7644no—
218C22—7642no—
219C22—7648no—
220C22—7642no—
221C22—7644no—
222C22—7642no—
223C22—7644no—
224C22#2025929212yes—
225C22#2025929211yescharacteristic
226C22#2025929712yes—
227C22#2025929711yescharacteristic
228C22#2025931911yescharacteristic
229C4—44no—
230C4—42no—
231C4—15281no—
232C4—7642no—
233C2—22no—
234C2—21no—
235C2—21no—
236C2—22no—
237C2—15282no—
238C2—7644no—
239C2#2713257311yescharacteristic
240C2#2713285112yes—
subgroupG/H
centerC22#20259292
commutator, cosocleC24×C191C23
FrattiniC24C22×D191
Fitting#342×C191C2
socleC22×C191#120
hypercenter#342D191
hypocenterC191#2021
LCSG ▷ C24×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #27133225C2semidirect
2. C2×#20259292C2semidirect
3. C2×#20259236C2semidirect
4. #27132518C2semidirect
5. #342×C191C2semidirect
25. C23×D191D4semidirect
26. C23×D191D4semidirect
37. C22×Dic191D4semidirect
45. C22×C4×C191D4semidirect
48. C22⋊C4×C191D4semidirect
120. C191#2021semidirect
126. #342D191semidirect
161. C22×C4D764semidirect
169. C22⋊C4D764semidirect

Maximal subgroups

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

subgroupindex
#271332252
C2×#202592922
C2×#202592362
#271325182
#342×C1912
#2021191