Finite Group Databasebeta

← #37575810

Subgroups — #37575810

Order 24448.

504 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 167 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
1C2×Q8×Dic191C211yesmaximal, characteristic
2C2×#20259287C211yesmaximal, characteristic
3#27132596C212yesmaximal
4#27132595C211yesmaximal, characteristic
5#27132593C211yesmaximal, characteristic
6#27132584C212yesmaximal
7#27132582C211yesmaximal, characteristic
8C4⋊C4×Dic191C212yesmaximal
9#27132514C212yesmaximal
10#27132508C211yesmaximal, characteristic
11#395×C191C211yesmaximal, characteristic
12C22×Dic382C2211yescharacteristic
13Q8×Dic191—24no—
14#20259287—24no—
15C2×C4⋊Dic191C2212yes—
16C2×C4⋊Dic191C2212yes—
17C2×C4⋊Dic191C2211yescharacteristic
18C2×Dic191⋊C4C2212yes—
19C2×Dic191⋊C4C2212yes—
20C2×Dic191⋊C4C2211yescharacteristic
21C2×Dic191⋊C4C2211yescharacteristic
22C2×C4×Dic191C2211yescharacteristic
23C2×C4×Dic191C2212yes—
24C2×C4×Dic191C2211yescharacteristic
25C2×C4×Dic191C2211yescharacteristic
26C2×C4×Dic191C2212yes—
27C191⋊#95C2211yescharacteristic
28C191⋊#95C2212yes—
29C191⋊#95C2212yes—
30C191⋊#95C2212yes—
31C191⋊#95C2212yes—
32C22×Q8×C191C2211yescharacteristic
33C2×C4⋊C4×C191C2212yes—
34C2×C4⋊C4×C191C2211yescharacteristic
35#95×C191C2211yescharacteristic
36#95×C191C2212yes—
37C2×Dic382—22no—
38C2×Dic382—22no—
39C2×Dic382—22no—
40C22×Dic191C2311yescharacteristic
41C22×Dic191C2312yes—
42C22×Dic191C2311yescharacteristic
43C22×Dic191C2312yes—
44C22×Dic191C2311yescharacteristic
45C22×Dic191C2311yescharacteristic
46C4⋊Dic191—24no—
47C4⋊Dic191—24no—
48C4⋊Dic191—22no—
49Dic191⋊C4—22no—
50Dic191⋊C4—22no—
51Dic191⋊C4—24no—
52Dic191⋊C4—24no—
53C4×Dic191—22no—
54C4×Dic191—22no—
55C4×Dic191—24no—
56C4×Dic191D414yes—
57C4×Dic191Q818yescomplemented
58C2×Q8×C191—22no—
59C2×Q8×C191—24no—
60C22×C4×C191C2311yescharacteristic
61C22×C4×C191C2311yescharacteristic
62C22×C4×C191C2312yes—
63C22×C4×C191C2311yescharacteristic
64C22×C4×C191C2312yes—
65C4⋊C4×C191—22no—
66C4⋊C4×C191—24no—
67Dic382—28no—
68C2×Dic191—21no—
69C2×Dic191—22no—
70C2×Dic191—22no—
71C2×Dic191—21no—
72C2×Dic191—21no—
73C2×Dic191—21no—
74C2×Dic191—21no—
75C2×Dic191—22no—
76C2×Dic191—22no—
77C2×Dic191—22no—
78C2×Dic191—22no—
79C2×Dic191C2×D412yes—
80C2×Dic191C2×D412yes—
81C2×Dic191C2×Q814yes—
82C2×Dic191C2×Q814yes—
83C2×Dic191#4112yes—
84C23×C191C2411yescharacteristic
85Q8×C191—28no—
86C2×C4×C191—21no—
87C2×C4×C191—22no—
88C2×C4×C191—22no—
89C2×C4×C191—22no—
90C2×C4×C191—22no—
91C2×C4×C191—22no—
92C2×C4×C191—21no—
93C2×C4×C191—21no—
94C2×C4×C191—22no—
95C2×C4×C191C2×D412yes—
96C2×C4×C191C2×Q814yes—
97C2×C4×C191#4114yes—
98C2×C4×C191#4112yes—
99C22×C191C22×D411yescharacteristic
100C22×C191C22×Q812yes—
101C22×C191C2×#4111yescharacteristic
102C22×C191C2×#4112yes—
103C22×C191C2×#4111yescharacteristic
104C4×C191—22no—
105C4×C191—24no—
106C4×C191—22no—
107C4×C191—24no—
108C4×C191—41no—
109Dic191—22no—
110Dic191—22no—
111Dic191—24no—
112Dic191—41no—
113Dic191—42no—
114Dic191C4⋊Q814yes—
115C2×C191#52511yescharacteristic
116C2×C191#52511yescharacteristic
117C2×C191C2×C4⋊Q811yescharacteristic
118C2×C191#53312yes—
119C2×C191#53312yes—
120C191#239911yescharacteristic, complemented, Sylow
121#2399—1911nomaximal, Sylow
122C2×C4×Q8—1911no—
123C2×C4×Q8—1911no—
124#398—1911no—
125#398—1912no—
126#398—1911no—
127#395—1911no—
128#395—1912no—
129#395D19111yescharacteristic
130C4×C4⋊C4—1912no—
131C4×C4⋊C4—1912no—
132#376—1911no—
133C22×Q8—1911no—
134C22×Q8C2×D19111yescharacteristic
135C4×Q8—3824no—
136C4×Q8—3824no—
137C2×C4⋊C4—1911no—
138C2×C4⋊C4—1912no—
139C2×C4⋊C4—1911no—
140C2×C4⋊C4—1911no—
141C2×C4⋊C4—1912no—
142C2×C4⋊C4—1912no—
143C2×C4⋊C4—1912no—
144C2×C4⋊C4C2×D19111yescharacteristic
145C2×C4⋊C4C2×D19112yes—
146C2×C42—1912no—
147C2×C42—1911no—
148C2×C42—1911no—
149C2×C42—1911no—
150C2×C42—1912no—
151#95—1911no—
152#95—1912no—
153#95—1912no—
154#95—1912no—
155#95—1912no—
156#95C2×D19111yescharacteristic
157#95C2×D19112yes—
158C2×Q8—22no—
159C2×Q8—24no—
160C2×Q8—3822no—
161C2×Q8—3822no—
162C2×Q8—3822no—
163C22×C4—1912no—
164C22×C4—1911no—
165C22×C4—1912no—
166C22×C4—1911no—
167C22×C4—1911no—
168C22×C4—1911no—
169C22×C4C22×D19111yescharacteristic
170C22×C4C22×D19111yescharacteristic
171C22×C4C22×D19112yes—
172C22×C4C22×D19112yes—
173C22×C4C22×D19111yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—24no—
176C4⋊C4—3822no—
177C4⋊C4—3824no—
178C4⋊C4—3824no—
179C4⋊C4—3822no—
180C4⋊C4—3822no—
181C4⋊C4—3824no—
182C4⋊C4—3824no—
183C42—3822no—
184C42—3824no—
185C42—3822no—
186C42—1914no—
187C42—1918no—
188C23C23×D19111yescharacteristic
189Q8—28no—
190Q8—3828no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—3821no—
201C2×C4—3821no—
202C2×C4—3822no—
203C2×C4—3822no—
204C2×C4—3821no—
205C2×C4—3821no—
206C2×C4—3821no—
207C2×C4—3822no—
208C2×C4—3822no—
209C2×C4—3822no—
210C2×C4—3822no—
211C2×C4—1912no—
212C2×C4—1914no—
213C2×C4—1912no—
214C2×C4—1912no—
215C2×C4—1914no—
216C2×C4D4×D19112yes—
217C2×C4Q8×D19114yes—
218C2×C4#1569028614yes—
219C2×C4#1569028812yes—
220C22C2×D4×D19111yescharacteristic
221C22C2×Q8×D19112yes—
222C22#41×D19111yescharacteristic
223C22C2×#1569028612yes—
224C22C2×#1569028811yescharacteristic
225C4—24no—
226C4—22no—
227C4—24no—
228C4—22no—
229C4—41no—
230C4—3824no—
231C4—3822no—
232C4—3822no—
233C4—1914no—
234C4—7641no—
235C4—7642no—
236C2#2713316911yescharacteristic
237C2#2713317611yescharacteristic
238C2C4⋊Q8×D19111yescharacteristic
239C2#2713321512yes—
240C2#2713321812yes—
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, prime radical, cosocleC23×C191C24
Fitting#395×C191C2
hypercenter#395D191
hypocenterC191#2399
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
57. C4×Dic191Q8semidirect
120. C191#2399semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic1912
C2×#202592872
#271325962
#271325952
#271325932
#271325842
#271325822
C4⋊C4×Dic1912
#271325142
#271325082
#395×C1912
#2399191