Finite Group Databasebeta

← #37571529

Subgroups — #37571529

Order 24448.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#27133292C211yesmaximal, characteristic
2#27132994C211yesmaximal, characteristic
3#27132991C211yesmaximal, characteristic
4#27132595C211yesmaximal, characteristic
5#27132399C211yesmaximal, characteristic
6#27132388C211yesmaximal, characteristic
7#328×C191C211yesmaximal, characteristic
8#20259321—21no—
9#20259320—21no—
10#20259312—21no—
11#20259312—21no—
12#20259301C2211yescharacteristic
13#20259299—21no—
14#20259278—21no—
15C2×C4⋊Dic191—21no—
16C2×C4⋊Dic191C2211yescharacteristic
17C2×Dic191⋊C4C2211yescharacteristic
18#20259254—21no—
19#20259253—21no—
20#20259247—21no—
21#20259246—21no—
22C22⋊(C191⋊C8)C2211yescharacteristic
23C191⋊#95—21no—
24C22⋊Q8×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic
26#95×C191C2211yescharacteristic
27C2×Dic382—21no—
28C2×Dic382D411yescharacteristic
29C22×Dic191—21no—
30C22×Dic191D411yescharacteristic
31C22×Dic191D411yescharacteristic
32C2×C191⋊C8—21no—
33C4⋊Dic191—21no—
34C4⋊Dic191—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191—42no—
37C4⋊Dic191D411yescharacteristic
38Dic191⋊C4—21no—
39Dic191⋊C4—21no—
40Dic191⋊C4—21no—
41Dic191⋊C4—21no—
42Dic191⋊C4—21no—
43Dic191⋊C4—21no—
44Dic191⋊C4—21no—
45C22⋊Dic191—21no—
46C4×Dic191—21no—
47C4×Dic191—21no—
48C2×Q8×C191D411yescharacteristic
49C22×C4×C191—21no—
50C22×C4×C191C2311yescharacteristic
51C2×C8×C191—21no—
52C4⋊C4×C191—21no—
53C4⋊C4×C191D411yescharacteristic
54C22⋊C4×C191—21no—
55Dic382—41no—
56Dic382—81no—
57C2×Dic191—21no—
58C2×Dic191—21no—
59C2×Dic191—21no—
60C2×Dic191—21no—
61C2×Dic191—21no—
62C2×Dic191—41no—
63C2×Dic191—41no—
64C2×Dic191—41no—
65C2×Dic191—41no—
66C2×Dic191SD1612yes—
67C191⋊C8—41no—
68C23×C191C2×D411yescharacteristic
69Q8×C191—41no—
70C2×C4×C191—22no—
71C2×C4×C191—21no—
72C2×C4×C191—21no—
73C2×C4×C191—41no—
74C2×C4×C191—41no—
75C2×C4×C191—41no—
76C2×C4×C191C2×D411yescharacteristic
77C2×C4×C191C2×D411yescharacteristic
78C8×C191—41no—
79C22×C191—21no—
80C22×C191—21no—
81C22×C191#12011yescharacteristic
82C22×C191C2×SD1611yescharacteristic
83C22×C191#13711yescharacteristic
84C4×C191—21no—
85C4×C191—21no—
86C4×C191—42no—
87C4×C191—41no—
88C4×C191—41no—
89Dic191—22no—
90Dic191—41no—
91Dic191—41no—
92Dic191—41no—
93Dic191—81no—
94C2×C191—21no—
95C2×C191—21no—
96C2×C191#44811yescharacteristic
97C2×C191#45611yescharacteristic
98C2×C191#45811yescharacteristic
99C191#161111yescharacteristic, complemented, Sylow
100#1611—1911nomaximal, Sylow
101#544—1911no—
102#483—1911no—
103#483—1911no—
104#398—1911no—
105#328—1911no—
106#328D19111yescharacteristic
107#324—1911no—
108C4⋊Q8—3821no—
109C4⋊Q8—3821no—
110#125—3821no—
111#125—3821no—
112C22⋊Q8—3821no—
113C22⋊Q8—1911no—
114C22⋊Q8C2×D19111yescharacteristic
115#117—3821no—
116C2×C4⋊C4—3821no—
117C2×C4⋊C4—1911no—
118C2×C4⋊C4—1911no—
119#106—3821no—
120#106—3821no—
121#103—3821no—
122#103—3821no—
123C22⋊C8—1911no—
124C22⋊C8C2×D19111yescharacteristic
125#95—3821no—
126#95C2×D19111yescharacteristic
127C2×Q8—3821no—
128C2×Q8—1911no—
129C2×Q8D76411yescharacteristic
130C22×C4—21no—
131C22×C4—3821no—
132C22×C4—1911no—
133C22×C4—1911no—
134C22×C4C22×D19111yescharacteristic
135C2×C8—21no—
136C2×C8—3821no—
137C4⋊C4—21no—
138C4⋊C4—3821no—
139C4⋊C4—3821no—
140C4⋊C4—3821no—
141C4⋊C4—3821no—
142C4⋊C4—3821no—
143C4⋊C4—3821no—
144C4⋊C4—3821no—
145C4⋊C4—3821no—
146C4⋊C4—3821no—
147C4⋊C4—3821no—
148C4⋊C4—1911no—
149C4⋊C4—7642no—
150C4⋊C4D76411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3821no—
153C42—3821no—
154C42—3821no—
155C23D4×D19111yescharacteristic
156Q8—41no—
157Q8—15281no—
158Q8—7641no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—3821no—
166C2×C4—3821no—
167C2×C4—3821no—
168C2×C4—3821no—
169C2×C4—3821no—
170C2×C4—1912no—
171C2×C4—7641no—
172C2×C4—7641no—
173C2×C4—7641no—
174C2×C4—7641no—
175C2×C4D4×D19111yescharacteristic
176C2×C4C2×D76411yescharacteristic
177C8—41no—
178C8—7641no—
179C22—21no—
180C22—21no—
181C22#2025929211yescharacteristic
182C22SD16×D19111yescharacteristic
183C22#2025935411yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—3822no—
190C4—15281no—
191C4—7641no—
192C4—7641no—
193C4—7641no—
194C2—21no—
195C2—21no—
196C2#2713280311yescharacteristic
197C2#2713284711yescharacteristic
198C2#2713285411yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#328×C191C2
socleC22×C191#120
prime radicalC23×C191C2×D4
hypercenter#328D191
hypocenterC191#1611
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C191#1611semidirect

Maximal subgroups

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

subgroupindex
#271332922
#271329942
#271329912
#271325952
#271323992
#271323882
#328×C1912
#1611191