Finite Group Databasebeta

← #37570890

Subgroups — #37570890

Order 24448.

214 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 69 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×#20259316C211yesmaximal, characteristic
2#27132716C211yesmaximal, characteristic, complemented
3#27132388C212yesmaximal, complemented
4#27132386C212yesmaximal
5#432×C191C211yesmaximal, characteristic, complemented
6#20259316—21no—
7#20259316—21no—
8#20259316—21no—
9#20259316—21no—
10C2×Dic191⋊C4C411yescharacteristic
11C2×Dic191⋊C4C411yescharacteristic
12C2×Dic191⋊C4C2211yescharacteristic
13C2×(C2×D191)⋊C4C411yescharacteristic
14C2×(C2×D191)⋊C4C411yescharacteristic
15C2×(C2×D191)⋊C4C2211yescharacteristic
16C4⋊(C191⋊C8)—21no—
17C22⋊(C191⋊C8)C2212yes—
18C4×C191⋊C8—21no—
19C2×C42×C191C2211yescharacteristic
20C4⋊C8×C191—21no—
21C22⋊C8×C191C2212yes—
22#97×C191—21no—
23C23×D191C2×C411yescharacteristic
24C22×Dic191C2×C411yescharacteristic
25C22×Dic191C2×C411yescharacteristic
26C22×Dic191C2×C411yescharacteristic
27C2×C191⋊C8—22no—
28Dic191⋊C4—21no—
29Dic191⋊C4—21no—
30Dic191⋊C4—21no—
31Dic191⋊C4—21no—
32Dic191⋊C4—21no—
33Dic191⋊C4—21no—
34(C2×D191)⋊C4—21no—
35(C2×D191)⋊C4—21no—
36(C2×D191)⋊C4—21no—
37(C2×D191)⋊C4—21no—
38(C2×D191)⋊C4—21no—
39(C2×D191)⋊C4—21no—
40C22×C4×C191C2×C411yescharacteristic
41C22×C4×C191C2×C411yescharacteristic
42C22×C4×C191C2311yescharacteristic
43C2×C8×C191—22no—
44C42×C191D411yescharacteristic
45C42×C191D411yescharacteristic
46C42×C191D411yescharacteristic
47C42×C191D411yescharacteristic
48C22×D191—21no—
49C22×D191—22no—
50C22×D191—41no—
51C22×D191—41no—
52C2×Dic191—21no—
53C2×Dic191—21no—
54C2×Dic191—21no—
55C2×Dic191—22no—
56C2×Dic191—41no—
57C2×Dic191—41no—
58C191⋊C8—42no—
59C23×C191C22×C411yescharacteristic
60C2×C4×C191—22no—
61C2×C4×C191—41no—
62C2×C4×C191—41no—
63C2×C4×C191C22⋊C411yescharacteristic
64C2×C4×C191C22⋊C411yescharacteristic
65C2×C4×C191C22⋊C411yescharacteristic
66C2×C4×C191C22⋊C411yescharacteristic
67C2×C4×C191C2×D411yescharacteristic
68C2×C4×C191C2×D411yescharacteristic
69C8×C191—42no—
70C22×C191—21no—
71C22×C191—21no—
72C22×C191C2×C22⋊C411yescharacteristic
73C22×C191#13112yes—
74C2×D191—41no—
75C2×D191—41no—
76C2×D191—41no—
77C2×D191—82no—
78C4×C191—21no—
79C4×C191—21no—
80C4×C191—21no—
81C4×C191—21no—
82C4×C191—21no—
83C4×C191—21no—
84Dic191—41no—
85Dic191—41no—
86Dic191—41no—
87C2×C191—22no—
88C2×C191#40811yescharacteristic
89C2×C191#41011yescharacteristic
90C2×C191#41311yescharacteristic
91D191—81no—
92C191#147311yescharacteristic, complemented, Sylow
93#1473—1911nomaximal, Sylow
94C2×#126—1911no—
95#432D19111yescharacteristic, complemented
96#431—1911no—
97#324—1912no—
98#323—1912no—
99#126—3821no—
100#126—3821no—
101#126—3821no—
102#126—3821no—
103C2×C4⋊C4—1911no—
104C2×C4⋊C4—1911no—
105C2×C4⋊C4—1911no—
106C2×C22⋊C4—1911no—
107C2×C22⋊C4—1911no—
108C2×C22⋊C4—1911no—
109C2×C42C2×D19111yescharacteristic
110C4⋊C8—21no—
111C4⋊C8—3821no—
112C22⋊C8—1912no—
113C22⋊C8C2×D19112yes—
114#97—21no—
115C4×C8—3821no—
116C24—1911no—
117C22×C4—1911no—
118C22×C4—1911no—
119C22×C4—1911no—
120C22×C4C4×D19111yescharacteristic
121C22×C4C4×D19111yescharacteristic
122C22×C4C22×D19111yescharacteristic
123C2×C8—22no—
124C2×C8—3822no—
125C4⋊C4—3821no—
126C4⋊C4—3821no—
127C4⋊C4—3821no—
128C4⋊C4—3821no—
129C4⋊C4—3821no—
130C4⋊C4—3821no—
131C22⋊C4—3821no—
132C22⋊C4—3821no—
133C22⋊C4—3821no—
134C22⋊C4—3821no—
135C22⋊C4—3821no—
136C22⋊C4—3821no—
137C42C22⋊D19111yescharacteristic
138C42C22⋊D19111yescharacteristic
139C42D76411yescharacteristic
140C42D76411yescharacteristic
141C23—3822no—
142C23—3821no—
143C23—7641no—
144C23—7641no—
145C23C2×C4×D19111yescharacteristic
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—3822no—
150C2×C4—3821no—
151C2×C4—3821no—
152C2×C4—3821no—
153C2×C4—7641no—
154C2×C4—7641no—
155C2×C4(C2×D191)⋊C411yescharacteristic
156C2×C4(C2×D191)⋊C411yescharacteristic
157C2×C4(C2×D191)⋊C411yescharacteristic
158C2×C4(C2×D191)⋊C411yescharacteristic
159C2×C4C2×C22⋊D19111yescharacteristic
160C2×C4C2×D76411yescharacteristic
161C8—42no—
162C8—7642no—
163C22—21no—
164C22—21no—
165C22—15282no—
166C22—7641no—
167C22—7641no—
168C22—7641no—
169C22C2×(C2×D191)⋊C411yescharacteristic
170C22#2025933012yes—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—7641no—
178C4—7641no—
179C4—7641no—
180C2—22no—
181C2—15281no—
182C2#2713263111yescharacteristic
183C2#2713263611yescharacteristic
184C2#2713264511yescharacteristic
subgroupG/H
centerC22C2×(C2×D191)⋊C4
commutatorC23×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#432×C191C2
socleC22×C191C2×C22⋊C4
prime radicalC23×D191C2×C4
cosocleC22×C4×C191C23
hypercenter#432D191
hypocenterC191#1473
LCSG ▷ C23×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #27132716C2semidirect
3. #27132388C2semidirect
5. #432×C191C2semidirect
92. C191#1473semidirect
95. #432D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593162
#271327162
#271323882
#271323862
#432×C1912
#1473191