Finite Group Databasebeta

← #37571069

Subgroups — #37571069

Order 24448.

208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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#27133215C211yesmaximal, characteristic
2#27132717C211yesmaximal, characteristic
3#27132530C211yesmaximal, characteristic
4#27132401C211yesmaximal, characteristic
5#27132400C211yesmaximal, characteristic
6#27132399C211yesmaximal, characteristic
7#328×C191C211yesmaximal, characteristic
8#20259321C411yescharacteristic, complemented
9#20259320C411yescharacteristic, complemented
10#20259312—21no—
11#20259301C2211yescharacteristic
12#20259299—21no—
13Q8×Dic191C411yescharacteristic, complemented
14#20259287—21no—
15#20259287C411yescharacteristic, complemented
16#20259278—21no—
17C2×C4×Dic191C2211yescharacteristic
18Dic191⋊C8—21no—
19C22⋊(C191⋊C8)C2211yescharacteristic
20#20259232—21no—
21C191⋊#95—21no—
22C191⋊#95—21no—
23C191⋊#95C2211yescharacteristic
24C22⋊Q8×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic
26#95×C191C2211yescharacteristic
27C2×Dic382—21no—
28C2×Dic382C2×C411yescharacteristic
29C22×Dic191—21no—
30C22×Dic191D411yescharacteristic
31C22×Dic191D411yescharacteristic
32C2×C191⋊C8—21no—
33C4⋊Dic191—21no—
34C4⋊Dic191C2×C411yescharacteristic
35Dic191⋊C4—21no—
36Dic191⋊C4—21no—
37Dic191⋊C4—21no—
38Dic191⋊C4—21no—
39Dic191⋊C4—21no—
40C22⋊Dic191—21no—
41C4×Dic191—21no—
42C4×Dic191—21no—
43C4×Dic191C2×C411yescharacteristic
44C4×Dic191C2×C411yescharacteristic
45C4×Dic191D411yescharacteristic
46C4×Dic191D411yescharacteristic
47C2×Q8×C191C2×C411yescharacteristic
48C22×C4×C191—21no—
49C22×C4×C191C2311yescharacteristic
50C2×C8×C191—21no—
51C4⋊C4×C191—21no—
52C4⋊C4×C191C2×C411yescharacteristic
53C22⋊C4×C191—21no—
54Dic382—42no—
55Dic382—41no—
56C2×Dic191—21no—
57C2×Dic191—21no—
58C2×Dic191—21no—
59C2×Dic191—21no—
60C2×Dic191—41no—
61C2×Dic191—41no—
62C2×Dic191—41no—
63C2×Dic191—41no—
64C2×Dic191C22⋊C411yescharacteristic
65C2×Dic191C22⋊C411yescharacteristic
66C2×Dic191C22⋊C411yescharacteristic
67C2×Dic191C22⋊C411yescharacteristic
68C191⋊C8—41no—
69C23×C191C2×D411yescharacteristic
70Q8×C191—41no—
71C2×C4×C191—21no—
72C2×C4×C191—21no—
73C2×C4×C191—41no—
74C2×C4×C191—41no—
75C2×C4×C191—41no—
76C2×C4×C191—41no—
77C2×C4×C191C22×C411yescharacteristic
78C2×C4×C191C2×D411yescharacteristic
79C8×C191—41no—
80C22×C191—21no—
81C22×C191—21no—
82C22×C191C2×C22⋊C411yescharacteristic
83C22×C191#13711yescharacteristic
84C22×C191#13711yescharacteristic
85C4×C191—21no—
86C4×C191—21no—
87C4×C191—41no—
88C4×C191—41no—
89C4×C191—81no—
90Dic191—21no—
91Dic191—21no—
92Dic191—21no—
93Dic191—21no—
94Dic191—41no—
95Dic191—41no—
96Dic191—81no—
97C2×C191—21no—
98C2×C191—21no—
99C2×C191#41011yescharacteristic
100C2×C191#41911yescharacteristic
101C2×C191#42111yescharacteristic
102C191#151511yescharacteristic, complemented, Sylow
103#1515—1911nomaximal, Sylow
104#533—1911no—
105#432—1911no—
106#383—1911no—
107#328—1911no—
108#328—1911no—
109#328—1911no—
110#328D19111yescharacteristic
111C4⋊Q8—1911no—
112C4⋊Q8—1911no—
113#125—3821no—
114C22⋊Q8—3821no—
115C22⋊Q8—1911no—
116C22⋊Q8C2×D19111yescharacteristic
117C4×Q8—3821no—
118C4×Q8—1911no—
119C4×Q8—1911no—
120#117—3821no—
121C2×C42—1911no—
122C4⋊C8—3821no—
123C22⋊C8—1911no—
124C22⋊C8C2×D19111yescharacteristic
125#97—3821no—
126#95—3821no—
127#95—3821no—
128#95—1911no—
129#95C2×D19111yescharacteristic
130C2×Q8—3821no—
131C2×Q8—1911no—
132C2×Q8C4×D19111yescharacteristic
133C22×C4—21no—
134C22×C4—3821no—
135C22×C4—1911no—
136C22×C4—1911no—
137C22×C4C22×D19111yescharacteristic
138C2×C8—21no—
139C2×C8—3821no—
140C4⋊C4—21no—
141C4⋊C4—3821no—
142C4⋊C4—3821no—
143C4⋊C4—3821no—
144C4⋊C4—3821no—
145C4⋊C4—3821no—
146C4⋊C4—3821no—
147C4⋊C4—1911no—
148C4⋊C4C4×D19111yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—3821no—
151C42—3821no—
152C42—3821no—
153C42—1911no—
154C42—1911no—
155C42—1911no—
156C42—1911no—
157C23D4×D19111yescharacteristic
158Q8—41no—
159Q8—7641no—
160Q8—7642no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—3821no—
168C2×C4—3821no—
169C2×C4—3821no—
170C2×C4—3821no—
171C2×C4—1911no—
172C2×C4—1911no—
173C2×C4—1911no—
174C2×C4—1911no—
175C2×C4—7641no—
176C2×C4—7641no—
177C2×C4—7641no—
178C2×C4—7641no—
179C2×C4C2×C4×D19111yescharacteristic
180C2×C4D4×D19111yescharacteristic
181C8—41no—
182C8—7641no—
183C22—21no—
184C22—21no—
185C22C22⋊C4×D19111yescharacteristic
186C22#2025935111yescharacteristic
187C22#2025935411yescharacteristic
188C4—21no—
189C4—21no—
190C4—41no—
191C4—41no—
192C4—81no—
193C4—3821no—
194C4—3821no—
195C4—3821no—
196C4—3821no—
197C4—15281no—
198C4—7641no—
199C4—7641no—
200C2—21no—
201C2—21no—
202C2#2713263511yescharacteristic
203C2#2713267011yescharacteristic
204C2#2713267811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D191
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#328×C191C2
socleC22×C191C2×C22⋊C4
prime radicalC23×C191C2×D4
cosocleC22×C4×C191C23
hypercenter#328D191
hypocenterC191#1515
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #20259321C4semidirect
9. #20259320C4semidirect
13. Q8×Dic191C4semidirect
15. #20259287C4semidirect
102. C191#1515semidirect

Maximal subgroups

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

subgroupindex
#271332152
#271327172
#271325302
#271324012
#271324002
#271323992
#328×C1912
#1515191