Finite Group Databasebeta

← #37571560

Subgroups — #37571560

Order 24448.

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

normal subgroups only

This group has 202 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#27132998C211yesmaximal, characteristic
3#27132601C211yesmaximal, characteristic
4#27132401C211yesmaximal, characteristic
5#27132400C211yesmaximal, characteristic
6#27132388C211yesmaximal, characteristic
7#484×C191C211yesmaximal, characteristic
8#20259321—21no—
9#20259320—21no—
10#20259312—21no—
11#20259312—21no—
12#20259301C2211yescharacteristic
13#20259299—21no—
14#20259278—21no—
15C2×Dic191⋊C4C2211yescharacteristic
16#20259255—21no—
17#20259245—21no—
18C22⋊(C191⋊C8)C2211yescharacteristic
19C191⋊#95—21no—
20C191⋊#95—21no—
21C191⋊#95C2211yescharacteristic
22C22⋊Q8×C191C2211yescharacteristic
23C2×C4⋊C4×C191C2211yescharacteristic
24#107×C191—21no—
25#103×C191—21no—
26C22⋊C8×C191C2211yescharacteristic
27C2×Dic382—21no—
28C2×Dic382D411yescharacteristic
29C22×Dic191—21no—
30C22×Dic191D411yescharacteristic
31C22×Dic191D411yescharacteristic
32C2×C191⋊C8—21no—
33C4⋊Dic191—21no—
34C4⋊Dic191D411yescharacteristic
35Dic191⋊C4—21no—
36Dic191⋊C4—21no—
37Dic191⋊C4—21no—
38Dic191⋊C4—21no—
39Dic191⋊C4—21no—
40Dic191⋊C4—21no—
41Dic191⋊C4—21no—
42C22⋊Dic191—21no—
43C4×Dic191—21no—
44C4×Dic191—21no—
45C2×Q8×C191D411yescharacteristic
46C22×C4×C191—21no—
47C22×C4×C191C2311yescharacteristic
48C2×C8×C191—21no—
49C4⋊C4×C191—21no—
50C4⋊C4×C191—21no—
51C4⋊C4×C191—21no—
52C4⋊C4×C191D411yescharacteristic
53C22⋊C4×C191—21no—
54Dic382—41no—
55Dic382—81no—
56C2×Dic191—21no—
57C2×Dic191—21no—
58C2×Dic191—21no—
59C2×Dic191—21no—
60C2×Dic191—21no—
61C2×Dic191—41no—
62C2×Dic191—41no—
63C2×Dic191—41no—
64C2×Dic191—41no—
65C2×Dic191Q1612yes—
66C191⋊C8—41no—
67C23×C191C2×D411yescharacteristic
68Q8×C191—41no—
69C2×C4×C191—21no—
70C2×C4×C191—21no—
71C2×C4×C191—41no—
72C2×C4×C191—42no—
73C2×C4×C191—41no—
74C2×C4×C191C2×D411yescharacteristic
75C2×C4×C191C2×D411yescharacteristic
76C8×C191—41no—
77C22×C191—21no—
78C22×C191—21no—
79C22×C191#12011yescharacteristic
80C22×C191C2×Q1611yescharacteristic
81C22×C191#13711yescharacteristic
82C4×C191—21no—
83C4×C191—21no—
84C4×C191—41no—
85C4×C191—41no—
86C4×C191—81no—
87Dic191—22no—
88Dic191—41no—
89Dic191—41no—
90Dic191—41no—
91Dic191—81no—
92C2×C191—21no—
93C2×C191—21no—
94C2×C191#45111yescharacteristic
95C2×C191#45411yescharacteristic
96C2×C191#45811yescharacteristic
97C191#161711yescharacteristic, complemented, Sylow
98#1617—1911nomaximal, Sylow
99#544—1911no—
100#484—1911no—
101#484D19111yescharacteristic
102#400—1911no—
103#328—1911no—
104#328—1911no—
105#324—1911no—
106C4⋊Q8—3821no—
107C4⋊Q8—3821no—
108#125—3821no—
109#125—3821no—
110C22⋊Q8—3821no—
111C22⋊Q8—1911no—
112C22⋊Q8C2×D19111yescharacteristic
113#117—3821no—
114C2×C4⋊C4—1911no—
115C2×C4⋊C4C2×D19111yescharacteristic
116#107—21no—
117#107—3821no—
118#103—21no—
119#103—3821no—
120C22⋊C8—1911no—
121C22⋊C8C2×D19111yescharacteristic
122#95—3821no—
123#95—3821no—
124#95—1911no—
125C2×Q8—3821no—
126C2×Q8—1911no—
127C2×Q8C22⋊D19111yescharacteristic
128C22×C4—21no—
129C22×C4—3821no—
130C22×C4—1911no—
131C22×C4—1911no—
132C22×C4C22×D19111yescharacteristic
133C2×C8—21no—
134C2×C8—3821no—
135C4⋊C4—21no—
136C4⋊C4—21no—
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—1911no—
147C4⋊C4C22⋊D19111yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—3821no—
150C42—3821no—
151C42—3821no—
152C23D4×D19111yescharacteristic
153Q8—41no—
154Q8—15281no—
155Q8—7641no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—3821no—
162C2×C4—3821no—
163C2×C4—3821no—
164C2×C4—3821no—
165C2×C4—3821no—
166C2×C4—1912no—
167C2×C4—7641no—
168C2×C4—7641no—
169C2×C4—7641no—
170C2×C4—7641no—
171C2×C4D4×D19111yescharacteristic
172C2×C4C2×C22⋊D19111yescharacteristic
173C8—41no—
174C8—7641no—
175C22—21no—
176C22—21no—
177C22#2025929011yescharacteristic
178C22Q16×D19111yescharacteristic
179C22#2025935411yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—3822no—
186C4—15281no—
187C4—7641no—
188C4—7641no—
189C4—7641no—
190C2—21no—
191C2—21no—
192C2#2713281711yescharacteristic
193C2#2713283411yescharacteristic
194C2#2713285211yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#484×C191C2
socleC22×C191#120
prime radicalC23×C191C2×D4
hypercenter#484D191
hypocenterC191#1617
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
97. C191#1617semidirect

Maximal subgroups

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

subgroupindex
#271332922
#271329982
#271326012
#271324012
#271324002
#271323882
#484×C1912
#1617191