Finite Group Databasebeta

← #37571554

Subgroups — #37571554

Order 24448.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#27133262C211yesmaximal, characteristic
2#27132996C211yesmaximal, characteristic, complemented
3#27132982C211yesmaximal, characteristic
4#27132603C211yesmaximal, characteristic, complemented
5#27132396C211yesmaximal, characteristic
6#27132388C211yesmaximal, characteristic, complemented
7#328×C191C211yesmaximal, characteristic, complemented
8#20259317—21no—
9#20259313—21no—
10#20259307—21no—
11#20259306—21no—
12#20259298—21no—
13#20259296C2211yescharacteristic
14(C22⋊D191)⋊C4—21no—
15C2×C4⋊Dic191C2211yescharacteristic
16C2×Dic191⋊C4C2211yescharacteristic
17#20259255—21no—
18#20259254—21no—
19#20259246—21no—
20#20259244—21no—
21C22⋊(C191⋊C8)C2211yescharacteristic
22C191⋊#95—21no—
23C191⋊#95—21no—
24C22⋊Q8×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic
26#95×C191C2211yescharacteristic
27C2×D764D411yescharacteristic
28C2×C22⋊D191—21no—
29C22×Dic191—21no—
30C22×Dic191D411yescharacteristic
31C22×Dic191D411yescharacteristic
32C2×C4×D191—21no—
33C2×C191⋊C8—21no—
34C4⋊Dic191—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191—21no—
37C4⋊Dic191—21no—
38C4⋊Dic191D411yescharacteristic
39Dic191⋊C4—21no—
40Dic191⋊C4—21no—
41Dic191⋊C4—21no—
42(C2×D191)⋊C4—21no—
43(C2×D191)⋊C4—21no—
44(C2×D191)⋊C4—21no—
45(C2×D191)⋊C4—21no—
46C4×Dic191—21no—
47C2×Q8×C191D411yescharacteristic
48C22×C4×C191—21no—
49C22×C4×C191C2311yescharacteristic
50C2×C8×C191—21no—
51C4⋊C4×C191—21no—
52C4⋊C4×C191D411yescharacteristic
53C22⋊C4×C191—21no—
54C22×D191—21no—
55D764—41no—
56C22⋊D191—41no—
57C22⋊D191—41no—
58C2×Dic191—21no—
59C2×Dic191—21no—
60C2×Dic191—21no—
61C2×Dic191—21no—
62C2×Dic191—21no—
63C2×Dic191—41no—
64C2×Dic191—42no—
65C2×Dic191—41no—
66C4×D191—81no—
67C191⋊C8—41no—
68C23×C191C2×D411yescharacteristic
69Q8×C191—41no—
70C2×C4×C191—21no—
71C2×C4×C191—21no—
72C2×C4×C191—41no—
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×C191#13511yescharacteristic
83C22×C191#13711yescharacteristic
84C2×D191—41no—
85C2×D191—41no—
86C2×D191—41no—
87C4×C191—21no—
88C4×C191—21no—
89C4×C191—41no—
90C4×C191—41no—
91C4×C191—81no—
92Dic191—41no—
93Dic191—41no—
94Dic191—41no—
95Dic191—81no—
96C2×C191—21no—
97C2×C191—21no—
98C2×C191#45211yescharacteristic
99C2×C191#45411yescharacteristic
100C2×C191#45811yescharacteristic
101D191—81no—
102C191#161511yescharacteristic, complemented, Sylow
103#1615—1911nomaximal, Sylow
104#539—1911no—
105#484—1911no—
106#481—1911no—
107#400—1911no—
108#328D19111yescharacteristic, complemented
109#327—1911no—
110#324—1911no—
111#126—3821no—
112#125—3821no—
113#123—3821no—
114#123—3821no—
115C22⋊Q8—3821no—
116C22⋊Q8C2×D19111yescharacteristic
117#121—1911no—
118C4×D4—3821no—
119C2×C4⋊C4—1911no—
120C2×C4⋊C4—1911no—
121#107—3821no—
122#106—3821no—
123#103—3821no—
124#102—3821no—
125C22⋊C8—1911no—
126C22⋊C8C2×D19111yescharacteristic
127#95—3821no—
128#95—3821no—
129#95C2×D19111yescharacteristic
130C2×Q8D76411yescharacteristic
131C2×D4—3821no—
132C2×D4—1911no—
133C22×C4—21no—
134C22×C4—3821no—
135C22×C4—3821no—
136C22×C4—1911no—
137C22×C4—1911no—
138C22×C4C22×D19111yescharacteristic
139C2×C8—21no—
140C2×C8—3821no—
141C4⋊C4—21no—
142C4⋊C4—3821no—
143C4⋊C4—3821no—
144C4⋊C4—3821no—
145C4⋊C4—3821no—
146C4⋊C4—3821no—
147C4⋊C4—3821no—
148C4⋊C4—3821no—
149C4⋊C4—1911no—
150C4⋊C4D76411yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3821no—
153C22⋊C4—3821no—
154C22⋊C4—3821no—
155C22⋊C4—3821no—
156C42—3821no—
157C23—3821no—
158C23D4×D19111yescharacteristic
159Q8—41no—
160D4—7641no—
161D4—7641no—
162D4—7641no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3821no—
170C2×C4—3821no—
171C2×C4—3821no—
172C2×C4—3821no—
173C2×C4—3821no—
174C2×C4—15281no—
175C2×C4—7642no—
176C2×C4—7641no—
177C2×C4—7641no—
178C2×C4D4×D19111yescharacteristic
179C2×C4C2×D76411yescharacteristic
180C8—41no—
181C8—7641no—
182C22—21no—
183C22—21no—
184C22—7641no—
185C22—7641no—
186C22—7641no—
187C22#2025929211yescharacteristic
188C22#2025934311yescharacteristic
189C22#2025935411yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—15281no—
196C4—7641no—
197C4—7641no—
198C4—7641no—
199C2—21no—
200C2—21no—
201C2—15281no—
202C2#2713282811yescharacteristic
203C2#2713283711yescharacteristic
204C2#2713285411yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#328×C191C2
socleC22×C191#120
prime radical#20259296C22
hypercenter#328D191
hypocenterC191#1615
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
2. #27132996C2semidirect
4. #27132603C2semidirect
6. #27132388C2semidirect
7. #328×C191C2semidirect
102. C191#1615semidirect
108. #328D191semidirect

Maximal subgroups

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

subgroupindex
#271332622
#271329962
#271329822
#271326032
#271323962
#271323882
#328×C1912
#1615191