Finite Group Databasebeta

← #37571589

Subgroups — #37571589

Order 24448.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#27133374C211yesmaximal, characteristic, complemented
2#27132860C211yesmaximal, characteristic, complemented
3#27132855C211yesmaximal, characteristic
4#27132412C211yesmaximal, characteristic, complemented
5#27132395C211yesmaximal, characteristic, complemented
6#27132392C211yesmaximal, characteristic, complemented
7#492×C191C211yesmaximal, characteristic, complemented
8C2×#15690275—21no—
9C2×#15690272—21no—
10#20259313—21no—
11#20259302—21no—
12#20259298—22no—
13C4×Dic382C2211yescharacteristic
14C4×D764C2211yescharacteristic
15#20259284—21no—
16C4⋊C4×D191—21no—
17C4⋊(C191⋊C8)C2211yescharacteristic
18C4⋊(C191⋊C8)C2211yescharacteristic
19#20259243—21no—
20#20259243—21no—
21C2×SD16×C191—22no—
22C4⋊Q8×C191C2211yescharacteristic
23#127×C191C2211yescharacteristic
24C4×C8×C191C2211yescharacteristic
25C2×Dic382D411yescharacteristic
26C2×D764D411yescharacteristic
27C2×C4×D191—22no—
28C2×C4×D191—21no—
29#15690275—42no—
30#15690272—42no—
31C2×C191⋊C8—21no—
32C2×C191⋊C8—21no—
33C4⋊Dic191—22no—
34C4⋊Dic191D411yescharacteristic
35C4⋊Dic191D411yescharacteristic
36Dic191⋊C4—22no—
37Dic191⋊C4—21no—
38(C2×D191)⋊C4—22no—
39(C2×D191)⋊C4—21no—
40C4×Dic191—21no—
41C2×Q8×C191D412yes—
42C2×D4×C191—21no—
43C2×D4×C191—21no—
44C2×D4×C191—21no—
45SD16×C191—44no—
46C2×C8×C191—21no—
47C4⋊C4×C191—21no—
48C4⋊C4×C191—21no—
49C42×C191C2311yescharacteristic
50C22×D191—21no—
51Dic382—21no—
52Dic382—21no—
53D764—21no—
54D764SD1612yescomplemented
55C2×Dic191—21no—
56C2×Dic191—21no—
57C2×Dic191—21no—
58C4×D191—41no—
59C4×D191—41no—
60C4×D191—82no—
61C191⋊C8—41no—
62C191⋊C8—41no—
63C23×C191—41no—
64Q8×C191—42no—
65D4×C191—42no—
66D4×C191—41no—
67D4×C191—41no—
68D4×C191—41no—
69D4×C191—41no—
70C2×C4×C191—22no—
71C2×C4×C191C2×D411yescharacteristic
72C2×C4×C191C2×D411yescharacteristic
73C2×C4×C191C2×D411yescharacteristic
74C8×C191—22no—
75C22×C191—81no—
76C22×C191—81no—
77C22×C191—81no—
78C22×C191#12011yescharacteristic
79C2×D191—22no—
80C2×D191—41no—
81C2×D191—41no—
82C4×C191—21no—
83C4×C191—42no—
84C4×C191C2×SD1611yescharacteristic
85C4×C191#13511yescharacteristic
86C4×C191AGL(1,ℤ/8)11yescharacteristic
87C4×C191#13711yescharacteristic
88Dic191—41no—
89Dic191—41no—
90Dic191—41no—
91C2×C191—161no—
92C2×C191#44811yescharacteristic
93C2×C191#44911yescharacteristic
94C2×C191#45311yescharacteristic
95D191—42no—
96C191#162211yescharacteristic, complemented, Sylow
97#1622—1911nomaximal, Sylow
98#554—1911no—
99#492D19111yescharacteristic, complemented
100#460—1911no—
101#459—1911no—
102#333—1911no—
103Q8⋊C8—1911no—
104D4⋊C8—1911no—
105C2×SD16—22no—
106C2×SD16—3821no—
107C2×D8—3821no—
108C4⋊Q8C2×D19111yescharacteristic
109#127C2×D19111yescharacteristic
110#125—3821no—
111C22⋊Q8—3821no—
112C22⋊Q8—3822no—
113C4×Q8—1911no—
114C4×D4—3821no—
115C4×D4—1911no—
116C2×C4⋊C4—3821no—
117C4⋊C8—1911no—
118C4⋊C8—1911no—
119#102—3821no—
120#102—3821no—
121C4×C8C2×D19111yescharacteristic
122C2×Q8—1911no—
123C2×Q8C22⋊D19112yes—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—1911no—
128C22×C4—3822no—
129C22×C4—3821no—
130SD16—44no—
131SD16—7642no—
132D8—7642no—
133C2×C8—21no—
134C2×C8—3821no—
135C2×C8—3821no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3822no—
139C4⋊C4—3822no—
140C4⋊C4—3821no—
141C4⋊C4—1911no—
142C4⋊C4—1911no—
143C22⋊C4—3822no—
144C22⋊C4—3821no—
145C42—3821no—
146C42C22×D19111yescharacteristic
147C23—41no—
148C23—3821no—
149Q8—42no—
150Q8—3821no—
151Q8—3821no—
152D4—42no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—3821no—
158D4—1912no—
159C2×C4—22no—
160C2×C4—3821no—
161C2×C4—3821no—
162C2×C4—3821no—
163C2×C4—15282no—
164C2×C4—7641no—
165C2×C4—7641no—
166C2×C4D4×D19111yescharacteristic
167C2×C4D4×D19111yescharacteristic
168C2×C4C2×C22⋊D19111yescharacteristic
169C8—22no—
170C8—7641no—
171C8—7641no—
172C22—81no—
173C22—81no—
174C22—81no—
175C22—3822no—
176C22—7641no—
177C22—7641no—
178C22#2025929011yescharacteristic
179C4—21no—
180C4—42no—
181C4—7641no—
182C4—7641no—
183C4—7641no—
184C4SD16×D19111yescharacteristic
185C4#2025934311yescharacteristic
186C4#2025934911yescharacteristic
187C4#2025935111yescharacteristic
188C2—161no—
189C2—7642no—
190C2#2713280011yescharacteristic
191C2#2713280711yescharacteristic
192C2#2713283011yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#492×C191C2
socleC22×C191#120
prime radical#27132855C2
hypercenter#492D191
hypocenterC191#1622
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #27133374C2semidirect
2. #27132860C2semidirect
4. #27132412C2semidirect
5. #27132395C2semidirect
6. #27132392C2semidirect
7. #492×C191C2semidirect
54. D764SD16semidirect
96. C191#1622semidirect
99. #492D191semidirect

Maximal subgroups

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

subgroupindex
#271333742
#271328602
#271328552
#271324122
#271323952
#271323922
#492×C1912
#1622191