Finite Group Databasebeta

← #37571602

Subgroups — #37571602

Order 24448.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#27133378C211yesmaximal, characteristic, complemented
2#27133035C211yesmaximal, characteristic, complemented
3#27132855C211yesmaximal, characteristic, complemented
4#27132411C211yesmaximal, characteristic, complemented
5D4⋊(C191⋊C8)C211yesmaximal, characteristic, complemented
6#27132390C211yesmaximal, characteristic, complemented
7#459×C191C211yesmaximal, characteristic, complemented
8C2×#15690275—22no—
9C2×#15690272—21no—
10#20259322C2211yescharacteristic
11#20259308—22no—
12#20259296—21no—
13#20259293—21no—
14C4×D764C2211yescharacteristic
15#20259281—21no—
16#20259280—21no—
17C4⋊(C191⋊C8)C2211yescharacteristic
18#20259243—21no—
19C4×C191⋊C8C2211yescharacteristic
20C2×D8×C191—21no—
21#127×C191C2211yescharacteristic
22C4×D4×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24#102×C191—21no—
25C2×Dic382D412yes—
26C2×D764D411yescharacteristic
27C2×C22⋊D191—22no—
28C2×C4×D191—21no—
29#15690275—44no—
30#15690272—42no—
31C2×C191⋊C8—21no—
32C2×C191⋊C8—21no—
33C4⋊Dic191—21no—
34C4⋊Dic191—21no—
35C4⋊Dic191D411yescharacteristic
36C22⋊Dic191—22no—
37(C2×D191)⋊C4—22no—
38(C2×D191)⋊C4—21no—
39C4×Dic191—22no—
40C2×D4×C191—21no—
41C2×D4×C191—21no—
42C2×D4×C191—21no—
43C2×D4×C191D411yescharacteristic
44C22×C4×C191—21no—
45D8×C191—42no—
46C2×C8×C191—21no—
47C4⋊C4×C191D411yescharacteristic
48C22⋊C4×C191—21no—
49C42×C191C2311yescharacteristic
50C22×D191—21no—
51Dic382—42no—
52D764—21no—
53D764—21no—
54C22⋊D191—82no—
55C2×Dic191—21no—
56C2×Dic191—22no—
57C4×D191—41no—
58C4×D191—41no—
59C191⋊C8—22no—
60C191⋊C8—41no—
61C23×C191—21no—
62C23×C191—41no—
63D4×C191—21no—
64D4×C191—21no—
65D4×C191—42no—
66D4×C191—41no—
67D4×C191—41no—
68D4×C191—41no—
69D4×C191—41no—
70C2×C4×C191—21no—
71C2×C4×C191—41no—
72C2×C4×C191—41no—
73C2×C4×C191C2×D411yescharacteristic
74C2×C4×C191C2×D411yescharacteristic
75C2×C4×C191C2×D411yescharacteristic
76C8×C191—41no—
77C22×C191—41no—
78C22×C191—41no—
79C22×C191—41no—
80C22×C191—81no—
81C22×C191—81no—
82C22×C191—81no—
83C22×C191#12011yescharacteristic
84C2×D191—41no—
85C2×D191—41no—
86C2×D191—41no—
87C4×C191—21no—
88C4×C191—41no—
89C4×C191#13511yescharacteristic
90C4×C191#13511yescharacteristic
91C4×C191AGL(1,ℤ/8)11yescharacteristic
92C4×C191AGL(1,ℤ/8)11yescharacteristic
93Dic191—41no—
94Dic191—42no—
95C2×C191—81no—
96C2×C191—161no—
97C2×C191#44911yescharacteristic
98C2×C191#44911yescharacteristic
99C2×C191#45311yescharacteristic
100D191—81no—
101C191#162411yescharacteristic, complemented, Sylow
102#1624—1911nomaximal, Sylow
103#555—1911no—
104#492—1911no—
105#459—1911no—
106#459D19111yescharacteristic, complemented
107#333—1911no—
108D4⋊C8—1911no—
109D4⋊C8—1911no—
110C2×SD16—3822no—
111C2×D8—21no—
112C2×D8—3821no—
113C4⋊Q8—1911no—
114#127C2×D19111yescharacteristic
115#124—3822no—
116#121—3821no—
117#121—3821no—
118C4×D4—1911no—
119C4×D4C2×D19111yescharacteristic
120#117—3821no—
121#117—3821no—
122C4⋊C8—1911no—
123C4⋊C8C2×D19111yescharacteristic
124#102—21no—
125#102—3821no—
126C4×C8—1911no—
127C2×Q8—1912no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—3822no—
132C2×D4—1911no—
133C2×D4C22⋊D19111yescharacteristic
134C22×C4—21no—
135C22×C4—3821no—
136SD16—7644no—
137D8—42no—
138D8—7642no—
139C2×C8—21no—
140C2×C8—3821no—
141C2×C8—3821no—
142C4⋊C4—3821no—
143C4⋊C4—3821no—
144C4⋊C4—1911no—
145C4⋊C4C22⋊D19111yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—3822no—
148C22⋊C4—3822no—
149C22⋊C4—3821no—
150C42—3822no—
151C42C22×D19111yescharacteristic
152C23—21no—
153C23—41no—
154C23—3821no—
155Q8—7642no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—3821no—
164D4—3821no—
165D4—15282no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3821no—
170C2×C4—3822no—
171C2×C4—7641no—
172C2×C4—7641no—
173C2×C4D4×D19111yescharacteristic
174C2×C4D4×D19111yescharacteristic
175C2×C4C2×C22⋊D19111yescharacteristic
176C8—41no—
177C8—3822no—
178C8—7641no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—7641no—
186C22—7641no—
187C22—7641no—
188C22#2025929011yescharacteristic
189C4—21no—
190C4—41no—
191C4—7641no—
192C4—7642no—
193C4#2025934111yescharacteristic
194C4#2025934211yescharacteristic
195C4#2025934611yescharacteristic
196C4#2025934811yescharacteristic
197C2—81no—
198C2—161no—
199C2—15281no—
200C2#2713280511yescharacteristic
201C2#2713280611yescharacteristic
202C2#2713282911yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#459×C191C2
socleC22×C191#120
hypercenter#459D191
hypocenterC191#1624
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #27133378C2semidirect
2. #27133035C2semidirect
3. #27132855C2semidirect
4. #27132411C2semidirect
5. D4⋊(C191⋊C8)C2semidirect
6. #27132390C2semidirect
7. #459×C191C2semidirect
101. C191#1624semidirect
106. #459D191semidirect

Maximal subgroups

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

subgroupindex
#271333782
#271330352
#271328552
#271324112
D4⋊(C191⋊C8)2
#271323902
#459×C1912
#1624191