Finite Group Databasebeta

← #37571612

Subgroups — #37571612

Order 24448.

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

normal subgroups only

This group has 256 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#27133318C211yesmaximal, characteristic, complemented
2#27133010C211yesmaximal, characteristic, complemented
3#27132859C211yesmaximal, characteristic, complemented
4#27132858C211yesmaximal, characteristic, complemented
5#27132410C211yesmaximal, characteristic, complemented
6#27132392C211yesmaximal, characteristic, complemented
7D4⋊C8×C191C211yesmaximal, characteristic, complemented
8C2×#15690287—21no—
9C2×D1528—21no—
10C2×#15690272—21no—
11#20259322C2211yescharacteristic
12#20259319C2211yescharacteristic
13#20259304—22no—
14#20259301—21no—
15#20259293—21no—
16C4×D764C2211yescharacteristic
17C4⋊C4×D191—21no—
18C4⋊(C191⋊C8)C2211yescharacteristic
19#20259244—22no—
20#20259244—21no—
21#20259242—21no—
22C4×D4×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24C4×C8×C191C2211yescharacteristic
25#15690287—42no—
26#15690287—42no—
27C2×Dic382—21no—
28C2×D764—21no—
29C2×D764—21no—
30C2×D764—21no—
31C2×D764D411yescharacteristic
32C2×C22⋊D191—22no—
33C2×C4×D191—22no—
34C2×C4×D191—21no—
35D1528—42no—
36#15690272—42no—
37C2×C191⋊C8—21no—
38C4⋊Dic191—21no—
39C4⋊Dic191D411yescharacteristic
40C4⋊Dic191D412yes—
41Dic191⋊C4—22no—
42C22⋊Dic191—22no—
43(C2×D191)⋊C4—21no—
44C2×D4×C191D411yescharacteristic
45C22×C4×C191—21no—
46C2×C8×C191—21no—
47C2×C8×C191—21no—
48C4⋊C4×C191D411yescharacteristic
49C22⋊C4×C191—21no—
50C42×C191C2311yescharacteristic
51C22×D191—21no—
52C22×D191—41no—
53Dic382—41no—
54Dic382—41no—
55D764—21no—
56D764—42no—
57D764—41no—
58D764—41no—
59D764—41no—
60D764—41no—
61D764D812yescomplemented
62C22⋊D191—44no—
63C2×Dic191—21no—
64C2×Dic191—22no—
65C4×D191—44no—
66C4×D191—41no—
67C4×D191—41no—
68C191⋊C8—41no—
69C23×C191—21no—
70D4×C191—21no—
71D4×C191—21no—
72C2×C4×C191—21no—
73C2×C4×C191—41no—
74C2×C4×C191—41no—
75C2×C4×C191C2×D411yescharacteristic
76C2×C4×C191C2×D411yescharacteristic
77C2×C4×C191C2×D411yescharacteristic
78C8×C191—41no—
79C8×C191—41no—
80C22×C191—41no—
81C22×C191—41no—
82C22×C191—41no—
83C22×C191#12011yescharacteristic
84C2×D191—22no—
85C2×D191—41no—
86C2×D191—41no—
87C2×D191—81no—
88C2×D191—81no—
89C2×D191—81no—
90C4×C191—21no—
91C4×C191—41no—
92C4×C191C2×D811yescharacteristic
93C4×C191#13511yescharacteristic
94C4×C191AGL(1,ℤ/8)11yescharacteristic
95C4×C191AGL(1,ℤ/8)11yescharacteristic
96Dic191—42no—
97Dic191—41no—
98C2×C191—81no—
99C2×C191#44711yescharacteristic
100C2×C191#44911yescharacteristic
101C2×C191#45411yescharacteristic
102D191—42no—
103D191—161no—
104C191#162511yescharacteristic, complemented, Sylow
105#1625—1911nomaximal, Sylow
106#547—1911no—
107#486—1911no—
108#459—1911no—
109#459—1911no—
110#332—1911no—
111D4⋊C8—1911no—
112D4⋊C8D19111yescharacteristic, complemented
113C2×#41—3821no—
114C2×D8—3821no—
115C2×D8—3821no—
116C4⋊Q8—1911no—
117#127—1911no—
118#123—3822no—
119C22⋊Q8—3821no—
120#121—3821no—
121C4×D4—1911no—
122C4×D4C2×D19111yescharacteristic
123C2×C4⋊C4—3821no—
124C4⋊C8—1911no—
125C4⋊C8C2×D19111yescharacteristic
126#102—3821no—
127#102—3822no—
128#102—3821no—
129C4×C8C2×D19111yescharacteristic
130#41—7642no—
131#41—7642no—
132C2×Q8—3821no—
133C2×D4—3822no—
134C2×D4—3821no—
135C2×D4—3821no—
136C2×D4—3821no—
137C2×D4—1911no—
138C2×D4D76411yescharacteristic
139C22×C4—21no—
140C22×C4—3822no—
141C22×C4—3821no—
142D8—7642no—
143D8—7642no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—3821no—
147C4⋊C4—3822no—
148C4⋊C4—3821no—
149C4⋊C4—1911no—
150C4⋊C4—1912no—
151C4⋊C4D76411yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—3822no—
154C22⋊C4—3821no—
155C42C22×D19111yescharacteristic
156C23—21no—
157C23—3821no—
158C23—7641no—
159Q8—7641no—
160Q8—7641no—
161D4—21no—
162D4—21no—
163D4—3821no—
164D4—1912no—
165D4—7642no—
166D4—7644no—
167D4—7641no—
168D4—7641no—
169D4—7641no—
170D4—7641no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—3821no—
175C2×C4—3822no—
176C2×C4—7644no—
177C2×C4—7641no—
178C2×C4—7641no—
179C2×C4D4×D19111yescharacteristic
180C2×C4D4×D19111yescharacteristic
181C2×C4C2×D76411yescharacteristic
182C8—41no—
183C8—41no—
184C8—7641no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—3822no—
189C22—15281no—
190C22—15281no—
191C22—15281no—
192C22—7641no—
193C22—7641no—
194C22#2025929211yescharacteristic
195C4—21no—
196C4—41no—
197C4—7642no—
198C4—7641no—
199C4D8×D19111yescharacteristic
200C4#2025934411yescharacteristic
201C4#2025934911yescharacteristic
202C4#2025935011yescharacteristic
203C2—81no—
204C2—30561no—
205C2—7642no—
206C2#2713279811yescharacteristic
207C2#2713281011yescharacteristic
208C2#2713283711yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
FittingD4⋊C8×C191C2
socleC22×C191#120
hypercenterD4⋊C8D191
hypocenterC191#1625
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #27133318C2semidirect
2. #27133010C2semidirect
3. #27132859C2semidirect
4. #27132858C2semidirect
5. #27132410C2semidirect
6. #27132392C2semidirect
7. D4⋊C8×C191C2semidirect
61. D764D8semidirect
104. C191#1625semidirect
112. D4⋊C8D191semidirect

Maximal subgroups

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

subgroupindex
#271333182
#271330102
#271328592
#271328582
#271324102
#271323922
D4⋊C8×C1912
#1625191