Finite Group Databasebeta

← #37571686

Subgroups — #37571686

Order 24448.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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#27133328C211yesmaximal, characteristic
2#27133015C211yesmaximal, characteristic, complemented
3#27132959C211yesmaximal, characteristic, complemented
4#27132954C211yesmaximal, characteristic
5#27132393C211yesmaximal, characteristic, complemented
6#27132390C211yesmaximal, characteristic
7#332×C191C211yesmaximal, characteristic, complemented
8C2×Q8×D191—21no—
9#20259322C2211yescharacteristic
10#20259321—21no—
11#20259300—22no—
12#20259298—21no—
13C4×Dic382C2211yescharacteristic
14C4×D764C2211yescharacteristic
15#20259284—21no—
16#20259256—21no—
17#20259254—21no—
18#20259247—21no—
19#20259245—22no—
20#20259244—21no—
21C4×C191⋊C8C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24C4⋊C8×C191C2211yescharacteristic
25C2×Dic382—22no—
26C2×Dic382—21no—
27C2×Dic382D411yescharacteristic
28Q8×D191—42no—
29Q8×D191—42no—
30C2×D764D411yescharacteristic
31C2×C4×D191—22no—
32C2×C4×D191—21no—
33C2×C191⋊C8—21no—
34C4⋊Dic191—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191D411yescharacteristic
37C4⋊Dic191D411yescharacteristic
38Dic191⋊C4—22no—
39Dic191⋊C4—21no—
40(C2×D191)⋊C4—22no—
41(C2×D191)⋊C4—21no—
42C4×Dic191—21no—
43C2×Q8×C191—21no—
44C2×C8×C191—21no—
45C2×C8×C191—21no—
46C4⋊C4×C191—21no—
47C4⋊C4×C191D412yes—
48C42×C191C2311yescharacteristic
49C22×D191—21no—
50Dic382—21no—
51Dic382—44no—
52Dic382—42no—
53Dic382SD1612yes—
54D764—21no—
55D764Q1612yes—
56C2×Dic191—21no—
57C2×Dic191—21no—
58C2×Dic191—21no—
59C2×Dic191—41no—
60C4×D191—44no—
61C4×D191—41no—
62C4×D191—41no—
63C191⋊C8—41no—
64Q8×C191—41no—
65Q8×C191—41no—
66C2×C4×C191—22no—
67C2×C4×C191C2×D411yescharacteristic
68C2×C4×C191C2×D411yescharacteristic
69C2×C4×C191C2×D411yescharacteristic
70C8×C191—41no—
71C8×C191—41no—
72C22×C191#12011yescharacteristic
73C2×D191—22no—
74C2×D191—41no—
75C2×D191—41no—
76C4×C191—21no—
77C4×C191—42no—
78C4×C191C2×SD1611yescharacteristic
79C4×C191C2×Q1611yescharacteristic
80C4×C191AGL(1,ℤ/8)11yescharacteristic
81C4×C191#13711yescharacteristic
82Dic191—22no—
83Dic191—41no—
84Dic191—41no—
85Dic191—81no—
86C2×C191#45011yescharacteristic
87C2×C191#45111yescharacteristic
88C2×C191#45411yescharacteristic
89D191—42no—
90C191#163711yescharacteristic, complemented, Sylow
91#1637—1911nomaximal, Sylow
92D4×Q8—1911no—
93#487—1911no—
94#477—1911no—
95#476—1911no—
96#332D19111yescharacteristic, complemented
97Q8⋊C8—1911no—
98D4⋊C8—1911no—
99C22×Q8—3821no—
100C4⋊Q8—3821no—
101C4⋊Q8—1911no—
102C4⋊Q8C2×D19111yescharacteristic
103C22⋊Q8—3821no—
104C22⋊Q8—3822no—
105C4×Q8—1911no—
106C4×D4—3821no—
107C4×D4—1911no—
108#107—3821no—
109#106—3821no—
110C4⋊C8C2×D19111yescharacteristic
111C4⋊C8C2×D19111yescharacteristic
112#103—3821no—
113#103—3822no—
114#102—3821no—
115C4×C8—1911no—
116C2×Q8—21no—
117C2×Q8—3822no—
118C2×Q8—3821no—
119C2×Q8—1911no—
120C2×Q8—7642no—
121C2×Q8—7642no—
122C2×D4—1911no—
123C22×C4—3822no—
124C22×C4—3821no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—3821no—
128C4⋊C4—21no—
129C4⋊C4—3822no—
130C4⋊C4—3821no—
131C4⋊C4—3821no—
132C4⋊C4—3821no—
133C4⋊C4—1911no—
134C4⋊C4—1911no—
135C4⋊C4D76412yes—
136C22⋊C4—3822no—
137C22⋊C4—3821no—
138C42—3821no—
139C42C22×D19111yescharacteristic
140C23—3821no—
141Q8—41no—
142Q8—41no—
143Q8—3821no—
144Q8—1912no—
145Q8—7642no—
146Q8—7644no—
147D4—3821no—
148D4—1912no—
149C2×C4—22no—
150C2×C4—3821no—
151C2×C4—3821no—
152C2×C4—3821no—
153C2×C4—7644no—
154C2×C4—7641no—
155C2×C4—7641no—
156C2×C4—7641no—
157C2×C4D4×D19111yescharacteristic
158C2×C4D4×D19111yescharacteristic
159C2×C4C2×D76411yescharacteristic
160C8—41no—
161C8—41no—
162C8—7641no—
163C22—3822no—
164C22—7641no—
165C22—7641no—
166C22#2025929211yescharacteristic
167C4—21no—
168C4—42no—
169C4—3822no—
170C4—15281no—
171C4—7641no—
172C4—7641no—
173C4SD16×D19111yescharacteristic
174C4Q16×D19111yescharacteristic
175C4#2025934611yescharacteristic
176C4#2025935111yescharacteristic
177C2—7642no—
178C2#2713281511yescharacteristic
179C2#2713282011yescharacteristic
180C2#2713283811yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#332×C191C2
socleC22×C191#120
prime radicalC2×D764D4
hypercenter#332D191
hypocenterC191#1637
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #27133015C2semidirect
3. #27132959C2semidirect
5. #27132393C2semidirect
7. #332×C191C2semidirect
90. C191#1637semidirect
96. #332D191semidirect

Maximal subgroups

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

subgroupindex
#271333282
#271330152
#271329592
#271329542
#271323932
#271323902
#332×C1912
#1637191