Finite Group Databasebeta

← #37571682

Subgroups — #37571682

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#27132955C211yesmaximal, characteristic, complemented
3#27132950C211yesmaximal, characteristic
4#27132409C211yesmaximal, characteristic, complemented
5#27132395C211yesmaximal, characteristic, complemented
6#27132392C211yesmaximal, characteristic
7#487×C191C211yesmaximal, characteristic, complemented
8C2×Q8×D191—21no—
9#20259321—21no—
10#20259300—22no—
11#20259298—21no—
12C4×Dic382C2211yescharacteristic
13C4×D764C2211yescharacteristic
14#20259284—21no—
15#20259255—21no—
16#20259253—21no—
17C4⋊(C191⋊C8)C2211yescharacteristic
18C4⋊(C191⋊C8)C2211yescharacteristic
19#20259245—21no—
20#20259242—21no—
21C4⋊Q8×C191C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23#103×C191—22no—
24C4×C8×C191C2211yescharacteristic
25C2×Dic382—22no—
26C2×Dic382D411yescharacteristic
27Q8×D191—42no—
28Q8×D191—42no—
29C2×D764D411yescharacteristic
30C2×C4×D191—22no—
31C2×C4×D191—21no—
32C2×C191⋊C8—21no—
33C2×C191⋊C8—21no—
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×C191—21no—
42C2×Q8×C191—21no—
43C2×C8×C191—21no—
44C4⋊C4×C191—21no—
45C4⋊C4×C191—21no—
46C4⋊C4×C191—21no—
47C4⋊C4×C191D412yes—
48C42×C191C2311yescharacteristic
49C22×D191—21no—
50Dic382—21no—
51Dic382—44no—
52Dic382SD1612yes—
53D764—21no—
54D764Q1612yes—
55C2×Dic191—21no—
56C2×Dic191—21no—
57C2×Dic191—21no—
58C4×D191—44no—
59C4×D191—41no—
60C4×D191—41no—
61C191⋊C8—41no—
62C191⋊C8—41no—
63Q8×C191—42no—
64Q8×C191—41no—
65Q8×C191—41no—
66C2×C4×C191—22no—
67C2×C4×C191—41no—
68C2×C4×C191C2×D411yescharacteristic
69C2×C4×C191C2×D411yescharacteristic
70C2×C4×C191C2×D411yescharacteristic
71C8×C191—41no—
72C22×C191#12011yescharacteristic
73C2×D191—22no—
74C2×D191—41no—
75C2×D191—41no—
76C4×C191—21no—
77C4×C191—42no—
78C4×C191—81no—
79C4×C191C2×SD1611yescharacteristic
80C4×C191C2×Q1611yescharacteristic
81C4×C191AGL(1,ℤ/8)11yescharacteristic
82C4×C191#13711yescharacteristic
83Dic191—22no—
84Dic191—41no—
85Dic191—41no—
86C2×C191#45011yescharacteristic
87C2×C191#45111yescharacteristic
88C2×C191#45411yescharacteristic
89D191—42no—
90C191#163711yescharacteristic, complemented, Sylow
91#1637—1911nomaximal, Sylow
92D4×Q8—1911no—
93#487D19111yescharacteristic, complemented
94#477—1911no—
95#476—1911no—
96#332—1911no—
97Q8⋊C8—1911no—
98D4⋊C8—1911no—
99C22×Q8—3821no—
100C4⋊Q8—3821no—
101C4⋊Q8C2×D19111yescharacteristic
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⋊C8—1911no—
111C4⋊C8—1911no—
112#103—22no—
113#103—3821no—
114#102—3821no—
115C4×C8C2×D19111yescharacteristic
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—3822no—
119C2×Q8—1911no—
120C2×Q8—7642no—
121C2×Q8—7642no—
122C2×D4—1911no—
123C22×C4—3822no—
124C22×C4—3821no—
125C2×C8—21no—
126C2×C8—3821no—
127C2×C8—3821no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—3822no—
132C4⋊C4—3821no—
133C4⋊C4—1911no—
134C4⋊C4—1911no—
135C4⋊C4C22⋊D19112yes—
136C22⋊C4—3822no—
137C22⋊C4—3821no—
138C42—3821no—
139C42C22×D19111yescharacteristic
140C23—3821no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—3821no—
145Q8—1912no—
146Q8—7644no—
147D4—3821no—
148D4—1912no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—3821no—
152C2×C4—3821no—
153C2×C4—3821no—
154C2×C4—7644no—
155C2×C4—7641no—
156C2×C4—7641no—
157C2×C4D4×D19111yescharacteristic
158C2×C4D4×D19111yescharacteristic
159C2×C4C2×C22⋊D19111yescharacteristic
160C8—41no—
161C8—7641no—
162C8—7641no—
163C22—3822no—
164C22—7641no—
165C22—7641no—
166C22#2025929011yescharacteristic
167C4—21no—
168C4—42no—
169C4—81no—
170C4—3822no—
171C4—7641no—
172C4—7641no—
173C4SD16×D19111yescharacteristic
174C4Q16×D19111yescharacteristic
175C4#2025934911yescharacteristic
176C4#2025935411yescharacteristic
177C2—7642no—
178C2#2713281211yescharacteristic
179C2#2713281711yescharacteristic
180C2#2713283511yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#487×C191C2
socleC22×C191#120
prime radicalC2×D764D4
hypercenter#487D191
hypocenterC191#1637
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #27132955C2semidirect
4. #27132409C2semidirect
5. #27132395C2semidirect
7. #487×C191C2semidirect
90. C191#1637semidirect
93. #487D191semidirect

Maximal subgroups

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

subgroupindex
#271333282
#271329552
#271329502
#271324092
#271323952
#271323922
#487×C1912
#1637191