Finite Group Databasebeta

← #37571853

Subgroups — #37571853

Order 24448.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#27133413C211yesmaximal, characteristic
2#27133069C211yesmaximal, characteristic, complemented
3#27133031C211yesmaximal, characteristic, complemented
4#27132404C211yesmaximal, characteristic, complemented
5#27132404C211yesmaximal, characteristic, complemented
6#27132403C211yesmaximal, characteristic
7#489×C191C211yesmaximal, characteristic
8#20259320—21no—
9#20259315—21no—
10#20259315—21no—
11#20259314C2211yescharacteristic
12#20259314C2211yescharacteristic
13#20259303—21no—
14#20259299—21no—
15#20259299—21no—
16#20259255—21no—
17#20259253—21no—
18#20259246—21no—
19#20259246—21no—
20#20259233C2211yescharacteristic
21#20259233C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23#124×C191C2211yescharacteristic
24#103×C191—21no—
25#102×C191—21no—
26#97×C191C2211yescharacteristic
27C2×Dic382—21no—
28C22×Dic191—21no—
29C2×C191⋊C8—21no—
30C2×C191⋊C8—21no—
31C4⋊Dic191D411yescharacteristic
32C4⋊Dic191D411yescharacteristic
33C4⋊Dic191D411yescharacteristic
34C4⋊Dic191D411yescharacteristic
35Dic191⋊C4—21no—
36Dic191⋊C4—21no—
37Dic191⋊C4—21no—
38Dic191⋊C4—21no—
39Dic191⋊C4—21no—
40Dic191⋊C4—21no—
41C22⋊Dic191—21no—
42C22⋊Dic191—21no—
43C22⋊Dic191—21no—
44C4×Dic191—21no—
45C2×Q8×C191—21no—
46C2×Q8×C191D411yescharacteristic
47C2×D4×C191D411yescharacteristic
48C2×C8×C191—21no—
49C4⋊C4×C191—21no—
50C4⋊C4×C191—21no—
51C22⋊C4×C191—21no—
52C22⋊C4×C191—21no—
53C42×C191C2311yescharacteristic
54Dic382—81no—
55C2×Dic191—21no—
56C2×Dic191—21no—
57C2×Dic191—21no—
58C2×Dic191—21no—
59C2×Dic191—81no—
60C191⋊C8—22no—
61C191⋊C8—41no—
62C23×C191—21no—
63Q8×C191—41no—
64Q8×C191—42no—
65D4×C191—41no—
66C2×C4×C191—21no—
67C2×C4×C191—41no—
68C2×C4×C191C2×D411yescharacteristic
69C2×C4×C191C2×D411yescharacteristic
70C2×C4×C191C2×D411yescharacteristic
71C8×C191—41no—
72C22×C191—41no—
73C22×C191—41no—
74C22×C191—41no—
75C22×C191#12011yescharacteristic
76C4×C191—21no—
77C4×C191—21no—
78C4×C191—21no—
79C4×C191—41no—
80C4×C191—81no—
81Dic191—41no—
82Dic191—41no—
83Dic191—41no—
84Dic191—41no—
85C2×C191—81no—
86C2×C191#45411yescharacteristic
87C2×C191#45511yescharacteristic
88C2×C191#45611yescharacteristic
89C191#166411yescharacteristic, complemented, Sylow
90#1664—1911nomaximal, Sylow
91#563—1911no—
92#501—1911no—
93#491—1911no—
94#489D19111yescharacteristic
95#330—1911no—
96#330—1911no—
97#329—1911no—
98C4⋊Q8—3821no—
99C4⋊Q8C2×D19111yescharacteristic
100#126—3821no—
101#126—3821no—
102#125—1911no—
103#125—1911no—
104#124C2×D19111yescharacteristic
105#123—3821no—
106C22⋊Q8—3821no—
107C22⋊Q8—3821no—
108#107—3821no—
109#106—3821no—
110#103—21no—
111#103—3821no—
112#103—3821no—
113#102—21no—
114#97—1911no—
115#97—1911no—
116#97C2×D19111yescharacteristic
117C2×Q8—21no—
118C2×Q8—3821no—
119C2×Q8C22⋊D19111yescharacteristic
120C2×D4C22⋊D19111yescharacteristic
121C22×C4—3821no—
122C2×C8—21no—
123C2×C8—3821no—
124C2×C8—3821no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—3821no—
128C4⋊C4—3821no—
129C4⋊C4—3821no—
130C4⋊C4—3821no—
131C4⋊C4—3821no—
132C4⋊C4—3821no—
133C4⋊C4—1911no—
134C4⋊C4—1911no—
135C4⋊C4—1911no—
136C4⋊C4—1911no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—3821no—
140C22⋊C4—3821no—
141C22⋊C4—3821no—
142C42—3821no—
143C42C22×D19111yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—42no—
147Q8—15281no—
148D4—41no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—3821no—
152C2×C4—3821no—
153C2×C4—3821no—
154C2×C4—3821no—
155C2×C4—15281no—
156C2×C4D4×D19111yescharacteristic
157C2×C4D4×D19111yescharacteristic
158C2×C4C2×C22⋊D19111yescharacteristic
159C8—41no—
160C8—3822no—
161C8—7641no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#2025929011yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—81no—
171C4—7641no—
172C4—7641no—
173C4—7641no—
174C4—7641no—
175C2—81no—
176C2#2713283411yescharacteristic
177C2#2713284011yescharacteristic
178C2#2713284411yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#489×C191C2
socleC22×C191#120
prime radicalC2×D4×C191D4
hypercenter#489D191
hypocenterC191#1664
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #27133069C2semidirect
3. #27133031C2semidirect
4. #27132404C2semidirect
5. #27132404C2semidirect
89. C191#1664semidirect

Maximal subgroups

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

subgroupindex
#271334132
#271330692
#271330312
#271324042
#271324032
#489×C1912
#1664191