Finite Group Databasebeta

← #37571664

Subgroups — #37571664

Order 24448.

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

normal subgroups only

This group has 218 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
2#27133042C211yesmaximal, characteristic, complemented
3#27132950C211yesmaximal, characteristic, complemented
4#27132411C211yesmaximal, characteristic, complemented
5D4⋊(C191⋊C8)C211yesmaximal, characteristic, complemented
6#27132390C211yesmaximal, characteristic, complemented
7#476×C191C211yesmaximal, characteristic, complemented
8C2×#15690277—22no—
9#20259322C2211yescharacteristic
10#20259308—22no—
11#20259296—21no—
12#20259293—21no—
13C4×D764C2211yescharacteristic
14#20259281—21no—
15#20259280—21no—
16#20259253—21no—
17C4⋊(C191⋊C8)C2211yescharacteristic
18#20259242—21no—
19C4×C191⋊C8C2211yescharacteristic
20C4⋊Q8×C191C2211yescharacteristic
21C4×D4×C191C2211yescharacteristic
22#106×C191—21no—
23C4⋊C8×C191C2211yescharacteristic
24#102×C191—21no—
25C2×Dic382D412yes—
26C2×D764D411yescharacteristic
27C2×C22⋊D191—22no—
28C2×C4×D191—21no—
29#15690277—44no—
30C2×C191⋊C8—21no—
31C2×C191⋊C8—21no—
32C4⋊Dic191—21no—
33C4⋊Dic191—21no—
34C4⋊Dic191D411yescharacteristic
35C22⋊Dic191—22no—
36(C2×D191)⋊C4—22no—
37(C2×D191)⋊C4—21no—
38C4×Dic191—22no—
39C2×Q8×C191—21no—
40C2×D4×C191D411yescharacteristic
41C22×C4×C191—21no—
42C2×C8×C191—21no—
43C4⋊C4×C191—21no—
44C4⋊C4×C191—21no—
45C4⋊C4×C191D411yescharacteristic
46C22⋊C4×C191—21no—
47C42×C191C2311yescharacteristic
48C22×D191—21no—
49Dic382—42no—
50D764—21no—
51D764—21no—
52C22⋊D191—82no—
53C2×Dic191—21no—
54C2×Dic191—22no—
55C4×D191—41no—
56C4×D191—41no—
57C191⋊C8—22no—
58C191⋊C8—41no—
59C23×C191—21no—
60Q8×C191—42no—
61D4×C191—21no—
62D4×C191—21no—
63C2×C4×C191—21no—
64C2×C4×C191—41no—
65C2×C4×C191—41no—
66C2×C4×C191—41no—
67C2×C4×C191C2×D411yescharacteristic
68C2×C4×C191C2×D411yescharacteristic
69C2×C4×C191C2×D411yescharacteristic
70C8×C191—41no—
71C22×C191—41no—
72C22×C191—41no—
73C22×C191—41no—
74C22×C191#12011yescharacteristic
75C2×D191—41no—
76C2×D191—41no—
77C2×D191—41no—
78C4×C191—21no—
79C4×C191—41no—
80C4×C191—81no—
81C4×C191#13511yescharacteristic
82C4×C191#13511yescharacteristic
83C4×C191#13711yescharacteristic
84C4×C191#13711yescharacteristic
85Dic191—41no—
86Dic191—42no—
87C2×C191—81no—
88C2×C191#45211yescharacteristic
89C2×C191#45211yescharacteristic
90C2×C191#45311yescharacteristic
91D191—81no—
92C191#163411yescharacteristic, complemented, Sylow
93#1634—1911nomaximal, Sylow
94#555—1911no—
95#494—1911no—
96#476—1911no—
97#476D19111yescharacteristic, complemented
98#333—1911no—
99D4⋊C8—1911no—
100D4⋊C8—1911no—
101C2×Q16—3822no—
102C4⋊Q8—1911no—
103C4⋊Q8C2×D19111yescharacteristic
104#124—3822no—
105#121—3821no—
106#121—3821no—
107C4×D4—1911no—
108C4×D4C2×D19111yescharacteristic
109#117—3821no—
110#117—3821no—
111#106—21no—
112#106—3821no—
113C4⋊C8—1911no—
114C4⋊C8C2×D19111yescharacteristic
115#102—21no—
116#102—3821no—
117C4×C8—1911no—
118C2×Q8—21no—
119C2×Q8—1912no—
120C2×D4—3822no—
121C2×D4—1911no—
122C2×D4C22⋊D19111yescharacteristic
123C22×C4—21no—
124C22×C4—3821no—
125Q16—7644no—
126C2×C8—21no—
127C2×C8—3821no—
128C2×C8—3821no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—3821no—
132C4⋊C4—3821no—
133C4⋊C4—1911no—
134C4⋊C4C22⋊D19111yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—3822no—
137C22⋊C4—3822no—
138C22⋊C4—3821no—
139C42—3822no—
140C42C22×D19111yescharacteristic
141C23—21no—
142C23—3821no—
143Q8—42no—
144Q8—7642no—
145D4—21no—
146D4—21no—
147D4—3821no—
148D4—3821no—
149D4—15282no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—3821no—
155C2×C4—3822no—
156C2×C4—7641no—
157C2×C4—7641no—
158C2×C4D4×D19111yescharacteristic
159C2×C4D4×D19111yescharacteristic
160C2×C4C2×C22⋊D19111yescharacteristic
161C8—41no—
162C8—3822no—
163C8—7641no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—7641no—
168C22—7641no—
169C22—7641no—
170C22#2025929011yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—7641no—
175C4—7642no—
176C4#2025934211yescharacteristic
177C4#2025934311yescharacteristic
178C4#2025935111yescharacteristic
179C4#2025935311yescharacteristic
180C2—81no—
181C2—15281no—
182C2#2713282211yescharacteristic
183C2#2713282311yescharacteristic
184C2#2713282911yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#476×C191C2
socleC22×C191#120
prime radical#27133378C2
hypercenter#476D191
hypocenterC191#1634
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #27133042C2semidirect
3. #27132950C2semidirect
4. #27132411C2semidirect
5. D4⋊(C191⋊C8)C2semidirect
6. #27132390C2semidirect
7. #476×C191C2semidirect
92. C191#1634semidirect
97. #476D191semidirect

Maximal subgroups

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

subgroupindex
#271333782
#271330422
#271329502
#271324112
D4⋊(C191⋊C8)2
#271323902
#476×C1912
#1634191