Finite Group Databasebeta

← #37574430

Subgroups — #37574430

Order 24448.

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

normal subgroups only

This group has 266 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
1C2×D8×D191C211yesmaximal, characteristic, complemented
2C2×#20259263C211yesmaximal, characteristic, complemented
3#27132896C211yesmaximal, characteristic, complemented
4#27132465C211yesmaximal, characteristic, complemented
5#27132464C211yesmaximal, characteristic, complemented
6(C2×D191)⋊C16C211yesmaximal, characteristic, complemented
7C2×D16×C191C211yesmaximal, characteristic, complemented
8C2×D4×D191—21no—
9C2×D1528C2211yescharacteristic
10C2×#15690272—21no—
11D8×D191—22no—
12D8×D191—22no—
13C2×C8×D191C2211yescharacteristic
14#20259293—21no—
15#20259263—22no—
16C2×C191⋊C16C2211yescharacteristic, complemented
17#20259256C2211yescharacteristic, complemented
18#20259243—21no—
19C2×D8×C191C2211yescharacteristic
20C2×D8×C191C2211yescharacteristic, complemented
21D16×C191—22no—
22C2×C16×C191C2211yescharacteristic, complemented
23C23×D191—41no—
24C2×D764—21no—
25C2×C22⋊D191—41no—
26C2×C22⋊D191—41no—
27D4×D191—24no—
28D4×D191—42no—
29C2×C4×D191D411yescharacteristic
30D1528—21no—
31D1528D412yescomplemented
32#15690272—24no—
33C2×C191⋊C8D411yescharacteristic
34C8×D191—21no—
35C8×D191—21no—
36C4⋊Dic191—21no—
37C22⋊Dic191—41no—
38C191⋊C16—21no—
39C2×D4×C191—21no—
40C2×D4×C191—21no—
41D8×C191—21no—
42D8×C191—21no—
43D8×C191—21no—
44D8×C191D412yescomplemented
45C2×C8×C191C2311yescharacteristic
46C16×C191—21no—
47C22×D191—44no—
48C22×D191—41no—
49C22×D191—82no—
50C22×D191—82no—
51C22×D191D811yescharacteristic
52D764—22no—
53D764—41no—
54C22⋊D191—44no—
55C22⋊D191—82no—
56C2×Dic191—41no—
57C2×Dic191D811yescharacteristic
58C4×D191—21no—
59C4×D191—21no—
60C191⋊C8—21no—
61C23×C191—41no—
62C23×C191—41no—
63D4×C191—22no—
64D4×C191—41no—
65D4×C191—41no—
66D4×C191—41no—
67C2×C4×C191C2×D411yescharacteristic
68C8×C191C2×D411yescharacteristic
69C8×C191C2×D411yescharacteristic
70C22×C191—42no—
71C22×C191—81no—
72C22×C191—81no—
73C22×C191—81no—
74C22×C191—81no—
75C22×C191—81no—
76C22×C191C2×D811yescharacteristic
77C2×D191—21no—
78C2×D191—21no—
79C2×D191—42no—
80C2×D191—88no—
81C2×D191—81no—
82C2×D191—81no—
83C2×D191D1612yescomplemented
84C4×C191#12011yescharacteristic
85C4×C191AGL(1,ℤ/8)11yescharacteristic
86Dic191—21no—
87Dic191—81no—
88C2×C191—82no—
89C2×C191—161no—
90C2×C191#44711yescharacteristic
91C2×C191C2×D1611yescharacteristic
92C2×C191#50911yescharacteristic
93D191—22no—
94D191—82no—
95C191#218411yescharacteristic, complemented, Sylow
96#2184—1911nomaximal, Sylow
97C22×D8—1911no—
98C2×D16—1911no—
99C2×D16D19111yescharacteristic, complemented
100#466—1911no—
101#357—1911no—
102#357—1911no—
103C22⋊C16—1911no—
104C22×D4—3821no—
105C2×D8—3822no—
106C2×D8—3822no—
107C2×D8—3821no—
108C2×D8—1911no—
109C2×D8C2×D19111yescharacteristic
110C2×D8C2×D19111yescharacteristic, complemented
111C22×C8—1911no—
112#121—3821no—
113D16—22no—
114D16—3822no—
115C2×C16—1911no—
116C2×C16C2×D19111yescharacteristic, complemented
117#107—1911no—
118#102—3821no—
119C24—7641no—
120C2×D4—21no—
121C2×D4—21no—
122C2×D4—3824no—
123C2×D4—3821no—
124C2×D4—7642no—
125C2×D4—7641no—
126C2×D4—7641no—
127C22×C4—1911no—
128D8—21no—
129D8—21no—
130D8—21no—
131D8—3824no—
132D8—3821no—
133D8—1912no—
134D8C22⋊D19112yescomplemented
135C2×C8—3821no—
136C2×C8—3821no—
137C2×C8—1911no—
138C2×C8C22×D19111yescharacteristic
139C4⋊C4—3821no—
140C22⋊C4—7641no—
141C16—21no—
142C16—3821no—
143C23—41no—
144C23—41no—
145C23—1911no—
146C23—15282no—
147C23—15282no—
148C23—7644no—
149C23—7641no—
150D4—22no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—3822no—
155D4—15282no—
156D4—7644no—
157D4—7641no—
158C2×C4—3821no—
159C2×C4—3821no—
160C2×C4—1911no—
161C2×C4—7641no—
162C2×C4D4×D19111yescharacteristic
163C8—3821no—
164C8D4×D19111yescharacteristic
165C8C2×C22⋊D19111yescharacteristic
166C22—42no—
167C22—81no—
168C22—81no—
169C22—81no—
170C22—81no—
171C22—81no—
172C22—3821no—
173C22—3821no—
174C22—1912no—
175C22—15288no—
176C22—15281no—
177C22—15281no—
178C22—7642no—
179C22D8×D19111yescharacteristic
180C4—3821no—
181C4—15281no—
182C4#2025929011yescharacteristic
183C4#2025934611yescharacteristic
184C2—82no—
185C2—161no—
186C2—3822no—
187C2—15282no—
188C2#2713279511yescharacteristic
189C2D16×D19111yescharacteristic
190C2#2713309711yescharacteristic
subgroupG/H
centerC22D8×D191
commutator, cosocleC2×C8×C191C23
FrattiniC2×C8C22×D191
FittingC2×D16×C191C2
socleC22×C191C2×D8
hypercenterC2×D16D191
hypocenterC191#2184
LCSG ▷ C2×C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×D8×D191C2semidirect
2. C2×#20259263C2semidirect
3. #27132896C2semidirect
4. #27132465C2semidirect
5. #27132464C2semidirect
6. (C2×D191)⋊C16C2semidirect
7. C2×D16×C191C2semidirect
16. C2×C191⋊C16C22semidirect
17. #20259256C22semidirect
20. C2×D8×C191C22semidirect
22. C2×C16×C191C22semidirect
31. D1528D4semidirect
44. D8×C191D4semidirect
83. C2×D191D16semidirect
95. C191#2184semidirect
99. C2×D16D191semidirect
110. C2×D8C2×D191semidirect
116. C2×C16C2×D191semidirect
134. D8C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1912
C2×#202592632
#271328962
#271324652
#271324642
(C2×D191)⋊C162
C2×D16×C1912
#2184191