Finite Group Databasebeta

← #37573587

Subgroups — #37573587

Order 24448.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#27133463C211yesmaximal, characteristic, complemented
2#27133174C212yesmaximal, complemented
3#27132679C212yesmaximal, complemented
4#27132420C211yesmaximal, characteristic, complemented
5#407×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C2212yes—
7#20259355—22no—
8#20259350—22no—
9#20259344—22no—
10#20259305—22no—
11#20259301—22no—
12#20259296—22no—
13#20259291—22no—
14C4×C22⋊D191—24no—
15#20259281C2212yes—
16#20259248—24no—
17C23×C4×C191C2211yescharacteristic
18C2×M16×C191C2211yescharacteristic
19C2×M16×C191C2211yescharacteristic
20C22⋊C8×C191—22no—
21#15690287—22no—
22#15690287—22no—
23#15690287—22no—
24#15690287—22no—
25C2×Dic382D412yescomplemented
26C2×D764D412yescomplemented
27C2×C22⋊D191—24no—
28C2×C22⋊D191—22no—
29C2×C4×D191—22no—
30Dic764—22no—
31#15690276—24no—
32D1528—22no—
33C4⋊Dic191—22no—
34Dic191⋊C4—24no—
35C22⋊Dic191—24no—
36C22⋊Dic191—22no—
37(C2×D191)⋊C4—24no—
38C4×Dic191D414yescomplemented
39C24×C191D411yescharacteristic
40C22×C4×C191—21no—
41C22×C4×C191—22no—
42C22×C4×C191—22no—
43C22×C4×C191—21no—
44C22×C4×C191D411yescharacteristic
45C22×C4×C191C2311yescharacteristic
46M16×C191—22no—
47M16×C191—22no—
48C2×C8×C191—21no—
49C2×C8×C191D412yescomplemented
50C22×D191—22no—
51Dic382—22no—
52Dic382—22no—
53D764—22no—
54D764—22no—
55C22⋊D191—48no—
56C22⋊D191—42no—
57C22⋊D191—42no—
58C2×Dic191—24no—
59C2×Dic191—22no—
60C4×D191—42no—
61C4×D191—42no—
62C23×C191—22no—
63C23×C191—21no—
64C23×C191—42no—
65C23×C191C2×D411yescharacteristic
66C2×C4×C191—22no—
67C2×C4×C191—21no—
68C2×C4×C191—41no—
69C2×C4×C191—42no—
70C2×C4×C191—41no—
71C2×C4×C191C2×D412yes—
72C2×C4×C191C2×D412yes—
73C2×C4×C191C2×D411yescharacteristic
74C2×C4×C191#4111yescharacteristic
75C8×C191—22no—
76C8×C191—41no—
77C22×C191—22no—
78C22×C191—24no—
79C22×C191—41no—
80C22×C191—42no—
81C22×C191—41no—
82C22×C191—41no—
83C22×C191#12012yes—
84C22×C191#12111yescharacteristic
85C2×D191—44no—
86C2×D191—42no—
87C4×C191—41no—
88C4×C191#12011yescharacteristic
89C4×C191#12112yes—
90C4×C191#12711yescharacteristic
91Dic191—44no—
92Dic191—42no—
93C2×C191—22no—
94C2×C191—21no—
95C2×C191—42no—
96C2×C191#39211yescharacteristic
97D191—82no—
98C191#201011yescharacteristic, complemented, Sylow
99#2010—1911nomaximal, Sylow
100#575—1911no—
101#525—1912no—
102#421—1912no—
103#407D19111yescharacteristic, complemented
104H(3,ℤ/4)—1911no—
105C2×#41—1912no—
106C23×C4C2×D19111yescharacteristic
107#137—3822no—
108AGL(1,ℤ/8)—3822no—
109#135—3822no—
110C2×M16C2×D19111yescharacteristic
111C2×M16C2×D19111yescharacteristic
112#123—3822no—
113C22⋊Q8—3822no—
114#121—3822no—
115#120—3822no—
116C4×D4—3824no—
117#117—1912no—
118#104—3824no—
119C22⋊C8—22no—
120C24D76411yescharacteristic
121#41—3822no—
122#41—3822no—
123#41—3822no—
124#41—3822no—
125C2×Q8—1912no—
126C2×D4—3824no—
127C2×D4—3822no—
128C2×D4—1912no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—3822no—
134C22×C4D76411yescharacteristic
135C22×C4C22×D19111yescharacteristic
136Q16—3822no—
137SD16—3824no—
138D8—3822no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D19112yescomplemented
143C4⋊C4—3824no—
144C4⋊C4—3822no—
145C22⋊C4—3824no—
146C22⋊C4—3824no—
147C22⋊C4—3822no—
148C42—1914no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—3822no—
153C23C2×D76411yescharacteristic
154Q8—3822no—
155Q8—3822no—
156D4—3822no—
157D4—3822no—
158D4—7648no—
159D4—7642no—
160D4—7642no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—3824no—
167C2×C4—3822no—
168C2×C4—7642no—
169C2×C4—7642no—
170C2×C4D4×D19112yes—
171C2×C4D4×D19112yes—
172C2×C4C2×C22⋊D19111yescharacteristic
173C2×C4#1569028711yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—7644no—
183C22—7642no—
184C22#2025929212yes—
185C22#2025929611yescharacteristic
186C4—41no—
187C4—7644no—
188C4—7642no—
189C4#2025929011yescharacteristic
190C4#2025929512yes—
191C4#2025931811yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—15282no—
196C2#2713257211yescharacteristic
subgroupG/H
centerC4#20259318
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#407×C191C2
socleC2×C191#392
hypercenter#407D191
hypocenterC191#2010
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #27133463C2semidirect
2. #27133174C2semidirect
3. #27132679C2semidirect
4. #27132420C2semidirect
5. #407×C191C2semidirect
25. C2×Dic382D4semidirect
26. C2×D764D4semidirect
38. C4×Dic191D4semidirect
49. C2×C8×C191D4semidirect
98. C191#2010semidirect
103. #407D191semidirect
142. C2×C8C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
#271334632
#271331742
#271326792
#271324202
#407×C1912
#2010191