Finite Group Databasebeta

← #37573588

Subgroups — #37573588

Order 24448.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#27133175C212yesmaximal, complemented
3#27132681C212yesmaximal, complemented
4#27132626C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C2212yes—
7C22×C4×D191C2211yescharacteristic
8#20259355—22no—
9#20259350—22no—
10#20259344—22no—
11C2×#15690271C2211yescharacteristic
12#20259306—22no—
13#20259302—22no—
14#20259297—22no—
15#20259292—22no—
16C4×D764—24no—
17#20259250—24no—
18(C2×D191)⋊C8—22no—
19C2×M16×C191C2211yescharacteristic
20#117×C191C2212yes—
21C23×D191D411yescharacteristic
22#15690287—22no—
23#15690287—22no—
24#15690287—22no—
25#15690287—22no—
26C2×Dic382D412yescomplemented
27C2×D764—24no—
28C2×D764D412yescomplemented
29C2×C22⋊D191—22no—
30C22×Dic191D411yescharacteristic
31C2×C4×D191—21no—
32C2×C4×D191—22no—
33C2×C4×D191—22no—
34C2×C4×D191—22no—
35C2×C4×D191—21no—
36Dic764—22no—
37#15690276—24no—
38D1528—22no—
39#15690271—22no—
40C2×C191⋊C8—21no—
41C4⋊Dic191—24no—
42(C2×D191)⋊C4—24no—
43(C2×D191)⋊C4—24no—
44C22×C4×C191C2311yescharacteristic
45M16×C191—22no—
46C2×C8×C191D412yescomplemented
47C4⋊C4×C191—22no—
48C22⋊C4×C191—22no—
49C42×C191D414yescomplemented
50C22×D191—22no—
51C22×D191—21no—
52C22×D191—22no—
53C22×D191—42no—
54Dic382—22no—
55Dic382—22no—
56D764—22no—
57D764—22no—
58D764—48no—
59C22⋊D191—42no—
60C22⋊D191—42no—
61C2×Dic191—22no—
62C2×Dic191—22no—
63C2×Dic191—21no—
64C4×D191—41no—
65C4×D191—42no—
66C4×D191—42no—
67C4×D191—41no—
68C4×D191—42no—
69C191⋊C8—41no—
70C23×C191C2×D411yescharacteristic
71C2×C4×C191—24no—
72C2×C4×C191C2×D412yes—
73C2×C4×C191C2×D411yescharacteristic
74C2×C4×C191C2×D412yes—
75C2×C4×C191#4111yescharacteristic
76C8×C191—22no—
77C22×C191—41no—
78C22×C191#12012yes—
79C22×C191#12111yescharacteristic
80C2×D191—24no—
81C2×D191—22no—
82C2×D191—42no—
83C2×D191—41no—
84C2×D191—41no—
85C2×D191—44no—
86C2×D191—42no—
87C4×C191—44no—
88C4×C191#12011yescharacteristic
89C4×C191#12112yes—
90C4×C191#12711yescharacteristic
91Dic191—41no—
92Dic191—42no—
93C2×C191—22no—
94C2×C191—21no—
95C2×C191#39211yescharacteristic
96D191—42no—
97D191—82no—
98C191#201011yescharacteristic, complemented, Sylow
99#2010—1911nomaximal, Sylow
100#575—1911no—
101#525—1912no—
102#421—1912no—
103#407—1911no—
104H(3,ℤ/4)D19111yescharacteristic, complemented
105C2×#41—1912no—
106C23×C4—1911no—
107#137—3822no—
108AGL(1,ℤ/8)—3822no—
109#135—3822no—
110C2×M16—1911no—
111C2×M16C2×D19111yescharacteristic
112#123—3822no—
113C22⋊Q8—3822no—
114#121—3822no—
115#120—3822no—
116C4×D4—3824no—
117#117C2×D19112yes—
118#104—3824no—
119C22⋊C8—3822no—
120C24—1911no—
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—3822no—
130C22×C4—3821no—
131C22×C4—3822no—
132C22×C4—3822no—
133C22×C4—3821no—
134C22×C4—1911no—
135C22×C4C22×D19111yescharacteristic
136Q16—3822no—
137SD16—3824no—
138D8—3822no—
139M16—22no—
140M16—3822no—
141C2×C8—3821no—
142C2×C8D76412yescomplemented
143C4⋊C4—22no—
144C4⋊C4—3824no—
145C22⋊C4—22no—
146C22⋊C4—3824no—
147C22⋊C4—3824no—
148C42D76414yescomplemented
149C23—3822no—
150C23—3821no—
151C23—3822no—
152C23—7642no—
153C23D4×D19111yescharacteristic
154Q8—3822no—
155Q8—3822no—
156D4—3822no—
157D4—3822no—
158D4—7648no—
159D4—7642no—
160D4—7642no—
161C2×C4—24no—
162C2×C4—3822no—
163C2×C4—3822no—
164C2×C4—3821no—
165C2×C4—7641no—
166C2×C4—7642no—
167C2×C4—7642no—
168C2×C4—7641no—
169C2×C4—7642no—
170C2×C4D4×D19112yes—
171C2×C4C2×D76411yescharacteristic
172C2×C4C2×D76412yes—
173C2×C4#1569028811yescharacteristic
174C8—22no—
175C8—7641no—
176C22—41no—
177C22—3824no—
178C22—3822no—
179C22—7644no—
180C22—7642no—
181C22—7641no—
182C22—7642no—
183C22—7641no—
184C22#2025929212yes—
185C22#2025929711yescharacteristic
186C4—44no—
187C4—7641no—
188C4—7642no—
189C4#2025929211yescharacteristic
190C4#2025929712yes—
191C4#2025931911yescharacteristic
192C2—22no—
193C2—21no—
194C2—15282no—
195C2—7642no—
196C2#2713257311yescharacteristic
subgroupG/H
centerC4#20259319
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
FittingH(3,ℤ/4)×C191C2
socleC2×C191#392
hypercenterH(3,ℤ/4)D191
hypocenterC191#2010
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #27133463C2semidirect
2. #27133175C2semidirect
3. #27132681C2semidirect
4. #27132626C2semidirect
5. H(3,ℤ/4)×C191C2semidirect
26. C2×Dic382D4semidirect
28. C2×D764D4semidirect
46. C2×C8×C191D4semidirect
49. C42×C191D4semidirect
98. C191#2010semidirect
104. H(3,ℤ/4)D191semidirect
142. C2×C8D764semidirect
148. C42D764semidirect

Maximal subgroups

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

subgroupindex
#271334632
#271331752
#271326812
#271326262
H(3,ℤ/4)×C1912
#2010191