Finite Group Databasebeta

← #37573584

Subgroups — #37573584

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#27133170C212yesmaximal, complemented
2#27132680C212yesmaximal, complemented
3#27132626C211yesmaximal, characteristic, complemented
4#27132420C211yesmaximal, characteristic, complemented
5#575×C191C211yesmaximal, characteristic, complemented
6C22×C4×D191C2211yescharacteristic
7C2×#15690271C2211yescharacteristic
8#20259303—22no—
9#20259298—22no—
10#20259293—22no—
11#20259290—22no—
12C4×C22⋊D191—24no—
13#20259281C2212yes—
14#20259249—24no—
15(C2×D191)⋊C8—22no—
16C2×#41×C191C2212yes—
17#137×C191—22no—
18AGL(1,ℤ/8)×C191—22no—
19#135×C191—22no—
20C2×M16×C191C2211yescharacteristic
21C23×D191D411yescharacteristic
22C2×C22⋊D191—24no—
23C22×Dic191D411yescharacteristic
24C2×C4×D191—21no—
25C2×C4×D191—22no—
26C2×C4×D191—22no—
27C2×C4×D191—21no—
28#15690271—22no—
29C2×C191⋊C8—21no—
30C4⋊Dic191—22no—
31Dic191⋊C4—24no—
32C22⋊Dic191—24no—
33C22⋊Dic191—22no—
34(C2×D191)⋊C4—24no—
35C4×Dic191D414yescomplemented
36#41×C191—22no—
37#41×C191—22no—
38#41×C191—22no—
39#41×C191—22no—
40C2×Q8×C191D412yescomplemented
41C2×D4×C191—22no—
42C2×D4×C191D412yescomplemented
43C22×C4×C191—22no—
44C22×C4×C191C2311yescharacteristic
45Q16×C191—22no—
46SD16×C191—24no—
47D8×C191—22no—
48M16×C191—22no—
49C2×C8×C191D412yescomplemented
50C22×D191—22no—
51C22×D191—21no—
52C22×D191—42no—
53C22⋊D191—48no—
54C2×Dic191—24no—
55C2×Dic191—22no—
56C2×Dic191—21no—
57C4×D191—41no—
58C4×D191—42no—
59C4×D191—41no—
60C191⋊C8—41no—
61C23×C191—22no—
62C23×C191C2×D411yescharacteristic
63Q8×C191—22no—
64Q8×C191—22no—
65D4×C191—22no—
66D4×C191—22no—
67D4×C191—42no—
68D4×C191—42no—
69C2×C4×C191—22no—
70C2×C4×C191—42no—
71C2×C4×C191—42no—
72C2×C4×C191C2×D412yes—
73C2×C4×C191C2×D412yes—
74C2×C4×C191C2×D411yescharacteristic
75C2×C4×C191#4111yescharacteristic
76C8×C191—22no—
77C22×C191—41no—
78C22×C191—44no—
79C22×C191—42no—
80C22×C191#12012yes—
81C22×C191#12111yescharacteristic
82C2×D191—24no—
83C2×D191—22no—
84C2×D191—42no—
85C2×D191—41no—
86C2×D191—41no—
87C4×C191—42no—
88C4×C191#12011yescharacteristic
89C4×C191#12112yes—
90C4×C191#12711yescharacteristic
91Dic191—44no—
92Dic191—41no—
93C2×C191—22no—
94C2×C191—21no—
95C2×C191—82no—
96C2×C191#39211yescharacteristic
97D191—42no—
98C191#201011yescharacteristic, complemented, Sylow
99#2010—1911nomaximal, Sylow
100#575D19111yescharacteristic, complemented
101#525—1912no—
102#421—1912no—
103#407—1911no—
104H(3,ℤ/4)—1911no—
105C2×#41C2×D19112yes—
106C23×C4—1911no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—1911no—
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—3822no—
120C24—1911no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D19112yescomplemented
126C2×D4—22no—
127C2×D4—3824no—
128C2×D4C22⋊D19112yescomplemented
129C22×C4—22no—
130C22×C4—3822no—
131C22×C4—3821no—
132C22×C4—3822no—
133C22×C4—3821no—
134C22×C4—1911no—
135C22×C4C22×D19111yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—3822no—
141C2×C8—3821no—
142C2×C8C22⋊D19112yescomplemented
143C4⋊C4—3824no—
144C4⋊C4—3822no—
145C22⋊C4—3824no—
146C22⋊C4—3824no—
147C22⋊C4—3822no—
148C42—1914no—
149C23—22no—
150C23—3822no—
151C23—3821no—
152C23—7642no—
153C23D4×D19111yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—7648no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—3824no—
165C2×C4—3822no—
166C2×C4—3821no—
167C2×C4—7641no—
168C2×C4—7642no—
169C2×C4—7641no—
170C2×C4D4×D19112yes—
171C2×C4C2×C22⋊D19112yes—
172C2×C4C2×C22⋊D19111yescharacteristic
173C2×C4#1569028611yescharacteristic
174C8—22no—
175C8—7641no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—3824no—
180C22—3822no—
181C22—7642no—
182C22—7641no—
183C22—7641no—
184C22#2025929012yes—
185C22#2025929311yescharacteristic
186C4—42no—
187C4—7644no—
188C4—7641no—
189C4#2025929111yescharacteristic
190C4#2025929412yes—
191C4#2025931811yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—7642no—
196C2#2713257111yescharacteristic
subgroupG/H
centerC4#20259318
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#575×C191C2
socleC2×C191#392
hypercenter#575D191
hypocenterC191#2010
LCSG ▷ C22×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #27133170C2semidirect
2. #27132680C2semidirect
3. #27132626C2semidirect
4. #27132420C2semidirect
5. #575×C191C2semidirect
35. C4×Dic191D4semidirect
40. C2×Q8×C191D4semidirect
42. C2×D4×C191D4semidirect
49. C2×C8×C191D4semidirect
98. C191#2010semidirect
100. #575D191semidirect
125. C2×Q8C22⋊D191semidirect
128. C2×D4C22⋊D191semidirect
142. C2×C8C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
#271331702
#271326802
#271326262
#271324202
#575×C1912
#2010191