Finite Group Databasebeta

← #37571745

Subgroups — #37571745

Order 24448.

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

normal subgroups only

This group has 212 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#27133379C211yesmaximal, characteristic
2#27132940C211yesmaximal, characteristic, complemented
3#27132865C211yesmaximal, characteristic, complemented
4#27132412C211yesmaximal, characteristic, complemented
5#27132392C211yesmaximal, characteristic, complemented
6#27132392C211yesmaximal, characteristic, complemented
7#487×C191C211yesmaximal, characteristic, complemented
8C2×#15690274—21no—
9#20259311—22no—
10#20259297—21no—
11#20259297—21no—
12C4×D764C2211yescharacteristic
13C4×D764C2211yescharacteristic
14#20259280—21no—
15#20259280—21no—
16#20259255—21no—
17C4⋊(C191⋊C8)C2211yescharacteristic
18C4⋊(C191⋊C8)C2211yescharacteristic
19#20259246—21no—
20#20259242—21no—
21C4⋊Q8×C191C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23#103×C191—22no—
24C4×C8×C191C2211yescharacteristic
25C2×D764—22no—
26C2×D764D411yescharacteristic
27C2×D764D411yescharacteristic
28C2×C4×D191—21no—
29C2×C4×D191—21no—
30#15690274—42no—
31C2×C191⋊C8—21no—
32C2×C191⋊C8—21no—
33C4⋊Dic191D411yescharacteristic
34C4⋊Dic191D411yescharacteristic
35(C2×D191)⋊C4—22no—
36(C2×D191)⋊C4—22no—
37(C2×D191)⋊C4—21no—
38(C2×D191)⋊C4—21no—
39C4×Dic191—22no—
40C2×Q8×C191—21no—
41C2×Q8×C191D412yes—
42C2×C8×C191—21no—
43C4⋊C4×C191—21no—
44C4⋊C4×C191—21no—
45C4⋊C4×C191—21no—
46C4⋊C4×C191—21no—
47C42×C191C2311yescharacteristic
48C22×D191—21no—
49C22×D191—21no—
50D764—21no—
51D764—21no—
52D764—21no—
53D764—21no—
54D764—82no—
55C2×Dic191—21no—
56C2×Dic191—21no—
57C4×D191—41no—
58C4×D191—41no—
59C4×D191—41no—
60C4×D191—41no—
61C191⋊C8—41no—
62C191⋊C8—41no—
63Q8×C191—42no—
64Q8×C191—41no—
65Q8×C191—41no—
66C2×C4×C191—22no—
67C2×C4×C191—41no—
68C2×C4×C191C2×D411yescharacteristic
69C2×C4×C191C2×D411yescharacteristic
70C2×C4×C191C2×D411yescharacteristic
71C8×C191—41no—
72C22×C191#12011yescharacteristic
73C2×D191—41no—
74C2×D191—41no—
75C2×D191—41no—
76C2×D191—41no—
77C2×D191—41no—
78C2×D191—41no—
79C4×C191—21no—
80C4×C191—42no—
81C4×C191—81no—
82C4×C191#13511yescharacteristic
83C4×C191#13511yescharacteristic
84C4×C191AGL(1,ℤ/8)11yescharacteristic
85C4×C191#13711yescharacteristic
86Dic191—41no—
87Dic191—41no—
88C2×C191#44911yescharacteristic
89C2×C191#45211yescharacteristic
90C2×C191#45511yescharacteristic
91D191—81no—
92D191—81no—
93C191#164611yescharacteristic, complemented, Sylow
94#1646—1911nomaximal, Sylow
95#555—1911no—
96#487D19111yescharacteristic, complemented
97#474—1911no—
98#461—1911no—
99#333—1911no—
100D4⋊C8—1911no—
101D4⋊C8—1911no—
102C2×SD16—3821no—
103C4⋊Q8C2×D19111yescharacteristic
104C4⋊Q8C2×D19111yescharacteristic
105#124—3822no—
106#121—3821no—
107#121—3821no—
108C4×D4—1911no—
109C4×D4—1911no—
110#117—3821no—
111#117—3821no—
112#107—3821no—
113C4⋊C8—1911no—
114C4⋊C8—1911no—
115#103—22no—
116#103—3821no—
117#102—3821no—
118C4×C8C2×D19111yescharacteristic
119C2×Q8—21no—
120C2×Q8C22⋊D19112yes—
121C2×D4—3822no—
122C2×D4—1911no—
123C2×D4—1911no—
124C22×C4—3821no—
125C22×C4—3821no—
126SD16—7642no—
127C2×C8—21no—
128C2×C8—3821no—
129C2×C8—3821no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—1911no—
135C4⋊C4—1911no—
136C22⋊C4—3822no—
137C22⋊C4—3822no—
138C22⋊C4—3821no—
139C22⋊C4—3821no—
140C42—3822no—
141C42C22×D19111yescharacteristic
142C23—3821no—
143C23—3821no—
144Q8—42no—
145Q8—41no—
146Q8—41no—
147D4—3821no—
148D4—3821no—
149D4—3821no—
150D4—3821no—
151D4—15282no—
152C2×C4—22no—
153C2×C4—41no—
154C2×C4—3821no—
155C2×C4—3821no—
156C2×C4—7641no—
157C2×C4—7641no—
158C2×C4—7641no—
159C2×C4—7641no—
160C2×C4D4×D19111yescharacteristic
161C2×C4D4×D19111yescharacteristic
162C2×C4C2×C22⋊D19111yescharacteristic
163C8—41no—
164C8—7641no—
165C8—7641no—
166C22—7641no—
167C22—7641no—
168C22—7641no—
169C22—7641no—
170C22—7641no—
171C22—7641no—
172C22#2025929011yescharacteristic
173C4—21no—
174C4—42no—
175C4—81no—
176C4—7641no—
177C4—7641no—
178C4#2025934311yescharacteristic
179C4#2025934511yescharacteristic
180C4#2025934911yescharacteristic
181C4#2025935411yescharacteristic
182C2—15281no—
183C2—15281no—
184C2#2713280711yescharacteristic
185C2#2713282411yescharacteristic
186C2#2713284011yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#487×C191C2
socleC22×C191#120
prime radical#27133379C2
hypercenter#487D191
hypocenterC191#1646
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #27132940C2semidirect
3. #27132865C2semidirect
4. #27132412C2semidirect
5. #27132392C2semidirect
6. #27132392C2semidirect
7. #487×C191C2semidirect
93. C191#1646semidirect
96. #487D191semidirect

Maximal subgroups

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

subgroupindex
#271333792
#271329402
#271328652
#271324122
#271323922
#487×C1912
#1646191