Finite Group Databasebeta

← #37571672

Subgroups — #37571672

Order 24448.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#27133316C211yesmaximal, characteristic
2#27133015C211yesmaximal, characteristic, complemented
3#27132954C211yesmaximal, characteristic, complemented
4#27132954C211yesmaximal, characteristic, complemented
5#27132390C211yesmaximal, characteristic, complemented
6#27132390C211yesmaximal, characteristic, complemented
7#332×C191C211yesmaximal, characteristic, complemented
8C2×#15690288—21no—
9#20259322C2211yescharacteristic
10#20259307—22no—
11#20259298—21no—
12#20259297—21no—
13C4×D764C2211yescharacteristic
14C4×D764C2211yescharacteristic
15C4⋊C4×D191—21no—
16#20259254—21no—
17#20259254—21no—
18#20259245—22no—
19#20259244—21no—
20#20259244—21no—
21C4×C191⋊C8C2211yescharacteristic
22C4⋊Q8×C191C2211yescharacteristic
23C4⋊C8×C191C2211yescharacteristic
24C4⋊C8×C191C2211yescharacteristic
25#15690288—42no—
26#15690288—42no—
27C2×Dic382—21no—
28C2×D764—22no—
29C2×D764D411yescharacteristic
30C2×D764D411yescharacteristic
31C2×C4×D191—22no—
32C2×C4×D191—21no—
33C2×C4×D191—21no—
34C2×C191⋊C8—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191—21no—
37C4⋊Dic191D411yescharacteristic
38C4⋊Dic191D411yescharacteristic
39Dic191⋊C4—22no—
40(C2×D191)⋊C4—22no—
41(C2×D191)⋊C4—21no—
42(C2×D191)⋊C4—21no—
43C2×Q8×C191—21no—
44C2×C8×C191—21no—
45C2×C8×C191—21no—
46C4⋊C4×C191—21no—
47C4⋊C4×C191D412yes—
48C42×C191C2311yescharacteristic
49C22×D191—21no—
50C22×D191—21no—
51Dic382—42no—
52D764—21no—
53D764—21no—
54D764—21no—
55D764—44no—
56D764SD1612yes—
57C2×Dic191—21no—
58C2×Dic191—21no—
59C2×Dic191—41no—
60C4×D191—44no—
61C4×D191—41no—
62C4×D191—41no—
63C4×D191—41no—
64C4×D191—41no—
65C191⋊C8—41no—
66Q8×C191—41no—
67Q8×C191—41no—
68C2×C4×C191—22no—
69C2×C4×C191C2×D411yescharacteristic
70C2×C4×C191C2×D411yescharacteristic
71C2×C4×C191C2×D411yescharacteristic
72C8×C191—41no—
73C8×C191—41no—
74C22×C191#12011yescharacteristic
75C2×D191—22no—
76C2×D191—41no—
77C2×D191—41no—
78C2×D191—41no—
79C2×D191—41no—
80C2×D191—41no—
81C4×C191—21no—
82C4×C191—42no—
83C4×C191C2×SD1611yescharacteristic
84C4×C191#13511yescharacteristic
85C4×C191AGL(1,ℤ/8)11yescharacteristic
86C4×C191#13711yescharacteristic
87Dic191—41no—
88Dic191—41no—
89Dic191—81no—
90C2×C191#45011yescharacteristic
91C2×C191#45211yescharacteristic
92C2×C191#45411yescharacteristic
93D191—42no—
94D191—81no—
95C191#163511yescharacteristic, complemented, Sylow
96#1635—1911nomaximal, Sylow
97#547—1911no—
98#487—1911no—
99#476—1911no—
100#476—1911no—
101#332D19111yescharacteristic, complemented
102D4⋊C8—1911no—
103D4⋊C8—1911no—
104C2×#41—3821no—
105C4⋊Q8—1911no—
106C4⋊Q8C2×D19111yescharacteristic
107#123—3822no—
108C22⋊Q8—3821no—
109#121—3821no—
110C4×D4—1911no—
111C4×D4—1911no—
112C2×C4⋊C4—3821no—
113#106—3821no—
114#106—3821no—
115C4⋊C8C2×D19111yescharacteristic
116C4⋊C8C2×D19111yescharacteristic
117#103—3822no—
118#102—3821no—
119#102—3821no—
120C4×C8—1911no—
121#41—7642no—
122#41—7642no—
123C2×Q8—21no—
124C2×Q8—3821no—
125C2×D4—3822no—
126C2×D4—1911no—
127C2×D4—1911no—
128C22×C4—3822no—
129C22×C4—3821no—
130C22×C4—3821no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—3821no—
134C4⋊C4—21no—
135C4⋊C4—3822no—
136C4⋊C4—3821no—
137C4⋊C4—3821no—
138C4⋊C4—1911no—
139C4⋊C4—1911no—
140C4⋊C4D76412yes—
141C22⋊C4—3822no—
142C22⋊C4—3821no—
143C22⋊C4—3821no—
144C42C22×D19111yescharacteristic
145C23—3821no—
146C23—3821no—
147Q8—41no—
148Q8—41no—
149Q8—7642no—
150D4—3821no—
151D4—3821no—
152D4—3821no—
153D4—1912no—
154D4—7644no—
155C2×C4—22no—
156C2×C4—3821no—
157C2×C4—3821no—
158C2×C4—7644no—
159C2×C4—7641no—
160C2×C4—7641no—
161C2×C4—7641no—
162C2×C4—7641no—
163C2×C4—7641no—
164C2×C4D4×D19111yescharacteristic
165C2×C4D4×D19111yescharacteristic
166C2×C4C2×D76411yescharacteristic
167C8—41no—
168C8—41no—
169C8—7641no—
170C22—3822no—
171C22—7641no—
172C22—7641no—
173C22—7641no—
174C22—7641no—
175C22—7641no—
176C22#2025929211yescharacteristic
177C4—21no—
178C4—42no—
179C4—15281no—
180C4—7641no—
181C4—7641no—
182C4SD16×D19111yescharacteristic
183C4#2025934311yescharacteristic
184C4#2025934611yescharacteristic
185C4#2025935411yescharacteristic
186C2—15281no—
187C2—7642no—
188C2#2713281511yescharacteristic
189C2#2713282811yescharacteristic
190C2#2713283811yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC42×C191C23
FrattiniC42C22×D191
Fitting#332×C191C2
socleC22×C191#120
prime radical#27133316C2
hypercenter#332D191
hypocenterC191#1635
LCSG ▷ C42×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #27133015C2semidirect
3. #27132954C2semidirect
4. #27132954C2semidirect
5. #27132390C2semidirect
6. #27132390C2semidirect
7. #332×C191C2semidirect
95. C191#1635semidirect
101. #332D191semidirect

Maximal subgroups

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

subgroupindex
#271333162
#271330152
#271329542
#271323902
#332×C1912
#1635191