Finite Group Databasebeta

← #37571525

Subgroups — #37571525

Order 24448.

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

normal subgroups only

This group has 254 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#27133244C211yesmaximal, characteristic
2#27132977C212yesmaximal, complemented
3#27132593C211yesmaximal, characteristic, complemented
4#27132398C212yesmaximal, complemented
5#324×C191C211yesmaximal, characteristic, complemented
6C2×#15690287—21no—
7#20259302—22no—
8#20259297—22no—
9#20259296—21no—
10#20259296C2212yes—
11C2×C4⋊Dic191C2211yescharacteristic
12C2×Dic191⋊C4—21no—
13#20259256—22no—
14#20259244—22no—
15C191⋊#95—21no—
16C191⋊#95C2211yescharacteristic
17C2×C4⋊C4×C191C2211yescharacteristic
18C22⋊C8×C191C2212yes—
19#15690287—42no—
20#15690287—42no—
21C2×Dic382—21no—
22C2×D764—21no—
23C2×D764—21no—
24C2×D764D412yes—
25C2×C22⋊D191—22no—
26C22×Dic191—21no—
27C22×Dic191—21no—
28C2×C4×D191—22no—
29C4⋊Dic191—21no—
30C4⋊Dic191—22no—
31C4⋊Dic191D412yes—
32Dic191⋊C4—42no—
33(C2×D191)⋊C4—22no—
34(C2×D191)⋊C4—22no—
35C22×C4×C191D411yescharacteristic
36C22×C4×C191D411yescharacteristic
37C22×C4×C191C2311yescharacteristic
38C2×C8×C191—22no—
39C4⋊C4×C191—22no—
40C22×D191—22no—
41Dic382—42no—
42D764—42no—
43D764—42no—
44D764—81no—
45C22⋊D191—42no—
46C22⋊D191—42no—
47C2×Dic191—22no—
48C2×Dic191—22no—
49C2×Dic191—41no—
50C2×Dic191—41no—
51C2×Dic191—41no—
52C2×Dic191—41no—
53C2×Dic191—41no—
54C4×D191—44no—
55C23×C191C2×D411yescharacteristic
56C2×C4×C191—21no—
57C2×C4×C191—21no—
58C2×C4×C191—21no—
59C2×C4×C191—41no—
60C2×C4×C191—41no—
61C2×C4×C191D812yes—
62C2×C4×C191C2×D412yes—
63C8×C191—42no—
64C22×C191—21no—
65C22×C191—21no—
66C22×C191#12011yescharacteristic
67C22×C191C2×D811yescharacteristic
68C22×C191AGL(1,ℤ/8)11yescharacteristic
69C2×D191—42no—
70C2×D191—42no—
71C2×D191—42no—
72C4×C191—22no—
73C4×C191—22no—
74C4×C191—41no—
75Dic191—42no—
76Dic191—42no—
77Dic191—81no—
78C2×C191—21no—
79C2×C191—21no—
80C2×C191#44711yescharacteristic
81C2×C191#45611yescharacteristic
82C2×C191#45811yescharacteristic
83D191—82no—
84C191#161011yescharacteristic, complemented, Sylow
85#1610—1911nomaximal, Sylow
86#537—1911no—
87#480—1912no—
88#398—1911no—
89#327—1912no—
90#324D19111yescharacteristic, complemented
91C2×#41—3821no—
92C22⋊Q8—3822no—
93#121—3822no—
94#121—3821no—
95#121—1912no—
96C2×C4⋊C4—3821no—
97C2×C4⋊C4—1911no—
98C2×C4⋊C4C2×D19111yescharacteristic
99#107—3822no—
100#102—3822no—
101C22⋊C8C2×D19112yes—
102#95—3821no—
103#95—1911no—
104#41—7642no—
105#41—7642no—
106C2×Q8—3821no—
107C2×D4—3821no—
108C2×D4—3821no—
109C2×D4—3822no—
110C2×D4—1912no—
111C22×C4—3822no—
112C22×C4—3821no—
113C22×C4—3821no—
114C22×C4D76411yescharacteristic
115C22×C4D76411yescharacteristic
116C22×C4C22×D19111yescharacteristic
117C2×C8—22no—
118C4⋊C4—22no—
119C4⋊C4—3821no—
120C4⋊C4—3822no—
121C4⋊C4—1912no—
122C4⋊C4—7642no—
123C22⋊C4—3822no—
124C22⋊C4—3822no—
125C23—3822no—
126C23C2×D76411yescharacteristic
127Q8—7642no—
128D4—15281no—
129D4—7642no—
130D4—7642no—
131D4—7642no—
132D4—7642no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—3822no—
139C2×C4—3822no—
140C2×C4—7644no—
141C2×C4—7641no—
142C2×C4—7641no—
143C2×C4—7641no—
144C2×C4—7641no—
145C2×C4—7641no—
146C2×C4D152812yes—
147C2×C4D4×D19112yes—
148C8—42no—
149C22—21no—
150C22—21no—
151C22—7642no—
152C22—7642no—
153C22—7642no—
154C22#2025929211yescharacteristic
155C22C2×D152811yescharacteristic
156C22#2025935011yescharacteristic
157C4—22no—
158C4—22no—
159C4—41no—
160C4—15281no—
161C4—7642no—
162C4—7642no—
163C2—21no—
164C2—21no—
165C2—15282no—
166C2#2713279911yescharacteristic
167C2#2713284811yescharacteristic
168C2#2713285411yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#324×C191C2
socleC22×C191#120
prime radical#27133244C2
hypercenter#324D191
hypocenterC191#1610
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #27132977C2semidirect
3. #27132593C2semidirect
4. #27132398C2semidirect
5. #324×C191C2semidirect
84. C191#1610semidirect
90. #324D191semidirect

Maximal subgroups

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

subgroupindex
#271332442
#271329772
#271325932
#271323982
#324×C1912
#1610191