Finite Group Databasebeta

← #37571547

Subgroups — #37571547

Order 24448.

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

normal subgroups only

This group has 236 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#27133289C211yesmaximal, characteristic
2#27132999C212yesmaximal, complemented
3#27132599C211yesmaximal, characteristic
4#27132401C212yesmaximal, complemented
5#323×C191C211yesmaximal, characteristic
6#20259301—21no—
7#20259301C2212yes—
8#20259299—22no—
9#20259299—22no—
10C2×C4⋊Dic191C2211yescharacteristic
11C2×Dic191⋊C4—21no—
12C2×C22⋊Dic191—21no—
13C2×C22⋊Dic191—21no—
14#20259256—22no—
15#20259247—22no—
16C191⋊#95C2211yescharacteristic
17C2×C22⋊C4×C191C2211yescharacteristic
18C22⋊C8×C191C2212yes—
19C2×Dic382—21no—
20C2×Dic382D412yes—
21C22×Dic191—21no—
22C22×Dic191—21no—
23C22×Dic191—21no—
24C22×Dic191—21no—
25C4⋊Dic191—21no—
26C4⋊Dic191—22no—
27C4⋊Dic191D412yes—
28Dic191⋊C4—22no—
29Dic191⋊C4—22no—
30Dic191⋊C4—42no—
31C22⋊Dic191—22no—
32C22⋊Dic191—22no—
33C22⋊Dic191—42no—
34C24×C191D411yescharacteristic
35C22×C4×C191D411yescharacteristic
36C22×C4×C191C2311yescharacteristic
37C2×C8×C191—22no—
38C22⋊C4×C191—22no—
39Dic382—42no—
40Dic382—81no—
41C2×Dic191—22no—
42C2×Dic191—22no—
43C2×Dic191—22no—
44C2×Dic191—41no—
45C2×Dic191—41no—
46C2×Dic191—41no—
47C2×Dic191—41no—
48C2×Dic191—41no—
49C2×Dic191—81no—
50C2×Dic191—81no—
51C23×C191—21no—
52C23×C191—21no—
53C23×C191—41no—
54C23×C191—41no—
55C23×C191Q1612yes—
56C23×C191C2×D411yescharacteristic
57C2×C4×C191—21no—
58C2×C4×C191—41no—
59C2×C4×C191—41no—
60C2×C4×C191C2×D412yes—
61C8×C191—42no—
62C22×C191—21no—
63C22×C191—21no—
64C22×C191—22no—
65C22×C191—42no—
66C22×C191—41no—
67C22×C191—41no—
68C22×C191—81no—
69C22×C191#12011yescharacteristic
70C22×C191C2×Q1611yescharacteristic
71C22×C191#13711yescharacteristic
72C4×C191—22no—
73C4×C191—41no—
74Dic191—42no—
75Dic191—42no—
76Dic191—42no—
77Dic191—81no—
78C2×C191—21no—
79C2×C191—21no—
80C2×C191—42no—
81C2×C191#45111yescharacteristic
82C2×C191#45311yescharacteristic
83C2×C191#45811yescharacteristic
84C191#161411yescharacteristic, complemented, Sylow
85#1614—1911nomaximal, Sylow
86#543—1911no—
87#484—1912no—
88#399—1911no—
89#328—1912no—
90#323D19111yescharacteristic
91C22⋊Q8—3822no—
92C22⋊Q8—3822no—
93C22⋊Q8—3821no—
94C22⋊Q8—1912no—
95C2×C4⋊C4—3821no—
96C2×C4⋊C4—1911no—
97C2×C22⋊C4—3821no—
98C2×C22⋊C4—3821no—
99C2×C22⋊C4C2×D19111yescharacteristic
100#107—3822no—
101#103—3822no—
102C22⋊C8C2×D19112yes—
103#95—1911no—
104C24D76411yescharacteristic
105C2×Q8—3821no—
106C2×Q8—1912no—
107C22×C4—3821no—
108C22×C4—3821no—
109C22×C4—3821no—
110C22×C4—3821no—
111C22×C4D76411yescharacteristic
112C22×C4C22×D19111yescharacteristic
113C2×C8—22no—
114C4⋊C4—3822no—
115C4⋊C4—3821no—
116C4⋊C4—3822no—
117C4⋊C4—3822no—
118C4⋊C4—1912no—
119C4⋊C4—7642no—
120C22⋊C4—22no—
121C22⋊C4—3822no—
122C22⋊C4—3822no—
123C22⋊C4—7642no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23Dic76412yes—
129C23C2×D76411yescharacteristic
130Q8—15281no—
131Q8—7642no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—3822no—
136C2×C4—3822no—
137C2×C4—3822no—
138C2×C4—15281no—
139C2×C4—15281no—
140C2×C4—7641no—
141C2×C4—7641no—
142C2×C4—7641no—
143C2×C4—7641no—
144C2×C4—7641no—
145C2×C4D4×D19112yes—
146C8—42no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#2025929211yescharacteristic
155C22C2×Dic76411yescharacteristic
156C22#2025935511yescharacteristic
157C4—22no—
158C4—41no—
159C4—15281no—
160C4—7642no—
161C4—7642no—
162C4—7642no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#2713282111yescharacteristic
167C2#2713283311yescharacteristic
168C2#2713285411yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#323×C191C2
socleC22×C191#120
prime radicalC24×C191D4
hypercenter#323D191
hypocenterC191#1614
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #27132999C2semidirect
4. #27132401C2semidirect
84. C191#1614semidirect

Maximal subgroups

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

subgroupindex
#271332892
#271329992
#271325992
#271324012
#323×C1912
#1614191