Finite Group Databasebeta

← #37573055

Subgroups — #37573055

Order 24448.

314 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 85 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#27133237C211yesmaximal, characteristic
2#27133141C211yesmaximal, characteristic, complemented
3#27132679C212yesmaximal
4#27132420C212yesmaximal, complemented
5C2×#101×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C2211yescharacteristic
7#20259320C412yescomplemented
8#20259311C412yescomplemented
9#20259305—22no—
10#20259298—22no—
11Q8×Dic191—24no—
12#20259281—22no—
13#20259281C2211yescharacteristic
14#20259281C2212yes—
15#20259248—24no—
16C22×Q8×C191C2211yescharacteristic
17C2×M16×C191C2212yes—
18#101×C191—22no—
19#15690287—22no—
20#15690287—22no—
21C2×Dic382C2×C411yescharacteristic
22C2×D764C2×C411yescharacteristic
23C2×C22⋊D191—21no—
24C2×C4×D191—21no—
25C4⋊Dic191—24no—
26C4⋊Dic191—22no—
27C4⋊Dic191—21no—
28Dic191⋊C4—24no—
29C22⋊Dic191—22no—
30C22⋊Dic191—21no—
31(C2×D191)⋊C4—24no—
32C4×Dic191—24no—
33C4×Dic191C2×C412yes—
34C4×Dic191D414yes—
35C2×Q8×C191—22no—
36C2×Q8×C191—22no—
37C2×Q8×C191C2×C412yes—
38C2×Q8×C191D412yes—
39C22×C4×C191D412yes—
40C22×C4×C191C2311yescharacteristic
41M16×C191—22no—
42M16×C191—22no—
43C2×C8×C191—22no—
44C22×D191—21no—
45Dic382—22no—
46D764—22no—
47C22⋊D191—41no—
48C22⋊D191—41no—
49C2×Dic191—22no—
50C2×Dic191—21no—
51C2×Dic191—24no—
52C4×D191—42no—
53C23×C191C2×D411yescharacteristic
54Q8×C191—24no—
55Q8×C191—24no—
56C2×C4×C191—22no—
57C2×C4×C191—22no—
58C2×C4×C191C22⋊C414yes—
59C2×C4×C191C22×C411yescharacteristic
60C2×C4×C191C2×D412yes—
61C2×C4×C191C2×D411yescharacteristic
62C2×C4×C191#4112yes—
63C8×C191—42no—
64C22×C191—41no—
65C22×C191C2×C22⋊C411yescharacteristic
66C22×C191#12011yescharacteristic
67C22×C191#12311yescharacteristic
68C2×D191—42no—
69C2×D191—41no—
70C4×C191—24no—
71C4×C191C4×D412yes—
72C4×C191#12112yes—
73Dic191—44no—
74Dic191—42no—
75Dic191—41no—
76C2×C191—21no—
77C2×C191—21no—
78C2×C191—21no—
79C2×C191#38611yescharacteristic
80D191—81no—
81C191#191211yescharacteristic, complemented, Sylow
82#1912—1911nomaximal, Sylow
83#536—1911no—
84#519—1911no—
85#421—1912no—
86C2×#101D19111yescharacteristic, complemented
87H(3,ℤ/4)—1912no—
88C2×#41—1911no—
89C22×Q8C2×D19111yescharacteristic
90C2×M16C2×D19112yes—
91C4⋊Q8—1912no—
92#124—1912no—
93#123—3822no—
94C22⋊Q8—3822no—
95C4×Q8—3824no—
96#117—3822no—
97#117—1912no—
98#117—1911no—
99#104—3824no—
100#101—22no—
101#41—3822no—
102#41—3822no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—1911no—
106C2×Q8C4×D19112yes—
107C2×Q8C22⋊D19112yes—
108C2×D4—3821no—
109C2×D4—1911no—
110C22×C4—3821no—
111C22×C4D76412yes—
112C22×C4C22×D19111yescharacteristic
113M16—22no—
114M16—22no—
115C2×C8—22no—
116C4⋊C4—3824no—
117C4⋊C4—3824no—
118C4⋊C4—3822no—
119C4⋊C4—3821no—
120C22⋊C4—3822no—
121C22⋊C4—3821no—
122C22⋊C4—3824no—
123C42—3824no—
124C42—1912no—
125C42—1914no—
126C23—3821no—
127C23C2×D76411yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—3822no—
131D4—3822no—
132D4—7641no—
133D4—7641no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—3822no—
137C2×C4—3821no—
138C2×C4—3824no—
139C2×C4—7642no—
140C2×C4(C2×D191)⋊C414yes—
141C2×C4C2×C4×D19111yescharacteristic
142C2×C4D4×D19112yes—
143C2×C4C2×C22⋊D19111yescharacteristic
144C2×C4#1569028612yes—
145C8—42no—
146C22—41no—
147C22—7642no—
148C22—7641no—
149C22C2×(C2×D191)⋊C411yescharacteristic
150C22#2025929211yescharacteristic
151C22#2025930611yescharacteristic
152C4—24no—
153C4—7644no—
154C4—7642no—
155C4—7641no—
156C4(C22⋊D191)⋊C412yes—
157C4#2025929412yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—15281no—
162C2#2713254011yescharacteristic
subgroupG/H
centerC2#27132540
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
FittingC2×#101×C191C2
socleC2×C191#386
prime radicalC2×#15690287C22
cosocleC22×C4×C191C23
hypercenterC2×#101D191
hypocenterC191#1912
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #27133141C2semidirect
4. #27132420C2semidirect
5. C2×#101×C191C2semidirect
7. #20259320C4semidirect
8. #20259311C4semidirect
81. C191#1912semidirect
86. C2×#101D191semidirect

Maximal subgroups

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

subgroupindex
#271332372
#271331412
#271326792
#271324202
C2×#101×C1912
#1912191