Finite Group Databasebeta

← #34101824

Subgroups — #34101824

Order 20096.

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

normal subgroups only

This group has 230 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#23757848C211yesmaximal, characteristic
2#101×D157C212yesmaximal, complemented
3#23757072C211yesmaximal, characteristic, complemented
4#23757069C212yesmaximal, complemented
5#356×C157C211yesmaximal, characteristic, complemented
6C2×#14578955C411yescharacteristic
7C2×Q8×D157C2211yescharacteristic
8M16×D157—22no—
9#19097769C411yescharacteristic
10#19097760C2211yescharacteristic
11#19097759C411yescharacteristic
12#19097756—22no—
13#19097749—22no—
14#19097728C411yescharacteristic
15#19097690C2212yes—
16#19097689—22no—
17C4⋊Q8×C157C2211yescharacteristic
18#101×C157C2212yes—
19#14578955—42no—
20C2×Dic314C2×C411yescharacteristic
21C2×Dic314D412yes—
22Q8×D157—42no—
23C2×D628—21no—
24C2×D628C2×C411yescharacteristic
25C2×C4×D157—21no—
26C2×C4×D157C2×C411yescharacteristic
27C2×C4×D157D412yes—
28#14578938—22no—
29#14578937—42no—
30C8×D157—42no—
31#14578933—21no—
32#14578933—22no—
33#14578931—21no—
34#14578931—22no—
35#14578931—22no—
36C4×Dic157C2×C411yescharacteristic
37C2×Q8×C157C2×C411yescharacteristic
38C2×Q8×C157C2311yescharacteristic
39M16×C157—22no—
40C4⋊C4×C157—22no—
41C42×C157C2×C411yescharacteristic
42C22×D157—21no—
43C22×D157C22⋊C411yescharacteristic
44Dic314—41no—
45Dic314—42no—
46D628—41no—
47D628—42no—
48C2×Dic157—21no—
49C2×Dic157C22⋊C411yescharacteristic
50C2×Dic157C22⋊C412yes—
51C4×D157—22no—
52C4×D157—22no—
53C4×D157—22no—
54C4×D157—42no—
55#11929434—42no—
56Q8×C157—41no—
57Q8×C157—41no—
58C2×C4×C157—21no—
59C2×C4×C157—21no—
60C2×C4×C157C22×C411yescharacteristic
61C2×C4×C157C2×D412yes—
62C8×C157—42no—
63C22×C157C2×C22⋊C411yescharacteristic
64C2×D157—41no—
65C2×D157—42no—
66C2×D157—41no—
67C2×D157#9912yes—
68C4×C157—22no—
69C4×C157—21no—
70C4×C157—41no—
71C4×C157—41no—
72Dic157—21no—
73Dic157—22no—
74Dic157—41no—
75C2×C157—21no—
76C2×C157C2×#9911yescharacteristic
77D157—22no—
78D157—81no—
79C157#213311yescharacteristic, complemented, Sylow
80#2133—1571nomaximal, Sylow
81#536—1571no—
82C2×#101—1572no—
83#356—1571no—
84#356D15711yescharacteristic, complemented
85#355—1572no—
86C2×#41—1571no—
87C22×Q8—1571no—
88C2×M16—3142no—
89C4⋊Q8—1571no—
90C4⋊Q8C2×D15711yescharacteristic
91#124—1571no—
92#124—1571no—
93#123—3142no—
94C22⋊Q8—3142no—
95#117—1571no—
96#101—3142no—
97#101—1572no—
98#101C2×D15712yes—
99#41—6282no—
100C2×Q8—6282no—
101C2×Q8—1571no—
102C2×Q8—1572no—
103C2×Q8C4×D15711yescharacteristic
104C2×Q8C22×D15711yescharacteristic
105C2×D4—3141no—
106C2×D4—1571no—
107C22×C4—3141no—
108C22×C4—1571no—
109C22×C4—1572no—
110M16—22no—
111M16—3142no—
112M16—6282no—
113C2×C8—6282no—
114C4⋊C4—22no—
115C4⋊C4—3141no—
116C4⋊C4—3142no—
117C22⋊C4—3141no—
118C22⋊C4—3142no—
119C22⋊C4—3142no—
120C42—1571no—
121C42C4×D15711yescharacteristic
122C23—3141no—
123C23—1571no—
124Q8—41no—
125Q8—41no—
126Q8—6282no—
127Q8—6281no—
128D4—6281no—
129D4—6282no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—3142no—
133C2×C4—3142no—
134C2×C4—3142no—
135C2×C4—3141no—
136C2×C4—6282no—
137C2×C4—1572no—
138C2×C4—1571no—
139C2×C4C2×C4×D15711yescharacteristic
140C2×C4D4×D15712yes—
141C8—42no—
142C8—6282no—
143C22—6281no—
144C22—6282no—
145C22—6281no—
146C22—1572no—
147C22C22⋊C4×D15711yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—41no—
152C4—3141no—
153C4—3142no—
154C4—6281no—
155C2—21no—
156C2—3142no—
157C2—12561no—
158C2#99×D15711yescharacteristic
subgroupG/H
centerC2#99×D157
commutatorC2×C4×C157C22×C4
FrattiniC2×Q8C22×D157
Fitting#356×C157C2
socleC2×C157C2×#99
prime radicalC2×#14578955C4
cosocleC2×Q8×C157C23
hypercenter#356D157
hypocenterC157#2133
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
2. #101×D157C2semidirect
3. #23757072C2semidirect
4. #23757069C2semidirect
5. #356×C157C2semidirect
79. C157#2133semidirect
84. #356D157semidirect

Maximal subgroups

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

subgroupindex
#237578482
#101×D1572
#237570722
#237570692
#356×C1572
#2133157