Finite Group Databasebeta

← #34100095

Subgroups — #34100095

Order 20096.

552 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#19097698C212yesmaximal, complemented
2#23757274C212yesmaximal, complemented
3C2×#19097690C211yesmaximal, characteristic, complemented
4#23757180C211yesmaximal, characteristic, complemented
5C2×2−1+4×C157C211yesmaximal, characteristic
6C2×#14578938C2212yes—
7C2×C4⋊Dic157C2211yescharacteristic
8C2×C4×Dic157C2211yescharacteristic
9#19097698—24no—
10#19097695—22no—
11#19097692—22no—
12#19097690—22no—
13#19097678—22no—
142−1+4×C157—24no—
152−1+4×C157—22no—
162−1+4×C157C414yescomplemented
17C2×#41×C157—22no—
18C2×#41×C157—22no—
19C2×#41×C157C2212yes—
20C22×Q8×C157—22no—
21C22×Q8×C157C2211yescharacteristic
22C22×Dic157—21no—
23C22×Dic157—21no—
24#14578938—22no—
25#14578938—22no—
26C2×#11929434—22no—
27C4⋊Dic157—22no—
28C4×Dic157—22no—
29#41×C157—28no—
30#41×C157—28no—
31#41×C157—28no—
32#41×C157—28no—
33#41×C157—22no—
34#41×C157—22no—
35#41×C157C2×C414yes—
36#41×C157D414yes—
37C2×Q8×C157—22no—
38C2×Q8×C157—28no—
39C2×Q8×C157—28no—
40C2×Q8×C157—22no—
41C2×Q8×C157—22no—
42C2×Q8×C157C2×C412yes—
43C2×Q8×C157D412yes—
44C2×Q8×C157D412yes—
45C2×D4×C157—22no—
46C2×D4×C157—22no—
47C2×D4×C157D412yes—
48C22×C4×C157—24no—
49C22×C4×C157—22no—
50C22×C4×C157D412yes—
51C22×C4×C157C2311yescharacteristic
52C2×Dic157—22no—
53C2×Dic157—41no—
54C2×Dic157—41no—
55C2×Dic157—42no—
56C2×Dic157—41no—
57#11929434—42no—
58C23×C157—22no—
59C23×C157C2×D411yescharacteristic
60Q8×C157—28no—
61Q8×C157—24no—
62Q8×C157—22no—
63Q8×C157—24no—
64Q8×C157C22⋊C414yes—
65D4×C157—28no—
66D4×C157—24no—
67D4×C157—24no—
68D4×C157—22no—
69D4×C157C22⋊C414yes—
70C2×C4×C157—216no—
71C2×C4×C157—22no—
72C2×C4×C157—22no—
73C2×C4×C157—22no—
74C2×C4×C157—24no—
75C2×C4×C157—24no—
76C2×C4×C157C22⋊C414yes—
77C2×C4×C157C22×C411yescharacteristic
78C2×C4×C157C2×D412yes—
79C2×C4×C157C2×D412yes—
80C2×C4×C157C2×D411yescharacteristic
81C22×C157—21no—
82C22×C157—21no—
83C22×C157—24no—
84C22×C157—42no—
85C22×C157—42no—
86C22×C157C2×C22⋊C411yescharacteristic
87C22×C157#12011yescharacteristic
88C22×C157#12011yescharacteristic
89C4×C157—24no—
90C4×C157—24no—
91C4×C157C2×C22⋊C412yes—
92C4×C157#12012yes—
93Dic157—42no—
94Dic157—81no—
95C2×C157—21no—
96C2×C157—21no—
97C2×C157—44no—
98C2×C157#37911yescharacteristic
99C2×C157#45411yescharacteristic
100C2×C157#45611yescharacteristic
101C157#179311yescharacteristic, complemented, Sylow
102#1793—1571nomaximal, Sylow
103C2×2−1+4D15711yescharacteristic
104C2×#104—1572no—
105#417—1572no—
106C2×#101—1571no—
107#391—1571no—
1082−1+4—24no—
1092−1+4—22no—
1102−1+4Dic15714yescomplemented
111C2×#41—22no—
112C2×#41—22no—
113C2×#41C2×D15712yes—
114C22×Q8—22no—
115C22×Q8C2×D15711yescharacteristic
116C2×M16—1572no—
117C2×C4⋊C4—1571no—
118C2×C42—1571no—
119#104—3144no—
120#103—3142no—
121#102—3142no—
122#101—3142no—
123#95—3142no—
124#41—28no—
125#41—28no—
126#41—28no—
127#41—22no—
128#41—22no—
129#41—28no—
130#41C2×Dic15714yes—
131#41C22⋊D15714yes—
132C2×Q8—22no—
133C2×Q8—28no—
134C2×Q8—28no—
135C2×Q8—22no—
136C2×Q8—22no—
137C2×Q8C2×Dic15712yes—
138C2×Q8C22⋊D15712yes—
139C2×Q8C22⋊D15712yes—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22⋊D15712yes—
143C22×C4—24no—
144C22×C4—22no—
145C22×C4—3141no—
146C22×C4—3141no—
147C22×C4C22⋊D15712yes—
148C22×C4C22×D15711yescharacteristic
149M16—3142no—
150M16—3142no—
151C2×C8—3142no—
152C4⋊C4—3142no—
153C42—3142no—
154C23—22no—
155C23C2×C22⋊D15711yescharacteristic
156Q8—28no—
157Q8—24no—
158Q8—22no—
159Q8—24no—
160Q8C22⋊Dic15714yes—
161D4—28no—
162D4—24no—
163D4—24no—
164D4—22no—
165D4C22⋊Dic15714yes—
166C2×C4—216no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—3142no—
173C2×C4—6281no—
174C2×C4—6281no—
175C2×C4—6282no—
176C2×C4—6281no—
177C2×C4C22⋊Dic15714yes—
178C2×C4C22×Dic15711yescharacteristic
179C2×C4C2×C22⋊D15712yes—
180C2×C4C2×C22⋊D15712yes—
181C2×C4C2×C22⋊D15711yescharacteristic
182C8—6282no—
183C22—21no—
184C22—21no—
185C22—24no—
186C22—42no—
187C22—42no—
188C22C2×C22⋊Dic15711yescharacteristic
189C22#1909774011yescharacteristic
190C22#1909774011yescharacteristic
191C4—24no—
192C4—24no—
193C4—6282no—
194C4—12561no—
195C4C2×C22⋊Dic15712yes—
196C4#1909774012yes—
197C2—21no—
198C2—21no—
199C2—44no—
200C2#2375712911yescharacteristic
201C2#2375744611yescharacteristic
202C2#2375745611yescharacteristic
subgroupG/H
centerC22#19097740
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting, prime radicalC2×2−1+4×C157C2
socleC22×C157#120
cosocleC22×C4×C157C23
hypercenterC2×2−1+4D157
hypocenterC157#1793
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×#19097698C2semidirect
2. #23757274C2semidirect
3. C2×#19097690C2semidirect
4. #23757180C2semidirect
16. 2−1+4×C157C4semidirect
101. C157#1793semidirect
110. 2−1+4Dic157semidirect

Maximal subgroups

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

subgroupindex
C2×#190976982
#237572742
C2×#190976902
#237571802
C2×2−1+4×C1572
#1793157