Finite Group Databasebeta

← #34100526

Subgroups — #34100526

Order 20096.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19097769C211yesmaximal, characteristic
2#23757750C211yesmaximal, characteristic
3#23757282C211yesmaximal, characteristic
4C2×#19097689C211yesmaximal, characteristic
5#23757034C211yesmaximal, characteristic
6#23757032C211yesmaximal, characteristic
7#419×C157C211yesmaximal, characteristic
8C22×Dic314C2211yescharacteristic
9C2×#14578938C2211yescharacteristic
10#19097769—22no—
11#19097769C414yescomplemented
12C4×Dic314—22no—
13#19097736—22no—
14#19097730C2211yescharacteristic
15#19097727—22no—
16C2×#14578933—22no—
17C2×C4×Dic157C2211yescharacteristic
18#19097695—22no—
19#19097689—22no—
20C22×Q8×C157C2211yescharacteristic
21C2×M16×C157C2211yescharacteristic
22#117×C157C2211yescharacteristic
23#103×C157—22no—
24C2×Dic314—21no—
25C2×Dic314—21no—
26C2×Dic314—21no—
27C2×Dic314—21no—
28C2×Dic314C2×C412yes—
29C2×Dic314D412yes—
30C22×Dic157—21no—
31C22×Dic157D412yes—
32#14578938—21no—
33#14578938—21no—
34C2×#11929434—21no—
35C4⋊Dic157D412yes—
36#14578933—24no—
37#14578933—28no—
38C22⋊Dic157—21no—
39C4×Dic157—24no—
40C4×Dic157—21no—
41C4×Dic157—21no—
42C4×Dic157C2×C412yes—
43C2×Q8×C157—21no—
44C2×Q8×C157—21no—
45C2×Q8×C157—21no—
46C2×Q8×C157—21no—
47C2×Q8×C157—21no—
48C2×Q8×C157C2×C412yes—
49C22×C4×C157—21no—
50C22×C4×C157C2311yescharacteristic
51M16×C157—21no—
52M16×C157—21no—
53C2×C8×C157—21no—
54C4⋊C4×C157D412yes—
55C22⋊C4×C157—21no—
56C42×C157—21no—
57Dic314—22no—
58Dic314—22no—
59Dic314—22no—
60Dic314—22no—
61C2×Dic157—24no—
62C2×Dic157—22no—
63C2×Dic157—22no—
64C2×Dic157—22no—
65C2×Dic157—22no—
66C2×Dic157C22⋊C414yes—
67#11929434—41no—
68C23×C157C2×D411yescharacteristic
69Q8×C157—22no—
70Q8×C157—22no—
71Q8×C157—41no—
72Q8×C157—41no—
73C2×C4×C157—22no—
74C2×C4×C157—22no—
75C2×C4×C157—41no—
76C2×C4×C157—41no—
77C2×C4×C157C22×C411yescharacteristic
78C2×C4×C157C2×D411yescharacteristic
79C2×C4×C157C2×D411yescharacteristic
80C2×C4×C157C2×D411yescharacteristic
81C2×C4×C157#4111yescharacteristic
82C2×C4×C157#4111yescharacteristic
83C8×C157—41no—
84C22×C157—22no—
85C22×C157C2×C22⋊C411yescharacteristic
86C22×C157#12011yescharacteristic
87C22×C157#12311yescharacteristic
88C4×C157—42no—
89C4×C157—42no—
90C4×C157C4×D411yescharacteristic
91C4×C157C4×D411yescharacteristic
92C4×C157#12111yescharacteristic
93C4×C157#12111yescharacteristic
94Dic157—24no—
95Dic157—24no—
96Dic157—42no—
97C2×C157—21no—
98C2×C157—21no—
99C2×C157#38611yescharacteristic
100C2×C157#45612yes—
101C157#188611yescharacteristic, complemented, Sylow
102#1886—1571nomaximal, Sylow
103C2×C4⋊Q8—1571no—
104#519—1571no—
105#419—1571no—
106#419D15711yescharacteristic
107C2×#101—1571no—
108#339—1571no—
109#339—1571no—
110C22×Q8—1571no—
111C22×Q8C2×D15711yescharacteristic
112C2×M16—1571no—
113C2×M16C2×D15711yescharacteristic
114C4⋊Q8—3142no—
115C4⋊Q8—1574no—
116C4×Q8—3142no—
117C4×Q8—3142no—
118#117—3142no—
119#117—1571no—
120#117C2×D15711yescharacteristic
121C2×C4⋊C4—3142no—
122C2×C42—1571no—
123#103—22no—
124#103—3142no—
125#101—3142no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—3141no—
132C2×Q8—3141no—
133C2×Q8—3141no—
134C2×Q8—3141no—
135C2×Q8—1572no—
136C2×Q8—1572no—
137C2×Q8C4×D15712yes—
138C22×C4—21no—
139C22×C4—3141no—
140C22×C4—1572no—
141C22×C4C22×D15711yescharacteristic
142M16—21no—
143M16—21no—
144M16—3141no—
145M16—3141no—
146C2×C8—21no—
147C2×C8—3141no—
148C4⋊C4—3144no—
149C4⋊C4—3148no—
150C4⋊C4—1572no—
151C4⋊C4C22⋊D15712yes—
152C22⋊C4—21no—
153C22⋊C4—3141no—
154C42—21no—
155C42—3144no—
156C42—3141no—
157C42—3141no—
158C42—1572no—
159C23D4×D15711yescharacteristic
160Q8—22no—
161Q8—22no—
162Q8—41no—
163Q8—41no—
164Q8—3142no—
165Q8—3142no—
166Q8—3142no—
167Q8—3142no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—3144no—
173C2×C4—3142no—
174C2×C4—3142no—
175C2×C4—3142no—
176C2×C4—3142no—
177C2×C4—1574no—
178C2×C4C2×C4×D15711yescharacteristic
179C2×C4D4×D15711yescharacteristic
180C2×C4D4×D15711yescharacteristic
181C2×C4C2×C22⋊D15711yescharacteristic
182C2×C4#1457895311yescharacteristic
183C2×C4#1457895411yescharacteristic
184C8—41no—
185C8—6281no—
186C22—22no—
187C22C22⋊C4×D15711yescharacteristic
188C22#1909773911yescharacteristic
189C22#1909775311yescharacteristic
190C4—42no—
191C4—42no—
192C4—3144no—
193C4—3144no—
194C4—6282no—
195C4#1909773111yescharacteristic
196C4C4×C22⋊D15711yescharacteristic
197C4#1909774211yescharacteristic
198C4#1909774411yescharacteristic
199C2—21no—
200C2—21no—
201C2#2375714911yescharacteristic
202C2#2375745412yes—
subgroupG/H
centerC22#19097739
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#419×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
cosocleC22×C4×C157C23
hypercenter#419D157
hypocenterC157#1886
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
11. #19097769C4semidirect
101. C157#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#190977692
#237577502
#237572822
C2×#190976892
#237570342
#237570322
#419×C1572
#1886157