Finite Group Databasebeta

← #34110422

Subgroups — #34110422

Order 20096.

382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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#23757750C211yesmaximal, characteristic, complemented
2#23757594C212yesmaximal, complemented
3#23757577C212yesmaximal, complemented
4#23757470C212yesmaximal, complemented
5#23757411C212yesmaximal, complemented
6#23757373C212yesmaximal, complemented
7C4×#14578942C212yesmaximal, complemented
8#23757334C211yesmaximal, characteristic, complemented
9#540×C157C211yesmaximal, characteristic
10C22×Dic314C2211yescharacteristic
11C2×#14578942C2212yes—
12C2×#14578942C2212yes—
13C4×Dic314C2212yes—
14C4×Dic314C2212yes—
15#19097736—22no—
16#19097730C2211yescharacteristic
17#19097727—22no—
18#19097704C2212yes—
19#19097702C2212yes—
20C4⋊#11929434C2212yes—
21#19097694C2212yes—
22#19097694C2212yes—
23#19097692C2212yes—
24#19097692C2212yes—
25C22⋊#11929434C2212yes—
26#19097682C2211yescharacteristic
27C4×#11929434C2211yescharacteristic
28#127×C157C2211yescharacteristic
29#125×C157C2211yescharacteristic
30#123×C157—22no—
31#121×C157—22no—
32#121×C157C2212yes—
33C4×D4×C157C2212yes—
34#117×C157C2211yescharacteristic
35C2×Dic314—24no—
36C2×Dic314—21no—
37C2×Dic314C2312yes—
38C22×Dic157—21no—
39#14578942—24no—
40#14578942—24no—
41C2×#11929434C2312yes—
42C2×#11929434C2312yes—
43C4⋊Dic157C2312yes—
44#14578933—22no—
45#14578933—22no—
46C22⋊Dic157—21no—
47C4×Dic157—22no—
48C4×Dic157—22no—
49C4×Dic157—21no—
50C2×D4×C157—22no—
51C2×D4×C157—22no—
52C2×D4×C157C2312yes—
53C22×C4×C157—22no—
54C22×C4×C157C2311yescharacteristic
55C4⋊C4×C157—22no—
56C4⋊C4×C157D412yes—
57C4⋊C4×C157C2312yes—
58C22⋊C4×C157—22no—
59C22⋊C4×C157—22no—
60C22⋊C4×C157D412yes—
61C42×C157C2311yescharacteristic
62C42×C157C2311yescharacteristic
63Dic314—24no—
64Dic314—22no—
65Dic314#4114yes—
66C2×Dic157—24no—
67C2×Dic157—22no—
68C2×Dic157—22no—
69#11929434—22no—
70#11929434—22no—
71C23×C157—22no—
72C23×C157C2×D411yescharacteristic
73D4×C157—22no—
74D4×C157—22no—
75D4×C157—82no—
76D4×C157—82no—
77C2×C4×C157—22no—
78C2×C4×C157—22no—
79C2×C4×C157—82no—
80C2×C4×C157C2×D411yescharacteristic
81C2×C4×C157C2×D412yes—
82C2×C4×C157C2×D412yes—
83C2×C4×C157C2411yescharacteristic
84C22×C157—21no—
85C22×C157—22no—
86C22×C157—42no—
87C22×C157—42no—
88C22×C157—42no—
89C22×C157C22×D411yescharacteristic
90C4×C157—21no—
91C4×C157—22no—
92C4×C157—22no—
93C4×C157—42no—
94C4×C157C2×#4112yes—
95Dic157—24no—
96Dic157—42no—
97C2×C157—41no—
98C2×C157—82no—
99C2×C157#52511yescharacteristic
100C2×C157#57712yes—
101C157#312611yescharacteristic, complemented, Sylow
102#3126—1571nomaximal, Sylow
103#540D15711yescharacteristic
104#519—1571no—
105#482—1572no—
106#479—1572no—
107#460—1572no—
108#448—1572no—
109#440—1572no—
110C4×SD16—1572no—
111#433—1571no—
112C22×Q8—1571no—
113C2×SD16—1572no—
114C2×SD16—1572no—
115#127C2×D15711yescharacteristic
116#125C2×D15711yescharacteristic
117#123—22no—
118#121—22no—
119#121C2×D15712yes—
120C4×Q8—3142no—
121C4×Q8—1572no—
122C4×Q8—1572no—
123C4×D4C2×D15712yes—
124#117—3142no—
125#117—1571no—
126#117C2×D15711yescharacteristic
127#107—1572no—
128#106—1572no—
129C4⋊C8—1572no—
130#103—1572no—
131#103—1572no—
132#102—1572no—
133#102—1572no—
134C22⋊C8—1572no—
135#97—1571no—
136C4×C8—1571no—
137C2×Q8—3144no—
138C2×Q8—3141no—
139C2×Q8—1572no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4C22×D15712yes—
143C22×C4—22no—
144C22×C4—3141no—
145C22×C4C22×D15711yescharacteristic
146SD16—3144no—
147SD16—3144no—
148C2×C8—1572no—
149C2×C8—1572no—
150C4⋊C4—22no—
151C4⋊C4—3142no—
152C4⋊C4—3142no—
153C4⋊C4—1572no—
154C4⋊C4C22⋊D15712yes—
155C4⋊C4C22×D15712yes—
156C22⋊C4—22no—
157C22⋊C4—22no—
158C22⋊C4—3141no—
159C22⋊C4C22⋊D15712yes—
160C42—3142no—
161C42—3142no—
162C42—3141no—
163C42C22×D15711yescharacteristic
164C42C22×D15711yescharacteristic
165C23—22no—
166C23C2×C22⋊D15711yescharacteristic
167Q8—3144no—
168Q8—3142no—
169Q8—1574no—
170D4—22no—
171D4—22no—
172D4—82no—
173D4—82no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—82no—
177C2×C4—3144no—
178C2×C4—3142no—
179C2×C4—3142no—
180C2×C4C2×C22⋊D15712yes—
181C2×C4C2×C22⋊D15712yes—
182C2×C4C2×C22⋊D15711yescharacteristic
183C2×C4C23×D15711yescharacteristic
184C8—3142no—
185C8—3142no—
186C22—22no—
187C22—21no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C22×C22⋊D15711yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—42no—
196C4—3144no—
197C4—6282no—
198C4#41×D15712yes—
199C2—41no—
200C2—82no—
201C2#2375778011yescharacteristic
202C2#2375808412yes—
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting, prime radical#540×C157C2
socleC22×C157C22×D4
hypercenter#540D157
hypocenterC157#3126
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #23757750C2semidirect
2. #23757594C2semidirect
3. #23757577C2semidirect
4. #23757470C2semidirect
5. #23757411C2semidirect
6. #23757373C2semidirect
7. C4×#14578942C2semidirect
8. #23757334C2semidirect
101. C157#3126semidirect

Maximal subgroups

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

subgroupindex
#237577502
#237575942
#237575772
#237574702
#237574112
#237573732
C4×#145789422
#237573342
#540×C1572
#3126157