Finite Group Databasebeta

← #34101277

Subgroups — #34101277

Order 20096.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19097771C211yesmaximal, characteristic
2C2×#19097695C212yesmaximal
3#23757035C212yesmaximal
4#23757028C211yesmaximal, characteristic
5#391×C157C211yesmaximal, characteristic
6C22×Dic314—21no—
7C22×#11929434C2212yes—
8#19097771—24no—
9C2×C4⋊Dic157—21no—
10C2×C4⋊Dic157C2212yes—
11#19097695—24no—
12C22×Q8×C157C2211yescharacteristic
13C2×C4⋊C4×C157C2211yescharacteristic
14C2×C42×C157C2211yescharacteristic
15#95×C157—21no—
16#95×C157—21no—
17C2×Dic314—24no—
18C2×Dic314—42no—
19C2×Dic314—42no—
20C22×Dic157—22no—
21C2×#11929434—22no—
22C2×#11929434—22no—
23C2×#11929434—22no—
24C4⋊Dic157—24no—
25C4⋊Dic157—22no—
26C4⋊Dic157D414yes—
27C2×Q8×C157—21no—
28C2×Q8×C157—22no—
29C2×Q8×C157—22no—
30C2×Q8×C157Q812yescomplemented
31C22×C4×C157—21no—
32C22×C4×C157—21no—
33C22×C4×C157D411yescharacteristic
34C22×C4×C157D411yescharacteristic
35C22×C4×C157C2311yescharacteristic
36C4⋊C4×C157—22no—
37C42×C157—22no—
38Dic314—48no—
39C2×Dic157—24no—
40C2×Dic157—42no—
41C2×Dic157—42no—
42#11929434—42no—
43C23×C157C2×D411yescharacteristic
44Q8×C157—24no—
45Q8×C157—42no—
46C2×C4×C157—21no—
47C2×C4×C157—21no—
48C2×C4×C157—21no—
49C2×C4×C157—21no—
50C2×C4×C157—22no—
51C2×C4×C157—41no—
52C2×C4×C157—41no—
53C2×C4×C157—41no—
54C2×C4×C157—41no—
55C2×C4×C157—41no—
56C2×C4×C157SD1612yes—
57C2×C4×C157Q1612yes—
58C2×C4×C157C2×D412yes—
59C2×C4×C157C2×Q811yescharacteristic
60C2×C4×C157#4112yes—
61C2×C4×C157#4111yescharacteristic
62C22×C157#12011yescharacteristic
63C22×C157C22⋊Q811yescharacteristic
64C22×C157#12411yescharacteristic
65C22×C157C2×SD1611yescharacteristic
66C22×C157C2×Q1611yescharacteristic
67C22×C157AGL(1,ℤ/8)11yescharacteristic
68C22×C157#13711yescharacteristic
69C4×C157—22no—
70C4×C157—22no—
71C4×C157—42no—
72C4×C157—81no—
73C4×C157C22⋊Q812yes—
74C4×C157#12412yes—
75Dic157—44no—
76C2×C157#39311yescharacteristic
77C2×C157#45011yescharacteristic
78C2×C157#45111yescharacteristic
79C2×C157#47511yescharacteristic
80C2×C157#47711yescharacteristic
81C2×C157#48711yescharacteristic
82C2×C157#48911yescharacteristic
83C157#202411yescharacteristic, complemented, Sylow
84#2024—1571nomaximal, Sylow
85C2×C4⋊Q8—1571no—
86C2×#103—1572no—
87#391D15711yescharacteristic
88#340—1572no—
89#336—1571no—
90C22×Q8—3141no—
91C22×Q8C2×D15711yescharacteristic
92C22×C8—1572no—
93C4⋊Q8—3144no—
94C2×C4⋊C4—3141no—
95C2×C4⋊C4—1572no—
96C2×C4⋊C4C2×D15711yescharacteristic
97C2×C42C2×D15711yescharacteristic
98#103—3144no—
99#95—21no—
100#95—21no—
101C2×Q8—21no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—3144no—
105C2×Q8—6282no—
106C2×Q8—6282no—
107C2×Q8Dic31412yescomplemented
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—3142no—
111C22×C4C22⋊D15711yescharacteristic
112C22×C4C22⋊D15711yescharacteristic
113C22×C4C22×D15711yescharacteristic
114C2×C8—3142no—
115C2×C8—3142no—
116C2×C8—3142no—
117C4⋊C4—22no—
118C4⋊C4—3144no—
119C4⋊C4—3142no—
120C4⋊C4—1574no—
121C42—22no—
122C23C2×C22⋊D15711yescharacteristic
123Q8—24no—
124Q8—42no—
125Q8—6288no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—3144no—
137C2×C4—6282no—
138C2×C4—6282no—
139C2×C4#1457894112yes—
140C2×C4#1457894412yes—
141C2×C4D4×D15712yes—
142C2×C4C2×Dic31411yescharacteristic
143C2×C4#1457895312yes—
144C2×C4#1457895411yescharacteristic
145C8—6282no—
146C22#1909773911yescharacteristic
147C22#1909775011yescharacteristic
148C22#1909775811yescharacteristic
149C22C2×#1457894111yescharacteristic
150C22C2×#1457894411yescharacteristic
151C22#1909779611yescharacteristic
152C22#1909780111yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—81no—
157C4—6284no—
158C4#1909774812yes—
159C4#1909775712yes—
160C2#2375718511yescharacteristic
161C2#2375742311yescharacteristic
162C2#2375742811yescharacteristic
163C2#2375755811yescharacteristic
164C2#2375756811yescharacteristic
165C2#2375762311yescharacteristic
166C2#2375763211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D157
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#391×C157C2
socle, prime radicalC23×C157C2×D4
hypercenter#391D157
hypocenterC157#2024
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C157Q8semidirect
83. C157#2024semidirect
107. C2×Q8Dic314semidirect

Maximal subgroups

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

subgroupindex
C2×#190977712
C2×#190976952
#237570352
#237570282
#391×C1572
#2024157