Finite Group Databasebeta

← #34099160

Subgroups — #34099160

Order 20096.

236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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#23757899C211yesmaximal, characteristic
2#23757608C212yesmaximal, complemented
3#23757009C212yesmaximal, complemented
4#23756997C211yesmaximal, characteristic
5#399×C157C211yesmaximal, characteristic
6#19097750—21no—
7#19097750C2212yes—
8#19097748—22no—
9#19097748—22no—
10C2×C22⋊Dic157—21no—
11#19097704—22no—
12#19097694—22no—
13C22⋊#11929434C2212yes—
14C2×C4⋊C4×C157—21no—
15C2×C4⋊C4×C157C2211yescharacteristic
16C2×C22⋊C4×C157—21no—
17C2×C22⋊C4×C157C2211yescharacteristic
18#95×C157C2211yescharacteristic
19C2×Dic314—21no—
20C2×Dic314D412yes—
21C22×Dic157—21no—
22C22×Dic157—21no—
23C2×#11929434—22no—
24C4⋊Dic157—21no—
25C4⋊Dic157D412yes—
26#14578933—22no—
27#14578933—22no—
28C22⋊Dic157—22no—
29C22⋊Dic157—22no—
30C24×C157D411yescharacteristic
31C22×C4×C157—21no—
32C22×C4×C157—21no—
33C22×C4×C157D411yescharacteristic
34C22×C4×C157C2311yescharacteristic
35C4⋊C4×C157—22no—
36C4⋊C4×C157—42no—
37C22⋊C4×C157—22no—
38C22⋊C4×C157—42no—
39Dic314—42no—
40Dic314—81no—
41C2×Dic157—22no—
42C2×Dic157—22no—
43C2×Dic157—81no—
44C2×Dic157—81no—
45#11929434—42no—
46C23×C157—21no—
47C23×C157—21no—
48C23×C157—41no—
49C23×C157—41no—
50C23×C157Q1612yes—
51C23×C157C2×D411yescharacteristic
52C2×C4×C157—22no—
53C2×C4×C157—21no—
54C2×C4×C157—41no—
55C2×C4×C157—41no—
56C2×C4×C157—41no—
57C2×C4×C157—41no—
58C2×C4×C157—41no—
59C2×C4×C157—41no—
60C2×C4×C157—41no—
61C2×C4×C157C2×D412yes—
62C22×C157—21no—
63C22×C157—21no—
64C22×C157—22no—
65C22×C157—42no—
66C22×C157—41no—
67C22×C157—41no—
68C22×C157—81no—
69C22×C157#12011yescharacteristic
70C22×C157C2×Q1611yescharacteristic
71C22×C157#13711yescharacteristic
72C4×C157—22no—
73C4×C157—42no—
74C4×C157—41no—
75C4×C157—81no—
76Dic157—42no—
77Dic157—42no—
78C2×C157—21no—
79C2×C157—21no—
80C2×C157—42no—
81C2×C157#45111yescharacteristic
82C2×C157#45311yescharacteristic
83C2×C157#45811yescharacteristic
84C157#161411yescharacteristic, complemented, Sylow
85#1614—1571nomaximal, Sylow
86#543—1571no—
87#484—1572no—
88#399D15711yescharacteristic
89#328—1572no—
90#323—1571no—
91C22⋊Q8—3142no—
92C22⋊Q8—3142no—
93C22⋊Q8—3141no—
94C22⋊Q8—1572no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4C2×D15711yescharacteristic
97C2×C22⋊C4—21no—
98C2×C22⋊C4—3141no—
99C2×C22⋊C4C2×D15711yescharacteristic
100#107—3142no—
101#103—3142no—
102C22⋊C8—1572no—
103#95C2×D15711yescharacteristic
104C24C22⋊D15711yescharacteristic
105C2×Q8—3141no—
106C2×Q8—1572no—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—3141no—
110C22×C4—3141no—
111C22×C4C22⋊D15711yescharacteristic
112C22×C4C22×D15711yescharacteristic
113C2×C8—3142no—
114C4⋊C4—22no—
115C4⋊C4—42no—
116C4⋊C4—3142no—
117C4⋊C4—3141no—
118C4⋊C4—3142no—
119C4⋊C4—1572no—
120C22⋊C4—22no—
121C22⋊C4—42no—
122C22⋊C4—3142no—
123C22⋊C4—3142no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23#1457894412yes—
129C23C2×C22⋊D15711yescharacteristic
130Q8—6282no—
131Q8—12561no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—3142no—
142C2×C4—3142no—
143C2×C4—12561no—
144C2×C4—12561no—
145C2×C4D4×D15712yes—
146C8—6282no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1909773911yescharacteristic
155C22C2×#1457894411yescharacteristic
156C22#1909780111yescharacteristic
157C4—22no—
158C4—42no—
159C4—41no—
160C4—81no—
161C4—6282no—
162C4—6282no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#2375742811yescharacteristic
167C2#2375744011yescharacteristic
168C2#2375746211yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#399×C157C2
socleC22×C157#120
prime radicalC24×C157D4
hypercenter#399D157
hypocenterC157#1614
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #23757608C2semidirect
3. #23757009C2semidirect
84. C157#1614semidirect

Maximal subgroups

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

subgroupindex
#237578992
#237576082
#237570092
#237569972
#399×C1572
#1614157