Finite Group Databasebeta

← #34101748

Subgroups — #34101748

Order 20096.

228 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 79 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×#19097777C211yesmaximal, characteristic
2C2×#19097710C211yesmaximal, characteristic, complemented
3C2×C16×D157C211yesmaximal, characteristic, complemented
4C22⋊#14578929C211yesmaximal, characteristic, complemented
5#23757052C211yesmaximal, characteristic, complemented
6#23757052C211yesmaximal, characteristic, complemented
7C22⋊C16×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C411yescharacteristic
9#19097777—22no—
10#19097777—22no—
11C2×#14578938C411yescharacteristic
12C2×#14578937C411yescharacteristic
13C2×#14578937C411yescharacteristic
14C2×C8×D157C2211yescharacteristic
15C2×C8×D157C2211yescharacteristic
16#19097710—22no—
17C2×#14578929C2211yescharacteristic
18C2×#14578929C2211yescharacteristic
19C16×D157—22no—
20C22×C8×C157C2211yescharacteristic
21C2×C16×C157C2211yescharacteristic
22C2×C16×C157C2211yescharacteristic
23#14578954—22no—
24#14578954—22no—
25C2×Dic314C811yescharacteristic
26C2×D628C811yescharacteristic
27C2×C22⋊D157C811yescharacteristic
28C2×C22⋊D157C811yescharacteristic
29C2×C4×D157C2×C411yescharacteristic
30C2×C4×D157C2×C411yescharacteristic
31#14578938—22no—
32#14578937—22no—
33#14578937—22no—
34C2×#11929434C2×C411yescharacteristic
35C2×#11929434C2×C411yescharacteristic
36C8×D157—21no—
37C8×D157—21no—
38C8×D157D412yes—
39C8×D157D412yes—
40#14578929—21no—
41#14578929—21no—
42C22×C4×C157C2×C411yescharacteristic
43C2×C8×C157—21no—
44C2×C8×C157—21no—
45C2×C8×C157C2×C411yescharacteristic
46C2×C8×C157C2311yescharacteristic
47C16×C157—21no—
48C16×C157—21no—
49C22×D157C2×C811yescharacteristic
50C22×D157C2×C811yescharacteristic
51Dic314—22no—
52D628—22no—
53C22⋊D157—22no—
54C22⋊D157—22no—
55C2×Dic157C2×C811yescharacteristic
56C2×Dic157C2×C811yescharacteristic
57C4×D157—21no—
58C4×D157—21no—
59C4×D157C22⋊C412yes—
60C4×D157M1612yes—
61#11929434—21no—
62#11929434C22⋊C412yes—
63C23×C157C2×C811yescharacteristic
64C2×C4×C157—21no—
65C2×C4×C157—21no—
66C2×C4×C157C2×C811yescharacteristic
67C2×C4×C157C22×C411yescharacteristic
68C8×C157—21no—
69C8×C157C2×D411yescharacteristic
70C8×C157C2×D411yescharacteristic
71C22×C157—21no—
72C22×C157—21no—
73C22×C157—21no—
74C22×C157C22×C811yescharacteristic
75C2×D157—21no—
76C2×D157—21no—
77C2×D157—21no—
78C2×D157—21no—
79C2×D157—21no—
80C2×D157C22⋊C812yes—
81C4×C157—21no—
82C4×C157C2×C22⋊C411yescharacteristic
83C4×C157C2×M1611yescharacteristic
84Dic157—21no—
85Dic157C22⋊C812yes—
86C2×C157—41no—
87C2×C157C2×C22⋊C811yescharacteristic
88C2×C157#50411yescharacteristic
89C2×C157#50411yescharacteristic
90D157—22no—
91D157—41no—
92C157#211311yescharacteristic, complemented, Sylow
93#2113—1571nomaximal, Sylow
94C2×#131—1571no—
95C2×M32—1571no—
96C22×C16—1571no—
97C22⋊C16—1571no—
98C22⋊C16—1571no—
99C22⋊C16—1571no—
100C22⋊C16D15711yescharacteristic, complemented
101C2×#41—1571no—
102#131—3142no—
103#131—3142no—
104C2×M16—1571no—
105C2×M16—1571no—
106C2×M16—1571no—
107C22×C8—1571no—
108C22×C8—1571no—
109C22×C8C2×D15711yescharacteristic
110M32—3142no—
111C2×C16—3142no—
112C2×C16—1571no—
113C2×C16—1571no—
114C2×C16C2×D15711yescharacteristic
115C2×C16C2×D15711yescharacteristic
116#41—3142no—
117#41—3142no—
118C2×Q8—1571no—
119C2×D4—1571no—
120C2×D4—1571no—
121C2×D4—1571no—
122C22×C4—1571no—
123C22×C4—1571no—
124C22×C4C4×D15711yescharacteristic
125M16—3142no—
126M16—3142no—
127M16—3142no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—3141no—
131C2×C8—3141no—
132C2×C8—1571no—
133C2×C8—1571no—
134C2×C8—1572no—
135C2×C8—1572no—
136C2×C8C4×D15711yescharacteristic
137C2×C8C22×D15711yescharacteristic
138C16—21no—
139C16—21no—
140C16—3141no—
141C16—3141no—
142C23—1571no—
143C23—1571no—
144C23C8×D15711yescharacteristic
145Q8—3142no—
146D4—3142no—
147D4—3142no—
148D4—3142no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—3141no—
152C2×C4—3141no—
153C2×C4—1571no—
154C2×C4—1571no—
155C2×C4—1572no—
156C2×C4—1572no—
157C2×C4C8×D15711yescharacteristic
158C2×C4C2×C4×D15711yescharacteristic
159C8—21no—
160C8—3141no—
161C8—1572no—
162C8D4×D15711yescharacteristic
163C8D4×D15711yescharacteristic
164C22—21no—
165C22—21no—
166C22—21no—
167C22—3141no—
168C22—3141no—
169C22—3141no—
170C22—3141no—
171C22—3141no—
172C22—1572no—
173C22C2×C8×D15711yescharacteristic
174C4—21no—
175C4—3141no—
176C4—1572no—
177C4C22⋊C4×D15711yescharacteristic
178C4M16×D15711yescharacteristic
179C2—41no—
180C2—3142no—
181C2—6281no—
182C2C22⋊C8×D15711yescharacteristic
183C2#2375768911yescharacteristic
184C2#2375769111yescharacteristic
subgroupG/H
center, FrattiniC2×C8C22×D157
commutator, socleC22×C157C22×C8
FittingC22⋊C16×C157C2
prime radicalC2×#14578954C4
cosocleC2×C8×C157C23
hypercenterC22⋊C16D157
hypocenterC157#2113
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C2×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#19097710C2semidirect
3. C2×C16×D157C2semidirect
4. C22⋊#14578929C2semidirect
5. #23757052C2semidirect
6. #23757052C2semidirect
7. C22⋊C16×C157C2semidirect
92. C157#2113semidirect
100. C22⋊C16D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977772
C2×#190977102
C2×C16×D1572
C22⋊#145789292
#237570522
C22⋊C16×C1572
#2113157