Finite Group Databasebeta

← #30639394

Subgroups — #30639394

Order 16256.

232 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 81 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#22549918C211yesmaximal, characteristic, complemented
2#22549881C211yesmaximal, characteristic
3C2×#16861130C211yesmaximal, characteristic
4#22549834C211yesmaximal, characteristic, complemented
5#22549644C211yesmaximal, characteristic, complemented
6#22549640C211yesmaximal, characteristic, complemented
7C2×#100×C127C211yesmaximal, characteristic
8C2×#14523232C2211yescharacteristic
9C22×C127⋊C8C2211yescharacteristic
10#16861168C2211yescharacteristic
11C2×C4⋊Dic127C2211yescharacteristic
12#16861143—21no—
13#16861141—21no—
14#16861130—21no—
15#16861130—21no—
16#16861130—21no—
17#16861130—21no—
18#16861119—21no—
19C8×Dic127—21no—
20C22×D4×C127C2211yescharacteristic
21C2×M16×C127C2211yescharacteristic
22C2×M16×C127C2211yescharacteristic
23#100×C127C414yescomplemented
24C22×Dic127—21no—
25#14523232—21no—
26#14523232—21no—
27C2×C127⋊C8—21no—
28C2×C127⋊C8—21no—
29C2×C127⋊C8—21no—
30C2×C127⋊C8D411yescharacteristic
31C2×C127⋊C8D411yescharacteristic
32C4⋊Dic127—21no—
33C4⋊Dic127—21no—
34C4⋊Dic127D411yescharacteristic
35C4⋊Dic127D411yescharacteristic
36C22⋊Dic127—21no—
37C4×Dic127—21no—
38C24×C127—21no—
39C2×D4×C127—21no—
40C2×D4×C127—21no—
41C2×D4×C127—21no—
42C2×D4×C127—21no—
43C2×D4×C127—21no—
44C2×D4×C127C2×C412yes—
45C22×C4×C127C2311yescharacteristic
46M16×C127—21no—
47M16×C127—21no—
48M16×C127C2×C412yes—
49M16×C127C2×C412yes—
50C2×C8×C127—21no—
51C2×C8×C127—21no—
52C2×Dic127—21no—
53C2×Dic127—21no—
54C2×Dic127—41no—
55C2×Dic127—81no—
56C127⋊C8—21no—
57C127⋊C8—21no—
58C127⋊C8—41no—
59C23×C127—22no—
60C23×C127—41no—
61C23×C127—41no—
62C23×C127—81no—
63C23×C127—81no—
64C23×C127#4111yescharacteristic
65D4×C127—22no—
66D4×C127—22no—
67D4×C127—41no—
68D4×C127—41no—
69C2×C4×C127C22×C411yescharacteristic
70C2×C4×C127C2×D411yescharacteristic
71C2×C4×C127C2×D411yescharacteristic
72C2×C4×C127#4111yescharacteristic
73C2×C4×C127#4111yescharacteristic
74C2×C4×C127#4111yescharacteristic
75C8×C127—22no—
76C8×C127—22no—
77C22×C127—21no—
78C22×C127—21no—
79C22×C127—42no—
80C22×C127—82no—
81C22×C127—82no—
82C22×C127—81no—
83C22×C127—81no—
84C22×C127#11711yescharacteristic
85C22×C127#12111yescharacteristic
86C22×C127#12611yescharacteristic
87C4×C127C4×D411yescharacteristic
88C4×C127C4×D411yescharacteristic
89C4×C127#12311yescharacteristic
90C4×C127#12411yescharacteristic
91Dic127—41no—
92Dic127—41no—
93Dic127—81no—
94C2×C127—21no—
95C2×C127—21no—
96C2×C127—82no—
97C2×C127#38811yescharacteristic
98C2×C127#47111yescharacteristic
99C2×C127#47211yescharacteristic
100#1931—1271nomaximal, Sylow
101C127#193111yescharacteristic, complemented, Sylow
102#428—1271no—
103#418—1271no—
104C2×#102—1271no—
105C2×#100D12711yescharacteristic
106#405—1271no—
107#343—1271no—
108#341—1271no—
109C22×D4C2×D12711yescharacteristic
110C2×M16—1271no—
111C2×M16C2×D12711yescharacteristic
112C2×M16C2×D12711yescharacteristic
113C22×C8—1271no—
114#117—1271no—
115C2×C4⋊C4—1271no—
116#107—2541no—
117#106—2541no—
118#102—2541no—
119#102—2541no—
120#102—2541no—
121#102—2541no—
122#100Dic12714yescomplemented
123#97—2541no—
124C4×C8—2541no—
125C24—21no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4C2×Dic12712yes—
132C22×C4—2541no—
133C22×C4C22×D12711yescharacteristic
134M16—21no—
135M16—21no—
136M16—2541no—
137M16—2541no—
138M16C2×Dic12712yes—
139M16C2×Dic12712yes—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—1271no—
143C2×C8—1271no—
144C2×C8—2541no—
145C2×C8—2541no—
146C2×C8—2541no—
147C4⋊C4—1271no—
148C4⋊C4—1271no—
149C4⋊C4—2541no—
150C4⋊C4—2541no—
151C22⋊C4—2541no—
152C42—2541no—
153C23—22no—
154C23—41no—
155C23—41no—
156C23—81no—
157C23—81no—
158C23#1452324811yescharacteristic
159D4—22no—
160D4—22no—
161D4—41no—
162D4—41no—
163C2×C4—10161no—
164C2×C4—5081no—
165C2×C4—2541no—
166C2×C4—2541no—
167C2×C4C22×Dic12711yescharacteristic
168C2×C4D4×D12711yescharacteristic
169C2×C4D4×D12711yescharacteristic
170C2×C4#1452324711yescharacteristic
171C2×C4#1452324711yescharacteristic
172C2×C4#1452324811yescharacteristic
173C8—22no—
174C8—22no—
175C8—5081no—
176C8—2541no—
177C8—2541no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—82no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22#1686116811yescharacteristic
186C22#1686118211yescharacteristic
187C22#1686120211yescharacteristic
188C4—10161no—
189C4—5081no—
190C4—5081no—
191C4D4×Dic12711yescharacteristic
192C4D4×Dic12711yescharacteristic
193C4#1686119111yescharacteristic
194C4#1686119511yescharacteristic
195C2—21no—
196C2—21no—
197C2—82no—
198C2#2254976911yescharacteristic
199C2#2255013811yescharacteristic
200C2#2255014511yescharacteristic
subgroupG/H
centerC22#16861182
commutatorC2×C4×C127C22×C4
FrattiniC22×C4C22×D127
FittingC2×#100×C127C2
socleC22×C127#121
prime radicalC22×D4×C127C22
cosocleC22×C4×C127C23
hypercenterC2×#100D127
hypocenterC127#1931
LCSG ▷ C2×C4×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. #22549918C2semidirect
4. #22549834C2semidirect
5. #22549644C2semidirect
6. #22549640C2semidirect
23. #100×C127C4semidirect
101. C127#1931semidirect
122. #100Dic127semidirect

Maximal subgroups

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

subgroupindex
#225499182
#225498812
C2×#168611302
#225498342
#225496442
#225496402
C2×#100×C1272
#1931127