Finite Group Databasebeta

← #30637305

Subgroups — #30637305

Order 16256.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#22550410C211yesmaximal, characteristic
2#22549929C211yesmaximal, characteristic, complemented
3#22549612C212yesmaximal, complemented
4#22549609C212yesmaximal
5#383×C127C211yesmaximal, characteristic, complemented
6#16861203—21no—
7#16861201C411yescharacteristic, complemented
8#16861197C411yescharacteristic, complemented
9#16861192—21no—
10#16861188C2211yescharacteristic
11#16861183C2211yescharacteristic
12C4×Dic254C411yescharacteristic, complemented
13C4×D508C411yescharacteristic, complemented
14C4×C22⋊D127—21no—
15#16861166—21no—
16C4⋊(C127⋊C8)—21no—
17C22⋊(C127⋊C8)C2212yes—
18C4×C127⋊C8—21no—
19C2×C42×C127C2211yescharacteristic
20#95×C127—21no—
21#95×C127—21no—
22#95×C127C2212yes—
23C2×Dic254C2×C411yescharacteristic
24C2×D508C2×C411yescharacteristic
25C2×C22⋊D127—21no—
26C2×C4×D127—21no—
27C2×C127⋊C8—22no—
28C4⋊Dic127C2×C411yescharacteristic
29C4⋊Dic127C2×C411yescharacteristic
30Dic127⋊C4—21no—
31Dic127⋊C4—21no—
32Dic127⋊C4—21no—
33Dic127⋊C4—21no—
34C22⋊Dic127—21no—
35(C2×D127)⋊C4—21no—
36(C2×D127)⋊C4—21no—
37(C2×D127)⋊C4—21no—
38(C2×D127)⋊C4—21no—
39C4×Dic127—21no—
40C22×C4×C127—22no—
41C22×C4×C127D411yescharacteristic
42C22×C4×C127D411yescharacteristic
43C22×C4×C127C2311yescharacteristic
44C42×C127C2×C411yescharacteristic
45C42×C127C2×C411yescharacteristic
46C42×C127D411yescharacteristic
47C42×C127D411yescharacteristic
48C22×D127—21no—
49Dic254—41no—
50D508—41no—
51C22⋊D127—42no—
52C2×Dic127—21no—
53C2×Dic127—21no—
54C2×Dic127—21no—
55C4×D127—42no—
56C127⋊C8—42no—
57C23×C127C2×D411yescharacteristic
58C2×C4×C127—22no—
59C2×C4×C127—41no—
60C2×C4×C127—41no—
61C2×C4×C127—42no—
62C2×C4×C127—42no—
63C2×C4×C127—42no—
64C2×C4×C127C22⋊C411yescharacteristic
65C2×C4×C127C22⋊C411yescharacteristic
66C2×C4×C127C22⋊C411yescharacteristic
67C2×C4×C127C22⋊C411yescharacteristic
68C2×C4×C127C22×C411yescharacteristic
69C2×C4×C127C2×D411yescharacteristic
70C22×C127—21no—
71C22×C127—21no—
72C22×C127C2×C22⋊C411yescharacteristic
73C22×C127#13512yes—
74C2×D127—41no—
75C2×D127—41no—
76C2×D127—41no—
77C4×C127—21no—
78C4×C127—21no—
79C4×C127—21no—
80C4×C127—21no—
81C4×C127—21no—
82C4×C127—21no—
83C4×C127—82no—
84Dic127—41no—
85Dic127—41no—
86Dic127—41no—
87C2×C127—22no—
88C2×C127#41011yescharacteristic
89C2×C127#41611yescharacteristic
90C2×C127#42111yescharacteristic
91D127—81no—
92#1521—1271nomaximal, Sylow
93C127#152111yescharacteristic, complemented, Sylow
94#529—1271no—
95#431—1271no—
96#383D12711yescharacteristic, complemented
97#328—1272no—
98#327—1272no—
99#126—2541no—
100#125—1271no—
101#124—1271no—
102#123—2541no—
103C22⋊Q8—1271no—
104#121—1271no—
105C4×Q8—1271no—
106C4×D4—1271no—
107C4×D4—2541no—
108#117—2541no—
109C2×C42C2×D12711yescharacteristic
110C4⋊C8—2541no—
111C22⋊C8—1272no—
112C4×C8—2541no—
113#95—21no—
114#95—21no—
115#95C2×D12712yes—
116C2×Q8—1271no—
117C2×D4—1271no—
118C2×D4—2541no—
119C22×C4—22no—
120C22×C4—2541no—
121C22×C4C22⋊D12711yescharacteristic
122C22×C4C22⋊D12711yescharacteristic
123C22×C4C22×D12711yescharacteristic
124C2×C8—2542no—
125C4⋊C4—1271no—
126C4⋊C4—1271no—
127C4⋊C4—2541no—
128C4⋊C4—2541no—
129C4⋊C4—2541no—
130C4⋊C4—2541no—
131C22⋊C4—2541no—
132C22⋊C4—2541no—
133C22⋊C4—2541no—
134C22⋊C4—2541no—
135C22⋊C4—2541no—
136C42—2541no—
137C42C4×D12711yescharacteristic
138C42C4×D12711yescharacteristic
139C42D50811yescharacteristic
140C42D50811yescharacteristic
141C23—2541no—
142C23C2×C22⋊D12711yescharacteristic
143Q8—5081no—
144D4—5081no—
145D4—5082no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—5082no—
153C2×C4—2541no—
154C2×C4—2541no—
155C2×C4—2541no—
156C2×C4(C2×D127)⋊C411yescharacteristic
157C2×C4(C2×D127)⋊C411yescharacteristic
158C2×C4(C2×D127)⋊C411yescharacteristic
159C2×C4(C2×D127)⋊C411yescharacteristic
160C2×C4C2×C4×D12711yescharacteristic
161C2×C4C2×D50811yescharacteristic
162C8—5082no—
163C22—21no—
164C22—21no—
165C22—5081no—
166C22—5081no—
167C22—5081no—
168C22C2×(C2×D127)⋊C411yescharacteristic
169C22#1686122912yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—5081no—
178C4—5081no—
179C4—5081no—
180C2—22no—
181C2—10161no—
182C2#2254984911yescharacteristic
183C2#2254987011yescharacteristic
184C2#2254989411yescharacteristic
subgroupG/H
centerC22C2×(C2×D127)⋊C4
commutatorC2×C4×C127C22×C4
FrattiniC22×C4C22×D127
Fitting#383×C127C2
socleC22×C127C2×C22⋊C4
prime radical#16861183C22
cosocleC22×C4×C127C23
hypercenter#383D127
hypocenterC127#1521
LCSG ▷ C2×C4×C127 ▷ C22×C127 ▷ C127
UCSC1 ◁ C22 ◁ C2×C42 ◁ #383

Complements

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

NH ≅ G/Ntype
2. #22549929C2semidirect
3. #22549612C2semidirect
5. #383×C127C2semidirect
7. #16861201C4semidirect
8. #16861197C4semidirect
12. C4×Dic254C4semidirect
13. C4×D508C4semidirect
93. C127#1521semidirect
96. #383D127semidirect

Maximal subgroups

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

subgroupindex
#225504102
#225499292
#225496122
#225496092
#383×C1272
#1521127