Finite Group Databasebeta

← C2×#22549665 #30640365

Subgroups — C2×#22549665 #30640365

Order 16256.

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

normal subgroups only

This group has 278 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
1C2×#16861190C211yesmaximal, characteristic
2C2×#16861126C211yesmaximal, characteristic
3#22549665C214yesmaximal, direct product factor
4C2×#99×C127C211yesmaximal, characteristic
5C23×Dic127C411yescharacteristic, complemented
6C2×#14523232—21no—
7#16861190—21no—
8#16861190—21no—
9#16861190C412yescomplemented
10#16861190C2212yes—
11C2×Dic127⋊C4—21no—
12C2×C22⋊Dic127—21no—
13C2×C22⋊Dic127C411yescharacteristic, complemented
14#16861126—21no—
15#16861126C2212yes—
16C22×D4×C127C2211yescharacteristic
17C2×C22⋊C4×C127—21no—
18#99×C127—21no—
19#99×C127C2212yes—
20C22×Dic127—21no—
21C22×Dic127—21no—
22C22×Dic127—21no—
23C22×Dic127—41no—
24C22×Dic127—41no—
25C22×Dic127C2×C412yescomplemented
26#14523232—22no—
27#14523232—41no—
28C2×C127⋊C8—41no—
29Dic127⋊C4—22no—
30Dic127⋊C4—22no—
31C22⋊Dic127—21no—
32C22⋊Dic127—22no—
33C22⋊Dic127—22no—
34C22⋊Dic127C2×C412yescomplemented
35C24×C127C2×C411yescharacteristic
36C24×C127D411yescharacteristic
37C2×D4×C127—41no—
38C2×D4×C127—41no—
39C2×D4×C127C2×C411yescharacteristic
40C2×D4×C127D411yescharacteristic
41C2×D4×C127D411yescharacteristic
42C2×D4×C127C2311yescharacteristic
43C22×C4×C127—41no—
44C22×C4×C127D411yescharacteristic
45C22⋊C4×C127—22no—
46C22⋊C4×C127—41no—
47C2×Dic127—22no—
48C2×Dic127—22no—
49C2×Dic127—42no—
50C2×Dic127—42no—
51C2×Dic127—41no—
52C2×Dic127—41no—
53C2×Dic127—42no—
54C127⋊C8—42no—
55C23×C127—21no—
56C23×C127—21no—
57C23×C127—21no—
58C23×C127—21no—
59C23×C127—42no—
60C23×C127—42no—
61C23×C127C22⋊C411yescharacteristic
62C23×C127C22⋊C411yescharacteristic
63C23×C127C22⋊C411yescharacteristic
64C23×C127C22×C411yescharacteristic
65C23×C127C2×D411yescharacteristic
66D4×C127—41no—
67D4×C127—41no—
68D4×C127—41no—
69D4×C127—41no—
70C2×C4×C127—21no—
71C2×C4×C127—21no—
72C2×C4×C127—42no—
73C2×C4×C127—82no—
74C2×C4×C127C22⋊C411yescharacteristic
75C2×C4×C127C2×D411yescharacteristic
76C22×C127—22no—
77C22×C127—21no—
78C22×C127—21no—
79C22×C127—21no—
80C22×C127—21no—
81C22×C127—41no—
82C22×C127—41no—
83C22×C127—41no—
84C22×C127—41no—
85C22×C127—42no—
86C22×C127—42no—
87C22×C127—42no—
88C22×C127—81no—
89C22×C127#9911yescharacteristic
90C22×C127#9911yescharacteristic
91C22×C127C2×C22⋊C411yescharacteristic
92C4×C127—21no—
93C4×C127—21no—
94C4×C127—82no—
95Dic127—42no—
96Dic127—42no—
97C2×C127—21no—
98C2×C127—21no—
99C2×C127—41no—
100C2×C127—41no—
101C2×C127—41no—
102C2×C127—41no—
103C2×C127#35212yescomplemented
104C2×C127C2×#9911yescharacteristic
105C2×#352—1271nomaximal, Sylow
106C127C2×#35211yescharacteristic, complemented, Sylow
107C2×#123—1271no—
108C2×#100—1271no—
109C2×#99D12711yescharacteristic
110#352—1274no—
111C22×D4C2×D12711yescharacteristic
112C23×C4—1271no—
113C2×M16—2541no—
114#123—1272no—
115#123—1272no—
116#123—2541no—
117#123—2541no—
118C2×C4⋊C4—2541no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4—1271no—
121C2×C22⋊C4—2541no—
122#100—1272no—
123#100—2541no—
124#99—21no—
125#99C2×D12712yes—
126C24C4×D12711yescharacteristic
127C24C22⋊D12711yescharacteristic
128C2×D4—41no—
129C2×D4—41no—
130C2×D4C4×D12711yescharacteristic
131C2×D4C22⋊D12711yescharacteristic
132C2×D4D50811yescharacteristic
133C2×D4C22×D12711yescharacteristic
134C22×C4—41no—
135C22×C4—1272no—
136C22×C4—5081no—
137C22×C4—5081no—
138C22×C4—2541no—
139C22×C4—2541no—
140C22×C4—2541no—
141C22×C4D50811yescharacteristic
142M16—5081no—
143M16—2542no—
144C2×C8—5081no—
145C4⋊C4—2542no—
146C4⋊C4—2542no—
147C22⋊C4—22no—
148C22⋊C4—41no—
149C22⋊C4—1272no—
150C22⋊C4—2541no—
151C22⋊C4—2542no—
152C22⋊C4—2542no—
153C23—21no—
154C23—21no—
155C23—21no—
156C23—21no—
157C23—42no—
158C23—42no—
159C23(C2×D127)⋊C411yescharacteristic
160C23(C2×D127)⋊C411yescharacteristic
161C23(C2×D127)⋊C411yescharacteristic
162C23C2×C4×D12711yescharacteristic
163C23C2×C22⋊D12711yescharacteristic
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—82no—
172C2×C4—5082no—
173C2×C4—5082no—
174C2×C4—5081no—
175C2×C4—5081no—
176C2×C4—5082no—
177C2×C4—2542no—
178C2×C4—2542no—
179C2×C4(C2×D127)⋊C411yescharacteristic
180C2×C4C2×D50811yescharacteristic
181C8—5082no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22#1686112311yescharacteristic
196C22#1686112311yescharacteristic
197C22C2×(C2×D127)⋊C411yescharacteristic
198C4—21no—
199C4—21no—
200C4—82no—
201C4—5082no—
202C4—5082no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—41no—
208C2—41no—
209C2#2254966512yesdirect product factor
210C2C2×#1686112311yescharacteristic
subgroupG/H
centerC22#16861123
commutatorC23×C127C22×C4
FrattiniC2×D4C22×D127
FittingC2×#99×C127C2
socleC22×C127#99
prime radicalC22×D4×C127C22
cosocleC2×D4×C127C23
hypercenterC2×#99D127
hypocenterC127C2×#352
LCSG ▷ C23×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #22549665C2direct (N × H)
5. C23×Dic127C4semidirect
9. #16861190C4semidirect
13. C2×C22⋊Dic127C4semidirect
25. C22×Dic127C2×C4semidirect
34. C22⋊Dic127C2×C4semidirect
103. C2×C127#352semidirect
106. C127C2×#352semidirect
209. C2#22549665direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611902
C2×#168611262
#225496652
C2×#99×C1272
C2×#352127