Finite Group Databasebeta

← C2×#22549664 #30640363

Subgroups — C2×#22549664 #30640363

Order 16256.

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

normal subgroups only

This group has 438 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×#16861177C211yesmaximal, characteristic
2C2×#16861124C211yesmaximal, characteristic, complemented
3#22549664C214yesmaximal, direct product factor
4C2×#100×C127C211yesmaximal, characteristic, complemented
5C24×D127C411yescharacteristic, complemented
6C22×C22⋊D127—21no—
7#16861177—21no—
8#16861177—21no—
9#16861177C412yescomplemented
10#16861177C2212yes—
11C2×C22⋊Dic127—21no—
12C2×C22⋊Dic127C411yescharacteristic, complemented
13C2×(C2×D127)⋊C4—21no—
14#16861124—21no—
15#16861124C2212yescomplemented
16C22×D4×C127C2211yescharacteristic
17C2×M16×C127—21no—
18#100×C127—21no—
19#100×C127C2212yescomplemented
20C23×D127—21no—
21C23×D127—21no—
22C23×D127—41no—
23C23×D127—41no—
24C23×D127—44no—
25C23×D127C2×C412yescomplemented
26C2×C22⋊D127—22no—
27C2×C22⋊D127—22no—
28C2×C22⋊D127—44no—
29C22×Dic127—21no—
30C22×Dic127—41no—
31C22⋊Dic127—21no—
32C22⋊Dic127—22no—
33C22⋊Dic127—41no—
34C22⋊Dic127C2×C412yescomplemented
35(C2×D127)⋊C4—22no—
36(C2×D127)⋊C4—22no—
37C24×C127C2×C411yescharacteristic
38C24×C127D411yescharacteristic
39C2×D4×C127—41no—
40C2×D4×C127—41no—
41C2×D4×C127C2×C411yescharacteristic
42C2×D4×C127D411yescharacteristic
43C2×D4×C127D411yescharacteristic
44C2×D4×C127C2311yescharacteristic
45C22×C4×C127D411yescharacteristic
46M16×C127—22no—
47M16×C127—41no—
48C2×C8×C127—41no—
49C22×D127—24no—
50C22×D127—22no—
51C22×D127—44no—
52C22×D127—44no—
53C22×D127—42no—
54C22×D127—42no—
55C22×D127—48no—
56C22×D127—44no—
57C22×D127—41no—
58C22×D127—41no—
59C22×D127—42no—
60C22×D127—44no—
61C22⋊D127—44no—
62C22⋊D127—44no—
63C2×Dic127—22no—
64C2×Dic127—42no—
65C2×Dic127—42no—
66C2×Dic127—82no—
67C23×C127—21no—
68C23×C127—21no—
69C23×C127—21no—
70C23×C127—21no—
71C23×C127—42no—
72C23×C127—42no—
73C23×C127C22⋊C411yescharacteristic
74C23×C127C22⋊C411yescharacteristic
75C23×C127C22⋊C411yescharacteristic
76C23×C127C22×C411yescharacteristic
77C23×C127C2×D411yescharacteristic
78D4×C127—41no—
79D4×C127—41no—
80D4×C127—41no—
81D4×C127—41no—
82C2×C4×C127—21no—
83C2×C4×C127—21no—
84C2×C4×C127C22⋊C411yescharacteristic
85C2×C4×C127C2×D411yescharacteristic
86C8×C127—42no—
87C22×C127—22no—
88C22×C127—21no—
89C22×C127—21no—
90C22×C127—21no—
91C22×C127—21no—
92C22×C127—41no—
93C22×C127—41no—
94C22×C127—41no—
95C22×C127—41no—
96C22×C127—42no—
97C22×C127—42no—
98C22×C127—42no—
99C22×C127—81no—
100C22×C127#9911yescharacteristic
101C22×C127#9911yescharacteristic
102C22×C127C2×C22⋊C411yescharacteristic
103C2×D127—24no—
104C2×D127—42no—
105C2×D127—44no—
106C2×D127—48no—
107C2×D127—44no—
108C2×D127—44no—
109C2×D127—42no—
110C2×D127—44no—
111C4×C127—21no—
112C4×C127—21no—
113Dic127—42no—
114Dic127—82no—
115C2×C127—21no—
116C2×C127—21no—
117C2×C127—41no—
118C2×C127—41no—
119C2×C127—41no—
120C2×C127—41no—
121C2×C127AΣL(1,𝔽16)12yescomplemented
122C2×C127C2×#9911yescharacteristic
123D127—44no—
124C2×AΣL(1,𝔽16)—1271nomaximal, Sylow
125C127C2×AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
126C2×#120—1271no—
127C2×#100D12711yescharacteristic, complemented
128C2×#99—1271no—
129AΣL(1,𝔽16)—1274no—
130C25—1271no—
131C22×D4—2541no—
132C22×D4C2×D12711yescharacteristic
133C2×M16—21no—
134#120—1272no—
135#120—1272no—
136#120—2541no—
137#120—2541no—
138C2×C22⋊C4—1271no—
139C2×C22⋊C4—2541no—
140C2×C22⋊C4—2541no—
141#100—21no—
142#100C2×D12712yescomplemented
143#99—1272no—
144#99—2541no—
145C24—1272no—
146C24—5081no—
147C24—5081no—
148C24—5084no—
149C24—2541no—
150C24—2541no—
151C24C4×D12711yescharacteristic
152C24D50811yescharacteristic
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—5084no—
156C2×D4—2542no—
157C2×D4—2542no—
158C2×D4C4×D12711yescharacteristic
159C2×D4C22⋊D12711yescharacteristic
160C2×D4D50811yescharacteristic
161C2×D4C22×D12711yescharacteristic
162C22×C4—5081no—
163C22×C4—2541no—
164C22×C4C22⋊D12711yescharacteristic
165M16—22no—
166M16—41no—
167C2×C8—41no—
168C22⋊C4—1272no—
169C22⋊C4—5081no—
170C22⋊C4—2542no—
171C22⋊C4—2541no—
172C22⋊C4—2542no—
173C22⋊C4—2542no—
174C23—21no—
175C23—21no—
176C23—21no—
177C23—21no—
178C23—42no—
179C23—42no—
180C23—5082no—
181C23—5082no—
182C23—5082no—
183C23—5084no—
184C23—5088no—
185C23—5084no—
186C23—5084no—
187C23—5084no—
188C23—5081no—
189C23—5081no—
190C23—2544no—
191C23—2542no—
192C23(C2×D127)⋊C411yescharacteristic
193C23(C2×D127)⋊C411yescharacteristic
194C23(C2×D127)⋊C411yescharacteristic
195C23C2×C4×D12711yescharacteristic
196C23C2×D50811yescharacteristic
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—5084no—
202D4—5084no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—10162no—
206C2×C4—5082no—
207C2×C4—5082no—
208C2×C4—2542no—
209C2×C4(C2×D127)⋊C411yescharacteristic
210C2×C4C2×C22⋊D12711yescharacteristic
211C8—42no—
212C22—22no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22—81no—
225C22—5082no—
226C22—5084no—
227C22—5084no—
228C22—5084no—
229C22—5088no—
230C22—5082no—
231C22—5084no—
232C22—2544no—
233C22#1686112311yescharacteristic
234C22#1686112311yescharacteristic
235C22C2×(C2×D127)⋊C411yescharacteristic
236C4—21no—
237C4—21no—
238C4—10162no—
239C4—5082no—
240C2—21no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2—41no—
245C2—41no—
246C2—5084no—
247C2#2254966412yesdirect product factor
248C2C2×#1686112311yescharacteristic
subgroupG/H
centerC22#16861123
commutatorC23×C127C22×C4
FrattiniC2×D4C22×D127
FittingC2×#100×C127C2
socleC22×C127#99
prime radicalC2×#16861177C2
cosocleC2×D4×C127C23
hypercenterC2×#100D127
hypocenterC127C2×AΣL(1,𝔽16)
LCSG ▷ C23×C127 ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. C2×#16861124C2semidirect
3. #22549664C2direct (N × H)
4. C2×#100×C127C2semidirect
5. C24×D127C4semidirect
9. #16861177C4semidirect
12. C2×C22⋊Dic127C4semidirect
15. #16861124C22semidirect
19. #100×C127C22semidirect
25. C23×D127C2×C4semidirect
34. C22⋊Dic127C2×C4semidirect
121. C2×C127AΣL(1,𝔽16)semidirect
125. C127C2×AΣL(1,𝔽16)semidirect
127. C2×#100D127semidirect
142. #100C2×D127semidirect
247. C2#22549664direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168611772
C2×#168611242
#225496642
C2×#100×C1272
C2×AΣL(1,𝔽16)127