Finite Group Databasebeta

← C4×#16861123 #30638519

Subgroups — C4×#16861123 #30638519

Order 16256.

412 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 117 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×C4×C22⋊D127C211yesmaximal, characteristic
2C2×#16861123C212yesmaximal
3C4×C22⋊Dic127C211yesmaximal, characteristic, complemented
4#22549642C212yesmaximal, complemented
5C4×C22⋊C4×C127C211yesmaximal, characteristic, complemented
6C22×C22⋊D127C2211yescharacteristic
7C22×C4×D127C411yescharacteristic, complemented
8C4×C22⋊D127—21no—
9C4×C22⋊D127—21no—
10C4×C22⋊D127—21no—
11C4×C22⋊D127—21no—
12C2×Dic127⋊C4C411yescharacteristic, complemented
13C2×C22⋊Dic127C2211yescharacteristic
14C2×C22⋊Dic127C2212yes—
15C2×(C2×D127)⋊C4C411yescharacteristic, complemented
16C2×C4×Dic127—21no—
17C2×C4×Dic127C411yescharacteristic, complemented
18#16861123C418yesdirect product factor
19C127⋊#95—21no—
20C23×C4×C127C2211yescharacteristic
21C2×C22⋊C4×C127C2212yes—
22C2×C42×C127—21no—
23#95×C127—21no—
24C23×D127C2×C411yescharacteristic
25C2×C22⋊D127—21no—
26C2×C22⋊D127—21no—
27C2×C22⋊D127—22no—
28C2×C22⋊D127C2×C414yes—
29C22×Dic127—22no—
30C22×Dic127C2×C411yescharacteristic
31C22×Dic127C2×C411yescharacteristic
32C22×Dic127C2×C411yescharacteristic
33C2×C4×D127—21no—
34C2×C4×D127—21no—
35C2×C4×D127—42no—
36Dic127⋊C4—21no—
37Dic127⋊C4—21no—
38C22⋊Dic127—21no—
39C22⋊Dic127—21no—
40C22⋊Dic127—22no—
41C22⋊Dic127C2×C414yescomplemented
42(C2×D127)⋊C4—21no—
43(C2×D127)⋊C4—21no—
44C4×Dic127—21no—
45C4×Dic127—21no—
46C4×Dic127—42no—
47C24×C127C2311yescharacteristic
48C22×C4×C127—22no—
49C22×C4×C127—42no—
50C22×C4×C127C2×C411yescharacteristic
51C22×C4×C127C2×C411yescharacteristic
52C22×C4×C127D411yescharacteristic
53C22×C4×C127D411yescharacteristic
54C22×C4×C127D411yescharacteristic
55C22×C4×C127D411yescharacteristic
56C22⋊C4×C127—22no—
57C22⋊C4×C127C2×C414yescomplemented
58C42×C127—42no—
59C22×D127—21no—
60C22×D127—21no—
61C22×D127—41no—
62C22×D127—41no—
63C22×D127C4212yescomplemented
64C22⋊D127—24no—
65C22⋊D127—24no—
66C2×Dic127—21no—
67C2×Dic127—21no—
68C2×Dic127—21no—
69C2×Dic127—21no—
70C2×Dic127—24no—
71C2×Dic127—42no—
72C2×Dic127—42no—
73C2×Dic127—41no—
74C2×Dic127—41no—
75C2×Dic127C4212yescomplemented
76C4×D127—42no—
77C4×D127—42no—
78C23×C127—41no—
79C23×C127—41no—
80C23×C127C22×C411yescharacteristic
81C23×C127C22×C412yes—
82C23×C127C2×D411yescharacteristic
83C23×C127C2×D411yescharacteristic
84C23×C127#4112yes—
85C2×C4×C127—22no—
86C2×C4×C127—22no—
87C2×C4×C127—22no—
88C2×C4×C127—24no—
89C2×C4×C127—41no—
90C2×C4×C127—41no—
91C2×C4×C127—41no—
92C2×C4×C127—42no—
93C2×C4×C127—42no—
94C2×C4×C127C22⋊C411yescharacteristic
95C2×C4×C127C22⋊C411yescharacteristic
96C2×C4×C127C22⋊C411yescharacteristic
97C2×C4×C127C22⋊C411yescharacteristic
98C22×C127—21no—
99C22×C127—21no—
100C22×C127—21no—
101C22×C127—21no—
102C22×C127—21no—
103C22×C127—21no—
104C22×C127—42no—
105C22×C127—42no—
106C22×C127C2×C4211yescharacteristic
107C22×C127C2×C22⋊C411yescharacteristic
108C22×C127#11711yescharacteristic
109C22×C127C4×D412yes—
110C22×C127C4×D412yes—
111C2×D127—22no—
112C2×D127—42no—
113C2×D127—41no—
114C2×D127—41no—
115C2×D127—42no—
116C4×C127—21no—
117C4×C127—21no—
118C4×C127—21no—
119C4×C127—44no—
120C4×C127#9912yescomplemented
121Dic127—22no—
122Dic127—44no—
123Dic127—41no—
124Dic127—41no—
125C2×C127—22no—
126C2×C127—22no—
127C2×C127—21no—
128C2×C127—21no—
129C2×C127C4×C22⋊C411yescharacteristic
130C2×C127C2×#9911yescharacteristic
131C2×C127#41011yescharacteristic
132D127—42no—
133C4×#99—1271nomaximal, Sylow
134C127C4×#9911yescharacteristic, complemented, Sylow
135C2×C4×D4—1271no—
136C2×#99—1272no—
137C4×C22⋊C4—1271no—
138C4×C22⋊C4D12711yescharacteristic, complemented
139#342—1272no—
140C22×D4—1271no—
141C23×C4—1271no—
142C23×C4C2×D12711yescharacteristic
143C4×D4—2541no—
144C4×D4—2541no—
145C4×D4—2541no—
146C4×D4—2541no—
147C2×C4⋊C4—1271no—
148C2×C22⋊C4—1272no—
149C2×C22⋊C4—1271no—
150C2×C22⋊C4—1271no—
151C2×C22⋊C4C2×D12712yes—
152C2×C42—21no—
153C2×C42—1271no—
154C2×C42—2541no—
155#99—1278no—
156#95—21no—
157#95—2541no—
158C24—1271no—
159C24C22×D12711yescharacteristic
160C2×D4—1274no—
161C2×D4—2541no—
162C2×D4—2541no—
163C2×D4—2542no—
164C22×C4—22no—
165C22×C4—42no—
166C22×C4—1271no—
167C22×C4—1271no—
168C22×C4—1271no—
169C22×C4—5082no—
170C22×C4—2542no—
171C22×C4—2541no—
172C22×C4—2541no—
173C22×C4C4×D12711yescharacteristic
174C22×C4C4×D12711yescharacteristic
175C22×C4C22⋊D12711yescharacteristic
176C22×C4C22⋊D12711yescharacteristic
177C22×C4D50811yescharacteristic
178C22×C4D50811yescharacteristic
179C4⋊C4—2541no—
180C4⋊C4—2541no—
181C22⋊C4—22no—
182C22⋊C4—1274no—
183C22⋊C4—2541no—
184C22⋊C4—2541no—
185C22⋊C4—2542no—
186C22⋊C4—2541no—
187C22⋊C4—2541no—
188C22⋊C4C4×D12714yescomplemented
189C42—42no—
190C42—5082no—
191C42—2541no—
192C42—2541no—
193C23—41no—
194C23—41no—
195C23—1272no—
196C23—5081no—
197C23—5081no—
198C23—2541no—
199C23—2541no—
200C23C2×C4×D12711yescharacteristic
201C23C2×C4×D12712yes—
202C23C2×C22⋊D12711yescharacteristic
203C23C2×D50811yescharacteristic
204C23#1452324812yes—
205D4—2544no—
206D4—2544no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—24no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—1272no—
217C2×C4—5082no—
218C2×C4—5082no—
219C2×C4—5082no—
220C2×C4—5082no—
221C2×C4—5081no—
222C2×C4—5081no—
223C2×C4—2541no—
224C2×C4—2541no—
225C2×C4—2544no—
226C2×C4—2541no—
227C2×C4—2541no—
228C2×C4(C2×D127)⋊C411yescharacteristic
229C2×C4(C2×D127)⋊C411yescharacteristic
230C2×C4(C2×D127)⋊C411yescharacteristic
231C2×C4(C2×D127)⋊C411yescharacteristic
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—42no—
240C22—5082no—
241C22—5082no—
242C22—5081no—
243C22—5081no—
244C22—2542no—
245C22C42×D12711yescharacteristic
246C22C2×(C2×D127)⋊C411yescharacteristic
247C22#1686116611yescharacteristic
248C22C4×C22⋊D12712yes—
249C22C4×D50812yes—
250C4—21no—
251C4—21no—
252C4—21no—
253C4—44no—
254C4—5084no—
255C4—5081no—
256C4—5081no—
257C4—2542no—
258C4#1686112312yesdirect product factor
259C2—22no—
260C2—22no—
261C2—21no—
262C2—21no—
263C2—5082no—
264C2C4×(C2×D127)⋊C411yescharacteristic
265C2C2×#1686112311yescharacteristic
266C2#2254984911yescharacteristic
subgroupG/H
centerC2×C4(C2×D127)⋊C4
commutatorC22×C127C2×C42
FrattiniC24C22×D127
FittingC4×C22⋊C4×C127C2
socleC22×C127C2×C22⋊C4
prime radicalC22×C22⋊D127C22
cosocleC24×C127C23
hypercenterC4×C22⋊C4D127
hypocenterC127C4×#99
LCSG ▷ C22×C127 ▷ C2×C127 ▷ C127
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C4×C22⋊Dic127C2semidirect
4. #22549642C2semidirect
5. C4×C22⋊C4×C127C2semidirect
7. C22×C4×D127C4semidirect
12. C2×Dic127⋊C4C4semidirect
15. C2×(C2×D127)⋊C4C4semidirect
17. C2×C4×Dic127C4semidirect
18. #16861123C4direct (N × H)
41. C22⋊Dic127C2×C4semidirect
57. C22⋊C4×C127C2×C4semidirect
63. C22×D127C42semidirect
75. C2×Dic127C42semidirect
120. C4×C127#99semidirect
134. C127C4×#99semidirect
138. C4×C22⋊C4D127semidirect
188. C22⋊C4C4×D127semidirect
258. C4#16861123direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1272
C2×#168611232
C4×C22⋊Dic1272
#225496422
C4×C22⋊C4×C1272
C4×#99127