Finite Group Databasebeta

← C4×#15692169 #27170921

Subgroups — C4×#15692169 #27170921

Order 12928.

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⋊D101C211yesmaximal, characteristic
2C2×#15692169C212yesmaximal
3C4×C22⋊Dic101C211yesmaximal, characteristic, complemented
4#20264943C212yesmaximal, complemented
5C4×C22⋊C4×C101C211yesmaximal, characteristic, complemented
6C22×C22⋊D101C2211yescharacteristic
7C22×C4×D101C411yescharacteristic, complemented
8C4×C22⋊D101—21no—
9C4×C22⋊D101—21no—
10C4×C22⋊D101—21no—
11C4×C22⋊D101—21no—
12C2×#13108053C411yescharacteristic, complemented
13C2×C22⋊Dic101C2211yescharacteristic
14C2×C22⋊Dic101C2212yes—
15C2×#13108051C411yescharacteristic, complemented
16C2×C4×Dic101—21no—
17C2×C4×Dic101C411yescharacteristic, complemented
18#15692169C418yesdirect product factor
19#15692162—21no—
20C23×C4×C101C2211yescharacteristic
21C2×C22⋊C4×C101C2212yes—
22C2×C42×C101—21no—
23#95×C101—21no—
24C23×D101C2×C411yescharacteristic
25C2×C22⋊D101—21no—
26C2×C22⋊D101—21no—
27C2×C22⋊D101—22no—
28C2×C22⋊D101C2×C414yes—
29C22×Dic101—22no—
30C22×Dic101C2×C411yescharacteristic
31C22×Dic101C2×C411yescharacteristic
32C22×Dic101C2×C411yescharacteristic
33C2×C4×D101—21no—
34C2×C4×D101—21no—
35C2×C4×D101—42no—
36#13108053—21no—
37#13108053—21no—
38C22⋊Dic101—21no—
39C22⋊Dic101—21no—
40C22⋊Dic101—22no—
41C22⋊Dic101C2×C414yescomplemented
42#13108051—21no—
43#13108051—21no—
44C4×Dic101—21no—
45C4×Dic101—21no—
46C4×Dic101—42no—
47C24×C101C2311yescharacteristic
48C22×C4×C101—22no—
49C22×C4×C101—42no—
50C22×C4×C101C2×C411yescharacteristic
51C22×C4×C101C2×C411yescharacteristic
52C22×C4×C101D411yescharacteristic
53C22×C4×C101D411yescharacteristic
54C22×C4×C101D411yescharacteristic
55C22×C4×C101D411yescharacteristic
56C22⋊C4×C101—22no—
57C22⋊C4×C101C2×C414yescomplemented
58C42×C101—42no—
59C23×C101—41no—
60C23×C101—41no—
61C23×C101C22×C411yescharacteristic
62C23×C101C22×C412yes—
63C23×C101C2×D411yescharacteristic
64C23×C101C2×D411yescharacteristic
65C23×C101#4112yes—
66C22×D101—21no—
67C22×D101—21no—
68C22×D101—41no—
69C22×D101—41no—
70C22×D101C4212yescomplemented
71C2×C4×C101—22no—
72C2×C4×C101—22no—
73C2×C4×C101—22no—
74C2×C4×C101—24no—
75C2×C4×C101—41no—
76C2×C4×C101—41no—
77C2×C4×C101—41no—
78C2×C4×C101—42no—
79C2×C4×C101—42no—
80C2×C4×C101C22⋊C411yescharacteristic
81C2×C4×C101C22⋊C411yescharacteristic
82C2×C4×C101C22⋊C411yescharacteristic
83C2×C4×C101C22⋊C411yescharacteristic
84C22⋊D101—24no—
85C22⋊D101—24no—
86C2×Dic101—21no—
87C2×Dic101—21no—
88C2×Dic101—21no—
89C2×Dic101—21no—
90C2×Dic101—24no—
91C2×Dic101—42no—
92C2×Dic101—42no—
93C2×Dic101—41no—
94C2×Dic101—41no—
95C2×Dic101C4212yescomplemented
96C4×D101—42no—
97C4×D101—42no—
98C22×C101—21no—
99C22×C101—21no—
100C22×C101—21no—
101C22×C101—21no—
102C22×C101—21no—
103C22×C101—21no—
104C22×C101—42no—
105C22×C101—42no—
106C22×C101C2×C4211yescharacteristic
107C22×C101C2×C22⋊C411yescharacteristic
108C22×C101#11711yescharacteristic
109C22×C101C4×D412yes—
110C22×C101C4×D412yes—
111C2×D101—22no—
112C2×D101—42no—
113C2×D101—41no—
114C2×D101—41no—
115C2×D101—42no—
116C4×C101—21no—
117C4×C101—21no—
118C4×C101—21no—
119C4×C101—44no—
120C4×C101#9912yescomplemented
121Dic101—22no—
122Dic101—44no—
123Dic101—41no—
124Dic101—41no—
125C2×C101—22no—
126C2×C101—22no—
127C2×C101—21no—
128C2×C101—21no—
129C2×C101C4×C22⋊C411yescharacteristic
130C2×C101C2×#9911yescharacteristic
131C2×C101#41011yescharacteristic
132D101—42no—
133C4×#99—1011nomaximal, Sylow
134C101C4×#9911yescharacteristic, complemented, Sylow
135C2×C4×D4—1011no—
136C2×#99—1012no—
137C4×C22⋊C4—1011no—
138C4×C22⋊C4D10111yescharacteristic, complemented
139#342—1012no—
140C22×D4—1011no—
141C23×C4—1011no—
142C23×C4C2×D10111yescharacteristic
143C4×D4—2021no—
144C4×D4—2021no—
145C4×D4—2021no—
146C4×D4—2021no—
147C2×C4⋊C4—1011no—
148C2×C22⋊C4—1012no—
149C2×C22⋊C4—1011no—
150C2×C22⋊C4—1011no—
151C2×C22⋊C4C2×D10112yes—
152C2×C42—21no—
153C2×C42—1011no—
154C2×C42—2021no—
155#99—1018no—
156#95—21no—
157#95—2021no—
158C24—1011no—
159C24C22×D10111yescharacteristic
160C2×D4—1014no—
161C2×D4—2021no—
162C2×D4—2021no—
163C2×D4—2022no—
164C22×C4—22no—
165C22×C4—42no—
166C22×C4—1011no—
167C22×C4—1011no—
168C22×C4—1011no—
169C22×C4—4042no—
170C22×C4—2022no—
171C22×C4—2021no—
172C22×C4—2021no—
173C22×C4C4×D10111yescharacteristic
174C22×C4C4×D10111yescharacteristic
175C22×C4D40411yescharacteristic
176C22×C4D40411yescharacteristic
177C22×C4C22⋊D10111yescharacteristic
178C22×C4C22⋊D10111yescharacteristic
179C4⋊C4—2021no—
180C4⋊C4—2021no—
181C22⋊C4—22no—
182C22⋊C4—1014no—
183C22⋊C4—2021no—
184C22⋊C4—2021no—
185C22⋊C4—2022no—
186C22⋊C4—2021no—
187C22⋊C4—2021no—
188C22⋊C4C4×D10114yescomplemented
189C42—42no—
190C42—4042no—
191C42—2021no—
192C42—2021no—
193C23—41no—
194C23—41no—
195C23—1012no—
196C23—4041no—
197C23—4041no—
198C23—2021no—
199C23—2021no—
200C23C2×C4×D10111yescharacteristic
201C23C2×C4×D10112yes—
202C23C2×C22⋊D10111yescharacteristic
203C23C2×D40411yescharacteristic
204C23#1310807412yes—
205D4—2024no—
206D4—2024no—
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—1012no—
217C2×C4—4042no—
218C2×C4—4042no—
219C2×C4—4042no—
220C2×C4—4042no—
221C2×C4—4041no—
222C2×C4—4041no—
223C2×C4—2021no—
224C2×C4—2021no—
225C2×C4—2024no—
226C2×C4—2021no—
227C2×C4—2021no—
228C2×C4#1310805111yescharacteristic
229C2×C4#1310805111yescharacteristic
230C2×C4#1310805111yescharacteristic
231C2×C4#1310805111yescharacteristic
232C22—21no—
233C22—21no—
234C22—21no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—42no—
240C22—4042no—
241C22—4042no—
242C22—4041no—
243C22—4041no—
244C22—2022no—
245C22C42×D10111yescharacteristic
246C22C2×#1310805111yescharacteristic
247C22#1569221211yescharacteristic
248C22C4×C22⋊D10112yes—
249C22C4×D40412yes—
250C4—21no—
251C4—21no—
252C4—21no—
253C4—44no—
254C4—4044no—
255C4—4041no—
256C4—4041no—
257C4—2022no—
258C4#1569216912yesdirect product factor
259C2—22no—
260C2—22no—
261C2—21no—
262C2—21no—
263C2—4042no—
264C2C4×#1310805111yescharacteristic
265C2C2×#1569216911yescharacteristic
266C2#2026515011yescharacteristic
subgroupG/H
centerC2×C4#13108051
commutatorC22×C101C2×C42
FrattiniC24C22×D101
FittingC4×C22⋊C4×C101C2
socleC22×C101C2×C22⋊C4
prime radicalC22×C22⋊D101C22
cosocleC24×C101C23
hypercenterC4×C22⋊C4D101
hypocenterC101C4×#99
LCSG ▷ C22×C101 ▷ C2×C101 ▷ C101
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⋊Dic101C2semidirect
4. #20264943C2semidirect
5. C4×C22⋊C4×C101C2semidirect
7. C22×C4×D101C4semidirect
12. C2×#13108053C4semidirect
15. C2×#13108051C4semidirect
17. C2×C4×Dic101C4semidirect
18. #15692169C4direct (N × H)
41. C22⋊Dic101C2×C4semidirect
57. C22⋊C4×C101C2×C4semidirect
70. C22×D101C42semidirect
95. C2×Dic101C42semidirect
120. C4×C101#99semidirect
134. C101C4×#99semidirect
138. C4×C22⋊C4D101semidirect
188. C22⋊C4C4×D101semidirect
258. C4#15692169direct (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⋊D1012
C2×#156921692
C4×C22⋊Dic1012
#202649432
C4×C22⋊C4×C1012
C4×#99101