Finite Group Databasebeta

← C4×#10622180 #14668951

Subgroups — C4×#10622180 #14668951

Order 2816.

532 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10622180C212yesmaximal
2C4×#66900C212yesmaximal, complemented
3#13066743C212yesmaximal, complemented
4C4×C11×#124C211yesmaximal, characteristic
5C2×C11×#124C2211yescharacteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C4×D4×C11C411yescharacteristic
8C11×#391C2211yescharacteristic
9C11×#390C411yescharacteristic
10C11×#388—22no—
11C11×#382C411yescharacteristic
12C4×C11×C22⋊C4—22no—
13C43×C11C411yescharacteristic
14C2×#66900C2214yes—
15C4×#4318—22no—
16#10622180C418yesdirect product factor
17#10622168—22no—
18C22×Q8×C11C2311yescharacteristic
19C22×D4×C11C2×C411yescharacteristic
20C23×C4×C11—21no—
21C11×#124—22no—
22C11×#124C2×C414yes—
23C4×Q8×C11—41no—
24C4×Q8×C11—41no—
25C4×D4×C11—41no—
26C4×D4×C11—41no—
27C2×C11×C4⋊C4C2×C411yescharacteristic
28C2×C11×C4⋊C4C2×C411yescharacteristic
29C2×C11×C4⋊C4D412yes—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—21no—
33C2×C42×C11—21no—
34C2×C42×C11—21no—
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11D412yes—
39C2×#4318—24no—
40C11×#95—22no—
41C11×#95—22no—
42#66900—24no—
43#66900C2×C418yescomplemented
44#66867—42no—
45C4×C11⋊C8—42no—
46C4×#355—111nomaximal, Sylow
47C24×C11—21no—
48C2×Q8×C11—41no—
49C2×Q8×C11—41no—
50C2×Q8×C11C22×C412yes—
51C2×Q8×C11#4112yes—
52C2×D4×C11—21no—
53C2×D4×C11—41no—
54C2×D4×C11—41no—
55C2×D4×C11C4212yes—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—44no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22⋊C412yes—
64C22×C4×C11C22⋊C411yescharacteristic
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D412yes—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—42no—
69C11×C4⋊C4—41no—
70C11×C22⋊C4—28no—
71C11×C22⋊C4—44no—
72C11×C22⋊C4—42no—
73C42×C11—22no—
74C42×C11—22no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—42no—
79C42×C11—42no—
80C42×C11—41no—
81C42×C11C4212yes—
82#4318—28no—
83#4318—44no—
84C2×C11⋊C8—44no—
85C4×#124D1111yescharacteristic
86C2×#355—112no—
87C4×#101—112no—
88#1394—112no—
89C23×C11—22no—
90C23×C11—42no—
91C23×C11—42no—
92C23×C11—41no—
93C23×C11—41no—
94C23×C11C2×C22⋊C411yescharacteristic
95Q8×C11—42no—
96Q8×C11—42no—
97D4×C11—42no—
98D4×C11—42no—
99C2×C4×C11—22no—
100C2×C4×C11—21no—
101C2×C4×C11—22no—
102C2×C4×C11—21no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11—21no—
107C2×C4×C11—22no—
108C2×C4×C11—41no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—41no—
116C2×C4×C11—82no—
117C2×C4×C11—82no—
118C2×C4×C11#9911yescharacteristic
119C2×C4×C11#9911yescharacteristic
120C2×C4×C11C2×C4211yescharacteristic
121C2×C4×C11#11711yescharacteristic
122C2×C4×C11C4×D414yes—
123C11⋊C8—48no—
124C2×#124C2×D1111yescharacteristic
125C2×C4×Q8C2×D1111yescharacteristic
126C2×C4×D4Dic1111yescharacteristic
127C2×#101—114no—
128C4×M16—222no—
129#391C2×D1111yescharacteristic
130#390Dic1111yescharacteristic
131#388—22no—
132#382Dic1111yescharacteristic
133C4×C22⋊C4—22no—
134C43Dic1111yescharacteristic
135#355—118no—
136#343—222no—
137C22×C11—21no—
138C22×C11—21no—
139C22×C11—44no—
140C22×C11—42no—
141C22×C11—82no—
142C22×C11—81no—
143C22×C11—81no—
144C22×C11C4×C22⋊C411yescharacteristic
145C22×C11C2×#9911yescharacteristic
146C22×C11#41011yescharacteristic
147C4×C11—21no—
148C4×C11—21no—
149C4×C11—21no—
150C4×C11—24no—
151C4×C11—42no—
152C4×C11—42no—
153C4×C11—41no—
154C4×C11—42no—
155C4×C11—81no—
156C4×C11#35512yescomplemented
157C22×Q8C22×D1111yescharacteristic
158C22×D4C2×Dic1111yescharacteristic
159C23×C4—21no—
160C2×M16—224no—
161#124—22no—
162#124C4×D1114yes—
163C4×Q8—41no—
164C4×Q8—41no—
165C4×D4—41no—
166C4×D4—41no—
167C2×C4⋊C4C2×Dic1111yescharacteristic
168C2×C4⋊C4C2×Dic1111yescharacteristic
169C2×C4⋊C4C22⋊D1112yes—
170C2×C22⋊C4—22no—
171C2×C22⋊C4—21no—
172C2×C22⋊C4—22no—
173C2×C42—21no—
174C2×C42—21no—
175C2×C42C2×Dic1111yescharacteristic
176C2×C42C2×Dic1111yescharacteristic
177C2×C42C2×Dic1111yescharacteristic
178C2×C42C22⋊D1112yes—
179#101—118no—
180#101—224no—
181#97—442no—
182C4×C8—442no—
183#95—22no—
184#95—22no—
185C2×C11—21no—
186C2×C11—21no—
187C2×C11—82no—
188C2×C11C4×#9911yescharacteristic
189C2×C11C2×#35511yescharacteristic
190C2×C11#213211yescharacteristic
191C24—21no—
192C2×Q8—41no—
193C2×Q8—41no—
194C2×Q8C2×C4×D1112yes—
195C2×Q8#433912yes—
196C2×D4—21no—
197C2×D4—41no—
198C2×D4—41no—
199C2×D4C4×Dic1112yes—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—44no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4C22⋊Dic1112yes—
207C22×C4C22⋊Dic1111yescharacteristic
208C22×C4C22⋊Dic1111yescharacteristic
209C22×C4C22×Dic1111yescharacteristic
210C22×C4C2×C22⋊D1112yes—
211M16—228no—
212M16—444no—
213C2×C8—444no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—41no—
217C22⋊C4—28no—
218C22⋊C4—42no—
219C22⋊C4—44no—
220C42—22no—
221C42—21no—
222C42—22no—
223C42—21no—
224C42—21no—
225C42—41no—
226C42—42no—
227C42—42no—
228C42C4×Dic1112yes—
229C11C4×#35511yescharacteristic, complemented, Sylow
230C23—22no—
231C23—42no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23C2×C22⋊Dic1111yescharacteristic
236Q8—42no—
237Q8—42no—
238D4—42no—
239D4—42no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4#6689811yescharacteristic
260C2×C4#6689811yescharacteristic
261C2×C4C2×C4×Dic1111yescharacteristic
262C2×C4#6697911yescharacteristic
263C2×C4C4×C22⋊D1114yes—
264C8—448no—
265C22—21no—
266C22—21no—
267C22—44no—
268C22—42no—
269C22—82no—
270C22—81no—
271C22—81no—
272C22C4×C22⋊Dic1111yescharacteristic
273C22C2×#6689811yescharacteristic
274C22#1062285311yescharacteristic
275C4—24no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—42no—
280C4—42no—
281C4—41no—
282C4—42no—
283C4—81no—
284C4#1062218012yesdirect product factor
285C2—21no—
286C2—21no—
287C2—82no—
288C2C4×#6689811yescharacteristic
289C2C2×#1062218011yescharacteristic
290C2#1307030111yescharacteristic
subgroupG/H
centerC2×C4#66898
commutatorC2×C4×C11C2×C42
FrattiniC22×Q8C22×D11
FittingC4×C11×#124C2
socleC22×C11C2×#99
prime radicalC22×D4×C11C2×C4
cosocleC22×Q8×C11C23
hypercenterC4×#124D11
hypocenterC11C4×#355
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
2. C4×#66900C2semidirect
3. #13066743C2semidirect
16. #10622180C4direct (N × H)
43. #66900C2×C4semidirect
156. C4×C11#355semidirect
229. C11C4×#355semidirect
284. C4#10622180direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106221802
C4×#669002
#130667432
C4×C11×#1242
C4×#35511