Finite Group Databasebeta

← #13074090

Subgroups — #13074090

Order 1408.

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

normal subgroups only

This group has 596 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×#66991C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3C11×#394C211yesmaximal, characteristic, complemented
4#10622835C211yesmaximal, characteristic, complemented
5#10622599C211yesmaximal, characteristic, complemented
6#10622569C212yesmaximal, complemented
7#10622569C212yesmaximal, complemented
8#10622564C212yesmaximal, complemented
9#10622557C212yesmaximal, complemented
10#10622279C211yesmaximal, characteristic, complemented
11#10622272C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×C22⋊D11C2212yes—
14C22×C4×D11C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C22×C4×D11C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2212yes—
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23#66991—24no—
24C2×(C2×D11)⋊C4C2212yes—
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2211yescharacteristic
29C2×C4×Dic11C2212yes—
30C4⋊C4×D11—24no—
31C11×#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2312yes—
38C23×D11C2311yescharacteristic
39C2×D4×C11—22no—
40C2×D4×C11—42no—
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C2×C22⋊D11—24no—
46C2×C22⋊D11—24no—
47C2×C22⋊D11—24no—
48C22×Dic11C2312yes—
49C22×Dic11C2312yes—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2311yescharacteristic
52C22×Dic11C2311yescharacteristic
53C2×C4×D11—22no—
54C2×C4×D11—22no—
55C2×C4×D11—22no—
56C2×C4×D11—22no—
57C2×C4×D11—42no—
58C2×C4×D11—42no—
59C2×C4×D11D414yes—
60C11×C4⋊C4—22no—
61C11×C22⋊C4—24no—
62C11×C22⋊C4—42no—
63C22⋊Dic11—24no—
64C22⋊Dic11—24no—
65C22⋊Dic11—42no—
66(C2×D11)⋊C4—24no—
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69Dic11⋊C4—22no—
70Dic11⋊C4—22no—
71C4×Dic11—42no—
72#2591—111nomaximal, Sylow
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—22no—
78C23×C11—22no—
79C23×C11—22no—
80C23×C11C2411yescharacteristic
81C22×D11—21no—
82C22×D11—21no—
83C22×D11—22no—
84C22×D11C2×D412yes—
85C22×D11#4114yes—
86D4×C11—44no—
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11C2×D412yes—
96C2×C4×C11#4112yes—
97C22⋊D11—48no—
98C2×Dic11—21no—
99C2×Dic11—21no—
100C2×Dic11—22no—
101C2×Dic11—21no—
102C2×Dic11—22no—
103C2×Dic11—22no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11C2×D412yes—
110C2×Dic11#4112yes—
111C4×D11—28no—
112C4×D11—44no—
113C4×D11—44no—
114C2×#121—111no—
115C22×C4⋊C4—111no—
116#400—111no—
117#400—111no—
118#394—111no—
119#394D1111yescharacteristic, complemented
120#388—112no—
121#388—112no—
122#386—112no—
123#386—112no—
124C4×C22⋊C4—111no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11C22×D411yescharacteristic
133C22×C11C2×#4111yescharacteristic
134C22×C11C2×#4111yescharacteristic
135C22×C11C2×#4112yes—
136C22×C11H(5,𝔽2)12yes—
137C2×D11—22no—
138C2×D11—22no—
139C2×D11—24no—
140C2×D11—24no—
141C2×D11#12414yes—
142C4×C11—22no—
143C4×C11—22no—
144C4×C11—41no—
145C4×C11—42no—
146Dic11—22no—
147Dic11—22no—
148Dic11—42no—
149Dic11—41no—
150Dic11—42no—
151C22×D4—112no—
152C22×D4C2×D1111yescharacteristic
153C23×C4—111no—
154C23×C4—111no—
155C23×C4—111no—
156#121—224no—
157C2×C4⋊C4—111no—
158C2×C4⋊C4—111no—
159C2×C4⋊C4—111no—
160C2×C4⋊C4—111no—
161C2×C4⋊C4—224no—
162C2×C4⋊C4C2×D1111yescharacteristic
163C2×C22⋊C4—112no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4—112no—
167C2×C22⋊C4C2×D1112yes—
168C2×C22⋊C4C2×D1112yes—
169C2×C42—112no—
170#95—111no—
171#95—112no—
172#95—112no—
173#95—112no—
174#95—112no—
175#95C2×D1111yescharacteristic
176C2×C11—82no—
177C2×C11#52511yescharacteristic
178C2×C11C2×#12411yescharacteristic
179C2×C11#53411yescharacteristic
180C2×C11#55312yes—
181C2×C11#55312yes—
182D11—24no—
183C24—111no—
184C24C22×D1112yes—
185C2×D4—22no—
186C2×D4—42no—
187C2×D4—224no—
188C2×D4—224no—
189C2×D4—224no—
190C22×C4—111no—
191C22×C4—111no—
192C22×C4—114no—
193C22×C4—112no—
194C22×C4—112no—
195C22×C4—111no—
196C22×C4—222no—
197C22×C4—222no—
198C22×C4—222no—
199C22×C4—222no—
200C22×C4—442no—
201C22×C4—442no—
202C22×C4C22×D1112yes—
203C22×C4C22×D1111yescharacteristic
204C22×C4C22×D1111yescharacteristic
205C22×C4C22×D1111yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—222no—
208C4⋊C4—222no—
209C4⋊C4—222no—
210C4⋊C4—222no—
211C22⋊C4—24no—
212C22⋊C4—42no—
213C22⋊C4—224no—
214C22⋊C4—224no—
215C22⋊C4—224no—
216C22⋊C4—442no—
217C42—442no—
218C11#259111yescharacteristic, complemented, Sylow
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—112no—
227C23—114no—
228C23—221no—
229C23—222no—
230C23—221no—
231C23C23×D1111yescharacteristic
232D4—44no—
233D4—448no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—112no—
243C2×C4—112no—
244C2×C4—228no—
245C2×C4—221no—
246C2×C4—221no—
247C2×C4—222no—
248C2×C4—222no—
249C2×C4—221no—
250C2×C4—222no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—222no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—444no—
257C2×C4—444no—
258C2×C4D4×D1112yes—
259C2×C4#434112yes—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—114no—
268C22—222no—
269C22—222no—
270C22—224no—
271C22—224no—
272C22C2×D4×D1111yescharacteristic
273C22C2×#434111yescharacteristic
274C22#6703712yes—
275C22#41×D1111yescharacteristic
276C22#41×D1112yes—
277C4—22no—
278C4—22no—
279C4—41no—
280C4—42no—
281C4—222no—
282C4—222no—
283C4—441no—
284C4—442no—
285C4—442no—
286C2—82no—
287C2—224no—
288C2#1062312011yescharacteristic
289C2#1062313711yescharacteristic
290C2#1062314512yes—
291C2#1062319212yes—
292C2D11×#12411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#394C2
prime radicalC2×#66991C2
hypercenter#394D11
hypocenterC11#2591
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D11C2semidirect
3. C11×#394C2semidirect
4. #10622835C2semidirect
5. #10622599C2semidirect
6. #10622569C2semidirect
7. #10622569C2semidirect
8. #10622564C2semidirect
9. #10622557C2semidirect
10. #10622279C2semidirect
11. #10622272C2semidirect
119. #394D11semidirect
218. C11#2591semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×C4⋊C4×D112
C11×#3942
#106228352
#106225992
#106225692
#106225642
#106225572
#106222792
#106222722
#259111