Finite Group Databasebeta

← #13074095

Subgroups — #13074095

Order 1408.

596 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 145 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×#66992C211yesmaximal, characteristic
2C22×Dic11⋊C4C211yesmaximal, characteristic, complemented
3C11×#386C211yesmaximal, characteristic, complemented
4#10622833C211yesmaximal, characteristic, complemented
5#10622826C211yesmaximal, characteristic, complemented
6#10622572C212yesmaximal, complemented
7#10622571C211yesmaximal, characteristic, complemented
8#10622557C212yesmaximal, complemented
9C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
10#10622282C212yesmaximal, complemented
11#10622271C212yesmaximal, complemented
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C22×C22⋊D11C2211yescharacteristic
16C23×Dic11C2211yescharacteristic
17C23×Dic11C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊Dic11C2212yes—
23#66992—24no—
24C2×(C2×D11)⋊C4C2211yescharacteristic
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×Dic11⋊C4—24no—
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×Dic11⋊C4C2212yes—
31C2×C4×Dic11C2212yes—
32C11×#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C24×C11C2311yescharacteristic
39C23×D11C2311yescharacteristic
40C2×D4×C11—22no—
41C2×D4×C11—22no—
42C2×D4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11—42no—
45C22×C4×C11C2311yescharacteristic
46C22×C4×C11C2312yes—
47C22×C4×C11C2312yes—
48C2×C22⋊D11—22no—
49C2×C22⋊D11—22no—
50C2×C22⋊D11—22no—
51C2×C22⋊D11—22no—
52C2×C22⋊D11—42no—
53C22×Dic11—24no—
54C22×Dic11—22no—
55C22×Dic11—42no—
56C22×Dic11D414yes—
57C22×Dic11C2311yescharacteristic
58C22×Dic11C2312yes—
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2312yes—
62C11×C22⋊C4—22no—
63C11×C22⋊C4—42no—
64C22⋊Dic11—22no—
65C22⋊Dic11—24no—
66C22⋊Dic11—22no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—24no—
69(C2×D11)⋊C4—42no—
70Dic11⋊C4—24no—
71Dic11⋊C4—24no—
72Dic11⋊C4—22no—
73C4×Dic11—42no—
74#2591—111nomaximal, Sylow
75C23×C11—22no—
76C23×C11—22no—
77C23×C11—21no—
78C23×C11—22no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—22no—
82C23×C11C2×D412yes—
83C23×C11#4112yes—
84C23×C11#4112yes—
85C23×C11C2411yescharacteristic
86C22×D11—21no—
87C22×D11—22no—
88C22×D11—21no—
89C22×D11—21no—
90C22×D11—22no—
91D4×C11—44no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—22no—
99C2×C4×C11—22no—
100C2×C4×C11—22no—
101C2×C4×C11—44no—
102C22⋊D11—44no—
103C22⋊D11—44no—
104C2×Dic11—28no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—21no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—22no—
115C2×Dic11—44no—
116C2×Dic11C2×D412yes—
117C2×Dic11C2×D412yes—
118C2×Dic11#4114yes—
119C2×#121—111no—
120C22×C4⋊C4—111no—
121#400—112no—
122#394—112no—
123#388—112no—
124#388—112no—
125#386—111no—
126#386—111no—
127#386—111no—
128#386D1111yescharacteristic, complemented
129C4×C22⋊C4—111no—
130C22×C11—22no—
131C22×C11—22no—
132C22×C11—24no—
133C22×C11—24no—
134C22×C11—41no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11—42no—
138C22×C11—42no—
139C22×C11#12414yes—
140C22×C11C22×D411yescharacteristic
141C22×C11C2×#4111yescharacteristic
142C22×C11C2×#4111yescharacteristic
143C22×C11C2×#4112yes—
144C22×C11H(5,𝔽2)12yes—
145C2×D11—41no—
146C2×D11—41no—
147C2×D11—41no—
148C2×D11—42no—
149C2×D11—42no—
150C4×C11—41no—
151C4×C11—42no—
152C4×C11—42no—
153Dic11—24no—
154Dic11—22no—
155Dic11—22no—
156Dic11—41no—
157Dic11—42no—
158C22×D4—111no—
159C22×D4—111no—
160C22×D4C2×D1111yescharacteristic
161C23×C4—111no—
162C23×C4—111no—
163C23×C4C2×D1111yescharacteristic
164#121—224no—
165C2×C4⋊C4—112no—
166C2×C4⋊C4—112no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—224no—
169C2×C22⋊C4—111no—
170C2×C22⋊C4—111no—
171C2×C22⋊C4—112no—
172C2×C22⋊C4—111no—
173C2×C22⋊C4—112no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4C2×D1111yescharacteristic
176C2×C22⋊C4C2×D1112yes—
177C2×C42—112no—
178#95—112no—
179#95—112no—
180#95—112no—
181#95—112no—
182#95C2×D1112yes—
183C2×C11—24no—
184C2×C11—81no—
185C2×C11#52511yescharacteristic
186C2×C11C2×#12411yescharacteristic
187C2×C11#53411yescharacteristic
188C2×C11#55312yes—
189C2×C11#55312yes—
190D11—81no—
191C24—111no—
192C24C22×D1111yescharacteristic
193C24C22×D1111yescharacteristic
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—222no—
198C2×D4—222no—
199C2×D4—222no—
200C2×D4—222no—
201C2×D4—442no—
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—112no—
205C22×C4—111no—
206C22×C4—111no—
207C22×C4—114no—
208C22×C4—111no—
209C22×C4—112no—
210C22×C4—224no—
211C22×C4—222no—
212C22×C4—442no—
213C22×C4C22×D1111yescharacteristic
214C22×C4C22×D1112yes—
215C22×C4C22×D1112yes—
216C4⋊C4—224no—
217C4⋊C4—224no—
218C4⋊C4—222no—
219C22⋊C4—22no—
220C22⋊C4—42no—
221C22⋊C4—222no—
222C22⋊C4—224no—
223C22⋊C4—222no—
224C22⋊C4—224no—
225C22⋊C4—222no—
226C22⋊C4—442no—
227C42—442no—
228C11#259111yescharacteristic, complemented, Sylow
229C23—22no—
230C23—22no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23—22no—
235C23—22no—
236C23—221no—
237C23—221no—
238C23—221no—
239C23—222no—
240C23—222no—
241C23#433912yes—
242C23D4×D1112yes—
243C23#434112yes—
244C23C23×D1111yescharacteristic
245D4—44no—
246D4—444no—
247D4—444no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—44no—
258C2×C4—112no—
259C2×C4—112no—
260C2×C4—114no—
261C2×C4—228no—
262C2×C4—222no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—221no—
270C2×C4—222no—
271C2×C4—222no—
272C2×C4—444no—
273C22—24no—
274C22—22no—
275C22—24no—
276C22—22no—
277C22—41no—
278C22—42no—
279C22—41no—
280C22—42no—
281C22—41no—
282C22—441no—
283C22—442no—
284C22—441no—
285C22—442no—
286C22—441no—
287C22#6693814yes—
288C22C2×#433911yescharacteristic
289C22C2×D4×D1111yescharacteristic
290C22C2×#434111yescharacteristic
291C22#6703712yes—
292C22#41×D1112yes—
293C4—41no—
294C4—42no—
295C4—42no—
296C4—222no—
297C4—222no—
298C4—224no—
299C4—441no—
300C4—442no—
301C2—24no—
302C2—81no—
303C2—881no—
304C2C2×#6693811yescharacteristic
305C2#1062307112yes—
306C2#1062312011yescharacteristic
307C2#1062313212yes—
308C2#1062318711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
prime radicalC2×#66992C2
hypercenter#386D11
hypocenterC11#2591
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×Dic11⋊C4C2semidirect
3. C11×#386C2semidirect
4. #10622833C2semidirect
5. #10622826C2semidirect
6. #10622572C2semidirect
7. #10622571C2semidirect
8. #10622557C2semidirect
9. C22⋊C4×Dic11C2semidirect
10. #10622282C2semidirect
11. #10622271C2semidirect
128. #386D11semidirect
228. C11#2591semidirect

Maximal subgroups

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

subgroupindex
C2×#669922
C22×Dic11⋊C42
C11×#3862
#106228332
#106228262
#106225722
#106225712
#106225572
C22⋊C4×Dic112
#106222822
#106222712
#259111