Finite Group Databasebeta

← #13074545

Subgroups — #13074545

Order 1408.

576 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 133 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×#66999C211yesmaximal, characteristic, complemented
2C2×#66937C211yesmaximal, characteristic
3C11×#393C211yesmaximal, characteristic, complemented
4#10622844C211yesmaximal, characteristic, complemented
5#10622572C212yesmaximal, complemented
6#10622569C212yesmaximal, complemented
7#10622566C211yesmaximal, characteristic, complemented
8#10622287C211yesmaximal, characteristic, complemented
9#10622278C212yesmaximal, complemented
10D11×#95C211yesmaximal, characteristic, complemented
11#10622271C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×C22⋊D11C2211yescharacteristic
15C22×D44C2211yescharacteristic
16C22×C4×D11C2212yes—
17C22×C4×D11C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2212yes—
21#66999—24no—
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2212yes—
29#66937—24no—
30C11×#95C2212yes—
31C11×#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
37C24×C11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C23×D11C2311yescharacteristic
40C2×Q8×C11—22no—
41C2×Q8×C11—42no—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×C4×C11C2312yes—
45C22×C4×C11C2311yescharacteristic
46C2×C22⋊D11—22no—
47C2×C22⋊D11—22no—
48C2×C22⋊D11—24no—
49C2×C22⋊D11—42no—
50C22×Dic11C2311yescharacteristic
51C22×Dic11C2312yes—
52C22×Dic11C2312yes—
53C22×Dic11C2311yescharacteristic
54C2×D44—22no—
55C2×D44—24no—
56C2×C4×D11—24no—
57C2×C4×D11—42no—
58C2×C4×D11—42no—
59C2×C4×D11—42no—
60C2×C4×D11D414yes—
61C11×C22⋊C4—22no—
62C11×C22⋊C4—42no—
63C22⋊Dic11—42no—
64(C2×D11)⋊C4—24no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—42no—
67(C2×D11)⋊C4—42no—
68C4⋊Dic11—22no—
69Dic11⋊C4—22no—
70Dic11⋊C4—24no—
71#2639—111nomaximal, Sylow
72C23×C11—21no—
73C23×C11—22no—
74C23×C11—21no—
75C23×C11—22no—
76C23×C11—21no—
77C23×C11C2411yescharacteristic
78C22×D11—22no—
79C22×D11—21no—
80C22×D11—21no—
81C22×D11—21no—
82C22×D11—22no—
83C22×D11—21no—
84C22×D11—22no—
85C22×D11—21no—
86C22×D11C2×D412yes—
87C22×D11#4114yes—
88Q8×C11—44no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—21no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11—22no—
98C2×C4×C11C2×D412yes—
99C22⋊D11—44no—
100C22⋊D11—44no—
101C2×Dic11—22no—
102C2×Dic11—22no—
103C2×Dic11—21no—
104C2×Dic11—22no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11C2×D412yes—
111D44—44no—
112C4×D11—44no—
113C4×D11—48no—
114C2×C22⋊Q8—111no—
115C2×#121—111no—
116#400—112no—
117#397—111no—
118#397—111no—
119#394—112no—
120#393—111no—
121#393D1111yescharacteristic, complemented
122#386—112no—
123#386—112no—
124C2×#95—111no—
125C22×C11—41no—
126C22×C11—41no—
127C22×C11—41no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11C22×D411yescharacteristic
131C22×C11C2×#4112yes—
132C22×C11H(5,𝔽2)12yes—
133C22×C11H(5,𝔽2)11yescharacteristic
134C22×C112−1+411yescharacteristic
135C2×D11—22no—
136C2×D11—22no—
137C2×D11—24no—
138C2×D11—24no—
139C2×D11—41no—
140C2×D11—41no—
141C2×D11—41no—
142C2×D11—42no—
143C2×D11—42no—
144C2×D11#12414yes—
145C4×C11—22no—
146C4×C11—41no—
147C4×C11—42no—
148C4×C11—42no—
149Dic11—22no—
150Dic11—41no—
151Dic11—42no—
152Dic11—42no—
153C22×Q8C2×D1111yescharacteristic
154C22×D4—111no—
155C22×D4—111no—
156C22×D4—111no—
157C23×C4—111no—
158C23×C4—112no—
159C22⋊Q8—224no—
160#121—224no—
161C2×C4⋊C4—111no—
162C2×C4⋊C4—112no—
163C2×C4⋊C4—111no—
164C2×C22⋊C4—111no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4—112no—
167C2×C22⋊C4—112no—
168C2×C22⋊C4—112no—
169C2×C22⋊C4C2×D1111yescharacteristic
170C2×C22⋊C4C2×D1112yes—
171#95—111no—
172#95—112no—
173#95—112no—
174#95—112no—
175#95—112no—
176#95C2×D1111yescharacteristic
177#95C2×D1112yes—
178C2×C11—81no—
179C2×C11C2×#12411yescharacteristic
180C2×C11#53411yescharacteristic
181C2×C11#53711yescharacteristic
182C2×C11#53812yes—
183C2×C11#53912yes—
184D11—24no—
185D11—81no—
186C24—111no—
187C24—111no—
188C24C22×D1111yescharacteristic
189C2×Q8—22no—
190C2×Q8—42no—
191C2×D4—222no—
192C2×D4—224no—
193C2×D4—222no—
194C2×D4—222no—
195C2×D4—224no—
196C2×D4—442no—
197C22×C4—111no—
198C22×C4—114no—
199C22×C4—112no—
200C22×C4—111no—
201C22×C4—112no—
202C22×C4—224no—
203C22×C4—442no—
204C22×C4—442no—
205C22×C4—442no—
206C22×C4C22×D1112yes—
207C22×C4C22×D1111yescharacteristic
208C22×C4C22×D1112yes—
209C22×C4C22×D1111yescharacteristic
210C4⋊C4—222no—
211C4⋊C4—224no—
212C4⋊C4—222no—
213C22⋊C4—22no—
214C22⋊C4—42no—
215C22⋊C4—224no—
216C22⋊C4—222no—
217C22⋊C4—442no—
218C22⋊C4—442no—
219C22⋊C4—442no—
220C11#263911yescharacteristic, complemented, Sylow
221C23—21no—
222C23—22no—
223C23—21no—
224C23—22no—
225C23—21no—
226C23—112no—
227C23—114no—
228C23—222no—
229C23—221no—
230C23—221no—
231C23—221no—
232C23—222no—
233C23—221no—
234C23—222no—
235C23—221no—
236C23C23×D1111yescharacteristic
237Q8—44no—
238D4—444no—
239D4—444no—
240D4—444no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—112no—
251C2×C4—222no—
252C2×C4—222no—
253C2×C4—221no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—222no—
257C2×C4—222no—
258C2×C4—222no—
259C2×C4—222no—
260C2×C4—444no—
261C2×C4—448no—
262C2×C4D4×D1112yes—
263C22—41no—
264C22—41no—
265C22—42no—
266C22—41no—
267C22—42no—
268C22—114no—
269C22—222no—
270C22—222no—
271C22—224no—
272C22—224no—
273C22—441no—
274C22—441no—
275C22—442no—
276C22—441no—
277C22—442no—
278C22C2×D4×D1111yescharacteristic
279C22#6703712yes—
280C22#6704011yescharacteristic
281C22#41×D1112yes—
282C22#6704211yescharacteristic
283C4—22no—
284C4—42no—
285C4—41no—
286C4—42no—
287C4—222no—
288C4—442no—
289C4—441no—
290C4—442no—
291C2—81no—
292C2—224no—
293C2—881no—
294C2#1062312011yescharacteristic
295C2#1062316011yescharacteristic
296C2#1062316912yes—
297C2D11×#12411yescharacteristic
298C2#1062320912yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC2×#66937C2
hypercenter#393D11
hypocenterC11#2639
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#66999C2semidirect
3. C11×#393C2semidirect
4. #10622844C2semidirect
5. #10622572C2semidirect
6. #10622569C2semidirect
7. #10622566C2semidirect
8. #10622287C2semidirect
9. #10622278C2semidirect
10. D11×#95C2semidirect
11. #10622271C2semidirect
121. #393D11semidirect
220. C11#2639semidirect

Maximal subgroups

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

subgroupindex
C2×#669992
C2×#669372
C11×#3932
#106228442
#106225722
#106225692
#106225662
#106222872
#106222782
D11×#952
#106222712
#263911