Finite Group Databasebeta

← #13074409

Subgroups — #13074409

Order 1408.

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

normal subgroups only

This group has 548 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×#66945C211yesmaximal, characteristic, complemented
2C2×#66937C211yesmaximal, characteristic
3C11×#399C211yesmaximal, characteristic, complemented
4#10622605C211yesmaximal, characteristic, complemented
5#10622604C212yesmaximal, complemented
6#10622585C212yesmaximal, complemented
7#10622572C212yesmaximal, complemented
8#10622570C212yesmaximal, complemented
9#10622566C211yesmaximal, characteristic, complemented
10#10622287C211yesmaximal, characteristic, complemented
11#10622280C211yesmaximal, characteristic, complemented
12C22×C22⋊D11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×D44C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2212yes—
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2212yes—
21C2×(C2×D11)⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×C4⋊Dic11C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2212yes—
31#66945—24no—
32#66937—24no—
33C11×#95C2211yescharacteristic
34C11⋊#95C2211yescharacteristic
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C23×D11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2312yes—
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C2×C22⋊D11—22no—
45C2×C22⋊D11—24no—
46C2×C22⋊D11—22no—
47C2×C22⋊D11—42no—
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2312yes—
51C22×Dic11C2311yescharacteristic
52C2×D44—22no—
53C2×D44—42no—
54C2×C4×D11—24no—
55C2×C4×D11D414yes—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—42no—
58C11×C22⋊C4—22no—
59C11×C22⋊C4—42no—
60C22⋊Dic11—42no—
61(C2×D11)⋊C4—24no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—42no—
64(C2×D11)⋊C4—42no—
65(C2×D11)⋊C4—42no—
66C4⋊Dic11—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4—24no—
69Dic11⋊C4—42no—
70C4×Dic11—24no—
71#2624—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—22no—
81C22×D11—21no—
82C22×D11—21no—
83C22×D11—22no—
84C22×D11—21no—
85C22×D11—22no—
86C22×D11—21no—
87C22×D11C2×D412yes—
88C2×C4×C11—22no—
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×C11—22no—
96C2×C4×C11—22no—
97C2×C4×C11C2×D412yes—
98C22⋊D11—44no—
99C22⋊D11—44no—
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×Dic11C2×D412yes—
109C2×Dic11#4114yes—
110D44—44no—
111C4×D11—28no—
112C2×#121—111no—
113C2×#117—111no—
114#399—111no—
115#399D1111yescharacteristic, complemented
116#397—111no—
117#397—111no—
118#394—112no—
119#394—112no—
120#390—112no—
121#389—112no—
122#380—111no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11—42no—
127C22×C11—42no—
128C22×C11C22×D411yescharacteristic
129C22×C11C2×#4112yes—
130C22×C11H(5,𝔽2)12yes—
131C22×C11H(5,𝔽2)11yescharacteristic
132C22×C112−1+411yescharacteristic
133C2×D11—22no—
134C2×D11—22no—
135C2×D11—22no—
136C2×D11—42no—
137C2×D11—42no—
138C2×D11—41no—
139C2×D11—41no—
140C2×D11—41no—
141C2×D11—42no—
142C2×D11—42no—
143C4×C11—22no—
144C4×C11—42no—
145C4×C11—41no—
146C4×C11—42no—
147Dic11—41no—
148Dic11—42no—
149Dic11—42no—
150Dic11#12314yes—
151C22×D4—111no—
152C22×D4—111no—
153C22×D4—111no—
154C23×C4—111no—
155#121—224no—
156#117—224no—
157C2×C4⋊C4—111no—
158C2×C4⋊C4—111no—
159C2×C4⋊C4—112no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4C2×D1111yescharacteristic
162C2×C4⋊C4C2×D1112yes—
163C2×C22⋊C4—112no—
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—
171C2×C42—112no—
172#95—111no—
173#95—112no—
174#95—112no—
175#95C2×D1111yescharacteristic
176C2×C11—81no—
177C2×C11C2×#12311yescharacteristic
178C2×C11#53511yescharacteristic
179C2×C11#53711yescharacteristic
180C2×C11#54012yes—
181C2×C11#54212yes—
182D11—42no—
183D11—81no—
184C24—111no—
185C24—111no—
186C24C22×D1111yescharacteristic
187C2×D4—222no—
188C2×D4—222no—
189C2×D4—224no—
190C2×D4—222no—
191C2×D4—442no—
192C2×D4—442no—
193C22×C4—111no—
194C22×C4—114no—
195C22×C4—112no—
196C22×C4—112no—
197C22×C4—111no—
198C22×C4—224no—
199C22×C4C22×D1111yescharacteristic
200C22×C4C22×D1112yes—
201C22×C4C22×D1112yes—
202C22×C4C22×D1111yescharacteristic
203C4⋊C4—22no—
204C4⋊C4—42no—
205C4⋊C4—222no—
206C4⋊C4—224no—
207C4⋊C4—222no—
208C4⋊C4—442no—
209C22⋊C4—22no—
210C22⋊C4—42no—
211C22⋊C4—224no—
212C22⋊C4—222no—
213C22⋊C4—442no—
214C22⋊C4—442no—
215C22⋊C4—442no—
216C22⋊C4—442no—
217C42—224no—
218C11#262411yescharacteristic, complemented, Sylow
219C23—21no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—21no—
224C23—112no—
225C23—222no—
226C23—221no—
227C23—222no—
228C23—221no—
229C23—221no—
230C23—222no—
231C23—221no—
232C23—222no—
233C23—221no—
234C23C23×D1111yescharacteristic
235D4—444no—
236D4—444no—
237D4—444no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—112no—
248C2×C4—114no—
249C2×C4—228no—
250C2×C4—222no—
251C2×C4—221no—
252C2×C4—222no—
253C2×C4—222no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—222no—
257C2×C4—222no—
258C2×C4D4×D1112yes—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—41no—
263C22—42no—
264C22—222no—
265C22—222no—
266C22—222no—
267C22—442no—
268C22—442no—
269C22—441no—
270C22—441no—
271C22—442no—
272C22—441no—
273C22—442no—
274C22C2×D4×D1111yescharacteristic
275C22#6703712yes—
276C22#6704011yescharacteristic
277C22#41×D1112yes—
278C22#6704211yescharacteristic
279C4—22no—
280C4—41no—
281C4—42no—
282C4—42no—
283C4—114no—
284C4—441no—
285C4—442no—
286C4—442no—
287C2—81no—
288C2—442no—
289C2—881no—
290C2#1062316011yescharacteristic
291C2#1062317112yes—
292C2D11×#12311yescharacteristic
293C2#1062319412yes—
294C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
prime radicalC2×#66937C2
hypercenter#399D11
hypocenterC11#2624
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#66945C2semidirect
3. C11×#399C2semidirect
4. #10622605C2semidirect
5. #10622604C2semidirect
6. #10622585C2semidirect
7. #10622572C2semidirect
8. #10622570C2semidirect
9. #10622566C2semidirect
10. #10622287C2semidirect
11. #10622280C2semidirect
115. #399D11semidirect
218. C11#2624semidirect

Maximal subgroups

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

subgroupindex
C2×#669452
C2×#669372
C11×#3992
#106226052
#106226042
#106225852
#106225722
#106225702
#106225662
#106222872
#106222802
#262411