Finite Group Databasebeta

← #13073103

Subgroups — #13073103

Order 1408.

596 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 141 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×C4⋊C4×D11C211yesmaximal, characteristic, complemented
2C2×#66937C211yesmaximal, characteristic
3C11×#397C211yesmaximal, characteristic, complemented
4#10622606C211yesmaximal, characteristic, complemented
5#10622570C212yesmaximal, complemented
6#10622569C212yesmaximal, complemented
7#10622566C211yesmaximal, characteristic, complemented
8#10622287C211yesmaximal, characteristic, complemented
9#10622279C211yesmaximal, characteristic, complemented
10#10622278C212yesmaximal, complemented
11#10622263C212yesmaximal, complemented
12C22×C22⋊D11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×D44C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C22×C4×D11C2212yes—
17C2×C11×C4⋊C4C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2212yes—
28C2×C4×Dic11C2212yes—
29C4⋊C4×D11—24no—
30#66937—24no—
31C11×#95C2212yes—
32C11×#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2211yescharacteristic
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—24no—
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2312yes—
50C22×Dic11C2312yes—
51C22×Dic11C2311yescharacteristic
52C2×D44—22no—
53C2×D44—24no—
54C2×C4×D11—24no—
55C2×C4×D11—24no—
56C2×C4×D11—42no—
57C2×C4×D11—42no—
58C2×C4×D11D414yes—
59C11×C4⋊C4—22no—
60C11×C22⋊C4—22no—
61C11×C22⋊C4—42no—
62C22⋊Dic11—42no—
63(C2×D11)⋊C4—24no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—42no—
66(C2×D11)⋊C4—42no—
67C4⋊Dic11—22no—
68Dic11⋊C4—22no—
69Dic11⋊C4—24no—
70C4×Dic11—24no—
71#2504—111nomaximal, Sylow
72C23×C11—21no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—21no—
76C23×C11—21no—
77C23×C11C2411yescharacteristic
78C22×D11—22no—
79C22×D11—21no—
80C22×D11—21no—
81C22×D11—21no—
82C22×D11—22no—
83C22×D11—22no—
84C22×D11—21no—
85C22×D11—21no—
86C22×D11C2×D412yes—
87C22×D11#4114yes—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
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—
112C4×D11—48no—
113C2×#121—111no—
114C22×C4⋊C4—111no—
115#397—111no—
116#397—111no—
117#397—111no—
118#397D1111yescharacteristic, complemented
119#390—112no—
120#386—112no—
121#386—112no—
122#382—112no—
123C4×C22⋊C4—111no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11—41no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11C22×D411yescharacteristic
130C22×C11C2×#4112yes—
131C22×C11C2×#4112yes—
132C22×C11H(5,𝔽2)11yescharacteristic
133C22×C11H(5,𝔽2)11yescharacteristic
134C2×D11—22no—
135C2×D11—22no—
136C2×D11—24no—
137C2×D11—24no—
138C2×D11—41no—
139C2×D11—41no—
140C2×D11—41no—
141C2×D11—42no—
142C2×D11—42no—
143C2×D11#12414yes—
144C4×C11—22no—
145C4×C11—41no—
146C4×C11—42no—
147C4×C11—42no—
148Dic11—41no—
149Dic11—42no—
150Dic11—42no—
151Dic11#12314yes—
152C22×D4—111no—
153C22×D4—111no—
154C22×D4—111no—
155C23×C4—111no—
156C23×C4—112no—
157#121—224no—
158C2×C4⋊C4—112no—
159C2×C4⋊C4—111no—
160C2×C4⋊C4—111no—
161C2×C4⋊C4—224no—
162C2×C4⋊C4C2×D1111yescharacteristic
163C2×C22⋊C4—111no—
164C2×C22⋊C4—112no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4—112no—
167C2×C22⋊C4—112no—
168C2×C22⋊C4C2×D1111yescharacteristic
169C2×C22⋊C4C2×D1112yes—
170C2×C42—112no—
171#95—111no—
172#95—112no—
173#95—112no—
174#95—112no—
175#95C2×D1111yescharacteristic
176#95C2×D1112yes—
177C2×C11—81no—
178C2×C11C2×#12311yescharacteristic
179C2×C11C2×#12411yescharacteristic
180C2×C11#53511yescharacteristic
181C2×C11#55312yes—
182C2×C11#55312yes—
183D11—24no—
184D11—81no—
185C24—111no—
186C24—111no—
187C24C22×D1111yescharacteristic
188C2×D4—222no—
189C2×D4—224no—
190C2×D4—222no—
191C2×D4—224no—
192C2×D4—222no—
193C2×D4—224no—
194C22×C4—111no—
195C22×C4—114no—
196C22×C4—111no—
197C22×C4—112no—
198C22×C4—112no—
199C22×C4—224no—
200C22×C4—224no—
201C22×C4—442no—
202C22×C4—442no—
203C22×C4C22×D1111yescharacteristic
204C22×C4C22×D1112yes—
205C22×C4C22×D1112yes—
206C22×C4C22×D1111yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—224no—
209C4⋊C4—222no—
210C4⋊C4—222no—
211C22⋊C4—22no—
212C22⋊C4—42no—
213C22⋊C4—224no—
214C22⋊C4—222no—
215C22⋊C4—442no—
216C22⋊C4—442no—
217C22⋊C4—442no—
218C42—224no—
219C11#250411yescharacteristic, complemented, Sylow
220C23—21no—
221C23—21no—
222C23—22no—
223C23—22no—
224C23—21no—
225C23—112no—
226C23—114no—
227C23—221no—
228C23—222no—
229C23—221no—
230C23—221no—
231C23—221no—
232C23—222no—
233C23—222no—
234C23—221no—
235C23C23×D1111yescharacteristic
236D4—444no—
237D4—444no—
238D4—444no—
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—22no—
248C2×C4—112no—
249C2×C4—114no—
250C2×C4—228no—
251C2×C4—221no—
252C2×C4—222no—
253C2×C4—222no—
254C2×C4—222no—
255C2×C4—222no—
256C2×C4—222no—
257C2×C4—222no—
258C2×C4—222no—
259C2×C4—448no—
260C2×C4D4×D1112yes—
261C22—42no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22—41no—
266C22—114no—
267C22—224no—
268C22—222no—
269C22—222no—
270C22—224no—
271C22—442no—
272C22—441no—
273C22—441no—
274C22—442no—
275C22—441no—
276C22C2×D4×D1111yescharacteristic
277C22#6703711yescharacteristic
278C22#41×D1112yes—
279C22#41×D1112yes—
280C22#6704211yescharacteristic
281C4—22no—
282C4—42no—
283C4—42no—
284C4—41no—
285C4—114no—
286C4—442no—
287C4—442no—
288C4—441no—
289C2—81no—
290C2—224no—
291C2—881no—
292C2#1062313811yescharacteristic
293C2D11×#12311yescharacteristic
294C2#1062319212yes—
295C2D11×#12411yescharacteristic
296C2#1062324012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC2×#66937C2
hypercenter#397D11
hypocenterC11#2504
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊C4×D11C2semidirect
3. C11×#397C2semidirect
4. #10622606C2semidirect
5. #10622570C2semidirect
6. #10622569C2semidirect
7. #10622566C2semidirect
8. #10622287C2semidirect
9. #10622279C2semidirect
10. #10622278C2semidirect
11. #10622263C2semidirect
118. #397D11semidirect
219. C11#2504semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D112
C2×#669372
C11×#3972
#106226062
#106225702
#106225692
#106225662
#106222872
#106222792
#106222782
#106222632
#250411