Finite Group Databasebeta

← #13076645

Subgroups — #13076645

Order 1408.

528 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 125 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×#66950C211yesmaximal, characteristic, complemented
2C2×#66937C211yesmaximal, characteristic
3C11×#399C211yesmaximal, characteristic, complemented
4#10622605C211yesmaximal, characteristic, complemented
5#10622604C212yesmaximal, complemented
6#10622597C212yesmaximal, complemented
7#10622574C212yesmaximal, complemented
8#10622572C212yesmaximal, complemented
9#10622560C211yesmaximal, characteristic, complemented
10#10622286C211yesmaximal, characteristic, complemented
11#10622277C211yesmaximal, characteristic, complemented
12C22×C22⋊D11C2211yescharacteristic
13C22×C22⋊D11C2211yescharacteristic
14C22×D44C2211yescharacteristic
15C22×C4×D11C2211yescharacteristic
16C22×Dic22C2211yescharacteristic
17C2×C11×C4⋊C4C2211yescharacteristic
18C2×C11×C4⋊C4C2212yes—
19C2×C11×C22⋊C4C2211yescharacteristic
20C2×C11×C22⋊C4C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×(C2×D11)⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×C4⋊Dic11C2212yes—
28C2×Dic11⋊C4C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30#66950—24no—
31#66937—24no—
32C11×#95C2211yescharacteristic
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C23×D11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2312yes—
43C22×C4×C11C2311yescharacteristic
44C2×C22⋊D11—22no—
45C2×C22⋊D11—22no—
46C2×C22⋊D11—42no—
47C2×C22⋊D11—42no—
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C22×Dic11C2312yes—
51C22×Dic11C2311yescharacteristic
52C2×D44—22no—
53C2×D44—42no—
54C2×C4×D11—42no—
55C2×C4×D11D414yes—
56C2×Dic22—22no—
57C2×Dic22—42no—
58C11×C4⋊C4—22no—
59C11×C4⋊C4—42no—
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—
67(C2×D11)⋊C4—42no—
68C4⋊Dic11—24no—
69Dic11⋊C4—22no—
70Dic11⋊C4—42no—
71#2816—111nomaximal, Sylow
72C23×C11—21no—
73C23×C11—22no—
74C23×C11—22no—
75C23×C11—21no—
76C23×C11—21no—
77C23×C11C2411yescharacteristic
78C22×D11—22no—
79C22×D11—22no—
80C22×D11—21no—
81C22×D11—21no—
82C22×D11—21no—
83C22×D11—22no—
84C22×D11—22no—
85C22×D11—21no—
86C22×D11—21no—
87C22×D11C2×D412yes—
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×Dic11—22no—
109C2×Dic11C2×D412yes—
110D44—44no—
111C4×D11—44no—
112Dic22—44no—
113C2×C22⋊Q8—111no—
114C2×#121—111no—
115#399—111no—
116#399D1111yescharacteristic, complemented
117#398—112no—
118#394—112no—
119#394—112no—
120#394—112no—
121#393—111no—
122#393—111no—
123#381—111no—
124C22×C11—41no—
125C22×C11—41no—
126C22×C11—41no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11C22×D411yescharacteristic
130C22×C11H(5,𝔽2)12yes—
131C22×C11H(5,𝔽2)12yes—
132C22×C112−1+411yescharacteristic
133C22×C112−1+411yescharacteristic
134C2×D11—22no—
135C2×D11—22no—
136C2×D11—22no—
137C2×D11—42no—
138C2×D11—42no—
139C2×D11—41no—
140C2×D11—41no—
141C2×D11—41no—
142C2×D11—42no—
143C2×D11—42no—
144C4×C11—22no—
145C4×C11—42no—
146C4×C11—41no—
147C4×C11—42no—
148Dic11—22no—
149Dic11—42no—
150Dic11—41no—
151Dic11—42no—
152C22×Q8—111no—
153C22×D4—111no—
154C22×D4—111no—
155C22×D4—111no—
156C23×C4—111no—
157C22⋊Q8—224no—
158#121—224no—
159C2×C4⋊C4—111no—
160C2×C4⋊C4—112no—
161C2×C4⋊C4—112no—
162C2×C4⋊C4C2×D1111yescharacteristic
163C2×C4⋊C4C2×D1112yes—
164C2×C22⋊C4—111no—
165C2×C22⋊C4—112no—
166C2×C22⋊C4—112no—
167C2×C22⋊C4—112no—
168C2×C22⋊C4—112no—
169C2×C22⋊C4—112no—
170C2×C22⋊C4C2×D1111yescharacteristic
171C2×C22⋊C4C2×D1112yes—
172#95—111no—
173#95—112no—
174#95—112no—
175#95—112no—
176#95C2×D1111yescharacteristic
177C2×C11—81no—
178C2×C11#53411yescharacteristic
179C2×C11#53511yescharacteristic
180C2×C11#53611yescharacteristic
181C2×C11#56212yes—
182C2×C11#56212yes—
183D11—42no—
184D11—81no—
185C24—111no—
186C24—111no—
187C24C22×D1111yescharacteristic
188C2×Q8—222no—
189C2×Q8—442no—
190C2×D4—222no—
191C2×D4—222no—
192C2×D4—222no—
193C2×D4—442no—
194C2×D4—442no—
195C2×D4—442no—
196C22×C4—111no—
197C22×C4—114no—
198C22×C4—112no—
199C22×C4—112no—
200C22×C4—111no—
201C22×C4—442no—
202C22×C4C22×D1112yes—
203C22×C4C22×D1111yescharacteristic
204C22×C4C22×D1112yes—
205C22×C4C22×D1111yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—42no—
208C4⋊C4—222no—
209C4⋊C4—224no—
210C4⋊C4—442no—
211C22⋊C4—22no—
212C22⋊C4—42no—
213C22⋊C4—224no—
214C22⋊C4—222no—
215C22⋊C4—442no—
216C22⋊C4—442no—
217C22⋊C4—442no—
218C22⋊C4—442no—
219C11#281611yescharacteristic, complemented, Sylow
220C23—21no—
221C23—22no—
222C23—21no—
223C23—22no—
224C23—21no—
225C23—112no—
226C23—222no—
227C23—221no—
228C23—222no—
229C23—221no—
230C23—221no—
231C23—222no—
232C23—221no—
233C23—222no—
234C23—221no—
235C23C23×D1111yescharacteristic
236Q8—444no—
237D4—444no—
238D4—444no—
239D4—444no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—112no—
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×C4—222no—
259C2×C4—444no—
260C2×C4D4×D1112yes—
261C22—41no—
262C22—41no—
263C22—42no—
264C22—41no—
265C22—42no—
266C22—222no—
267C22—222no—
268C22—222no—
269C22—442no—
270C22—442no—
271C22—441no—
272C22—441no—
273C22—442no—
274C22—441no—
275C22—442no—
276C22C2×D4×D1111yescharacteristic
277C22#6703712yes—
278C22#6704011yescharacteristic
279C22#6704212yes—
280C22#6704311yescharacteristic
281C4—22no—
282C4—41no—
283C4—42no—
284C4—42no—
285C4—222no—
286C4—441no—
287C4—442no—
288C4—442no—
289C2—81no—
290C2—442no—
291C2—881no—
292C2#1062315911yescharacteristic
293C2#1062317812yes—
294C2#1062318411yescharacteristic
295C2#1062319812yes—
296C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
prime radicalC2×#66937C2
hypercenter#399D11
hypocenterC11#2816
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#66950C2semidirect
3. C11×#399C2semidirect
4. #10622605C2semidirect
5. #10622604C2semidirect
6. #10622597C2semidirect
7. #10622574C2semidirect
8. #10622572C2semidirect
9. #10622560C2semidirect
10. #10622286C2semidirect
11. #10622277C2semidirect
116. #399D11semidirect
219. C11#2816semidirect

Maximal subgroups

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

subgroupindex
C2×#669502
C2×#669372
C11×#3992
#106226052
#106226042
#106225972
#106225742
#106225722
#106225602
#106222862
#106222772
#281611