Finite Group Databasebeta

← #13076655

Subgroups — #13076655

Order 1408.

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

normal subgroups only

This group has 630 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×#66993C211yesmaximal, characteristic, complemented
2C2×#66932C211yesmaximal, characteristic, complemented
3C11×#392C211yesmaximal, characteristic, complemented
4#10622836C212yesmaximal, complemented
5#10622836C212yesmaximal, complemented
6#10622835C211yesmaximal, characteristic, complemented
7#10622574C212yesmaximal, complemented
8#10622573C211yesmaximal, characteristic, complemented
9#10622572C212yesmaximal, complemented
10#10622285C211yesmaximal, characteristic, complemented
11#10622264C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C22×D4×C11C2212yes—
14C22×C22⋊D11C2212yes—
15C22×C22⋊D11C2212yes—
16C22×C22⋊D11C2212yes—
17C22×D44C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C2212yes—
20C2×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊Dic11C2211yescharacteristic
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2212yes—
24#66993—24no—
25C2×(C2×D11)⋊C4C2212yes—
26C2×(C2×D11)⋊C4C2212yes—
27C2×(C2×D11)⋊C4C2212yes—
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2211yescharacteristic
30C2×Dic11⋊C4C2211yescharacteristic
31C2×C4×Dic11C2211yescharacteristic
32#66932—24no—
33C11×#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C24×C11C2312yes—
39C23×D11C2312yes—
40C2×D4×C11—22no—
41C2×D4×C11—42no—
42C2×D4×C11—42no—
43C2×D4×C11—42no—
44C2×D4×C11—42no—
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×C4×C11C2311yescharacteristic
48C2×C22⋊D11—24no—
49C2×C22⋊D11—24no—
50C2×C22⋊D11—42no—
51C2×C22⋊D11—42no—
52C2×C22⋊D11—42no—
53C2×C22⋊D11—42no—
54C2×C22⋊D11—42no—
55C2×C22⋊D11—42no—
56C2×C22⋊D11—42no—
57C22×Dic11C2312yes—
58C22×Dic11C2311yescharacteristic
59C22×Dic11C2311yescharacteristic
60C22×Dic11C2311yescharacteristic
61C22×Dic11C2311yescharacteristic
62C2×D44—22no—
63C2×D44—42no—
64C11×C22⋊C4—22no—
65C11×C22⋊C4—42no—
66C22⋊Dic11—22no—
67C22⋊Dic11—22no—
68C22⋊Dic11—42no—
69C22⋊Dic11—42no—
70(C2×D11)⋊C4—42no—
71(C2×D11)⋊C4—42no—
72(C2×D11)⋊C4—42no—
73C4⋊Dic11—22no—
74Dic11⋊C4—22no—
75Dic11⋊C4—22no—
76C4×Dic11D414yescomplemented
77#2818—111nomaximal, Sylow
78C23×C11—21no—
79C23×C11—22no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—21no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—22no—
88C23×C11—22no—
89C23×C11—21no—
90C23×C11C2411yescharacteristic
91C22×D11—22no—
92C22×D11—22no—
93C22×D11—22no—
94C22×D11—22no—
95C22×D11—22no—
96C22×D11—22no—
97C22×D11—22no—
98D4×C11—44no—
99D4×C11—48no—
100C2×C4×C11—22no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—22no—
104C2×C4×C11—22no—
105C2×C4×C11—22no—
106C2×C4×C11C2×D412yes—
107C22⋊D11—48no—
108C22⋊D11—48no—
109C22⋊D11—48no—
110C2×Dic11—22no—
111C2×Dic11—21no—
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—22no—
117C2×Dic11—22no—
118C2×Dic11—21no—
119C2×Dic11—22no—
120C2×Dic11—22no—
121C2×Dic11C2×D412yes—
122C2×Dic11C2×D412yes—
123D44—44no—
124C2×#127—111no—
125C2×#126—111no—
126#394—111no—
127#394—112no—
128#394—112no—
129#394—111no—
130#392—112no—
131#392—112no—
132#392—111no—
133#392D1111yescharacteristic, complemented
134#383—111no—
135C22×C11—42no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11—42no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—42no—
145C22×C11—42no—
146C22×C11—42no—
147C22×C11C22×D411yescharacteristic
148C22×C11H(5,𝔽2)12yes—
149C22×C11H(5,𝔽2)12yes—
150C22×C11H(5,𝔽2)11yescharacteristic
151C22×C11H(5,𝔽2)11yescharacteristic
152C2×D11—42no—
153C2×D11—42no—
154C2×D11—42no—
155C2×D11—42no—
156C2×D11—42no—
157C2×D11—42no—
158C2×D11—42no—
159C4×C11—22no—
160C4×C11—41no—
161C4×C11—42no—
162Dic11—22no—
163Dic11—22no—
164Dic11—41no—
165Dic11—41no—
166Dic11—42no—
167C22×D4—112no—
168C22×D4—112no—
169C22×D4—112no—
170C22×D4—111no—
171C22×D4C2×D1111yescharacteristic
172C22×D4C2×D1112yes—
173#127—224no—
174#126—224no—
175C2×C4⋊C4—111no—
176C2×C4⋊C4—111no—
177C2×C4⋊C4—111no—
178C2×C22⋊C4—111no—
179C2×C22⋊C4—111no—
180C2×C22⋊C4—112no—
181C2×C22⋊C4—112no—
182C2×C22⋊C4—112no—
183C2×C22⋊C4—112no—
184C2×C22⋊C4—112no—
185C2×C22⋊C4C2×D1111yescharacteristic
186C2×C22⋊C4C2×D1112yes—
187C2×C42—111no—
188#95—112no—
189#95—112no—
190#95—111no—
191#95C2×D1111yescharacteristic
192C2×C11—82no—
193C2×C11—81no—
194C2×C11#53511yescharacteristic
195C2×C11#53511yescharacteristic
196C2×C11#53511yescharacteristic
197C2×C11#56012yes—
198C2×C11#56012yes—
199D11—82no—
200C24—112no—
201C24C22×D1111yescharacteristic
202C24C22×D1112yes—
203C2×D4—22no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—42no—
208C2×D4—224no—
209C2×D4—224no—
210C2×D4—222no—
211C2×D4—442no—
212C2×D4—442no—
213C2×D4—442no—
214C2×D4—442no—
215C2×D4—442no—
216C2×D4—442no—
217C2×D4—442no—
218C2×D4—442no—
219C22×C4—111no—
220C22×C4—111no—
221C22×C4—112no—
222C22×C4—111no—
223C22×C4—111no—
224C22×C4C22×D1112yes—
225C22×C4C22×D1111yescharacteristic
226C22×C4C22×D1111yescharacteristic
227C4⋊C4—222no—
228C4⋊C4—222no—
229C4⋊C4—222no—
230C22⋊C4—22no—
231C22⋊C4—42no—
232C22⋊C4—222no—
233C22⋊C4—222no—
234C22⋊C4—442no—
235C22⋊C4—442no—
236C22⋊C4—442no—
237C22⋊C4—442no—
238C22⋊C4—442no—
239C42—114no—
240C11#281811yescharacteristic, complemented, Sylow
241C23—21no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—21no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—21no—
253C23—222no—
254C23—222no—
255C23—222no—
256C23—222no—
257C23—222no—
258C23—222no—
259C23—222no—
260C23C23×D1111yescharacteristic
261D4—44no—
262D4—48no—
263D4—444no—
264D4—448no—
265D4—448no—
266D4—448no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—112no—
274C2×C4—112no—
275C2×C4—222no—
276C2×C4—221no—
277C2×C4—221no—
278C2×C4—221no—
279C2×C4—221no—
280C2×C4—222no—
281C2×C4—221no—
282C2×C4—222no—
283C2×C4—222no—
284C2×C4—221no—
285C2×C4—222no—
286C2×C4D4×D1112yes—
287C22—42no—
288C22—41no—
289C22—42no—
290C22—41no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—41no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—442no—
300C22—442no—
301C22—442no—
302C22—442no—
303C22—442no—
304C22—442no—
305C22—442no—
306C22C2×D4×D1111yescharacteristic
307C22#6703712yes—
308C22#6703712yes—
309C22#6703711yescharacteristic
310C22#6704211yescharacteristic
311C4—22no—
312C4—41no—
313C4—42no—
314C4—222no—
315C4—222no—
316C4—441no—
317C4—441no—
318C4—442no—
319C2—82no—
320C2—81no—
321C2—882no—
322C2#1062312311yescharacteristic
323C2#1062312612yes—
324C2#1062313811yescharacteristic
325C2#1062315112yes—
326C2#1062324611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#392C2
hypercenter#392D11
hypocenterC11#2818
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#66993C2semidirect
2. C2×#66932C2semidirect
3. C11×#392C2semidirect
4. #10622836C2semidirect
5. #10622836C2semidirect
6. #10622835C2semidirect
7. #10622574C2semidirect
8. #10622573C2semidirect
9. #10622572C2semidirect
10. #10622285C2semidirect
11. #10622264C2semidirect
76. C4×Dic11D4semidirect
133. #392D11semidirect
240. C11#2818semidirect

Maximal subgroups

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

subgroupindex
C2×#669932
C2×#669322
C11×#3922
#106228362
#106228352
#106225742
#106225732
#106225722
#106222852
#106222642
#281811