Finite Group Databasebeta

← #13072913

Subgroups — #13072913

Order 1408.

540 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C11C211yesmaximal, characteristic
2C2×#66979C211yesmaximal, characteristic, complemented
3#10622835C212yesmaximal
4#10622825C211yesmaximal, characteristic, complemented
5#10622825C211yesmaximal, characteristic, complemented
6#10622825C211yesmaximal, characteristic, complemented
7#10622591C212yesmaximal, complemented
8#10622565C212yesmaximal, complemented
9#10622557C212yesmaximal, complemented
10#10622541C211yesmaximal, characteristic, complemented
11#10622541C211yesmaximal, characteristic, complemented
12C22×D4×C11C2211yescharacteristic
13C23×C4×C11C2211yescharacteristic
14C23×C4×C11C2211yescharacteristic
15C4×D4×C11—24no—
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C22⋊C4C2211yescharacteristic
18C2×C11×C22⋊C4C2211yescharacteristic
19C2×C42×C11C2211yescharacteristic
20C2×C22⋊Dic11C2212yes—
21C2×C22⋊Dic11C2212yes—
22C2×C22⋊Dic11C2212yes—
23C2×C22⋊Dic11C2212yes—
24#66979—24no—
25C2×C4⋊Dic11C2211yescharacteristic
26C2×C4⋊Dic11C2211yescharacteristic
27C2×C4⋊Dic11C2211yescharacteristic
28C2×C4⋊Dic11C2211yescharacteristic
29C2×Dic11⋊C4C2212yes—
30C2×Dic11⋊C4C2212yes—
31C2×C4×Dic11C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C24×C11C2311yescharacteristic
39C2×D4×C11—22no—
40C2×D4×C11—22no—
41C2×D4×C11—22no—
42C22×C4×C11—22no—
43C22×C4×C11—22no—
44C22×C4×C11—22no—
45C22×C4×C11—22no—
46C22×C4×C11—22no—
47C22×C4×C11D414yes—
48C22×C4×C11C2311yescharacteristic
49C22×C4×C11C2311yescharacteristic
50C22×C4×C11C2311yescharacteristic
51C22×C4×C11C2311yescharacteristic
52C22×C4×C11C2311yescharacteristic
53C22×Dic11C2312yes—
54C22×Dic11C2312yes—
55C22×Dic11C2312yes—
56C22×Dic11C2312yes—
57C11×C4⋊C4—22no—
58C11×C22⋊C4—22no—
59C11×C22⋊C4—22no—
60C42×C11—22no—
61C22⋊Dic11—24no—
62C22⋊Dic11—24no—
63C22⋊Dic11—42no—
64C22⋊Dic11—42no—
65C4⋊Dic11—22no—
66C4⋊Dic11—22no—
67C4⋊Dic11—22no—
68C4⋊Dic11—22no—
69Dic11⋊C4—24no—
70Dic11⋊C4—42no—
71C4×Dic11—24no—
72#2485—111nomaximal, Sylow
73C23×C11—21no—
74C23×C11—21no—
75C23×C11—21no—
76C23×C11—21no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11—21no—
82C23×C11—21no—
83C23×C11—21no—
84C23×C11—21no—
85C23×C11C2×D412yes—
86C23×C11#4112yes—
87C23×C11C2411yescharacteristic
88D4×C11—28no—
89C2×C4×C11—21no—
90C2×C4×C11—21no—
91C2×C4×C11—21no—
92C2×C4×C11—21no—
93C2×C4×C11—28no—
94C2×C4×C11—21no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—44no—
101C2×C4×C11C2×D412yes—
102C2×C4×C11C2×D412yes—
103C2×C4×C11#4112yes—
104C2×C4×C11#4112yes—
105C2×C4×C11#4112yes—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—22no—
109C2×Dic11—22no—
110C2×Dic11—22no—
111C2×Dic11—22no—
112C2×Dic11—22no—
113C2×Dic11—22no—
114C2×Dic11—22no—
115C2×Dic11—22no—
116C2×Dic11—22no—
117C2×Dic11—22no—
118C2×C4×D4D1111yescharacteristic
119C2×#117—111no—
120#397—112no—
121#394—112no—
122#389—111no—
123#389—111no—
124#388—112no—
125#387—112no—
126#380—111no—
127#380—111no—
128#380—111no—
129C22×C11—22no—
130C22×C11—22no—
131C22×C11—22no—
132C22×C11—22no—
133C22×C11—22no—
134C22×C11—22no—
135C22×C11—41no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—41no—
142C22×C11—41no—
143C22×C11C22×D411yescharacteristic
144C22×C11C2×#4111yescharacteristic
145C22×C11C2×#4111yescharacteristic
146C22×C11C2×#4111yescharacteristic
147C22×C11C2×#4111yescharacteristic
148C22×C11H(5,𝔽2)11yescharacteristic
149C22×C112−1+411yescharacteristic
150C4×C11—22no—
151C4×C11—22no—
152C4×C11—41no—
153C4×C11—41no—
154C4×C11#12314yes—
155Dic11—42no—
156Dic11—42no—
157Dic11—42no—
158Dic11—42no—
159C22×D4C2×D1111yescharacteristic
160C23×C4C2×D1111yescharacteristic
161C23×C4C2×D1111yescharacteristic
162C4×D4—24no—
163#117—224no—
164C2×C4⋊C4—111no—
165C2×C4⋊C4—111no—
166C2×C4⋊C4—111no—
167C2×C4⋊C4—111no—
168C2×C4⋊C4—112no—
169C2×C4⋊C4—112no—
170C2×C4⋊C4C2×D1111yescharacteristic
171C2×C22⋊C4—112no—
172C2×C22⋊C4—112no—
173C2×C22⋊C4—112no—
174C2×C22⋊C4—112no—
175C2×C22⋊C4C2×D1111yescharacteristic
176C2×C22⋊C4C2×D1111yescharacteristic
177C2×C42—112no—
178C2×C42C2×D1111yescharacteristic
179#95—112no—
180#95—112no—
181#95—112no—
182#95—112no—
183#95—112no—
184C2×C11—42no—
185C2×C11—42no—
186C2×C11C2×#12311yescharacteristic
187C2×C11#52511yescharacteristic
188C2×C11#53711yescharacteristic
189C2×C11#55211yescharacteristic
190C2×C11#55311yescharacteristic
191C2×C11#55511yescharacteristic
192C2×C11#55611yescharacteristic
193C24C22×D1111yescharacteristic
194C24C22×D1111yescharacteristic
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—22no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—112no—
204C22×C4—112no—
205C22×C4—112no—
206C22×C4—112no—
207C22×C4C22⋊D1114yes—
208C22×C4C22×D1111yescharacteristic
209C22×C4C22×D1111yescharacteristic
210C22×C4C22×D1111yescharacteristic
211C22×C4C22×D1111yescharacteristic
212C22×C4C22×D1111yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—224no—
215C4⋊C4—222no—
216C4⋊C4—222no—
217C4⋊C4—222no—
218C4⋊C4—222no—
219C4⋊C4—442no—
220C22⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—224no—
223C22⋊C4—224no—
224C22⋊C4—442no—
225C22⋊C4—442no—
226C42—22no—
227C42—224no—
228C11#248511yescharacteristic, complemented, Sylow
229C23—21no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23#433912yes—
242C23C2×C22⋊D1112yes—
243C23C23×D1111yescharacteristic
244D4—28no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—28no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—44no—
257C2×C4—222no—
258C2×C4—222no—
259C2×C4—222no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—222no—
263C2×C4—222no—
264C2×C4—222no—
265C2×C4—222no—
266C2×C4—222no—
267C2×C4—222no—
268C2×C4—222no—
269C2×C4#433912yes—
270C2×C4#434112yes—
271C2×C4#434112yes—
272C2×C4C2×C22⋊D1112yes—
273C2×C4C2×C22⋊D1112yes—
274C22—22no—
275C22—22no—
276C22—22no—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—41no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22C2×#433911yescharacteristic
289C22C2×#433911yescharacteristic
290C22C2×#434111yescharacteristic
291C22C2×#434111yescharacteristic
292C22#6704211yescharacteristic
293C22#6704311yescharacteristic
294C22C22×C22⋊D1111yescharacteristic
295C4—22no—
296C4—22no—
297C4—41no—
298C4—41no—
299C4—442no—
300C4—442no—
301C4—442no—
302C4—442no—
303C4#6698814yes—
304C2—42no—
305C2—42no—
306C2#1062307211yescharacteristic
307C2#1062307311yescharacteristic
308C2#1062309411yescharacteristic
309C2#1062309611yescharacteristic
310C2#1062332211yescharacteristic
311C2C2×#6698811yescharacteristic
312C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C4×D4×C11C2
prime radicalC22×D4×C11C22
hypercenterC2×C4×D4D11
hypocenterC11#2485
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#66979C2semidirect
4. #10622825C2semidirect
5. #10622825C2semidirect
6. #10622825C2semidirect
7. #10622591C2semidirect
8. #10622565C2semidirect
9. #10622557C2semidirect
10. #10622541C2semidirect
11. #10622541C2semidirect
228. C11#2485semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C112
C2×#669792
#106228352
#106228252
#106225912
#106225652
#106225572
#106225412
#248511