Finite Group Databasebeta

← #13079007

Subgroups — #13079007

Order 1408.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#10623363C211yesmaximal, characteristic
2C2×#66941C211yesmaximal, characteristic, complemented
3C11×#417C211yesmaximal, characteristic, complemented
4#10622845C211yesmaximal, characteristic, complemented
5#10622746C211yesmaximal, characteristic, complemented
6M16×Dic11C211yesmaximal, characteristic, complemented
7#10622579C211yesmaximal, characteristic, complemented
8#10622408C212yesmaximal, complemented
9#10622405C212yesmaximal, complemented
10#10622378C212yesmaximal, complemented
11#10622373C212yesmaximal, complemented
12C2×C11×#41C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C22×Dic22—21no—
15C2×C11×M16C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17#67000C2211yescharacteristic
18#66997C2211yescharacteristic
19#66993C2211yescharacteristic
20#66992—21no—
21#66992—21no—
22#66989C2211yescharacteristic
23C4×C22⋊D11—21no—
24C4×C22⋊D11—21no—
25C2×C4⋊Dic11C2211yescharacteristic
26C2×Dic11⋊C4—21no—
27C2×C4×Dic11C2211yescharacteristic
28C2×#4318C2211yescharacteristic
29#66941—21no—
30#66941—21no—
31#66941C2212yes—
32#66941C2212yes—
33C11×#103C2212yes—
34C11×#102C2212yes—
35#66899C2212yes—
36#66896C2212yes—
37#66885C2212yes—
38#66880C2212yes—
39#66879C2212yes—
40C8×Dic11C2212yes—
41#66874C2212yes—
42#66873C2212yes—
43C11×#41—22no—
44C11×#41—22no—
45C2×Q8×C11C2311yescharacteristic
46C2×D4×C11—21no—
47C2×D4×C11C2311yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11C2311yescharacteristic
51C2×C22⋊D11—21no—
52C2×C22⋊D11—21no—
53C2×C22⋊D11—21no—
54C22×Dic11—21no—
55C22×Dic11D411yescharacteristic
56C22×Dic11D411yescharacteristic
57#4339—22no—
58#4339—22no—
59C2×D44C2311yescharacteristic
60C2×C4×D11—21no—
61C2×Dic22—22no—
62C2×Dic22—22no—
63C2×Dic22—44no—
64C2×Dic22C2311yescharacteristic
65C11×M16—22no—
66C2×C8×C11C2312yes—
67C11×C4⋊C4—21no—
68C11×C4⋊C4C2312yes—
69C22⋊Dic11—21no—
70C22⋊Dic11—21no—
71(C2×D11)⋊C4—21no—
72(C2×D11)⋊C4—21no—
73C4⋊Dic11—21no—
74C4⋊Dic11C2312yes—
75Dic11⋊C4—22no—
76Dic11⋊C4—22no—
77Dic11⋊C4—21no—
78Dic11⋊C4—21no—
79C4×Dic11D411yescharacteristic
80C4×Dic11D411yescharacteristic
81C4×Dic11C2311yescharacteristic
82C4×Dic11C2311yescharacteristic
83#4318—22no—
84C2×C11⋊C8C2312yes—
85#3141—111nomaximal, Sylow
86C23×C11—21no—
87C23×C11C2×D411yescharacteristic
88C22×D11—21no—
89Q8×C11—21no—
90Q8×C11—21no—
91D4×C11—21no—
92D4×C11—21no—
93D4×C11—42no—
94C2×C4×C11—21no—
95C2×C4×C11—22no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11C2×D411yescharacteristic
99C2×C4×C11#4112yes—
100C2×C4×C11#4112yes—
101C2×C4×C11C2411yescharacteristic
102C22⋊D11—42no—
103C22⋊D11—42no—
104C22⋊D11—42no—
105C2×Dic11—22no—
106C2×Dic11—22no—
107C2×Dic11—22no—
108C2×Dic11—21no—
109C2×Dic11—42no—
110C2×Dic11C2×D411yescharacteristic
111C2×Dic11C2×D411yescharacteristic
112C2×Dic11C2×D411yescharacteristic
113C2×Dic11C2×D411yescharacteristic
114D44—21no—
115D44—21no—
116C4×D11—42no—
117Dic22—21no—
118Dic22—21no—
119Dic22—44no—
120Dic22—44no—
121C8×C11—22no—
122C11⋊C8—22no—
123#532—111no—
124C2×C4⋊Q8—111no—
125#489—112no—
126#489—112no—
127#487—112no—
128#486—112no—
129#417—111no—
130#417—111no—
131#417—111no—
132#417D1111yescharacteristic, complemented
133C4×M16—111no—
134C22×C11—21no—
135C22×C11—21no—
136C22×C11—41no—
137C22×C11—41no—
138C22×C11—41no—
139C22×C11#12412yes—
140C22×C11C22×D411yescharacteristic
141C2×D11—41no—
142C2×D11—41no—
143C2×D11—41no—
144C4×C11—41no—
145C4×C11—42no—
146C4×C11#12412yes—
147C4×C11C2×#4111yescharacteristic
148C4×C11C2×#4111yescharacteristic
149Dic11—21no—
150Dic11—21no—
151Dic11—41no—
152Dic11—42no—
153Dic11AGL(1,ℤ/8)12yes—
154Dic11#13712yes—
155C2×#41—111no—
156C2×#41C2×D1111yescharacteristic
157C22×Q8—221no—
158C2×M16—111no—
159C2×M16C2×D1111yescharacteristic
160C4⋊Q8—112no—
161C4⋊Q8—112no—
162C4⋊Q8—111no—
163C4⋊Q8—221no—
164C4⋊Q8—221no—
165#127—111no—
166#124—111no—
167#124—111no—
168#121—221no—
169#121—221no—
170C4×D4—221no—
171C4×D4—221no—
172C2×C4⋊C4—111no—
173C2×C4⋊C4—221no—
174C2×C4⋊C4C2×D1111yescharacteristic
175C2×C42—111no—
176#103—112no—
177#103—112no—
178#103—112no—
179#103C2×D1112yes—
180#102—112no—
181#102—112no—
182#102—112no—
183#102C2×D1112yes—
184#97—112no—
185C4×C8—112no—
186C2×C11—22no—
187C2×C11—81no—
188C2×C11C2×#12411yescharacteristic
189C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C11C2×#13711yescharacteristic
191D11—81no—
192#41—22no—
193#41—22no—
194#41—222no—
195#41—222no—
196C2×Q8—111no—
197C2×Q8—222no—
198C2×Q8—222no—
199C2×Q8—444no—
200C2×Q8C22×D1111yescharacteristic
201C2×D4—21no—
202C2×D4—111no—
203C2×D4—221no—
204C2×D4—221no—
205C2×D4—221no—
206C2×D4C22×D1111yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—111no—
210C22×C4—111no—
211C22×C4—221no—
212C22×C4—221no—
213C22×C4C22×D1111yescharacteristic
214M16—22no—
215M16—222no—
216C2×C8—112no—
217C2×C8C22×D1112yes—
218C4⋊C4—21no—
219C4⋊C4—112no—
220C4⋊C4—222no—
221C4⋊C4—222no—
222C4⋊C4—221no—
223C4⋊C4—221no—
224C4⋊C4—221no—
225C4⋊C4C22×D1112yes—
226C22⋊C4—221no—
227C22⋊C4—221no—
228C22⋊C4—221no—
229C22⋊C4—221no—
230C42—111no—
231C42—111no—
232C42—111no—
233C42—111no—
234C11#314111yescharacteristic, complemented, Sylow
235C23—21no—
236C23—221no—
237C23D4×D1111yescharacteristic
238Q8—21no—
239Q8—21no—
240Q8—221no—
241Q8—221no—
242Q8—444no—
243Q8—444no—
244D4—21no—
245D4—21no—
246D4—42no—
247D4—221no—
248D4—221no—
249D4—442no—
250D4—442no—
251D4—442no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—111no—
257C2×C4—111no—
258C2×C4—111no—
259C2×C4—111no—
260C2×C4—222no—
261C2×C4—222no—
262C2×C4—221no—
263C2×C4—222no—
264C2×C4—442no—
265C2×C4—442no—
266C2×C4#433912yes—
267C2×C4D4×D1111yescharacteristic
268C2×C4#434112yes—
269C2×C4C23×D1111yescharacteristic
270C8—22no—
271C8—222no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22—441no—
278C22—441no—
279C22—441no—
280C22#6693812yes—
281C22C2×D4×D1111yescharacteristic
282C4—41no—
283C4—42no—
284C4—112no—
285C4—112no—
286C4—221no—
287C4—221no—
288C4—441no—
289C4—442no—
290C4#6693812yes—
291C4C2×#433911yescharacteristic
292C4C2×#434111yescharacteristic
293C2—22no—
294C2—81no—
295C2—881no—
296C2C2×#6693811yescharacteristic
297C2D11×AGL(1,ℤ/8)11yescharacteristic
298C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#417C2
socleC22×C11C22×D4
prime radical#10623363C2
hypercenter#417D11
hypocenterC11#3141
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#66941C2semidirect
3. C11×#417C2semidirect
4. #10622845C2semidirect
5. #10622746C2semidirect
6. M16×Dic11C2semidirect
7. #10622579C2semidirect
8. #10622408C2semidirect
9. #10622405C2semidirect
10. #10622378C2semidirect
11. #10622373C2semidirect
132. #417D11semidirect
234. C11#3141semidirect

Maximal subgroups

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

subgroupindex
#106233632
C2×#669412
C11×#4172
#106228452
#106227462
M16×Dic112
#106225792
#106224082
#106224052
#106223782
#106223732
#314111