Finite Group Databasebeta

← #13078593

Subgroups — #13078593

Order 1408.

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

normal subgroups only

This group has 398 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
1#10623364C211yesmaximal, characteristic
2#10623035C211yesmaximal, characteristic, complemented
3C11×#417C211yesmaximal, characteristic, complemented
4#10622846C211yesmaximal, characteristic, complemented
5#10622742C211yesmaximal, characteristic, complemented
6#10622734C211yesmaximal, characteristic, complemented
7C2×#66871C211yesmaximal, characteristic, complemented
8#10622428C212yesmaximal, complemented
9#10622422C212yesmaximal, complemented
10#10622392C212yesmaximal, complemented
11#10622387C212yesmaximal, complemented
12C2×C11×#41C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C2×C11×M16C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16#66999C2212yes—
17#66992—22no—
18#66991C2212yes—
19#66983—21no—
20C4×C22⋊D11—22no—
21#66979C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23#66977—21no—
24C22×C11⋊C8C2211yescharacteristic
25#66946—21no—
26#66945C2212yes—
27C4⋊C4×D11C2212yes—
28#66940—21no—
29C11×#103C2212yes—
30C11×#102C2212yes—
31#66899C2211yescharacteristic
32#66899C2211yescharacteristic
33#66896C2211yescharacteristic
34#66896C2211yescharacteristic
35(C2×D11)⋊C8C2212yes—
36(C2×D11)⋊C8C2212yes—
37#66882C2212yes—
38#66881C2212yes—
39#66871C2212yes—
40#66871C2212yes—
41C11×#41—22no—
42C11×#41—22no—
43C2×Q8×C11C2311yescharacteristic
44C2×D4×C11—21no—
45C2×D4×C11C2311yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C2311yescharacteristic
49C2×C22⋊D11—22no—
50C2×C22⋊D11D412yes—
51C22×Dic11—21no—
52#4339—22no—
53#4339—22no—
54C2×D44D411yescharacteristic
55C2×C4×D11—22no—
56C2×C4×D11C2312yes—
57C2×Dic22D411yescharacteristic
58C11×M16—22no—
59C2×C8×C11C2312yes—
60C11×C4⋊C4—21no—
61C11×C4⋊C4C2312yes—
62C22⋊Dic11—22no—
63C22⋊Dic11—21no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—22no—
66C4⋊Dic11—21no—
67C4⋊Dic11C2312yes—
68C4⋊Dic11C2311yescharacteristic
69C4⋊Dic11C2311yescharacteristic
70Dic11⋊C4—22no—
71Dic11⋊C4—22no—
72C4×Dic11—22no—
73C4×Dic11—21no—
74C2×C11⋊C8—22no—
75C2×C11⋊C8C2311yescharacteristic
76C2×C11⋊C8C2311yescharacteristic
77#3098—111nomaximal, Sylow
78C23×C11—21no—
79C23×C11C2×D411yescharacteristic
80C22×D11C2×D412yes—
81Q8×C11—21no—
82Q8×C11—21no—
83D4×C11—21no—
84D4×C11—21no—
85D4×C11—42no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—42no—
89C2×C4×C11—81no—
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11#4112yes—
92C2×C4×C11#4112yes—
93C2×C4×C11C2411yescharacteristic
94C22⋊D11—24no—
95C22⋊D11—82no—
96C2×Dic11—21no—
97C2×Dic11—21no—
98C2×Dic11—22no—
99C2×Dic11—81no—
100C2×Dic11C2×D412yes—
101D44—22no—
102C4×D11—22no—
103C4×D11—22no—
104C4×D11—82no—
105Dic22—22no—
106C8×C11—22no—
107C11⋊C8—21no—
108C11⋊C8—21no—
109#537—111no—
110#520—111no—
111#485—112no—
112#484—112no—
113#482—112no—
114#480—112no—
115#428—111no—
116C2×#107—111no—
117#417D1111yescharacteristic, complemented
118#416—111no—
119#408—111no—
120C22×C11—21no—
121C22×C11—21no—
122C22×C11—41no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11#12312yes—
126C22×C11C22×D411yescharacteristic
127C2×D11—22no—
128C2×D11—22no—
129C2×D11—22no—
130C4×C11—41no—
131C4×C11—42no—
132C4×C11#12312yes—
133C4×C11C2×#4111yescharacteristic
134C4×C11C2×#4111yescharacteristic
135Dic11—22no—
136Dic11—41no—
137Dic11—42no—
138Dic11—41no—
139C2×#41—111no—
140C2×#41C2×D1111yescharacteristic
141C2×M16C2×D1111yescharacteristic
142C22×C8—111no—
143C22⋊Q8—112no—
144C22⋊Q8—221no—
145#121—112no—
146#121—221no—
147#121—222no—
148C4×Q8—221no—
149C4×D4—221no—
150C4×D4—222no—
151#117—111no—
152#117—112no—
153C2×C4⋊C4—111no—
154C2×C4⋊C4—112no—
155C2×C4⋊C4C2×D1111yescharacteristic
156#107—112no—
157#107—112no—
158#107—112no—
159#106—112no—
160#103—111no—
161#103—111no—
162#103C2×D1112yes—
163#102—111no—
164#102—111no—
165#102C2×D1112yes—
166C22⋊C8—112no—
167C22⋊C8—112no—
168C2×C11—22no—
169C2×C11—81no—
170C2×C11C2×#12311yescharacteristic
171C2×C11#57611yescharacteristic
172C2×C11#57811yescharacteristic
173D11—42no—
174#41—22no—
175#41—22no—
176#41—222no—
177#41—222no—
178C2×Q8—111no—
179C2×Q8C22×D1111yescharacteristic
180C2×D4—21no—
181C2×D4—112no—
182C2×D4—111no—
183C2×D4—222no—
184C2×D4C22×D1111yescharacteristic
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—112no—
188C22×C4—222no—
189C22×C4—221no—
190C22×C4C22×D1111yescharacteristic
191M16—22no—
192C2×C8—111no—
193C2×C8—111no—
194C2×C8—222no—
195C2×C8C22×D1112yes—
196C4⋊C4—21no—
197C4⋊C4—111no—
198C4⋊C4—111no—
199C4⋊C4—112no—
200C4⋊C4—222no—
201C4⋊C4—222no—
202C4⋊C4—221no—
203C4⋊C4C22×D1112yes—
204C22⋊C4—222no—
205C22⋊C4—222no—
206C22⋊C4—222no—
207C22⋊C4—221no—
208C42—222no—
209C42—221no—
210C11#309811yescharacteristic, complemented, Sylow
211C23—21no—
212C23—112no—
213C23D4×D1111yescharacteristic
214Q8—21no—
215Q8—21no—
216Q8—222no—
217D4—21no—
218D4—21no—
219D4—42no—
220D4—224no—
221D4—222no—
222D4—882no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—81no—
227C2×C4—112no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4—222no—
233C2×C4—882no—
234C2×C4—881no—
235C2×C4#433912yes—
236C2×C4D4×D1111yescharacteristic
237C2×C4#434112yes—
238C2×C4C23×D1111yescharacteristic
239C8—22no—
240C8—221no—
241C8—221no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—222no—
248C22—222no—
249C22—222no—
250C22#6693612yes—
251C22C2×D4×D1111yescharacteristic
252C4—41no—
253C4—42no—
254C4—222no—
255C4—441no—
256C4—442no—
257C4—441no—
258C4#6693612yes—
259C4C2×#433911yescharacteristic
260C4C2×#434111yescharacteristic
261C2—22no—
262C2—81no—
263C2—442no—
264C2C2×#6693611yescharacteristic
265C2#1062330511yescharacteristic
266C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#417C2
socleC22×C11C22×D4
prime radical#10623364C2
hypercenter#417D11
hypocenterC11#3098
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. #10623035C2semidirect
3. C11×#417C2semidirect
4. #10622846C2semidirect
5. #10622742C2semidirect
6. #10622734C2semidirect
7. C2×#66871C2semidirect
8. #10622428C2semidirect
9. #10622422C2semidirect
10. #10622392C2semidirect
11. #10622387C2semidirect
117. #417D11semidirect
210. C11#3098semidirect

Maximal subgroups

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

subgroupindex
#106233642
#106230352
C11×#4172
#106228462
#106227422
#106227342
C2×#668712
#106224282
#106224222
#106223922
#106223872
#309811