Finite Group Databasebeta

← #13078583

Subgroups — #13078583

Order 1408.

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

normal subgroups only

This group has 386 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#10623347C211yesmaximal, characteristic
2#10623054C211yesmaximal, characteristic
3C11×#419C211yesmaximal, characteristic, complemented
4C2×#66899C211yesmaximal, characteristic, complemented
5#10622742C211yesmaximal, characteristic
6#10622734C211yesmaximal, characteristic, complemented
7#10622611C211yesmaximal, characteristic, complemented
8#10622428C212yesmaximal, complemented
9#10622427C212yesmaximal, complemented
10#10622422C212yesmaximal, complemented
11#10622418C212yesmaximal, complemented
12C22×Q8×C11C2211yescharacteristic
13C2×#4339C2211yescharacteristic
14C2×C11×M16C2211yescharacteristic
15C11×#117C2211yescharacteristic
16#67000—21no—
17#66999C2212yes—
18#66999C2212yes—
19#66997—21no—
20#66982—22no—
21#66979C2211yescharacteristic
22C2×C4⋊Dic11C2211yescharacteristic
23C22×C11⋊C8C2211yescharacteristic
24#66945C2212yes—
25C4⋊C4×D11C2212yes—
26(C22⋊D11)⋊C4—22no—
27C4×D44—21no—
28C4×Dic22—21no—
29C11×#103C2212yes—
30C11×#103C2212yes—
31#66899C2212yes—
32#66899C2212yes—
33(C2×D11)⋊C8C2212yes—
34(C2×D11)⋊C8C2212yes—
35#66882C2212yes—
36#66881C2212yes—
37#66872C2211yescharacteristic
38#66872C2211yescharacteristic
39#66871C2211yescharacteristic
40#66871C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×Q8×C11—22no—
43C2×Q8×C11—22no—
44C2×Q8×C11C2312yes—
45C22×C4×C11—21no—
46C22×C4×C11C2311yescharacteristic
47C2×C22⋊D11D412yes—
48C22×Dic11—21no—
49#4339—22no—
50#4339—22no—
51C2×D44D411yescharacteristic
52C2×C4×D11—22no—
53C2×C4×D11C2312yes—
54C2×Dic22D411yescharacteristic
55C11×M16—22no—
56C2×C8×C11C2312yes—
57C11×C4⋊C4C2311yescharacteristic
58C11×C4⋊C4C2311yescharacteristic
59C11×C22⋊C4—21no—
60C42×C11—21no—
61C22⋊Dic11—21no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—22no—
65C4⋊Dic11—21no—
66C4⋊Dic11C2311yescharacteristic
67C4⋊Dic11C2311yescharacteristic
68C4⋊Dic11C2312yes—
69Dic11⋊C4—22no—
70Dic11⋊C4—22no—
71Dic11⋊C4—22no—
72C4×Dic11—22no—
73C4×Dic11—21no—
74C2×C11⋊C8—22no—
75C2×C11⋊C8C2311yescharacteristic
76C2×C11⋊C8C2311yescharacteristic
77#3097—111nomaximal, Sylow
78C23×C11C2×D411yescharacteristic
79C22×D11C2×D412yes—
80Q8×C11—22no—
81Q8×C11—22no—
82Q8×C11—42no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—42no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11#4112yes—
89C2×C4×C11#4112yes—
90C2×C4×C11C2411yescharacteristic
91C22⋊D11—24no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—81no—
96C2×Dic11C2×D412yes—
97D44—22no—
98C4×D11—22no—
99C4×D11—22no—
100C4×D11—82no—
101Dic22—22no—
102C8×C11—22no—
103C11⋊C8—21no—
104C11⋊C8—21no—
105#536—111no—
106#520—111no—
107#485—112no—
108#485—112no—
109#484—112no—
110#483—112no—
111#428—111no—
112#427—111no—
113#419D1111yescharacteristic, complemented
114C2×#103—111no—
115#408—111no—
116C22×C11—21no—
117C22×C11—21no—
118C22×C11#12312yes—
119C22×C11C22×D411yescharacteristic
120C2×D11—22no—
121C2×D11—22no—
122C2×D11—22no—
123C4×C11—42no—
124C4×C11—41no—
125C4×C11—41no—
126C4×C11#12312yes—
127C4×C11C2×#4111yescharacteristic
128C4×C11C2×#4111yescharacteristic
129Dic11—22no—
130Dic11—42no—
131Dic11—41no—
132Dic11—41no—
133C2×#41—111no—
134C22×Q8C2×D1111yescharacteristic
135C2×M16C2×D1111yescharacteristic
136C22×C8—111no—
137C4⋊Q8—221no—
138#124—221no—
139#123—222no—
140C22⋊Q8—112no—
141C22⋊Q8—112no—
142C4×Q8—221no—
143C4×D4—221no—
144C4×D4—222no—
145#117—111no—
146#117—112no—
147#117C2×D1111yescharacteristic
148C2×C4⋊C4—111no—
149C2×C4⋊C4—112no—
150#107—112no—
151#107—111no—
152#107—111no—
153#106—112no—
154#106—111no—
155#106—111no—
156#103—112no—
157#103—112no—
158#103C2×D1112yes—
159#103C2×D1112yes—
160C22⋊C8—112no—
161C22⋊C8—112no—
162C2×C11—22no—
163C2×C11C2×#12311yescharacteristic
164C2×C11#57711yescharacteristic
165C2×C11#57811yescharacteristic
166D11—42no—
167#41—222no—
168#41—222no—
169C2×Q8—21no—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—111no—
173C2×Q8C22×D1112yes—
174C2×D4—112no—
175C2×D4—111no—
176C22×C4—21no—
177C22×C4—112no—
178C22×C4—222no—
179C22×C4—221no—
180C22×C4C22×D1111yescharacteristic
181M16—22no—
182C2×C8—111no—
183C2×C8—111no—
184C2×C8—222no—
185C2×C8C22×D1112yes—
186C4⋊C4—112no—
187C4⋊C4—111no—
188C4⋊C4—111no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—222no—
192C4⋊C4—221no—
193C4⋊C4C22×D1111yescharacteristic
194C4⋊C4C22×D1111yescharacteristic
195C22⋊C4—21no—
196C22⋊C4—222no—
197C22⋊C4—222no—
198C22⋊C4—222no—
199C22⋊C4—221no—
200C42—21no—
201C42—222no—
202C42—221no—
203C11#309711yescharacteristic, complemented, Sylow
204C23—112no—
205C23D4×D1111yescharacteristic
206Q8—22no—
207Q8—22no—
208Q8—42no—
209Q8—222no—
210D4—224no—
211D4—222no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—42no—
216C2×C4—112no—
217C2×C4—222no—
218C2×C4—222no—
219C2×C4—221no—
220C2×C4—221no—
221C2×C4—222no—
222C2×C4—882no—
223C2×C4—881no—
224C2×C4#433912yes—
225C2×C4D4×D1111yescharacteristic
226C2×C4#434112yes—
227C2×C4C23×D1111yescharacteristic
228C8—22no—
229C8—221no—
230C8—221no—
231C22—21no—
232C22—21no—
233C22—222no—
234C22—222no—
235C22—222no—
236C22#6693612yes—
237C22C2×D4×D1111yescharacteristic
238C4—42no—
239C4—41no—
240C4—41no—
241C4—222no—
242C4—442no—
243C4—441no—
244C4—441no—
245C4#6693612yes—
246C4C2×#433911yescharacteristic
247C4C2×#434111yescharacteristic
248C2—22no—
249C2—442no—
250C2C2×#6693611yescharacteristic
251C2#1062330911yescharacteristic
252C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#419C2
socleC22×C11C22×D4
prime radicalC2×#4339C22
hypercenter#419D11
hypocenterC11#3097
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. C11×#419C2semidirect
4. C2×#66899C2semidirect
6. #10622734C2semidirect
7. #10622611C2semidirect
8. #10622428C2semidirect
9. #10622427C2semidirect
10. #10622422C2semidirect
11. #10622418C2semidirect
113. #419D11semidirect
203. C11#3097semidirect

Maximal subgroups

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

subgroupindex
#106233472
#106230542
C11×#4192
C2×#668992
#106227422
#106227342
#106226112
#106224282
#106224272
#106224222
#106224182
#309711