Finite Group Databasebeta

← #13078268

Subgroups — #13078268

Order 1408.

460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C11×#536C211yesmaximal, characteristic
2#10623356C211yesmaximal, characteristic
3C2×#67001C211yesmaximal, characteristic
4C22×#4326C211yesmaximal, characteristic, complemented
5#10622838C211yesmaximal, characteristic, complemented
6#10622665C214yesmaximal, complemented
7#10622664C214yesmaximal, complemented
8#10622617C211yesmaximal, characteristic, complemented
9#10622611C211yesmaximal, characteristic, complemented
10C2×C11×#41C2211yescharacteristic
11C22×Q8×C11C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C11×C4⋊Q8—21no—
14C11×#124—21no—
15C11×#123—22no—
16C11×C22⋊Q8C2214yes—
17C11×#117C2211yescharacteristic
18#67001—24no—
19#66997—21no—
20C2×#4326—24no—
21C2×#4326C2212yes—
22C2×#4326C2212yes—
23#66989—21no—
24#66988—22no—
25#66979C2211yescharacteristic
26#66977C2214yes—
27C2×#4318C2211yescharacteristic
28C2×#4318C2212yes—
29C22×C11⋊C8C2212yes—
30C22×C11⋊C8C2211yescharacteristic
31#66899C2214yes—
32#66874C2214yes—
33#66872C2212yes—
34#66871C2212yes—
35C11×#41—22no—
36C11×#41—22no—
37C2×Q8×C11—21no—
38C2×Q8×C11—22no—
39C2×Q8×C11—22no—
40C2×Q8×C11D411yescharacteristic
41C2×Q8×C11C2312yes—
42C2×D4×C11D412yes—
43C2×D4×C11D411yescharacteristic
44C22×C4×C11—21no—
45C22×C4×C11C2312yes—
46C22×C4×C11C2311yescharacteristic
47C22×Dic11—21no—
48C2×Dic22—22no—
49C2×Dic22—21no—
50C2×Dic22—22no—
51C2×Dic22C2312yes—
52C11×C4⋊C4—24no—
53C11×C4⋊C4C2312yes—
54C11×C22⋊C4—21no—
55C11×C22⋊C4—24no—
56C42×C11—21no—
57C22⋊Dic11—24no—
58C22⋊Dic11—21no—
59#4326—24no—
60#4326—24no—
61C4⋊Dic11C2312yes—
62Dic11⋊C4—24no—
63C4×Dic11—21no—
64#4318—24no—
65#4318—22no—
66C2×C11⋊C8—24no—
67C2×C11⋊C8D414yes—
68C2×C11⋊C8C2312yes—
69C2×C11⋊C8C2311yescharacteristic
70C2×C11⋊C8C2311yescharacteristic
71#3059—111nomaximal, Sylow
72C23×C11C2×D412yes—
73C23×C11C2×D411yescharacteristic
74Q8×C11—22no—
75Q8×C11—22no—
76Q8×C11—22no—
77Q8×C11—42no—
78D4×C11—24no—
79D4×C11—22no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—42no—
85C2×C4×C11C2×D412yes—
86C2×C4×C11C2×D412yes—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11#4112yes—
89C2×C4×C11C2411yescharacteristic
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—42no—
93Dic22—22no—
94Dic22—22no—
95Dic22—42no—
96C11⋊C8—22no—
97C11⋊C8C2×D412yes—
98C11⋊C8C2×D412yes—
99C22×Q16—111no—
100C2×#131—111no—
101#536—111no—
102#536D1111yescharacteristic
103#470—114no—
104#467—114no—
105#427—111no—
106#419—111no—
107#419—111no—
108C22×C11—22no—
109C22×C11—22no—
110C22×C11—24no—
111C22×C11#12112yes—
112C22×C11C22×D411yescharacteristic
113C4×C11—22no—
114C4×C11—42no—
115C4×C11—42no—
116C4×C11#12112yes—
117C4×C11C22×D411yescharacteristic
118C4×C11C2×#4111yescharacteristic
119Dic11—42no—
120Dic11—42no—
121C2×#41C2×D1111yescharacteristic
122C22×Q8—111no—
123C22×Q8C2×D1111yescharacteristic
124C2×Q16—112no—
125C2×Q16—112no—
126C2×Q16—224no—
127#131—224no—
128C2×M16—111no—
129C2×M16—112no—
130C22×C8—111no—
131C22×C8—112no—
132C4⋊Q8—21no—
133C4⋊Q8—221no—
134#124—21no—
135#124—221no—
136#123—22no—
137#123—222no—
138C22⋊Q8—114no—
139C22⋊Q8C2×D1114yes—
140#117—111no—
141#117C2×D1111yescharacteristic
142#107—112no—
143#106—112no—
144#103—114no—
145#103—114no—
146C2×C11—22no—
147C2×C11—42no—
148C2×C11C2×#12111yescharacteristic
149C2×C11#57812yes—
150#41—22no—
151#41—22no—
152C2×Q8—21no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—112no—
156C2×Q8—221no—
157C2×Q8—222no—
158C2×Q8—222no—
159C2×Q8C22⋊D1111yescharacteristic
160C2×Q8C22×D1112yes—
161C2×D4C22⋊D1112yes—
162C2×D4C22⋊D1111yescharacteristic
163C22×C4—21no—
164C22×C4—221no—
165C22×C4C22×D1112yes—
166C22×C4C22×D1111yescharacteristic
167Q16—224no—
168Q16—224no—
169M16—224no—
170M16—222no—
171C2×C8—114no—
172C2×C8—111no—
173C2×C8—111no—
174C2×C8—112no—
175C2×C8—224no—
176C4⋊C4—24no—
177C4⋊C4—112no—
178C4⋊C4—224no—
179C4⋊C4C22×D1112yes—
180C22⋊C4—21no—
181C22⋊C4—24no—
182C22⋊C4—221no—
183C22⋊C4—224no—
184C42—21no—
185C42—221no—
186C11#305911yescharacteristic, complemented, Sylow
187C23C2×C22⋊D1112yes—
188C23C2×C22⋊D1111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—222no—
194Q8—222no—
195Q8—442no—
196D4—24no—
197D4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—442no—
206C2×C4D4×D1112yes—
207C2×C4#434112yes—
208C2×C4C2×C22⋊D1112yes—
209C2×C4C2×C22⋊D1111yescharacteristic
210C2×C4C23×D1111yescharacteristic
211C8—112no—
212C8—112no—
213C8—222no—
214C22—22no—
215C22—22no—
216C22—24no—
217C22#6699212yes—
218C22C22×C22⋊D1111yescharacteristic
219C4—22no—
220C4—42no—
221C4—42no—
222C4—442no—
223C4—442no—
224C4#6699212yes—
225C4C2×D4×D1111yescharacteristic
226C4C2×#434111yescharacteristic
227C2—22no—
228C2—42no—
229C2C2×#6699211yescharacteristic
230C2#1062336912yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#536C2
socleC22×C11C22×D4
prime radicalC2×C11×#41C22
hypercenter#536D11
hypocenterC11#3059
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
4. C22×#4326C2semidirect
5. #10622838C2semidirect
6. #10622665C2semidirect
7. #10622664C2semidirect
8. #10622617C2semidirect
9. #10622611C2semidirect
186. C11#3059semidirect

Maximal subgroups

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

subgroupindex
C11×#5362
#106233562
C2×#670012
C22×#43262
#106228382
#106226652
#106226642
#106226172
#106226112
#305911