Finite Group Databasebeta

← #14670619

Subgroups — #14670619

Order 2816.

408 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 99 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#13077687C211yesmaximal, characteristic
2#13069000C211yesmaximal, characteristic
3#13068838C212yesmaximal, complemented
4#13066746C212yesmaximal, complemented
5C11×#2132C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7#10623350C2211yescharacteristic
8C11×#413C2212yes—
9#10622853C2211yescharacteristic
10#10622849—21no—
11#10622847—21no—
12#10622847C2212yes—
13#10622738—22no—
14#10622624—22no—
15#10622624—22no—
16#10622539—21no—
17C11×#356C412yescomplemented
18C11×#355C412yescomplemented
19#10622196—22no—
20#10622161—21no—
21C2×C11×#41D411yescharacteristic
22C2×C11×#41C2311yescharacteristic
23C2×C11×M16—22no—
24C11×C4⋊Q8C2×C411yescharacteristic
25C11×#127Q811yescharacteristic
26C11×#124C2×C411yescharacteristic
27C11×#124Q811yescharacteristic
28C11×#121—22no—
29C4×D4×C11—22no—
30C2×C42×C11D411yescharacteristic
31#67001—42no—
32#66979—21no—
33C2×#4318—21no—
34C2×#4318—22no—
35C2×#4318—21no—
36C2×#4318D412yes—
37C22×C11⋊C8—21no—
38C22×C11⋊C8D412yes—
39C11×#101C2×C414yes—
40C11×#100—22no—
41#66901—42no—
42#66898—22no—
43C22⋊(C11⋊C8)—22no—
44C22⋊(C11⋊C8)—22no—
45C22⋊(C11⋊C8)—22no—
46#66883—44no—
47C4⋊(C11⋊C8)—21no—
48C4⋊(C11⋊C8)—21no—
49#66867—22no—
50#12974—111nomaximal, Sylow
51C11×#41—41no—
52C11×#41—41no—
53C11×#41—41no—
54C11×#41—41no—
55C2×Q8×C11C4⋊C411yescharacteristic
56C2×Q8×C11C22×C411yescharacteristic
57C2×D4×C11—22no—
58C2×D4×C11—21no—
59C2×D4×C11C4⋊C411yescharacteristic
60C2×D4×C11C2×Q811yescharacteristic
61C2×D4×C11#4112yes—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D412yes—
66C11×M16—24no—
67C11×M16—42no—
68C2×C8×C11—42no—
69C11×C4⋊C4—22no—
70C11×C22⋊C4—22no—
71C11×C22⋊C4—22no—
72C42×C11—21no—
73C42×C11C4⋊C411yescharacteristic
74C42×C11C4⋊C411yescharacteristic
75C22⋊Dic11—41no—
76C4⋊Dic11—41no—
77C4×Dic11—41no—
78#4318—24no—
79#4318—22no—
80#4318—42no—
81#4318—41no—
82#4318—81no—
83C2×C11⋊C8—22no—
84C2×C11⋊C8—22no—
85C2×C11⋊C8—42no—
86C2×C11⋊C8—42no—
87C2×C11⋊C8—41no—
88C2×C11⋊C8—81no—
89#2980—111no—
90#2132D1111yescharacteristic
91#1884—111no—
92#1858—112no—
93#1395—112no—
94C23×C11—21no—
95C23×C11C22⋊Q812yes—
96C23×C11#12311yescharacteristic
97Q8×C11—41no—
98Q8×C11—41no—
99D4×C11—41no—
100D4×C11—42no—
101D4×C11—41no—
102D4×C11—81no—
103D4×C11—82no—
104C2×C4×C11—22no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—41no—
112C2×C4×C11—41no—
113C2×C4×C11—81no—
114C2×C4×C11C2×C4⋊C411yescharacteristic
115C2×C4×C11C4×D412yes—
116C2×C4×C11#12011yescharacteristic
117C2×Dic11—81no—
118C8×C11—44no—
119C11⋊C8—42no—
120C11⋊C8—42no—
121C11⋊C8—42no—
122#568—111no—
123#532C2×D1111yescharacteristic
124#435—222no—
125#435—222no—
126#432—221no—
127#430—222no—
128#421—221no—
129#413C2×D1112yes—
130#410—111no—
131#408—112no—
132#408—221no—
133#356Dic1112yescomplemented
134#355Dic1112yescomplemented
135#341—222no—
136#339—221no—
137C22×C11—21no—
138C22×C11—22no—
139C22×C11—41no—
140C22×C11—42no—
141C22×C11—42no—
142C22×C11—41no—
143C22×C11#38511yescharacteristic
144C4×C11—21no—
145C4×C11—22no—
146C4×C11—41no—
147C4×C11—41no—
148C4×C11—41no—
149C4×C11B(4,𝔽2)11yescharacteristic
150C4×C11#45811yescharacteristic
151Dic11—161no—
152C2×#41D4411yescharacteristic
153C2×#41C22×D1111yescharacteristic
154#131—442no—
155C2×M16—22no—
156C2×M16—112no—
157C2×M16—221no—
158C2×M16—221no—
159C2×M16—222no—
160C22×C8—112no—
161C22×C8—221no—
162C4⋊Q8C2×Dic1111yescharacteristic
163#127Dic2211yescharacteristic
164#124Dic2211yescharacteristic
165#124C2×Dic1111yescharacteristic
166#121—22no—
167C4×D4—22no—
168#117—221no—
169C2×C42D4411yescharacteristic
170#108—444no—
171C4⋊C8—221no—
172C4⋊C8—221no—
173#104—442no—
174#101C2×Dic1114yes—
175#100—22no—
176#99—222no—
177C22⋊C8—222no—
178C22⋊C8—222no—
179C22⋊C8—222no—
180#97—222no—
181C2×C11—21no—
182C2×C11—41no—
183C2×C11—42no—
184C2×C11—81no—
185C2×C11#186711yescharacteristic
186#41—41no—
187#41—41no—
188#41—41no—
189#41—41no—
190C2×Q8C4⋊Dic1111yescharacteristic
191C2×Q8C22×Dic1111yescharacteristic
192C2×D4—22no—
193C2×D4—21no—
194C2×D4C4⋊Dic1111yescharacteristic
195C2×D4C2×Dic2211yescharacteristic
196C2×D4#434112yes—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4C2×D4411yescharacteristic
200C22×C4D4×D1112yes—
201M16—24no—
202M16—42no—
203M16—222no—
204M16—224no—
205M16—441no—
206M16—442no—
207M16—881no—
208C2×C8—42no—
209C2×C8—222no—
210C2×C8—222no—
211C2×C8—441no—
212C2×C8—442no—
213C2×C8—442no—
214C2×C8—881no—
215C4⋊C4—22no—
216C4⋊C4—441no—
217C22⋊C4—22no—
218C22⋊C4—22no—
219C22⋊C4—441no—
220C42—21no—
221C42—441no—
222C42C4⋊Dic1111yescharacteristic
223C42C4⋊Dic1111yescharacteristic
224C11#1297411yescharacteristic, complemented, Sylow
225C23—21no—
226C23#6693112yes—
227C23#6693911yescharacteristic
228Q8—41no—
229Q8—41no—
230D4—41no—
231D4—42no—
232D4—41no—
233D4—81no—
234D4—82no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—81no—
245C2×C4—881no—
246C2×C4#6693511yescharacteristic
247C2×C4C2×C4⋊Dic1111yescharacteristic
248C2×C4D4×Dic1112yes—
249C8—44no—
250C8—442no—
251C8—442no—
252C8—442no—
253C22—21no—
254C22—22no—
255C22—41no—
256C22—42no—
257C22—42no—
258C22—41no—
259C22#1062256311yescharacteristic
260C4—22no—
261C4—21no—
262C4—41no—
263C4—41no—
264C4—41no—
265C4—1761no—
266C4#1062235411yescharacteristic
267C4#1062235511yescharacteristic
268C2—21no—
269C2—41no—
270C2—42no—
271C2—81no—
272C2#1306889911yescharacteristic
subgroupG/H
centerC4#10622354
commutatorC2×Q8×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#2132C2
socleC2×C11#1867
prime radicalC11×#532C22
cosocleC2×C11×#41C23
hypercenter#2132D11
hypocenterC11#12974
LCSG ▷ C2×Q8×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #2132

Complements

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

NH ≅ G/Ntype
3. #13068838C2semidirect
4. #13066746C2semidirect
17. C11×#356C4semidirect
18. C11×#355C4semidirect
133. #356Dic11semidirect
134. #355Dic11semidirect
224. C11#12974semidirect

Maximal subgroups

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

subgroupindex
#130776872
#130690002
#130688382
#130667462
C11×#21322
#1297411