Finite Group Databasebeta

← #14672461

Subgroups — #14672461

Order 2816.

420 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 111 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#13068612C211yesmaximal, characteristic
2C4×#66900C211yesmaximal, characteristic
3#13066743C214yesmaximal
4C11×#2567C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C11×#395—21no—
8C11×#395—21no—
9C11×#391C2212yes—
10C11×#389—21no—
11C11×#389—21no—
12C11×#384C412yes—
13C4×C11×C4⋊C4C411yescharacteristic
14C2×#66900C2212yes—
15C2×#66900C2212yes—
16#10622537—21no—
17C4×#4318—21no—
18#10622168—21no—
19#10622168—21no—
20C22×Q8×C11—21no—
21C22×Q8×C11C2311yescharacteristic
22C11×C4⋊Q8—41no—
23C11×C4⋊Q8—41no—
24C4×Q8×C11—41no—
25C4×Q8×C11—41no—
26C2×C11×C4⋊C4—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—22no—
30C2×C11×C4⋊C4C2×C412yes—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C412yes—
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×#4318—22no—
39C2×#4318—22no—
40C11×#95—21no—
41C11×#95—22no—
42C11×#95—22no—
43#66900—22no—
44#66900—24no—
45#66900Q814yescomplemented
46C4⋊(C11⋊C8)—41no—
47C4⋊(C11⋊C8)—41no—
48#66867—41no—
49C4×C11⋊C8—41no—
50#13302—111nomaximal, Sylow
51C2×Q8×C11—41no—
52C2×Q8×C11—41no—
53C2×Q8×C11—42no—
54C2×Q8×C11—82no—
55C2×Q8×C11C2×Q812yes—
56C2×Q8×C11#4112yes—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C11×C4⋊C4—24no—
67C11×C4⋊C4—41no—
68C11×C4⋊C4—41no—
69C11×C4⋊C4—41no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—41no—
72C11×C4⋊C4—41no—
73C11×C4⋊C4—82no—
74C11×C4⋊C4—82no—
75C42×C11—21no—
76C42×C11—21no—
77C42×C11—21no—
78C42×C11—21no—
79C42×C11—21no—
80C42×C11—21no—
81C42×C11—42no—
82#4318—24no—
83#4318—42no—
84#4318—42no—
85#4318—42no—
86C2×C11⋊C8—42no—
87C2×C11⋊C8—42no—
88#2567D1111yescharacteristic
89#1801—111no—
90C4×#101—111no—
91#1394—114no—
92C23×C11C2×C22⋊C411yescharacteristic
93Q8×C11—42no—
94Q8×C11—42no—
95Q8×C11—84no—
96C2×C4×C11—21no—
97C2×C4×C11—21no—
98C2×C4×C11—21no—
99C2×C4×C11—21no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—22no—
103C2×C4×C11—24no—
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—42no—
108C2×C4×C11—42no—
109C2×C4×C11—41no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—42no—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11#9911yescharacteristic
116C2×C4×C11#9911yescharacteristic
117C2×C4×C11C4×Q812yes—
118C2×C4×C11C22⋊Q812yes—
119C2×C4×C11#12411yescharacteristic
120C2×C4×C11C4⋊Q811yescharacteristic
121C11⋊C8—44no—
122C11⋊C8—82no—
123C2×C4⋊Q8Dic1111yescharacteristic
124C2×C4×Q8C2×D1111yescharacteristic
125#423—221no—
126C2×#101—112no—
127C2×#101—112no—
128C4×M16—221no—
129#395—21no—
130#395—21no—
131#391C2×D1112yes—
132#389—21no—
133#389—21no—
134#384Dic1112yes—
135C4×C4⋊C4Dic1111yescharacteristic
136#343—221no—
137#343—221no—
138C22×C11—21no—
139C22×C11—21no—
140C22×C11#39111yescharacteristic
141C22×C11C2×#9911yescharacteristic
142C22×C11#41011yescharacteristic
143C4×C11—21no—
144C4×C11—22no—
145C4×C11—22no—
146C4×C11—21no—
147C4×C11—21no—
148C4×C11—44no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11—41no—
152C4×C11—82no—
153C4×C11#35612yes—
154C22×Q8—21no—
155C22×Q8C22×D1111yescharacteristic
156C2×M16—222no—
157C2×M16—222no—
158C4⋊Q8—41no—
159C4⋊Q8—41no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C2×Dic1112yes—
167C2×C4⋊C4C2×Dic1111yescharacteristic
168C2×C4⋊C4C22⋊D1111yescharacteristic
169C2×C4⋊C4C22⋊D1111yescharacteristic
170C2×C42C2×Dic1111yescharacteristic
171C2×C42C2×Dic1112yes—
172C2×C42C22⋊D1111yescharacteristic
173C2×C42C22⋊D1111yescharacteristic
174C4⋊C8—441no—
175C4⋊C8—441no—
176#101—114no—
177#101—222no—
178#101—224no—
179#97—441no—
180C4×C8—441no—
181#95—21no—
182#95—22no—
183#95—22no—
184C2×C11—21no—
185C2×C11—21no—
186C2×C11#199611yescharacteristic
187C2×C11C2×#35611yescharacteristic
188C2×C11#213411yescharacteristic
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—42no—
192C2×Q8—82no—
193C2×Q8Q8×D1112yes—
194C2×Q8#434312yes—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4C22⋊Dic1111yescharacteristic
198C22×C4C22⋊Dic1111yescharacteristic
199C22×C4C22⋊Dic1111yescharacteristic
200C22×C4C22⋊Dic1111yescharacteristic
201C22×C4C22×Dic1111yescharacteristic
202C22×C4C2×C22⋊D1111yescharacteristic
203C22×C4C2×C22⋊D1111yescharacteristic
204M16—224no—
205M16—442no—
206M16—442no—
207M16—442no—
208C2×C8—442no—
209C2×C8—442no—
210C4⋊C4—24no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—82no—
218C4⋊C4—82no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—42no—
226C11#1330211yescharacteristic, complemented, Sylow
227C23C2×C22⋊Dic1111yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—84no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4#6689811yescharacteristic
251C2×C4#6689811yescharacteristic
252C2×C4#6699711yescharacteristic
253C2×C4Q8×Dic1112yes—
254C2×C4#6699912yes—
255C2×C4#6700011yescharacteristic
256C8—444no—
257C8—882no—
258C22—21no—
259C22—21no—
260C22C2×#6689811yescharacteristic
261C22#1062284311yescharacteristic
262C22#1062285311yescharacteristic
263C4—22no—
264C4—21no—
265C4—21no—
266C4—22no—
267C4—21no—
268C4—44no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4#1062218612yes—
274C2—21no—
275C2—21no—
276C2#1306960211yescharacteristic
277C2C2×#1062218611yescharacteristic
278C2#1307030811yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC22×Q8C22×D11
FittingC11×#2567C2
socleC22×C11C2×#99
prime radicalC23×C11C2×C22⋊C4
cosocleC22×Q8×C11C23
hypercenter#2567D11
hypocenterC11#13302
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2567

Complements

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

NH ≅ G/Ntype
45. #66900Q8semidirect
226. C11#13302semidirect

Maximal subgroups

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

subgroupindex
#130686122
C4×#669002
#130667432
C11×#25672
#1330211