Finite Group Databasebeta

← #14669798

Subgroups — #14669798

Order 2816.

428 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 115 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#13070281C212yesmaximal
2#13068662C212yesmaximal, complemented
3#13066737C212yesmaximal, complemented
4C11×#2931C211yesmaximal, characteristic
5C2×C11×#131C411yescharacteristic, complemented
6C2×C11×#131C2211yescharacteristic
7C11×#532C2211yescharacteristic
8C11×#436—22no—
9C8×D4×C11—22no—
10C11×#423C411yescharacteristic, complemented
11C11×#408C411yescharacteristic, complemented
12C11×#408C2211yescharacteristic
13C2×C4×C8×C11C411yescharacteristic, complemented
14#10622853C2214yes—
15#10622719—22no—
16#10622195—22no—
17#10622183—22no—
18#10622179—22no—
19C2×C11×#41C2×C411yescharacteristic
20C2×C11×#41C2311yescharacteristic
21C11×#131—41no—
22C11×#131—41no—
23C11×#131—41no—
24C11×#131—41no—
25C2×C11×M16—21no—
26C2×C11×M16C2×C411yescharacteristic
27C2×C11×M16C2×C411yescharacteristic
28C2×C11×M16D412yes—
29C22×C8×C11—21no—
30C22×C8×C11C2×C411yescharacteristic
31C22×C8×C11C2×C411yescharacteristic
32C22×C8×C11D412yes—
33C11×C4⋊Q8Q811yescharacteristic
34C11×#127D411yescharacteristic
35C11×#124D411yescharacteristic
36C11×#124Q811yescharacteristic
37C11×#121—22no—
38C4×D4×C11—22no—
39C2×C42×C11C2×C411yescharacteristic
40#66979—24no—
41C11×C4⋊C8—22no—
42C11×C22⋊C8—22no—
43C11×C22⋊C8—22no—
44C4×C8×C11—21no—
45C4×C8×C11—21no—
46#66898—24no—
47#66898—24no—
48#66882—42no—
49#66881—42no—
50#12807—111nomaximal, Sylow
51C11×#41—41no—
52C11×#41—41no—
53C11×#41—41no—
54C11×#41—41no—
55C2×Q8×C11C4⋊C411yescharacteristic
56C2×Q8×C11C2×Q811yescharacteristic
57C2×D4×C11—21no—
58C2×D4×C11—22no—
59C2×D4×C11C4⋊C411yescharacteristic
60C2×D4×C11C2×D411yescharacteristic
61C2×D4×C11#4112yes—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D412yes—
66C11×M16—41no—
67C11×M16—42no—
68C11×M16—41no—
69C11×M16—42no—
70C2×C8×C11—22no—
71C2×C8×C11—22no—
72C2×C8×C11—21no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11C22⋊C412yes—
80C2×C8×C11C22⋊C411yescharacteristic
81C2×C8×C11C22⋊C411yescharacteristic
82C11×C4⋊C4—22no—
83C11×C22⋊C4—22no—
84C11×C22⋊C4—22no—
85C42×C11—21no—
86C42×C11C4⋊C411yescharacteristic
87C42×C11C4⋊C411yescharacteristic
88C22⋊Dic11—44no—
89C4⋊Dic11—44no—
90C4×Dic11—44no—
91#2931D1111yescharacteristic
92#2126—112no—
93#1812—112no—
94#1391—112no—
95C23×C11—21no—
96C23×C11#11711yescharacteristic
97C23×C11#12112yes—
98Q8×C11—41no—
99Q8×C11—41no—
100D4×C11—41no—
101D4×C11—42no—
102D4×C11—41no—
103D4×C11—44no—
104D4×C11—42no—
105C2×C4×C11—21no—
106C2×C4×C11—22no—
107C2×C4×C11—21no—
108C2×C4×C11—22no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—42no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11C2×C22⋊C411yescharacteristic
116C2×C4×C11C2×C4⋊C411yescharacteristic
117C2×C4×C11C22⋊Q812yes—
118C2×Dic11—84no—
119C8×C11—22no—
120C8×C11—21no—
121C8×C11—41no—
122C8×C11—41no—
123C8×C11#9911yescharacteristic
124C8×C11#9911yescharacteristic
125C2×#131Dic1111yescharacteristic, complemented
126C2×#131C2×D1111yescharacteristic
127#532C2×D1111yescharacteristic
128#436—22no—
129C8×D4—22no—
130#427—222no—
131#423Dic1111yescharacteristic, complemented
132#410—114no—
133#408Dic1111yescharacteristic, complemented
134#408C2×D1111yescharacteristic
135C2×C4×C8Dic1111yescharacteristic, complemented
136#354—222no—
137#353—222no—
138H(3,ℤ/4)—222no—
139C22×C11—21no—
140C22×C11—22no—
141C22×C11—41no—
142C22×C11—42no—
143C22×C11—42no—
144C22×C11—41no—
145C22×C11#38011yescharacteristic
146C4×C11—22no—
147C4×C11—21no—
148C4×C11—22no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11C2×#9911yescharacteristic
152C4×C11#41011yescharacteristic
153Dic11—164no—
154C2×#41C2×Dic1111yescharacteristic
155C2×#41C22×D1111yescharacteristic
156#131—41no—
157#131—41no—
158#131—41no—
159#131—41no—
160C2×M16—21no—
161C2×M16C2×Dic1111yescharacteristic
162C2×M16C2×Dic1111yescharacteristic
163C2×M16C22⋊D1112yes—
164C22×C8—21no—
165C22×C8C2×Dic1111yescharacteristic
166C22×C8C2×Dic1111yescharacteristic
167C22×C8C22⋊D1112yes—
168C4⋊Q8Dic2211yescharacteristic
169#127D4411yescharacteristic
170#124Dic2211yescharacteristic
171#124D4411yescharacteristic
172#121—22no—
173C4×D4—22no—
174#117—224no—
175C2×C42C2×Dic1111yescharacteristic
176#107—442no—
177#106—442no—
178C4⋊C8—22no—
179#99—224no—
180#99—224no—
181C22⋊C8—22no—
182C22⋊C8—22no—
183C4×C8—21no—
184C4×C8—21no—
185C2×C11—21no—
186C2×C11—42no—
187C2×C11—41no—
188C2×C11—81no—
189C2×C11#179911yescharacteristic
190#41—41no—
191#41—41no—
192#41—41no—
193#41—41no—
194C2×Q8C4⋊Dic1111yescharacteristic
195C2×Q8C2×Dic2211yescharacteristic
196C2×D4—21no—
197C2×D4—22no—
198C2×D4C4⋊Dic1111yescharacteristic
199C2×D4C2×D4411yescharacteristic
200C2×D4#433912yes—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4C22×Dic1111yescharacteristic
204C22×C4C2×C22⋊D1112yes—
205M16—41no—
206M16—42no—
207M16—42no—
208M16—41no—
209C2×C8—22no—
210C2×C8—22no—
211C2×C8—21no—
212C2×C8—21no—
213C2×C8—21no—
214C2×C8—21no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8C22⋊Dic1112yes—
219C2×C8C22⋊Dic1111yescharacteristic
220C2×C8C22⋊Dic1111yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—444no—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C22⋊C4—444no—
226C42—21no—
227C42—444no—
228C42C4⋊Dic1111yescharacteristic
229C42C4⋊Dic1111yescharacteristic
230C11#1280711yescharacteristic, complemented, Sylow
231C23—21no—
232C23#6697911yescharacteristic
233C23#6698312yes—
234Q8—41no—
235Q8—41no—
236D4—41no—
237D4—42no—
238D4—41no—
239D4—44no—
240D4—42no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—884no—
252C2×C4#6697712yes—
253C2×C4C2×C4⋊Dic1111yescharacteristic
254C2×C4C2×C22⋊Dic1111yescharacteristic
255C8—22no—
256C8—21no—
257C8—41no—
258C8—41no—
259C8#6689811yescharacteristic
260C8#6689811yescharacteristic
261C22—22no—
262C22—21no—
263C22—41no—
264C22—42no—
265C22—42no—
266C22—41no—
267C22#1062282511yescharacteristic
268C4—22no—
269C4—22no—
270C4—21no—
271C4—41no—
272C4—41no—
273C4—1764no—
274C4C2×#6689811yescharacteristic
275C4#1062285311yescharacteristic
276C2—21no—
277C2—42no—
278C2—41no—
279C2—81no—
280C2#1306860411yescharacteristic
subgroupG/H
centerC4#10622853
commutatorC22×C4×C11C22×C4
FrattiniC2×#41C22×D11
FittingC11×#2931C2
socleC2×C11#1799
prime radicalC11×#532C22
cosocleC2×C11×#41C23
hypercenter#2931D11
hypocenterC11#12807
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×#131 ◁ #2931

Complements

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

NH ≅ G/Ntype
2. #13068662C2semidirect
3. #13066737C2semidirect
5. C2×C11×#131C4semidirect
10. C11×#423C4semidirect
11. C11×#408C4semidirect
13. C2×C4×C8×C11C4semidirect
125. C2×#131Dic11semidirect
131. #423Dic11semidirect
133. #408Dic11semidirect
135. C2×C4×C8Dic11semidirect
230. C11#12807semidirect

Maximal subgroups

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

subgroupindex
#130702812
#130686622
#130667372
C11×#29312
#1280711