Finite Group Databasebeta

← #14910187

Subgroups — #14910187

Order 2816.

512 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 127 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#13079259C212yesmaximal, complemented
2#13070775C212yesmaximal, complemented
3#13070772C212yesmaximal, complemented
4#13070719C211yesmaximal, characteristic, complemented
5#13070700C212yesmaximal, complemented
6#13070650C212yesmaximal, complemented
7#13070649C212yesmaximal, complemented
8#13070376C211yesmaximal, characteristic, complemented
9C11×#2218C211yesmaximal, characteristic, complemented
10#10623150—22no—
11C2×C11×D16C2211yescharacteristic
12C2×C11×M32C2211yescharacteristic
13C11×#466C2212yes—
14#10622764C2212yes—
15D8×Dic11C2212yes—
16C2×#66890C2212yes—
17#10622728C2212yes—
18#10622714C2211yescharacteristic
19C22×C11⋊C16C2211yescharacteristic
20#10622652—22no—
21C2×D176C2211yescharacteristic
22#10622491C2212yes—
23#10622485C2212yes—
24#10622398—22no—
25#10622377—22no—
26C11×#367C2211yescharacteristic
27C11×#357C2212yes—
28#10622200C2212yes—
29#10622147C2212yes—
30#10622143C2211yescharacteristic
31Dic11⋊C16C2212yes—
32Dic11⋊C16C2212yes—
33#10622129C2212yes—
34#10622127C2212yes—
35C2×C11×D8C2312yes—
36C22×C8×C11C2311yescharacteristic
37C11×#121—22no—
38#66993—22no—
39#66992—42no—
40#66991—42no—
41D4×Dic11—22no—
42C2×#4323—22no—
43#66983—22no—
44#66979D411yescharacteristic
45C2×#4318D411yescharacteristic
46C2×D88C2312yes—
47#66946—22no—
48#66943—22no—
49#66939—42no—
50#66936—42no—
51C11×D16—41no—
52C11×M32—41no—
53C2×C11×C16C2311yescharacteristic
54C2×C11×C16C2311yescharacteristic
55C11×#107C2312yes—
56C11×#102—22no—
57#66896—22no—
58#66890—42no—
59#66885—22no—
60#66882C2312yes—
61#66879D412yes—
62C8×Dic11C2312yes—
63C2×C11⋊C16—41no—
64C2×C11⋊C16C2312yes—
65#66873—22no—
66#66872—22no—
67D176—41no—
68#33825—111nomaximal, Sylow
69C2×D4×C11—22no—
70C2×D4×C11—42no—
71C22×C4×C11C2×D411yescharacteristic
72C2×C22⋊D11—42no—
73C2×C22⋊D11—42no—
74C2×C22⋊D11—42no—
75C22×Dic11—42no—
76C2×D44—22no—
77C2×C4×D11—42no—
78C11×D8—22no—
79C11×D8—22no—
80C2×C8×C11—21no—
81C2×C8×C11—21no—
82C2×C8×C11C2×D411yescharacteristic
83C2×C8×C11C2411yescharacteristic
84C11×C4⋊C4—22no—
85C11×C22⋊C4—42no—
86C22⋊Dic11—42no—
87C22⋊Dic11D811yescharacteristic
88C22⋊Dic11D811yescharacteristic
89#4323—44no—
90(C2×D11)⋊C4—42no—
91(C2×D11)⋊C4—42no—
92C4⋊Dic11—22no—
93C4⋊Dic11—42no—
94C4⋊Dic11D812yes—
95Dic11⋊C4—42no—
96C4×Dic11C2×D412yes—
97#4318—41no—
98C2×C11⋊C8C2×D412yes—
99D88—22no—
100D88—22no—
101C11×C16—21no—
102C11×C16—21no—
103C11⋊C16—22no—
104#3176—112no—
105#2228—112no—
106#2228—112no—
107#2218—111no—
108#2218D1111yescharacteristic, complemented
109#2215—112no—
110#2206—112no—
111#2206—112no—
112#2151—111no—
113C23×C11—42no—
114C23×C11C2×D811yescharacteristic
115C22×D11—42no—
116D4×C11—42no—
117D4×C11—42no—
118D4×C11—162no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—42no—
122C2×C4×C11C2×D811yescharacteristic
123C2×C4×C11C22×D411yescharacteristic
124C22⋊D11—162no—
125C22⋊D11—162no—
126C22⋊D11—162no—
127C2×Dic11—42no—
128C2×Dic11—162no—
129C2×Dic11C2×D812yes—
130C2×Dic11C2×D812yes—
131D44—42no—
132D44—42no—
133C4×D11—162no—
134C8×C11—21no—
135C8×C11H(5,𝔽2)11yescharacteristic
136C8×C112−1+411yescharacteristic
137C11⋊C8—22no—
138#540—222no—
139C2×D16—112no—
140C2×D16—111no—
141C2×D16C2×D1111yescharacteristic
142C2×M32C2×D1111yescharacteristic
143C22×C16—111no—
144#499—112no—
145#493—112no—
146#490—222no—
147#469—222no—
148#466—112no—
149#466C2×D1112yes—
150#442—222no—
151C4×D8—112no—
152C4×D8—112no—
153#405—111no—
154#367—111no—
155#367C2×D1111yescharacteristic
156#366—112no—
157C4⋊C16—112no—
158C4⋊C16—112no—
159#357—112no—
160#357—112no—
161#357—112no—
162#357C2×D1112yes—
163C22×C11—22no—
164C22×C11—21no—
165C22×C11—82no—
166C22×C11—82no—
167C22×C11—82no—
168C22×C11C22×D811yescharacteristic
169C2×D11—82no—
170C2×D11—82no—
171C2×D11—82no—
172C4×C11—21no—
173C4×C11—82no—
174C4×C11#53711yescharacteristic
175C4×C11#57511yescharacteristic
176Dic11—22no—
177Dic11—22no—
178Dic11—82no—
179C2×D8—112no—
180C2×D8—222no—
181C2×D8C22×D1112yes—
182C2×M16—111no—
183C22×C8C22×D1111yescharacteristic
184#127—222no—
185#125—222no—
186#123—442no—
187#123—442no—
188#121—22no—
189#121—222no—
190#121—442no—
191#121—442no—
192C4×D4—222no—
193C4×D4—222no—
194#117—111no—
195D16—41no—
196D16—441no—
197D16—442no—
198M32—41no—
199C2×C16—112no—
200C2×C16—441no—
201C2×C16C22×D1111yescharacteristic
202C2×C16C22×D1111yescharacteristic
203#107—112no—
204#107C22×D1112yes—
205#106—222no—
206#102—22no—
207#102—222no—
208#102—222no—
209#102—222no—
210#97—112no—
211C4×C8—112no—
212C2×C11—41no—
213C2×C11—162no—
214C2×C11#324511yescharacteristic
215C2×C11#341512yes—
216D11—162no—
217C2×D4—22no—
218C2×D4—42no—
219C2×D4—222no—
220C2×D4—442no—
221C2×D4—442no—
222C2×D4—442no—
223C22×C4—442no—
224C22×C4—442no—
225C22×C4D4×D1111yescharacteristic
226D8—22no—
227D8—22no—
228D8—222no—
229D8—222no—
230D8—444no—
231M16—441no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—112no—
235C2×C8D4×D1111yescharacteristic
236C2×C8C23×D1111yescharacteristic
237C4⋊C4—22no—
238C4⋊C4—112no—
239C4⋊C4—222no—
240C4⋊C4—442no—
241C4⋊C4—442no—
242C22⋊C4—42no—
243C22⋊C4—111no—
244C22⋊C4—111no—
245C22⋊C4—442no—
246C22⋊C4—442no—
247C22⋊C4—442no—
248C42—112no—
249C16—21no—
250C16—21no—
251C16—222no—
252C11#3382511yescharacteristic, complemented, Sylow
253C23—42no—
254C23—442no—
255C23D8×D1111yescharacteristic
256D4—42no—
257D4—42no—
258D4—162no—
259D4—442no—
260D4—442no—
261D4—1762no—
262D4—1762no—
263D4—1762no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—42no—
267C2×C4—112no—
268C2×C4—112no—
269C2×C4—442no—
270C2×C4—1762no—
271C2×C4—1762no—
272C2×C4D8×D1111yescharacteristic
273C2×C4C2×D4×D1111yescharacteristic
274C8—21no—
275C8—222no—
276C8#6703711yescharacteristic
277C8#6704311yescharacteristic
278C22—21no—
279C22—22no—
280C22—82no—
281C22—82no—
282C22—82no—
283C22—882no—
284C22—882no—
285C22—882no—
286C22C2×D8×D1111yescharacteristic
287C4—21no—
288C4—82no—
289C4—222no—
290C4—222no—
291C4—882no—
292C4#1062312811yescharacteristic
293C4#1062329911yescharacteristic
294C2—41no—
295C2—162no—
296C2—1762no—
297C2#1307992211yescharacteristic
298C2#1308175612yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2218C2
socleC22×C11C22×D8
hypercenter#2218D11
hypocenterC11#33825
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2218

Complements

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

NH ≅ G/Ntype
1. #13079259C2semidirect
2. #13070775C2semidirect
3. #13070772C2semidirect
4. #13070719C2semidirect
5. #13070700C2semidirect
6. #13070650C2semidirect
7. #13070649C2semidirect
8. #13070376C2semidirect
9. C11×#2218C2semidirect
108. #2218D11semidirect
252. C11#33825semidirect

Maximal subgroups

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

subgroupindex
#130792592
#130707752
#130707722
#130707192
#130707002
#130706502
#130706492
#130703762
C11×#22182
#3382511