Finite Group Databasebeta

← #14658111

Subgroups — #14658111

Order 2816.

500 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 81 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#13069080C212yesmaximal, complemented
2#13068798C211yesmaximal, characteristic, complemented
3#13067132C212yesmaximal, complemented
4#13066493C211yesmaximal, characteristic, complemented
5C11×#3186C211yesmaximal, characteristic
6C2×C11×#121C2212yes—
7C22×#4318C2211yescharacteristic
8C11×#480—22no—
9C11×#466—21no—
10C11×#466—21no—
11C11×#447—22no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C2×#66897—22no—
14C4×C22⋊Dic11C2211yescharacteristic
15#10622820C2212yes—
16C2×Dic11⋊C8—21no—
17#10622188—21no—
18#10622175—22no—
19#10622175—22no—
20#10622168—22no—
21C22×D4×C11—22no—
22C22×D4×C11D412yes—
23C23×C4×C11C2311yescharacteristic
24C2×C11×D8—21no—
25C2×C11×D8—21no—
26C22×C8×C11D411yescharacteristic
27C22×C8×C11D411yescharacteristic
28C11×#121—22no—
29C11×#121—22no—
30C11×#121—22no—
31C11×#121—22no—
32C2×C11×C4⋊C4D412yes—
33C2×C11×C22⋊C4—22no—
34C2×C22⋊Dic11—21no—
35C2×C4×Dic11—21no—
36C2×#4318—22no—
37C2×#4318—22no—
38C2×#4318—42no—
39C22×C11⋊C8—21no—
40C11×#107—21no—
41C11×#107—21no—
42C11×#102—22no—
43C11×#102—22no—
44C11×C22⋊C8—22no—
45#66897—44no—
46C11⋊#95D411yescharacteristic
47C11⋊#95D411yescharacteristic
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—22no—
50Dic11⋊C8—42no—
51#10557—111nomaximal, Sylow
52C24×C11—22no—
53C24×C11#4111yescharacteristic
54C2×D4×C11—22no—
55C2×D4×C11—22no—
56C2×D4×C11—42no—
57C2×D4×C11—42no—
58C2×D4×C11—42no—
59C2×D4×C11—42no—
60C2×D4×C11—82no—
61C2×D4×C11—82no—
62C22×C4×C11—22no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11C2×D412yes—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11#4112yes—
69C22×Dic11—21no—
70C22×Dic11—21no—
71C11×D8—81no—
72C11×D8—81no—
73C2×C8×C11—21no—
74C2×C8×C11—21no—
75C2×C8×C11—41no—
76C2×C8×C11—41no—
77C11×C4⋊C4—22no—
78C11×C4⋊C4—22no—
79C11×C22⋊C4—42no—
80C11×C22⋊C4—42no—
81C22⋊Dic11—42no—
82C4×Dic11—41no—
83C4×Dic11—41no—
84#4318—24no—
85#4318—42no—
86#4318—42no—
87#4318—42no—
88C2×C11⋊C8—22no—
89C2×C11⋊C8—41no—
90C2×C11⋊C8—41no—
91C2×C11⋊C8—42no—
92#3186D1111yescharacteristic
93#1900—112no—
94#1851—111no—
95#1507—112no—
96#1293—111no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—41no—
100C23×C11—41no—
101C23×C11—44no—
102C23×C11—42no—
103C23×C11—82no—
104C23×C11—82no—
105C23×C11#12111yescharacteristic
106C23×C11#12312yes—
107D4×C11—42no—
108D4×C11—42no—
109D4×C11—82no—
110D4×C11—84no—
111D4×C11—82no—
112D4×C11—82no—
113C2×C4×C11—21no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—82no—
121C2×C4×C11#12011yescharacteristic
122C2×C4×C11#12112yes—
123C2×C4×C11#12411yescharacteristic
124C2×Dic11—22no—
125C2×Dic11—41no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130C8×C11—41no—
131C8×C11—41no—
132C11⋊C8—42no—
133C11⋊C8—82no—
134C22×M16—111no—
135C2×#121C2×D1112yes—
136#480—22no—
137#466—21no—
138#466—21no—
139#447—22no—
140C2×C4⋊C8—221no—
141C2×#100—222no—
142#407—112no—
143C2×C22⋊C8C2×D1111yescharacteristic
144C4×C22⋊C4—111no—
145#343—222no—
146#336—221no—
147#327—222no—
148#327—222no—
149C22×C11—21no—
150C22×C11—21no—
151C22×C11—22no—
152C22×C11—22no—
153C22×C11—22no—
154C22×C11—81no—
155C22×C11—81no—
156C22×C11—82no—
157C22×C11—82no—
158C22×C11—82no—
159C22×C11—164no—
160C22×C11#39411yescharacteristic
161C22×C11#47211yescharacteristic
162C22×C11#47211yescharacteristic
163C4×C11—22no—
164C4×C11—21no—
165C4×C11—82no—
166C4×C11B(4,𝔽2)11yescharacteristic
167C4×C11#45811yescharacteristic
168Dic11—42no—
169Dic11—81no—
170C22×D4—22no—
171C22×D4C22⋊D1112yes—
172C23×C4C22×D1111yescharacteristic
173C2×D8—21no—
174C2×D8—21no—
175C2×M16—222no—
176C2×M16—222no—
177C2×M16—442no—
178C22×C8—221no—
179C22×C8C22⋊D1111yescharacteristic
180C22×C8C22⋊D1111yescharacteristic
181#121—22no—
182#121—22no—
183#121—22no—
184#121—22no—
185C2×C4⋊C4C22⋊D1112yes—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—221no—
188C2×C42—221no—
189#107—21no—
190#107—21no—
191C4⋊C8—442no—
192#102—22no—
193#102—22no—
194#100—444no—
195C22⋊C8—22no—
196C22⋊C8—222no—
197C22⋊C8—222no—
198#95—111no—
199#95—111no—
200C2×C11—21no—
201C2×C11—21no—
202C2×C11—42no—
203C2×C11—162no—
204C2×C11#204411yescharacteristic
205C2×C11#204511yescharacteristic
206C2×C11#205011yescharacteristic
207C24—22no—
208C24#434111yescharacteristic
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—82no—
216C2×D4—82no—
217C22×C4—22no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—221no—
221C22×C4—221no—
222C22×C4D4×D1111yescharacteristic
223C22×C4#434112yes—
224C22×C4C2×C22⋊D1111yescharacteristic
225C22×C4C2×C22⋊D1112yes—
226D8—81no—
227D8—81no—
228M16—224no—
229M16—442no—
230M16—442no—
231M16—442no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—222no—
237C2×C8—441no—
238C2×C8—441no—
239C2×C8—442no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—442no—
245C42—441no—
246C42—441no—
247C11#1055711yescharacteristic, complemented, Sylow
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—44no—
253C23—42no—
254C23—82no—
255C23—82no—
256C23#6698812yes—
257C23#6699111yescharacteristic
258D4—42no—
259D4—42no—
260D4—82no—
261D4—84no—
262D4—82no—
263D4—82no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—82no—
272C2×C4—222no—
273C2×C4—441no—
274C2×C4—441no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4#6698911yescharacteristic
279C2×C4#6699212yes—
280C2×C4#6700611yescharacteristic
281C8—41no—
282C8—41no—
283C8—442no—
284C8—882no—
285C22—21no—
286C22—21no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—81no—
291C22—81no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22—164no—
296C22#1062277311yescharacteristic
297C22#1062277311yescharacteristic
298C22#1062283511yescharacteristic
299C4—22no—
300C4—21no—
301C4—82no—
302C4—442no—
303C4—881no—
304C4#1062285611yescharacteristic
305C4#1062285711yescharacteristic
306C2—21no—
307C2—21no—
308C2—42no—
309C2—162no—
310C2#1306986411yescharacteristic
311C2#1306986911yescharacteristic
312C2#1306990011yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#3186C2
socleC22×C11#394
hypercenter#3186D11
hypocenterC11#10557
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3186

Complements

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

NH ≅ G/Ntype
1. #13069080C2semidirect
2. #13068798C2semidirect
3. #13067132C2semidirect
4. #13066493C2semidirect
247. C11#10557semidirect

Maximal subgroups

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

subgroupindex
#130690802
#130687982
#130671322
#130664932
C11×#31862
#1055711