Finite Group Databasebeta

← #14658114

Subgroups — #14658114

Order 2816.

500 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 79 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#13079367C211yesmaximal, characteristic
2#13069079C212yesmaximal, complemented
3#13067131C212yesmaximal, complemented
4#13066493C211yesmaximal, characteristic, complemented
5C11×#1851C211yesmaximal, characteristic, complemented
6C22×C11×M16C2211yescharacteristic
7C2×#66983C2212yes—
8C2×C11×C4⋊C8—21no—
9C2×C11×C22⋊C8C2211yescharacteristic
10C4×C11×C22⋊C4C2211yescharacteristic
11#10622820C2212yes—
12C2×#66887—22no—
13#10622728—21no—
14#10622728—21no—
15#10622349—22no—
16#10622345—22no—
17C11×#336—21no—
18#10622192—22no—
19#10622089—22no—
20#10622089—22no—
21C23×C4×C11C2311yescharacteristic
22C22×C22⋊D11—22no—
23C22×D44D412yes—
24C2×C11×M16—22no—
25C2×C11×M16—42no—
26C22×C8×C11—21no—
27C22×C8×C11D411yescharacteristic
28C22×C8×C11D411yescharacteristic
29C2×C11×C22⋊C4—21no—
30C2×C42×C11—21no—
31#66983—22no—
32#66983—22no—
33#66983—22no—
34#66983—22no—
35C2×(C2×D11)⋊C4—22no—
36C2×C4⋊Dic11D412yes—
37C2×#4318—22no—
38C2×D88—21no—
39C2×D88—21no—
40C11×C4⋊C8—42no—
41C11×C22⋊C8—22no—
42C11×#95D411yescharacteristic
43C11×#95D411yescharacteristic
44C22⋊(C11⋊C8)—22no—
45C22⋊(C11⋊C8)—22no—
46#66887—44no—
47#66885—22no—
48#66885—22no—
49#66882—21no—
50#66882—21no—
51#10557—111nomaximal, Sylow
52C24×C11#4111yescharacteristic
53C23×D11—22no—
54C22×C4×C11—21no—
55C22×C4×C11—21no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11C2×D412yes—
59C22×C4×C11C2×D411yescharacteristic
60C22×C4×C11C2×D411yescharacteristic
61C22×C4×C11#4112yes—
62C2×C22⋊D11—42no—
63C2×C22⋊D11—42no—
64C2×C22⋊D11—82no—
65C2×C22⋊D11—82no—
66C22×Dic11—22no—
67C2×D44—22no—
68C2×D44—22no—
69C2×D44—42no—
70C2×D44—42no—
71C11×M16—24no—
72C11×M16—42no—
73C2×C8×C11—22no—
74C2×C8×C11—21no—
75C2×C8×C11—21no—
76C2×C8×C11—41no—
77C2×C8×C11—41no—
78C2×C8×C11—41no—
79C2×C8×C11—41no—
80C11×C22⋊C4—42no—
81C42×C11—41no—
82C42×C11—41no—
83(C2×D11)⋊C4—42no—
84(C2×D11)⋊C4—42no—
85C4⋊Dic11—22no—
86C4⋊Dic11—22no—
87#4318—42no—
88#4318—42no—
89C2×C11⋊C8—42no—
90D88—81no—
91D88—81no—
92#3186—111no—
93#1900—112no—
94#1851D1111yescharacteristic, complemented
95#1507—112no—
96#1293—111no—
97C23×C11—21no—
98C23×C11—21no—
99C23×C11—41no—
100C23×C11—41no—
101C23×C11#12111yescharacteristic
102C23×C11#12312yes—
103C22×D11—42no—
104C22×D11—44no—
105C22×D11—82no—
106C22×D11—82no—
107C2×C4×C11—22no—
108C2×C4×C11—21no—
109C2×C4×C11—22no—
110C2×C4×C11—21no—
111C2×C4×C11—22no—
112C2×C4×C11—41no—
113C2×C4×C11—42no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11#12112yes—
121C2×C4×C11#12411yescharacteristic
122C22⋊D11—84no—
123C22⋊D11—82no—
124C22⋊D11—82no—
125C2×Dic11—42no—
126C2×Dic11—82no—
127D44—42no—
128D44—42no—
129D44—82no—
130C8×C11—41no—
131C8×C11—42no—
132C8×C11—41no—
133C11⋊C8—82no—
134C22×M16C2×D1111yescharacteristic
135C2×#121—112no—
136#480—222no—
137#466—221no—
138#466—221no—
139#447—222no—
140C2×C4⋊C8—21no—
141C2×#100—222no—
142#407—112no—
143C2×C22⋊C8C2×D1111yescharacteristic
144C4×C22⋊C4C2×D1111yescharacteristic
145#343—222no—
146#336—21no—
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#39411yescharacteristic
157C22×C11#47211yescharacteristic
158C22×C11#47211yescharacteristic
159C2×D11—82no—
160C2×D11—82no—
161C2×D11—82no—
162C2×D11—164no—
163C4×C11—22no—
164C4×C11—21no—
165C4×C11—42no—
166C4×C11—81no—
167C4×C11B(4,𝔽2)11yescharacteristic
168C4×C11#45811yescharacteristic
169Dic11—82no—
170C22×D4—112no—
171C22×D4—222no—
172C23×C4C22×D1111yescharacteristic
173C2×D8—221no—
174C2×D8—221no—
175C2×M16—22no—
176C2×M16—42no—
177C2×M16—222no—
178C22×C8—21no—
179C22×C8C22⋊D1111yescharacteristic
180C22×C8C22⋊D1111yescharacteristic
181#121—222no—
182#121—222no—
183#121—222no—
184#121—222no—
185C2×C4⋊C4—112no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—222no—
188C2×C42—21no—
189#107—221no—
190#107—221no—
191C4⋊C8—42no—
192#102—222no—
193#102—222no—
194#100—444no—
195C22⋊C8—22no—
196C22⋊C8—222no—
197C22⋊C8—222no—
198#95D4411yescharacteristic
199#95D4411yescharacteristic
200C2×C11—21no—
201C2×C11—21no—
202C2×C11—42no—
203C2×C11#204411yescharacteristic
204C2×C11#204511yescharacteristic
205C2×C11#205011yescharacteristic
206D11—162no—
207C24—222no—
208C24#433911yescharacteristic
209C2×D4—222no—
210C2×D4—222no—
211C2×D4—442no—
212C2×D4—442no—
213C2×D4—442no—
214C2×D4—442no—
215C2×D4—882no—
216C2×D4—882no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—222no—
222C22×C4C2×D4411yescharacteristic
223C22×C4D4×D1112yes—
224C22×C4#434312yes—
225C22×C4C2×C22⋊D1111yescharacteristic
226D8—881no—
227D8—881no—
228M16—24no—
229M16—42no—
230M16—442no—
231M16—442no—
232C2×C8—22no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—442no—
240C4⋊C4—222no—
241C4⋊C4—222no—
242C22⋊C4—42no—
243C22⋊C4—442no—
244C22⋊C4—442no—
245C42—41no—
246C42—41no—
247C11#1055711yescharacteristic, complemented, Sylow
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—444no—
253C23—442no—
254C23—882no—
255C23—882no—
256C23#6694712yes—
257C23#6698311yescharacteristic
258D4—442no—
259D4—442no—
260D4—882no—
261D4—884no—
262D4—882no—
263D4—882no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—442no—
277C2×C4—882no—
278C2×C4#6694812yes—
279C2×C4#6699011yescharacteristic
280C2×C4#6700011yescharacteristic
281C8—42no—
282C8—41no—
283C8—41no—
284C8—882no—
285C22—21no—
286C22—21no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—81no—
291C22—81no—
292C22—882no—
293C22—882no—
294C22—882no—
295C22—1764no—
296C22#1062260411yescharacteristic
297C22#1062275511yescharacteristic
298C22#1062275511yescharacteristic
299C4—22no—
300C4—21no—
301C4—42no—
302C4—81no—
303C4—882no—
304C4#1062264511yescharacteristic
305C4#1062266611yescharacteristic
306C2—21no—
307C2—21no—
308C2—42no—
309C2—1762no—
310C2#1306986711yescharacteristic
311C2#1306987211yescharacteristic
312C2#1306990311yescharacteristic
subgroupG/H
centerC22#10622604
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1851C2
socleC22×C11#394
prime radical#13079367C2
hypercenter#1851D11
hypocenterC11#10557
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
2. #13069079C2semidirect
3. #13067131C2semidirect
4. #13066493C2semidirect
5. C11×#1851C2semidirect
94. #1851D11semidirect
247. C11#10557semidirect

Maximal subgroups

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

subgroupindex
#130793672
#130690792
#130671312
#130664932
C11×#18512
#1055711