Finite Group Databasebeta

← #14648845

Subgroups — #14648845

Order 2816.

484 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077701C211yesmaximal, characteristic
2#13071907C211yesmaximal, characteristic
3#13067064C212yesmaximal
4#13066510C212yesmaximal
5C4×C11×#101C211yesmaximal, characteristic
6C2×C4×Q8×C11C2211yescharacteristic
7C2×C4×Dic22C2211yescharacteristic
8C2×C11×#101—21no—
9C4×C11×M16C2212yes—
10#10622842—21no—
11#10622637—24no—
12#10622596C411yescharacteristic
13#10622596C411yescharacteristic
14#10622593—21no—
15#10622592C411yescharacteristic
16#10622592C411yescharacteristic
17#10622545C2211yescharacteristic
18C4×Dic11⋊C4—21no—
19C4×Dic11⋊C4—21no—
20#10622539—21no—
21#10622539C2212yes—
22#10622538—21no—
23C11×#343—21no—
24#10622094—24no—
25C22×Q8×C11D411yescharacteristic
26C22×Dic22C2×C411yescharacteristic
27C2×C11×M16—22no—
28C4×Q8×C11—22no—
29C4×Q8×C11—22no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×C4⋊Dic11C2×C411yescharacteristic
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11—21no—
43C2×C4×Dic11—21no—
44C4×Dic22—22no—
45C4×Dic22—22no—
46C11×#101—24no—
47C11×#97—22no—
48C4×C8×C11—22no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95C2×C411yescharacteristic
55C11⋊#95C2×C411yescharacteristic
56C22⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58C4⋊(C11⋊C8)—22no—
59C4⋊(C11⋊C8)D414yes—
60#66867—22no—
61#66867—22no—
62C4×C11⋊C8—22no—
63#9030—111nomaximal, Sylow
64C2×Q8×C11—22no—
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C2×Dic22—22no—
79C2×Dic22—42no—
80C11×M16—24no—
81C11×M16—42no—
82C2×C8×C11—42no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—22no—
85C11×C4⋊C4—22no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11C2×D412yes—
91C42×C11#4112yes—
92C4⋊Dic11—22no—
93Dic11⋊C4—42no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96Dic11⋊C4—42no—
97Dic11⋊C4—42no—
98C4×Dic11—24no—
99C4×Dic11—41no—
100C4×Dic11—41no—
101C2×C11⋊C8—24no—
102#2983—111no—
103#2399—111no—
104C4×#101D1111yescharacteristic
105#1491—112no—
106#1300—112no—
107C23×C11C2×C22⋊C411yescharacteristic
108Q8×C11—44no—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—22no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11#10412yes—
123C2×C4×C11C4×D412yes—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12112yes—
126C2×C4×C11#12311yescharacteristic
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139Dic22—24no—
140Dic22—42no—
141C8×C11—44no—
142C11⋊C8—44no—
143C2×C4×Q8—111no—
144C2×C4×Q8C2×D1111yescharacteristic
145#446—224no—
146#432—112no—
147#432—221no—
148#431—221no—
149C2×#101—21no—
150C4×M16C2×D1112yes—
151#398—111no—
152#398—111no—
153#398—221no—
154#395—111no—
155#395—111no—
156#395—221no—
157C4×C4⋊C4—221no—
158C4×C4⋊C4—221no—
159#376—111no—
160#343—21no—
161Q8⋊C8—224no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11#38611yescharacteristic
165C22×C11C2×#10411yescharacteristic
166C22×C11#42111yescharacteristic
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—21no—
170C4×C11—22no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11#45612yes—
175Dic11—42no—
176Dic11—42no—
177Dic11—42no—
178Dic11—81no—
179C22×Q8—111no—
180C22×Q8C22⋊D1111yescharacteristic
181C2×M16—22no—
182C4×Q8—22no—
183C4×Q8—22no—
184C4×Q8—222no—
185C4×Q8—222no—
186C2×C4⋊C4—111no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—221no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4C4×D1111yescharacteristic
193C2×C4⋊C4C4×D1111yescharacteristic
194C2×C4⋊C4C22⋊D1111yescharacteristic
195C2×C42—221no—
196C2×C42—221no—
197C2×C42D4411yescharacteristic
198C2×C42D4411yescharacteristic
199C2×C42C22×D1111yescharacteristic
200C4⋊C8—114no—
201C4⋊C8—222no—
202C4⋊C8—222no—
203#101—24no—
204C22⋊C8—222no—
205#97—22no—
206#97—222no—
207#97—222no—
208C4×C8—22no—
209C4×C8—222no—
210#95—111no—
211#95—111no—
212#95—221no—
213#95—221no—
214#95—221no—
215#95—221no—
216#95—221no—
217C2×C11—21no—
218C2×C11—21no—
219C2×C11#187111yescharacteristic
220C2×C11#188611yescharacteristic
221C2×C11#189111yescharacteristic
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—41no—
225C2×Q8—222no—
226C2×Q8—442no—
227C22×C4—221no—
228C22×C4—221no—
229C22×C4—221no—
230C22×C4—221no—
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4(C2×D11)⋊C411yescharacteristic
233C22×C4(C2×D11)⋊C411yescharacteristic
234C22×C4(C2×D11)⋊C411yescharacteristic
235C22×C4C2×C4×D1111yescharacteristic
236C22×C4C2×D4411yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238M16—24no—
239M16—42no—
240C2×C8—42no—
241C2×C8—224no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—222no—
246C4⋊C4—442no—
247C4⋊C4—442no—
248C4⋊C4—442no—
249C4⋊C4—442no—
250C4⋊C4—442no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—224no—
256C42—441no—
257C42—441no—
258C42D4×D1112yes—
259C42#434112yes—
260C11#903011yescharacteristic, complemented, Sylow
261C23C2×(C2×D11)⋊C411yescharacteristic
262Q8—44no—
263Q8—224no—
264Q8—442no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—222no—
279C2×C4—222no—
280C2×C4—222no—
281C2×C4—441no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—441no—
288C2×C4—441no—
289C2×C4—441no—
290C2×C4#6686912yes—
291C2×C4(C22⋊D11)⋊C412yes—
292C2×C4#6693511yescharacteristic
293C2×C4#6693911yescharacteristic
294C2×C4#6699212yes—
295C8—44no—
296C8—444no—
297C22—21no—
298C22—21no—
299C22C2×#6686911yescharacteristic
300C22#1062257111yescharacteristic
301C22#1062261811yescharacteristic
302C4—22no—
303C4—22no—
304C4—21no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—442no—
310C4—442no—
311C4—442no—
312C4—881no—
313C4#1062236512yes—
314C2—21no—
315C2—21no—
316C2#1306891611yescharacteristic
317C2#1306900711yescharacteristic
318C2#1306903211yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC4×C11×#101C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenterC4×#101D11
hypocenterC11#9030
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
260. C11#9030semidirect

Maximal subgroups

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

subgroupindex
#130777012
#130719072
#130670642
#130665102
C4×C11×#1012
#903011