Finite Group Databasebeta

← #14651152

Subgroups — #14651152

Order 2816.

470 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 117 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#13077696C211yesmaximal, characteristic
2#13073831C211yesmaximal, characteristic
3#13068609C211yesmaximal, characteristic
4#13067302C211yesmaximal, characteristic
5#13067300C211yesmaximal, characteristic
6#13066519C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66888—21no—
14#10622587—22no—
15#10622549—21no—
16#10622542—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622443—22no—
20#10622331—22no—
21C8×Dic22—22no—
22#10622272C414yes—
23#10622192—21no—
24#10622124—22no—
25#10622120—22no—
26C22×Dic22—21no—
27C22×Dic22D411yescharacteristic
28C2×C11×M16—21no—
29C2×C11×C4⋊C4—21no—
30C2×C42×C11—21no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11C2×C412yes—
34C2×C4⋊Dic11D411yescharacteristic
35C2×Dic11⋊C4C2×C412yes—
36C2×C4×Dic11D412yes—
37C2×#4318—21no—
38#66922—21no—
39#66922—21no—
40#66922—21no—
41#66922—21no—
42C4×Dic22—21no—
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22—21no—
46C11×C4⋊C8—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8D412yes—
49C11×C22⋊C8—21no—
50C4×C8×C11—21no—
51C11×#95C2×C412yes—
52C11⋊#95—24no—
53C11⋊#95—24no—
54C22⋊(C11⋊C8)—21no—
55#66888—42no—
56Dic11⋊C8—24no—
57C8×Dic11—24no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61C4×C11⋊C8—21no—
62#9396—111nomaximal, Sylow
63C22×C4×C11—22no—
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×Dic11—22no—
68C22×Dic11C22⋊C412yes—
69C22×Dic11C22⋊C412yes—
70C2×Dic22—21no—
71C2×Dic22—21no—
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22—44no—
75C2×Dic22—41no—
76C2×Dic22—41no—
77C2×Dic22SD1612yes—
78C2×Dic22Q1612yes—
79C11×M16—41no—
80C11×M16—41no—
81C2×C8×C11—22no—
82C2×C8×C11—41no—
83C11×C4⋊C4—42no—
84C42×C11—41no—
85C42×C11—41no—
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11#4111yescharacteristic
89C42×C11#4111yescharacteristic
90C4⋊Dic11—22no—
91C4⋊Dic11—22no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96Dic11⋊C4—22no—
97Dic11⋊C4—22no—
98C4×Dic11—22no—
99C4×Dic11—22no—
100#4318—41no—
101#4318—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104#2982—111no—
105#2568—111no—
106#1801—111no—
107#1549—111no—
108#1549—111no—
109#1303—111no—
110#1303D1111yescharacteristic
111C23×C11C2×C22⋊C411yescharacteristic
112C2×C4×C11—22no—
113C2×C4×C11—41no—
114C2×C4×C11—42no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11C4×D411yescharacteristic
118C2×C4×C11C4×D411yescharacteristic
119C2×C4×C11#12011yescharacteristic
120C2×C4×C11#12111yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12311yescharacteristic
123C2×C4×C11C2×SD1611yescharacteristic
124C2×C4×C11C2×Q1611yescharacteristic
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11#13511yescharacteristic
127C2×Dic11—22no—
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—42no—
131C2×Dic11—44no—
132C2×Dic11—42no—
133C2×Dic11#10314yes—
134Dic22—22no—
135Dic22—22no—
136Dic22—22no—
137Dic22—22no—
138Dic22—82no—
139Dic22—82no—
140C8×C11—42no—
141C8×C11—81no—
142C11⋊C8—42no—
143C11⋊C8—81no—
144C2×C4⋊Q8—111no—
145C2×C4×Q8—111no—
146C8×Q8—222no—
147C8×Q8—222no—
148#431—111no—
149#431—222no—
150#431C2×D1111yescharacteristic
151#423—111no—
152#423C2×D1111yescharacteristic
153C2×#101—221no—
154#400—114no—
155#391—221no—
156#391—222no—
157#382—221no—
158C4×C4⋊C4C2×D1111yescharacteristic
159#343—221no—
160#332—222no—
161#332—222no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11#38611yescharacteristic
165C22×C11C2×#10311yescharacteristic
166C22×C11#41611yescharacteristic
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—82no—
171C4×C11#45412yes—
172C4×C11#46511yescharacteristic
173C4×C11#46511yescharacteristic
174C4×C11#46711yescharacteristic
175C4×C11#46711yescharacteristic
176Dic11—24no—
177Dic11—42no—
178Dic11—82no—
179C22×Q8—111no—
180C22×Q8—221no—
181C2×M16—21no—
182C2×M16—221no—
183C4⋊Q8—221no—
184C4⋊Q8—221no—
185C4⋊Q8—221no—
186C4⋊Q8—221no—
187C4×Q8—221no—
188C4×Q8—221no—
189C4×Q8—221no—
190C4×Q8—221no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—112no—
193C2×C4⋊C4—111no—
194C2×C4⋊C4—112no—
195C2×C4⋊C4—221no—
196C2×C42—21no—
197C2×C42—112no—
198C2×C42C22×D1111yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—112no—
202C4⋊C8—224no—
203C4⋊C8—221no—
204C4⋊C8—221no—
205C4⋊C8D4412yes—
206#101—442no—
207C22⋊C8—21no—
208C22⋊C8—221no—
209C4×C8—21no—
210C4×C8—224no—
211C4×C8—221no—
212#95—224no—
213#95—224no—
214#95C4×D1112yes—
215C2×C11—21no—
216C2×C11—21no—
217C2×C11#188811yescharacteristic
218C2×C11#189211yescharacteristic
219C2×C11#191511yescharacteristic
220C2×Q8—112no—
221C2×Q8—112no—
222C2×Q8—221no—
223C2×Q8—221no—
224C2×Q8—221no—
225C2×Q8—221no—
226C2×Q8—444no—
227C2×Q8—441no—
228C2×Q8—441no—
229C22×C4—22no—
230C22×C4—112no—
231C22×C4—112no—
232C22×C4—222no—
233C22×C4C2×C4×D1111yescharacteristic
234C22×C4D4×D1111yescharacteristic
235C22×C4D4×D1111yescharacteristic
236M16—41no—
237M16—41no—
238M16—441no—
239M16—441no—
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—222no—
243C2×C8—441no—
244C4⋊C4—42no—
245C4⋊C4—222no—
246C4⋊C4—221no—
247C4⋊C4—222no—
248C4⋊C4—221no—
249C4⋊C4—222no—
250C4⋊C4—222no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C42—41no—
254C42—41no—
255C42—222no—
256C42—222no—
257C42C2×D4411yescharacteristic
258C42#433911yescharacteristic
259C42D4×D1111yescharacteristic
260C42#434311yescharacteristic
261C11#939611yescharacteristic, complemented, Sylow
262C23C22⋊C4×D1111yescharacteristic
263Q8—222no—
264Q8—222no—
265Q8—222no—
266Q8—222no—
267Q8—882no—
268Q8—882no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—114no—
275C2×C4—222no—
276C2×C4—222no—
277C2×C4—222no—
278C2×C4—442no—
279C2×C4—444no—
280C2×C4—442no—
281C2×C4C4×D4411yescharacteristic
282C2×C4#6693511yescharacteristic
283C2×C4#6693711yescharacteristic
284C2×C4#6694611yescharacteristic
285C2×C4#6694711yescharacteristic
286C2×C4#6694811yescharacteristic
287C2×C4#6696511yescharacteristic
288C2×C4SD16×D1111yescharacteristic
289C2×C4#6696911yescharacteristic
290C2×C4Q16×D1111yescharacteristic
291C8—42no—
292C8—81no—
293C8—442no—
294C8—881no—
295C22—21no—
296C22—21no—
297C22#1062227811yescharacteristic
298C22#1062238511yescharacteristic
299C22D11×#10311yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—82no—
304C4—224no—
305C4—442no—
306C4—882no—
307C4#1062239111yescharacteristic
308C4#1062242611yescharacteristic
309C4#1062244012yes—
310C4#1062247711yescharacteristic
311C4#1062250011yescharacteristic
312C2—21no—
313C2—21no—
314C2#1306901811yescharacteristic
315C2#1306903811yescharacteristic
316C2#1306916711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#386
prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1303D11
hypocenterC11#9396
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
261. C11#9396semidirect

Maximal subgroups

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

subgroupindex
#130776962
#130738312
#130686092
#130673022
#130673002
#130665192
C11×#13032
#939611