Finite Group Databasebeta

← #14651172

Subgroups — #14651172

Order 2816.

466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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#13077699C211yesmaximal, characteristic
2#13073824C211yesmaximal, characteristic
3#13068609C211yesmaximal, characteristic
4#13067298C211yesmaximal, characteristic
5#13067296C211yesmaximal, characteristic
6#13066519C211yesmaximal, characteristic
7C11×#1303C211yesmaximal, characteristic
8C2×#66922C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66888—21no—
14#10622598—22no—
15#10622548—21no—
16#10622542—21no—
17#10622538C2211yescharacteristic
18#10622537C2211yescharacteristic
19#10622444—22no—
20#10622332—22no—
21#10622292—22no—
22#10622269C414yes—
23#10622192—21no—
24#10622119—22no—
25#10622119—22no—
26C22×Dic22C2×C412yes—
27C22×Dic22D411yescharacteristic
28C2×C11×M16—21no—
29C2×C11×C4⋊C4—21no—
30C2×C42×C11—21no—
31C2×C42×C11C2311yescharacteristic
32C2×C4⋊Dic11—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—24no—
35C2×C4⋊Dic11D411yescharacteristic
36C2×Dic11⋊C4C2×C412yes—
37C2×C4×Dic11D412yes—
38C2×#4318—21no—
39#66922—21no—
40#66922—21no—
41#66922—21no—
42#66922—21no—
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8D412yes—
50C11×C22⋊C8—21no—
51C4×C8×C11—21no—
52C11×#95C2×C412yes—
53C11⋊#95—24no—
54C22⋊(C11⋊C8)—21no—
55#66888—42no—
56#66879—24no—
57Dic11⋊C8—24no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)D412yes—
61C4×C11⋊C8—21no—
62#9400—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—22no—
71C2×Dic22—22no—
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22—21no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22—82no—
79C11×M16—41no—
80C11×M16—41no—
81C2×C8×C11—22no—
82C2×C8×C11—41no—
83C11×C4⋊C4—24no—
84C42×C11—41no—
85C42×C11—41no—
86C42×C11C2×D411yescharacteristic
87C42×C11C2×D411yescharacteristic
88C42×C11#4111yescharacteristic
89C42×C11#4111yescharacteristic
90C4⋊Dic11—21no—
91C4⋊Dic11—21no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94C4⋊Dic11—41no—
95C4⋊Dic11—41no—
96C4⋊Dic11—84no—
97Dic11⋊C4—22no—
98Dic11⋊C4—22no—
99C4×Dic11—22no—
100C4×Dic11—22no—
101#4318—41no—
102#4318—41no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—41no—
105#2983—111no—
106#2567—111no—
107#1801—111no—
108#1548—111no—
109#1548—111no—
110#1303—111no—
111#1303D1111yescharacteristic
112C23×C11C2×C22⋊C411yescharacteristic
113C2×C4×C11—22no—
114C2×C4×C11—24no—
115C2×C4×C11—41no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11C4×D411yescharacteristic
119C2×C4×C11C4×D411yescharacteristic
120C2×C4×C11#12011yescharacteristic
121C2×C4×C11#12111yescharacteristic
122C2×C4×C11#12111yescharacteristic
123C2×C4×C11#12311yescharacteristic
124C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C11#13711yescharacteristic
126C2×C4×C11#13711yescharacteristic
127C2×C4×C11#13711yescharacteristic
128C2×Dic11—22no—
129C2×Dic11—22no—
130C2×Dic11—22no—
131C2×Dic11—22no—
132C2×Dic11—42no—
133C2×Dic11—44no—
134C2×Dic11—42no—
135Dic22—41no—
136Dic22—41no—
137Dic22—41no—
138Dic22—41no—
139Dic22—82no—
140Dic22—82no—
141C8×C11—42no—
142C8×C11—81no—
143C11⋊C8—42no—
144C11⋊C8—81no—
145C2×C4⋊Q8—111no—
146C2×C4×Q8—111no—
147#446—222no—
148#446—222no—
149#432—222no—
150#431—111no—
151#431C2×D1111yescharacteristic
152#423—111no—
153#423C2×D1111yescharacteristic
154C2×#101—221no—
155#395—114no—
156#391—221no—
157#389—222no—
158#384—221no—
159C4×C4⋊C4C2×D1111yescharacteristic
160#343—221no—
161#333—222no—
162#333—222no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11#38611yescharacteristic
166C22×C11#41711yescharacteristic
167C22×C11#41911yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—44no—
172C4×C11#45612yes—
173C4×C11#46811yescharacteristic
174C4×C11#46811yescharacteristic
175C4×C11#47011yescharacteristic
176C4×C11#47011yescharacteristic
177Dic11—42no—
178Dic11—42no—
179Dic11—82no—
180C22×Q8—111no—
181C22×Q8—112no—
182C2×M16—21no—
183C2×M16—221no—
184C4⋊Q8—221no—
185C4⋊Q8—221no—
186C4⋊Q8—221no—
187C4⋊Q8—221no—
188C4×Q8—221no—
189C4×Q8—221no—
190C4×Q8—221no—
191C4×Q8—221no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—112no—
194C2×C4⋊C4—111no—
195C2×C4⋊C4—221no—
196C2×C4⋊C4—221no—
197C2×C4⋊C4—224no—
198C2×C42—21no—
199C2×C42—112no—
200C2×C42C22×D1111yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—112no—
204C4⋊C8—224no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8D4412yes—
208#101—442no—
209C22⋊C8—21no—
210C22⋊C8—221no—
211#97—224no—
212C4×C8—21no—
213C4×C8—221no—
214#95—224no—
215#95C4×D1112yes—
216C2×C11—21no—
217C2×C11—21no—
218C2×C11#188611yescharacteristic
219C2×C11#189411yescharacteristic
220C2×C11#191411yescharacteristic
221C2×Q8—221no—
222C2×Q8—221no—
223C2×Q8—221no—
224C2×Q8—221no—
225C2×Q8—221no—
226C2×Q8—221no—
227C2×Q8—222no—
228C2×Q8—222no—
229C2×Q8—882no—
230C22×C4—22no—
231C22×C4—112no—
232C22×C4—112no—
233C22×C4—222no—
234C22×C4C2×C4×D1111yescharacteristic
235C22×C4D4×D1111yescharacteristic
236C22×C4D4×D1111yescharacteristic
237M16—41no—
238M16—41no—
239M16—441no—
240M16—441no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—222no—
244C2×C8—441no—
245C4⋊C4—24no—
246C4⋊C4—222no—
247C4⋊C4—221no—
248C4⋊C4—222no—
249C4⋊C4—221no—
250C4⋊C4—441no—
251C4⋊C4—441no—
252C4⋊C4—441no—
253C4⋊C4—441no—
254C4⋊C4—884no—
255C42—41no—
256C42—41no—
257C42—222no—
258C42—222no—
259C42C2×D4411yescharacteristic
260C42#433911yescharacteristic
261C42D4×D1111yescharacteristic
262C42#434311yescharacteristic
263C11#940011yescharacteristic, complemented, Sylow
264C23C22⋊C4×D1111yescharacteristic
265Q8—441no—
266Q8—441no—
267Q8—441no—
268Q8—441no—
269Q8—882no—
270Q8—882no—
271C2×C4—22no—
272C2×C4—24no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—222no—
277C2×C4—222no—
278C2×C4—222no—
279C2×C4—222no—
280C2×C4—442no—
281C2×C4—444no—
282C2×C4—442no—
283C2×C4C4×D4411yescharacteristic
284C2×C4#6693511yescharacteristic
285C2×C4#6693711yescharacteristic
286C2×C4#6694611yescharacteristic
287C2×C4#6694711yescharacteristic
288C2×C4#6694811yescharacteristic
289C2×C4#6696411yescharacteristic
290C2×C4#6696811yescharacteristic
291C2×C4#6696811yescharacteristic
292C2×C4#6697111yescharacteristic
293C8—42no—
294C8—81no—
295C8—442no—
296C8—881no—
297C22—21no—
298C22—21no—
299C22#1062227811yescharacteristic
300C22#1062238411yescharacteristic
301C22#1062241511yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—44no—
306C4—442no—
307C4—442no—
308C4—882no—
309C4#1062239311yescharacteristic
310C4#1062242911yescharacteristic
311C4#1062243912yes—
312C4#1062248111yescharacteristic
313C4#1062249911yescharacteristic
314C2—21no—
315C2—21no—
316C2#1306900811yescharacteristic
317C2#1306904811yescharacteristic
318C2#1306916211yescharacteristic
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#9400
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
263. C11#9400semidirect

Maximal subgroups

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

subgroupindex
#130776992
#130738242
#130686092
#130672982
#130672962
#130665192
C11×#13032
#940011