Finite Group Databasebeta

← #14657555

Subgroups — #14657555

Order 2816.

366 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 93 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#13078417C211yesmaximal, characteristic
2#13068628C211yesmaximal, characteristic
3#13067391C211yesmaximal, characteristic
4#13067273C211yesmaximal, characteristic
5#13066939C211yesmaximal, characteristic
6#13066474C211yesmaximal, characteristic
7C11×#1518C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Dic22C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#382C2211yescharacteristic
12#10622707—21no—
13#10622704—21no—
14#10622676—22no—
15#10622617—21no—
16#10622608—21no—
17C2×#66874—21no—
18#10622538C2211yescharacteristic
19#10622537C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21C11×#328—22no—
22#10622185—21no—
23#10622184—21no—
24#10622167—21no—
25#10622107—22no—
26#10622096—22no—
27C22×Dic22D411yescharacteristic
28C11×C4⋊Q8D411yescharacteristic
29C11×C4⋊Q8D411yescharacteristic
30C11×#125—21no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C11×#117—21no—
36C2×C11×C4⋊C4—21no—
37C2×C42×C11C2311yescharacteristic
38C2×C4⋊Dic11D411yescharacteristic
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11—21no—
41C2×#4318—21no—
42C22×C11⋊C8—21no—
43C4×Dic22—21no—
44C4×Dic22—21no—
45C4×Dic22—21no—
46C4×Dic22—21no—
47C11×C4⋊C8—21no—
48C11×C22⋊C8D412yes—
49C4×C8×C11—21no—
50C11×#95—21no—
51C11×#95—21no—
52C22⋊(C11⋊C8)—21no—
53#66874—22no—
54#66874—22no—
55#66874—42no—
56#66872—22no—
57#66871—22no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)D412yes—
63C4×C11⋊C8—21no—
64#10471—111nomaximal, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—21no—
72C22×Dic11—21no—
73C2×Dic22—21no—
74C2×Dic22—21no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—21no—
78C2×Dic22Q1612yes—
79C2×C8×C11—22no—
80C11×C4⋊C4—21no—
81C11×C4⋊C4—21no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C22⋊C4—41no—
89C42×C11—41no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96Dic11⋊C4—41no—
97Dic11⋊C4—41no—
98C4×Dic11—41no—
99C4×Dic11—41no—
100#4318—41no—
101#4318—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#3078—111no—
108#1805—111no—
109#1571—111no—
110#1542—111no—
111#1518D1111yescharacteristic
112#1461—111no—
113#1286—111no—
114C23×C11#12111yescharacteristic
115Q8×C11—81no—
116Q8×C11—81no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12111yescharacteristic
127C2×C4×C11#12311yescharacteristic
128C2×C4×C11#12311yescharacteristic
129C2×C4×C11#12411yescharacteristic
130C2×C4×C11C2×Q1611yescharacteristic
131C2×C4×C11#13511yescharacteristic
132C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C11#13711yescharacteristic
134C2×Dic11—22no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—81no—
139Dic22—22no—
140Dic22—22no—
141Dic22—41no—
142Dic22—41no—
143C8×C11—42no—
144C11⋊C8—42no—
145C11⋊C8—81no—
146C11⋊C8—81no—
147#533C2×D1111yescharacteristic
148C2×C4×Q8—111no—
149#479—222no—
150#477—221no—
151#475—221no—
152#431—111no—
153#431C2×D1111yescharacteristic
154#428—221no—
155#423—111no—
156C2×C4⋊C8—111no—
157#419—221no—
158C2×#103—221no—
159#382C2×D1111yescharacteristic
160#340—221no—
161#335—222no—
162#333—221no—
163#332—221no—
164#328—22no—
165#324—222no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#39411yescharacteristic
169C22×C11#46711yescharacteristic
170C22×C11#46811yescharacteristic
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—81no—
176C4×C11—81no—
177C4×C11—161no—
178C4×C11#44911yescharacteristic
179C4×C11#45111yescharacteristic
180C4×C11#48411yescharacteristic
181C4×C11#48511yescharacteristic
182Dic11—42no—
183Dic11—81no—
184C22×Q8—111no—
185C2×M16—221no—
186C22×C8—221no—
187C4⋊Q8D4411yescharacteristic
188C4⋊Q8D4411yescharacteristic
189#125—21no—
190C22⋊Q8—21no—
191C22⋊Q8—21no—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×Q8—221no—
195C4×Q8—221no—
196C4×Q8—221no—
197C4×Q8—221no—
198#117—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—111no—
201C2×C4⋊C4—221no—
202C2×C42—221no—
203C2×C42C22×D1111yescharacteristic
204#107—222no—
205#106—222no—
206C4⋊C8—21no—
207C4⋊C8—112no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8—221no—
212#103—222no—
213#103—222no—
214#103—442no—
215C22⋊C8—221no—
216C22⋊C8C22⋊D1112yes—
217C4×C8—21no—
218C4×C8—221no—
219#95—21no—
220#95—21no—
221C2×C11—21no—
222C2×C11—21no—
223C2×C11#203611yescharacteristic
224C2×C11#204911yescharacteristic
225C2×C11#205311yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—112no—
229C2×Q8—221no—
230C2×Q8—221no—
231C2×Q8—221no—
232C2×Q8—221no—
233C2×Q8—221no—
234C22×C4—41no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4D4×D1111yescharacteristic
238C22×C4#434111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240M16—441no—
241M16—441no—
242C2×C8—22no—
243C2×C8—222no—
244C2×C8—441no—
245C2×C8—441no—
246C2×C8—441no—
247C2×C8—441no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C22⋊C4—41no—
261C42—41no—
262C42—441no—
263C42—441no—
264C42C2×D4411yescharacteristic
265C42#433911yescharacteristic
266C42D4×D1111yescharacteristic
267C42#434111yescharacteristic
268C11#1047111yescharacteristic, complemented, Sylow
269C23#6699111yescharacteristic
270Q8—81no—
271Q8—81no—
272Q8—222no—
273Q8—222no—
274Q8—441no—
275Q8—441no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—222no—
284C2×C4—441no—
285C2×C4—441no—
286C2×C4—441no—
287C2×C4—881no—
288C2×C4#6693511yescharacteristic
289C2×C4#6693611yescharacteristic
290C2×C4#6693811yescharacteristic
291C2×C4#6693911yescharacteristic
292C2×C4#6696711yescharacteristic
293C2×C4#6696811yescharacteristic
294C2×C4Q16×D1111yescharacteristic
295C2×C4#6697211yescharacteristic
296C2×C4#6698311yescharacteristic
297C2×C4#6699211yescharacteristic
298C8—42no—
299C8—442no—
300C8—881no—
301C8—881no—
302C22—21no—
303C22—21no—
304C22#1062257411yescharacteristic
305C22#1062278711yescharacteristic
306C22#1062280111yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—81no—
313C4—161no—
314C4—442no—
315C4—881no—
316C4#1062242111yescharacteristic
317C4#1062242211yescharacteristic
318C4#1062242411yescharacteristic
319C4#1062242711yescharacteristic
320C2—21no—
321C2—21no—
322C2#1306981811yescharacteristic
323C2#1306989711yescharacteristic
324C2#1306992111yescharacteristic
subgroupG/H
centerC22#10622574
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1518C2
socleC22×C11#394
prime radicalC23×C11#121
hypercenter#1518D11
hypocenterC11#10471
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
268. C11#10471semidirect

Maximal subgroups

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

subgroupindex
#130784172
#130686282
#130673912
#130672732
#130669392
#130664742
C11×#15182
#1047111