Finite Group Databasebeta

← #14657553

Subgroups — #14657553

Order 2816.

366 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 97 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#13068631C211yesmaximal, characteristic
2#13067392C211yesmaximal, characteristic
3#13067273C211yesmaximal, characteristic
4#13067180C211yesmaximal, characteristic
5#13066940C211yesmaximal, characteristic
6#13066476C211yesmaximal, characteristic
7C11×#3078C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C11×#479—22no—
11C11×#477—21no—
12C11×#475—21no—
13C11×#428—21no—
14C11×#423C2211yescharacteristic
15C11×#419—21no—
16C2×#66899—21no—
17#10622549C2211yescharacteristic
18#10622538C2211yescharacteristic
19#10622538C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622185—21no—
22#10622184—21no—
23#10622176—22no—
24#10622167—21no—
25#10622166—22no—
26#10622117—22no—
27C22×Q8×C11D411yescharacteristic
28C2×C11×M16—21no—
29C11×C4⋊Q8D411yescharacteristic
30C11×C4⋊Q8D411yescharacteristic
31C11×#125—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C4×Q8×C11—21no—
40C11×#117—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4D411yescharacteristic
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45C2×C4⋊Dic11—21no—
46C22×C11⋊C8—21no—
47C11×#107—22no—
48C11×#106—22no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C11×#103—22no—
52C11×#103—22no—
53#66899—42no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C22⋊(C11⋊C8)—21no—
57C22⋊(C11⋊C8)D412yes—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#10471—111nomaximal, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11Q1612yes—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11C2×D411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11#4111yescharacteristic
78C22×Dic11—41no—
79C11×M16—41no—
80C11×M16—41no—
81C2×C8×C11—22no—
82C11×C4⋊C4—21no—
83C11×C4⋊C4—21no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93C42×C11—41no—
94C42×C11—41no—
95C42×C11—41no—
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11#4111yescharacteristic
99C42×C11#4111yescharacteristic
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107#3078D1111yescharacteristic
108#1805—111no—
109#1571—111no—
110#1542—111no—
111#1518—111no—
112#1461—111no—
113#1286—111no—
114C23×C11#12111yescharacteristic
115Q8×C11—22no—
116Q8×C11—22no—
117Q8×C11—41no—
118Q8×C11—41no—
119Q8×C11—81no—
120Q8×C11—81no—
121C2×C4×C11—22no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—81no—
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12111yescharacteristic
132C2×C4×C11#12111yescharacteristic
133C2×C4×C11#12311yescharacteristic
134C2×C4×C11#12311yescharacteristic
135C2×C4×C11#12411yescharacteristic
136C2×C4×C11C2×Q1611yescharacteristic
137C2×C4×C11#13511yescharacteristic
138C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C11#13711yescharacteristic
140C2×Dic11—81no—
141C2×Dic11—81no—
142C2×Dic11—81no—
143C8×C11—42no—
144C11⋊C8—42no—
145C11⋊C8—81no—
146C11⋊C8—81no—
147#533C2×D1111yescharacteristic
148C2×C4×Q8C2×D1111yescharacteristic
149#479—22no—
150#477—21no—
151#475—21no—
152#431—111no—
153#431—111no—
154#428—21no—
155#423C2×D1111yescharacteristic
156C2×C4⋊C8—111no—
157#419—21no—
158C2×#103—221no—
159#382—111no—
160#340—221no—
161#335—222no—
162#333—221no—
163#332—221no—
164#328—222no—
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—42no—
176C4×C11—81no—
177C4×C11—81no—
178C4×C11—81no—
179C4×C11#44911yescharacteristic
180C4×C11#45111yescharacteristic
181C4×C11#48411yescharacteristic
182C4×C11#48511yescharacteristic
183Dic11—161no—
184C22×Q8C22⋊D1111yescharacteristic
185C2×M16—21no—
186C22×C8—221no—
187C4⋊Q8C22⋊D1111yescharacteristic
188C4⋊Q8C22⋊D1111yescharacteristic
189#125—21no—
190C22⋊Q8—21no—
191C22⋊Q8—21no—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195C4×Q8—21no—
196C4×Q8—21no—
197C4×Q8—21no—
198#117—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4C22⋊D1111yescharacteristic
202C2×C42—21no—
203C2×C42C22×D1111yescharacteristic
204#107—22no—
205#106—22no—
206C4⋊C8—21no—
207C4⋊C8—221no—
208C4⋊C8—221no—
209C4⋊C8—221no—
210C4⋊C8—221no—
211C4⋊C8C22⋊D1112yes—
212#103—22no—
213#103—22no—
214#103—442no—
215C22⋊C8—112no—
216C22⋊C8—221no—
217C4×C8—221no—
218C4×C8—221no—
219#95—221no—
220#95—221no—
221C2×C11—21no—
222C2×C11—21no—
223C2×C11#203611yescharacteristic
224C2×C11#204911yescharacteristic
225C2×C11#205311yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8#432612yes—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—441no—
237C22×C4D4×D1111yescharacteristic
238C22×C4#434111yescharacteristic
239C22×C4C2×C22⋊D1111yescharacteristic
240M16—41no—
241M16—41no—
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—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C22⋊C4—41no—
261C42—41no—
262C42—41no—
263C42—41no—
264C42#434111yescharacteristic
265C42#434111yescharacteristic
266C42C2×C22⋊D1111yescharacteristic
267C42C2×C22⋊D1111yescharacteristic
268C11#1047111yescharacteristic, complemented, Sylow
269C23#6699211yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274Q8—81no—
275Q8—81no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—81no—
285C2×C4—881no—
286C2×C4—881no—
287C2×C4—881no—
288C2×C4#6698811yescharacteristic
289C2×C4#6698811yescharacteristic
290C2×C4#6698911yescharacteristic
291C2×C4#6699111yescharacteristic
292C2×C4#6699211yescharacteristic
293C2×C4#6699511yescharacteristic
294C2×C4C2×#432611yescharacteristic
295C2×C4#6700211yescharacteristic
296C2×C4#6700311yescharacteristic
297C2×C4#6700611yescharacteristic
298C8—42no—
299C8—442no—
300C8—881no—
301C8—881no—
302C22—21no—
303C22—21no—
304C22#1062266211yescharacteristic
305C22#1062266411yescharacteristic
306C22#1062283511yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—42no—
312C4—81no—
313C4—81no—
314C4—81no—
315C4—1761no—
316C4#1062265711yescharacteristic
317C4#1062265811yescharacteristic
318C4#1062284111yescharacteristic
319C4#1062285111yescharacteristic
320C2—21no—
321C2—21no—
322C2#1306981611yescharacteristic
323C2#1306989311yescharacteristic
324C2#1306991911yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3078C2
socleC22×C11#394
prime radicalC23×C11#121
hypercenter#3078D11
hypocenterC11#10471
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

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
#130686312
#130673922
#130672732
#130671802
#130669402
#130664762
C11×#30782
#1047111