Finite Group Databasebeta

← #14655657

Subgroups — #14655657

Order 2816.

476 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 113 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#13079769C211yesmaximal, characteristic
2#13079162C211yesmaximal, characteristic
3C2×#10622295C211yesmaximal, characteristic
4#13069605C211yesmaximal, characteristic
5#13067296C211yesmaximal, characteristic
6#13067072C211yesmaximal, characteristic
7C11×#1278C211yesmaximal, characteristic
8#10623001C2211yescharacteristic
9C2×#66922C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14#10622734—22no—
15C2×#66882—22no—
16#10622537C2211yescharacteristic
17#10622463—22no—
18#10622335—22no—
19#10622315—22no—
20#10622295—22no—
21#10622295—21no—
22#10622295—21no—
23#10622295—22no—
24#10622294—21no—
25#10622293—21no—
26#10622192—22no—
27#10622119—22no—
28#10622094—22no—
29C22×Dic22—21no—
30C22×Dic22—21no—
31C2×C11×M16D412yes—
32C22×C8×C11—21no—
33C2×C42×C11C2311yescharacteristic
34#66979—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11D412yes—
39#66977—21no—
40#66977—21no—
41C2×#4318—21no—
42#66923—21no—
43#66922—21no—
44#66922—21no—
45#66922—21no—
46#66922—21no—
47#66922—21no—
48#66922—21no—
49#66922—21no—
50#66922D412yes—
51#66922D411yescharacteristic
52#66922D411yescharacteristic
53C4×Dic22—21no—
54C4×Dic22—21no—
55C11×C4⋊C8D412yes—
56C11×C22⋊C8—21no—
57C11×#97—21no—
58C4×C8×C11—21no—
59C4×C8×C11—21no—
60C4×C8×C11—21no—
61C4×C8×C11D412yes—
62#66882—24no—
63#66882—28no—
64#66882—24no—
65#66881—24no—
66#66880—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69#10165—111nomaximal, Sylow
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11#4111yescharacteristic
73C22×Dic11—22no—
74C22×Dic11—41no—
75C2×Dic22—21no—
76C2×Dic22—21no—
77C2×Dic22—22no—
78C2×Dic22—41no—
79C2×Dic22—41no—
80C2×Dic22—41no—
81C2×Dic22—82no—
82C2×Dic22—82no—
83C11×M16—22no—
84C11×M16Q1614yes—
85C2×C8×C11—24no—
86C2×C8×C11—22no—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C42×C11C2×D411yescharacteristic
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C22⋊Dic11—41no—
94C4⋊Dic11—22no—
95C4⋊Dic11—21no—
96C4⋊Dic11—22no—
97C4⋊Dic11—21no—
98C4⋊Dic11—22no—
99C4⋊Dic11—22no—
100C4⋊Dic11—21no—
101C4⋊Dic11—21no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—41no—
109#4318—42no—
110C2×C11⋊C8—41no—
111#3230—111no—
112#3165—111no—
113C2×#500—111no—
114#1997—111no—
115#1548—111no—
116#1493—111no—
117#1278D1111yescharacteristic
118C23×C11#12111yescharacteristic
119C2×C4×C11—22no—
120C2×C4×C11—22no—
121C2×C4×C11#12011yescharacteristic
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11#12011yescharacteristic
124C2×C4×C11#12111yescharacteristic
125C2×C4×C11#12111yescharacteristic
126C2×C4×C11#12711yescharacteristic
127C2×C4×C11C2×Q1612yes—
128C2×C4×C11#13712yes—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—82no—
134C2×Dic11—82no—
135Dic22—42no—
136Dic22—42no—
137Dic22—82no—
138Dic22—82no—
139Dic22—82no—
140Dic22—82no—
141C8×C11—24no—
142C8×C11—24no—
143C8×C11—42no—
144C11⋊C8—81no—
145#533—111no—
146C2×C4⋊Q8—111no—
147C2×C4⋊Q8—111no—
148#501—222no—
149#500—222no—
150#500—221no—
151#500—221no—
152#500—222no—
153#498—221no—
154#487—221no—
155#484—222no—
156#477—222no—
157#431C2×D1111yescharacteristic
158#428—222no—
159C2×#107—222no—
160#423—111no—
161C4×M16C2×D1111yescharacteristic
162C2×C4×C8C2×D1111yescharacteristic
163#343—222no—
164#333—222no—
165Q8⋊C8—222no—
166C22×C11—21no—
167C22×C11—21no—
168C22×C11#39211yescharacteristic
169C22×C11#46212yes—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11#45112yes—
173C4×C11#45612yes—
174C4×C11#47212yes—
175C4×C11#49411yescharacteristic
176C4×C11#49711yescharacteristic
177Dic11—81no—
178Dic11—81no—
179Dic11—82no—
180Dic11—82no—
181C22×Q8—221no—
182C22×Q8—221no—
183C2×M16—221no—
184C2×M16D4412yes—
185C22×C8—21no—
186C4⋊Q8—112no—
187C4⋊Q8—111no—
188C4⋊Q8—111no—
189C4⋊Q8—221no—
190C4⋊Q8—221no—
191C4⋊Q8—221no—
192C4⋊Q8—221no—
193C4⋊Q8—221no—
194C4⋊Q8—221no—
195C4⋊Q8—221no—
196#125—221no—
197C22⋊Q8—221no—
198C22⋊Q8—221no—
199C4×Q8—221no—
200C4×Q8—221no—
201#117—221no—
202C2×C4⋊C4—112no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C42C22×D1111yescharacteristic
207#107—228no—
208#107—224no—
209#107—224no—
210#106—224no—
211C4⋊C8—221no—
212C4⋊C8—221no—
213C4⋊C8D4412yes—
214#103—224no—
215C22⋊C8—21no—
216#97—21no—
217C4×C8—21no—
218C4×C8—21no—
219C4×C8—21no—
220C4×C8D4412yes—
221C2×C11—22no—
222C2×C11#200511yescharacteristic
223C2×C11#201611yescharacteristic
224C2×C11#201811yescharacteristic
225C2×Q8—221no—
226C2×Q8—221no—
227C2×Q8—222no—
228C2×Q8—441no—
229C2×Q8—441no—
230C2×Q8—441no—
231C2×Q8—882no—
232C2×Q8—882no—
233C22×C4—222no—
234C22×C4—441no—
235C22×C4C2×D4411yescharacteristic
236C22×C4D4×D1111yescharacteristic
237C22×C4#434311yescharacteristic
238M16—22no—
239M16—442no—
240M16Dic4414yes—
241C2×C8—24no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8—22no—
245C2×C8—441no—
246C4⋊C4—222no—
247C4⋊C4—221no—
248C4⋊C4—222no—
249C4⋊C4—222no—
250C4⋊C4—222no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—441no—
255C4⋊C4—441no—
256C4⋊C4—441no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C22⋊C4—441no—
261C42—441no—
262C42C2×D4411yescharacteristic
263C42C2×D4411yescharacteristic
264C42D4×D1111yescharacteristic
265C42D4×D1111yescharacteristic
266C11#1016511yescharacteristic, complemented, Sylow
267C23#6694811yescharacteristic
268Q8—442no—
269Q8—442no—
270Q8—882no—
271Q8—882no—
272Q8—882no—
273Q8—882no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—442no—
279C2×C4—442no—
280C2×C4—882no—
281C2×C4—882no—
282C2×C4#6692711yescharacteristic
283C2×C4#6693511yescharacteristic
284C2×C4#6693511yescharacteristic
285C2×C4#6693511yescharacteristic
286C2×C4#6694811yescharacteristic
287C2×C4#6694811yescharacteristic
288C2×C4C2×Dic4412yes—
289C2×C4#6696212yes—
290C8—24no—
291C8—24no—
292C8—42no—
293C8—881no—
294C22—21no—
295C22—21no—
296C22#1062228411yescharacteristic
297C22#1062246212yes—
298C4—21no—
299C4—21no—
300C4—881no—
301C4—882no—
302C4—882no—
303C4—881no—
304C4#1062231211yescharacteristic
305C4#1062232811yescharacteristic
306C4#1062235212yes—
307C4#1062243912yes—
308C4#1062251012yes—
309C2—22no—
310C2#1306965511yescharacteristic
311C2#1306971811yescharacteristic
312C2#1306972611yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1278C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1278D11
hypocenterC11#10165
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1278

Complements

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

NH ≅ G/Ntype
266. C11#10165semidirect

Maximal subgroups

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

subgroupindex
#130797692
#130791622
C2×#106222952
#130696052
#130672962
#130670722
C11×#12782
#1016511