Finite Group Databasebeta

← #14655638

Subgroups — #14655638

Order 2816.

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

normal subgroups only

This group has 488 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#13079561C211yesmaximal, characteristic
2C2×#10622706C211yesmaximal, characteristic
3#13069605C211yesmaximal, characteristic
4#13067297C211yesmaximal, characteristic
5#13067071C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic
7C11×#3165C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#501—22no—
12C11×#500—21no—
13C11×#498—21no—
14C11×#428—22no—
15C4×C11×M16C2211yescharacteristic
16#10622706—21no—
17#10622706—22no—
18#10622706—22no—
19#10622705—21no—
20#10622663—22no—
21#10622644—22no—
22C2×#66874—22no—
23#10622538C2211yescharacteristic
24#10622537C2211yescharacteristic
25C2×C4×C11⋊C8C2211yescharacteristic
26#10622192—22no—
27#10622184—22no—
28Q8⋊(C11⋊C8)—22no—
29C22×Q8×C11—21no—
30C22×Dic22D412yes—
31C2×C11×M16D412yes—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D412yes—
38C11×#125—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C4×Q8×C11—21no—
42C4×Q8×C11—21no—
43C11×#117—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4326—24no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×#4318—21no—
51C22×C11⋊C8—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56C11×#107—24no—
57C11×#106—24no—
58C11×#97—21no—
59C4×C8×C11—21no—
60C22⋊(C11⋊C8)—21no—
61#66874—28no—
62#66874—24no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)D412yes—
66C4×C11⋊C8—21no—
67C4×C11⋊C8—21no—
68C4×C11⋊C8D412yes—
69#10163—111nomaximal, Sylow
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—22no—
73C2×Q8×C11—41no—
74C2×Q8×C11—82no—
75C22×C4×C11—41no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11#4111yescharacteristic
79C22×Dic11—22no—
80C2×Dic22—22no—
81C2×Dic22—22no—
82C2×Dic22—44no—
83C11×M16—22no—
84C11×M16Q1614yescomplemented
85C2×C8×C11—22no—
86C11×C4⋊C4—22no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—41no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C22⋊C4—41no—
97C42×C11—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102#4326—84no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107#4318—42no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—42no—
111C2×C11⋊C8—41no—
112#3209—111no—
113#3165D1111yescharacteristic
114C2×#487—111no—
115#1997—111no—
116#1548—111no—
117#1493—111no—
118#1278—111no—
119C23×C11#12111yescharacteristic
120Q8×C11—42no—
121Q8×C11—42no—
122Q8×C11—82no—
123Q8×C11—82no—
124C2×C4×C11—22no—
125C2×C4×C11—22no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—42no—
129C2×C4×C11—82no—
130C2×C4×C11#12011yescharacteristic
131C2×C4×C11#12011yescharacteristic
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12111yescharacteristic
134C2×C4×C11#12111yescharacteristic
135C2×C4×C11#12711yescharacteristic
136C2×C4×C11C2×Q1612yes—
137C2×C4×C11#13712yes—
138C2×Dic11—42no—
139C2×Dic11—82no—
140Dic22—44no—
141Dic22—44no—
142C8×C11—24no—
143C11⋊C8—42no—
144C11⋊C8—42no—
145C11⋊C8—81no—
146#533C2×D1111yescharacteristic
147C2×C4⋊Q8—111no—
148C2×C4⋊Q8C2×D1111yescharacteristic
149#501—22no—
150#500—21no—
151#498—21no—
152#494—221no—
153#487—222no—
154#487—222no—
155#487—221no—
156#462—222no—
157#451—222no—
158#431—111no—
159#428—22no—
160#423—111no—
161C2×#103—222no—
162C4×M16C2×D1111yescharacteristic
163C2×C4×C8—111no—
164#343—222no—
165#333—222no—
166Q8⋊C8—222no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11#39211yescharacteristic
170C22×C11#46212yes—
171C4×C11—21no—
172C4×C11—21no—
173C4×C11—81no—
174C4×C11—82no—
175C4×C11—81no—
176C4×C11#45112yes—
177C4×C11#45512yes—
178C4×C11#47112yes—
179C4×C11#49411yescharacteristic
180C4×C11#49711yescharacteristic
181Dic11—82no—
182C22×Q8—21no—
183C22×Q8—112no—
184C2×Q16—224no—
185C2×M16—221no—
186C2×M16C22⋊D1112yes—
187C22×C8—221no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—221no—
192C4⋊Q8—221no—
193C4⋊Q8—221no—
194C4⋊Q8—221no—
195C4⋊Q8C22⋊D1112yes—
196C4⋊Q8C22⋊D1111yescharacteristic
197C4⋊Q8C22⋊D1111yescharacteristic
198#125—21no—
199C22⋊Q8—21no—
200C22⋊Q8—21no—
201C4×Q8—21no—
202C4×Q8—21no—
203#117—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C42C22×D1111yescharacteristic
209#107—24no—
210#106—24no—
211C4⋊C8—112no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214#103—228no—
215#103—224no—
216C22⋊C8—221no—
217#97—21no—
218C4×C8—21no—
219C4×C8—112no—
220C4×C8—221no—
221C4×C8—221no—
222C2×C11—22no—
223C2×C11#200411yescharacteristic
224C2×C11#201611yescharacteristic
225C2×C11#201911yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—22no—
229C2×Q8—41no—
230C2×Q8—82no—
231C2×Q8—222no—
232C2×Q8—222no—
233C2×Q8—444no—
234C22×C4—41no—
235C22×C4—222no—
236C22×C4D4×D1111yescharacteristic
237C22×C4#434111yescharacteristic
238C22×C4C2×C22⋊D1111yescharacteristic
239Q16—884no—
240M16—22no—
241M16—442no—
242M16#432614yescomplemented
243C2×C8—22no—
244C2×C8—222no—
245C2×C8—222no—
246C2×C8—442no—
247C2×C8—441no—
248C4⋊C4—22no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—22no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—441no—
259C4⋊C4—441no—
260C4⋊C4—441no—
261C4⋊C4—441no—
262C22⋊C4—41no—
263C42—41no—
264C42D4×D1111yescharacteristic
265C42D4×D1111yescharacteristic
266C42C2×C22⋊D1111yescharacteristic
267C42C2×C22⋊D1111yescharacteristic
268C11#1016311yescharacteristic, complemented, Sylow
269C23#6699111yescharacteristic
270Q8—42no—
271Q8—42no—
272Q8—82no—
273Q8—82no—
274Q8—444no—
275Q8—444no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—82no—
282C2×C4—442no—
283C2×C4—882no—
284C2×C4#6699011yescharacteristic
285C2×C4#6699011yescharacteristic
286C2×C4#6699211yescharacteristic
287C2×C4#6699211yescharacteristic
288C2×C4#6699311yescharacteristic
289C2×C4#6699512yes—
290C2×C4C2×#432612yes—
291C2×C4#6700611yescharacteristic
292C8—24no—
293C8—442no—
294C8—442no—
295C8—881no—
296C22—21no—
297C22—21no—
298C22#1062270312yes—
299C22#1062283611yescharacteristic
300C4—21no—
301C4—21no—
302C4—81no—
303C4—82no—
304C4—81no—
305C4—882no—
306C4#1062269911yescharacteristic
307C4#1062270511yescharacteristic
308C4#1062281312yes—
309C4#1062281512yes—
310C4#1062284112yes—
311C2—22no—
312C2#1306964211yescharacteristic
313C2#1306971611yescharacteristic
314C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3165C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3165D11
hypocenterC11#10163
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
84. C11×M16Q16semidirect
242. M16#4326semidirect
268. C11#10163semidirect

Maximal subgroups

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

subgroupindex
#130795612
C2×#106227062
#130696052
#130672972
#130670712
#130664542
C11×#31652
#1016311