Finite Group Databasebeta

← #14655694

Subgroups — #14655694

Order 2816.

488 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 105 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#13067288C211yesmaximal, characteristic
5#13067071C211yesmaximal, characteristic
6#13066454C211yesmaximal, characteristic
7C11×#3139C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#491—22no—
12C11×#487—21no—
13C11×#487—21no—
14C11×#419—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#10622185—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⋊Q8D412yes—
36C11×C4⋊Q8D411yescharacteristic
37C11×C4⋊Q8D411yescharacteristic
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×#103—24no—
57C11×#103—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#10171—111nomaximal, Sylow
70C2×Q8×C11—22no—
71C2×Q8×C11—21no—
72C2×Q8×C11—21no—
73C2×Q8×C11—41no—
74C2×Q8×C11—42no—
75C2×Q8×C11—42no—
76C22×C4×C11—41no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×Dic11—22no—
81C2×Dic22—22no—
82C2×Dic22—22no—
83C2×Dic22—44no—
84C11×M16—22no—
85C11×M16—22no—
86C2×C8×C11—22no—
87C11×C4⋊C4—22no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—22no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C42×C11—41no—
99C42×C11C2×D411yescharacteristic
100C42×C11C2×D411yescharacteristic
101C42×C11C2×D411yescharacteristic
102C42×C11C2×D411yescharacteristic
103#4326—84no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108#4318—42no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—22no—
111C2×C11⋊C8—42no—
112C2×C11⋊C8—41no—
113#3209—111no—
114#3139D1111yescharacteristic
115C2×#487—111no—
116#1997—111no—
117#1546—111no—
118#1493—111no—
119#1278—111no—
120C23×C11#12111yescharacteristic
121Q8×C11—44no—
122Q8×C11—42no—
123Q8×C11—42no—
124Q8×C11—81no—
125Q8×C11—81no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—42no—
131C2×C4×C11—82no—
132C2×C4×C11#12011yescharacteristic
133C2×C4×C11#12011yescharacteristic
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12111yescharacteristic
136C2×C4×C11#12111yescharacteristic
137C2×C4×C11#12711yescharacteristic
138C2×C4×C11#13512yes—
139C2×C4×C11#13712yes—
140C2×Dic11—42no—
141C2×Dic11—82no—
142Dic22—44no—
143Dic22—44no—
144C8×C11—42no—
145C11⋊C8—42no—
146C11⋊C8—42no—
147C11⋊C8—81no—
148#533C2×D1111yescharacteristic
149C2×C4⋊Q8—111no—
150C2×C4⋊Q8C2×D1111yescharacteristic
151#494—221no—
152#491—22no—
153#487—21no—
154#487—21no—
155#487—222no—
156#487—222no—
157#487—221no—
158#462—222no—
159#451—222no—
160#431—111no—
161#423—111no—
162#419—22no—
163C2×#103—222no—
164C4×M16C2×D1111yescharacteristic
165C2×C4×C8—111no—
166#343—222no—
167#332—222no—
168Q8⋊C8—222no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#39211yescharacteristic
172C22×C11#46412yes—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—81no—
176C4×C11—82no—
177C4×C11—81no—
178C4×C11#45212yes—
179C4×C11#45512yes—
180C4×C11#47312yes—
181C4×C11#49511yescharacteristic
182C4×C11#49711yescharacteristic
183Dic11—82no—
184C22×Q8—21no—
185C22×Q8—112no—
186C2×Q16—224no—
187C2×M16—221no—
188C2×M16C22⋊D1112yes—
189C22×C8—221no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—221no—
194C4⋊Q8—221no—
195C4⋊Q8—221no—
196C4⋊Q8—221no—
197C4⋊Q8C22⋊D1112yes—
198C4⋊Q8C22⋊D1111yescharacteristic
199C4⋊Q8C22⋊D1111yescharacteristic
200#125—21no—
201C22⋊Q8—21no—
202C22⋊Q8—21no—
203C4×Q8—21no—
204C4×Q8—21no—
205#117—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C42C22×D1111yescharacteristic
211C4⋊C8—112no—
212C4⋊C8—221no—
213C4⋊C8—221no—
214#103—24no—
215#103—24no—
216#103—228no—
217#103—224no—
218C22⋊C8—221no—
219#97—21no—
220C4×C8—21no—
221C4×C8—112no—
222C4×C8—221no—
223C4×C8—221no—
224C2×C11—22no—
225C2×C11#200411yescharacteristic
226C2×C11#201511yescharacteristic
227C2×C11#202011yescharacteristic
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—222no—
235C2×Q8—222no—
236C2×Q8—444no—
237C22×C4—41no—
238C22×C4—222no—
239C22×C4D4×D1111yescharacteristic
240C22×C4#434111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242Q16—884no—
243M16—22no—
244M16—22no—
245M16—442no—
246C2×C8—22no—
247C2×C8—222no—
248C2×C8—222no—
249C2×C8—442no—
250C2×C8—441no—
251C4⋊C4—22no—
252C4⋊C4—21no—
253C4⋊C4—22no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—441no—
265C22⋊C4—41no—
266C42—41no—
267C42D4×D1111yescharacteristic
268C42D4×D1111yescharacteristic
269C42C2×C22⋊D1111yescharacteristic
270C42C2×C22⋊D1111yescharacteristic
271C11#1017111yescharacteristic, complemented, Sylow
272C23#6699111yescharacteristic
273Q8—42no—
274Q8—42no—
275Q8—44no—
276Q8—81no—
277Q8—81no—
278Q8—444no—
279Q8—444no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—82no—
286C2×C4—442no—
287C2×C4—882no—
288C2×C4#6699011yescharacteristic
289C2×C4#6699011yescharacteristic
290C2×C4#6699211yescharacteristic
291C2×C4#6699211yescharacteristic
292C2×C4#6699311yescharacteristic
293C2×C4#6700312yes—
294C2×C4#6700412yes—
295C2×C4#6700611yescharacteristic
296C8—42no—
297C8—442no—
298C8—442no—
299C8—881no—
300C22—21no—
301C22—21no—
302C22#1062266712yes—
303C22#1062283611yescharacteristic
304C4—21no—
305C4—21no—
306C4—81no—
307C4—82no—
308C4—81no—
309C4—882no—
310C4#1062267211yescharacteristic
311C4#1062267311yescharacteristic
312C4#1062281512yes—
313C4#1062281712yes—
314C4#1062285212yes—
315C2—22no—
316C2#1306964211yescharacteristic
317C2#1306971011yescharacteristic
318C2#1306973411yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3139C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#3139D11
hypocenterC11#10171
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
271. C11#10171semidirect

Maximal subgroups

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

subgroupindex
#130795612
C2×#106227062
#130696052
#130672882
#130670712
#130664542
C11×#31392
#1017111