Finite Group Databasebeta

← #14666769

Subgroups — #14666769

Order 2816.

394 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 57 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#13073985C211yesmaximal, characteristic
2#13069958C211yesmaximal, characteristic
3#13067624C211yesmaximal, characteristic
4#13066623C211yesmaximal, characteristic
5#13066622C211yesmaximal, characteristic
6#13066561C211yesmaximal, characteristic
7C11×#1611C211yesmaximal, characteristic
8C11×#544C2211yescharacteristic
9C2×#66940—21no—
10C11×#483—21no—
11C11×#398C2211yescharacteristic
12#10622656—21no—
13#10622608—21no—
14#10622597—21no—
15#10622596C2211yescharacteristic
16#10622589C2211yescharacteristic
17#10622585—21no—
18#10622260—21no—
19#10622259—21no—
20#10622259—21no—
21C11×#328—21no—
22C11×#324C2211yescharacteristic
23#10622176—21no—
24#10622170—21no—
25#10622168C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×Dic22—21no—
28C11×C4⋊Q8—41no—
29C11×#125—41no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—21no—
32C11×#117—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4C2311yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—21no—
44C2×C4×Dic11—21no—
45C2×C4×Dic11D411yescharacteristic
46C2×#4318—21no—
47#66940—42no—
48#66940—42no—
49C11×#106—41no—
50C11×#103—41no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95D411yescharacteristic
54#66899—41no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66872—41no—
62#66872—41no—
63#66871—41no—
64#12247—111nomaximal, Sylow
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C2×Dic22—24no—
77C2×Dic22—42no—
78C2×Dic22—42no—
79C2×C8×C11—41no—
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×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C22⋊C4—41no—
91C42×C11—41no—
92C4⋊Dic11—41no—
93C4⋊Dic11—41no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96Dic11⋊C4—42no—
97Dic11⋊C4—41no—
98Dic11⋊C4—41no—
99Dic11⋊C4—81no—
100C4×Dic11—21no—
101C4×Dic11—42no—
102C4×Dic11—42no—
103C4×Dic11SD1612yes—
104#4318—22no—
105#4318—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108#2582—111no—
109#2060—111no—
110#1611—111no—
111#1611D1111yescharacteristic
112#1346—111no—
113#1346—111no—
114#1325—111no—
115C23×C11#12011yescharacteristic
116Q8×C11—81no—
117Q8×C11—81no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—22no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
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—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11C2×SD1611yescharacteristic
133C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
134C2×Dic11—22no—
135C2×Dic11—22no—
136C2×Dic11—22no—
137C2×Dic11—22no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146Dic22—48no—
147C8×C11—81no—
148C11⋊C8—42no—
149C11⋊C8—81no—
150#544C2×D1111yescharacteristic
151C2×C4×Q8—221no—
152#483—21no—
153#483—221no—
154#428—221no—
155#398—111no—
156#398—221no—
157#398C2×D1111yescharacteristic
158#391—221no—
159#391—221no—
160#389—221no—
161#389—221no—
162#384—111no—
163#343—111no—
164#339—221no—
165#328—21no—
166#328—221no—
167#324—111no—
168#324C2×D1111yescharacteristic
169C22×C11—21no—
170C22×C11—21no—
171C22×C11#45011yescharacteristic
172C22×C11#45611yescharacteristic
173C22×C11B(4,𝔽2)11yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—42no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11—81no—
180C4×C11—81no—
181C4×C11—81no—
182Dic11—24no—
183Dic11—42no—
184Dic11—81no—
185Dic11—81no—
186C22×Q8—221no—
187C2×M16—221no—
188C4⋊Q8—41no—
189#125—41no—
190C22⋊Q8—21no—
191C22⋊Q8—21no—
192C4×Q8—442no—
193C4×Q8—442no—
194#117—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—111no—
197C2×C4⋊C4—111no—
198C2×C4⋊C4—221no—
199C2×C4⋊C4—221no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4C22⋊D1111yescharacteristic
204C2×C4⋊C4C22×D1111yescharacteristic
205C2×C42—111no—
206C2×C42—221no—
207C2×C42—221no—
208#107—441no—
209#106—41no—
210#106—441no—
211#106—441no—
212#103—41no—
213#103—441no—
214C22⋊C8—21no—
215C22⋊C8—221no—
216#95—21no—
217#95—111no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95C22⋊D1111yescharacteristic
223C2×C11—21no—
224C2×C11—21no—
225C2×C11#160411yescharacteristic
226C2×C11#219811yescharacteristic
227C2×C11#220511yescharacteristic
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—224no—
231C2×Q8—442no—
232C2×Q8—442no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—221no—
236C22×C4—221no—
237C22×C4—221no—
238C22×C4—221no—
239C22×C4D4×D1111yescharacteristic
240C22×C4D4×D1111yescharacteristic
241C22×C4C2×C22⋊D1111yescharacteristic
242M16—222no—
243M16—441no—
244C2×C8—41no—
245C2×C8—441no—
246C2×C8—441no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—441no—
258C4⋊C4—441no—
259C4⋊C4—442no—
260C4⋊C4—442no—
261C4⋊C4—442no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—881no—
265C22⋊C4—41no—
266C42—41no—
267C42—112no—
268C42—221no—
269C42—442no—
270C42—442no—
271C11#1224711yescharacteristic, complemented, Sylow
272C23#6699011yescharacteristic
273Q8—81no—
274Q8—81no—
275Q8—448no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—222no—
291C2×C4—222no—
292C2×C4—222no—
293C2×C4—222no—
294C2×C4—441no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—441no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4SD16×D1111yescharacteristic
303C2×C4#6696711yescharacteristic
304C8—81no—
305C8—442no—
306C8—881no—
307C22—21no—
308C22—21no—
309C22#1062264511yescharacteristic
310C22#1062278211yescharacteristic
311C22#1062281811yescharacteristic
312C4—21no—
313C4—21no—
314C4—42no—
315C4—41no—
316C4—41no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—224no—
321C4—442no—
322C4—881no—
323C4—881no—
324C2—21no—
325C2—21no—
326C2#1306758311yescharacteristic
327C2#1307061011yescharacteristic
328C2#1307064511yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1611C2
socleC22×C11B(4,𝔽2)
prime radicalC23×C11#120
hypercenter#1611D11
hypocenterC11#12247
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1611

Complements

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

NH ≅ G/Ntype
271. C11#12247semidirect

Maximal subgroups

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

subgroupindex
#130739852
#130699582
#130676242
#130666232
#130666222
#130665612
C11×#16112
#1224711