Finite Group Databasebeta

← #14735674

Subgroups — #14735674

Order 2816.

806 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 171 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#13079814C212yesmaximal
2#13078964C211yesmaximal, characteristic
3#13067944C214yesmaximal, complemented
4#13067918C214yesmaximal, complemented
5#13067254C211yesmaximal, characteristic, complemented
6#13067231C212yesmaximal, complemented
7C11×#3556C211yesmaximal, characteristic, complemented
8C11×#564C2214yes—
9C11×#557—22no—
10C11×#557—22no—
11C11×#557—22no—
12C11×#541—22no—
13C11×#541—24no—
14C11×#533C2212yes—
15C11×#533C2211yescharacteristic
16#10623008C2211yescharacteristic
17#10622702—22no—
18#10622700—22no—
19#10622697—22no—
20#10622682C2212yes—
21#10622680C2214yes—
22#10622680C2212yes—
23#10622678C2214yes—
24#10622616—24no—
25#10622615—22no—
26#10622539C2212yes—
27C2×#66867C2211yescharacteristic
28#10622181C2218yes—
29#10622181C2214yes—
30C2×#4339—21no—
31C11×C4⋊Q8—24no—
32C11×C4⋊Q8—22no—
33C11×C4⋊Q8D412yes—
34C11×C4⋊Q8D412yes—
35C11×C4⋊Q8D412yes—
36C11×#126—28no—
37C11×#125—24no—
38C11×#125—22no—
39C11×#125—28no—
40C11×#125—28no—
41C11×#125—28no—
42C11×#125C2314yes—
43C11×#125C2312yes—
44C11×C22⋊Q8—22no—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—22no—
47C4×Q8×C11—24no—
48C4×Q8×C11—24no—
49C4×Q8×C11—24no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C11×#117D412yes—
54C11×#117D414yes—
55C2×C42×C11C2311yescharacteristic
56#66983—22no—
57C22×C11⋊C8—21no—
58#66928—21no—
59#66927C2311yescharacteristic
60C4×D44—22no—
61#66922C2311yescharacteristic
62C22⋊(C11⋊C8)—22no—
63#66874—24no—
64#66873—24no—
65#66873—24no—
66#66873—24no—
67#66872—24no—
68#66871—24no—
69C4⋊(C11⋊C8)—22no—
70#66867—21no—
71#66867C2312yes—
72#66867C2314yes—
73#19063—111nomaximal, Sylow
74C2×Q8×C11—22no—
75C2×Q8×C11—22no—
76C2×Q8×C11—22no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D412yes—
79C2×C22⋊D11—41no—
80#4339—44no—
81C2×D44—22no—
82C2×D44—21no—
83C2×C4×D11—41no—
84C2×Dic22—21no—
85C11×C4⋊C4—28no—
86C11×C4⋊C4—28no—
87C11×C4⋊C4—28no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—22no—
90C11×C4⋊C4—22no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—24no—
94C11×C4⋊C4C2×D414yes—
95C11×C4⋊C4C2×D414yes—
96C11×C4⋊C4C2×D414yes—
97C11×C22⋊C4—22no—
98C11×C22⋊C4—24no—
99C42×C11—28no—
100C42×C11—24no—
101C42×C11—22no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D412yes—
104C42×C11C2411yescharacteristic
105(C2×D11)⋊C4—42no—
106C4⋊Dic11—22no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—24no—
109C2×C11⋊C8—42no—
110#3556D1111yescharacteristic, complemented
111#3235—112no—
112#3135—111no—
113#1663—114no—
114#1658—114no—
115#1537—111no—
116#1531—112no—
117C23×C11#12011yescharacteristic
118C22×D11—41no—
119Q8×C11—44no—
120Q8×C11—44no—
121Q8×C11—44no—
122C2×C4×C11—22no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—24no—
126C2×C4×C11—42no—
127C2×C4×C11#12012yes—
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11C22×D412yes—
130C2×C4×C11C22×D411yescharacteristic
131C22⋊D11—82no—
132C2×Dic11—41no—
133D44—44no—
134D44—42no—
135C4×D11—82no—
136Dic22—42no—
137C11⋊C8—44no—
138C11⋊C8—42no—
139#564C2×D1114yes—
140#557—22no—
141#557—22no—
142#557—22no—
143#541—22no—
144#541—24no—
145#533C2×D1111yescharacteristic
146#533C2×D1112yes—
147#532—111no—
148#501—114no—
149#491—112no—
150#490—112no—
151#490—114no—
152#489—222no—
153#482—224no—
154#476—222no—
155#474—222no—
156#432—112no—
157#416—222no—
158C2×#97—111no—
159#330—114no—
160#330—118no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11C2×#12011yescharacteristic
164C2×D11—81no—
165C2×D11—82no—
166C4×C11—21no—
167C4×C11—22no—
168C4×C11—22no—
169C4×C11—44no—
170C4×C11—44no—
171C4×C11—44no—
172C4×C11#45412yes—
173Dic11—81no—
174C2×#41—221no—
175C22×C8—221no—
176C4⋊Q8—24no—
177C4⋊Q8—22no—
178C4⋊Q8—111no—
179C4⋊Q8C22⋊D1112yes—
180C4⋊Q8C22⋊D1112yes—
181C4⋊Q8C22⋊D1112yes—
182#127—111no—
183#126—28no—
184#125—24no—
185#125—22no—
186#125—28no—
187#125—28no—
188#125—28no—
189#125C22×D1112yes—
190#125C22×D1114yes—
191#124—221no—
192C22⋊Q8—22no—
193C22⋊Q8—22no—
194C22⋊Q8—22no—
195#121—222no—
196C4×Q8—24no—
197C4×Q8—24no—
198C4×Q8—24no—
199C4×Q8—22no—
200C4×Q8—22no—
201C4×Q8—22no—
202C4×D4—222no—
203#117C22⋊D1112yes—
204#117C22⋊D1114yes—
205C2×C42C22×D1111yescharacteristic
206#107—224no—
207#106—224no—
208C4⋊C8—222no—
209#103—224no—
210#102—224no—
211#102—224no—
212#102—224no—
213C22⋊C8—222no—
214#97—112no—
215#97—114no—
216#97—221no—
217C2×C11—41no—
218C2×C11C2×#45411yescharacteristic
219C2×C11#302012yes—
220D11—161no—
221#41—444no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—221no—
226C2×D4—222no—
227C2×D4—221no—
228C2×D4—441no—
229C22×C4—441no—
230C22×C4C2×C22⋊D1111yescharacteristic
231C22×C4C2×C22⋊D1112yes—
232C2×C8—222no—
233C2×C8—224no—
234C2×C8—442no—
235C4⋊C4—28no—
236C4⋊C4—28no—
237C4⋊C4—28no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—24no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—222no—
245C4⋊C4C2×C22⋊D1114yes—
246C4⋊C4C2×C22⋊D1114yes—
247C4⋊C4C2×C22⋊D1114yes—
248C22⋊C4—22no—
249C22⋊C4—24no—
250C22⋊C4—442no—
251C42—28no—
252C42—24no—
253C42—22no—
254C42C2×C22⋊D1111yescharacteristic
255C42C2×C22⋊D1112yes—
256C42C23×D1111yescharacteristic
257C11#1906311yescharacteristic, complemented, Sylow
258C23—441no—
259C23#6700611yescharacteristic
260Q8—44no—
261Q8—44no—
262Q8—44no—
263Q8—442no—
264D4—442no—
265D4—444no—
266D4—882no—
267C2×C4—22no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—42no—
272C2×C4—441no—
273C2×C4—882no—
274C2×C4#6700612yes—
275C2×C4#6700611yescharacteristic
276C2×C4C22×C22⋊D1112yes—
277C2×C4C22×C22⋊D1111yescharacteristic
278C8—442no—
279C8—444no—
280C22—21no—
281C22—22no—
282C22—881no—
283C22—882no—
284C22C2×#6700611yescharacteristic
285C4—21no—
286C4—22no—
287C4—22no—
288C4—44no—
289C4—44no—
290C4—44no—
291C4—881no—
292C4#1062285812yes—
293C2—41no—
294C2—1761no—
295C2C2×#1062285811yescharacteristic
296C2#1307798012yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3556C2
socleC22×C11C2×#120
prime radical#10623008C22
hypercenter#3556D11
hypocenterC11#19063
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3556

Complements

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

NH ≅ G/Ntype
3. #13067944C2semidirect
4. #13067918C2semidirect
5. #13067254C2semidirect
6. #13067231C2semidirect
7. C11×#3556C2semidirect
110. #3556D11semidirect
257. C11#19063semidirect

Maximal subgroups

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

subgroupindex
#130798142
#130789642
#130679442
#130679182
#130672542
#130672312
C11×#35562
#1906311