Finite Group Databasebeta

← #14667643

Subgroups — #14667643

Order 2816.

306 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 65 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#13081626C211yesmaximal, characteristic
2#13070841C211yesmaximal, characteristic
3#13068007C211yesmaximal, characteristic, complemented
4#13066663C211yesmaximal, characteristic
5#13066594C211yesmaximal, characteristic, complemented
6#13066580C211yesmaximal, characteristic, complemented
7C11×#2225C211yesmaximal, characteristic, complemented
8#10623116—21no—
9C11×#500C2211yescharacteristic
10C4×C11×Q16C2211yescharacteristic
11#10622804—21no—
12#10622703—21no—
13#10622640—21no—
14#10622485—21no—
15#10622432—22no—
16#10622308C2211yescharacteristic
17C8×Dic22C2211yescharacteristic
18C11×#367—21no—
19C11×C4⋊C16C2211yescharacteristic
20C11×#358—21no—
21#10622185—21no—
22#10622129—22no—
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C11×C4⋊Q8—21no—
27C4×Q8×C11—21no—
28#67000—22no—
29C2×#4326—41no—
30C2×#4325—22no—
31C2×D88—21no—
32C2×D88D412yes—
33#66947—42no—
34#66946—22no—
35#66928—41no—
36#66927—21no—
37C4×D44—41no—
38C4×Dic22D411yescharacteristic
39C2×C11×C16—21no—
40C11×#107—21no—
41C11×#107—21no—
42C11×#107D411yescharacteristic
43C11×#103—21no—
44C4×C8×C11C2311yescharacteristic
45#66899—41no—
46Dic11⋊C8—21no—
47C8×Dic11—21no—
48C2×C11⋊C16—21no—
49#66873—22no—
50C4⋊(C11⋊C8)—21no—
51C4⋊(C11⋊C8)D411yescharacteristic
52#12381—111nomaximal, Sylow
53C2×Q8×C11—21no—
54C2×Q8×C11—41no—
55C2×D44—22no—
56C2×D44—41no—
57C2×D44—41no—
58C2×C4×D11—42no—
59C2×Dic22D811yescharacteristic
60C11×Q16—21no—
61C11×Q16—21no—
62C2×C8×C11C2×D411yescharacteristic
63C2×C8×C11C2×D411yescharacteristic
64C11×C4⋊C4—21no—
65C11×C4⋊C4—41no—
66C11×C4⋊C4—41no—
67C11×C4⋊C4—41no—
68C42×C11—41no—
69C42×C11C2×D411yescharacteristic
70#4326—82no—
71#4325—82no—
72(C2×D11)⋊C4—42no—
73(C2×D11)⋊C4—42no—
74(C2×D11)⋊C4—42no—
75C4⋊Dic11D811yescharacteristic
76Dic11⋊C4—21no—
77C4×Dic11—21no—
78C2×C11⋊C8—21no—
79C2×C11⋊C8—41no—
80D88—42no—
81D88—41no—
82D88—41no—
83C11×C16—41no—
84C11⋊C16—41no—
85#3396—111no—
86#2240—111no—
87#2225D1111yescharacteristic, complemented
88#1674—111no—
89#1361—111no—
90Q8⋊C16—111no—
91#1332—111no—
92C22×D11—42no—
93Q8×C11—41no—
94Q8×C11—41no—
95Q8×C11—81no—
96Q8×C11—81no—
97C2×C4×C11—41no—
98C2×C4×C11—41no—
99C2×C4×C11—81no—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11C2×D811yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
103C2×Dic11—21no—
104C2×Dic11—21no—
105D44—42no—
106D44—42no—
107D44—81no—
108D44—81no—
109D44—161no—
110C4×D11—162no—
111Dic22—21no—
112Dic22—21no—
113C8×C11—21no—
114C8×C11#13511yescharacteristic
115C8×C11#13711yescharacteristic
116C11⋊C8—41no—
117C11⋊C8—81no—
118#559—221no—
119#500C2×D1111yescharacteristic
120#495—221no—
121#493—111no—
122#463—222no—
123#462—221no—
124#460—221no—
125C8×Q8—111no—
126C4×Q16C2×D1111yescharacteristic
127C4×D8—221no—
128#367—21no—
129C4⋊C16C2×D1111yescharacteristic
130#358—21no—
131#357—222no—
132C4×C16—111no—
133#335—111no—
134#332—221no—
135C22×C11#44711yescharacteristic
136C2×D11—82no—
137C2×D11—82no—
138C2×D11—82no—
139C4×C11—21no—
140C4×C11—81no—
141C4×C11—81no—
142C4×C11—161no—
143C4×C11#45211yescharacteristic
144C4×C11#45511yescharacteristic
145C4×C11#50811yescharacteristic
146C4×C11#50911yescharacteristic
147Dic11—41no—
148Dic11—41no—
149C2×Q16—441no—
150C2×Q16C22⋊D1111yescharacteristic
151C2×SD16—222no—
152C2×D8—112no—
153C2×D8—221no—
154C4⋊Q8—21no—
155#127—221no—
156#124—222no—
157#124—441no—
158#123—442no—
159C4×Q8—21no—
160C4×Q8—111no—
161C4×D4—222no—
162C4×D4—441no—
163C2×C16—21no—
164C2×C16—221no—
165#107—21no—
166#107—21no—
167#107C22⋊D1111yescharacteristic
168C4⋊C8—111no—
169C4⋊C8—221no—
170C4⋊C8—221no—
171#103—21no—
172#103—441no—
173#102—222no—
174C4×C8—221no—
175C4×C8C22×D1111yescharacteristic
176C2×C11#164111yescharacteristic
177C2×C11#218611yescharacteristic
178C2×C11#219411yescharacteristic
179D11—162no—
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8—111no—
183C2×D4—222no—
184C2×D4—441no—
185C2×D4—441no—
186C22×C4—442no—
187Q16—21no—
188Q16—21no—
189Q16—882no—
190SD16—882no—
191D8—442no—
192D8—441no—
193D8—441no—
194C2×C8—221no—
195C2×C8—441no—
196C2×C8D4×D1111yescharacteristic
197C2×C8C2×C22⋊D1111yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—111no—
203C4⋊C4—221no—
204C22⋊C4—442no—
205C22⋊C4—442no—
206C22⋊C4—442no—
207C42—41no—
208C42—221no—
209C42D4×D1111yescharacteristic
210C16—41no—
211C16—441no—
212C11#1238111yescharacteristic, complemented, Sylow
213C23—442no—
214Q8—41no—
215Q8—41no—
216Q8—81no—
217Q8—81no—
218Q8—221no—
219Q8—221no—
220D4—442no—
221D4—442no—
222D4—881no—
223D4—881no—
224D4—1761no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—81no—
228C2×C4—221no—
229C2×C4—221no—
230C2×C4—1762no—
231C2×C4D8×D1111yescharacteristic
232C2×C4#6696411yescharacteristic
233C2×C4#6699011yescharacteristic
234C8—21no—
235C8—441no—
236C8—881no—
237C8#6699511yescharacteristic
238C8#6700311yescharacteristic
239C22—882no—
240C22—882no—
241C22—882no—
242C22#1062276911yescharacteristic
243C4—21no—
244C4—81no—
245C4—81no—
246C4—161no—
247C4—441no—
248C4—441no—
249C4#1062252711yescharacteristic
250C4#1062252911yescharacteristic
251C4#1062266011yescharacteristic
252C4#1062281511yescharacteristic
253C2—1762no—
254C2#1306780811yescharacteristic
255C2#1307053811yescharacteristic
256C2#1307058411yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2225C2
socleC22×C11#447
prime radical#10622308C22
hypercenter#2225D11
hypocenterC11#12381
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2225

Complements

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

NH ≅ G/Ntype
3. #13068007C2semidirect
5. #13066594C2semidirect
6. #13066580C2semidirect
7. C11×#2225C2semidirect
87. #2225D11semidirect
212. C11#12381semidirect

Maximal subgroups

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

subgroupindex
#130816262
#130708412
#130680072
#130666632
#130665942
#130665802
C11×#22252
#1238111