Finite Group Databasebeta

← #14667323

Subgroups — #14667323

Order 2816.

306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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#13070868C211yesmaximal, characteristic
2#13070666C211yesmaximal, characteristic
3#13067986C211yesmaximal, characteristic
4#13066665C211yesmaximal, characteristic
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic
6#13066580C211yesmaximal, characteristic
7C11×#3395C211yesmaximal, characteristic
8C11×#557—21no—
9C11×#494—21no—
10C11×#494C2211yescharacteristic
11C11×#462—22no—
12C11×#462—21no—
13C8×Q8×C11C2211yescharacteristic
14C4×C11×Q16—21no—
15C4×C11×Q16C2211yescharacteristic
16C2×#66893—22no—
17C2×#66893—21no—
18#10622633—21no—
19#10622312C2211yescharacteristic
20#10622130—21no—
21#10622120—21no—
22C4⋊(C11⋊C16)C2211yescharacteristic
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16—22no—
26C2×C11×Q16—21no—
27C2×C11×Q16D411yescharacteristic
28C2×C11×Q16D412yes—
29C11×C4⋊Q8—22no—
30C11×C4⋊Q8—21no—
31C11×#125—42no—
32C11×#125—41no—
33C4×Q8×C11—22no—
34C4×Q8×C11—21no—
35C4×Q8×C11—41no—
36C4×Q8×C11D411yescharacteristic
37C2×Dic44—21no—
38C2×Dic44—21no—
39#66922—21no—
40C11×#107D411yescharacteristic
41C11×C4⋊C8—21no—
42C11×C4⋊C8D411yescharacteristic
43C11×#103—22no—
44C11×#103—21no—
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66899—41no—
48#66893—44no—
49#66893—42no—
50C2×C11⋊C16—21no—
51C2×C11⋊C16—21no—
52#66872—41no—
53C4⋊(C11⋊C8)—21no—
54#12334—111nomaximal, Sylow
55C2×Q8×C11—21no—
56C2×Q8×C11—22no—
57C2×Q8×C11D811yescharacteristic
58C2×Dic22—41no—
59C11×Q16—21no—
60C11×Q16—21no—
61C11×Q16—41no—
62C11×Q16—41no—
63C11×Q16—42no—
64C11×Q16—82no—
65C2×C8×C11—21no—
66C2×C8×C11C2×D411yescharacteristic
67C2×C8×C11C2×D411yescharacteristic
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—41no—
74C11×C4⋊C4—41no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4D811yescharacteristic
77C42×C11—21no—
78C42×C11—42no—
79C42×C11—41no—
80C42×C11C2×D411yescharacteristic
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83C2×C11⋊C8—41no—
84Dic44—42no—
85Dic44—41no—
86Dic44—41no—
87C11⋊C16—22no—
88C11⋊C16—41no—
89#3395D1111yescharacteristic
90#2247—111no—
91#2209—111no—
92#1670—111no—
93#1362—111no—
94Q8⋊C16—111no—
95#1332—111no—
96Q8×C11—21no—
97Q8×C11—41no—
98Q8×C11—42no—
99Q8×C11—42no—
100Q8×C11—41no—
101Q8×C11Q3212yescomplemented
102C2×C4×C11—21no—
103C2×C4×C11—21no—
104C2×C4×C11—41no—
105C2×C4×C11—42no—
106C2×C4×C11—41no—
107C2×C4×C11#12011yescharacteristic
108C2×C4×C11C2×D811yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
110C2×Dic11—81no—
111Dic22—81no—
112Dic22—81no—
113C8×C11—21no—
114C8×C11—41no—
115C8×C11#13511yescharacteristic
116C8×C11AGL(1,ℤ/8)11yescharacteristic
117C11⋊C8—81no—
118#557—21no—
119C2×Q32—221no—
120C2×Q32—222no—
121#494—21no—
122#494—111no—
123#494C2×D1111yescharacteristic
124#475—221no—
125#462—22no—
126#462—21no—
127C8×Q8C2×D1111yescharacteristic
128C4×Q16—21no—
129C4×Q16C2×D1111yescharacteristic
130C4⋊C16—111no—
131#358—221no—
132C4×C16—111no—
133#335—111no—
134#332—221no—
135C22×C11#44711yescharacteristic
136C4×C11—22no—
137C4×C11—21no—
138C4×C11—41no—
139C4×C11—81no—
140C4×C11—82no—
141C4×C11—81no—
142C4×C11#44911yescharacteristic
143C4×C11#45311yescharacteristic
144C4×C11C2×Q3211yescharacteristic
145C4×C11#51011yescharacteristic
146Dic11—161no—
147C2×Q16—22no—
148C2×Q16—21no—
149C2×Q16—221no—
150C2×Q16—221no—
151C2×Q16C22⋊D1111yescharacteristic
152C2×Q16C22⋊D1112yes—
153C4⋊Q8—22no—
154C4⋊Q8—21no—
155C4⋊Q8—221no—
156#125—42no—
157#125—41no—
158C4×Q8—22no—
159C4×Q8—21no—
160C4×Q8—41no—
161C4×Q8C22⋊D1111yescharacteristic
162Q32—444no—
163Q32—442no—
164C2×C16—221no—
165C2×C16—221no—
166#107C22⋊D1111yescharacteristic
167#106—441no—
168C4⋊C8—21no—
169C4⋊C8—221no—
170C4⋊C8C22⋊D1111yescharacteristic
171#103—22no—
172#103—21no—
173#103—441no—
174C4×C8—21no—
175C4×C8C22×D1111yescharacteristic
176C2×C11#162111yescharacteristic
177C2×C11#218811yescharacteristic
178C2×C11#219511yescharacteristic
179C2×Q8—21no—
180C2×Q8—22no—
181C2×Q8—441no—
182C2×Q8#432311yescharacteristic
183Q16—21no—
184Q16—21no—
185Q16—42no—
186Q16—41no—
187Q16—41no—
188Q16—82no—
189Q16—442no—
190Q16—441no—
191Q16—441no—
192C2×C8—21no—
193C2×C8—441no—
194C2×C8C2×C22⋊D1111yescharacteristic
195C2×C8C2×C22⋊D1111yescharacteristic
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—42no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—441no—
205C4⋊C4—441no—
206C4⋊C4#432311yescharacteristic
207C42—21no—
208C42—42no—
209C42—41no—
210C42C2×C22⋊D1111yescharacteristic
211C16—222no—
212C16—441no—
213C11#1233411yescharacteristic, complemented, Sylow
214Q8—21no—
215Q8—41no—
216Q8—42no—
217Q8—42no—
218Q8—41no—
219Q8—881no—
220Q8—881no—
221Q8#6689312yescomplemented
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—881no—
228C2×C4C2×#432311yescharacteristic
229C2×C4#6698511yescharacteristic
230C2×C4#6700611yescharacteristic
231C8—21no—
232C8—41no—
233C8—881no—
234C8#6700211yescharacteristic
235C8#6700311yescharacteristic
236C22#1062283011yescharacteristic
237C4—21no—
238C4—22no—
239C4—41no—
240C4—81no—
241C4—81no—
242C4—82no—
243C4—1761no—
244C4#1062279211yescharacteristic
245C4C2×#6689311yescharacteristic
246C4#1062285111yescharacteristic
247C4#1062285411yescharacteristic
248C2#1306768111yescharacteristic
249C2#1307055011yescharacteristic
250C2#1307059411yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3395C2
socle, prime radicalC22×C11#447
hypercenter#3395D11
hypocenterC11#12334
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3395

Complements

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

NH ≅ G/Ntype
101. Q8×C11Q32semidirect
213. C11#12334semidirect
221. Q8#66893semidirect

Maximal subgroups

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

subgroupindex
#130708682
#130706662
#130679862
#130666652
Q8⋊(C11⋊C16)2
#130665802
C11×#33952
#1233411