Finite Group Databasebeta

← #14667295

Subgroups — #14667295

Order 2816.

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

normal subgroups only

This group has 322 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#13070873C211yesmaximal, characteristic
2#13070656C211yesmaximal, characteristic
3#13067976C211yesmaximal, characteristic
4#13066665C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066580C211yesmaximal, characteristic, complemented
7C11×#3395C211yesmaximal, characteristic, complemented
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×#66892—22no—
17C2×#66892—21no—
18#10622640—21no—
19#10622308C2211yescharacteristic
20#10622129—21no—
21#10622123—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×#4325—41no—
38C2×D88—21no—
39C2×D88—21no—
40#66927—21no—
41C11×#107D411yescharacteristic
42C11×C4⋊C8—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×#103—22no—
45C11×#103—21no—
46C4×C8×C11—21no—
47C4×C8×C11C2311yescharacteristic
48#66892—44no—
49#66892—42no—
50C2×C11⋊C16—21no—
51C2×C11⋊C16—21no—
52#66873—41no—
53C4⋊(C11⋊C8)—21no—
54#12330—111nomaximal, Sylow
55C2×Q8×C11—21no—
56C2×Q8×C11—22no—
57C2×Q8×C11D811yescharacteristic
58C2×D44—41no—
59C2×D44—41no—
60C2×D44—41no—
61C11×Q16—21no—
62C11×Q16—21no—
63C11×Q16—41no—
64C11×Q16—41no—
65C11×Q16—42no—
66C11×Q16—82no—
67C2×C8×C11—21no—
68C2×C8×C11C2×D411yescharacteristic
69C2×C8×C11C2×D411yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—42no—
74C11×C4⋊C4—42no—
75C11×C4⋊C4—41no—
76C11×C4⋊C4—41no—
77C11×C4⋊C4—41no—
78C11×C4⋊C4D811yescharacteristic
79C42×C11—21no—
80C42×C11—42no—
81C42×C11—41no—
82C42×C11C2×D411yescharacteristic
83#4325—82no—
84C2×C11⋊C8—41no—
85D88—42no—
86D88—41no—
87D88—41no—
88C11⋊C16—22no—
89C11⋊C16—41no—
90#3395D1111yescharacteristic, complemented
91#2248—111no—
92#2207—111no—
93#1668—111no—
94#1362—111no—
95Q8⋊C16—111no—
96#1332—111no—
97C22×D11—81no—
98Q8×C11—21no—
99Q8×C11—41no—
100Q8×C11—42no—
101Q8×C11—42no—
102Q8×C11—41no—
103Q8×C11SD3212yescomplemented
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11—41no—
107C2×C4×C11—42no—
108C2×C4×C11—41no—
109C2×C4×C11#12011yescharacteristic
110C2×C4×C11C2×D811yescharacteristic
111C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
112D44—81no—
113D44—81no—
114D44—81no—
115D44—81no—
116D44—161no—
117C8×C11—21no—
118C8×C11—41no—
119C8×C11#13511yescharacteristic
120C8×C11AGL(1,ℤ/8)11yescharacteristic
121C11⋊C8—81no—
122#557—21no—
123C2×SD32—221no—
124C2×SD32—222no—
125#494—21no—
126#494C2×D1111yescharacteristic
127#493—111no—
128#462—22no—
129#462—21no—
130#460—221no—
131C8×Q8C2×D1111yescharacteristic
132C4×Q16—21no—
133C4×Q16C2×D1111yescharacteristic
134C4⋊C16—111no—
135#357—221no—
136C4×C16—111no—
137#335—111no—
138#331—221no—
139C22×C11#44711yescharacteristic
140C2×D11—161no—
141C2×D11—161no—
142C2×D11—161no—
143C4×C11—22no—
144C4×C11—21no—
145C4×C11—41no—
146C4×C11—81no—
147C4×C11—82no—
148C4×C11—81no—
149C4×C11#44911yescharacteristic
150C4×C11#45311yescharacteristic
151C4×C11C2×SD3211yescharacteristic
152C4×C11#51011yescharacteristic
153C2×Q16—22no—
154C2×Q16—21no—
155C2×Q16C22⋊D1111yescharacteristic
156C2×Q16C22⋊D1112yes—
157C2×SD16—441no—
158C2×D8—221no—
159C2×D8—221no—
160C4⋊Q8—22no—
161C4⋊Q8—21no—
162#127—221no—
163#125—42no—
164#125—41no—
165C4×Q8—22no—
166C4×Q8—21no—
167C4×Q8—41no—
168C4×Q8C22⋊D1111yescharacteristic
169SD32—444no—
170SD32—442no—
171C2×C16—221no—
172C2×C16—221no—
173#107C22⋊D1111yescharacteristic
174C4⋊C8—21no—
175C4⋊C8—221no—
176C4⋊C8C22⋊D1111yescharacteristic
177#103—22no—
178#103—21no—
179#102—441no—
180C4×C8—21no—
181C4×C8C22×D1111yescharacteristic
182C2×C11#162111yescharacteristic
183C2×C11#218511yescharacteristic
184C2×C11#219311yescharacteristic
185D11—321no—
186C2×Q8—21no—
187C2×Q8—22no—
188C2×Q8#432311yescharacteristic
189C2×D4—441no—
190C2×D4—441no—
191C2×D4—441no—
192Q16—21no—
193Q16—21no—
194Q16—42no—
195Q16—41no—
196Q16—41no—
197Q16—82no—
198SD16—882no—
199D8—442no—
200D8—441no—
201D8—441no—
202C2×C8—21no—
203C2×C8—441no—
204C2×C8C2×C22⋊D1111yescharacteristic
205C2×C8C2×C22⋊D1111yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4#432311yescharacteristic
215C42—21no—
216C42—42no—
217C42—41no—
218C42C2×C22⋊D1111yescharacteristic
219C16—222no—
220C16—441no—
221C11#1233011yescharacteristic, complemented, Sylow
222C23—881no—
223Q8—21no—
224Q8—41no—
225Q8—42no—
226Q8—42no—
227Q8—41no—
228Q8#6689212yescomplemented
229D4—881no—
230D4—881no—
231D4—881no—
232D4—881no—
233D4—1761no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4C2×#432311yescharacteristic
240C2×C4#6698511yescharacteristic
241C2×C4#6700611yescharacteristic
242C8—21no—
243C8—41no—
244C8—881no—
245C8#6700211yescharacteristic
246C8#6700311yescharacteristic
247C22—1761no—
248C22—1761no—
249C22—1761no—
250C22#1062283011yescharacteristic
251C4—22no—
252C4—21no—
253C4—41no—
254C4—81no—
255C4—82no—
256C4—81no—
257C4C2×#6689211yescharacteristic
258C4#1062279211yescharacteristic
259C4#1062285111yescharacteristic
260C4#1062285411yescharacteristic
261C2—3521no—
262C2#1306768111yescharacteristic
263C2#1307053311yescharacteristic
264C2#1307058011yescharacteristic
subgroupG/H
centerC22#10622830
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#3395C2
socleC22×C11#447
prime radical#10622308C22
hypercenter#3395D11
hypocenterC11#12330
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
4. #13066665C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
6. #13066580C2semidirect
7. C11×#3395C2semidirect
90. #3395D11semidirect
103. Q8×C11SD32semidirect
221. C11#12330semidirect
228. Q8#66892semidirect

Maximal subgroups

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

subgroupindex
#130708732
#130706562
#130679762
#130666652
Q8⋊(C11⋊C16)2
#130665802
C11×#33952
#1233011