Finite Group Databasebeta

← #14667918

Subgroups — #14667918

Order 2816.

234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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#13070764C211yesmaximal, characteristic
2#13070662C211yesmaximal, characteristic
3#13068213C211yesmaximal, characteristic, complemented
4C8×D88C211yesmaximal, characteristic
5#13066673C211yesmaximal, characteristic, complemented
6#13066666C211yesmaximal, characteristic, complemented
7C11×#1367C211yesmaximal, characteristic, complemented
8C2×#66864—21no—
9#10622312C2211yescharacteristic
10C4×D88C2211yescharacteristic
11C8×D44—21no—
12#10622295C2211yescharacteristic
13#10622294—21no—
14#10622293—21no—
15C11×C4⋊C16C2211yescharacteristic
16C11×C4⋊C16C2211yescharacteristic
17C82×C11C2211yescharacteristic
18#10622147—21no—
19#10622143—21no—
20#10622141—21no—
21#10622097—21no—
22#10622096C2211yescharacteristic
23C2×Dic44—21no—
24C2×Dic44—21no—
25C2×D88D411yescharacteristic
26C2×C8×D11—41no—
27C4×D44—21no—
28#66922—21no—
29#66922—21no—
30C2×C11×C16—21no—
31C2×C11×C16—21no—
32C4×C8×C11D411yescharacteristic
33C4×C8×C11D411yescharacteristic
34C4×C8×C11C2311yescharacteristic
35#66885—21no—
36(C2×D11)⋊C8—41no—
37#66882—21no—
38#66882—21no—
39#66882D411yescharacteristic
40#66881—41no—
41#66881—41no—
42#66880—42no—
43C4⋊(C11⋊C8)—21no—
44#66864—42no—
45#12420—111nomaximal, Sylow
46C2×D44—21no—
47C2×C4×D11—41no—
48C2×Dic22—41no—
49C2×Dic22—41no—
50C2×C8×C11—21no—
51C2×C8×C11D811yescharacteristic
52C2×C8×C11D811yescharacteristic
53C2×C8×C11C2×D411yescharacteristic
54C2×C8×C11#4111yescharacteristic
55C42×C11C2×D411yescharacteristic
56(C2×D11)⋊C4—41no—
57C4⋊Dic11—21no—
58C4⋊Dic11—41no—
59C4⋊Dic11—41no—
60C4⋊Dic11—41no—
61C4⋊Dic11—41no—
62C2×C11⋊C8—41no—
63Dic44—41no—
64Dic44—41no—
65Dic44—81no—
66D88—21no—
67D88SD1612yes—
68C8×D11—82no—
69C11×C16—41no—
70C11×C16—41no—
71#2226—111no—
72#2208—111no—
73#1707—111no—
74C8×D8—111no—
75#1367D1111yescharacteristic, complemented
76#1365—111no—
77#1362—111no—
78C22×D11—41no—
79C2×C4×C11#12111yescharacteristic
80C2×C4×C11C2×D811yescharacteristic
81C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
82C2×Dic11—41no—
83C2×Dic11—81no—
84C2×Dic11—81no—
85D44—22no—
86D44—41no—
87C4×D11—81no—
88C4×D11—81no—
89Dic22—82no—
90Dic22—81no—
91Dic22—81no—
92C8×C11—21no—
93C8×C11—21no—
94C8×C11—41no—
95C8×C11SD3212yescomplemented
96C8×C11C2×SD1611yescharacteristic
97C8×C11#13511yescharacteristic
98C11⋊C8—81no—
99C2×SD32—221no—
100#500—111no—
101#498—221no—
102#494—111no—
103#487—221no—
104C4×D8—111no—
105C8×D4—221no—
106#367—221no—
107C4⋊C16C2×D1111yescharacteristic
108C4⋊C16C2×D1111yescharacteristic
109#358—221no—
110#357—221no—
111#335—111no—
112D4⋊C8—221no—
113C82C2×D1111yescharacteristic
114C22×C11#45911yescharacteristic
115C2×D11—42no—
116C2×D11—81no—
117C2×D11—81no—
118C4×C11—21no—
119C4×C11#46511yescharacteristic
120C4×C11#47111yescharacteristic
121C4×C11C2×SD3211yescharacteristic
122C4×C11#51011yescharacteristic
123Dic11—81no—
124Dic11—161no—
125Dic11—161no—
126C2×Q16—221no—
127C2×Q16—221no—
128C2×D8—111no—
129C22×C8—441no—
130C4⋊Q8—221no—
131C4⋊Q8—221no—
132C4×D4—221no—
133SD32—442no—
134C2×C16—21no—
135C2×C16—21no—
136#107—111no—
137#107—221no—
138#107—221no—
139#106—441no—
140#106—441no—
141C4⋊C8—221no—
142#103—442no—
143#102—221no—
144C22⋊C8—441no—
145C4×C8D4411yescharacteristic
146C4×C8D4411yescharacteristic
147C4×C8C22×D1111yescharacteristic
148C2×C11#166511yescharacteristic
149C2×C11#220811yescharacteristic
150C2×C11#221211yescharacteristic
151D11—82no—
152C2×Q8—441no—
153C2×Q8—441no—
154C2×D4—221no—
155C22×C4—441no—
156Q16—441no—
157Q16—441no—
158Q16—881no—
159D8—112no—
160D8—221no—
161C2×C8—21no—
162C2×C8—441no—
163C2×C8—882no—
164C2×C8D8811yescharacteristic
165C2×C8D8811yescharacteristic
166C2×C8D4×D1111yescharacteristic
167C2×C8#434311yescharacteristic
168C4⋊C4—221no—
169C4⋊C4—441no—
170C4⋊C4—441no—
171C4⋊C4—441no—
172C4⋊C4—441no—
173C22⋊C4—441no—
174C42C2×D4411yescharacteristic
175C16—41no—
176C16—41no—
177C11#1242011yescharacteristic, complemented, Sylow
178C23—441no—
179Q8—882no—
180Q8—881no—
181Q8—881no—
182D4—222no—
183D4—441no—
184C2×C4—441no—
185C2×C4—881no—
186C2×C4—881no—
187C2×C4—881no—
188C2×C4—881no—
189C2×C4#6694811yescharacteristic
190C2×C4C2×D8811yescharacteristic
191C2×C4#6696111yescharacteristic
192C8—21no—
193C8—21no—
194C8—41no—
195C8—881no—
196C8#6686412yescomplemented
197C8SD16×D1111yescharacteristic
198C8#6696911yescharacteristic
199C22—442no—
200C22—881no—
201C22—881no—
202C22#1062245611yescharacteristic
203C4—21no—
204C4—881no—
205C4—1761no—
206C4—1761no—
207C4#1062247711yescharacteristic
208C4#1062251111yescharacteristic
209C4C2×#6686411yescharacteristic
210C4#1062252211yescharacteristic
211C2—882no—
212C2#1306795811yescharacteristic
213C2#1307066211yescharacteristic
214C2#1307068611yescharacteristic
subgroupG/H
centerC22#10622456
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1367C2
socleC22×C11#459
prime radicalC2×D88D4
hypercenter#1367D11
hypocenterC11#12420
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1367

Complements

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

NH ≅ G/Ntype
3. #13068213C2semidirect
5. #13066673C2semidirect
6. #13066666C2semidirect
7. C11×#1367C2semidirect
75. #1367D11semidirect
95. C8×C11SD32semidirect
177. C11#12420semidirect
196. C8#66864semidirect

Maximal subgroups

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

subgroupindex
#130707642
#130706622
#130682132
C8×D882
#130666732
#130666662
C11×#13672
#1242011