Finite Group Databasebeta

← #14667917

Subgroups — #14667917

Order 2816.

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

normal subgroups only

This group has 234 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#13070763C211yesmaximal, characteristic
2#13070661C211yesmaximal, characteristic
3#13068213C211yesmaximal, characteristic, complemented
4#13066680C211yesmaximal, characteristic, complemented
5#13066675C211yesmaximal, characteristic, complemented
6#13066664C211yesmaximal, characteristic, complemented
7C8×C11×D8C211yesmaximal, characteristic
8C4×C11×D8C2211yescharacteristic
9C8×D4×C11—21no—
10C2×#66891—21no—
11#10622312C2211yescharacteristic
12#10622295C2211yescharacteristic
13#10622294—21no—
14#10622293—21no—
15C11×#335C2211yescharacteristic
16C11×D4⋊C8—21no—
17C82×C11C2211yescharacteristic
18#10622200—21no—
19#10622130—21no—
20#10622128—21no—
21C4⋊(C11⋊C16)C2211yescharacteristic
22C4⋊(C11⋊C16)C2211yescharacteristic
23C2×C11×D8D411yescharacteristic
24C22×C8×C11—41no—
25C4×D4×C11—21no—
26C2×Dic44—21no—
27C2×Dic44—21no—
28#66922—21no—
29#66922—21no—
30C11×#107D411yescharacteristic
31C11×C4⋊C8—21no—
32C11×#102—21no—
33C11×C22⋊C8—41no—
34C4×C8×C11D411yescharacteristic
35C4×C8×C11D411yescharacteristic
36C4×C8×C11C2311yescharacteristic
37#66891—42no—
38#66882—21no—
39#66882—21no—
40#66881—41no—
41#66881—41no—
42#66880—42no—
43C2×C11⋊C16—21no—
44C2×C11⋊C16—21no—
45#12420—111nomaximal, Sylow
46C2×D4×C11—21no—
47C22×C4×C11—41no—
48C2×Dic22—41no—
49C2×Dic22—41no—
50C11×D8—21no—
51C11×D8SD1612yes—
52C2×C8×C11—21no—
53C2×C8×C11—41no—
54C2×C8×C11—82no—
55C2×C8×C11D811yescharacteristic
56C2×C8×C11D811yescharacteristic
57C2×C8×C11C2×D411yescharacteristic
58C2×C8×C11#4111yescharacteristic
59C11×C4⋊C4—21no—
60C11×C22⋊C4—41no—
61C42×C11C2×D411yescharacteristic
62C4⋊Dic11—41no—
63C4⋊Dic11—41no—
64C4⋊Dic11—41no—
65C4⋊Dic11—41no—
66Dic44—41no—
67Dic44—41no—
68Dic44—81no—
69C11⋊C16—41no—
70C11⋊C16—41no—
71#2226—111no—
72#2208—111no—
73#1707—111no—
74C8×D8D1111yescharacteristic
75#1367—111no—
76#1365—111no—
77#1362—111no—
78C23×C11—41no—
79D4×C11—22no—
80D4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11—81no—
83C2×C4×C11—81no—
84C2×C4×C11#12111yescharacteristic
85C2×C4×C11C2×D811yescharacteristic
86C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
87C2×Dic11—81no—
88C2×Dic11—81no—
89Dic22—82no—
90Dic22—81no—
91Dic22—81no—
92C8×C11—21no—
93C8×C11—21no—
94C8×C11—41no—
95C8×C11—81no—
96C8×C11SD3212yescomplemented
97C8×C11C2×SD1611yescharacteristic
98C8×C11#13511yescharacteristic
99C2×SD32—221no—
100#500—111no—
101#498—221no—
102#494—111no—
103#487—221no—
104C4×D8C2×D1111yescharacteristic
105C8×D4—21no—
106#367—221no—
107C4⋊C16—111no—
108C4⋊C16—111no—
109#358—221no—
110#357—221no—
111#335C2×D1111yescharacteristic
112D4⋊C8—21no—
113C82C2×D1111yescharacteristic
114C22×C11—42no—
115C22×C11—81no—
116C22×C11—81no—
117C22×C11#45911yescharacteristic
118C4×C11—21no—
119C4×C11—81no—
120C4×C11#46511yescharacteristic
121C4×C11#47111yescharacteristic
122C4×C11C2×SD3211yescharacteristic
123C4×C11#51011yescharacteristic
124Dic11—161no—
125Dic11—161no—
126C2×Q16—221no—
127C2×Q16—221no—
128C2×D8D4411yescharacteristic
129C22×C8—41no—
130C4⋊Q8—221no—
131C4⋊Q8—221no—
132C4×D4—21no—
133SD32—442no—
134C2×C16—221no—
135C2×C16—221no—
136#107—221no—
137#107—221no—
138#107D4411yescharacteristic
139#106—441no—
140#106—441no—
141C4⋊C8—21no—
142#103—442no—
143#102—21no—
144C22⋊C8—41no—
145C4×C8C22⋊D1111yescharacteristic
146C4×C8C22⋊D1111yescharacteristic
147C4×C8C22×D1111yescharacteristic
148C2×C11—82no—
149C2×C11#166511yescharacteristic
150C2×C11#220811yescharacteristic
151C2×C11#221211yescharacteristic
152C2×Q8—441no—
153C2×Q8—441no—
154C2×D4—21no—
155C22×C4—41no—
156Q16—441no—
157Q16—441no—
158Q16—881no—
159D8—21no—
160D8#431412yes—
161C2×C8—21no—
162C2×C8—41no—
163C2×C8—82no—
164C2×C8#432311yescharacteristic
165C2×C8#432311yescharacteristic
166C2×C8C2×D4411yescharacteristic
167C2×C8#433911yescharacteristic
168C4⋊C4—21no—
169C4⋊C4—441no—
170C4⋊C4—441no—
171C4⋊C4—441no—
172C4⋊C4—441no—
173C22⋊C4—41no—
174C42C2×C22⋊D1111yescharacteristic
175C16—441no—
176C16—441no—
177C11#1242011yescharacteristic, complemented, Sylow
178C23—41no—
179Q8—882no—
180Q8—881no—
181Q8—881no—
182D4—22no—
183D4—41no—
184C2×C4—41no—
185C2×C4—81no—
186C2×C4—81no—
187C2×C4—881no—
188C2×C4—881no—
189C2×C4#6698311yescharacteristic
190C2×C4C2×#432311yescharacteristic
191C2×C4#6700211yescharacteristic
192C8—21no—
193C8—21no—
194C8—41no—
195C8—81no—
196C8#6689112yescomplemented
197C8C2×#431411yescharacteristic
198C8#6695711yescharacteristic
199C22—42no—
200C22—81no—
201C22—81no—
202C22#1062262811yescharacteristic
203C4—21no—
204C4—81no—
205C4—1761no—
206C4—1761no—
207C4#1062272711yescharacteristic
208C4#1062275411yescharacteristic
209C4C2×#6689111yescharacteristic
210C4#1062280811yescharacteristic
211C2—82no—
212C2#1306795711yescharacteristic
213C2#1307066111yescharacteristic
214C2#1307068511yescharacteristic
subgroupG/H
centerC22#10622628
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC8×C11×D8C2
socleC22×C11#459
prime radicalC2×C11×D8D4
hypercenterC8×D8D11
hypocenterC11#12420
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
3. #13068213C2semidirect
4. #13066680C2semidirect
5. #13066675C2semidirect
6. #13066664C2semidirect
96. C8×C11SD32semidirect
177. C11#12420semidirect
196. C8#66891semidirect

Maximal subgroups

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

subgroupindex
#130707632
#130706612
#130682132
#130666802
#130666752
#130666642
C8×C11×D82
#1242011