Finite Group Databasebeta

← #14665760

Subgroups — #14665760

Order 2816.

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

normal subgroups only

This group has 224 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
1C4×#66891C211yesmaximal, characteristic
2#13067512C211yesmaximal, characteristic, complemented
3#13067501C211yesmaximal, characteristic
4#13066689C211yesmaximal, characteristic, complemented
5#13066581C211yesmaximal, characteristic, complemented
6C16×C11⋊C8C211yesmaximal, characteristic, complemented
7C11×#1331C211yesmaximal, characteristic
8C4×C11×D8C2211yescharacteristic
9C2×#66891C411yescharacteristic
10#10622625—21no—
11#10622444—21no—
12C4×Dic44C2211yescharacteristic
13C4×C11×C16C2211yescharacteristic
14C11×#335C2211yescharacteristic
15#10622200C411yescharacteristic
16D4⋊(C11⋊C8)—21no—
17#10622130C411yescharacteristic
18#10622128C411yescharacteristic
19#10622122—21no—
20C4×C11⋊C16C2211yescharacteristic
21#10622096C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C2×C11×D8C2×C411yescharacteristic
24C4×D4×C11—21no—
25C2×#4318—41no—
26C2×Dic44C2×C411yescharacteristic
27C4×Dic22—21no—
28C2×C11×C16—21no—
29C11×#107C2×C411yescharacteristic
30C11×C4⋊C8—21no—
31C11×#102—21no—
32C4×C8×C11C2311yescharacteristic
33C22⋊(C11⋊C8)—41no—
34#66891—22no—
35#66882C2×C411yescharacteristic
36#66880—21no—
37#66879—41no—
38Dic11⋊C8—41no—
39C2×C11⋊C16C2×C411yescharacteristic
40C2×C11⋊C16C2×C411yescharacteristic
41C4⋊(C11⋊C8)—21no—
42C4×C11⋊C8D411yescharacteristic
43C4×C11⋊C8D411yescharacteristic
44#12082—111nomaximal, Sylow
45C2×D4×C11—21no—
46C22×C4×C11—41no—
47C2×Dic22—21no—
48C11×D8—21no—
49C11×D8—21no—
50C2×C8×C11—41no—
51C2×C8×C11C22×C411yescharacteristic
52C2×C8×C11#4111yescharacteristic
53C11×C4⋊C4—21no—
54C11×C22⋊C4—41no—
55C42×C11C2×D411yescharacteristic
56C4⋊Dic11—21no—
57Dic11⋊C4—41no—
58C4×Dic11—41no—
59#4318—82no—
60C2×C11⋊C8—21no—
61C2×C11⋊C8—41no—
62C2×C11⋊C8D811yescharacteristic
63C2×C11⋊C8D811yescharacteristic
64Dic44—21no—
65Dic44—21no—
66C11×C16—22no—
67C11⋊C16—21no—
68C11⋊C16M1612yescomplemented
69C4×SD32—111no—
70#1591—111no—
71#1589—111no—
72#1372—111no—
73#1332—111no—
74#1331D1111yescharacteristic
75C8×C16—111no—
76C23×C11—41no—
77D4×C11—41no—
78D4×C11—41no—
79C2×C4×C11—41no—
80C2×C4×C11—81no—
81C2×C4×C11—81no—
82C2×C4×C11C4×D411yescharacteristic
83C2×C4×C11C2×D811yescharacteristic
84C2×C4×C11#13511yescharacteristic
85C2×Dic11—41no—
86C2×Dic11—41no—
87Dic22—41no—
88Dic22—41no—
89C8×C11—21no—
90C8×C11—81no—
91C8×C11C2×M1611yescharacteristic
92C8×C11#13111yescharacteristic
93C11⋊C8—22no—
94C11⋊C8—21no—
95C11⋊C8—81no—
96C11⋊C8SD3212yescomplemented
97C2×SD32—111no—
98#446—221no—
99C4×Q16—111no—
100C4×D8C2×D1111yescharacteristic
101#436—221no—
102#367—111no—
103#358—111no—
104#357—111no—
105C4×C16—111no—
106C4×C16C2×D1111yescharacteristic
107#335—111no—
108#335C2×D1111yescharacteristic
109Q8⋊C8—221no—
110D4⋊C8—221no—
111C82—111no—
112C22×C11—81no—
113C22×C11—81no—
114C22×C11—81no—
115C22×C11C4×D811yescharacteristic
116C4×C11—21no—
117C4×C11—81no—
118C4×C11#43611yescharacteristic
119C4×C11#44311yescharacteristic
120C4×C11C2×SD3211yescharacteristic
121C4×C11#50811yescharacteristic
122Dic11—81no—
123Dic11—81no—
124C2×Q16—111no—
125C2×D8C4×D1111yescharacteristic
126C2×M16—441no—
127C4×Q8—221no—
128C4×D4—21no—
129SD32—222no—
130C2×C16—21no—
131C2×C16—111no—
132C2×C16—111no—
133#107—111no—
134#107C4×D1111yescharacteristic
135C4⋊C8—21no—
136C4⋊C8—221no—
137C4⋊C8—441no—
138#103—221no—
139#102—21no—
140C22⋊C8—441no—
141#97—441no—
142C4×C8—111no—
143C4×C8—111no—
144C4×C8C22×D1111yescharacteristic
145C2×C11—161no—
146C2×C11#158911yescharacteristic
147C2×C11C4×SD3211yescharacteristic
148C2×C11#217811yescharacteristic
149C2×Q8—221no—
150C2×D4—21no—
151C22×C4—41no—
152Q16—221no—
153Q16—221no—
154D8—21no—
155D8—21no—
156M16—882no—
157C2×C8—41no—
158C2×C8—111no—
159C2×C8—111no—
160C2×C8—221no—
161C2×C8—441no—
162C2×C8C2×C4×D1111yescharacteristic
163C2×C8#434111yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—221no—
166C4⋊C4—441no—
167C22⋊C4—41no—
168C42—441no—
169C42D4×D1111yescharacteristic
170C16—22no—
171C16—112no—
172C16—221no—
173C11#1208211yescharacteristic, complemented, Sylow
174C23—41no—
175Q8—441no—
176Q8—441no—
177D4—41no—
178D4—41no—
179C2×C4—41no—
180C2×C4—81no—
181C2×C4—81no—
182C2×C4—441no—
183C2×C4—441no—
184C2×C4(C22⋊D11)⋊C411yescharacteristic
185C2×C4D8×D1111yescharacteristic
186C2×C4#6696911yescharacteristic
187C8—21no—
188C8—81no—
189C8—112no—
190C8—222no—
191C8—221no—
192C8—881no—
193C8#6695411yescharacteristic
194C8M16×D1111yescharacteristic
195C22—81no—
196C22—81no—
197C22—81no—
198C22#1062236911yescharacteristic
199C4—21no—
200C4—81no—
201C4—881no—
202C4—881no—
203C4#1062234211yescharacteristic
204C4#1062243711yescharacteristic
205C4#1062252511yescharacteristic
206C4D11×SD3211yescharacteristic
207C2—161no—
208C2#1306749811yescharacteristic
209C2#1307047111yescharacteristic
210C2#1307049411yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1331C2
socleC22×C11C4×D8
prime radicalC2×C11×D8C2×C4
cosocleC4×C8×C11C23
hypercenter#1331D11
hypocenterC11#12082
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #13067512C2semidirect
4. #13066689C2semidirect
5. #13066581C2semidirect
6. C16×C11⋊C8C2semidirect
68. C11⋊C16M16semidirect
96. C11⋊C8SD32semidirect
173. C11#12082semidirect

Maximal subgroups

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

subgroupindex
C4×#668912
#130675122
#130675012
#130666892
#130665812
C16×C11⋊C82
C11×#13312
#1208211