Finite Group Databasebeta

← #14665756

Subgroups — #14665756

Order 2816.

224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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×#66864C211yesmaximal, characteristic
2#13067512C211yesmaximal, characteristic, complemented
3#13067500C211yesmaximal, characteristic
4#13066579C211yesmaximal, characteristic, complemented
5#13066576C211yesmaximal, characteristic
6C16×C11⋊C8C211yesmaximal, characteristic, complemented
7C11×#1372C211yesmaximal, characteristic, complemented
8C2×#66864C411yescharacteristic
9#10622451—21no—
10#10622444—21no—
11C4×Dic44C2211yescharacteristic
12C4×D88C2211yescharacteristic
13C4×C11×C16C2211yescharacteristic
14C11×#335C2211yescharacteristic
15C11×#335C2211yescharacteristic
16#10622147C411yescharacteristic
17#10622143C411yescharacteristic
18#10622141C411yescharacteristic
19#10622122—21no—
20#10622121—21no—
21C4×C11⋊C16C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C2×Dic44C2×C411yescharacteristic
24C2×D88C2×C411yescharacteristic
25C2×#4313—41no—
26C4×D44—21no—
27C4×Dic22—21no—
28C2×C11×C16C2×C411yescharacteristic
29C2×C11×C16C2×C411yescharacteristic
30C11×C4⋊C8—21no—
31C11×C4⋊C8—21no—
32C4×C8×C11C2311yescharacteristic
33#66885—21no—
34(C2×D11)⋊C8—41no—
35#66882C2×C411yescharacteristic
36#66882C2×C411yescharacteristic
37#66880—21no—
38#66879—41no—
39Dic11⋊C8—41no—
40C2×C11⋊C16—21no—
41C4×C11⋊C8D411yescharacteristic
42C4×C11⋊C8D411yescharacteristic
43#66864—22no—
44#12082—111nomaximal, Sylow
45C2×D44—21no—
46C2×C4×D11—41no—
47C2×Dic22—21no—
48C2×C8×C11—41no—
49C2×C8×C11—41no—
50C2×C8×C11C22×C411yescharacteristic
51C2×C8×C11#4111yescharacteristic
52C42×C11C2×D411yescharacteristic
53(C2×D11)⋊C4—41no—
54C4⋊Dic11—21no—
55C4⋊Dic11—21no—
56Dic11⋊C4—41no—
57C4×Dic11—41no—
58C2×C11⋊C8—21no—
59C2×C11⋊C8D811yescharacteristic
60C2×C11⋊C8D811yescharacteristic
61Dic44—21no—
62Dic44—21no—
63D88—21no—
64D88—21no—
65#4313—82no—
66C11×C16—21no—
67C11×C16M1612yescomplemented
68C11⋊C16—22no—
69C4×SD32—111no—
70#1591—111no—
71#1589—111no—
72#1372D1111yescharacteristic, complemented
73#1332—111no—
74#1331—111no—
75C8×C16—111no—
76C22×D11—41no—
77C2×C4×C11C4×D411yescharacteristic
78C2×C4×C11C2×D811yescharacteristic
79C2×C4×C11#13511yescharacteristic
80C2×Dic11—41no—
81C2×Dic11—41no—
82C2×Dic11—41no—
83D44—41no—
84D44—41no—
85C4×D11—81no—
86C4×D11—81no—
87Dic22—41no—
88Dic22—41no—
89C8×C11—21no—
90C8×C11—81no—
91C8×C11—81no—
92C8×C11C2×M1611yescharacteristic
93C8×C11#13111yescharacteristic
94C11⋊C8—22no—
95C11⋊C8—21no—
96C11⋊C8SD3212yescomplemented
97C2×SD32—111no—
98#446—221no—
99C4×Q16—111no—
100C4×D8—111no—
101#436—221no—
102#367—111no—
103#358—111no—
104#357—111no—
105C4×C16—111no—
106C4×C16C2×D1111yescharacteristic
107#335C2×D1111yescharacteristic
108#335C2×D1111yescharacteristic
109Q8⋊C8—221no—
110D4⋊C8—221no—
111C82—111no—
112C22×C11C4×D811yescharacteristic
113C2×D11—81no—
114C2×D11—81no—
115C2×D11—81no—
116C4×C11—21no—
117C4×C11#43611yescharacteristic
118C4×C11#44311yescharacteristic
119C4×C11C2×SD3211yescharacteristic
120C4×C11#50811yescharacteristic
121Dic11—81no—
122Dic11—81no—
123Dic11—81no—
124C2×Q16—111no—
125C2×D8—111no—
126C2×M16—441no—
127C4×Q8—221no—
128C4×D4—221no—
129SD32—222no—
130C2×C16—221no—
131C2×C16C4×D1111yescharacteristic
132C2×C16C4×D1111yescharacteristic
133#107—111no—
134#107—111no—
135C4⋊C8—21no—
136C4⋊C8—21no—
137C4⋊C8—441no—
138#103—221no—
139#102—221no—
140C22⋊C8—441no—
141#97—441no—
142C4×C8—111no—
143C4×C8—111no—
144C4×C8C22×D1111yescharacteristic
145C2×C11#158911yescharacteristic
146C2×C11C4×SD3211yescharacteristic
147C2×C11#217811yescharacteristic
148D11—161no—
149C2×Q8—221no—
150C2×D4—221no—
151C22×C4—441no—
152Q16—221no—
153Q16—221no—
154D8—221no—
155D8—221no—
156M16—882no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—111no—
160C2×C8—111no—
161C2×C8—221no—
162C2×C8C2×C4×D1111yescharacteristic
163C2×C8#434311yescharacteristic
164C4⋊C4—221no—
165C4⋊C4—221no—
166C4⋊C4—441no—
167C22⋊C4—441no—
168C42—441no—
169C42D4×D1111yescharacteristic
170C16—21no—
171C16—222no—
172C16#431312yescomplemented
173C11#1208211yescharacteristic, complemented, Sylow
174C23—441no—
175Q8—441no—
176Q8—441no—
177D4—441no—
178D4—441no—
179C2×C4—441no—
180C2×C4—441no—
181C2×C4—441no—
182C2×C4—881no—
183C2×C4—881no—
184C2×C4#6694611yescharacteristic
185C2×C4D8×D1111yescharacteristic
186C2×C4#6697211yescharacteristic
187C8—21no—
188C8—81no—
189C8—81no—
190C8—112no—
191C8—222no—
192C8—221no—
193C8C2×#431311yescharacteristic
194C8#6696011yescharacteristic
195C22—881no—
196C22—881no—
197C22—881no—
198C22#1062248511yescharacteristic
199C4—21no—
200C4—881no—
201C4—881no—
202C4—881no—
203C4#1062245111yescharacteristic
204C4#1062250811yescharacteristic
205C4D11×SD3211yescharacteristic
206C4#1062252911yescharacteristic
207C2—1761no—
208C2#1306750011yescharacteristic
209C2#1307046711yescharacteristic
210C2#1307049611yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutatorC2×C8×C11C22×C4
FrattiniC4×C8C22×D11
FittingC11×#1372C2
socleC22×C11C4×D8
prime radicalC2×D88C2×C4
cosocleC4×C8×C11C23
hypercenter#1372D11
hypocenterC11#12082
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1372

Complements

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

NH ≅ G/Ntype
2. #13067512C2semidirect
4. #13066579C2semidirect
6. C16×C11⋊C8C2semidirect
7. C11×#1372C2semidirect
67. C11×C16M16semidirect
72. #1372D11semidirect
96. C11⋊C8SD32semidirect
172. C16#4313semidirect
173. C11#12082semidirect

Maximal subgroups

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

subgroupindex
C4×#668642
#130675122
#130675002
#130665792
#130665762
C16×C11⋊C82
C11×#13722
#1208211