Finite Group Databasebeta

← #14667975

Subgroups — #14667975

Order 2816.

240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 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#13070663C211yesmaximal, characteristic, complemented
2#13070657C211yesmaximal, characteristic
3#13068223C211yesmaximal, characteristic
4#13067422C211yesmaximal, characteristic, complemented
5#13066685C211yesmaximal, characteristic, complemented
6#13066661C211yesmaximal, characteristic
7C11×#1362C211yesmaximal, characteristic, complemented
8C11×#494C2211yescharacteristic
9C2×#66893—21no—
10#10622701—21no—
11#10622701—21no—
12C2×#66864—21no—
13#10622443—21no—
14C4×Dic44C2211yescharacteristic
15#10622308C2211yescharacteristic
16C11×C4⋊C16C2211yescharacteristic
17C11×#335C2211yescharacteristic
18#10622202—21no—
19#10622147—21no—
20#10622122—21no—
21C4⋊(C11⋊C16)C2211yescharacteristic
22C8×C11⋊C8C2211yescharacteristic
23C2×C11×Q16—21no—
24C2×C11×Q16—21no—
25C11×C4⋊Q8—21no—
26C2×Dic44D411yescharacteristic
27C2×D88—21no—
28C2×D88—21no—
29#66927—21no—
30C4×Dic22—21no—
31C2×C11×C16—21no—
32C11×C4⋊C8—21no—
33C4×C8×C11C2311yescharacteristic
34#66893—42no—
35#66882D411yescharacteristic
36#66880—21no—
37Dic11⋊C8—41no—
38C8×Dic11—41no—
39C2×C11⋊C16—21no—
40#66873—42no—
41#66873—41no—
42#66873—41no—
43C4×C11⋊C8D411yescharacteristic
44C4×C11⋊C8D411yescharacteristic
45#66864—42no—
46#12429—111nomaximal, Sylow
47C2×Q8×C11—41no—
48C2×D44—41no—
49C2×D44—41no—
50C2×D44—41no—
51C2×Dic22—21no—
52C11×Q16—41no—
53C11×Q16—41no—
54C11×Q16—81no—
55C2×C8×C11—41no—
56C2×C8×C11C2×D411yescharacteristic
57C2×C8×C11#4111yescharacteristic
58C11×C4⋊C4—41no—
59C11×C4⋊C4—41no—
60C42×C11C2×D411yescharacteristic
61C4⋊Dic11—21no—
62Dic11⋊C4—41no—
63C4×Dic11—41no—
64C2×C11⋊C8—21no—
65C2×C11⋊C8D811yescharacteristic
66C2×C11⋊C8D811yescharacteristic
67Dic44—21no—
68Dic44D812yes—
69D88—41no—
70D88—41no—
71D88—81no—
72C11×C16—41no—
73C11⋊C16—41no—
74#2209—111no—
75#2207—111no—
76#1709—111no—
77C8×Q16—111no—
78#1370—111no—
79#1362D1111yescharacteristic, complemented
80#1361—111no—
81C22×D11—81no—
82Q8×C11—81no—
83Q8×C11—81no—
84C2×C4×C11—81no—
85C2×C4×C11#12111yescharacteristic
86C2×C4×C11C2×D811yescharacteristic
87C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
88C2×Dic11—41no—
89C2×Dic11—41no—
90D44—82no—
91D44—81no—
92D44—81no—
93D44—81no—
94D44—81no—
95Dic22—22no—
96Dic22—41no—
97C8×C11—21no—
98C8×C11—81no—
99C8×C11C2×D811yescharacteristic
100C8×C11#13511yescharacteristic
101C11⋊C8—21no—
102C11⋊C8—21no—
103C11⋊C8—41no—
104C2×Q32—221no—
105C2×SD32—221no—
106#494C2×D1111yescharacteristic
107#493—111no—
108#486—221no—
109#486—221no—
110C8×Q8—221no—
111C4×Q16—111no—
112C4⋊C16—111no—
113C4⋊C16C2×D1111yescharacteristic
114#358—221no—
115#357—221no—
116#335C2×D1111yescharacteristic
117Q8⋊C8—221no—
118C82—111no—
119C22×C11#45911yescharacteristic
120C2×D11—161no—
121C2×D11—161no—
122C2×D11—161no—
123C4×C11—21no—
124C4×C11—161no—
125C4×C11#46611yescharacteristic
126C4×C11#47211yescharacteristic
127C4×C11#50811yescharacteristic
128C4×C11#51011yescharacteristic
129Dic11—42no—
130Dic11—81no—
131C2×Q16—21no—
132C2×Q16—21no—
133C2×Q16—111no—
134C2×D8—221no—
135C2×D8—221no—
136C4⋊Q8—21no—
137#127—221no—
138C4×Q8—221no—
139Q32—442no—
140SD32—442no—
141C2×C16—21no—
142C2×C16—221no—
143#107—111no—
144C4⋊C8—21no—
145C4⋊C8—441no—
146#103—221no—
147#102—441no—
148#102—441no—
149#102—442no—
150C4×C8—111no—
151C4×C8—111no—
152C4×C8—441no—
153C4×C8C22×D1111yescharacteristic
154C2×C11#166711yescharacteristic
155C2×C11#221111yescharacteristic
156C2×C11#221211yescharacteristic
157D11—321no—
158C2×Q8—41no—
159C2×Q8—221no—
160C2×D4—441no—
161C2×D4—441no—
162C2×D4—441no—
163Q16—41no—
164Q16—41no—
165Q16—81no—
166Q16—112no—
167Q16—221no—
168D8—441no—
169D8—441no—
170D8—881no—
171C2×C8—41no—
172C2×C8—111no—
173C2×C8—111no—
174C2×C8—221no—
175C2×C8#433911yescharacteristic
176C2×C8D4×D1111yescharacteristic
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—221no—
180C4⋊C4—441no—
181C42—441no—
182C42D4×D1111yescharacteristic
183C16—41no—
184C16—441no—
185C11#1242911yescharacteristic, complemented, Sylow
186C23—881no—
187Q8—81no—
188Q8—81no—
189Q8—222no—
190Q8—441no—
191D4—882no—
192D4—881no—
193D4—881no—
194D4—881no—
195D4—881no—
196C2×C4—81no—
197C2×C4—441no—
198C2×C4—441no—
199C2×C4#6693711yescharacteristic
200C2×C4D8×D1111yescharacteristic
201C2×C4#6696711yescharacteristic
202C8—21no—
203C8—81no—
204C8—221no—
205C8—221no—
206C8—441no—
207C8D8×D1111yescharacteristic
208C8#6696911yescharacteristic
209C22—1761no—
210C22—1761no—
211C22—1761no—
212C22#1062239911yescharacteristic
213C4—21no—
214C4—161no—
215C4—442no—
216C4—881no—
217C4#1062236211yescharacteristic
218C4#1062238811yescharacteristic
219C4#1062252911yescharacteristic
220C4#1062253111yescharacteristic
221C2—3521no—
222C2#1306797011yescharacteristic
223C2#1307068111yescharacteristic
224C2#1307068811yescharacteristic
subgroupG/H
centerC22#10622399
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1362C2
socleC22×C11#459
prime radical#10622308C22
hypercenter#1362D11
hypocenterC11#12429
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #13070663C2semidirect
4. #13067422C2semidirect
5. #13066685C2semidirect
7. C11×#1362C2semidirect
79. #1362D11semidirect
185. C11#12429semidirect

Maximal subgroups

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

subgroupindex
#130706632
#130706572
#130682232
#130674222
#130666852
#130666612
C11×#13622
#1242911