Finite Group Databasebeta

← #14673590

Subgroups — #14673590

Order 2816.

314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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#13070329C212yesmaximal
2#13069504C211yesmaximal, characteristic
3#13068780C211yesmaximal, characteristic, complemented
4#13066725C212yesmaximal, complemented
5C11×#1376C211yesmaximal, characteristic, complemented
6C2×#66957C2211yescharacteristic
7C2×C11×M32C2212yes—
8C2×C4×C8×C11C2211yescharacteristic
9#10622723—21no—
10C2×#66883C2211yescharacteristic
11C2×#66882C2212yes—
12C2×#66881—21no—
13#10622549—21no—
14C2×#66869—21no—
15#10622147—22no—
16#10622141—22no—
17C2×#4339—21no—
18C22×C8×C11D411yescharacteristic
19C22×C8×C11C2311yescharacteristic
20C2×C42×C11D411yescharacteristic
21C2×C4⋊Dic11—22no—
22C2×#4318—21no—
23C2×Dic44D411yescharacteristic
24#66957—22no—
25#66957—22no—
26C2×D88D411yescharacteristic
27C2×#4314—21no—
28C11×M32—22no—
29C11×M32—22no—
30C2×C11×C16—22no—
31C4×C8×C11—22no—
32C11⋊#95—42no—
33(C2×D11)⋊C8—42no—
34#66883—22no—
35#66882—22no—
36#66882—22no—
37#66881—42no—
38#66869—42no—
39#13485—111nomaximal, Sylow
40C22×C4×C11—21no—
41C22×C4×C11C2×D411yescharacteristic
42C2×C22⋊D11—41no—
43C22×Dic11—42no—
44#4339—41no—
45#4339—41no—
46#4339—41no—
47#4339—41no—
48C2×D44—21no—
49C2×C4×D11—41no—
50C2×Dic22—21no—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11D812yes—
54C2×C8×C11C2×D411yescharacteristic
55C2×C8×C11#4111yescharacteristic
56C2×C8×C11#4112yes—
57C2×C8×C11#4112yes—
58C42×C11—21no—
59C42×C11SD1612yes—
60C4⋊Dic11—42no—
61C4⋊Dic11—42no—
62#4318—41no—
63#4318—41no—
64C2×C11⋊C8—41no—
65Dic44—22no—
66D88—22no—
67#4314—42no—
68C11×C16—42no—
69#2139—112no—
70#1974—111no—
71#1846—111no—
72#1387—112no—
73#1376D1111yescharacteristic, complemented
74C23×C11AGL(1,ℤ/8)11yescharacteristic
75C22×D11—41no—
76C2×C4×C11—22no—
77C2×C4×C11—42no—
78C2×C4×C11#12111yescharacteristic
79C2×C4×C11#12311yescharacteristic
80C2×C4×C11#12411yescharacteristic
81C2×C4×C11C2×D811yescharacteristic
82C2×C4×C11C2×SD1611yescharacteristic
83C2×C4×C11#13711yescharacteristic
84C22⋊D11—81no—
85C22⋊D11—81no—
86C2×Dic11—41no—
87C2×Dic11—84no—
88C2×Dic11—82no—
89D44—41no—
90D44—41no—
91C4×D11—81no—
92C4×D11—81no—
93Dic22—41no—
94Dic22—41no—
95C8×C11—22no—
96C8×C11#12312yes—
97C8×C11#12612yes—
98C11⋊C8—81no—
99C2×#135—111no—
100C2×M32C2×D1112yes—
101C2×#108—111no—
102C2×#107—112no—
103C2×#106—221no—
104C2×#104—221no—
105#408—221no—
106C2×C4×C8C2×D1111yescharacteristic
107#382—221no—
108#358—222no—
109#357—222no—
110C22×C11—22no—
111C22×C11#45911yescharacteristic
112C22×C11#48111yescharacteristic
113C22×C11#48911yescharacteristic
114C2×D11—81no—
115C2×D11—82no—
116C4×C11—42no—
117C4×C11#39711yescharacteristic
118C4×C11#46111yescharacteristic
119C4×C11#48011yescharacteristic
120C4×C11#48611yescharacteristic
121Dic11—81no—
122Dic11—162no—
123C2×#41—221no—
124#135—222no—
125#135—222no—
126C2×Q16—111no—
127C2×SD16—221no—
128C2×D8—111no—
129C2×M16—221no—
130C22×C8D4411yescharacteristic
131C22×C8C22×D1111yescharacteristic
132C2×C4⋊C4—222no—
133C2×C42D4411yescharacteristic
134M32—22no—
135M32—22no—
136C2×C16—22no—
137#108—222no—
138#107—222no—
139#107—222no—
140#106—442no—
141#104—442no—
142C22⋊C8—442no—
143C4×C8—22no—
144#95—442no—
145C2×C11—21no—
146C2×C11—21no—
147C2×C11#207111yescharacteristic
148C2×C11#221212yes—
149D11—161no—
150#41—441no—
151#41—441no—
152#41—441no—
153#41—441no—
154C2×Q8—221no—
155C2×D4—221no—
156C2×D4—441no—
157C22×C4—21no—
158C22×C4—441no—
159C22×C4—442no—
160C22×C4C2×D4411yescharacteristic
161Q16—222no—
162SD16—442no—
163D8—222no—
164M16—441no—
165M16—441no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—441no—
169C2×C8D8812yes—
170C2×C8#433912yes—
171C2×C8D4×D1111yescharacteristic
172C2×C8#434112yes—
173C2×C8#434311yescharacteristic
174C4⋊C4—442no—
175C4⋊C4—442no—
176C42—21no—
177C42#431412yes—
178C16—42no—
179C11#1348511yescharacteristic, complemented, Sylow
180C23—441no—
181C23#6696111yescharacteristic
182Q8—441no—
183Q8—441no—
184D4—441no—
185D4—441no—
186D4—881no—
187D4—881no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—441no—
191C2×C4—881no—
192C2×C4—881no—
193C2×C4—884no—
194C2×C4—882no—
195C2×C4#6692811yescharacteristic
196C2×C4#6693911yescharacteristic
197C2×C4#6694811yescharacteristic
198C2×C4C2×#431411yescharacteristic
199C2×C4C2×D8811yescharacteristic
200C2×C4#6696211yescharacteristic
201C8—22no—
202C8—881no—
203C8#6693612yes—
204C8#6695112yes—
205C22—22no—
206C22—882no—
207C22—881no—
208C22#1062232711yescharacteristic
209C22#1062234811yescharacteristic
210C22#1062245611yescharacteristic
211C4—42no—
212C4—881no—
213C4—1762no—
214C4#1062228711yescharacteristic
215C4#1062230711yescharacteristic
216C4#1062234911yescharacteristic
217C4#1062245411yescharacteristic
218C2—21no—
219C2—21no—
220C2—1761no—
221C2#1307002111yescharacteristic
222C2#1307068612yes—
subgroupG/H
centerC22#10622456
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1376C2
socleC22×C11#459
prime radicalC2×#66957C22
hypercenter#1376D11
hypocenterC11#13485
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1376

Complements

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

NH ≅ G/Ntype
3. #13068780C2semidirect
4. #13066725C2semidirect
5. C11×#1376C2semidirect
73. #1376D11semidirect
179. C11#13485semidirect

Maximal subgroups

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

subgroupindex
#130703292
#130695042
#130687802
#130667252
C11×#13762
#1348511