Finite Group Databasebeta

← #14673573

Subgroups — #14673573

Order 2816.

362 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#10622200C212yesmaximal
2#13068780C211yesmaximal, characteristic, complemented
3#13066707C212yesmaximal, complemented
4#13066694C211yesmaximal, characteristic, complemented
5C11×#1970C211yesmaximal, characteristic
6C22×C11×D8C2211yescharacteristic
7C2×C11×#107C2211yescharacteristic
8C2×C11×#102—21no—
9C2×C4×C8×C11C2211yescharacteristic
10C11×#390—21no—
11C2×#66882C2212yes—
12C2×#66881—21no—
13C22×C11⋊C16C2212yes—
14#10622549—21no—
15#10622200—24no—
16C22×D4×C11—21no—
17C2×C11×D8—22no—
18C2×C11×D8—22no—
19C2×C11×D8—21no—
20C2×C11×D8D412yes—
21C22×C8×C11D411yescharacteristic
22C22×C8×C11C2311yescharacteristic
23C2×C11×C4⋊C4—21no—
24C2×C11×C22⋊C4—42no—
25C2×C42×C11D411yescharacteristic
26C2×C4⋊Dic11—22no—
27C11×#107—22no—
28C11×#102—42no—
29C4×C8×C11—22no—
30C11⋊#95—42no—
31#66882—22no—
32#66882—22no—
33#66881—42no—
34C2×C11⋊C16—22no—
35C2×C11⋊C16—22no—
36C2×C11⋊C16—22no—
37#13482—111nomaximal, Sylow
38C24×C11—41no—
39C2×D4×C11—22no—
40C2×D4×C11—41no—
41C2×D4×C11—41no—
42C2×D4×C11—41no—
43C2×D4×C11—41no—
44C2×D4×C11—41no—
45C22×C4×C11—41no—
46C22×C4×C11D812yes—
47C22×C4×C11C2×D411yescharacteristic
48C22×Dic11—42no—
49C11×D8—24no—
50C11×D8—42no—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11SD1612yes—
54C2×C8×C11C2×D411yescharacteristic
55C2×C8×C11#4111yescharacteristic
56C2×C8×C11#4112yes—
57C2×C8×C11#4112yes—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—41no—
60C11×C22⋊C4—84no—
61C42×C11—21no—
62C42×C11—21no—
63C4⋊Dic11—42no—
64C4⋊Dic11—42no—
65C11⋊C16—42no—
66C2×#357—112no—
67#1970D1111yescharacteristic
68#1846—111no—
69#1380—112no—
70#1374—111no—
71C23×C11—42no—
72C23×C11—81no—
73C23×C11—81no—
74C23×C11—82no—
75C23×C11—82no—
76C23×C11C2×D811yescharacteristic
77D4×C11—42no—
78D4×C11—42no—
79D4×C11—81no—
80D4×C11—81no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—81no—
85C2×C4×C11—82no—
86C2×C4×C11#12111yescharacteristic
87C2×C4×C11#12311yescharacteristic
88C2×C4×C11#12411yescharacteristic
89C2×C4×C11C2×SD1611yescharacteristic
90C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
91C2×C4×C11#13711yescharacteristic
92C2×Dic11—82no—
93C2×Dic11—82no—
94C2×Dic11—82no—
95C8×C11—22no—
96C8×C11#12312yes—
97C8×C11#12612yes—
98C22×D8C2×D1111yescharacteristic
99C22×C16—112no—
100C2×#107—112no—
101C2×#107C2×D1111yescharacteristic
102C2×#106—221no—
103C2×#102—21no—
104C2×C4×C8C2×D1111yescharacteristic
105#390—21no—
106#382—221no—
107#357—224no—
108C22×C11—82no—
109C22×C11—84no—
110C22×C11—162no—
111C22×C11—161no—
112C22×C11—161no—
113C22×C11#45911yescharacteristic
114C22×C11#48011yescharacteristic
115C22×C11#48611yescharacteristic
116C22×C11#50812yes—
117C22×C11#50912yes—
118C4×C11—42no—
119C4×C11—161no—
120C4×C11#39711yescharacteristic
121C4×C11#46111yescharacteristic
122C4×C11#48111yescharacteristic
123C4×C11#48911yescharacteristic
124Dic11—162no—
125C22×D4—21no—
126C2×D8—21no—
127C2×D8—22no—
128C2×D8—22no—
129C2×D8D4412yes—
130C22×C8C22⋊D1111yescharacteristic
131C22×C8C22×D1111yescharacteristic
132C2×C4⋊C4—21no—
133C2×C4⋊C4—222no—
134C2×C22⋊C4—42no—
135C2×C42C22⋊D1111yescharacteristic
136C2×C16—222no—
137C2×C16—222no—
138C2×C16—222no—
139#107—22no—
140#107—222no—
141#107—222no—
142#106—442no—
143#102—42no—
144C4×C8—22no—
145#95—442no—
146C2×C11—162no—
147C2×C11#207111yescharacteristic
148C2×C11#221012yes—
149C2×C11#223412yes—
150C2×C11#224211yescharacteristic
151C2×C11#224411yescharacteristic
152C24—41no—
153C2×D4—22no—
154C2×D4—41no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159C22×C4—41no—
160C22×C4—442no—
161C22×C4#432312yes—
162C22×C4C2×C22⋊D1111yescharacteristic
163D8—24no—
164D8—42no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8#432412yes—
168C2×C8C2×D4411yescharacteristic
169C2×C8#433911yescharacteristic
170C2×C8#434112yes—
171C2×C8#434112yes—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—442no—
175C4⋊C4—442no—
176C22⋊C4—84no—
177C42—21no—
178C42—21no—
179C16—442no—
180C11#1348211yescharacteristic, complemented, Sylow
181C23—42no—
182C23—82no—
183C23—82no—
184C23—81no—
185C23—81no—
186C23C2×#432311yescharacteristic
187D4—42no—
188D4—42no—
189D4—81no—
190D4—81no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—82no—
195C2×C4—81no—
196C2×C4—882no—
197C2×C4—882no—
198C2×C4—882no—
199C2×C4#6698311yescharacteristic
200C2×C4C2×#432411yescharacteristic
201C2×C4#6698811yescharacteristic
202C2×C4#6698911yescharacteristic
203C2×C4#6700211yescharacteristic
204C2×C4#6700411yescharacteristic
205C8—22no—
206C8#6693212yes—
207C8#6693912yes—
208C22—84no—
209C22—82no—
210C22—161no—
211C22—162no—
212C22—161no—
213C22#1062262811yescharacteristic
214C22#1062264611yescharacteristic
215C22#1062268311yescharacteristic
216C22#1062276012yes—
217C22#1062280712yes—
218C4—42no—
219C4—161no—
220C4—1762no—
221C4#1062256611yescharacteristic
222C4#1062263211yescharacteristic
223C4#1062264711yescharacteristic
224C4#1062266811yescharacteristic
225C2—162no—
226C2#1307001911yescharacteristic
227C2#1307067112yes—
228C2#1307080412yes—
229C2#1307084711yescharacteristic
230C2#1307085711yescharacteristic
subgroupG/H
centerC23C2×#4323
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1970C2
socleC23×C11C2×D8
prime radicalC22×C11×D8C22
hypercenter#1970D11
hypocenterC11#13482
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. #13068780C2semidirect
3. #13066707C2semidirect
4. #13066694C2semidirect
180. C11#13482semidirect

Maximal subgroups

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

subgroupindex
C2×#106222002
#130687802
#130667072
#130666942
C11×#19702
#1348211