Finite Group Databasebeta

← #13070033

Subgroups — #13070033

Order 1408.

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

normal subgroups only

This group has 258 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
1C2×#66885C211yesmaximal, characteristic
2#10622601C211yesmaximal, characteristic
3#10622590C211yesmaximal, characteristic, complemented
4C2×#66873C211yesmaximal, characteristic
5C11×#340C211yesmaximal, characteristic, complemented
6#10622188C211yesmaximal, characteristic, complemented
7#10622167C211yesmaximal, characteristic, complemented
8C22×D44C2211yescharacteristic
9C22×C8×C11C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×(C2×D11)⋊C4—21no—
13C2×(C2×D11)⋊C4—21no—
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4×Dic11C2211yescharacteristic
16C22×C11⋊C8C2211yescharacteristic
17C11⋊#95—21no—
18C11⋊#95—21no—
19#66885—22no—
20#66873—22no—
21C23×D11—21no—
22C22×C4×C11—21no—
23C22×C4×C11—21no—
24C22×C4×C11C2311yescharacteristic
25C22×Dic11—21no—
26C22×Dic11D411yescharacteristic
27C22×Dic11D411yescharacteristic
28C2×D44—21no—
29C2×D44—21no—
30C2×D44—21no—
31C2×D44—21no—
32C2×D44—21no—
33C2×D44D412yes—
34C2×C8×C11—21no—
35C2×C8×C11—21no—
36C2×C8×C11—21no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4—21no—
39C11×C4⋊C4—21no—
40C11×C4⋊C4—21no—
41(C2×D11)⋊C4—42no—
42(C2×D11)⋊C4—42no—
43C4⋊Dic11—21no—
44C4⋊Dic11—21no—
45C4×Dic11—21no—
46C4×Dic11—21no—
47C2×C11⋊C8—21no—
48C2×C11⋊C8—21no—
49C2×C11⋊C8—21no—
50#2073—111nomaximal, Sylow
51C23×C11C2×D411yescharacteristic
52C22×D11—22no—
53C22×D11—41no—
54C22×D11—41no—
55C22×D11—41no—
56C22×D11—41no—
57C22×D11—41no—
58C22×D11—41no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11—41no—
65C2×C4×C11C2×D411yescharacteristic
66C2×C4×C11#4111yescharacteristic
67C2×C4×C11#4111yescharacteristic
68C2×C4×C11#4111yescharacteristic
69C2×C4×C11#4111yescharacteristic
70C2×C4×C11#4111yescharacteristic
71C2×Dic11—21no—
72C2×Dic11—21no—
73C2×Dic11—21no—
74C2×Dic11—21no—
75C2×Dic11—21no—
76C2×Dic11—21no—
77C2×Dic11—41no—
78C2×Dic11—41no—
79C2×Dic11—41no—
80D44—22no—
81D44—22no—
82D44—41no—
83D44—41no—
84C8×C11—41no—
85C11⋊C8—41no—
86C2×#102—111no—
87C2×#102—111no—
88#390—111no—
89#382—111no—
90#340—111no—
91#340D1111yescharacteristic, complemented
92#336—111no—
93C22×C11#12111yescharacteristic
94C22×C11#12311yescharacteristic
95C22×C11#12411yescharacteristic
96C22×C11#13511yescharacteristic
97C22×C11#13511yescharacteristic
98C22×C11AGL(1,ℤ/8)11yescharacteristic
99C22×C11AGL(1,ℤ/8)11yescharacteristic
100C2×D11—42no—
101C2×D11—42no—
102C2×D11—42no—
103C2×D11—81no—
104C2×D11—81no—
105C2×D11—81no—
106C2×D11—81no—
107C4×C11—81no—
108C4×C11—81no—
109C4×C11#12311yescharacteristic
110C4×C11#12311yescharacteristic
111C4×C11#12611yescharacteristic
112C4×C11#12611yescharacteristic
113Dic11—41no—
114Dic11—41no—
115Dic11—81no—
116C22×D4—111no—
117C22×C8—111no—
118C22×C8C2×D1111yescharacteristic
119C2×C4⋊C4—111no—
120C2×C4⋊C4C2×D1111yescharacteristic
121C2×C4⋊C4C2×D1111yescharacteristic
122C2×C22⋊C4—221no—
123C2×C22⋊C4—221no—
124C2×C42—111no—
125#102—222no—
126#102—222no—
127#95—221no—
128#95—221no—
129C2×C11#39711yescharacteristic
130C2×C11#46311yescharacteristic
131C2×C11#46311yescharacteristic
132C2×C11#48211yescharacteristic
133C2×C11#48211yescharacteristic
134C2×C11#48811yescharacteristic
135C2×C11#49011yescharacteristic
136D11—82no—
137C24—221no—
138C2×D4—112no—
139C2×D4—221no—
140C2×D4—221no—
141C2×D4—221no—
142C2×D4—221no—
143C2×D4—221no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—111no—
147C22×C4—111no—
148C22×C4—221no—
149C22×C4C22×D1111yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—221no—
154C2×C8—221no—
155C2×C8—221no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—221no—
161C4⋊C4—221no—
162C22⋊C4—442no—
163C22⋊C4—442no—
164C42—221no—
165C42—221no—
166C11#207311yescharacteristic, complemented, Sylow
167C23—222no—
168C23—441no—
169C23—441no—
170C23—441no—
171C23—441no—
172C23—441no—
173C23—441no—
174C23D4×D1111yescharacteristic
175D4—222no—
176D4—222no—
177D4—441no—
178D4—441no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—221no—
186C2×C4—221no—
187C2×C4—221no—
188C2×C4—221no—
189C2×C4—221no—
190C2×C4—221no—
191C2×C4—441no—
192C2×C4—441no—
193C2×C4—441no—
194C2×C4#433911yescharacteristic
195C2×C4#433911yescharacteristic
196C2×C4#433911yescharacteristic
197C2×C4D4×D1111yescharacteristic
198C2×C4#434111yescharacteristic
199C2×C4#434311yescharacteristic
200C8—41no—
201C8—441no—
202C22—442no—
203C22—442no—
204C22—442no—
205C22—881no—
206C22—881no—
207C22—881no—
208C22—881no—
209C22#6693711yescharacteristic
210C22#6693811yescharacteristic
211C22#6694711yescharacteristic
212C22#6696411yescharacteristic
213C22#6696711yescharacteristic
214C22#6696911yescharacteristic
215C22#6697211yescharacteristic
216C4—81no—
217C4—81no—
218C4—441no—
219C4—441no—
220C4—881no—
221C4#6692911yescharacteristic
222C4#6693611yescharacteristic
223C4#6694711yescharacteristic
224C4#6695111yescharacteristic
225C2—882no—
226C2#1062228811yescharacteristic
227C2#1062237711yescharacteristic
228C2#1062240011yescharacteristic
229C2#1062241311yescharacteristic
230C2#1062243211yescharacteristic
231C2#1062247911yescharacteristic
232C2#1062249811yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#340C2
socleC23×C11C2×D4
prime radicalC22×D44C22
hypercenter#340D11
hypocenterC11#2073
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
3. #10622590C2semidirect
5. C11×#340C2semidirect
6. #10622188C2semidirect
7. #10622167C2semidirect
91. #340D11semidirect
166. C11#2073semidirect

Maximal subgroups

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

subgroupindex
C2×#668852
#106226012
#106225902
C2×#668732
C11×#3402
#106221882
#106221672
#207311