Finite Group Databasebeta

← #13070023

Subgroups — #13070023

Order 1408.

274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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#10622589C211yesmaximal, 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×Dic11⋊C4—21no—
16C2×Dic11⋊C4—21no—
17C2×C4×Dic11C2211yescharacteristic
18C22×C11⋊C8C2211yescharacteristic
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—
45Dic11⋊C4—42no—
46Dic11⋊C4—42no—
47C4×Dic11—21no—
48C4×Dic11—21no—
49C2×C11⋊C8—21no—
50C2×C11⋊C8—21no—
51C2×C11⋊C8—21no—
52#2071—111nomaximal, Sylow
53C23×C11C2×D411yescharacteristic
54C22×D11—22no—
55C22×D11—41no—
56C22×D11—41no—
57C22×D11—41no—
58C22×D11—41no—
59C22×D11—41no—
60C22×D11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—41no—
63C2×C4×C11—41no—
64C2×C4×C11—41no—
65C2×C4×C11—41no—
66C2×C4×C11—41no—
67C2×C4×C11C2×D411yescharacteristic
68C2×C4×C11#4111yescharacteristic
69C2×C4×C11#4111yescharacteristic
70C2×C4×C11#4111yescharacteristic
71C2×C4×C11#4111yescharacteristic
72C2×C4×C11#4111yescharacteristic
73C2×Dic11—21no—
74C2×Dic11—21no—
75C2×Dic11—21no—
76C2×Dic11—21no—
77C2×Dic11—41no—
78C2×Dic11—41no—
79C2×Dic11—41no—
80C2×Dic11D812yes—
81C2×Dic11SD1612yes—
82D44—22no—
83D44—22no—
84D44—41no—
85D44—41no—
86C8×C11—41no—
87C11⋊C8—41no—
88C2×#102—111no—
89C2×#102—111no—
90#390—111no—
91#384—111no—
92#340—111no—
93#340D1111yescharacteristic, complemented
94#336—111no—
95C22×C11#12111yescharacteristic
96C22×C11#12311yescharacteristic
97C22×C11#12411yescharacteristic
98C22×C11C2×D811yescharacteristic
99C22×C11C2×SD1611yescharacteristic
100C22×C11AGL(1,ℤ/8)11yescharacteristic
101C22×C11#13711yescharacteristic
102C2×D11—42no—
103C2×D11—42no—
104C2×D11—42no—
105C2×D11—81no—
106C2×D11—81no—
107C2×D11—81no—
108C2×D11—81no—
109C4×C11—81no—
110C4×C11—81no—
111C4×C11#12311yescharacteristic
112C4×C11#12311yescharacteristic
113C4×C11#12611yescharacteristic
114C4×C11#12611yescharacteristic
115Dic11—22no—
116Dic11—22no—
117Dic11—81no—
118C22×D4—111no—
119C22×C8—111no—
120C22×C8C2×D1111yescharacteristic
121C2×C4⋊C4—111no—
122C2×C4⋊C4—221no—
123C2×C4⋊C4—221no—
124C2×C4⋊C4C2×D1111yescharacteristic
125C2×C4⋊C4C2×D1111yescharacteristic
126C2×C22⋊C4—221no—
127C2×C22⋊C4—221no—
128C2×C42—111no—
129#102—222no—
130#102—222no—
131C2×C11#39711yescharacteristic
132C2×C11#45911yescharacteristic
133C2×C11#46111yescharacteristic
134C2×C11#48011yescharacteristic
135C2×C11#48111yescharacteristic
136C2×C11#48611yescharacteristic
137C2×C11#48911yescharacteristic
138D11—82no—
139C24—221no—
140C2×D4—112no—
141C2×D4—221no—
142C2×D4—221no—
143C2×D4—221no—
144C2×D4—221no—
145C2×D4—221no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—111no—
149C22×C4—111no—
150C22×C4—221no—
151C22×C4C22×D1111yescharacteristic
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—221no—
156C2×C8—221no—
157C2×C8—221no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—221no—
163C4⋊C4—221no—
164C4⋊C4—442no—
165C4⋊C4—442no—
166C22⋊C4—442no—
167C22⋊C4—442no—
168C42—221no—
169C42—221no—
170C11#207111yescharacteristic, complemented, Sylow
171C23—222no—
172C23—441no—
173C23—441no—
174C23—441no—
175C23—441no—
176C23—441no—
177C23—441no—
178C23D4×D1111yescharacteristic
179D4—222no—
180D4—222no—
181D4—441no—
182D4—441no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—112no—
190C2×C4—112no—
191C2×C4—221no—
192C2×C4—221no—
193C2×C4—221no—
194C2×C4—221no—
195C2×C4—441no—
196C2×C4—441no—
197C2×C4—441no—
198C2×C4#433911yescharacteristic
199C2×C4#433911yescharacteristic
200C2×C4#433911yescharacteristic
201C2×C4D4×D1111yescharacteristic
202C2×C4#434111yescharacteristic
203C2×C4#434311yescharacteristic
204C8—41no—
205C8—441no—
206C22—442no—
207C22—442no—
208C22—442no—
209C22—881no—
210C22—881no—
211C22—881no—
212C22—881no—
213C22#6693711yescharacteristic
214C22#6693811yescharacteristic
215C22#6694711yescharacteristic
216C22D8×D1111yescharacteristic
217C22SD16×D1111yescharacteristic
218C22#6696711yescharacteristic
219C22#6697111yescharacteristic
220C4—81no—
221C4—81no—
222C4—222no—
223C4—222no—
224C4—881no—
225C4#6692911yescharacteristic
226C4#6693611yescharacteristic
227C4#6694711yescharacteristic
228C4#6695111yescharacteristic
229C2—882no—
230C2#1062228811yescharacteristic
231C2#1062237311yescharacteristic
232C2#1062239911yescharacteristic
233C2#1062240811yescharacteristic
234C2#1062243111yescharacteristic
235C2#1062247611yescharacteristic
236C2#1062249511yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#340C2
socleC23×C11C2×D4
prime radicalC22×D44C22
hypercenter#340D11
hypocenterC11#2071
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. #10622589C2semidirect
5. C11×#340C2semidirect
6. #10622188C2semidirect
7. #10622167C2semidirect
93. #340D11semidirect
170. C11#2071semidirect

Maximal subgroups

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

subgroupindex
C2×#668852
#106226012
#106225892
C2×#668732
C11×#3402
#106221882
#106221672
#207111