Finite Group Databasebeta

← #13074105

Subgroups — #13074105

Order 1408.

520 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 153 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×C11×#124C211yesmaximal, characteristic
2C2×C4×Dic22C211yesmaximal, characteristic, complemented
3#10622843C212yesmaximal, complemented
4#10622834C212yesmaximal
5#10622566C212yesmaximal, complemented
6#10622560C212yesmaximal, complemented
7#10622558C214yesmaximal, complemented
8C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
9C22×Q8×C11C2211yescharacteristic
10C22×D4×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C11×#124—24no—
13C2×C11×C22⋊C4C2212yes—
14C2×C11×C22⋊C4C2212yes—
15C2×C42×C11C2211yescharacteristic
16C2×C22⋊Dic11C2214yes—
17C2×C22⋊Dic11C2214yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×C4×Dic11C2212yes—
22C2×C4×Dic11C2212yes—
23C4×Dic22—24no—
24C11⋊#95C2212yes—
25C11⋊#95C2214yes—
26C11⋊#95C2214yes—
27C24×C11C2312yes—
28C2×Q8×C11—22no—
29C2×Q8×C11—24no—
30C2×D4×C11—22no—
31C2×D4×C11—24no—
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2314yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C2×Dic22—24no—
40C2×Dic22—22no—
41C11×C22⋊C4—24no—
42C11×C22⋊C4—24no—
43C42×C11D414yes—
44C22⋊Dic11—28no—
45C22⋊Dic11—44no—
46C4⋊Dic11—22no—
47C4⋊Dic11—24no—
48Dic11⋊C4—24no—
49C4×Dic11—24no—
50C4×Dic11—42no—
51#2592—111nomaximal, Sylow
52C23×C11—22no—
53C23×C11—24no—
54C23×C11—24no—
55C23×C11—22no—
56C23×C11—22no—
57C23×C11C2411yescharacteristic
58Q8×C11—44no—
59D4×C11—44no—
60C2×C4×C11—22no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—24no—
65C2×C4×C11C2×D412yes—
66C2×C4×C11C2×D412yes—
67C2×C4×C11C2×D412yes—
68C2×C4×C11#4114yes—
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—24no—
73C2×Dic11—24no—
74C2×Dic11—24no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11#4114yes—
78Dic22—28no—
79C2×#124D1111yescharacteristic
80C2×C4×Q8—111no—
81#397—112no—
82#393—112no—
83#391—112no—
84#390—112no—
85#388—114no—
86C4×C4⋊C4—111no—
87C22×C11—42no—
88C22×C11—42no—
89C22×C11—42no—
90C22×C11—44no—
91C22×C11—44no—
92C22×C11C22×D411yescharacteristic
93C22×C11C2×#4112yes—
94C22×C11C2×#4112yes—
95C22×C11H(5,𝔽2)11yescharacteristic
96C22×C112−1+411yescharacteristic
97C4×C11—22no—
98C4×C11—22no—
99C4×C11—42no—
100C4×C11#12414yes—
101Dic11—24no—
102Dic11—42no—
103Dic11—44no—
104C22×Q8—111no—
105C22×Q8C2×D1111yescharacteristic
106C22×D4C2×D1111yescharacteristic
107#124—24no—
108C4×Q8—224no—
109C2×C4⋊C4—112no—
110C2×C4⋊C4—111no—
111C2×C4⋊C4—112no—
112C2×C22⋊C4—114no—
113C2×C22⋊C4—114no—
114C2×C22⋊C4C2×D1112yes—
115C2×C22⋊C4C2×D1112yes—
116C2×C42—112no—
117C2×C42—112no—
118C2×C42C2×D1111yescharacteristic
119#95—112no—
120#95—114no—
121#95—114no—
122C2×C11—82no—
123C2×C11#52511yescharacteristic
124C2×C11C2×#12411yescharacteristic
125C2×C11#53711yescharacteristic
126C2×C11#55612yes—
127C2×C11#55912yes—
128C24C22×D1112yes—
129C2×Q8—24no—
130C2×Q8—22no—
131C2×Q8—224no—
132C2×Q8—222no—
133C2×D4—24no—
134C2×D4—22no—
135C22×C4—112no—
136C22×C4—114no—
137C22×C4—112no—
138C22×C4C22×D1112yes—
139C22×C4C22×D1111yescharacteristic
140C22×C4C22×D1111yescharacteristic
141C22×C4C22×D1111yescharacteristic
142C4⋊C4—224no—
143C4⋊C4—224no—
144C4⋊C4—222no—
145C22⋊C4—24no—
146C22⋊C4—24no—
147C22⋊C4—228no—
148C22⋊C4—444no—
149C42—224no—
150C42—442no—
151C42C22⋊D1114yes—
152C11#259211yescharacteristic, complemented, Sylow
153C23—24no—
154C23—24no—
155C23—22no—
156C23—22no—
157C23—22no—
158C23C23×D1111yescharacteristic
159Q8—44no—
160Q8—228no—
161D4—44no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—114no—
168C2×C4—222no—
169C2×C4—222no—
170C2×C4—224no—
171C2×C4—224no—
172C2×C4—224no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4#434114yes—
177C2×C4C2×C22⋊D1112yes—
178C2×C4C2×C22⋊D1112yes—
179C2×C4C2×C22⋊D1112yes—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—44no—
184C22—44no—
185C22C2×#434112yes—
186C22#41×D1112yes—
187C22#6704211yescharacteristic
188C22#6704311yescharacteristic
189C22C22×C22⋊D1111yescharacteristic
190C4—22no—
191C4—22no—
192C4—42no—
193C4—224no—
194C4—442no—
195C4—444no—
196C4#6698914yes—
197C2—82no—
198C2#1062320212yes—
199C2#1062321212yes—
200C2C2×#6698911yescharacteristic
201C2#1062335911yescharacteristic
202C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#124C2
prime radicalC22×D4×C11C22
hypercenterC2×#124D11
hypocenterC11#2592
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic22C2semidirect
3. #10622843C2semidirect
5. #10622566C2semidirect
6. #10622560C2semidirect
7. #10622558C2semidirect
8. C4×C4⋊Dic11C2semidirect
152. C11#2592semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
C2×C4×Dic222
#106228432
#106228342
#106225662
#106225602
#106225582
C4×C4⋊Dic112
#259211