Finite Group Databasebeta

← #13081223

Subgroups — #13081223

Order 1408.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#10623089C212yesmaximal, complemented
2C4×C11×D8C211yesmaximal, characteristic, complemented
3#10622772C212yesmaximal, complemented
4#10622622C212yesmaximal, complemented
5#10622494C212yesmaximal, complemented
6#10622397C212yesmaximal, complemented
7#10622387C212yesmaximal, complemented
8#10622301C211yesmaximal, characteristic, complemented
9#10622296C211yesmaximal, characteristic, complemented
10C2×C11×D8C2211yescharacteristic
11C4×D4×C11C2212yes—
12#66991C2212yes—
13#66991C2212yes—
14#66982—22no—
15C4×C22⋊D11—22no—
16C2×#4313C2212yes—
17#66945C2212yes—
18C4⋊C4×D11C2212yes—
19#66937—22no—
20#66932—22no—
21C4×D44C2211yescharacteristic
22#66923C2212yes—
23C11×#107C2211yescharacteristic
24C11×#102C2212yes—
25C4×C8×C11C2211yescharacteristic
26#66896C2212yes—
27#66896C2212yes—
28(C2×D11)⋊C8C2212yes—
29#66882C2211yescharacteristic
30#66882C2211yescharacteristic
31#66881C2212yes—
32#66872C2212yes—
33#66871C2212yes—
34C4⋊(C11⋊C8)C2211yescharacteristic
35C2×D4×C11C2312yes—
36C22×C4×C11—22no—
37C2×C22⋊D11—22no—
38C2×C22⋊D11—22no—
39C2×D44D411yescharacteristic
40C2×C4×D11—22no—
41C2×C4×D11C2312yes—
42C11×D8—22no—
43C2×C8×C11C2311yescharacteristic
44C2×C8×C11C2311yescharacteristic
45C11×C4⋊C4C2312yes—
46C11×C22⋊C4—22no—
47C42×C11C2311yescharacteristic
48C22⋊Dic11—22no—
49C22⋊Dic11—22no—
50(C2×D11)⋊C4—22no—
51(C2×D11)⋊C4D412yes—
52C4⋊Dic11D411yescharacteristic
53C4⋊Dic11C2312yes—
54C4⋊Dic11C2312yes—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58C4×Dic11—22no—
59C2×C11⋊C8C2312yes—
60#4313—24no—
61#3355—111nomaximal, Sylow
62C23×C11—22no—
63C22×D11C2×D412yes—
64D4×C11—22no—
65D4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—82no—
68C2×C4×C11C2×D411yescharacteristic
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11C2411yescharacteristic
71C22⋊D11—44no—
72C22⋊D11—82no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11C2×D412yes—
76D44—41no—
77C4×D11—22no—
78C4×D11—22no—
79C4×D11—82no—
80C8×C11—21no—
81C8×C11#4112yes—
82C11⋊C8—22no—
83#553—112no—
84#499—111no—
85#482—112no—
86#480—112no—
87#478—112no—
88#469—112no—
89C4×D8D1111yescharacteristic, complemented
90#436—111no—
91#428—112no—
92C22×C11—42no—
93C22×C11—42no—
94C22×C11—42no—
95C22×C11C22×D411yescharacteristic
96C2×D11—22no—
97C2×D11—22no—
98C2×D11—22no—
99C4×C11—21no—
100C4×C11—21no—
101C4×C11—42no—
102C4×C11C2×#4111yescharacteristic
103C4×C112−1+411yescharacteristic
104Dic11—22no—
105Dic11—42no—
106Dic11—42no—
107C2×D8C2×D1111yescharacteristic
108C2×M16—112no—
109#126—222no—
110#125—112no—
111#123—222no—
112#121—112no—
113#121—112no—
114#121—222no—
115C4×D4—111no—
116C4×D4—222no—
117C4×D4C2×D1112yes—
118#117—112no—
119C2×C4⋊C4—112no—
120#107—111no—
121#107—111no—
122#107—112no—
123#107C2×D1111yescharacteristic
124#106—112no—
125#106—112no—
126C4⋊C8—111no—
127#102—112no—
128#102—112no—
129#102C2×D1112yes—
130C22⋊C8—112no—
131C4×C8C2×D1111yescharacteristic
132C2×C11—82no—
133C2×C11#54711yescharacteristic
134C2×C11#57511yescharacteristic
135C2×C11#57611yescharacteristic
136D11—42no—
137C2×D4—111no—
138C2×D4—222no—
139C2×D4—222no—
140C2×D4C22×D1112yes—
141C22×C4—22no—
142C22×C4—112no—
143C22×C4—222no—
144D8—22no—
145M16—224no—
146C2×C8—112no—
147C2×C8C22×D1111yescharacteristic
148C2×C8C22×D1111yescharacteristic
149C4⋊C4—111no—
150C4⋊C4—112no—
151C4⋊C4—112no—
152C4⋊C4—222no—
153C4⋊C4—222no—
154C4⋊C4—222no—
155C4⋊C4C22×D1112yes—
156C22⋊C4—22no—
157C22⋊C4—112no—
158C22⋊C4—222no—
159C22⋊C4—222no—
160C22⋊C4—222no—
161C42—222no—
162C42C22×D1111yescharacteristic
163C11#335511yescharacteristic, complemented, Sylow
164C23—22no—
165C23—112no—
166D4—22no—
167D4—22no—
168D4—441no—
169D4—444no—
170D4—882no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—112no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4—222no—
178C2×C4—882no—
179C2×C4D4×D1111yescharacteristic
180C2×C4D4×D1111yescharacteristic
181C2×C4C23×D1111yescharacteristic
182C8—21no—
183C8—222no—
184C8#433912yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—222no—
189C22—222no—
190C22—222no—
191C22C2×D4×D1111yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—222no—
196C4—442no—
197C4—442no—
198C4C2×#433911yescharacteristic
199C4#6704311yescharacteristic
200C2—82no—
201C2—442no—
202C2#1062308211yescharacteristic
203C2#1062328811yescharacteristic
204C2#1062329911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×D8C2
socleC22×C11C22×D4
hypercenterC4×D8D11
hypocenterC11#3355
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10623089C2semidirect
2. C4×C11×D8C2semidirect
3. #10622772C2semidirect
4. #10622622C2semidirect
5. #10622494C2semidirect
6. #10622397C2semidirect
7. #10622387C2semidirect
8. #10622301C2semidirect
9. #10622296C2semidirect
89. C4×D8D11semidirect
163. C11#3355semidirect

Maximal subgroups

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

subgroupindex
#106230892
C4×C11×D82
#106227722
#106226222
#106224942
#106223972
#106223872
#106223012
#106222962
#335511