Finite Group Databasebeta

← #13069353

Subgroups — #13069353

Order 1408.

240 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 99 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×#66879C211yesmaximal, characteristic
2#10622598C211yesmaximal, characteristic
3#10622586C211yesmaximal, characteristic
4C2×#66872C211yesmaximal, characteristic
5C2×#66871C211yesmaximal, characteristic
6C11×#340C211yesmaximal, characteristic
7#10622189C211yesmaximal, characteristic
8C22×C8×C11C2211yescharacteristic
9C2×C11×C4⋊C4C2211yescharacteristic
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic11—21no—
12C2×C4⋊Dic11C2211yescharacteristic
13C2×C4⋊Dic11C2211yescharacteristic
14C2×Dic11⋊C4—21no—
15C2×C4×Dic11C2211yescharacteristic
16C22×C11⋊C8C2211yescharacteristic
17C11⋊#95—21no—
18C11⋊#95—21no—
19#66879—22no—
20#66872—22no—
21#66871C414yescomplemented
22C22×C4×C11—21no—
23C22×C4×C11—21no—
24C22×C4×C11C2311yescharacteristic
25C22×Dic11—21no—
26C22×Dic11—21no—
27C22×Dic11D411yescharacteristic
28C22×Dic11D411yescharacteristic
29C2×C8×C11—21no—
30C2×C8×C11—21no—
31C2×C8×C11Q812yes—
32C11×C4⋊C4—21no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—21no—
35C11×C4⋊C4C2×C412yes—
36C4⋊Dic11—21no—
37C4⋊Dic11—21no—
38C4⋊Dic11—21no—
39C4⋊Dic11—42no—
40C4⋊Dic11C2×C412yes—
41Dic11⋊C4—42no—
42C4×Dic11—21no—
43C4×Dic11—21no—
44C2×C11⋊C8C2×C412yes—
45C2×C11⋊C8D412yes—
46C2×C11⋊C8Q812yes—
47#1943—111nomaximal, Sylow
48C23×C11C2×D411yescharacteristic
49C2×C4×C11—22no—
50C2×C4×C11—41no—
51C2×C4×C11—41no—
52C2×C4×C11—41no—
53C2×C4×C11—41no—
54C2×C4×C11—41no—
55C2×C4×C11C22×C411yescharacteristic
56C2×C4×C11C2×D411yescharacteristic
57C2×C4×C11C2×Q811yescharacteristic
58C2×C4×C11C2×Q811yescharacteristic
59C2×C4×C11#4111yescharacteristic
60C2×C4×C11#4111yescharacteristic
61C2×Dic11—22no—
62C2×Dic11—21no—
63C2×Dic11—21no—
64C2×Dic11—21no—
65C2×Dic11—21no—
66C2×Dic11—21no—
67C2×Dic11—21no—
68C2×Dic11—41no—
69C2×Dic11—41no—
70C2×Dic11—41no—
71C2×Dic11—41no—
72C2×Dic11—41no—
73C8×C11—22no—
74C11⋊C8C4⋊C414yescomplemented
75C2×#107—111no—
76C2×#106—111no—
77C2×#97—111no—
78#389—111no—
79#389—111no—
80#340—111no—
81#340D1111yescharacteristic
82C22×C11C4×D411yescharacteristic
83C22×C11#12111yescharacteristic
84C22×C11C4⋊Q811yescharacteristic
85C22×C11AGL(1,ℤ/8)11yescharacteristic
86C22×C11AGL(1,ℤ/8)11yescharacteristic
87C22×C11#13711yescharacteristic
88C22×C11#13711yescharacteristic
89C4×C11—42no—
90C4×C11—81no—
91C4×C11C2×C4⋊C411yescharacteristic
92C4×C11C4×Q811yescharacteristic
93C4×C11C22⋊Q811yescharacteristic
94C4×C11#12511yescharacteristic
95Dic11—42no—
96Dic11—41no—
97Dic11—41no—
98Dic11—81no—
99C22×C8—111no—
100C22×C8C2×D1111yescharacteristic
101C2×C4⋊C4—111no—
102C2×C4⋊C4—111no—
103C2×C4⋊C4—221no—
104C2×C4⋊C4—221no—
105C2×C4⋊C4C2×D1111yescharacteristic
106C2×C4⋊C4C2×D1111yescharacteristic
107C2×C42—111no—
108#107—114no—
109#106—222no—
110#97—222no—
111#95—221no—
112#95—221no—
113C2×C11#38911yescharacteristic
114C2×C11#44111yescharacteristic
115C2×C11#44211yescharacteristic
116C2×C11#46811yescharacteristic
117C2×C11#46811yescharacteristic
118C2×C11#50111yescharacteristic
119C2×C11#50111yescharacteristic
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—111no—
123C22×C4—111no—
124C22×C4—221no—
125C22×C4—221no—
126C22×C4C22×D1111yescharacteristic
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—112no—
130C2×C8—112no—
131C2×C8—112no—
132C2×C8Dic2212yes—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—112no—
137C4⋊C4—221no—
138C4⋊C4—221no—
139C4⋊C4—221no—
140C4⋊C4—442no—
141C4⋊C4—442no—
142C4⋊C4C4×D1112yes—
143C42—221no—
144C42—221no—
145C11#194311yescharacteristic, complemented, Sylow
146C23D4×D1111yescharacteristic
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—222no—
154C2×C4—221no—
155C2×C4—221no—
156C2×C4—221no—
157C2×C4—221no—
158C2×C4—221no—
159C2×C4—221no—
160C2×C4—441no—
161C2×C4—441no—
162C2×C4—441no—
163C2×C4—441no—
164C2×C4—441no—
165C2×C4C2×Dic2211yescharacteristic
166C2×C4C2×C4×D1111yescharacteristic
167C2×C4#433911yescharacteristic
168C2×C4D4×D1111yescharacteristic
169C2×C4#434111yescharacteristic
170C2×C4Q8×D1111yescharacteristic
171C8—22no—
172C8—114no—
173C22(C22⋊D11)⋊C411yescharacteristic
174C22#6693711yescharacteristic
175C22#6694111yescharacteristic
176C22#6696411yescharacteristic
177C22#6696711yescharacteristic
178C22#6696811yescharacteristic
179C22#6697111yescharacteristic
180C4—42no—
181C4—81no—
182C4—441no—
183C4—442no—
184C4—441no—
185C4—881no—
186C4C4×Dic2211yescharacteristic
187C4#6693111yescharacteristic
188C4#6694211yescharacteristic
189C4C4⋊C4×D1111yescharacteristic
190C2#1062226011yescharacteristic
191C2#1062239311yescharacteristic
192C2#1062239811yescharacteristic
193C2#1062240211yescharacteristic
194C2#1062242511yescharacteristic
195C2#1062246911yescharacteristic
196C2#1062248911yescharacteristic
subgroupG/H
centerC23D4×D11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#340C2
socle, prime radicalC23×C11C2×D4
cosocleC22×C4×C11C23
hypercenter#340D11
hypocenterC11#1943
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
21. #66871C4semidirect
74. C11⋊C8C4⋊C4semidirect
145. C11#1943semidirect

Maximal subgroups

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

subgroupindex
C2×#668792
#106225982
#106225862
C2×#668722
C2×#668712
C11×#3402
#106221892
#194311