Finite Group Databasebeta

← #28389765

Subgroups — #28389765

Order 14464.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#20299270C211yesmaximal, characteristic
2#20298946C211yesmaximal, characteristic, complemented
3#20298875C211yesmaximal, characteristic, complemented
4#20298341C211yesmaximal, characteristic, complemented
5Q8⋊#11744751C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic, complemented
7#462×C113C211yesmaximal, characteristic, complemented
8C2×#14268648—21no—
9#16813619—21no—
10#16813619C2211yescharacteristic
11#16813597—22no—
12#16813597—21no—
13C4×D452—21no—
14C4×D452C2211yescharacteristic
15#16813555—21no—
16C4⋊#11744751C2211yescharacteristic
17#16813542—21no—
18#16813542—22no—
19C4×#11744751C2211yescharacteristic
20C2×Q16×C113—21no—
21C4⋊Q8×C113C2211yescharacteristic
22C4×Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24#103×C113—21no—
25#14268648—42no—
26#14268648—42no—
27C2×D452—22no—
28C2×D452—21no—
29C2×D452—21no—
30C2×D452—22no—
31C2×D452D411yescharacteristic
32C2×D452D412yes—
33C2×C4×D113—22no—
34C2×C4×D113—21no—
35C2×#11744751—21no—
36C2×#11744751—21no—
37C4⋊Dic113D411yescharacteristic
38#14268624—22no—
39#14268624—21no—
40C2×Q8×C113—21no—
41C2×Q8×C113D411yescharacteristic
42Q16×C113—42no—
43C2×C8×C113—21no—
44C4⋊C4×C113—21no—
45C4⋊C4×C113—21no—
46C4⋊C4×C113—21no—
47C4⋊C4×C113D411yescharacteristic
48C42×C113—21no—
49C42×C113C2311yescharacteristic
50C22×D113—21no—
51C22×D113—22no—
52Q8×C113—21no—
53Q8×C113—41no—
54Q8×C113—41no—
55Q8×C113D812yes—
56C2×C4×C113—21no—
57C2×C4×C113—21no—
58C2×C4×C113—41no—
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113C2×D411yescharacteristic
62C2×Dic113—21no—
63D452—21no—
64D452—21no—
65D452—42no—
66D452—44no—
67D452—41no—
68D452—41no—
69D452—41no—
70D452—41no—
71D452—82no—
72C4×D113—44no—
73C4×D113—41no—
74C4×D113—41no—
75C8×C113—41no—
76#11744751—41no—
77#11744751—41no—
78C22×C113#12011yescharacteristic
79C2×D113—42no—
80C2×D113—41no—
81C2×D113—41no—
82C2×D113—42no—
83C2×D113—42no—
84C2×D113—41no—
85C4×C113—22no—
86C4×C113—21no—
87C4×C113—41no—
88C4×C113—81no—
89C4×C113C2×D811yescharacteristic
90C4×C113#13511yescharacteristic
91C4×C113AGL(1,ℤ/8)11yescharacteristic
92C4×C113#13711yescharacteristic
93Dic113—41no—
94C2×C113#44711yescharacteristic
95C2×C113#45211yescharacteristic
96C2×C113#45511yescharacteristic
97D113—81no—
98D113—82no—
99#1641—1131nomaximal, Sylow
100C113#164111yescharacteristic, complemented, Sylow
101#550—1131no—
102#486—1131no—
103#474—1131no—
104#462D11311yescharacteristic, complemented
105#331—1131no—
106Q8⋊C8—1131no—
107D4⋊C8—1131no—
108C2×#41—2261no—
109C2×Q16—21no—
110C4⋊Q8C2×D11311yescharacteristic
111#127—1131no—
112#127—2261no—
113#121—2262no—
114#121—2261no—
115C4×Q8C2×D11311yescharacteristic
116C4×D4—1131no—
117C4×D4—2261no—
118#107—2261no—
119C4⋊C8—1131no—
120C4⋊C8C2×D11311yescharacteristic
121#103—21no—
122#102—2261no—
123#102—2262no—
124C4×C8—1131no—
125#41—4522no—
126#41—4522no—
127C2×Q8—21no—
128C2×Q8C22⋊D11311yescharacteristic
129C2×D4—1132no—
130C2×D4—1131no—
131C2×D4—2262no—
132C2×D4—2262no—
133C2×D4—2261no—
134C2×D4—2261no—
135C22×C4—2262no—
136C22×C4—2261no—
137Q16—42no—
138C2×C8—21no—
139C2×C8—2261no—
140C2×C8—2261no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—1131no—
145C4⋊C4C22⋊D11311yescharacteristic
146C22⋊C4—2262no—
147C22⋊C4—2261no—
148C42—21no—
149C42C22×D11311yescharacteristic
150C23—2262no—
151C23—2261no—
152Q8—21no—
153Q8—41no—
154Q8—41no—
155Q8#1426863212yes—
156D4—9042no—
157D4—4522no—
158D4—4524no—
159D4—4521no—
160D4—4521no—
161D4—4521no—
162D4—4521no—
163D4—2261no—
164D4—2261no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—4524no—
169C2×C4—4521no—
170C2×C4—4521no—
171C2×C4—2261no—
172C2×C4D4×D11311yescharacteristic
173C2×C4D4×D11311yescharacteristic
174C2×C4C2×C22⋊D11311yescharacteristic
175C8—41no—
176C8—4521no—
177C8—4521no—
178C22—4522no—
179C22—4521no—
180C22—4521no—
181C22—4522no—
182C22—4522no—
183C22—4521no—
184C22#1681359011yescharacteristic
185C4—21no—
186C4—22no—
187C4—41no—
188C4—81no—
189C4—4521no—
190C4C2×#1426863211yescharacteristic
191C4#1681364511yescharacteristic
192C4#1681364711yescharacteristic
193C4#1681365411yescharacteristic
194C2—9042no—
195C2—9041no—
196C2#2029873111yescharacteristic
197C2#2029875911yescharacteristic
198C2#2029877411yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#462×C113C2
socleC22×C113#120
prime radical#20299270C2
hypercenter#462D113
hypocenterC113#1641
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #20298946C2semidirect
3. #20298875C2semidirect
4. #20298341C2semidirect
5. Q8⋊#11744751C2semidirect
6. #20298325C2semidirect
7. #462×C113C2semidirect
100. C113#1641semidirect
104. #462D113semidirect

Maximal subgroups

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

subgroupindex
#202992702
#202989462
#202988752
#202983412
Q8⋊#117447512
#202983252
#462×C1132
#1641113