Finite Group Databasebeta

← #28389767

Subgroups — #28389767

Order 14464.

250 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 61 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#20298944C211yesmaximal, characteristic, complemented
2#20298878C211yesmaximal, characteristic, complemented
3#20298808C211yesmaximal, characteristic, complemented
4#20298342C211yesmaximal, characteristic, complemented
5Q8⋊#11744751C211yesmaximal, characteristic, complemented
6D4⋊#11744751C211yesmaximal, characteristic, complemented
7#550×C113C211yesmaximal, characteristic
8C2×#14268637—21no—
9#16813622C2211yescharacteristic
10#16813555—21no—
11C4⋊#11744751C2211yescharacteristic
12C4⋊#11744751C2211yescharacteristic
13#16813545—21no—
14#16813543—21no—
15#16813543—22no—
16C4×#11744751C2211yescharacteristic
17C2×#41×C113—21no—
18#127×C113—21no—
19#127×C113C2211yescharacteristic
20#121×C113—22no—
21#121×C113—21no—
22C4×Q8×C113C2211yescharacteristic
23C4×D4×C113—21no—
24C4×D4×C113C2211yescharacteristic
25C2×Dic226—21no—
26#14268637—42no—
27C2×#11744751—21no—
28C2×#11744751—21no—
29C2×#11744751—21no—
30C4⋊Dic113—21no—
31C4⋊Dic113—21no—
32#41×C113—42no—
33#41×C113—42no—
34C2×Q8×C113D411yescharacteristic
35C2×D4×C113—22no—
36C2×D4×C113—22no—
37C2×D4×C113—21no—
38C2×D4×C113—21no—
39C2×D4×C113D411yescharacteristic
40C2×D4×C113D412yes—
41C22×C4×C113—22no—
42C22×C4×C113—21no—
43C4⋊C4×C113—21no—
44C4⋊C4×C113D411yescharacteristic
45C4⋊C4×C113D411yescharacteristic
46C22⋊C4×C113—22no—
47C22⋊C4×C113—21no—
48C42×C113—21no—
49C42×C113C2311yescharacteristic
50C23×C113—21no—
51C23×C113—22no—
52Q8×C113—21no—
53Q8×C113D812yes—
54D4×C113—21no—
55D4×C113—21no—
56D4×C113—42no—
57D4×C113—44no—
58D4×C113—41no—
59D4×C113—41no—
60D4×C113—41no—
61D4×C113—41no—
62D4×C113—82no—
63C2×C4×C113—21no—
64C2×C4×C113—21no—
65C2×C4×C113—21no—
66C2×C4×C113—44no—
67C2×C4×C113—41no—
68C2×C4×C113—41no—
69C2×C4×C113C2×D411yescharacteristic
70C2×C4×C113C2×D411yescharacteristic
71C2×C4×C113C2×D411yescharacteristic
72C2×Dic113—41no—
73Dic226—41no—
74Dic226—41no—
75#11744751—41no—
76#11744751—41no—
77#11744751—41no—
78C22×C113—42no—
79C22×C113—41no—
80C22×C113—41no—
81C22×C113—42no—
82C22×C113—42no—
83C22×C113—41no—
84C22×C113#12011yescharacteristic
85C4×C113—22no—
86C4×C113—21no—
87C4×C113—41no—
88C4×C113—41no—
89C4×C113C2×D811yescharacteristic
90C4×C113#13511yescharacteristic
91C4×C113AGL(1,ℤ/8)11yescharacteristic
92C4×C113#13711yescharacteristic
93Dic113—81no—
94C2×C113—81no—
95C2×C113—82no—
96C2×C113#44711yescharacteristic
97C2×C113#45211yescharacteristic
98C2×C113#45511yescharacteristic
99#1641—1131nomaximal, Sylow
100C113#164111yescharacteristic, complemented, Sylow
101#550D11311yescharacteristic
102#486—1131no—
103#474—1131no—
104#462—1131no—
105#331—1131no—
106Q8⋊C8—1131no—
107D4⋊C8—1131no—
108C2×#41—21no—
109C2×Q16—2261no—
110C4⋊Q8—1131no—
111#127—21no—
112#127C2×D11311yescharacteristic
113#121—22no—
114#121—21no—
115C4×Q8C2×D11311yescharacteristic
116C4×D4—21no—
117C4×D4C2×D11311yescharacteristic
118#107—2261no—
119C4⋊C8—1131no—
120C4⋊C8—1131no—
121#103—2261no—
122#102—2261no—
123#102—2262no—
124C4×C8—1131no—
125#41—42no—
126#41—42no—
127C2×Q8—2261no—
128C2×Q8C22⋊D11311yescharacteristic
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4C22⋊D11311yescharacteristic
134C2×D4C22⋊D11312yes—
135C22×C4—22no—
136C22×C4—21no—
137Q16—4522no—
138C2×C8—2261no—
139C2×C8—2261no—
140C2×C8—2261no—
141C4⋊C4—21no—
142C4⋊C4—2261no—
143C4⋊C4—2261no—
144C4⋊C4C22⋊D11311yescharacteristic
145C4⋊C4C22⋊D11311yescharacteristic
146C22⋊C4—22no—
147C22⋊C4—21no—
148C42—21no—
149C42C22×D11311yescharacteristic
150C23—21no—
151C23—22no—
152Q8—21no—
153Q8—4521no—
154Q8—4521no—
155Q8#1426863212yes—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—44no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—41no—
164D4—82no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—44no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—4521no—
172C2×C4C2×C22⋊D11311yescharacteristic
173C2×C4C2×C22⋊D11311yescharacteristic
174C2×C4C2×C22⋊D11311yescharacteristic
175C8—4521no—
176C8—4521no—
177C8—4521no—
178C22—41no—
179C22—42no—
180C22—42no—
181C22—41no—
182C22—42no—
183C22—41no—
184C22#1681359111yescharacteristic
185C4—21no—
186C4—22no—
187C4—41no—
188C4—41no—
189C4—9041no—
190C4C2×#1426863211yescharacteristic
191C4#1681364211yescharacteristic
192C4#1681364811yescharacteristic
193C4#1681365211yescharacteristic
194C2—81no—
195C2—82no—
196C2#2029873211yescharacteristic
197C2#2029876011yescharacteristic
198C2#2029877611yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting, prime radical#550×C113C2
socleC22×C113#120
hypercenter#550D113
hypocenterC113#1641
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #20298944C2semidirect
2. #20298878C2semidirect
3. #20298808C2semidirect
4. #20298342C2semidirect
5. Q8⋊#11744751C2semidirect
6. D4⋊#11744751C2semidirect
100. C113#1641semidirect

Maximal subgroups

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

subgroupindex
#202989442
#202988782
#202988082
#202983422
Q8⋊#117447512
D4⋊#117447512
#550×C1132
#1641113