Finite Group Databasebeta

← #27194376

Subgroups — #27194376

Order 13184.

240 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 55 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#20268444C211yesmaximal, characteristic
2#20268068C211yesmaximal, characteristic, complemented
3#20267993C211yesmaximal, characteristic, complemented
4#20267537C211yesmaximal, characteristic, complemented
5#20267520C211yesmaximal, characteristic, complemented
6#20267520C211yesmaximal, characteristic, complemented
7#500×C103C211yesmaximal, characteristic, complemented
8C2×#13110106—21no—
9C2×#13110092—21no—
10#15693006—22no—
11#15692997—21no—
12#15692996—21no—
13C4×D412C2211yescharacteristic
14C4×D412C2211yescharacteristic
15C4⋊C4×D103—21no—
16#15692954—21no—
17C4⋊(C103⋊C8)C2211yescharacteristic
18C4⋊(C103⋊C8)C2211yescharacteristic
19#15692945—21no—
20#15692941—21no—
21C4⋊Q8×C103C2211yescharacteristic
22C4⋊Q8×C103C2211yescharacteristic
23#107×C103—22no—
24C4×C8×C103C2211yescharacteristic
25#13110106—42no—
26#13110106—42no—
27C2×D412—22no—
28C2×D412D411yescharacteristic
29C2×D412D411yescharacteristic
30C2×C4×D103—22no—
31C2×C4×D103—21no—
32C2×C4×D103—21no—
33#13110092—42no—
34C2×C103⋊C8—21no—
35C2×C103⋊C8—21no—
36C4⋊Dic103D411yescharacteristic
37C4⋊Dic103D411yescharacteristic
38Dic103⋊C4—22no—
39(C2×D103)⋊C4—22no—
40(C2×D103)⋊C4—21no—
41(C2×D103)⋊C4—21no—
42C2×Q8×C103—21no—
43C2×Q8×C103—21no—
44C2×C8×C103—21no—
45C4⋊C4×C103—21no—
46C4⋊C4×C103—21no—
47C4⋊C4×C103—21no—
48C4⋊C4×C103D412yes—
49C42×C103C2311yescharacteristic
50C22×D103—21no—
51C22×D103—21no—
52Q8×C103—41no—
53Q8×C103—41no—
54Q8×C103—41no—
55Q8×C103—41no—
56C2×C4×C103—22no—
57C2×C4×C103—41no—
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×Dic103—21no—
62C2×Dic103—21no—
63D412—21no—
64D412—21no—
65D412—21no—
66D412—44no—
67D412D812yes—
68C4×D103—44no—
69C4×D103—41no—
70C4×D103—41no—
71C4×D103—41no—
72C4×D103—41no—
73C8×C103—22no—
74C103⋊C8—41no—
75C103⋊C8—41no—
76C22×C103#12011yescharacteristic
77C2×D103—22no—
78C2×D103—41no—
79C2×D103—41no—
80C2×D103—41no—
81C2×D103—41no—
82C2×D103—41no—
83C4×C103—21no—
84C4×C103—42no—
85C4×C103—81no—
86C4×C103C2×D811yescharacteristic
87C4×C103#13511yescharacteristic
88C4×C103AGL(1,ℤ/8)11yescharacteristic
89C4×C103#13711yescharacteristic
90Dic103—41no—
91Dic103—41no—
92C2×C103#44711yescharacteristic
93C2×C103#45211yescharacteristic
94C2×C103#45611yescharacteristic
95D103—42no—
96D103—81no—
97#1647—1031nomaximal, Sylow
98C103#164711yescharacteristic, complemented, Sylow
99#547—1031no—
100#500D10311yescharacteristic, complemented
101#474—1031no—
102#461—1031no—
103#332—1031no—
104D4⋊C8—1031no—
105D4⋊C8—1031no—
106C2×#41—2061no—
107C2×SD16—2061no—
108C4⋊Q8C2×D10311yescharacteristic
109C4⋊Q8C2×D10311yescharacteristic
110#123—2062no—
111C22⋊Q8—2061no—
112#121—2061no—
113C4×D4—1031no—
114C4×D4—1031no—
115C2×C4⋊C4—2061no—
116#107—22no—
117#107—2061no—
118C4⋊C8—1031no—
119C4⋊C8—1031no—
120#103—2061no—
121#102—2061no—
122C4×C8C2×D10311yescharacteristic
123#41—4122no—
124#41—4122no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×D4—1031no—
128C2×D4—1031no—
129C2×D4—2062no—
130C22×C4—2062no—
131C22×C4—2061no—
132C22×C4—2061no—
133SD16—4122no—
134C2×C8—21no—
135C2×C8—2061no—
136C2×C8—2061no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1031no—
141C4⋊C4—1031no—
142C4⋊C4—2062no—
143C4⋊C4C22⋊D10312yes—
144C22⋊C4—2062no—
145C22⋊C4—2061no—
146C22⋊C4—2061no—
147C42C22×D10311yescharacteristic
148C23—2061no—
149C23—2061no—
150Q8—41no—
151Q8—41no—
152Q8—41no—
153Q8—41no—
154D4—1032no—
155D4—4124no—
156D4—2061no—
157D4—2061no—
158D4—2061no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—4124no—
162C2×C4—4121no—
163C2×C4—4121no—
164C2×C4—4121no—
165C2×C4—4121no—
166C2×C4—2061no—
167C2×C4—2061no—
168C2×C4D4×D10311yescharacteristic
169C2×C4D4×D10311yescharacteristic
170C2×C4C2×C22⋊D10311yescharacteristic
171C8—22no—
172C8—4121no—
173C8—4121no—
174C22—4121no—
175C22—4121no—
176C22—4121no—
177C22—4121no—
178C22—4121no—
179C22—2062no—
180C22#1569298911yescharacteristic
181C4—21no—
182C4—42no—
183C4—81no—
184C4—4121no—
185C4—4121no—
186C4D8×D10311yescharacteristic
187C4#1569304411yescharacteristic
188C4#1569304511yescharacteristic
189C4#1569305311yescharacteristic
190C2—8241no—
191C2—4122no—
192C2#2026792311yescharacteristic
193C2#2026795211yescharacteristic
194C2#2026797311yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC42×C103C23
FrattiniC42C22×D103
Fitting#500×C103C2
socleC22×C103#120
prime radical#20268444C2
hypercenter#500D103
hypocenterC103#1647
LCSG ▷ C42×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. #20268068C2semidirect
3. #20267993C2semidirect
4. #20267537C2semidirect
5. #20267520C2semidirect
6. #20267520C2semidirect
7. #500×C103C2semidirect
98. C103#1647semidirect
100. #500D103semidirect

Maximal subgroups

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

subgroupindex
#202684442
#202680682
#202679932
#202675372
#202675202
#500×C1032
#1647103