Finite Group Databasebeta

← #27193605

Subgroups — #27193605

Order 13184.

230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 77 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#20268325C211yesmaximal, characteristic
2#20267848C211yesmaximal, characteristic, complemented
3#20267523C212yesmaximal, complemented
4#20267520C212yesmaximal, complemented
5C2×C4×C8×C103C211yesmaximal, characteristic, complemented
6#15693015—21no—
7#15693013C411yescharacteristic
8#15693009C411yescharacteristic
9#15693004—21no—
10#15693000C411yescharacteristic
11#15692995C411yescharacteristic
12C4×Dic206C2211yescharacteristic
13C4×D412C2211yescharacteristic
14C4×C22⋊D103—21no—
15#15692978—21no—
16C4⋊(C103⋊C8)C2212yes—
17C22⋊(C103⋊C8)—21no—
18#15692932—21no—
19C22×C8×C103—21no—
20C2×C42×C103C2211yescharacteristic
21C4×C8×C103—21no—
22C4×C8×C103C2212yes—
23C2×Dic206C2×C411yescharacteristic
24C2×D412C2×C411yescharacteristic
25C2×C22⋊D103—21no—
26C2×C4×D103—21no—
27C2×C103⋊C8—22no—
28C4⋊Dic103C2×C411yescharacteristic
29C4⋊Dic103C2×C411yescharacteristic
30Dic103⋊C4—21no—
31Dic103⋊C4—21no—
32Dic103⋊C4—21no—
33Dic103⋊C4—21no—
34C22⋊Dic103—21no—
35(C2×D103)⋊C4—21no—
36(C2×D103)⋊C4—21no—
37(C2×D103)⋊C4—21no—
38(C2×D103)⋊C4—21no—
39C4×Dic103—21no—
40C22×C4×C103C2×C411yescharacteristic
41C22×C4×C103D411yescharacteristic
42C22×C4×C103D411yescharacteristic
43C2×C8×C103—24no—
44C2×C8×C103—22no—
45C42×C103C2×C411yescharacteristic
46C42×C103D411yescharacteristic
47C42×C103D411yescharacteristic
48C42×C103C2311yescharacteristic
49C23×C103C22⋊C411yescharacteristic
50C22×D103—21no—
51C2×C4×C103—22no—
52C2×C4×C103—22no—
53C2×C4×C103—22no—
54C2×C4×C103C22⋊C411yescharacteristic
55C2×C4×C103C22⋊C411yescharacteristic
56C2×C4×C103C22⋊C411yescharacteristic
57C2×C4×C103C22×C411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×D411yescharacteristic
60C22⋊D103—42no—
61C2×Dic103—21no—
62C2×Dic103—21no—
63C2×Dic103—21no—
64D412—22no—
65C4×D103—42no—
66Dic206—22no—
67C8×C103—24no—
68C103⋊C8—42no—
69C22×C103—21no—
70C22×C103—21no—
71C22×C103#10412yes—
72C22×C103C2×C22⋊C411yescharacteristic
73C2×D103—41no—
74C2×D103—41no—
75C2×D103—41no—
76C4×C103—21no—
77C4×C103—21no—
78C4×C103—21no—
79C4×C103—21no—
80C4×C103#13112yes—
81C4×C103#13512yes—
82Dic103—41no—
83Dic103—41no—
84Dic103—41no—
85C2×C103—22no—
86C2×C103#40811yescharacteristic
87C2×C103#41611yescharacteristic
88C2×C103C2×#10411yescharacteristic
89D103—81no—
90#1494—1031nomaximal, Sylow
91C103#149411yescharacteristic, complemented, Sylow
92#529—1031no—
93#432—1031no—
94C2×C4×C8D10311yescharacteristic, complemented
95Q8⋊C8—1032no—
96D4⋊C8—1032no—
97C22×C8—21no—
98#126—2061no—
99#125—1031no—
100#124—1031no—
101#123—2061no—
102C22⋊Q8—1031no—
103#121—1031no—
104C4×Q8—1031no—
105C4×D4—1031no—
106C4×D4—2061no—
107#117—2061no—
108C2×C42C2×D10311yescharacteristic
109C4⋊C8—1032no—
110C22⋊C8—2061no—
111#97—2061no—
112C4×C8—21no—
113C4×C8C2×D10312yes—
114C2×Q8—1031no—
115C2×D4—1031no—
116C2×D4—2061no—
117C22×C4—2061no—
118C22×C4C4×D10311yescharacteristic
119C22×C4D41211yescharacteristic
120C22×C4C22⋊D10311yescharacteristic
121C2×C8—24no—
122C2×C8—22no—
123C2×C8—2062no—
124C4⋊C4—1031no—
125C4⋊C4—1031no—
126C4⋊C4—2061no—
127C4⋊C4—2061no—
128C4⋊C4—2061no—
129C4⋊C4—2061no—
130C22⋊C4—2061no—
131C22⋊C4—2061no—
132C22⋊C4—2061no—
133C22⋊C4—2061no—
134C22⋊C4—2061no—
135C42—2061no—
136C42C4×D10311yescharacteristic
137C42D41211yescharacteristic
138C42C22⋊D10311yescharacteristic
139C42C22×D10311yescharacteristic
140C23—2061no—
141C23(C2×D103)⋊C411yescharacteristic
142Q8—2062no—
143D4—4122no—
144D4—2062no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—4122no—
149C2×C4—2061no—
150C2×C4—2061no—
151C2×C4—2061no—
152C2×C4(C2×D103)⋊C411yescharacteristic
153C2×C4(C2×D103)⋊C411yescharacteristic
154C2×C4(C2×D103)⋊C411yescharacteristic
155C2×C4C2×C4×D10311yescharacteristic
156C2×C4C2×C22⋊D10311yescharacteristic
157C2×C4C2×D41211yescharacteristic
158C8—24no—
159C8—4122no—
160C22—21no—
161C22—21no—
162C22—4121no—
163C22—4121no—
164C22—4121no—
165C22#1569294912yes—
166C22C2×(C2×D103)⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—4121no—
172C4—4121no—
173C4—4121no—
174C4#1569302712yes—
175C4#1569304312yes—
176C2—22no—
177C2—8241no—
178C2#2026775711yescharacteristic
179C2#2026778811yescharacteristic
180C2C2×#1569294911yescharacteristic
subgroupG/H
centerC2×C4C2×D412
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
FittingC2×C4×C8×C103C2
socleC22×C103C2×C22⋊C4
prime radical#15692995C4
cosocleC42×C103C23
hypercenterC2×C4×C8D103
hypocenterC103#1494
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. #20267848C2semidirect
3. #20267523C2semidirect
4. #20267520C2semidirect
5. C2×C4×C8×C103C2semidirect
91. C103#1494semidirect
94. C2×C4×C8D103semidirect

Maximal subgroups

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

subgroupindex
#202683252
#202678482
#202675232
#202675202
C2×C4×C8×C1032
#1494103