Finite Group Databasebeta

← #27193777

Subgroups — #27193777

Order 13184.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#20268340C211yesmaximal, characteristic
2#20267846C212yesmaximal, complemented
3#20267531C211yesmaximal, characteristic, complemented
4#20267530C212yesmaximal, complemented
5#329×C103C211yesmaximal, characteristic, complemented
6C2×#13110106C411yescharacteristic
7C2×#13110104C411yescharacteristic
8#15693019C411yescharacteristic
9#15693017C411yescharacteristic
10#15693009C2211yescharacteristic
11#15692994—22no—
12(C22⋊D103)⋊C4—22no—
13C42×D103C2211yescharacteristic
14Dic103⋊C8—22no—
15(C2×D103)⋊C8—22no—
16#15692932C2212yes—
17#124×C103C2211yescharacteristic
18#97×C103C2212yes—
19#13110106—42no—
20#13110104—42no—
21C2×Dic206C2×C411yescharacteristic
22C2×D412—21no—
23C2×D412C2×C411yescharacteristic
24C2×C22⋊D103—21no—
25C2×C22⋊D103—22no—
26C22×Dic103—21no—
27C2×C4×D103—21no—
28C2×C4×D103C2×C411yescharacteristic
29C2×C4×D103D412yes—
30C2×C103⋊C8—22no—
31Dic103⋊C4—22no—
32(C2×D103)⋊C4—22no—
33C4×Dic103C2×C411yescharacteristic
34C4×Dic103D412yes—
35C2×Q8×C103C2×C411yescharacteristic
36C2×D4×C103C2×C411yescharacteristic
37C2×C8×C103—22no—
38C22⋊C4×C103—22no—
39C42×C103C2311yescharacteristic
40C23×C103—21no—
41C22×D103—21no—
42C22×D103C22⋊C411yescharacteristic
43Q8×C103—41no—
44D4×C103—41no—
45C2×C4×C103—21no—
46C2×C4×C103C22×C411yescharacteristic
47C2×C4×C103C2×D412yes—
48C22⋊D103—44no—
49C22⋊D103—42no—
50C2×Dic103—21no—
51C2×Dic103—42no—
52C2×Dic103C22⋊C412yes—
53C2×Dic103C22⋊C411yescharacteristic
54D412—41no—
55D412—42no—
56C4×D103—22no—
57C4×D103—42no—
58C4×D103—42no—
59Dic206—41no—
60C8×C103—42no—
61C103⋊C8—42no—
62C22×C103—41no—
63C22×C103—42no—
64C22×C103C2×C22⋊C411yescharacteristic
65C2×D103—21no—
66C2×D103—22no—
67C2×D103—41no—
68C2×D103—42no—
69C4×C103—21no—
70C4×C103—22no—
71C4×C103—41no—
72Dic103—22no—
73Dic103—41no—
74Dic103#10012yes—
75C2×C103—81no—
76C2×C103C2×#10011yescharacteristic
77C2×C103#42112yes—
78D103—41no—
79D103—81no—
80#1536—1031nomaximal, Sylow
81C103#153611yescharacteristic, complemented, Sylow
82#532—1031no—
83#432—1032no—
84#329—1031no—
85#329—1032no—
86#329D10311yescharacteristic, complemented
87C2×#41—1031no—
88C2×#41—1031no—
89C4⋊Q8—1031no—
90#127—1031no—
91#124—1031no—
92#124C2×D10311yescharacteristic
93#121—2062no—
94C4×D4—2062no—
95C2×C42—1031no—
96C4⋊C8—2062no—
97C22⋊C8—2062no—
98#97—1032no—
99#97C2×D10312yes—
100#41—4122no—
101#41—4122no—
102C2×Q8—1031no—
103C2×Q8C4×D10311yescharacteristic
104C2×D4—1031no—
105C2×D4—2061no—
106C2×D4—2062no—
107C2×D4—2061no—
108C2×D4C4×D10311yescharacteristic
109C22×C4—1032no—
110C22×C4—1031no—
111C22×C4—2061no—
112C22×C4—2061no—
113C2×C8—22no—
114C2×C8—2062no—
115C4⋊C4—2062no—
116C22⋊C4—22no—
117C22⋊C4—2062no—
118C42—1031no—
119C42—1032no—
120C42C22×D10311yescharacteristic
121C23—21no—
122C23—1031no—
123C23—2061no—
124Q8—41no—
125Q8—4121no—
126D4—41no—
127D4—4121no—
128D4—4122no—
129D4—4122no—
130D4—4124no—
131C2×C4—21no—
132C2×C4—1031no—
133C2×C4—1032no—
134C2×C4—4122no—
135C2×C4—4122no—
136C2×C4—4122no—
137C2×C4—2062no—
138C2×C4—2061no—
139C2×C4C2×C4×D10311yescharacteristic
140C2×C4D4×D10312yes—
141C8—42no—
142C8—4122no—
143C22—42no—
144C22—41no—
145C22—4122no—
146C22—4121no—
147C22—2062no—
148C22—2061no—
149C22C22⋊C4×D10311yescharacteristic
150C4—22no—
151C4—21no—
152C4—41no—
153C4—1032no—
154C4—4121no—
155C4—2062no—
156C2—81no—
157C2—8241no—
158C2—4121no—
159C2#100×D10311yescharacteristic
160C2#2026780612yes—
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC42C22×D103
Fitting#329×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268340C2
cosocleC42×C103C23
hypercenter#329D103
hypocenterC103#1536
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20267846C2semidirect
3. #20267531C2semidirect
4. #20267530C2semidirect
5. #329×C103C2semidirect
81. C103#1536semidirect
86. #329D103semidirect

Maximal subgroups

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

subgroupindex
#202683402
#202678462
#202675312
#202675302
#329×C1032
#1536103