Finite Group Databasebeta

← #27195679

Subgroups — #27195679

Order 13184.

314 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 85 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#20268365C211yesmaximal, characteristic
2#20268269C211yesmaximal, characteristic, complemented
3#20267807C212yesmaximal
4#20267548C212yesmaximal, complemented
5C2×#101×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C2211yescharacteristic
7#15693019C412yescomplemented
8#15693010C412yescomplemented
9#15693004—22no—
10#15692997—22no—
11Q8×Dic103—24no—
12#15692980—22no—
13#15692980C2211yescharacteristic
14#15692980C2212yes—
15#15692947—24no—
16C22×Q8×C103C2211yescharacteristic
17C2×M16×C103C2212yes—
18#101×C103—22no—
19#13110105—22no—
20#13110105—22no—
21C2×Dic206C2×C411yescharacteristic
22C2×D412C2×C411yescharacteristic
23C2×C22⋊D103—21no—
24C2×C4×D103—21no—
25C4⋊Dic103—24no—
26C4⋊Dic103—22no—
27C4⋊Dic103—21no—
28Dic103⋊C4—24no—
29C22⋊Dic103—22no—
30C22⋊Dic103—21no—
31(C2×D103)⋊C4—24no—
32C4×Dic103—24no—
33C4×Dic103C2×C412yes—
34C4×Dic103D414yes—
35C2×Q8×C103—22no—
36C2×Q8×C103—22no—
37C2×Q8×C103C2×C412yes—
38C2×Q8×C103D412yes—
39C22×C4×C103D412yes—
40C22×C4×C103C2311yescharacteristic
41M16×C103—22no—
42M16×C103—22no—
43C2×C8×C103—22no—
44C23×C103C2×D411yescharacteristic
45C22×D103—21no—
46Q8×C103—24no—
47Q8×C103—24no—
48C2×C4×C103—22no—
49C2×C4×C103—22no—
50C2×C4×C103C22⋊C414yes—
51C2×C4×C103C22×C411yescharacteristic
52C2×C4×C103C2×D412yes—
53C2×C4×C103C2×D411yescharacteristic
54C2×C4×C103#4112yes—
55C22⋊D103—41no—
56C22⋊D103—41no—
57C2×Dic103—22no—
58C2×Dic103—21no—
59C2×Dic103—24no—
60D412—22no—
61C4×D103—42no—
62Dic206—22no—
63C8×C103—42no—
64C22×C103—41no—
65C22×C103C2×C22⋊C411yescharacteristic
66C22×C103#12011yescharacteristic
67C22×C103#12311yescharacteristic
68C2×D103—42no—
69C2×D103—41no—
70C4×C103—24no—
71C4×C103C4×D412yes—
72C4×C103#12112yes—
73Dic103—44no—
74Dic103—42no—
75Dic103—41no—
76C2×C103—21no—
77C2×C103—21no—
78C2×C103—21no—
79C2×C103#38611yescharacteristic
80D103—81no—
81#1912—1031nomaximal, Sylow
82C103#191211yescharacteristic, complemented, Sylow
83#536—1031no—
84#519—1031no—
85#421—1032no—
86C2×#101D10311yescharacteristic, complemented
87H(3,ℤ/4)—1032no—
88C2×#41—1031no—
89C22×Q8C2×D10311yescharacteristic
90C2×M16C2×D10312yes—
91C4⋊Q8—1032no—
92#124—1032no—
93#123—2062no—
94C22⋊Q8—2062no—
95C4×Q8—2064no—
96#117—1032no—
97#117—1031no—
98#117—2062no—
99#104—2064no—
100#101—22no—
101#41—2062no—
102#41—2062no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—1031no—
106C2×Q8C4×D10312yes—
107C2×Q8C22⋊D10312yes—
108C2×D4—1031no—
109C2×D4—2061no—
110C22×C4—2061no—
111C22×C4D41212yes—
112C22×C4C22×D10311yescharacteristic
113M16—22no—
114M16—22no—
115C2×C8—22no—
116C4⋊C4—2064no—
117C4⋊C4—2064no—
118C4⋊C4—2062no—
119C4⋊C4—2061no—
120C22⋊C4—2062no—
121C22⋊C4—2061no—
122C22⋊C4—2064no—
123C42—1032no—
124C42—1034no—
125C42—2064no—
126C23—2061no—
127C23C2×D41211yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—2062no—
131D4—4121no—
132D4—4121no—
133D4—2062no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—4122no—
137C2×C4—2062no—
138C2×C4—2061no—
139C2×C4—2064no—
140C2×C4(C2×D103)⋊C414yes—
141C2×C4C2×C4×D10311yescharacteristic
142C2×C4D4×D10312yes—
143C2×C4C2×C22⋊D10311yescharacteristic
144C2×C4#1311010412yes—
145C8—42no—
146C22—41no—
147C22—4122no—
148C22—4121no—
149C22C2×(C2×D103)⋊C411yescharacteristic
150C22#1569299111yescharacteristic
151C22#1569300511yescharacteristic
152C4—24no—
153C4—4124no—
154C4—4122no—
155C4—4121no—
156C4(C22⋊D103)⋊C412yes—
157C4#1569299312yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—8241no—
162C2#2026766811yescharacteristic
subgroupG/H
centerC2#20267668
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×#101×C103C2
socleC2×C103#386
prime radicalC2×#13110105C22
cosocleC22×C4×C103C23
hypercenterC2×#101D103
hypocenterC103#1912
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #20268269C2semidirect
4. #20267548C2semidirect
5. C2×#101×C103C2semidirect
7. #15693019C4semidirect
8. #15693010C4semidirect
82. C103#1912semidirect
86. C2×#101D103semidirect

Maximal subgroups

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

subgroupindex
#202683652
#202682692
#202678072
#202675482
C2×#101×C1032
#1912103