Finite Group Databasebeta

← #27196835

Subgroups — #27196835

Order 13184.

262 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 65 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#20268355C211yesmaximal, characteristic
2#20267775C211yesmaximal, characteristic, complemented
3#20267587C214yesmaximal, complemented
4#413×C103C211yesmaximal, characteristic, complemented
5C22×D412C411yescharacteristic
6C2×#13110089—21no—
7#15693017C412yes—
8#15693010C2212yes—
9#15692995—21no—
10#15692995—21no—
11#15692989—21no—
12#15692989—21no—
13#15692980C411yescharacteristic
14#15692940C2212yescomplemented
15#15692938—21no—
16C2×#41×C103C2211yescharacteristic
17C2×M16×C103—21no—
18#101×C103C2212yescomplemented
19#100×C103—21no—
20C23×D103—21no—
21C2×D412—21no—
22C2×D412—41no—
23C2×D412—41no—
24C2×D412C2×C412yes—
25C2×C22⋊D103—22no—
26C2×C22⋊D103—22no—
27#13110089—22no—
28#13110089—41no—
29C2×C103⋊C8—41no—
30C4⋊Dic103—21no—
31C22⋊Dic103—21no—
32(C2×D103)⋊C4—22no—
33(C2×D103)⋊C4—22no—
34C4×Dic103C2×C412yes—
35#41×C103—41no—
36#41×C103—41no—
37C2×Q8×C103C2311yescharacteristic
38C2×D4×C103C2×C411yescharacteristic
39C2×D4×C103D411yescharacteristic
40C2×D4×C103D411yescharacteristic
41C22×C4×C103C2×C411yescharacteristic
42C22×C4×C103D411yescharacteristic
43C22×C4×C103D411yescharacteristic
44M16×C103—22no—
45M16×C103—41no—
46C2×C8×C103—41no—
47C23×C103C22⋊C411yescharacteristic
48C23×C103C22⋊C411yescharacteristic
49C23×C103C22⋊C411yescharacteristic
50C22×D103—22no—
51C22×D103—42no—
52C22×D103—82no—
53Q8×C103—41no—
54D4×C103—41no—
55D4×C103—41no—
56D4×C103—41no—
57C2×C4×C103—21no—
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—21no—
62C2×C4×C103—21no—
63C2×C4×C103C22⋊C411yescharacteristic
64C2×C4×C103C22×C411yescharacteristic
65C2×C4×C103C2×D411yescharacteristic
66C2×C4×C103C2×D411yescharacteristic
67C22⋊D103—82no—
68C22⋊D103—82no—
69C2×Dic103—22no—
70D412—42no—
71D412—41no—
72D412—41no—
73C8×C103—42no—
74C103⋊C8—42no—
75C22×C103—21no—
76C22×C103—21no—
77C22×C103—21no—
78C22×C103—41no—
79C22×C103—41no—
80C22×C103—41no—
81C22×C103C2×C22⋊C411yescharacteristic
82C2×D103—42no—
83C2×D103—42no—
84C2×D103—42no—
85C2×D103—84no—
86C4×C103—21no—
87C4×C103—21no—
88C4×C103—21no—
89C4×C103#9911yescharacteristic
90C4×C103#9911yescharacteristic
91Dic103—42no—
92C2×C103—21no—
93C2×C103—41no—
94C2×C103—41no—
95C2×C103—41no—
96C2×C103C2×#9911yescharacteristic
97D103—82no—
98#2134—1031nomaximal, Sylow
99C103#213411yescharacteristic, complemented, Sylow
100#535—1031no—
101#413—1031no—
102#413D10311yescharacteristic, complemented
103#355—1034no—
104C2×#41C2×D10311yescharacteristic
105C22×D4—1031no—
106C2×M16—21no—
107C2×M16—2061no—
108#127—1032no—
109#124—1032no—
110#121—2061no—
111#121—2061no—
112#120—2061no—
113#120—2061no—
114#117—1031no—
115#101—1032no—
116#101C2×D10312yescomplemented
117#100—21no—
118#100—2061no—
119C24—2061no—
120#41—41no—
121#41—41no—
122C2×Q8C22×D10311yescharacteristic
123C2×D4—1032no—
124C2×D4—4121no—
125C2×D4—4121no—
126C2×D4—2062no—
127C2×D4—2062no—
128C2×D4—2061no—
129C2×D4C4×D10311yescharacteristic
130C2×D4D41211yescharacteristic
131C2×D4C22⋊D10311yescharacteristic
132C22×C4C4×D10311yescharacteristic
133C22×C4D41211yescharacteristic
134C22×C4C22⋊D10311yescharacteristic
135M16—22no—
136M16—41no—
137M16—4121no—
138M16—2062no—
139C2×C8—41no—
140C2×C8—4121no—
141C4⋊C4—2061no—
142C22⋊C4—2061no—
143C22⋊C4—2062no—
144C22⋊C4—2062no—
145C42—1032no—
146C23—8242no—
147C23—4122no—
148C23—2062no—
149C23(C2×D103)⋊C411yescharacteristic
150C23(C2×D103)⋊C411yescharacteristic
151C23(C2×D103)⋊C411yescharacteristic
152Q8—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—8242no—
157D4—8242no—
158D4—4122no—
159D4—4121no—
160D4—4121no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—2062no—
168C2×C4(C2×D103)⋊C411yescharacteristic
169C2×C4C2×C4×D10311yescharacteristic
170C2×C4C2×C22⋊D10311yescharacteristic
171C2×C4C2×D41211yescharacteristic
172C8—42no—
173C8—4122no—
174C22—21no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—41no—
180C22—8244no—
181C22—4122no—
182C22—4122no—
183C22—4122no—
184C22C2×(C2×D103)⋊C411yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—4122no—
189C4#1569293511yescharacteristic
190C4#1569293511yescharacteristic
191C2—21no—
192C2—41no—
193C2—41no—
194C2—41no—
195C2—8242no—
196C2C2×#1569293511yescharacteristic
subgroupG/H
centerC2C2×#15692935
commutatorC2×C4×C103C22×C4
FrattiniC2×Q8C22×D103
Fitting#413×C103C2
socleC2×C103C2×#99
prime radical#20268355C2
cosocleC2×Q8×C103C23
hypercenter#413D103
hypocenterC103#2134
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #20267775C2semidirect
3. #20267587C2semidirect
4. #413×C103C2semidirect
14. #15692940C22semidirect
18. #101×C103C22semidirect
99. C103#2134semidirect
102. #413D103semidirect
116. #101C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683552
#202677752
#202675872
#413×C1032
#2134103