Finite Group Databasebeta

← #27195560

Subgroups — #27195560

Order 13184.

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

normal subgroups only

This group has 342 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#20268558C211yesmaximal, characteristic, complemented
2#20268298C211yesmaximal, characteristic
3#20267754C212yesmaximal, complemented
4#20267563C212yesmaximal, complemented
5#413×C103C211yesmaximal, characteristic, complemented
6C22×C4×D103C2211yescharacteristic
7#15693028—24no—
8C2×#13110089—22no—
9C2×#13110089C2212yes—
10#15693002C412yes—
11#15692997—21no—
12#15692992—21no—
13#15692989C412yes—
14C4×C22⋊D103—22no—
15#15692980C2211yescharacteristic
16(C2×D103)⋊C8—24no—
17C2×#41×C103C2211yescharacteristic
18C2×M16×C103C2212yes—
19#101×C103—21no—
20#100×C103—21no—
21C23×D103C2×C411yescharacteristic
22C2×C22⋊D103—22no—
23C22×Dic103C2×C411yescharacteristic
24C2×C4×D103—22no—
25C2×C4×D103—21no—
26C2×C4×D103—21no—
27C2×C4×D103—22no—
28#13110089—24no—
29#13110089—22no—
30#13110089—22no—
31C2×C103⋊C8—24no—
32C2×C103⋊C8D414yescomplemented
33C4⋊Dic103—21no—
34Dic103⋊C4—22no—
35C22⋊Dic103—22no—
36C22⋊Dic103C2×C412yes—
37(C2×D103)⋊C4—22no—
38C4×Dic103—21no—
39#41×C103—22no—
40#41×C103—22no—
41C2×Q8×C103D411yescharacteristic
42C2×D4×C103C2×C412yes—
43C2×D4×C103D411yescharacteristic
44C22×C4×C103D412yes—
45C22×C4×C103C2311yescharacteristic
46M16×C103—22no—
47M16×C103—22no—
48C2×C8×C103—22no—
49C23×C103C22⋊C412yes—
50C23×C103C22×C411yescharacteristic
51C22×D103—21no—
52C22×D103—22no—
53C22×D103—42no—
54Q8×C103—22no—
55D4×C103—24no—
56D4×C103—22no—
57C2×C4×C103—22no—
58C2×C4×C103—22no—
59C2×C4×C103C22⋊C412yes—
60C2×C4×C103C2×D412yes—
61C2×C4×C103C2×D411yescharacteristic
62C2×C4×C103C2×D411yescharacteristic
63C2×C4×C103#4112yes—
64C22⋊D103—44no—
65C2×Dic103—22no—
66C2×Dic103—21no—
67C2×Dic103—22no—
68C4×D103—41no—
69C4×D103—42no—
70C4×D103—41no—
71C8×C103—42no—
72C103⋊C8—24no—
73C22×C103—22no—
74C22×C103—41no—
75C22×C103—42no—
76C22×C103C2×C22⋊C411yescharacteristic
77C22×C103C4×D412yes—
78C2×D103—22no—
79C2×D103—24no—
80C2×D103—41no—
81C2×D103—42no—
82C2×D103—41no—
83C4×C103—22no—
84C4×C103#12011yescharacteristic
85C4×C103#12112yes—
86C4×C103#12311yescharacteristic
87Dic103—42no—
88Dic103—41no—
89C2×C103—21no—
90C2×C103—22no—
91C2×C103—42no—
92C2×C103#38611yescharacteristic
93D103—42no—
94#1891—1031nomaximal, Sylow
95C103#189111yescharacteristic, complemented, Sylow
96#568—1031no—
97#525—1031no—
98#413D10311yescharacteristic, complemented
99#407—1032no—
100#344—1032no—
101C2×#41C2×D10311yescharacteristic
102C23×C4—1031no—
103#131—2064no—
104C2×M16—1032no—
105C2×M16—2062no—
106C2×M16C2×D10312yes—
107#123—1032no—
108C22⋊Q8—2061no—
109#121—2061no—
110#120—1032no—
111C4×D4—2062no—
112#117—1031no—
113#101—21no—
114#100—21no—
115C22⋊C8—2064no—
116C24—1031no—
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D10311yescharacteristic
120C2×D4—2062no—
121C2×D4C4×D10312yes—
122C2×D4C22⋊D10311yescharacteristic
123C22×C4—1031no—
124C22×C4—2062no—
125C22×C4—2061no—
126C22×C4—2061no—
127C22×C4—2062no—
128C22×C4D41212yes—
129C22×C4C22×D10311yescharacteristic
130M16—22no—
131M16—22no—
132M16—2064no—
133M16—2062no—
134M16—2062no—
135C2×C8—22no—
136C2×C8—1034no—
137C2×C8—2064no—
138C4⋊C4—2062no—
139C4⋊C4—2061no—
140C22⋊C4—1032no—
141C22⋊C4—2062no—
142C22⋊C4—2062no—
143C42—2061no—
144C23—4122no—
145C23—2061no—
146C23—2062no—
147C23(C2×D103)⋊C412yes—
148C23C2×C4×D10311yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—4124no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—4121no—
156C2×C4—4122no—
157C2×C4—4121no—
158C2×C4—2062no—
159C2×C4—2061no—
160C2×C4—2062no—
161C2×C4(C2×D103)⋊C412yes—
162C2×C4D4×D10312yes—
163C2×C4C2×C22⋊D10311yescharacteristic
164C2×C4C2×D41211yescharacteristic
165C2×C4#1311010412yes—
166C8—42no—
167C8—2064no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—4121no—
172C22—4122no—
173C22—4121no—
174C22—2062no—
175C22—2064no—
176C22C2×(C2×D103)⋊C411yescharacteristic
177C22(C22⋊D103)⋊C412yes—
178C4—22no—
179C4—4122no—
180C4—4121no—
181C4#1569299111yescharacteristic
182C4#1569299312yes—
183C4#1569300511yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—4122no—
188C2#2026766811yescharacteristic
subgroupG/H
centerC4#15692991
commutatorC23×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#413×C103C2
socleC2×C103#386
prime radical#20268298C2
cosocleC22×C4×C103C23
hypercenter#413D103
hypocenterC103#1891
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #20268558C2semidirect
3. #20267754C2semidirect
4. #20267563C2semidirect
5. #413×C103C2semidirect
32. C2×C103⋊C8D4semidirect
95. C103#1891semidirect
98. #413D103semidirect

Maximal subgroups

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

subgroupindex
#202685582
#202682982
#202677542
#202675632
#413×C1032
#1891103