Finite Group Databasebeta

← #27195640

Subgroups — #27195640

Order 13184.

310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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#20268269C211yesmaximal, characteristic, complemented
2#20267808C211yesmaximal, characteristic
3#20267800C211yesmaximal, characteristic, complemented
4#20267765C211yesmaximal, characteristic
5#20267562C211yesmaximal, characteristic, complemented
6#20267548C211yesmaximal, characteristic, complemented
7C2×#137×C103C211yesmaximal, characteristic
8C2×#13110089C2211yescharacteristic
9Q8×Dic103—22no—
10Q8×Dic103—22no—
11#15692980—22no—
12#15692980C2211yescharacteristic
13#15692980C2211yescharacteristic
14#15692980C2211yescharacteristic
15#15692948—22no—
16#15692945—22no—
17#15692936—22no—
18C2×#41×C103C2211yescharacteristic
19C22×Q8×C103C2211yescharacteristic
20#137×C103—22no—
21#137×C103—22no—
22C2×Q16×C103C412yescomplemented
23C2×SD16×C103C412yescomplemented
24C2×M16×C103C2211yescharacteristic
25#13110089—21no—
26#13110089—21no—
27C2×C103⋊C8—21no—
28C4⋊Dic103—24no—
29C4⋊Dic103—21no—
30C4⋊Dic103—21no—
31C4⋊Dic103—21no—
32C22⋊Dic103—21no—
33C22⋊Dic103—21no—
34C22⋊Dic103D412yes—
35C4×Dic103—24no—
36C4×Dic103—21no—
37C4×Dic103—21no—
38C4×Dic103D412yes—
39#41×C103—21no—
40#41×C103—21no—
41#41×C103—21no—
42#41×C103—21no—
43C2×Q8×C103—21no—
44C2×Q8×C103—21no—
45C2×Q8×C103—21no—
46C2×Q8×C103C2×C411yescharacteristic
47C2×Q8×C103C2×C412yes—
48C2×Q8×C103D412yes—
49C2×Q8×C103D412yes—
50C2×D4×C103—21no—
51C2×D4×C103C2×C411yescharacteristic
52C22×C4×C103—21no—
53C22×C4×C103—21no—
54C22×C4×C103C2311yescharacteristic
55Q16×C103—24no—
56SD16×C103—24no—
57M16×C103—21no—
58M16×C103—21no—
59C2×C8×C103C2×C412yes—
60C23×C103—21no—
61C23×C103C2×D411yescharacteristic
62Q8×C103—22no—
63Q8×C103—22no—
64Q8×C103—22no—
65Q8×C103—21no—
66Q8×C103—21no—
67Q8×C103C22⋊C414yes—
68D4×C103—21no—
69D4×C103—21no—
70D4×C103—41no—
71D4×C103—41no—
72C2×C4×C103—22no—
73C2×C4×C103—22no—
74C2×C4×C103—22no—
75C2×C4×C103—21no—
76C2×C4×C103—41no—
77C2×C4×C103—41no—
78C2×C4×C103C22×C411yescharacteristic
79C2×C4×C103C2×D411yescharacteristic
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103C2×D411yescharacteristic
82C2×C4×C103#4111yescharacteristic
83C2×C4×C103#4111yescharacteristic
84C2×Dic103—22no—
85C2×Dic103—22no—
86C2×Dic103—41no—
87C8×C103—22no—
88C103⋊C8—41no—
89C22×C103—41no—
90C22×C103—41no—
91C22×C103—81no—
92C22×C103C4×D411yescharacteristic
93C22×C103#12011yescharacteristic
94C22×C103#12111yescharacteristic
95C4×C103—24no—
96C4×C103—41no—
97C4×C103C2×C22⋊C411yescharacteristic
98C4×C103C4×D411yescharacteristic
99C4×C103#12111yescharacteristic
100C4×C103#12311yescharacteristic
101Dic103—42no—
102Dic103—42no—
103Dic103—81no—
104C2×C103—21no—
105C2×C103—21no—
106C2×C103—21no—
107C2×C103—81no—
108C2×C103#38611yescharacteristic
109#1905—1031nomaximal, Sylow
110C103#190511yescharacteristic, complemented, Sylow
111C2×#137D10311yescharacteristic
112#519—1031no—
113#421—1031no—
114#419—1031no—
115#410—1031no—
116#344—1031no—
117H(3,ℤ/4)—1031no—
118C2×#41C2×D10311yescharacteristic
119C22×Q8C2×D10311yescharacteristic
120#137—22no—
121#137—22no—
122C2×Q16Dic10312yescomplemented
123C2×SD16Dic10312yescomplemented
124C2×M16—1031no—
125C2×M16C2×D10311yescharacteristic
126C4×Q8—2062no—
127C4×Q8—2062no—
128#117—1031no—
129#117—1031no—
130#117—1031no—
131#117—2062no—
132#104—2062no—
133#103—2062no—
134#99—2062no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8C2×Dic10311yescharacteristic
143C2×Q8C2×Dic10312yes—
144C2×Q8C22⋊D10312yes—
145C2×Q8C22⋊D10312yes—
146C2×D4—21no—
147C2×D4C2×Dic10311yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4C22×D10311yescharacteristic
151Q16—24no—
152SD16—24no—
153M16—21no—
154M16—21no—
155M16—2061no—
156M16—2061no—
157C2×C8—2061no—
158C2×C8C2×Dic10312yes—
159C4⋊C4—2064no—
160C4⋊C4—2061no—
161C4⋊C4—2061no—
162C4⋊C4—2061no—
163C22⋊C4—1032no—
164C22⋊C4—2061no—
165C22⋊C4—2061no—
166C42—1032no—
167C42—2064no—
168C42—2061no—
169C42—2061no—
170C23—21no—
171C23D4×D10311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—22no—
175Q8—21no—
176Q8—21no—
177Q8C22⋊Dic10314yes—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—4121no—
189C2×C4—2062no—
190C2×C4—2062no—
191C2×C4C22×Dic10311yescharacteristic
192C2×C4D4×D10311yescharacteristic
193C2×C4C2×C22⋊D10311yescharacteristic
194C2×C4C2×C22⋊D10311yescharacteristic
195C2×C4#1311010411yescharacteristic
196C2×C4#1311010411yescharacteristic
197C8—22no—
198C8—4121no—
199C22—41no—
200C22—41no—
201C22—81no—
202C22D4×Dic10311yescharacteristic
203C22#1569298911yescharacteristic
204C22#1569299311yescharacteristic
205C4—24no—
206C4—41no—
207C4—8241no—
208C4—4122no—
209C4—4122no—
210C4C2×C22⋊Dic10311yescharacteristic
211C4D4×Dic10311yescharacteristic
212C4#1569299311yescharacteristic
213C4#1569300211yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#2026767111yescharacteristic
subgroupG/H
centerC2#20267671
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×#137×C103C2
socleC2×C103#386
prime radicalC2×#41×C103C22
cosocleC22×C4×C103C23
hypercenterC2×#137D103
hypocenterC103#1905
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. #20268269C2semidirect
3. #20267800C2semidirect
5. #20267562C2semidirect
6. #20267548C2semidirect
22. C2×Q16×C103C4semidirect
23. C2×SD16×C103C4semidirect
110. C103#1905semidirect
122. C2×Q16Dic103semidirect
123. C2×SD16Dic103semidirect

Maximal subgroups

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

subgroupindex
#202682692
#202678082
#202678002
#202677652
#202675622
#202675482
C2×#137×C1032
#1905103