Finite Group Databasebeta

← #27195638

Subgroups — #27195638

Order 13184.

310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#15693052C211yesmaximal, characteristic
2#20267809C211yesmaximal, characteristic
3#20267800C211yesmaximal, characteristic, complemented
4#20267764C211yesmaximal, characteristic
5#20267561C211yesmaximal, characteristic, complemented
6#20267547C211yesmaximal, characteristic, complemented
7#519×C103C211yesmaximal, characteristic, complemented
8C2×#13110105C2211yescharacteristic
9#15693052—22no—
10#15693052—22no—
11C2×#13110095C412yescomplemented
12C2×#13110092C412yescomplemented
13C2×#13110089C2211yescharacteristic
14C2×#13110089C2211yescharacteristic
15#15692980C2211yescharacteristic
16#15692949—22no—
17#15692945—22no—
18#15692935—22no—
19C22×Q8×C103C2211yescharacteristic
20C4×Q8×C103—22no—
21C4×Q8×C103—22no—
22#117×C103—22no—
23#117×C103C2211yescharacteristic
24#117×C103C2211yescharacteristic
25#13110105—21no—
26#13110105—21no—
27#13110105—21no—
28#13110105—21no—
29C2×Dic206C2×C411yescharacteristic
30C2×D412C2×C411yescharacteristic
31C2×C22⋊D103—21no—
32C2×C4×D103—21no—
33#13110095—24no—
34#13110092—24no—
35#13110089—21no—
36#13110089—21no—
37#13110089—21no—
38#13110089—21no—
39C2×C103⋊C8—21no—
40C2×C103⋊C8C2×C412yes—
41C4⋊Dic103—21no—
42C22⋊Dic103—21no—
43C4×Dic103—21no—
44C2×Q8×C103—21no—
45C2×Q8×C103—21no—
46C2×Q8×C103—21no—
47C2×Q8×C103C2×C412yes—
48C2×Q8×C103D412yes—
49C2×Q8×C103D412yes—
50C22×C4×C103—21no—
51C22×C4×C103C2311yescharacteristic
52C4⋊C4×C103—24no—
53C4⋊C4×C103—21no—
54C4⋊C4×C103—21no—
55C22⋊C4×C103—21no—
56C22⋊C4×C103D412yes—
57C42×C103—24no—
58C42×C103—21no—
59C42×C103D412yes—
60C23×C103C2×D411yescharacteristic
61C22×D103—21no—
62Q8×C103—22no—
63Q8×C103—22no—
64Q8×C103—22no—
65Q8×C103C22⋊C414yes—
66C2×C4×C103—22no—
67C2×C4×C103—22no—
68C2×C4×C103—22no—
69C2×C4×C103—22no—
70C2×C4×C103—22no—
71C2×C4×C103C22×C411yescharacteristic
72C2×C4×C103C2×D411yescharacteristic
73C2×C4×C103C2×D411yescharacteristic
74C2×C4×C103C2×D411yescharacteristic
75C2×C4×C103#4111yescharacteristic
76C2×C4×C103#4111yescharacteristic
77C22⋊D103—41no—
78C22⋊D103—41no—
79C2×Dic103—21no—
80C2×Dic103—41no—
81D412—21no—
82D412—21no—
83C4×D103—41no—
84C4×D103—41no—
85Dic206—21no—
86Dic206—21no—
87C103⋊C8—22no—
88C103⋊C8—41no—
89C22×C103—41no—
90C22×C103C4×D411yescharacteristic
91C22×C103#12011yescharacteristic
92C22×C103#12111yescharacteristic
93C2×D103—41no—
94C2×D103—81no—
95C4×C103—24no—
96C4×C103—42no—
97C4×C103—42no—
98C4×C103C2×C22⋊C411yescharacteristic
99C4×C103C4×D411yescharacteristic
100C4×C103#12111yescharacteristic
101C4×C103#12311yescharacteristic
102Dic103—41no—
103Dic103—81no—
104C2×C103—21no—
105C2×C103—21no—
106C2×C103—21no—
107C2×C103#38611yescharacteristic
108D103—81no—
109#1905—1031nomaximal, Sylow
110C103#190511yescharacteristic, complemented, Sylow
111C2×#137—1031no—
112#519D10311yescharacteristic, complemented
113#421—1031no—
114#419—1031no—
115#410—1031no—
116#344—1031no—
117H(3,ℤ/4)—1031no—
118C2×#41—1031no—
119C22×Q8C2×D10311yescharacteristic
120#137—2062no—
121#137—2062no—
122C2×Q16—1032no—
123C2×SD16—1032no—
124C2×M16—1031no—
125C2×M16—1031no—
126C4×Q8—22no—
127C4×Q8—22no—
128#117—22no—
129#117—1031no—
130#117C2×D10311yescharacteristic
131#117C2×D10311yescharacteristic
132#104—2062no—
133#103—2062no—
134#99—2062no—
135#41—2061no—
136#41—2061no—
137#41—2061no—
138#41—2061no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—1031no—
143C2×Q8C4×D10312yes—
144C2×Q8D41212yes—
145C2×Q8C22⋊D10312yes—
146C2×D4—1031no—
147C2×D4—2061no—
148C22×C4—21no—
149C22×C4—2061no—
150C22×C4C22×D10311yescharacteristic
151Q16—2064no—
152SD16—2064no—
153M16—2061no—
154M16—2061no—
155M16—2061no—
156M16—2061no—
157C2×C8—1032no—
158C2×C8—2061no—
159C4⋊C4—24no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—2061no—
163C22⋊C4—21no—
164C22⋊C4—2061no—
165C22⋊C4C22⋊D10312yes—
166C42—24no—
167C42—21no—
168C42—2061no—
169C42C22⋊D10312yes—
170C23—2061no—
171C23C2×C22⋊D10311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—22no—
175Q8—2061no—
176Q8—2061no—
177Q8(C2×D103)⋊C414yes—
178D4—4121no—
179D4—4121no—
180D4—2061no—
181D4—2061no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—4121no—
188C2×C4—4121no—
189C2×C4—4121no—
190C2×C4—2061no—
191C2×C4C2×C4×D10311yescharacteristic
192C2×C4C2×C22⋊D10311yescharacteristic
193C2×C4C2×C22⋊D10311yescharacteristic
194C2×C4C2×D41211yescharacteristic
195C2×C4#1311010511yescharacteristic
196C2×C4#1311010511yescharacteristic
197C8—4121no—
198C8—2062no—
199C22—41no—
200C22—8241no—
201C22—4121no—
202C22C4×C22⋊D10311yescharacteristic
203C22#1569299011yescharacteristic
204C22#1569299511yescharacteristic
205C4—24no—
206C4—42no—
207C4—42no—
208C4—8241no—
209C4—4121no—
210C4C2×(C2×D103)⋊C411yescharacteristic
211C4C4×C22⋊D10311yescharacteristic
212C4#1569299511yescharacteristic
213C4#1569300411yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—8241no—
218C2#2026767011yescharacteristic
subgroupG/H
centerC2#20267670
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#519×C103C2
socleC2×C103#386
prime radicalC2×#13110105C22
cosocleC22×C4×C103C23
hypercenter#519D103
hypocenterC103#1905
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
3. #20267800C2semidirect
5. #20267561C2semidirect
6. #20267547C2semidirect
7. #519×C103C2semidirect
11. C2×#13110095C4semidirect
12. C2×#13110092C4semidirect
110. C103#1905semidirect
112. #519D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930522
#202678092
#202678002
#202677642
#202675612
#202675472
#519×C1032
#1905103