Finite Group Databasebeta

← #27195678

Subgroups — #27195678

Order 13184.

314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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#20268362C211yesmaximal, characteristic
2#20268268C211yesmaximal, characteristic, complemented
3#20267808C211yesmaximal, characteristic
4C2×#15692939C211yesmaximal, characteristic, complemented
5#20267548C211yesmaximal, characteristic, complemented
6#20267547C211yesmaximal, characteristic, complemented
7#421×C103C211yesmaximal, characteristic
8C22×Dic206C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10#15693019C412yescomplemented
11#15693008C412yescomplemented
12#15693002—22no—
13#15693000—22no—
14C4×Dic206—22no—
15#15692986—22no—
16#15692980C2211yescharacteristic
17#15692980C2211yescharacteristic
18#15692977—22no—
19#15692948—22no—
20#15692939—22no—
21C2×#41×C103C2211yescharacteristic
22C2×M16×C103C2211yescharacteristic
23#117×C103C2211yescharacteristic
24#104×C103—22no—
25C2×Dic206—21no—
26C2×Dic206—21no—
27C2×Dic206—21no—
28C2×Dic206—21no—
29C2×Dic206C2×C412yes—
30C2×Dic206D412yes—
31C22×Dic103D412yes—
32#13110089—21no—
33#13110089—21no—
34C2×C103⋊C8—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103—21no—
37Dic103⋊C4—24no—
38Dic103⋊C4—24no—
39C22⋊Dic103—21no—
40C22⋊Dic103—21no—
41C22⋊Dic103—24no—
42C4×Dic103—24no—
43C4×Dic103C2×C412yes—
44C4×Dic103D412yes—
45#41×C103—21no—
46#41×C103—21no—
47#41×C103—21no—
48#41×C103—21no—
49C2×Q8×C103C2×C411yescharacteristic
50C2×D4×C103—21no—
51C2×D4×C103C2×C411yescharacteristic
52C22×C4×C103—21no—
53C22×C4×C103C2311yescharacteristic
54M16×C103—21no—
55M16×C103—21no—
56C2×C8×C103—21no—
57C4⋊C4×C103—21no—
58C22⋊C4×C103—21no—
59C42×C103D412yes—
60C23×C103—21no—
61C23×C103C2×D411yescharacteristic
62Q8×C103—21no—
63Q8×C103—21no—
64D4×C103—21no—
65D4×C103—21no—
66D4×C103—41no—
67D4×C103—41no—
68C2×C4×C103—21no—
69C2×C4×C103—22no—
70C2×C4×C103—41no—
71C2×C4×C103—41no—
72C2×C4×C103C22×C411yescharacteristic
73C2×C4×C103C2×D411yescharacteristic
74C2×C4×C103C2×D411yescharacteristic
75C2×C4×C103C2×D411yescharacteristic
76C2×C4×C103#4111yescharacteristic
77C2×C4×C103#4111yescharacteristic
78C2×Dic103—22no—
79C2×Dic103—22no—
80C2×Dic103—22no—
81C2×Dic103—22no—
82C2×Dic103C22⋊C414yes—
83Dic206—22no—
84Dic206—22no—
85Dic206—22no—
86Dic206—22no—
87C8×C103—41no—
88C103⋊C8—41no—
89C22×C103—41no—
90C22×C103—42no—
91C22×C103—41no—
92C22×C103C2×C22⋊C411yescharacteristic
93C22×C103#12011yescharacteristic
94C22×C103#12311yescharacteristic
95C4×C103—42no—
96C4×C103—41no—
97C4×C103C4×D411yescharacteristic
98C4×C103C4×D411yescharacteristic
99C4×C103#12111yescharacteristic
100C4×C103#12111yescharacteristic
101Dic103—24no—
102Dic103—42no—
103Dic103—42no—
104C2×C103—21no—
105C2×C103—21no—
106C2×C103—21no—
107C2×C103—81no—
108C2×C103#38611yescharacteristic
109#1912—1031nomaximal, Sylow
110C103#191211yescharacteristic, complemented, Sylow
111#536—1031no—
112#519—1031no—
113#421—1031no—
114#421D10311yescharacteristic
115C2×#101—1031no—
116H(3,ℤ/4)—1031no—
117H(3,ℤ/4)—1031no—
118C2×#41C2×D10311yescharacteristic
119C22×Q8—1031no—
120C2×M16—1031no—
121C2×M16C2×D10311yescharacteristic
122C4⋊Q8—1032no—
123#124—1032no—
124#123—2062no—
125C22⋊Q8—2062no—
126C4×Q8—2062no—
127C4×Q8—2062no—
128#117—1031no—
129#117—1031no—
130#117—2062no—
131#117C2×D10311yescharacteristic
132#104—22no—
133#104—2062no—
134#101—2062no—
135#41—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139C2×Q8—1032no—
140C2×Q8—1032no—
141C2×Q8—2061no—
142C2×Q8—2061no—
143C2×Q8—2061no—
144C2×Q8—2061no—
145C2×Q8C4×D10311yescharacteristic
146C2×D4—21no—
147C2×D4C4×D10311yescharacteristic
148C22×C4—21no—
149C22×C4—1032no—
150C22×C4C22×D10311yescharacteristic
151M16—21no—
152M16—21no—
153M16—2061no—
154M16—2061no—
155C2×C8—21no—
156C2×C8—2061no—
157C4⋊C4—21no—
158C4⋊C4—2064no—
159C4⋊C4—2064no—
160C4⋊C4—2061no—
161C4⋊C4—2061no—
162C22⋊C4—21no—
163C22⋊C4—2064no—
164C22⋊C4—2061no—
165C22⋊C4—2061no—
166C42—1032no—
167C42—1032no—
168C42—2064no—
169C42C22⋊D10312yes—
170C23—21no—
171C23D4×D10311yescharacteristic
172Q8—21no—
173Q8—21no—
174Q8—2062no—
175Q8—2062no—
176Q8—2062no—
177Q8—2062no—
178D4—21no—
179D4—21no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—1034no—
187C2×C4—2062no—
188C2×C4—2062no—
189C2×C4—2062no—
190C2×C4—2062no—
191C2×C4C2×C4×D10311yescharacteristic
192C2×C4D4×D10311yescharacteristic
193C2×C4D4×D10311yescharacteristic
194C2×C4C2×C22⋊D10311yescharacteristic
195C2×C4#1311010411yescharacteristic
196C2×C4#1311010511yescharacteristic
197C8—41no—
198C8—4121no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22C22⋊C4×D10311yescharacteristic
203C22#1569298911yescharacteristic
204C22#1569300311yescharacteristic
205C4—42no—
206C4—41no—
207C4—4122no—
208C4—4122no—
209C4—2064no—
210C4(C22⋊D103)⋊C411yescharacteristic
211C4C4×C22⋊D10311yescharacteristic
212C4#1569299211yescharacteristic
213C4#1569299411yescharacteristic
214C2—21no—
215C2—21no—
216C2—21no—
217C2—81no—
218C2#2026766711yescharacteristic
subgroupG/H
centerC2#20267667
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#421×C103C2
socleC2×C103#386
prime radicalC2×#41×C103C22
cosocleC22×C4×C103C23
hypercenter#421D103
hypocenterC103#1912
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #20268268C2semidirect
4. C2×#15692939C2semidirect
5. #20267548C2semidirect
6. #20267547C2semidirect
10. #15693019C4semidirect
11. #15693008C4semidirect
110. C103#1912semidirect

Maximal subgroups

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

subgroupindex
#202683622
#202682682
#202678082
C2×#156929392
#202675482
#202675472
#421×C1032
#1912103