Finite Group Databasebeta

← #27195246

Subgroups — #27195246

Order 13184.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#20268259C211yesmaximal, characteristic
2#20267773C211yesmaximal, characteristic
3#20267764C211yesmaximal, characteristic
4#20267552C211yesmaximal, characteristic, complemented
5#20267550C211yesmaximal, characteristic, complemented
6#20267547C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C103C211yesmaximal, characteristic, complemented
8C2×#13110105C2211yescharacteristic
9C2×#13110089C2211yescharacteristic
10#15692986—21no—
11#15692983—21no—
12(C22⋊D103)⋊C4—22no—
13#15692980C2211yescharacteristic
14#15692978C412yescomplemented
15C2×C4×Dic103C2211yescharacteristic
16C42×D103C412yescomplemented
17#15692939—21no—
18#15692937—21no—
19#15692935—22no—
20C2×M16×C103C2211yescharacteristic
21#117×C103C2211yescharacteristic
22#117×C103C2211yescharacteristic
23#13110105—21no—
24#13110105—21no—
25#13110105—21no—
26#13110105—21no—
27C2×Dic206D411yescharacteristic
28C2×D412D411yescharacteristic
29C2×C22⋊D103D412yes—
30C22×Dic103—21no—
31C2×C4×D103—22no—
32C2×C4×D103C2×C412yes—
33#13110089—21no—
34#13110089—21no—
35C2×C103⋊C8—21no—
36C4⋊Dic103—21no—
37Dic103⋊C4—22no—
38C22⋊Dic103—21no—
39(C2×D103)⋊C4—22no—
40C4×Dic103—21no—
41C4×Dic103—22no—
42C4×Dic103—21no—
43C4×Dic103C2×C411yescharacteristic
44C4×Dic103C2×C411yescharacteristic
45C22×C4×C103C2311yescharacteristic
46M16×C103—21no—
47M16×C103—21no—
48C2×C8×C103—21no—
49C4⋊C4×C103—21no—
50C4⋊C4×C103—21no—
51C22⋊C4×C103—21no—
52C22⋊C4×C103—21no—
53C42×C103—21no—
54C42×C103C2×C412yes—
55C23×C103C2×D411yescharacteristic
56C22×D103C22⋊C412yes—
57C2×C4×C103—22no—
58C2×C4×C103—41no—
59C2×C4×C103C22×C411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×C4×C103#4111yescharacteristic
62C2×C4×C103#4111yescharacteristic
63C2×C4×C103#4111yescharacteristic
64C2×C4×C103#4111yescharacteristic
65C22⋊D103—22no—
66C22⋊D103—22no—
67C2×Dic103—21no—
68C2×Dic103—21no—
69C2×Dic103—42no—
70C2×Dic103—41no—
71C2×Dic103C22⋊C412yes—
72D412—21no—
73D412—21no—
74C4×D103—22no—
75C4×D103—22no—
76C4×D103—44no—
77Dic206—21no—
78Dic206—21no—
79C8×C103—41no—
80C103⋊C8—41no—
81C22×C103—41no—
82C22×C103C2×C22⋊C411yescharacteristic
83C22×C103#12311yescharacteristic
84C22×C103#12311yescharacteristic
85C2×D103—22no—
86C2×D103—42no—
87C4×C103—42no—
88C4×C103—81no—
89C4×C103#11711yescharacteristic
90C4×C103#11711yescharacteristic
91C4×C103#12311yescharacteristic
92C4×C103#12311yescharacteristic
93Dic103—22no—
94Dic103—22no—
95Dic103—41no—
96Dic103—81no—
97C2×C103—21no—
98C2×C103—21no—
99C2×C103—21no—
100C2×C103#38111yescharacteristic
101D103—42no—
102#1827—1031nomaximal, Sylow
103C103#182711yescharacteristic, complemented, Sylow
104C4×#41—1031no—
105#413—1031no—
106#410—1031no—
107#339—1031no—
108#339—1031no—
109H(3,ℤ/4)—1031no—
110H(3,ℤ/4)D10311yescharacteristic, complemented
111C2×#41—1031no—
112C2×M16—1031no—
113C2×M16C2×D10311yescharacteristic
114C4×Q8—2061no—
115C4×D4—2062no—
116C4×D4—2061no—
117#117—1032no—
118#117—1031no—
119#117C2×D10311yescharacteristic
120#117C2×D10311yescharacteristic
121C2×C42—1031no—
122C2×C42—1032no—
123#101—2061no—
124#100—2061no—
125#99—2062no—
126#41—2061no—
127#41—2061no—
128#41—2061no—
129#41—2061no—
130C2×Q8—1031no—
131C2×D4—1032no—
132C2×D4—1031no—
133C22×C4—1032no—
134C22×C4—2062no—
135C22×C4—2061no—
136C22×C4C22×D10311yescharacteristic
137M16—21no—
138M16—21no—
139M16—2061no—
140M16—2061no—
141C2×C8—21no—
142C2×C8—2061no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2062no—
146C4⋊C4—2061no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—2062no—
150C22⋊C4—2061no—
151C42—21no—
152C42—1031no—
153C42—1031no—
154C42—2062no—
155C42—2061no—
156C42—2061no—
157C42C4×D10312yes—
158C23—1032no—
159C23D4×D10311yescharacteristic
160Q8—2061no—
161Q8—2061no—
162D4—2062no—
163D4—2062no—
164D4—2061no—
165D4—2061no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—1032no—
169C2×C4—4124no—
170C2×C4—4121no—
171C2×C4—4122no—
172C2×C4—2061no—
173C2×C4—2061no—
174C2×C4—2062no—
175C2×C4—2062no—
176C2×C4C2×C4×D10311yescharacteristic
177C2×C4D4×D10311yescharacteristic
178C2×C4#1311010411yescharacteristic
179C2×C4#1311010511yescharacteristic
180C2×C4#1311010511yescharacteristic
181C2×C4#1311010611yescharacteristic
182C8—41no—
183C8—4121no—
184C22—41no—
185C22—4122no—
186C22—2062no—
187C22C22⋊C4×D10311yescharacteristic
188C22#1569300311yescharacteristic
189C22#1569300611yescharacteristic
190C4—42no—
191C4—81no—
192C4—8241no—
193C4—4121no—
194C4—2062no—
195C4—2062no—
196C4#1569297811yescharacteristic
197C4#1569297911yescharacteristic
198C4#1569300311yescharacteristic
199C4#1569300611yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—4122no—
204C2#2026765311yescharacteristic
subgroupG/H
centerC4#15692978
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingH(3,ℤ/4)×C103C2
socleC2×C103#381
prime radicalC2×#13110105C22
cosocleC22×C4×C103C23
hypercenterH(3,ℤ/4)D103
hypocenterC103#1827
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #20267552C2semidirect
5. #20267550C2semidirect
6. #20267547C2semidirect
7. H(3,ℤ/4)×C103C2semidirect
14. #15692978C4semidirect
16. C42×D103C4semidirect
103. C103#1827semidirect
110. H(3,ℤ/4)D103semidirect

Maximal subgroups

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

subgroupindex
#202682592
#202677732
#202677642
#202675522
#202675502
#202675472
H(3,ℤ/4)×C1032
#1827103