Finite Group Databasebeta

← #27194163

Subgroups — #27194163

Order 13184.

288 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 53 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#20268353C211yesmaximal, characteristic
2#20268109C212yesmaximal, complemented
3#20267524C212yesmaximal, complemented
4#20267515C211yesmaximal, characteristic, complemented
5#399×C103C211yesmaximal, characteristic, complemented
6C22×C22⋊D103—21no—
7#15693005—22no—
8#15692995—21no—
9#15692995C2212yes—
10#15692991—22no—
11#15692952—22no—
12#15692941—22no—
13C22⋊(C103⋊C8)C2212yescomplemented
14C2×C4⋊C4×C103—21no—
15C2×C4⋊C4×C103C2211yescharacteristic, complemented
16C2×C22⋊C4×C103—21no—
17C2×C22⋊C4×C103C2211yescharacteristic
18#95×C103C2211yescharacteristic, complemented
19C23×D103—21no—
20C2×D412—21no—
21C2×D412D412yes—
22C2×C22⋊D103—22no—
23C2×C22⋊D103—22no—
24C2×C22⋊D103—42no—
25C2×C22⋊D103—42no—
26C22×Dic103—21no—
27C2×C103⋊C8—22no—
28C4⋊Dic103—21no—
29C4⋊Dic103D412yes—
30(C2×D103)⋊C4—22no—
31(C2×D103)⋊C4—22no—
32C24×C103D411yescharacteristic
33C22×C4×C103—21no—
34C22×C4×C103—21no—
35C22×C4×C103D411yescharacteristic
36C22×C4×C103C2311yescharacteristic
37C4⋊C4×C103—22no—
38C4⋊C4×C103—42no—
39C22⋊C4×C103—22no—
40C22⋊C4×C103—42no—
41C23×C103—21no—
42C23×C103—21no—
43C23×C103—41no—
44C23×C103—41no—
45C23×C103SD1612yes—
46C23×C103C2×D411yescharacteristic
47C22×D103—22no—
48C22×D103—42no—
49C22×D103—81no—
50C22×D103—81no—
51C2×C4×C103—22no—
52C2×C4×C103—21no—
53C2×C4×C103—41no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103—41no—
58C2×C4×C103—41no—
59C2×C4×C103—41no—
60C2×C4×C103C2×D412yes—
61C22⋊D103—44no—
62C22⋊D103—42no—
63C22⋊D103—42no—
64C2×Dic103—22no—
65C2×Dic103—42no—
66D412—42no—
67D412—81no—
68C103⋊C8—42no—
69C22×C103—21no—
70C22×C103—21no—
71C22×C103—22no—
72C22×C103—42no—
73C22×C103—41no—
74C22×C103—41no—
75C22×C103—81no—
76C22×C103#12011yescharacteristic
77C22×C103C2×SD1611yescharacteristic
78C22×C103AGL(1,ℤ/8)11yescharacteristic
79C2×D103—42no—
80C2×D103—42no—
81C2×D103—42no—
82C2×D103—84no—
83C4×C103—22no—
84C4×C103—42no—
85C4×C103—41no—
86C4×C103—81no—
87Dic103—42no—
88C2×C103—21no—
89C2×C103—21no—
90C2×C103—42no—
91C2×C103#45011yescharacteristic
92C2×C103#45311yescharacteristic
93C2×C103#45811yescharacteristic
94D103—82no—
95#1613—1031nomaximal, Sylow
96C103#161311yescharacteristic, complemented, Sylow
97#534—1031no—
98#481—1032no—
99#399D10311yescharacteristic, complemented
100#327—1032no—
101#323—1031no—
102C22×D4—2061no—
103#123—2062no—
104#121—1032no—
105#121—2061no—
106#120—2062no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4C2×D10311yescharacteristic, complemented
109C2×C22⋊C4—21no—
110C2×C22⋊C4C2×D10311yescharacteristic
111#106—2062no—
112#102—2062no—
113C22⋊C8—1032no—
114#95C2×D10311yescharacteristic, complemented
115C24—2061no—
116C24C22⋊D10311yescharacteristic
117C2×D4—1032no—
118C2×D4—4122no—
119C2×D4—4122no—
120C2×D4—2061no—
121C2×D4—2062no—
122C2×D4—2062no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—2061no—
126C22×C4C22⋊D10311yescharacteristic
127C22×C4C22×D10311yescharacteristic
128C2×C8—2062no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4—1032no—
132C4⋊C4—2061no—
133C22⋊C4—22no—
134C22⋊C4—42no—
135C22⋊C4—2062no—
136C22⋊C4—2062no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—8241no—
142C23—8241no—
143C23—4122no—
144C23—2062no—
145C23#1311009212yes—
146C23C2×C22⋊D10311yescharacteristic
147D4—8241no—
148D4—4122no—
149D4—4124no—
150D4—4122no—
151D4—4122no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—4122no—
162C2×C4—2062no—
163C2×C4D4×D10312yes—
164C8—4122no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—8244no—
173C22—4122no—
174C22—4122no—
175C22—4122no—
176C22#1569298911yescharacteristic
177C22C2×#1311009211yescharacteristic
178C22#1569304611yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—81no—
183C4—4122no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—8242no—
188C2#2026794111yescharacteristic
189C2#2026795811yescharacteristic
190C2#2026798011yescharacteristic
subgroupG/H
centerC22#15692989
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#399×C103C2
socleC22×C103#120
prime radical#20268353C2
hypercenter#399D103
hypocenterC103#1613
LCSG ▷ C22×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #20268109C2semidirect
3. #20267524C2semidirect
4. #20267515C2semidirect
5. #399×C103C2semidirect
13. C22⋊(C103⋊C8)C22semidirect
15. C2×C4⋊C4×C103C22semidirect
18. #95×C103C22semidirect
96. C103#1613semidirect
99. #399D103semidirect
108. C2×C4⋊C4C2×D103semidirect
114. #95C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683532
#202681092
#202675242
#202675152
#399×C1032
#1613103