Finite Group Databasebeta

← #27196674

Subgroups — #27196674

Order 13184.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#15692952C211yesmaximal, characteristic, complemented
2C2×#15692943C211yesmaximal, characteristic
3C2×#15692941C211yesmaximal, characteristic
4#20267692C211yesmaximal, characteristic
5#20267660C211yesmaximal, characteristic, complemented
6#20267545C211yesmaximal, characteristic, complemented
7C2×#106×C103C211yesmaximal, characteristic, complemented
8C22×D412C2211yescharacteristic
9C22×C103⋊C8C2211yescharacteristic
10C2×C4⋊Dic103C2211yescharacteristic
11C2×Dic103⋊C4—22no—
12C2×(C2×D103)⋊C4—22no—
13C2×C4×Dic103C2211yescharacteristic
14#15692952—22no—
15#15692943—22no—
16#15692941—22no—
17C22×C8×C103C2211yescharacteristic
18C2×C4⋊C4×C103C2211yescharacteristic
19C2×C4⋊C4×C103C2211yescharacteristic
20#106×C103—22no—
21C23×D103—21no—
22C2×D412—21no—
23C2×D412—21no—
24C2×D412—21no—
25C2×D412—21no—
26C2×D412—21no—
27C2×D412Q812yes—
28C22×Dic103—21no—
29C22×Dic103D412yes—
30C2×C103⋊C8—21no—
31C2×C103⋊C8—21no—
32C2×C103⋊C8D412yes—
33C4⋊Dic103—21no—
34C4⋊Dic103—21no—
35Dic103⋊C4—44no—
36(C2×D103)⋊C4—44no—
37C4×Dic103—21no—
38C4×Dic103—21no—
39C22×C4×C103—21no—
40C22×C4×C103—21no—
41C22×C4×C103C2311yescharacteristic
42C2×C8×C103—21no—
43C2×C8×C103—21no—
44C2×C8×C103D412yes—
45C4⋊C4×C103—21no—
46C4⋊C4×C103—21no—
47C4⋊C4×C103—21no—
48C4⋊C4×C103—21no—
49C23×C103C2×D411yescharacteristic
50C22×D103—22no—
51C22×D103—41no—
52C22×D103—41no—
53C22×D103—42no—
54C22×D103—42no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103—42no—
58C2×C4×C103—42no—
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×D411yescharacteristic
61C2×C4×C103C2×Q811yescharacteristic
62C2×C4×C103#4111yescharacteristic
63C2×C4×C103#4111yescharacteristic
64C2×C4×C103#4111yescharacteristic
65C2×Dic103—22no—
66C2×Dic103—22no—
67C2×Dic103—41no—
68C2×Dic103—42no—
69C2×Dic103SD1614yes—
70D412—22no—
71D412—22no—
72D412—41no—
73D412—41no—
74C8×C103—22no—
75C103⋊C8—22no—
76C22×C103C22⋊Q811yescharacteristic
77C22×C103#12311yescharacteristic
78C22×C103#12711yescharacteristic
79C22×C103C2×SD1612yes—
80C22×C103AGL(1,ℤ/8)12yes—
81C2×D103—42no—
82C2×D103—44no—
83C2×D103—82no—
84C2×D103—81no—
85C2×D103—81no—
86C4×C103—81no—
87C4×C103—81no—
88C4×C103C22⋊Q811yescharacteristic
89C4×C103C22⋊Q811yescharacteristic
90C4×C103#12311yescharacteristic
91C4×C103#12311yescharacteristic
92Dic103—24no—
93Dic103—81no—
94C2×C103#39911yescharacteristic
95C2×C103#47612yes—
96C2×C103#48112yes—
97C2×C103#49211yescharacteristic
98C2×C103#49611yescharacteristic
99D103—82no—
100#2094—1031nomaximal, Sylow
101C103#209411yescharacteristic, complemented, Sylow
102C2×#106—1031no—
103C2×#106D10311yescharacteristic, complemented
104C2×#102—1031no—
105C2×#102—1031no—
106#390—1031no—
107#384—1031no—
108#336—1031no—
109C22×D4—1031no—
110C22×C8—1031no—
111C22×C8C2×D10311yescharacteristic
112C2×C4⋊C4—1031no—
113C2×C4⋊C4—2062no—
114C2×C4⋊C4C2×D10311yescharacteristic
115C2×C4⋊C4C2×D10311yescharacteristic
116C2×C22⋊C4—2062no—
117C2×C42—1031no—
118#106—22no—
119#106—2062no—
120#102—2062no—
121#102—2062no—
122C24—2061no—
123C2×D4—1032no—
124C2×D4—2061no—
125C2×D4—2061no—
126C2×D4—2061no—
127C2×D4—2061no—
128C2×D4—2061no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—1032no—
132C22×C4—2061no—
133C22×C4C22×D10311yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1032no—
137C2×C8—2061no—
138C2×C8—2061no—
139C2×C8C22⋊D10312yes—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—4124no—
145C4⋊C4—2061no—
146C4⋊C4—2061no—
147C22⋊C4—4124no—
148C42—2061no—
149C42—2061no—
150C23—4121no—
151C23—4121no—
152C23—4122no—
153C23—4122no—
154C23—2062no—
155C23D4×D10311yescharacteristic
156D4—4121no—
157D4—4121no—
158D4—2062no—
159D4—2062no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—1034no—
165C2×C4—4121no—
166C2×C4—4122no—
167C2×C4—2062no—
168C2×C4—2062no—
169C2×C4D4×D10311yescharacteristic
170C2×C4C2×C22⋊D10311yescharacteristic
171C2×C4Q8×D10311yescharacteristic
172C2×C4#1311010511yescharacteristic
173C2×C4#1311010511yescharacteristic
174C2×C4#1311010611yescharacteristic
175C8—22no—
176C8—2062no—
177C22—8242no—
178C22—8241no—
179C22—8241no—
180C22—4124no—
181C22—4122no—
182C22#1569299911yescharacteristic
183C22#1569300611yescharacteristic
184C22#1569301711yescharacteristic
185C22SD16×D10312yes—
186C22#1569304812yes—
187C4—81no—
188C4—81no—
189C4—8241no—
190C4—2064no—
191C4#1569299711yescharacteristic
192C4#1569299911yescharacteristic
193C4#1569300411yescharacteristic
194C4#1569300611yescharacteristic
195C2—8242no—
196C2#2026772611yescharacteristic
197C2#2026808012yes—
198C2#2026811112yes—
199C2#2026816211yescharacteristic
200C2#2026817711yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
FittingC2×#106×C103C2
socleC23×C103C2×D4
prime radicalC22×D412C22
hypercenterC2×#106D103
hypocenterC103#2094
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. C2×#15692952C2semidirect
5. #20267660C2semidirect
6. #20267545C2semidirect
7. C2×#106×C103C2semidirect
101. C103#2094semidirect
103. C2×#106D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929522
C2×#156929432
C2×#156929412
#202676922
#202676602
#202675452
C2×#106×C1032
#2094103