Finite Group Databasebeta

← #27195486

Subgroups — #27195486

Order 13184.

338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×Dic412C211yesmaximal, characteristic
2C2×#15692986C211yesmaximal, characteristic
3C2×#15692944C211yesmaximal, characteristic
4C2×#15692944C211yesmaximal, characteristic
5#20267696C211yesmaximal, characteristic
6#20267545C211yesmaximal, characteristic
7#340×C103C211yesmaximal, characteristic
8C22×Dic206C2211yescharacteristic
9C22×Dic206C2211yescharacteristic
10C2×Dic412—22no—
11C2×Dic412—22no—
12C2×Dic412C414yescomplemented
13C22×C103⋊C8C2211yescharacteristic
14#15692986—22no—
15#15692986—22no—
16C2×Dic103⋊C4—21no—
17C2×C4×Dic103—21no—
18C2×C4×Dic103C2211yescharacteristic
19#15692944—22no—
20#15692944—22no—
21C103⋊#95—21no—
22C103⋊#95—21no—
23C22×C8×C103C2211yescharacteristic
24C2×C4⋊C4×C103C2211yescharacteristic
25C2×C4⋊C4×C103C2211yescharacteristic
26C2×Dic206—21no—
27C2×Dic206—21no—
28C2×Dic206—21no—
29C2×Dic206—21no—
30C2×Dic206—21no—
31C2×Dic206—21no—
32C2×Dic206—21no—
33C2×Dic206—21no—
34C2×Dic206C2×C412yes—
35C2×Dic206C2×C412yes—
36C2×Dic206D412yes—
37C2×Dic206D412yes—
38C22×Dic103—21no—
39C22×Dic103—21no—
40C22×Dic103D411yescharacteristic
41C22×Dic103D411yescharacteristic
42Dic412—28no—
43C2×C103⋊C8—21no—
44C2×C103⋊C8—21no—
45C2×C103⋊C8—21no—
46Dic103⋊C4—24no—
47C4×Dic103—24no—
48C4×Dic103—21no—
49C4×Dic103—21no—
50C22×C4×C103—21no—
51C22×C4×C103—21no—
52C22×C4×C103C2311yescharacteristic
53C2×C8×C103—21no—
54C2×C8×C103—21no—
55C2×C8×C103C2×C412yes—
56C4⋊C4×C103—21no—
57C4⋊C4×C103—21no—
58C4⋊C4×C103—21no—
59C4⋊C4×C103D412yes—
60C23×C103C2×D411yescharacteristic
61C2×C4×C103—22no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103—41no—
67C2×C4×C103C22×C411yescharacteristic
68C2×C4×C103C2×D411yescharacteristic
69C2×C4×C103C2×D411yescharacteristic
70C2×C4×C103C2×D411yescharacteristic
71C2×C4×C103#4111yescharacteristic
72C2×C4×C103#4111yescharacteristic
73C2×Dic103—22no—
74C2×Dic103—21no—
75C2×Dic103—22no—
76C2×Dic103—22no—
77C2×Dic103—21no—
78C2×Dic103—22no—
79C2×Dic103—21no—
80C2×Dic103—21no—
81C2×Dic103—21no—
82C2×Dic103—41no—
83C2×Dic103—41no—
84C2×Dic103Q1612yescomplemented
85Dic206—22no—
86Dic206—22no—
87Dic206—22no—
88Dic206—22no—
89Dic206—22no—
90Dic206—41no—
91Dic206—41no—
92Dic206C22⋊C414yes—
93C8×C103—22no—
94C103⋊C8—41no—
95C22×C103C4×D411yescharacteristic
96C22×C103#12011yescharacteristic
97C22×C103#12111yescharacteristic
98C22×C103C2×Q1611yescharacteristic
99C22×C103#13511yescharacteristic
100C22×C103#13711yescharacteristic
101C22×C103#13711yescharacteristic
102C4×C103—42no—
103C4×C103—81no—
104C4×C103C2×C22⋊C411yescharacteristic
105C4×C103C4×D411yescharacteristic
106C4×C103#12111yescharacteristic
107C4×C103#12311yescharacteristic
108Dic103—24no—
109Dic103—22no—
110Dic103—42no—
111Dic103—41no—
112C2×C103#38611yescharacteristic
113C2×C103C4×Q1611yescharacteristic
114C2×C103#44111yescharacteristic
115C2×C103#45111yescharacteristic
116C2×C103#45211yescharacteristic
117C2×C103#46211yescharacteristic
118C2×C103#46411yescharacteristic
119#1878—1031nomaximal, Sylow
120C103#187811yescharacteristic, complemented, Sylow
121C22×Q16—1031no—
122C2×C4×Q8—1031no—
123C2×#103—1031no—
124C2×#103—1031no—
125#391—1031no—
126#340D10311yescharacteristic
127#336—1031no—
128C22×Q8—1031no—
129C22×Q8—1031no—
130C2×Q16—1034no—
131C2×Q16—2062no—
132C2×Q16—2062no—
133C22×C8—1031no—
134C22×C8C2×D10311yescharacteristic
135C4×Q8—2062no—
136C4×Q8—2062no—
137C2×C4⋊C4—2061no—
138C2×C4⋊C4C2×D10311yescharacteristic
139C2×C4⋊C4C2×D10311yescharacteristic
140C2×C42—1031no—
141C2×C42—2061no—
142#103—2062no—
143#103—2062no—
144#95—2061no—
145#95—2061no—
146C2×Q8—1032no—
147C2×Q8—1032no—
148C2×Q8—1032no—
149C2×Q8—1032no—
150C2×Q8—2061no—
151C2×Q8—2061no—
152C2×Q8—2061no—
153C2×Q8—2061no—
154C2×Q8—2061no—
155C2×Q8—2061no—
156C2×Q8—2061no—
157C2×Q8—2061no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—1031no—
161C22×C4—1031no—
162C22×C4—2061no—
163C22×C4—2061no—
164C22×C4C22×D10311yescharacteristic
165Q16—2068no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—2061no—
169C2×C8—2061no—
170C2×C8—2061no—
171C2×C8C4×D10312yes—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—2064no—
176C4⋊C4D41212yes—
177C42—2064no—
178C42—2061no—
179C42—2061no—
180C23D4×D10311yescharacteristic
181Q8—1034no—
182Q8—4121no—
183Q8—4121no—
184Q8—2062no—
185Q8—2062no—
186Q8—2062no—
187Q8—2062no—
188Q8—2062no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—1032no—
196C2×C4—4121no—
197C2×C4—4121no—
198C2×C4—2062no—
199C2×C4—2061no—
200C2×C4—2061no—
201C2×C4—2061no—
202C2×C4—2062no—
203C2×C4—2061no—
204C2×C4—2062no—
205C2×C4—2062no—
206C2×C4—2061no—
207C2×C4C2×C4×D10311yescharacteristic
208C2×C4D4×D10311yescharacteristic
209C2×C4D4×D10311yescharacteristic
210C2×C4C2×D41211yescharacteristic
211C2×C4#1311010511yescharacteristic
212C2×C4#1311010611yescharacteristic
213C8—22no—
214C8—4121no—
215C22#1569298311yescharacteristic
216C22#1569299111yescharacteristic
217C22#1569299411yescharacteristic
218C22Q16×D10311yescharacteristic
219C22#1569304011yescharacteristic
220C22#1569305011yescharacteristic
221C22#1569305011yescharacteristic
222C4—42no—
223C4—81no—
224C4—4122no—
225C4—4121no—
226C4—2064no—
227C4—2062no—
228C4C22⋊C4×D10311yescharacteristic
229C4C4×D41211yescharacteristic
230C4#1569299611yescharacteristic
231C4#1569300611yescharacteristic
232C2#2026766911yescharacteristic
233C2#2026788511yescharacteristic
234C2#2026789711yescharacteristic
235C2#2026794811yescharacteristic
236C2#2026795411yescharacteristic
237C2#2026800011yescharacteristic
238C2#2026801211yescharacteristic
subgroupG/H
centerC23D4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#340×C103C2
socle, prime radicalC23×C103C2×D4
cosocleC22×C4×C103C23
hypercenter#340D103
hypocenterC103#1878
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
12. C2×Dic412C4semidirect
84. C2×Dic103Q16semidirect
120. C103#1878semidirect

Maximal subgroups

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

subgroupindex
C22×Dic4122
C2×#156929862
C2×#156929442
#202676962
#202675452
#340×C1032
#1878103