Finite Group Databasebeta

← #27196284

Subgroups — #27196284

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×#15693020C211yesmaximal, characteristic
2C2×#15692946C211yesmaximal, characteristic
3C2×#15692944C211yesmaximal, characteristic
4#20267696C211yesmaximal, characteristic
5#20267553C211yesmaximal, characteristic
6#20267545C211yesmaximal, characteristic
7#340×C103C211yesmaximal, characteristic
8C22×Dic206—21no—
9C22×Dic206C2211yescharacteristic
10C22×C103⋊C8C2211yescharacteristic
11#15693020—22no—
12#15693020—22no—
13C2×C4⋊Dic103C2211yescharacteristic
14C2×Dic103⋊C4—21no—
15C2×C4×Dic103C2211yescharacteristic
16#15692946—22no—
17#15692944—22no—
18C103⋊#95—21no—
19C103⋊#95—21no—
20C22×C8×C103C2211yescharacteristic
21C2×C4⋊C4×C103C2211yescharacteristic
22C2×C4⋊C4×C103C2211yescharacteristic
23C2×Dic206—21no—
24C2×Dic206—21no—
25C2×Dic206—21no—
26C2×Dic206—21no—
27C2×Dic206—24no—
28C2×Dic206—21no—
29C2×Dic206—42no—
30C2×Dic206—42no—
31C2×Dic206Q812yescomplemented
32C22×Dic103—21no—
33C22×Dic103—21no—
34C22×Dic103D411yescharacteristic
35C22×Dic103D411yescharacteristic
36C2×C103⋊C8—21no—
37C2×C103⋊C8—21no—
38C2×C103⋊C8—21no—
39C4⋊Dic103—21no—
40C4⋊Dic103D412yes—
41Dic103⋊C4—24no—
42C4×Dic103—21no—
43C4×Dic103—21no—
44C22×C4×C103—21no—
45C22×C4×C103—21no—
46C22×C4×C103C2311yescharacteristic
47C2×C8×C103—21no—
48C2×C8×C103—21no—
49C2×C8×C103—21no—
50C4⋊C4×C103—21no—
51C4⋊C4×C103—21no—
52C4⋊C4×C103—21no—
53C4⋊C4×C103D412yes—
54C23×C103C2×D411yescharacteristic
55C2×C4×C103—22no—
56C2×C4×C103—41no—
57C2×C4×C103—41no—
58C2×C4×C103—41no—
59C2×C4×C103—41no—
60C2×C4×C103—41no—
61C2×C4×C103C2×D411yescharacteristic
62C2×C4×C103C2×D411yescharacteristic
63C2×C4×C103C2×Q811yescharacteristic
64C2×C4×C103#4111yescharacteristic
65C2×C4×C103#4111yescharacteristic
66C2×C4×C103#4111yescharacteristic
67C2×Dic103—21no—
68C2×Dic103—21no—
69C2×Dic103—21no—
70C2×Dic103—21no—
71C2×Dic103—22no—
72C2×Dic103—22no—
73C2×Dic103—41no—
74C2×Dic103—41no—
75C2×Dic103—41no—
76C2×Dic103—41no—
77C2×Dic103SD1612yes—
78C2×Dic103Q1612yes—
79Dic206—22no—
80Dic206—22no—
81Dic206—48no—
82Dic206—41no—
83Dic206—41no—
84C8×C103—41no—
85C103⋊C8—41no—
86C22×C103#12011yescharacteristic
87C22×C103C22⋊Q811yescharacteristic
88C22×C103#12411yescharacteristic
89C22×C103C2×SD1611yescharacteristic
90C22×C103C2×Q1611yescharacteristic
91C22×C103AGL(1,ℤ/8)11yescharacteristic
92C22×C103#13711yescharacteristic
93C4×C103—42no—
94C4×C103—81no—
95C4×C103C22⋊Q811yescharacteristic
96C4×C103C22⋊Q811yescharacteristic
97C4×C103#12411yescharacteristic
98C4×C103#12411yescharacteristic
99Dic103—22no—
100Dic103—22no—
101Dic103—42no—
102Dic103—42no—
103C2×C103#39311yescharacteristic
104C2×C103#45011yescharacteristic
105C2×C103#45111yescharacteristic
106C2×C103#47511yescharacteristic
107C2×C103#47711yescharacteristic
108C2×C103#48711yescharacteristic
109C2×C103#48911yescharacteristic
110#2024—1031nomaximal, Sylow
111C103#202411yescharacteristic, complemented, Sylow
112C2×C4⋊Q8—1031no—
113C2×#103—1031no—
114C2×#103—1031no—
115#391—1031no—
116#340—1031no—
117#340D10311yescharacteristic
118#336—1031no—
119C22×Q8—1031no—
120C22×Q8—2061no—
121C22×C8—1031no—
122C22×C8C2×D10311yescharacteristic
123C4⋊Q8—2062no—
124C4⋊Q8—2062no—
125C2×C4⋊C4—1031no—
126C2×C4⋊C4—2061no—
127C2×C4⋊C4C2×D10311yescharacteristic
128C2×C4⋊C4C2×D10311yescharacteristic
129C2×C42—1031no—
130#103—2062no—
131#103—2062no—
132#95—2061no—
133#95—2061no—
134C2×Q8—1032no—
135C2×Q8—4122no—
136C2×Q8—4122no—
137C2×Q8—2064no—
138C2×Q8—2061no—
139C2×Q8—2061no—
140C2×Q8—2061no—
141C2×Q8—2061no—
142C2×Q8—2061no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—1031no—
146C22×C4—1031no—
147C22×C4—2061no—
148C22×C4—2061no—
149C22×C4C22×D10311yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—2061no—
154C2×C8—2061no—
155C2×C8—2061no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—1032no—
160C4⋊C4—2064no—
161C4⋊C4—2061no—
162C4⋊C4D41212yes—
163C42—2061no—
164C42—2061no—
165C23D4×D10311yescharacteristic
166Q8—4128no—
167Q8—4121no—
168Q8—4121no—
169Q8—2062no—
170Q8—2062no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—1032no—
178C2×C4—1032no—
179C2×C4—4121no—
180C2×C4—4121no—
181C2×C4—4121no—
182C2×C4—4121no—
183C2×C4—2062no—
184C2×C4—2062no—
185C2×C4—2061no—
186C2×C4—2061no—
187C2×C4—2061no—
188C2×C4—2061no—
189C2×C4D4×D10311yescharacteristic
190C2×C4C2×D41211yescharacteristic
191C2×C4Q8×D10311yescharacteristic
192C2×C4#1311010411yescharacteristic
193C2×C4#1311010511yescharacteristic
194C2×C4#1311010511yescharacteristic
195C8—41no—
196C8—4121no—
197C22#1569299111yescharacteristic
198C22#1569299911yescharacteristic
199C22#1569300711yescharacteristic
200C22SD16×D10311yescharacteristic
201C22Q16×D10311yescharacteristic
202C22#1569304511yescharacteristic
203C22#1569305011yescharacteristic
204C4—42no—
205C4—81no—
206C4—4122no—
207C4—4122no—
208C4—2062no—
209C4—2062no—
210C4#1569299911yescharacteristic
211C4#1569300111yescharacteristic
212C4#1569300711yescharacteristic
213C4#1569300911yescharacteristic
214C2#2026770411yescharacteristic
215C2#2026794311yescharacteristic
216C2#2026794811yescharacteristic
217C2#2026807511yescharacteristic
218C2#2026808511yescharacteristic
219C2#2026814011yescharacteristic
220C2#2026814911yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#340×C103C2
socle, prime radicalC23×C103C2×D4
hypercenter#340D103
hypocenterC103#2024
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
31. C2×Dic206Q8semidirect
111. C103#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#156930202
C2×#156929462
C2×#156929442
#202676962
#202675532
#202675452
#340×C1032
#2024103