Finite Group Databasebeta

← #27207817

Subgroups — #27207817

Order 13184.

336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q8×Dic206C211yesmaximal, characteristic
2#20268516C211yesmaximal, characteristic
3#20268141C211yesmaximal, characteristic
4#20268140C212yesmaximal
5#20268087C211yesmaximal, characteristic
6#20268084C212yesmaximal
7#20267999C212yesmaximal
8#20267915C211yesmaximal, characteristic
9Q16×Dic103C212yesmaximal
10C4×#13110095C211yesmaximal, characteristic
11#462×C103C211yesmaximal, characteristic
12C2×#13110095C2211yescharacteristic
13#15693021—21no—
14#15693021C2211yescharacteristic
15#15693020—22no—
16#15693020C2212yes—
17#15693019C2212yes—
18#15693012—21no—
19#15693011—22no—
20Q8×Dic103C2212yes—
21Q8×Dic103C2212yes—
22C4×Dic206—21no—
23C4×Dic206C2211yescharacteristic
24C4×Dic206C2211yescharacteristic
25#15692986—21no—
26#15692955C2212yes—
27#15692954C2211yescharacteristic
28Dic103⋊C8C2212yes—
29#15692946C2212yes—
30#15692945C2212yes—
31#15692945C2211yescharacteristic
32#15692945C2212yes—
33#15692944C2211yescharacteristic
34C4×C103⋊C8C2211yescharacteristic
35C8×Dic103C2212yes—
36C2×Q16×C103C2212yes—
37C4⋊Q8×C103C2211yescharacteristic
38C4×Q8×C103C2211yescharacteristic
39C4⋊C8×C103C2211yescharacteristic
40#103×C103C2212yes—
41C2×Dic206—21no—
42C2×Dic206—22no—
43C2×Dic206D411yescharacteristic
44C2×Dic206C2311yescharacteristic
45#13110095—22no—
46C2×C103⋊C8C2311yescharacteristic
47C2×C103⋊C8C2311yescharacteristic
48C4⋊Dic103—21no—
49C4⋊Dic103—22no—
50C4⋊Dic103—22no—
51C4⋊Dic103D411yescharacteristic
52C4⋊Dic103C2312yes—
53C4⋊Dic103C2311yescharacteristic
54Dic103⋊C4—21no—
55Dic103⋊C4—22no—
56Dic103⋊C4—22no—
57Dic103⋊C4—22no—
58Dic103⋊C4D412yes—
59C4×Dic103—21no—
60C4×Dic103—22no—
61C4×Dic103—22no—
62C4×Dic103C2312yes—
63C2×Q8×C103C2312yes—
64C2×Q8×C103C2311yescharacteristic
65Q16×C103—24no—
66C2×C8×C103C2312yes—
67C4⋊C4×C103—21no—
68C4⋊C4×C103—21no—
69C4⋊C4×C103—21no—
70C4⋊C4×C103C2311yescharacteristic
71C42×C103—21no—
72C42×C103C2311yescharacteristic
73Q8×C103—21no—
74Q8×C103—22no—
75Q8×C103—22no—
76Q8×C103#4112yes—
77C2×C4×C103—21no—
78C2×C4×C103—21no—
79C2×C4×C103—22no—
80C2×C4×C103C2×D411yescharacteristic
81C2×C4×C103C2×D411yescharacteristic
82C2×C4×C103C2411yescharacteristic
83C2×Dic103—21no—
84C2×Dic103—21no—
85C2×Dic103—22no—
86C2×Dic103C2×D412yes—
87C2×Dic103C2×D412yes—
88Dic206—21no—
89Dic206—21no—
90Dic206—82no—
91Dic206—81no—
92Dic206Q1614yescomplemented
93C8×C103—22no—
94C103⋊C8—21no—
95C103⋊C8—21no—
96C22×C103C22×D411yescharacteristic
97C4×C103—22no—
98C4×C103—21no—
99C4×C103—42no—
100C4×C103—41no—
101C4×C103C2×Q1612yes—
102C4×C103C2×#4111yescharacteristic
103C4×C1032−1+411yescharacteristic
104Dic103—22no—
105Dic103—41no—
106Dic103—42no—
107Dic103—41no—
108Dic103C2×Q1614yes—
109C2×C103#54811yescharacteristic
110C2×C103C22×Q1611yescharacteristic
111C2×C103#57711yescharacteristic
112#3363—1031nomaximal, Sylow
113C103#336311yescharacteristic, complemented, Sylow
114Q82—1031no—
115#557—1031no—
116#487—1031no—
117#487—1032no—
118#477—1031no—
119#477—1032no—
120#462—1032no—
121#462D10311yescharacteristic
122C8×Q8—1031no—
123C4×Q16—1032no—
124C4×Q16—1031no—
125C2×Q16—1031no—
126C2×Q16C2×D10312yes—
127C4⋊Q8—1032no—
128C4⋊Q8—1032no—
129C4⋊Q8—1031no—
130C4⋊Q8—2061no—
131C4⋊Q8—2062no—
132C4⋊Q8C2×D10311yescharacteristic
133#125—2062no—
134#125—2061no—
135C4×Q8—1031no—
136C4×Q8—1032no—
137C4×Q8—1032no—
138C4×Q8—1031no—
139C4×Q8—2061no—
140C4×Q8—2061no—
141C4×Q8C2×D10311yescharacteristic
142#107—1032no—
143#107—1031no—
144C4⋊C8—1032no—
145C4⋊C8C2×D10311yescharacteristic
146#103—1031no—
147#103—1032no—
148#103—1032no—
149#103—1032no—
150#103—1031no—
151#103C2×D10312yes—
152C4×C8—1032no—
153C4×C8—1031no—
154C2×Q8—1031no—
155C2×Q8—1031no—
156C2×Q8—2062no—
157C2×Q8—2061no—
158C2×Q8C22×D10312yes—
159C2×Q8C22×D10311yescharacteristic
160Q16—24no—
161Q16—2062no—
162C2×C8—1031no—
163C2×C8—1031no—
164C2×C8C22×D10312yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—1032no—
169C4⋊C4—1031no—
170C4⋊C4—1032no—
171C4⋊C4—1031no—
172C4⋊C4—2062no—
173C4⋊C4—2062no—
174C4⋊C4—2062no—
175C4⋊C4—2062no—
176C4⋊C4—2062no—
177C4⋊C4—2061no—
178C4⋊C4—2061no—
179C4⋊C4C22×D10311yescharacteristic
180C42—21no—
181C42—1032no—
182C42—2062no—
183C42—2062no—
184C42—2061no—
185C42C22×D10311yescharacteristic
186Q8—21no—
187Q8—22no—
188Q8—22no—
189Q8—8241no—
190Q8—8242no—
191Q8—1034no—
192Q8—2061no—
193Q8—2061no—
194Q8#1311010412yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—1032no—
199C2×C4—1032no—
200C2×C4—2061no—
201C2×C4—2062no—
202C2×C4—2061no—
203C2×C4D4×D10311yescharacteristic
204C2×C4D4×D10311yescharacteristic
205C2×C4C23×D10311yescharacteristic
206C8—22no—
207C8—2061no—
208C8—2061no—
209C22C2×D4×D10311yescharacteristic
210C4—21no—
211C4—22no—
212C4—41no—
213C4—42no—
214C4—1034no—
215C4—4122no—
216C4—4121no—
217C4—4121no—
218C4—2062no—
219C4Q16×D10312yes—
220C4C2×#1311010411yescharacteristic
221C4#1569306811yescharacteristic
222C2#2026844711yescharacteristic
223C2C2×Q16×D10311yescharacteristic
224C2#2026860011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#462×C103C2
socle, prime radicalC22×C103C22×D4
hypercenter#462D103
hypocenterC103#3363
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
92. Dic206Q16semidirect
113. C103#3363semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic2062
#202685162
#202681412
#202681402
#202680872
#202680842
#202679992
#202679152
Q16×Dic1032
C4×#131100952
#462×C1032
#3363103