Finite Group Databasebeta

← #27195864

Subgroups — #27195864

Order 13184.

248 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 105 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×Dic103⋊C8C211yesmaximal, characteristic
2C2×Dic103⋊C8C211yesmaximal, characteristic
3C2×#15692931C211yesmaximal, characteristic
4C4×Dic103⋊C4C211yesmaximal, characteristic
5#20267546C211yesmaximal, characteristic
6#20267545C211yesmaximal, characteristic
7C2×C4⋊C8×C103C211yesmaximal, characteristic
8C22×C103⋊C8C2211yescharacteristic
9C22×C103⋊C8C2211yescharacteristic
10C2×Dic103⋊C4C411yescharacteristic
11C2×Dic103⋊C4C411yescharacteristic
12C2×C4×Dic103C2211yescharacteristic
13C2×C4×Dic103C2211yescharacteristic
14Dic103⋊C8—22no—
15Dic103⋊C8—22no—
16#15692931—22no—
17C103⋊#95C411yescharacteristic
18C103⋊#95C411yescharacteristic
19C22×C8×C103C2211yescharacteristic
20C22×C8×C103C2211yescharacteristic
21C2×C42×C103C2211yescharacteristic
22C4⋊C8×C103—22no—
23C22×Dic103C2×C411yescharacteristic
24C22×Dic103C2×C411yescharacteristic
25C22×Dic103C2×C411yescharacteristic
26C22×Dic103C2×C411yescharacteristic
27C2×C103⋊C8—21no—
28C2×C103⋊C8—21no—
29C2×C103⋊C8—21no—
30C2×C103⋊C8—21no—
31C2×C103⋊C8—21no—
32C2×C103⋊C8Q812yes—
33Dic103⋊C4—22no—
34Dic103⋊C4—22no—
35C4×Dic103—21no—
36C4×Dic103—21no—
37C4×Dic103D412yes—
38C4×Dic103Q812yes—
39C22×C4×C103C2×C411yescharacteristic
40C22×C4×C103C2×C411yescharacteristic
41C22×C4×C103C2311yescharacteristic
42C2×C8×C103—21no—
43C2×C8×C103—21no—
44C2×C8×C103—21no—
45C2×C8×C103—21no—
46C2×C8×C103—21no—
47C2×C8×C103D412yes—
48C42×C103—21no—
49C42×C103—21no—
50C23×C103C22×C411yescharacteristic
51C2×C4×C103—21no—
52C2×C4×C103—21no—
53C2×C4×C103—21no—
54C2×C4×C103—21no—
55C2×C4×C103—21no—
56C2×C4×C103M1612yes—
57C2×C4×C103C2×D411yescharacteristic
58C2×C4×C103C2×D411yescharacteristic
59C2×C4×C103C2×Q811yescharacteristic
60C2×C4×C103C2×Q811yescharacteristic
61C2×C4×C103#4111yescharacteristic
62C2×C4×C103#4111yescharacteristic
63C2×Dic103—21no—
64C2×Dic103—21no—
65C2×Dic103—21no—
66C2×Dic103—21no—
67C2×Dic103—21no—
68C2×Dic103—21no—
69C2×Dic103—21no—
70C2×Dic103—21no—
71C2×Dic103—21no—
72C2×Dic103C4⋊C412yes—
73C2×Dic103C4⋊C412yes—
74C2×Dic103M1612yes—
75C8×C103—22no—
76C8×C103—41no—
77C103⋊C8—22no—
78C103⋊C8—41no—
79C22×C103C2×C4⋊C411yescharacteristic
80C22×C103C4×D411yescharacteristic
81C22×C103C4×Q811yescharacteristic
82C22×C103C2×M1611yescharacteristic
83C22×C103C2×M1611yescharacteristic
84C22×C103#13111yescharacteristic
85C22×C103#13111yescharacteristic
86C4×C103—22no—
87C4×C103—41no—
88C4×C103#12111yescharacteristic
89C4×C103C22⋊Q811yescharacteristic
90C4×C103#12511yescharacteristic
91C4×C103C4⋊Q811yescharacteristic
92Dic103—22no—
93Dic103—22no—
94Dic103—22no—
95Dic103—41no—
96C2×C103#38911yescharacteristic
97C2×C103#42311yescharacteristic
98C2×C103#42411yescharacteristic
99C2×C103#43511yescharacteristic
100C2×C103#43511yescharacteristic
101C2×C103#44611yescharacteristic
102C2×C103#44611yescharacteristic
103#1940—1031nomaximal, Sylow
104C103#194011yescharacteristic, complemented, Sylow
105C2×C4⋊C8—1031no—
106C2×C4⋊C8—1031no—
107C2×C4⋊C8D10311yescharacteristic
108C2×#97—1031no—
109C4×C4⋊C4—1031no—
110#336—1031no—
111#336—1031no—
112C22×C8—1031no—
113C22×C8—1031no—
114C22×C8C2×D10311yescharacteristic
115C22×C8C2×D10311yescharacteristic
116C2×C4⋊C4—1031no—
117C2×C4⋊C4—1031no—
118C2×C42—1031no—
119C2×C42—1031no—
120C2×C42C2×D10311yescharacteristic
121C4⋊C8—22no—
122C4⋊C8—2062no—
123C4⋊C8—2062no—
124#97—2062no—
125#95—1031no—
126#95—1031no—
127C22×C4—1031no—
128C22×C4—1031no—
129C22×C4—1031no—
130C22×C4—1031no—
131C22×C4C4×D10311yescharacteristic
132C22×C4C4×D10311yescharacteristic
133C22×C4C22×D10311yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—1032no—
140C2×C8—2061no—
141C2×C8—2061no—
142C2×C8—2061no—
143C2×C8—2061no—
144C2×C8—2061no—
145C2×C8C22⋊D10312yes—
146C4⋊C4—2062no—
147C4⋊C4—2062no—
148C42—21no—
149C42—21no—
150C42—1032no—
151C42—1032no—
152C42—2061no—
153C42—2061no—
154C23C2×C4×D10311yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—1032no—
161C2×C4—1032no—
162C2×C4—1032no—
163C2×C4—2061no—
164C2×C4—2061no—
165C2×C4—2061no—
166C2×C4—2061no—
167C2×C4—2061no—
168C2×C4—2061no—
169C2×C4—2061no—
170C2×C4—2061no—
171C2×C4—2061no—
172C2×C4#1311008812yes—
173C2×C4D4×D10311yescharacteristic
174C2×C4C2×C22⋊D10311yescharacteristic
175C2×C4Q8×D10311yescharacteristic
176C2×C4Q8×D10311yescharacteristic
177C2×C4#1311010411yescharacteristic
178C2×C4#1311010511yescharacteristic
179C8—22no—
180C8—41no—
181C8—4121no—
182C8—2062no—
183C22C4⋊C4×D10311yescharacteristic
184C22C4×C22⋊D10311yescharacteristic
185C22#1569298611yescharacteristic
186C22M16×D10311yescharacteristic
187C22C2×#1311008811yescharacteristic
188C22#1569302711yescharacteristic
189C22#1569302911yescharacteristic
190C4—22no—
191C4—41no—
192C4—4121no—
193C4—2062no—
194C4—2062no—
195C4—2062no—
196C4#1569299311yescharacteristic
197C4#1569299911yescharacteristic
198C4#1569301111yescharacteristic
199C4#1569301911yescharacteristic
200C2#2026768611yescharacteristic
201C2#2026781311yescharacteristic
202C2#2026781611yescharacteristic
203C2#2026786011yescharacteristic
204C2#2026786211yescharacteristic
205C2#2026791811yescharacteristic
206C2#2026792011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D103
commutator, socle, prime radicalC23×C103C22×C4
FittingC2×C4⋊C8×C103C2
cosocleC22×C4×C103C23
hypercenterC2×C4⋊C8D103
hypocenterC103#1940
LCSG ▷ C23×C103 ▷ C103
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
104. C103#1940semidirect

Maximal subgroups

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

subgroupindex
C2×Dic103⋊C82
C2×#156929312
C4×Dic103⋊C42
#202675462
#202675452
C2×C4⋊C8×C1032
#1940103