Finite Group Databasebeta

← #27196640

Subgroups — #27196640

Order 13184.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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×#15692954C211yesmaximal, characteristic
2C2×C4⋊(C103⋊C8)C211yesmaximal, characteristic
3#20267689C211yesmaximal, characteristic
4#20267553C211yesmaximal, characteristic
5#20267553C211yesmaximal, characteristic
6#20267553C211yesmaximal, characteristic
7#389×C103C211yesmaximal, characteristic
8C22×C103⋊C8C2211yescharacteristic
9C22×C103⋊C8C2211yescharacteristic
10C2×C4⋊Dic103C2211yescharacteristic
11C2×C4⋊Dic103C2211yescharacteristic
12C2×Dic103⋊C4—21no—
13#15692954—22no—
14C4⋊(C103⋊C8)—22no—
15C103⋊#95—21no—
16C2×C4⋊C4×C103—21no—
17C2×C4⋊C4×C103C2211yescharacteristic
18C2×C4⋊C4×C103C2211yescharacteristic
19C2×C42×C103C2211yescharacteristic
20#95×C103—21no—
21C22×Dic103—21no—
22C22×Dic103—21no—
23C2×C103⋊C8—21no—
24C2×C103⋊C8—21no—
25C2×C103⋊C8—21no—
26C2×C103⋊C8—21no—
27C2×C103⋊C8—21no—
28C2×C103⋊C8D412yes—
29C4⋊Dic103—21no—
30C4⋊Dic103—21no—
31C4⋊Dic103—21no—
32C4⋊Dic103Q812yes—
33Dic103⋊C4—42no—
34C22×C4×C103—21no—
35C22×C4×C103—21no—
36C22×C4×C103D411yescharacteristic
37C22×C4×C103D411yescharacteristic
38C22×C4×C103C2311yescharacteristic
39C4⋊C4×C103—21no—
40C4⋊C4×C103—21no—
41C4⋊C4×C103—21no—
42C4⋊C4×C103—42no—
43C4⋊C4×C103Q812yes—
44C42×C103—21no—
45C42×C103—21no—
46C23×C103C2×D411yescharacteristic
47C2×C4×C103—21no—
48C2×C4×C103—21no—
49C2×C4×C103—21no—
50C2×C4×C103—22no—
51C2×C4×C103—21no—
52C2×C4×C103—21no—
53C2×C4×C103—41no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103—41no—
57C2×C4×C103—41no—
58C2×C4×C103Q1612yes—
59C2×C4×C103C2×D411yescharacteristic
60C2×C4×C103C2×Q811yescharacteristic
61C2×C4×C103C2×Q811yescharacteristic
62C2×C4×C103#4111yescharacteristic
63C2×C4×C103#4111yescharacteristic
64C2×C4×C103#4111yescharacteristic
65C2×Dic103—22no—
66C2×Dic103—41no—
67C2×Dic103—41no—
68C2×Dic103—41no—
69C2×Dic103—41no—
70C2×Dic103—41no—
71C103⋊C8—22no—
72C103⋊C8—41no—
73C22×C103#12111yescharacteristic
74C22×C103C22⋊Q811yescharacteristic
75C22×C103C22⋊Q811yescharacteristic
76C22×C103C2×Q1611yescharacteristic
77C22×C103#13511yescharacteristic
78C22×C103AGL(1,ℤ/8)11yescharacteristic
79C22×C103AGL(1,ℤ/8)11yescharacteristic
80C4×C103—22no—
81C4×C103—41no—
82C4×C103—42no—
83C4×C103—81no—
84C4×C103#12311yescharacteristic
85C4×C103#12511yescharacteristic
86C4×C103#12511yescharacteristic
87C4×C103C4⋊Q811yescharacteristic
88Dic103—42no—
89Dic103—81no—
90C2×C103#39811yescharacteristic
91C2×C103#46711yescharacteristic
92C2×C103#46911yescharacteristic
93C2×C103#47711yescharacteristic
94C2×C103#47711yescharacteristic
95C2×C103#47811yescharacteristic
96C2×C103#47811yescharacteristic
97#2087—1031nomaximal, Sylow
98C103#208711yescharacteristic, complemented, Sylow
99C2×#107—1031no—
100C2×C4⋊C8—1031no—
101#389—1031no—
102#389D10311yescharacteristic
103#340—1031no—
104#340—1031no—
105#340—1031no—
106C22×C8—1031no—
107C22×C8—1031no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—1031no—
110C2×C4⋊C4—1031no—
111C2×C4⋊C4—2061no—
112C2×C4⋊C4C2×D10311yescharacteristic
113C2×C4⋊C4C2×D10311yescharacteristic
114C2×C42C2×D10311yescharacteristic
115#107—2062no—
116C4⋊C8—2062no—
117#95—21no—
118#95—2061no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—2061no—
122C22×C4—2061no—
123C22×C4C22⋊D10311yescharacteristic
124C22×C4C22⋊D10311yescharacteristic
125C22×C4C22×D10311yescharacteristic
126C2×C8—1032no—
127C2×C8—2061no—
128C2×C8—2061no—
129C2×C8—2061no—
130C2×C8—2061no—
131C2×C8—2061no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—42no—
136C4⋊C4—1032no—
137C4⋊C4—4122no—
138C4⋊C4—2061no—
139C4⋊C4—2061no—
140C4⋊C4—2061no—
141C4⋊C4Dic20612yes—
142C42—21no—
143C42—21no—
144C23C2×C22⋊D10311yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—4121no—
157C2×C4—4121no—
158C2×C4—4121no—
159C2×C4—4121no—
160C2×C4—4121no—
161C2×C4—2062no—
162C2×C4#1311009512yes—
163C2×C4D4×D10311yescharacteristic
164C2×C4Q8×D10311yescharacteristic
165C2×C4C2×Dic20611yescharacteristic
166C2×C4#1311010411yescharacteristic
167C2×C4#1311010511yescharacteristic
168C2×C4#1311010611yescharacteristic
169C8—4121no—
170C8—2062no—
171C22#1569299311yescharacteristic
172C22#1569299711yescharacteristic
173C22#1569300011yescharacteristic
174C22C2×#1311009511yescharacteristic
175C22#1569304111yescharacteristic
176C22#1569304611yescharacteristic
177C22#1569304711yescharacteristic
178C4—22no—
179C4—41no—
180C4—42no—
181C4—81no—
182C4—8241no—
183C4—4122no—
184C4#1569300611yescharacteristic
185C4#1569301111yescharacteristic
186C4#1569301211yescharacteristic
187C4#1569302011yescharacteristic
188C2#2026772411yescharacteristic
189C2#2026803011yescharacteristic
190C2#2026804211yescharacteristic
191C2#2026808311yescharacteristic
192C2#2026808611yescharacteristic
193C2#2026808811yescharacteristic
194C2#2026809111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#389×C103C2
socle, prime radicalC23×C103C2×D4
hypercenter#389D103
hypocenterC103#2087
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
98. C103#2087semidirect

Maximal subgroups

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

subgroupindex
C2×#156929542
C2×C4⋊(C103⋊C8)2
#202676892
#202675532
#389×C1032
#2087103