Finite Group Databasebeta

← #27196482

Subgroups — #27196482

Order 13184.

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

normal subgroups only

This group has 250 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×#15693013C211yesmaximal, characteristic
2C2×#15692954C211yesmaximal, characteristic
3C2×#15692952C211yesmaximal, characteristic
4#20267553C211yesmaximal, characteristic
5#20267553C211yesmaximal, characteristic
6#20267546C211yesmaximal, characteristic
7#389×C103C211yesmaximal, characteristic
8C22×C103⋊C8C2211yescharacteristic
9C22×C103⋊C8C2211yescharacteristic
10#15693013—22no—
11#15693013—22no—
12C2×C4⋊Dic103C2211yescharacteristic
13C2×C4⋊Dic103C2211yescharacteristic
14C2×Dic103⋊C4—21no—
15C2×Dic103⋊C4—21no—
16#15692954—22no—
17#15692952—22no—
18C2×C4⋊C4×C103—21no—
19C2×C4⋊C4×C103C2211yescharacteristic
20C2×C4⋊C4×C103C2211yescharacteristic
21C2×C42×C103C2211yescharacteristic
22#95×C103—21no—
23C22×Dic103—21no—
24C22×Dic103—21no—
25C2×C103⋊C8—21no—
26C2×C103⋊C8—21no—
27C2×C103⋊C8—21no—
28C2×C103⋊C8—21no—
29C2×C103⋊C8Q812yes—
30C2×C103⋊C8Q812yes—
31C4⋊Dic103—21no—
32C4⋊Dic103—21no—
33C4⋊Dic103D412yes—
34C4⋊Dic103D412yes—
35Dic103⋊C4—24no—
36Dic103⋊C4—24no—
37C22×C4×C103—21no—
38C22×C4×C103—21no—
39C22×C4×C103D411yescharacteristic
40C22×C4×C103D411yescharacteristic
41C22×C4×C103C2311yescharacteristic
42C4⋊C4×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103—42no—
46C4⋊C4×C103Q812yes—
47C42×C103—21no—
48C42×C103—21no—
49C23×C103C2×D411yescharacteristic
50C2×C4×C103—21no—
51C2×C4×C103—21no—
52C2×C4×C103—22no—
53C2×C4×C103—21no—
54C2×C4×C103—21no—
55C2×C4×C103—21no—
56C2×C4×C103—21no—
57C2×C4×C103—41no—
58C2×C4×C103—41no—
59C2×C4×C103—41no—
60C2×C4×C103—41no—
61C2×C4×C103—41no—
62C2×C4×C103C2×D411yescharacteristic
63C2×C4×C103C2×D411yescharacteristic
64C2×C4×C103C2×Q811yescharacteristic
65C2×C4×C103C2×Q811yescharacteristic
66C2×C4×C103C2×Q811yescharacteristic
67C2×C4×C103#4111yescharacteristic
68C2×Dic103—22no—
69C2×Dic103—22no—
70C2×Dic103—41no—
71C2×Dic103—41no—
72C2×Dic103—41no—
73C2×Dic103—41no—
74C103⋊C8—22no—
75C103⋊C8—22no—
76C22×C103#12011yescharacteristic
77C22×C103C22⋊Q811yescharacteristic
78C22×C103C4⋊Q811yescharacteristic
79C22×C103#13511yescharacteristic
80C22×C103#13511yescharacteristic
81C22×C103AGL(1,ℤ/8)11yescharacteristic
82C22×C103#13711yescharacteristic
83C4×C103—41no—
84C4×C103—41no—
85C4×C103—42no—
86C4×C103—81no—
87C4×C103C22⋊Q811yescharacteristic
88C4×C103C22⋊Q811yescharacteristic
89C4×C103C4⋊Q811yescharacteristic
90C4×C103C4⋊Q811yescharacteristic
91Dic103—42no—
92Dic103—42no—
93C2×C103#39511yescharacteristic
94C2×C103#44911yescharacteristic
95C2×C103#45211yescharacteristic
96C2×C103#47811yescharacteristic
97C2×C103#47911yescharacteristic
98C2×C103#49911yescharacteristic
99C2×C103#50111yescharacteristic
100#2059—1031nomaximal, Sylow
101C103#205911yescharacteristic, complemented, Sylow
102C2×#125—1031no—
103C2×#107—1031no—
104C2×#106—1031no—
105#389D10311yescharacteristic
106#340—1031no—
107#340—1031no—
108#336—1031no—
109C22×C8—1031no—
110C22×C8—1031no—
111#125—2062no—
112#125—2062no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—1031no—
115C2×C4⋊C4—1031no—
116C2×C4⋊C4—2061no—
117C2×C4⋊C4—2061no—
118C2×C4⋊C4C2×D10311yescharacteristic
119C2×C4⋊C4C2×D10311yescharacteristic
120C2×C42C2×D10311yescharacteristic
121#107—2062no—
122#106—2062no—
123#95—21no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—2061no—
127C22×C4—2061no—
128C22×C4C22⋊D10311yescharacteristic
129C22×C4C22⋊D10311yescharacteristic
130C22×C4C22×D10311yescharacteristic
131C2×C8—1032no—
132C2×C8—1032no—
133C2×C8—2061no—
134C2×C8—2061no—
135C2×C8—2061no—
136C2×C8—2061no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—42no—
141C4⋊C4—1032no—
142C4⋊C4—1032no—
143C4⋊C4—2064no—
144C4⋊C4—2064no—
145C4⋊C4—2061no—
146C4⋊C4—2061no—
147C4⋊C4Dic20612yes—
148C42—21no—
149C42—21no—
150C23C2×C22⋊D10311yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—4121no—
164C2×C4—4121no—
165C2×C4—4121no—
166C2×C4—4121no—
167C2×C4—2062no—
168C2×C4—2062no—
169C2×C4D4×D10311yescharacteristic
170C2×C4D4×D10311yescharacteristic
171C2×C4Q8×D10311yescharacteristic
172C2×C4Q8×D10311yescharacteristic
173C2×C4C2×Dic20611yescharacteristic
174C2×C4#1311010511yescharacteristic
175C8—2062no—
176C8—2062no—
177C22#1569298911yescharacteristic
178C22#1569300011yescharacteristic
179C22#1569301911yescharacteristic
180C22#1569304111yescharacteristic
181C22#1569304111yescharacteristic
182C22#1569304711yescharacteristic
183C22#1569305211yescharacteristic
184C4—42no—
185C4—41no—
186C4—41no—
187C4—81no—
188C4—4122no—
189C4—4122no—
190C4#1569299911yescharacteristic
191C4#1569299911yescharacteristic
192C4#1569302011yescharacteristic
193C4#1569302011yescharacteristic
194C2#2026771111yescharacteristic
195C2#2026793411yescharacteristic
196C2#2026795111yescharacteristic
197C2#2026809111yescharacteristic
198C2#2026809811yescharacteristic
199C2#2026819011yescharacteristic
200C2#2026819711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#389×C103C2
socle, prime radicalC23×C103C2×D4
hypercenter#389D103
hypocenterC103#2059
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
101. C103#2059semidirect

Maximal subgroups

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

subgroupindex
C2×#156930132
C2×#156929542
C2×#156929522
#202675532
#202675462
#389×C1032
#2059103