Finite Group Databasebeta

← #27196539

Subgroups — #27196539

Order 13184.

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

normal subgroups only

This group has 248 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
3C2×#15692945C211yesmaximal, characteristic
4C2×#15692945C211yesmaximal, characteristic
5#20267689C211yesmaximal, characteristic
6#20267553C211yesmaximal, characteristic
7#391×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—
15#15692945—22no—
16#15692945—22no—
17C103⋊#95—21no—
18C22×Q8×C103C2211yescharacteristic
19C2×C4⋊C4×C103C2211yescharacteristic
20C2×C42×C103C2211yescharacteristic
21#95×C103—21no—
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⋊C8—21no—
30C2×C103⋊C8D412yes—
31C4⋊Dic103—21no—
32C4⋊Dic103—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103D412yes—
35Dic103⋊C4—42no—
36C2×Q8×C103—21no—
37C2×Q8×C103—21no—
38C2×Q8×C103—21no—
39C2×Q8×C103—21no—
40C2×Q8×C103—21no—
41C2×Q8×C103Q812yes—
42C22×C4×C103—21no—
43C22×C4×C103—21no—
44C22×C4×C103D411yescharacteristic
45C22×C4×C103D411yescharacteristic
46C22×C4×C103C2311yescharacteristic
47C4⋊C4×C103—21no—
48C4⋊C4×C103—21no—
49C42×C103—21no—
50C42×C103—21no—
51C23×C103C2×D411yescharacteristic
52Q8×C103—22no—
53Q8×C103—22no—
54Q8×C103—41no—
55Q8×C103—41no—
56C2×C4×C103—21no—
57C2×C4×C103—21no—
58C2×C4×C103—21no—
59C2×C4×C103—22no—
60C2×C4×C103—21no—
61C2×C4×C103—21no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103—41no—
67C2×C4×C103Q1612yes—
68C2×C4×C103C2×D411yescharacteristic
69C2×C4×C103C2×D411yescharacteristic
70C2×C4×C103C2×Q811yescharacteristic
71C2×C4×C103#4111yescharacteristic
72C2×C4×C103#4111yescharacteristic
73C2×C4×C103#4111yescharacteristic
74C2×Dic103—22no—
75C2×Dic103—41no—
76C2×Dic103—41no—
77C2×Dic103—41no—
78C2×Dic103—41no—
79C2×Dic103—41no—
80C103⋊C8—22no—
81C103⋊C8—41no—
82C22×C103#12111yescharacteristic
83C22×C103#12111yescharacteristic
84C22×C103C22⋊Q811yescharacteristic
85C22×C103C2×Q1611yescharacteristic
86C22×C103#13511yescharacteristic
87C22×C103AGL(1,ℤ/8)11yescharacteristic
88C22×C103#13711yescharacteristic
89C4×C103—22no—
90C4×C103—42no—
91C4×C103—41no—
92C4×C103—81no—
93C4×C103#12111yescharacteristic
94C4×C103C22⋊Q811yescharacteristic
95C4×C103C22⋊Q811yescharacteristic
96C4×C103#12611yescharacteristic
97Dic103—42no—
98Dic103—81no—
99C2×C103#39611yescharacteristic
100C2×C103#46211yescharacteristic
101C2×C103#46311yescharacteristic
102C2×C103#46711yescharacteristic
103C2×C103#46811yescharacteristic
104C2×C103#47711yescharacteristic
105C2×C103#47911yescharacteristic
106#2068—1031nomaximal, Sylow
107C103#206811yescharacteristic, complemented, Sylow
108C2×#107—1031no—
109C2×C4⋊C8—1031no—
110C2×#103—1031no—
111C2×#103—1031no—
112#391D10311yescharacteristic
113#389—1031no—
114#340—1031no—
115C22×Q8C2×D10311yescharacteristic
116C22×C8—1031no—
117C22×C8—1031no—
118C2×C4⋊C4—1031no—
119C2×C4⋊C4—1031no—
120C2×C4⋊C4—2061no—
121C2×C4⋊C4C2×D10311yescharacteristic
122C2×C42C2×D10311yescharacteristic
123#107—2062no—
124C4⋊C8—2062no—
125#103—2062no—
126#103—2062no—
127#95—21no—
128#95—21no—
129#95—2061no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8Dic20612yes—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—2061no—
139C22×C4—2061no—
140C22×C4C22⋊D10311yescharacteristic
141C22×C4C22⋊D10311yescharacteristic
142C22×C4C22×D10311yescharacteristic
143C2×C8—1032no—
144C2×C8—2061no—
145C2×C8—2061no—
146C2×C8—2061no—
147C2×C8—2061no—
148C2×C8—2061no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—1032no—
152C4⋊C4—4122no—
153C4⋊C4—2061no—
154C4⋊C4—2061no—
155C4⋊C4—2061no—
156C42—21no—
157C42—21no—
158C23C2×C22⋊D10311yescharacteristic
159Q8—22no—
160Q8—22no—
161Q8—41no—
162Q8—41no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—4121no—
175C2×C4—4121no—
176C2×C4—4121no—
177C2×C4—4121no—
178C2×C4—4121no—
179C2×C4—2062no—
180C2×C4#1311009512yes—
181C2×C4D4×D10311yescharacteristic
182C2×C4D4×D10311yescharacteristic
183C2×C4C2×Dic20611yescharacteristic
184C2×C4#1311010411yescharacteristic
185C2×C4#1311010411yescharacteristic
186C2×C4#1311010511yescharacteristic
187C8—4121no—
188C8—2062no—
189C22#1569299211yescharacteristic
190C22#1569299311yescharacteristic
191C22#1569300011yescharacteristic
192C22C2×#1311009511yescharacteristic
193C22#1569304111yescharacteristic
194C22#1569304611yescharacteristic
195C22#1569305211yescharacteristic
196C4—22no—
197C4—41no—
198C4—42no—
199C4—81no—
200C4—8241no—
201C4—4122no—
202C4#1569299411yescharacteristic
203C4#1569299811yescharacteristic
204C4#1569299811yescharacteristic
205C4#1569301411yescharacteristic
206C2#2026771411yescharacteristic
207C2#2026799811yescharacteristic
208C2#2026800311yescharacteristic
209C2#2026803011yescharacteristic
210C2#2026803911yescharacteristic
211C2#2026808611yescharacteristic
212C2#2026809811yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#391×C103C2
socle, prime radicalC23×C103C2×D4
hypercenter#391D103
hypocenterC103#2068
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
107. C103#2068semidirect

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
C2×#156929452
#202676892
#202675532
#391×C1032
#2068103