Finite Group Databasebeta

← #27196636

Subgroups — #27196636

Order 13184.

224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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×Dic103⋊C8C211yesmaximal, characteristic
3#20267690C211yesmaximal, characteristic
4#20267687C211yesmaximal, characteristic
5#20267554C211yesmaximal, characteristic
6#20267553C211yesmaximal, characteristic
7#340×C103C211yesmaximal, characteristic
8C22×C103⋊C8C2211yescharacteristic
9C2×C4⋊Dic103—21no—
10C2×C4⋊Dic103C2211yescharacteristic
11C2×C4⋊Dic103C2211yescharacteristic
12C2×Dic103⋊C4—21no—
13C2×C4×Dic103C2211yescharacteristic
14#15692954—22no—
15Dic103⋊C8—22no—
16C103⋊#95—21no—
17C103⋊#95—21no—
18C22×C8×C103C2211yescharacteristic
19C2×C4⋊C4×C103C2211yescharacteristic
20C2×C4⋊C4×C103C2211yescharacteristic
21C22×Dic103—21no—
22C22×Dic103—21no—
23C22×Dic103D411yescharacteristic
24C22×Dic103D411yescharacteristic
25C2×C103⋊C8—21no—
26C2×C103⋊C8—21no—
27C2×C103⋊C8D412yes—
28C4⋊Dic103—21no—
29C4⋊Dic103—21no—
30C4⋊Dic103—21no—
31C4⋊Dic103—42no—
32C4⋊Dic103Q812yes—
33Dic103⋊C4—42no—
34C4×Dic103—21no—
35C4×Dic103—21no—
36C22×C4×C103—21no—
37C22×C4×C103—21no—
38C22×C4×C103C2311yescharacteristic
39C2×C8×C103—21no—
40C2×C8×C103—21no—
41C2×C8×C103—21no—
42C4⋊C4×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—21no—
45C4⋊C4×C103Q812yes—
46C23×C103C2×D411yescharacteristic
47C2×C4×C103—22no—
48C2×C4×C103—41no—
49C2×C4×C103—41no—
50C2×C4×C103—41no—
51C2×C4×C103—41no—
52C2×C4×C103—41no—
53C2×C4×C103C2×D411yescharacteristic
54C2×C4×C103C2×Q811yescharacteristic
55C2×C4×C103C2×Q811yescharacteristic
56C2×C4×C103#4111yescharacteristic
57C2×C4×C103#4111yescharacteristic
58C2×C4×C103#4111yescharacteristic
59C2×Dic103—21no—
60C2×Dic103—21no—
61C2×Dic103—21no—
62C2×Dic103—22no—
63C2×Dic103—21no—
64C2×Dic103—21no—
65C2×Dic103—41no—
66C2×Dic103—41no—
67C2×Dic103—41no—
68C2×Dic103—41no—
69C2×Dic103—41no—
70C2×Dic103D812yes—
71C8×C103—41no—
72C103⋊C8—22no—
73C22×C103#12111yescharacteristic
74C22×C103C22⋊Q811yescharacteristic
75C22×C103C22⋊Q811yescharacteristic
76C22×C103C2×D811yescharacteristic
77C22×C103#13511yescharacteristic
78C22×C103#13711yescharacteristic
79C22×C103#13711yescharacteristic
80C4×C103—42no—
81C4×C103—81no—
82C4×C103#12311yescharacteristic
83C4×C103#12511yescharacteristic
84C4×C103#12511yescharacteristic
85C4×C103C4⋊Q811yescharacteristic
86Dic103—22no—
87Dic103—41no—
88Dic103—42no—
89Dic103—81no—
90C2×C103#39811yescharacteristic
91C2×C103#46611yescharacteristic
92C2×C103#47011yescharacteristic
93C2×C103#47411yescharacteristic
94C2×C103#47411yescharacteristic
95C2×C103#47911yescharacteristic
96C2×C103#47911yescharacteristic
97#2086—1031nomaximal, Sylow
98C103#208611yescharacteristic, complemented, Sylow
99C2×#107—1031no—
100C2×C4⋊C8—1031no—
101#389—1031no—
102#389—1031no—
103#340—1031no—
104#340—1031no—
105#340D10311yescharacteristic
106C22×C8—1031no—
107C22×C8C2×D10311yescharacteristic
108C2×C4⋊C4—1031no—
109C2×C4⋊C4—1031no—
110C2×C4⋊C4—2061no—
111C2×C4⋊C4—2061no—
112C2×C4⋊C4C2×D10311yescharacteristic
113C2×C4⋊C4C2×D10311yescharacteristic
114C2×C42—1031no—
115#107—2062no—
116C4⋊C8—2062no—
117#95—2061no—
118#95—2061no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—1031no—
122C22×C4—1031no—
123C22×C4—2061no—
124C22×C4—2061no—
125C22×C4C22×D10311yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—1032no—
130C2×C8—2061no—
131C2×C8—2061no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—1032no—
136C4⋊C4—4122no—
137C4⋊C4—4122no—
138C4⋊C4—2061no—
139C4⋊C4—2061no—
140C4⋊C4—2061no—
141C4⋊C4Dic20612yes—
142C42—2061no—
143C42—2061no—
144C23D4×D10311yescharacteristic
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—1032no—
152C2×C4—4121no—
153C2×C4—4121no—
154C2×C4—4121no—
155C2×C4—4121no—
156C2×C4—4121no—
157C2×C4—2061no—
158C2×C4—2062no—
159C2×C4—2061no—
160C2×C4—2061no—
161C2×C4—2061no—
162C2×C4—2061no—
163C2×C4D4×D10311yescharacteristic
164C2×C4Q8×D10311yescharacteristic
165C2×C4C2×Dic20611yescharacteristic
166C2×C4#1311010411yescharacteristic
167C2×C4#1311010511yescharacteristic
168C2×C4#1311010511yescharacteristic
169C8—41no—
170C8—2062no—
171C22#1569299411yescharacteristic
172C22#1569299811yescharacteristic
173C22#1569299911yescharacteristic
174C22D8×D10311yescharacteristic
175C22#1569304211yescharacteristic
176C22#1569305011yescharacteristic
177C22#1569305311yescharacteristic
178C4—42no—
179C4—81no—
180C4—8241no—
181C4—4121no—
182C4—4122no—
183C4—2062no—
184C4#1569300311yescharacteristic
185C4#1569301111yescharacteristic
186C4#1569301311yescharacteristic
187C4#1569302011yescharacteristic
188C2#2026772511yescharacteristic
189C2#2026802611yescharacteristic
190C2#2026804811yescharacteristic
191C2#2026806911yescharacteristic
192C2#2026807011yescharacteristic
193C2#2026809611yescharacteristic
194C2#2026810111yescharacteristic
subgroupG/H
centerC23D4×D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#340×C103C2
socle, prime radicalC23×C103C2×D4
hypercenter#340D103
hypocenterC103#2086
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
98. C103#2086semidirect

Maximal subgroups

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

subgroupindex
C2×#156929542
C2×Dic103⋊C82
#202676902
#202676872
#202675542
#202675532
#340×C1032
#2086103