Finite Group Databasebeta

← #27196711

Subgroups — #27196711

Order 13184.

198 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#20267689C211yesmaximal, characteristic
2#20267553C211yesmaximal, characteristic
3#20267553C211yesmaximal, characteristic
4#20267553C211yesmaximal, characteristic
5#20267553C211yesmaximal, characteristic
6#20267546C211yesmaximal, characteristic
7#382×C103C211yesmaximal, characteristic
8C22×C103⋊C8C2211yescharacteristic
9C22×C103⋊C8C2211yescharacteristic
10C2×C4⋊Dic103C2211yescharacteristic
11C2×C4⋊Dic103C2211yescharacteristic
12C2×Dic103⋊C4—21no—
13C103⋊#95—21no—
14C2×C4⋊C4×C103C2211yescharacteristic
15C2×C4⋊C4×C103C2211yescharacteristic
16C2×C42×C103C2211yescharacteristic
17#95×C103—21no—
18#95×C103—21no—
19C22×Dic103—21no—
20C22×Dic103—21no—
21C2×C103⋊C8—21no—
22C2×C103⋊C8—21no—
23C2×C103⋊C8—21no—
24C2×C103⋊C8—21no—
25C2×C103⋊C8—21no—
26C2×C103⋊C8—21no—
27C4⋊Dic103—21no—
28C4⋊Dic103—21no—
29C4⋊Dic103—21no—
30C4⋊Dic103Q812yes—
31Dic103⋊C4—42no—
32C22×C4×C103—21no—
33C22×C4×C103—21no—
34C22×C4×C103D411yescharacteristic
35C22×C4×C103D411yescharacteristic
36C22×C4×C103C2311yescharacteristic
37C4⋊C4×C103—21no—
38C4⋊C4×C103—21no—
39C4⋊C4×C103—21no—
40C4⋊C4×C103—21no—
41C42×C103—21no—
42C42×C103—21no—
43C23×C103C2×D411yescharacteristic
44C2×C4×C103—21no—
45C2×C4×C103—21no—
46C2×C4×C103—21no—
47C2×C4×C103—21no—
48C2×C4×C103—21no—
49C2×C4×C103—21no—
50C2×C4×C103—41no—
51C2×C4×C103—41no—
52C2×C4×C103—41no—
53C2×C4×C103—41no—
54C2×C4×C103—41no—
55C2×C4×C103—41no—
56C2×C4×C103C2×Q811yescharacteristic
57C2×C4×C103#4111yescharacteristic
58C2×C4×C103#4111yescharacteristic
59C2×C4×C103#4111yescharacteristic
60C2×C4×C103#4111yescharacteristic
61C2×C4×C103#4111yescharacteristic
62C2×Dic103—22no—
63C2×Dic103—41no—
64C2×Dic103—41no—
65C2×Dic103—41no—
66C2×Dic103—41no—
67C2×Dic103—41no—
68C103⋊C8—41no—
69C103⋊C8—41no—
70C22×C103C22⋊Q811yescharacteristic
71C22×C103#12311yescharacteristic
72C22×C103#12411yescharacteristic
73C22×C103#13511yescharacteristic
74C22×C103#13511yescharacteristic
75C22×C103AGL(1,ℤ/8)11yescharacteristic
76C22×C103#13711yescharacteristic
77C4×C103—41no—
78C4×C103—41no—
79C4×C103—81no—
80C4×C103—81no—
81C4×C103#12511yescharacteristic
82C4×C103#12511yescharacteristic
83C4×C103#12611yescharacteristic
84C4×C103#12611yescharacteristic
85Dic103—42no—
86Dic103—81no—
87C2×C103#40011yescharacteristic
88C2×C103#47811yescharacteristic
89C2×C103#47911yescharacteristic
90C2×C103#48211yescharacteristic
91C2×C103#48511yescharacteristic
92C2×C103#48811yescharacteristic
93C2×C103#48911yescharacteristic
94#2101—1031nomaximal, Sylow
95C103#210111yescharacteristic, complemented, Sylow
96#389—1031no—
97#382D10311yescharacteristic
98#340—1031no—
99#340—1031no—
100#340—1031no—
101#340—1031no—
102#336—1031no—
103C22×C8—1031no—
104C22×C8—1031no—
105C2×C4⋊C4—1031no—
106C2×C4⋊C4—1031no—
107C2×C4⋊C4—2061no—
108C2×C4⋊C4C2×D10311yescharacteristic
109C2×C4⋊C4C2×D10311yescharacteristic
110C2×C42C2×D10311yescharacteristic
111#95—21no—
112#95—21no—
113#95—2061no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—2061no—
117C22×C4—2061no—
118C22×C4C22⋊D10311yescharacteristic
119C22×C4C22⋊D10311yescharacteristic
120C22×C4C22×D10311yescharacteristic
121C2×C8—2061no—
122C2×C8—2061no—
123C2×C8—2061no—
124C2×C8—2061no—
125C2×C8—2061no—
126C2×C8—2061no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—1032no—
132C4⋊C4—4122no—
133C4⋊C4—2061no—
134C4⋊C4—2061no—
135C4⋊C4—2061no—
136C42—21no—
137C42—21no—
138C23C2×C22⋊D10311yescharacteristic
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—4121no—
152C2×C4—4121no—
153C2×C4—4121no—
154C2×C4—4121no—
155C2×C4—4121no—
156C2×C4—2062no—
157C2×C4Q8×D10311yescharacteristic
158C2×C4#1311010411yescharacteristic
159C2×C4#1311010411yescharacteristic
160C2×C4#1311010511yescharacteristic
161C2×C4#1311010511yescharacteristic
162C2×C4#1311010611yescharacteristic
163C8—4121no—
164C8—4121no—
165C22#1569299711yescharacteristic
166C22#1569300411yescharacteristic
167C22#1569300811yescharacteristic
168C22#1569304111yescharacteristic
169C22#1569304111yescharacteristic
170C22#1569304611yescharacteristic
171C22#1569305111yescharacteristic
172C4—41no—
173C4—41no—
174C4—81no—
175C4—81no—
176C4—8241no—
177C4—4122no—
178C4#1569301111yescharacteristic
179C4#1569301111yescharacteristic
180C4#1569301611yescharacteristic
181C4#1569301611yescharacteristic
182C2#2026772911yescharacteristic
183C2#2026808811yescharacteristic
184C2#2026809511yescharacteristic
185C2#2026811511yescharacteristic
186C2#2026813211yescharacteristic
187C2#2026814511yescharacteristic
188C2#2026815011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutator, cosocleC22×C4×C103C23
FrattiniC22×C4C22×D103
Fitting#382×C103C2
socle, prime radicalC23×C103C2×D4
hypercenter#382D103
hypocenterC103#2101
LCSG ▷ C22×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
95. C103#2101semidirect

Maximal subgroups

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

subgroupindex
#202676892
#202675532
#202675462
#382×C1032
#2101103