Finite Group Databasebeta

← #20276109

Subgroups — #20276109

Order 6784.

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×#13133151C211yesmaximal, characteristic
2C2×#13133142C211yesmaximal, characteristic
3C2×#13133142C211yesmaximal, characteristic
4#16810529C211yesmaximal, characteristic
5#16810521C211yesmaximal, characteristic
6#16810386C211yesmaximal, characteristic
7C2×C4⋊C8×C53C211yesmaximal, characteristic
8C22×Dic106C2211yescharacteristic
9C2×C4⋊Dic53C2211yescharacteristic
10C2×C4⋊Dic53C2211yescharacteristic
11C2×C4⋊Dic53C2211yescharacteristic
12C2×#11719919—21no—
13#13133151—22no—
14#13133142—22no—
15#13133142—22no—
16#13133124—21no—
17#13133124—21no—
18#13133124—21no—
19C22×C8×C53C2211yescharacteristic
20C22×C8×C53C2211yescharacteristic
21C2×C42×C53C2211yescharacteristic
22C4⋊C8×C53—22no—
23C22×C4×C53D411yescharacteristic
24C22×C4×C53D411yescharacteristic
25C22×C4×C53C2311yescharacteristic
26C22×Dic53—21no—
27C22×Dic53—21no—
28C22×Dic53—21no—
29C22×Dic53—21no—
30C2×Dic106—21no—
31C2×Dic106—21no—
32C2×Dic106—21no—
33C2×Dic106—21no—
34C2×Dic106—21no—
35C2×Dic106Q812yes—
36C2×C8×C53—21no—
37C2×C8×C53—21no—
38C2×C8×C53—21no—
39C2×C8×C53—21no—
40C2×C8×C53—21no—
41C2×C8×C53D412yes—
42C42×C53—21no—
43C42×C53—21no—
44C4⋊Dic53—21no—
45C4⋊Dic53—21no—
46C4⋊Dic53—21no—
47C4⋊Dic53—21no—
48C4⋊Dic53—21no—
49C4⋊Dic53D412yes—
50#11719919—42no—
51C23×C53C2×D411yescharacteristic
52C2×C4×C53—21no—
53C2×C4×C53—21no—
54C2×C4×C53—21no—
55C2×C4×C53—21no—
56C2×C4×C53—21no—
57C2×C4×C53Q1612yes—
58C2×C4×C53C2×D411yescharacteristic
59C2×C4×C53C2×D411yescharacteristic
60C2×C4×C53C2×Q811yescharacteristic
61C2×C4×C53#4111yescharacteristic
62C2×C4×C53#4111yescharacteristic
63C2×C4×C53#4111yescharacteristic
64C2×Dic53—22no—
65C2×Dic53—22no—
66C2×Dic53—41no—
67C2×Dic53—41no—
68C2×Dic53—41no—
69C2×Dic53—41no—
70C2×Dic53—41no—
71C2×Dic53—41no—
72C2×Dic53—41no—
73C2×Dic53—41no—
74C2×Dic53—41no—
75C2×Dic53—41no—
76Dic106—22no—
77Dic106—22no—
78Dic106—41no—
79Dic106—41no—
80C8×C53—22no—
81C8×C53—41no—
82C22×C53#12111yescharacteristic
83C22×C53#12111yescharacteristic
84C22×C53C22⋊Q811yescharacteristic
85C22×C53C2×Q1611yescharacteristic
86C22×C53#13511yescharacteristic
87C22×C53AGL(1,ℤ/8)11yescharacteristic
88C22×C53#13711yescharacteristic
89C4×C53—22no—
90C4×C53—41no—
91C4×C53#12111yescharacteristic
92C4×C53C22⋊Q811yescharacteristic
93C4×C53C22⋊Q811yescharacteristic
94C4×C53#12611yescharacteristic
95Dic53—42no—
96Dic53—42no—
97Dic53—81no—
98Dic53—81no—
99#2068—531nomaximal, Sylow
100C2×C53#39611yescharacteristic
101C2×C53#46211yescharacteristic
102C2×C53#46311yescharacteristic
103C2×C53#46711yescharacteristic
104C2×C53#46811yescharacteristic
105C2×C53#47711yescharacteristic
106C2×C53#47911yescharacteristic
107C2×#107—531no—
108C2×C4⋊C8D5311yescharacteristic
109C2×#103—531no—
110C2×#103—531no—
111#391—531no—
112#389—531no—
113#340—531no—
114C53#206811yescharacteristic, complemented, Sylow
115C22×Q8—531no—
116C22×C8C2×D5311yescharacteristic
117C22×C8C2×D5311yescharacteristic
118C2×C4⋊C4—531no—
119C2×C4⋊C4—531no—
120C2×C4⋊C4—531no—
121C2×C4⋊C4—1061no—
122C2×C42C2×D5311yescharacteristic
123#107—1062no—
124C4⋊C8—22no—
125#103—1062no—
126#103—1062no—
127#95—1061no—
128#95—1061no—
129#95—1061no—
130C2×Q8—532no—
131C2×Q8—1061no—
132C2×Q8—1061no—
133C2×Q8—1061no—
134C2×Q8—1061no—
135C2×Q8—1061no—
136C22×C4—1061no—
137C22×C4—1061no—
138C22×C4—1061no—
139C22×C4—1061no—
140C22×C4D21211yescharacteristic
141C22×C4D21211yescharacteristic
142C22×C4C22×D5311yescharacteristic
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8C22⋊D5312yes—
149C4⋊C4—532no—
150C4⋊C4—1061no—
151C4⋊C4—1061no—
152C4⋊C4—1061no—
153C4⋊C4—1061no—
154C4⋊C4—1061no—
155C4⋊C4—2122no—
156C42—21no—
157C42—21no—
158C23C2×D21211yescharacteristic
159Q8—1062no—
160Q8—1062no—
161Q8—2121no—
162Q8—2121no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—1062no—
169C2×C4—1062no—
170C2×C4—2121no—
171C2×C4—2121no—
172C2×C4—2121no—
173C2×C4—2121no—
174C2×C4—2121no—
175C2×C4—2121no—
176C2×C4—2121no—
177C2×C4—2121no—
178C2×C4—2121no—
179C2×C4—2121no—
180C2×C4Dic21212yes—
181C2×C4#1171994511yescharacteristic
182C2×C4D4×D5311yescharacteristic
183C2×C4#1171994711yescharacteristic
184C2×C4Q8×D5311yescharacteristic
185C2×C4#1171994911yescharacteristic
186C2×C4C2×C22⋊D5311yescharacteristic
187C8—22no—
188C8—41no—
189C22#1313319111yescharacteristic
190C22#1313319211yescharacteristic
191C22#1313319711yescharacteristic
192C22C2×Dic21211yescharacteristic
193C22#1313323911yescharacteristic
194C22#1313324511yescharacteristic
195C22#1313325011yescharacteristic
196C4—22no—
197C4—41no—
198C4—4241no—
199C4—4241no—
200C4—2122no—
201C4—2122no—
202C4#1313318911yescharacteristic
203C4#1313319311yescharacteristic
204C4#1313319511yescharacteristic
205C4#1313321211yescharacteristic
206C2#1681054511yescharacteristic
207C2#1681083411yescharacteristic
208C2#1681083911yescharacteristic
209C2#1681086411yescharacteristic
210C2#1681086911yescharacteristic
211C2#1681091911yescharacteristic
212C2#1681093111yescharacteristic
subgroupG/H
centerC23C2×D212
commutatorC22×C4×C53C23
FrattiniC22×C4C22×D53
FittingC2×C4⋊C8×C53C2
socleC23×C53C2×D4
hypercenterC2×C4⋊C8D53
hypocenterC53#2068
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
114. C53#2068semidirect