Finite Group Databasebeta

← #21447163

Subgroups — #21447163

Order 7808.

246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 75 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#16840390C211yesmaximal, characteristic
2#16839805C211yesmaximal, characteristic
3#16839804C211yesmaximal, characteristic
4#16839632C211yesmaximal, characteristic
5#16839530C211yesmaximal, characteristic
6#16839522C211yesmaximal, characteristic
7C61×#339C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9#14519777—21no—
10#14519776—21no—
11#14519769—21no—
12#14519768—21no—
13#14519754—22no—
14#14519736C2211yescharacteristic
15C2×C4⋊Dic61—22no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18#14519711—21no—
19#14519710—21no—
20#14519709—21no—
21#14519708—21no—
22C2×M16×C61C2211yescharacteristic
23#117×C61C2211yescharacteristic
24C2×C42×C61C2211yescharacteristic
25C22×C4×C61—21no—
26C22×C4×C61C2311yescharacteristic
27C22×Dic61—21no—
28C22×Dic61D412yes—
29C2×Dic122—22no—
30M16×C61—21no—
31M16×C61Q812yescomplemented
32C2×C8×C61—21no—
33C4⋊C4×C61D411yescharacteristic
34C4⋊C4×C61D411yescharacteristic
35C22⋊C4×C61—21no—
36C42×C61—21no—
37C42×C61—21no—
38C42×C61Q812yescomplemented
39C22⋊Dic61—21no—
40C4⋊Dic61—22no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—44no—
46C4⋊Dic61D411yescharacteristic
47C4⋊Dic61D411yescharacteristic
48#11758196—22no—
49#11758196—22no—
50C4×Dic61—21no—
51#11758194—21no—
52#11758194Q812yescomplemented
53C2×#92418—21no—
54C23×C61C2×D411yescharacteristic
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×Q811yescharacteristic
63C2×C4×C61C2×Q811yescharacteristic
64C2×C4×C61C2×Q811yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—22no—
69C2×Dic61—42no—
70C2×Dic61—42no—
71C2×Dic61—41no—
72Dic122—82no—
73C8×C61—22no—
74#92418—22no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61#12011yescharacteristic
78C22×C61C22⋊Q811yescharacteristic
79C22×C61C4⋊Q811yescharacteristic
80C4×C61—24no—
81C4×C61—41no—
82C4×C61—41no—
83C4×C61C22⋊Q811yescharacteristic
84C4×C61C22⋊Q811yescharacteristic
85C4×C61C4⋊Q811yescharacteristic
86C4×C61C4⋊Q811yescharacteristic
87Dic61—41no—
88Dic61—42no—
89Dic61—41no—
90Dic61—81no—
91#2060—611nomaximal, Sylow
92C2×C61—21no—
93C2×C61—21no—
94C2×C61#39511yescharacteristic
95C2×C61#45311yescharacteristic
96C2×C61#45611yescharacteristic
97#544—611no—
98#428—611no—
99#428—611no—
100#384—611no—
101#343—611no—
102#339—611no—
103#339D6111yescharacteristic
104C61#206011yescharacteristic, complemented, Sylow
105C2×M16—611no—
106C2×M16C2×D6111yescharacteristic
107C4⋊Q8—1221no—
108C4⋊Q8—1221no—
109#125—1221no—
110#125—1221no—
111C22⋊Q8—1222no—
112#117—611no—
113#117C2×D6111yescharacteristic
114C2×C4⋊C4—611no—
115C2×C4⋊C4—611no—
116C2×C4⋊C4—1222no—
117C2×C42C2×D6111yescharacteristic
118#107—1221no—
119#107—1221no—
120#106—1221no—
121#106—1221no—
122C2×Q8—1222no—
123C22×C4—21no—
124C22×C4—612no—
125C22×C4—1221no—
126C22×C4C22×D6111yescharacteristic
127M16—21no—
128M16—612no—
129M16—1221no—
130M16Dic12212yescomplemented
131C2×C8—21no—
132C2×C8—1221no—
133C4⋊C4—611no—
134C4⋊C4—611no—
135C4⋊C4—1222no—
136C4⋊C4—1222no—
137C4⋊C4—1222no—
138C4⋊C4—1221no—
139C4⋊C4—1221no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4—2444no—
143C4⋊C4D24411yescharacteristic
144C4⋊C4D24411yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—1221no—
147C42—21no—
148C42—21no—
149C42—1221no—
150C42Dic12212yescomplemented
151C23D4×D6111yescharacteristic
152Q8—4882no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—1221no—
159C2×C4—1221no—
160C2×C4—1222no—
161C2×C4—2442no—
162C2×C4—2441no—
163C2×C4—2442no—
164C2×C4C2×Dic12211yescharacteristic
165C2×C4C2×Dic12211yescharacteristic
166C2×C4C2×D24411yescharacteristic
167C2×C4D4×D6111yescharacteristic
168C2×C4#1175822411yescharacteristic
169C2×C4Q8×D6111yescharacteristic
170C8—22no—
171C8—1222no—
172C22—21no—
173C22—21no—
174C22#1451974711yescharacteristic
175C22#1451975411yescharacteristic
176C22#1451977611yescharacteristic
177C4—24no—
178C4—41no—
179C4—41no—
180C4—4881no—
181C4—2441no—
182C4—2442no—
183C4—2441no—
184C4#1451975411yescharacteristic
185C4#1451975711yescharacteristic
186C4#1451977611yescharacteristic
187C4#1451977711yescharacteristic
188C2—21no—
189C2—21no—
190C2#1683968311yescharacteristic
191C2#1683993111yescharacteristic
192C2#1683994611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61#120
hypercenter#339D61
hypocenterC61#2060
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
31. M16×C61Q8semidirect
38. C42×C61Q8semidirect
52. #11758194Q8semidirect
104. C61#2060semidirect
130. M16Dic122semidirect
150. C42Dic122semidirect