Finite Group Databasebeta

← #21444741

Subgroups — #21444741

Order 7808.

316 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 53 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#16840388C211yesmaximal, characteristic, complemented
2#16839913C212yesmaximal, complemented
3#16839498C212yesmaximal, complemented
4#16839486C211yesmaximal, characteristic, complemented
5C61×#392C211yesmaximal, characteristic
6C2×#11758200—22no—
7#14519756—21no—
8#14519756C2212yes—
9#14519754—22no—
10#14519754—22no—
11C2×C22⋊Dic61—21no—
12#14519698—22no—
13C22⋊#92418C2212yes—
14C22×D4×C61—21no—
15C22×D4×C61C2211yescharacteristic
16C2×C22⋊C4×C61—21no—
17C2×C22⋊C4×C61C2211yescharacteristic
18#95×C61C2211yescharacteristic
19C24×C61—21no—
20C24×C61D411yescharacteristic
21C2×D4×C61—22no—
22C2×D4×C61—42no—
23C2×D4×C61—42no—
24C2×D4×C61—42no—
25C2×D4×C61—42no—
26C22×C4×C61—21no—
27C22×C4×C61D411yescharacteristic
28C22×C4×C61C2311yescharacteristic
29C22×Dic61—21no—
30C22×Dic61—21no—
31C2×Dic122—21no—
32C2×Dic122D412yescomplemented
33C22⋊C4×C61—22no—
34C22⋊C4×C61—42no—
35C22⋊Dic61—22no—
36C22⋊Dic61—22no—
37#11758200—44no—
38C4⋊Dic61—21no—
39C4⋊Dic61D412yescomplemented
40#11758196—22no—
41#11758196—22no—
42C2×#92418—22no—
43C23×C61—21no—
44C23×C61—21no—
45C23×C61—22no—
46C23×C61—41no—
47C23×C61—41no—
48C23×C61—41no—
49C23×C61—41no—
50C23×C61—41no—
51C23×C61—41no—
52C23×C61—41no—
53C23×C61—41no—
54C23×C61SD1612yescomplemented
55C23×C61C2×D411yescharacteristic
56D4×C61—24no—
57D4×C61—42no—
58D4×C61—48no—
59C2×C4×C61—22no—
60C2×C4×C61—21no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61C2×D412yes—
66C2×Dic61—22no—
67C2×Dic61—22no—
68C2×Dic61—81no—
69C2×Dic61—81no—
70Dic122—42no—
71Dic122—81no—
72#92418—42no—
73C22×C61—21no—
74C22×C61—21no—
75C22×C61—22no—
76C22×C61—42no—
77C22×C61—42no—
78C22×C61—42no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61—42no—
82C22×C61—81no—
83C22×C61—81no—
84C22×C61—81no—
85C22×C61—81no—
86C22×C61—81no—
87C22×C61#12011yescharacteristic
88C22×C61C2×SD1611yescharacteristic
89C22×C61#13711yescharacteristic
90C4×C61—22no—
91C4×C61—42no—
92C4×C61—41no—
93Dic61—42no—
94Dic61—42no—
95#1596—611nomaximal, Sylow
96C2×C61—21no—
97C2×C61—21no—
98C2×C61—42no—
99C2×C61—82no—
100C2×C61#44811yescharacteristic
101C2×C61#45311yescharacteristic
102C2×C61B(4,𝔽2)11yescharacteristic
103#543—611no—
104#450—612no—
105#392D6111yescharacteristic
106#328—612no—
107#323—611no—
108C61#159611yescharacteristic, complemented, Sylow
109C22×D4—21no—
110C22×D4C2×D6111yescharacteristic
111C2×SD16—1222no—
112C22⋊Q8—612no—
113C22⋊Q8—1222no—
114C22⋊Q8—1222no—
115C22⋊Q8—1221no—
116C2×C22⋊C4—21no—
117C2×C22⋊C4—1221no—
118C2×C22⋊C4C2×D6111yescharacteristic
119#102—1222no—
120C22⋊C8—612no—
121#95C2×D6111yescharacteristic
122C24—21no—
123C24C22⋊D6111yescharacteristic
124C2×Q8—612no—
125C2×Q8—1221no—
126C2×D4—22no—
127C2×D4—42no—
128C2×D4—42no—
129C2×D4—42no—
130C2×D4—42no—
131C22×C4—21no—
132C22×C4—1221no—
133C22×C4—1221no—
134C22×C4C22⋊D6111yescharacteristic
135C22×C4C22×D6111yescharacteristic
136SD16—2444no—
137C2×C8—1222no—
138C4⋊C4—612no—
139C4⋊C4—1222no—
140C4⋊C4—1221no—
141C4⋊C4—1222no—
142C22⋊C4—22no—
143C22⋊C4—42no—
144C22⋊C4—1222no—
145C22⋊C4—1222no—
146C23—21no—
147C23—21no—
148C23—22no—
149C23—41no—
150C23—41no—
151C23—41no—
152C23—41no—
153C23—41no—
154C23—41no—
155C23—41no—
156C23—41no—
157C23#1175820012yescomplemented
158C23C2×C22⋊D6111yescharacteristic
159Q8—4881no—
160Q8—2442no—
161D4—24no—
162D4—42no—
163D4—48no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—1222no—
171C2×C4—1222no—
172C2×C4—4881no—
173C2×C4—4881no—
174C2×C4D4×D6112yes—
175C8—2442no—
176C22—21no—
177C22—21no—
178C22—22no—
179C22—42no—
180C22—42no—
181C22—42no—
182C22—41no—
183C22—41no—
184C22—42no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22—81no—
189C22—81no—
190C22#1451974511yescharacteristic
191C22C2×#1175820011yescharacteristic
192C22#1451980711yescharacteristic
193C4—22no—
194C4—42no—
195C4—41no—
196C4—2442no—
197C4—2442no—
198C2—21no—
199C2—21no—
200C2—42no—
201C2—82no—
202C2#1683990011yescharacteristic
203C2#1683992911yescharacteristic
204C2#1683994811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#392C2
socleC22×C61#120
hypercenter#392D61
hypocenterC61#1596
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #16840388C2semidirect
2. #16839913C2semidirect
3. #16839498C2semidirect
4. #16839486C2semidirect
32. C2×Dic122D4semidirect
39. C4⋊Dic61D4semidirect
54. C23×C61SD16semidirect
108. C61#1596semidirect
157. C23#11758200semidirect