Finite Group Databasebeta

← #21455950

Subgroups — #21455950

Order 7808.

380 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 129 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#16840319C211yesmaximal, characteristic
2C2×C4×Dic122C211yesmaximal, characteristic
3#16840093C212yesmaximal
4#16840048C212yesmaximal, complemented
5#16839973C212yesmaximal, complemented
6#16839920C212yesmaximal
7#16839870C214yesmaximal, complemented
8C61×#432C211yesmaximal, characteristic
9C22×Dic122C2211yescharacteristic
10C2×Dic244C2214yes—
11#14519777C2211yescharacteristic
12#14519777C2211yescharacteristic
13#14519769—21no—
14#14519756—21no—
15#14519756C2212yes—
16C4×Dic122—21no—
17C4×Dic122—21no—
18C4×Dic122—21no—
19C4×Dic122C2212yes—
20C4×Dic122C2212yes—
21C4×Dic122C2212yes—
22#14519736—21no—
23C2×C4⋊Dic61C2211yescharacteristic
24C2×#11758196—21no—
25C2×C4×Dic61—21no—
26#14519709C2214yes—
27#14519702C2214yes—
28#14519702C2214yes—
29C2×C42×C61C2211yescharacteristic
30C4⋊C8×C61C2212yes—
31C22⋊C8×C61C2212yes—
32#97×C61C2212yes—
33C22×C4×C61D411yescharacteristic
34C22×C4×C61D411yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—21no—
37C22×Dic61—21no—
38C2×Dic122—21no—
39C2×Dic122—24no—
40C2×Dic122—21no—
41C2×Dic122C2312yes—
42C2×Dic122C2312yes—
43C2×C8×C61C2314yes—
44C42×C61D411yescharacteristic
45C42×C61D411yescharacteristic
46C42×C61C2311yescharacteristic
47C42×C61C2311yescharacteristic
48C22⋊Dic61—22no—
49C4⋊Dic61—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61—21no—
52C4⋊Dic61—21no—
53C4⋊Dic61C2312yes—
54C4⋊Dic61C2312yes—
55#11758196—22no—
56#11758196—22no—
57#11758196—22no—
58#11758196—22no—
59C4×Dic61—22no—
60C4×Dic61—22no—
61C4×Dic61—22no—
62Dic244—28no—
63C23×C61C2×D411yescharacteristic
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2411yescharacteristic
73C2×Dic61—24no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—42no—
79Dic122—24no—
80Dic122—22no—
81Dic122—24no—
82Dic122—42no—
83Dic122#4114yes—
84C8×C61—24no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61#13712yes—
88C22×C61C22×D411yescharacteristic
89C4×C61—21no—
90C4×C61—21no—
91C4×C61—21no—
92C4×C61—21no—
93C4×C61#13712yes—
94C4×C61C2×#4112yes—
95Dic61—24no—
96Dic61—42no—
97Dic61—42no—
98Dic61—42no—
99#3113—611nomaximal, Sylow
100C2×C61—22no—
101C2×C61#52511yescharacteristic
102C2×C61C2×#13711yescharacteristic
103C2×C61C2×#13711yescharacteristic
104#533—611no—
105C2×C4×Q8—611no—
106#483—612no—
107#475—612no—
108#462—612no—
109#451—612no—
110#441—614no—
111#432D6111yescharacteristic
112C61#311311yescharacteristic, complemented, Sylow
113C22×Q8—611no—
114C2×Q16—614no—
115C4⋊Q8—611no—
116C4⋊Q8—611no—
117#125—1221no—
118C22⋊Q8—612no—
119C22⋊Q8—1221no—
120C4×Q8—612no—
121C4×Q8—612no—
122C4×Q8—612no—
123C4×Q8—1221no—
124C4×Q8—1221no—
125C4×Q8—1221no—
126#117—1221no—
127C2×C4⋊C4—611no—
128C2×C4⋊C4—1221no—
129C2×C42—1221no—
130C2×C42C2×D6111yescharacteristic
131#106—614no—
132C4⋊C8C2×D6112yes—
133#103—614no—
134#103—614no—
135C22⋊C8C2×D6112yes—
136#97C2×D6112yes—
137C2×Q8—612no—
138C2×Q8—612no—
139C2×Q8—1224no—
140C2×Q8—1221no—
141C2×Q8—1221no—
142C22×C4—1221no—
143C22×C4—1221no—
144C22×C4D24411yescharacteristic
145C22×C4D24411yescharacteristic
146C22×C4C22×D6111yescharacteristic
147Q16—1228no—
148C2×C8C22×D6114yes—
149C4⋊C4—612no—
150C4⋊C4—612no—
151C4⋊C4—1221no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4—1221no—
159C22⋊C4—1222no—
160C42—1222no—
161C42—1222no—
162C42—1222no—
163C42D24411yescharacteristic
164C42D24411yescharacteristic
165C42C22×D6111yescharacteristic
166C42C22×D6111yescharacteristic
167C23C2×D24411yescharacteristic
168Q8—614no—
169Q8—1224no—
170Q8—1222no—
171Q8—1224no—
172Q8—2442no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—1224no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—2442no—
182C2×C4C2×D24411yescharacteristic
183C2×C4C2×D24411yescharacteristic
184C2×C4C2×D24411yescharacteristic
185C2×C4C2×D24411yescharacteristic
186C2×C4C2×D24411yescharacteristic
187C2×C4C23×D6111yescharacteristic
188C8—24no—
189C22—21no—
190C22—21no—
191C22#1451981012yes—
192C22C22×D24411yescharacteristic
193C4—21no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—1224no—
198C4—2442no—
199C4—2442no—
200C4—2442no—
201C4#1451981012yes—
202C4#41×D6112yes—
203C2—22no—
204C2#1684027411yescharacteristic
205C2C2×#1451981011yescharacteristic
206C2C2×#1451981011yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3113
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
4. #16840048C2semidirect
5. #16839973C2semidirect
7. #16839870C2semidirect
112. C61#3113semidirect