Finite Group Databasebeta

← #21451200

Subgroups — #21451200

Order 7808.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C22×#11758196C211yesmaximal, characteristic
2#16839693C212yesmaximal, complemented
3#16839681C212yesmaximal, complemented
4#16839657C214yesmaximal, complemented
5#16839634C212yesmaximal
6#16839634C212yesmaximal
7C4×C22⋊Dic61C211yesmaximal, characteristic
8C2×C22⋊Q8×C61C211yesmaximal, characteristic
9C23×Dic61C2211yescharacteristic
10C23×Dic61C2211yescharacteristic
11C2×#11758196—24no—
12C2×#11758196C2212yes—
13C2×#11758196C2214yes—
14C2×#11758196C2212yes—
15C2×#11758196C2214yes—
16C2×C22⋊Dic61C2212yes—
17C2×C4×Dic61C2212yes—
18#14519684C2212yes—
19#14519684C2214yes—
20#14519684C2214yes—
21C22×Q8×C61C2211yescharacteristic
22C23×C4×C61C2211yescharacteristic
23C22⋊Q8×C61—24no—
24C2×C4⋊C4×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2212yes—
26C2×C22⋊C4×C61C2212yes—
27C24×C61C2311yescharacteristic
28C2×Q8×C61—22no—
29C2×Q8×C61—42no—
30C22×C4×C61—42no—
31C22×C4×C61D414yes—
32C22×C4×C61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—22no—
37C22×Dic61—24no—
38C22×Dic61—22no—
39C22×Dic61—42no—
40C22×Dic61C2312yes—
41C22×Dic61C2314yes—
42C22×Dic61C2312yes—
43C4⋊C4×C61—22no—
44C4⋊C4×C61—24no—
45C22⋊C4×C61—24no—
46C22⋊Dic61Q818yescomplemented
47#11758196—24no—
48#11758196—24no—
49#11758196—28no—
50#11758196—44no—
51C4×Dic61—42no—
52C23×C61—22no—
53C23×C61—22no—
54C23×C61C2×D412yes—
55C23×C61C2×Q814yes—
56C23×C61C2411yescharacteristic
57Q8×C61—44no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—24no—
63C2×C4×C61—24no—
64C2×C4×C61—44no—
65C2×C4×C61C2×D412yes—
66C2×C4×C61C2×D412yes—
67C2×Dic61—28no—
68C2×Dic61—22no—
69C2×Dic61—24no—
70C2×Dic61—22no—
71C2×Dic61—24no—
72C2×Dic61—22no—
73C2×Dic61—24no—
74C2×Dic61—44no—
75C2×Dic61C2×Q818yes—
76C2×Dic61#4114yes—
77C22×C61—22no—
78C22×C61—22no—
79C22×C61—28no—
80C22×C61C4⋊Q814yes—
81C22×C61C22×D411yescharacteristic
82C22×C61C22×Q812yes—
83C22×C61C2×#4112yes—
84C22×C61H(5,𝔽2)12yes—
85C4×C61—22no—
86C4×C61—22no—
87C4×C61—42no—
88C4×C61—42no—
89Dic61—24no—
90Dic61—28no—
91Dic61—42no—
92#2583—611nomaximal, Sylow
93C2×C61—24no—
94C2×C61#52511yescharacteristic
95C2×C61C2×C4⋊Q811yescharacteristic
96C2×C61#53411yescharacteristic
97C2×C61#55414yes—
98C2×C22⋊Q8D6111yescharacteristic
99C22×C4⋊C4—611no—
100#398—612no—
101#395—612no—
102#389—614no—
103#385—612no—
104#385—612no—
105C4×C22⋊C4—611no—
106C61#258311yescharacteristic, complemented, Sylow
107C22×Q8C2×D6111yescharacteristic
108C23×C4—611no—
109C23×C4—611no—
110C23×C4C2×D6111yescharacteristic
111C22⋊Q8—24no—
112C2×C4⋊C4—612no—
113C2×C4⋊C4—612no—
114C2×C4⋊C4—614no—
115C2×C4⋊C4—614no—
116C2×C4⋊C4—1224no—
117C2×C4⋊C4C2×D6112yes—
118C2×C4⋊C4C2×D6111yescharacteristic
119C2×C22⋊C4—612no—
120C2×C22⋊C4C2×D6112yes—
121C2×C42—612no—
122#95—612no—
123#95—614no—
124#95—614no—
125C24C22×D6111yescharacteristic
126C2×Q8—22no—
127C2×Q8—42no—
128C22×C4—42no—
129C22×C4—614no—
130C22×C4—612no—
131C22×C4—612no—
132C22×C4—1224no—
133C22×C4—1222no—
134C22×C4—1222no—
135C22×C4—2442no—
136C22×C4C22⋊D6114yes—
137C22×C4C22×D6112yes—
138C22×C4C22×D6112yes—
139C22×C4C22×D6111yescharacteristic
140C22×C4C22×D6111yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—24no—
143C4⋊C4—1228no—
144C4⋊C4—1224no—
145C4⋊C4—1224no—
146C4⋊C4—2444no—
147C22⋊C4—24no—
148C22⋊C4—618no—
149C42—2442no—
150C23—22no—
151C23—22no—
152C23Q8×D6114yes—
153C23C2×C22⋊D6112yes—
154C23C23×D6111yescharacteristic
155Q8—44no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—24no—
162C2×C4—44no—
163C2×C4—618no—
164C2×C4—614no—
165C2×C4—1228no—
166C2×C4—1222no—
167C2×C4—1224no—
168C2×C4—1222no—
169C2×C4—1224no—
170C2×C4—1222no—
171C2×C4—1224no—
172C2×C4—2444no—
173C2×C4C2×C22⋊D6112yes—
174C2×C4C2×C22⋊D6112yes—
175C22—28no—
176C22—22no—
177C22—22no—
178C22#1451977514yes—
179C22C22×C22⋊D6111yescharacteristic
180C22C2×Q8×D6112yes—
181C22#41×D6112yes—
182C22#1451982212yes—
183C4—22no—
184C4—22no—
185C4—42no—
186C4—42no—
187C4—1228no—
188C4—1224no—
189C4—2442no—
190C2—24no—
191C2#1684026911yescharacteristic
192C2C2×#1451977511yescharacteristic
193C2#1684032111yescharacteristic
194C2#1684046614yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C22⋊Q8×C61C2
hypercenterC2×C22⋊Q8D61
hypocenterC61#2583
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16839693C2semidirect
3. #16839681C2semidirect
4. #16839657C2semidirect
46. C22⋊Dic61Q8semidirect
106. C61#2583semidirect