Finite Group Databasebeta

← #21450271

Subgroups — #21450271

Order 7808.

484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14519753C211yesmaximal, characteristic
2C2×#14519735C211yesmaximal, characteristic
3#16839691C214yesmaximal
4#16839669C211yesmaximal, characteristic, complemented
5#16839644C214yesmaximal, complemented
6#16839631C211yesmaximal, characteristic, complemented
7#16839628C211yesmaximal, characteristic, complemented
8C4×#11758198C211yesmaximal, characteristic
9C61×#391C211yesmaximal, characteristic, complemented
10C22×C4×D61C2211yescharacteristic
11#14519753—24no—
12#14519735—24no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196C2214yes—
16C2×#11758196C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×C4×Dic61C2212yes—
21C2×C4×Dic61C2211yescharacteristic
22#14519684C2214yes—
23#14519684C2214yes—
24#14519684C2212yes—
25C22×Q8×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C42×C61C2211yescharacteristic
28#95×C61C2214yes—
29C23×D61C2311yescharacteristic
30C2×Q8×C61—22no—
31C2×Q8×C61—22no—
32C2×Q8×C61—22no—
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2311yescharacteristic
40C22×Dic61C2312yes—
41C2×C4×D61—22no—
42C2×C4×D61—22no—
43C2×C4×D61D414yes—
44C4⋊C4×C61—22no—
45C42×C61—22no—
46#11758198—24no—
47#11758198—24no—
48#11758198—24no—
49C4⋊Dic61—22no—
50C4⋊Dic61—22no—
51#11758196—24no—
52#11758196—28no—
53C4×Dic61—22no—
54C4×Dic61—24no—
55C23×C61C2411yescharacteristic
56C22×D61—22no—
57C22×D61—21no—
58C22×D61—21no—
59C22×D61—22no—
60C22×D61C2×D412yes—
61Q8×C61—44no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—24no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61C2×D412yes—
71C2×C4×C61#4112yes—
72C2×C4×C61#4112yes—
73C2×Dic61—22no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—24no—
80C2×Dic61—24no—
81C2×Dic61C2×D412yes—
82C2×Dic61#4114yes—
83C4×D61—28no—
84C22×C61C22×D411yescharacteristic
85C22×C61C2×#4112yes—
86C22×C61C2×#4111yescharacteristic
87C22×C61C2×#4111yescharacteristic
88C22×C612−1+412yes—
89C2×D61—22no—
90C2×D61—22no—
91C2×D61—22no—
92C2×D61—42no—
93C2×D61—42no—
94C4×C61—42no—
95C4×C61—42no—
96C4×C61—42no—
97C4×C61#12314yes—
98Dic61—22no—
99Dic61—24no—
100Dic61—42no—
101Dic61—42no—
102#2499—611nomaximal, Sylow
103C2×C61C2×#12311yescharacteristic
104C2×C61#53211yescharacteristic
105C2×C61#53611yescharacteristic
106C2×C61#55212yes—
107C2×C61#55612yes—
108D61—42no—
109C2×C22⋊Q8—611no—
110C2×#117—611no—
111#397—614no—
112#391—611no—
113#391D6111yescharacteristic, complemented
114#387—614no—
115#384—611no—
116#382—611no—
117C4×C22⋊C4—611no—
118C61#249911yescharacteristic, complemented, Sylow
119C22×Q8C2×D6111yescharacteristic
120C23×C4—611no—
121C22⋊Q8—1224no—
122#117—1224no—
123C2×C4⋊C4—611no—
124C2×C4⋊C4—611no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—614no—
127C2×C4⋊C4C2×D6111yescharacteristic
128C2×C22⋊C4—612no—
129C2×C22⋊C4—612no—
130C2×C22⋊C4—612no—
131C2×C42—612no—
132C2×C42—611no—
133C2×C42C2×D6111yescharacteristic
134#95—612no—
135#95—614no—
136#95—614no—
137#95C2×D6114yes—
138C24—611no—
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—22no—
142C22×C4—612no—
143C22×C4—611no—
144C22×C4—614no—
145C22×C4—612no—
146C22×C4—612no—
147C22×C4—1222no—
148C22×C4—1222no—
149C22×C4C22×D6112yes—
150C22×C4C22×D6112yes—
151C22×C4C22×D6112yes—
152C22×C4C22×D6111yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—1228no—
155C4⋊C4—1224no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C22⋊C4—1224no—
159C22⋊C4—1224no—
160C22⋊C4—1224no—
161C42—22no—
162C42—1224no—
163C42—1222no—
164C23—612no—
165C23—1222no—
166C23—1221no—
167C23—1221no—
168C23—1222no—
169C23C23×D6111yescharacteristic
170Q8—44no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—612no—
180C2×C4—614no—
181C2×C4—1221no—
182C2×C4—1222no—
183C2×C4—1221no—
184C2×C4—1222no—
185C2×C4—1228no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1224no—
189C2×C4—1224no—
190C2×C4#1175822212yes—
191C2×C4D4×D6112yes—
192C2×C4#1175822412yes—
193C22—1222no—
194C22—1222no—
195C22—1222no—
196C22—2442no—
197C22—2442no—
198C22C2×D4×D6111yescharacteristic
199C22#41×D6112yes—
200C22C2×#1175822411yescharacteristic
201C22C2×#1175822211yescharacteristic
202C22#1451982512yes—
203C4—42no—
204C4—42no—
205C4—42no—
206C4—1224no—
207C4—1222no—
208C4—2442no—
209C4—2442no—
210C4#1451975914yes—
211C2—2442no—
212C2C2×#1451975911yescharacteristic
213C2#1684031111yescharacteristic
214C2#1684033711yescharacteristic
215C2#1684045312yes—
216C2#1684048312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#391C2
hypercenter#391D61
hypocenterC61#2499
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
4. #16839669C2semidirect
5. #16839644C2semidirect
6. #16839631C2semidirect
7. #16839628C2semidirect
9. C61×#391C2semidirect
113. #391D61semidirect
118. C61#2499semidirect