Finite Group Databasebeta

← #21452746

Subgroups — #21452746

Order 7808.

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

normal subgroups only

This group has 504 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
1C2×#14519762C212yesmaximal
2#16839692C211yesmaximal, characteristic, complemented
3#16839691C212yesmaximal, complemented
4#16839691C212yesmaximal, complemented
5#16839663C211yesmaximal, characteristic
6#16839657C212yesmaximal, complemented
7#16839636C212yesmaximal, complemented
8#16839633C212yesmaximal, complemented
9C61×#398C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C4×D61C2212yes—
12#14519762—28no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196C2212yes—
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×C4×Dic61C2211yescharacteristic
23#14519684C2211yescharacteristic
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C2×C4⋊C4×C61C2212yes—
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2211yescharacteristic
30#95×C61C2211yescharacteristic
31#95×C61C2212yes—
32C23×D61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C2×D244—41no—
42C2×D244—41no—
43C2×D244D414yes—
44C2×C4×D61—24no—
45C2×C4×D61—42no—
46C2×C4×D61—42no—
47C4⋊C4×C61—24no—
48C4⋊C4×C61—41no—
49C4⋊C4×C61—41no—
50#11758198—24no—
51#11758198—24no—
52#11758198—24no—
53#11758198—24no—
54#11758198—24no—
55C4⋊Dic61—41no—
56#11758196—24no—
57#11758196—24no—
58#11758196—42no—
59C4×Dic61—41no—
60C23×C61C2411yescharacteristic
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—22no—
66C22×D61—22no—
67C22×D61C2×D414yes—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61C2×D412yes—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61#4114yes—
90D244—44no—
91C4×D61—48no—
92C22×C61C22×D411yescharacteristic
93C22×C61C2×#4112yes—
94C22×C61H(5,𝔽2)11yescharacteristic
95C22×C61H(5,𝔽2)11yescharacteristic
96C22×C612−1+412yes—
97C2×D61—24no—
98C2×D61—24no—
99C2×D61—24no—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—42no—
104C4×C61—22no—
105C4×C61—42no—
106C4×C61—42no—
107C4×C61—41no—
108C4×C61—41no—
109Dic61—24no—
110Dic61—42no—
111Dic61—42no—
112#2724—611nomaximal, Sylow
113C2×C61#53411yescharacteristic
114C2×C61#53912yes—
115C2×C61#54712yes—
116C2×C61#55911yescharacteristic
117C2×C61#56311yescharacteristic
118D61—44no—
119C2×#123—612no—
120#398—611no—
121#398D6111yescharacteristic, complemented
122#397—612no—
123#397—612no—
124#390—611no—
125#389—612no—
126#385—612no—
127#385—612no—
128C61#272411yescharacteristic, complemented, Sylow
129C22×D4—611no—
130C23×C4—612no—
131#123—1228no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—612no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4C2×D6112yes—
137C2×C4⋊C4C2×D6111yescharacteristic
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C22⋊C4—612no—
140C2×C22⋊C4—612no—
141C2×C22⋊C4—612no—
142C2×C22⋊C4—612no—
143C2×C22⋊C4—612no—
144C2×C42—611no—
145#95—612no—
146#95—612no—
147#95—612no—
148#95—611no—
149#95C2×D6112yes—
150#95C2×D6111yescharacteristic
151C24—612no—
152C2×D4—614no—
153C2×D4—2441no—
154C2×D4—2441no—
155C22×C4—612no—
156C22×C4—612no—
157C22×C4—612no—
158C22×C4—1224no—
159C22×C4—2442no—
160C22×C4—2442no—
161C22×C4C22×D6111yescharacteristic
162C22×C4C22×D6112yes—
163C22×C4C22×D6111yescharacteristic
164C22×C4C22×D6112yes—
165C22×C4C22×D6111yescharacteristic
166C4⋊C4—24no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—1224no—
170C4⋊C4—1224no—
171C4⋊C4—2442no—
172C4⋊C4—2441no—
173C22⋊C4—1224no—
174C22⋊C4—1224no—
175C22⋊C4—1224no—
176C22⋊C4—1224no—
177C22⋊C4—1224no—
178C42—2441no—
179C23—614no—
180C23—1222no—
181C23—1222no—
182C23—1222no—
183C23—1222no—
184C23—1222no—
185C23—1222no—
186C23C23×D6111yescharacteristic
187D4—2444no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—614no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—2448no—
210C2×C4D4×D6112yes—
211C22—1224no—
212C22—1224no—
213C22—1224no—
214C22—2442no—
215C22—2442no—
216C22—2442no—
217C22—2442no—
218C22C2×D4×D6111yescharacteristic
219C22#41×D6112yes—
220C22#1451982211yescharacteristic
221C22#1451982311yescharacteristic
222C22#1451982512yes—
223C4—22no—
224C4—41no—
225C4—41no—
226C4—42no—
227C4—42no—
228C4—1224no—
229C4—2442no—
230C4—2442no—
231C2—2444no—
232C2#1684032011yescharacteristic
233C2#1684036012yes—
234C2#1684041412yes—
235C2#1684049611yescharacteristic
236C2#1684051111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2724
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #16839692C2semidirect
3. #16839691C2semidirect
4. #16839691C2semidirect
6. #16839657C2semidirect
7. #16839636C2semidirect
8. #16839633C2semidirect
9. C61×#398C2semidirect
121. #398D61semidirect
128. C61#2724semidirect