Finite Group Databasebeta

← #21450792

Subgroups — #21450792

Order 7808.

704 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14519774C211yesmaximal, characteristic
2C2×#14519766C211yesmaximal, characteristic, complemented
3C2×#14519766C211yesmaximal, characteristic, complemented
4C2×#14519739C211yesmaximal, characteristic, complemented
5#16839680C214yesmaximal, complemented
6#16839663C211yesmaximal, characteristic, complemented
7#16839640C214yesmaximal, complemented
8C4×#11758196C211yesmaximal, characteristic, complemented
9C61×#391C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×D244C2214yes—
12C22×D244C2211yescharacteristic
13C22×C4×D61C2212yes—
14#14519774—24no—
15#14519766—24no—
16#14519766—24no—
17#14519739—24no—
18C2×#11758196C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2214yes—
22C2×#11758198C2212yes—
23C2×#11758198C2214yes—
24C2×C4×Dic61C2211yescharacteristic
25C2×C4×Dic61C2211yescharacteristic
26#14519684C2212yes—
27C22×Q8×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C42×C61C2211yescharacteristic
30#95×C61C2214yes—
31C23×D61C2312yes—
32C23×D61C2312yes—
33C2×Q8×C61—22no—
34C2×Q8×C61—22no—
35C2×Q8×C61—22no—
36C22×C4×C61C2312yes—
37C22×C4×C61C2312yes—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×Dic61C2312yes—
41C22×Dic61C2311yescharacteristic
42C22×Dic61C2311yescharacteristic
43C2×D244—22no—
44C2×D244—22no—
45C2×D244—28no—
46C2×D244—22no—
47C2×D244—22no—
48C2×D244—28no—
49C2×D244—22no—
50C2×D244—44no—
51C2×D244D414yes—
52C2×C4×D61—24no—
53C2×C4×D61—44no—
54C4⋊C4×C61—22no—
55C42×C61—22no—
56#11758198—28no—
57#11758198—24no—
58#11758198—24no—
59#11758198—24no—
60#11758198—44no—
61#11758196—24no—
62C4×Dic61—22no—
63C4×Dic61D414yescomplemented
64C23×C61C2411yescharacteristic
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—24no—
68C22×D61—24no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72C22×D61—24no—
73C22×D61—24no—
74C22×D61C2×D414yes—
75Q8×C61—44no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—24no—
83C2×C4×C61C2×D412yes—
84C2×C4×C61C2×D412yes—
85C2×C4×C61#4114yes—
86C2×C4×C61#4112yes—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61C2×D412yes—
93C2×Dic61C2×D412yes—
94D244—28no—
95D244—416no—
96D244—44no—
97C4×D61—48no—
98C22×C61C22×D411yescharacteristic
99C22×C61C22×D411yescharacteristic
100C22×C61C2×#4111yescharacteristic
101C22×C61C2×#4112yes—
102C22×C61H(5,𝔽2)12yes—
103C2×D61—24no—
104C2×D61—28no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—44no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—44no—
112C2×D61—44no—
113C4×C61—24no—
114C4×C61—42no—
115C4×C61—42no—
116C4×C61#12114yes—
117Dic61—22no—
118Dic61—22no—
119Dic61—42no—
120#2544—611nomaximal, Sylow
121C2×C61C2×#12111yescharacteristic
122C2×C61#53211yescharacteristic
123C2×C61#53511yescharacteristic
124C2×C61#54612yes—
125C2×C61#55912yes—
126D61—44no—
127D61—82no—
128C2×#127—611no—
129C2×#124—611no—
130C2×#124—611no—
131C2×C4×D4—611no—
132#394—614no—
133#391D6111yescharacteristic, complemented
134#390—611no—
135#386—614no—
136C4×C4⋊C4—611no—
137C61#254411yescharacteristic, complemented, Sylow
138C22×Q8C2×D6111yescharacteristic
139C22×D4—611no—
140C22×D4—611no—
141C22×D4—614no—
142C23×C4—612no—
143#127—1224no—
144#124—1224no—
145#124—1224no—
146C4×D4—1224no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4C2×D6111yescharacteristic
149C2×C22⋊C4—612no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4—614no—
152C2×C22⋊C4—612no—
153C2×C22⋊C4—614no—
154C2×C42—611no—
155C2×C42—611no—
156C2×C42C2×D6111yescharacteristic
157#95—612no—
158#95C2×D6114yes—
159C24—612no—
160C24—612no—
161C2×Q8—22no—
162C2×Q8—22no—
163C2×Q8—22no—
164C2×D4—614no—
165C2×D4—1228no—
166C2×D4—1222no—
167C2×D4—1222no—
168C2×D4—1222no—
169C2×D4—1222no—
170C2×D4—1222no—
171C2×D4—1228no—
172C2×D4—2444no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—612no—
176C22×C4—1224no—
177C22×C4—2444no—
178C22×C4C22×D6112yes—
179C22×C4C22×D6112yes—
180C22×C4C22×D6112yes—
181C22×C4C22×D6111yescharacteristic
182C4⋊C4—22no—
183C4⋊C4—1224no—
184C22⋊C4—1224no—
185C22⋊C4—1224no—
186C22⋊C4—1224no—
187C22⋊C4—1228no—
188C22⋊C4—2444no—
189C42—22no—
190C42—614no—
191C42—1222no—
192C23—614no—
193C23—1222no—
194C23—1222no—
195C23—1224no—
196C23—1224no—
197C23—1222no—
198C23—1222no—
199C23—1222no—
200C23—1224no—
201C23—1224no—
202C23C23×D6111yescharacteristic
203Q8—44no—
204D4—1228no—
205D4—24416no—
206D4—2444no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—24no—
214C2×C4—612no—
215C2×C4—612no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—2448no—
222C2×C4#1175822212yes—
223C2×C4D4×D6112yes—
224C2×C4D4×D6112yes—
225C2×C4#1175822614yes—
226C22—1224no—
227C22—1228no—
228C22—2444no—
229C22—2442no—
230C22—2442no—
231C22—2442no—
232C22—2444no—
233C22—2444no—
234C22—2442no—
235C22—2442no—
236C22C2×D4×D6111yescharacteristic
237C22C2×D4×D6111yescharacteristic
238C22C2×#1175822211yescharacteristic
239C22C2×#1175822612yes—
240C22#1451982312yes—
241C4—24no—
242C4—42no—
243C4—42no—
244C4—1222no—
245C4—1222no—
246C4—2442no—
247C4#1451975014yes—
248C2—4882no—
249C2—2444no—
250C2C2×#1451975011yescharacteristic
251C2#1684031311yescharacteristic
252C2#1684033011yescharacteristic
253C2#1684040312yes—
254C2#1684049712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#391C2
hypercenter#391D61
hypocenterC61#2544
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#14519766C2semidirect
3. C2×#14519766C2semidirect
4. C2×#14519739C2semidirect
5. #16839680C2semidirect
6. #16839663C2semidirect
7. #16839640C2semidirect
8. C4×#11758196C2semidirect
9. C61×#391C2semidirect
63. C4×Dic61D4semidirect
133. #391D61semidirect
137. C61#2544semidirect