Finite Group Databasebeta

← #21447071

Subgroups — #21447071

Order 7808.

382 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 67 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#16840324C211yesmaximal, characteristic
2C2×#14519691C212yesmaximal, complemented
3#16839639C212yesmaximal, complemented
4#16839634C211yesmaximal, characteristic, complemented
5C61×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D61C2212yes—
7C23×Dic61C2211yescharacteristic
8#14519761—22no—
9#14519751—21no—
10#14519751—21no—
11#14519747—22no—
12C2×#11758196—21no—
13C2×C22⋊Dic61C2211yescharacteristic
14C2×#11758198—22no—
15#14519691—24no—
16#14519684—21no—
17#14519684—22no—
18C2×C22⋊C4×C61C2212yes—
19C2×C22⋊C4×C61C2211yescharacteristic
20C24×C61C2311yescharacteristic
21C23×D61D412yes—
22C22×C4×C61—22no—
23C22×C4×C61D411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C2×C22⋊D61—22no—
26C2×C22⋊D61—22no—
27C2×C22⋊D61—22no—
28C2×C22⋊D61—22no—
29C2×C22⋊D61—22no—
30C2×C22⋊D61—22no—
31C22×Dic61—22no—
32C22×Dic61—21no—
33C22×Dic61—21no—
34C22×Dic61—42no—
35C22×Dic61D412yes—
36C2×D244—21no—
37C2×D244—21no—
38C22⋊C4×C61—22no—
39C22⋊C4×C61—22no—
40C22⋊C4×C61—22no—
41C22⋊Dic61—21no—
42C22⋊Dic61D412yescomplemented
43#11758198—22no—
44#11758198—22no—
45#11758198—44no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48#11758196—42no—
49C23×C61—41no—
50C23×C61—41no—
51C23×C61C2×D412yes—
52C23×C61C2×D411yescharacteristic
53C23×C61C2×D411yescharacteristic
54C23×C61#4111yescharacteristic
55C23×C61#4112yes—
56C22×D61—22no—
57C22×D61—22no—
58C22×D61—22no—
59C22×D61—42no—
60C22×D61—42no—
61C2×C4×C61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61—42no—
68C22⋊D61—42no—
69C22⋊D61—42no—
70C22⋊D61—42no—
71C22⋊D61—42no—
72C2×Dic61—22no—
73C2×Dic61—24no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61—42no—
82C2×Dic61—41no—
83D244—81no—
84D244—81no—
85C22×C61—21no—
86C22×C61—22no—
87C22×C61—21no—
88C22×C61—22no—
89C22×C61—41no—
90C22×C61—42no—
91C22×C61—41no—
92C22×C61#12011yescharacteristic
93C22×C61#12112yes—
94C22×C61#12111yescharacteristic
95C22×C61#12312yes—
96C22×C61#12411yescharacteristic
97C2×D61—44no—
98C2×D61—42no—
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—82no—
102C4×C61—41no—
103C4×C61—41no—
104C4×C61—82no—
105Dic61—42no—
106Dic61—42no—
107Dic61—42no—
108#2044—611nomaximal, Sylow
109C2×C61—21no—
110C2×C61—22no—
111C2×C61—22no—
112C2×C61—21no—
113C2×C61#39411yescharacteristic
114C2×C61B(4,𝔽2)11yescharacteristic
115C2×C61#45811yescharacteristic
116D61—82no—
117#534—611no—
118C2×#99—612no—
119#386—612no—
120#385—611no—
121#342D6111yescharacteristic, complemented
122C61#204411yescharacteristic, complemented, Sylow
123C22×D4—612no—
124C23×C4—611no—
125#123—1222no—
126#121—1221no—
127#121—1221no—
128#120—1222no—
129C2×C4⋊C4—1221no—
130C2×C22⋊C4—611no—
131C2×C22⋊C4—1222no—
132C2×C22⋊C4C2×D6112yes—
133C2×C22⋊C4C2×D6111yescharacteristic
134#99—1224no—
135#95—1222no—
136#95—1221no—
137C24—612no—
138C24C22×D6111yescharacteristic
139C2×D4—1221no—
140C2×D4—1221no—
141C2×D4—1222no—
142C2×D4—1222no—
143C2×D4—1222no—
144C2×D4—1222no—
145C2×D4—1222no—
146C2×D4—1222no—
147C22×C4—22no—
148C22×C4—612no—
149C22×C4—1221no—
150C22×C4—1221no—
151C22×C4—1222no—
152C22×C4—2442no—
153C22×C4D24411yescharacteristic
154C22×C4D24411yescharacteristic
155C4⋊C4—1221no—
156C4⋊C4—1221no—
157C4⋊C4—2442no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—612no—
162C22⋊C4—1222no—
163C22⋊C4—1222no—
164C22⋊C4—1221no—
165C22⋊C4—2444no—
166C23—41no—
167C23—41no—
168C23—1222no—
169C23—1222no—
170C23—1222no—
171C23—2442no—
172C23—2442no—
173C23C2×D24411yescharacteristic
174C23#1175822212yes—
175C23D4×D6112yes—
176C23D4×D6111yescharacteristic
177C23#1175822611yescharacteristic
178D4—4881no—
179D4—4881no—
180D4—2442no—
181D4—2442no—
182D4—2442no—
183D4—2442no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—1224no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4—2442no—
201C2×C4—2441no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—42no—
207C22—41no—
208C22—41no—
209C22—4882no—
210C22—2444no—
211C22—2442no—
212C22—2442no—
213C22—2442no—
214C22#1451974711yescharacteristic
215C22#1451975012yes—
216C22#1451975211yescharacteristic
217C22#1451976212yes—
218C22#1451976511yescharacteristic
219C4—41no—
220C4—41no—
221C4—82no—
222C4—2442no—
223C4—2442no—
224C4—2442no—
225C2—22no—
226C2—21no—
227C2—22no—
228C2—21no—
229C2—4882no—
230C2#1683968011yescharacteristic
231C2#1683995011yescharacteristic
232C2#1683995311yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC24×C61C23
FrattiniC24C22×D61
FittingC61×#342C2
socleC22×C61#120
hypercenter#342D61
hypocenterC61#2044
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#14519691C2semidirect
3. #16839639C2semidirect
4. #16839634C2semidirect
5. C61×#342C2semidirect
42. C22⋊Dic61D4semidirect
121. #342D61semidirect
122. C61#2044semidirect