Finite Group Databasebeta

← #21446261

Subgroups — #21446261

Order 7808.

442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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#16840274C211yesmaximal, characteristic
2C2×C42×D61C211yesmaximal, characteristic, complemented
3C2×#14519705C211yesmaximal, characteristic, complemented
4C2×#14519703C211yesmaximal, characteristic, complemented
5#16839725C211yesmaximal, characteristic, complemented
6#16839521C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×C4×D61—21no—
10C22×C4×D61C2211yescharacteristic
11C2×#11758194C2211yescharacteristic
12#14519761—21no—
13#14519757C412yescomplemented
14#14519752C412yescomplemented
15#14519747—21no—
16C4×D244—22no—
17C2×C4×Dic61—21no—
18C2×C4×Dic61C2211yescharacteristic
19C42×D61—22no—
20C42×D61—22no—
21#14519705—22no—
22#14519703—22no—
23#14519689—22no—
24C2×M16×C61C2211yescharacteristic
25#117×C61C2211yescharacteristic
26C2×C42×C61C2211yescharacteristic
27C23×D61D411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31C22×Dic61—21no—
32C22×Dic61D411yescharacteristic
33#11758222—21no—
34#11758222—21no—
35#11758222—21no—
36#11758222—21no—
37C2×D244—22no—
38C2×D244C2×C411yescharacteristic, complemented
39C2×C4×D61—28no—
40C2×C4×D61—24no—
41C2×C4×D61—21no—
42C2×C4×D61—21no—
43C2×C4×D61—21no—
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61C2×C412yes—
47C2×C4×D61D412yes—
48C2×Dic122C2×C411yescharacteristic, complemented
49M16×C61—21no—
50M16×C61—21no—
51C2×C8×C61—21no—
52C4⋊C4×C61C2×C412yescomplemented
53C22⋊C4×C61—21no—
54C42×C61—21no—
55C42×C61—21no—
56C42×C61D412yescomplemented
57#11758198—22no—
58#11758198—22no—
59C4⋊Dic61—22no—
60C4×Dic61—24no—
61C4×Dic61—21no—
62C4×Dic61D412yescomplemented
63#11758194—21no—
64#11758194—21no—
65C2×#92418—21no—
66C23×C61C2×D411yescharacteristic
67C22×D61—21no—
68C22×D61—21no—
69C22×D61—24no—
70C22×D61—21no—
71C22×D61C22⋊C412yes—
72C2×C4×C61—24no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61C22×C411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61#4111yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C22⋊D61—41no—
82C22⋊D61—41no—
83C2×Dic61—24no—
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61C22⋊C412yes—
89D244—21no—
90D244—21no—
91D244—44no—
92C4×D61—216no—
93C4×D61—22no—
94C4×D61—22no—
95C4×D61—22no—
96C4×D61—22no—
97C4×D61—41no—
98C4×D61—41no—
99Dic122—21no—
100Dic122—21no—
101C8×C61—41no—
102#92418—41no—
103C22×C61—22no—
104C22×C61C2×C22⋊C411yescharacteristic
105C22×C61#12011yescharacteristic
106C22×C61#12311yescharacteristic
107C2×D61—24no—
108C2×D61—24no—
109C2×D61—22no—
110C2×D61—22no—
111C2×D61—41no—
112C2×D61—42no—
113C2×D61#10414yescomplemented
114C4×C61—24no—
115C4×C61—42no—
116C4×C61C4×D411yescharacteristic
117C4×C61C4×D411yescharacteristic
118C4×C61#12111yescharacteristic
119C4×C61#12111yescharacteristic
120Dic61—24no—
121Dic61—22no—
122Dic61—41no—
123#1896—611nomaximal, Sylow
124C2×C61—21no—
125C2×C61—21no—
126C2×C61#38611yescharacteristic
127C2×C61C2×#10412yes—
128D61—24no—
129D61—81no—
130#525—611no—
131C22×C42—611no—
132C2×#104—611no—
133C2×#104—611no—
134#407—611no—
135#339—611no—
136#339D6111yescharacteristic, complemented
137C61#189611yescharacteristic, complemented, Sylow
138C2×#41—611no—
139C23×C4—611no—
140C23×C4—1221no—
141C2×M16—611no—
142C2×M16C2×D6111yescharacteristic
143#123—1221no—
144C22⋊Q8—612no—
145#121—612no—
146#120—1221no—
147C4×D4—1222no—
148#117C2×D6111yescharacteristic
149C2×C42—611no—
150C2×C42—1222no—
151C2×C42—1221no—
152C2×C42—1222no—
153C2×C42C2×D6111yescharacteristic
154#104—1222no—
155#104—1222no—
156C22⋊C8—1222no—
157C24—611no—
158#41—1221no—
159#41—1221no—
160#41—1221no—
161#41—1221no—
162C2×Q8—611no—
163C2×D4—611no—
164C2×D4—1222no—
165C2×D4—1221no—
166C22×C4—21no—
167C22×C4—611no—
168C22×C4—612no—
169C22×C4—612no—
170C22×C4—1224no—
171C22×C4—1228no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4—1221no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4—1221no—
178C22×C4C22×D6111yescharacteristic
179M16—21no—
180M16—21no—
181M16—1221no—
182M16—1221no—
183C2×C8—21no—
184C2×C8—1221no—
185C4⋊C4—1222no—
186C4⋊C4C4×D6112yescomplemented
187C22⋊C4—21no—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C42—21no—
191C42—21no—
192C42—612no—
193C42—1224no—
194C42—1221no—
195C42D24412yescomplemented
196C23—612no—
197C23—1224no—
198C23—1221no—
199C23—1221no—
200C23—1221no—
201C23D4×D6111yescharacteristic
202Q8—1221no—
203Q8—1221no—
204D4—1221no—
205D4—1221no—
206D4—2444no—
207D4—2441no—
208D4—2441no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—612no—
213C2×C4—12216no—
214C2×C4—1224no—
215C2×C4—1222no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1221no—
223C2×C4—2441no—
224C2×C4—2441no—
225C2×C4C2×C4×D6111yescharacteristic
226C2×C4C2×D24411yescharacteristic
227C2×C4#1175822211yescharacteristic
228C2×C4D4×D6111yescharacteristic
229C2×C4D4×D6111yescharacteristic
230C2×C4#1175822611yescharacteristic
231C8—41no—
232C8—2441no—
233C22—22no—
234C22—614no—
235C22—1224no—
236C22—1224no—
237C22—1222no—
238C22—1222no—
239C22—2442no—
240C22—2441no—
241C22C22⋊C4×D6111yescharacteristic
242C22#1451974711yescharacteristic
243C22#1451976211yescharacteristic
244C4—24no—
245C4—42no—
246C4—1224no—
247C4—1222no—
248C4—2441no—
249C4#1451973911yescharacteristic
250C4C4×D24411yescharacteristic
251C4#1451975011yescharacteristic
252C4#1451975211yescharacteristic
253C2—21no—
254C2—21no—
255C2—1224no—
256C2—4881no—
257C2#1683964011yescharacteristic
258C2#104×D6112yes—
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61C2×C22⋊C4
hypercenter#339D61
hypocenterC61#1896
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×C42×D61C2semidirect
3. C2×#14519705C2semidirect
4. C2×#14519703C2semidirect
5. #16839725C2semidirect
6. #16839521C2semidirect
7. C61×#339C2semidirect
13. #14519757C4semidirect
14. #14519752C4semidirect
38. C2×D244C2×C4semidirect
48. C2×Dic122C2×C4semidirect
52. C4⋊C4×C61C2×C4semidirect
56. C42×C61D4semidirect
62. C4×Dic61D4semidirect
113. C2×D61#104semidirect
136. #339D61semidirect
137. C61#1896semidirect
186. C4⋊C4C4×D61semidirect
195. C42D244semidirect