Finite Group Databasebeta

← #21457012

Subgroups — #21457012

Order 7808.

366 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 111 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#16840318C211yesmaximal, characteristic, complemented
2#16840310C211yesmaximal, characteristic
3#16840172C211yesmaximal, characteristic, complemented
4#16840171C211yesmaximal, characteristic, complemented
5#16840126C211yesmaximal, characteristic, complemented
6#16840085C212yesmaximal, complemented
7#16840084C212yesmaximal, complemented
8#16840050C212yesmaximal, complemented
9#16840040C212yesmaximal, complemented
10#16839817C211yesmaximal, characteristic, complemented
11C61×#490C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13#14519777C2211yescharacteristic
14#14519776C2211yescharacteristic
15#14519776C2211yescharacteristic
16#14519769C2211yescharacteristic
17#14519764—21no—
18#14519755—21no—
19#14519755—21no—
20#14519748—21no—
21#14519748C2212yes—
22#14519742—21no—
23#14519742—21no—
24D4×Dic61—21no—
25D4×Dic61C2212yes—
26#14519735C2211yescharacteristic
27#14519735C2211yescharacteristic
28C42×D61C2211yescharacteristic
29#14519711C2212yes—
30#14519710C2212yes—
31#14519709C2212yes—
32#14519708C2212yes—
33#14519706C2212yes—
34#14519698C2212yes—
35#14519698C2212yes—
36#14519689C2212yes—
37#14519688C2211yescharacteristic
38#127×C61C2211yescharacteristic
39#125×C61C2211yescharacteristic
40#102×C61C2212yes—
41#102×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×D4×C61—21no—
44C2×D4×C61—21no—
45C2×D4×C61C2312yes—
46C2×C22⋊D61—22no—
47C22×Dic61—22no—
48#11758224—44no—
49C2×C4×D61D411yescharacteristic
50C2×C4×D61D411yescharacteristic
51C2×C4×D61C2311yescharacteristic
52C2×Dic122—21no—
53C2×Dic122—21no—
54C2×Dic122—21no—
55C2×C8×C61C2312yes—
56C4⋊C4×C61—21no—
57C4⋊C4×C61—21no—
58C4⋊C4×C61C2311yescharacteristic
59C4⋊C4×C61C2311yescharacteristic
60C42×C61C2311yescharacteristic
61C22⋊Dic61—22no—
62C22⋊Dic61—22no—
63#11758198—21no—
64#11758198—21no—
65C4⋊Dic61—21no—
66C4⋊Dic61C2311yescharacteristic
67C4⋊Dic61C2311yescharacteristic
68C4⋊Dic61C2312yes—
69#11758196—21no—
70#11758196—21no—
71#11758196—21no—
72#11758196—21no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61D411yescharacteristic
76C4×Dic61D411yescharacteristic
77C4×Dic61C2311yescharacteristic
78C2×#92418C2312yes—
79C23×C61—22no—
80C22×D61C2×D411yescharacteristic
81D4×C61—24no—
82D4×C61—42no—
83D4×C61—42no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2411yescharacteristic
89C22⋊D61—44no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—22no—
93C2×Dic61—44no—
94C2×Dic61C2×D411yescharacteristic
95C2×Dic61C2×D411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97C4×D61—22no—
98C4×D61—22no—
99C4×D61—41no—
100Dic122—42no—
101Dic122—42no—
102Dic122—42no—
103C8×C61—22no—
104#92418—22no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61C22×D411yescharacteristic
109C2×D61—21no—
110C2×D61—21no—
111C2×D61—21no—
112C4×C61—21no—
113C4×C61—21no—
114C4×C61—41no—
115C4×C61—41no—
116C4×C612−1+412yes—
117Dic61—21no—
118Dic61—21no—
119Dic61—41no—
120Dic61—42no—
121Dic61—41no—
122Dic61AGL(1,ℤ/8)12yes—
123#3235—611nomaximal, Sylow
124C2×C61—82no—
125C2×C61#53611yescharacteristic
126C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
127C2×C61#57511yescharacteristic
128D61—41no—
129#533—611no—
130#532—611no—
131#501—611no—
132#501—611no—
133#490—611no—
134#490D6111yescharacteristic, complemented
135#482—612no—
136#482—612no—
137#476—612no—
138#474—612no—
139#432—611no—
140C61#323511yescharacteristic, complemented, Sylow
141C2×#41—1221no—
142C4⋊Q8—611no—
143C4⋊Q8—611no—
144C4⋊Q8—611no—
145#127C2×D6111yescharacteristic
146#125—611no—
147#125C2×D6111yescharacteristic
148#124—1221no—
149C22⋊Q8—1221no—
150C22⋊Q8—1221no—
151#121—612no—
152#121—1221no—
153C4×Q8—1221no—
154C4×Q8—1221no—
155C4×D4—612no—
156C4×D4—1221no—
157#117—611no—
158#117—611no—
159C2×C42—611no—
160#107—612no—
161#107—612no—
162#106—612no—
163#106—612no—
164C4⋊C8—612no—
165#102—612no—
166#102—612no—
167#102C2×D6112yes—
168#102C2×D6112yes—
169C22⋊C8—612no—
170#97—611no—
171#97C2×D6111yescharacteristic
172#41—2444no—
173C2×Q8—1221no—
174C2×Q8—1221no—
175C2×Q8—1221no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—1222no—
179C2×D4C22×D6112yes—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—1222no—
184C2×C8—612no—
185C2×C8C22×D6112yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—611no—
189C4⋊C4—611no—
190C4⋊C4—612no—
191C4⋊C4—1221no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C4⋊C4C22×D6111yescharacteristic
197C4⋊C4C22×D6111yescharacteristic
198C22⋊C4—1221no—
199C22⋊C4—1221no—
200C22⋊C4—1222no—
201C22⋊C4—1222no—
202C42—611no—
203C42—611no—
204C42—611no—
205C42—1221no—
206C42—1221no—
207C42C22×D6111yescharacteristic
208C23—22no—
209C23—611no—
210Q8—2442no—
211Q8—2442no—
212Q8—2442no—
213D4—24no—
214D4—42no—
215D4—42no—
216D4—2444no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1222no—
227C2×C4—2441no—
228C2×C4—2444no—
229C2×C4D4×D6111yescharacteristic
230C2×C4D4×D6111yescharacteristic
231C2×C4C23×D6111yescharacteristic
232C8—22no—
233C8—1222no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—1221no—
238C22—1221no—
239C22—1221no—
240C22C2×D4×D6111yescharacteristic
241C4—21no—
242C4—21no—
243C4—41no—
244C4—41no—
245C4—612no—
246C4—1221no—
247C4—1221no—
248C4—2442no—
249C4—2441no—
250C4—2441no—
251C4#1451982412yes—
252C2—82no—
253C2—2441no—
254C2#1684033211yescharacteristic
255C2AGL(1,ℤ/8)×D6111yescharacteristic
256C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#490C2
socleC22×C61C22×D4
hypercenter#490D61
hypocenterC61#3235
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #16840318C2semidirect
3. #16840172C2semidirect
4. #16840171C2semidirect
5. #16840126C2semidirect
6. #16840085C2semidirect
7. #16840084C2semidirect
8. #16840050C2semidirect
9. #16840040C2semidirect
10. #16839817C2semidirect
11. C61×#490C2semidirect
134. #490D61semidirect
140. C61#3235semidirect