Finite Group Databasebeta

← #21456216

Subgroups — #21456216

Order 7808.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840311C211yesmaximal, characteristic
2#125×D61C211yesmaximal, characteristic, complemented
3#16840129C212yesmaximal, complemented
4#16840125C212yesmaximal, complemented
5#16840119C211yesmaximal, characteristic, complemented
6#16840117C211yesmaximal, characteristic, complemented
7#16840116C211yesmaximal, characteristic, complemented
8#16839762C212yesmaximal, complemented
9#16839760C212yesmaximal, complemented
10C4×#11758189C211yesmaximal, characteristic, complemented
11C61×#488C211yesmaximal, characteristic, complemented
12C2×#11758226C2211yescharacteristic
13C2×#11758224C2211yescharacteristic
14C2×#11758189C2212yes—
15#14519775C2211yescharacteristic
16#14519773C2211yescharacteristic
17#14519769C2211yescharacteristic
18#14519768C2212yes—
19#14519767—22no—
20#14519765C2211yescharacteristic
21#14519750—22no—
22#14519737—22no—
23C4⋊C4×D61—22no—
24C4⋊C4×D61C2212yes—
25C42×D61C2211yescharacteristic
26#14519702C2212yes—
27#14519701C2212yes—
28#14519700C2212yes—
29#14519699C2212yes—
30#14519698C2212yes—
31#14519697C2212yes—
32#14519687C2212yes—
33C4×#92418C2211yescharacteristic
34#125×C61C2211yescharacteristic
35#124×C61C2211yescharacteristic
36#103×C61C2212yes—
37#102×C61C2212yes—
38C4×C8×C61C2211yescharacteristic
39C2×Q8×C61C2311yescharacteristic
40C2×D4×C61C2311yescharacteristic
41C2×C22⋊D61—21no—
42C2×C22⋊D61—22no—
43C22×Dic61—21no—
44#11758226—24no—
45#11758224—24no—
46C2×D244—21no—
47C2×D244C2311yescharacteristic
48C2×C4×D61—22no—
49C2×C4×D61—21no—
50C2×C4×D61D412yes—
51C2×C4×D61C2311yescharacteristic
52C2×Dic122C2311yescharacteristic
53C2×C8×C61C2312yes—
54C4⋊C4×C61—22no—
55C4⋊C4×C61C2312yes—
56C22⋊C4×C61—22no—
57C42×C61C2311yescharacteristic
58#11758198—22no—
59C4⋊Dic61—22no—
60C4⋊Dic61C2312yes—
61#11758196—22no—
62#11758196—22no—
63#11758196—22no—
64#11758196—22no—
65C4×Dic61D412yes—
66C4×Dic61C2311yescharacteristic
67C2×#92418C2312yes—
68#11758189—24no—
69C23×C61—21no—
70C22×D61—21no—
71C22×D61C2×D411yescharacteristic
72Q8×C61—22no—
73D4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2411yescharacteristic
78C22⋊D61—44no—
79C22⋊D61—42no—
80C2×Dic61—22no—
81C2×Dic61—21no—
82C2×Dic61—42no—
83C2×Dic61C2×D412yes—
84C2×Dic61C2×D411yescharacteristic
85D244—22no—
86D244—42no—
87C4×D61—42no—
88C4×D61—44no—
89C4×D61—42no—
90C4×D61#4114yes—
91Dic122—22no—
92C8×C61—22no—
93#92418—22no—
94C22×C61—41no—
95C22×C61—42no—
96C22×C61C22×D411yescharacteristic
97C2×D61—22no—
98C2×D61—41no—
99C2×D61—42no—
100C2×D61#12412yes—
101C4×C61—22no—
102C4×C61—41no—
103C4×C61—42no—
104C4×C61C2×#4112yes—
105Dic61—22no—
106Dic61—41no—
107Dic61—42no—
108Dic61#12412yes—
109#3142—611nomaximal, Sylow
110C2×C61—81no—
111C2×C61C2×#12411yescharacteristic
112C2×C61#57512yes—
113D61—22no—
114D61—81no—
115#532—611no—
116C2×#125—611no—
117#491—612no—
118#490—612no—
119#488—611no—
120#488—611no—
121#488—611no—
122#488D6111yescharacteristic, complemented
123#417—612no—
124#417—612no—
125C4×M16—611no—
126C61#314211yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C2×#41—611no—
129C2×M16—612no—
130C4⋊Q8—611no—
131#127—611no—
132#125—612no—
133#125—611no—
134#125—1222no—
135#125C2×D6111yescharacteristic
136#124—611no—
137#124C2×D6111yescharacteristic
138#121—1222no—
139C4×D4—1222no—
140C2×C4⋊C4—612no—
141C2×C4⋊C4—1222no—
142C2×C42—611no—
143#103—612no—
144#103—612no—
145#103—612no—
146#103C2×D6112yes—
147#102—612no—
148#102—612no—
149#102—612no—
150#102C2×D6112yes—
151#97—612no—
152C4×C8—611no—
153C4×C8C2×D6111yescharacteristic
154#41—1224no—
155#41—1224no—
156C2×Q8—611no—
157C2×Q8C22×D6111yescharacteristic
158C2×D4—611no—
159C2×D4—1221no—
160C2×D4—1222no—
161C2×D4—1221no—
162C2×D4C22×D6111yescharacteristic
163C22×C4—611no—
164C22×C4—612no—
165C22×C4—1221no—
166C22×C4—1222no—
167C22×C4—1221no—
168M16—1224no—
169C2×C8—612no—
170C2×C8C22×D6112yes—
171C4⋊C4—22no—
172C4⋊C4—612no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4C22×D6112yes—
179C22⋊C4—22no—
180C22⋊C4—1222no—
181C42—612no—
182C42—611no—
183C42C22×D6111yescharacteristic
184C23—21no—
185C23—611no—
186C23—1221no—
187Q8—22no—
188Q8—1222no—
189D4—22no—
190D4—1222no—
191D4—2442no—
192D4—2444no—
193D4—2442no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—611no—
197C2×C4—614no—
198C2×C4—612no—
199C2×C4—1221no—
200C2×C4—1222no—
201C2×C4—2442no—
202C2×C4—2442no—
203C2×C4—2444no—
204C2×C4—2442no—
205C2×C4D4×D6112yes—
206C2×C4C23×D6111yescharacteristic
207C8—22no—
208C8—1222no—
209C22—41no—
210C22—42no—
211C22—612no—
212C22—1222no—
213C22—2441no—
214C22—2442no—
215C22C2×D4×D6111yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—612no—
220C4—1222no—
221C4—2441no—
222C4—2442no—
223C4#41×D6112yes—
224C2—81no—
225C2—1222no—
226C2—4881no—
227C2#124×D6111yescharacteristic
228C2#1684055912yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#488C2
socleC22×C61C22×D4
hypercenter#488D61
hypocenterC61#3142
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #125×D61C2semidirect
3. #16840129C2semidirect
4. #16840125C2semidirect
5. #16840119C2semidirect
6. #16840117C2semidirect
7. #16840116C2semidirect
8. #16839762C2semidirect
9. #16839760C2semidirect
10. C4×#11758189C2semidirect
11. C61×#488C2semidirect
122. #488D61semidirect
126. C61#3142semidirect