Finite Group Databasebeta

← #21456467

Subgroups — #21456467

Order 7808.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840363C212yesmaximal, complemented
2#16840162C211yesmaximal, characteristic, complemented
3#16840137C211yesmaximal, characteristic, complemented
4#16840125C212yesmaximal, complemented
5#16840016C211yesmaximal, characteristic, complemented
6#16840012C211yesmaximal, characteristic, complemented
7#16839997C212yesmaximal, complemented
8#16839875C211yesmaximal, characteristic, complemented
9C4×#11758199C212yesmaximal, complemented
10#16839719C211yesmaximal, characteristic, complemented
11C61×#442C211yesmaximal, characteristic, complemented
12C2×D488C2211yescharacteristic
13C2×#11758199C2212yes—
14C2×#11758189C2211yescharacteristic
15C2×C8×D61C2211yescharacteristic
16#14519773C2212yes—
17#14519768C2212yes—
18#14519760—22no—
19#14519759—22no—
20#14519752C2212yes—
21#14519751—22no—
22#14519750—22no—
23#14519748C2212yes—
24C4×D244C2212yes—
25#14519734C2211yescharacteristic
26#14519710C2212yes—
27#14519709C2211yescharacteristic
28#14519699C2212yes—
29#14519698C2212yes—
30#14519697C2212yes—
31#14519687C2211yescharacteristic
32C4×#92418C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34C2×D8×C61C2211yescharacteristic
35C4×D4×C61C2212yes—
36#106×C61C2211yescharacteristic
37#102×C61C2212yes—
38#97×C61C2211yescharacteristic
39C2×D4×C61C2312yes—
40C22×C4×C61—22no—
41C2×C22⋊D61—22no—
42C2×C22⋊D61—22no—
43C2×C22⋊D61—22no—
44C2×D244—22no—
45C2×D244C2312yes—
46C2×C4×D61—22no—
47C2×C4×D61C2311yescharacteristic
48D8×C61—22no—
49C2×C8×C61C2311yescharacteristic
50C2×C8×C61C2311yescharacteristic
51C4⋊C4×C61C2312yes—
52C22⋊C4×C61—22no—
53C42×C61C2311yescharacteristic
54C22⋊Dic61—22no—
55#11758199—24no—
56#11758198—22no—
57#11758198—22no—
58#11758198D412yes—
59C4⋊Dic61—22no—
60C4⋊Dic61C2312yes—
61#11758196—22no—
62#11758196D412yes—
63C4×Dic61C2311yescharacteristic
64C2×#92418C2311yescharacteristic
65C2×#92418C2311yescharacteristic
66D488—22no—
67#11758189—22no—
68C8×D61—22no—
69C23×C61—22no—
70C22×D61—22no—
71C22×D61C2×D411yescharacteristic
72D4×C61—22no—
73D4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—82no—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2411yescharacteristic
78C22⋊D61—82no—
79C22⋊D61—82no—
80C22⋊D61—82no—
81C2×Dic61—22no—
82C2×Dic61C2×D412yes—
83C2×Dic61C2×D411yescharacteristic
84D244—22no—
85D244—22no—
86D244—82no—
87C4×D61—21no—
88C4×D61—21no—
89C4×D61—82no—
90C8×C61—21no—
91C8×C61#4112yes—
92#92418—21no—
93#92418#4112yes—
94C22×C61—42no—
95C22×C61—42no—
96C22×C61—42no—
97C22×C61C22×D411yescharacteristic
98C2×D61—21no—
99C2×D61—22no—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C4×C61—22no—
104C4×C61—42no—
105C4×C61C2×#4111yescharacteristic
106C4×C61C2×#4111yescharacteristic
107Dic61—21no—
108Dic61—22no—
109Dic61—42no—
110#3176—611nomaximal, Sylow
111C2×C61—82no—
112C2×C61#53211yescharacteristic
113C2×C61#57612yes—
114D61—41no—
115D61—82no—
116#540—612no—
117#499—611no—
118#493—611no—
119#490—612no—
120#469—611no—
121#469—611no—
122#466—612no—
123#442—611no—
124#442D6111yescharacteristic, complemented
125C4×D8—612no—
126#405—611no—
127C61#317611yescharacteristic, complemented, Sylow
128C2×D8—612no—
129C2×D8—611no—
130C2×D8C2×D6111yescharacteristic
131C2×M16—611no—
132C22×C8—611no—
133#127—612no—
134#125—612no—
135#123—1222no—
136#123—1222no—
137#121—612no—
138#121—612no—
139#121—1222no—
140#121—1222no—
141C4×D4—612no—
142C4×D4C2×D6112yes—
143#117—611no—
144#107—612no—
145#106—611no—
146#106C2×D6111yescharacteristic
147#102—612no—
148#102—612no—
149#102—612no—
150#102C2×D6112yes—
151#97—611no—
152#97C2×D6111yescharacteristic
153C4×C8—611no—
154C4×C8—611no—
155C2×D4—612no—
156C2×D4—1222no—
157C2×D4—1222no—
158C2×D4—1222no—
159C2×D4—1222no—
160C2×D4C22×D6112yes—
161C22×C4—22no—
162C22×C4—611no—
163C22×C4—1222no—
164D8—22no—
165D8—1224no—
166D8—1222no—
167M16—1222no—
168C2×C8—611no—
169C2×C8—611no—
170C2×C8—1222no—
171C2×C8C22×D6111yescharacteristic
172C2×C8C22×D6111yescharacteristic
173C4⋊C4—612no—
174C4⋊C4—612no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4C22×D6112yes—
178C22⋊C4—22no—
179C22⋊C4—612no—
180C22⋊C4—1222no—
181C22⋊C4—1222no—
182C22⋊C4—1222no—
183C42—611no—
184C42C22×D6111yescharacteristic
185C23—22no—
186C23—611no—
187C23—1222no—
188D4—22no—
189D4—22no—
190D4—1222no—
191D4—1222no—
192D4—4882no—
193D4—4882no—
194D4—4882no—
195D4—4882no—
196C2×C4—22no—
197C2×C4—82no—
198C2×C4—612no—
199C2×C4—611no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1222no—
203C2×C4—4882no—
204C2×C4D4×D6112yes—
205C2×C4C23×D6111yescharacteristic
206C8—21no—
207C8—612no—
208C8—1221no—
209C8#1175822212yes—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—1221no—
214C22—1222no—
215C22—2442no—
216C22—2442no—
217C22—2442no—
218C22C2×D4×D6111yescharacteristic
219C4—22no—
220C4—42no—
221C4—1221no—
222C4—1222no—
223C4—2442no—
224C4#41×D6111yescharacteristic
225C4C2×#1175822211yescharacteristic
226C2—82no—
227C2—4882no—
228C2—2441no—
229C2#1684030911yescharacteristic
230C2#1684056612yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#442C2
socleC22×C61C22×D4
hypercenter#442D61
hypocenterC61#3176
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #16840363C2semidirect
2. #16840162C2semidirect
3. #16840137C2semidirect
4. #16840125C2semidirect
5. #16840016C2semidirect
6. #16840012C2semidirect
7. #16839997C2semidirect
8. #16839875C2semidirect
9. C4×#11758199C2semidirect
10. #16839719C2semidirect
11. C61×#442C2semidirect
124. #442D61semidirect
127. C61#3176semidirect