Finite Group Databasebeta

← #21456468

Subgroups — #21456468

Order 7808.

386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840368C211yesmaximal, characteristic, complemented
2#16840366C211yesmaximal, characteristic, complemented
3#16840161C211yesmaximal, characteristic, complemented
4#16840138C211yesmaximal, characteristic, complemented
5#16840127C211yesmaximal, characteristic, complemented
6#16840014C212yesmaximal, complemented
7#16839997C212yesmaximal, complemented
8#16839871C212yesmaximal, complemented
9#16839842C212yesmaximal, complemented
10#16839719C211yesmaximal, characteristic, complemented
11C61×#490C211yesmaximal, characteristic, complemented
12C2×#11758199C2212yes—
13C2×#11758199C2212yes—
14C2×#11758189C2211yescharacteristic
15C2×C8×D61C2211yescharacteristic
16#14519774C2211yescharacteristic
17#14519769C2211yescharacteristic
18#14519762—22no—
19#14519758—22no—
20#14519752—22no—
21#14519752C2212yes—
22#14519749—22no—
23#14519748C2212yes—
24D4×Dic61C2212yes—
25#14519739C2212yes—
26#14519734C2211yescharacteristic
27#14519710C2212yes—
28#14519708C2212yes—
29#14519699C2212yes—
30#14519699C2212yes—
31#14519687C2211yescharacteristic
32C4×#92418C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34#127×C61C2211yescharacteristic
35#125×C61C2211yescharacteristic
36#102×C61C2212yes—
37#102×C61C2212yes—
38#97×C61C2211yescharacteristic
39C2×D4×C61—22no—
40C2×D4×C61C2312yes—
41C2×C22⋊D61—22no—
42C22×Dic61—22no—
43C2×D244—22no—
44C2×D244—22no—
45C2×D244C2312yes—
46C2×C4×D61—22no—
47C2×C4×D61C2311yescharacteristic
48C2×C8×C61C2311yescharacteristic
49C2×C8×C61C2311yescharacteristic
50C4⋊C4×C61—22no—
51C4⋊C4×C61C2312yes—
52C42×C61C2311yescharacteristic
53C22⋊Dic61—22no—
54C22⋊Dic61—22no—
55#11758199—24no—
56#11758199—24no—
57#11758198—22no—
58#11758198—22no—
59#11758198D412yes—
60C4⋊Dic61C2312yes—
61#11758196—22no—
62#11758196D412yes—
63C4×Dic61C2311yescharacteristic
64C2×#92418C2311yescharacteristic
65C2×#92418C2311yescharacteristic
66#11758189—22no—
67C8×D61—22no—
68C23×C61—22no—
69C22×D61—22no—
70C22×D61C2×D411yescharacteristic
71D4×C61—22no—
72D4×C61—22no—
73D4×C61—82no—
74C2×C4×C61—22no—
75C2×C4×C61C2×D412yes—
76C2×C4×C61C2411yescharacteristic
77C22⋊D61—82no—
78C2×Dic61—22no—
79C2×Dic61—82no—
80C2×Dic61C2×D412yes—
81C2×Dic61C2×D411yescharacteristic
82D244—22no—
83D244—22no—
84D244—82no—
85D244—82no—
86C4×D61—21no—
87C4×D61—21no—
88C4×D61—82no—
89C8×C61—21no—
90C8×C61—21no—
91#92418#4112yes—
92#92418#4112yes—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61—42no—
96C22×C61C22×D411yescharacteristic
97C2×D61—21no—
98C2×D61—22no—
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—42no—
102C4×C61—22no—
103C4×C61—42no—
104C4×C61C2×#4111yescharacteristic
105C4×C61C2×#4111yescharacteristic
106Dic61—21no—
107Dic61—22no—
108Dic61—42no—
109#3176—611nomaximal, Sylow
110C2×C61—82no—
111C2×C61#53211yescharacteristic
112C2×C61#57612yes—
113D61—41no—
114D61—82no—
115#540—611no—
116#540—611no—
117#499—611no—
118#493—611no—
119#490—611no—
120#490D6111yescharacteristic, complemented
121#469—612no—
122#466—612no—
123#442—612no—
124C4×D8—612no—
125#405—611no—
126C61#317611yescharacteristic, complemented, Sylow
127C2×D8—612no—
128C2×D8—612no—
129C2×M16—611no—
130C22×C8—611no—
131#127—611no—
132#127C2×D6111yescharacteristic
133#125—611no—
134#125C2×D6111yescharacteristic
135#123—1222no—
136#123—1222no—
137#121—612no—
138#121—612no—
139#121—1222no—
140#121—1222no—
141C4×D4—612no—
142C4×D4—612no—
143#117—611no—
144#107—612no—
145#106—612no—
146#102—612no—
147#102—612no—
148#102C2×D6112yes—
149#102C2×D6112yes—
150#97—611no—
151#97C2×D6111yescharacteristic
152C4×C8—611no—
153C4×C8—611no—
154C2×D4—22no—
155C2×D4—612no—
156C2×D4—1222no—
157C2×D4—1222no—
158C2×D4—1222no—
159C2×D4C22×D6112yes—
160C22×C4—611no—
161C22×C4—1222no—
162C22×C4—1222no—
163D8—1224no—
164D8—1224no—
165M16—1222no—
166C2×C8—611no—
167C2×C8—611no—
168C2×C8—1222no—
169C2×C8C22×D6111yescharacteristic
170C2×C8C22×D6111yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—612no—
173C4⋊C4—612no—
174C4⋊C4—1222no—
175C4⋊C4C22×D6112yes—
176C22⋊C4—612no—
177C22⋊C4—1222no—
178C22⋊C4—1222no—
179C22⋊C4—1222no—
180C22⋊C4—1222no—
181C42—611no—
182C42C22×D6111yescharacteristic
183C23—22no—
184C23—611no—
185C23—1222no—
186D4—22no—
187D4—22no—
188D4—82no—
189D4—1222no—
190D4—1222no—
191D4—4882no—
192D4—4882no—
193D4—4882no—
194C2×C4—22no—
195C2×C4—612no—
196C2×C4—611no—
197C2×C4—1221no—
198C2×C4—1221no—
199C2×C4—1222no—
200C2×C4—4882no—
201C2×C4—4882no—
202C2×C4D4×D6112yes—
203C2×C4C23×D6111yescharacteristic
204C8—21no—
205C8—21no—
206C8—612no—
207C8—612no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—1222no—
212C22—1221no—
213C22—2442no—
214C22—2442no—
215C22—2442no—
216C22C2×D4×D6111yescharacteristic
217C4—22no—
218C4—42no—
219C4—1222no—
220C4—1221no—
221C4—2442no—
222C4#41×D6111yescharacteristic
223C4#41×D6111yescharacteristic
224C2—82no—
225C2—4882no—
226C2—2441no—
227C2#1684031111yescharacteristic
228C2#1684056612yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#490C2
socleC22×C61C22×D4
hypercenter#490D61
hypocenterC61#3176
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. #16840368C2semidirect
2. #16840366C2semidirect
3. #16840161C2semidirect
4. #16840138C2semidirect
5. #16840127C2semidirect
6. #16840014C2semidirect
7. #16839997C2semidirect
8. #16839871C2semidirect
9. #16839842C2semidirect
10. #16839719C2semidirect
11. C61×#490C2semidirect
120. #490D61semidirect
126. C61#3176semidirect