Finite Group Databasebeta

← #21456463

Subgroups — #21456463

Order 7808.

386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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#16840367C211yesmaximal, characteristic, complemented
2#16840161C211yesmaximal, characteristic, complemented
3#16840138C211yesmaximal, characteristic, complemented
4#16840128C211yesmaximal, characteristic, complemented
5#16840126C211yesmaximal, characteristic, complemented
6#16840013C212yesmaximal, complemented
7#16839996C212yesmaximal, complemented
8#16839872C212yesmaximal, complemented
9C4×#11758199C212yesmaximal, complemented
10#16839718C211yesmaximal, characteristic, complemented
11C61×#540C211yesmaximal, characteristic, complemented
12C2×#11758199C2212yes—
13C2×#11758199C2212yes—
14C2×#11758194C2211yescharacteristic
15C22×#92418C2211yescharacteristic
16#14519774C2211yescharacteristic
17#14519769C2211yescharacteristic
18#14519762—22no—
19#14519751C2212yes—
20#14519750—22no—
21C4×D244C2212yes—
22#14519710C2212yes—
23#14519708C2212yes—
24#14519698C2212yes—
25#14519698C2212yes—
26#14519697C2212yes—
27#14519697C2212yes—
28#14519688C2211yescharacteristic
29#14519688C2211yescharacteristic
30C4×#92418C2211yescharacteristic
31C4×#92418C2211yescharacteristic
32#127×C61C2211yescharacteristic
33#125×C61C2211yescharacteristic
34#123×C61—22no—
35#121×C61—22no—
36#121×C61C2212yes—
37C4×D4×C61C2212yes—
38#117×C61C2211yescharacteristic
39C2×D4×C61—22no—
40C2×D4×C61—22no—
41C2×D4×C61C2312yes—
42C22×C4×C61—22no—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—22no—
45C2×D244—22no—
46C2×D244C2312yes—
47C2×C4×D61—22no—
48C4⋊C4×C61—22no—
49C4⋊C4×C61D412yes—
50C4⋊C4×C61C2312yes—
51C22⋊C4×C61—22no—
52C22⋊C4×C61—22no—
53C22⋊C4×C61D412yes—
54C42×C61C2311yescharacteristic
55C42×C61C2311yescharacteristic
56#11758199—24no—
57#11758199—24no—
58#11758198—22no—
59#11758198—22no—
60C4⋊Dic61C2312yes—
61#11758196—22no—
62#11758194—22no—
63C2×#92418—22no—
64C2×#92418C2311yescharacteristic
65C2×#92418C2311yescharacteristic
66C2×#92418C2311yescharacteristic
67C2×#92418C2311yescharacteristic
68C23×C61—22no—
69C23×C61C2×D411yescharacteristic
70C22×D61—22no—
71D4×C61—22no—
72D4×C61—22no—
73D4×C61—82no—
74D4×C61—82no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—82no—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2411yescharacteristic
83C22⋊D61—82no—
84C2×Dic61—22no—
85D244—22no—
86D244—22no—
87D244—82no—
88C4×D61—82no—
89#92418—21no—
90#92418—21no—
91#92418#4112yes—
92#92418#4112yes—
93C22×C61—21no—
94C22×C61—22no—
95C22×C61—42no—
96C22×C61—42no—
97C22×C61—42no—
98C22×C61C22×D411yescharacteristic
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—42no—
102C4×C61—21no—
103C4×C61—22no—
104C4×C61—22no—
105C4×C61—42no—
106C4×C61C2×#4111yescharacteristic
107C4×C61C2×#4111yescharacteristic
108Dic61—42no—
109#3176—611nomaximal, Sylow
110C2×C61—41no—
111C2×C61—82no—
112C2×C61#53211yescharacteristic
113C2×C61#57612yes—
114D61—82no—
115#540—611no—
116#540D6111yescharacteristic, complemented
117#499—611no—
118#493—611no—
119#490—611no—
120#490—611no—
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—22no—
136#123—1222no—
137#121—22no—
138#121—612no—
139#121—1222no—
140#121C2×D6112yes—
141C4×D4—612no—
142C4×D4C2×D6112yes—
143#117C2×D6111yescharacteristic
144#107—612no—
145#106—612no—
146#102—612no—
147#102—612no—
148#102—612no—
149#102—612no—
150#97—611no—
151#97—611no—
152C4×C8—611no—
153C4×C8—611no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—612no—
157C2×D4—1222no—
158C2×D4—1222no—
159C2×D4C22×D6112yes—
160C22×C4—22no—
161C22×C4—1222no—
162C22×C4C22×D6111yescharacteristic
163D8—1224no—
164D8—1224no—
165M16—1222no—
166C2×C8—611no—
167C2×C8—611no—
168C2×C8—611no—
169C2×C8—611no—
170C2×C8—1222no—
171C4⋊C4—22no—
172C4⋊C4—612no—
173C4⋊C4—1222no—
174C4⋊C4C22⋊D6112yes—
175C4⋊C4C22×D6112yes—
176C22⋊C4—22no—
177C22⋊C4—22no—
178C22⋊C4—1222no—
179C22⋊C4—1222no—
180C22⋊C4C22⋊D6112yes—
181C42C22×D6111yescharacteristic
182C42C22×D6111yescharacteristic
183C23—22no—
184C23—1222no—
185C23C2×C22⋊D6111yescharacteristic
186D4—22no—
187D4—22no—
188D4—82no—
189D4—82no—
190D4—1222no—
191D4—1222no—
192D4—4882no—
193D4—4882no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—82no—
198C2×C4—1222no—
199C2×C4—4882no—
200C2×C4C2×C22⋊D6112yes—
201C2×C4C2×C22⋊D6112yes—
202C2×C4C2×C22⋊D6111yescharacteristic
203C2×C4C23×D6111yescharacteristic
204C8—612no—
205C8—612no—
206C8—1221no—
207C8—1221no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—2442no—
214C22—2442no—
215C22—2442no—
216C22C22×C22⋊D6111yescharacteristic
217C4—21no—
218C4—22no—
219C4—22no—
220C4—42no—
221C4—2442no—
222C4#41×D6111yescharacteristic
223C4#41×D6111yescharacteristic
224C2—41no—
225C2—82no—
226C2—4882no—
227C2#1684030811yescharacteristic
228C2#1684056512yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#540C2
socleC22×C61C22×D4
hypercenter#540D61
hypocenterC61#3176
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #16840367C2semidirect
2. #16840161C2semidirect
3. #16840138C2semidirect
4. #16840128C2semidirect
5. #16840126C2semidirect
6. #16840013C2semidirect
7. #16839996C2semidirect
8. #16839872C2semidirect
9. C4×#11758199C2semidirect
10. #16839718C2semidirect
11. C61×#540C2semidirect
116. #540D61semidirect
126. C61#3176semidirect