Finite Group Databasebeta

← #21456771

Subgroups — #21456771

Order 7808.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840312C211yesmaximal, characteristic
2#16840141C211yesmaximal, characteristic, complemented
3#16840136C211yesmaximal, characteristic, complemented
4#16840114C211yesmaximal, characteristic, complemented
5#16840110C211yesmaximal, characteristic, complemented
6#16839984C214yesmaximal, complemented
7#16839922C214yesmaximal, complemented
8#16839815C211yesmaximal, characteristic, complemented
9C61×#533C211yesmaximal, characteristic, complemented
10C2×#11758222C2212yes—
11C2×#11758202C2214yes—
12C2×#11758201C2214yes—
13#14519777C2211yescharacteristic
14#14519774C2211yescharacteristic
15#14519765C2212yes—
16#14519751—21no—
17#14519751—21no—
18C4×D244—21no—
19C4×D244—21no—
20C4⋊#92418C2212yes—
21#14519700C2214yes—
22#14519697C2214yes—
23C22⋊#92418C2212yes—
24C4×#92418C2211yescharacteristic
25C4×#92418C2211yescharacteristic
26C4⋊Q8×C61C2211yescharacteristic
27C4⋊Q8×C61C2211yescharacteristic
28#125×C61—21no—
29C22⋊Q8×C61—21no—
30C22⋊Q8×C61C2212yes—
31C4×Q8×C61—21no—
32C4×Q8×C61C2212yes—
33#117×C61—21no—
34C2×C42×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×Q8×C61C2312yes—
37C22×C4×C61D411yescharacteristic
38C22×C4×C61D411yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—22no—
41#11758222—44no—
42C2×D244—21no—
43C2×D244—21no—
44C2×D244C2312yes—
45C2×C4×D61—22no—
46C2×Dic122C2312yes—
47C4⋊C4×C61—21no—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—22no—
52C4⋊C4×C61C2312yes—
53C22⋊C4×C61—22no—
54C42×C61—22no—
55C42×C61D411yescharacteristic
56C42×C61D411yescharacteristic
57C42×C61C2311yescharacteristic
58C42×C61C2311yescharacteristic
59#11758202—44no—
60#11758201—44no—
61#11758198—22no—
62#11758198—22no—
63C4⋊Dic61—21no—
64C4⋊Dic61—21no—
65C2×#92418C2312yes—
66C2×#92418C2312yes—
67C23×C61C2×D411yescharacteristic
68C22×D61—22no—
69Q8×C61—24no—
70Q8×C61—42no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C22⋊D61—44no—
83C2×Dic61—22no—
84D244—24no—
85D244—42no—
86D244—42no—
87C4×D61—44no—
88Dic122—24no—
89#92418—22no—
90#92418—22no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61C22×D411yescharacteristic
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—42no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—21no—
101C4×C61—42no—
102C4×C61—42no—
103C4×C61#13512yes—
104C4×C61#13712yes—
105C4×C61H(5,𝔽2)12yes—
106Dic61—42no—
107#3210—611nomaximal, Sylow
108C2×C61—41no—
109C2×C61#53511yescharacteristic
110C2×C61C2×#13511yescharacteristic
111C2×C61C2×#13711yescharacteristic
112D61—82no—
113#533D6111yescharacteristic, complemented
114#532—611no—
115#494—611no—
116#492—611no—
117#487—611no—
118#486—611no—
119#464—614no—
120#452—614no—
121#431—611no—
122C61#321011yescharacteristic, complemented, Sylow
123C2×#41—612no—
124C2×Q16—614no—
125C2×SD16—614no—
126C4⋊Q8—611no—
127C4⋊Q8C2×D6111yescharacteristic
128C4⋊Q8C2×D6111yescharacteristic
129#127—611no—
130#125—21no—
131#124—612no—
132C22⋊Q8—21no—
133C22⋊Q8C2×D6112yes—
134#121—1221no—
135#121—1221no—
136C4×Q8—21no—
137C4×Q8C2×D6112yes—
138C4×D4—1221no—
139C4×D4—1221no—
140#117—21no—
141C2×C42C2×D6111yescharacteristic
142C4⋊C8—612no—
143#103—614no—
144#102—614no—
145C22⋊C8—612no—
146C4×C8—611no—
147C4×C8—611no—
148#41—2444no—
149C2×Q8—21no—
150C2×Q8—612no—
151C2×Q8C22×D6112yes—
152C2×D4—612no—
153C2×D4—1222no—
154C2×D4—1221no—
155C2×D4—1221no—
156C22×C4—1222no—
157C22×C4C22⋊D6111yescharacteristic
158C22×C4C22⋊D6111yescharacteristic
159C22×C4C22×D6111yescharacteristic
160Q16—2444no—
161SD16—2444no—
162C2×C8—612no—
163C2×C8—612no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—1221no—
170C4⋊C4—1221no—
171C4⋊C4C22×D6112yes—
172C22⋊C4—22no—
173C22⋊C4—1222no—
174C22⋊C4—1222no—
175C42—22no—
176C42C22⋊D6111yescharacteristic
177C42C22⋊D6111yescharacteristic
178C42C22×D6111yescharacteristic
179C42C22×D6111yescharacteristic
180C23—1222no—
181C23C2×C22⋊D6111yescharacteristic
182Q8—24no—
183Q8—42no—
184Q8—1224no—
185D4—1224no—
186D4—2444no—
187D4—2442no—
188D4—2442no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—1222no—
195C2×C4—2444no—
196C2×C4C2×C22⋊D6111yescharacteristic
197C2×C4C2×C22⋊D6111yescharacteristic
198C2×C4C2×C22⋊D6111yescharacteristic
199C2×C4C2×C22⋊D6111yescharacteristic
200C2×C4C2×C22⋊D6111yescharacteristic
201C2×C4C23×D6111yescharacteristic
202C8—1222no—
203C8—1222no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—2442no—
208C22—2442no—
209C22—2442no—
210C22C22×C22⋊D6111yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—42no—
216C4—2442no—
217C4#1451979712yes—
218C4#1451980812yes—
219C4#1451982312yes—
220C2—41no—
221C2—4882no—
222C2#1684032611yescharacteristic
223C2C2×#1451979711yescharacteristic
224C2C2×#1451980811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3210
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16840141C2semidirect
3. #16840136C2semidirect
4. #16840114C2semidirect
5. #16840110C2semidirect
6. #16839984C2semidirect
7. #16839922C2semidirect
8. #16839815C2semidirect
9. C61×#533C2semidirect
113. #533D61semidirect
122. C61#3210semidirect