Finite Group Databasebeta

← #21456745

Subgroups — #21456745

Order 7808.

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

normal subgroups only

This group has 428 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#16840313C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3#16840136C211yesmaximal, characteristic, complemented
4#16840135C211yesmaximal, characteristic, complemented
5#16840114C211yesmaximal, characteristic, complemented
6#16839966C214yesmaximal, complemented
7#16839902C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic, complemented
9C61×#487C211yesmaximal, characteristic, complemented
10C2×#11758226—21no—
11C2×Q8×D61C2212yes—
12C2×#11758190C2214yes—
13C2×#11758201C2214yes—
14#14519777C2211yescharacteristic
15#14519776—21no—
16#14519776—21no—
17#14519775C2212yes—
18#14519774C2211yescharacteristic
19#14519766—21no—
20#14519752—21no—
21#14519752C2212yes—
22#14519739—21no—
23#14519739C2212yes—
24C4⋊C4×D61—21no—
25C4⋊C4×D61—21no—
26C42×D61C2211yescharacteristic
27#14519706C2212yes—
28#14519700C2214yes—
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic
31C4⋊Q8×C61C2211yescharacteristic
32C4⋊Q8×C61C2211yescharacteristic
33#103×C61C2214yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×Q8×C61C2312yes—
37#11758226—44no—
38Q8×D61—44no—
39C2×D244—22no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244C2312yes—
43C2×C4×D61—22no—
44C2×C4×D61—22no—
45C2×C4×D61D411yescharacteristic
46C2×C4×D61D411yescharacteristic
47C2×C4×D61C2311yescharacteristic
48C2×Dic122—22no—
49C2×Dic122C2312yes—
50C2×C8×C61C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2312yes—
55C42×C61C2311yescharacteristic
56#11758201—44no—
57#11758198—22no—
58#11758198—22no—
59C4⋊Dic61—21no—
60C4⋊Dic61—21no—
61#11758196—22no—
62#11758196—22no—
63C4×Dic61D411yescharacteristic
64C4×Dic61D411yescharacteristic
65C4×Dic61C2311yescharacteristic
66C2×#92418C2312yes—
67#11758190—44no—
68C22×D61—22no—
69C22×D61C2×D411yescharacteristic
70Q8×C61—24no—
71Q8×C61—42no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2411yescharacteristic
77C2×Dic61—22no—
78C2×Dic61C2×D411yescharacteristic
79C2×Dic61C2×D411yescharacteristic
80C2×Dic61C2×D411yescharacteristic
81D244—24no—
82D244—44no—
83D244—42no—
84D244—42no—
85C4×D61—22no—
86C4×D61—22no—
87C4×D61—44no—
88C4×D61—44no—
89C4×D61SD1614yescomplemented
90Dic122—24no—
91Dic122—44no—
92C8×C61—22no—
93#92418—22no—
94C22×C61C22×D411yescharacteristic
95C2×D61—21no—
96C2×D61—21no—
97C2×D61—42no—
98C2×D61—42no—
99C2×D61—42no—
100C2×D61C2×SD1612yes—
101C4×C61—42no—
102C4×C61—42no—
103C4×C61C2×SD1612yes—
104C4×C61#13712yes—
105C4×C61H(5,𝔽2)12yes—
106Dic61—21no—
107Dic61—21no—
108Dic61—42no—
109Dic61C2×SD1612yes—
110#3206—611nomaximal, Sylow
111C2×C61#53511yescharacteristic
112C2×C61C22×SD1611yescharacteristic
113C2×C61C2×#13711yescharacteristic
114D61—22no—
115D61—82no—
116#532—611no—
117C2×C4⋊Q8—611no—
118#492—611no—
119#492—611no—
120#487—611no—
121#487D6111yescharacteristic, complemented
122#461—614no—
123#448—614no—
124#431—611no—
125C61#320611yescharacteristic, complemented, Sylow
126C2×#41—1221no—
127C22×Q8—612no—
128C2×SD16—614no—
129C2×SD16—614no—
130C4⋊Q8—612no—
131C4⋊Q8—611no—
132C4⋊Q8—1221no—
133C4⋊Q8—1221no—
134C4⋊Q8C2×D6111yescharacteristic
135C4⋊Q8C2×D6111yescharacteristic
136#127—611no—
137#124—1221no—
138#121—612no—
139#121—1221no—
140C4×D4—612no—
141C4×D4—1221no—
142C2×C4⋊C4—1221no—
143C2×C4⋊C4—1221no—
144C2×C42—611no—
145C4⋊C8—612no—
146#103—614no—
147#103C2×D6114yes—
148C22⋊C8—612no—
149C4×C8—611no—
150C4×C8C2×D6111yescharacteristic
151#41—2444no—
152C2×Q8—21no—
153C2×Q8—612no—
154C2×Q8—1222no—
155C2×Q8—2444no—
156C2×Q8C22×D6112yes—
157C2×D4—612no—
158C2×D4—1222no—
159C2×D4—1221no—
160C2×D4—1221no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—611no—
164C22×C4—1222no—
165C22×C4—1222no—
166SD16—2444no—
167SD16—2444no—
168C2×C8—612no—
169C2×C8C22×D6112yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C4⋊C4C22×D6112yes—
178C22⋊C4—1222no—
179C22⋊C4—1222no—
180C42—611no—
181C42—611no—
182C42—611no—
183C42C22×D6111yescharacteristic
184C23—611no—
185C23—1222no—
186Q8—24no—
187Q8—42no—
188Q8—1224no—
189Q8—2444no—
190D4—1224no—
191D4—2444no—
192D4—2442no—
193D4—2442no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—611no—
197C2×C4—614no—
198C2×C4—611no—
199C2×C4—611no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—2444no—
204C2×C4—2444no—
205C2×C4D4×D6111yescharacteristic
206C2×C4D4×D6111yescharacteristic
207C2×C4C23×D6111yescharacteristic
208C8—22no—
209C8—1222no—
210C22—612no—
211C22—1221no—
212C22—1221no—
213C22—2442no—
214C22—2442no—
215C22—2442no—
216C22C2×D4×D6111yescharacteristic
217C4—42no—
218C4—42no—
219C4—612no—
220C4—1221no—
221C4—1221no—
222C4—2442no—
223C4SD16×D6112yes—
224C4#1451980912yes—
225C4#1451982312yes—
226C2—1222no—
227C2—4882no—
228C2#1684033011yescharacteristic
229C2C2×SD16×D6111yescharacteristic
230C2C2×#1451980911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#487C2
socleC22×C61C22×D4
hypercenter#487D61
hypocenterC61#3206
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D61C2semidirect
3. #16840136C2semidirect
4. #16840135C2semidirect
5. #16840114C2semidirect
6. #16839966C2semidirect
7. #16839902C2semidirect
8. #16839813C2semidirect
9. C61×#487C2semidirect
89. C4×D61SD16semidirect
121. #487D61semidirect
125. C61#3206semidirect