Finite Group Databasebeta

← #21456740

Subgroups — #21456740

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#16840310C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3#16840134C211yesmaximal, characteristic, complemented
4#16840113C211yesmaximal, characteristic, complemented
5#16840112C211yesmaximal, characteristic, complemented
6#16839965C214yesmaximal, complemented
7#16839899C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic, complemented
9C61×#492C211yesmaximal, characteristic, complemented
10C2×#11758224—21no—
11C2×Q8×D61C2212yes—
12C2×#11758200C2214yes—
13#14519777C2211yescharacteristic
14#14519777C2211yescharacteristic
15#14519776—21no—
16#14519776—21no—
17#14519775C2212yes—
18#14519764—21no—
19#14519748—21no—
20#14519748C2212yes—
21D4×Dic61—21no—
22D4×Dic61C2212yes—
23C4⋊C4×D61—21no—
24C4⋊C4×D61—21no—
25C42×D61C2211yescharacteristic
26#14519706C2212yes—
27#14519702C2214yes—
28#14519701C2214yes—
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic
31C2×SD16×C61C2214yes—
32C4⋊Q8×C61C2211yescharacteristic
33#127×C61C2211yescharacteristic
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61C2312yes—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61C2312yes—
39C2×C22⋊D61—22no—
40C22×Dic61—22no—
41Q8×D61—44no—
42#11758224—44no—
43C2×C4×D61—22no—
44C2×C4×D61D411yescharacteristic
45C2×C4×D61D411yescharacteristic
46C2×C4×D61C2311yescharacteristic
47C2×Dic122—21no—
48C2×Dic122—22no—
49C2×Dic122C2312yes—
50SD16×C61—44no—
51C2×C8×C61C2312yes—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—21no—
54C42×C61C2311yescharacteristic
55C22⋊Dic61—22no—
56C22⋊Dic61—22no—
57#11758200—44no—
58C4⋊Dic61—21no—
59C4⋊Dic61—21no—
60C4⋊Dic61—21no—
61C4⋊Dic61C2312yes—
62#11758196—22no—
63#11758196—22no—
64C4×Dic61D411yescharacteristic
65C4×Dic61D411yescharacteristic
66C4×Dic61C2311yescharacteristic
67C2×#92418C2312yes—
68C23×C61—22no—
69C22×D61C2×D411yescharacteristic
70Q8×C61—24no—
71D4×C61—24no—
72D4×C61—42no—
73D4×C61—42no—
74C2×C4×C61—22no—
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2411yescharacteristic
78C22⋊D61—44no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—44no—
82C2×Dic61C2×D411yescharacteristic
83C2×Dic61C2×D411yescharacteristic
84C2×Dic61C2×D411yescharacteristic
85C4×D61—22no—
86C4×D61—22no—
87C4×D61—44no—
88C4×D61SD1614yescomplemented
89Dic122—24no—
90Dic122—44no—
91Dic122—42no—
92C8×C61—22no—
93#92418—22no—
94C22×C61—42no—
95C22×C61—42no—
96C22×C61—42no—
97C22×C61C22×D411yescharacteristic
98C2×D61—21no—
99C2×D61—21no—
100C2×D61C2×SD1612yes—
101C4×C61—42no—
102C4×C61C2×SD1612yes—
103C4×C61#13712yes—
104C4×C61H(5,𝔽2)12yes—
105Dic61—21no—
106Dic61—21no—
107Dic61—42no—
108Dic61—42no—
109Dic61C2×SD1612yes—
110#3206—611nomaximal, Sylow
111C2×C61—82no—
112C2×C61#53511yescharacteristic
113C2×C61C22×SD1611yescharacteristic
114C2×C61C2×#13711yescharacteristic
115D61—22no—
116#532—611no—
117C2×C4⋊Q8—611no—
118#492—611no—
119#492D6111yescharacteristic, complemented
120#487—611no—
121#487—611no—
122#461—614no—
123#448—614no—
124#431—611no—
125C61#320611yescharacteristic, complemented, Sylow
126C2×#41—1221no—
127C22×Q8—612no—
128C2×SD16—614no—
129C2×SD16C2×D6114yes—
130C4⋊Q8—612no—
131C4⋊Q8—611no—
132C4⋊Q8—611no—
133C4⋊Q8—1221no—
134C4⋊Q8—1221no—
135C4⋊Q8C2×D6111yescharacteristic
136#127C2×D6111yescharacteristic
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#103—614no—
148C22⋊C8—612no—
149C4×C8—611no—
150C4×C8C2×D6111yescharacteristic
151#41—2444no—
152C2×Q8—612no—
153C2×Q8—1222no—
154C2×Q8—1221no—
155C2×Q8—2444no—
156C2×Q8C22×D6112yes—
157C2×D4—21no—
158C2×D4—21no—
159C2×D4—1222no—
160C2×D4C22×D6112yes—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4—611no—
164C22×C4—1222no—
165C22×C4—1222no—
166SD16—44no—
167SD16—2444no—
168C2×C8—612no—
169C2×C8C22×D6112yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—612no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C4⋊C4—1221no—
178C22⋊C4—1222no—
179C22⋊C4—1222no—
180C42—611no—
181C42—611no—
182C42—611no—
183C42C22×D6111yescharacteristic
184C23—22no—
185C23—611no—
186Q8—24no—
187Q8—1224no—
188Q8—2444no—
189Q8—2442no—
190D4—24no—
191D4—42no—
192D4—42no—
193D4—2444no—
194C2×C4—22no—
195C2×C4—611no—
196C2×C4—614no—
197C2×C4—611no—
198C2×C4—611no—
199C2×C4—1222no—
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—42no—
211C22—42no—
212C22—42no—
213C22—612no—
214C22—1221no—
215C22—1221no—
216C22C2×D4×D6111yescharacteristic
217C4—42no—
218C4—612no—
219C4—1221no—
220C4—1221no—
221C4—2442no—
222C4—2442no—
223C4SD16×D6112yes—
224C4#1451980612yes—
225C4#1451982212yes—
226C2—82no—
227C2—1222no—
228C2#1684032511yescharacteristic
229C2C2×SD16×D6111yescharacteristic
230C2C2×#1451980611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#492C2
socleC22×C61C22×D4
hypercenter#492D61
hypocenterC61#3206
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D61C2semidirect
3. #16840134C2semidirect
4. #16840113C2semidirect
5. #16840112C2semidirect
6. #16839965C2semidirect
7. #16839899C2semidirect
8. #16839813C2semidirect
9. C61×#492C2semidirect
88. C4×D61SD16semidirect
119. #492D61semidirect
125. C61#3206semidirect