Finite Group Databasebeta

← #21457536

Subgroups — #21457536

Order 7808.

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

normal subgroups only

This group has 484 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
1C2×#14519798C212yesmaximal, complemented
2#16840416C211yesmaximal, characteristic, complemented
3#16840415C211yesmaximal, characteristic, complemented
4#16840141C211yesmaximal, characteristic, complemented
5#16840002C212yesmaximal, complemented
6#16839968C211yesmaximal, characteristic, complemented
7#16839927C212yesmaximal, complemented
8#16839921C212yesmaximal, complemented
9C4×#11758199C211yesmaximal, characteristic, complemented
10#16839827C211yesmaximal, characteristic, complemented
11C61×#461C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yes—
13C2×#11758224C2212yes—
14#14519798—28no—
15C2×#11758202C2212yes—
16C2×#11758202C2212yes—
17C2×#11758190C2212yes—
18C2×#11758199C2211yescharacteristic
19C2×C8×D61C2212yes—
20#14519777C2211yescharacteristic
21#14519762—22no—
22#14519761—22no—
23#14519757C2212yes—
24#14519753C2212yes—
25#14519752—21no—
26#14519751—21no—
27C4×D244C2211yescharacteristic
28C4×D244C2211yescharacteristic
29C2×C4⋊Dic61—21no—
30C4⋊C4×D61—21no—
31#14519710C2211yescharacteristic
32#14519702C2212yes—
33#14519698C2211yescharacteristic
34#14519697C2211yescharacteristic
35#14519689C2212yes—
36C4×#92418C2211yescharacteristic
37C2×SD16×C61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×D4×C61C2211yescharacteristic
40C4⋊C8×C61C2211yescharacteristic
41#103×C61C2212yes—
42C2×Q8×C61C2312yes—
43C2×D4×C61C2311yescharacteristic
44C22×C4×C61—21no—
45C2×C22⋊D61—22no—
46C22×Dic61—22no—
47#11758226—24no—
48#11758226—42no—
49#11758224—24no—
50#11758224—42no—
51C2×D244—22no—
52C2×D244D411yescharacteristic
53C2×D244C2311yescharacteristic
54C2×C4×D61—21no—
55C2×C4×D61—22no—
56C2×C4×D61C2312yes—
57C2×Dic122C2312yes—
58SD16×C61—24no—
59C2×C8×C61C2312yes—
60C4⋊C4×C61—21no—
61C4⋊C4×C61—21no—
62C4⋊C4×C61C2311yescharacteristic
63C22⋊C4×C61—21no—
64C42×C61C2311yescharacteristic
65#11758202—24no—
66#11758202—42no—
67#11758199D414yescomplemented
68#11758198—22no—
69#11758198—22no—
70#11758198—21no—
71#11758198D412yes—
72C4⋊Dic61—21no—
73C4⋊Dic61—21no—
74C4⋊Dic61—22no—
75C4⋊Dic61D411yescharacteristic
76C4⋊Dic61C2311yescharacteristic
77#11758196—22no—
78C2×#92418C2311yescharacteristic
79C2×#92418C2311yescharacteristic
80#11758190—24no—
81C8×D61—24no—
82C23×C61—21no—
83C22×D61—21no—
84C22×D61C2×D412yes—
85Q8×C61—22no—
86Q8×C61—22no—
87D4×C61—21no—
88D4×C61C2×D412yes—
89C2×C4×C61—22no—
90C2×C4×C61—21no—
91C2×C4×C61—42no—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2411yescharacteristic
95C22⋊D61—44no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61—44no—
99C2×Dic61C2×D412yes—
100D244—22no—
101D244—21no—
102D244—44no—
103D244C2×D412yes—
104C4×D61—22no—
105C4×D61—22no—
106C4×D61—44no—
107C4×D61—42no—
108Dic122—22no—
109Dic122—22no—
110C8×C61—22no—
111#92418—21no—
112#92418C2×D412yes—
113C22×C61—22no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61C22×D411yescharacteristic
117C2×D61—22no—
118C2×D61—22no—
119C2×D61—22no—
120C2×D61—22no—
121C2×D61—41no—
122C2×D61—41no—
123C4×C61—21no—
124C4×C61—42no—
125C4×C61—41no—
126C4×C61#13512yescomplemented
127C4×C61C22×D411yescharacteristic
128C4×C61H(5,𝔽2)11yescharacteristic
129Dic61—22no—
130Dic61—42no—
131Dic61—41no—
132#3283—611nomaximal, Sylow
133C2×C61—42no—
134C2×C61D4211yescharacteristic
135C2×C61C2×#13511yescharacteristic
136C2×C61#57811yescharacteristic
137D61—42no—
138D61—42no—
139C2×#135—612no—
140#547—611no—
141#547—611no—
142#494—611no—
143#467—612no—
144#461—611no—
145#461D6111yescharacteristic, complemented
146#452—612no—
147#452—612no—
148C4×D8—611no—
149C8×D4—611no—
150C61#328311yescharacteristic, complemented, Sylow
151C2×#41—612no—
152C2×#41—612no—
153#135—1228no—
154C2×Q16—612no—
155C2×Q16—612no—
156C2×SD16—612no—
157C2×SD16C2×D6112yes—
158C2×D8—611no—
159C22×C8—612no—
160C4⋊Q8—611no—
161C4⋊Q8C2×D6111yescharacteristic
162#123—1222no—
163#123—1222no—
164C22⋊Q8—612no—
165C22⋊Q8—612no—
166#121—1221no—
167#121—1221no—
168C4×D4—611no—
169C4×D4—611no—
170C4×D4C2×D6111yescharacteristic
171C2×C4⋊C4—1221no—
172C2×C4⋊C4—1221no—
173#107—611no—
174C4⋊C8C2×D6111yescharacteristic
175#103—612no—
176#103C2×D6112yes—
177#102—611no—
178#102—611no—
179C22⋊C8—612no—
180C4×C8—611no—
181#41—1224no—
182#41—1224no—
183#41—2442no—
184#41—2442no—
185C2×Q8—612no—
186C2×Q8C22×D6112yes—
187C2×D4—611no—
188C2×D4—611no—
189C2×D4—1222no—
190C2×D4—1222no—
191C2×D4C22×D6111yescharacteristic
192C22×C4—21no—
193C22×C4—612no—
194C22×C4—1222no—
195C22×C4—1222no—
196C22×C4—1221no—
197Q16—1224no—
198Q16—2442no—
199SD16—24no—
200SD16—1224no—
201D8—614no—
202C2×C8—611no—
203C2×C8—611no—
204C2×C8—1224no—
205C2×C8C22×D6112yes—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—611no—
209C4⋊C4—611no—
210C4⋊C4—1222no—
211C4⋊C4—1222no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4C22×D6111yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—612no—
217C22⋊C4—1222no—
218C22⋊C4—1222no—
219C22⋊C4—1221no—
220C42C22×D6111yescharacteristic
221C23—21no—
222C23—612no—
223C23—1221no—
224Q8—22no—
225Q8—22no—
226Q8—1222no—
227Q8—1222no—
228D4—21no—
229D4—612no—
230D4—1221no—
231D4—1222no—
232D4—2444no—
233D4—2444no—
234D4D4×D6112yes—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—612no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1221no—
242C2×C4—1222no—
243C2×C4—2444no—
244C2×C4—2444no—
245C2×C4—2442no—
246C2×C4D4×D6111yescharacteristic
247C2×C4D4×D6111yescharacteristic
248C2×C4C23×D6111yescharacteristic
249C8—22no—
250C8—612no—
251C8—1221no—
252C22—22no—
253C22—41no—
254C22—41no—
255C22—1222no—
256C22—1222no—
257C22—1222no—
258C22—1222no—
259C22—2441no—
260C22—2441no—
261C22C2×D4×D6111yescharacteristic
262C4—21no—
263C4—41no—
264C4—42no—
265C4—1222no—
266C4—2441no—
267C4—2442no—
268C4#1451979812yescomplemented
269C4C2×D4×D6111yescharacteristic
270C4#1451982311yescharacteristic
271C2—42no—
272C2—2442no—
273C2—2442no—
274C2#1684039611yescharacteristic
275C2C2×#1451979811yescharacteristic
276C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3283
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. C2×#14519798C2semidirect
2. #16840416C2semidirect
3. #16840415C2semidirect
4. #16840141C2semidirect
5. #16840002C2semidirect
6. #16839968C2semidirect
7. #16839927C2semidirect
8. #16839921C2semidirect
9. C4×#11758199C2semidirect
10. #16839827C2semidirect
11. C61×#461C2semidirect
67. #11758199D4semidirect
126. C4×C61#135semidirect
145. #461D61semidirect
150. C61#3283semidirect
268. C4#14519798semidirect