Finite Group Databasebeta

← #21456859

Subgroups — #21456859

Order 7808.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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, complemented
2#16840297C211yesmaximal, characteristic, complemented
3#16840154C211yesmaximal, characteristic, complemented
4#16840151C211yesmaximal, characteristic, complemented
5#16840128C211yesmaximal, characteristic, complemented
6#16839987C212yesmaximal, complemented
7#16839980C212yesmaximal, complemented
8#16839927C212yesmaximal, complemented
9#16839910C212yesmaximal, complemented
10#16839817C211yesmaximal, characteristic, complemented
11C61×#491C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yes—
13C2×#11758202C2212yes—
14C2×#11758190C2212yes—
15C2×#11758201C2212yes—
16C2×D488C2212yes—
17#14519774C2211yescharacteristic
18#14519772—21no—
19#14519766C2212yes—
20#14519765C2211yescharacteristic
21#14519762—21no—
22#14519757C2211yescharacteristic
23#14519752—21no—
24#14519752—21no—
25#14519752C2211yescharacteristic
26#14519742C2211yescharacteristic
27#14519739—21no—
28#14519739—21no—
29#14519739—21no—
30#14519739C2211yescharacteristic
31#14519735—21no—
32C42×D61C2211yescharacteristic
33#14519706C2212yes—
34#14519697C2212yes—
35#14519697C2212yes—
36#14519689C2212yes—
37#14519688C2211yescharacteristic
38C4⋊Q8×C61C2211yescharacteristic
39#125×C61C2211yescharacteristic
40#103×C61C2212yes—
41#103×C61C2212yes—
42#97×C61C2211yescharacteristic
43C2×Q8×C61C2312yes—
44#11758226—42no—
45#11758226—42no—
46C2×D244—22no—
47C2×D244—21no—
48C2×D244—21no—
49C2×D244—21no—
50C2×D244C2312yes—
51C2×D244C2311yescharacteristic
52C2×C4×D61—22no—
53C2×C4×D61—21no—
54C2×C4×D61D411yescharacteristic
55C2×C4×D61D411yescharacteristic
56C2×C4×D61C2311yescharacteristic
57C2×Dic122C2311yescharacteristic
58C2×C8×C61C2312yes—
59C4⋊C4×C61—21no—
60C4⋊C4×C61—21no—
61C4⋊C4×C61—21no—
62C4⋊C4×C61—21no—
63C4⋊C4×C61C2311yescharacteristic
64C4⋊C4×C61C2311yescharacteristic
65C42×C61C2311yescharacteristic
66#11758202—42no—
67#11758201—42no—
68#11758198—21no—
69#11758198—21no—
70#11758198—21no—
71#11758198—21no—
72#11758198—22no—
73#11758198—22no—
74#11758198—21no—
75C4⋊Dic61—21no—
76#11758196—21no—
77C4×Dic61—21no—
78C4×Dic61D411yescharacteristic
79C4×Dic61D411yescharacteristic
80C4×Dic61C2311yescharacteristic
81C2×#92418C2312yes—
82D488—42no—
83#11758190—42no—
84C22×D61—21no—
85C22×D61—22no—
86C22×D61C2×D411yescharacteristic
87Q8×C61—22no—
88Q8×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2411yescharacteristic
95C2×Dic61—21no—
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99D244—22no—
100D244—22no—
101D244—22no—
102D244—42no—
103D244—42no—
104D244—42no—
105D244—44no—
106C4×D61—22no—
107C4×D61—41no—
108C4×D61—41no—
109C4×D61—42no—
110C4×D61—44no—
111Dic122—22no—
112C8×C61—22no—
113#92418—22no—
114C22×C61C22×D411yescharacteristic
115C2×D61—21no—
116C2×D61—21no—
117C2×D61—21no—
118C2×D61—42no—
119C2×D61—41no—
120C2×D61—41no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—41no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—42no—
127C4×C61—41no—
128C4×C61—41no—
129C4×C61H(5,𝔽2)12yes—
130Dic61—21no—
131Dic61—21no—
132Dic61—21no—
133Dic61—41no—
134#3219—611nomaximal, Sylow
135C2×C61#53511yescharacteristic
136C2×C61#57511yescharacteristic
137C2×C61#57511yescharacteristic
138D61—41no—
139D61—82no—
140D61—81no—
141#532—611no—
142#529—611no—
143#497—611no—
144#496—611no—
145#491D6111yescharacteristic, complemented
146#490—611no—
147#464—612no—
148#463—612no—
149#452—612no—
150#449—612no—
151#432—611no—
152C61#321911yescharacteristic, complemented, Sylow
153C2×#41—612no—
154C2×Q16—612no—
155C2×SD16—612no—
156C2×SD16—612no—
157C2×D8—612no—
158C4⋊Q8C2×D6111yescharacteristic
159#127—611no—
160#126—1221no—
161#125C2×D6111yescharacteristic
162#124—612no—
163#124—611no—
164#123—1221no—
165C22⋊Q8—611no—
166#121—611no—
167#121—1221no—
168#121—1221no—
169C4×Q8—611no—
170C4×D4—611no—
171C4×D4—1221no—
172C4×D4—1221no—
173C4×D4—1221no—
174#117—1221no—
175C2×C42—611no—
176C4⋊C8—612no—
177#103C2×D6112yes—
178#103C2×D6112yes—
179#102—612no—
180#102—612no—
181C22⋊C8—612no—
182#97—611no—
183#97C2×D6111yescharacteristic
184#41—2442no—
185#41—2442no—
186C2×Q8—611no—
187C2×Q8C22×D6112yes—
188C2×D4—612no—
189C2×D4—611no—
190C2×D4—1221no—
191C2×D4—1222no—
192C2×D4—1221no—
193C2×D4—1221no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—1221no—
198C22×C4—1222no—
199Q16—2442no—
200SD16—2442no—
201SD16—2442no—
202D8—2442no—
203C2×C8—612no—
204C2×C8C22×D6112yes—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C4⋊C4C22×D6111yescharacteristic
212C4⋊C4C22×D6111yescharacteristic
213C22⋊C4—1221no—
214C22⋊C4—1221no—
215C22⋊C4—1222no—
216C22⋊C4—1222no—
217C22⋊C4—1221no—
218C22⋊C4—1221no—
219C22⋊C4—1221no—
220C42—611no—
221C42—611no—
222C42—611no—
223C42—1221no—
224C42C22×D6111yescharacteristic
225C23—611no—
226C23—1221no—
227C23—1222no—
228Q8—22no—
229Q8—22no—
230Q8—1222no—
231D4—1222no—
232D4—1222no—
233D4—1222no—
234D4—2442no—
235D4—2442no—
236D4—2442no—
237D4—2444no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—1222no—
245C2×C4—1221no—
246C2×C4—2441no—
247C2×C4—2441no—
248C2×C4—2442no—
249C2×C4—2444no—
250C2×C4D4×D6111yescharacteristic
251C2×C4D4×D6111yescharacteristic
252C2×C4C23×D6111yescharacteristic
253C8—22no—
254C8—1222no—
255C22—1221no—
256C22—1221no—
257C22—1221no—
258C22—2441no—
259C22—2442no—
260C22—2442no—
261C22—2441no—
262C22—2442no—
263C22—2441no—
264C22C2×D4×D6111yescharacteristic
265C4—21no—
266C4—21no—
267C4—41no—
268C4—41no—
269C4—42no—
270C4—1221no—
271C4—1221no—
272C4—1221no—
273C4—2441no—
274C4#1451982312yes—
275C2—4881no—
276C2—4882no—
277C2—2441no—
278C2#1684033011yescharacteristic
279C2#1684056111yescharacteristic
280C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#491C2
socleC22×C61C22×D4
hypercenter#491D61
hypocenterC61#3219
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #16840313C2semidirect
2. #16840297C2semidirect
3. #16840154C2semidirect
4. #16840151C2semidirect
5. #16840128C2semidirect
6. #16839987C2semidirect
7. #16839980C2semidirect
8. #16839927C2semidirect
9. #16839910C2semidirect
10. #16839817C2semidirect
11. C61×#491C2semidirect
145. #491D61semidirect
152. C61#3219semidirect