Finite Group Databasebeta

← #21456797

Subgroups — #21456797

Order 7808.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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, complemented
2#16840296C211yesmaximal, characteristic, complemented
3#16840146C212yesmaximal, complemented
4#16840117C212yesmaximal, complemented
5#16839973C211yesmaximal, characteristic, complemented
6#16839968C211yesmaximal, characteristic, complemented
7#16839963C211yesmaximal, characteristic, complemented
8#16839958C211yesmaximal, characteristic, complemented
9#16839926C212yesmaximal, complemented
10#16839909C212yesmaximal, complemented
11C61×#431C211yesmaximal, characteristic, complemented
12C2×#11758222C2212yes—
13C2×Dic244C2212yes—
14C2×#11758190C2212yes—
15C2×#11758190C2212yes—
16C2×D488C2212yes—
17#14519777C2211yescharacteristic
18#14519774C2211yescharacteristic
19#14519771—21no—
20#14519769C2211yescharacteristic
21#14519765C2211yescharacteristic
22#14519765C2212yes—
23#14519760—21no—
24#14519756C2211yescharacteristic
25#14519751—21no—
26#14519751—21no—
27#14519751C2211yescharacteristic
28C4×Dic122C2211yescharacteristic
29C4×D244—21no—
30C4×D244—21no—
31C4×D244C2211yescharacteristic
32C4×C22⋊D61—21no—
33#14519734—21no—
34#14519702C2212yes—
35#14519702C2212yes—
36#14519699C2212yes—
37#14519699C2212yes—
38C2×C42×C61C2211yescharacteristic
39C4⋊C8×C61C2211yescharacteristic
40C4⋊C8×C61C2211yescharacteristic
41C22⋊C8×C61C2212yes—
42C4×C8×C61C2212yes—
43C22×C4×C61D411yescharacteristic
44C22×C4×C61D411yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—22no—
47C2×C22⋊D61—21no—
48#11758222—42no—
49#11758222—42no—
50C2×D244—21no—
51C2×D244—21no—
52C2×D244C2312yes—
53C2×D244C2311yescharacteristic
54C2×C4×D61—22no—
55C2×C4×D61—21no—
56C2×Dic122C2312yes—
57C2×Dic122C2311yescharacteristic
58C2×C8×C61C2312yes—
59C2×C8×C61C2312yes—
60C42×C61D411yescharacteristic
61C42×C61D411yescharacteristic
62C42×C61C2311yescharacteristic
63C42×C61C2311yescharacteristic
64C22⋊Dic61—21no—
65#11758198—21no—
66#11758198—21no—
67#11758198—21no—
68#11758198—22no—
69#11758198—22no—
70#11758198—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61C2311yescharacteristic
74C4⋊Dic61C2311yescharacteristic
75#11758196—21no—
76#11758196—21no—
77#11758196—21no—
78#11758196—21no—
79C4×Dic61—21no—
80Dic244—42no—
81D488—42no—
82#11758190—42no—
83#11758190—42no—
84C23×C61C2×D411yescharacteristic
85C22×D61—21no—
86C22×D61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2411yescharacteristic
97C22⋊D61—44no—
98C22⋊D61—42no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—22no—
103D244—21no—
104D244—22no—
105D244—21no—
106D244—22no—
107D244—42no—
108D244—42no—
109C4×D61—44no—
110C4×D61—42no—
111Dic122—21no—
112Dic122—22no—
113Dic122—21no—
114Dic122—22no—
115C8×C61—22no—
116C8×C61—22no—
117C22×C61—21no—
118C22×C61—21no—
119C22×C61—21no—
120C22×C61C22×D411yescharacteristic
121C2×D61—42no—
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—41no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—21no—
131C4×C61#13512yes—
132C4×C61H(5,𝔽2)11yescharacteristic
133C4×C61H(5,𝔽2)11yescharacteristic
134Dic61—42no—
135Dic61—41no—
136Dic61—41no—
137Dic61—41no—
138#3212—611nomaximal, Sylow
139C2×C61—41no—
140C2×C61#53511yescharacteristic
141C2×C61C2×#13511yescharacteristic
142C2×C61#57511yescharacteristic
143D61—82no—
144D61—81no—
145#532—611no—
146#529—611no—
147#495—612no—
148#488—612no—
149#462—611no—
150#461—611no—
151#460—611no—
152#459—611no—
153#452—612no—
154#449—612no—
155#431D6111yescharacteristic, complemented
156C61#321211yescharacteristic, complemented, Sylow
157C2×#41—612no—
158C2×Q16—612no—
159C2×SD16—612no—
160C2×SD16—612no—
161C2×D8—612no—
162C4⋊Q8—611no—
163#127—611no—
164#126—1221no—
165#125—611no—
166#124—611no—
167#124—612no—
168#123—1221no—
169C22⋊Q8—611no—
170#121—611no—
171#121—1221no—
172#121—1221no—
173C4×Q8—611no—
174C4×D4—611no—
175C4×D4—1221no—
176C4×D4—1221no—
177C4×D4—1221no—
178#117—1221no—
179C2×C42C2×D6111yescharacteristic
180C4⋊C8C2×D6111yescharacteristic
181C4⋊C8C2×D6111yescharacteristic
182#103—612no—
183#103—612no—
184#102—612no—
185#102—612no—
186C22⋊C8C2×D6112yes—
187C4×C8C2×D6112yes—
188#41—2442no—
189#41—2442no—
190C2×Q8—612no—
191C2×Q8—611no—
192C2×D4—612no—
193C2×D4—611no—
194C2×D4—1221no—
195C2×D4—1222no—
196C2×D4—1221no—
197C2×D4—1221no—
198C22×C4—1221no—
199C22×C4—1222no—
200C22×C4D24411yescharacteristic
201C22×C4D24411yescharacteristic
202C22×C4C22×D6111yescharacteristic
203Q16—2442no—
204SD16—2442no—
205SD16—2442no—
206D8—2442no—
207C2×C8C22×D6112yes—
208C2×C8C22×D6112yes—
209C4⋊C4—611no—
210C4⋊C4—611no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4—1221no—
215C4⋊C4—1221no—
216C4⋊C4—1221no—
217C22⋊C4—1221no—
218C22⋊C4—1221no—
219C22⋊C4—1221no—
220C22⋊C4—1221no—
221C22⋊C4—1222no—
222C22⋊C4—1222no—
223C22⋊C4—1221no—
224C42—1221no—
225C42D24411yescharacteristic
226C42D24411yescharacteristic
227C42C22×D6111yescharacteristic
228C42C22×D6111yescharacteristic
229C23—1221no—
230C23—1222no—
231C23C2×D24411yescharacteristic
232Q8—1221no—
233Q8—1222no—
234Q8—1221no—
235Q8—1222no—
236D4—1221no—
237D4—1222no—
238D4—1221no—
239D4—1222no—
240D4—2442no—
241D4—2442no—
242D4—2444no—
243D4—2442no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1222no—
252C2×C4—2444no—
253C2×C4—2442no—
254C2×C4C2×D24411yescharacteristic
255C2×C4C2×D24411yescharacteristic
256C2×C4C2×D24411yescharacteristic
257C2×C4C2×D24411yescharacteristic
258C2×C4C2×D24411yescharacteristic
259C2×C4C23×D6111yescharacteristic
260C8—22no—
261C8—22no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—2441no—
266C22—2442no—
267C22—2442no—
268C22—2441no—
269C22—2442no—
270C22—2441no—
271C22C22×D24411yescharacteristic
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—2441no—
277C4—2441no—
278C4—2442no—
279C4—2441no—
280C4#1451979912yes—
281C4#1451982311yescharacteristic
282C4#1451982311yescharacteristic
283C2—41no—
284C2—4881no—
285C2—4882no—
286C2#1684033111yescharacteristic
287C2C2×#1451979911yescharacteristic
288C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#431C2
socleC22×C61C22×D4
hypercenter#431D61
hypocenterC61#3212
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #16840312C2semidirect
2. #16840296C2semidirect
3. #16840146C2semidirect
4. #16840117C2semidirect
5. #16839973C2semidirect
6. #16839968C2semidirect
7. #16839963C2semidirect
8. #16839958C2semidirect
9. #16839926C2semidirect
10. #16839909C2semidirect
11. C61×#431C2semidirect
155. #431D61semidirect
156. C61#3212semidirect