Finite Group Databasebeta

← #21457141

Subgroups — #21457141

Order 7808.

398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 115 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, complemented
2#16840294C211yesmaximal, characteristic, complemented
3#16840060C212yesmaximal, complemented
4#16840058C211yesmaximal, characteristic, complemented
5#16840052C211yesmaximal, characteristic, complemented
6#16839995C212yesmaximal, complemented
7#16839990C212yesmaximal, complemented
8#16839975C212yesmaximal, complemented
9#16839959C211yesmaximal, characteristic, complemented
10C4⋊C8×D61C211yesmaximal, characteristic, complemented
11C61×#459C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13C2×#11758200C2212yes—
14C2×C8×D61C2212yes—
15#14519777C2211yescharacteristic
16#14519770—21no—
17#14519768C2211yescharacteristic
18#14519764—21no—
19#14519764C2211yescharacteristic
20#14519759—21no—
21#14519757C2211yescharacteristic
22#14519748—21no—
23#14519748C2212yes—
24#14519748C2211yescharacteristic
25C4×Dic122C2211yescharacteristic
26D4×Dic61—21no—
27D4×Dic61C2212yes—
28C4×C22⋊D61—21no—
29#14519736—21no—
30C42×D61C2211yescharacteristic
31#14519711C2212yes—
32#14519708C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519702C2212yes—
36#14519698C2212yes—
37#14519698C2212yes—
38C2×D8×C61C2212yes—
39#127×C61C2211yescharacteristic
40C4×D4×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42#102×C61C2212yes—
43C2×D4×C61—21no—
44C2×D4×C61—21no—
45C2×D4×C61C2312yes—
46C2×D4×C61C2311yescharacteristic
47C22×C4×C61—21no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61—21no—
50C22×Dic61—22no—
51#11758224—44no—
52C2×C4×D61D411yescharacteristic
53C2×C4×D61D411yescharacteristic
54C2×C4×D61C2311yescharacteristic
55C2×Dic122—21no—
56C2×Dic122C2311yescharacteristic
57D8×C61—42no—
58C2×C8×C61C2312yes—
59C4⋊C4×C61C2311yescharacteristic
60C22⋊C4×C61—21no—
61C42×C61C2311yescharacteristic
62C22⋊Dic61—21no—
63C22⋊Dic61—21no—
64C22⋊Dic61—21no—
65C22⋊Dic61—22no—
66C22⋊Dic61—22no—
67#11758200—42no—
68#11758198—21no—
69C4⋊Dic61—21no—
70C4⋊Dic61—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61C2311yescharacteristic
73C4⋊Dic61C2312yes—
74#11758196—21no—
75#11758196—21no—
76C4×Dic61—21no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81C8×D61—42no—
82C23×C61—21no—
83C23×C61—22no—
84C22×D61C2×D411yescharacteristic
85D4×C61—22no—
86D4×C61—21no—
87D4×C61—22no—
88D4×C61—21no—
89D4×C61—42no—
90D4×C61—42no—
91C2×C4×C61—21no—
92C2×C4×C61—42no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—44no—
97C22⋊D61—42no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—22no—
101C2×Dic61—44no—
102C2×Dic61C2×D411yescharacteristic
103C2×Dic61C2×D411yescharacteristic
104C2×Dic61C2×D411yescharacteristic
105C4×D61—22no—
106C4×D61—22no—
107C4×D61—21no—
108C4×D61—21no—
109Dic122—21no—
110Dic122—21no—
111Dic122—42no—
112C8×C61—22no—
113#92418—22no—
114C22×C61—42no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61—41no—
120C22×C61C22×D411yescharacteristic
121C2×D61—21no—
122C2×D61—21no—
123C2×D61AGL(1,ℤ/8)12yes—
124C4×C61—21no—
125C4×C61—41no—
126C4×C61#13512yes—
127C4×C61H(5,𝔽2)11yescharacteristic
128C4×C612−1+411yescharacteristic
129Dic61—21no—
130Dic61—21no—
131Dic61—21no—
132Dic61—41no—
133Dic61—42no—
134Dic61—41no—
135#3247—611nomaximal, Sylow
136C2×C61—81no—
137C2×C61—82no—
138C2×C61#53711yescharacteristic
139C2×C61C2×#13511yescharacteristic
140C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
141D61—22no—
142#532—611no—
143#529—611no—
144#478—612no—
145#477—611no—
146#476—611no—
147#466—612no—
148#465—612no—
149#463—612no—
150#460—611no—
151#459D6111yescharacteristic, complemented
152C2×C4⋊C8—611no—
153C61#324711yescharacteristic, complemented, Sylow
154C2×#41—1221no—
155C2×SD16—612no—
156C2×D8C2×D6112yes—
157C22×C8—612no—
158C4⋊Q8—611no—
159#127C2×D6111yescharacteristic
160#126—1221no—
161#125—611no—
162#124—611no—
163#124—1221no—
164#123—1221no—
165C22⋊Q8—611no—
166#121—611no—
167#121—612no—
168#121—1221no—
169C4×Q8—611no—
170C4×D4—612no—
171C4×D4—1221no—
172C4×D4—1221no—
173C4×D4C2×D6111yescharacteristic
174#117—1221no—
175C2×C42—611no—
176#107—612no—
177#106—612no—
178C4⋊C8—612no—
179C4⋊C8—611no—
180C4⋊C8C2×D6111yescharacteristic
181#103—612no—
182#102—612no—
183#102—612no—
184#102C2×D6112yes—
185#41—2444no—
186C2×Q8—611no—
187C2×Q8—1221no—
188C2×D4—21no—
189C2×D4—21no—
190C2×D4—1221no—
191C2×D4—1222no—
192C2×D4C22×D6111yescharacteristic
193C2×D4C22×D6112yes—
194C22×C4—21no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—1222no—
199SD16—2442no—
200D8—42no—
201C2×C8—612no—
202C2×C8—2442no—
203C2×C8C22×D6112yes—
204C4⋊C4—611no—
205C4⋊C4—612no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C4⋊C4C22×D6111yescharacteristic
212C22⋊C4—21no—
213C22⋊C4—1221no—
214C22⋊C4—1221no—
215C22⋊C4—1221no—
216C22⋊C4—1222no—
217C22⋊C4—1222no—
218C22⋊C4—1221no—
219C42—611no—
220C42—611no—
221C42—611no—
222C42—1221no—
223C42C22×D6111yescharacteristic
224C23—21no—
225C23—22no—
226C23—611no—
227Q8—1221no—
228Q8—1221no—
229Q8—2442no—
230D4—21no—
231D4—22no—
232D4—21no—
233D4—22no—
234D4—42no—
235D4—42no—
236D4—2442no—
237D4—2444no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—1222no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1222no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1222no—
250C2×C4—2444no—
251C2×C4D4×D6111yescharacteristic
252C2×C4D4×D6111yescharacteristic
253C2×C4C23×D6111yescharacteristic
254C8—22no—
255C8—1222no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—42no—
262C22—612no—
263C22—1221no—
264C22—1221no—
265C22C2×D4×D6111yescharacteristic
266C4—21no—
267C4—41no—
268C4—1221no—
269C4—1221no—
270C4—1221no—
271C4—2442no—
272C4—2441no—
273C4—2441no—
274C4#1451979612yes—
275C4#1451982211yescharacteristic
276C4#1451982411yescharacteristic
277C2—81no—
278C2—82no—
279C2—1222no—
280C2#1684034111yescharacteristic
281C2C2×#1451979611yescharacteristic
282C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3247
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16840310C2semidirect
2. #16840294C2semidirect
3. #16840060C2semidirect
4. #16840058C2semidirect
5. #16840052C2semidirect
6. #16839995C2semidirect
7. #16839990C2semidirect
8. #16839975C2semidirect
9. #16839959C2semidirect
10. C4⋊C8×D61C2semidirect
11. C61×#459C2semidirect
151. #459D61semidirect
153. C61#3247semidirect