Finite Group Databasebeta

← #21457147

Subgroups — #21457147

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#16840313C211yesmaximal, characteristic, complemented
2#16840294C211yesmaximal, characteristic, complemented
3#16840061C212yesmaximal, complemented
4#16840054C211yesmaximal, characteristic, complemented
5#16839997C212yesmaximal, complemented
6#16839992C212yesmaximal, complemented
7#16839976C212yesmaximal, complemented
8#16839963C211yesmaximal, characteristic, complemented
9#16839957C211yesmaximal, characteristic, complemented
10C4⋊C8×D61C211yesmaximal, characteristic, complemented
11C61×#476C211yesmaximal, characteristic, complemented
12C2×#11758226—21no—
13C2×#11758190C2212yes—
14C2×#11758199C2212yes—
15C2×C8×D61C2212yes—
16#14519774C2211yescharacteristic
17#14519770—21no—
18#14519768C2211yescharacteristic
19#14519766—21no—
20#14519764C2211yescharacteristic
21#14519759—21no—
22#14519757C2211yescharacteristic
23#14519752—21no—
24#14519752C2212yes—
25#14519748C2211yescharacteristic
26C4×Dic122C2211yescharacteristic
27#14519739—21no—
28#14519739C2212yes—
29C4×C22⋊D61—21no—
30#14519736—21no—
31C42×D61C2211yescharacteristic
32#14519710C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519700C2212yes—
36#14519699C2212yes—
37#14519697C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×D4×C61C2211yescharacteristic
40#106×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#102×C61C2212yes—
43C2×Q8×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—21no—
47#11758226—44no—
48C2×D244—22no—
49C2×D244—21no—
50C2×D244—21no—
51C2×D244C2312yes—
52C2×C4×D61—22no—
53C2×C4×D61D411yescharacteristic
54C2×C4×D61D411yescharacteristic
55C2×C4×D61C2311yescharacteristic
56C2×Dic122C2311yescharacteristic
57C2×C8×C61C2312yes—
58C4⋊C4×C61—21no—
59C4⋊C4×C61C2312yes—
60C4⋊C4×C61C2311yescharacteristic
61C22⋊C4×C61—21no—
62C42×C61C2311yescharacteristic
63C22⋊Dic61—21no—
64C22⋊Dic61—21no—
65C22⋊Dic61—21no—
66#11758199—42no—
67#11758198—21no—
68#11758198—22no—
69#11758198—22no—
70C4⋊Dic61—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61C2311yescharacteristic
73#11758196—21no—
74#11758196—21no—
75C4×Dic61—21no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80#11758190—42no—
81C8×D61—42no—
82C23×C61—21no—
83C22×D61—22no—
84C22×D61C2×D411yescharacteristic
85Q8×C61—42no—
86D4×C61—21no—
87D4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—42no—
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2411yescharacteristic
94C22⋊D61—42no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100D244—22no—
101D244—22no—
102D244—42no—
103D244—44no—
104D244—42no—
105C4×D61—22no—
106C4×D61—22no—
107C4×D61—21no—
108C4×D61—21no—
109C4×D61—44no—
110Dic122—21no—
111Dic122—21no—
112C8×C61—22no—
113#92418—22no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61C22×D411yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61AGL(1,ℤ/8)12yes—
124C4×C61—21no—
125C4×C61—41no—
126C4×C61—42no—
127C4×C61#13512yes—
128C4×C61H(5,𝔽2)11yescharacteristic
129C4×C612−1+411yescharacteristic
130Dic61—21no—
131Dic61—21no—
132Dic61—21no—
133Dic61—41no—
134Dic61—41no—
135#3247—611nomaximal, Sylow
136C2×C61—81no—
137C2×C61#53711yescharacteristic
138C2×C61C2×#13511yescharacteristic
139C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
140D61—22no—
141D61—82no—
142#532—611no—
143#529—611no—
144#478—612no—
145#477—611no—
146#476D6111yescharacteristic, complemented
147#466—612no—
148#465—612no—
149#463—612no—
150#460—611no—
151#459—611no—
152C2×C4⋊C8—611no—
153C61#324711yescharacteristic, complemented, Sylow
154C2×#41—1221no—
155C2×SD16—612no—
156C2×D8—612no—
157C22×C8—612no—
158C4⋊Q8C2×D6111yescharacteristic
159#127—611no—
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#106C2×D6112yes—
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—21no—
187C2×Q8—611no—
188C2×D4—612no—
189C2×D4—1222no—
190C2×D4—1221no—
191C2×D4—1221no—
192C2×D4—1221no—
193C2×D4C22×D6111yescharacteristic
194C22×C4—21no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—1222no—
199SD16—2442no—
200D8—2442no—
201C2×C8—612no—
202C2×C8—2442no—
203C2×C8C22×D6112yes—
204C4⋊C4—21no—
205C4⋊C4—611no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4C22×D6111yescharacteristic
211C4⋊C4C22×D6112yes—
212C22⋊C4—21no—
213C22⋊C4—1222no—
214C22⋊C4—1222no—
215C22⋊C4—1221no—
216C22⋊C4—1221no—
217C22⋊C4—1221no—
218C22⋊C4—1221no—
219C42—611no—
220C42—611no—
221C42—611no—
222C42—1221no—
223C42C22×D6111yescharacteristic
224C23—21no—
225C23—611no—
226C23—1222no—
227Q8—42no—
228Q8—1221no—
229Q8—1221no—
230D4—21no—
231D4—21no—
232D4—1222no—
233D4—1222no—
234D4—2442no—
235D4—2444no—
236D4—2442no—
237D4—2442no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—42no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—1222no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1222no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—2444no—
251C2×C4D4×D6111yescharacteristic
252C2×C4D4×D6111yescharacteristic
253C2×C4C23×D6111yescharacteristic
254C8—22no—
255C8—1222no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—612no—
260C22—1221no—
261C22—1221no—
262C22—2442no—
263C22—2442no—
264C22—2442no—
265C22C2×D4×D6111yescharacteristic
266C4—21no—
267C4—41no—
268C4—42no—
269C4—1221no—
270C4—1221no—
271C4—1221no—
272C4—2441no—
273C4—2441no—
274C4#1451979812yes—
275C4#1451982311yescharacteristic
276C4#1451982511yescharacteristic
277C2—81no—
278C2—1222no—
279C2—4882no—
280C2#1684034211yescharacteristic
281C2C2×#1451979811yescharacteristic
282C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#476C2
socleC22×C61C22×D4
hypercenter#476D61
hypocenterC61#3247
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16840313C2semidirect
2. #16840294C2semidirect
3. #16840061C2semidirect
4. #16840054C2semidirect
5. #16839997C2semidirect
6. #16839992C2semidirect
7. #16839976C2semidirect
8. #16839963C2semidirect
9. #16839957C2semidirect
10. C4⋊C8×D61C2semidirect
11. C61×#476C2semidirect
146. #476D61semidirect
153. C61#3247semidirect