Finite Group Databasebeta

← #21457148

Subgroups — #21457148

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#16840299C211yesmaximal, characteristic, complemented
3#16840065C212yesmaximal, complemented
4#16840049C211yesmaximal, characteristic, complemented
5#16839999C212yesmaximal, complemented
6#16839994C212yesmaximal, complemented
7#16839980C212yesmaximal, complemented
8#16839962C211yesmaximal, characteristic, complemented
9#16839958C211yesmaximal, characteristic, complemented
10C4⋊C8×D61C211yesmaximal, characteristic, complemented
11C61×#477C211yesmaximal, characteristic, complemented
12C2×#11758226—21no—
13C2×#11758201C2212yes—
14C2×D488C2212yes—
15C2×C8×D61C2212yes—
16#14519774C2211yescharacteristic
17#14519772—21no—
18#14519768C2211yescharacteristic
19#14519766—21no—
20#14519766C2211yescharacteristic
21#14519762—21no—
22#14519753C2211yescharacteristic
23#14519752—21no—
24#14519752C2212yes—
25#14519752C2211yescharacteristic
26C4×D244—21no—
27C4×D244C2211yescharacteristic
28#14519739—21no—
29#14519739C2212yes—
30#14519734—21no—
31C42×D61C2211yescharacteristic
32#14519708C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519699C2212yes—
36#14519697C2212yes—
37#14519697C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×Q8×C61C2211yescharacteristic
40#107×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45#11758226—44no—
46C2×D244—22no—
47C2×D244—21no—
48C2×D244—21no—
49C2×D244—21no—
50C2×D244C2311yescharacteristic
51C2×D244C2312yes—
52C2×C4×D61—21no—
53C2×C4×D61—22no—
54C2×C4×D61D411yescharacteristic
55C2×C4×D61D411yescharacteristic
56C2×C4×D61C2311yescharacteristic
57C2×C8×C61C2312yes—
58C4⋊C4×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2312yes—
61C4⋊C4×C61C2311yescharacteristic
62C42×C61—21no—
63C42×C61C2311yescharacteristic
64#11758201—42no—
65#11758198—21no—
66#11758198—21no—
67#11758198—21no—
68#11758198—21no—
69#11758198—22no—
70#11758198—22no—
71#11758198—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61C2311yescharacteristic
74#11758196—21no—
75#11758196—21no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80D488—42no—
81C8×D61—42no—
82C22×D61—21no—
83C22×D61—22no—
84C22×D61C2×D411yescharacteristic
85Q8×C61—21no—
86Q8×C61—21no—
87Q8×C61—42no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2411yescharacteristic
94C2×Dic61—21no—
95C2×Dic61C2×D411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98D244—21no—
99D244—22no—
100D244—21no—
101D244—22no—
102D244—42no—
103D244—42no—
104D244—44no—
105D244—42no—
106C4×D61—22no—
107C4×D61—22no—
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—44no—
111C4×D61—42no—
112C8×C61—22no—
113#92418—22no—
114C22×C61C22×D411yescharacteristic
115C2×D61—21no—
116C2×D61—21no—
117C2×D61—41no—
118C2×D61—42no—
119C2×D61—41no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—41no—
123C2×D61AGL(1,ℤ/8)12yes—
124C4×C61—21no—
125C4×C61—41no—
126C4×C61—42no—
127C4×C61—41no—
128C4×C61#13512yes—
129C4×C61H(5,𝔽2)11yescharacteristic
130C4×C612−1+411yescharacteristic
131Dic61—21no—
132Dic61—21no—
133Dic61—21no—
134Dic61—41no—
135#3247—611nomaximal, Sylow
136C2×C61#53711yescharacteristic
137C2×C61C2×#13511yescharacteristic
138C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
139D61—22no—
140D61—81no—
141D61—82no—
142#532—611no—
143#529—611no—
144#478—612no—
145#477D6111yescharacteristic, complemented
146#476—611no—
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×Q8C2×D6111yescharacteristic
170C4×D4—612no—
171C4×D4—611no—
172C4×D4—1221no—
173C4×D4—1221no—
174#117—1221no—
175C2×C42—611no—
176#107C2×D6112yes—
177#106—612no—
178C4⋊C8—612no—
179C4⋊C8—611no—
180C4⋊C8C2×D6111yescharacteristic
181#103C2×D6112yes—
182#102—612no—
183#102—612no—
184#102—612no—
185#41—2444no—
186C2×Q8—21no—
187C2×Q8C22×D6111yescharacteristic
188C2×D4—611no—
189C2×D4—612no—
190C2×D4—1221no—
191C2×D4—1222no—
192C2×D4—1221no—
193C2×D4—1221no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—1222no—
198C22×C4—1221no—
199SD16—2442no—
200D8—2442no—
201C2×C8—612no—
202C2×C8—2442no—
203C2×C8C22×D6112yes—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—611no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4C22×D6111yescharacteristic
211C4⋊C4C22×D6112yes—
212C22⋊C4—1221no—
213C22⋊C4—1221no—
214C22⋊C4—1222no—
215C22⋊C4—1222no—
216C22⋊C4—1221no—
217C22⋊C4—1221no—
218C22⋊C4—1221no—
219C42—21no—
220C42—611no—
221C42—611no—
222C42—611no—
223C42C22×D6111yescharacteristic
224C23—611no—
225C23—1221no—
226C23—1222no—
227Q8—21no—
228Q8—21no—
229Q8—42no—
230D4—1221no—
231D4—1222no—
232D4—1221no—
233D4—1222no—
234D4—2442no—
235D4—2442no—
236D4—2444no—
237D4—2442no—
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—1221no—
247C2×C4—1222no—
248C2×C4—1221no—
249C2×C4—2444no—
250C2×C4—2442no—
251C2×C4D4×D6111yescharacteristic
252C2×C4D4×D6111yescharacteristic
253C2×C4C23×D6111yescharacteristic
254C8—22no—
255C8—1222no—
256C22—612no—
257C22—1221no—
258C22—1221no—
259C22—2441no—
260C22—2442no—
261C22—2442no—
262C22—2441no—
263C22—2441no—
264C22—2442no—
265C22C2×D4×D6111yescharacteristic
266C4—21no—
267C4—42no—
268C4—41no—
269C4—41no—
270C4—1221no—
271C4—1221no—
272C4—1221no—
273C4—2441no—
274C4#1451980012yes—
275C4#1451982311yescharacteristic
276C4#1451982511yescharacteristic
277C2—1222no—
278C2—4881no—
279C2—4882no—
280C2#1684034211yescharacteristic
281C2C2×#1451980011yescharacteristic
282C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#477C2
socleC22×C61C22×D4
hypercenter#477D61
hypocenterC61#3247
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #16840313C2semidirect
2. #16840299C2semidirect
3. #16840065C2semidirect
4. #16840049C2semidirect
5. #16839999C2semidirect
6. #16839994C2semidirect
7. #16839980C2semidirect
8. #16839962C2semidirect
9. #16839958C2semidirect
10. C4⋊C8×D61C2semidirect
11. C61×#477C2semidirect
145. #477D61semidirect
153. C61#3247semidirect