Finite Group Databasebeta

← #21456794

Subgroups — #21456794

Order 7808.

400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840143C212yesmaximal, complemented
4#16840118C212yesmaximal, complemented
5#16839969C211yesmaximal, characteristic, complemented
6#16839963C211yesmaximal, characteristic, complemented
7#16839957C211yesmaximal, characteristic, complemented
8#16839927C212yesmaximal, complemented
9#16839906C212yesmaximal, complemented
10#16839814C211yesmaximal, characteristic, complemented
11C61×#461C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yes—
13C2×#11758202C2212yes—
14C2×#11758190C2212yes—
15C2×#11758199C2212yes—
16#14519774C2211yescharacteristic
17#14519770—21no—
18#14519768C2211yescharacteristic
19#14519766C2212yes—
20#14519764C2211yescharacteristic
21#14519759—21no—
22#14519757C2211yescharacteristic
23#14519752—21no—
24#14519752—21no—
25#14519748C2211yescharacteristic
26C4×Dic122C2211yescharacteristic
27#14519739—21no—
28#14519739—21no—
29C4×C22⋊D61—21no—
30#14519736—21no—
31C42×D61C2211yescharacteristic
32C4⋊#92418C2211yescharacteristic
33#14519701C2212yes—
34#14519699C2212yes—
35#14519697C2212yes—
36#14519689C2212yes—
37C8×Dic61C2212yes—
38C2×SD16×C61C2212yes—
39C4⋊Q8×C61C2211yescharacteristic
40C4×D4×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61C2312yes—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—21no—
47#11758226—42no—
48#11758226—42no—
49C2×D244—22no—
50C2×D244—21no—
51C2×D244—21no—
52C2×D244C2312yes—
53C2×C4×D61—22no—
54C2×C4×D61D411yescharacteristic
55C2×C4×D61D411yescharacteristic
56C2×C4×D61C2311yescharacteristic
57C2×Dic122C2311yescharacteristic
58SD16×C61—42no—
59C2×C8×C61C2312yes—
60C4⋊C4×C61—21no—
61C4⋊C4×C61—21no—
62C4⋊C4×C61C2311yescharacteristic
63C22⋊C4×C61—21no—
64C42×C61C2311yescharacteristic
65C22⋊Dic61—21no—
66C22⋊Dic61—21no—
67C22⋊Dic61—21no—
68#11758202—42no—
69#11758199—42no—
70#11758198—21no—
71#11758198—22no—
72#11758198—22no—
73C4⋊Dic61—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61C2311yescharacteristic
76#11758196—21no—
77#11758196—21no—
78C4×Dic61—21no—
79C4×Dic61D411yescharacteristic
80C4×Dic61D411yescharacteristic
81C4×Dic61C2311yescharacteristic
82C2×#92418C2312yes—
83#11758190—42no—
84C23×C61—21no—
85C22×D61—22no—
86C22×D61C2×D411yescharacteristic
87Q8×C61—22no—
88Q8×C61—22no—
89D4×C61—21no—
90D4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—42no—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2411yescharacteristic
97C22⋊D61—42no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C2×Dic61C2×D411yescharacteristic
103D244—22no—
104D244—22no—
105D244—42no—
106D244—44no—
107D244—42no—
108C4×D61—22no—
109C4×D61—21no—
110C4×D61—21no—
111C4×D61—41no—
112C4×D61—44no—
113Dic122—21no—
114Dic122—21no—
115C8×C61—22no—
116#92418—22no—
117C22×C61—41no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61C22×D411yescharacteristic
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—21no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—42no—
127C4×C61—21no—
128C4×C61—42no—
129C4×C61—41no—
130C4×C61#13512yes—
131C4×C61H(5,𝔽2)11yescharacteristic
132C4×C61H(5,𝔽2)11yescharacteristic
133Dic61—21no—
134Dic61—21no—
135Dic61—21no—
136Dic61—41no—
137Dic61—41no—
138#3212—611nomaximal, Sylow
139C2×C61—81no—
140C2×C61#53511yescharacteristic
141C2×C61C2×#13511yescharacteristic
142C2×C61#57511yescharacteristic
143D61—41no—
144D61—82no—
145#532—611no—
146#529—611no—
147#495—612no—
148#488—612no—
149#462—611no—
150#461D6111yescharacteristic, complemented
151#460—611no—
152#459—611no—
153#452—612no—
154#449—612no—
155#431—611no—
156C61#321211yescharacteristic, complemented, Sylow
157C2×#41—612no—
158C2×Q16—612no—
159C2×SD16—612no—
160C2×SD16C2×D6112yes—
161C2×D8—612no—
162C4⋊Q8C2×D6111yescharacteristic
163#127—611no—
164#126—1221no—
165#125—611no—
166#124—612no—
167#124—611no—
168#123—1221no—
169C22⋊Q8—611no—
170#121—611no—
171#121—1221no—
172#121—1221no—
173C4×Q8—611no—
174C4×D4—1221no—
175C4×D4—1221no—
176C4×D4—1221no—
177C4×D4C2×D6111yescharacteristic
178#117—1221no—
179C2×C42—611no—
180C4⋊C8—611no—
181C4⋊C8C2×D6111yescharacteristic
182#103—612no—
183#103C2×D6112yes—
184#102—612no—
185#102—612no—
186C22⋊C8—612no—
187C4×C8—612no—
188#41—2442no—
189#41—2442no—
190C2×Q8—611no—
191C2×Q8C22×D6112yes—
192C2×D4—612no—
193C2×D4—1222no—
194C2×D4—1221no—
195C2×D4—1221no—
196C2×D4—1221no—
197C2×D4C22×D6111yescharacteristic
198C22×C4—21no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—1222no—
203Q16—2442no—
204SD16—42no—
205SD16—2442no—
206D8—2442no—
207C2×C8—612no—
208C2×C8C22×D6112yes—
209C4⋊C4—21no—
210C4⋊C4—21no—
211C4⋊C4—611no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4—1221no—
215C4⋊C4—1221no—
216C4⋊C4C22×D6111yescharacteristic
217C22⋊C4—21no—
218C22⋊C4—1222no—
219C22⋊C4—1222no—
220C22⋊C4—1221no—
221C22⋊C4—1221no—
222C22⋊C4—1221no—
223C22⋊C4—1221no—
224C42—611no—
225C42—611no—
226C42—611no—
227C42—1221no—
228C42C22×D6111yescharacteristic
229C23—21no—
230C23—611no—
231C23—1222no—
232Q8—22no—
233Q8—22no—
234Q8—1221no—
235Q8—1221no—
236D4—21no—
237D4—21no—
238D4—1222no—
239D4—1222no—
240D4—2442no—
241D4—2444no—
242D4—2442no—
243D4—2442no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—611no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—1222no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—2441no—
256C2×C4—2444no—
257C2×C4D4×D6111yescharacteristic
258C2×C4D4×D6111yescharacteristic
259C2×C4C23×D6111yescharacteristic
260C8—22no—
261C8—1222no—
262C22—41no—
263C22—41no—
264C22—41no—
265C22—1221no—
266C22—1221no—
267C22—1221no—
268C22—2442no—
269C22—2442no—
270C22—2442no—
271C22C2×D4×D6111yescharacteristic
272C4—21no—
273C4—41no—
274C4—42no—
275C4—1221no—
276C4—1221no—
277C4—1221no—
278C4—2441no—
279C4—2441no—
280C4#1451979812yes—
281C4#1451982211yescharacteristic
282C4#1451982311yescharacteristic
283C2—81no—
284C2—4882no—
285C2—2441no—
286C2#1684032811yescharacteristic
287C2C2×#1451979811yescharacteristic
288C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3212
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #16840313C2semidirect
2. #16840294C2semidirect
3. #16840143C2semidirect
4. #16840118C2semidirect
5. #16839969C2semidirect
6. #16839963C2semidirect
7. #16839957C2semidirect
8. #16839927C2semidirect
9. #16839906C2semidirect
10. #16839814C2semidirect
11. C61×#461C2semidirect
150. #461D61semidirect
156. C61#3212semidirect