Finite Group Databasebeta

← #21456828

Subgroups — #21456828

Order 7808.

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

normal subgroups only

This group has 390 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#16840316C211yesmaximal, characteristic, complemented
2#16840310C211yesmaximal, characteristic
3#16840153C212yesmaximal, complemented
4#16840120C212yesmaximal, complemented
5#16839973C211yesmaximal, characteristic, complemented
6#16839972C211yesmaximal, characteristic, complemented
7#16839959C211yesmaximal, characteristic, complemented
8#16839925C212yesmaximal, complemented
9#16839921C212yesmaximal, complemented
10#16839818C211yesmaximal, characteristic, complemented
11C61×#460C211yesmaximal, characteristic, complemented
12C2×#11758224C2212yes—
13C2×Dic244C2212yes—
14C2×#11758202C2212yes—
15C2×#11758200C2212yes—
16#14519777C2211yescharacteristic
17#14519776C2211yescharacteristic
18#14519775C2211yescharacteristic
19#14519767—21no—
20#14519764C2212yes—
21#14519757C2211yescharacteristic
22#14519755—21no—
23#14519753C2211yescharacteristic
24#14519748—21no—
25#14519748—21no—
26C4×Dic122—21no—
27C4×Dic122C2211yescharacteristic
28D4×Dic61—21no—
29D4×Dic61—21no—
30#14519734—21no—
31C42×D61C2211yescharacteristic
32C4⋊#92418C2211yescharacteristic
33#14519702C2212yes—
34#14519700C2212yes—
35#14519698C2212yes—
36#14519689C2212yes—
37#14519687C2212yes—
38C2×SD16×C61C2212yes—
39#127×C61C2211yescharacteristic
40C4×Q8×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42#102×C61C2212yes—
43C2×Q8×C61C2311yescharacteristic
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C2×D4×C61C2312yes—
47C2×C22⋊D61—22no—
48C22×Dic61—22no—
49#11758224—42no—
50#11758224—42no—
51C2×C4×D61D411yescharacteristic
52C2×C4×D61D411yescharacteristic
53C2×C4×D61C2311yescharacteristic
54C2×Dic122—21no—
55C2×Dic122C2312yes—
56C2×Dic122C2311yescharacteristic
57SD16×C61—42no—
58C2×C8×C61C2312yes—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2311yescharacteristic
61C42×C61—21no—
62C42×C61C2311yescharacteristic
63C22⋊Dic61—22no—
64C22⋊Dic61—22no—
65#11758202—42no—
66#11758200—42no—
67#11758198—21no—
68#11758198—21no—
69C4⋊Dic61—21no—
70C4⋊Dic61—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61C2311yescharacteristic
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76#11758196—21no—
77#11758196—21no—
78C4×Dic61—21no—
79C4×Dic61D411yescharacteristic
80C4×Dic61D411yescharacteristic
81C4×Dic61C2311yescharacteristic
82C2×#92418C2312yes—
83Dic244—42no—
84C23×C61—22no—
85C22×D61C2×D411yescharacteristic
86Q8×C61—21no—
87Q8×C61—21no—
88D4×C61—22no—
89D4×C61—22no—
90D4×C61—42no—
91D4×C61—42no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2411yescharacteristic
97C22⋊D61—44no—
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—21no—
107C4×D61—21no—
108C4×D61—41no—
109Dic122—21no—
110Dic122—22no—
111Dic122—21no—
112Dic122—22no—
113Dic122—42no—
114C8×C61—22no—
115#92418—22no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61C22×D411yescharacteristic
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—21no—
123C4×C61—21no—
124C4×C61—41no—
125C4×C61—41no—
126C4×C61#13712yes—
127C4×C61H(5,𝔽2)11yescharacteristic
128C4×C61H(5,𝔽2)11yescharacteristic
129Dic61—21no—
130Dic61—21no—
131Dic61—21no—
132Dic61—41no—
133Dic61—42no—
134Dic61—41no—
135#3216—611nomaximal, Sylow
136C2×C61—82no—
137C2×C61#53511yescharacteristic
138C2×C61C2×#13711yescharacteristic
139C2×C61#57511yescharacteristic
140D61—41no—
141#533—611no—
142#532—611no—
143#497—612no—
144#489—612no—
145#462—611no—
146#462—611no—
147#460—611no—
148#460D6111yescharacteristic, complemented
149#452—612no—
150#452—612no—
151#432—611no—
152C61#321611yescharacteristic, complemented, Sylow
153C2×#41—612no—
154C2×Q16—612no—
155C2×Q16—612no—
156C2×SD16—612no—
157C2×SD16C2×D6112yes—
158C4⋊Q8—611no—
159C4⋊Q8—611no—
160C4⋊Q8—611no—
161#127C2×D6111yescharacteristic
162#125—1221no—
163#124—612no—
164C22⋊Q8—611no—
165C22⋊Q8—611no—
166C22⋊Q8—1221no—
167#121—1221no—
168#121—1221no—
169C4×Q8—611no—
170C4×Q8—1221no—
171C4×Q8C2×D6111yescharacteristic
172C4×D4—1221no—
173C4×D4—1221no—
174#117—1221no—
175C2×C42—611no—
176C4⋊C8—611no—
177C4⋊C8C2×D6111yescharacteristic
178#103—612no—
179#103—612no—
180#102—612no—
181#102C2×D6112yes—
182C22⋊C8—612no—
183#97—612no—
184#41—2442no—
185#41—2442no—
186C2×Q8—612no—
187C2×Q8—611no—
188C2×Q8—1221no—
189C2×Q8C22×D6111yescharacteristic
190C2×D4—21no—
191C2×D4—21no—
192C2×D4—1222no—
193C2×D4C22×D6112yes—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—1222no—
198Q16—2442no—
199Q16—2442no—
200SD16—42no—
201SD16—2442no—
202C2×C8—612no—
203C2×C8C22×D6112yes—
204C4⋊C4—21no—
205C4⋊C4—611no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C4⋊C4—1221no—
214C4⋊C4C22×D6111yescharacteristic
215C22⋊C4—1221no—
216C22⋊C4—1221no—
217C22⋊C4—1222no—
218C22⋊C4—1222no—
219C42—21no—
220C42—611no—
221C42—611no—
222C42—611no—
223C42—1221no—
224C42C22×D6111yescharacteristic
225C23—22no—
226C23—611no—
227Q8—21no—
228Q8—21no—
229Q8—1221no—
230Q8—1222no—
231Q8—1221no—
232Q8—1222no—
233Q8—2442no—
234D4—22no—
235D4—22no—
236D4—42no—
237D4—42no—
238D4—2444no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1222no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1222no—
250C2×C4—2441no—
251C2×C4—2444no—
252C2×C4D4×D6111yescharacteristic
253C2×C4D4×D6111yescharacteristic
254C2×C4C23×D6111yescharacteristic
255C8—22no—
256C8—1222no—
257C22—42no—
258C22—42no—
259C22—42no—
260C22—1221no—
261C22—1221no—
262C22—1221no—
263C22C2×D4×D6111yescharacteristic
264C4—21no—
265C4—41no—
266C4—41no—
267C4—1221no—
268C4—1221no—
269C4—1221no—
270C4—2441no—
271C4—2442no—
272C4—2441no—
273C4#1451980612yes—
274C4#1451982211yescharacteristic
275C4#1451982311yescharacteristic
276C2—82no—
277C2—2441no—
278C2#1684032811yescharacteristic
279C2C2×#1451980611yescharacteristic
280C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#460C2
socleC22×C61C22×D4
hypercenter#460D61
hypocenterC61#3216
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #16840316C2semidirect
3. #16840153C2semidirect
4. #16840120C2semidirect
5. #16839973C2semidirect
6. #16839972C2semidirect
7. #16839959C2semidirect
8. #16839925C2semidirect
9. #16839921C2semidirect
10. #16839818C2semidirect
11. C61×#460C2semidirect
148. #460D61semidirect
152. C61#3216semidirect