Finite Group Databasebeta

← #21456858

Subgroups — #21456858

Order 7808.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840312C211yesmaximal, characteristic, complemented
2#16840296C211yesmaximal, characteristic, complemented
3#16840156C211yesmaximal, characteristic, complemented
4#16840151C211yesmaximal, characteristic, complemented
5#16840131C211yesmaximal, characteristic, complemented
6#16840127C211yesmaximal, characteristic, complemented
7#16839985C212yesmaximal, complemented
8#16839978C212yesmaximal, complemented
9#16839926C212yesmaximal, complemented
10#16839909C212yesmaximal, complemented
11C61×#432C211yesmaximal, characteristic, complemented
12C2×#11758222C2212yes—
13C2×Dic244C2212yes—
14C2×#11758190C2212yes—
15C2×#11758190C2212yes—
16C2×D488C2212yes—
17#14519777C2211yescharacteristic
18#14519774C2211yescharacteristic
19#14519771—21no—
20#14519769C2211yescharacteristic
21#14519765C2212yes—
22#14519765C2211yescharacteristic
23#14519760—21no—
24#14519756C2211yescharacteristic
25#14519751—21no—
26#14519751—21no—
27#14519751C2211yescharacteristic
28C4×Dic122C2211yescharacteristic
29C4×D244—21no—
30C4×D244—21no—
31C4×D244C2211yescharacteristic
32C4×C22⋊D61—21no—
33#14519734—21no—
34#14519702C2212yes—
35#14519702C2212yes—
36#14519699C2212yes—
37#14519699C2212yes—
38C2×C42×C61C2211yescharacteristic
39C4⋊C8×C61C2212yes—
40C22⋊C8×C61C2212yes—
41#97×C61C2211yescharacteristic
42#97×C61C2211yescharacteristic
43C22×C4×C61D411yescharacteristic
44C22×C4×C61D411yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—22no—
47C2×C22⋊D61—21no—
48#11758222—42no—
49#11758222—42no—
50C2×D244—21no—
51C2×D244—21no—
52C2×D244C2312yes—
53C2×D244C2311yescharacteristic
54C2×C4×D61—22no—
55C2×C4×D61—21no—
56C2×Dic122C2312yes—
57C2×Dic122C2311yescharacteristic
58C2×C8×C61C2312yes—
59C2×C8×C61C2312yes—
60C42×C61D411yescharacteristic
61C42×C61D411yescharacteristic
62C42×C61C2311yescharacteristic
63C42×C61C2311yescharacteristic
64C22⋊Dic61—21no—
65#11758198—21no—
66#11758198—21no—
67#11758198—21no—
68#11758198—22no—
69#11758198—22no—
70#11758198—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61C2311yescharacteristic
74C4⋊Dic61C2311yescharacteristic
75#11758196—21no—
76#11758196—21no—
77#11758196—21no—
78#11758196—21no—
79C4×Dic61—21no—
80Dic244—42no—
81D488—42no—
82#11758190—42no—
83#11758190—42no—
84C23×C61C2×D411yescharacteristic
85C22×D61—21no—
86C22×D61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
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—21no—
101C2×Dic61—22no—
102D244—22no—
103D244—22no—
104D244—22no—
105D244—42no—
106D244—42no—
107C4×D61—42no—
108C4×D61—44no—
109Dic122—22no—
110Dic122—22no—
111Dic122—22no—
112C8×C61—22no—
113C8×C61—22no—
114C22×C61—21no—
115C22×C61—21no—
116C22×C61—21no—
117C22×C61C22×D411yescharacteristic
118C2×D61—42no—
119C2×D61—41no—
120C2×D61—41no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—41no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61H(5,𝔽2)12yes—
130Dic61—42no—
131Dic61—41no—
132Dic61—41no—
133Dic61—41no—
134#3219—611nomaximal, Sylow
135C2×C61—41no—
136C2×C61#53511yescharacteristic
137C2×C61#57511yescharacteristic
138C2×C61#57511yescharacteristic
139D61—82no—
140D61—81no—
141#532—611no—
142#529—611no—
143#497—611no—
144#496—611no—
145#491—611no—
146#490—611no—
147#464—612no—
148#463—612no—
149#452—612no—
150#449—612no—
151#432D6111yescharacteristic, complemented
152C61#321911yescharacteristic, complemented, Sylow
153C2×#41—612no—
154C2×Q16—612no—
155C2×SD16—612no—
156C2×SD16—612no—
157C2×D8—612no—
158C4⋊Q8—611no—
159#127—611no—
160#126—1221no—
161#125—611no—
162#124—611no—
163#124—612no—
164#123—1221no—
165C22⋊Q8—611no—
166#121—611no—
167#121—1221no—
168#121—1221no—
169C4×Q8—611no—
170C4×D4—611no—
171C4×D4—1221no—
172C4×D4—1221no—
173C4×D4—1221no—
174#117—1221no—
175C2×C42C2×D6111yescharacteristic
176C4⋊C8C2×D6112yes—
177#103—612no—
178#103—612no—
179#102—612no—
180#102—612no—
181C22⋊C8C2×D6112yes—
182#97C2×D6111yescharacteristic
183#97C2×D6111yescharacteristic
184#41—2442no—
185#41—2442no—
186C2×Q8—612no—
187C2×Q8—611no—
188C2×D4—612no—
189C2×D4—611no—
190C2×D4—1221no—
191C2×D4—1222no—
192C2×D4—1221no—
193C2×D4—1221no—
194C22×C4—1221no—
195C22×C4—1222no—
196C22×C4D24411yescharacteristic
197C22×C4D24411yescharacteristic
198C22×C4C22×D6111yescharacteristic
199Q16—2442no—
200SD16—2442no—
201SD16—2442no—
202D8—2442no—
203C2×C8C22×D6112yes—
204C2×C8C22×D6112yes—
205C4⋊C4—611no—
206C4⋊C4—611no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4—1221no—
213C22⋊C4—1221no—
214C22⋊C4—1221no—
215C22⋊C4—1221no—
216C22⋊C4—1221no—
217C22⋊C4—1222no—
218C22⋊C4—1222no—
219C22⋊C4—1221no—
220C42—1221no—
221C42D24411yescharacteristic
222C42D24411yescharacteristic
223C42C22×D6111yescharacteristic
224C42C22×D6111yescharacteristic
225C23—1221no—
226C23—1222no—
227C23C2×D24411yescharacteristic
228Q8—1222no—
229Q8—1222no—
230Q8—1222no—
231D4—1222no—
232D4—1222no—
233D4—1222no—
234D4—2442no—
235D4—2442no—
236D4—2442no—
237D4—2444no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1222no—
245C2×C4—2442no—
246C2×C4—2444no—
247C2×C4C2×D24411yescharacteristic
248C2×C4C2×D24411yescharacteristic
249C2×C4C2×D24411yescharacteristic
250C2×C4C2×D24411yescharacteristic
251C2×C4C2×D24411yescharacteristic
252C2×C4C23×D6111yescharacteristic
253C8—22no—
254C8—22no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—2441no—
259C22—2442no—
260C22—2442no—
261C22—2441no—
262C22—2442no—
263C22—2441no—
264C22C22×D24411yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—2441no—
271C4—2441no—
272C4—2442no—
273C4—2441no—
274C4#1451982312yes—
275C2—41no—
276C2—4881no—
277C2—4882no—
278C2#1684033111yescharacteristic
279C2#1684056211yescharacteristic
280C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3219
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #16840312C2semidirect
2. #16840296C2semidirect
3. #16840156C2semidirect
4. #16840151C2semidirect
5. #16840131C2semidirect
6. #16840127C2semidirect
7. #16839985C2semidirect
8. #16839978C2semidirect
9. #16839926C2semidirect
10. #16839909C2semidirect
11. C61×#432C2semidirect
151. #432D61semidirect
152. C61#3219semidirect