Finite Group Databasebeta

← #21456721

Subgroups — #21456721

Order 7808.

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

normal subgroups only

This group has 402 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#16840340C212yesmaximal, complemented
2#16840098C212yesmaximal, complemented
3#16840076C212yesmaximal, complemented
4#16840008C212yesmaximal, complemented
5#16840003C211yesmaximal, characteristic, complemented
6#16839998C211yesmaximal, characteristic, complemented
7#16839926C212yesmaximal, complemented
8#16839909C212yesmaximal, complemented
9C61×#408C211yesmaximal, characteristic, complemented
10C2×#11758222C2212yes—
11C2×Dic244C2211yescharacteristic
12C2×#11758190C2212yes—
13C2×D488C2211yescharacteristic
14#14519756C2212yes—
15#14519756C2212yes—
16#14519753—22no—
17#14519751C2212yes—
18#14519751C2212yes—
19#14519749—22no—
20#14519749—22no—
21#14519748—22no—
22C2×C4⋊Dic61C2212yes—
23#14519711C2211yescharacteristic
24#14519711C2211yescharacteristic
25#14519711C2212yes—
26#14519702C2212yes—
27#14519702C2212yes—
28#14519699C2212yes—
29#14519699C2212yes—
30C2×#41×C61C2211yescharacteristic
31C2×M16×C61C2211yescharacteristic
32C22×C8×C61C2211yescharacteristic
33C22⋊C8×C61C2212yes—
34C22⋊C8×C61C2212yes—
35#41×C61—41no—
36#41×C61—41no—
37C2×Q8×C61D411yescharacteristic
38C2×D4×C61D412yes—
39C2×D4×C61D411yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—22no—
43C2×C22⋊D61—22no—
44C2×C22⋊D61—22no—
45C22×Dic61—22no—
46#11758222—42no—
47#11758222—42no—
48C2×D244C2312yes—
49C2×C4×D61—22no—
50C2×Dic122C2312yes—
51M16×C61—41no—
52C2×C8×C61—41no—
53C2×C8×C61C2311yescharacteristic
54C2×C8×C61C2311yescharacteristic
55C2×C8×C61C2312yes—
56C22⋊Dic61—22no—
57C22⋊Dic61—22no—
58#11758198—22no—
59#11758198—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61C2312yes—
62C4⋊Dic61C2312yes—
63#11758196—22no—
64#11758196—22no—
65Dic244—41no—
66D488—41no—
67#11758190—42no—
68C23×C61C2×D411yescharacteristic
69C23×C61C2×D412yes—
70C22×D61—22no—
71Q8×C61—41no—
72D4×C61—42no—
73D4×C61—41no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2411yescharacteristic
81C22⋊D61—44no—
82C22⋊D61—82no—
83C22⋊D61—82no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—82no—
88D244—22no—
89D244—22no—
90C4×D61—44no—
91Dic122—22no—
92Dic122—22no—
93C8×C61—22no—
94C8×C61—21no—
95C8×C61—21no—
96C22×C61—22no—
97C22×C61—21no—
98C22×C61—22no—
99C22×C61—21no—
100C22×C61—21no—
101C22×C61—22no—
102C22×C61C22×D411yescharacteristic
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—42no—
106C4×C61—22no—
107C4×C61—21no—
108C4×C61H(5,𝔽2)11yescharacteristic
109C4×C61H(5,𝔽2)11yescharacteristic
110Dic61—42no—
111Dic61—42no—
112Dic61—42no—
113#3203—611nomaximal, Sylow
114C2×C61—42no—
115C2×C61—41no—
116C2×C61#53411yescharacteristic
117C2×C61#57611yescharacteristic
118C2×C61#57811yescharacteristic
119D61—82no—
120#537—612no—
121#484—612no—
122#480—612no—
123#468—612no—
124#467—611no—
125#466—611no—
126#452—612no—
127#449—612no—
128#408D6111yescharacteristic, complemented
129C61#320311yescharacteristic, complemented, Sylow
130C2×#41—612no—
131C2×#41C2×D6111yescharacteristic
132C2×Q16—611no—
133C2×SD16—612no—
134C2×D8—611no—
135C2×M16C2×D6111yescharacteristic
136C22×C8C2×D6111yescharacteristic
137C22⋊Q8—612no—
138C22⋊Q8—612no—
139C22⋊Q8—1222no—
140#121—612no—
141#121—612no—
142#121—1222no—
143#121—1222no—
144#121—1222no—
145C2×C4⋊C4—612no—
146#107—611no—
147#107—611no—
148#107—612no—
149#103—612no—
150#103—612no—
151#102—612no—
152#102—612no—
153C22⋊C8C2×D6112yes—
154C22⋊C8C2×D6112yes—
155#41—41no—
156#41—41no—
157#41—2442no—
158#41—2442no—
159C2×Q8—612no—
160C2×Q8D24411yescharacteristic
161C2×D4—612no—
162C2×D4—1222no—
163C2×D4—1222no—
164C2×D4—1222no—
165C2×D4D24411yescharacteristic
166C2×D4D24412yes—
167C22×C4—1222no—
168C22×C4—1222no—
169C22×C4C22×D6112yes—
170C22×C4C22×D6111yescharacteristic
171Q16—2441no—
172SD16—2442no—
173D8—2441no—
174M16—41no—
175C2×C8—41no—
176C2×C8C22×D6111yescharacteristic
177C2×C8C22×D6112yes—
178C2×C8C22×D6111yescharacteristic
179C4⋊C4—612no—
180C4⋊C4—612no—
181C4⋊C4—1222no—
182C4⋊C4—1222no—
183C4⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C22⋊C4—1222no—
187C22⋊C4—1222no—
188C23—1222no—
189C23C2×D24411yescharacteristic
190C23C2×D24412yes—
191Q8—41no—
192Q8—1222no—
193Q8—1222no—
194D4—42no—
195D4—41no—
196D4—1222no—
197D4—1222no—
198D4—4882no—
199D4—4882no—
200D4—2444no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1222no—
208C2×C4—4882no—
209C2×C4—2444no—
210C2×C4C2×D24411yescharacteristic
211C2×C4C2×D24412yes—
212C2×C4C23×D6111yescharacteristic
213C8—21no—
214C8—21no—
215C8—22no—
216C22—22no—
217C22—21no—
218C22—21no—
219C22—22no—
220C22—22no—
221C22—21no—
222C22—2442no—
223C22—2442no—
224C22—2442no—
225C22C22×D24411yescharacteristic
226C4—22no—
227C4—21no—
228C4—2442no—
229C4—2442no—
230C4—2442no—
231C4#1451982211yescharacteristic
232C4#1451982211yescharacteristic
233C2—42no—
234C2—41no—
235C2—4882no—
236C2#1684032411yescharacteristic
237C2#1684056711yescharacteristic
238C2#1684057911yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#408C2
socleC22×C61C22×D4
hypercenter#408D61
hypocenterC61#3203
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #16840340C2semidirect
2. #16840098C2semidirect
3. #16840076C2semidirect
4. #16840008C2semidirect
5. #16840003C2semidirect
6. #16839998C2semidirect
7. #16839926C2semidirect
8. #16839909C2semidirect
9. C61×#408C2semidirect
128. #408D61semidirect
129. C61#3203semidirect