Finite Group Databasebeta

← #21456882

Subgroups — #21456882

Order 7808.

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

normal subgroups only

This group has 388 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#16840367C211yesmaximal, characteristic, complemented
2#16840338C211yesmaximal, characteristic, complemented
3#16840151C211yesmaximal, characteristic, complemented
4#16840135C211yesmaximal, characteristic, complemented
5#16840131C211yesmaximal, characteristic, complemented
6#16840117C211yesmaximal, characteristic, complemented
7#16839978C212yesmaximal, complemented
8#16839968C212yesmaximal, complemented
9#16839909C212yesmaximal, complemented
10#16839903C212yesmaximal, complemented
11C61×#433C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14C2×#11758190C2212yes—
15C2×#11758190C2212yes—
16C2×#11758190C2212yes—
17C2×D488C2212yes—
18#14519777C2211yescharacteristic
19#14519777C2211yescharacteristic
20#14519774C2211yescharacteristic
21#14519769C2211yescharacteristic
22#14519765C2211yescharacteristic
23#14519765C2211yescharacteristic
24#14519762—22no—
25#14519761—22no—
26#14519757—22no—
27#14519751C2212yes—
28#14519750—22no—
29C4×D244C2212yes—
30#14519702C2212yes—
31#14519702C2212yes—
32#14519702C2212yes—
33#14519699C2212yes—
34#117×C61C2211yescharacteristic
35C4⋊C8×C61C2212yes—
36C22⋊C8×C61C2212yes—
37#97×C61C2211yescharacteristic
38C4×C8×C61C2211yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C2×C22⋊D61—21no—
41C2×C22⋊D61—22no—
42C22×Dic61—21no—
43#11758222—42no—
44C2×D244—22no—
45C2×D244C2311yescharacteristic
46C2×D244C2312yes—
47C2×C4×D61—21no—
48C2×C4×D61—22no—
49C2×Dic122—21no—
50C2×Dic122—42no—
51C2×Dic122C2311yescharacteristic
52C2×Dic122C2311yescharacteristic
53C2×Dic122C2311yescharacteristic
54C2×C8×C61C2312yes—
55C2×C8×C61C2312yes—
56C4⋊C4×C61D412yes—
57C22⋊C4×C61D412yes—
58C42×C61C2311yescharacteristic
59C42×C61C2311yescharacteristic
60#11758198—22no—
61#11758198—22no—
62#11758198—22no—
63#11758198—22no—
64C4⋊Dic61—22no—
65C4⋊Dic61—22no—
66C4⋊Dic61C2312yes—
67#11758196—22no—
68D488—42no—
69#11758190—42no—
70#11758190—42no—
71#11758190—42no—
72C23×C61C2×D411yescharacteristic
73C22×D61—21no—
74C22×D61—22no—
75C2×C4×C61—22no—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2411yescharacteristic
80C22⋊D61—42no—
81C22⋊D61—82no—
82C2×Dic61—22no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—42no—
87D244—22no—
88D244—22no—
89D244—22no—
90D244—82no—
91C4×D61—42no—
92C4×D61—82no—
93Dic122—22no—
94Dic122—22no—
95Dic122—22no—
96Dic122—42no—
97C8×C61—22no—
98C8×C61—22no—
99C22×C61—21no—
100C22×C61—22no—
101C22×C61C22×D411yescharacteristic
102C2×D61—41no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—42no—
106C2×D61—42no—
107C4×C61—21no—
108C4×C61—22no—
109C4×C61—22no—
110C4×C61H(5,𝔽2)12yes—
111Dic61—41no—
112Dic61—41no—
113Dic61—41no—
114Dic61—42no—
115#3221—611nomaximal, Sylow
116C2×C61—41no—
117C2×C61#53511yescharacteristic
118C2×C61#57712yes—
119D61—81no—
120D61—82no—
121#540—611no—
122#536—611no—
123#496—611no—
124#492—611no—
125#491—611no—
126#488—611no—
127#463—612no—
128#461—612no—
129#449—612no—
130#448—612no—
131#433D6111yescharacteristic, complemented
132C61#322111yescharacteristic, complemented, Sylow
133C2×#41—611no—
134C22×Q8—611no—
135C2×SD16—612no—
136C2×SD16—612no—
137C2×SD16—612no—
138C2×D8—612no—
139C4⋊Q8—611no—
140C4⋊Q8—611no—
141#127—611no—
142#125—611no—
143#124—611no—
144#124—611no—
145#123—1222no—
146#123—1222no—
147C22⋊Q8—1222no—
148#121—612no—
149#121—1222no—
150C4×D4—612no—
151#117C2×D6111yescharacteristic
152C4⋊C8C2×D6112yes—
153#103—612no—
154#103—612no—
155#103—612no—
156#102—612no—
157C22⋊C8C2×D6112yes—
158#97C2×D6111yescharacteristic
159C4×C8C2×D6111yescharacteristic
160#41—2442no—
161C2×Q8—611no—
162C2×Q8—611no—
163C2×Q8—611no—
164C2×Q8—1221no—
165C2×Q8—2442no—
166C2×D4—611no—
167C2×D4—612no—
168C2×D4—1222no—
169C2×D4—1221no—
170C2×D4—1222no—
171C22×C4—1221no—
172C22×C4—1222no—
173C22×C4—1221no—
174C22×C4C22×D6111yescharacteristic
175SD16—2442no—
176SD16—2442no—
177SD16—2442no—
178D8—2442no—
179C2×C8C22×D6112yes—
180C2×C8C22×D6112yes—
181C4⋊C4—612no—
182C4⋊C4—1222no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C4⋊C4D24412yes—
186C22⋊C4—1222no—
187C22⋊C4—1222no—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C22⋊C4D24412yes—
191C42C22×D6111yescharacteristic
192C42C22×D6111yescharacteristic
193C23—1221no—
194C23—1222no—
195C23C2×D24411yescharacteristic
196Q8—1222no—
197Q8—1222no—
198Q8—1222no—
199Q8—2442no—
200D4—1222no—
201D4—1222no—
202D4—1222no—
203D4—4882no—
204D4—4882no—
205D4—2442no—
206C2×C4—22no—
207C2×C4—1222no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—4882no—
212C2×C4—2442no—
213C2×C4—2442no—
214C2×C4C2×D24412yes—
215C2×C4C2×D24412yes—
216C2×C4C2×D24411yescharacteristic
217C2×C4C23×D6111yescharacteristic
218C8—22no—
219C8—22no—
220C22—22no—
221C22—21no—
222C22—2442no—
223C22—2442no—
224C22—2442no—
225C22—2441no—
226C22—2442no—
227C22C22×D24411yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—2442no—
232C4—2441no—
233C4—2441no—
234C4—2441no—
235C4#1451982312yes—
236C2—41no—
237C2—4882no—
238C2—4881no—
239C2#1684033111yescharacteristic
240C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#433C2
socleC22×C61C22×D4
hypercenter#433D61
hypocenterC61#3221
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #16840367C2semidirect
2. #16840338C2semidirect
3. #16840151C2semidirect
4. #16840135C2semidirect
5. #16840131C2semidirect
6. #16840117C2semidirect
7. #16839978C2semidirect
8. #16839968C2semidirect
9. #16839909C2semidirect
10. #16839903C2semidirect
11. C61×#433C2semidirect
131. #433D61semidirect
132. C61#3221semidirect