Finite Group Databasebeta

← #21456522

Subgroups — #21456522

Order 7808.

366 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840296C211yesmaximal, characteristic
2#16840168C211yesmaximal, characteristic, complemented
3#16840154C211yesmaximal, characteristic, complemented
4#16840130C211yesmaximal, characteristic, complemented
5#16840124C211yesmaximal, characteristic, complemented
6#16840001C212yesmaximal, complemented
7#16839993C212yesmaximal
8#16839867C212yesmaximal, complemented
9#16839860C212yesmaximal, complemented
10C2×#14519688C211yesmaximal, characteristic, complemented
11C61×#533C211yesmaximal, characteristic, complemented
12C2×#11758202C2212yes—
13C2×#11758201C2212yes—
14C22×#92418C2212yes—
15#14519771—21no—
16#14519769C2211yescharacteristic
17#14519765C2211yescharacteristic
18#14519760—21no—
19#14519756C2211yescharacteristic
20#14519751C2211yescharacteristic
21C4×Dic122C2211yescharacteristic
22C4×D244C2211yescharacteristic
23C4×C22⋊D61—21no—
24#14519734—21no—
25#14519710C2212yes—
26#14519708C2212yes—
27#14519701C2212yes—
28#14519701C2212yes—
29#14519700C2212yes—
30#14519697C2212yes—
31#14519688C2212yes—
32#14519688C2211yescharacteristic
33#14519688C2211yescharacteristic
34C4⋊Q8×C61C2211yescharacteristic
35C4⋊Q8×C61C2211yescharacteristic
36#125×C61—21no—
37C22⋊Q8×C61—21no—
38C22⋊Q8×C61C2212yes—
39C4×Q8×C61—21no—
40C4×Q8×C61C2212yes—
41#117×C61—21no—
42C2×C42×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61C2312yes—
45C22×C4×C61D411yescharacteristic
46C22×C4×C61D411yescharacteristic
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—21no—
49C2×D244C2311yescharacteristic
50C2×C4×D61—21no—
51C2×Dic122C2311yescharacteristic
52C4⋊C4×C61—21no—
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—22no—
57C4⋊C4×C61C2312yes—
58C22⋊C4×C61—22no—
59C42×C61—22no—
60C42×C61D411yescharacteristic
61C42×C61D411yescharacteristic
62C42×C61C2311yescharacteristic
63C42×C61C2311yescharacteristic
64C22⋊Dic61—21no—
65#11758202—24no—
66#11758201—24no—
67#11758198—21no—
68#11758198—21no—
69#11758198—21no—
70#11758198—21no—
71C4⋊Dic61C2311yescharacteristic
72C4⋊Dic61C2311yescharacteristic
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76#11758196—21no—
77C4×Dic61—21no—
78C2×#92418—24no—
79C2×#92418C2312yes—
80C2×#92418C2312yes—
81C23×C61C2×D411yescharacteristic
82C22×D61—21no—
83Q8×C61—22no—
84Q8×C61—22no—
85Q8×C61—42no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—41no—
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2411yescharacteristic
97C22⋊D61—42no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101D244—22no—
102C4×D61—42no—
103Dic122—22no—
104#92418—22no—
105#92418#4114yes—
106C22×C61—21no—
107C22×C61—21no—
108C22×C61#13712yes—
109C22×C61C22×D411yescharacteristic
110C2×D61—41no—
111C2×D61—41no—
112C2×D61—41no—
113C4×C61—21no—
114C4×C61—21no—
115C4×C61—21no—
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—42no—
119C4×C61—42no—
120C4×C61C2×#4112yes—
121Dic61—41no—
122Dic61—41no—
123Dic61—41no—
124#3181—611nomaximal, Sylow
125C2×C61—22no—
126C2×C61#53211yescharacteristic
127C2×C61C2×#13711yescharacteristic
128C2×C61#57511yescharacteristic
129D61—81no—
130#533D6111yescharacteristic, complemented
131#529—611no—
132#501—611no—
133#497—611no—
134#491—611no—
135#489—611no—
136#467—612no—
137#465—612no—
138#441—612no—
139#440—612no—
140C2×#97—611no—
141C61#318111yescharacteristic, complemented, Sylow
142C2×Q16—612no—
143C2×SD16—612no—
144C22×C8—612no—
145C4⋊Q8C2×D6111yescharacteristic
146C4⋊Q8C2×D6111yescharacteristic
147#126—1221no—
148#125—21no—
149#125—611no—
150#124—611no—
151#123—1221no—
152C22⋊Q8—21no—
153C22⋊Q8—611no—
154C22⋊Q8C2×D6112yes—
155#121—611no—
156C4×Q8—21no—
157C4×Q8—611no—
158C4×Q8C2×D6112yes—
159C4×D4—611no—
160C4×D4—1221no—
161#117—21no—
162#117—1221no—
163C2×C42C2×D6111yescharacteristic
164#107—612no—
165#106—612no—
166#103—612no—
167#103—612no—
168#103—612no—
169#102—612no—
170#97—612no—
171#97—611no—
172#97—611no—
173C2×Q8—21no—
174C2×Q8—611no—
175C2×Q8C22×D6112yes—
176C2×D4—611no—
177C2×D4—1221no—
178C22×C4—1221no—
179C22×C4C22⋊D6111yescharacteristic
180C22×C4C22⋊D6111yescharacteristic
181C22×C4C22×D6111yescharacteristic
182Q16—1224no—
183SD16—1224no—
184C2×C8—612no—
185C2×C8—612no—
186C2×C8—1224no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—611no—
193C4⋊C4—611no—
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C4⋊C4—1221no—
197C4⋊C4—1221no—
198C4⋊C4C22×D6112yes—
199C22⋊C4—22no—
200C22⋊C4—1221no—
201C22⋊C4—1221no—
202C22⋊C4—1221no—
203C22⋊C4—1221no—
204C22⋊C4—1221no—
205C42—22no—
206C42—1221no—
207C42C22⋊D6111yescharacteristic
208C42C22⋊D6111yescharacteristic
209C42C22×D6111yescharacteristic
210C42C22×D6111yescharacteristic
211C23—1221no—
212C23C2×C22⋊D6111yescharacteristic
213Q8—22no—
214Q8—22no—
215Q8—42no—
216Q8—1222no—
217D4—1222no—
218D4—2442no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—2442no—
228C2×C4C2×C22⋊D6111yescharacteristic
229C2×C4C2×C22⋊D6111yescharacteristic
230C2×C4C2×C22⋊D6111yescharacteristic
231C2×C4C2×C22⋊D6111yescharacteristic
232C2×C4C2×C22⋊D6111yescharacteristic
233C2×C4C23×D6111yescharacteristic
234C8—614no—
235C8—1222no—
236C22—21no—
237C22—21no—
238C22—2441no—
239C22—2441no—
240C22—2441no—
241C22#1451980812yes—
242C22C22×C22⋊D6111yescharacteristic
243C4—21no—
244C4—21no—
245C4—21no—
246C4—21no—
247C4—21no—
248C4—42no—
249C4—42no—
250C4—2441no—
251C4—2441no—
252C4—2441no—
253C4#41×D6112yes—
254C2—22no—
255C2—4881no—
256C2#1684030811yescharacteristic
257C2C2×#1451980811yescharacteristic
258C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3181
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16840168C2semidirect
3. #16840154C2semidirect
4. #16840130C2semidirect
5. #16840124C2semidirect
6. #16840001C2semidirect
8. #16839867C2semidirect
9. #16839860C2semidirect
10. C2×#14519688C2semidirect
11. C61×#533C2semidirect
130. #533D61semidirect
141. C61#3181semidirect