Finite Group Databasebeta

← #21456525

Subgroups — #21456525

Order 7808.

366 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 119 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#16840317C211yesmaximal, characteristic, complemented
2#16840291C211yesmaximal, characteristic
3#16840171C211yesmaximal, characteristic, complemented
4#16840130C211yesmaximal, characteristic, complemented
5#16840121C211yesmaximal, characteristic, complemented
6#16840000C212yesmaximal, complemented
7#16839988C212yesmaximal
8#16839869C212yesmaximal, complemented
9#16839863C212yesmaximal, complemented
10#97×D61C211yesmaximal, characteristic, complemented
11C61×#497C211yesmaximal, characteristic, complemented
12C2×C8×D61C2212yes—
13#14519777C2211yescharacteristic
14#14519770—21no—
15#14519769C2211yescharacteristic
16#14519768—21no—
17#14519759—21no—
18#14519757—21no—
19#14519753C2212yes—
20#14519753C2211yescharacteristic
21#14519748C2211yescharacteristic
22Q8×Dic61C2211yescharacteristic
23Q8×Dic61C2212yes—
24#14519742—21no—
25D4×Dic61C2211yescharacteristic
26#14519737—21no—
27#14519735—21no—
28#14519733—21no—
29C42×D61C2211yescharacteristic
30#14519711C2212yes—
31#14519709C2212yes—
32#14519701C2212yes—
33#14519701C2212yes—
34#14519701C2212yes—
35#14519698C2212yes—
36#14519688C2211yescharacteristic
37#14519687C2212yes—
38C2×Q16×C61C2212yes—
39C2×SD16×C61C2212yes—
40C4⋊Q8×C61C2211yescharacteristic
41#124×C61C2211yescharacteristic
42#97×C61C2211yescharacteristic
43C2×Q8×C61C2311yescharacteristic
44C2×Q8×C61C2312yes—
45C2×D4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C22×Dic61—21no—
48C2×C4×D61D411yescharacteristic
49C2×C4×D61D411yescharacteristic
50C2×C4×D61C2311yescharacteristic
51C2×Dic122—21no—
52Q16×C61—24no—
53SD16×C61—24no—
54C2×C8×C61C2312yes—
55C4⋊C4×C61—21no—
56C4⋊C4×C61—21no—
57C22⋊C4×C61—21no—
58C22⋊C4×C61—21no—
59C42×C61C2311yescharacteristic
60C22⋊Dic61—21no—
61C22⋊Dic61—21no—
62#11758198—22no—
63#11758198—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61—22no—
66C4⋊Dic61—21no—
67C4⋊Dic61C2312yes—
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2311yescharacteristic
70#11758196—21no—
71#11758196—21no—
72#11758196—21no—
73#11758196—22no—
74C4×Dic61—21no—
75C4×Dic61—22no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80C8×D61—24no—
81C23×C61—21no—
82C22×D61C2×D411yescharacteristic
83Q8×C61—22no—
84Q8×C61—22no—
85Q8×C61—22no—
86D4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2411yescharacteristic
92C22⋊D61—42no—
93C2×Dic61—21no—
94C2×Dic61—22no—
95C2×Dic61—21no—
96C2×Dic61—42no—
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100C4×D61—22no—
101C4×D61—22no—
102C4×D61—41no—
103Dic122—42no—
104C8×C61#4114yes—
105#92418—22no—
106C22×C61—41no—
107C22×C61—41no—
108C22×C61—41no—
109C22×C61C22×D411yescharacteristic
110C2×D61—21no—
111C2×D61—21no—
112C2×D61#13712yes—
113C4×C61—21no—
114C4×C61—21no—
115C4×C61—41no—
116C4×C61—42no—
117C4×C61C2×#4112yes—
118Dic61—21no—
119Dic61—21no—
120Dic61—21no—
121Dic61—41no—
122Dic61—42no—
123Dic61—41no—
124#3181—611nomaximal, Sylow
125C2×C61—81no—
126C2×C61#53211yescharacteristic
127C2×C61C2×#13711yescharacteristic
128C2×C61#57511yescharacteristic
129D61—22no—
130#533—611no—
131#529—611no—
132#501—611no—
133#497D6111yescharacteristic, complemented
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×Q16C2×D6112yes—
143C2×SD16C2×D6112yes—
144C22×C8—612no—
145C4⋊Q8—611no—
146C4⋊Q8C2×D6111yescharacteristic
147#126—1221no—
148#125—611no—
149#125—1221no—
150#124C2×D6111yescharacteristic
151#123—1221no—
152C22⋊Q8—611no—
153C22⋊Q8—612no—
154C22⋊Q8—1221no—
155#121—611no—
156C4×Q8—611no—
157C4×Q8—612no—
158C4×Q8—1221no—
159C4×D4—611no—
160C4×D4—1221no—
161#117—1221no—
162#117—1221no—
163C2×C42—611no—
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#97C2×D6111yescharacteristic
173C2×Q8—1221no—
174C2×Q8C22×D6111yescharacteristic
175C2×Q8C22×D6112yes—
176C2×D4—1221no—
177C2×D4C22×D6111yescharacteristic
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—1221no—
182Q16—24no—
183SD16—24no—
184C2×C8—612no—
185C2×C8—1224no—
186C2×C8C22×D6112yes—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—612no—
190C4⋊C4—611no—
191C4⋊C4—611no—
192C4⋊C4—1221no—
193C4⋊C4—1222no—
194C4⋊C4—1222no—
195C4⋊C4—1221no—
196C4⋊C4—1221no—
197C4⋊C4—1221no—
198C4⋊C4—1221no—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—1222no—
202C22⋊C4—1221no—
203C22⋊C4—1221no—
204C22⋊C4—1221no—
205C42—611no—
206C42—611no—
207C42—611no—
208C42—1221no—
209C42—1222no—
210C42C22×D6111yescharacteristic
211C23—21no—
212C23—611no—
213Q8—22no—
214Q8—22no—
215Q8—22no—
216Q8—2442no—
217D4—22no—
218D4—2442no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—611no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1221no—
227C2×C4—1222no—
228C2×C4—1221no—
229C2×C4—2441no—
230C2×C4—2442no—
231C2×C4D4×D6111yescharacteristic
232C2×C4D4×D6111yescharacteristic
233C2×C4C23×D6111yescharacteristic
234C8—1222no—
235C8#1175822414yes—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—612no—
240C22—1221no—
241C22—1221no—
242C22C2×D4×D6111yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—42no—
247C4—1221no—
248C4—1221no—
249C4—1221no—
250C4—2441no—
251C4—2441no—
252C4—2442no—
253C4C2×#1175822412yes—
254C2—81no—
255C2—1222no—
256C2#1684031011yescharacteristic
257C2#137×D6111yescharacteristic
258C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#497C2
socleC22×C61C22×D4
hypercenter#497D61
hypocenterC61#3181
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840171C2semidirect
4. #16840130C2semidirect
5. #16840121C2semidirect
6. #16840000C2semidirect
8. #16839869C2semidirect
9. #16839863C2semidirect
10. #97×D61C2semidirect
11. C61×#497C2semidirect
133. #497D61semidirect
141. C61#3181semidirect