Finite Group Databasebeta

← #21455992

Subgroups — #21455992

Order 7808.

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

normal subgroups only

This group has 386 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
2C2×C4×Dic122C211yesmaximal, characteristic, complemented
3#16840098C211yesmaximal, characteristic, complemented
4#16840081C211yesmaximal, characteristic
5#16840070C212yesmaximal, complemented
6#16839985C212yesmaximal, complemented
7#16839920C211yesmaximal, characteristic, complemented
8#16839903C211yesmaximal, characteristic
9#16839870C212yesmaximal, complemented
10#16839864C212yesmaximal, complemented
11C61×#432C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C2×Dic244C2212yes—
14C2×#11758190C2212yes—
15#14519771—21no—
16#14519769C2211yescharacteristic
17#14519765C2211yescharacteristic
18#14519760—21no—
19#14519756C2211yescharacteristic
20#14519751C2211yescharacteristic
21C4×Dic122—21no—
22C4×Dic122—21no—
23C4×Dic122C2212yes—
24C4×Dic122C2212yes—
25C4×Dic122C2211yescharacteristic
26C4×D244C2211yescharacteristic
27C4×C22⋊D61—21no—
28#14519734—21no—
29C2×C4⋊Dic61C2211yescharacteristic
30C2×#11758196—21no—
31C2×C4×Dic61—21no—
32#14519711C2212yes—
33#14519709C2212yes—
34#14519702C2212yes—
35#14519702C2212yes—
36#14519702C2212yes—
37#14519699C2212yes—
38C2×C42×C61C2211yescharacteristic
39C4⋊C8×C61C2212yes—
40C22⋊C8×C61C2211yescharacteristic
41C22⋊C8×C61C2211yescharacteristic
42#97×C61C2212yes—
43C22×C4×C61D411yescharacteristic
44C22×C4×C61D411yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C2×C22⋊D61—21no—
47C22×Dic61—21no—
48C22×Dic61—21no—
49C2×D244C2311yescharacteristic
50C2×C4×D61—21no—
51C2×Dic122—21no—
52C2×Dic122—24no—
53C2×Dic122C2311yescharacteristic
54C2×Dic122C2312yes—
55C2×C8×C61C2312yes—
56C2×C8×C61C2312yes—
57C42×C61D411yescharacteristic
58C42×C61D411yescharacteristic
59C42×C61C2311yescharacteristic
60C42×C61C2311yescharacteristic
61C22⋊Dic61—21no—
62#11758198—21no—
63#11758198—21no—
64#11758198—21no—
65#11758198—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61C2312yes—
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2311yescharacteristic
70#11758196—22no—
71#11758196—22no—
72#11758196—21no—
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76C4×Dic61—22no—
77C4×Dic61—22no—
78C4×Dic61—21no—
79Dic244—24no—
80#11758190—24no—
81C23×C61C2×D411yescharacteristic
82C22×D61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—41no—
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2411yescharacteristic
92C22⋊D61—42no—
93C2×Dic61—24no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—42no—
100D244—22no—
101C4×D61—42no—
102Dic122—24no—
103Dic122—22no—
104Dic122—22no—
105Dic122#4114yes—
106C8×C61—22no—
107C8×C61—22no—
108C22×C61—21no—
109C22×C61—21no—
110C22×C61#13712yes—
111C22×C61C22×D411yescharacteristic
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—41no—
115C4×C61—21no—
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—21no—
120C4×C61C2×#4112yes—
121Dic61—24no—
122Dic61—41no—
123Dic61—41no—
124Dic61—41no—
125Dic61—42no—
126#3117—611nomaximal, Sylow
127C2×C61—22no—
128C2×C61#52511yescharacteristic
129C2×C61C2×#13711yescharacteristic
130C2×C61#57511yescharacteristic
131D61—81no—
132#529—611no—
133C2×C4×Q8—611no—
134#484—611no—
135#481—611no—
136#479—612no—
137#464—612no—
138#451—611no—
139#448—611no—
140#441—612no—
141#440—612no—
142#432D6111yescharacteristic, complemented
143C61#311711yescharacteristic, complemented, Sylow
144C22×Q8—611no—
145C2×Q16—612no—
146C2×SD16—612no—
147#126—1221no—
148#125—611no—
149#124—611no—
150#123—1221no—
151C22⋊Q8—611no—
152#121—611no—
153C4×Q8—612no—
154C4×Q8—612no—
155C4×Q8—611no—
156C4×Q8—1221no—
157C4×Q8—1221no—
158C4×D4—611no—
159C4×D4—1221no—
160#117—1221no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—1221no—
163C2×C42—1221no—
164C2×C42C2×D6111yescharacteristic
165#107—612no—
166#106—612no—
167C4⋊C8C2×D6112yes—
168#103—612no—
169#103—612no—
170#103—612no—
171#102—612no—
172C22⋊C8C2×D6111yescharacteristic
173C22⋊C8C2×D6111yescharacteristic
174#97C2×D6112yes—
175C2×Q8—612no—
176C2×Q8—611no—
177C2×Q8—1224no—
178C2×Q8—1221no—
179C2×D4—611no—
180C2×D4—1221no—
181C22×C4—1221no—
182C22×C4—1221no—
183C22×C4—1221no—
184C22×C4D24411yescharacteristic
185C22×C4D24411yescharacteristic
186C22×C4C22×D6111yescharacteristic
187Q16—1224no—
188SD16—1224no—
189C2×C8C22×D6112yes—
190C2×C8C22×D6112yes—
191C4⋊C4—612no—
192C4⋊C4—611no—
193C4⋊C4—611no—
194C4⋊C4—1221no—
195C4⋊C4—1222no—
196C4⋊C4—1222no—
197C4⋊C4—1221no—
198C4⋊C4—1221no—
199C4⋊C4—1221no—
200C4⋊C4—1221no—
201C22⋊C4—1221no—
202C22⋊C4—1221no—
203C22⋊C4—1221no—
204C22⋊C4—1221no—
205C22⋊C4—1221no—
206C42—1222no—
207C42—1222no—
208C42—1221no—
209C42D24411yescharacteristic
210C42D24411yescharacteristic
211C42C22×D6111yescharacteristic
212C42C22×D6111yescharacteristic
213C23—1221no—
214C23C2×D24411yescharacteristic
215Q8—614no—
216Q8—1224no—
217Q8—1222no—
218Q8—1222no—
219D4—1222no—
220D4—2442no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—1224no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—2442no—
231C2×C4—2442no—
232C2×C4C2×D24411yescharacteristic
233C2×C4C2×D24411yescharacteristic
234C2×C4C2×D24411yescharacteristic
235C2×C4C2×D24411yescharacteristic
236C2×C4C2×D24411yescharacteristic
237C2×C4C23×D6111yescharacteristic
238C8—22no—
239C8—22no—
240C22—21no—
241C22—21no—
242C22—2441no—
243C22—2441no—
244C22—2441no—
245C22#1451981012yes—
246C22C22×D24411yescharacteristic
247C4—21no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—21no—
252C4—1224no—
253C4—2441no—
254C4—2441no—
255C4—2441no—
256C4—2442no—
257C4#41×D6112yes—
258C2—22no—
259C2—4881no—
260C2#1684027411yescharacteristic
261C2C2×#1451981011yescharacteristic
262C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3117
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
2. C2×C4×Dic122C2semidirect
3. #16840098C2semidirect
5. #16840070C2semidirect
6. #16839985C2semidirect
7. #16839920C2semidirect
9. #16839870C2semidirect
10. #16839864C2semidirect
11. C61×#432C2semidirect
142. #432D61semidirect
143. C61#3117semidirect