Finite Group Databasebeta

← #21456989

Subgroups — #21456989

Order 7808.

334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14519769C211yesmaximal, characteristic, complemented
3#16840164C212yesmaximal, complemented
4#16840117C212yesmaximal, complemented
5#16840098C211yesmaximal, characteristic, complemented
6#16840093C211yesmaximal, characteristic, complemented
7#16840081C211yesmaximal, characteristic
8#16840076C211yesmaximal, characteristic
9#16840070C212yesmaximal, complemented
10#16840063C212yesmaximal, complemented
11C61×#431C211yesmaximal, characteristic, complemented
12#14519771—21no—
13#14519769—21no—
14#14519769—21no—
15#14519769C2212yes—
16#14519769C2212yes—
17#14519769C2211yescharacteristic
18#14519765C2211yescharacteristic
19#14519760—21no—
20#14519756C2211yescharacteristic
21#14519751C2211yescharacteristic
22C4×Dic122C2211yescharacteristic
23C4×D244C2211yescharacteristic
24C4×C22⋊D61—21no—
25#14519734—21no—
26C2×C4⋊Dic61C2211yescharacteristic
27C2×C4⋊Dic61C2211yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30#14519711C2212yes—
31#14519711C2212yes—
32#14519709C2212yes—
33#14519709C2212yes—
34#14519702C2212yes—
35#14519702C2212yes—
36#14519699C2212yes—
37#14519699C2212yes—
38C2×C42×C61C2211yescharacteristic
39C4⋊C8×C61C2212yes—
40C22⋊C8×C61C2211yescharacteristic
41C22⋊C8×C61C2211yescharacteristic
42C4×C8×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×Dic122C2311yescharacteristic
52C2×C8×C61C2312yes—
53C2×C8×C61C2312yes—
54C42×C61D411yescharacteristic
55C42×C61D411yescharacteristic
56C42×C61C2311yescharacteristic
57C42×C61C2311yescharacteristic
58C22⋊Dic61—21no—
59#11758198—21no—
60#11758198—21no—
61#11758198—21no—
62#11758198—21no—
63C4⋊Dic61—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61C2312yes—
66C4⋊Dic61C2312yes—
67C4⋊Dic61C2311yescharacteristic
68C4⋊Dic61C2311yescharacteristic
69#11758196—22no—
70#11758196—22no—
71#11758196—22no—
72#11758196—22no—
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76#11758196—21no—
77C4×Dic61—21no—
78C23×C61C2×D411yescharacteristic
79C22×D61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—41no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2411yescharacteristic
89C22⋊D61—42no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97D244—22no—
98C4×D61—42no—
99Dic122—22no—
100C8×C61—22no—
101C8×C61—22no—
102C22×C61—21no—
103C22×C61—21no—
104C22×C61#13512yes—
105C22×C61C22×D411yescharacteristic
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—41no—
109C4×C61—21no—
110C4×C61—21no—
111C4×C61—21no—
112C4×C61—21no—
113C4×C61—21no—
114C4×C612−1+412yes—
115Dic61—41no—
116Dic61—42no—
117Dic61—41no—
118Dic61—41no—
119Dic61—42no—
120#3232—611nomaximal, Sylow
121C2×C61—22no—
122C2×C61#53611yescharacteristic
123C2×C61C2×#13511yescharacteristic
124C2×C61#57511yescharacteristic
125D61—81no—
126#529—611no—
127C2×#125—611no—
128#499—612no—
129#488—612no—
130#484—611no—
131#483—611no—
132#481—611no—
133#480—611no—
134#479—612no—
135#478—612no—
136#431D6111yescharacteristic, complemented
137C61#323211yescharacteristic, complemented, Sylow
138#126—1221no—
139#125—612no—
140#125—612no—
141#125—611no—
142#125—1221no—
143#125—1221no—
144#124—611no—
145#123—1221no—
146C22⋊Q8—611no—
147#121—611no—
148C4×Q8—611no—
149C4×D4—611no—
150C4×D4—1221no—
151#117—1221no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4—611no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4—1221no—
156C2×C42C2×D6111yescharacteristic
157#107—612no—
158#107—612no—
159#106—612no—
160#106—612no—
161C4⋊C8C2×D6112yes—
162#103—612no—
163#103—612no—
164#102—612no—
165#102—612no—
166C22⋊C8C2×D6111yescharacteristic
167C22⋊C8C2×D6111yescharacteristic
168C4×C8C2×D6112yes—
169C2×Q8—611no—
170C2×D4—611no—
171C2×D4—1221no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4—1221no—
175C22×C4D24411yescharacteristic
176C22×C4D24411yescharacteristic
177C22×C4C22×D6111yescharacteristic
178C2×C8C22×D6112yes—
179C2×C8C22×D6112yes—
180C4⋊C4—612no—
181C4⋊C4—612no—
182C4⋊C4—611no—
183C4⋊C4—611no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4—1222no—
187C4⋊C4—1222no—
188C4⋊C4—1222no—
189C4⋊C4—1222no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C22⋊C4—1221no—
195C22⋊C4—1221no—
196C22⋊C4—1221no—
197C22⋊C4—1221no—
198C22⋊C4—1221no—
199C42—1221no—
200C42D24411yescharacteristic
201C42D24411yescharacteristic
202C42C22×D6111yescharacteristic
203C42C22×D6111yescharacteristic
204C23—1221no—
205C23C2×D24411yescharacteristic
206Q8—1222no—
207D4—1222no—
208D4—2442no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—2442no—
218C2×C4—2442no—
219C2×C4—2442no—
220C2×C4C2×D24411yescharacteristic
221C2×C4C2×D24411yescharacteristic
222C2×C4C2×D24411yescharacteristic
223C2×C4C2×D24411yescharacteristic
224C2×C4C2×D24411yescharacteristic
225C2×C4C23×D6111yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—2441no—
231C22—2441no—
232C22—2441no—
233C22#1451979912yes—
234C22C22×D24411yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—2442no—
241C4—2441no—
242C4—2441no—
243C4—2442no—
244C4—2441no—
245C4#1451982412yes—
246C2—22no—
247C2—4881no—
248C2#1684033811yescharacteristic
249C2C2×#1451979911yescharacteristic
250C2#1684056211yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#431C2
socleC22×C61C22×D4
hypercenter#431D61
hypocenterC61#3232
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C2×#14519769C2semidirect
3. #16840164C2semidirect
4. #16840117C2semidirect
5. #16840098C2semidirect
6. #16840093C2semidirect
9. #16840070C2semidirect
10. #16840063C2semidirect
11. C61×#431C2semidirect
136. #431D61semidirect
137. C61#3232semidirect