Finite Group Databasebeta

← #21456998

Subgroups — #21456998

Order 7808.

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

normal subgroups only

This group has 332 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
2#16840161C212yesmaximal, complemented
3#16840119C212yesmaximal, complemented
4#16840103C212yesmaximal, complemented
5#16840086C212yesmaximal
6#16840054C211yesmaximal, characteristic, complemented
7#16840049C211yesmaximal, characteristic, complemented
8#16840044C211yesmaximal, characteristic, complemented
9#16840039C211yesmaximal, characteristic, complemented
10#16839815C211yesmaximal, characteristic, complemented
11C61×#533C211yesmaximal, characteristic, complemented
12#14519771—21no—
13#14519769C2211yescharacteristic
14#14519765C2211yescharacteristic
15#14519760—21no—
16#14519756C2211yescharacteristic
17#14519751C2211yescharacteristic
18C4×Dic122C2211yescharacteristic
19C4×D244C2211yescharacteristic
20C4×C22⋊D61—21no—
21#14519734—21no—
22#14519710C2212yes—
23#14519710C2212yes—
24#14519708C2212yes—
25#14519708C2212yes—
26C4⋊#92418C2211yescharacteristic
27C4⋊#92418C2211yescharacteristic
28#14519700C2212yes—
29#14519700C2212yes—
30#14519697C2212yes—
31#14519697C2212yes—
32C22⋊#92418C2212yes—
33C4×#92418C2212yes—
34C4⋊Q8×C61C2211yescharacteristic
35C4⋊Q8×C61C2211yescharacteristic
36#125×C61C2212yes—
37C22⋊Q8×C61—21no—
38C22⋊Q8×C61—21no—
39C4×Q8×C61—21no—
40C4×Q8×C61—21no—
41#117×C61C2212yes—
42C2×C42×C61C2211yescharacteristic
43C2×Q8×C61—21no—
44C2×Q8×C61—21no—
45C22×C4×C61D411yescharacteristic
46C22×C4×C61D411yescharacteristic
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—21no—
49C2×D244C2311yescharacteristic
50C2×C4×D61—21no—
51C2×Dic122C2311yescharacteristic
52C4⋊C4×C61—22no—
53C4⋊C4×C61—22no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56C4⋊C4×C61C2312yes—
57C4⋊C4×C61C2312yes—
58C22⋊C4×C61—22no—
59C42×C61—22no—
60C42×C61D411yescharacteristic
61C42×C61D411yescharacteristic
62C42×C61C2311yescharacteristic
63C42×C61C2311yescharacteristic
64C22⋊Dic61—21no—
65#11758198—21no—
66#11758198—21no—
67#11758198—21no—
68#11758198—21no—
69C4⋊Dic61C2311yescharacteristic
70C4⋊Dic61C2311yescharacteristic
71#11758196—21no—
72#11758196—21no—
73#11758196—21no—
74#11758196—21no—
75C4×Dic61—21no—
76C2×#92418C2312yes—
77C2×#92418C2312yes—
78C23×C61C2×D411yescharacteristic
79C22×D61—21no—
80Q8×C61—42no—
81Q8×C61—42no—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—41no—
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2411yescharacteristic
94C22⋊D61—42no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98D244—21no—
99D244—21no—
100C4×D61—42no—
101Dic122—21no—
102Dic122—21no—
103#92418—22no—
104#92418—22no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61—21no—
108C22×C61C22×D411yescharacteristic
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—41no—
112C4×C61—21no—
113C4×C61—21no—
114C4×C61—21no—
115C4×C61—21no—
116C4×C61—42no—
117C4×C61—42no—
118C4×C61#13512yes—
119C4×C612−1+411yescharacteristic
120C4×C612−1+411yescharacteristic
121Dic61—41no—
122Dic61—41no—
123Dic61—41no—
124#3233—611nomaximal, Sylow
125C2×C61—41no—
126C2×C61#53611yescharacteristic
127C2×C61C2×#13511yescharacteristic
128C2×C61#57511yescharacteristic
129D61—81no—
130#533D6111yescharacteristic, complemented
131#529—611no—
132#499—612no—
133#488—612no—
134#485—612no—
135#482—612no—
136#477—611no—
137#476—611no—
138#475—611no—
139#474—611no—
140#431—611no—
141C61#323311yescharacteristic, complemented, Sylow
142C4⋊Q8C2×D6111yescharacteristic
143C4⋊Q8C2×D6111yescharacteristic
144#126—1221no—
145#125—611no—
146#125C2×D6112yes—
147#124—611no—
148#123—1221no—
149C22⋊Q8—21no—
150C22⋊Q8—21no—
151C22⋊Q8—611no—
152#121—611no—
153C4×Q8—21no—
154C4×Q8—21no—
155C4×Q8—611no—
156C4×D4—611no—
157C4×D4—1221no—
158#117—1221no—
159#117C2×D6112yes—
160C2×C42C2×D6111yescharacteristic
161#107—612no—
162#107—612no—
163#106—612no—
164#106—612no—
165C4⋊C8—611no—
166C4⋊C8—611no—
167#103—612no—
168#103—612no—
169#102—612no—
170#102—612no—
171C22⋊C8—612no—
172C4×C8—612no—
173C2×Q8—21no—
174C2×Q8—21no—
175C2×Q8—611no—
176C2×D4—611no—
177C2×D4—1221no—
178C22×C4—1221no—
179C22×C4C22⋊D6111yescharacteristic
180C22×C4C22⋊D6111yescharacteristic
181C22×C4C22×D6111yescharacteristic
182C2×C8—612no—
183C2×C8—612no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—611no—
189C4⋊C4—611no—
190C4⋊C4—1221no—
191C4⋊C4—1221no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4C22×D6112yes—
195C4⋊C4C22×D6112yes—
196C22⋊C4—22no—
197C22⋊C4—1221no—
198C22⋊C4—1221no—
199C22⋊C4—1221no—
200C22⋊C4—1221no—
201C22⋊C4—1221no—
202C42—22no—
203C42—1221no—
204C42C22⋊D6111yescharacteristic
205C42C22⋊D6111yescharacteristic
206C42C22×D6111yescharacteristic
207C42C22×D6111yescharacteristic
208C23—1221no—
209C23C2×C22⋊D6111yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—1221no—
213Q8—1221no—
214D4—1221no—
215D4—1221no—
216D4—2442no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—2442no—
227C2×C4C2×C22⋊D6111yescharacteristic
228C2×C4C2×C22⋊D6111yescharacteristic
229C2×C4C2×C22⋊D6111yescharacteristic
230C2×C4C2×C22⋊D6111yescharacteristic
231C2×C4C2×C22⋊D6111yescharacteristic
232C2×C4C23×D6111yescharacteristic
233C8—1222no—
234C8—1222no—
235C22—21no—
236C22—21no—
237C22—21no—
238C22—2441no—
239C22—2441no—
240C22—2441no—
241C22C22×C22⋊D6111yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—42no—
248C4—2441no—
249C4—2441no—
250C4—2441no—
251C4#1451979712yes—
252C4#1451982511yescharacteristic
253C4#1451982511yescharacteristic
254C2—41no—
255C2—4881no—
256C2#1684033611yescharacteristic
257C2C2×#1451979711yescharacteristic
258C2#1684056011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3233
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. #16840161C2semidirect
3. #16840119C2semidirect
4. #16840103C2semidirect
6. #16840054C2semidirect
7. #16840049C2semidirect
8. #16840044C2semidirect
9. #16840039C2semidirect
10. #16839815C2semidirect
11. C61×#533C2semidirect
130. #533D61semidirect
141. C61#3233semidirect