Finite Group Databasebeta

← #21457003

Subgroups — #21457003

Order 7808.

332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840299C211yesmaximal, characteristic
3#16840163C212yesmaximal, complemented
4#16840118C212yesmaximal, complemented
5#16840102C212yesmaximal, complemented
6#16840089C212yesmaximal
7#16840049C211yesmaximal, characteristic, complemented
8#16840047C211yesmaximal, characteristic, complemented
9#16840043C211yesmaximal, characteristic, complemented
10#16839814C211yesmaximal, characteristic, complemented
11C61×#477C211yesmaximal, characteristic, complemented
12#14519777C2211yescharacteristic
13#14519772—21no—
14#14519768C2211yescharacteristic
15#14519768C2212yes—
16#14519766C2211yescharacteristic
17#14519762—21no—
18#14519757—21no—
19#14519753—21no—
20#14519753C2211yescharacteristic
21#14519752C2211yescharacteristic
22Q8×Dic61—21no—
23#14519742—21no—
24C4×D244—21no—
25C4×D244C2211yescharacteristic
26#14519735C2212yes—
27#14519734—21no—
28C42×D61C2211yescharacteristic
29#14519711C2212yes—
30#14519708C2212yes—
31#14519708C2212yes—
32C4⋊#92418C2211yescharacteristic
33#14519701C2212yes—
34#14519699C2212yes—
35#14519697C2212yes—
36#14519689C2212yes—
37C8×Dic61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×Q8×C61C2211yescharacteristic
40#107×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45C2×D244—21no—
46C2×D244C2311yescharacteristic
47C2×C4×D61—21no—
48C2×C4×D61D411yescharacteristic
49C2×C4×D61D411yescharacteristic
50C2×C4×D61C2311yescharacteristic
51C2×Dic122—21no—
52C2×C8×C61C2312yes—
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61C2312yes—
56C4⋊C4×C61C2311yescharacteristic
57C42×C61—21no—
58C42×C61C2311yescharacteristic
59#11758198—22no—
60#11758198—21no—
61#11758198—21no—
62#11758198—21no—
63#11758198—21no—
64#11758198—21no—
65C4⋊Dic61—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61—22no—
68C4⋊Dic61C2312yes—
69C4⋊Dic61C2311yescharacteristic
70#11758196—21no—
71#11758196—21no—
72#11758196—22no—
73C4×Dic61—22no—
74C4×Dic61D411yescharacteristic
75C4×Dic61D411yescharacteristic
76C4×Dic61C2311yescharacteristic
77C2×#92418C2312yes—
78C22×D61—21no—
79C22×D61C2×D411yescharacteristic
80Q8×C61—21no—
81Q8×C61—21no—
82Q8×C61—42no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2411yescharacteristic
89C2×Dic61—22no—
90C2×Dic61—21no—
91C2×Dic61C2×D411yescharacteristic
92C2×Dic61C2×D411yescharacteristic
93C2×Dic61C2×D411yescharacteristic
94D244—21no—
95D244—21no—
96D244—42no—
97C4×D61—22no—
98C4×D61—21no—
99C4×D61—21no—
100C4×D61—41no—
101C4×D61—42no—
102Dic122—42no—
103C8×C61—22no—
104#92418—22no—
105C22×C61C22×D411yescharacteristic
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—21no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—41no—
112C4×C61—21no—
113C4×C61—41no—
114C4×C61—41no—
115C4×C61—42no—
116C4×C61#13512yes—
117C4×C612−1+411yescharacteristic
118C4×C612−1+411yescharacteristic
119Dic61—21no—
120Dic61—21no—
121Dic61—21no—
122Dic61—42no—
123Dic61—41no—
124#3233—611nomaximal, Sylow
125C2×C61#53611yescharacteristic
126C2×C61C2×#13511yescharacteristic
127C2×C61#57511yescharacteristic
128D61—41no—
129D61—81no—
130#533—611no—
131#529—611no—
132#499—612no—
133#488—612no—
134#485—612no—
135#482—612no—
136#477D6111yescharacteristic, complemented
137#476—611no—
138#475—611no—
139#474—611no—
140#431—611no—
141C61#323311yescharacteristic, complemented, Sylow
142C4⋊Q8—611no—
143C4⋊Q8C2×D6111yescharacteristic
144#126—1221no—
145#125—611no—
146#125—612no—
147#124—611no—
148#123—1221no—
149C22⋊Q8—611no—
150C22⋊Q8—1221no—
151C22⋊Q8—1221no—
152#121—611no—
153C4×Q8—1221no—
154C4×Q8—1221no—
155C4×Q8C2×D6111yescharacteristic
156C4×D4—611no—
157C4×D4—1221no—
158#117—612no—
159#117—1221no—
160C2×C42—611no—
161#107—612no—
162#107C2×D6112yes—
163#106—612no—
164#106—612no—
165C4⋊C8—611no—
166C4⋊C8C2×D6111yescharacteristic
167#103—612no—
168#103C2×D6112yes—
169#102—612no—
170#102—612no—
171C22⋊C8—612no—
172C4×C8—612no—
173C2×Q8—21no—
174C2×Q8—1221no—
175C2×Q8C22×D6111yescharacteristic
176C2×D4—611no—
177C2×D4—1221no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—1221no—
182C2×C8—612no—
183C2×C8C22×D6112yes—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—612no—
187C4⋊C4—611no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C4⋊C4—1222no—
191C4⋊C4—1221no—
192C4⋊C4—1222no—
193C4⋊C4—1221no—
194C4⋊C4C22×D6112yes—
195C4⋊C4C22×D6111yescharacteristic
196C22⋊C4—1221no—
197C22⋊C4—1221no—
198C22⋊C4—1221no—
199C22⋊C4—1222no—
200C22⋊C4—1221no—
201C22⋊C4—1221no—
202C42—21no—
203C42—611no—
204C42—611no—
205C42—611no—
206C42—1222no—
207C42C22×D6111yescharacteristic
208C23—611no—
209C23—1221no—
210Q8—21no—
211Q8—21no—
212Q8—42no—
213Q8—2442no—
214D4—1221no—
215D4—1221no—
216D4—2442no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1221no—
228C2×C4—2441no—
229C2×C4—2442no—
230C2×C4D4×D6111yescharacteristic
231C2×C4D4×D6111yescharacteristic
232C2×C4C23×D6111yescharacteristic
233C8—22no—
234C8—1222no—
235C22—1221no—
236C22—1221no—
237C22—1221no—
238C22—2441no—
239C22—2441no—
240C22—2441no—
241C22C2×D4×D6111yescharacteristic
242C4—21no—
243C4—41no—
244C4—42no—
245C4—41no—
246C4—1221no—
247C4—1221no—
248C4—1221no—
249C4—2441no—
250C4—2442no—
251C4#1451980012yes—
252C4#1451982411yescharacteristic
253C4#1451982511yescharacteristic
254C2—4881no—
255C2—2441no—
256C2#1684033511yescharacteristic
257C2C2×#1451980011yescharacteristic
258C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#477C2
socleC22×C61C22×D4
hypercenter#477D61
hypocenterC61#3233
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840163C2semidirect
4. #16840118C2semidirect
5. #16840102C2semidirect
7. #16840049C2semidirect
8. #16840047C2semidirect
9. #16840043C2semidirect
10. #16839814C2semidirect
11. C61×#477C2semidirect
136. #477D61semidirect
141. C61#3233semidirect