Finite Group Databasebeta

← #21457038

Subgroups — #21457038

Order 7808.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#14519776C211yesmaximal, characteristic, complemented
2#16840293C211yesmaximal, characteristic
3#16840170C212yesmaximal, complemented
4#16840120C212yesmaximal, complemented
5#16840093C211yesmaximal, characteristic, complemented
6#16840092C211yesmaximal, characteristic, complemented
7#16840073C211yesmaximal, characteristic
8#16840056C212yesmaximal, complemented
9#16840050C212yesmaximal, complemented
10#16839816C211yesmaximal, characteristic, complemented
11C61×#480C211yesmaximal, characteristic
12C22×Dic122—21no—
13#14519776—21no—
14#14519776—21no—
15#14519776C2212yes—
16#14519776C2212yes—
17#14519770—21no—
18#14519768C2211yescharacteristic
19#14519764C2211yescharacteristic
20#14519758—21no—
21#14519756C2211yescharacteristic
22#14519742C2211yescharacteristic
23D4×Dic61—21no—
24D4×Dic61C2211yescharacteristic
25#14519733—21no—
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196—21no—
28C2×C4×Dic61C2211yescharacteristic
29#14519710C2212yes—
30#14519709C2212yes—
31#14519708C2212yes—
32#14519706C2212yes—
33#14519702C2212yes—
34#14519700C2212yes—
35#14519698C2212yes—
36C22⋊#92418C2211yescharacteristic
37#14519687C2212yes—
38#121×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#107×C61C2212yes—
41#102×C61C2212yes—
42C22⋊C8×C61C2211yescharacteristic
43C2×D4×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C22×Dic61—21no—
48C22×Dic61—21no—
49C22×Dic61D411yescharacteristic
50C22×Dic61D411yescharacteristic
51C2×Dic122—22no—
52C2×Dic122—22no—
53C2×Dic122—44no—
54C2×Dic122C2311yescharacteristic
55C2×C8×C61C2312yes—
56C4⋊C4×C61—21no—
57C4⋊C4×C61C2312yes—
58C4⋊C4×C61C2311yescharacteristic
59C22⋊C4×C61—21no—
60C22⋊Dic61—21no—
61C22⋊Dic61—21no—
62C22⋊Dic61—21no—
63C22⋊Dic61—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61—21no—
66C4⋊Dic61C2312yes—
67C4⋊Dic61C2311yescharacteristic
68#11758196—21no—
69#11758196—22no—
70#11758196—22no—
71#11758196—21no—
72#11758196—21no—
73C4×Dic61—21no—
74C4×Dic61D411yescharacteristic
75C4×Dic61D411yescharacteristic
76C4×Dic61C2311yescharacteristic
77C4×Dic61C2311yescharacteristic
78C2×#92418C2312yes—
79C23×C61—21no—
80C23×C61C2×D411yescharacteristic
81D4×C61—22no—
82D4×C61—42no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—42no—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2411yescharacteristic
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100Dic122—22no—
101Dic122—44no—
102Dic122—44no—
103C8×C61—22no—
104#92418—22no—
105C22×C61—21no—
106C22×C61—21no—
107C22×C61—41no—
108C22×C61—41no—
109C22×C61—41no—
110C22×C61AGL(1,ℤ/8)12yes—
111C22×C61C22×D411yescharacteristic
112C4×C61—21no—
113C4×C61—42no—
114C4×C61—41no—
115C4×C612−1+412yes—
116Dic61—21no—
117Dic61—21no—
118Dic61—21no—
119Dic61—41no—
120Dic61—42no—
121Dic61—41no—
122Dic61#13712yes—
123#3238—611nomaximal, Sylow
124C2×C61—22no—
125C2×C61—81no—
126C2×C61#53611yescharacteristic
127C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C61C2×#13711yescharacteristic
129C2×C4⋊Q8—611no—
130#529—611no—
131#501—612no—
132#489—612no—
133#483—611no—
134#483—611no—
135#480—611no—
136#480D6111yescharacteristic
137#477—612no—
138#476—612no—
139#432—611no—
140C61#323811yescharacteristic, complemented, Sylow
141C22×Q8—1221no—
142C4⋊Q8—612no—
143C4⋊Q8—612no—
144C4⋊Q8—1221no—
145C4⋊Q8—1221no—
146#126—1221no—
147#125—611no—
148#124—611no—
149#123—1221no—
150C22⋊Q8—611no—
151#121C2×D6111yescharacteristic
152C4×Q8—611no—
153C4×D4—611no—
154C4×D4—1221no—
155#117—1221no—
156C2×C4⋊C4—611no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4C2×D6111yescharacteristic
159C2×C42—611no—
160#107—612no—
161#107C2×D6112yes—
162#106—612no—
163#106—612no—
164C4⋊C8—612no—
165#103—612no—
166#103—612no—
167#102—612no—
168#102C2×D6112yes—
169C22⋊C8—611no—
170C22⋊C8C2×D6111yescharacteristic
171#97—612no—
172C2×Q8—611no—
173C2×Q8—1222no—
174C2×Q8—1222no—
175C2×Q8—2444no—
176C2×D4—21no—
177C2×D4C22×D6111yescharacteristic
178C22×C4—21no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—1221no—
182C22×C4—1221no—
183C22×C4C22×D6111yescharacteristic
184C2×C8—612no—
185C2×C8C22×D6112yes—
186C4⋊C4—21no—
187C4⋊C4—612no—
188C4⋊C4—611no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1221no—
192C4⋊C4—1221no—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C4⋊C4—1221no—
196C4⋊C4C22×D6112yes—
197C4⋊C4C22×D6111yescharacteristic
198C22⋊C4—21no—
199C22⋊C4—1221no—
200C22⋊C4—1221no—
201C22⋊C4—1221no—
202C22⋊C4—1221no—
203C42—611no—
204C42—611no—
205C42—611no—
206C42—611no—
207C42—1221no—
208C23—21no—
209C23D4×D6111yescharacteristic
210Q8—1222no—
211Q8—2444no—
212Q8—2444no—
213D4—22no—
214D4—42no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1222no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4D4×D6111yescharacteristic
231C2×C4C23×D6111yescharacteristic
232C8—22no—
233C8—1222no—
234C22—21no—
235C22—21no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22#1451980112yes—
240C22C2×D4×D6111yescharacteristic
241C4—21no—
242C4—42no—
243C4—41no—
244C4—612no—
245C4—1221no—
246C4—1221no—
247C4—1221no—
248C4—2442no—
249C4—2441no—
250C4—2441no—
251C4#1451982412yes—
252C2—22no—
253C2—81no—
254C2#1684033411yescharacteristic
255C2C2×#1451980111yescharacteristic
256C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#480C2
socleC22×C61C22×D4
hypercenter#480D61
hypocenterC61#3238
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. C2×#14519776C2semidirect
3. #16840170C2semidirect
4. #16840120C2semidirect
5. #16840093C2semidirect
6. #16840092C2semidirect
8. #16840056C2semidirect
9. #16840050C2semidirect
10. #16839816C2semidirect
140. C61#3238semidirect