Finite Group Databasebeta

← #21458520

Subgroups — #21458520

Order 7808.

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

normal subgroups only

This group has 348 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
1#16840498C211yesmaximal, characteristic
2#16840487C211yesmaximal, characteristic, complemented
3#16840115C212yesmaximal, complemented
4#16840060C212yesmaximal, complemented
5#16840044C211yesmaximal, characteristic, complemented
6#16839983C212yesmaximal, complemented
7#16839959C211yesmaximal, characteristic
8C8×Dic122C211yesmaximal, characteristic, complemented
9C4×Dic244C211yesmaximal, characteristic, complemented
10#16839853C212yesmaximal, complemented
11C61×#486C211yesmaximal, characteristic
12C2×Dic244C2211yescharacteristic
13C2×#11758200C2212yes—
14#14519775—21no—
15#14519768C2212yes—
16#14519767—22no—
17#14519764—21no—
18#14519764C2212yes—
19#14519758—22no—
20Q8×Dic61—21no—
21C4×Dic122C2211yescharacteristic
22C4×Dic122C2211yescharacteristic
23C4×Dic122C2211yescharacteristic
24#14519742C2212yes—
25D4×Dic61—21no—
26D4×Dic61C2212yes—
27#14519711C2211yescharacteristic
28#14519708C2212yes—
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519702C2211yescharacteristic
33#14519700C2212yes—
34#14519698C2212yes—
35C8×Dic61C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37#127×C61C2211yescharacteristic
38#102×C61C2212yes—
39#102×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61C2312yes—
45C22×Dic61—22no—
46C2×Dic122D411yescharacteristic
47C2×Dic122C2311yescharacteristic
48C2×Dic122C2311yescharacteristic
49C2×C8×C61C2311yescharacteristic
50C2×C8×C61C2311yescharacteristic
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2312yes—
53C42×C61C2311yescharacteristic
54C22⋊Dic61—22no—
55C22⋊Dic61—22no—
56C22⋊Dic61—22no—
57#11758200—24no—
58C4⋊Dic61—22no—
59C4⋊Dic61D411yescharacteristic
60C4⋊Dic61C2311yescharacteristic
61C4⋊Dic61C2311yescharacteristic
62#11758196—21no—
63#11758196—21no—
64#11758196—22no—
65#11758196—22no—
66#11758196D412yes—
67C4×Dic61—21no—
68C4×Dic61—21no—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2312yes—
72Dic244—22no—
73C23×C61—22no—
74Q8×C61—42no—
75D4×C61—22no—
76D4×C61—22no—
77D4×C61—42no—
78D4×C61—81no—
79C2×C4×C61—22no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—82no—
88C2×Dic61C2×D412yes—
89C2×Dic61C2×D412yes—
90Dic122—22no—
91Dic122—21no—
92Dic122—21no—
93Dic122—21no—
94Dic122#4112yes—
95C8×C61—21no—
96C8×C61—21no—
97#92418—22no—
98C22×C61—42no—
99C22×C61—42no—
100C22×C61—42no—
101C22×C61C22×D411yescharacteristic
102C4×C61—21no—
103C4×C61—42no—
104C4×C61#13512yes—
105C4×C61C2×#4111yescharacteristic
106C4×C612−1+411yescharacteristic
107Dic61—22no—
108Dic61—22no—
109Dic61—22no—
110Dic61—41no—
111Dic61—41no—
112Dic61—41no—
113#3365—611nomaximal, Sylow
114C2×C61—82no—
115C2×C61#54811yescharacteristic
116C2×C61C2×#13511yescharacteristic
117C2×C61#57711yescharacteristic
118#559—611no—
119#557—611no—
120#488—612no—
121#486D6111yescharacteristic
122#478—612no—
123#475—611no—
124#464—612no—
125#460—611no—
126C8×Q8—611no—
127C4×Q16—611no—
128C4×SD16—612no—
129C61#336511yescharacteristic, complemented, Sylow
130C2×Q16—611no—
131C2×SD16—612no—
132C4⋊Q8—1221no—
133C4⋊Q8C2×D6111yescharacteristic
134#127C2×D6111yescharacteristic
135#125—612no—
136#125—1222no—
137#124—612no—
138#124—1221no—
139#123—1222no—
140C4×Q8—611no—
141C4×Q8—612no—
142C4×Q8—611no—
143C4×Q8—611no—
144C4×Q8—1221no—
145C4×D4—612no—
146C4×D4—1221no—
147#107—611no—
148#106—612no—
149C4⋊C8—612no—
150C4⋊C8—611no—
151#103—611no—
152#103—611no—
153#103—612no—
154#102—612no—
155#102C2×D6112yes—
156#102C2×D6112yes—
157C4×C8—612no—
158C4×C8C2×D6111yescharacteristic
159C2×Q8—21no—
160C2×Q8—611no—
161C2×Q8—611no—
162C2×Q8—611no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4C22×D6112yes—
166C22×C4—1222no—
167Q16—1222no—
168SD16—1224no—
169C2×C8—612no—
170C2×C8C22×D6111yescharacteristic
171C2×C8C22×D6111yescharacteristic
172C4⋊C4—21no—
173C4⋊C4—612no—
174C4⋊C4—611no—
175C4⋊C4—611no—
176C4⋊C4—611no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1221no—
181C4⋊C4—1221no—
182C4⋊C4C22×D6112yes—
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C42—612no—
187C42—1222no—
188C42—1221no—
189C42—1221no—
190C42C22×D6111yescharacteristic
191C23—22no—
192Q8—42no—
193Q8—612no—
194Q8—1221no—
195Q8—1222no—
196Q8—1221no—
197Q8—1221no—
198D4—22no—
199D4—22no—
200D4—42no—
201D4—81no—
202C2×C4—22no—
203C2×C4—612no—
204C2×C4—612no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—4882no—
210C2×C4D4×D6111yescharacteristic
211C2×C4D4×D6111yescharacteristic
212C2×C4C23×D6111yescharacteristic
213C8—21no—
214C8—21no—
215C8—1222no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22C2×D4×D6111yescharacteristic
220C4—21no—
221C4—42no—
222C4—1222no—
223C4—1222no—
224C4—1222no—
225C4—2441no—
226C4—2441no—
227C4—2441no—
228C4#1451979612yes—
229C4#41×D6111yescharacteristic
230C4#1451982411yescharacteristic
231C2—82no—
232C2#1684042011yescharacteristic
233C2C2×#1451979611yescharacteristic
234C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3365
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #16840487C2semidirect
3. #16840115C2semidirect
4. #16840060C2semidirect
5. #16840044C2semidirect
6. #16839983C2semidirect
8. C8×Dic122C2semidirect
9. C4×Dic244C2semidirect
10. #16839853C2semidirect
129. C61#3365semidirect