Finite Group Databasebeta

← #21457757

Subgroups — #21457757

Order 7808.

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

normal subgroups only

This group has 396 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#16840486C211yesmaximal, characteristic, complemented
2#16840432C211yesmaximal, characteristic
3#16840084C212yesmaximal, complemented
4#16840044C211yesmaximal, characteristic, complemented
5#16839990C212yesmaximal, complemented
6#16839959C211yesmaximal, characteristic, complemented
7#16839925C212yesmaximal, complemented
8C4×Dic244C211yesmaximal, characteristic, complemented
9C8×D244C211yesmaximal, characteristic, complemented
10#16839755C212yesmaximal, complemented
11C61×#486C211yesmaximal, characteristic, complemented
12C2×#11758224C2212yes—
13C2×Dic244C2211yescharacteristic
14C2×#11758200C2212yes—
15C2×C8×D61C2212yes—
16#14519773—21no—
17#14519772—22no—
18#14519766—21no—
19#14519757C2212yes—
20#14519749—22no—
21#14519748C2212yes—
22Q8×Dic61—21no—
23C4×Dic122C2211yescharacteristic
24C4×Dic122C2211yescharacteristic
25C4×D244C2211yescharacteristic
26D4×Dic61—21no—
27#14519735C2212yes—
28#14519711C2211yescharacteristic
29#14519708C2212yes—
30C4⋊#92418C2211yescharacteristic
31#14519702C2211yescharacteristic
32#14519702C2211yescharacteristic
33#14519700C2212yes—
34#14519698C2212yes—
35#14519689C2212yes—
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—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—22no—
47C22×Dic61—22no—
48#11758224—24no—
49#11758224—42no—
50C2×D244D411yescharacteristic
51C2×C4×D61C2312yes—
52C2×Dic122C2311yescharacteristic
53C2×Dic122C2311yescharacteristic
54C2×C8×C61C2311yescharacteristic
55C2×C8×C61C2311yescharacteristic
56C4⋊C4×C61—21no—
57C4⋊C4×C61C2312yes—
58C42×C61C2311yescharacteristic
59C22⋊Dic61—22no—
60#11758200—42no—
61#11758198—22no—
62#11758198—22no—
63#11758198D412yes—
64C4⋊Dic61—22no—
65C4⋊Dic61D411yescharacteristic
66C4⋊Dic61C2311yescharacteristic
67C4⋊Dic61C2311yescharacteristic
68#11758196—21no—
69#11758196—21no—
70C4×Dic61—21no—
71C4×Dic61—21no—
72C4×Dic61—22no—
73C2×#92418C2312yes—
74Dic244—22no—
75C8×D61—42no—
76C23×C61—22no—
77C22×D61C2×D412yes—
78Q8×C61—42no—
79D4×C61—22no—
80D4×C61—22no—
81D4×C61—42no—
82D4×C61—81no—
83C2×C4×C61—22no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C22⋊D61—44no—
88C22⋊D61—82no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—44no—
94C2×Dic61C2×D412yes—
95D244—22no—
96C4×D61—22no—
97C4×D61—22no—
98Dic122—21no—
99Dic122—21no—
100Dic122—21no—
101Dic122#4112yes—
102C8×C61—21no—
103C8×C61—21no—
104#92418—22no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61C22×D411yescharacteristic
109C2×D61—22no—
110C2×D61—22no—
111C2×D61—22no—
112C4×C61—21no—
113C4×C61—42no—
114C4×C61#13512yes—
115C4×C61C2×#4111yescharacteristic
116C4×C61H(5,𝔽2)11yescharacteristic
117Dic61—22no—
118Dic61—22no—
119Dic61—41no—
120Dic61—41no—
121Dic61—41no—
122#3304—611nomaximal, Sylow
123C2×C61—82no—
124C2×C61#54611yescharacteristic
125C2×C61C2×#13511yescharacteristic
126C2×C61#57711yescharacteristic
127D61—42no—
128#556—611no—
129#550—611no—
130#486D6111yescharacteristic, complemented
131#482—612no—
132#475—611no—
133#465—612no—
134#460—611no—
135#452—612no—
136C4×Q16—611no—
137C8×D4—611no—
138#416—612no—
139C61#330411yescharacteristic, complemented, Sylow
140C2×#41—612no—
141C2×Q16—611no—
142C2×SD16—612no—
143C22×C8—612no—
144C4⋊Q8C2×D6111yescharacteristic
145#127—1221no—
146#127C2×D6111yescharacteristic
147#126—1222no—
148#124—1221no—
149C22⋊Q8—612no—
150#121—612no—
151#121—1222no—
152C4×Q8—611no—
153C4×Q8—611no—
154C4×Q8—1221no—
155C4×D4—611no—
156C4×D4—1221no—
157#117—612no—
158#107—611no—
159#106—612no—
160C4⋊C8—611no—
161#103—611no—
162#103—611no—
163#103—612no—
164#102—612no—
165#102C2×D6112yes—
166#102C2×D6112yes—
167C22⋊C8—612no—
168C4×C8C2×D6111yescharacteristic
169#41—1224no—
170#41—2442no—
171C2×Q8—21no—
172C2×Q8—611no—
173C2×Q8—611no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—611no—
177C2×D4—1222no—
178C2×D4—1222no—
179C2×D4C22×D6112yes—
180C22×C4—612no—
181C22×C4—1222no—
182Q16—1222no—
183SD16—2442no—
184C2×C8—612no—
185C2×C8—2442no—
186C2×C8C22×D6111yescharacteristic
187C2×C8C22×D6111yescharacteristic
188C4⋊C4—21no—
189C4⋊C4—611no—
190C4⋊C4—611no—
191C4⋊C4—611no—
192C4⋊C4—1222no—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C4⋊C4C22×D6112yes—
196C22⋊C4—612no—
197C22⋊C4—1222no—
198C22⋊C4—1222no—
199C22⋊C4—1222no—
200C42—1222no—
201C42—1221no—
202C42—1221no—
203C42C22×D6111yescharacteristic
204C23—22no—
205C23—612no—
206Q8—42no—
207Q8—612no—
208Q8—1221no—
209Q8—1221no—
210Q8—1221no—
211D4—22no—
212D4—22no—
213D4—42no—
214D4—81no—
215D4—1222no—
216D4—4882no—
217D4—2444no—
218C2×C4—22no—
219C2×C4—612no—
220C2×C4—1221no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—2444no—
227C2×C4D4×D6111yescharacteristic
228C2×C4D4×D6111yescharacteristic
229C2×C4C23×D6111yescharacteristic
230C8—21no—
231C8—21no—
232C8—1222no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—1222no—
237C22—1222no—
238C22—1222no—
239C22C2×D4×D6111yescharacteristic
240C4—21no—
241C4—42no—
242C4—1222no—
243C4—1222no—
244C4—2441no—
245C4—2441no—
246C4—2441no—
247C4#1451979612yes—
248C4#41×D6111yescharacteristic
249C4#1451982311yescharacteristic
250C2—82no—
251C2—2442no—
252C2#1684040511yescharacteristic
253C2C2×#1451979611yescharacteristic
254C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#486C2
socleC22×C61C22×D4
hypercenter#486D61
hypocenterC61#3304
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
1. #16840486C2semidirect
3. #16840084C2semidirect
4. #16840044C2semidirect
5. #16839990C2semidirect
6. #16839959C2semidirect
7. #16839925C2semidirect
8. C4×Dic244C2semidirect
9. C8×D244C2semidirect
10. #16839755C2semidirect
11. C61×#486C2semidirect
130. #486D61semidirect
139. C61#3304semidirect