Finite Group Databasebeta

← #21457746

Subgroups — #21457746

Order 7808.

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

normal subgroups only

This group has 398 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#16840478C211yesmaximal, characteristic, complemented
2#16840415C211yesmaximal, characteristic, complemented
3#16840102C212yesmaximal, complemented
4#16840049C211yesmaximal, characteristic, complemented
5#16839994C212yesmaximal, complemented
6#16839964C211yesmaximal, characteristic, complemented
7#16839910C212yesmaximal, complemented
8C4×D488C211yesmaximal, characteristic, complemented
9C8×D244C211yesmaximal, characteristic, complemented
10#16839757C212yesmaximal, complemented
11C61×#487C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yes—
13C2×#11758201C2212yes—
14C2×D488C2211yescharacteristic
15C2×C8×D61C2212yes—
16#14519766—22no—
17#14519762—22no—
18#14519753C2212yes—
19#14519752—21no—
20#14519752—21no—
21#14519752C2212yes—
22C4×D244C2211yescharacteristic
23C4×D244C2211yescharacteristic
24C4×D244C2211yescharacteristic
25#14519735—21no—
26#14519735C2212yes—
27C4⋊C4×D61—21no—
28#14519711C2211yescharacteristic
29#14519708C2212yes—
30C4⋊#92418C2211yescharacteristic
31#14519701C2212yes—
32#14519699C2211yescharacteristic
33#14519699C2211yescharacteristic
34#14519697C2212yes—
35#14519689C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37C4⋊Q8×C61C2211yescharacteristic
38#103×C61C2212yes—
39#103×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×Q8×C61C2312yes—
43#11758226—24no—
44#11758226—42no—
45C2×D244—22no—
46C2×D244—22no—
47C2×D244D411yescharacteristic
48C2×D244C2311yescharacteristic
49C2×D244C2311yescharacteristic
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—22no—
53C2×C4×D61C2312yes—
54C2×C8×C61C2311yescharacteristic
55C2×C8×C61C2311yescharacteristic
56C4⋊C4×C61—21no—
57C4⋊C4×C61—21no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61C2312yes—
60C42×C61C2311yescharacteristic
61#11758201—42no—
62#11758198—22no—
63#11758198—22no—
64#11758198—21no—
65#11758198—21no—
66#11758198—22no—
67#11758198D412yes—
68C4⋊Dic61D411yescharacteristic
69C4⋊Dic61C2311yescharacteristic
70C4⋊Dic61C2311yescharacteristic
71#11758196—22no—
72C4×Dic61—22no—
73C2×#92418C2312yes—
74D488—22no—
75C8×D61—42no—
76C22×D61—21no—
77C22×D61—21no—
78C22×D61C2×D412yes—
79Q8×C61—22no—
80Q8×C61—22no—
81Q8×C61—81no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2411yescharacteristic
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61C2×D412yes—
90D244—22no—
91D244—21no—
92D244—21no—
93D244—21no—
94D244—44no—
95D244—82no—
96D244#4112yes—
97C4×D61—22no—
98C4×D61—22no—
99C4×D61—44no—
100C4×D61—42no—
101C4×D61—42no—
102C8×C61—21no—
103C8×C61—21no—
104#92418—22no—
105C22×C61C22×D411yescharacteristic
106C2×D61—22no—
107C2×D61—22no—
108C2×D61—22no—
109C2×D61—22no—
110C2×D61—41no—
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—41no—
115C4×C61—21no—
116C4×C61—42no—
117C4×C61—42no—
118C4×C61#13512yes—
119C4×C61C2×#4111yescharacteristic
120C4×C61H(5,𝔽2)11yescharacteristic
121Dic61—22no—
122Dic61—41no—
123Dic61—41no—
124#3303—611nomaximal, Sylow
125C2×C61#54611yescharacteristic
126C2×C61C2×#13511yescharacteristic
127C2×C61#57711yescharacteristic
128D61—42no—
129D61—42no—
130D61—81no—
131#555—611no—
132#547—611no—
133#487D6111yescharacteristic, complemented
134#485—612no—
135#476—611no—
136#465—612no—
137#461—611no—
138#449—612no—
139C4×D8—611no—
140C8×D4—611no—
141#416—612no—
142C61#330311yescharacteristic, complemented, Sylow
143C2×#41—612no—
144C2×SD16—612no—
145C2×D8—611no—
146C22×C8—612no—
147C4⋊Q8C2×D6111yescharacteristic
148C4⋊Q8C2×D6111yescharacteristic
149#124—1222no—
150#123—1222no—
151C22⋊Q8—612no—
152#121—612no—
153#121—1221no—
154#121—1221no—
155C4×D4—611no—
156C4×D4—611no—
157C4×D4—611no—
158#117—612no—
159#117—1221no—
160C2×C4⋊C4—1221no—
161#107—611no—
162#106—612no—
163C4⋊C8—611no—
164#103—612no—
165#103C2×D6112yes—
166#103C2×D6112yes—
167#102—611no—
168#102—611no—
169#102—612no—
170C22⋊C8—612no—
171C4×C8C2×D6111yescharacteristic
172#41—1224no—
173#41—2442no—
174C2×Q8—21no—
175C2×Q8C22×D6112yes—
176C2×D4—611no—
177C2×D4—611no—
178C2×D4—611no—
179C2×D4—1222no—
180C2×D4—1222no—
181C22×C4—612no—
182C22×C4—1222no—
183C22×C4—1221no—
184C22×C4—1221no—
185SD16—2442no—
186D8—1222no—
187C2×C8—612no—
188C2×C8—2442no—
189C2×C8C22×D6111yescharacteristic
190C2×C8C22×D6111yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—611no—
195C4⋊C4—611no—
196C4⋊C4—611no—
197C4⋊C4—1222no—
198C4⋊C4C22×D6112yes—
199C22⋊C4—612no—
200C22⋊C4—1222no—
201C22⋊C4—1222no—
202C22⋊C4—1222no—
203C22⋊C4—1221no—
204C22⋊C4—1221no—
205C42—1222no—
206C42C22×D6111yescharacteristic
207C23—612no—
208C23—1221no—
209C23—1221no—
210Q8—22no—
211Q8—22no—
212Q8—81no—
213D4—612no—
214D4—1221no—
215D4—1221no—
216D4—1221no—
217D4—1222no—
218D4—4882no—
219D4—2444no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—612no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—2444no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4D4×D6111yescharacteristic
231C2×C4D4×D6111yescharacteristic
232C2×C4C23×D6111yescharacteristic
233C8—21no—
234C8—21no—
235C8—1222no—
236C22—1222no—
237C22—1222no—
238C22—1222no—
239C22—1222no—
240C22—2441no—
241C22—2441no—
242C22—2441no—
243C22—2441no—
244C22—2441no—
245C22C2×D4×D6111yescharacteristic
246C4—21no—
247C4—42no—
248C4—42no—
249C4—1222no—
250C4—2441no—
251C4—2441no—
252C4#1451980012yes—
253C4#41×D6111yescharacteristic
254C4#1451982311yescharacteristic
255C2—4881no—
256C2—2442no—
257C2—2442no—
258C2#1684040511yescharacteristic
259C2C2×#1451980011yescharacteristic
260C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#487C2
socleC22×C61C22×D4
hypercenter#487D61
hypocenterC61#3303
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #16840478C2semidirect
2. #16840415C2semidirect
3. #16840102C2semidirect
4. #16840049C2semidirect
5. #16839994C2semidirect
6. #16839964C2semidirect
7. #16839910C2semidirect
8. C4×D488C2semidirect
9. C8×D244C2semidirect
10. #16839757C2semidirect
11. C61×#487C2semidirect
133. #487D61semidirect
142. C61#3303semidirect