Finite Group Databasebeta

← #21456839

Subgroups — #21456839

Order 7808.

490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14519774C211yesmaximal, characteristic, complemented
2#16840296C211yesmaximal, characteristic, complemented
3#16840151C212yesmaximal, complemented
4#16840127C212yesmaximal, complemented
5#16839963C212yesmaximal, complemented
6#16839958C212yesmaximal, complemented
7#16839915C212yesmaximal, complemented
8#16839898C212yesmaximal, complemented
9C61×#432C211yesmaximal, characteristic, complemented
10C22×D244—21no—
11C22×D244—21no—
12C22×D244C2212yes—
13C2×#11758190C2214yescomplemented
14C2×D488C2214yescomplemented
15#14519774—21no—
16#14519774—21no—
17#14519774C2212yes—
18#14519774C2212yes—
19#14519771—21no—
20#14519769C2211yescharacteristic, complemented
21#14519765C2211yescharacteristic, complemented
22#14519760—21no—
23#14519756C2211yescharacteristic
24#14519751C2211yescharacteristic
25C4×Dic122C2211yescharacteristic, complemented
26C4×D244C2211yescharacteristic, complemented
27C4×C22⋊D61—21no—
28#14519734—21no—
29#14519699C2214yescomplemented
30#14519699C2214yescomplemented
31C2×C42×C61C2211yescharacteristic
32C4⋊C8×C61C2212yescomplemented
33C22⋊C8×C61C2212yes—
34#97×C61C2212yescomplemented
35C23×D61—22no—
36C22×C4×C61D411yescharacteristic
37C22×C4×C61D411yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—21no—
40C2×D244—22no—
41C2×D244—22no—
42C2×D244—22no—
43C2×D244—22no—
44C2×D244—22no—
45C2×D244—44no—
46C2×D244—44no—
47C2×D244—44no—
48C2×D244C2314yes—
49C2×D244C2311yescharacteristic
50C2×C4×D61—21no—
51C2×Dic122C2311yescharacteristic
52C2×C8×C61C2314yes—
53C42×C61D411yescharacteristic
54C42×C61D411yescharacteristic
55C42×C61C2311yescharacteristic
56C42×C61C2311yescharacteristic
57C22⋊Dic61—21no—
58#11758198—21no—
59#11758198—21no—
60#11758198—21no—
61#11758198—21no—
62C4⋊Dic61C2311yescharacteristic
63C4⋊Dic61C2311yescharacteristic
64#11758196—21no—
65#11758196—21no—
66#11758196—21no—
67#11758196—21no—
68C4×Dic61—21no—
69D488—44no—
70#11758190—44no—
71C23×C61C2×D411yescharacteristic
72C22×D61—21no—
73C22×D61—24no—
74C22×D61—44no—
75C22×D61—44no—
76C22×D61—44no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2411yescharacteristic
86C22⋊D61—42no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90D244—24no—
91D244—22no—
92D244—24no—
93D244—44no—
94D244—44no—
95D244—44no—
96D244—44no—
97D244—44no—
98C4×D61—42no—
99Dic122—22no—
100C8×C61—24no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61AGL(1,ℤ/8)12yes—
104C22×C61C22×D411yescharacteristic
105C2×D61—44no—
106C2×D61—41no—
107C2×D61—41no—
108C2×D61—44no—
109C2×D61—44no—
110C2×D61—41no—
111C2×D61—88no—
112C4×C61—21no—
113C4×C61—21no—
114C4×C61—21no—
115C4×C61—21no—
116C4×C61AGL(1,ℤ/8)12yes—
117C4×C61H(5,𝔽2)12yes—
118Dic61—41no—
119Dic61—41no—
120Dic61—41no—
121#3217—611nomaximal, Sylow
122C2×C61—22no—
123C2×C61#53511yescharacteristic
124C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
125C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
126D61—81no—
127D61—84no—
128C2×#127—611no—
129#529—611no—
130#496—612no—
131#490—612no—
132#460—612no—
133#459—612no—
134#450—612no—
135#447—612no—
136#432D6111yescharacteristic, complemented
137C61#321711yescharacteristic, complemented, Sylow
138C22×D4—612no—
139C22×D4—1221no—
140C22×D4—1221no—
141C2×SD16—614no—
142C2×D8—614no—
143#127—612no—
144#127—612no—
145#127—1221no—
146#127—1221no—
147#126—1221no—
148#125—611no—
149#124—611no—
150#123—1221no—
151C22⋊Q8—611no—
152#121—611no—
153C4×Q8—611no—
154C4×D4—611no—
155C4×D4—1221no—
156#117—1221no—
157C2×C42C2×D6111yescharacteristic
158C4⋊C8C2×D6112yescomplemented
159#102—614no—
160#102—614no—
161C22⋊C8C2×D6112yes—
162#97C2×D6112yescomplemented
163C24—1222no—
164C2×Q8—611no—
165C2×D4—614no—
166C2×D4—611no—
167C2×D4—1221no—
168C2×D4—1222no—
169C2×D4—1222no—
170C2×D4—1222no—
171C2×D4—1222no—
172C2×D4—1222no—
173C2×D4—2444no—
174C2×D4—2444no—
175C2×D4—2444no—
176C22×C4—1221no—
177C22×C4D24411yescharacteristic
178C22×C4D24411yescharacteristic
179C22×C4C22×D6111yescharacteristic
180SD16—2444no—
181D8—2444no—
182C2×C8C22×D6114yes—
183C4⋊C4—611no—
184C4⋊C4—611no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C4⋊C4—1221no—
189C22⋊C4—1221no—
190C22⋊C4—1221no—
191C22⋊C4—1221no—
192C22⋊C4—1221no—
193C22⋊C4—1221no—
194C42—1221no—
195C42D24411yescharacteristic
196C42D24411yescharacteristic
197C42C22×D6111yescharacteristic
198C42C22×D6111yescharacteristic
199C23—1221no—
200C23—1224no—
201C23—2444no—
202C23—2444no—
203C23—2444no—
204C23C2×D24411yescharacteristic
205Q8—1222no—
206D4—1222no—
207D4—1224no—
208D4—1224no—
209D4—2444no—
210D4—2444no—
211D4—2444no—
212D4—2444no—
213D4—2442no—
214D4—2444no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—2442no—
222C2×C4C2×D24411yescharacteristic
223C2×C4C2×D24411yescharacteristic
224C2×C4C2×D24411yescharacteristic
225C2×C4C2×D24411yescharacteristic
226C2×C4C2×D24411yescharacteristic
227C2×C4C23×D6111yescharacteristic
228C8—24no—
229C22—21no—
230C22—21no—
231C22—4888no—
232C22—2441no—
233C22—2444no—
234C22—2444no—
235C22—2441no—
236C22—2444no—
237C22—2441no—
238C22#1451980512yes—
239C22C22×D24411yescharacteristic
240C4—21no—
241C4—21no—
242C4—21no—
243C4—21no—
244C4—2441no—
245C4—2441no—
246C4—2441no—
247C4#1451980512yes—
248C4#1451982312yes—
249C2—22no—
250C2—4884no—
251C2—4881no—
252C2#1684033111yescharacteristic
253C2C2×#1451980511yescharacteristic
254C2C2×#1451980511yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#432C2
socleC22×C61C22×D4
hypercenter#432D61
hypocenterC61#3217
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. C2×#14519774C2semidirect
2. #16840296C2semidirect
3. #16840151C2semidirect
4. #16840127C2semidirect
5. #16839963C2semidirect
6. #16839958C2semidirect
7. #16839915C2semidirect
8. #16839898C2semidirect
9. C61×#432C2semidirect
13. C2×#11758190C22semidirect
14. C2×D488C22semidirect
20. #14519769C22semidirect
21. #14519765C22semidirect
25. C4×Dic122C22semidirect
26. C4×D244C22semidirect
29. #14519699C22semidirect
30. #14519699C22semidirect
32. C4⋊C8×C61C22semidirect
34. #97×C61C22semidirect
136. #432D61semidirect
137. C61#3217semidirect
158. C4⋊C8C2×D61semidirect
162. #97C2×D61semidirect