Finite Group Databasebeta

← #21456834

Subgroups — #21456834

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#16840152C212yesmaximal, complemented
3#16840128C212yesmaximal, complemented
4#16839962C212yesmaximal, complemented
5#16839957C212yesmaximal, complemented
6#16839912C212yesmaximal, complemented
7#16839895C212yesmaximal, complemented
8#16839819C211yesmaximal, characteristic, complemented
9C61×#529C211yesmaximal, characteristic, complemented
10C22×D244—21no—
11C22×D244—21no—
12C22×D244C2212yes—
13C2×#11758201C2214yescomplemented
14C2×#11758199C2214yescomplemented
15#14519774—21no—
16#14519774—21no—
17#14519774C2212yes—
18#14519774C2212yes—
19C4⋊#92418C2212yescomplemented
20#14519697C2214yescomplemented
21#14519697C2214yescomplemented
22C22⋊#92418C2212yes—
23#14519688C2212yescomplemented
24#126×C61—21no—
25#125×C61C2211yescharacteristic, complemented
26#124×C61C2211yescharacteristic, complemented
27#123×C61—21no—
28C22⋊Q8×C61C2211yescharacteristic
29#121×C61C2211yescharacteristic
30C4×Q8×C61C2211yescharacteristic, complemented
31C4×D4×C61—21no—
32C4×D4×C61C2211yescharacteristic, complemented
33#117×C61—21no—
34C2×C42×C61C2211yescharacteristic
35C23×D61—22no—
36C2×Q8×C61C2311yescharacteristic
37C2×D4×C61—21no—
38C2×D4×C61C2311yescharacteristic
39C22×C4×C61—21no—
40C22×C4×C61D411yescharacteristic
41C22×C4×C61D411yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C2×D244—22no—
44C2×D244—22no—
45C2×D244—22no—
46C2×D244—22no—
47C2×D244—22no—
48C2×D244—44no—
49C2×D244—44no—
50C2×D244—44no—
51C2×D244C2314yes—
52C4⋊C4×C61—21no—
53C4⋊C4×C61—21no—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56C4⋊C4×C61C2311yescharacteristic
57C4⋊C4×C61C2311yescharacteristic
58C22⋊C4×C61—21no—
59C22⋊C4×C61—21no—
60C22⋊C4×C61—21no—
61C22⋊C4×C61—21no—
62C22⋊C4×C61—21no—
63C42×C61—21no—
64C42×C61D411yescharacteristic
65C42×C61D411yescharacteristic
66C42×C61C2311yescharacteristic
67C42×C61C2311yescharacteristic
68#11758201—44no—
69#11758199—44no—
70C2×#92418C2314yes—
71C23×C61—21no—
72C23×C61C2×D411yescharacteristic
73C22×D61—24no—
74C22×D61—44no—
75C22×D61—44no—
76C22×D61—44no—
77Q8×C61—22no—
78D4×C61—22no—
79D4×C61—42no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—42no—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93D244—24no—
94D244—24no—
95D244—44no—
96D244—44no—
97D244—44no—
98D244—44no—
99D244—44no—
100#92418—24no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61AGL(1,ℤ/8)12yes—
107C22×C61C22×D411yescharacteristic
108C2×D61—44no—
109C2×D61—44no—
110C2×D61—44no—
111C2×D61—88no—
112C4×C61—21no—
113C4×C61—21no—
114C4×C61—21no—
115C4×C61—21no—
116C4×C61—41no—
117C4×C61—41no—
118C4×C61—41no—
119C4×C61AGL(1,ℤ/8)12yes—
120C4×C61H(5,𝔽2)12yes—
121#3217—611nomaximal, Sylow
122C2×C61—22no—
123C2×C61—81no—
124C2×C61#53511yescharacteristic
125C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
126C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
127D61—84no—
128C2×#127—611no—
129#529D6111yescharacteristic, complemented
130#496—612no—
131#490—612no—
132#460—612no—
133#459—612no—
134#450—612no—
135#447—612no—
136#432—611no—
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—21no—
148#125C2×D6111yescharacteristic, complemented
149#124C2×D6111yescharacteristic, complemented
150#123—21no—
151C22⋊Q8C2×D6111yescharacteristic
152#121C2×D6111yescharacteristic
153C4×Q8C2×D6111yescharacteristic, complemented
154C4×D4—21no—
155C4×D4C2×D6111yescharacteristic, complemented
156#117—21no—
157C2×C42C2×D6111yescharacteristic
158C4⋊C8—612no—
159#102—614no—
160#102—614no—
161C22⋊C8—612no—
162#97—612no—
163C24—1222no—
164C2×Q8C22×D6111yescharacteristic
165C2×D4—21no—
166C2×D4—614no—
167C2×D4—1222no—
168C2×D4—1222no—
169C2×D4—1222no—
170C2×D4—1222no—
171C2×D4—1222no—
172C2×D4—2444no—
173C2×D4—2444no—
174C2×D4—2444no—
175C2×D4C22×D6111yescharacteristic
176C22×C4—21no—
177C22×C4C22⋊D6111yescharacteristic
178C22×C4C22⋊D6111yescharacteristic
179C22×C4C22×D6111yescharacteristic
180SD16—2444no—
181D8—2444no—
182C2×C8—614no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4C22×D6111yescharacteristic
188C4⋊C4C22×D6111yescharacteristic
189C22⋊C4—21no—
190C22⋊C4—21no—
191C22⋊C4—21no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C42—21no—
195C42C22⋊D6111yescharacteristic
196C42C22⋊D6111yescharacteristic
197C42C22×D6111yescharacteristic
198C42C22×D6111yescharacteristic
199C23—21no—
200C23—1224no—
201C23—2444no—
202C23—2444no—
203C23—2444no—
204C23C2×C22⋊D6111yescharacteristic
205Q8—22no—
206D4—22no—
207D4—42no—
208D4—1224no—
209D4—1224no—
210D4—2444no—
211D4—2444no—
212D4—2444no—
213D4—2444no—
214D4—2444no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4C2×C22⋊D6111yescharacteristic
223C2×C4C2×C22⋊D6111yescharacteristic
224C2×C4C2×C22⋊D6111yescharacteristic
225C2×C4C2×C22⋊D6111yescharacteristic
226C2×C4C2×C22⋊D6111yescharacteristic
227C2×C4C23×D6111yescharacteristic
228C8—1224no—
229C22—21no—
230C22—21no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—4888no—
235C22—2444no—
236C22—2444no—
237C22—2444no—
238C22#1451980212yes—
239C22C22×C22⋊D6111yescharacteristic
240C4—21no—
241C4—21no—
242C4—21no—
243C4—21no—
244C4—41no—
245C4—41no—
246C4—41no—
247C4#1451980212yes—
248C4#1451982312yes—
249C2—22no—
250C2—81no—
251C2—4884no—
252C2#1684032611yescharacteristic
253C2C2×#1451980211yescharacteristic
254C2C2×#1451980211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#529C2
socleC22×C61C22×D4
hypercenter#529D61
hypocenterC61#3217
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C2×#14519774C2semidirect
2. #16840152C2semidirect
3. #16840128C2semidirect
4. #16839962C2semidirect
5. #16839957C2semidirect
6. #16839912C2semidirect
7. #16839895C2semidirect
8. #16839819C2semidirect
9. C61×#529C2semidirect
13. C2×#11758201C22semidirect
14. C2×#11758199C22semidirect
19. C4⋊#92418C22semidirect
20. #14519697C22semidirect
21. #14519697C22semidirect
23. #14519688C22semidirect
25. #125×C61C22semidirect
26. #124×C61C22semidirect
30. C4×Q8×C61C22semidirect
32. C4×D4×C61C22semidirect
129. #529D61semidirect
137. C61#3217semidirect
148. #125C2×D61semidirect
149. #124C2×D61semidirect
153. C4×Q8C2×D61semidirect
155. C4×D4C2×D61semidirect