Finite Group Databasebeta

← #21458044

Subgroups — #21458044

Order 7808.

448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 123 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
1D4×D244C211yesmaximal, characteristic
2#16840110C211yesmaximal, characteristic, complemented
3#16840086C212yesmaximal, complemented
4#16840039C211yesmaximal, characteristic, complemented
5#16840010C212yesmaximal, complemented
6#16839962C211yesmaximal, characteristic, complemented
7#16839912C212yesmaximal, complemented
8C4×#11758201C211yesmaximal, characteristic, complemented
9#16839840C211yesmaximal, characteristic, complemented
10#16839766C212yesmaximal, complemented
11C61×#556C211yesmaximal, characteristic, complemented
12C22×D244C2212yes—
13C2×D4×D61—21no—
14C2×#11758201C2211yescharacteristic
15C2×#11758201C2212yescomplemented
16C2×#11758194C2212yescomplemented
17#14519774C2211yescharacteristic
18#14519752—21no—
19#14519751C2212yes—
20#14519747—22no—
21C4×D244C2211yescharacteristic
22#14519710C2212yescomplemented
23#14519708C2211yescharacteristic, complemented
24C4⋊#92418C2211yescharacteristic, complemented
25#14519701C2211yescharacteristic, complemented
26#14519697C2211yescharacteristic
27#14519697C2212yes—
28#14519697C2212yescomplemented
29#14519697C2212yescomplemented
30#14519697C2212yescomplemented
31C22⋊#92418C2212yescomplemented
32C4×#92418C2211yescharacteristic, complemented
33C4⋊Q8×C61C2211yescharacteristic, complemented
34#126×C61—22no—
35#124×C61—21no—
36C22⋊Q8×C61C2212yescomplemented
37C4×Q8×C61—21no—
38C4×Q8×C61C2211yescharacteristic, complemented
39C4×D4×C61C2211yescharacteristic
40#117×C61C2212yescomplemented
41C23×D61—22no—
42C2×Q8×C61—21no—
43C2×Q8×C61C2311yescharacteristic
44C2×D4×C61D411yescharacteristic
45C22×C4×C61C2312yes—
46C2×C22⋊D61—22no—
47D4×D61—44no—
48C2×D244—24no—
49C2×D244—21no—
50C2×D244—22no—
51C2×D244—21no—
52C2×D244—42no—
53C2×D244C2312yes—
54C2×D244C2311yescharacteristic
55C2×C4×D61—21no—
56C4⋊C4×C61—22no—
57C4⋊C4×C61—21no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61D411yescharacteristic
60C4⋊C4×C61C2311yescharacteristic
61C4⋊C4×C61C2312yes—
62C22⋊C4×C61—22no—
63C22⋊C4×C61—22no—
64C22⋊C4×C61D412yes—
65C42×C61—22no—
66C42×C61—21no—
67C42×C61C2311yescharacteristic
68#11758201—22no—
69#11758201—42no—
70#11758198—21no—
71#11758198—22no—
72C4⋊Dic61C2311yescharacteristic
73#11758194—42no—
74C2×#92418C2311yescharacteristic
75C2×#92418C2311yescharacteristic
76C2×#92418C2312yes—
77C23×C61C2×D412yes—
78C22×D61—21no—
79C22×D61—22no—
80C22×D61—44no—
81C22×D61—44no—
82C22×D61—82no—
83Q8×C61—21no—
84Q8×C61—21no—
85Q8×C61—42no—
86D4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61C2×D412yes—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—44no—
97C2×Dic61—21no—
98D244—22no—
99D244—21no—
100D244—22no—
101D244—44no—
102D244—42no—
103D244—81no—
104D244#4112yes—
105C4×D61—42no—
106#92418—21no—
107#92418—21no—
108#92418—22no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—22no—
112C22×C61C22×D411yescharacteristic
113C2×D61—22no—
114C2×D61—41no—
115C2×D61—41no—
116C2×D61—42no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—88no—
120C4×C61—22no—
121C4×C61—21no—
122C4×C61—41no—
123C4×C61—42no—
124C4×C61—41no—
125C4×C61AGL(1,ℤ/8)12yes—
126C4×C61C2×#4111yescharacteristic
127C4×C61H(5,𝔽2)11yescharacteristic
128Dic61—41no—
129#3324—611nomaximal, Sylow
130C2×C61—42no—
131C2×C61#54611yescharacteristic
132C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
133C2×C61#57711yescharacteristic
134D61—42no—
135D61—82no—
136#556D6111yescharacteristic, complemented
137D42—611no—
138#486—611no—
139#482—612no—
140#474—611no—
141#468—612no—
142#460—611no—
143#450—612no—
144C4×SD16—611no—
145#436—611no—
146#418—612no—
147C61#332411yescharacteristic, complemented, Sylow
148C22×D4—612no—
149C22×D4—1221no—
150C2×SD16—611no—
151C2×SD16—612no—
152C2×M16—612no—
153C4⋊Q8C2×D6111yescharacteristic, complemented
154#127—611no—
155#126—22no—
156#124—21no—
157C22⋊Q8C2×D6112yescomplemented
158#121—612no—
159#121—1221no—
160#120—1222no—
161C4×Q8—21no—
162C4×Q8C2×D6111yescharacteristic, complemented
163C4×D4—611no—
164C4×D4C2×D6111yescharacteristic
165#117C2×D6112yescomplemented
166#107—612no—
167#106—611no—
168C4⋊C8—611no—
169#103—611no—
170#102—611no—
171#102—612no—
172#102—612no—
173#102—612no—
174#102—612no—
175C22⋊C8—612no—
176C4×C8—611no—
177C24—1222no—
178C2×Q8—21no—
179C2×Q8C22×D6111yescharacteristic
180C2×D4—611no—
181C2×D4—612no—
182C2×D4—1224no—
183C2×D4—1222no—
184C2×D4—1221no—
185C2×D4—1222no—
186C2×D4—1221no—
187C2×D4—2442no—
188C2×D4—2444no—
189C2×D4C22⋊D6111yescharacteristic
190C22×C4—1221no—
191C22×C4C22×D6112yes—
192SD16—1222no—
193SD16—2442no—
194M16—2442no—
195C2×C8—611no—
196C2×C8—611no—
197C2×C8—612no—
198C4⋊C4—22no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—611no—
202C4⋊C4C22⋊D6111yescharacteristic
203C4⋊C4C22×D6111yescharacteristic
204C4⋊C4C22×D6112yes—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—1221no—
208C22⋊C4—1222no—
209C22⋊C4C22⋊D6112yes—
210C42—22no—
211C42—21no—
212C42C22×D6111yescharacteristic
213C23—1221no—
214C23—1222no—
215C23—4882no—
216C23—2444no—
217C23—2444no—
218C23C2×C22⋊D6112yes—
219Q8—21no—
220Q8—21no—
221Q8—42no—
222D4—22no—
223D4—612no—
224D4—1222no—
225D4—1221no—
226D4—1222no—
227D4—4881no—
228D4—2444no—
229D4—2444no—
230D4—2442no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—1221no—
237C2×C4—2442no—
238C2×C4C2×C22⋊D6112yes—
239C2×C4C2×C22⋊D6111yescharacteristic
240C2×C4C2×C22⋊D6111yescharacteristic
241C2×C4C23×D6111yescharacteristic
242C8—1221no—
243C8—1221no—
244C8—1222no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—1222no—
249C22—4888no—
250C22—2442no—
251C22—2442no—
252C22—2442no—
253C22—2441no—
254C22—2441no—
255C22C22×C22⋊D6111yescharacteristic
256C4—21no—
257C4—22no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—2441no—
262C4#1451980212yes—
263C4#41×D6111yescharacteristic
264C4#1451982311yescharacteristic
265C2—42no—
266C2—4882no—
267C2—2442no—
268C2#1684040011yescharacteristic
269C2C2×#1451980211yescharacteristic
270C2#1684057011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#556C2
socleC22×C61C22×D4
hypercenter#556D61
hypocenterC61#3324
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #16840110C2semidirect
3. #16840086C2semidirect
4. #16840039C2semidirect
5. #16840010C2semidirect
6. #16839962C2semidirect
7. #16839912C2semidirect
8. C4×#11758201C2semidirect
9. #16839840C2semidirect
10. #16839766C2semidirect
11. C61×#556C2semidirect
15. C2×#11758201C22semidirect
16. C2×#11758194C22semidirect
22. #14519710C22semidirect
23. #14519708C22semidirect
24. C4⋊#92418C22semidirect
25. #14519701C22semidirect
28. #14519697C22semidirect
29. #14519697C22semidirect
30. #14519697C22semidirect
31. C22⋊#92418C22semidirect
32. C4×#92418C22semidirect
33. C4⋊Q8×C61C22semidirect
36. C22⋊Q8×C61C22semidirect
38. C4×Q8×C61C22semidirect
40. #117×C61C22semidirect
136. #556D61semidirect
147. C61#3324semidirect
153. C4⋊Q8C2×D61semidirect
157. C22⋊Q8C2×D61semidirect
162. C4×Q8C2×D61semidirect
165. #117C2×D61semidirect