Finite Group Databasebeta

← #21456869

Subgroups — #21456869

Order 7808.

420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840367C211yesmaximal, characteristic, complemented
2#16840152C211yesmaximal, characteristic, complemented
3#16840138C211yesmaximal, characteristic, complemented
4#16840126C211yesmaximal, characteristic, complemented
5#16840116C211yesmaximal, characteristic, complemented
6#16839974C212yesmaximal, complemented
7#16839954C212yesmaximal, complemented
8#16839907C212yesmaximal, complemented
9#16839896C212yesmaximal, complemented
10#16839823C211yesmaximal, characteristic, complemented
11C61×#535C211yesmaximal, characteristic, complemented
12C2×#11758201C2212yescomplemented
13C2×#11758199C2212yes—
14C2×#11758199C2212yes—
15C2×#11758199C2212yescomplemented
16#14519774C2211yescharacteristic, complemented
17#14519769C2211yescharacteristic, complemented
18#14519762—22no—
19#14519751C2212yes—
20#14519750—22no—
21C4×D244C2212yescomplemented
22C4⋊#92418C2212yescomplemented
23#14519701C2212yescomplemented
24#14519698C2212yes—
25#14519698C2212yes—
26#14519698C2212yescomplemented
27C22⋊#92418C2212yes—
28#14519688C2211yescharacteristic, complemented
29C4×#92418C2211yescharacteristic, complemented
30C2×#41×C61C2211yescharacteristic
31C22×D4×C61C2211yescharacteristic
32#127×C61C2211yescharacteristic
33#127×C61C2211yescharacteristic
34#124×C61C2211yescharacteristic
35#124×C61C2211yescharacteristic
36#121×C61—22no—
37#120×C61—22no—
38#117×C61C2211yescharacteristic
39C24×C61—21no—
40#41×C61—42no—
41C2×Q8×C61C2311yescharacteristic
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61—22no—
45C2×D4×C61—22no—
46C2×D4×C61—42no—
47C2×D4×C61C2311yescharacteristic
48C2×D4×C61C2311yescharacteristic
49C2×D4×C61C2311yescharacteristic
50C22×C4×C61—21no—
51C22×C4×C61C2311yescharacteristic
52C2×C22⋊D61—22no—
53C2×D244—22no—
54C2×D244C2312yes—
55C2×C4×D61—22no—
56C4⋊C4×C61D412yes—
57C22⋊C4×C61—22no—
58C22⋊C4×C61—22no—
59C22⋊C4×C61D412yes—
60C42×C61C2311yescharacteristic
61C42×C61C2311yescharacteristic
62#11758201—42no—
63#11758199—42no—
64#11758199—42no—
65#11758199—42no—
66#11758198—22no—
67#11758198—22no—
68C4⋊Dic61C2312yes—
69#11758196—22no—
70C2×#92418C2312yes—
71C2×#92418C2312yes—
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61—42no—
76C23×C61—82no—
77C23×C61C2×D411yescharacteristic
78C22×D61—22no—
79Q8×C61—22no—
80D4×C61—22no—
81D4×C61—22no—
82D4×C61—22no—
83D4×C61—42no—
84D4×C61—42no—
85D4×C61—82no—
86D4×C61—82no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—42no—
90C2×C4×C61C2×D412yes—
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D412yes—
93C2×C4×C61C2411yescharacteristic
94C22⋊D61—82no—
95C2×Dic61—22no—
96D244—22no—
97D244—22no—
98D244—82no—
99C4×D61—82no—
100#92418—22no—
101#92418—22no—
102C22×C61—21no—
103C22×C61—22no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61—84no—
111C22×C61C22×D411yescharacteristic
112C2×D61—42no—
113C2×D61—42no—
114C2×D61—42no—
115C4×C61—21no—
116C4×C61—22no—
117C4×C61—22no—
118C4×C61—41no—
119C4×C61H(5,𝔽2)12yes—
120Dic61—42no—
121#3220—611nomaximal, Sylow
122C2×C61—41no—
123C2×C61—81no—
124C2×C61—81no—
125C2×C61—81no—
126C2×C61#53511yescharacteristic
127C2×C61#57612yes—
128D61—82no—
129#540—611no—
130#535D6111yescharacteristic, complemented
131#496—611no—
132#493—611no—
133#490—611no—
134#488—611no—
135#463—612no—
136#459—612no—
137#449—612no—
138#447—612no—
139#433—611no—
140C61#322011yescharacteristic, complemented, Sylow
141C2×#41C2×D6111yescharacteristic
142C22×D4C2×D6111yescharacteristic
143C2×SD16—612no—
144C2×D8—612no—
145C2×D8—612no—
146C2×D8—612no—
147#127—611no—
148#127C2×D6111yescharacteristic
149#127C2×D6111yescharacteristic
150#125—611no—
151#124C2×D6111yescharacteristic
152#124C2×D6111yescharacteristic
153#123—1222no—
154#121—22no—
155#121—612no—
156#121—1222no—
157#120—22no—
158C4×D4—612no—
159#117C2×D6111yescharacteristic
160C4⋊C8—612no—
161#103—612no—
162#102—612no—
163#102—612no—
164#102—612no—
165C22⋊C8—612no—
166#97—611no—
167C4×C8—611no—
168C24—21no—
169#41—42no—
170C2×Q8C22×D6111yescharacteristic
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—42no—
176C2×D4—612no—
177C2×D4—1222no—
178C2×D4—1222no—
179C2×D4C22×D6111yescharacteristic
180C2×D4C22×D6111yescharacteristic
181C2×D4C22×D6111yescharacteristic
182C22×C4—21no—
183C22×C4—1222no—
184C22×C4C22×D6111yescharacteristic
185SD16—2442no—
186D8—2442no—
187D8—2442no—
188D8—2442no—
189C2×C8—612no—
190C2×C8—612no—
191C4⋊C4—612no—
192C4⋊C4—1222no—
193C4⋊C4C22⋊D6112yes—
194C22⋊C4—22no—
195C22⋊C4—22no—
196C22⋊C4—1222no—
197C22⋊C4—1222no—
198C22⋊C4C22⋊D6112yes—
199C42C22×D6111yescharacteristic
200C42C22×D6111yescharacteristic
201C23—21no—
202C23—21no—
203C23—21no—
204C23—42no—
205C23—82no—
206C23—1222no—
207C23C2×C22⋊D6111yescharacteristic
208Q8—22no—
209D4—22no—
210D4—22no—
211D4—22no—
212D4—42no—
213D4—42no—
214D4—82no—
215D4—82no—
216D4—1222no—
217D4—1222no—
218D4—4882no—
219D4—4882no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—1222no—
224C2×C4—4882no—
225C2×C4C2×C22⋊D6112yes—
226C2×C4C2×C22⋊D6112yes—
227C2×C4C2×C22⋊D6111yescharacteristic
228C2×C4C23×D6111yescharacteristic
229C8—1222no—
230C8—1222no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—84no—
240C22—2442no—
241C22—2442no—
242C22—2442no—
243C22C22×C22⋊D6111yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—41no—
248C4—2442no—
249C4#1451982212yes—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—81no—
254C2—4882no—
255C2#1684032911yescharacteristic
256C2#1684056512yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#535C2
socleC22×C61C22×D4
hypercenter#535D61
hypocenterC61#3220
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #16840367C2semidirect
2. #16840152C2semidirect
3. #16840138C2semidirect
4. #16840126C2semidirect
5. #16840116C2semidirect
6. #16839974C2semidirect
7. #16839954C2semidirect
8. #16839907C2semidirect
9. #16839896C2semidirect
10. #16839823C2semidirect
11. C61×#535C2semidirect
12. C2×#11758201C22semidirect
15. C2×#11758199C22semidirect
16. #14519774C22semidirect
17. #14519769C22semidirect
21. C4×D244C22semidirect
22. C4⋊#92418C22semidirect
23. #14519701C22semidirect
26. #14519698C22semidirect
28. #14519688C22semidirect
29. C4×#92418C22semidirect
130. #535D61semidirect
140. C61#3220semidirect