Finite Group Databasebeta

← #21455651

Subgroups — #21455651

Order 7808.

398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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#16840390C211yesmaximal, characteristic, complemented
2#16840236C211yesmaximal, characteristic
3#16840063C212yesmaximal, complemented
4#16840063C212yesmaximal, complemented
5#16840053C212yesmaximal, complemented
6#16840043C212yesmaximal, complemented
7#16839804C211yesmaximal, characteristic, complemented
8#16839800C211yesmaximal, characteristic, complemented
9#16839768C211yesmaximal, characteristic
10C2×#14519699C211yesmaximal, characteristic
11C61×#424C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13#14519777C2212yescomplemented
14#14519776—21no—
15#14519769C2212yescomplemented
16#14519768—21no—
17#14519754—22no—
18C4×D244C2212yes—
19C4×D244C2212yes—
20#14519739—21no—
21#14519739—21no—
22#14519736C2211yescharacteristic
23#14519736C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C22⋊C4×D61—22no—
26#14519711C2211yescharacteristic, complemented
27#14519711C2212yescomplemented
28#14519711C2211yescharacteristic, complemented
29#14519709C2211yescharacteristic, complemented
30#14519709C2212yescomplemented
31#14519709C2211yescharacteristic, complemented
32#14519699C2212yes—
33#14519699C2212yes—
34#14519699C2212yes—
35#14519699C2212yes—
36C2×M16×C61C2211yescharacteristic
37C22×C8×C61C2211yescharacteristic
38#117×C61C2211yescharacteristic
39C4⋊C8×C61C2212yescomplemented
40C4⋊C8×C61C2212yescomplemented
41C23×D61—21no—
42C22×C4×C61C2311yescharacteristic
43C22×Dic61—21no—
44C2×D244—21no—
45C2×D244—22no—
46C2×D244Q814yescomplemented
47C2×D244C2312yes—
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×Dic122—22no—
51M16×C61—22no—
52C2×C8×C61—22no—
53C2×C8×C61C2311yescharacteristic
54C2×C8×C61C2311yescharacteristic
55C2×C8×C61C2312yes—
56C4⋊C4×C61D411yescharacteristic
57C4⋊C4×C61D411yescharacteristic
58C22⋊C4×C61D412yes—
59C42×C61C2312yes—
60C22⋊Dic61—21no—
61C22⋊Dic61—21no—
62#11758198—22no—
63#11758198—22no—
64C4⋊Dic61—21no—
65C4⋊Dic61—22no—
66C4⋊Dic61C2312yes—
67C4⋊Dic61C2311yescharacteristic
68C4⋊Dic61C2311yescharacteristic
69C4⋊Dic61C2311yescharacteristic
70C4⋊Dic61C2311yescharacteristic
71#11758196—22no—
72#11758196—22no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C23×C61C2×D411yescharacteristic
76C22×D61—22no—
77C22×D61—24no—
78C22×D61—81no—
79C22×D61—81no—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×Q812yes—
84C2×C4×C61#4112yes—
85C2×C4×C61C2411yescharacteristic
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—22no—
91C2×Dic61—81no—
92D244—24no—
93D244—22no—
94D244C2×Q814yes—
95C4×D61—82no—
96C4×D61—82no—
97Dic122—82no—
98C8×C61—21no—
99C8×C61—21no—
100C8×C61—22no—
101C22×C61—21no—
102C22×C61—21no—
103C22×C61C22⋊Q812yes—
104C22×C61C22×D411yescharacteristic
105C2×D61—24no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—84no—
109C4×C61—22no—
110C4×C61—22no—
111C4×C61C22⋊Q812yes—
112C4×C61C22×Q811yescharacteristic
113C4×C61C2×#4111yescharacteristic
114Dic61—41no—
115Dic61—42no—
116Dic61—41no—
117Dic61—41no—
118Dic61—41no—
119#3081—611nomaximal, Sylow
120C2×C61—22no—
121C2×C61C2×C22⋊Q811yescharacteristic
122C2×C61#57611yescharacteristic
123C2×C61#57711yescharacteristic
124D61—44no—
125#544—611no—
126#518—611no—
127#478—612no—
128#478—612no—
129#476—612no—
130#474—612no—
131#428—611no—
132#427—611no—
133#424D6111yescharacteristic, complemented
134#418—611no—
135C2×#102—611no—
136C61#308111yescharacteristic, complemented, Sylow
137C22×D4—611no—
138C2×M16C2×D6111yescharacteristic
139C22×C8C2×D6111yescharacteristic
140C4⋊Q8—612no—
141C4⋊Q8—1221no—
142#125—612no—
143#125—1221no—
144C22⋊Q8—1222no—
145C4×D4—612no—
146C4×D4—612no—
147C4×D4—1221no—
148C4×D4—1221no—
149#117—611no—
150#117—611no—
151#117C2×D6111yescharacteristic
152C2×C4⋊C4—611no—
153C2×C22⋊C4—1222no—
154#107—611no—
155#107—611no—
156#107—612no—
157#106—611no—
158#106—611no—
159#106—612no—
160C4⋊C8C2×D6112yescomplemented
161C4⋊C8C2×D6112yescomplemented
162#102—612no—
163#102—612no—
164#102—612no—
165#102—612no—
166C24—1221no—
167C2×Q8—1222no—
168C2×D4—614no—
169C2×D4—612no—
170C2×D4—1221no—
171C2×D4—1222no—
172C22×C4—1221no—
173C22×C4—1222no—
174C22×C4—1222no—
175C22×C4C22×D6111yescharacteristic
176M16—22no—
177C2×C8—22no—
178C2×C8C22×D6111yescharacteristic
179C2×C8C22×D6112yes—
180C2×C8C22×D6111yescharacteristic
181C4⋊C4—612no—
182C4⋊C4—611no—
183C4⋊C4—611no—
184C4⋊C4—611no—
185C4⋊C4—611no—
186C4⋊C4—1221no—
187C4⋊C4—1222no—
188C4⋊C4—1222no—
189C4⋊C4—1222no—
190C4⋊C4D24411yescharacteristic
191C4⋊C4D24411yescharacteristic
192C22⋊C4—1221no—
193C22⋊C4—1221no—
194C22⋊C4—1222no—
195C22⋊C4—1222no—
196C22⋊C4D24412yes—
197C42—1221no—
198C42—1221no—
199C42C22×D6112yes—
200C23—1224no—
201C23—1222no—
202C23—4881no—
203C23—4881no—
204C23C2×D24411yescharacteristic
205Q8—4882no—
206D4—614no—
207D4—1222no—
208D4—1224no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1222no—
214C2×C4—4882no—
215C2×C4—4882no—
216C2×C4—4881no—
217C2×C4C2×D24412yes—
218C2×C4C2×D24412yes—
219C2×C4C2×D24411yescharacteristic
220C2×C4#1175822412yes—
221C2×C4Q8×D6112yes—
222C2×C4C23×D6111yescharacteristic
223C8—21no—
224C8—21no—
225C8—22no—
226C22—21no—
227C22—21no—
228C22—1224no—
229C22—4884no—
230C22—2442no—
231C22—2442no—
232C22#1451975712yes—
233C22C22×D24411yescharacteristic
234C4—22no—
235C4—22no—
236C4—2441no—
237C4—2442no—
238C4—2441no—
239C4—2441no—
240C4—2441no—
241C4#1451975712yes—
242C4C2×Q8×D6111yescharacteristic
243C4C2×#1175822411yescharacteristic
244C2—22no—
245C2—2444no—
246C2C2×#1451975711yescharacteristic
247C2#1684056711yescharacteristic
248C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#424C2
socleC22×C61C22×D4
hypercenter#424D61
hypocenterC61#3081
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #16840390C2semidirect
3. #16840063C2semidirect
4. #16840063C2semidirect
5. #16840053C2semidirect
6. #16840043C2semidirect
7. #16839804C2semidirect
8. #16839800C2semidirect
11. C61×#424C2semidirect
13. #14519777C22semidirect
15. #14519769C22semidirect
26. #14519711C22semidirect
27. #14519711C22semidirect
28. #14519711C22semidirect
29. #14519709C22semidirect
30. #14519709C22semidirect
31. #14519709C22semidirect
39. C4⋊C8×C61C22semidirect
40. C4⋊C8×C61C22semidirect
46. C2×D244Q8semidirect
133. #424D61semidirect
136. C61#3081semidirect
160. C4⋊C8C2×D61semidirect
161. C4⋊C8C2×D61semidirect