Finite Group Databasebeta

← #21456884

Subgroups — #21456884

Order 7808.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840373C211yesmaximal, characteristic, complemented
2#16840325C211yesmaximal, characteristic
3#16840154C211yesmaximal, characteristic, complemented
4#16840126C211yesmaximal, characteristic, complemented
5#16840117C211yesmaximal, characteristic, complemented
6#16839982C212yesmaximal, complemented
7#16839960C212yesmaximal, complemented
8#16839921C212yesmaximal, complemented
9#16839911C212yesmaximal, complemented
10#16839821C211yesmaximal, characteristic, complemented
11C61×#492C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic
13C2×D4×D61C2211yescharacteristic
14C2×#11758202C2212yescomplemented
15C2×#11758201C2212yes—
16#14519773C2211yescharacteristic
17#14519772—22no—
18#14519769C2211yescharacteristic, complemented
19#14519767—22no—
20#14519765C2211yescharacteristic
21#14519764C2211yescharacteristic
22#14519753C2212yes—
23#14519749—22no—
24#14519745—22no—
25Q8×Dic61C2212yescomplemented
26#14519734C2211yescharacteristic
27#14519706C2212yescomplemented
28#14519702C2212yescomplemented
29#14519699C2212yes—
30#14519698C2212yes—
31#14519698C2212yescomplemented
32#14519689C2212yes—
33#14519688C2211yescharacteristic, complemented
34C2×SD16×C61C2212yes—
35C2×SD16×C61C2212yescomplemented
36C4⋊Q8×C61C2211yescharacteristic, complemented
37#127×C61C2211yescharacteristic
38C4×C8×C61C2211yescharacteristic, complemented
39C23×D61—21no—
40C2×Q8×C61C2312yes—
41C2×D4×C61—22no—
42C2×D4×C61C2311yescharacteristic
43C2×D4×C61C2311yescharacteristic
44C2×C22⋊D61—21no—
45C2×C22⋊D61—21no—
46C2×C22⋊D61—22no—
47C22×Dic61—21no—
48#11758224—42no—
49D4×D61—42no—
50C2×D244C2311yescharacteristic
51C2×C4×D61C2311yescharacteristic
52C2×Dic122C2311yescharacteristic
53SD16×C61—42no—
54SD16×C61—42no—
55C2×C8×C61C2312yes—
56C4⋊C4×C61—22no—
57C42×C61C2311yescharacteristic
58C22⋊Dic61—22no—
59#11758202—42no—
60#11758201—42no—
61#11758198—22no—
62#11758198—22no—
63#11758198D412yes—
64C4⋊Dic61—22no—
65C4⋊Dic61C2312yes—
66#11758196—22no—
67#11758196—22no—
68#11758196D412yes—
69C4×Dic61—22no—
70C4×Dic61C2311yescharacteristic
71C2×#92418C2312yes—
72C23×C61—21no—
73C23×C61—21no—
74C22×D61—21no—
75C22×D61—42no—
76C22×D61—82no—
77C22×D61C2×D411yescharacteristic
78Q8×C61—22no—
79Q8×C61—22no—
80D4×C61—22no—
81D4×C61—22no—
82D4×C61—82no—
83C2×C4×C61—22no—
84C2×C4×C61C2×D412yes—
85C2×C4×C61C2411yescharacteristic
86C22⋊D61—42no—
87C22⋊D61—42no—
88C22⋊D61—82no—
89C2×Dic61—22no—
90C2×Dic61—21no—
91C2×Dic61—42no—
92C2×Dic61C2×D412yes—
93C2×Dic61C2×D411yescharacteristic
94D244—22no—
95C4×D61—22no—
96Dic122—22no—
97C8×C61—22no—
98#92418—22no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—42no—
102C22×C61—42no—
103C22×C61C22×D411yescharacteristic
104C2×D61—21no—
105C2×D61—22no—
106C2×D61—41no—
107C2×D61—42no—
108C2×D61—84no—
109C4×C61—22no—
110C4×C61—42no—
111C4×C61H(5,𝔽2)12yes—
112Dic61—21no—
113Dic61—22no—
114Dic61—41no—
115Dic61—42no—
116#3222—611nomaximal, Sylow
117C2×C61—81no—
118C2×C61—81no—
119C2×C61#53511yescharacteristic
120C2×C61#57712yes—
121D61—41no—
122D61—81no—
123#541—611no—
124#535—611no—
125#497—611no—
126#492D6111yescharacteristic, complemented
127#490—611no—
128#488—611no—
129#464—612no—
130#460—612no—
131#452—612no—
132#450—612no—
133#433—611no—
134C61#322211yescharacteristic, complemented, Sylow
135C2×#41—611no—
136C22×D4—611no—
137C2×Q16—612no—
138C2×SD16—612no—
139C2×SD16C2×D6112yes—
140C2×SD16C2×D6112yescomplemented
141C4⋊Q8C2×D6111yescharacteristic, complemented
142#127—611no—
143#127C2×D6111yescharacteristic
144#126—1222no—
145#125—611no—
146#125—1222no—
147#124—611no—
148#124—611no—
149C22⋊Q8—612no—
150#121—1222no—
151#120—1222no—
152C4×Q8—612no—
153#117—611no—
154C4⋊C8—612no—
155#103—612no—
156#102—612no—
157#102—612no—
158#102—612no—
159C22⋊C8—612no—
160#97—611no—
161C4×C8C2×D6111yescharacteristic, complemented
162C24—1221no—
163#41—2442no—
164C2×Q8—611no—
165C2×Q8C22×D6112yes—
166C2×D4—22no—
167C2×D4—611no—
168C2×D4—1222no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—2442no—
172C2×D4C22×D6111yescharacteristic
173C2×D4C22×D6111yescharacteristic
174C22×C4—611no—
175C22×C4—1221no—
176Q16—2442no—
177SD16—42no—
178SD16—42no—
179SD16—2442no—
180C2×C8—612no—
181C2×C8C22×D6112yes—
182C4⋊C4—22no—
183C4⋊C4—612no—
184C4⋊C4—612no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1222no—
188C22⋊C4—612no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C22⋊C4—1222no—
192C42—611no—
193C42—1222no—
194C42C22×D6111yescharacteristic
195C23—21no—
196C23—21no—
197C23—611no—
198C23—1221no—
199C23—4882no—
200C23—2442no—
201Q8—22no—
202Q8—22no—
203Q8—1222no—
204D4—22no—
205D4—22no—
206D4—82no—
207D4—1222no—
208D4—4882no—
209D4—2442no—
210D4—2442no—
211C2×C4—22no—
212C2×C4—612no—
213C2×C4—611no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1221no—
217C2×C4—2442no—
218C2×C4D4×D6112yes—
219C2×C4C23×D6111yescharacteristic
220C8—22no—
221C8—1222no—
222C22—42no—
223C22—42no—
224C22—41no—
225C22—41no—
226C22—1222no—
227C22—1221no—
228C22—4884no—
229C22—2442no—
230C22—2441no—
231C22C2×D4×D6111yescharacteristic
232C4—22no—
233C4—42no—
234C4—1222no—
235C4—1221no—
236C4—2442no—
237C4—2441no—
238C4#1451982212yes—
239C2—81no—
240C2—81no—
241C2—4881no—
242C2—2441no—
243C2#1684032511yescharacteristic
244C2#1684056812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#492C2
socleC22×C61C22×D4
hypercenter#492D61
hypocenterC61#3222
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #16840373C2semidirect
3. #16840154C2semidirect
4. #16840126C2semidirect
5. #16840117C2semidirect
6. #16839982C2semidirect
7. #16839960C2semidirect
8. #16839921C2semidirect
9. #16839911C2semidirect
10. #16839821C2semidirect
11. C61×#492C2semidirect
14. C2×#11758202C22semidirect
18. #14519769C22semidirect
25. Q8×Dic61C22semidirect
27. #14519706C22semidirect
28. #14519702C22semidirect
31. #14519698C22semidirect
33. #14519688C22semidirect
35. C2×SD16×C61C22semidirect
36. C4⋊Q8×C61C22semidirect
38. C4×C8×C61C22semidirect
126. #492D61semidirect
134. C61#3222semidirect
140. C2×SD16C2×D61semidirect
141. C4⋊Q8C2×D61semidirect
161. C4×C8C2×D61semidirect