Finite Group Databasebeta

← #21458806

Subgroups — #21458806

Order 7808.

360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840486C211yesmaximal, characteristic, complemented
2#16840482C211yesmaximal, characteristic, complemented
3#16840143C212yesmaximal
4#16840141C211yesmaximal, characteristic, complemented
5#16839987C212yesmaximal, complemented
6#16839982C212yesmaximal, complemented
7#16839968C211yesmaximal, characteristic, complemented
8#16839886C211yesmaximal, characteristic, complemented
9#16839854C212yesmaximal, complemented
10C4×#11758199C211yesmaximal, characteristic
11C61×#461C211yesmaximal, characteristic, complemented
12C2×#11758202C2212yes—
13C2×#11758202C2212yes—
14C2×#11758190C2212yes—
15C2×#11758199C2211yescharacteristic
16#14519777C2211yescharacteristic
17#14519772—22no—
18#14519770—22no—
19#14519766C2212yes—
20#14519764C2212yes—
21#14519757—21no—
22#14519756—21no—
23Q8×Dic61C2212yes—
24C4×Dic122C2211yescharacteristic
25#14519742C2212yes—
26C4×D244C2211yescharacteristic
27#14519736—21no—
28#14519735—21no—
29#14519710C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2212yes—
32#14519698C2211yescharacteristic
33#14519697C2211yescharacteristic
34C4×#92418C2211yescharacteristic
35C8×Dic61C2212yes—
36C2×SD16×C61C2212yes—
37C4⋊Q8×C61C2211yescharacteristic
38C4×D4×C61C2211yescharacteristic
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61C2312yes—
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C2×D244C2311yescharacteristic
45C2×C4×D61—21no—
46C2×Dic122D411yescharacteristic
47C2×Dic122C2312yes—
48SD16×C61—42no—
49C2×C8×C61C2312yes—
50C4⋊C4×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2311yescharacteristic
53C22⋊C4×C61—21no—
54C42×C61C2311yescharacteristic
55C22⋊Dic61—22no—
56C22⋊Dic61—22no—
57#11758202—24no—
58#11758202—42no—
59#11758199—22no—
60#11758198—21no—
61#11758198—22no—
62#11758198—22no—
63C4⋊Dic61—21no—
64C4⋊Dic61—21no—
65C4⋊Dic61—22no—
66C4⋊Dic61D411yescharacteristic
67C4⋊Dic61C2311yescharacteristic
68#11758196—22no—
69#11758196D412yes—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61C2312yes—
73C2×#92418C2311yescharacteristic
74C2×#92418C2311yescharacteristic
75#11758190—42no—
76C23×C61—21no—
77C22×D61—21no—
78Q8×C61—22no—
79Q8×C61—22no—
80D4×C61—21no—
81D4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—42no—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2411yescharacteristic
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61C2×D412yes—
91C2×Dic61C2×D412yes—
92D244—21no—
93D244—21no—
94C4×D61—42no—
95Dic122—22no—
96Dic122—22no—
97Dic122—22no—
98C8×C61—22no—
99#92418—21no—
100#92418#4112yes—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61C22×D411yescharacteristic
105C2×D61—41no—
106C2×D61—41no—
107C2×D61—41no—
108C4×C61—21no—
109C4×C61—42no—
110C4×C61—41no—
111C4×C61#13512yes—
112C4×C61C2×#4111yescharacteristic
113C4×C61H(5,𝔽2)11yescharacteristic
114Dic61—22no—
115Dic61—22no—
116Dic61—42no—
117Dic61—41no—
118#3393—611nomaximal, Sylow
119C2×C61—81no—
120C2×C61#55011yescharacteristic
121C2×C61C2×#13511yescharacteristic
122C2×C61#57811yescharacteristic
123D61—81no—
124#556—611no—
125#556—611no—
126#495—612no—
127#494—611no—
128#464—612no—
129#464—612no—
130#461—611no—
131#461D6111yescharacteristic, complemented
132C8×Q8—611no—
133C4×Q16—612no—
134C4×D8—611no—
135C61#339311yescharacteristic, complemented, Sylow
136C2×Q16—612no—
137C2×Q16—612no—
138C2×SD16—612no—
139C2×SD16C2×D6112yes—
140C2×D8—611no—
141C4⋊Q8—611no—
142C4⋊Q8C2×D6111yescharacteristic
143#126—1222no—
144#126—1222no—
145#124—612no—
146#124—612no—
147C22⋊Q8—1221no—
148C22⋊Q8—1221no—
149C4×Q8—611no—
150C4×Q8—612no—
151C4×Q8—612no—
152C4×D4—611no—
153C4×D4C2×D6111yescharacteristic
154#117—1221no—
155#117—1221no—
156#107—611no—
157C4⋊C8—612no—
158C4⋊C8C2×D6111yescharacteristic
159#103—612no—
160#103C2×D6112yes—
161#102—611no—
162#102—611no—
163C4×C8—612no—
164C4×C8—611no—
165C2×Q8—611no—
166C2×Q8—612no—
167C2×Q8C22×D6112yes—
168C2×D4—611no—
169C2×D4C22×D6111yescharacteristic
170C22×C4—21no—
171C22×C4—1221no—
172Q16—1224no—
173Q16—2442no—
174SD16—42no—
175SD16—2442no—
176D8—1222no—
177C2×C8—611no—
178C2×C8—611no—
179C2×C8C22×D6112yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—612no—
183C4⋊C4—611no—
184C4⋊C4—611no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1221no—
188C4⋊C4—1221no—
189C4⋊C4C22×D6111yescharacteristic
190C22⋊C4—21no—
191C22⋊C4—1222no—
192C22⋊C4—1222no—
193C22⋊C4—1222no—
194C22⋊C4—1222no—
195C22⋊C4—1221no—
196C42—612no—
197C42—1222no—
198C42—1222no—
199C42C22×D6111yescharacteristic
200C23—21no—
201C23—1221no—
202Q8—22no—
203Q8—22no—
204Q8—1222no—
205Q8—1222no—
206Q8—1222no—
207D4—21no—
208D4—21no—
209D4—1221no—
210D4—1221no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—612no—
215C2×C4—612no—
216C2×C4—1221no—
217C2×C4—1222no—
218C2×C4—2442no—
219C2×C4D4×D6111yescharacteristic
220C2×C4D4×D6111yescharacteristic
221C2×C4C23×D6111yescharacteristic
222C8—22no—
223C8—612no—
224C8—1221no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—2441no—
229C22—2441no—
230C22—2441no—
231C22C2×D4×D6111yescharacteristic
232C4—21no—
233C4—41no—
234C4—42no—
235C4—1222no—
236C4—1222no—
237C4—2441no—
238C4—2442no—
239C4#1451979812yes—
240C4#41×D6111yescharacteristic
241C4#1451982211yescharacteristic
242C2—81no—
243C2—4881no—
244C2#1684043011yescharacteristic
245C2C2×#1451979811yescharacteristic
246C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3393
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #16840486C2semidirect
2. #16840482C2semidirect
4. #16840141C2semidirect
5. #16839987C2semidirect
6. #16839982C2semidirect
7. #16839968C2semidirect
8. #16839886C2semidirect
9. #16839854C2semidirect
11. C61×#461C2semidirect
131. #461D61semidirect
135. C61#3393semidirect