Finite Group Databasebeta

← #21458910

Subgroups — #21458910

Order 7808.

380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840494C212yesmaximal, complemented
2#16840148C212yesmaximal, complemented
3#16839986C212yesmaximal, complemented
4#16839974C212yesmaximal, complemented
5#16839955C212yesmaximal, complemented
6#16839892C211yesmaximal, characteristic, complemented
7#16839863C212yesmaximal, complemented
8C4×D488C211yesmaximal, characteristic, complemented
9C61×#495C211yesmaximal, characteristic, complemented
10C2×#11758201C2212yes—
11C2×D488C2211yescharacteristic
12C2×#11758199C2212yes—
13#14519773C2212yes—
14#14519766C2212yes—
15#14519763—22no—
16#14519761—22no—
17#14519759—22no—
18Q8×Dic61C2212yes—
19C4×Dic122C2211yescharacteristic
20C4×D244C2212yes—
21D4×Dic61C2212yes—
22#14519737—22no—
23#14519711C2211yescharacteristic
24C4⋊#92418C2211yescharacteristic
25#14519706C2212yes—
26#14519701C2212yes—
27#14519699C2212yes—
28#14519698C2212yes—
29#14519687C2212yes—
30C2×Q16×C61C2211yescharacteristic
31C2×SD16×C61C2212yes—
32C2×D8×C61C2211yescharacteristic
33#124×C61C2212yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61C2312yes—
36C2×D4×C61C2312yes—
37C2×C22⋊D61—22no—
38C2×C22⋊D61—22no—
39C22×Dic61—22no—
40C2×D244C2312yes—
41C2×C4×D61—22no—
42C2×Dic122D411yescharacteristic
43Q16×C61—41no—
44SD16×C61—24no—
45D8×C61—41no—
46C2×C8×C61C2311yescharacteristic
47C2×C8×C61C2311yescharacteristic
48C22⋊C4×C61—22no—
49C22⋊C4×C61—22no—
50C42×C61C2311yescharacteristic
51C22⋊Dic61—22no—
52#11758201—42no—
53#11758199—42no—
54#11758198—22no—
55#11758198—22no—
56#11758198—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61D411yescharacteristic
59C4⋊Dic61C2312yes—
60#11758196D412yes—
61C4×Dic61—22no—
62C4×Dic61C2312yes—
63C2×#92418C2312yes—
64D488—22no—
65C23×C61—22no—
66C22×D61—22no—
67Q8×C61—22no—
68Q8×C61—22no—
69D4×C61—22no—
70D4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2411yescharacteristic
75C22⋊D61—44no—
76C22⋊D61—82no—
77C2×Dic61—22no—
78C2×Dic61—82no—
79C2×Dic61C2×D412yes—
80C2×Dic61C2×D412yes—
81D244—22no—
82D244—22no—
83C4×D61—82no—
84Dic122—41no—
85C8×C61—21no—
86C8×C61#4112yes—
87#92418—22no—
88C22×C61—42no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61C22×D411yescharacteristic
92C2×D61—42no—
93C2×D61—42no—
94C2×D61—42no—
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—42no—
98C4×C61C2×#4111yescharacteristic
99C4×C61H(5,𝔽2)11yescharacteristic
100Dic61—22no—
101Dic61—22no—
102Dic61—42no—
103#3403—611nomaximal, Sylow
104C2×C61—82no—
105C2×C61#55011yescharacteristic
106C2×C61#57511yescharacteristic
107C2×C61#57611yescharacteristic
108D61—82no—
109#559—612no—
110#496—612no—
111#495D6111yescharacteristic, complemented
112#464—612no—
113#463—612no—
114#459—612no—
115#446—611no—
116#440—612no—
117C4×D8—611no—
118C61#340311yescharacteristic, complemented, Sylow
119C2×Q16C2×D6111yescharacteristic
120C2×SD16—612no—
121C2×SD16C2×D6112yes—
122C2×D8—612no—
123C2×D8—611no—
124C2×D8C2×D6111yescharacteristic
125#127—612no—
126#124—612no—
127#124—1222no—
128#124C2×D6112yes—
129#123—1222no—
130#123—1222no—
131C4×Q8—611no—
132C4×Q8—612no—
133C4×D4—612no—
134C4×D4—612no—
135C4×D4—1222no—
136#107—611no—
137C4⋊C8—612no—
138C4⋊C8—611no—
139#103—612no—
140#102—612no—
141#102—612no—
142#97—612no—
143C4×C8C2×D6111yescharacteristic
144C2×Q8—611no—
145C2×Q8C22×D6112yes—
146C2×D4—612no—
147C2×D4—1222no—
148C2×D4—1222no—
149C2×D4C22×D6112yes—
150C22×C4—1222no—
151C22×C4—1222no—
152Q16—41no—
153SD16—24no—
154SD16—2442no—
155D8—41no—
156D8—1222no—
157D8—2442no—
158C2×C8—612no—
159C2×C8C22×D6111yescharacteristic
160C2×C8C22×D6111yescharacteristic
161C4⋊C4—612no—
162C4⋊C4—611no—
163C4⋊C4—612no—
164C4⋊C4—1222no—
165C22⋊C4—22no—
166C22⋊C4—22no—
167C22⋊C4—1222no—
168C22⋊C4—1222no—
169C22⋊C4—1222no—
170C22⋊C4—1222no—
171C42—612no—
172C42—1222no—
173C42C22×D6111yescharacteristic
174C23—22no—
175C23—1222no—
176Q8—22no—
177Q8—22no—
178Q8—2441no—
179D4—22no—
180D4—22no—
181D4—1222no—
182D4—1222no—
183D4—4882no—
184D4—2444no—
185C2×C4—22no—
186C2×C4—612no—
187C2×C4—612no—
188C2×C4—1222no—
189C2×C4—4882no—
190C2×C4—4882no—
191C2×C4D4×D6111yescharacteristic
192C2×C4D4×D6111yescharacteristic
193C2×C4C23×D6111yescharacteristic
194C8—21no—
195C8—1222no—
196C8#1175822412yes—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—2442no—
201C22—2442no—
202C22—2442no—
203C22C2×D4×D6111yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—1222no—
208C4—1222no—
209C4—2442no—
210C4C2×#1175822411yescharacteristic
211C4#1451982211yescharacteristic
212C2—82no—
213C2—4882no—
214C2#1684043211yescharacteristic
215C2#1684055911yescharacteristic
216C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#495C2
socleC22×C61C22×D4
hypercenter#495D61
hypocenterC61#3403
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #16840494C2semidirect
2. #16840148C2semidirect
3. #16839986C2semidirect
4. #16839974C2semidirect
5. #16839955C2semidirect
6. #16839892C2semidirect
7. #16839863C2semidirect
8. C4×D488C2semidirect
9. C61×#495C2semidirect
111. #495D61semidirect
118. C61#3403semidirect