Finite Group Databasebeta

← #21458563

Subgroups — #21458563

Order 7808.

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

normal subgroups only

This group has 338 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
1Q8×Dic122C211yesmaximal, characteristic, complemented
2#16840486C211yesmaximal, characteristic
3#16840123C212yesmaximal
4#16840112C211yesmaximal, characteristic, complemented
5#16840053C211yesmaximal, characteristic
6#16840045C212yesmaximal, complemented
7#16839986C212yesmaximal
8#16839889C211yesmaximal, characteristic, complemented
9#16839869C212yesmaximal, complemented
10C4×#11758201C211yesmaximal, characteristic
11C61×#462C211yesmaximal, characteristic, complemented
12C2×#11758201C2211yescharacteristic
13#14519777—21no—
14#14519777C2211yescharacteristic
15#14519776—22no—
16#14519776C2212yes—
17#14519772—22no—
18#14519766C2212yes—
19#14519757—21no—
20Q8×Dic61C2212yes—
21Q8×Dic61C2212yes—
22C4×Dic122—21no—
23C4×Dic122C2211yescharacteristic
24C4×D244C2211yescharacteristic
25#14519735—21no—
26#14519709C2212yes—
27#14519708C2211yescharacteristic
28#14519706C2212yes—
29#14519701C2212yes—
30#14519701C2211yescharacteristic
31#14519701C2212yes—
32#14519699C2212yes—
33#14519697C2211yescharacteristic
34#14519687C2212yes—
35C4×#92418C2211yescharacteristic
36C2×Q16×C61C2212yes—
37C4⋊Q8×C61C2211yescharacteristic
38C4×Q8×C61C2211yescharacteristic
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61C2312yes—
42C2×Q8×C61C2311yescharacteristic
43C2×D244C2311yescharacteristic
44C2×C4×D61—21no—
45C2×Dic122—21no—
46C2×Dic122—22no—
47C2×Dic122D411yescharacteristic
48Q16×C61—24no—
49C2×C8×C61C2312yes—
50C4⋊C4×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53C4⋊C4×C61C2311yescharacteristic
54C42×C61—21no—
55C42×C61C2311yescharacteristic
56#11758201—22no—
57#11758198—21no—
58#11758198—22no—
59#11758198—22no—
60C4⋊Dic61—21no—
61C4⋊Dic61—22no—
62C4⋊Dic61—22no—
63C4⋊Dic61D411yescharacteristic
64C4⋊Dic61C2312yes—
65C4⋊Dic61C2311yescharacteristic
66#11758196—22no—
67#11758196D412yes—
68C4×Dic61—22no—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2311yescharacteristic
72C2×#92418C2311yescharacteristic
73C22×D61—21no—
74Q8×C61—21no—
75Q8×C61—22no—
76Q8×C61—22no—
77Q8×C61#4112yes—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2411yescharacteristic
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61C2×D412yes—
87C2×Dic61C2×D412yes—
88D244—21no—
89D244—21no—
90C4×D61—42no—
91Dic122—22no—
92Dic122—82no—
93Dic122—81no—
94C8×C61—22no—
95#92418—21no—
96#92418—21no—
97C22×C61C22×D411yescharacteristic
98C2×D61—41no—
99C2×D61—41no—
100C2×D61—41no—
101C4×C61—22no—
102C4×C61—21no—
103C4×C61—42no—
104C4×C61—41no—
105C4×C61#13712yes—
106C4×C61C2×#4111yescharacteristic
107C4×C612−1+411yescharacteristic
108Dic61—22no—
109Dic61—22no—
110Dic61—41no—
111Dic61—42no—
112#3369—611nomaximal, Sylow
113C2×C61#54811yescharacteristic
114C2×C61C2×#13711yescharacteristic
115C2×C61#57711yescharacteristic
116D61—81no—
117Q82—611no—
118#556—611no—
119#489—612no—
120#487—611no—
121#476—611no—
122#475—612no—
123#464—612no—
124#462D6111yescharacteristic, complemented
125#446—611no—
126#441—612no—
127C4×SD16—611no—
128C61#336911yescharacteristic, complemented, Sylow
129C2×Q16C2×D6112yes—
130C2×SD16—611no—
131C4⋊Q8—612no—
132C4⋊Q8—611no—
133C4⋊Q8—1221no—
134C4⋊Q8—1222no—
135C4⋊Q8C2×D6111yescharacteristic
136#126—1222no—
137#124—612no—
138C22⋊Q8—1221no—
139C4×Q8—611no—
140C4×Q8—612no—
141C4×Q8—612no—
142C4×Q8—1221no—
143C4×Q8C2×D6111yescharacteristic
144C4×D4—611no—
145#117—1221no—
146#106—612no—
147#106—611no—
148C4⋊C8—612no—
149C4⋊C8C2×D6111yescharacteristic
150#103—611no—
151#103—612no—
152#103—612no—
153#103C2×D6112yes—
154#102—612no—
155#102—611no—
156#97—612no—
157C4×C8—611no—
158C2×Q8—611no—
159C2×Q8—1222no—
160C2×Q8—1221no—
161C2×Q8C22×D6112yes—
162C2×Q8C22×D6111yescharacteristic
163C2×D4—611no—
164C22×C4—1221no—
165Q16—24no—
166SD16—1222no—
167C2×C8—611no—
168C2×C8—611no—
169C2×C8C22×D6112yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—612no—
174C4⋊C4—611no—
175C4⋊C4—612no—
176C4⋊C4—611no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1221no—
181C4⋊C4C22×D6111yescharacteristic
182C22⋊C4—1222no—
183C22⋊C4—1222no—
184C22⋊C4—1221no—
185C42—21no—
186C42—612no—
187C42—1222no—
188C42—1222no—
189C42C22×D6111yescharacteristic
190C23—1221no—
191Q8—21no—
192Q8—22no—
193Q8—22no—
194Q8—1222no—
195Q8—4881no—
196Q8—4882no—
197Q8#1175822412yes—
198D4—1221no—
199D4—1221no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—612no—
204C2×C4—612no—
205C2×C4—1221no—
206C2×C4—1222no—
207C2×C4—2442no—
208C2×C4D4×D6111yescharacteristic
209C2×C4D4×D6111yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—22no—
212C8—1221no—
213C8—1221no—
214C22—2441no—
215C22—2441no—
216C22—2441no—
217C22C2×D4×D6111yescharacteristic
218C4—21no—
219C4—22no—
220C4—41no—
221C4—42no—
222C4—1222no—
223C4—1222no—
224C4—2441no—
225C4—2442no—
226C4#1451980912yes—
227C4C2×#1175822411yescharacteristic
228C4#1451982411yescharacteristic
229C2—4881no—
230C2#1684041811yescharacteristic
231C2C2×#1451980911yescharacteristic
232C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#462C2
socleC22×C61C22×D4
hypercenter#462D61
hypocenterC61#3369
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. Q8×Dic122C2semidirect
4. #16840112C2semidirect
6. #16840045C2semidirect
8. #16839889C2semidirect
9. #16839869C2semidirect
11. C61×#462C2semidirect
124. #462D61semidirect
128. C61#3369semidirect