Finite Group Databasebeta

← #21458509

Subgroups — #21458509

Order 7808.

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

normal subgroups only

This group has 336 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#16840487C211yesmaximal, characteristic, complemented
2#16840486C211yesmaximal, characteristic
3#16840118C212yesmaximal
4#16840067C212yesmaximal, complemented
5#16840039C211yesmaximal, characteristic
6#16839987C212yesmaximal
7#16839969C211yesmaximal, characteristic, complemented
8C8×Dic122C211yesmaximal, characteristic, complemented
9#16839854C212yesmaximal, complemented
10C4×#11758190C211yesmaximal, characteristic
11C61×#487C211yesmaximal, characteristic, complemented
12C2×#11758202C2212yes—
13C2×#11758190C2211yescharacteristic
14#14519775—21no—
15#14519772—22no—
16#14519768C2212yes—
17#14519767—22no—
18#14519766C2212yes—
19#14519757—21no—
20Q8×Dic61—21no—
21Q8×Dic61C2212yes—
22C4×Dic122C2211yescharacteristic
23C4×Dic122C2211yescharacteristic
24#14519742C2212yes—
25C4×D244C2211yescharacteristic
26#14519735—21no—
27#14519710C2212yes—
28#14519709C2211yescharacteristic
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519701C2212yes—
33#14519699C2211yescharacteristic
34#14519697C2212yes—
35C8×Dic61C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37C4⋊Q8×C61C2211yescharacteristic
38#103×C61C2212yes—
39#103×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×Q8×C61C2312yes—
43C2×D244C2311yescharacteristic
44C2×C4×D61—21no—
45C2×Dic122D411yescharacteristic
46C2×Dic122C2311yescharacteristic
47C2×C8×C61C2311yescharacteristic
48C2×C8×C61C2311yescharacteristic
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2312yes—
53C42×C61C2311yescharacteristic
54#11758202—24no—
55#11758198—21no—
56#11758198—22no—
57#11758198—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61—22no—
60C4⋊Dic61D411yescharacteristic
61C4⋊Dic61C2311yescharacteristic
62C4⋊Dic61C2311yescharacteristic
63#11758196—21no—
64#11758196—22no—
65#11758196—22no—
66#11758196D412yes—
67C4×Dic61—21no—
68C4×Dic61—22no—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2312yes—
72#11758190—22no—
73C22×D61—21no—
74Q8×C61—22no—
75Q8×C61—22no—
76Q8×C61—42no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61C2×D412yes—
86C2×Dic61C2×D412yes—
87D244—21no—
88D244—21no—
89C4×D61—42no—
90Dic122—22no—
91Dic122—21no—
92Dic122#4112yes—
93C8×C61—21no—
94C8×C61—21no—
95#92418—22no—
96C22×C61C22×D411yescharacteristic
97C2×D61—41no—
98C2×D61—41no—
99C2×D61—41no—
100C4×C61—21no—
101C4×C61—42no—
102C4×C61—42no—
103C4×C61#13512yes—
104C4×C61C2×#4111yescharacteristic
105C4×C612−1+411yescharacteristic
106Dic61—22no—
107Dic61—22no—
108Dic61—22no—
109Dic61—41no—
110Dic61—41no—
111#3364—611nomaximal, Sylow
112C2×C61#54811yescharacteristic
113C2×C61C2×#13511yescharacteristic
114C2×C61#57811yescharacteristic
115D61—81no—
116#557—611no—
117#556—611no—
118#488—612no—
119#487D6111yescharacteristic, complemented
120#479—612no—
121#474—611no—
122#464—612no—
123#462—611no—
124C8×Q8—611no—
125C4×Q16—612no—
126C4×SD16—611no—
127C61#336411yescharacteristic, complemented, Sylow
128C2×Q16—612no—
129C2×SD16—611no—
130C4⋊Q8—1221no—
131C4⋊Q8C2×D6111yescharacteristic
132C4⋊Q8C2×D6111yescharacteristic
133#126—1222no—
134#125—612no—
135#125—1222no—
136#124—612no—
137C22⋊Q8—1221no—
138C4×Q8—611no—
139C4×Q8—612no—
140C4×Q8—612no—
141C4×Q8—611no—
142C4×Q8—1221no—
143C4×D4—611no—
144#117—1221no—
145#107—612no—
146#106—611no—
147C4⋊C8—612no—
148C4⋊C8—611no—
149#103—612no—
150#103—611no—
151#103C2×D6112yes—
152#103C2×D6112yes—
153#102—611no—
154#102—612no—
155C4×C8—612no—
156C4×C8C2×D6111yescharacteristic
157C2×Q8—21no—
158C2×Q8—611no—
159C2×Q8—611no—
160C2×Q8C22×D6112yes—
161C2×D4—611no—
162C22×C4—1221no—
163Q16—1224no—
164SD16—1222no—
165C2×C8—612no—
166C2×C8C22×D6111yescharacteristic
167C2×C8C22×D6111yescharacteristic
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—612no—
172C4⋊C4—611no—
173C4⋊C4—611no—
174C4⋊C4—611no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1221no—
180C4⋊C4C22×D6112yes—
181C22⋊C4—1222no—
182C22⋊C4—1222no—
183C22⋊C4—1221no—
184C42—612no—
185C42—1222no—
186C42—1222no—
187C42—1221no—
188C42C22×D6111yescharacteristic
189C23—1221no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—612no—
194Q8—1221no—
195Q8—1222no—
196D4—1221no—
197D4—1221no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—612no—
201C2×C4—612no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—2442no—
206C2×C4D4×D6111yescharacteristic
207C2×C4D4×D6111yescharacteristic
208C2×C4C23×D6111yescharacteristic
209C8—21no—
210C8—21no—
211C8—1222no—
212C22—2441no—
213C22—2441no—
214C22—2441no—
215C22C2×D4×D6111yescharacteristic
216C4—21no—
217C4—42no—
218C4—42no—
219C4—1222no—
220C4—1222no—
221C4—1222no—
222C4—2441no—
223C4—2441no—
224C4#1451979812yes—
225C4#41×D6111yescharacteristic
226C4#1451982411yescharacteristic
227C2—4881no—
228C2#1684042011yescharacteristic
229C2C2×#1451979811yescharacteristic
230C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#487C2
socleC22×C61C22×D4
hypercenter#487D61
hypocenterC61#3364
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #16840487C2semidirect
4. #16840067C2semidirect
7. #16839969C2semidirect
8. C8×Dic122C2semidirect
9. #16839854C2semidirect
11. C61×#487C2semidirect
119. #487D61semidirect
127. C61#3364semidirect