Finite Group Databasebeta

← #21458519

Subgroups — #21458519

Order 7808.

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

normal subgroups only

This group has 348 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
1#16840498C211yesmaximal, characteristic
2#16840491C211yesmaximal, characteristic, complemented
3#16840115C212yesmaximal, complemented
4#16840108C211yesmaximal, characteristic
5#16840064C212yesmaximal, complemented
6#16840048C211yesmaximal, characteristic, complemented
7#16839982C212yesmaximal, complemented
8#16839886C211yesmaximal, characteristic, complemented
9C4×#11758202C211yesmaximal, characteristic, complemented
10SD16×Dic61C212yesmaximal, complemented
11C61×#460C211yesmaximal, characteristic
12C2×#11758202C2211yescharacteristic
13#14519777—21no—
14#14519777C2211yescharacteristic
15#14519768—22no—
16#14519768C2212yes—
17#14519764—21no—
18#14519764C2212yes—
19#14519758—22no—
20Q8×Dic61C2212yes—
21C4×Dic122—21no—
22C4×Dic122C2211yescharacteristic
23C4×Dic122C2211yescharacteristic
24D4×Dic61—21no—
25D4×Dic61C2212yes—
26#14519710C2211yescharacteristic
27#14519709C2212yes—
28#14519706C2212yes—
29#14519702C2212yes—
30#14519701C2211yescharacteristic
31#14519700C2211yescharacteristic
32#14519698C2212yes—
33#14519698C2212yes—
34C4×#92418C2211yescharacteristic
35C8×Dic61C2212yes—
36C2×SD16×C61C2212yes—
37#127×C61C2211yescharacteristic
38C4×Q8×C61C2211yescharacteristic
39C4⋊C8×C61C2211yescharacteristic
40#102×C61C2212yes—
41C2×Q8×C61C2311yescharacteristic
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61C2312yes—
45C22×Dic61—22no—
46C2×Dic122—21no—
47C2×Dic122D411yescharacteristic
48C2×Dic122C2311yescharacteristic
49SD16×C61—24no—
50C2×C8×C61C2312yes—
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2311yescharacteristic
53C42×C61—21no—
54C42×C61C2311yescharacteristic
55C22⋊Dic61—22no—
56C22⋊Dic61—22no—
57C22⋊Dic61—22no—
58#11758202—22no—
59C4⋊Dic61—21no—
60C4⋊Dic61—22no—
61C4⋊Dic61—22no—
62C4⋊Dic61D411yescharacteristic
63C4⋊Dic61C2312yes—
64C4⋊Dic61C2311yescharacteristic
65#11758196—21no—
66#11758196—22no—
67#11758196D412yes—
68C4×Dic61—21no—
69C4×Dic61—22no—
70C4×Dic61C2312yes—
71C2×#92418C2311yescharacteristic
72C2×#92418C2311yescharacteristic
73C23×C61—22no—
74Q8×C61—21no—
75Q8×C61#4112yes—
76D4×C61—22no—
77D4×C61—22no—
78D4×C61—42no—
79D4×C61—81no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C2×Dic61—22no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—82no—
89C2×Dic61C2×D412yes—
90C2×Dic61C2×D412yes—
91Dic122—22no—
92Dic122—21no—
93Dic122—21no—
94Dic122—42no—
95C8×C61—22no—
96#92418—21no—
97#92418—21no—
98C22×C61—42no—
99C22×C61—42no—
100C22×C61—42no—
101C22×C61C22×D411yescharacteristic
102C4×C61—22no—
103C4×C61—21no—
104C4×C61—41no—
105C4×C61#13512yes—
106C4×C61C2×#4111yescharacteristic
107C4×C612−1+411yescharacteristic
108Dic61—22no—
109Dic61—22no—
110Dic61—41no—
111Dic61—42no—
112Dic61—41no—
113#3365—611nomaximal, Sylow
114C2×C61—82no—
115C2×C61#54811yescharacteristic
116C2×C61C2×#13511yescharacteristic
117C2×C61#57711yescharacteristic
118#559—611no—
119#557—611no—
120#488—612no—
121#486—611no—
122#478—612no—
123#475—611no—
124#464—612no—
125#460D6111yescharacteristic
126C8×Q8—611no—
127C4×Q16—611no—
128C4×SD16—612no—
129C61#336511yescharacteristic, complemented, Sylow
130C2×Q16—611no—
131C2×SD16C2×D6112yes—
132C4⋊Q8—611no—
133C4⋊Q8—1221no—
134#127C2×D6111yescharacteristic
135#125—612no—
136#125—1222no—
137#124—612no—
138#124—1221no—
139#123—1222no—
140C4×Q8—611no—
141C4×Q8—612no—
142C4×Q8—611no—
143C4×Q8—1221no—
144C4×Q8C2×D6111yescharacteristic
145C4×D4—612no—
146C4×D4—1221no—
147#107—611no—
148#106—612no—
149C4⋊C8—612no—
150C4⋊C8C2×D6111yescharacteristic
151#103—611no—
152#103—612no—
153#103—611no—
154#102—612no—
155#102—612no—
156#102C2×D6112yes—
157C4×C8—612no—
158C4×C8—611no—
159C2×Q8—611no—
160C2×Q8—611no—
161C2×Q8—1221no—
162C2×Q8C22×D6111yescharacteristic
163C2×D4—21no—
164C2×D4—21no—
165C2×D4C22×D6112yes—
166C22×C4—1222no—
167Q16—1222no—
168SD16—24no—
169C2×C8—611no—
170C2×C8—611no—
171C2×C8C22×D6112yes—
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⋊C4—1221no—
182C4⋊C4C22×D6111yescharacteristic
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C42—21no—
187C42—612no—
188C42—1222no—
189C42—1221no—
190C42C22×D6111yescharacteristic
191C23—22no—
192Q8—21no—
193Q8—1222no—
194Q8—1221no—
195Q8—1221no—
196Q8—2442no—
197Q8#1175822412yes—
198D4—22no—
199D4—22no—
200D4—42no—
201D4—81no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—612no—
205C2×C4—612no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1222no—
209C2×C4—4882no—
210C2×C4D4×D6111yescharacteristic
211C2×C4D4×D6111yescharacteristic
212C2×C4C23×D6111yescharacteristic
213C8—22no—
214C8—1221no—
215C8—1221no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22C2×D4×D6111yescharacteristic
220C4—21no—
221C4—22no—
222C4—41no—
223C4—1222no—
224C4—1222no—
225C4—2442no—
226C4—2441no—
227C4—2441no—
228C4#1451979812yes—
229C4C2×#1175822411yescharacteristic
230C4#1451982411yescharacteristic
231C2—82no—
232C2#1684041811yescharacteristic
233C2C2×#1451979811yescharacteristic
234C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#460C2
socleC22×C61C22×D4
hypercenter#460D61
hypocenterC61#3365
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #16840491C2semidirect
3. #16840115C2semidirect
5. #16840064C2semidirect
6. #16840048C2semidirect
7. #16839982C2semidirect
8. #16839886C2semidirect
9. C4×#11758202C2semidirect
10. SD16×Dic61C2semidirect
129. C61#3365semidirect