Finite Group Databasebeta

← #21446916

Subgroups — #21446916

Order 7808.

390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×Dic244C211yesmaximal, characteristic, complemented
2C22×#11758190C211yesmaximal, characteristic
3C2×#14519765C211yesmaximal, characteristic
4C2×#14519702C211yesmaximal, characteristic, complemented
5C2×#14519699C211yesmaximal, characteristic
6#16839668C211yesmaximal, characteristic, complemented
7C61×#336C211yesmaximal, characteristic, complemented
8C22×Dic122C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10C22×D244C2211yescharacteristic
11C2×Dic244—22no—
12C2×Dic244—22no—
13C2×Dic244—22no—
14C2×#11758190—22no—
15C2×#11758190—22no—
16C2×#11758190—22no—
17#14519765—22no—
18#14519765—22no—
19C2×C4⋊Dic61C2211yescharacteristic
20C2×#11758198—22no—
21#14519702—22no—
22#14519699—22no—
23#14519684—22no—
24C22×C8×C61C2211yescharacteristic
25C22×C8×C61C2211yescharacteristic
26C2×C42×C61C2211yescharacteristic
27C23×D61—21no—
28C22×C4×C61D412yes—
29C22×C4×C61C2311yescharacteristic
30C22×Dic61—21no—
31C22×Dic61—21no—
32C22×Dic61—21no—
33C2×D244—21no—
34C2×D244—21no—
35C2×D244—21no—
36C2×D244—21no—
37C2×D244—21no—
38C2×D244D412yes—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122—21no—
45C2×Dic122—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122D412yes—
50C2×Dic122D412yes—
51C2×C8×C61—21no—
52C2×C8×C61—21no—
53C2×C8×C61—21no—
54C2×C8×C61—21no—
55C2×C8×C61D412yes—
56C2×C8×C61D412yes—
57C42×C61—21no—
58C42×C61—21no—
59#11758198—28no—
60C4⋊Dic61—21no—
61C4⋊Dic61—21no—
62Dic244—28no—
63#11758190—28no—
64C23×C61C2×D411yescharacteristic
65C22×D61—22no—
66C22×D61—41no—
67C22×D61—41no—
68C22×D61—42no—
69C22×D61—42no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61#4111yescharacteristic
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86C2×Dic61—42no—
87D244—22no—
88D244—22no—
89D244—41no—
90D244—41no—
91Dic122—22no—
92Dic122—22no—
93Dic122—22no—
94Dic122—22no—
95Dic122—41no—
96Dic122—41no—
97Dic122—41no—
98Dic122—41no—
99C8×C61—22no—
100C8×C61—22no—
101C22×C61#12011yescharacteristic
102C22×C61#12111yescharacteristic
103C22×C61#12711yescharacteristic
104C22×C61#13512yes—
105C22×C61#13712yes—
106C2×D61—42no—
107C2×D61—44no—
108C2×D61—82no—
109C2×D61—81no—
110C2×D61—81no—
111C4×C61—42no—
112C4×C61#12011yescharacteristic
113C4×C61#12011yescharacteristic
114C4×C61#12111yescharacteristic
115C4×C61#12111yescharacteristic
116Dic61—42no—
117Dic61—42no—
118Dic61—81no—
119#2015—611nomaximal, Sylow
120C2×C61#39211yescharacteristic
121C2×C61#45212yes—
122C2×C61#46412yes—
123C2×C61#49511yescharacteristic
124C2×C61#49711yescharacteristic
125D61—82no—
126C22×Q16—611no—
127C22×SD16—611no—
128C2×#124—611no—
129C2×#103—611no—
130C2×#102—611no—
131#391—611no—
132#336D6111yescharacteristic, complemented
133C61#201511yescharacteristic, complemented, Sylow
134C22×Q8—611no—
135C22×Q8—611no—
136C22×D4—611no—
137C2×Q16—1222no—
138C2×Q16—1222no—
139C2×Q16—1222no—
140C2×SD16—1222no—
141C2×SD16—1222no—
142C2×SD16—1222no—
143C22×C8C2×D6111yescharacteristic
144C22×C8C2×D6111yescharacteristic
145#124—1222no—
146#124—1222no—
147C2×C4⋊C4—611no—
148C2×C22⋊C4—1222no—
149C2×C42C2×D6111yescharacteristic
150#103—1222no—
151#102—1222no—
152#95—1222no—
153C24—1221no—
154C2×Q8—612no—
155C2×Q8—612no—
156C2×Q8—1221no—
157C2×Q8—1221no—
158C2×Q8—1221no—
159C2×Q8—1221no—
160C2×Q8—1221no—
161C2×Q8—1221no—
162C2×Q8—1221no—
163C2×Q8—1221no—
164C2×Q8—1221no—
165C2×Q8—1221no—
166C2×D4—612no—
167C2×D4—1221no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—1221no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4—1221no—
175C22×C4D24412yes—
176C22×C4C22×D6111yescharacteristic
177Q16—1228no—
178SD16—1228no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8D24412yes—
184C2×C8D24412yes—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C22⋊C4—1228no—
188C42—21no—
189C42—21no—
190C23—1222no—
191C23—2442no—
192C23—2441no—
193C23—2441no—
194C23—2442no—
195C23C2×D24411yescharacteristic
196Q8—1222no—
197Q8—1222no—
198Q8—1222no—
199Q8—1222no—
200Q8—2441no—
201Q8—2441no—
202Q8—2441no—
203Q8—2441no—
204D4—1222no—
205D4—1222no—
206D4—2441no—
207D4—2441no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—1222no—
212C2×C4—1222no—
213C2×C4—2441no—
214C2×C4—2442no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4C2×D24411yescharacteristic
220C2×C4C2×D24411yescharacteristic
221C2×C4D4×D6111yescharacteristic
222C2×C4D4×D6111yescharacteristic
223C2×C4D4×D6111yescharacteristic
224C2×C4#1175822611yescharacteristic
225C8—22no—
226C8—22no—
227C22—4882no—
228C22—4881no—
229C22—4881no—
230C22—2444no—
231C22—2442no—
232C22#1451974711yescharacteristic
233C22#1451975211yescharacteristic
234C22#1451977411yescharacteristic
235C22#1451979912yes—
236C22#1451981012yes—
237C4—42no—
238C4—4881no—
239C4—2442no—
240C4—2442no—
241C4#1451974711yescharacteristic
242C4#1451974711yescharacteristic
243C4#1451975211yescharacteristic
244C4#1451975211yescharacteristic
245C2—4882no—
246C2#1683967211yescharacteristic
247C2#1683992612yes—
248C2#1683998512yes—
249C2#1684014611yescharacteristic
250C2#1684015611yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#336C2
socleC23×C61C2×D4
hypercenter#336D61
hypocenterC61#2015
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
1. C22×Dic244C2semidirect
4. C2×#14519702C2semidirect
6. #16839668C2semidirect
7. C61×#336C2semidirect
132. #336D61semidirect
133. C61#2015semidirect