Finite Group Databasebeta

← #21446898

Subgroups — #21446898

Order 7808.

426 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11758190C211yesmaximal, characteristic, complemented
2C22×#11758199C211yesmaximal, characteristic
3C2×#14519764C211yesmaximal, characteristic, complemented
4C2×#14519700C211yesmaximal, characteristic, complemented
5#16839663C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic, complemented
8C22×Dic122C2211yescharacteristic
9C22×D244C2211yescharacteristic
10C2×#11758190—22no—
11C2×#11758190—22no—
12C2×#11758190—22no—
13C2×#11758199—22no—
14C2×#11758199—22no—
15C2×#11758199—22no—
16C22×#92418C2211yescharacteristic
17#14519764—22no—
18#14519764—22no—
19C2×C22⋊Dic61—22no—
20C2×#11758198—22no—
21C2×C4×Dic61C2211yescharacteristic
22#14519700—22no—
23C22×D4×C61C2211yescharacteristic
24C22×C8×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2211yescharacteristic
26#102×C61—22no—
27C24×C61—21no—
28C23×D61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61D412yes—
35C22×C4×C61—21no—
36C22×C4×C61C2311yescharacteristic
37C22×Dic61—21no—
38C22×Dic61D412yes—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—21no—
43C2×D244—21no—
44C2×D244D412yes—
45C2×Dic122—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122D412yes—
51C2×C8×C61—21no—
52C2×C8×C61—21no—
53C2×C8×C61D412yes—
54C4⋊C4×C61—21no—
55C4⋊C4×C61—21no—
56C22⋊Dic61—28no—
57#11758199—28no—
58#11758198—44no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C2×#92418—21no—
62C2×#92418—21no—
63C2×#92418D412yes—
64#11758190—28no—
65C23×C61—22no—
66C23×C61—41no—
67C23×C61—41no—
68C23×C61—42no—
69C23×C61—42no—
70C23×C61C2×D411yescharacteristic
71C22×D61—22no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61—42no—
75C22×D61—42no—
76D4×C61—22no—
77D4×C61—22no—
78D4×C61—41no—
79D4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—42no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61#4111yescharacteristic
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94D244—22no—
95D244—22no—
96D244—41no—
97D244—41no—
98Dic122—22no—
99Dic122—22no—
100Dic122—41no—
101Dic122—41no—
102C8×C61—22no—
103#92418—22no—
104C22×C61—42no—
105C22×C61—44no—
106C22×C61—82no—
107C22×C61—81no—
108C22×C61—81no—
109C22×C61#12011yescharacteristic
110C22×C61#12111yescharacteristic
111C22×C61#12711yescharacteristic
112C22×C61#13512yes—
113C22×C61AGL(1,ℤ/8)12yes—
114C2×D61—42no—
115C2×D61—44no—
116C2×D61—82no—
117C2×D61—81no—
118C2×D61—81no—
119C4×C61—81no—
120C4×C61#12011yescharacteristic
121C4×C61#12011yescharacteristic
122C4×C61#12111yescharacteristic
123C4×C61#12111yescharacteristic
124Dic61—42no—
125Dic61—42no—
126#2012—611nomaximal, Sylow
127C2×C61—82no—
128C2×C61#39211yescharacteristic
129C2×C61#44912yes—
130C2×C61#46312yes—
131C2×C61#49511yescharacteristic
132C2×C61#49611yescharacteristic
133D61—82no—
134C22×SD16—611no—
135C22×D8—611no—
136C2×#124—611no—
137C2×#103—611no—
138C2×#102D6111yescharacteristic, complemented
139#390—611no—
140#336—611no—
141C61#201211yescharacteristic, complemented, Sylow
142C22×Q8—611no—
143C22×D4—611no—
144C22×D4C2×D6111yescharacteristic
145C2×SD16—1222no—
146C2×SD16—1222no—
147C2×SD16—1222no—
148C2×D8—1222no—
149C2×D8—1222no—
150C2×D8—1222no—
151C22×C8—611no—
152C22×C8C2×D6111yescharacteristic
153#124—1222no—
154#124—1222no—
155C2×C4⋊C4C2×D6111yescharacteristic
156C2×C22⋊C4—1222no—
157C2×C22⋊C4—1222no—
158C2×C42—611no—
159#103—1222no—
160#102—22no—
161C24—21no—
162C24—1221no—
163C2×Q8—612no—
164C2×Q8—1221no—
165C2×Q8—1221no—
166C2×Q8—1221no—
167C2×Q8—1221no—
168C2×Q8—1221no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—612no—
175C2×D4—1221no—
176C2×D4—1221no—
177C2×D4—1221no—
178C2×D4—1221no—
179C2×D4—1221no—
180C2×D4D24412yes—
181C22×C4—21no—
182C22×C4—612no—
183C22×C4—1221no—
184C22×C4C22×D6111yescharacteristic
185SD16—1228no—
186D8—1228no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—612no—
190C2×C8—1221no—
191C2×C8—1221no—
192C2×C8C22⋊D6112yes—
193C4⋊C4—21no—
194C4⋊C4—21no—
195C22⋊C4—1228no—
196C22⋊C4—2444no—
197C42—1221no—
198C42—1221no—
199C23—22no—
200C23—41no—
201C23—41no—
202C23—42no—
203C23—42no—
204C23—1222no—
205C23—2441no—
206C23—2441no—
207C23—2442no—
208C23—2442no—
209C23D4×D6111yescharacteristic
210Q8—1222no—
211Q8—1222no—
212Q8—2441no—
213Q8—2441no—
214D4—22no—
215D4—22no—
216D4—41no—
217D4—41no—
218D4—1222no—
219D4—1222no—
220D4—2441no—
221D4—2441no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—2441no—
229C2×C4—2441no—
230C2×C4C2×D24411yescharacteristic
231C2×C4#1175822211yescharacteristic
232C2×C4D4×D6111yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C2×C4D4×D6111yescharacteristic
235C2×C4C2×C22⋊D6111yescharacteristic
236C8—22no—
237C8—1222no—
238C22—44no—
239C22—42no—
240C22—82no—
241C22—81no—
242C22—81no—
243C22—4881no—
244C22—4881no—
245C22—4882no—
246C22—2444no—
247C22—2442no—
248C22#1451974711yescharacteristic
249C22#1451975011yescharacteristic
250C22#1451977311yescharacteristic
251C22#1451979812yes—
252C22#1451980112yes—
253C4—81no—
254C4—2442no—
255C4—2442no—
256C4#1451974511yescharacteristic
257C4#1451974711yescharacteristic
258C4#1451975011yescharacteristic
259C4#1451975111yescharacteristic
260C2—82no—
261C2—4882no—
262C2#1683967111yescharacteristic
263C2#1683990812yes—
264C2#1683997612yes—
265C2#1684014311yescharacteristic
266C2#1684015011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#2012
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#11758190C2semidirect
3. C2×#14519764C2semidirect
4. C2×#14519700C2semidirect
5. #16839663C2semidirect
6. #16839516C2semidirect
7. C2×#102×C61C2semidirect
138. C2×#102D61semidirect
141. C61#2012semidirect