Finite Group Databasebeta

← #21446894

Subgroups — #21446894

Order 7808.

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

normal subgroups only

This group has 426 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×#11758200C211yesmaximal, characteristic, complemented
2C2×#14519764C211yesmaximal, characteristic, complemented
3C2×#14519702C211yesmaximal, characteristic, complemented
4C2×#14519698C211yesmaximal, characteristic, complemented
5#16839665C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C22×D8×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758200—22no—
10C2×#11758200—22no—
11C2×#11758200—22no—
12C22×#92418C2211yescharacteristic
13#14519764—22no—
14#14519764—22no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C22⋊Dic61—22no—
17C2×C22⋊Dic61—22no—
18C2×C4×Dic61C2211yescharacteristic
19#14519702—22no—
20#14519698—22no—
21C22×D4×C61C2211yescharacteristic
22C22×D4×C61C2211yescharacteristic
23C2×D8×C61—22no—
24C2×D8×C61—22no—
25C2×D8×C61—22no—
26C22×C8×C61C2211yescharacteristic
27C24×C61—21no—
28C24×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—21no—
35C2×D4×C61—21no—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61D412yes—
40C2×D4×C61D412yes—
41C22×C4×C61C2311yescharacteristic
42C22×Dic61—21no—
43C22×Dic61—21no—
44C22×Dic61D412yes—
45C2×Dic122—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122D412yes—
51D8×C61—28no—
52C2×C8×C61—21no—
53C2×C8×C61—21no—
54C2×C8×C61D412yes—
55C22⋊Dic61—28no—
56C22⋊Dic61—44no—
57#11758200—28no—
58C4⋊Dic61—21no—
59C4⋊Dic61—21no—
60C4×Dic61—21no—
61C4×Dic61—21no—
62C2×#92418—21no—
63C2×#92418—21no—
64C2×#92418D412yes—
65C23×C61—22no—
66C23×C61—22no—
67C23×C61—41no—
68C23×C61—41no—
69C23×C61—41no—
70C23×C61—41no—
71C23×C61—42no—
72C23×C61—42no—
73C23×C61—42no—
74C23×C61—42no—
75C23×C61C2×D411yescharacteristic
76D4×C61—22no—
77D4×C61—22no—
78D4×C61—22no—
79D4×C61—22no—
80D4×C61—41no—
81D4×C61—41no—
82D4×C61—41no—
83D4×C61—41no—
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61#4111yescharacteristic
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—41no—
95C2×Dic61—41no—
96C2×Dic61—41no—
97C2×Dic61—42no—
98Dic122—22no—
99Dic122—22no—
100Dic122—41no—
101Dic122—41no—
102C8×C61—22no—
103#92418—22no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—44no—
107C22×C61—44no—
108C22×C61—82no—
109C22×C61—82no—
110C22×C61—81no—
111C22×C61—81no—
112C22×C61—81no—
113C22×C61—81no—
114C22×C61#12011yescharacteristic
115C22×C61#12111yescharacteristic
116C22×C61#12711yescharacteristic
117C22×C61#13512yes—
118C22×C61AGL(1,ℤ/8)12yes—
119C4×C61#12011yescharacteristic
120C4×C61#12011yescharacteristic
121C4×C61#12111yescharacteristic
122C4×C61#12111yescharacteristic
123Dic61—42no—
124Dic61—42no—
125Dic61—81no—
126#2012—611nomaximal, Sylow
127C2×C61—82no—
128C2×C61—82no—
129C2×C61#39211yescharacteristic
130C2×C61#44912yes—
131C2×C61#46312yes—
132C2×C61#49511yescharacteristic
133C2×C61#49611yescharacteristic
134C22×SD16—611no—
135C22×D8D6111yescharacteristic
136C2×#124—611no—
137C2×#103—611no—
138C2×#102—611no—
139#390—611no—
140#336—611no—
141C61#201211yescharacteristic, complemented, Sylow
142C22×Q8—611no—
143C22×D4C2×D6111yescharacteristic
144C22×D4C2×D6111yescharacteristic
145C2×SD16—1222no—
146C2×SD16—1222no—
147C2×SD16—1222no—
148C2×D8—22no—
149C2×D8—22no—
150C2×D8—22no—
151C22×C8—611no—
152C22×C8C2×D6111yescharacteristic
153#124—1222no—
154#124—1222no—
155C2×C4⋊C4—611no—
156C2×C22⋊C4—1222no—
157C2×C22⋊C4—1222no—
158C2×C42—611no—
159#103—1222no—
160#102—1222no—
161C24—21no—
162C24—21no—
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—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4C22⋊D6112yes—
180C2×D4C22⋊D6112yes—
181C22×C4—612no—
182C22×C4—1221no—
183C22×C4—1221no—
184C22×C4C22×D6111yescharacteristic
185SD16—1228no—
186D8—28no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—612no—
190C2×C8—1221no—
191C2×C8—1221no—
192C2×C8C22⋊D6112yes—
193C4⋊C4—1221no—
194C4⋊C4—1221no—
195C22⋊C4—1228no—
196C22⋊C4—2444no—
197C42—1221no—
198C42—1221no—
199C23—22no—
200C23—22no—
201C23—41no—
202C23—41no—
203C23—41no—
204C23—41no—
205C23—42no—
206C23—42no—
207C23—42no—
208C23—42no—
209C23D4×D6111yescharacteristic
210Q8—1222no—
211Q8—1222no—
212Q8—2441no—
213Q8—2441no—
214D4—22no—
215D4—22no—
216D4—22no—
217D4—22no—
218D4—41no—
219D4—41no—
220D4—41no—
221D4—41no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—2441no—
227C2×C4—2442no—
228C2×C4—2441no—
229C2×C4—2441no—
230C2×C4D4×D6111yescharacteristic
231C2×C4D4×D6111yescharacteristic
232C2×C4#1175822411yescharacteristic
233C2×C4C2×C22⋊D6111yescharacteristic
234C2×C4C2×C22⋊D6111yescharacteristic
235C2×C4C2×C22⋊D6111yescharacteristic
236C8—22no—
237C8—1222no—
238C22—44no—
239C22—44no—
240C22—42no—
241C22—42no—
242C22—82no—
243C22—81no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—82no—
248C22#1451974511yescharacteristic
249C22#1451974911yescharacteristic
250C22#1451977311yescharacteristic
251C22#1451979612yes—
252C22#1451980112yes—
253C4—4881no—
254C4—2442no—
255C4—2442no—
256C4#1451974511yescharacteristic
257C4#1451974611yescharacteristic
258C4#1451974811yescharacteristic
259C4#1451974911yescharacteristic
260C2—82no—
261C2—82no—
262C2#1683967011yescharacteristic
263C2#1683990412yes—
264C2#1683997512yes—
265C2#1684014511yescharacteristic
266C2#1684015011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC22×D8×C61C2
socleC23×C61C2×D4
hypercenterC22×D8D61
hypocenterC61#2012
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×#11758200C2semidirect
2. C2×#14519764C2semidirect
3. C2×#14519702C2semidirect
4. C2×#14519698C2semidirect
5. #16839665C2semidirect
6. #16839516C2semidirect
141. C61#2012semidirect