Finite Group Databasebeta

← #21446963

Subgroups — #21446963

Order 7808.

294 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#14519768C211yesmaximal, characteristic, complemented
2C2×#14519698C211yesmaximal, characteristic
3#16839665C211yesmaximal, characteristic
4#16839525C211yesmaximal, characteristic, complemented
5#16839524C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9#14519768—22no—
10#14519768—22no—
11C2×C4⋊Dic61—21no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196—21no—
15C2×C22⋊Dic61—21no—
16C2×C22⋊Dic61—21no—
17C2×C4×Dic61C2211yescharacteristic
18#14519698—22no—
19C22×D4×C61C2211yescharacteristic
20C22×C8×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22#102×C61—22no—
23C24×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61Q812yes—
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C22×Dic61—21no—
33C22×Dic61—21no—
34C22×Dic61D411yescharacteristic
35C22×Dic61D411yescharacteristic
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61D412yes—
41C22⋊Dic61—42no—
42C22⋊Dic61—42no—
43C4⋊Dic61—24no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61D412yes—
48#11758196—24no—
49C4×Dic61—21no—
50C4×Dic61—21no—
51C2×#92418—21no—
52C2×#92418—21no—
53C2×#92418—21no—
54C23×C61—22no—
55C23×C61—41no—
56C23×C61—41no—
57C23×C61—41no—
58C23×C61—41no—
59C23×C61—41no—
60C23×C61—41no—
61C23×C61C2×D411yescharacteristic
62D4×C61—22no—
63D4×C61—22no—
64D4×C61—41no—
65D4×C61—41no—
66C2×C4×C61—22no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×Q811yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—22no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86C2×Dic61—41no—
87C8×C61—41no—
88#92418—41no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61—81no—
93C22×C61—81no—
94C22×C61—81no—
95C22×C61—81no—
96C22×C61#12011yescharacteristic
97C22×C61C22⋊Q811yescharacteristic
98C22×C61#12411yescharacteristic
99C22×C61#13511yescharacteristic
100C22×C61#13511yescharacteristic
101C22×C61AGL(1,ℤ/8)11yescharacteristic
102C22×C61AGL(1,ℤ/8)11yescharacteristic
103C4×C61—42no—
104C4×C61C22⋊Q811yescharacteristic
105C4×C61C22⋊Q811yescharacteristic
106C4×C61#12411yescharacteristic
107C4×C61#12411yescharacteristic
108Dic61—41no—
109Dic61—41no—
110Dic61—42no—
111Dic61—81no—
112#2025—611nomaximal, Sylow
113C2×C61—82no—
114C2×C61#39311yescharacteristic
115C2×C61#44911yescharacteristic
116C2×C61#44911yescharacteristic
117C2×C61#47811yescharacteristic
118C2×C61#47811yescharacteristic
119C2×C61#48811yescharacteristic
120C2×C61#49011yescharacteristic
121C2×#125—611no—
122C2×#102—611no—
123C2×#102D6111yescharacteristic
124#390—611no—
125#340—611no—
126#340—611no—
127#336—611no—
128C61#202511yescharacteristic, complemented, Sylow
129C22×D4C2×D6111yescharacteristic
130C22×C8—611no—
131C22×C8C2×D6111yescharacteristic
132#125—1222no—
133#125—1222no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4—1221no—
137C2×C4⋊C4—1221no—
138C2×C4⋊C4C2×D6111yescharacteristic
139C2×C22⋊C4—1221no—
140C2×C22⋊C4—1221no—
141C2×C42—611no—
142#102—22no—
143#102—1222no—
144C24—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4Dic12212yes—
151C22×C4—21no—
152C22×C4—611no—
153C22×C4—611no—
154C22×C4—1221no—
155C22×C4—1221no—
156C22×C4C22×D6111yescharacteristic
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—1221no—
161C2×C8—1221no—
162C2×C8—1221no—
163C4⋊C4—21no—
164C4⋊C4—612no—
165C4⋊C4—1224no—
166C4⋊C4—1224no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C4⋊C4—1221no—
170C4⋊C4C22⋊D6112yes—
171C22⋊C4—2442no—
172C22⋊C4—2442no—
173C42—1221no—
174C42—1221no—
175C23—22no—
176C23—41no—
177C23—41no—
178C23—41no—
179C23—41no—
180C23—41no—
181C23—41no—
182C23D4×D6111yescharacteristic
183D4—22no—
184D4—22no—
185D4—41no—
186D4—41no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1222no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4—2441no—
201C2×C4—2441no—
202C2×C4C2×Dic12211yescharacteristic
203C2×C4#1175822211yescharacteristic
204C2×C4D4×D6111yescharacteristic
205C2×C4#1175822411yescharacteristic
206C2×C4#1175822411yescharacteristic
207C2×C4C2×C22⋊D6111yescharacteristic
208C8—41no—
209C8—2441no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—81no—
214C22—81no—
215C22—81no—
216C22—81no—
217C22#1451974511yescharacteristic
218C22#1451975411yescharacteristic
219C22#1451976311yescharacteristic
220C22#1451979611yescharacteristic
221C22#1451979811yescharacteristic
222C22#1451980111yescharacteristic
223C22#1451980411yescharacteristic
224C4—42no—
225C4—4881no—
226C4—2441no—
227C4—2441no—
228C4—2442no—
229C4#1451975411yescharacteristic
230C4#1451975611yescharacteristic
231C4#1451976311yescharacteristic
232C4#1451976411yescharacteristic
233C2—82no—
234C2#1683967411yescharacteristic
235C2#1683990411yescharacteristic
236C2#1683990611yescharacteristic
237C2#1684006011yescharacteristic
238C2#1684006411yescharacteristic
239C2#1684011511yescharacteristic
240C2#1684012511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#2025
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. C2×#14519768C2semidirect
4. #16839525C2semidirect
5. #16839524C2semidirect
6. #16839516C2semidirect
128. C61#2025semidirect