Finite Group Databasebeta

← #21447235

Subgroups — #21447235

Order 7808.

258 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 79 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×#14519698C211yesmaximal, characteristic
2#16839665C211yesmaximal, characteristic
3#16839627C211yesmaximal, characteristic, complemented
4#16839525C211yesmaximal, characteristic, complemented
5#16839524C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C2×C4⋊Dic61C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C22⋊Dic61—21no—
12C2×C22⋊Dic61—21no—
13C2×C4×Dic61C2211yescharacteristic
14#14519698—22no—
15#14519684—21no—
16#14519684—21no—
17C22×D4×C61C2211yescharacteristic
18C22×C8×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20#102×C61—22no—
21C24×C61—21no—
22C2×D4×C61—21no—
23C2×D4×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61D412yes—
28C22×C4×C61—21no—
29C22×C4×C61C2311yescharacteristic
30C22×Dic61—21no—
31C22×Dic61—21no—
32C22×Dic61D411yescharacteristic
33C22×Dic61D411yescharacteristic
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C22⋊Dic61—42no—
40C22⋊Dic61—42no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4×Dic61—21no—
46C4×Dic61—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C23×C61—22no—
51C23×C61—41no—
52C23×C61—41no—
53C23×C61—41no—
54C23×C61—41no—
55C23×C61—41no—
56C23×C61—41no—
57C23×C61C2×D411yescharacteristic
58D4×C61—22no—
59D4×C61—22no—
60D4×C61—41no—
61D4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×C4×C61#4111yescharacteristic
68C2×C4×C61#4111yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83C8×C61—41no—
84#92418—41no—
85C22×C61—42no—
86C22×C61—42no—
87C22×C61—42no—
88C22×C61—81no—
89C22×C61—81no—
90C22×C61—81no—
91C22×C61—81no—
92C22×C61#12111yescharacteristic
93C22×C61#12311yescharacteristic
94C22×C61#12411yescharacteristic
95C22×C61#13511yescharacteristic
96C22×C61#13511yescharacteristic
97C22×C61AGL(1,ℤ/8)11yescharacteristic
98C22×C61AGL(1,ℤ/8)11yescharacteristic
99C4×C61—81no—
100C4×C61#12311yescharacteristic
101C4×C61#12311yescharacteristic
102C4×C61#12611yescharacteristic
103C4×C61#12611yescharacteristic
104Dic61—41no—
105Dic61—41no—
106Dic61—81no—
107Dic61—81no—
108#2073—611nomaximal, Sylow
109C2×C61—82no—
110C2×C61#39711yescharacteristic
111C2×C61#46311yescharacteristic
112C2×C61#46311yescharacteristic
113C2×C61#48211yescharacteristic
114C2×C61#48211yescharacteristic
115C2×C61#48811yescharacteristic
116C2×C61#49011yescharacteristic
117C2×#102—611no—
118C2×#102D6111yescharacteristic
119#390—611no—
120#382—611no—
121#340—611no—
122#340—611no—
123#336—611no—
124C61#207311yescharacteristic, complemented, Sylow
125C22×D4C2×D6111yescharacteristic
126C22×C8—611no—
127C22×C8C2×D6111yescharacteristic
128C2×C4⋊C4—611no—
129C2×C4⋊C4—611no—
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C22⋊C4—1221no—
132C2×C22⋊C4—1221no—
133C2×C42—611no—
134#102—22no—
135#102—1222no—
136#95—1221no—
137#95—1221no—
138C24—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4C22⋊D6112yes—
145C22×C4—21no—
146C22×C4—611no—
147C22×C4—611no—
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4C22×D6111yescharacteristic
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—1221no—
155C2×C8—1221no—
156C2×C8—1221no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C22⋊C4—2442no—
164C22⋊C4—2442no—
165C42—1221no—
166C42—1221no—
167C23—22no—
168C23—41no—
169C23—41no—
170C23—41no—
171C23—41no—
172C23—41no—
173C23—41no—
174C23D4×D6111yescharacteristic
175D4—22no—
176D4—22no—
177D4—41no—
178D4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—1221no—
185C2×C4—1221no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4—2441no—
194C2×C4#1175822211yescharacteristic
195C2×C4#1175822211yescharacteristic
196C2×C4#1175822411yescharacteristic
197C2×C4#1175822411yescharacteristic
198C2×C4#1175822411yescharacteristic
199C2×C4C2×C22⋊D6111yescharacteristic
200C8—41no—
201C8—2441no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—81no—
206C22—81no—
207C22—81no—
208C22—81no—
209C22#1451974911yescharacteristic
210C22#1451975911yescharacteristic
211C22#1451976311yescharacteristic
212C22#1451979611yescharacteristic
213C22#1451979811yescharacteristic
214C22#1451980111yescharacteristic
215C22#1451980411yescharacteristic
216C4—81no—
217C4—4881no—
218C4—4881no—
219C4—2441no—
220C4—2441no—
221C4#1451975811yescharacteristic
222C4#1451976011yescharacteristic
223C4#1451977011yescharacteristic
224C4#1451977011yescharacteristic
225C2—82no—
226C2#1683969011yescharacteristic
227C2#1683997511yescharacteristic
228C2#1683997911yescharacteristic
229C2#1684008411yescharacteristic
230C2#1684008511yescharacteristic
231C2#1684011511yescharacteristic
232C2#1684012511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#2073
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
3. #16839627C2semidirect
4. #16839525C2semidirect
5. #16839524C2semidirect
6. #16839516C2semidirect
124. C61#2073semidirect