Finite Group Databasebeta

← #21447236

Subgroups — #21447236

Order 7808.

258 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 77 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×#14519699C211yesmaximal, characteristic
2C2×#14519697C211yesmaximal, characteristic
3#16839663C211yesmaximal, characteristic
4#16839627C211yesmaximal, characteristic, complemented
5#16839524C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C61×#340C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×#11758198—21no—
12C2×#11758198—21no—
13C2×C4×Dic61C2211yescharacteristic
14#14519699—22no—
15#14519697—22no—
16#14519684—21no—
17#14519684—21no—
18C22×C8×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21C23×D61—21no—
22C22×C4×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61D411yescharacteristic
27C22×Dic61D411yescharacteristic
28C2×D244—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244D412yes—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41#11758198—42no—
42#11758198—42no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4×Dic61—21no—
46C4×Dic61—21no—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C23×C61C2×D411yescharacteristic
51C22×D61—22no—
52C22×D61—41no—
53C22×D61—41no—
54C22×D61—41no—
55C22×D61—41no—
56C22×D61—41no—
57C22×D61—41no—
58C2×C4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×C4×C61#4111yescharacteristic
68C2×C4×C61#4111yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—21no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79D244—22no—
80D244—22no—
81D244—41no—
82D244—41no—
83C8×C61—41no—
84#92418—41no—
85C22×C61#12111yescharacteristic
86C22×C61#12311yescharacteristic
87C22×C61#12411yescharacteristic
88C22×C61#13511yescharacteristic
89C22×C61#13511yescharacteristic
90C22×C61AGL(1,ℤ/8)11yescharacteristic
91C22×C61AGL(1,ℤ/8)11yescharacteristic
92C2×D61—42no—
93C2×D61—42no—
94C2×D61—42no—
95C2×D61—81no—
96C2×D61—81no—
97C2×D61—81no—
98C2×D61—81no—
99C4×C61—81no—
100C4×C61—81no—
101C4×C61#12311yescharacteristic
102C4×C61#12311yescharacteristic
103C4×C61#12611yescharacteristic
104C4×C61#12611yescharacteristic
105Dic61—41no—
106Dic61—41no—
107Dic61—81no—
108#2073—611nomaximal, Sylow
109C2×C61#39711yescharacteristic
110C2×C61#46311yescharacteristic
111C2×C61#46311yescharacteristic
112C2×C61#48211yescharacteristic
113C2×C61#48211yescharacteristic
114C2×C61#48811yescharacteristic
115C2×C61#49011yescharacteristic
116D61—82no—
117C2×#102—611no—
118C2×#102—611no—
119#390—611no—
120#382—611no—
121#340—611no—
122#340D6111yescharacteristic, complemented
123#336—611no—
124C61#207311yescharacteristic, complemented, Sylow
125C22×D4—611no—
126C22×C8—611no—
127C22×C8C2×D6111yescharacteristic
128C2×C4⋊C4—611no—
129C2×C4⋊C4C2×D6111yescharacteristic
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C22⋊C4—1221no—
132C2×C22⋊C4—1221no—
133C2×C42—611no—
134#102—1222no—
135#102—1222no—
136#95—1221no—
137#95—1221no—
138C24—1221no—
139C2×D4—612no—
140C2×D4—1221no—
141C2×D4—1221no—
142C2×D4—1221no—
143C2×D4—1221no—
144C2×D4—1221no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—611no—
148C22×C4—611no—
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—21no—
160C4⋊C4—21no—
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C22⋊C4—2442no—
164C22⋊C4—2442no—
165C42—1221no—
166C42—1221no—
167C23—1222no—
168C23—2441no—
169C23—2441no—
170C23—2441no—
171C23—2441no—
172C23—2441no—
173C23—2441no—
174C23D4×D6111yescharacteristic
175D4—1222no—
176D4—1222no—
177D4—2441no—
178D4—2441no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—1221no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4—2441no—
194C2×C4#1175822211yescharacteristic
195C2×C4#1175822211yescharacteristic
196C2×C4#1175822211yescharacteristic
197C2×C4D4×D6111yescharacteristic
198C2×C4#1175822411yescharacteristic
199C2×C4#1175822611yescharacteristic
200C8—41no—
201C8—2441no—
202C22—4881no—
203C22—4881no—
204C22—4881no—
205C22—4881no—
206C22—2442no—
207C22—2442no—
208C22—2442no—
209C22#1451975011yescharacteristic
210C22#1451976211yescharacteristic
211C22#1451976311yescharacteristic
212C22#1451979811yescharacteristic
213C22#1451980011yescharacteristic
214C22#1451980111yescharacteristic
215C22#1451980411yescharacteristic
216C4—81no—
217C4—81no—
218C4—4881no—
219C4—2441no—
220C4—2441no—
221C4#1451975911yescharacteristic
222C4#1451976211yescharacteristic
223C4#1451977111yescharacteristic
224C4#1451977211yescharacteristic
225C2—4882no—
226C2#1683969111yescharacteristic
227C2#1683997611yescharacteristic
228C2#1683998011yescharacteristic
229C2#1684008811yescharacteristic
230C2#1684008911yescharacteristic
231C2#1684011811yescharacteristic
232C2#1684012511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#2073
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
4. #16839627C2semidirect
5. #16839524C2semidirect
6. #16839516C2semidirect
7. C61×#340C2semidirect
122. #340D61semidirect
124. C61#2073semidirect