Finite Group Databasebeta

← #21447253

Subgroups — #21447253

Order 7808.

256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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×#14519689C211yesmaximal, characteristic
2#16839619C211yesmaximal, characteristic
3#16839619C211yesmaximal, characteristic
4#16839525C211yesmaximal, characteristic, complemented
5#16839524C211yesmaximal, characteristic, complemented
6#16839524C211yesmaximal, characteristic, complemented
7C2×#106×C61C211yesmaximal, characteristic, complemented
8C22×C4×D61C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758198—21no—
13C2×#11758198—21no—
14#14519689—22no—
15#14519684—21no—
16#14519684—21no—
17C22×C8×C61C2211yescharacteristic
18C2×C4⋊C4×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20#106×C61—22no—
21C23×D61D411yescharacteristic
22C22×C4×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61—21no—
27C22×Dic61D411yescharacteristic
28C2×C4×D61—21no—
29C2×C4×D61—21no—
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×C4×D61—21no—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C2×C8×C61D412yes—
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—21no—
52C22×D61—21no—
53C22×D61—21no—
54C22×D61—21no—
55C22×D61—21no—
56C22×D61—21no—
57C22×D61SD1612yes—
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—41no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C4×D61—41no—
80C4×D61—41no—
81C4×D61—41no—
82C4×D61—41no—
83C8×C61—22no—
84#92418—41no—
85C22×C61#12111yescharacteristic
86C22×C61#12311yescharacteristic
87C22×C61#12311yescharacteristic
88C22×C61C2×SD1611yescharacteristic
89C22×C61#13511yescharacteristic
90C22×C61AGL(1,ℤ/8)11yescharacteristic
91C22×C61#13711yescharacteristic
92C2×D61—22no—
93C2×D61—22no—
94C2×D61—22no—
95C2×D61—41no—
96C2×D61—41no—
97C2×D61—41no—
98C2×D61—41no—
99C4×C61—81no—
100C4×C61—81no—
101C4×C61#12311yescharacteristic
102C4×C61#12411yescharacteristic
103C4×C61#12611yescharacteristic
104C4×C61#12611yescharacteristic
105Dic61—41no—
106Dic61—81no—
107Dic61—81no—
108#2077—611nomaximal, Sylow
109C2×C61#39711yescharacteristic
110C2×C61#46511yescharacteristic
111C2×C61#46811yescharacteristic
112C2×C61#48111yescharacteristic
113C2×C61#48211yescharacteristic
114C2×C61#48311yescharacteristic
115C2×C61#48511yescharacteristic
116D61—42no—
117C2×#106D6111yescharacteristic, complemented
118C2×C22⋊C8—611no—
119#380—611no—
120#380—611no—
121#340—611no—
122#340—611no—
123#340—611no—
124C61#207711yescharacteristic, complemented, Sylow
125C23×C4—611no—
126C22×C8—611no—
127C22×C8C2×D6111yescharacteristic
128C2×C4⋊C4—611no—
129C2×C4⋊C4—611no—
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C4⋊C4C2×D6111yescharacteristic
132C2×C22⋊C4—1221no—
133C2×C22⋊C4—1221no—
134#106—22no—
135C22⋊C8—1222no—
136#95—1221no—
137#95—1221no—
138C24—611no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—611no—
142C22×C4—1221no—
143C22×C4—1221no—
144C22×C4—1221no—
145C22×C4—1221no—
146C22×C4—1221no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4C22×D6111yescharacteristic
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—1221no—
154C2×C8—1221no—
155C2×C8—1221no—
156C2×C8C22⋊D6112yes—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C4⋊C4—1221no—
164C4⋊C4—1221no—
165C22⋊C4—2442no—
166C22⋊C4—2442no—
167C23—612no—
168C23—1221no—
169C23—1221no—
170C23—1221no—
171C23—1221no—
172C23—1221no—
173C23—1221no—
174C23D4×D6111yescharacteristic
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4—2441no—
187C2×C4—2441no—
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#1175822611yescharacteristic
198C2×C4#1175822611yescharacteristic
199C2×C4C2×C22⋊D6111yescharacteristic
200C8—22no—
201C8—2441no—
202C22—1222no—
203C22—1222no—
204C22—1222no—
205C22—2441no—
206C22—2441no—
207C22—2441no—
208C22—2441no—
209C22#1451974811yescharacteristic
210C22#1451976211yescharacteristic
211C22#1451976211yescharacteristic
212C22SD16×D6111yescharacteristic
213C22#1451979811yescharacteristic
214C22#1451980411yescharacteristic
215C22#1451980611yescharacteristic
216C4—81no—
217C4—81no—
218C4—4881no—
219C4—4881no—
220C4—2441no—
221C4#1451976011yescharacteristic
222C4#1451976611yescharacteristic
223C4#1451977211yescharacteristic
224C4#1451977211yescharacteristic
225C2—2442no—
226C2#1683968811yescharacteristic
227C2#1683998811yescharacteristic
228C2#1684000511yescharacteristic
229C2#1684008211yescharacteristic
230C2#1684008811yescharacteristic
231C2#1684009411yescharacteristic
232C2#1684010611yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#106×C61C2
socleC23×C61C2×D4
hypercenterC2×#106D61
hypocenterC61#2077
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
4. #16839525C2semidirect
5. #16839524C2semidirect
6. #16839524C2semidirect
7. C2×#106×C61C2semidirect
117. C2×#106D61semidirect
124. C61#2077semidirect