Finite Group Databasebeta

← #21446674

Subgroups — #21446674

Order 7808.

348 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 103 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
2C2×#14519708C211yesmaximal, characteristic, complemented
3C2×#14519702C211yesmaximal, characteristic, complemented
4C2×C8×Dic61C211yesmaximal, characteristic, complemented
5#16839667C211yesmaximal, characteristic, complemented
6#16839665C211yesmaximal, characteristic
7C2×#102×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758200—22no—
10C2×#11758200—22no—
11C2×#11758200C414yescomplemented
12C22×#92418C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C22⋊Dic61—22no—
15C2×C4×Dic61C2211yescharacteristic
16#14519708—22no—
17#14519702—22no—
18C8×Dic61—22no—
19#14519684—22no—
20C22×D4×C61C2211yescharacteristic
21C22×C8×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23#102×C61—22no—
24C24×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61C2×C412yes—
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33C22×Dic61—21no—
34C22×Dic61—21no—
35C22×Dic61D412yes—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122C2×C412yes—
42C2×C8×C61—21no—
43C2×C8×C61—21no—
44C2×C8×C61D412yes—
45C4⋊C4×C61—21no—
46C4⋊C4×C61—21no—
47C22⋊Dic61—44no—
48#11758200—28no—
49C4⋊Dic61—21no—
50C4⋊Dic61—21no—
51C4×Dic61—21no—
52C4×Dic61—21no—
53C2×#92418C2×C412yes—
54C2×#92418D412yes—
55C2×#92418D412yes—
56C23×C61—22no—
57C23×C61—41no—
58C23×C61—41no—
59C23×C61—42no—
60C23×C61—42no—
61C23×C61C2×D411yescharacteristic
62D4×C61—22no—
63D4×C61—22no—
64D4×C61—41no—
65D4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—42no—
68C2×C4×C61C22×C411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61—42no—
81C2×Dic61SD1614yescomplemented
82Dic122—22no—
83Dic122—22no—
84Dic122—41no—
85Dic122—41no—
86C8×C61—22no—
87#92418C22⋊C414yescomplemented
88C22×C61—42no—
89C22×C61—44no—
90C22×C61—82no—
91C22×C61—81no—
92C22×C61—81no—
93C22×C61C4×D411yescharacteristic
94C22×C61#12111yescharacteristic
95C22×C61#12711yescharacteristic
96C22×C61C2×SD1612yes—
97C22×C61#13512yes—
98C4×C61—81no—
99C4×C61C2×C22⋊C411yescharacteristic
100C4×C61C4×D411yescharacteristic
101C4×C61#12111yescharacteristic
102C4×C61#12411yescharacteristic
103Dic61—24no—
104Dic61—42no—
105Dic61—81no—
106#1968—611nomaximal, Sylow
107C2×C61—82no—
108C2×C61#39011yescharacteristic
109C2×C61C4×SD1612yes—
110C2×C61#46512yes—
111C2×C61#49211yescharacteristic
112C2×C61#49511yescharacteristic
113C22×SD16—611no—
114C2×#106—611no—
115C2×#103—611no—
116C2×#102D6111yescharacteristic
117C2×C4×C8—611no—
118#391—611no—
119#390—611no—
120C61#196811yescharacteristic, complemented, Sylow
121C22×Q8—611no—
122C22×D4C2×D6111yescharacteristic
123C2×SD16—614no—
124C2×SD16—1222no—
125C2×SD16—1222no—
126C22×C8—611no—
127C22×C8C2×D6111yescharacteristic
128C2×C4⋊C4—611no—
129C2×C4⋊C4C2×D6111yescharacteristic
130C2×C22⋊C4—1222no—
131C2×C42—611no—
132#106—1222no—
133#103—1222no—
134#102—22no—
135C4×C8—1222no—
136#95—1222no—
137C24—21no—
138C2×Q8—612no—
139C2×Q8—1221no—
140C2×Q8—1221no—
141C2×Q8—1221no—
142C2×Q8—1221no—
143C2×Q8—1221no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4C4×D6112yes—
150C22×C4—21no—
151C22×C4—612no—
152C22×C4—1221no—
153C22×C4—1221no—
154C22×C4C22×D6111yescharacteristic
155SD16—1228no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—612no—
159C2×C8—612no—
160C2×C8—612no—
161C2×C8C22⋊D6112yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C22⋊C4—2444no—
167C42—1221no—
168C42—1221no—
169C23—22no—
170C23—41no—
171C23—41no—
172C23—42no—
173C23—42no—
174C23D4×D6111yescharacteristic
175Q8—1222no—
176Q8—1222no—
177Q8—2441no—
178Q8—2441no—
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—41no—
184C2×C4—42no—
185C2×C4—614no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—2441no—
190C2×C4—2442no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4C2×C4×D6111yescharacteristic
194C2×C4#1175822211yescharacteristic
195C2×C4D4×D6111yescharacteristic
196C2×C4D4×D6111yescharacteristic
197C2×C4#1175822411yescharacteristic
198C2×C4C2×C22⋊D6111yescharacteristic
199C8—22no—
200C8—614no—
201C22—44no—
202C22—42no—
203C22—82no—
204C22—81no—
205C22—81no—
206C22#1451973711yescharacteristic
207C22#1451975011yescharacteristic
208C22#1451977311yescharacteristic
209C22SD16×D6112yes—
210C22#1451979612yes—
211C4—81no—
212C4—1224no—
213C4—4881no—
214C4—2442no—
215C4C22⋊C4×D6111yescharacteristic
216C4C4×C22⋊D6111yescharacteristic
217C4#1451974911yescharacteristic
218C4#1451976311yescharacteristic
219C2—82no—
220C2#1683966211yescharacteristic
221C2#1683985312yes—
222C2#1683999012yes—
223C2#1684013311yescharacteristic
224C2#1684014511yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#1968
LCSG ▷ C2×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
2. C2×#14519708C2semidirect
3. C2×#14519702C2semidirect
4. C2×C8×Dic61C2semidirect
5. #16839667C2semidirect
11. C2×#11758200C4semidirect
81. C2×Dic61SD16semidirect
87. #92418C22⋊C4semidirect
120. C61#1968semidirect