Finite Group Databasebeta

← #21446778

Subgroups — #21446778

Order 7808.

300 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14519776C211yesmaximal, characteristic
2C2×C8×Dic61C211yesmaximal, characteristic
3#16839631C211yesmaximal, characteristic
4#16839525C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic
6#16839524C211yesmaximal, characteristic
7C61×#340C211yesmaximal, characteristic
8C22×Dic122—21no—
9C22×#92418C2211yescharacteristic
10#14519776—22no—
11#14519776C414yescomplemented
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196—21no—
15C2×#11758196—21no—
16C2×#11758196—21no—
17C2×C4×Dic61C2211yescharacteristic
18C8×Dic61—22no—
19C22×C8×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C22×C4×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61—21no—
27C22×Dic61D411yescharacteristic
28C22×Dic61D411yescharacteristic
29C2×Dic122—24no—
30C2×Dic122—42no—
31C2×Dic122—42no—
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C2×C8×C61Q812yescomplemented
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61C2×C412yes—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61C2×C412yes—
43#11758196—24no—
44#11758196—42no—
45#11758196—42no—
46C4×Dic61C2×C412yes—
47C4×Dic61D412yes—
48C2×#92418—21no—
49C2×#92418—21no—
50C2×#92418Q812yescomplemented
51C23×C61C2×D411yescharacteristic
52C2×C4×C61—22no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61C22×C411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×Q811yescharacteristic
61C2×C4×C61C2×Q811yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×Dic61—22no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61C22⋊C412yes—
71C2×Dic61C22⋊C412yes—
72C2×Dic61D812yes—
73C2×Dic61SD1612yes—
74C2×Dic61SD1612yes—
75C2×Dic61Q1612yes—
76Dic122—48no—
77C8×C61—22no—
78#92418—22no—
79C22×C61C2×C22⋊C411yescharacteristic
80C22×C61#12411yescharacteristic
81C22×C61C4⋊Q811yescharacteristic
82C22×C61C2×D811yescharacteristic
83C22×C61C2×SD1611yescharacteristic
84C22×C61C2×SD1611yescharacteristic
85C22×C61C2×Q1611yescharacteristic
86C4×C61—42no—
87C4×C61—81no—
88C4×C61C4×Q811yescharacteristic
89C4×C61C4×Q811yescharacteristic
90C4×C61C22⋊Q811yescharacteristic
91C4×C61C22⋊Q811yescharacteristic
92Dic61—42no—
93Dic61—81no—
94Dic61#10214yes—
95Dic61#10314yes—
96#1990—611nomaximal, Sylow
97C2×C61#39111yescharacteristic
98C2×C61C2×#10211yescharacteristic
99C2×C61C2×#10311yescharacteristic
100C2×C61#48611yescharacteristic
101C2×C61#48711yescharacteristic
102C2×C61#49811yescharacteristic
103C2×C61#50011yescharacteristic
104C2×C4⋊Q8—611no—
105C2×C4×C8—611no—
106#384—611no—
107#340—611no—
108#340—611no—
109#340—611no—
110#340D6111yescharacteristic
111C61#199011yescharacteristic, complemented, Sylow
112C22×Q8—1221no—
113C22×C8—611no—
114C22×C8C2×D6111yescharacteristic
115C4⋊Q8—614no—
116C4⋊Q8—1222no—
117C2×C4⋊C4—611no—
118C2×C4⋊C4—611no—
119C2×C4⋊C4—1221no—
120C2×C4⋊C4—1221no—
121C2×C4⋊C4—1221no—
122C2×C4⋊C4C2×D6111yescharacteristic
123C2×C4⋊C4C2×D6111yescharacteristic
124C2×C42—611no—
125C4×C8—1222no—
126C2×Q8—1224no—
127C2×Q8—2442no—
128C2×Q8—2442no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—1221no—
134C22×C4—1221no—
135C22×C4C22×D6111yescharacteristic
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—612no—
139C2×C8—1221no—
140C2×C8—1221no—
141C2×C8Dic12212yescomplemented
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—612no—
146C4⋊C4—1224no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4—2442no—
151C4⋊C4—2442no—
152C4⋊C4C4×D6112yes—
153C42—612no—
154C42—612no—
155C23D4×D6111yescharacteristic
156Q8—2448no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—612no—
164C2×C4—612no—
165C2×C4—612no—
166C2×C4—612no—
167C2×C4—612no—
168C2×C4—612no—
169C2×C4—1222no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4—2441no—
174C2×C4—2441no—
175C2×C4C2×Dic12211yescharacteristic
176C2×C4C2×C4×D6111yescharacteristic
177C2×C4#1175822211yescharacteristic
178C2×C4D4×D6111yescharacteristic
179C2×C4#1175822411yescharacteristic
180C2×C4Q8×D6111yescharacteristic
181C8—22no—
182C8—1222no—
183C22C22⋊C4×D6111yescharacteristic
184C22#1451976311yescharacteristic
185C22#1451977611yescharacteristic
186C22D8×D6111yescharacteristic
187C22SD16×D6111yescharacteristic
188C22SD16×D6111yescharacteristic
189C22Q16×D6111yescharacteristic
190C4—42no—
191C4—81no—
192C4—614no—
193C4—614no—
194C4—4881no—
195C4—2442no—
196C4#1451974211yescharacteristic
197C4C4×Dic12211yescharacteristic
198C4#1451975411yescharacteristic
199C4#1451975511yescharacteristic
200C2#1683966611yescharacteristic
201C2#102×D6111yescharacteristic
202C2#103×D6111yescharacteristic
203C2#1684010711yescharacteristic
204C2#1684011111yescharacteristic
205C2#1684015911yescharacteristic
206C2#1684016611yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1990
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
11. #14519776C4semidirect
34. C2×C8×C61Q8semidirect
50. C2×#92418Q8semidirect
111. C61#1990semidirect
141. C2×C8Dic122semidirect