Finite Group Databasebeta

← #21447349

Subgroups — #21447349

Order 7808.

290 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14519708C211yesmaximal, characteristic, complemented
2C2×#14519699C211yesmaximal, characteristic
3C2×#14519697C211yesmaximal, characteristic
4#16839663C211yesmaximal, characteristic
5#16839631C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#106×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×#11758196—22no—
12C2×#11758198—22no—
13C2×C4×Dic61C2211yescharacteristic
14#14519708—22no—
15#14519699—22no—
16#14519697—22no—
17C22×C8×C61C2211yescharacteristic
18C2×C4⋊C4×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20#106×C61—22no—
21C23×D61—21no—
22C22×C4×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61D412yes—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244Q812yes—
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C2×C8×C61D412yes—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40#11758198—44no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43#11758196—44no—
44C4×Dic61—21no—
45C4×Dic61—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C2×#92418D412yes—
49C23×C61C2×D411yescharacteristic
50C22×D61—22no—
51C22×D61—41no—
52C22×D61—41no—
53C22×D61—42no—
54C22×D61—42no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61—42no—
58C2×C4×C61—42no—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×Q811yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×Dic61—22no—
66C2×Dic61—22no—
67C2×Dic61—41no—
68C2×Dic61—42no—
69C2×Dic61SD1614yes—
70D244—22no—
71D244—22no—
72D244—41no—
73D244—41no—
74C8×C61—22no—
75#92418—22no—
76C22×C61C22⋊Q811yescharacteristic
77C22×C61#12311yescharacteristic
78C22×C61#12711yescharacteristic
79C22×C61C2×SD1612yes—
80C22×C61AGL(1,ℤ/8)12yes—
81C2×D61—42no—
82C2×D61—44no—
83C2×D61—82no—
84C2×D61—81no—
85C2×D61—81no—
86C4×C61—81no—
87C4×C61—81no—
88C4×C61C22⋊Q811yescharacteristic
89C4×C61C22⋊Q811yescharacteristic
90C4×C61#12311yescharacteristic
91C4×C61#12311yescharacteristic
92Dic61—24no—
93Dic61—81no—
94#2094—611nomaximal, Sylow
95C2×C61#39911yescharacteristic
96C2×C61#47612yes—
97C2×C61#48112yes—
98C2×C61#49211yescharacteristic
99C2×C61#49611yescharacteristic
100D61—82no—
101C2×#106—611no—
102C2×#106D6111yescharacteristic, complemented
103C2×#102—611no—
104C2×#102—611no—
105#390—611no—
106#384—611no—
107#336—611no—
108C61#209411yescharacteristic, complemented, Sylow
109C22×D4—611no—
110C22×C8—611no—
111C22×C8C2×D6111yescharacteristic
112C2×C4⋊C4—611no—
113C2×C4⋊C4—1222no—
114C2×C4⋊C4C2×D6111yescharacteristic
115C2×C4⋊C4C2×D6111yescharacteristic
116C2×C22⋊C4—1222no—
117C2×C42—611no—
118#106—22no—
119#106—1222no—
120#102—1222no—
121#102—1222no—
122C24—1221no—
123C2×D4—612no—
124C2×D4—1221no—
125C2×D4—1221no—
126C2×D4—1221no—
127C2×D4—1221no—
128C2×D4—1221no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—612no—
132C22×C4—1221no—
133C22×C4C22×D6111yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—612no—
137C2×C8—1221no—
138C2×C8—1221no—
139C2×C8C22⋊D6112yes—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C4⋊C4—2444no—
147C22⋊C4—2444no—
148C42—1221no—
149C42—1221no—
150C23—1222no—
151C23—2441no—
152C23—2441no—
153C23—2442no—
154C23—2442no—
155C23D4×D6111yescharacteristic
156D4—1222no—
157D4—1222no—
158D4—2441no—
159D4—2441no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—614no—
165C2×C4—1222no—
166C2×C4—1222no—
167C2×C4—2441no—
168C2×C4—2442no—
169C2×C4#1175822211yescharacteristic
170C2×C4#1175822211yescharacteristic
171C2×C4D4×D6111yescharacteristic
172C2×C4Q8×D6111yescharacteristic
173C2×C4#1175822611yescharacteristic
174C2×C4C2×C22⋊D6111yescharacteristic
175C8—22no—
176C8—1222no—
177C22—4882no—
178C22—4881no—
179C22—4881no—
180C22—2442no—
181C22—2444no—
182C22#1451975511yescharacteristic
183C22#1451976211yescharacteristic
184C22#1451977311yescharacteristic
185C22SD16×D6112yes—
186C22#1451980412yes—
187C4—81no—
188C4—81no—
189C4—1224no—
190C4—4881no—
191C4#1451975311yescharacteristic
192C4#1451975511yescharacteristic
193C4#1451976011yescharacteristic
194C4#1451976211yescharacteristic
195C2—4882no—
196C2#1683969711yescharacteristic
197C2#1684005112yes—
198C2#1684008212yes—
199C2#1684013311yescharacteristic
200C2#1684014811yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#106×C61C2
socleC23×C61C2×D4
hypercenterC2×#106D61
hypocenterC61#2094
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
1. C2×#14519708C2semidirect
5. #16839631C2semidirect
6. #16839516C2semidirect
7. C2×#106×C61C2semidirect
102. C2×#106D61semidirect
108. C61#2094semidirect