Finite Group Databasebeta

← #21446397

Subgroups — #21446397

Order 7808.

230 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 97 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
2#16839660C211yesmaximal, characteristic
3#16839524C211yesmaximal, characteristic
4#16839524C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic
6#16839517C211yesmaximal, characteristic
7C4×C4⋊C4×C61C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196—21no—
13#14519708C414yescomplemented
14#14519684—21no—
15C2×C4⋊C4×C61C2211yescharacteristic
16C2×C4⋊C4×C61C2211yescharacteristic
17C2×C42×C61—21no—
18C2×C42×C61C2211yescharacteristic
19#95×C61—21no—
20C22×C4×C61—21no—
21C22×C4×C61—21no—
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61—21no—
27C4⋊C4×C61—21no—
28C4⋊C4×C61—21no—
29C4⋊C4×C61C2×C412yes—
30C4⋊C4×C61Q812yes—
31C42×C61—21no—
32C42×C61—21no—
33C42×C61—42no—
34C4⋊Dic61—21no—
35C4⋊Dic61—21no—
36C4⋊Dic61—21no—
37C4⋊Dic61C2×C412yes—
38#11758196—42no—
39C2×#92418—21no—
40C2×#92418—21no—
41C2×#92418—21no—
42C2×#92418—21no—
43C2×#92418—21no—
44C2×#92418C2×C412yes—
45C23×C61C2×D411yescharacteristic
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61—22no—
49C2×C4×C61—22no—
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61SD1612yes—
58C2×C4×C61C22×C411yescharacteristic
59C2×C4×C61C2×Q811yescharacteristic
60C2×C4×C61#4111yescharacteristic
61C2×C4×C61#4111yescharacteristic
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—
70#92418—22no—
71#92418—41no—
72C22×C61C4×D411yescharacteristic
73C22×C61C22⋊Q811yescharacteristic
74C22×C61#12311yescharacteristic
75C22×C61C2×SD1611yescharacteristic
76C22×C61#13511yescharacteristic
77C22×C61AGL(1,ℤ/8)11yescharacteristic
78C22×C61#13711yescharacteristic
79C4×C61—22no—
80C4×C61—42no—
81C4×C61—42no—
82C4×C61—41no—
83C4×C61#11711yescharacteristic
84C4×C61C4×Q811yescharacteristic
85C4×C61#12511yescharacteristic
86C4×C61#12611yescharacteristic
87Dic61—42no—
88Dic61—81no—
89#1919—611nomaximal, Sylow
90C2×C61#38711yescharacteristic
91C2×C61C4×SD1611yescharacteristic
92C2×C61#44011yescharacteristic
93C2×C61#47511yescharacteristic
94C2×C61#47811yescharacteristic
95C2×C61#48111yescharacteristic
96C2×C61#48511yescharacteristic
97C2×#106—611no—
98#389—611no—
99C4×C4⋊C4D6111yescharacteristic
100#340—611no—
101#340—611no—
102#340—611no—
103#336—611no—
104C61#191911yescharacteristic, complemented, Sylow
105C22×C8—611no—
106C22×C8—611no—
107C2×C4⋊C4—611no—
108C2×C4⋊C4—611no—
109C2×C4⋊C4—1221no—
110C2×C4⋊C4C2×D6111yescharacteristic
111C2×C4⋊C4C2×D6111yescharacteristic
112C2×C42—21no—
113C2×C42C2×D6111yescharacteristic
114#106—614no—
115#95—21no—
116#95—1221no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—1221no—
120C22×C4—1221no—
121C22×C4C22⋊D6111yescharacteristic
122C22×C4C22⋊D6111yescharacteristic
123C22×C4C22×D6111yescharacteristic
124C2×C8—612no—
125C2×C8—1221no—
126C2×C8—1221no—
127C2×C8—1221no—
128C2×C8—1221no—
129C2×C8—1221no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—612no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4—2442no—
137C4⋊C4Dic12212yes—
138C4⋊C4C4×D6112yes—
139C42—21no—
140C42—21no—
141C42—42no—
142C23C2×C22⋊D6111yescharacteristic
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—1222no—
155C2×C4—2441no—
156C2×C4—2441no—
157C2×C4—2441no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4#1175820112yes—
161C2×C4C2×Dic12211yescharacteristic
162C2×C4C2×C4×D6111yescharacteristic
163C2×C4#1175822211yescharacteristic
164C2×C4#1175822211yescharacteristic
165C2×C4#1175822211yescharacteristic
166C2×C4#1175822211yescharacteristic
167C8—1222no—
168C8—2441no—
169C22C4×C22⋊D6111yescharacteristic
170C22#1451975611yescharacteristic
171C22#1451976011yescharacteristic
172C22C2×#1175820111yescharacteristic
173C22#1451979711yescharacteristic
174C22#1451980311yescharacteristic
175C22#1451980711yescharacteristic
176C4—22no—
177C4—42no—
178C4—41no—
179C4—42no—
180C4—4881no—
181C4—2442no—
182C4#1451973411yescharacteristic
183C4C4×Dic12211yescharacteristic
184C4#1451976911yescharacteristic
185C4#1451977111yescharacteristic
186C2#1683964611yescharacteristic
187C2C4×#1175820111yescharacteristic
188C2#1683986211yescharacteristic
189C2#1684004711yescharacteristic
190C2#1684006211yescharacteristic
191C2#1684008011yescharacteristic
192C2#1684010311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC4×C4⋊C4×C61C2
socleC23×C61C2×D4
hypercenterC4×C4⋊C4D61
hypocenterC61#1919
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
13. #14519708C4semidirect
104. C61#1919semidirect