Finite Group Databasebeta

← #21446584

Subgroups — #21446584

Order 7808.

240 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 99 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
2C2×#14519706C211yesmaximal, characteristic
3#16839627C211yesmaximal, characteristic
4C4⋊C4×Dic61C211yesmaximal, characteristic
5#16839525C211yesmaximal, characteristic
6#16839524C211yesmaximal, characteristic
7C2×#107×C61C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C2×C4⋊Dic61C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4×Dic61—21no—
12C2×C4×Dic61C2211yescharacteristic
13#14519708—22no—
14#14519706C414yescomplemented
15#14519684—21no—
16#14519684—21no—
17#14519684—21no—
18C22×C8×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21#107×C61—22no—
22C22×C4×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61—21no—
27C22×Dic61D411yescharacteristic
28C22×Dic61D411yescharacteristic
29C2×C8×C61—21no—
30C2×C8×C61—21no—
31C2×C8×C61C2×C412yes—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61D412yes—
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61—21no—
39C4⋊Dic61Q812yes—
40C4×Dic61—42no—
41C4×Dic61C2×C412yes—
42C4×Dic61Q812yes—
43C2×#92418—21no—
44C2×#92418—21no—
45C2×#92418C2×C412yes—
46C23×C61C2×D411yescharacteristic
47C2×C4×C61—22no—
48C2×C4×C61—41no—
49C2×C4×C61—41no—
50C2×C4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61C22×C411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×Q811yescharacteristic
56C2×C4×C61C2×Q811yescharacteristic
57C2×C4×C61#4111yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—22no—
64C2×Dic61—41no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61C4⋊C412yes—
70C2×Dic61C4⋊C412yes—
71C8×C61—22no—
72#92418—22no—
73C22×C61C2×C4⋊C411yescharacteristic
74C22×C61#12111yescharacteristic
75C22×C61C22⋊Q811yescharacteristic
76C22×C61#13511yescharacteristic
77C22×C61#13511yescharacteristic
78C22×C61AGL(1,ℤ/8)11yescharacteristic
79C22×C61#13711yescharacteristic
80C4×C61—42no—
81C4×C61—81no—
82C4×C61C4×D411yescharacteristic
83C4×C61C4×Q811yescharacteristic
84C4×C61#12511yescharacteristic
85C4×C61C4⋊Q811yescharacteristic
86Dic61—22no—
87Dic61—22no—
88Dic61—42no—
89Dic61—81no—
90#1949—611nomaximal, Sylow
91C2×C61#38911yescharacteristic
92C2×C61#42711yescharacteristic
93C2×C61#42811yescharacteristic
94C2×C61#46311yescharacteristic
95C2×C61#46411yescharacteristic
96C2×C61#47811yescharacteristic
97C2×C61#47911yescharacteristic
98C2×#107D6111yescharacteristic
99C2×#106—611no—
100C2×C4⋊C8—611no—
101#382—611no—
102C4×C4⋊C4—611no—
103#340—611no—
104#340—611no—
105C61#194911yescharacteristic, complemented, Sylow
106C22×C8—611no—
107C22×C8C2×D6111yescharacteristic
108C2×C4⋊C4—611no—
109C2×C4⋊C4—611no—
110C2×C4⋊C4C2×D6111yescharacteristic
111C2×C4⋊C4C2×D6111yescharacteristic
112C2×C42—611no—
113C2×C42—1221no—
114#107—22no—
115#106—1222no—
116C4⋊C8—614no—
117#95—1221no—
118#95—1221no—
119#95—1221no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—611no—
123C22×C4—611no—
124C22×C4—1221no—
125C22×C4—1221no—
126C22×C4C22×D6111yescharacteristic
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—612no—
130C2×C8—1221no—
131C2×C8—1221no—
132C2×C8C4×D6112yes—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—612no—
137C4⋊C4—1221no—
138C4⋊C4—1221no—
139C4⋊C4—1221no—
140C4⋊C4C22⋊D6112yes—
141C42—612no—
142C42—612no—
143C42—2442no—
144C23D4×D6111yescharacteristic
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—612no—
152C2×C4—612no—
153C2×C4—1221no—
154C2×C4—1221no—
155C2×C4—1221no—
156C2×C4—1221no—
157C2×C4—1222no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4—2441no—
163C2×C4C2×C4×D6111yescharacteristic
164C2×C4#1175822211yescharacteristic
165C2×C4#1175822411yescharacteristic
166C2×C4Q8×D6111yescharacteristic
167C2×C4Q8×D6111yescharacteristic
168C2×C4C2×C22⋊D6111yescharacteristic
169C8—22no—
170C8—1222no—
171C22C4⋊C4×D6111yescharacteristic
172C22#1451974911yescharacteristic
173C22#1451975511yescharacteristic
174C22#1451979611yescharacteristic
175C22#1451980011yescharacteristic
176C22#1451980111yescharacteristic
177C22#1451980911yescharacteristic
178C4—42no—
179C4—81no—
180C4—1222no—
181C4—1222no—
182C4—4881no—
183C4—2442no—
184C4C4×C22⋊D6111yescharacteristic
185C4#1451974211yescharacteristic
186C4#1451976711yescharacteristic
187C4#1451977511yescharacteristic
188C2#1683965711yescharacteristic
189C2#1683979911yescharacteristic
190C2#1683980311yescharacteristic
191C2#1683997511yescharacteristic
192C2#1683998611yescharacteristic
193C2#1684006511yescharacteristic
194C2#1684006811yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#107×C61C2
socleC23×C61C2×D4
hypercenterC2×#107D61
hypocenterC61#1949
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
14. #14519706C4semidirect
105. C61#1949semidirect