Finite Group Databasebeta

← #21447303

Subgroups — #21447303

Order 7808.

214 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 85 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#16839661C211yesmaximal, characteristic
3#16839627C211yesmaximal, characteristic
4#16839525C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic
6#16839516C211yesmaximal, characteristic
7C2×#107×C61C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C2×C4⋊Dic61—21no—
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×C4×Dic61C2211yescharacteristic
13#14519708—22no—
14#14519684—21no—
15#14519684—21no—
16#14519684—21no—
17C22×C8×C61C2211yescharacteristic
18C2×C4⋊C4×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20#107×C61—22no—
21C22×C4×C61—21no—
22C22×C4×C61—21no—
23C22×C4×C61C2311yescharacteristic
24C22×Dic61—21no—
25C22×Dic61—21no—
26C22×Dic61D411yescharacteristic
27C22×Dic61D411yescharacteristic
28C2×C8×C61—21no—
29C2×C8×C61—21no—
30C2×C8×C61Q812yes—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61D412yes—
35C4⋊Dic61—21no—
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61—21no—
39C4⋊Dic61—42no—
40C4×Dic61—21no—
41C4×Dic61—21no—
42C2×#92418—21no—
43C2×#92418—21no—
44C2×#92418Q812yes—
45C23×C61C2×D411yescharacteristic
46C2×C4×C61—22no—
47C2×C4×C61—41no—
48C2×C4×C61—41no—
49C2×C4×C61—41no—
50C2×C4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×Q811yescharacteristic
54C2×C4×C61C2×Q811yescharacteristic
55C2×C4×C61#4111yescharacteristic
56C2×C4×C61#4111yescharacteristic
57C2×C4×C61#4111yescharacteristic
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—41no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C8×C61—22no—
71#92418—22no—
72C22×C61#12111yescharacteristic
73C22×C61#12311yescharacteristic
74C22×C61C4⋊Q811yescharacteristic
75C22×C61#13511yescharacteristic
76C22×C61#13511yescharacteristic
77C22×C61AGL(1,ℤ/8)11yescharacteristic
78C22×C61#13711yescharacteristic
79C4×C61—42no—
80C4×C61—81no—
81C4×C61C22⋊Q811yescharacteristic
82C4×C61C22⋊Q811yescharacteristic
83C4×C61#12511yescharacteristic
84C4×C61#12511yescharacteristic
85Dic61—41no—
86Dic61—41no—
87Dic61—81no—
88Dic61—81no—
89#2085—611nomaximal, Sylow
90C2×C61#39811yescharacteristic
91C2×C61#46311yescharacteristic
92C2×C61#46411yescharacteristic
93C2×C61#48211yescharacteristic
94C2×C61#48511yescharacteristic
95C2×C61#49911yescharacteristic
96C2×C61#50111yescharacteristic
97C2×#107D6111yescharacteristic
98C2×#106—611no—
99#389—611no—
100#382—611no—
101#340—611no—
102#340—611no—
103#336—611no—
104C61#208511yescharacteristic, complemented, Sylow
105C22×C8—611no—
106C22×C8C2×D6111yescharacteristic
107C2×C4⋊C4—611no—
108C2×C4⋊C4—611no—
109C2×C4⋊C4—1221no—
110C2×C4⋊C4C2×D6111yescharacteristic
111C2×C4⋊C4C2×D6111yescharacteristic
112C2×C42—611no—
113#107—22no—
114#106—1222no—
115#95—1221no—
116#95—1221no—
117#95—1221no—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—1221no—
123C22×C4—1221no—
124C22×C4C22×D6111yescharacteristic
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—612no—
128C2×C8—1221no—
129C2×C8—1221no—
130C2×C8Dic12212yes—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4—2442no—
139C4⋊C4C22⋊D6112yes—
140C42—1221no—
141C42—1221no—
142C23D4×D6111yescharacteristic
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—1221no—
150C2×C4—1221no—
151C2×C4—1221no—
152C2×C4—1221no—
153C2×C4—1221no—
154C2×C4—1221no—
155C2×C4—2441no—
156C2×C4—2441no—
157C2×C4—2441no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4—2441no—
161C2×C4C2×Dic12211yescharacteristic
162C2×C4#1175822211yescharacteristic
163C2×C4#1175822411yescharacteristic
164C2×C4Q8×D6111yescharacteristic
165C2×C4#1175822611yescharacteristic
166C2×C4C2×C22⋊D6111yescharacteristic
167C8—22no—
168C8—1222no—
169C22#1451974911yescharacteristic
170C22#1451976211yescharacteristic
171C22#1451977611yescharacteristic
172C22#1451979611yescharacteristic
173C22#1451980011yescharacteristic
174C22#1451980111yescharacteristic
175C22#1451980911yescharacteristic
176C4—42no—
177C4—81no—
178C4—4881no—
179C4—4881no—
180C4—2441no—
181C4—2441no—
182C4#1451975311yescharacteristic
183C4#1451975611yescharacteristic
184C4#1451976711yescharacteristic
185C4#1451976811yescharacteristic
186C2#1683969511yescharacteristic
187C2#1683997511yescharacteristic
188C2#1683998611yescharacteristic
189C2#1684008911yescharacteristic
190C2#1684010511yescharacteristic
191C2#1684016311yescharacteristic
192C2#1684017011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#107×C61C2
socleC23×C61C2×D4
hypercenterC2×#107D61
hypocenterC61#2085
LCSG ▷ C22×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
104. C61#2085semidirect