Finite Group Databasebeta

← #21447322

Subgroups — #21447322

Order 7808.

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

normal subgroups only

This group has 224 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
2C2×#14519706C211yesmaximal, characteristic
3#16839661C211yesmaximal, characteristic
4#16839658C211yesmaximal, characteristic
5#16839525C211yesmaximal, characteristic
6#16839524C211yesmaximal, characteristic
7C61×#340C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C2×C4⋊Dic61—21no—
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196—21no—
13C2×C4×Dic61C2211yescharacteristic
14#14519708—22no—
15#14519706—22no—
16#14519684—21no—
17#14519684—21no—
18C22×C8×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
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×C61—21no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61Q812yes—
35C4⋊Dic61—21no—
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61—42no—
39C4⋊Dic61Q812yes—
40#11758196—42no—
41C4×Dic61—21no—
42C4×Dic61—21no—
43C2×#92418—21no—
44C2×#92418—21no—
45C2×#92418D412yes—
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×C61C2×D411yescharacteristic
54C2×C4×C61C2×Q811yescharacteristic
55C2×C4×C61C2×Q811yescharacteristic
56C2×C4×C61#4111yescharacteristic
57C2×C4×C61#4111yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—22no—
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61SD1612yes—
71C8×C61—41no—
72#92418—22no—
73C22×C61#12111yescharacteristic
74C22×C61C22⋊Q811yescharacteristic
75C22×C61C22⋊Q811yescharacteristic
76C22×C61C2×SD1611yescharacteristic
77C22×C61#13511yescharacteristic
78C22×C61AGL(1,ℤ/8)11yescharacteristic
79C22×C61#13711yescharacteristic
80C4×C61—42no—
81C4×C61—81no—
82C4×C61#12311yescharacteristic
83C4×C61#12511yescharacteristic
84C4×C61#12511yescharacteristic
85C4×C61C4⋊Q811yescharacteristic
86Dic61—22no—
87Dic61—41no—
88Dic61—42no—
89Dic61—81no—
90#2088—611nomaximal, Sylow
91C2×C61#39811yescharacteristic
92C2×C61#46511yescharacteristic
93C2×C61#46811yescharacteristic
94C2×C61#47511yescharacteristic
95C2×C61#47611yescharacteristic
96C2×C61#47811yescharacteristic
97C2×C61#47911yescharacteristic
98C2×#106—611no—
99C2×C4⋊C8—611no—
100#389—611no—
101#389—611no—
102#340—611no—
103#340—611no—
104#340D6111yescharacteristic
105C61#208811yescharacteristic, complemented, Sylow
106C22×C8—611no—
107C22×C8C2×D6111yescharacteristic
108C2×C4⋊C4—611no—
109C2×C4⋊C4—611no—
110C2×C4⋊C4—1221no—
111C2×C4⋊C4—1221no—
112C2×C4⋊C4C2×D6111yescharacteristic
113C2×C4⋊C4C2×D6111yescharacteristic
114C2×C42—611no—
115#106—1222no—
116C4⋊C8—1222no—
117#95—1221no—
118#95—1221no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—1221no—
124C22×C4—1221no—
125C22×C4C22×D6111yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—612no—
130C2×C8—1221no—
131C2×C8—1221no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—612no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4—1221no—
139C4⋊C4—2442no—
140C4⋊C4—2442no—
141C4⋊C4Dic12212yes—
142C42—1221no—
143C42—1221no—
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—1221no—
153C2×C4—1221no—
154C2×C4—1221no—
155C2×C4—1221no—
156C2×C4—1222no—
157C2×C4—1221no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4—2441no—
163C2×C4C2×Dic12211yescharacteristic
164C2×C4#1175822211yescharacteristic
165C2×C4#1175822211yescharacteristic
166C2×C4D4×D6111yescharacteristic
167C2×C4#1175822411yescharacteristic
168C2×C4Q8×D6111yescharacteristic
169C8—41no—
170C8—1222no—
171C22#1451975011yescharacteristic
172C22#1451975411yescharacteristic
173C22#1451975511yescharacteristic
174C22SD16×D6111yescharacteristic
175C22#1451979611yescharacteristic
176C22#1451980411yescharacteristic
177C22#1451980911yescharacteristic
178C4—42no—
179C4—81no—
180C4—1222no—
181C4—4881no—
182C4—2441no—
183C4—2442no—
184C4#1451975911yescharacteristic
185C4#1451976711yescharacteristic
186C4#1451976911yescharacteristic
187C4#1451977611yescharacteristic
188C2#1683969611yescharacteristic
189C2#1683999011yescharacteristic
190C2#1684001111yescharacteristic
191C2#1684004511yescharacteristic
192C2#1684005111yescharacteristic
193C2#1684006011yescharacteristic
194C2#1684006811yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#2088
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
105. C61#2088semidirect