Finite Group Databasebeta

← #21447310

Subgroups — #21447310

Order 7808.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14519710C211yesmaximal, characteristic
2C2×C4⋊#92418C211yesmaximal, characteristic
3#16839660C211yesmaximal, characteristic
4#16839524C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic
6#16839524C211yesmaximal, characteristic
7C61×#389C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196—21no—
13#14519710—22no—
14C4⋊#92418—22no—
15#14519684—21no—
16C2×C4⋊C4×C61—21no—
17C2×C4⋊C4×C61C2211yescharacteristic
18C2×C4⋊C4×C61C2211yescharacteristic
19C2×C42×C61C2211yescharacteristic
20#95×C61—21no—
21C22×C4×C61—21no—
22C22×C4×C61—21no—
23C22×C4×C61D411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—21no—
27C22×Dic61—21no—
28C4⋊C4×C61—21no—
29C4⋊C4×C61—21no—
30C4⋊C4×C61—21no—
31C4⋊C4×C61—42no—
32C4⋊C4×C61Q812yes—
33C42×C61—21no—
34C42×C61—21no—
35C4⋊Dic61—21no—
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61Q812yes—
39#11758196—42no—
40C2×#92418—21no—
41C2×#92418—21no—
42C2×#92418—21no—
43C2×#92418—21no—
44C2×#92418—21no—
45C2×#92418D412yes—
46C23×C61C2×D411yescharacteristic
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61—22no—
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×C61—41no—
58C2×C4×C61D812yes—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×Q811yescharacteristic
61C2×C4×C61C2×Q811yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×Dic61—22no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71#92418—22no—
72#92418—41no—
73C22×C61#12111yescharacteristic
74C22×C61C22⋊Q811yescharacteristic
75C22×C61C22⋊Q811yescharacteristic
76C22×C61C2×D811yescharacteristic
77C22×C61#13511yescharacteristic
78C22×C61#13711yescharacteristic
79C22×C61#13711yescharacteristic
80C4×C61—22no—
81C4×C61—41no—
82C4×C61—42no—
83C4×C61—81no—
84C4×C61#12311yescharacteristic
85C4×C61#12511yescharacteristic
86C4×C61#12511yescharacteristic
87C4×C61C4⋊Q811yescharacteristic
88Dic61—42no—
89Dic61—81no—
90#2086—611nomaximal, Sylow
91C2×C61#39811yescharacteristic
92C2×C61#46611yescharacteristic
93C2×C61#47011yescharacteristic
94C2×C61#47411yescharacteristic
95C2×C61#47411yescharacteristic
96C2×C61#47911yescharacteristic
97C2×C61#47911yescharacteristic
98C2×#107—611no—
99C2×C4⋊C8—611no—
100#389—611no—
101#389D6111yescharacteristic
102#340—611no—
103#340—611no—
104#340—611no—
105C61#208611yescharacteristic, complemented, Sylow
106C22×C8—611no—
107C22×C8—611no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—611no—
110C2×C4⋊C4—611no—
111C2×C4⋊C4—1221no—
112C2×C4⋊C4C2×D6111yescharacteristic
113C2×C4⋊C4C2×D6111yescharacteristic
114C2×C42C2×D6111yescharacteristic
115#107—1222no—
116C4⋊C8—1222no—
117#95—21no—
118#95—1221no—
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—1221no—
122C22×C4—1221no—
123C22×C4C22⋊D6111yescharacteristic
124C22×C4C22⋊D6111yescharacteristic
125C22×C4C22×D6111yescharacteristic
126C2×C8—612no—
127C2×C8—1221no—
128C2×C8—1221no—
129C2×C8—1221no—
130C2×C8—1221no—
131C2×C8—1221no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—42no—
136C4⋊C4—612no—
137C4⋊C4—1221no—
138C4⋊C4—1221no—
139C4⋊C4—1221no—
140C4⋊C4—2442no—
141C4⋊C4Dic12212yes—
142C42—21no—
143C42—21no—
144C23C2×C22⋊D6111yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—1222no—
157C2×C4—2441no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4#1175819912yes—
163C2×C4C2×Dic12211yescharacteristic
164C2×C4#1175822211yescharacteristic
165C2×C4D4×D6111yescharacteristic
166C2×C4#1175822411yescharacteristic
167C2×C4Q8×D6111yescharacteristic
168C2×C4#1175822611yescharacteristic
169C8—1222no—
170C8—2441no—
171C22#1451974911yescharacteristic
172C22#1451975311yescharacteristic
173C22#1451975611yescharacteristic
174C22C2×#1175819911yescharacteristic
175C22#1451979711yescharacteristic
176C22#1451980711yescharacteristic
177C22#1451980811yescharacteristic
178C4—22no—
179C4—41no—
180C4—42no—
181C4—81no—
182C4—4881no—
183C4—2442no—
184C4#1451976211yescharacteristic
185C4#1451976711yescharacteristic
186C4#1451976811yescharacteristic
187C4#1451977611yescharacteristic
188C2#1683969511yescharacteristic
189C2#1683999611yescharacteristic
190C2#1684001811yescharacteristic
191C2#1684003911yescharacteristic
192C2#1684004211yescharacteristic
193C2#1684006611yescharacteristic
194C2#1684006911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#389C2
socleC23×C61C2×D4
hypercenter#389D61
hypocenterC61#2086
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
105. C61#2086semidirect