Finite Group Databasebeta

← #21444880

Subgroups — #21444880

Order 7808.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#16840497C211yesmaximal, characteristic, complemented
2#16840139C211yesmaximal, characteristic
3#16839963C211yesmaximal, characteristic, complemented
4#16839962C211yesmaximal, characteristic, complemented
5#16839505C211yesmaximal, characteristic, complemented
6#16839494C211yesmaximal, characteristic, complemented
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758190—21no—
9C2×#11758201—21no—
10C2×D488—22no—
11#14519774C2211yescharacteristic
12#14519774C2211yescharacteristic
13#14519766—21no—
14#14519765—21no—
15#14519762—22no—
16C4×Dic122C2211yescharacteristic
17C4×D244—21no—
18#14519739—21no—
19C4⋊#92418C2211yescharacteristic
20#14519699—21no—
21#14519697—21no—
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61D411yescharacteristic
26C2×D244—21no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244D412yes—
32C2×C4×D61—22no—
33C2×Dic122D411yescharacteristic
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61D411yescharacteristic
38C42×C61—21no—
39C42×C61C2311yescharacteristic
40#11758201—42no—
41#11758198—22no—
42#11758198—22no—
43#11758198—22no—
44C4⋊Dic61D411yescharacteristic
45#11758196—21no—
46C4×Dic61—21no—
47C2×#92418—21no—
48D488—44no—
49#11758190—42no—
50C22×D61—22no—
51C22×D61—41no—
52Q8×C61—21no—
53Q8×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61D244—42no—
62D244—42no—
63D244—41no—
64D244—41no—
65D244—41no—
66D244—41no—
67D244—41no—
68D244—41no—
69D244—41no—
70D244—41no—
71C4×D61—82no—
72Dic122—21no—
73Dic122—21no—
74C8×C61—22no—
75C8×C61—41no—
76#92418—41no—
77C22×C61#12011yescharacteristic
78C2×D61—42no—
79C2×D61—42no—
80C2×D61—42no—
81C2×D61—81no—
82C2×D61—81no—
83C2×D61—81no—
84C4×C61—21no—
85C4×C61—41no—
86C4×C61—41no—
87C4×C61#13511yescharacteristic
88C4×C61#13511yescharacteristic
89C4×C61AGL(1,ℤ/8)11yescharacteristic
90C4×C61AGL(1,ℤ/8)11yescharacteristic
91Dic61—41no—
92Dic61—41no—
93#1620—611nomaximal, Sylow
94C2×C61#44911yescharacteristic
95C2×C61#44911yescharacteristic
96C2×C61#45311yescharacteristic
97D61—82no—
98D61—161no—
99#559—611no—
100#493—611no—
101#460—611no—
102#460—611no—
103#331—611no—
104Q8⋊C8—611no—
105Q8⋊C8D6111yescharacteristic, complemented
106C61#162011yescharacteristic, complemented, Sylow
107C2×SD16—1221no—
108C2×SD16—1221no—
109C2×D8—1222no—
110#127—611no—
111#127—611no—
112#124—1221no—
113#124—1221no—
114#123—1222no—
115C4×Q8—611no—
116C4×Q8C2×D6111yescharacteristic
117C4×D4—1221no—
118C4×D4—1221no—
119C4⋊C8—611no—
120C4⋊C8C2×D6111yescharacteristic
121#102—1221no—
122#102—1221no—
123C4×C8C2×D6111yescharacteristic
124C2×Q8—611no—
125C2×Q8D24411yescharacteristic
126C2×D4—612no—
127C2×D4—1221no—
128C2×D4—1221no—
129C2×D4—1221no—
130C2×D4—1221no—
131C2×D4—1221no—
132C22×C4—1222no—
133SD16—2442no—
134SD16—2442no—
135D8—2444no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—1221no—
139C4⋊C4—21no—
140C4⋊C4—611no—
141C4⋊C4—1221no—
142C4⋊C4D24411yescharacteristic
143C22⋊C4—1222no—
144C22⋊C4—1222no—
145C22⋊C4—1222no—
146C42—21no—
147C42—1221no—
148C42C22×D6111yescharacteristic
149C23—1222no—
150C23—2441no—
151Q8—21no—
152Q8—21no—
153Q8—1221no—
154Q8—1221no—
155D4—2442no—
156D4—2442no—
157D4—2441no—
158D4—2441no—
159D4—2441no—
160D4—2441no—
161D4—2441no—
162D4—2441no—
163D4—2441no—
164D4—2441no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—4882no—
170C2×C4C2×D24411yescharacteristic
171C2×C4D4×D6111yescharacteristic
172C2×C4D4×D6111yescharacteristic
173C8—22no—
174C8—41no—
175C8—2441no—
176C22—4881no—
177C22—4881no—
178C22—4881no—
179C22—2442no—
180C22—2442no—
181C22—2442no—
182C22#1451974711yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—2441no—
187C4—2441no—
188C4#1451979911yescharacteristic
189C4#1451980011yescharacteristic
190C4#1451980411yescharacteristic
191C4#1451980511yescharacteristic
192C2—9761no—
193C2—4882no—
194C2#1683990911yescharacteristic
195C2#1683991011yescharacteristic
196C2#1683993111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61#120
hypercenterQ8⋊C8D61
hypocenterC61#1620
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #16840497C2semidirect
3. #16839963C2semidirect
4. #16839962C2semidirect
5. #16839505C2semidirect
6. #16839494C2semidirect
7. C61×Q8⋊C8C2semidirect
105. Q8⋊C8D61semidirect
106. C61#1620semidirect