Finite Group Databasebeta

← #21444928

Subgroups — #21444928

Order 7808.

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

normal subgroups only

This group has 216 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#16840485C211yesmaximal, characteristic, complemented
2#16840108C211yesmaximal, characteristic, complemented
3#16839954C211yesmaximal, characteristic
4#16839507C211yesmaximal, characteristic, complemented
5Q8⋊#92418C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×#460C211yesmaximal, characteristic, complemented
8C2×#11758199—21no—
9#14519777C2211yescharacteristic
10#14519772—22no—
11#14519765—21no—
12#14519753—21no—
13C4×Dic122—21no—
14C4×D244C2211yescharacteristic
15#14519735—21no—
16C4⋊#92418C2211yescharacteristic
17#14519698—21no—
18#14519698—22no—
19C4×#92418C2211yescharacteristic
20C2×SD16×C61—21no—
21#127×C61C2211yescharacteristic
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24#102×C61—21no—
25C2×Q8×C61D411yescharacteristic
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D244D411yescharacteristic
30C2×C4×D61—21no—
31C2×Dic122—21no—
32SD16×C61—42no—
33C2×C8×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61D411yescharacteristic
36C42×C61—21no—
37C42×C61C2311yescharacteristic
38#11758199—42no—
39#11758198—22no—
40#11758198—22no—
41#11758198—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61D411yescharacteristic
44C4⋊Dic61D412yes—
45#11758196—22no—
46C4×Dic61—22no—
47C2×#92418—21no—
48C2×#92418—21no—
49C23×C61—41no—
50C22×D61—21no—
51Q8×C61—21no—
52Q8×C61—21no—
53D4×C61—42no—
54D4×C61—41no—
55D4×C61—41no—
56D4×C61—41no—
57D4×C61—41no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×Dic61—21no—
64C2×Dic61—22no—
65D244—21no—
66D244—21no—
67C4×D61—41no—
68C4×D61—41no—
69Dic122—41no—
70Dic122—41no—
71C8×C61—41no—
72#92418—41no—
73#92418—41no—
74C22×C61—81no—
75C22×C61—81no—
76C22×C61—81no—
77C22×C61#12011yescharacteristic
78C2×D61—41no—
79C2×D61—41no—
80C2×D61—41no—
81C4×C61—21no—
82C4×C61—41no—
83C4×C61—41no—
84C4×C61#13511yescharacteristic
85C4×C61#13511yescharacteristic
86C4×C61AGL(1,ℤ/8)11yescharacteristic
87C4×C61AGL(1,ℤ/8)11yescharacteristic
88Dic61—42no—
89Dic61—41no—
90#1628—611nomaximal, Sylow
91C2×C61—161no—
92C2×C61#44911yescharacteristic
93C2×C61#44911yescharacteristic
94C2×C61#45411yescharacteristic
95D61—81no—
96#556—611no—
97#486—611no—
98#460D6111yescharacteristic, complemented
99#459—611no—
100#332—611no—
101Q8⋊C8—611no—
102D4⋊C8—611no—
103C61#162811yescharacteristic, complemented, Sylow
104C2×SD16—21no—
105C2×D8—1221no—
106C4⋊Q8—611no—
107#127C2×D6111yescharacteristic
108#126—1222no—
109#124—1221no—
110C22⋊Q8—1221no—
111C4×Q8—1221no—
112C4×Q8C2×D6111yescharacteristic
113C4×D4—611no—
114#117—1221no—
115C4⋊C8—611no—
116C4⋊C8C2×D6111yescharacteristic
117#102—21no—
118#102—1221no—
119#102—1222no—
120C4×C8—611no—
121C2×Q8—1221no—
122C2×Q8C22⋊D6111yescharacteristic
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—611no—
127C22×C4—1221no—
128SD16—42no—
129D8—2442no—
130C2×C8—21no—
131C2×C8—1221no—
132C2×C8—1221no—
133C4⋊C4—21no—
134C4⋊C4—611no—
135C4⋊C4—612no—
136C4⋊C4—1222no—
137C4⋊C4—1221no—
138C4⋊C4C22⋊D6111yescharacteristic
139C22⋊C4—1222no—
140C22⋊C4—1222no—
141C22⋊C4—1221no—
142C42—21no—
143C42—1222no—
144C42C22×D6111yescharacteristic
145C23—41no—
146C23—1221no—
147Q8—21no—
148Q8—21no—
149Q8—2441no—
150Q8—2441no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—1221no—
157D4—1221no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—1221no—
161C2×C4—1222no—
162C2×C4—2441no—
163C2×C4—2441no—
164C2×C4D4×D6111yescharacteristic
165C2×C4D4×D6111yescharacteristic
166C2×C4C2×C22⋊D6111yescharacteristic
167C8—41no—
168C8—2441no—
169C8—2441no—
170C22—81no—
171C22—81no—
172C22—81no—
173C22—2441no—
174C22—2441no—
175C22—2441no—
176C22#1451974511yescharacteristic
177C4—21no—
178C4—41no—
179C4—41no—
180C4—2441no—
181C4—2442no—
182C4#1451979711yescharacteristic
183C4#1451979811yescharacteristic
184C4#1451980311yescharacteristic
185C4#1451980411yescharacteristic
186C2—161no—
187C2—4881no—
188C2#1683990511yescharacteristic
189C2#1683990611yescharacteristic
190C2#1683993311yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#460C2
socleC22×C61#120
hypercenter#460D61
hypocenterC61#1628
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #16840485C2semidirect
2. #16840108C2semidirect
4. #16839507C2semidirect
5. Q8⋊#92418C2semidirect
6. #16839489C2semidirect
7. C61×#460C2semidirect
98. #460D61semidirect
103. C61#1628semidirect