Finite Group Databasebeta

← #21447775

Subgroups — #21447775

Order 7808.

220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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#16840563C211yesmaximal, characteristic, complemented
2#16840198C211yesmaximal, characteristic, complemented
3#16840029C211yesmaximal, characteristic, complemented
4#16839575C211yesmaximal, characteristic, complemented
5#16839570C211yesmaximal, characteristic, complemented
6#16839545C211yesmaximal, characteristic, complemented
7C2×D16×C61C211yesmaximal, characteristic, complemented
8#14519822—21no—
9#14519803—21no—
10#14519803—21no—
11#14519801—22no—
12#14519799C2211yescharacteristic
13#14519796—21no—
14D8×D61—21no—
15#14519783C2211yescharacteristic
16#14519721—21no—
17#14519718—21no—
18#14519717C2211yescharacteristic, complemented
19#14519713C2211yescharacteristic, complemented
20#14519694—21no—
21C2×D8×C61C2211yescharacteristic
22C2×D8×C61C2211yescharacteristic, complemented
23D16×C61—22no—
24C2×C16×C61C2211yescharacteristic, complemented
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×C22⋊D61—42no—
28#11758224—22no—
29#11758224—41no—
30D4×D61—22no—
31D4×D61—41no—
32#11758222—21no—
33#11758222D411yescharacteristic
34D8×C61—21no—
35D8×C61—21no—
36D8×C61—21no—
37D8×C61D412yes—
38C2×C8×C61C2311yescharacteristic
39#11758200—22no—
40#11758200—41no—
41#11758199—22no—
42#11758199—41no—
43#11758194—21no—
44#11758194D411yescharacteristic
45Dic244D411yescharacteristic
46D488D411yescharacteristic
47#11758190—21no—
48#11758189—21no—
49C8×D61—21no—
50C16×C61—21no—
51#11758185—21no—
52C23×C61—41no—
53C23×C61—41no—
54C22×D61—42no—
55D4×C61—22no—
56D4×C61—41no—
57D4×C61—41no—
58D4×C61—41no—
59C2×C4×C61C2×D411yescharacteristic
60C22⋊D61—21no—
61C22⋊D61—42no—
62C22⋊D61—42no—
63C22⋊D61—41no—
64C2×Dic61—42no—
65D244—21no—
66D244D811yescharacteristic
67C4×D61—21no—
68C4×D61—41no—
69Dic122—21no—
70Dic122D811yescharacteristic
71C8×C61C2×D411yescharacteristic
72C8×C61C2×D411yescharacteristic
73#92418—21no—
74#92418—41no—
75C22×C61—42no—
76C22×C61—81no—
77C22×C61—161no—
78C22×C61—161no—
79C22×C61AGL(1,ℤ/8)11yescharacteristic
80C2×D61—21no—
81C2×D61—41no—
82C2×D61—162no—
83C4×C61#12011yescharacteristic
84C4×C61C2×D811yescharacteristic
85Dic61—21no—
86Dic61—41no—
87#2192—611nomaximal, Sylow
88C2×C61—21no—
89C2×C61—82no—
90C2×C61—161no—
91C2×C61#44711yescharacteristic
92D61—41no—
93D61—81no—
94#576—611no—
95#509—611no—
96C2×D16D6111yescharacteristic, complemented
97#472—611no—
98#361—611no—
99#359—611no—
100#350—611no—
101C61#219211yescharacteristic, complemented, Sylow
102H(5,𝔽2)—1221no—
103AGL(1,ℤ/8)—1221no—
104AGL(1,ℤ/8)—1222no—
105AGL(1,ℤ/8)—1221no—
106#135—611no—
107#135—1221no—
108C2×D8—1221no—
109C2×D8C2×D6111yescharacteristic
110C2×D8C2×D6111yescharacteristic, complemented
111#131—611no—
112SD32—1221no—
113D16—22no—
114D16—1221no—
115M32—611no—
116C2×C16C2×D6111yescharacteristic, complemented
117#108—611no—
118#100—1221no—
119#41—611no—
120#41—1222no—
121#41—1221no—
122#41—2441no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—1222no—
126C2×D4—2441no—
127C2×D4—2442no—
128Q16—611no—
129SD16—1222no—
130SD16—1221no—
131SD16—2441no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—611no—
136D8—1222no—
137D8—2441no—
138D8C22⋊D6112yes—
139M16—611no—
140M16—1221no—
141M16—1221no—
142C2×C8—1221no—
143C2×C8C22×D6111yescharacteristic
144C16—21no—
145C16—1221no—
146C23—41no—
147C23—41no—
148C23—2442no—
149Q8—611no—
150Q8—1221no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—611no—
156D4—1221no—
157D4—1221no—
158D4—2442no—
159D4—2442no—
160D4—2441no—
161C2×C4—1221no—
162C2×C4—2442no—
163C2×C4—2441no—
164C2×C4D4×D6111yescharacteristic
165C8—1221no—
166C8—2441no—
167C8D4×D6111yescharacteristic
168C8C2×C22⋊D6111yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—1221no—
174C22—9762no—
175C22—2441no—
176C22#1451980111yescharacteristic
177C4—1221no—
178C4—2441no—
179C4#1451974511yescharacteristic
180C4D8×D6111yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—4881no—
185C2—2441no—
186C2#1683989411yescharacteristic
subgroupG/H
centerC2#16839894
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC2×D16×C61C2
socleC2×C61#447
hypercenterC2×D16D61
hypocenterC61#2192
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #16840563C2semidirect
2. #16840198C2semidirect
3. #16840029C2semidirect
4. #16839575C2semidirect
5. #16839570C2semidirect
6. #16839545C2semidirect
7. C2×D16×C61C2semidirect
18. #14519717C22semidirect
19. #14519713C22semidirect
22. C2×D8×C61C22semidirect
24. C2×C16×C61C22semidirect
96. C2×D16D61semidirect
101. C61#2192semidirect
110. C2×D8C2×D61semidirect
116. C2×C16C2×D61semidirect