Finite Group Databasebeta

← #21447773

Subgroups — #21447773

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#16840564C211yesmaximal, characteristic, complemented
2C2×#14519718C211yesmaximal, characteristic, complemented
3#16840029C211yesmaximal, characteristic, complemented
4#16839576C211yesmaximal, characteristic, complemented
5#16839569C211yesmaximal, characteristic, complemented
6#16839547C211yesmaximal, characteristic, complemented
7C61×#509C211yesmaximal, characteristic, complemented
8#14519823—21no—
9#14519804—22no—
10#14519803—21no—
11#14519802—21no—
12#14519800—21no—
13C2×D488C2211yescharacteristic
14D8×D61—21no—
15#14519783C2211yescharacteristic
16#14519718—22no—
17C2×#11758185C2211yescharacteristic, complemented
18#14519713C2211yescharacteristic, complemented
19#14519694—21no—
20#135×C61C2211yescharacteristic
21C2×D8×C61C2211yescharacteristic, complemented
22SD32×C61—21no—
23D16×C61—21no—
24M32×C61C2211yescharacteristic, complemented
25#41×C61—21no—
26C2×D4×C61—21no—
27#11758226—22no—
28D4×D61—22no—
29D4×D61—42no—
30#11758222—41no—
31#11758222D411yescharacteristic
32C2×D244—21no—
33C2×D244—41no—
34Q16×C61D411yescharacteristic
35SD16×C61—21no—
36D8×C61—21no—
37D8×C61—21no—
38D8×C61D411yescharacteristic
39C2×C8×C61C2311yescharacteristic
40#11758201—22no—
41#11758200—41no—
42#11758199—22no—
43#11758199—41no—
44#11758194—21no—
45#11758194D411yescharacteristic
46D488—21no—
47D488D412yes—
48#11758189—21no—
49C8×D61—21no—
50C16×C61—21no—
51#11758185—21no—
52C23×C61—41no—
53C22×D61—42no—
54C22×D61—41no—
55Q8×C61—21no—
56D4×C61—21no—
57D4×C61—41no—
58D4×C61—41no—
59D4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61C2×D411yescharacteristic
62C22⋊D61—21no—
63C22⋊D61—42no—
64D244—22no—
65D244—42no—
66D244—41no—
67D244D811yescharacteristic
68C4×D61—21no—
69C4×D61—42no—
70Dic122D811yescharacteristic
71C8×C61C2×D411yescharacteristic
72C8×C61C2×D411yescharacteristic
73#92418—21no—
74#92418—41no—
75C22×C61—41no—
76C22×C61—81no—
77C22×C61—161no—
78C22×C61AGL(1,ℤ/8)11yescharacteristic
79C2×D61—21no—
80C2×D61—42no—
81C2×D61—162no—
82C2×D61—161no—
83C4×C61—41no—
84C4×C61#12011yescharacteristic
85C4×C61C2×D811yescharacteristic
86Dic61—21no—
87#2192—611nomaximal, Sylow
88C2×C61—21no—
89C2×C61—81no—
90C2×C61—161no—
91C2×C61#44711yescharacteristic
92D61—41no—
93D61—82no—
94#576—611no—
95#509D6111yescharacteristic, complemented
96C2×D16—611no—
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—1221no—
107#135C2×D6111yescharacteristic
108C2×D8—611no—
109C2×D8—1221no—
110C2×D8C2×D6111yescharacteristic, complemented
111#131—611no—
112SD32—21no—
113D16—21no—
114D16—1222no—
115M32C2×D6111yescharacteristic, complemented
116C2×C16—611no—
117#108—611no—
118#100—1221no—
119#41—21no—
120#41—611no—
121#41—1222no—
122#41—2441no—
123C2×D4—21no—
124C2×D4—1222no—
125C2×D4—1221no—
126C2×D4—2441no—
127C2×D4—2442no—
128Q16C22⋊D6111yescharacteristic
129SD16—21no—
130SD16—1222no—
131SD16—2441no—
132D8—21no—
133D8—21no—
134D8—612no—
135D8—1222no—
136D8—1221no—
137D8—2441no—
138D8C22⋊D6111yescharacteristic
139M16—611no—
140M16—1221no—
141M16—1221no—
142C2×C8—1221no—
143C2×C8C22×D6111yescharacteristic
144C16—21no—
145C16—1221no—
146C23—41no—
147C23—2442no—
148C23—2441no—
149Q8—21no—
150Q8—611no—
151D4—21no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—611no—
156D4—1221no—
157D4—1222no—
158D4—2442no—
159D4—2442no—
160D4—2441no—
161C2×C4—41no—
162C2×C4—1221no—
163C2×C4—2442no—
164C2×C4D4×D6111yescharacteristic
165C8—1221no—
166C8—2441no—
167C8D4×D6111yescharacteristic
168C8C2×C22⋊D6111yescharacteristic
169C22—41no—
170C22—81no—
171C22—161no—
172C22—1221no—
173C22—9761no—
174C22—9762no—
175C22—2442no—
176C22#1451980111yescharacteristic
177C4—41no—
178C4—1221no—
179C4#1451974511yescharacteristic
180C4D8×D6111yescharacteristic
181C2—21no—
182C2—81no—
183C2—161no—
184C2—4882no—
185C2—2441no—
186C2#1683989411yescharacteristic
subgroupG/H
centerC2#16839894
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#509C2
socleC2×C61#447
hypercenter#509D61
hypocenterC61#2192
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #16840564C2semidirect
2. C2×#14519718C2semidirect
3. #16840029C2semidirect
4. #16839576C2semidirect
5. #16839569C2semidirect
6. #16839547C2semidirect
7. C61×#509C2semidirect
17. C2×#11758185C22semidirect
18. #14519713C22semidirect
21. C2×D8×C61C22semidirect
24. M32×C61C22semidirect
95. #509D61semidirect
101. C61#2192semidirect
110. C2×D8C2×D61semidirect
115. M32C2×D61semidirect