Finite Group Databasebeta

← #23762576

Subgroups — #23762576

Order 10112.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#19099198C211yesmaximal, characteristic
2#19098840C211yesmaximal, characteristic, complemented
3#19098765C211yesmaximal, characteristic, complemented
4#19098307C211yesmaximal, characteristic, complemented
5#19098292C211yesmaximal, characteristic, complemented
6#19098292C211yesmaximal, characteristic, complemented
7#486×C79C211yesmaximal, characteristic, complemented
8C2×D4×D79—21no—
9C2×D4×D79—21no—
10C2×#11929611—21no—
11#14579132—21no—
12#14579132—21no—
13#14579129—22no—
14C4×D316C2211yescharacteristic
15C4×D316C2211yescharacteristic
16#14579094—21no—
17C4⋊(C79⋊C8)C2211yescharacteristic, complemented
18C4⋊(C79⋊C8)C2211yescharacteristic, complemented
19#14579085—21no—
20#14579081—21no—
21C4⋊Q8×C79C2211yescharacteristic, complemented
22#127×C79C2211yescharacteristic
23#102×C79—22no—
24C4×C8×C79C2211yescharacteristic, complemented
25C23×D79—22no—
26C2×D316D411yescharacteristic
27C2×D316D411yescharacteristic
28C2×C22⋊D79—22no—
29C2×C22⋊D79—22no—
30D4×D79—42no—
31D4×D79—42no—
32D4×D79—42no—
33D4×D79—42no—
34C2×C4×D79—21no—
35C2×C4×D79—21no—
36#11929611—42no—
37C2×C79⋊C8—21no—
38C2×C79⋊C8—21no—
39C4⋊Dic79D411yescharacteristic
40C4⋊Dic79D411yescharacteristic
41C22⋊Dic79—22no—
42(C2×D79)⋊C4—21no—
43(C2×D79)⋊C4—21no—
44C2×Q8×C79—21no—
45C2×D4×C79—21no—
46C2×D4×C79—21no—
47C2×D4×C79D412yes—
48C2×C8×C79—21no—
49C4⋊C4×C79—21no—
50C4⋊C4×C79—21no—
51C42×C79C2311yescharacteristic
52C23×C79—22no—
53C22×D79—21no—
54C22×D79—21no—
55C22×D79—44no—
56C22×D79—44no—
57C22×D79—82no—
58Q8×C79—41no—
59Q8×C79—41no—
60D4×C79—42no—
61D4×C79—41no—
62D4×C79—41no—
63D4×C79—41no—
64D4×C79—41no—
65C2×C4×C79—41no—
66C2×C4×C79C2×D411yescharacteristic
67C2×C4×C79C2×D411yescharacteristic
68C2×C4×C79C2×D411yescharacteristic
69C22⋊D79—44no—
70C22⋊D79—44no—
71C2×Dic79—21no—
72C2×Dic79—21no—
73D316—21no—
74D316—21no—
75D316D812yes—
76D316SD1612yescomplemented
77C4×D79—41no—
78C4×D79—41no—
79C4×D79—41no—
80C4×D79—41no—
81C8×C79—41no—
82C79⋊C8—41no—
83C79⋊C8—41no—
84C22×C79—42no—
85C22×C79—42no—
86C22×C79—42no—
87C22×C79#12011yescharacteristic
88C2×D79—22no—
89C2×D79—22no—
90C2×D79—41no—
91C2×D79—41no—
92C2×D79—41no—
93C2×D79—41no—
94C2×D79—88no—
95C4×C79—21no—
96C4×C79—81no—
97C4×C79C2×D811yescharacteristic
98C4×C79C2×SD1611yescharacteristic
99C4×C79AGL(1,ℤ/8)11yescharacteristic
100C4×C79AGL(1,ℤ/8)11yescharacteristic
101Dic79—41no—
102Dic79—41no—
103C2×C79—82no—
104C2×C79#44711yescharacteristic
105C2×C79#45011yescharacteristic
106C2×C79#45511yescharacteristic
107D79—42no—
108D79—42no—
109#1639—791nomaximal, Sylow
110C79#163911yescharacteristic, complemented, Sylow
111D42—791no—
112#486D7911yescharacteristic, complemented
113#474—791no—
114#461—791no—
115#331—791no—
116D4⋊C8—791no—
117D4⋊C8—791no—
118C22×D4—1581no—
119C22×D4—1581no—
120C2×SD16—1581no—
121C4⋊Q8C2×D7911yescharacteristic, complemented
122#127C2×D7911yescharacteristic
123#121—1581no—
124#121—1581no—
125#120—1582no—
126C4×D4—791no—
127C4×D4—791no—
128#107—1581no—
129C4⋊C8—791no—
130C4⋊C8—791no—
131#103—1581no—
132#102—22no—
133#102—1581no—
134C4×C8C2×D7911yescharacteristic, complemented
135C24—1582no—
136C2×Q8—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—3162no—
140C2×D4—3162no—
141C2×D4—3162no—
142C2×D4—3162no—
143C2×D4—791no—
144C2×D4—791no—
145C2×D4—1582no—
146C2×D4—1582no—
147C2×D4C22⋊D7912yes—
148C22×C4—1581no—
149C22×C4—1581no—
150SD16—3162no—
151C2×C8—21no—
152C2×C8—1581no—
153C2×C8—1581no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—791no—
157C4⋊C4—791no—
158C22⋊C4—1582no—
159C22⋊C4—1581no—
160C22⋊C4—1581no—
161C42C22×D7911yescharacteristic
162C23—22no—
163C23—3164no—
164C23—3164no—
165C23—6322no—
166C23—1581no—
167C23—1581no—
168Q8—41no—
169Q8—41no—
170D4—42no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—3164no—
176D4—3164no—
177D4—792no—
178D4—792no—
179D4—1581no—
180D4—1581no—
181C2×C4—41no—
182C2×C4—3161no—
183C2×C4—3161no—
184C2×C4—3161no—
185C2×C4—3161no—
186C2×C4—1581no—
187C2×C4—1581no—
188C2×C4D4×D7911yescharacteristic
189C2×C4D4×D7911yescharacteristic
190C2×C4C2×C22⋊D7911yescharacteristic
191C8—41no—
192C8—3161no—
193C8—3161no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—3161no—
198C22—3161no—
199C22—3161no—
200C22—3161no—
201C22—6328no—
202C22—1582no—
203C22—1582no—
204C22#1457912911yescharacteristic
205C4—21no—
206C4—81no—
207C4—3161no—
208C4—3161no—
209C4D8×D7911yescharacteristic
210C4SD16×D7911yescharacteristic
211C4#1457918511yescharacteristic
212C4#1457918811yescharacteristic
213C2—82no—
214C2—3162no—
215C2—3162no—
216C2#1909869511yescharacteristic
217C2#1909871211yescharacteristic
218C2#1909874011yescharacteristic
subgroupG/H
centerC22#14579129
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#486×C79C2
socleC22×C79#120
prime radical#19099198C2
hypercenter#486D79
hypocenterC79#1639
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #19098840C2semidirect
3. #19098765C2semidirect
4. #19098307C2semidirect
5. #19098292C2semidirect
6. #19098292C2semidirect
7. #486×C79C2semidirect
17. C4⋊(C79⋊C8)C22semidirect
18. C4⋊(C79⋊C8)C22semidirect
21. C4⋊Q8×C79C22semidirect
24. C4×C8×C79C22semidirect
76. D316SD16semidirect
110. C79#1639semidirect
112. #486D79semidirect
121. C4⋊Q8C2×D79semidirect
134. C4×C8C2×D79semidirect