Finite Group Databasebeta

← #23762714

Subgroups — #23762714

Order 10112.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#19099307C211yesmaximal, characteristic
2#19098969C211yesmaximal, characteristic, complemented
3#19098925C211yesmaximal, characteristic, complemented
4#19098304C211yesmaximal, characteristic, complemented
5#19098303C211yesmaximal, characteristic, complemented
6#19098302C211yesmaximal, characteristic, complemented
7#497×C79C211yesmaximal, characteristic, complemented
8#14579153C2211yescharacteristic
9#14579149C2211yescharacteristic
10#14579145—21no—
11#14579143—21no—
12#14579138—21no—
13#14579137—21no—
14#14579134—21no—
15#14579133—21no—
16#14579094—21no—
17#14579092—21no—
18#14579084—21no—
19#14579081—21no—
20#14579072C2211yescharacteristic
21#14579072C2211yescharacteristic
22C2×Q16×C79—21no—
23C2×SD16×C79—21no—
24C4⋊Q8×C79C2211yescharacteristic
25#124×C79C2211yescharacteristic
26#97×C79C2211yescharacteristic
27C2×Dic158D411yescharacteristic
28C2×D316D411yescharacteristic
29C2×C22⋊D79—21no—
30C2×C22⋊D79—21no—
31C22×Dic79—21no—
32C2×C4×D79—21no—
33C2×C79⋊C8—21no—
34C2×C79⋊C8—21no—
35C4⋊Dic79—21no—
36C4⋊Dic79D411yescharacteristic
37C4⋊Dic79D411yescharacteristic
38Dic79⋊C4—21no—
39Dic79⋊C4—21no—
40Dic79⋊C4—21no—
41C22⋊Dic79—21no—
42(C2×D79)⋊C4—21no—
43(C2×D79)⋊C4—21no—
44(C2×D79)⋊C4—21no—
45C2×Q8×C79—21no—
46C2×Q8×C79D411yescharacteristic
47C2×D4×C79D411yescharacteristic
48Q16×C79—42no—
49SD16×C79—42no—
50C2×C8×C79—21no—
51C4⋊C4×C79—21no—
52C4⋊C4×C79—21no—
53C22⋊C4×C79—21no—
54C22⋊C4×C79—21no—
55C42×C79C2311yescharacteristic
56C23×C79—21no—
57C22×D79—21no—
58Q8×C79—41no—
59Q8×C79—41no—
60Q8×C79—41no—
61D4×C79—41no—
62C2×C4×C79—21no—
63C2×C4×C79—41no—
64C2×C4×C79C2×D411yescharacteristic
65C2×C4×C79C2×D411yescharacteristic
66C2×C4×C79C2×D411yescharacteristic
67C22⋊D79—81no—
68C22⋊D79—81no—
69C2×Dic79—21no—
70C2×Dic79—21no—
71C2×Dic79—21no—
72C2×Dic79—81no—
73D316—41no—
74C4×D79—81no—
75Dic158—41no—
76C8×C79—22no—
77C79⋊C8—22no—
78C79⋊C8—41no—
79C22×C79—41no—
80C22×C79—41no—
81C22×C79—41no—
82C22×C79#12011yescharacteristic
83C2×D79—41no—
84C2×D79—41no—
85C2×D79—41no—
86C4×C79—21no—
87C4×C79—21no—
88C4×C79—21no—
89C4×C79—41no—
90C4×C79—81no—
91Dic79—41no—
92Dic79—41no—
93Dic79—41no—
94C2×C79—81no—
95C2×C79#45311yescharacteristic
96C2×C79#45511yescharacteristic
97C2×C79#45611yescharacteristic
98D79—81no—
99#1661—791nomaximal, Sylow
100C79#166111yescharacteristic, complemented, Sylow
101#562—791no—
102#501—791no—
103#497D7911yescharacteristic, complemented
104#489—791no—
105#330—791no—
106#329—791no—
107#329—791no—
108C2×Q16—21no—
109C2×SD16—21no—
110C4⋊Q8C2×D7911yescharacteristic
111#125—791no—
112#124—791no—
113#124C2×D7911yescharacteristic
114#123—1581no—
115#123—1581no—
116C22⋊Q8—1581no—
117C22⋊Q8—1581no—
118#121—1581no—
119#121—1581no—
120#107—1581no—
121#106—1581no—
122#103—1581no—
123#102—1581no—
124#97—791no—
125#97—791no—
126#97C2×D7911yescharacteristic
127C2×Q8—21no—
128C2×Q8—791no—
129C2×Q8C22⋊D7911yescharacteristic
130C2×D4—791no—
131C2×D4—1581no—
132C2×D4—1581no—
133C2×D4C22⋊D7911yescharacteristic
134C22×C4—1581no—
135C22×C4—1581no—
136Q16—42no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—1581no—
140C2×C8—1581no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—791no—
144C4⋊C4—791no—
145C4⋊C4—1581no—
146C4⋊C4—1581no—
147C4⋊C4—1581no—
148C4⋊C4—1581no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—1581no—
152C22⋊C4—1581no—
153C22⋊C4—1581no—
154C22⋊C4—1581no—
155C42C22×D7911yescharacteristic
156C23—21no—
157C23—1581no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—3161no—
162D4—41no—
163D4—3161no—
164D4—6321no—
165D4—6321no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—6321no—
169C2×C4—6321no—
170C2×C4—1581no—
171C2×C4—1581no—
172C2×C4—1581no—
173C2×C4D4×D7911yescharacteristic
174C2×C4D4×D7911yescharacteristic
175C2×C4C2×C22⋊D7911yescharacteristic
176C8—22no—
177C8—3161no—
178C8—1582no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—3161no—
183C22—3161no—
184C22—3161no—
185C22#1457912911yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—3161no—
192C4—3161no—
193C4—3161no—
194C2—81no—
195C2—6321no—
196C2#1909873011yescharacteristic
197C2#1909873911yescharacteristic
198C2#1909874411yescharacteristic
subgroupG/H
centerC22#14579129
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#497×C79C2
socleC22×C79#120
prime radical#19099307C2
hypercenter#497D79
hypocenterC79#1661
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #19098969C2semidirect
3. #19098925C2semidirect
4. #19098304C2semidirect
5. #19098303C2semidirect
6. #19098302C2semidirect
7. #497×C79C2semidirect
100. C79#1661semidirect
103. #497D79semidirect