Finite Group Databasebeta

← #23776219

Subgroups — #23776219

Order 10112.

350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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#19099299C211yesmaximal, characteristic
2#19099293C211yesmaximal, characteristic, complemented
3#19098921C212yesmaximal, complemented
4#19098855C211yesmaximal, characteristic, complemented
5#19098841C212yesmaximal, complemented
6#19098784C212yesmaximal, complemented
7#19098760C211yesmaximal, characteristic
8#19098693C211yesmaximal, characteristic, complemented
9#19098660C212yesmaximal, complemented
10C4×Dic316C211yesmaximal, characteristic, complemented
11#486×C79C211yesmaximal, characteristic
12C2×Dic316C2211yescharacteristic
13C2×#11929612C2212yes—
14#14579160—21no—
15#14579160C2212yes—
16#14579159—22no—
17#14579148—21no—
18#14579148C2212yes—
19#14579142—22no—
20C4×Dic158C2211yescharacteristic
21C4×Dic158C2211yescharacteristic
22C4×Dic158C2211yescharacteristic
23#14579126—21no—
24#14579126C2212yes—
25D4×Dic79—21no—
26D4×Dic79C2212yes—
27#14579095C2211yescharacteristic
28#14579094C2212yes—
29C4⋊(C79⋊C8)C2211yescharacteristic
30Dic79⋊C8C2212yes—
31#14579086C2211yescharacteristic
32#14579086C2211yescharacteristic
33#14579084C2212yes—
34#14579082C2212yes—
35#14579071C2212yes—
36C4⋊Q8×C79C2211yescharacteristic
37#127×C79C2211yescharacteristic
38#102×C79C2212yes—
39#102×C79C2212yes—
40C4×C8×C79C2211yescharacteristic
41C2×Dic158—22no—
42C2×Dic158D411yescharacteristic
43C2×Dic158C2311yescharacteristic
44C2×Dic158C2311yescharacteristic
45C22×Dic79—22no—
46Dic316—22no—
47#11929612—24no—
48C2×C79⋊C8C2312yes—
49C4⋊Dic79D411yescharacteristic
50C4⋊Dic79C2311yescharacteristic
51C4⋊Dic79C2311yescharacteristic
52Dic79⋊C4—22no—
53Dic79⋊C4—22no—
54Dic79⋊C4—21no—
55Dic79⋊C4—21no—
56Dic79⋊C4D412yes—
57C22⋊Dic79—22no—
58C22⋊Dic79—22no—
59C22⋊Dic79—22no—
60C4×Dic79—22no—
61C4×Dic79—21no—
62C4×Dic79—21no—
63C4×Dic79C2312yes—
64C2×Q8×C79—21no—
65C2×D4×C79—21no—
66C2×D4×C79—21no—
67C2×D4×C79C2312yes—
68C2×C8×C79C2311yescharacteristic
69C2×C8×C79C2311yescharacteristic
70C4⋊C4×C79—21no—
71C4⋊C4×C79C2312yes—
72C42×C79C2311yescharacteristic
73C23×C79—22no—
74Q8×C79—81no—
75D4×C79—22no—
76D4×C79—22no—
77D4×C79—42no—
78D4×C79—81no—
79C2×C4×C79—22no—
80C2×C4×C79C2×D411yescharacteristic
81C2×C4×C79C2×D411yescharacteristic
82C2×C4×C79C2411yescharacteristic
83C2×Dic79—21no—
84C2×Dic79—21no—
85C2×Dic79—21no—
86C2×Dic79—21no—
87C2×Dic79—82no—
88C2×Dic79C2×D412yes—
89C2×Dic79C2×D412yes—
90Dic158—22no—
91Dic158—21no—
92Dic158—21no—
93Dic158—21no—
94Dic158—82no—
95Dic158#4112yes—
96C8×C79—21no—
97C8×C79—21no—
98C79⋊C8—22no—
99C22×C79—42no—
100C22×C79—42no—
101C22×C79—42no—
102C22×C79C22×D411yescharacteristic
103C4×C79—21no—
104C4×C79—42no—
105C4×C79#13712yes—
106C4×C79C2×#4111yescharacteristic
107C4×C792−1+411yescharacteristic
108Dic79—22no—
109Dic79—22no—
110Dic79—22no—
111Dic79—41no—
112Dic79—41no—
113Dic79—41no—
114C2×C79—82no—
115C2×C79#54811yescharacteristic
116C2×C79C2×#13711yescharacteristic
117C2×C79#57611yescharacteristic
118#3375—791nomaximal, Sylow
119C79#337511yescharacteristic, complemented, Sylow
120#559—791no—
121Q82—791no—
122#489—792no—
123#486D7911yescharacteristic
124#477—791no—
125#474—792no—
126#464—792no—
127#460—791no—
128#446—791no—
129#440—792no—
130C4×Q16—791no—
131C2×Q16—791no—
132C2×SD16—792no—
133C4⋊Q8—792no—
134C4⋊Q8—1581no—
135C4⋊Q8—1582no—
136C4⋊Q8C2×D7911yescharacteristic
137#127C2×D7911yescharacteristic
138#124—792no—
139#124—1581no—
140#123—1582no—
141C4×Q8—791no—
142C4×Q8—792no—
143C4×Q8—791no—
144C4×Q8—791no—
145C4×Q8—1581no—
146C4×D4—792no—
147C4×D4—1581no—
148#107—791no—
149#107—792no—
150C4⋊C8—792no—
151C4⋊C8—791no—
152#103—791no—
153#103—791no—
154#103—792no—
155#102—792no—
156#102C2×D7912yes—
157#102C2×D7912yes—
158#97—792no—
159C4×C8C2×D7911yescharacteristic
160C2×Q8—21no—
161C2×Q8—791no—
162C2×Q8—791no—
163C2×Q8—791no—
164C2×Q8—1582no—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4C22×D7912yes—
168C22×C4—1582no—
169Q16—1582no—
170SD16—1584no—
171C2×C8—792no—
172C2×C8C22×D7911yescharacteristic
173C2×C8C22×D7911yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—792no—
176C4⋊C4—791no—
177C4⋊C4—791no—
178C4⋊C4—791no—
179C4⋊C4—1582no—
180C4⋊C4—1582no—
181C4⋊C4—1581no—
182C4⋊C4—1581no—
183C4⋊C4C22×D7912yes—
184C22⋊C4—1582no—
185C22⋊C4—1582no—
186C22⋊C4—1582no—
187C42—792no—
188C42—1582no—
189C42—1581no—
190C42—1581no—
191C42C22×D7911yescharacteristic
192C23—22no—
193Q8—81no—
194Q8—792no—
195Q8—6322no—
196Q8—1581no—
197Q8—1581no—
198Q8—1581no—
199Q8—1582no—
200D4—22no—
201D4—22no—
202D4—42no—
203D4—81no—
204C2×C4—22no—
205C2×C4—792no—
206C2×C4—792no—
207C2×C4—6322no—
208C2×C4—1581no—
209C2×C4—1581no—
210C2×C4—1581no—
211C2×C4—1581no—
212C2×C4D4×D7911yescharacteristic
213C2×C4D4×D7911yescharacteristic
214C2×C4C23×D7911yescharacteristic
215C8—21no—
216C8—21no—
217C8—1582no—
218C22—42no—
219C22—42no—
220C22—42no—
221C22C2×D4×D7911yescharacteristic
222C4—21no—
223C4—42no—
224C4—3161no—
225C4—3161no—
226C4—3161no—
227C4—1582no—
228C4—1582no—
229C4—1582no—
230C4#1457919012yes—
231C4#41×D7911yescharacteristic
232C4#1457920811yescharacteristic
233C2—82no—
234C2#1909922111yescharacteristic
235C2C2×#1457919011yescharacteristic
236C2#1909936411yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#486×C79C2
socleC22×C79C22×D4
prime radical#127×C79C22
hypercenter#486D79
hypocenterC79#3375
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #19099293C2semidirect
3. #19098921C2semidirect
4. #19098855C2semidirect
5. #19098841C2semidirect
6. #19098784C2semidirect
8. #19098693C2semidirect
9. #19098660C2semidirect
10. C4×Dic316C2semidirect
119. C79#3375semidirect