Finite Group Databasebeta

← #23763901

Subgroups — #23763901

Order 10112.

332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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#19099361C211yesmaximal, characteristic
2#19098580C211yesmaximal, characteristic, complemented
3C2×#14579089C211yesmaximal, characteristic, complemented
4#19098536C211yesmaximal, characteristic, complemented
5#19098333C211yesmaximal, characteristic, complemented
6#19098323C211yesmaximal, characteristic, complemented
7C4×#41×C79C211yesmaximal, characteristic, complemented
8C2×#11929624C2211yescharacteristic
9#14579192—21no—
10#14579191C412yescomplemented
11#14579187—21no—
12#14579186C412yescomplemented
13#14579181—22no—
14C2×#11929608C2211yescharacteristic
15C2×#11929608C2211yescharacteristic
16#14579120C2211yescharacteristic
17#14579089—21no—
18#14579089—21no—
19#14579088—22no—
20#14579075—22no—
21C2×#41×C79C2211yescharacteristic
22C4×Q8×C79—21no—
23C4×D4×C79—21no—
24C4×D4×C79—22no—
25#117×C79—21no—
26#117×C79C2211yescharacteristic
27C2×C42×C79—21no—
28C2×C42×C79C2211yescharacteristic
29#11929624—21no—
30#11929624—21no—
31#11929624—21no—
32#11929624—21no—
33C2×Dic158C2×C411yescharacteristic, complemented
34C2×D316C2×C411yescharacteristic, complemented
35C2×C22⋊D79—21no—
36C2×C4×D79—21no—
37#11929614—22no—
38#11929612—22no—
39#11929611—22no—
40#11929609—22no—
41#11929608—21no—
42#11929608—21no—
43#11929608—21no—
44#11929608C2×C412yescomplemented
45C2×C79⋊C8—21no—
46C2×C79⋊C8—21no—
47C4⋊Dic79—21no—
48C22⋊Dic79—21no—
49C4×Dic79—21no—
50#41×C79—21no—
51#41×C79—21no—
52#41×C79C2×C412yes—
53#41×C79D412yes—
54C2×Q8×C79D411yescharacteristic
55C2×D4×C79—21no—
56C2×D4×C79D411yescharacteristic
57C22×C4×C79—21no—
58C22×C4×C79—22no—
59C22×C4×C79—21no—
60C22×C4×C79C2311yescharacteristic
61C4⋊C4×C79—22no—
62C4⋊C4×C79—21no—
63C22⋊C4×C79—22no—
64C22⋊C4×C79D412yes—
65C42×C79—22no—
66C42×C79—21no—
67C42×C79—21no—
68C42×C79D411yescharacteristic
69C42×C79D411yescharacteristic
70C23×C79—21no—
71C23×C79C2×D411yescharacteristic
72C22×D79—21no—
73Q8×C79—21no—
74Q8×C79C22⋊C412yes—
75D4×C79—22no—
76D4×C79—22no—
77D4×C79—21no—
78D4×C79C22⋊C412yes—
79C2×C4×C79—21no—
80C2×C4×C79—21no—
81C2×C4×C79—22no—
82C2×C4×C79—22no—
83C2×C4×C79—22no—
84C2×C4×C79—21no—
85C2×C4×C79—42no—
86C2×C4×C79—44no—
87C2×C4×C79C22×C411yescharacteristic
88C2×C4×C79C2×D411yescharacteristic
89C2×C4×C79C2×D411yescharacteristic
90C2×C4×C79C2×D411yescharacteristic
91C2×C4×C79#4111yescharacteristic
92C2×C4×C79#4111yescharacteristic
93C22⋊D79—41no—
94C22⋊D79—41no—
95C2×Dic79—21no—
96C2×Dic79—41no—
97D316—21no—
98D316—21no—
99C4×D79—41no—
100C4×D79—41no—
101Dic158—21no—
102Dic158—21no—
103C79⋊C8—22no—
104C79⋊C8—41no—
105C22×C79—22no—
106C22×C79—41no—
107C22×C79—42no—
108C22×C79C4×D411yescharacteristic
109C22×C79#12011yescharacteristic
110C22×C79#12111yescharacteristic
111C2×D79—41no—
112C2×D79—81no—
113C4×C79—22no—
114C4×C79—22no—
115C4×C79—42no—
116C4×C79—41no—
117C4×C79C2×C22⋊C411yescharacteristic
118C4×C79C4×D411yescharacteristic
119C4×C79#12111yescharacteristic
120C4×C79#12311yescharacteristic
121Dic79—41no—
122Dic79—81no—
123C2×C79—21no—
124C2×C79—21no—
125C2×C79—21no—
126C2×C79—42no—
127C2×C79#38611yescharacteristic
128D79—81no—
129#1906—791nomaximal, Sylow
130C79#190611yescharacteristic, complemented, Sylow
131#575—791no—
132C4×#41D7911yescharacteristic, complemented
133#421—791no—
134C2×#104—791no—
135#410—791no—
136#344—791no—
137#339—791no—
138C2×#41—791no—
139C2×#41C2×D7911yescharacteristic
140#137—792no—
141#137—1581no—
142AGL(1,ℤ/8)—792no—
143AGL(1,ℤ/8)—1581no—
144#135—1582no—
145C2×M16—791no—
146C2×M16—791no—
147C4×Q8—21no—
148C4×D4—21no—
149C4×D4—22no—
150#117—21no—
151#117—791no—
152#117C2×D7911yescharacteristic
153C2×C42—21no—
154C2×C42C2×D7911yescharacteristic
155#104—1582no—
156#104—1581no—
157#104—1581no—
158#99—1582no—
159#41—21no—
160#41—21no—
161#41—1581no—
162#41—1581no—
163#41—1581no—
164#41—1581no—
165#41C4×D7912yes—
166#41D31612yes—
167C2×Q8—791no—
168C2×Q8C22⋊D7911yescharacteristic
169C2×D4—21no—
170C2×D4—791no—
171C2×D4—1581no—
172C2×D4C22⋊D7911yescharacteristic
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—1581no—
177C22×C4C22×D7911yescharacteristic
178Q16—1582no—
179SD16—1582no—
180SD16—1582no—
181D8—1582no—
182M16—792no—
183M16—1581no—
184M16—1581no—
185M16—1581no—
186C2×C8—1581no—
187C2×C8—1581no—
188C4⋊C4—22no—
189C4⋊C4—21no—
190C4⋊C4—1581no—
191C22⋊C4—22no—
192C22⋊C4—1581no—
193C22⋊C4C22⋊D7912yes—
194C42—22no—
195C42—21no—
196C42—21no—
197C42—1581no—
198C42C22⋊D7911yescharacteristic
199C42C22⋊D7911yescharacteristic
200C23—21no—
201C23—1581no—
202C23C2×C22⋊D7911yescharacteristic
203Q8—21no—
204Q8—1581no—
205Q8—1581no—
206Q8(C2×D79)⋊C412yes—
207D4—22no—
208D4—22no—
209D4—21no—
210D4—3161no—
211D4—3161no—
212D4—1581no—
213D4—1581no—
214D4(C2×D79)⋊C412yes—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4—44no—
223C2×C4—3161no—
224C2×C4—3161no—
225C2×C4—3161no—
226C2×C4—1581no—
227C2×C4C2×C4×D7911yescharacteristic
228C2×C4C2×C22⋊D7911yescharacteristic
229C2×C4C2×C22⋊D7911yescharacteristic
230C2×C4C2×D31611yescharacteristic
231C2×C4#1192962411yescharacteristic
232C2×C4#1192962411yescharacteristic
233C8—3161no—
234C8—1582no—
235C22—22no—
236C22—41no—
237C22—42no—
238C22—3161no—
239C22—6321no—
240C22C4×C22⋊D7911yescharacteristic
241C22#1457913011yescharacteristic
242C22#1457913511yescharacteristic
243C4—22no—
244C4—22no—
245C4—42no—
246C4—41no—
247C4—3161no—
248C4—6321no—
249C4C2×(C2×D79)⋊C411yescharacteristic
250C4C4×C22⋊D7911yescharacteristic
251C4#1457913511yescharacteristic
252C4#1457914411yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—42no—
257C2—6321no—
258C2#1909844211yescharacteristic
subgroupG/H
centerC4#14579135
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
FittingC4×#41×C79C2
socleC2×C79#386
prime radical#19099361C2
cosocleC22×C4×C79C23
hypercenterC4×#41D79
hypocenterC79#1906
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C4 ◁ C22×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. #19098580C2semidirect
3. C2×#14579089C2semidirect
4. #19098536C2semidirect
5. #19098333C2semidirect
6. #19098323C2semidirect
7. C4×#41×C79C2semidirect
10. #14579191C4semidirect
12. #14579186C4semidirect
33. C2×Dic158C2×C4semidirect
34. C2×D316C2×C4semidirect
44. #11929608C2×C4semidirect
130. C79#1906semidirect
132. C4×#41D79semidirect