Finite Group Databasebeta

← #23772980

Subgroups — #23772980

Order 10112.

520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#14579181C211yesmaximal, characteristic, complemented
2C22×C8×D79C211yesmaximal, characteristic, complemented
3#19099075C211yesmaximal, characteristic, complemented
4#19099070C211yesmaximal, characteristic, complemented
5#19098803C212yesmaximal, complemented
6#19098798C212yesmaximal, complemented
7#19098795C212yesmaximal, complemented
8#19098791C212yesmaximal, complemented
9#19098599C211yesmaximal, characteristic, complemented
10#19098560C211yesmaximal, characteristic, complemented
11#416×C79C211yesmaximal, characteristic, complemented
12C2×#11929624C2211yescharacteristic
13C22×C4×D79C2211yescharacteristic
14#14579181—24no—
15C2×#11929614C2211yescharacteristic, complemented
16C2×#11929612C2211yescharacteristic, complemented
17C2×#11929611C2211yescharacteristic, complemented
18C2×#11929609C2211yescharacteristic, complemented
19C22×C79⋊C8C2211yescharacteristic
20C2×C8×D79—24no—
21C2×C8×D79C2212yes—
22C2×C8×D79C2212yes—
23#14579145—21no—
24#14579142—21no—
25#14579141C2212yes—
26#14579137C2212yes—
27#14579136C2212yes—
28#14579132C2212yes—
29#14579131—21no—
30#14579129—21no—
31C4×D316—22no—
32C4×C22⋊D79—22no—
33#14579120C2211yescharacteristic
34#14579094C2212yescomplemented
35#14579092C2212yescomplemented
36#14579086C2212yescomplemented
37#14579083C2212yescomplemented
38C2×#41×C79C2211yescharacteristic
39C22×C8×C79C2211yescharacteristic
40#117×C79C2211yescharacteristic
41#103×C79C2212yescomplemented
42#102×C79C2212yescomplemented
43C23×D79D411yescharacteristic
44#11929624—22no—
45#11929624—22no—
46C2×Dic158C2311yescharacteristic
47C2×D316—22no—
48C2×D316C2311yescharacteristic
49C2×C22⋊D79—21no—
50C2×C22⋊D79—22no—
51C22×Dic79D411yescharacteristic
52C2×C4×D79—22no—
53C2×C4×D79—21no—
54C2×C4×D79—22no—
55C2×C4×D79D412yes—
56C2×C4×D79C2312yes—
57#11929614—22no—
58#11929612—22no—
59#11929611—22no—
60#11929609—22no—
61C2×C79⋊C8D414yescomplemented
62C2×C79⋊C8C2311yescharacteristic
63C2×C79⋊C8C2311yescharacteristic
64C8×D79—24no—
65C8×D79—24no—
66C4⋊Dic79—22no—
67C4⋊Dic79C2312yes—
68Dic79⋊C4—22no—
69C22⋊Dic79—22no—
70C22⋊Dic79—21no—
71(C2×D79)⋊C4—22no—
72(C2×D79)⋊C4—22no—
73(C2×D79)⋊C4—22no—
74C4×Dic79—21no—
75#41×C79—22no—
76#41×C79—22no—
77C2×Q8×C79C2311yescharacteristic
78C2×D4×C79—21no—
79C2×D4×C79C2311yescharacteristic
80C22×C4×C79—21no—
81C22×C4×C79C2311yescharacteristic
82C2×C8×C79—22no—
83C2×C8×C79C2312yes—
84C4⋊C4×C79C2312yes—
85C22⋊C4×C79—21no—
86C42×C79—21no—
87C23×C79—21no—
88C23×C79C2×D411yescharacteristic
89C22×D79—22no—
90C22×D79—24no—
91C22×D79—21no—
92C22×D79C2×D412yes—
93Q8×C79—21no—
94Q8×C79—21no—
95D4×C79—21no—
96D4×C79—21no—
97D4×C79—42no—
98C2×C4×C79—21no—
99C2×C4×C79—22no—
100C2×C4×C79—42no—
101C2×C4×C79C2×D412yes—
102C2×C4×C79C2×D411yescharacteristic
103C2×C4×C79#4112yes—
104C2×C4×C79C2411yescharacteristic
105C22⋊D79—42no—
106C22⋊D79—44no—
107C2×Dic79—22no—
108C2×Dic79—22no—
109C2×Dic79—21no—
110C2×Dic79C2×D412yes—
111D316—21no—
112D316—21no—
113D316—44no—
114C4×D79—24no—
115C4×D79—22no—
116C4×D79—22no—
117C4×D79—42no—
118Dic158—21no—
119Dic158—21no—
120C8×C79—22no—
121C79⋊C8C2×D412yes—
122C79⋊C8C2×D412yes—
123C22×C79—22no—
124C22×C79—41no—
125C22×C79—42no—
126C22×C79#12112yes—
127C22×C79C22×D411yescharacteristic
128C2×D79—28no—
129C2×D79—22no—
130C2×D79—22no—
131C2×D79—41no—
132C2×D79—42no—
133C2×D79#13514yescomplemented
134C4×C79—41no—
135C4×C79—42no—
136C4×C79#12112yes—
137C4×C79C22×D411yescharacteristic
138C4×C79C2×#4111yescharacteristic
139Dic79—22no—
140Dic79—41no—
141Dic79—42no—
142C2×C79—22no—
143C2×C79—81no—
144C2×C79C2×#12111yescharacteristic
145C2×C79C2×#13512yes—
146D79—24no—
147D79—81no—
148#3050—791nomaximal, Sylow
149C79#305011yescharacteristic, complemented, Sylow
150C2×#135—791no—
151C23×C8—791no—
152#525—791no—
153#525—791no—
154#467—792no—
155#466—792no—
156#465—792no—
157#465—792no—
158#427—791no—
159#416—791no—
160#416D7911yescharacteristic, complemented
161C2×#41—791no—
162C2×#41C2×D7911yescharacteristic
163C23×C4—791no—
164#135—1584no—
165C2×Q16—791no—
166C2×SD16—791no—
167C2×SD16—791no—
168C2×D8—791no—
169C22×C8—791no—
170C22×C8—792no—
171C22×C8—792no—
172C22×C8—1584no—
173C22×C8C2×D7911yescharacteristic
174#123—1581no—
175#123—1581no—
176C22⋊Q8—792no—
177C22⋊Q8—792no—
178#121—792no—
179#121—792no—
180#120—1581no—
181#120—1581no—
182C4×D4—1582no—
183C4×D4—1582no—
184#117—791no—
185#117C2×D7911yescharacteristic
186#107—792no—
187#106—792no—
188#103—792no—
189#103C2×D7912yescomplemented
190#102—792no—
191#102C2×D7912yescomplemented
192C24—791no—
193#41—22no—
194#41—22no—
195#41—1582no—
196#41—1582no—
197C2×Q8—791no—
198C2×Q8C22×D7911yescharacteristic
199C2×D4—21no—
200C2×D4—791no—
201C2×D4—1582no—
202C2×D4—1582no—
203C2×D4—1581no—
204C2×D4C22×D7911yescharacteristic
205C22×C4—21no—
206C22×C4—791no—
207C22×C4—792no—
208C22×C4—792no—
209C22×C4—1581no—
210C22×C4—1582no—
211C22×C4—1582no—
212C22×C4C22×D7911yescharacteristic
213Q16—1582no—
214SD16—1582no—
215SD16—1582no—
216D8—1582no—
217C2×C8—22no—
218C2×C8—794no—
219C2×C8—791no—
220C2×C8—791no—
221C2×C8—1584no—
222C2×C8—1584no—
223C2×C8C22×D7912yes—
224C4⋊C4—792no—
225C4⋊C4—1582no—
226C4⋊C4—1582no—
227C4⋊C4C22×D7912yes—
228C22⋊C4—21no—
229C22⋊C4—1582no—
230C22⋊C4—1582no—
231C22⋊C4—1582no—
232C22⋊C4—1582no—
233C22⋊C4—1581no—
234C42—21no—
235C42—1581no—
236C23—21no—
237C23—792no—
238C23—1584no—
239C23—1581no—
240C23—1582no—
241C23D4×D7911yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—1581no—
245Q8—1581no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—3164no—
250D4—3164no—
251D4—3162no—
252D4—1581no—
253D4—1581no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—3162no—
258C2×C4—792no—
259C2×C4—1582no—
260C2×C4—1581no—
261C2×C4—1582no—
262C2×C4—1582no—
263C2×C4—1584no—
264C2×C4—1582no—
265C2×C4D4×D7912yes—
266C2×C4D4×D7911yescharacteristic
267C2×C4#1192962412yes—
268C2×C4C23×D7911yescharacteristic
269C8—22no—
270C8—792no—
271C8—792no—
272C22—22no—
273C22—41no—
274C22—42no—
275C22—3161no—
276C22—3162no—
277C22—794no—
278C22—1588no—
279C22—1582no—
280C22—1582no—
281C22#1457913412yes—
282C22C2×D4×D7911yescharacteristic
283C4—41no—
284C4—42no—
285C4—3161no—
286C4—3162no—
287C4—1582no—
288C4#1457913412yes—
289C4C2×D4×D7911yescharacteristic
290C4C2×#1192962411yescharacteristic
291C2—22no—
292C2—81no—
293C2—6321no—
294C2—1584no—
295C2C2×#1457913411yescharacteristic
296C2#135×D7912yes—
subgroupG/H
centerC2×C4D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#416×C79C2
socleC22×C79C22×D4
hypercenter#416D79
hypocenterC79#3050
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#14579181C2semidirect
2. C22×C8×D79C2semidirect
3. #19099075C2semidirect
4. #19099070C2semidirect
5. #19098803C2semidirect
6. #19098798C2semidirect
7. #19098795C2semidirect
8. #19098791C2semidirect
9. #19098599C2semidirect
10. #19098560C2semidirect
11. #416×C79C2semidirect
15. C2×#11929614C22semidirect
16. C2×#11929612C22semidirect
17. C2×#11929611C22semidirect
18. C2×#11929609C22semidirect
34. #14579094C22semidirect
35. #14579092C22semidirect
36. #14579086C22semidirect
37. #14579083C22semidirect
41. #103×C79C22semidirect
42. #102×C79C22semidirect
61. C2×C79⋊C8D4semidirect
133. C2×D79#135semidirect
149. C79#3050semidirect
160. #416D79semidirect
189. #103C2×D79semidirect
191. #102C2×D79semidirect