Finite Group Databasebeta

← #23773646

Subgroups — #23773646

Order 10112.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099173C211yesmaximal, characteristic, complemented
2#19099038C211yesmaximal, characteristic
3#19098905C211yesmaximal, characteristic, complemented
4#19098901C211yesmaximal, characteristic, complemented
5#19098865C211yesmaximal, characteristic, complemented
6#19098861C211yesmaximal, characteristic, complemented
7#19098766C211yesmaximal, characteristic, complemented
8#19098766C211yesmaximal, characteristic, complemented
9#19098714C211yesmaximal, characteristic
10#19098664C211yesmaximal, characteristic, complemented
11#19098660C211yesmaximal, characteristic, complemented
12#19098654C211yesmaximal, characteristic, complemented
13SD16×Dic79C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#450×C79C211yesmaximal, characteristic
16C2×#11929612C2211yescharacteristic
17C2×#11929612C2211yescharacteristic
18#14579159C2211yescharacteristic, complemented
19#14579154—21no—
20#14579154—21no—
21#14579152—21no—
22#14579152C2211yescharacteristic, complemented
23#14579151—21no—
24#14579140C2211yescharacteristic
25Q8×Dic79C2211yescharacteristic, complemented
26#14579126C2211yescharacteristic, complemented
27D4×Dic79—21no—
28D4×Dic79—21no—
29D4×Dic79C2211yescharacteristic
30D4×Dic79C2211yescharacteristic
31D4×Dic79C2211yescharacteristic
32D4×Dic79C2211yescharacteristic
33#14579120C2211yescharacteristic
34#14579120C2211yescharacteristic
35C2×C22⋊Dic79—21no—
36C2×C22⋊Dic79—21no—
37#14579095C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579085C2211yescharacteristic, complemented
46#14579085C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59C2×Dic158C2311yescharacteristic
60C22×Dic79—21no—
61C22×Dic79—21no—
62C22×Dic79—21no—
63C22×Dic79—21no—
64#11929612—22no—
65#11929612—22no—
66C2×C79⋊C8C2311yescharacteristic
67C2×C79⋊C8C2311yescharacteristic
68C4⋊Dic79—21no—
69C4⋊Dic79—21no—
70C4⋊Dic79D411yescharacteristic
71C4⋊Dic79D411yescharacteristic
72C4⋊Dic79C2311yescharacteristic
73C4⋊Dic79C2311yescharacteristic
74C4⋊Dic79C2311yescharacteristic
75Dic79⋊C4—21no—
76Dic79⋊C4—21no—
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80C22⋊Dic79—21no—
81C22⋊Dic79—21no—
82C22⋊Dic79—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79D411yescharacteristic
87C22⋊Dic79D411yescharacteristic
88C4×Dic79—21no—
89C4×Dic79—21no—
90C4×Dic79—21no—
91C4×Dic79C2311yescharacteristic
92C4×Dic79C2311yescharacteristic
93C24×C79—21no—
94C2×Q8×C79C2311yescharacteristic
95C2×D4×C79—22no—
96C2×D4×C79—22no—
97C2×D4×C79—21no—
98C2×D4×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101SD16×C79—22no—
102SD16×C79—22no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C4⋊C4×C79—21no—
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C23×C79—24no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79—81no—
112C23×C79—81no—
113C23×C79C2×D411yescharacteristic
114Q8×C79—21no—
115Q8×C79—21no—
116D4×C79—24no—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79#4112yes—
120D4×C79#4112yes—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2411yescharacteristic
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—81no—
132C2×Dic79—81no—
133C2×Dic79—81no—
134C2×Dic79—81no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139Dic158—21no—
140Dic158—21no—
141C8×C79—21no—
142C8×C79—21no—
143C79⋊C8—21no—
144C79⋊C8—21no—
145C22×C79—21no—
146C22×C79—22no—
147C22×C79—22no—
148C22×C79—21no—
149C22×C79—21no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79—84no—
155C22×C79C22×D411yescharacteristic
156C4×C79—21no—
157C4×C79—41no—
158C4×C79—41no—
159C4×C79C2×#4111yescharacteristic
160C4×C79C2×#4111yescharacteristic
161Dic79—21no—
162Dic79—21no—
163Dic79—21no—
164Dic79—21no—
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169C2×C79—41no—
170C2×C79—42no—
171C2×C79—42no—
172C2×C79#52511yescharacteristic
173C2×C79#57711yescharacteristic
174C2×C79#57711yescharacteristic
175#3123—791nomaximal, Sylow
176C79#312311yescharacteristic, complemented, Sylow
177#541—791no—
178#518—791no—
179#485—791no—
180#485—791no—
181#478—791no—
182#478—791no—
183#461—791no—
184#461—791no—
185#450—791no—
186#450D7911yescharacteristic
187#440—791no—
188#440—791no—
189C4×SD16—791no—
190C4×SD16—791no—
191#433—791no—
192C22×D4C2×D7911yescharacteristic
193C2×SD16—791no—
194C2×SD16—791no—
195C2×SD16C2×D7911yescharacteristic
196C2×SD16C2×D7911yescharacteristic
197C4⋊Q8—791no—
198#126—1581no—
199#126—1581no—
200#125—791no—
201#125—1581no—
202#125—1581no—
203C22⋊Q8—791no—
204C22⋊Q8C2×D7911yescharacteristic
205C4×Q8—791no—
206C4×Q8—791no—
207C4×D4—791no—
208C4×D4—791no—
209C4×D4—791no—
210C4×D4—791no—
211C4×D4—1581no—
212C4×D4—1581no—
213#117—791no—
214#117—791no—
215C2×C22⋊C4—1581no—
216C2×C22⋊C4—1581no—
217#107—791no—
218#107—791no—
219#106—791no—
220#106—791no—
221C4⋊C8—791no—
222C4⋊C8—791no—
223#103—791no—
224#103—791no—
225#103—791no—
226#103—791no—
227#102—791no—
228#102—791no—
229#102C2×D7911yescharacteristic
230#102C2×D7911yescharacteristic
231C22⋊C8—791no—
232C22⋊C8C2×D7911yescharacteristic
233#97—791no—
234C4×C8—791no—
235C24—21no—
236C2×Q8—791no—
237C2×Q8C22×D7911yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4C22×D7911yescharacteristic
242C2×D4C22×D7911yescharacteristic
243C22×C4—1581no—
244C22×C4—1581no—
245C22×C4—1581no—
246C22×C4—1581no—
247C22×C4C22×D7911yescharacteristic
248SD16—22no—
249SD16—22no—
250SD16—1582no—
251SD16—1582no—
252C2×C8—791no—
253C2×C8—791no—
254C2×C8C22×D7911yescharacteristic
255C2×C8C22×D7911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—791no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—791no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4C22×D7911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—791no—
272C22⋊C4—791no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C42—791no—
280C42—791no—
281C42—1581no—
282C42—1581no—
283C42—1581no—
284C23—24no—
285C23—21no—
286C23—21no—
287C23—81no—
288C23—81no—
289C23D4×D7911yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—1581no—
293Q8—1581no—
294D4—24no—
295D4—21no—
296D4—21no—
297D4#1192962312yes—
298D4#1192962312yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—791no—
304C2×C4—791no—
305C2×C4—791no—
306C2×C4—791no—
307C2×C4—6321no—
308C2×C4—6321no—
309C2×C4—6321no—
310C2×C4—6321no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4D4×D7911yescharacteristic
316C2×C4C23×D7911yescharacteristic
317C8—21no—
318C8—21no—
319C8—1581no—
320C8—1581no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—84no—
331C22C2×D4×D7911yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—3161no—
336C4—3161no—
337C4—3161no—
338C4—3161no—
339C4—1581no—
340C4—1581no—
341C4—1581no—
342C4—1581no—
343C4C2×#1192962311yescharacteristic
344C4C2×#1192962311yescharacteristic
345C2—41no—
346C2—42no—
347C2—42no—
348C2#1909906911yescharacteristic
349C2#1909936911yescharacteristic
350C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#450×C79C2
socleC22×C79C22×D4
prime radicalC22×D4×C79C22
hypercenter#450D79
hypocenterC79#3123
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #19099173C2semidirect
3. #19098905C2semidirect
4. #19098901C2semidirect
5. #19098865C2semidirect
6. #19098861C2semidirect
7. #19098766C2semidirect
8. #19098766C2semidirect
10. #19098664C2semidirect
11. #19098660C2semidirect
12. #19098654C2semidirect
13. SD16×Dic79C2semidirect
14. #19098621C2semidirect
18. #14579159C22semidirect
22. #14579152C22semidirect
25. Q8×Dic79C22semidirect
26. #14579126C22semidirect
37. #14579095C22semidirect
38. #14579094C22semidirect
39. #14579093C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579086C22semidirect
45. #14579085C22semidirect
46. #14579085C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
176. C79#3123semidirect