Finite Group Databasebeta

← #23772976

Subgroups — #23772976

Order 10112.

520 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579182C211yesmaximal, characteristic, complemented
2C22×C8×D79C211yesmaximal, characteristic, complemented
3#19099076C211yesmaximal, characteristic, complemented
4#19099073C211yesmaximal, characteristic, complemented
5#19098803C211yesmaximal, characteristic, complemented
6#19098802C211yesmaximal, characteristic, complemented
7#19098798C211yesmaximal, characteristic, complemented
8#19098797C211yesmaximal, characteristic, complemented
9#19098793C211yesmaximal, characteristic, complemented
10#19098792C211yesmaximal, characteristic, complemented
11#19098789C211yesmaximal, characteristic, complemented
12#19098598C211yesmaximal, characteristic, complemented
13#19098558C211yesmaximal, characteristic, complemented
14#19098556C211yesmaximal, characteristic, complemented
15#465×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×#11929623C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19#14579182—24no—
20C2×#11929614C2211yescharacteristic, complemented
21C2×#11929613C2211yescharacteristic, complemented
22C2×#11929609C2211yescharacteristic, complemented
23C22×C79⋊C8C2211yescharacteristic
24C2×C8×D79—24no—
25C2×C8×D79C2211yescharacteristic
26C2×C8×D79C2211yescharacteristic
27C2×C8×D79C2211yescharacteristic
28C2×C8×D79C2211yescharacteristic
29#14579146—21no—
30#14579143—21no—
31#14579141C2211yescharacteristic
32#14579140C2211yescharacteristic
33#14579137C2211yescharacteristic
34#14579136C2211yescharacteristic
35#14579135C2211yescharacteristic
36#14579132C2211yescharacteristic
37#14579131—21no—
38#14579129—21no—
39D4×Dic79—21no—
40#14579123—21no—
41(C22⋊D79)⋊C4—21no—
42(C22⋊D79)⋊C4—21no—
43#14579119C2211yescharacteristic
44#14579119C2211yescharacteristic
45#14579094C2211yescharacteristic, complemented
46#14579094C2211yescharacteristic, complemented
47#14579093C2211yescharacteristic, complemented
48#14579086C2211yescharacteristic, complemented
49#14579085C2211yescharacteristic, complemented
50#14579084C2211yescharacteristic, complemented
51#14579083C2211yescharacteristic, complemented
52#14579082C2211yescharacteristic, complemented
53#14579081C2211yescharacteristic, complemented
54C2×SD16×C79C2211yescharacteristic, complemented
55C22×C8×C79C2211yescharacteristic
56C22⋊Q8×C79C2211yescharacteristic
57#121×C79C2211yescharacteristic
58#106×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic, complemented
61C23×D79D411yescharacteristic
62#11929625—22no—
63#11929625—22no—
64#11929623—22no—
65#11929623—22no—
66C2×Dic158C2311yescharacteristic
67C2×D316—21no—
68C2×D316—21no—
69C2×D316C2311yescharacteristic
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C22×Dic79—21no—
74C22×Dic79D411yescharacteristic
75C2×C4×D79—22no—
76C2×C4×D79—22no—
77C2×C4×D79—21no—
78C2×C4×D79D411yescharacteristic
79C2×C4×D79D411yescharacteristic
80C2×C4×D79C2311yescharacteristic
81C2×C4×D79C2311yescharacteristic
82#11929614—22no—
83#11929613—22no—
84#11929609—22no—
85C2×C79⋊C8—22no—
86C2×C79⋊C8C2311yescharacteristic
87C2×C79⋊C8C2311yescharacteristic
88C8×D79—22no—
89C8×D79—22no—
90C8×D79—22no—
91C8×D79D414yescomplemented
92C4⋊Dic79—21no—
93C4⋊Dic79C2311yescharacteristic
94C4⋊Dic79C2311yescharacteristic
95Dic79⋊C4—21no—
96Dic79⋊C4—21no—
97C22⋊Dic79—21no—
98C22⋊Dic79—21no—
99(C2×D79)⋊C4—21no—
100(C2×D79)⋊C4—21no—
101(C2×D79)⋊C4—21no—
102(C2×D79)⋊C4—21no—
103(C2×D79)⋊C4—21no—
104(C2×D79)⋊C4—21no—
105C4×Dic79—21no—
106C4×Dic79—21no—
107C2×Q8×C79C2311yescharacteristic
108C2×D4×C79—21no—
109C2×D4×C79C2311yescharacteristic
110C22×C4×C79C2311yescharacteristic
111SD16×C79—22no—
112C2×C8×C79—22no—
113C2×C8×C79C2311yescharacteristic
114C2×C8×C79C2311yescharacteristic
115C4⋊C4×C79—21no—
116C4⋊C4×C79C2311yescharacteristic
117C4⋊C4×C79C2311yescharacteristic
118C22⋊C4×C79—21no—
119C22⋊C4×C79—21no—
120C23×C79—21no—
121C23×C79C2×D411yescharacteristic
122C22×D79—22no—
123C22×D79—22no—
124C22×D79—22no—
125C22×D79—21no—
126C22×D79C2×D411yescharacteristic
127C22×D79C2×D411yescharacteristic
128Q8×C79—21no—
129Q8×C79—21no—
130D4×C79—21no—
131D4×C79—21no—
132D4×C79—42no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2411yescharacteristic
140C22⋊D79—42no—
141C22⋊D79—42no—
142C22⋊D79—42no—
143C2×Dic79—22no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—42no—
148C2×Dic79C2×D411yescharacteristic
149C2×Dic79C2×D411yescharacteristic
150D316—21no—
151D316—21no—
152D316—42no—
153D316—42no—
154C4×D79—22no—
155C4×D79—21no—
156C4×D79—21no—
157C4×D79—22no—
158C4×D79—42no—
159C4×D79C2×D412yes—
160C4×D79#4112yes—
161Dic158—21no—
162Dic158—21no—
163C8×C79—21no—
164C8×C79C2×D412yes—
165C79⋊C8—21no—
166C79⋊C8C2×D412yes—
167C22×C79—21no—
168C22×C79—21no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79#13512yescomplemented
173C22×C79C22×D411yescharacteristic
174C2×D79—28no—
175C2×D79—21no—
176C2×D79—21no—
177C2×D79—21no—
178C2×D79—21no—
179C2×D79—41no—
180C2×D79—41no—
181C2×D79—41no—
182C2×D79#12112yes—
183C2×D79#13512yescomplemented
184C4×C79—21no—
185C4×C79—41no—
186C4×C79—41no—
187C4×C79—41no—
188C4×C79C22×D411yescharacteristic
189C4×C79C2×#4111yescharacteristic
190Dic79—21no—
191Dic79—41no—
192Dic79—41no—
193Dic79—41no—
194Dic79#12112yes—
195C2×C79—22no—
196C2×C79—81no—
197C2×C79C2×#12111yescharacteristic
198C2×C79C2×#13511yescharacteristic
199C2×C79C2×#13511yescharacteristic
200D79—22no—
201D79—22no—
202D79—81no—
203#3050—791nomaximal, Sylow
204C79#305011yescharacteristic, complemented, Sylow
205C2×#135—791no—
206C23×C8—791no—
207#525—791no—
208#525—791no—
209#467—791no—
210#467—791no—
211#466—791no—
212#466—791no—
213#465—791no—
214#465—791no—
215#465—791no—
216#465D7911yescharacteristic, complemented
217#427—791no—
218#416—791no—
219#416—791no—
220C2×#41—791no—
221C2×#41—791no—
222C23×C4—791no—
223#135—1584no—
224C2×Q16—791no—
225C2×SD16—791no—
226C2×SD16C2×D7911yescharacteristic, complemented
227C2×D8—791no—
228C22×C8—791no—
229C22×C8—791no—
230C22×C8—791no—
231C22×C8—791no—
232C22×C8—791no—
233C22×C8—1584no—
234C22×C8C2×D7911yescharacteristic
235#123—1581no—
236#123—1581no—
237C22⋊Q8—791no—
238C22⋊Q8—791no—
239C22⋊Q8—791no—
240C22⋊Q8C2×D7911yescharacteristic
241#121—791no—
242#121—791no—
243#121—791no—
244#121C2×D7911yescharacteristic
245#120—1581no—
246#120—1581no—
247C4×D4—1581no—
248C4×D4—1581no—
249C4×D4—1581no—
250C4×D4—1581no—
251#117—791no—
252#117—791no—
253#107—791no—
254#107—791no—
255#106—791no—
256#106C2×D7911yescharacteristic, complemented
257#103—791no—
258#103—791no—
259#103—791no—
260#103C2×D7911yescharacteristic, complemented
261#102—791no—
262#102—791no—
263#102—791no—
264#102C2×D7911yescharacteristic, complemented
265C24—791no—
266#41—1582no—
267#41—1582no—
268#41—1582no—
269#41—1582no—
270C2×Q8—791no—
271C2×Q8C22×D7911yescharacteristic
272C2×D4—21no—
273C2×D4—791no—
274C2×D4—1581no—
275C2×D4—1581no—
276C2×D4—1581no—
277C2×D4—1581no—
278C2×D4—1581no—
279C2×D4C22×D7911yescharacteristic
280C22×C4—791no—
281C22×C4—791no—
282C22×C4—791no—
283C22×C4—791no—
284C22×C4—791no—
285C22×C4—1581no—
286C22×C4—1582no—
287C22×C4—1582no—
288C22×C4—1581no—
289C22×C4C22×D7911yescharacteristic
290Q16—1582no—
291SD16—22no—
292SD16—1582no—
293D8—1582no—
294C2×C8—22no—
295C2×C8—791no—
296C2×C8—794no—
297C2×C8—791no—
298C2×C8—1582no—
299C2×C8—1582no—
300C2×C8—1582no—
301C2×C8—1582no—
302C2×C8C22×D7911yescharacteristic
303C2×C8C22×D7911yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—791no—
306C4⋊C4—791no—
307C4⋊C4—1581no—
308C4⋊C4—1581no—
309C4⋊C4—1581no—
310C4⋊C4C22×D7911yescharacteristic
311C4⋊C4C22×D7911yescharacteristic
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—1581no—
315C22⋊C4—1581no—
316C22⋊C4—1581no—
317C22⋊C4—1581no—
318C22⋊C4—1581no—
319C22⋊C4—1581no—
320C22⋊C4—1581no—
321C22⋊C4—1581no—
322C42—1581no—
323C42—1581no—
324C23—21no—
325C23—791no—
326C23—791no—
327C23—1582no—
328C23—1582no—
329C23—1581no—
330C23—1582no—
331C23D4×D7911yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—1581no—
335Q8—1581no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—3162no—
340D4—3162no—
341D4—3162no—
342D4—3162no—
343D4—3162no—
344D4—1581no—
345D4—1581no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3162no—
352C2×C4—3162no—
353C2×C4—791no—
354C2×C4—792no—
355C2×C4—792no—
356C2×C4—791no—
357C2×C4—1582no—
358C2×C4—1582no—
359C2×C4—1581no—
360C2×C4—1581no—
361C2×C4—1581no—
362C2×C4—1582no—
363C2×C4—1581no—
364C2×C4—1581no—
365C2×C4D4×D7911yescharacteristic
366C2×C4C23×D7911yescharacteristic
367C8—21no—
368C8—792no—
369C8—1581no—
370C8D4×D7912yes—
371C22—21no—
372C22—21no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—3161no—
377C22—3161no—
378C22—3161no—
379C22—792no—
380C22—792no—
381C22—1588no—
382C22—1581no—
383C22—1581no—
384C22—1581no—
385C22—1581no—
386C22#1457918212yescomplemented
387C22C2×D4×D7911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—3161no—
393C4—3161no—
394C4—3161no—
395C4—792no—
396C4—1581no—
397C4C2×D4×D7911yescharacteristic
398C4#41×D7911yescharacteristic
399C2—22no—
400C2—81no—
401C2—6321no—
402C2—1582no—
403C2—1582no—
404C2#121×D7911yescharacteristic
405C2#135×D7911yescharacteristic
406C2C2×#1457918211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#465×C79C2
socleC22×C79C22×D4
hypercenter#465D79
hypocenterC79#3050
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#14579182C2semidirect
2. C22×C8×D79C2semidirect
3. #19099076C2semidirect
4. #19099073C2semidirect
5. #19098803C2semidirect
6. #19098802C2semidirect
7. #19098798C2semidirect
8. #19098797C2semidirect
9. #19098793C2semidirect
10. #19098792C2semidirect
11. #19098789C2semidirect
12. #19098598C2semidirect
13. #19098558C2semidirect
14. #19098556C2semidirect
15. #465×C79C2semidirect
20. C2×#11929614C22semidirect
21. C2×#11929613C22semidirect
22. C2×#11929609C22semidirect
45. #14579094C22semidirect
46. #14579094C22semidirect
47. #14579093C22semidirect
48. #14579086C22semidirect
49. #14579085C22semidirect
50. #14579084C22semidirect
51. #14579083C22semidirect
52. #14579082C22semidirect
53. #14579081C22semidirect
54. C2×SD16×C79C22semidirect
58. #106×C79C22semidirect
59. #103×C79C22semidirect
60. #102×C79C22semidirect
91. C8×D79D4semidirect
172. C22×C79#135semidirect
183. C2×D79#135semidirect
204. C79#3050semidirect
216. #465D79semidirect
226. C2×SD16C2×D79semidirect
256. #106C2×D79semidirect
260. #103C2×D79semidirect
264. #102C2×D79semidirect
386. C22#14579182semidirect