Finite Group Databasebeta

← #23773073

Subgroups — #23773073

Order 10112.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579188C211yesmaximal, characteristic, complemented
2C2×#14579167C211yesmaximal, characteristic, complemented
3#19099143C211yesmaximal, characteristic, complemented
4#19099129C211yesmaximal, characteristic, complemented
5#19098817C211yesmaximal, characteristic, complemented
6#19098814C211yesmaximal, characteristic, complemented
7#19098811C211yesmaximal, characteristic, complemented
8#19098806C211yesmaximal, characteristic, complemented
9#19098799C211yesmaximal, characteristic, complemented
10#19098798C211yesmaximal, characteristic, complemented
11#19098795C211yesmaximal, characteristic, complemented
12#19098602C211yesmaximal, characteristic, complemented
13#19098558C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#465×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×#11929624C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19#14579188—24no—
20C2×#11929611C2211yescharacteristic
21C2×D632C2211yescharacteristic
22C2×#11929609C2211yescharacteristic
23#14579167—24no—
24C2×#11929608C2211yescharacteristic, complemented
25C2×#11929607C2211yescharacteristic
26C2×#11929607C2211yescharacteristic, complemented
27C2×C8×D79C2211yescharacteristic
28C2×C8×D79C2211yescharacteristic, complemented
29#14579157—21no—
30#14579147—21no—
31#14579139—21no—
32#14579137C2211yescharacteristic, complemented
33#14579136—21no—
34#14579136C2211yescharacteristic
35#14579136C2211yescharacteristic, complemented
36#14579135C2211yescharacteristic
37#14579135C2211yescharacteristic, complemented
38#14579134—21no—
39#14579134—21no—
40#14579132C2211yescharacteristic
41#14579131—21no—
42#14579129—21no—
43#14579119C2211yescharacteristic
44C4⋊C4×D79C2211yescharacteristic
45#14579095C2211yescharacteristic, complemented
46#14579094C2211yescharacteristic, complemented
47#14579092C2211yescharacteristic, complemented
48#14579085C2211yescharacteristic, complemented
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic, complemented
51#14579082C2211yescharacteristic
52#14579081C2211yescharacteristic
53#14579081C2211yescharacteristic, complemented
54C2×SD16×C79C2211yescharacteristic
55C22×C8×C79C2211yescharacteristic, complemented
56C22⋊Q8×C79C2211yescharacteristic, complemented
57#121×C79C2211yescharacteristic
58#106×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic
61C23×D79—21no—
62#11929625—22no—
63#11929625—22no—
64#11929624—22no—
65#11929624—22no—
66C2×Dic158D411yescharacteristic
67C2×D316—21no—
68C2×D316—21no—
69C2×D316—21no—
70C2×D316D411yescharacteristic
71C2×D316C2311yescharacteristic
72C2×D316C2311yescharacteristic
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75C2×C22⋊D79—21no—
76C2×C22⋊D79—21no—
77C2×C22⋊D79D411yescharacteristic
78C2×C22⋊D79D411yescharacteristic
79D4×D79—22no—
80D4×D79—22no—
81C2×C4×D79—21no—
82C2×C4×D79—21no—
83C2×C4×D79C2311yescharacteristic
84C2×C4×D79C2311yescharacteristic
85#11929611—22no—
86D632—22no—
87#11929609—22no—
88#11929608—22no—
89#11929607—22no—
90#11929607D414yescomplemented
91C2×C79⋊C8C2311yescharacteristic
92C2×C79⋊C8C2311yescharacteristic
93C8×D79—22no—
94C8×D79—22no—
95C4⋊Dic79C2311yescharacteristic
96C4⋊Dic79C2311yescharacteristic
97Dic79⋊C4—21no—
98Dic79⋊C4—21no—
99C22⋊Dic79—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—
105(C2×D79)⋊C4—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—21no—
123C22×D79—21no—
124C22×D79—42no—
125C22×D79—81no—
126C22×D79—81no—
127C22×D79C2×D411yescharacteristic
128C22×D79C2×D411yescharacteristic
129Q8×C79—21no—
130Q8×C79—21no—
131D4×C79—21no—
132D4×C79—21no—
133D4×C79—81no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79C2×D411yescharacteristic
140C2×C4×C79C2411yescharacteristic
141C22⋊D79—22no—
142C22⋊D79—22no—
143C22⋊D79—42no—
144C22⋊D79—81no—
145C22⋊D79—81no—
146C22⋊D79—81no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79C2×D411yescharacteristic
150C2×Dic79C2×D411yescharacteristic
151D316—22no—
152D316—21no—
153D316—21no—
154D316—21no—
155D316—21no—
156D316—42no—
157D316—81no—
158D316—81no—
159C4×D79—21no—
160C4×D79—21no—
161C4×D79—42no—
162C4×D79—81no—
163C4×D79C2×D412yes—
164C4×D79#4112yes—
165Dic158—22no—
166C8×C79—21no—
167C8×C79C2×D412yes—
168C79⋊C8—21no—
169C79⋊C8C2×D412yes—
170C22×C79—21no—
171C22×C79—21no—
172C22×C79—21no—
173C22×C79—41no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79C22×D411yescharacteristic
177C2×D79—21no—
178C2×D79—21no—
179C2×D79—21no—
180C2×D79—21no—
181C2×D79—21no—
182C2×D79—41no—
183C2×D79—41no—
184C2×D79—41no—
185C2×D79—41no—
186C2×D79—41no—
187C2×D79—41no—
188C2×D79—84no—
189C2×D79#12112yes—
190C4×C79—21no—
191C4×C79—41no—
192C4×C79—41no—
193C4×C79—41no—
194C4×C79C22×D411yescharacteristic
195C4×C79C2×#4111yescharacteristic
196Dic79—21no—
197Dic79—41no—
198Dic79—41no—
199Dic79#12112yes—
200C2×C79—41no—
201C2×C79—81no—
202C2×C79C2×#12111yescharacteristic
203C2×C79#57611yescharacteristic
204C2×C79#57711yescharacteristic
205D79—22no—
206D79—41no—
207D79—81no—
208D79—81no—
209#3062—791nomaximal, Sylow
210C79#306211yescharacteristic, complemented, Sylow
211C2×AGL(1,ℤ/8)—791no—
212C2×#131—791no—
213#537—791no—
214#535—791no—
215#469—791no—
216#469—791no—
217#468—791no—
218#468—791no—
219#466—791no—
220#466—791no—
221#465—791no—
222#465D7911yescharacteristic, complemented
223#428—791no—
224#416—791no—
225C2×#102—791no—
226C2×#41—791no—
227C2×#41—791no—
228C22×D4—791no—
229AGL(1,ℤ/8)—1584no—
230C2×SD16—791no—
231C2×SD16C2×D7911yescharacteristic
232C2×D8—791no—
233C2×D8—791no—
234#131—1584no—
235C2×M16—791no—
236C2×M16—791no—
237C2×M16—791no—
238C22×C8—791no—
239C22×C8—791no—
240C22×C8C2×D7911yescharacteristic, complemented
241#127—1581no—
242#124—1581no—
243C22⋊Q8—791no—
244C22⋊Q8—1581no—
245C22⋊Q8C2×D7911yescharacteristic, complemented
246#121—791no—
247#121—791no—
248#121—791no—
249#121—791no—
250#121—791no—
251#121—1581no—
252#121—1581no—
253#121—1581no—
254#121C2×D7911yescharacteristic
255#120—1581no—
256#120—1581no—
257#117—791no—
258C2×C4⋊C4—791no—
259#107—791no—
260#107—791no—
261#106—791no—
262#106C2×D7911yescharacteristic, complemented
263#103—791no—
264#103C2×D7911yescharacteristic, complemented
265#102—791no—
266#102—791no—
267#102—791no—
268#102—791no—
269#102—791no—
270#102C2×D7911yescharacteristic
271C24—1581no—
272#41—1582no—
273#41—1582no—
274#41—1582no—
275#41—1582no—
276C2×Q8—791no—
277C2×Q8C22×D7911yescharacteristic
278C2×D4—21no—
279C2×D4—791no—
280C2×D4—791no—
281C2×D4—791no—
282C2×D4—791no—
283C2×D4—791no—
284C2×D4—1581no—
285C2×D4—1581no—
286C2×D4—1581no—
287C2×D4—1582no—
288C2×D4—1582no—
289C2×D4—1581no—
290C2×D4—1581no—
291C2×D4—1581no—
292C2×D4—1581no—
293C2×D4C22×D7911yescharacteristic
294C22×C4—791no—
295C22×C4—791no—
296C22×C4—1581no—
297C22×C4—1581no—
298C22×C4C22×D7911yescharacteristic
299SD16—22no—
300SD16—1582no—
301D8—1582no—
302D8—1582no—
303M16—794no—
304M16—1582no—
305M16—1582no—
306C2×C8—22no—
307C2×C8—791no—
308C2×C8—791no—
309C2×C8—1582no—
310C2×C8—1582no—
311C2×C8C22×D7911yescharacteristic
312C2×C8C22×D7911yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—791no—
315C4⋊C4—791no—
316C4⋊C4—1581no—
317C4⋊C4—1581no—
318C4⋊C4C22×D7911yescharacteristic
319C4⋊C4C22×D7911yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—1581no—
323C22⋊C4—1581no—
324C22⋊C4—1581no—
325C22⋊C4—1581no—
326C22⋊C4—1581no—
327C22⋊C4—1581no—
328C22⋊C4—1581no—
329C42—1581no—
330C23—21no—
331C23—3162no—
332C23—791no—
333C23—791no—
334C23—6321no—
335C23—6321no—
336C23—1581no—
337C23—1581no—
338C23D4×D7911yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—1582no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—3162no—
346D4—3162no—
347D4—6321no—
348D4—6321no—
349D4—6321no—
350D4—6321no—
351D4—6321no—
352D4—1582no—
353D4—1582no—
354D4—1582no—
355D4—1581no—
356D4—1581no—
357D4—1581no—
358D4—1581no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—3162no—
365C2×C4—791no—
366C2×C4—792no—
367C2×C4—792no—
368C2×C4—791no—
369C2×C4—6321no—
370C2×C4—1581no—
371C2×C4—1581no—
372C2×C4—1581no—
373C2×C4—1581no—
374C2×C4D4×D7911yescharacteristic
375C2×C4C23×D7911yescharacteristic
376C8—21no—
377C8—792no—
378C8—1581no—
379C8D4×D7912yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—3161no—
387C22—3161no—
388C22—3161no—
389C22—3161no—
390C22—3161no—
391C22—3161no—
392C22—792no—
393C22—6324no—
394C22—1581no—
395C22—1581no—
396C22—1581no—
397C22—1581no—
398C22—1581no—
399C22C2×D4×D7911yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—3161no—
405C4—3161no—
406C4—792no—
407C4—1581no—
408C4C2×D4×D7911yescharacteristic
409C4#41×D7911yescharacteristic
410C2—41no—
411C2—81no—
412C2—3161no—
413C2—6321no—
414C2—6321no—
415C2—1582no—
416C2#121×D7911yescharacteristic
417C2#1909936511yescharacteristic
418C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#465×C79C2
socleC22×C79C22×D4
hypercenter#465D79
hypocenterC79#3062
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×#14579188C2semidirect
2. C2×#14579167C2semidirect
3. #19099143C2semidirect
4. #19099129C2semidirect
5. #19098817C2semidirect
6. #19098814C2semidirect
7. #19098811C2semidirect
8. #19098806C2semidirect
9. #19098799C2semidirect
10. #19098798C2semidirect
11. #19098795C2semidirect
12. #19098602C2semidirect
13. #19098558C2semidirect
14. #102×D79C2semidirect
15. #465×C79C2semidirect
24. C2×#11929608C22semidirect
26. C2×#11929607C22semidirect
28. C2×C8×D79C22semidirect
32. #14579137C22semidirect
35. #14579136C22semidirect
37. #14579135C22semidirect
45. #14579095C22semidirect
46. #14579094C22semidirect
47. #14579092C22semidirect
48. #14579085C22semidirect
50. #14579083C22semidirect
53. #14579081C22semidirect
55. C22×C8×C79C22semidirect
56. C22⋊Q8×C79C22semidirect
58. #106×C79C22semidirect
59. #103×C79C22semidirect
90. #11929607D4semidirect
210. C79#3062semidirect
222. #465D79semidirect
240. C22×C8C2×D79semidirect
245. C22⋊Q8C2×D79semidirect
262. #106C2×D79semidirect
264. #103C2×D79semidirect