Finite Group Databasebeta

← #23772901

Subgroups — #23772901

Order 10112.

526 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579188C211yesmaximal, characteristic, complemented
2C2×D8×D79C211yesmaximal, characteristic, complemented
3#19099131C211yesmaximal, characteristic, complemented
4#19099035C211yesmaximal, characteristic, complemented
5#19098781C211yesmaximal, characteristic, complemented
6#19098780C211yesmaximal, characteristic, complemented
7#19098775C211yesmaximal, characteristic, complemented
8#19098759C211yesmaximal, characteristic, complemented
9#19098758C211yesmaximal, characteristic, complemented
10#19098757C211yesmaximal, characteristic, complemented
11#19098756C211yesmaximal, characteristic, complemented
12#19098588C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14#19098558C211yesmaximal, characteristic, complemented
15#463×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19#14579188—24no—
20C2×#11929611C2211yescharacteristic, complemented
21C2×D632C2211yescharacteristic
22C2×D632C2211yescharacteristic, complemented
23C2×#11929609C2211yescharacteristic
24C2×#11929609C2211yescharacteristic
25C2×#11929609C2211yescharacteristic, complemented
26D8×D79—24no—
27C2×#11929607C2211yescharacteristic
28C2×C8×D79C2211yescharacteristic
29#14579158C2211yescharacteristic, complemented
30#14579157C2211yescharacteristic, complemented
31#14579150C2211yescharacteristic, complemented
32#14579134—21no—
33#14579134—21no—
34#14579131—21no—
35#14579131—21no—
36C4×D316C2211yescharacteristic, complemented
37D4×Dic79C2211yescharacteristic, complemented
38#14579123C2211yescharacteristic, complemented
39C4×C22⋊D79—21no—
40(C22⋊D79)⋊C4—21no—
41#14579119C2211yescharacteristic
42#14579118C2211yescharacteristic
43C2×(C2×D79)⋊C4—21no—
44C22⋊C4×D79—21no—
45C4⋊(C79⋊C8)C2211yescharacteristic, complemented
46Dic79⋊C8C2211yescharacteristic, complemented
47Dic79⋊C8C2211yescharacteristic, complemented
48#14579085C2211yescharacteristic, complemented
49#14579083C2211yescharacteristic, complemented
50#14579083C2211yescharacteristic, complemented
51#14579082C2211yescharacteristic, complemented
52#14579081C2211yescharacteristic, complemented
53#14579081C2211yescharacteristic, complemented
54C2×SD16×C79C2211yescharacteristic, complemented
55C2×D8×C79C2211yescharacteristic
56#124×C79C2211yescharacteristic, complemented
57C4×D4×C79C2211yescharacteristic, complemented
58C4⋊C8×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62C23×D79—21no—
63#11929625—22no—
64#11929625—22no—
65C2×D316—21no—
66C2×D316—21no—
67C2×D316—21no—
68C2×D316C2311yescharacteristic
69C2×D316C2311yescharacteristic
70C2×D316C2311yescharacteristic
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75D4×D79—22no—
76D4×D79—22no—
77D4×D79—22no—
78D4×D79D414yescomplemented
79C22×Dic79—21no—
80C2×C4×D79—21no—
81C2×C4×D79—21no—
82C2×C4×D79—21no—
83C2×C4×D79C2311yescharacteristic
84#11929611—22no—
85D632—22no—
86D632—22no—
87#11929609—22no—
88#11929609—22no—
89#11929609—22no—
90#11929607—22no—
91C2×C79⋊C8C2311yescharacteristic
92C2×C79⋊C8C2311yescharacteristic
93C8×D79—22no—
94C4⋊Dic79C2311yescharacteristic
95Dic79⋊C4D411yescharacteristic
96Dic79⋊C4D411yescharacteristic
97C22⋊Dic79—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4—21no—
100(C2×D79)⋊C4—21no—
101(C2×D79)⋊C4—21no—
102(C2×D79)⋊C4—21no—
103(C2×D79)⋊C4D411yescharacteristic
104(C2×D79)⋊C4D411yescharacteristic
105C4×Dic79—21no—
106C4×Dic79C2311yescharacteristic
107C2×Q8×C79C2311yescharacteristic
108C2×D4×C79C2311yescharacteristic
109C2×D4×C79C2311yescharacteristic
110C22×C4×C79—21no—
111SD16×C79—22no—
112D8×C79—22no—
113C2×C8×C79C2311yescharacteristic
114C2×C8×C79C2311yescharacteristic
115C4⋊C4×C79C2311yescharacteristic
116C22⋊C4×C79—21no—
117C22⋊C4×C79—21no—
118C22⋊C4×C79—21no—
119C42×C79C2311yescharacteristic
120C23×C79—21no—
121C23×C79—21no—
122C22×D79—21no—
123C22×D79—24no—
124C22×D79—21no—
125C22×D79—21no—
126C22×D79—42no—
127C22×D79—81no—
128C22×D79—81no—
129C22×D79—81no—
130C22×D79—81no—
131C22×D79C2×D411yescharacteristic
132Q8×C79—21no—
133Q8×C79—21no—
134D4×C79—21no—
135D4×C79—21no—
136D4×C79—21no—
137D4×C79C2×D412yes—
138C2×C4×C79—21no—
139C2×C4×C79—21no—
140C2×C4×C79—81no—
141C2×C4×C79C2×D411yescharacteristic
142C2×C4×C79C2×D411yescharacteristic
143C2×C4×C79C2411yescharacteristic
144C22⋊D79—24no—
145C22⋊D79—42no—
146C22⋊D79—81no—
147C22⋊D79—81no—
148C2×Dic79—21no—
149C2×Dic79—81no—
150C2×Dic79C2×D411yescharacteristic
151C2×Dic79C2×D411yescharacteristic
152C2×Dic79C2×D411yescharacteristic
153D316—21no—
154D316—21no—
155D316—21no—
156D316—21no—
157D316—21no—
158D316—42no—
159D316—81no—
160D316—81no—
161D316C2×D412yes—
162C4×D79—42no—
163C4×D79—81no—
164C4×D79—81no—
165C4×D79C2×D412yes—
166C4×D79#4112yes—
167C8×C79—21no—
168C8×C79—21no—
169C79⋊C8—21no—
170C79⋊C8—21no—
171C22×C79—22no—
172C22×C79—41no—
173C22×C79—41no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79—41no—
177C22×C79C22×D411yescharacteristic
178C2×D79—21no—
179C2×D79—21no—
180C2×D79—22no—
181C2×D79—41no—
182C2×D79—41no—
183C2×D79—41no—
184C2×D79—41no—
185C2×D79—41no—
186C2×D79—41no—
187C2×D79—41no—
188C2×D79—41no—
189C2×D79—84no—
190C2×D79—84no—
191C2×D79#12112yes—
192C4×C79—21no—
193C4×C79—21no—
194C4×C79—41no—
195C4×C79—41no—
196C4×C79C22×D411yescharacteristic
197C4×C79C2×#4111yescharacteristic
198Dic79—21no—
199Dic79—21no—
200Dic79—41no—
201Dic79#12112yes—
202C2×C79—42no—
203C2×C79—81no—
204C2×C79C2×#12111yescharacteristic
205C2×C79#57611yescharacteristic
206C2×C79#57611yescharacteristic
207D79—22no—
208D79—42no—
209D79—81no—
210D79—81no—
211#3041—791nomaximal, Sylow
212C79#304111yescharacteristic, complemented, Sylow
213C2×AGL(1,ℤ/8)—791no—
214C22×D8—791no—
215#535—791no—
216#518—791no—
217#463—791no—
218#463—791no—
219#463—791no—
220#463D7911yescharacteristic, complemented
221#459—791no—
222#459—791no—
223#459—791no—
224#459—791no—
225#424—791no—
226#418—791no—
227#416—791no—
228C2×#41—791no—
229C22×D4—791no—
230C22×D4—791no—
231AGL(1,ℤ/8)—1584no—
232C2×SD16—791no—
233C2×SD16C2×D7911yescharacteristic, complemented
234C2×D8—791no—
235C2×D8—791no—
236C2×D8—791no—
237C2×D8—791no—
238C2×D8—791no—
239C2×D8—1584no—
240C2×D8C2×D7911yescharacteristic
241C2×M16—791no—
242C22×C8—791no—
243#127—791no—
244#127—791no—
245#124—791no—
246#124C2×D7911yescharacteristic, complemented
247#121—1581no—
248#121—1581no—
249#120—1581no—
250#120—1581no—
251C4×D4—791no—
252C4×D4—791no—
253C4×D4—791no—
254C4×D4—1581no—
255C4×D4—1581no—
256C4×D4C2×D7911yescharacteristic, complemented
257#117—791no—
258#117—791no—
259C2×C22⋊C4—1581no—
260C2×C22⋊C4—1581no—
261C4⋊C8—791no—
262C4⋊C8—791no—
263C4⋊C8—791no—
264C4⋊C8C2×D7911yescharacteristic, complemented
265#103—791no—
266#103C2×D7911yescharacteristic, complemented
267#102—791no—
268#102—791no—
269#102—791no—
270#102—791no—
271#102—791no—
272#102C2×D7911yescharacteristic, complemented
273C24—1581no—
274C24—1581no—
275#41—1582no—
276#41—1582no—
277C2×Q8C22×D7911yescharacteristic
278C2×D4—794no—
279C2×D4—791no—
280C2×D4—791no—
281C2×D4—791no—
282C2×D4—1581no—
283C2×D4—1582no—
284C2×D4—1582no—
285C2×D4—1582no—
286C2×D4—1581no—
287C2×D4—1581no—
288C2×D4—1581no—
289C2×D4—1581no—
290C2×D4—1581no—
291C2×D4—1581no—
292C2×D4C22×D7911yescharacteristic
293C2×D4C22×D7911yescharacteristic
294C22×C4—21no—
295C22×C4—791no—
296C22×C4—1581no—
297C22×C4—1581no—
298C22×C4—1581no—
299C22×C4—1581no—
300SD16—22no—
301SD16—1582no—
302D8—22no—
303D8—1582no—
304D8—1582no—
305D8—1582no—
306D8—1582no—
307D8—1582no—
308M16—1582no—
309C2×C8—791no—
310C2×C8—791no—
311C2×C8—1582no—
312C2×C8C22×D7911yescharacteristic
313C2×C8C22×D7911yescharacteristic
314C4⋊C4—791no—
315C4⋊C4—791no—
316C4⋊C4—791no—
317C4⋊C4C22×D7911yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—791no—
322C22⋊C4—791no—
323C22⋊C4—1581no—
324C22⋊C4—1581no—
325C22⋊C4—1581no—
326C22⋊C4—1581no—
327C22⋊C4—1581no—
328C22⋊C4—1581no—
329C42—791no—
330C42—1581no—
331C42C22×D7911yescharacteristic
332C23—21no—
333C23—21no—
334C23—3162no—
335C23—791no—
336C23—6321no—
337C23—6321no—
338C23—6321no—
339C23—6321no—
340C23—1584no—
341C23—1581no—
342C23—1581no—
343C23—1581no—
344Q8—21no—
345Q8—21no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—3162no—
350D4—3162no—
351D4—792no—
352D4—6321no—
353D4—6321no—
354D4—6321no—
355D4—6321no—
356D4—1584no—
357D4—1581no—
358D4—1581no—
359D4—1581no—
360D4—1581no—
361D4—1581no—
362D4D4×D7912yes—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—81no—
366C2×C4—3162no—
367C2×C4—791no—
368C2×C4—792no—
369C2×C4—792no—
370C2×C4—791no—
371C2×C4—791no—
372C2×C4—6321no—
373C2×C4—6321no—
374C2×C4—6321no—
375C2×C4—1581no—
376C2×C4D4×D7911yescharacteristic
377C2×C4D4×D7911yescharacteristic
378C2×C4C23×D7911yescharacteristic
379C8—21no—
380C8—21no—
381C8—1581no—
382C8—1581no—
383C22—22no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—3161no—
390C22—3161no—
391C22—3161no—
392C22—3161no—
393C22—3161no—
394C22—3161no—
395C22—3161no—
396C22—3161no—
397C22—792no—
398C22—6324no—
399C22—6324no—
400C22—1582no—
401C22—1581no—
402C22—1581no—
403C22C2×D4×D7911yescharacteristic
404C4—21no—
405C4—21no—
406C4—41no—
407C4—41no—
408C4—3161no—
409C4—792no—
410C4—1581no—
411C4—1581no—
412C4C2×D4×D7911yescharacteristic
413C4#41×D7911yescharacteristic
414C2—42no—
415C2—81no—
416C2—3162no—
417C2—6321no—
418C2—6321no—
419C2—1582no—
420C2#121×D7911yescharacteristic
421C2#1909936511yescharacteristic
422C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#463×C79C2
socleC22×C79C22×D4
hypercenter#463D79
hypocenterC79#3041
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#14579188C2semidirect
2. C2×D8×D79C2semidirect
3. #19099131C2semidirect
4. #19099035C2semidirect
5. #19098781C2semidirect
6. #19098780C2semidirect
7. #19098775C2semidirect
8. #19098759C2semidirect
9. #19098758C2semidirect
10. #19098757C2semidirect
11. #19098756C2semidirect
12. #19098588C2semidirect
13. #19098566C2semidirect
14. #19098558C2semidirect
15. #463×C79C2semidirect
20. C2×#11929611C22semidirect
22. C2×D632C22semidirect
25. C2×#11929609C22semidirect
29. #14579158C22semidirect
30. #14579157C22semidirect
31. #14579150C22semidirect
36. C4×D316C22semidirect
37. D4×Dic79C22semidirect
38. #14579123C22semidirect
45. C4⋊(C79⋊C8)C22semidirect
46. Dic79⋊C8C22semidirect
47. Dic79⋊C8C22semidirect
48. #14579085C22semidirect
49. #14579083C22semidirect
50. #14579083C22semidirect
51. #14579082C22semidirect
52. #14579081C22semidirect
53. #14579081C22semidirect
54. C2×SD16×C79C22semidirect
56. #124×C79C22semidirect
57. C4×D4×C79C22semidirect
58. C4⋊C8×C79C22semidirect
59. #103×C79C22semidirect
60. #102×C79C22semidirect
78. D4×D79D4semidirect
212. C79#3041semidirect
220. #463D79semidirect
233. C2×SD16C2×D79semidirect
246. #124C2×D79semidirect
256. C4×D4C2×D79semidirect
264. C4⋊C8C2×D79semidirect
266. #103C2×D79semidirect
272. #102C2×D79semidirect