Finite Group Databasebeta

← #23775093

Subgroups — #23775093

Order 10112.

546 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#11929613C211yesmaximal, characteristic, complemented
2C2×SD16×D79C211yesmaximal, characteristic, complemented
3#19099226C211yesmaximal, characteristic, complemented
4#19099197C211yesmaximal, characteristic
5#19098934C211yesmaximal, characteristic, complemented
6#19098793C211yesmaximal, characteristic, complemented
7#19098767C211yesmaximal, characteristic, complemented
8#19098762C211yesmaximal, characteristic, complemented
9#19098715C211yesmaximal, characteristic, complemented
10#19098713C211yesmaximal, characteristic, complemented
11#19098703C211yesmaximal, characteristic, complemented
12#19098701C211yesmaximal, characteristic, complemented
13#19098650C211yesmaximal, characteristic, complemented
14C8×C22⋊D79C211yesmaximal, characteristic, complemented
15#465×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic, complemented
17C2×Q8×D79C2211yescharacteristic, complemented
18C22×D316C2211yescharacteristic
19C2×D4×D79—21no—
20C2×D4×D79C2211yescharacteristic
21C2×#11929613—24no—
22C2×#11929613C2211yescharacteristic
23C2×#11929613C2211yescharacteristic
24C2×#11929613C2211yescharacteristic, complemented
25C2×#11929613C2211yescharacteristic, complemented
26C2×#11929612C2211yescharacteristic, complemented
27C2×#11929612C2211yescharacteristic, complemented
28C2×#11929611C2211yescharacteristic
29C2×#11929611C2211yescharacteristic, complemented
30SD16×D79—24no—
31C2×C8×D79C2211yescharacteristic, complemented
32#14579160—21no—
33#14579159C2211yescharacteristic, complemented
34#14579157C2211yescharacteristic
35#14579141C2211yescharacteristic, complemented
36#14579139—21no—
37#14579138—21no—
38#14579136C2211yescharacteristic
39#14579134—21no—
40#14579131—21no—
41#14579129—21no—
42#14579126C2211yescharacteristic, complemented
43#14579123C2211yescharacteristic
44C4×C22⋊D79C2211yescharacteristic
45(C22⋊D79)⋊C4—21no—
46Dic79⋊C8C2211yescharacteristic, complemented
47#14579084C2211yescharacteristic, complemented
48#14579084C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic
50#14579081C2211yescharacteristic, complemented
51C22⋊(C79⋊C8)C2211yescharacteristic, complemented
52(C2×D79)⋊C8C2211yescharacteristic, complemented
53C8×Dic79C2211yescharacteristic, complemented
54C2×SD16×C79C2211yescharacteristic, complemented
55C22×C8×C79C2211yescharacteristic, complemented
56C22⋊Q8×C79C2211yescharacteristic, complemented
57#121×C79C2211yescharacteristic
58#106×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62C23×D79—21no—
63C2×Dic158—22no—
64C2×Dic158—21no—
65C2×Dic158—21no—
66C2×Dic158—41no—
67C2×Dic158C2311yescharacteristic
68C2×Dic158C2311yescharacteristic
69Q8×D79—22no—
70Q8×D79—41no—
71C2×D316—21no—
72C2×D316—22no—
73C2×D316—21no—
74C2×D316—41no—
75C2×D316C2311yescharacteristic
76C2×D316C2311yescharacteristic
77C2×C22⋊D79—21no—
78C2×C22⋊D79—21no—
79C2×C22⋊D79—21no—
80C2×C22⋊D79D411yescharacteristic
81D4×D79—22no—
82D4×D79—41no—
83D4×D79—44no—
84C22×Dic79—21no—
85C2×C4×D79—21no—
86C2×C4×D79—21no—
87C2×C4×D79C2311yescharacteristic
88#11929613—22no—
89#11929613—22no—
90#11929613—22no—
91#11929613D414yescomplemented
92#11929612—22no—
93#11929612—41no—
94#11929611—22no—
95#11929611—41no—
96C2×C79⋊C8C2311yescharacteristic
97C2×C79⋊C8C2311yescharacteristic
98C8×D79—22no—
99C4⋊Dic79—21no—
100Dic79⋊C4—21no—
101Dic79⋊C4—21no—
102Dic79⋊C4—21no—
103Dic79⋊C4D411yescharacteristic
104C22⋊Dic79D411yescharacteristic
105(C2×D79)⋊C4—21no—
106(C2×D79)⋊C4—21no—
107(C2×D79)⋊C4—21no—
108(C2×D79)⋊C4D411yescharacteristic
109C4×Dic79—21no—
110C4×Dic79C2311yescharacteristic
111C2×Q8×C79C2311yescharacteristic
112C2×D4×C79—21no—
113C2×D4×C79C2311yescharacteristic
114C22×C4×C79C2311yescharacteristic
115SD16×C79—22no—
116C2×C8×C79—22no—
117C2×C8×C79C2311yescharacteristic
118C2×C8×C79C2311yescharacteristic
119C4⋊C4×C79—21no—
120C4⋊C4×C79C2311yescharacteristic
121C4⋊C4×C79C2311yescharacteristic
122C22⋊C4×C79—21no—
123C22⋊C4×C79—21no—
124C23×C79—21no—
125C23×C79C2×D411yescharacteristic
126C22×D79—21no—
127C22×D79—21no—
128C22×D79—42no—
129C22×D79—42no—
130C22×D79—42no—
131C22×D79—42no—
132C22×D79—81no—
133C22×D79—81no—
134C22×D79C2×D411yescharacteristic
135Q8×C79—21no—
136Q8×C79—21no—
137D4×C79—21no—
138D4×C79—21no—
139D4×C79—42no—
140C2×C4×C79—21no—
141C2×C4×C79—21no—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79C2×D411yescharacteristic
146C2×C4×C79C2411yescharacteristic
147C22⋊D79—42no—
148C22⋊D79—42no—
149C22⋊D79—81no—
150C22⋊D79SD1614yescomplemented
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79—42no—
154C2×Dic79C2×D411yescharacteristic
155C2×Dic79C2×D411yescharacteristic
156C2×Dic79C2×D411yescharacteristic
157D316—21no—
158D316—21no—
159D316—21no—
160D316—42no—
161D316—42no—
162D316C2×D412yes—
163C4×D79—21no—
164C4×D79—21no—
165C4×D79—42no—
166C4×D79—42no—
167Dic158—21no—
168Dic158—21no—
169Dic158—21no—
170Dic158—42no—
171Dic158—42no—
172Dic158C2×D412yescomplemented
173C8×C79—21no—
174C8×C79C2×D412yescomplemented
175C79⋊C8—21no—
176C79⋊C8—21no—
177C22×C79—21no—
178C22×C79—21no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79—41no—
182C22×C79C2×SD1612yescomplemented
183C22×C79C22×D411yescharacteristic
184C2×D79—21no—
185C2×D79—21no—
186C2×D79—22no—
187C2×D79—41no—
188C2×D79—41no—
189C2×D79—41no—
190C2×D79—41no—
191C2×D79—41no—
192C2×D79—84no—
193C2×D79—84no—
194C2×D79C2×SD1612yescomplemented
195C4×C79—21no—
196C4×C79—41no—
197C4×C79—41no—
198C4×C79—41no—
199C4×C79C22×D411yescharacteristic
200C4×C79H(5,𝔽2)11yescharacteristic
201Dic79—21no—
202Dic79—22no—
203Dic79—21no—
204Dic79—41no—
205Dic79C2×SD1612yescomplemented
206C2×C79—22no—
207C2×C79—81no—
208C2×C79D4211yescharacteristic
209C2×C79C22×SD1611yescharacteristic
210C2×C79#57711yescharacteristic
211D79—22no—
212D79—42no—
213D79—81no—
214D4×SD16—791nomaximal, Sylow
215C79D4×SD1611yescharacteristic, complemented, Sylow
216C22×SD16—791no—
217C22×SD16—791no—
218D4×Q8—791no—
219D42—791no—
220#492—791no—
221#465—791no—
222#465D7911yescharacteristic, complemented
223#461—791no—
224#460—791no—
225#450—791no—
226#450—791no—
227#448—791no—
228#448—791no—
229C4×SD16—791no—
230C8×D4—791no—
231C22×Q8—791no—
232C22×Q8—791no—
233C22×D4—791no—
234C22×D4—791no—
235C22×D4—1581no—
236C2×SD16—791no—
237C2×SD16—791no—
238C2×SD16—791no—
239C2×SD16—791no—
240C2×SD16—791no—
241C2×SD16—791no—
242C2×SD16—791no—
243C2×SD16—791no—
244C2×SD16—1584no—
245C2×SD16—1584no—
246C2×SD16C2×D7911yescharacteristic, complemented
247C22×C8—791no—
248C22×C8C2×D7911yescharacteristic, complemented
249C4⋊Q8—791no—
250C4⋊Q8—1581no—
251#127—791no—
252C22⋊Q8—791no—
253C22⋊Q8—1581no—
254C22⋊Q8—1581no—
255C22⋊Q8C2×D7911yescharacteristic, complemented
256#121—791no—
257#121—1581no—
258#121C2×D7911yescharacteristic
259#120—1581no—
260#120—1581no—
261C4×Q8—791no—
262C4×D4—791no—
263C4×D4—791no—
264C4×D4—1581no—
265#106C2×D7911yescharacteristic, complemented
266C4⋊C8—791no—
267#103—791no—
268#103—791no—
269#103C2×D7911yescharacteristic, complemented
270#102—791no—
271#102—791no—
272#102C2×D7911yescharacteristic, complemented
273C22⋊C8—791no—
274C22⋊C8—791no—
275C4×C8—791no—
276C24—1581no—
277C24—1581no—
278C2×Q8—3161no—
279C2×Q8—3161no—
280C2×Q8—791no—
281C2×Q8—791no—
282C2×Q8—1582no—
283C2×Q8—1581no—
284C2×Q8—1582no—
285C2×Q8—1581no—
286C2×Q8C22×D7911yescharacteristic
287C2×D4—21no—
288C2×D4—3161no—
289C2×D4—3164no—
290C2×D4—3161no—
291C2×D4—791no—
292C2×D4—791no—
293C2×D4—791no—
294C2×D4—1581no—
295C2×D4—1582no—
296C2×D4—1581no—
297C2×D4—1581no—
298C2×D4—1581no—
299C2×D4—1582no—
300C2×D4—1581no—
301C2×D4C22×D7911yescharacteristic
302C22×C4—791no—
303C22×C4—1581no—
304C22×C4—1581no—
305C22×C4—1581no—
306C22×C4C22×D7911yescharacteristic
307SD16—22no—
308SD16—3161no—
309SD16—3161no—
310SD16—794no—
311SD16—1582no—
312SD16—1582no—
313SD16—1582no—
314SD16—1582no—
315SD16—1582no—
316C2×C8—22no—
317C2×C8—791no—
318C2×C8—791no—
319C2×C8—1582no—
320C2×C8C22×D7911yescharacteristic
321C2×C8C22×D7911yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—791no—
324C4⋊C4—1581no—
325C4⋊C4—1581no—
326C4⋊C4—1581no—
327C4⋊C4—1581no—
328C4⋊C4C22×D7911yescharacteristic
329C4⋊C4C22×D7911yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—791no—
333C22⋊C4—791no—
334C22⋊C4—1581no—
335C22⋊C4—1581no—
336C22⋊C4—1581no—
337C42—791no—
338C42—1581no—
339C23—21no—
340C23—3162no—
341C23—3162no—
342C23—3162no—
343C23—3162no—
344C23—791no—
345C23—6321no—
346C23—6321no—
347C23—1581no—
348C23—1581no—
349C23D4×D7911yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—3162no—
353Q8—3162no—
354Q8—792no—
355Q8—1581no—
356Q8—1581no—
357Q8—1581no—
358D4—21no—
359D4—21no—
360D4—42no—
361D4—3162no—
362D4—3162no—
363D4—3162no—
364D4—3162no—
365D4—794no—
366D4—792no—
367D4—6321no—
368D4—1581no—
369D4—1581no—
370D4—1581no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—3162no—
377C2×C4—3162no—
378C2×C4—3162no—
379C2×C4—791no—
380C2×C4—791no—
381C2×C4—791no—
382C2×C4—1581no—
383C2×C4—1581no—
384C2×C4—1581no—
385C2×C4—1581no—
386C2×C4D4×D7911yescharacteristic
387C2×C4C23×D7911yescharacteristic
388C8—21no—
389C8—1581no—
390C8—1581no—
391C8D4×D7912yescomplemented
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—3161no—
398C22—3161no—
399C22—3161no—
400C22—3161no—
401C22—3161no—
402C22—792no—
403C22—6324no—
404C22—6324no—
405C22—1582no—
406C22—1581no—
407C22—1581no—
408C22SD16×D7912yescomplemented
409C22C2×D4×D7911yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—3161no—
415C4—792no—
416C4—1582no—
417C4—1581no—
418C4—1581no—
419C4C2×D4×D7911yescharacteristic
420C4#1457920711yescharacteristic
421C2—22no—
422C2—81no—
423C2—3162no—
424C2—6321no—
425C2—1582no—
426C2#1909919711yescharacteristic
427C2C2×SD16×D7911yescharacteristic
428C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#465×C79C2
socleC22×C79C22×D4
prime radical#19099197C2
hypercenter#465D79
hypocenterC79D4×SD16
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. C22×#11929613C2semidirect
2. C2×SD16×D79C2semidirect
3. #19099226C2semidirect
5. #19098934C2semidirect
6. #19098793C2semidirect
7. #19098767C2semidirect
8. #19098762C2semidirect
9. #19098715C2semidirect
10. #19098713C2semidirect
11. #19098703C2semidirect
12. #19098701C2semidirect
13. #19098650C2semidirect
14. C8×C22⋊D79C2semidirect
15. #465×C79C2semidirect
16. C22×Dic158C22semidirect
17. C2×Q8×D79C22semidirect
24. C2×#11929613C22semidirect
25. C2×#11929613C22semidirect
26. C2×#11929612C22semidirect
27. C2×#11929612C22semidirect
29. C2×#11929611C22semidirect
31. C2×C8×D79C22semidirect
33. #14579159C22semidirect
35. #14579141C22semidirect
42. #14579126C22semidirect
46. Dic79⋊C8C22semidirect
47. #14579084C22semidirect
48. #14579084C22semidirect
50. #14579081C22semidirect
51. C22⋊(C79⋊C8)C22semidirect
52. (C2×D79)⋊C8C22semidirect
53. C8×Dic79C22semidirect
54. C2×SD16×C79C22semidirect
55. C22×C8×C79C22semidirect
56. C22⋊Q8×C79C22semidirect
58. #106×C79C22semidirect
59. #103×C79C22semidirect
60. #102×C79C22semidirect
91. #11929613D4semidirect
150. C22⋊D79SD16semidirect
172. Dic158C2×D4semidirect
174. C8×C79C2×D4semidirect
182. C22×C79C2×SD16semidirect
194. C2×D79C2×SD16semidirect
205. Dic79C2×SD16semidirect
215. C79D4×SD16semidirect
222. #465D79semidirect
246. C2×SD16C2×D79semidirect
248. C22×C8C2×D79semidirect
255. C22⋊Q8C2×D79semidirect
265. #106C2×D79semidirect
269. #103C2×D79semidirect
272. #102C2×D79semidirect
391. C8D4×D79semidirect
408. C22SD16×D79semidirect