Finite Group Databasebeta

← #23775083

Subgroups — #23775083

Order 10112.

526 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579181C211yesmaximal, characteristic, complemented
2C2×D8×D79C211yesmaximal, characteristic, complemented
3#19099210C211yesmaximal, characteristic, complemented
4#19099201C211yesmaximal, characteristic, complemented
5#19098944C211yesmaximal, characteristic, complemented
6#19098803C211yesmaximal, characteristic, complemented
7#19098797C211yesmaximal, characteristic, complemented
8#19098781C211yesmaximal, characteristic, complemented
9#19098776C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098712C211yesmaximal, characteristic, complemented
12#19098710C211yesmaximal, characteristic, complemented
13#19098643C211yesmaximal, characteristic, complemented
14(C22⋊D79)⋊C8C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic, complemented
17C2×D4×D79C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19#14579181—24no—
20C2×#11929614C2211yescharacteristic, complemented
21C2×#11929613C2211yescharacteristic, complemented
22C2×#11929612C2211yescharacteristic, complemented
23C2×#11929611C2211yescharacteristic, complemented
24C2×D632C2211yescharacteristic
25C2×#11929609C2211yescharacteristic
26C2×#11929609C2211yescharacteristic
27D8×D79—24no—
28C22×C79⋊C8C2211yescharacteristic, complemented
29C2×C8×D79C2211yescharacteristic
30#14579150C2211yescharacteristic, complemented
31#14579148C2211yescharacteristic, complemented
32#14579144—21no—
33#14579143—21no—
34#14579141C2211yescharacteristic
35#14579137C2211yescharacteristic
36#14579135C2211yescharacteristic, complemented
37#14579133—21no—
38#14579132—21no—
39#14579129—21no—
40#14579129—21no—
41D4×Dic79C2211yescharacteristic, complemented
42#14579123C2211yescharacteristic, complemented
43C4×C22⋊D79C2211yescharacteristic
44C2×(C2×D79)⋊C4—21no—
45C22⋊C4×D79—21no—
46#14579094C2211yescharacteristic, complemented
47Dic79⋊C8C2211yescharacteristic, complemented
48#14579086C2211yescharacteristic, complemented
49#14579083C2211yescharacteristic, complemented
50#14579082C2211yescharacteristic, complemented
51#14579081C2211yescharacteristic, complemented
52(C2×D79)⋊C8C2211yescharacteristic
53C8×Dic79C2211yescharacteristic, complemented
54C2×#41×C79C2211yescharacteristic, complemented
55C2×SD16×C79C2211yescharacteristic, complemented
56C2×D8×C79C2211yescharacteristic
57#121×C79C2211yescharacteristic, complemented
58#103×C79C2211yescharacteristic, complemented
59#102×C79C2211yescharacteristic, complemented
60C22⋊C8×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62C23×D79—21no—
63#11929624—22no—
64#11929624—41no—
65C2×Dic158C2311yescharacteristic
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79D411yescharacteristic
73D4×D79—22no—
74D4×D79—22no—
75D4×D79—41no—
76D4×D79—41no—
77C22×Dic79—21no—
78C2×C4×D79—21no—
79C2×C4×D79—21no—
80C2×C4×D79C2311yescharacteristic
81#11929614—22no—
82#11929613—41no—
83#11929612—22no—
84#11929611—22no—
85D632—22no—
86#11929609—22no—
87#11929609D414yescomplemented
88C2×C79⋊C8—22no—
89C2×C79⋊C8C2311yescharacteristic
90C2×C79⋊C8C2311yescharacteristic
91C8×D79—22no—
92C4⋊Dic79—21no—
93C4⋊Dic79C2311yescharacteristic
94Dic79⋊C4—21no—
95Dic79⋊C4D411yescharacteristic
96C22⋊Dic79—21no—
97C22⋊Dic79—21no—
98C22⋊Dic79—21no—
99C22⋊Dic79D411yescharacteristic
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—
106(C2×D79)⋊C4D411yescharacteristic
107C4×Dic79C2311yescharacteristic
108#41×C79—22no—
109#41×C79—41no—
110C2×Q8×C79C2311yescharacteristic
111C2×D4×C79—21no—
112C2×D4×C79—21no—
113C2×D4×C79C2311yescharacteristic
114C2×D4×C79C2311yescharacteristic
115C22×C4×C79—21no—
116C22×C4×C79C2311yescharacteristic
117SD16×C79—41no—
118D8×C79—22no—
119C2×C8×C79C2311yescharacteristic
120C2×C8×C79C2311yescharacteristic
121C4⋊C4×C79C2311yescharacteristic
122C22⋊C4×C79—21no—
123C23×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—21no—
140D4×C79—42no—
141D4×C79—81no—
142D4×C79C2×D412yes—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79—21no—
146C2×C4×C79—21no—
147C2×C4×C79—42no—
148C2×C4×C79C2×D411yescharacteristic
149C2×C4×C79C2411yescharacteristic
150C22⋊D79—22no—
151C22⋊D79—42no—
152C22⋊D79—42no—
153C22⋊D79—42no—
154C22⋊D79—81no—
155C2×Dic79—21no—
156C2×Dic79—21no—
157C2×Dic79—81no—
158C2×Dic79C2×D411yescharacteristic
159C2×Dic79C2×D411yescharacteristic
160C2×Dic79C2×D411yescharacteristic
161D316—21no—
162D316—21no—
163D316—21no—
164D316C2×D412yes—
165C4×D79—21no—
166C4×D79—21no—
167C4×D79—42no—
168C4×D79—81no—
169Dic158—21no—
170Dic158—21no—
171C8×C79—21no—
172C8×C79—21no—
173C79⋊C8—21no—
174C79⋊C8C2×D412yes—
175C22×C79—21no—
176C22×C79—22no—
177C22×C79—21no—
178C22×C79—21no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79—41no—
182C22×C79—41no—
183C22×C79—41no—
184C22×C79C22×D411yescharacteristic
185C2×D79—21no—
186C2×D79—21no—
187C2×D79—22no—
188C2×D79—41no—
189C2×D79—41no—
190C2×D79—41no—
191C2×D79—41no—
192C2×D79—41no—
193C2×D79—84no—
194C2×D79—84no—
195C2×D79#13512yescomplemented
196C4×C79—21no—
197C4×C79—41no—
198C4×C79—41no—
199C4×C79C22×D411yescharacteristic
200C4×C79H(5,𝔽2)11yescharacteristic
201Dic79—21no—
202Dic79—21no—
203Dic79—21no—
204Dic79—41no—
205Dic79—41no—
206C2×C79—42no—
207C2×C79—41no—
208C2×C79—81no—
209C2×C79D4211yescharacteristic
210C2×C79C2×#13511yescharacteristic
211C2×C79#57611yescharacteristic
212D79—22no—
213D79—42no—
214D79—81no—
215#3280—791nomaximal, Sylow
216C79#328011yescharacteristic, complemented, Sylow
217C2×#135—791no—
218C22×D8—791no—
219#546—791no—
220#546—791no—
221#495—791no—
222#467—791no—
223#466—791no—
224#463—791no—
225#463—791no—
226#450—791no—
227#450—791no—
228#449—791no—
229#449D7911yescharacteristic, complemented
230C4×D8—791no—
231C8×D4—791no—
232C2×#41—791no—
233C2×#41C2×D7911yescharacteristic, complemented
234C22×D4—791no—
235C22×D4—791no—
236#135—1584no—
237C2×Q16—791no—
238C2×SD16—791no—
239C2×SD16—791no—
240C2×SD16—791no—
241C2×SD16C2×D7911yescharacteristic, complemented
242C2×D8—791no—
243C2×D8—791no—
244C2×D8—791no—
245C2×D8—1584no—
246C2×D8C2×D7911yescharacteristic
247C22×C8—791no—
248C22×C8—791no—
249#124—791no—
250#124—791no—
251#123—1581no—
252#123—1581no—
253C22⋊Q8—791no—
254C22⋊Q8—791no—
255#121—791no—
256#121—1581no—
257#121—1581no—
258#121C2×D7911yescharacteristic, complemented
259#120—1581no—
260#120—1581no—
261C4×D4—791no—
262C4×D4—791no—
263C4×D4—791no—
264C2×C22⋊C4—1581no—
265C2×C22⋊C4—1581no—
266#107—791no—
267C4⋊C8—791no—
268#103—791no—
269#103C2×D7911yescharacteristic, complemented
270#102—791no—
271#102—791no—
272#102—791no—
273#102C2×D7911yescharacteristic, complemented
274C22⋊C8—791no—
275C22⋊C8C2×D7911yescharacteristic, complemented
276C4×C8—791no—
277C24—1581no—
278C24—1581no—
279#41—22no—
280#41—41no—
281#41—3161no—
282#41—1582no—
283C2×Q8—791no—
284C2×Q8C22×D7911yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—3161no—
288C2×D4—3161no—
289C2×D4—791no—
290C2×D4—791no—
291C2×D4—791no—
292C2×D4—1581no—
293C2×D4—1581no—
294C2×D4—1582no—
295C2×D4—1581no—
296C2×D4—1582no—
297C2×D4—1581no—
298C2×D4C22×D7911yescharacteristic
299C2×D4C22×D7911yescharacteristic
300C22×C4—21no—
301C22×C4—791no—
302C22×C4—1581no—
303C22×C4—1581no—
304C22×C4—1581no—
305C22×C4C22×D7911yescharacteristic
306Q16—1582no—
307SD16—41no—
308SD16—3161no—
309SD16—1582no—
310SD16—1582no—
311D8—22no—
312D8—794no—
313D8—1582no—
314D8—1582no—
315C2×C8—791no—
316C2×C8—791no—
317C2×C8—1582no—
318C2×C8—1582no—
319C2×C8C22×D7911yescharacteristic
320C2×C8C22×D7911yescharacteristic
321C4⋊C4—791no—
322C4⋊C4—791no—
323C4⋊C4—1581no—
324C4⋊C4—1581no—
325C4⋊C4C22×D7911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—791no—
328C22⋊C4—791no—
329C22⋊C4—1581no—
330C22⋊C4—1581no—
331C22⋊C4—1581no—
332C22⋊C4—1581no—
333C22⋊C4—1581no—
334C22⋊C4—1581no—
335C22⋊C4—1581no—
336C22⋊C4—1581no—
337C22⋊C4—1581no—
338C42—791no—
339C23—21no—
340C23—21no—
341C23—3162no—
342C23—3162no—
343C23—3162no—
344C23—3162no—
345C23—791no—
346C23—6321no—
347C23—6321no—
348C23—1581no—
349C23—1581no—
350C23D4×D7911yescharacteristic
351Q8—21no—
352Q8—21no—
353Q8—1581no—
354Q8—1581no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4—81no—
360D4—3162no—
361D4—3162no—
362D4—3162no—
363D4—792no—
364D4—6321no—
365D4—1582no—
366D4—1581no—
367D4—1581no—
368D4—1581no—
369D4D4×D7912yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—42no—
375C2×C4—3162no—
376C2×C4—791no—
377C2×C4—791no—
378C2×C4—791no—
379C2×C4—6321no—
380C2×C4—6321no—
381C2×C4—1581no—
382C2×C4—1581no—
383C2×C4—1581no—
384C2×C4—1581no—
385C2×C4D4×D7911yescharacteristic
386C2×C4C23×D7911yescharacteristic
387C8—21no—
388C8—21no—
389C8—792no—
390C8—1581no—
391C22—21no—
392C22—22no—
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—3161no—
401C22—3161no—
402C22—3161no—
403C22—3161no—
404C22—3161no—
405C22—792no—
406C22—6324no—
407C22—6324no—
408C22—1582no—
409C22—1581no—
410C22—1581no—
411C22C2×D4×D7911yescharacteristic
412C4—21no—
413C4—41no—
414C4—41no—
415C4—3161no—
416C4—3161no—
417C4—1581no—
418C4—1581no—
419C4—1581no—
420C4C2×D4×D7911yescharacteristic
421C4#1457920611yescharacteristic
422C2—41no—
423C2—42no—
424C2—81no—
425C2—3162no—
426C2—6321no—
427C2—1582no—
428C2#1909919511yescharacteristic
429C2#135×D7911yescharacteristic
430C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3280
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#14579181C2semidirect
2. C2×D8×D79C2semidirect
3. #19099210C2semidirect
4. #19099201C2semidirect
5. #19098944C2semidirect
6. #19098803C2semidirect
7. #19098797C2semidirect
8. #19098781C2semidirect
9. #19098776C2semidirect
10. #19098715C2semidirect
11. #19098712C2semidirect
12. #19098710C2semidirect
13. #19098643C2semidirect
14. (C22⋊D79)⋊C8C2semidirect
15. #449×C79C2semidirect
16. C2×#11929624C22semidirect
20. C2×#11929614C22semidirect
21. C2×#11929613C22semidirect
22. C2×#11929612C22semidirect
23. C2×#11929611C22semidirect
28. C22×C79⋊C8C22semidirect
30. #14579150C22semidirect
31. #14579148C22semidirect
36. #14579135C22semidirect
41. D4×Dic79C22semidirect
42. #14579123C22semidirect
46. #14579094C22semidirect
47. Dic79⋊C8C22semidirect
48. #14579086C22semidirect
49. #14579083C22semidirect
50. #14579082C22semidirect
51. #14579081C22semidirect
53. C8×Dic79C22semidirect
54. C2×#41×C79C22semidirect
55. C2×SD16×C79C22semidirect
57. #121×C79C22semidirect
58. #103×C79C22semidirect
59. #102×C79C22semidirect
60. C22⋊C8×C79C22semidirect
87. #11929609D4semidirect
195. C2×D79#135semidirect
216. C79#3280semidirect
229. #449D79semidirect
233. C2×#41C2×D79semidirect
241. C2×SD16C2×D79semidirect
258. #121C2×D79semidirect
269. #103C2×D79semidirect
273. #102C2×D79semidirect
275. C22⋊C8C2×D79semidirect