Finite Group Databasebeta

← #23775094

Subgroups — #23775094

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×#11929612C211yesmaximal, characteristic, complemented
2C2×SD16×D79C211yesmaximal, characteristic, complemented
3#19099226C211yesmaximal, characteristic, complemented
4D4×C22⋊D79C211yesmaximal, characteristic
5#19098934C211yesmaximal, characteristic, complemented
6#19098794C211yesmaximal, characteristic, complemented
7#19098791C211yesmaximal, characteristic, complemented
8#19098766C211yesmaximal, characteristic, complemented
9#19098762C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098704C211yesmaximal, characteristic, complemented
12#19098700C211yesmaximal, characteristic, complemented
13#19098654C211yesmaximal, characteristic, complemented
14(C22⋊D79)⋊C8C211yesmaximal, characteristic, complemented
15#450×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic, complemented
17C2×Q8×D79C2211yescharacteristic, complemented
18C22×C22⋊D79—21no—
19C2×D4×D79C2211yescharacteristic
20C2×#11929613C2211yescharacteristic, complemented
21C2×#11929613C2211yescharacteristic, complemented
22C2×#11929612—24no—
23C2×#11929612C2211yescharacteristic
24C2×#11929612C2211yescharacteristic
25C2×#11929612C2211yescharacteristic, complemented
26C2×#11929612C2211yescharacteristic, complemented
27C2×#11929611C2211yescharacteristic, complemented
28SD16×D79—24no—
29C22×C79⋊C8C2211yescharacteristic, complemented
30C2×C8×D79C2211yescharacteristic, complemented
31#14579160—21no—
32#14579159C2211yescharacteristic, complemented
33#14579157C2211yescharacteristic
34#14579141C2211yescharacteristic, complemented
35#14579139—21no—
36#14579138—21no—
37#14579135C2211yescharacteristic
38#14579133—21no—
39#14579132C2211yescharacteristic
40#14579130—21no—
41#14579129—21no—
42#14579126C2211yescharacteristic, complemented
43D4×Dic79C2211yescharacteristic
44C4×C22⋊D79C2211yescharacteristic
45(C22⋊D79)⋊C4—21no—
46#14579092C2211yescharacteristic, complemented
47Dic79⋊C8C2211yescharacteristic, complemented
48#14579086C2211yescharacteristic, complemented
49#14579086C2211yescharacteristic, complemented
50#14579085C2211yescharacteristic, complemented
51#14579081C2211yescharacteristic, complemented
52(C2×D79)⋊C8C2211yescharacteristic, complemented
53C8×Dic79C2211yescharacteristic, complemented
54C22×D4×C79C2211yescharacteristic
55C2×SD16×C79C2211yescharacteristic
56C2×SD16×C79C2211yescharacteristic, complemented
57C22⋊Q8×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59#102×C79C2211yescharacteristic, complemented
60C22⋊C8×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62C2×Dic158—22no—
63C2×Dic158—21no—
64C2×Dic158—21no—
65C2×Dic158—41no—
66C2×Dic158C2311yescharacteristic
67C2×Dic158C2311yescharacteristic
68Q8×D79—22no—
69Q8×D79—41no—
70C2×D316C2311yescharacteristic
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75C2×C22⋊D79—21no—
76C2×C22⋊D79—44no—
77C2×C22⋊D79D411yescharacteristic
78D4×D79—22no—
79D4×D79—41no—
80C22×Dic79—21no—
81C22×Dic79—21no—
82C2×C4×D79—21no—
83C2×C4×D79C2311yescharacteristic
84#11929613—22no—
85#11929613—41no—
86#11929612—22no—
87#11929612—22no—
88#11929612—22no—
89#11929612D414yescomplemented
90#11929611—22no—
91C2×C79⋊C8—22no—
92C2×C79⋊C8C2311yescharacteristic
93C2×C79⋊C8C2311yescharacteristic
94C8×D79—22no—
95C4⋊Dic79—21no—
96C4⋊Dic79C2311yescharacteristic
97Dic79⋊C4—21no—
98Dic79⋊C4—21no—
99Dic79⋊C4—21no—
100Dic79⋊C4D411yescharacteristic
101C22⋊Dic79—21no—
102C22⋊Dic79—21no—
103C22⋊Dic79D411yescharacteristic
104(C2×D79)⋊C4—21no—
105(C2×D79)⋊C4—21no—
106(C2×D79)⋊C4D411yescharacteristic
107C4×Dic79—21no—
108C4×Dic79C2311yescharacteristic
109C24×C79—21no—
110C2×Q8×C79C2311yescharacteristic
111C2×D4×C79—22no—
112C2×D4×C79—21no—
113C2×D4×C79—41no—
114C2×D4×C79C2311yescharacteristic
115C2×D4×C79C2311yescharacteristic
116C22×C4×C79C2311yescharacteristic
117SD16×C79—22no—
118SD16×C79—41no—
119C2×C8×C79C2311yescharacteristic
120C2×C8×C79C2311yescharacteristic
121C4⋊C4×C79—21no—
122C4⋊C4×C79C2311yescharacteristic
123C22⋊C4×C79—21no—
124C23×C79—21no—
125C23×C79—21no—
126C23×C79—42no—
127C23×C79—42no—
128C23×C79—81no—
129C23×C79C2×D411yescharacteristic
130C22×D79—21no—
131C22×D79—42no—
132C22×D79—42no—
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×C79C2×D412yes—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79—21no—
146C2×C4×C79C2×D411yescharacteristic
147C2×C4×C79C2411yescharacteristic
148C22⋊D79—42no—
149C22⋊D79—42no—
150C22⋊D79—42no—
151C22⋊D79—42no—
152C22⋊D79—81no—
153C22⋊D79SD1614yescomplemented
154C2×Dic79—21no—
155C2×Dic79—21no—
156C2×Dic79—21no—
157C2×Dic79—42no—
158C2×Dic79—42no—
159C2×Dic79C2×D411yescharacteristic
160C2×Dic79C2×D411yescharacteristic
161C2×Dic79C2×D411yescharacteristic
162D316—21no—
163D316—21no—
164C4×D79—21no—
165C4×D79—21no—
166C4×D79—42no—
167Dic158—21no—
168Dic158—21no—
169Dic158—21no—
170Dic158—42no—
171Dic158—42no—
172Dic158C2×D412yescomplemented
173C8×C79—21no—
174C8×C79—21no—
175C79⋊C8—21no—
176C79⋊C8C2×D412yescomplemented
177C22×C79—21no—
178C22×C79—21no—
179C22×C79—22no—
180C22×C79—41no—
181C22×C79—41no—
182C22×C79—41no—
183C22×C79—41no—
184C22×C79—41no—
185C22×C79—84no—
186C22×C79C2×SD1612yescomplemented
187C22×C79C22×D411yescharacteristic
188C2×D79—21no—
189C2×D79—21no—
190C2×D79—41no—
191C2×D79—41no—
192C2×D79—41no—
193C2×D79—84no—
194C2×D79C2×SD1612yescomplemented
195C4×C79—21no—
196C4×C79—41no—
197C4×C79—41no—
198C4×C79C22×D411yescharacteristic
199C4×C79H(5,𝔽2)11yescharacteristic
200Dic79—21no—
201Dic79—22no—
202Dic79—21no—
203Dic79—41no—
204Dic79—41no—
205Dic79C2×SD1612yescomplemented
206C2×C79—22no—
207C2×C79—42no—
208C2×C79—81no—
209C2×C79D4211yescharacteristic
210C2×C79C22×SD1611yescharacteristic
211C2×C79#57711yescharacteristic
212D79—22no—
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#465—791no—
223#461—791no—
224#460—791no—
225#450—791no—
226#450D7911yescharacteristic, complemented
227#448—791no—
228#448—791no—
229C4×SD16—791no—
230C8×D4—791no—
231C22×Q8—791no—
232C22×Q8—791no—
233C22×D4—791no—
234C22×D4—1581no—
235C22×D4C2×D7911yescharacteristic
236C2×SD16—791no—
237C2×SD16—791no—
238C2×SD16—791no—
239C2×SD16—791no—
240C2×SD16—791no—
241C2×SD16—791no—
242C2×SD16—791no—
243C2×SD16—1584no—
244C2×SD16—1584no—
245C2×SD16C2×D7911yescharacteristic
246C2×SD16C2×D7911yescharacteristic, complemented
247C22×C8—791no—
248C22×C8—791no—
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—791no—
258#121—1581no—
259#120—1581no—
260#120—1581no—
261C4×Q8—791no—
262C4×D4—791no—
263C4×D4—791no—
264C4×D4—1581no—
265#106—791no—
266C4⋊C8—791no—
267#103—791no—
268#103—791no—
269#103—791no—
270#102—791no—
271#102C2×D7911yescharacteristic
272#102C2×D7911yescharacteristic, complemented
273C22⋊C8—791no—
274C22⋊C8C2×D7911yescharacteristic, complemented
275C4×C8—791no—
276C24—21no—
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—22no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—3164no—
291C2×D4—3161no—
292C2×D4—791no—
293C2×D4—791no—
294C2×D4—1581no—
295C2×D4—1581no—
296C2×D4—1581no—
297C2×D4—1581no—
298C2×D4—1581no—
299C2×D4—1582no—
300C2×D4C22×D7911yescharacteristic
301C2×D4C22×D7911yescharacteristic
302C22×C4—791no—
303C22×C4—1581no—
304C22×C4—1581no—
305C22×C4—1581no—
306C22×C4C22×D7911yescharacteristic
307SD16—22no—
308SD16—41no—
309SD16—3161no—
310SD16—794no—
311SD16—1582no—
312SD16—1582no—
313SD16—1582no—
314SD16—1582no—
315SD16—1582no—
316C2×C8—791no—
317C2×C8—791no—
318C2×C8—1582no—
319C2×C8—1582no—
320C2×C8C22×D7911yescharacteristic
321C2×C8C22×D7911yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—791no—
324C4⋊C4—791no—
325C4⋊C4—1581no—
326C4⋊C4—1581no—
327C4⋊C4—1581no—
328C4⋊C4—1581no—
329C4⋊C4C22×D7911yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—791no—
332C22⋊C4—791no—
333C22⋊C4—1581no—
334C22⋊C4—1581no—
335C22⋊C4—1581no—
336C22⋊C4—1581no—
337C42—791no—
338C42—1581no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—3162no—
345C23—3162no—
346C23—791no—
347C23—6321no—
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—21no—
361D4—42no—
362D4—3162no—
363D4—3162no—
364D4—3162no—
365D4—3162no—
366D4—794no—
367D4—6321no—
368D4—1581no—
369D4—1581no—
370D4D4×D7912yes—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—3162no—
376C2×C4—3162no—
377C2×C4—3162no—
378C2×C4—791no—
379C2×C4—791no—
380C2×C4—791no—
381C2×C4—1581no—
382C2×C4—1581no—
383C2×C4—1581no—
384C2×C4—1581no—
385C2×C4—1581no—
386C2×C4D4×D7911yescharacteristic
387C2×C4C23×D7911yescharacteristic
388C8—21no—
389C8—21no—
390C8—792no—
391C8—1581no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—84no—
401C22—3161no—
402C22—3161no—
403C22—3161no—
404C22—792no—
405C22—6324no—
406C22—1581no—
407C22—1581no—
408C22SD16×D7912yescomplemented
409C22C2×D4×D7911yescharacteristic
410C4—21no—
411C4—41no—
412C4—41no—
413C4—3161no—
414C4—3161no—
415C4—792no—
416C4—1582no—
417C4—1581no—
418C4—1581no—
419C4C2×D4×D7911yescharacteristic
420C4#1457920611yescharacteristic
421C2—22no—
422C2—42no—
423C2—81no—
424C2—6321no—
425C2—1582no—
426C2#1909919511yescharacteristic
427C2C2×SD16×D7911yescharacteristic
428C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#450×C79C2
socleC22×C79C22×D4
prime radicalD4×C22⋊D79C2
hypercenter#450D79
hypocenterC79D4×SD16
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C22×#11929612C2semidirect
2. C2×SD16×D79C2semidirect
3. #19099226C2semidirect
5. #19098934C2semidirect
6. #19098794C2semidirect
7. #19098791C2semidirect
8. #19098766C2semidirect
9. #19098762C2semidirect
10. #19098715C2semidirect
11. #19098704C2semidirect
12. #19098700C2semidirect
13. #19098654C2semidirect
14. (C22⋊D79)⋊C8C2semidirect
15. #450×C79C2semidirect
16. C22×Dic158C22semidirect
17. C2×Q8×D79C22semidirect
20. C2×#11929613C22semidirect
21. C2×#11929613C22semidirect
25. C2×#11929612C22semidirect
26. C2×#11929612C22semidirect
27. C2×#11929611C22semidirect
29. C22×C79⋊C8C22semidirect
30. C2×C8×D79C22semidirect
32. #14579159C22semidirect
34. #14579141C22semidirect
42. #14579126C22semidirect
46. #14579092C22semidirect
47. Dic79⋊C8C22semidirect
48. #14579086C22semidirect
49. #14579086C22semidirect
50. #14579085C22semidirect
51. #14579081C22semidirect
52. (C2×D79)⋊C8C22semidirect
53. C8×Dic79C22semidirect
56. C2×SD16×C79C22semidirect
57. C22⋊Q8×C79C22semidirect
59. #102×C79C22semidirect
60. C22⋊C8×C79C22semidirect
89. #11929612D4semidirect
153. C22⋊D79SD16semidirect
172. Dic158C2×D4semidirect
176. C79⋊C8C2×D4semidirect
186. C22×C79C2×SD16semidirect
194. C2×D79C2×SD16semidirect
205. Dic79C2×SD16semidirect
215. C79D4×SD16semidirect
226. #450D79semidirect
246. C2×SD16C2×D79semidirect
255. C22⋊Q8C2×D79semidirect
272. #102C2×D79semidirect
274. C22⋊C8C2×D79semidirect
408. C22SD16×D79semidirect