Finite Group Databasebeta

← #23775363

Subgroups — #23775363

Order 10112.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099217C211yesmaximal, characteristic, complemented
2#19099209C211yesmaximal, characteristic, complemented
3#19098923C211yesmaximal, characteristic, complemented
4#19098894C211yesmaximal, characteristic, complemented
5#19098882C211yesmaximal, characteristic, complemented
6#19098854C211yesmaximal, characteristic, complemented
7#19098816C211yesmaximal, characteristic, complemented
8#19098792C211yesmaximal, characteristic, complemented
9#19098779C211yesmaximal, characteristic, complemented
10#19098710C211yesmaximal, characteristic, complemented
11#19098699C211yesmaximal, characteristic, complemented
12#19098676C211yesmaximal, characteristic, complemented
13#19098565C211yesmaximal, characteristic, complemented
14C2×#14579083C211yesmaximal, characteristic, complemented
15#435×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929623—21no—
18C22×D316C2211yescharacteristic
19C2×#11929613C2211yescharacteristic, complemented
20C2×D632C2211yescharacteristic
21C2×D632C2211yescharacteristic
22#14579161C2211yescharacteristic, complemented
23#14579149C2211yescharacteristic
24#14579146—21no—
25#14579145—21no—
26#14579145—21no—
27#14579141—21no—
28#14579140C2211yescharacteristic
29#14579135C2211yescharacteristic
30#14579135C2211yescharacteristic
31#14579135C2211yescharacteristic, complemented
32#14579134—21no—
33#14579129—21no—
34C4×D316C2211yescharacteristic
35C4×D316C2211yescharacteristic, complemented
36C2×C4⋊Dic79C2211yescharacteristic
37C2×C4⋊Dic79C2211yescharacteristic, complemented
38C22⋊C4×D79—21no—
39#14579093C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic
51#14579083C2211yescharacteristic, complemented
52C2×M16×C79C2211yescharacteristic, complemented
53C22×C8×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic
55C4⋊C8×C79C2211yescharacteristic, complemented
56C22⋊C8×C79C2211yescharacteristic
57C22⋊C8×C79C2211yescharacteristic, complemented
58#97×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—22no—
61#11929624—41no—
62#11929623—44no—
63C2×Dic158—21no—
64C2×Dic158C2311yescharacteristic
65C2×D316—22no—
66C2×D316—21no—
67C2×D316—41no—
68C2×D316C2311yescharacteristic
69C2×D316C2311yescharacteristic
70C2×D316C2311yescharacteristic
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75C22×Dic79—21no—
76C22×Dic79—21no—
77C2×C4×D79—21no—
78C2×C4×D79—21no—
79C2×C4×D79—21no—
80#11929613—41no—
81D632—22no—
82D632—41no—
83C4⋊Dic79—21no—
84C4⋊Dic79—21no—
85C4⋊Dic79—21no—
86C4⋊Dic79C2311yescharacteristic
87C4⋊Dic79C2311yescharacteristic
88C4⋊Dic79C2311yescharacteristic
89C4⋊Dic79C2311yescharacteristic
90Dic79⋊C4—21no—
91C22⋊Dic79—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99C2×D4×C79D411yescharacteristic
100C22×C4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102M16×C79—41no—
103C2×C8×C79—41no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79D411yescharacteristic
109C22⋊C4×C79D411yescharacteristic
110C22⋊C4×C79D411yescharacteristic
111C42×C79C2311yescharacteristic
112C23×C79C2×D411yescharacteristic
113C23×C79C2×D411yescharacteristic
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—42no—
118C22×D79—42no—
119C22×D79—81no—
120D4×C79—22no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—42no—
131C22⋊D79—42no—
132C22⋊D79—42no—
133C22⋊D79—81no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—42no—
140C2×Dic79—42no—
141D316—21no—
142D316—21no—
143D316—21no—
144D316—21no—
145D316—21no—
146D316—42no—
147D316#4112yescomplemented
148C4×D79—42no—
149C4×D79—42no—
150C4×D79—81no—
151Dic158—21no—
152Dic158—21no—
153Dic158—42no—
154C8×C79—21no—
155C8×C79—21no—
156C8×C79—21no—
157C8×C79—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79AGL(1,ℤ/8)12yes—
164C22×C79C22×D411yescharacteristic
165C2×D79—22no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—84no—
175C4×C79—21no—
176C4×C79—21no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79C2×#4111yescharacteristic
180C4×C79H(5,𝔽2)11yescharacteristic
181Dic79—41no—
182Dic79—41no—
183Dic79—41no—
184Dic79—41no—
185Dic79—41no—
186C2×C79—22no—
187C2×C79—41no—
188C2×C79#54611yescharacteristic
189C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
190C2×C79#57711yescharacteristic
191D79—42no—
192D79—81no—
193D79—81no—
194#3306—791nomaximal, Sylow
195C79#330611yescharacteristic, complemented, Sylow
196#547—791no—
197#546—791no—
198#489—791no—
199#483—791no—
200#481—791no—
201#476—791no—
202#469—791no—
203#465—791no—
204#463—791no—
205#449—791no—
206#447—791no—
207#442—791no—
208#435D7911yescharacteristic, complemented
209#417—791no—
210C2×#102—791no—
211C2×#41—791no—
212C2×#41—1581no—
213C22×D4—791no—
214C2×SD16—791no—
215C2×D8—791no—
216C2×D8—791no—
217C2×M16C2×D7911yescharacteristic, complemented
218C22×C8C2×D7911yescharacteristic
219C4⋊Q8—791no—
220#124—791no—
221#123—1581no—
222#123—1581no—
223#123—1581no—
224C22⋊Q8—791no—
225C22⋊Q8—1581no—
226#121—791no—
227#121—791no—
228#121—791no—
229#121—1581no—
230#120—1581no—
231C4×D4—791no—
232C4×D4—791no—
233C4×D4C2×D7911yescharacteristic
234C2×C4⋊C4—791no—
235C2×C4⋊C4—791no—
236C2×C22⋊C4—1581no—
237#106—791no—
238#106—791no—
239#106—791no—
240C4⋊C8C2×D7911yescharacteristic, complemented
241#103—791no—
242#103—791no—
243#103—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251C22⋊C8C2×D7911yescharacteristic
252C22⋊C8C2×D7911yescharacteristic, complemented
253#97C2×D7911yescharacteristic, complemented
254C24—1581no—
255#41—3161no—
256#41—3164no—
257#41—1582no—
258C2×Q8—791no—
259C2×Q8—1581no—
260C2×D4—3161no—
261C2×D4—791no—
262C2×D4—791no—
263C2×D4—791no—
264C2×D4—1582no—
265C2×D4—1581no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4D31611yescharacteristic
271C22×C4—1581no—
272C22×C4—1581no—
273C22×C4—1581no—
274C22×C4—1581no—
275C22×C4—1581no—
276C22×C4C22×D7911yescharacteristic
277C22×C4C22×D7911yescharacteristic
278SD16—3161no—
279D8—3161no—
280D8—1582no—
281M16—41no—
282C2×C8—41no—
283C2×C8C22×D7911yescharacteristic
284C2×C8C22×D7911yescharacteristic
285C2×C8C22×D7911yescharacteristic
286C2×C8C22×D7911yescharacteristic
287C4⋊C4—791no—
288C4⋊C4—791no—
289C4⋊C4—791no—
290C4⋊C4—791no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4D31611yescharacteristic
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4D31611yescharacteristic
305C22⋊C4D31611yescharacteristic
306C42C22×D7911yescharacteristic
307C23—3162no—
308C23—3162no—
309C23—6321no—
310C23—1581no—
311C23—1581no—
312C23—1581no—
313C23C2×D31611yescharacteristic
314C23C2×D31611yescharacteristic
315Q8—3162no—
316Q8—1581no—
317Q8—1581no—
318D4—22no—
319D4—3162no—
320D4—3162no—
321D4—3162no—
322D4—3162no—
323D4—792no—
324D4—6321no—
325D4—1581no—
326D4—1581no—
327D4—1581no—
328D4—1581no—
329D4—1581no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—3162no—
335C2×C4—3162no—
336C2×C4—3162no—
337C2×C4—3162no—
338C2×C4—6321no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4C2×D31611yescharacteristic
345C2×C4C2×D31611yescharacteristic
346C2×C4C2×D31611yescharacteristic
347C2×C4C2×D31611yescharacteristic
348C2×C4C23×D7911yescharacteristic
349C8—21no—
350C8—21no—
351C8—21no—
352C8—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—3161no—
359C22—3161no—
360C22—3161no—
361C22—3161no—
362C22—3161no—
363C22—3161no—
364C22—3161no—
365C22—3161no—
366C22—6324no—
367C22—1582no—
368C22#1457918912yes—
369C22C22×D31611yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—3161no—
375C4—3161no—
376C4—3161no—
377C4—3161no—
378C4—3161no—
379C4#41×D7911yescharacteristic
380C4#1457920611yescharacteristic
381C2—22no—
382C2—41no—
383C2—3162no—
384C2—6321no—
385C2—6321no—
386C2#1909920811yescharacteristic
387C2C2×#1457918911yescharacteristic
388C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#435×C79C2
socleC22×C79C22×D4
hypercenter#435D79
hypocenterC79#3306
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #19099217C2semidirect
2. #19099209C2semidirect
3. #19098923C2semidirect
4. #19098894C2semidirect
5. #19098882C2semidirect
6. #19098854C2semidirect
7. #19098816C2semidirect
8. #19098792C2semidirect
9. #19098779C2semidirect
10. #19098710C2semidirect
11. #19098699C2semidirect
12. #19098676C2semidirect
13. #19098565C2semidirect
14. C2×#14579083C2semidirect
15. #435×C79C2semidirect
19. C2×#11929613C22semidirect
22. #14579161C22semidirect
31. #14579135C22semidirect
35. C4×D316C22semidirect
37. C2×C4⋊Dic79C22semidirect
39. #14579093C22semidirect
40. #14579093C22semidirect
41. #14579093C22semidirect
42. #14579086C22semidirect
43. #14579086C22semidirect
44. #14579086C22semidirect
51. #14579083C22semidirect
52. C2×M16×C79C22semidirect
55. C4⋊C8×C79C22semidirect
57. C22⋊C8×C79C22semidirect
58. #97×C79C22semidirect
147. D316#41semidirect
195. C79#3306semidirect
208. #435D79semidirect
217. C2×M16C2×D79semidirect
240. C4⋊C8C2×D79semidirect
252. C22⋊C8C2×D79semidirect
253. #97C2×D79semidirect