Finite Group Databasebeta

← #23773586

Subgroups — #23773586

Order 10112.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099184C211yesmaximal, characteristic, complemented
2#19099037C211yesmaximal, characteristic, complemented
3#19098905C211yesmaximal, characteristic, complemented
4#19098888C211yesmaximal, characteristic, complemented
5#19098854C211yesmaximal, characteristic, complemented
6#19098844C211yesmaximal, characteristic, complemented
7#19098779C211yesmaximal, characteristic, complemented
8#19098779C211yesmaximal, characteristic, complemented
9#19098716C211yesmaximal, characteristic, complemented
10#19098699C211yesmaximal, characteristic
11#19098676C211yesmaximal, characteristic, complemented
12#19098665C211yesmaximal, characteristic, complemented
13C4×#11929613C211yesmaximal, characteristic, complemented
14C4×D632C211yesmaximal, characteristic, complemented
15#433×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C2×#11929613C2211yescharacteristic
18C2×#11929613C2211yescharacteristic
19C2×D632C2211yescharacteristic
20C2×D632C2211yescharacteristic
21#14579161C2211yescharacteristic, complemented
22#14579156—21no—
23#14579149C2211yescharacteristic, complemented
24#14579147—21no—
25#14579143—21no—
26#14579140C2211yescharacteristic
27#14579139—21no—
28#14579135C2211yescharacteristic
29C4×Dic158C2211yescharacteristic, complemented
30C4×D316C2211yescharacteristic
31C4×D316C2211yescharacteristic
32C4×D316C2211yescharacteristic
33C4×D316C2211yescharacteristic
34C4×D316C2211yescharacteristic, complemented
35#14579123—21no—
36#14579123—21no—
37#14579120C2211yescharacteristic
38C22⋊C4×D79—21no—
39C22⋊C4×D79—21no—
40#14579095C2211yescharacteristic, complemented
41#14579095C2211yescharacteristic, complemented
42#14579093C2211yescharacteristic, complemented
43#14579093C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579086C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic, complemented
51#14579083C2211yescharacteristic, complemented
52#117×C79C2211yescharacteristic
53C4⋊C8×C79C2211yescharacteristic, complemented
54C4⋊C8×C79C2211yescharacteristic, complemented
55C22⋊C8×C79C2211yescharacteristic
56C22⋊C8×C79C2211yescharacteristic
57#97×C79C2211yescharacteristic, complemented
58C4×C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62C2×D316—22no—
63C2×D316—22no—
64C2×D316—21no—
65C2×D316C2311yescharacteristic
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74#11929613—22no—
75#11929613—22no—
76D632—22no—
77D632—22no—
78C4⋊Dic79—21no—
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95C4×Dic79—21no—
96C4×Dic79—21no—
97C22×C4×C79C2311yescharacteristic
98C2×C8×C79C2311yescharacteristic
99C2×C8×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C4⋊C4×C79D411yescharacteristic
103C4⋊C4×C79D411yescharacteristic
104C22⋊C4×C79D411yescharacteristic
105C22⋊C4×C79D411yescharacteristic
106C42×C79C2311yescharacteristic
107C42×C79C2311yescharacteristic
108C23×C79C2×D411yescharacteristic
109C22×D79—21no—
110C22×D79—21no—
111C22×D79—24no—
112C22×D79—21no—
113C22×D79—81no—
114C22×D79—81no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79C2×D411yescharacteristic
118C2×C4×C79C2×D411yescharacteristic
119C2×C4×C79C2×D411yescharacteristic
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2×D411yescharacteristic
122C2×C4×C79C2411yescharacteristic
123C22⋊D79—81no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129D316—24no—
130D316—21no—
131D316—21no—
132D316—21no—
133D316—21no—
134D316#4112yes—
135D316#4112yes—
136C4×D79—81no—
137C4×D79—81no—
138C4×D79—81no—
139C4×D79—81no—
140C4×D79—81no—
141Dic158—21no—
142Dic158—21no—
143Dic158—81no—
144C8×C79—21no—
145C8×C79—21no—
146C8×C79—21no—
147C8×C79—21no—
148C22×C79—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79C22×D411yescharacteristic
152C2×D79—22no—
153C2×D79—22no—
154C2×D79—41no—
155C2×D79—41no—
156C2×D79—41no—
157C2×D79—41no—
158C2×D79—41no—
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—84no—
162C4×C79—21no—
163C4×C79—21no—
164C4×C79—21no—
165C4×C79—21no—
166C4×C79—21no—
167C4×C79C2×#4111yescharacteristic
168C4×C79C2×#4111yescharacteristic
169Dic79—41no—
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174C2×C79—41no—
175C2×C79#52511yescharacteristic
176C2×C79#57611yescharacteristic
177C2×C79#57711yescharacteristic
178D79—42no—
179D79—42no—
180D79—81no—
181#3118—791nomaximal, Sylow
182C79#311811yescharacteristic, complemented, Sylow
183#542—791no—
184#518—791no—
185#485—791no—
186#482—791no—
187#476—791no—
188#474—791no—
189#463—791no—
190#463—791no—
191#450—791no—
192#447—791no—
193#442—791no—
194#440—791no—
195C4×SD16—791no—
196C4×D8—791no—
197#433D7911yescharacteristic, complemented
198C22×D4—791no—
199C2×SD16—791no—
200C2×SD16—791no—
201C2×D8—791no—
202C2×D8—791no—
203C4⋊Q8—791no—
204#126—1581no—
205#124—791no—
206#124—1581no—
207#123—1581no—
208C22⋊Q8—791no—
209C22⋊Q8—1581no—
210#121—791no—
211C4×Q8—791no—
212C4×D4—791no—
213C4×D4—791no—
214C4×D4—791no—
215C4×D4—791no—
216C4×D4—791no—
217C4×D4—1581no—
218C4×D4—1581no—
219#117—791no—
220#117C2×D7911yescharacteristic
221C2×C22⋊C4—1581no—
222C2×C22⋊C4—1581no—
223#107—791no—
224#107—791no—
225#106—791no—
226#106—791no—
227C4⋊C8C2×D7911yescharacteristic, complemented
228C4⋊C8C2×D7911yescharacteristic, complemented
229#103—791no—
230#103—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235#102—791no—
236#102—791no—
237C22⋊C8C2×D7911yescharacteristic
238C22⋊C8C2×D7911yescharacteristic
239#97C2×D7911yescharacteristic, complemented
240C4×C8C2×D7911yescharacteristic, complemented
241C24—1581no—
242C2×Q8—791no—
243C2×Q8—1581no—
244C2×D4—791no—
245C2×D4—791no—
246C2×D4—791no—
247C2×D4—1582no—
248C2×D4—1582no—
249C2×D4—1581no—
250C2×D4—1581no—
251C22×C4—1581no—
252C22×C4—1581no—
253C22×C4—1581no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4C22×D7911yescharacteristic
257SD16—1582no—
258SD16—1582no—
259D8—1582no—
260D8—1582no—
261C2×C8C22×D7911yescharacteristic
262C2×C8C22×D7911yescharacteristic
263C2×C8C22×D7911yescharacteristic
264C2×C8C22×D7911yescharacteristic
265C4⋊C4—791no—
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4D31611yescharacteristic
273C4⋊C4D31611yescharacteristic
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4D31611yescharacteristic
285C22⋊C4D31611yescharacteristic
286C42—1581no—
287C42—1581no—
288C42C22×D7911yescharacteristic
289C42C22×D7911yescharacteristic
290C23—6321no—
291C23—6321no—
292C23—1584no—
293C23—1581no—
294C23—1581no—
295C23—1581no—
296C23C2×D31611yescharacteristic
297Q8—6321no—
298Q8—1581no—
299Q8—1581no—
300D4—792no—
301D4—792no—
302D4—6321no—
303D4—1584no—
304D4—1581no—
305D4—1581no—
306D4—1581no—
307D4—1581no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—6321no—
311C2×C4—6321no—
312C2×C4—6321no—
313C2×C4—6321no—
314C2×C4—6321no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4C2×D31611yescharacteristic
321C2×C4C2×D31611yescharacteristic
322C2×C4C2×D31611yescharacteristic
323C2×C4C2×D31611yescharacteristic
324C2×C4C2×D31611yescharacteristic
325C2×C4C23×D7911yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—3161no—
334C22—3161no—
335C22—3161no—
336C22—3161no—
337C22—3161no—
338C22—3161no—
339C22—3161no—
340C22—6324no—
341C22—1582no—
342C22—1582no—
343C22C22×D31611yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—3161no—
350C4—3161no—
351C4—3161no—
352C4—3161no—
353C4—3161no—
354C4#41×D7911yescharacteristic
355C4#41×D7911yescharacteristic
356C2—41no—
357C2—3162no—
358C2—3162no—
359C2—6321no—
360C2#1909907511yescharacteristic
361C2#1909936811yescharacteristic
362C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#433×C79C2
socleC22×C79C22×D4
prime radical#19098699C2
hypercenter#433D79
hypocenterC79#3118
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #19099184C2semidirect
2. #19099037C2semidirect
3. #19098905C2semidirect
4. #19098888C2semidirect
5. #19098854C2semidirect
6. #19098844C2semidirect
7. #19098779C2semidirect
8. #19098779C2semidirect
9. #19098716C2semidirect
11. #19098676C2semidirect
12. #19098665C2semidirect
13. C4×#11929613C2semidirect
14. C4×D632C2semidirect
15. #433×C79C2semidirect
21. #14579161C22semidirect
23. #14579149C22semidirect
29. C4×Dic158C22semidirect
34. C4×D316C22semidirect
40. #14579095C22semidirect
41. #14579095C22semidirect
42. #14579093C22semidirect
43. #14579093C22semidirect
44. #14579086C22semidirect
45. #14579086C22semidirect
50. #14579083C22semidirect
51. #14579083C22semidirect
53. C4⋊C8×C79C22semidirect
54. C4⋊C8×C79C22semidirect
57. #97×C79C22semidirect
58. C4×C8×C79C22semidirect
182. C79#3118semidirect
197. #433D79semidirect
227. C4⋊C8C2×D79semidirect
228. C4⋊C8C2×D79semidirect
239. #97C2×D79semidirect
240. C4×C8C2×D79semidirect