Finite Group Databasebeta

← #23774185

Subgroups — #23774185

Order 10112.

420 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099075C211yesmaximal, characteristic
2C22⋊Q8×D79C211yesmaximal, characteristic, complemented
3#19098904C211yesmaximal, characteristic, complemented
4#19098895C211yesmaximal, characteristic, complemented
5#19098878C211yesmaximal, characteristic, complemented
6#19098805C211yesmaximal, characteristic, complemented
7#19098803C211yesmaximal, characteristic, complemented
8#19098795C211yesmaximal, characteristic, complemented
9#19098793C211yesmaximal, characteristic, complemented
10#19098727C211yesmaximal, characteristic, complemented
11#19098723C211yesmaximal, characteristic, complemented
12#19098720C211yesmaximal, characteristic, complemented
13#19098703C211yesmaximal, characteristic, complemented
14C22⋊C8×D79C211yesmaximal, characteristic, complemented
15#485×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C2×Dic316C2211yescharacteristic, complemented
20C2×#11929614C2211yescharacteristic, complemented
21C2×#11929613C2211yescharacteristic, complemented
22C2×#11929611C2211yescharacteristic, complemented
23C2×C8×D79C2211yescharacteristic
24C2×C8×D79C2211yescharacteristic
25#14579145—21no—
26#14579141C2211yescharacteristic
27#14579141C2211yescharacteristic
28#14579141C2211yescharacteristic
29#14579140C2211yescharacteristic
30#14579139—21no—
31#14579138—21no—
32#14579137C2211yescharacteristic
33#14579136C2211yescharacteristic
34#14579136C2211yescharacteristic
35#14579131—21no—
36C4×D316—21no—
37C4×D316—21no—
38C4⋊C4×D79—21no—
39C4⋊C4×D79C2211yescharacteristic
40C22⋊C4×D79—21no—
41#14579094C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579084C2211yescharacteristic, complemented
47#14579083C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52C22⋊Q8×C79C2211yescharacteristic
53#117×C79C2211yescharacteristic
54#107×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic
59C23×D79D411yescharacteristic
60#11929624—41no—
61#11929624—41no—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64C2×Dic158C2311yescharacteristic
65Q8×D79—41no—
66Q8×D79—41no—
67C2×D316—21no—
68C2×D316—21no—
69C2×D316C2311yescharacteristic
70C2×C22⋊D79—21no—
71C22×Dic79D411yescharacteristic
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—41no—
76C2×C4×D79—41no—
77C2×C4×D79D411yescharacteristic
78C2×C4×D79D411yescharacteristic
79C2×C4×D79C2311yescharacteristic
80C2×C4×D79C2311yescharacteristic
81Dic316—41no—
82#11929614—41no—
83#11929613—41no—
84#11929611—41no—
85C2×C79⋊C8C2311yescharacteristic
86C2×C79⋊C8C2311yescharacteristic
87C8×D79—41no—
88C8×D79—41no—
89C4⋊Dic79—21no—
90C4⋊Dic79—21no—
91C4⋊Dic79—21no—
92C4⋊Dic79C2311yescharacteristic
93Dic79⋊C4—21no—
94Dic79⋊C4—21no—
95Dic79⋊C4—21no—
96C22⋊Dic79—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4—21no—
100(C2×D79)⋊C4—21no—
101(C2×D79)⋊C4—21no—
102(C2×D79)⋊C4—21no—
103C2×Q8×C79C2311yescharacteristic
104C22×C4×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79—21no—
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
111C22⋊C4×C79—21no—
112C22⋊C4×C79—21no—
113C42×C79—21no—
114C23×C79C2×D411yescharacteristic
115C22×D79—22no—
116C22×D79—22no—
117C22×D79—21no—
118C22×D79—41no—
119C22×D79C2×D411yescharacteristic
120C22×D79C2×D411yescharacteristic
121Q8×C79—21no—
122Q8×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C22⋊D79—42no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—41no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138D316—21no—
139D316—21no—
140D316—42no—
141D316—42no—
142C4×D79—21no—
143C4×D79—21no—
144C4×D79—21no—
145C4×D79—21no—
146C4×D79—41no—
147C4×D79—41no—
148C4×D79—42no—
149C4×D79—42no—
150C4×D79—42no—
151Dic158—21no—
152Dic158—21no—
153Dic158—21no—
154Dic158—21no—
155Dic158—42no—
156C8×C79—21no—
157C8×C79—21no—
158C79⋊C8—21no—
159C79⋊C8—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79C22×D411yescharacteristic
164C2×D79—21no—
165C2×D79—21no—
166C2×D79—21no—
167C2×D79—21no—
168C2×D79—44no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79#13512yes—
173C2×D79#13712yes—
174C4×C79—21no—
175C4×C79—41no—
176C4×C79—41no—
177C4×C79—41no—
178C4×C79—41no—
179C4×C79H(5,𝔽2)11yescharacteristic
180C4×C79H(5,𝔽2)11yescharacteristic
181Dic79—21no—
182Dic79—21no—
183Dic79—41no—
184Dic79—41no—
185Dic79—41no—
186C2×C79—41no—
187C2×C79#53411yescharacteristic
188C2×C79C2×#13511yescharacteristic
189C2×C79C2×#13711yescharacteristic
190D79—22no—
191D79—22no—
192D79—81no—
193#3190—791nomaximal, Sylow
194C79#319011yescharacteristic, complemented, Sylow
195#525—791no—
196C2×C22⋊Q8—791no—
197#485—791no—
198#485D7911yescharacteristic, complemented
199#483—791no—
200#480—791no—
201#467—791no—
202#467—791no—
203#465—791no—
204#465—791no—
205#452—791no—
206#452—791no—
207#451—791no—
208#448—791no—
209C2×C22⋊C8—791no—
210C2×#41—791no—
211C22×Q8—791no—
212C23×C4—791no—
213C2×Q16—791no—
214C2×Q16—791no—
215C2×SD16—791no—
216C2×SD16—791no—
217C22×C8—791no—
218C22×C8—791no—
219#123—1581no—
220C22⋊Q8—791no—
221C22⋊Q8—791no—
222C22⋊Q8—791no—
223C22⋊Q8—791no—
224C22⋊Q8—791no—
225C22⋊Q8—1581no—
226C22⋊Q8—1581no—
227C22⋊Q8C2×D7911yescharacteristic
228#121—791no—
229#121—791no—
230#120—1581no—
231C4×D4—1581no—
232C4×D4—1581no—
233#117C2×D7911yescharacteristic
234C2×C4⋊C4—791no—
235C2×C4⋊C4—1581no—
236C2×C22⋊C4—1581no—
237#107—791no—
238#107C2×D7911yescharacteristic, complemented
239#106—791no—
240#106C2×D7911yescharacteristic, complemented
241#103—791no—
242#103—791no—
243#103—791no—
244#103—791no—
245#103C2×D7911yescharacteristic, complemented
246#103C2×D7911yescharacteristic, complemented
247#102—791no—
248#102—791no—
249C22⋊C8—791no—
250C22⋊C8—791no—
251C22⋊C8—791no—
252C22⋊C8C2×D7911yescharacteristic
253C24—791no—
254#41—3161no—
255#41—3161no—
256C2×Q8—3161no—
257C2×Q8—3161no—
258C2×Q8—791no—
259C2×Q8—791no—
260C2×Q8—1581no—
261C2×Q8C22×D7911yescharacteristic
262C2×D4—791no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4—1581no—
266C22×C4—3161no—
267C22×C4—3161no—
268C22×C4—791no—
269C22×C4—791no—
270C22×C4—791no—
271C22×C4—791no—
272C22×C4—791no—
273C22×C4—1581no—
274C22×C4—1581no—
275C22×C4—1581no—
276C22×C4C22×D7911yescharacteristic
277Q16—3161no—
278Q16—3161no—
279SD16—3161no—
280SD16—3161no—
281C2×C8—3161no—
282C2×C8—3161no—
283C2×C8—791no—
284C2×C8—791no—
285C2×C8C22×D7911yescharacteristic
286C2×C8C22×D7911yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—791no—
289C4⋊C4—1581no—
290C4⋊C4—1581no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4C22×D7911yescharacteristic
296C4⋊C4C22×D7911yescharacteristic
297C4⋊C4C22×D7911yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C42—21no—
308C23—3161no—
309C23—791no—
310C23—791no—
311C23—1582no—
312C23—1582no—
313C23—1581no—
314C23D4×D7911yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—3162no—
318Q8—1581no—
319Q8—1581no—
320Q8—1581no—
321Q8—1581no—
322D4—3162no—
323D4—3162no—
324D4—3162no—
325D4—1581no—
326D4—1581no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—3162no—
334C2×C4—3161no—
335C2×C4—3161no—
336C2×C4—3162no—
337C2×C4—3162no—
338C2×C4—3161no—
339C2×C4—791no—
340C2×C4—791no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4D4×D7911yescharacteristic
349C2×C4C23×D7911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1581no—
353C8—1581no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—3164no—
358C22—3161no—
359C22—3161no—
360C22—3161no—
361C22—792no—
362C22—792no—
363C22—1581no—
364C22—1581no—
365C22—1581no—
366C22—1581no—
367C22C2×D4×D7911yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—3161no—
374C4—3161no—
375C4—3161no—
376C4—1581no—
377C4—1581no—
378C4#1457920711yescharacteristic
379C4#1457920711yescharacteristic
380C2—41no—
381C2—6321no—
382C2—1582no—
383C2—1582no—
384C2#1909912411yescharacteristic
385C2#135×D7911yescharacteristic
386C2#137×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#485×C79C2
socleC22×C79C22×D4
prime radical#19099075C2
hypercenter#485D79
hypocenterC79#3190
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D79C2semidirect
3. #19098904C2semidirect
4. #19098895C2semidirect
5. #19098878C2semidirect
6. #19098805C2semidirect
7. #19098803C2semidirect
8. #19098795C2semidirect
9. #19098793C2semidirect
10. #19098727C2semidirect
11. #19098723C2semidirect
12. #19098720C2semidirect
13. #19098703C2semidirect
14. C22⋊C8×D79C2semidirect
15. #485×C79C2semidirect
19. C2×Dic316C22semidirect
20. C2×#11929614C22semidirect
21. C2×#11929613C22semidirect
22. C2×#11929611C22semidirect
41. #14579094C22semidirect
42. #14579092C22semidirect
43. #14579086C22semidirect
44. #14579084C22semidirect
45. #14579084C22semidirect
46. #14579084C22semidirect
47. #14579083C22semidirect
48. #14579081C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
56. #103×C79C22semidirect
57. #103×C79C22semidirect
194. C79#3190semidirect
198. #485D79semidirect
238. #107C2×D79semidirect
240. #106C2×D79semidirect
245. #103C2×D79semidirect
246. #103C2×D79semidirect