Finite Group Databasebeta

← #23775415

Subgroups — #23775415

Order 10112.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×D316C211yesmaximal, characteristic
2#19098929C211yesmaximal, characteristic, complemented
3#19098887C211yesmaximal, characteristic, complemented
4#19098876C211yesmaximal, characteristic, complemented
5#19098860C211yesmaximal, characteristic, complemented
6#19098811C211yesmaximal, characteristic, complemented
7#19098794C211yesmaximal, characteristic, complemented
8#19098763C211yesmaximal, characteristic, complemented
9#19098713C211yesmaximal, characteristic, complemented
10#19098713C211yesmaximal, characteristic, complemented
11#19098661C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098567C211yesmaximal, characteristic, complemented
14C2×#14579081C211yesmaximal, characteristic, complemented
15#552×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×D4×D79—21no—
19C2×#11929611C2211yescharacteristic
20C2×#11929611C2211yescharacteristic, complemented
21C2×#11929611C2211yescharacteristic, complemented
22C2×#11929608C2211yescharacteristic, complemented
23C22×C79⋊C8C2211yescharacteristic, complemented
24#14579158C2211yescharacteristic
25#14579136—21no—
26#14579135C2211yescharacteristic
27#14579135C2211yescharacteristic
28#14579131—21no—
29#14579131—21no—
30C4×D316C2211yescharacteristic
31#14579094C2211yescharacteristic, complemented
32#14579094C2211yescharacteristic, complemented
33#14579092C2211yescharacteristic, complemented
34C4⋊(C79⋊C8)C2211yescharacteristic, complemented
35#14579085C2211yescharacteristic, complemented
36#14579081C2211yescharacteristic
37#14579081C2211yescharacteristic
38#14579081C2211yescharacteristic
39#14579081C2211yescharacteristic, complemented
40#14579081C2211yescharacteristic, complemented
41#14579081C2211yescharacteristic, complemented
42#14579081C2211yescharacteristic, complemented
43#14579081C2211yescharacteristic, complemented
44#14579081C2211yescharacteristic, complemented
45C22⋊(C79⋊C8)C2211yescharacteristic, complemented
46C22⋊(C79⋊C8)C2211yescharacteristic, complemented
47#14579072C2211yescharacteristic, complemented
48#126×C79—21no—
49#125×C79—21no—
50#125×C79C2211yescharacteristic, complemented
51#123×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic, complemented
53C22⋊Q8×C79C2211yescharacteristic, complemented
54C4×Q8×C79C2211yescharacteristic, complemented
55C4×D4×C79C2211yescharacteristic
56#117×C79—21no—
57#117×C79C2211yescharacteristic, complemented
58C2×C4⋊C4×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79—21no—
61C2×D316—22no—
62C2×D316—22no—
63C2×D316—21no—
64C2×D316—21no—
65C2×D316—21no—
66C2×D316—21no—
67C2×D316—41no—
68C2×D316—41no—
69C2×D316C2311yescharacteristic
70C2×D316C2311yescharacteristic
71C2×D316C2311yescharacteristic
72C2×C22⋊D79—21no—
73C2×C22⋊D79—21no—
74D4×D79—44no—
75C2×C4×D79—21no—
76#11929611—22no—
77#11929611—41no—
78#11929611—41no—
79#11929608—41no—
80C2×C79⋊C8—41no—
81C2×C79⋊C8C2311yescharacteristic
82C2×C79⋊C8C2311yescharacteristic
83C2×C79⋊C8C2311yescharacteristic
84C2×C79⋊C8C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89C2×Q8×C79C2311yescharacteristic
90C2×D4×C79D411yescharacteristic
91C22×C4×C79—21no—
92C22×C4×C79C2311yescharacteristic
93C22×C4×C79C2311yescharacteristic
94C4⋊C4×C79—21no—
95C4⋊C4×C79—21no—
96C4⋊C4×C79—21no—
97C4⋊C4×C79—21no—
98C4⋊C4×C79—21no—
99C4⋊C4×C79—21no—
100C4⋊C4×C79D411yescharacteristic
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C42×C79—21no—
110C42×C79—21no—
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—42no—
120C22×D79—42no—
121C22×D79—81no—
122C22×D79—81no—
123Q8×C79—21no—
124Q8×C79—21no—
125D4×C79—22no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—42no—
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2411yescharacteristic
140C22⋊D79—42no—
141C22⋊D79—42no—
142C2×Dic79—21no—
143D316—21no—
144D316—21no—
145D316—21no—
146D316—21no—
147D316—21no—
148D316—42no—
149D316—42no—
150D316—42no—
151D316—81no—
152D316#4112yes—
153C4×D79—42no—
154C79⋊C8—21no—
155C79⋊C8—21no—
156C79⋊C8—21no—
157C79⋊C8—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—
175C2×D79—84no—
176C4×C79—21no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79—21no—
180C4×C79—41no—
181C4×C79—41no—
182C4×C79—41no—
183C4×C79—41no—
184C4×C79C2×#4111yescharacteristic
185C4×C79H(5,𝔽2)11yescharacteristic
186Dic79—41no—
187C2×C79—22no—
188C2×C79—41no—
189C2×C79#54611yescharacteristic
190C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C79#57711yescharacteristic
192D79—42no—
193D79—81no—
194D79—81no—
195#3310—791nomaximal, Sylow
196C79#331011yescharacteristic, complemented, Sylow
197#552D7911yescharacteristic, complemented
198D42—791no—
199#490—791no—
200#482—791no—
201#480—791no—
202#478—791no—
203#468—791no—
204#465—791no—
205#460—791no—
206#450—791no—
207#450—791no—
208#440—791no—
209#435—791no—
210#418—791no—
211C2×#102—791no—
212C22×D4—791no—
213C22×D4—791no—
214C22×D4—1581no—
215C2×SD16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×M16—791no—
219C22×C8—791no—
220#127—791no—
221#126—21no—
222#125—21no—
223#125C2×D7911yescharacteristic, complemented
224#123—21no—
225C22⋊Q8C2×D7911yescharacteristic, complemented
226C22⋊Q8C2×D7911yescharacteristic, complemented
227#121—791no—
228#121—791no—
229#121—1581no—
230#120—1581no—
231#120—1581no—
232C4×Q8C2×D7911yescharacteristic, complemented
233C4×D4—791no—
234C4×D4C2×D7911yescharacteristic
235#117—21no—
236#117C2×D7911yescharacteristic, complemented
237C2×C4⋊C4C2×D7911yescharacteristic, complemented
238#107—791no—
239#107—791no—
240#106—791no—
241C4⋊C8—791no—
242#103—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251#102—791no—
252C22⋊C8—791no—
253C22⋊C8—791no—
254#97—791no—
255C24—1581no—
256C24—1581no—
257C2×Q8C22×D7911yescharacteristic
258C2×D4—3161no—
259C2×D4—3161no—
260C2×D4—3164no—
261C2×D4—791no—
262C2×D4—791no—
263C2×D4—791no—
264C2×D4—1582no—
265C2×D4—1582no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4C22⋊D7911yescharacteristic
273C22×C4—21no—
274C22×C4—1581no—
275C22×C4C22×D7911yescharacteristic
276C22×C4C22×D7911yescharacteristic
277SD16—3161no—
278SD16—3161no—
279SD16—1582no—
280M16—3161no—
281C2×C8—3161no—
282C2×C8—791no—
283C2×C8—791no—
284C2×C8—791no—
285C2×C8—791no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—791no—
293C4⋊C4C22⋊D7911yescharacteristic
294C4⋊C4C22×D7911yescharacteristic
295C4⋊C4C22×D7911yescharacteristic
296C4⋊C4C22×D7911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4C22⋊D7911yescharacteristic
304C22⋊C4C22⋊D7911yescharacteristic
305C42—21no—
306C42—21no—
307C42C22×D7911yescharacteristic
308C23—3162no—
309C23—3162no—
310C23—3162no—
311C23—3162no—
312C23—6321no—
313C23—6321no—
314C23—1581no—
315C23—1581no—
316C23—1581no—
317C23C2×C22⋊D7911yescharacteristic
318C23C2×C22⋊D7911yescharacteristic
319Q8—21no—
320Q8—21no—
321D4—22no—
322D4—3162no—
323D4—3162no—
324D4—3162no—
325D4—3162no—
326D4—3162no—
327D4—792no—
328D4—6321no—
329D4—1581no—
330D4—1581no—
331D4—1581no—
332D4—1581no—
333D4—1581no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—3162no—
344C2×C4—1581no—
345C2×C4C2×C22⋊D7911yescharacteristic
346C2×C4C2×C22⋊D7911yescharacteristic
347C2×C4C2×C22⋊D7911yescharacteristic
348C2×C4C2×C22⋊D7911yescharacteristic
349C2×C4C23×D7911yescharacteristic
350C8—1581no—
351C8—1581no—
352C8—1581no—
353C8—1581no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—3161no—
360C22—3161no—
361C22—3161no—
362C22—3161no—
363C22—3161no—
364C22—3161no—
365C22—3161no—
366C22—3161no—
367C22—6324no—
368C22—6324no—
369C22—1582no—
370C22#1457918612yes—
371C22C22×C22⋊D7911yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3161no—
381C4#41×D7911yescharacteristic
382C4#1457920711yescharacteristic
383C2—22no—
384C2—41no—
385C2—3162no—
386C2—6321no—
387C2—6321no—
388C2#1909920111yescharacteristic
389C2C2×#1457918611yescharacteristic
390C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#552×C79C2
socleC22×C79C22×D4
prime radicalD4×D316C2
hypercenter#552D79
hypocenterC79#3310
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #19098929C2semidirect
3. #19098887C2semidirect
4. #19098876C2semidirect
5. #19098860C2semidirect
6. #19098811C2semidirect
7. #19098794C2semidirect
8. #19098763C2semidirect
9. #19098713C2semidirect
10. #19098713C2semidirect
11. #19098661C2semidirect
12. #19098635C2semidirect
13. #19098567C2semidirect
14. C2×#14579081C2semidirect
15. #552×C79C2semidirect
20. C2×#11929611C22semidirect
21. C2×#11929611C22semidirect
22. C2×#11929608C22semidirect
23. C22×C79⋊C8C22semidirect
31. #14579094C22semidirect
32. #14579094C22semidirect
33. #14579092C22semidirect
34. C4⋊(C79⋊C8)C22semidirect
35. #14579085C22semidirect
39. #14579081C22semidirect
40. #14579081C22semidirect
41. #14579081C22semidirect
42. #14579081C22semidirect
43. #14579081C22semidirect
44. #14579081C22semidirect
45. C22⋊(C79⋊C8)C22semidirect
46. C22⋊(C79⋊C8)C22semidirect
47. #14579072C22semidirect
50. #125×C79C22semidirect
52. C22⋊Q8×C79C22semidirect
53. C22⋊Q8×C79C22semidirect
54. C4×Q8×C79C22semidirect
57. #117×C79C22semidirect
58. C2×C4⋊C4×C79C22semidirect
196. C79#3310semidirect
197. #552D79semidirect
223. #125C2×D79semidirect
225. C22⋊Q8C2×D79semidirect
226. C22⋊Q8C2×D79semidirect
232. C4×Q8C2×D79semidirect
236. #117C2×D79semidirect
237. C2×C4⋊C4C2×D79semidirect