Finite Group Databasebeta

← #23775209

Subgroups — #23775209

Order 10112.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099214C211yesmaximal, characteristic, complemented
2D4×C22⋊D79C211yesmaximal, characteristic, complemented
3#19098908C211yesmaximal, characteristic, complemented
4#19098876C211yesmaximal, characteristic, complemented
5#19098875C211yesmaximal, characteristic, complemented
6#19098841C211yesmaximal, characteristic, complemented
7#19098799C211yesmaximal, characteristic, complemented
8#19098798C211yesmaximal, characteristic, complemented
9#19098757C211yesmaximal, characteristic, complemented
10#19098698C211yesmaximal, characteristic, complemented
11#19098697C211yesmaximal, characteristic, complemented
12#19098643C211yesmaximal, characteristic, complemented
13C8×C22⋊D79C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15C2×#102×C79C211yesmaximal, characteristic, complemented
16C2×#11929624—21no—
17C22×C22⋊D79—21no—
18C2×D4×D79C2211yescharacteristic
19C2×D632C2211yescharacteristic, complemented
20C2×#11929609C2211yescharacteristic
21C2×#11929609C2211yescharacteristic, complemented
22C2×C8×D79C2211yescharacteristic, complemented
23#14579160C2211yescharacteristic, complemented
24#14579157C2211yescharacteristic
25#14579146—21no—
26#14579144—21no—
27#14579139—21no—
28#14579136C2211yescharacteristic, complemented
29#14579135C2211yescharacteristic
30#14579135C2211yescharacteristic, complemented
31#14579133—21no—
32#14579132C2211yescharacteristic
33#14579130—21no—
34#14579129—21no—
35D4×Dic79C2211yescharacteristic
36#14579123C2211yescharacteristic, complemented
37C4×C22⋊D79C2211yescharacteristic
38C4⋊C4×D79C2211yescharacteristic, complemented
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579094C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic, complemented
54C2×C4⋊C4×C79C2211yescharacteristic, complemented
55#102×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—44no—
61C2×Dic158—21no—
62C2×D316—21no—
63C2×D316C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—44no—
72C2×C22⋊D79D411yescharacteristic
73D4×D79—22no—
74D4×D79—41no—
75C22×Dic79—21no—
76C2×C4×D79—21no—
77C2×C4×D79—21no—
78C2×C4×D79C2311yescharacteristic
79D632—41no—
80#11929609—22no—
81#11929609—41no—
82C2×C79⋊C8C2311yescharacteristic
83C2×C79⋊C8C2311yescharacteristic
84C8×D79—41no—
85C4⋊Dic79C2311yescharacteristic
86C4⋊Dic79C2311yescharacteristic
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4D411yescharacteristic
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79D411yescharacteristic
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4D411yescharacteristic
98C4×Dic79C2311yescharacteristic
99C24×C79—21no—
100C2×D4×C79—22no—
101C2×D4×C79—21no—
102C2×D4×C79—41no—
103C2×D4×C79C2311yescharacteristic
104C2×D4×C79C2311yescharacteristic
105C22×C4×C79—21no—
106C22×C4×C79C2311yescharacteristic
107C2×C8×C79—41no—
108C2×C8×C79C2311yescharacteristic
109C2×C8×C79C2311yescharacteristic
110C4⋊C4×C79—21no—
111C4⋊C4×C79C2311yescharacteristic
112C4⋊C4×C79C2311yescharacteristic
113C23×C79—21no—
114C23×C79—21no—
115C23×C79—42no—
116C23×C79—42no—
117C23×C79—81no—
118C23×C79C2×D411yescharacteristic
119C22×D79—21no—
120C22×D79—21no—
121C22×D79—42no—
122C22×D79—42no—
123C22×D79—81no—
124C22×D79C2×D411yescharacteristic
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—42no—
129D4×C79#4112yescomplemented
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×C79C2411yescharacteristic
137C22⋊D79—42no—
138C22⋊D79—42no—
139C22⋊D79—42no—
140C22⋊D79—42no—
141C22⋊D79—42no—
142C22⋊D79—81no—
143C22⋊D79D814yescomplemented
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—42no—
147C2×Dic79C2×D411yescharacteristic
148C2×Dic79C2×D411yescharacteristic
149C2×Dic79C2×D411yescharacteristic
150D316—21no—
151D316—21no—
152D316—21no—
153D316—21no—
154D316—42no—
155C4×D79—21no—
156C4×D79—21no—
157C4×D79—42no—
158C4×D79—42no—
159Dic158—42no—
160C8×C79—21no—
161C8×C79—21no—
162C79⋊C8—21no—
163C79⋊C8—21no—
164C22×C79—21no—
165C22×C79—21no—
166C22×C79—22no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—84no—
173C22×C79C2×D812yes—
174C22×C79C22×D411yescharacteristic
175C2×D79—21no—
176C2×D79—21no—
177C2×D79—41no—
178C2×D79—41no—
179C2×D79—41no—
180C2×D79—41no—
181C2×D79—41no—
182C2×D79—41no—
183C2×D79—84no—
184C2×D79C2×D812yes—
185C4×C79—21no—
186C4×C79—41no—
187C4×C79—41no—
188C4×C79C2×#4111yescharacteristic
189C4×C79H(5,𝔽2)11yescharacteristic
190Dic79—21no—
191Dic79—21no—
192Dic79—41no—
193Dic79—41no—
194Dic79C2×D812yes—
195C2×C79—22no—
196C2×C79—42no—
197C2×C79—81no—
198C2×C79#54611yescharacteristic
199C2×C79C22×D811yescharacteristic
200C2×C79#57711yescharacteristic
201D79—22no—
202D79—81no—
203D79—81no—
204#3294—791nomaximal, Sylow
205C79#329411yescharacteristic, complemented, Sylow
206#547—791no—
207D42—791no—
208#486—791no—
209#480—791no—
210#480—791no—
211#474—791no—
212#466—791no—
213#466—791no—
214#459—791no—
215#447—791no—
216#447—791no—
217C4×D8—791no—
218C8×D4—791no—
219C2×#102—791no—
220C2×#102D7911yescharacteristic, complemented
221C2×#41—1581no—
222C22×D4—791no—
223C22×D4—1581no—
224C22×D4C2×D7911yescharacteristic
225C2×D8—791no—
226C2×D8—791no—
227C2×D8—791no—
228C22×C8—791no—
229C22×C8C2×D7911yescharacteristic, complemented
230C4⋊Q8—791no—
231#127—791no—
232#123—1581no—
233#123—1581no—
234C22⋊Q8—1581no—
235#121—791no—
236#121—791no—
237#121—791no—
238#121—791no—
239#121—1581no—
240#120—1581no—
241#120—1581no—
242C4×D4—791no—
243C4×D4—791no—
244C4×D4—791no—
245C2×C4⋊C4—791no—
246C2×C4⋊C4C2×D7911yescharacteristic, complemented
247#107—791no—
248#107—791no—
249#107—791no—
250C4⋊C8—791no—
251#102—791no—
252#102—791no—
253#102—791no—
254#102—791no—
255#102—791no—
256#102—791no—
257#102C2×D7911yescharacteristic
258#102C2×D7911yescharacteristic
259#102C2×D7911yescharacteristic, complemented
260#102C2×D7911yescharacteristic, complemented
261C22⋊C8—791no—
262C22⋊C8—791no—
263C4×C8—791no—
264C24—21no—
265C24—1581no—
266#41—3164no—
267C2×Q8—1581no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—3164no—
272C2×D4—3161no—
273C2×D4—791no—
274C2×D4—791no—
275C2×D4—791no—
276C2×D4—1581no—
277C2×D4—1581no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4—1581no—
281C2×D4—1581no—
282C2×D4—1581no—
283C2×D4—1582no—
284C2×D4C22×D7911yescharacteristic
285C2×D4C22×D7911yescharacteristic
286C22×C4—21no—
287C22×C4—791no—
288C22×C4—1581no—
289C22×C4—1581no—
290C22×C4—1581no—
291C22×C4C22×D7911yescharacteristic
292D8—3161no—
293D8—3161no—
294D8—1582no—
295C2×C8—41no—
296C2×C8—3161no—
297C2×C8—791no—
298C2×C8—791no—
299C2×C8C22×D7911yescharacteristic
300C2×C8C22×D7911yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—791no—
303C4⋊C4—791no—
304C4⋊C4—791no—
305C4⋊C4—1581no—
306C4⋊C4—1581no—
307C4⋊C4C22×D7911yescharacteristic
308C4⋊C4C22×D7911yescharacteristic
309C22⋊C4—791no—
310C22⋊C4—791no—
311C22⋊C4—1581no—
312C22⋊C4—1581no—
313C22⋊C4—1581no—
314C22⋊C4—1581no—
315C22⋊C4—1581no—
316C22⋊C4—1581no—
317C42—791no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—3162no—
324C23—3162no—
325C23—791no—
326C23—6321no—
327C23—1581no—
328C23—1581no—
329C23D4×D7911yescharacteristic
330Q8—3162no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—3162no—
336D4—3162no—
337D4—3162no—
338D4—3162no—
339D4—3162no—
340D4—3162no—
341D4—794no—
342D4—6321no—
343D4—1581no—
344D4—1581no—
345D4—1581no—
346D4—1581no—
347D4#1192962412yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—3162no—
354C2×C4—3162no—
355C2×C4—3162no—
356C2×C4—791no—
357C2×C4—791no—
358C2×C4—791no—
359C2×C4—1581no—
360C2×C4—1581no—
361C2×C4—1581no—
362C2×C4—1581no—
363C2×C4D4×D7911yescharacteristic
364C2×C4C23×D7911yescharacteristic
365C8—21no—
366C8—21no—
367C8—1581no—
368C8—1581no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—3161no—
379C22—3161no—
380C22—3161no—
381C22—3161no—
382C22—3161no—
383C22—3161no—
384C22—792no—
385C22—6324no—
386C22—1581no—
387C22—1581no—
388C22D8×D7912yes—
389C22C2×D4×D7911yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—3161no—
394C4—3161no—
395C4—792no—
396C4—1581no—
397C4—1581no—
398C4C2×#1192962411yescharacteristic
399C4#1457920611yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—6321no—
404C2—6321no—
405C2—1582no—
406C2#1909920311yescharacteristic
407C2C2×D8×D7911yescharacteristic
408C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×#102×C79C2
socleC22×C79C22×D4
hypercenterC2×#102D79
hypocenterC79#3294
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #19099214C2semidirect
2. D4×C22⋊D79C2semidirect
3. #19098908C2semidirect
4. #19098876C2semidirect
5. #19098875C2semidirect
6. #19098841C2semidirect
7. #19098799C2semidirect
8. #19098798C2semidirect
9. #19098757C2semidirect
10. #19098698C2semidirect
11. #19098697C2semidirect
12. #19098643C2semidirect
13. C8×C22⋊D79C2semidirect
14. #102×D79C2semidirect
15. C2×#102×C79C2semidirect
19. C2×D632C22semidirect
21. C2×#11929609C22semidirect
22. C2×C8×D79C22semidirect
23. #14579160C22semidirect
28. #14579136C22semidirect
30. #14579135C22semidirect
36. #14579123C22semidirect
38. C4⋊C4×D79C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579094C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579083C22semidirect
44. #14579083C22semidirect
46. #14579082C22semidirect
47. #14579081C22semidirect
48. #14579081C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. C8×Dic79C22semidirect
53. C22×C8×C79C22semidirect
54. C2×C4⋊C4×C79C22semidirect
57. #102×C79C22semidirect
58. #102×C79C22semidirect
129. D4×C79#41semidirect
143. C22⋊D79D8semidirect
205. C79#3294semidirect
220. C2×#102D79semidirect
229. C22×C8C2×D79semidirect
246. C2×C4⋊C4C2×D79semidirect
259. #102C2×D79semidirect
260. #102C2×D79semidirect
347. D4#11929624semidirect