Finite Group Databasebeta

← #23774253

Subgroups — #23774253

Order 10112.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099143C211yesmaximal, characteristic, complemented
2#19099129C211yesmaximal, characteristic, complemented
3#19098902C211yesmaximal, characteristic, complemented
4#19098890C211yesmaximal, characteristic, complemented
5#19098880C211yesmaximal, characteristic, complemented
6#19098878C211yesmaximal, characteristic, complemented
7#19098816C211yesmaximal, characteristic, complemented
8#19098797C211yesmaximal, characteristic, complemented
9#19098794C211yesmaximal, characteristic, complemented
10#19098712C211yesmaximal, characteristic, complemented
11#19098711C211yesmaximal, characteristic, complemented
12#19098707C211yesmaximal, characteristic, complemented
13#19098698C211yesmaximal, characteristic, complemented
14#19098531C211yesmaximal, characteristic, complemented
15#468×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic, complemented
17C2×#11929624C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×D632C2211yescharacteristic
21C2×#11929609C2211yescharacteristic
22C22×C79⋊C8C2211yescharacteristic, complemented
23#14579157—21no—
24#14579147—21no—
25#14579139—21no—
26#14579137C2211yescharacteristic
27#14579136—21no—
28#14579136C2211yescharacteristic
29#14579136C2211yescharacteristic
30#14579135C2211yescharacteristic
31#14579135C2211yescharacteristic, complemented
32#14579134—21no—
33#14579134—21no—
34#14579132C2211yescharacteristic
35#14579131—21no—
36#14579129—21no—
37#14579119C2211yescharacteristic
38C4⋊C4×D79C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic
46#14579081C2211yescharacteristic
47#14579081C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic, complemented
54C22⋊Q8×C79C2211yescharacteristic, complemented
55#121×C79C2211yescharacteristic
56#107×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60#11929625—41no—
61#11929625—41no—
62#11929624—41no—
63#11929624—41no—
64C2×Dic158D411yescharacteristic
65C2×D316—21no—
66C2×D316—21no—
67C2×D316—21no—
68C2×D316D411yescharacteristic
69C2×D316C2311yescharacteristic
70C2×D316C2311yescharacteristic
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75C2×C22⋊D79D411yescharacteristic
76C2×C22⋊D79D411yescharacteristic
77D4×D79—41no—
78D4×D79—41no—
79C2×C4×D79—21no—
80C2×C4×D79—21no—
81C2×C4×D79C2311yescharacteristic
82C2×C4×D79C2311yescharacteristic
83#11929611—41no—
84D632—41no—
85#11929609—41no—
86C2×C79⋊C8—41no—
87C2×C79⋊C8C2311yescharacteristic
88C2×C79⋊C8C2311yescharacteristic
89C4⋊Dic79C2311yescharacteristic
90C4⋊Dic79C2311yescharacteristic
91Dic79⋊C4—21no—
92Dic79⋊C4—21no—
93C22⋊Dic79—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—
99(C2×D79)⋊C4—21no—
100C4×Dic79—21no—
101C2×Q8×C79C2311yescharacteristic
102C2×D4×C79—21no—
103C2×D4×C79C2311yescharacteristic
104C22×C4×C79C2311yescharacteristic
105SD16×C79—41no—
106M16×C79—41no—
107C2×C8×C79C2311yescharacteristic
108C2×C8×C79C2311yescharacteristic
109C4⋊C4×C79—21no—
110C4⋊C4×C79C2311yescharacteristic
111C4⋊C4×C79C2311yescharacteristic
112C22⋊C4×C79—21no—
113C22⋊C4×C79—21no—
114C23×C79—21no—
115C23×C79C2×D411yescharacteristic
116C22×D79—21no—
117C22×D79—21no—
118C22×D79—42no—
119C22×D79—81no—
120C22×D79—81no—
121C22×D79C2×D411yescharacteristic
122C22×D79C2×D411yescharacteristic
123Q8×C79—21no—
124Q8×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—81no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2411yescharacteristic
135C22⋊D79—41no—
136C22⋊D79—41no—
137C22⋊D79—42no—
138C22⋊D79—81no—
139C22⋊D79—81no—
140C22⋊D79—81no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79C2×D411yescharacteristic
144C2×Dic79C2×D411yescharacteristic
145D316—21no—
146D316—21no—
147D316—21no—
148D316—21no—
149D316—41no—
150D316—42no—
151D316—81no—
152D316—81no—
153C4×D79—21no—
154C4×D79—21no—
155C4×D79—21no—
156C4×D79—21no—
157C4×D79—42no—
158C4×D79—81no—
159Dic158—41no—
160C8×C79—21no—
161C8×C79—21no—
162C79⋊C8—21no—
163C79⋊C8—21no—
164C22×C79—21no—
165C22×C79—21no—
166C22×C79—21no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79C22×D411yescharacteristic
171C2×D79—21no—
172C2×D79—21no—
173C2×D79—21no—
174C2×D79—21no—
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—
184C4×C79—21no—
185C4×C79—41no—
186C4×C79—41no—
187C4×C79—41no—
188C4×C79H(5,𝔽2)11yescharacteristic
189C4×C79H(5,𝔽2)11yescharacteristic
190Dic79—21no—
191Dic79—21no—
192Dic79—41no—
193Dic79—41no—
194C2×C79—41no—
195C2×C79—81no—
196C2×C79#53411yescharacteristic
197C2×C79#57611yescharacteristic
198C2×C79#57711yescharacteristic
199D79—41no—
200D79—41no—
201D79—81no—
202D79—81no—
203#3198—791nomaximal, Sylow
204C79#319811yescharacteristic, complemented, Sylow
205#537—791no—
206#535—791no—
207#485—791no—
208#482—791no—
209#481—791no—
210#480—791no—
211#469—791no—
212#468D7911yescharacteristic, complemented
213#466—791no—
214#465—791no—
215#450—791no—
216#449—791no—
217#449—791no—
218#447—791no—
219#408—791no—
220C2×#41—791no—
221C2×#41—791no—
222C22×D4—791no—
223C2×SD16—791no—
224C2×SD16C2×D7911yescharacteristic
225C2×D8—791no—
226C2×D8—791no—
227C2×M16C2×D7911yescharacteristic, complemented
228C22×C8—791no—
229#127—1581no—
230#124—1581no—
231C22⋊Q8—791no—
232C22⋊Q8—1581no—
233C22⋊Q8C2×D7911yescharacteristic, complemented
234#121—791no—
235#121—791no—
236#121—791no—
237#121—791no—
238#121—791no—
239#121—1581no—
240#121—1581no—
241#121—1581no—
242#121C2×D7911yescharacteristic
243#120—1581no—
244#120—1581no—
245#117—791no—
246C2×C4⋊C4—791no—
247#107—791no—
248#107C2×D7911yescharacteristic, complemented
249#106—791no—
250#106—791no—
251#103—791no—
252#103C2×D7911yescharacteristic, complemented
253#102—791no—
254#102—791no—
255#102—791no—
256#102—791no—
257#102—791no—
258#102C2×D7911yescharacteristic
259C22⋊C8—791no—
260C22⋊C8—791no—
261C22⋊C8—791no—
262C22⋊C8—791no—
263C24—1581no—
264#41—3161no—
265#41—3161no—
266#41—3161no—
267#41—3161no—
268C2×Q8—791no—
269C2×Q8C22×D7911yescharacteristic
270C2×D4—21no—
271C2×D4—3161no—
272C2×D4—3161no—
273C2×D4—791no—
274C2×D4—791no—
275C2×D4—791no—
276C2×D4—791no—
277C2×D4—791no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4—1581no—
281C2×D4—1581no—
282C2×D4—1581no—
283C2×D4—1581no—
284C2×D4—1581no—
285C2×D4C22×D7911yescharacteristic
286C22×C4—791no—
287C22×C4—791no—
288C22×C4—1581no—
289C22×C4—1581no—
290C22×C4C22×D7911yescharacteristic
291SD16—41no—
292SD16—3161no—
293D8—3161no—
294D8—3161no—
295M16—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—1581no—
305C4⋊C4—1581no—
306C4⋊C4C22×D7911yescharacteristic
307C4⋊C4C22×D7911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—1581no—
311C22⋊C4—1581no—
312C22⋊C4—1581no—
313C22⋊C4—1581no—
314C22⋊C4—1581no—
315C22⋊C4—1581no—
316C22⋊C4—1581no—
317C42—1581no—
318C23—21no—
319C23—3162no—
320C23—791no—
321C23—791no—
322C23—6321no—
323C23—6321no—
324C23—1581no—
325C23—1581no—
326C23D4×D7911yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—3161no—
330D4—21no—
331D4—21no—
332D4—81no—
333D4—3161no—
334D4—3162no—
335D4—3161no—
336D4—3161no—
337D4—3162no—
338D4—6321no—
339D4—6321no—
340D4—6321no—
341D4—6321no—
342D4—6321no—
343D4—1581no—
344D4—1581no—
345D4—1581no—
346D4—1581no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—3162no—
353C2×C4—791no—
354C2×C4—791no—
355C2×C4—6321no—
356C2×C4—1581no—
357C2×C4—1581no—
358C2×C4—1581no—
359C2×C4—1581no—
360C2×C4—1581no—
361C2×C4—1581no—
362C2×C4D4×D7911yescharacteristic
363C2×C4C23×D7911yescharacteristic
364C8—21no—
365C8—21no—
366C8—1581no—
367C8—1581no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—3161no—
375C22—3161no—
376C22—3161no—
377C22—3161no—
378C22—3161no—
379C22—3161no—
380C22—6324no—
381C22—1581no—
382C22—1581no—
383C22—1581no—
384C22—1581no—
385C22—1581no—
386C22—1581no—
387C22C2×D4×D7911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—3161no—
393C4—3161no—
394C4—1581no—
395C4—1581no—
396C4#1457920611yescharacteristic
397C4#1457920711yescharacteristic
398C2—41no—
399C2—81no—
400C2—3161no—
401C2—3161no—
402C2—6321no—
403C2—6321no—
404C2#1909912111yescharacteristic
405C2#1909936711yescharacteristic
406C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#468×C79C2
socleC22×C79C22×D4
hypercenter#468D79
hypocenterC79#3198
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #19099143C2semidirect
2. #19099129C2semidirect
3. #19098902C2semidirect
4. #19098890C2semidirect
5. #19098880C2semidirect
6. #19098878C2semidirect
7. #19098816C2semidirect
8. #19098797C2semidirect
9. #19098794C2semidirect
10. #19098712C2semidirect
11. #19098711C2semidirect
12. #19098707C2semidirect
13. #19098698C2semidirect
14. #19098531C2semidirect
15. #468×C79C2semidirect
16. C2×#11929625C22semidirect
22. C22×C79⋊C8C22semidirect
31. #14579135C22semidirect
38. C4⋊C4×D79C22semidirect
39. #14579094C22semidirect
40. #14579093C22semidirect
41. #14579092C22semidirect
42. #14579085C22semidirect
44. #14579083C22semidirect
47. #14579081C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. (C2×D79)⋊C8C22semidirect
53. C2×M16×C79C22semidirect
54. C22⋊Q8×C79C22semidirect
56. #107×C79C22semidirect
57. #103×C79C22semidirect
204. C79#3198semidirect
212. #468D79semidirect
227. C2×M16C2×D79semidirect
233. C22⋊Q8C2×D79semidirect
248. #107C2×D79semidirect
252. #103C2×D79semidirect