Finite Group Databasebeta

← #23774256

Subgroups — #23774256

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#19099130C211yesmaximal, characteristic, complemented
3#19098901C211yesmaximal, characteristic, complemented
4#19098888C211yesmaximal, characteristic, complemented
5#19098880C211yesmaximal, characteristic, complemented
6#19098875C211yesmaximal, characteristic, complemented
7#19098815C211yesmaximal, characteristic, complemented
8#19098806C211yesmaximal, characteristic, complemented
9#19098798C211yesmaximal, characteristic, complemented
10#19098789C211yesmaximal, characteristic, complemented
11#19098707C211yesmaximal, characteristic, complemented
12#19098707C211yesmaximal, characteristic, complemented
13#19098697C211yesmaximal, characteristic, complemented
14#19098528C211yesmaximal, characteristic, complemented
15#450×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic, complemented
17C2×#11929624C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×#11929607C2211yescharacteristic, complemented
21C2×C8×D79C2211yescharacteristic, complemented
22#14579157—21no—
23#14579148—21no—
24#14579139—21no—
25#14579137C2211yescharacteristic, complemented
26#14579136—21no—
27#14579136C2211yescharacteristic, complemented
28#14579135C2211yescharacteristic
29#14579134—21no—
30#14579134—21no—
31#14579132C2211yescharacteristic
32#14579132C2211yescharacteristic
33#14579132C2211yescharacteristic
34#14579132C2211yescharacteristic
35#14579130—21no—
36#14579130—21no—
37#14579120C2211yescharacteristic
38C4⋊C4×D79C2211yescharacteristic, complemented
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59#11929625—41no—
60#11929625—41no—
61#11929624—41no—
62#11929624—41no—
63C2×Dic158D411yescharacteristic
64C2×D316—21no—
65C2×D316—21no—
66C2×D316D411yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79D411yescharacteristic
74C2×C22⋊D79D411yescharacteristic
75C2×C4×D79—21no—
76C2×C4×D79—21no—
77C2×C4×D79C2311yescharacteristic
78C2×C4×D79C2311yescharacteristic
79#11929609—41no—
80#11929609—41no—
81#11929607—41no—
82C2×C79⋊C8C2311yescharacteristic
83C2×C79⋊C8C2311yescharacteristic
84C8×D79—41no—
85C4⋊Dic79C2311yescharacteristic
86C4⋊Dic79C2311yescharacteristic
87C4⋊Dic79C2311yescharacteristic
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94C22⋊Dic79—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98C4×Dic79—21no—
99C24×C79—21no—
100C2×Q8×C79C2311yescharacteristic
101C2×D4×C79—21no—
102C2×D4×C79—41no—
103C2×D4×C79—41no—
104C2×D4×C79C2311yescharacteristic
105C2×D4×C79C2311yescharacteristic
106C22×C4×C79C2311yescharacteristic
107SD16×C79—41no—
108SD16×C79—41no—
109C2×C8×C79C2311yescharacteristic
110C2×C8×C79C2311yescharacteristic
111C4⋊C4×C79—21no—
112C4⋊C4×C79C2311yescharacteristic
113C22⋊C4×C79—21no—
114C23×C79—21no—
115C23×C79—21no—
116C23×C79—42no—
117C23×C79—81no—
118C23×C79—81no—
119C23×C79C2×D411yescharacteristic
120C22×D79—21no—
121C22×D79C2×D411yescharacteristic
122C22×D79C2×D411yescharacteristic
123Q8×C79—21no—
124Q8×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—21no—
129D4×C79—42no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2411yescharacteristic
136C22⋊D79—41no—
137C22⋊D79—41no—
138C22⋊D79—81no—
139C22⋊D79—81no—
140C22⋊D79—81no—
141C22⋊D79—81no—
142C22⋊D79—81no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79C2×D411yescharacteristic
147C2×Dic79C2×D411yescharacteristic
148D316—21no—
149D316—21no—
150D316—41no—
151D316—42no—
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×C79—41no—
171C22×C79—41no—
172C22×C79—41no—
173C22×C79—84no—
174C22×C79C22×D411yescharacteristic
175C2×D79—21no—
176C2×D79—21no—
177C2×D79—21no—
178C2×D79—21no—
179C2×D79—21no—
180C2×D79—21no—
181C2×D79—41no—
182C2×D79—41no—
183C2×D79—41no—
184C4×C79—21no—
185C4×C79—41no—
186C4×C79—41no—
187C4×C79H(5,𝔽2)11yescharacteristic
188C4×C79H(5,𝔽2)11yescharacteristic
189Dic79—21no—
190Dic79—21no—
191Dic79—41no—
192Dic79—41no—
193Dic79—41no—
194C2×C79—41no—
195C2×C79—81no—
196C2×C79—81no—
197C2×C79#53411yescharacteristic
198C2×C79#57611yescharacteristic
199C2×C79#57711yescharacteristic
200D79—41no—
201D79—41no—
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#468—791no—
213#466—791no—
214#465—791no—
215#450D7911yescharacteristic, complemented
216#449—791no—
217#449—791no—
218#447—791no—
219#408—791no—
220C2×#41—791no—
221C2×#41—791no—
222C22×D4C2×D7911yescharacteristic
223C2×SD16C2×D7911yescharacteristic
224C2×SD16C2×D7911yescharacteristic
225C2×D8—791no—
226C2×D8—791no—
227C2×M16—791no—
228C22×C8—791no—
229#127—1581no—
230#124—1581no—
231C22⋊Q8—791no—
232C22⋊Q8—1581no—
233C22⋊Q8C2×D7911yescharacteristic
234#121—791no—
235#121—791no—
236#121—791no—
237#121—791no—
238#121—791no—
239#121—791no—
240#121—1581no—
241#121—1581no—
242#121—1581no—
243#120—1581no—
244#120—1581no—
245#117—791no—
246C2×C4⋊C4—791no—
247#107—791no—
248#107—791no—
249#106—791no—
250#106—791no—
251#103—791no—
252#103—791no—
253#102—791no—
254#102—791no—
255#102—791no—
256#102—791no—
257#102C2×D7911yescharacteristic
258#102C2×D7911yescharacteristic
259C22⋊C8—791no—
260C22⋊C8—791no—
261C22⋊C8—791no—
262C22⋊C8C2×D7911yescharacteristic
263C24—21no—
264#41—3161no—
265#41—3161no—
266#41—3161no—
267#41—3161no—
268C2×Q8—791no—
269C2×Q8C22×D7911yescharacteristic
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—791no—
274C2×D4—791no—
275C2×D4—791no—
276C2×D4—791no—
277C2×D4—1581no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4—1581no—
281C2×D4—1581no—
282C2×D4—1581no—
283C2×D4—1581no—
284C2×D4C22×D7911yescharacteristic
285C2×D4C22×D7911yescharacteristic
286C22×C4—791no—
287C22×C4—791no—
288C22×C4—1581no—
289C22×C4—1581no—
290C22×C4C22×D7911yescharacteristic
291SD16—41no—
292SD16—41no—
293D8—3161no—
294D8—3161no—
295M16—3161no—
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
308C22⋊C4—21no—
309C22⋊C4—1581no—
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—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—791no—
324C23—791no—
325C23—1581no—
326C23D4×D7911yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—3161no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—3161no—
336D4—3162no—
337D4—3161no—
338D4—3161no—
339D4—6321no—
340D4—6321no—
341D4—6321no—
342D4—6321no—
343D4—6321no—
344D4—6321no—
345D4—1581no—
346D4—1581no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—3162no—
352C2×C4—791no—
353C2×C4—791no—
354C2×C4—6321no—
355C2×C4—1581no—
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—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—3161no—
379C22—3161no—
380C22—3161no—
381C22—1581no—
382C22—1581no—
383C22—1581no—
384C22—1581no—
385C22—1581no—
386C22—1581no—
387C22C2×D4×D7911yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—3161no—
392C4—3161no—
393C4—3161no—
394C4—1581no—
395C4—1581no—
396C4#1457920611yescharacteristic
397C4#1457920611yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—3161no—
402C2—3161no—
403C2—6321no—
404C2#1909912311yescharacteristic
405C2#1909936711yescharacteristic
406C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#450×C79C2
socleC22×C79C22×D4
hypercenter#450D79
hypocenterC79#3198
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #19099143C2semidirect
2. #19099130C2semidirect
3. #19098901C2semidirect
4. #19098888C2semidirect
5. #19098880C2semidirect
6. #19098875C2semidirect
7. #19098815C2semidirect
8. #19098806C2semidirect
9. #19098798C2semidirect
10. #19098789C2semidirect
11. #19098707C2semidirect
12. #19098707C2semidirect
13. #19098697C2semidirect
14. #19098528C2semidirect
15. #450×C79C2semidirect
16. C2×#11929625C22semidirect
20. C2×#11929607C22semidirect
21. C2×C8×D79C22semidirect
25. #14579137C22semidirect
27. #14579136C22semidirect
38. C4⋊C4×D79C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579093C22semidirect
42. #14579092C22semidirect
43. #14579085C22semidirect
44. #14579085C22semidirect
45. #14579083C22semidirect
46. #14579083C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. (C2×D79)⋊C8C22semidirect
204. C79#3198semidirect
215. #450D79semidirect