Finite Group Databasebeta

← #23774491

Subgroups — #23774491

Order 10112.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099178C211yesmaximal, characteristic, complemented
2#19099126C211yesmaximal, characteristic, complemented
3#19098951C211yesmaximal, characteristic, complemented
4#19098946C211yesmaximal, characteristic, complemented
5#19098921C211yesmaximal, characteristic, complemented
6#19098908C211yesmaximal, characteristic, complemented
7#19098786C211yesmaximal, characteristic, complemented
8#19098778C211yesmaximal, characteristic, complemented
9#19098760C211yesmaximal, characteristic, complemented
10#19098726C211yesmaximal, characteristic, complemented
11#19098715C211yesmaximal, characteristic, complemented
12#19098705C211yesmaximal, characteristic, complemented
13#19098695C211yesmaximal, characteristic, complemented
14#19098623C211yesmaximal, characteristic, complemented
15#459×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×Dic316C2211yescharacteristic, complemented
19C2×#11929613C2211yescharacteristic
20C2×#11929612C2211yescharacteristic
21C2×#11929612C2211yescharacteristic, complemented
22C2×#11929612C2211yescharacteristic, complemented
23C2×#11929609C2211yescharacteristic
24#14579160C2211yescharacteristic, complemented
25#14579157C2211yescharacteristic
26#14579154—21no—
27#14579149C2211yescharacteristic
28#14579148C2211yescharacteristic
29#14579148C2211yescharacteristic, complemented
30#14579147—21no—
31#14579144—21no—
32#14579141C2211yescharacteristic
33#14579140—21no—
34#14579133—21no—
35#14579133—21no—
36#14579132C2211yescharacteristic
37#14579129—21no—
38#14579129—21no—
39C4×Dic158C2211yescharacteristic, complemented
40#14579118C2211yescharacteristic
41C4⋊(C79⋊C8)C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C2×D8×C79C2211yescharacteristic
53C2×D8×C79C2211yescharacteristic, complemented
54#127×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic, complemented
56C4⋊C8×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929623—41no—
61#11929623—41no—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64C2×Dic158C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71D4×D79—41no—
72D4×D79—41no—
73C22×Dic79—21no—
74C2×C4×D79C2311yescharacteristic
75Dic316—41no—
76#11929613—41no—
77#11929612—41no—
78#11929612—41no—
79#11929612—41no—
80#11929609—41no—
81C2×C79⋊C8C2311yescharacteristic
82C2×C79⋊C8C2311yescharacteristic
83C4⋊Dic79—21no—
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4D411yescharacteristic
88Dic79⋊C4D411yescharacteristic
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4D411yescharacteristic
98(C2×D79)⋊C4D411yescharacteristic
99C4×Dic79—21no—
100C4×Dic79C2311yescharacteristic
101C2×D4×C79—21no—
102C2×D4×C79—21no—
103C2×D4×C79C2311yescharacteristic
104C2×D4×C79C2311yescharacteristic
105C2×D4×C79C2311yescharacteristic
106C22×C4×C79—21no—
107D8×C79—41no—
108D8×C79—41no—
109C2×C8×C79C2311yescharacteristic
110C2×C8×C79C2311yescharacteristic
111C4⋊C4×C79C2311yescharacteristic
112C22⋊C4×C79—21no—
113C42×C79C2311yescharacteristic
114C23×C79—21no—
115C23×C79—21no—
116C23×C79—21no—
117C22×D79—21no—
118C22×D79—42no—
119C22×D79—81no—
120C22×D79—81no—
121C22×D79C2×D411yescharacteristic
122D4×C79—21no—
123D4×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—81no—
129D4×C79—81no—
130C2×C4×C79—21no—
131C2×C4×C79—81no—
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2411yescharacteristic
135C22⋊D79—42no—
136C22⋊D79—42no—
137C22⋊D79—81no—
138C22⋊D79—81no—
139C22⋊D79—81no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—42no—
144C2×Dic79C2×D411yescharacteristic
145C2×Dic79C2×D411yescharacteristic
146C2×Dic79C2×D411yescharacteristic
147D316—21no—
148D316—21no—
149C4×D79—21no—
150C4×D79—21no—
151Dic158—21no—
152Dic158—21no—
153Dic158—21no—
154Dic158—21no—
155Dic158—81no—
156C8×C79—21no—
157C8×C79—21no—
158C79⋊C8—21no—
159C79⋊C8—21no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79C22×D411yescharacteristic
170C2×D79—21no—
171C2×D79—21no—
172C2×D79—21no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—84no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79—41no—
180C4×C79H(5,𝔽2)11yescharacteristic
181C4×C79H(5,𝔽2)11yescharacteristic
182Dic79—21no—
183Dic79—21no—
184Dic79—21no—
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188C2×C79—81no—
189C2×C79—81no—
190C2×C79—81no—
191C2×C79#53511yescharacteristic
192C2×C79#57611yescharacteristic
193C2×C79#57711yescharacteristic
194D79—41no—
195D79—81no—
196#3224—791nomaximal, Sylow
197C79#322411yescharacteristic, complemented, Sylow
198#542—791no—
199#535—791no—
200#496—791no—
201#495—791no—
202#489—791no—
203#486—791no—
204#464—791no—
205#463—791no—
206#460—791no—
207#459D7911yescharacteristic, complemented
208#452—791no—
209#450—791no—
210#449—791no—
211#447—791no—
212#433—791no—
213C2×#41—791no—
214C22×D4—791no—
215C2×Q16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×SD16—791no—
219C2×SD16—791no—
220C2×D8—791no—
221C2×D8C2×D7911yescharacteristic
222C2×D8C2×D7911yescharacteristic, complemented
223C4⋊Q8—791no—
224#127—791no—
225#127C2×D7911yescharacteristic
226#126—1581no—
227#124—791no—
228#124—791no—
229#124—791no—
230#124—1581no—
231#123—1581no—
232C22⋊Q8—791no—
233C22⋊Q8—1581no—
234#121—791no—
235#121—1581no—
236#121—1581no—
237#120—1581no—
238#120—1581no—
239C4×Q8—791no—
240C4×D4C2×D7911yescharacteristic, complemented
241#117—791no—
242C4⋊C8—791no—
243C4⋊C8C2×D7911yescharacteristic, complemented
244#103—791no—
245#103—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102C2×D7911yescharacteristic
251#102C2×D7911yescharacteristic, complemented
252C22⋊C8—791no—
253C22⋊C8—791no—
254#97—791no—
255C4×C8—791no—
256C24—1581no—
257#41—3161no—
258#41—3161no—
259C2×Q8—791no—
260C2×Q8—791no—
261C2×Q8—1581no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—3161no—
265C2×D4—3161no—
266C2×D4—791no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4C22×D7911yescharacteristic
273C2×D4C22×D7911yescharacteristic
274C2×D4C22×D7911yescharacteristic
275C22×C4—21no—
276C22×C4—791no—
277C22×C4—1581no—
278Q16—3161no—
279SD16—3161no—
280SD16—3161no—
281SD16—3161no—
282SD16—3161no—
283D8—41no—
284D8—41no—
285D8—3161no—
286C2×C8—791no—
287C2×C8—791no—
288C2×C8C22×D7911yescharacteristic
289C2×C8C22×D7911yescharacteristic
290C4⋊C4—791no—
291C4⋊C4—791no—
292C4⋊C4—791no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4—1581no—
296C4⋊C4C22×D7911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—791no—
299C22⋊C4—791no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C42—791no—
309C42—1581no—
310C42C22×D7911yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—3162no—
315C23—791no—
316C23—6321no—
317C23—6321no—
318C23—1581no—
319Q8—6321no—
320Q8—1581no—
321Q8—1581no—
322Q8—1581no—
323Q8—1581no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—81no—
331D4—81no—
332D4—3162no—
333D4—3162no—
334D4—6321no—
335D4—6321no—
336D4—6321no—
337D4—1581no—
338D4—1581no—
339C2×C4—21no—
340C2×C4—81no—
341C2×C4—3162no—
342C2×C4—791no—
343C2×C4—791no—
344C2×C4—791no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4D4×D7911yescharacteristic
351C2×C4D4×D7911yescharacteristic
352C2×C4C23×D7911yescharacteristic
353C8—21no—
354C8—21no—
355C8—1581no—
356C8—1581no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—3161no—
367C22—3161no—
368C22—3161no—
369C22—6324no—
370C22—1581no—
371C22—1581no—
372C22—1581no—
373C22C2×D4×D7911yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—3161no—
378C4—3161no—
379C4—3161no—
380C4—1581no—
381C4—1581no—
382C4—1581no—
383C4#1457920611yescharacteristic
384C4#1457920711yescharacteristic
385C2—81no—
386C2—81no—
387C2—81no—
388C2—3161no—
389C2—6321no—
390C2#1909912911yescharacteristic
391C2#1909936411yescharacteristic
392C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#459×C79C2
socleC22×C79C22×D4
hypercenter#459D79
hypocenterC79#3224
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #19099178C2semidirect
2. #19099126C2semidirect
3. #19098951C2semidirect
4. #19098946C2semidirect
5. #19098921C2semidirect
6. #19098908C2semidirect
7. #19098786C2semidirect
8. #19098778C2semidirect
9. #19098760C2semidirect
10. #19098726C2semidirect
11. #19098715C2semidirect
12. #19098705C2semidirect
13. #19098695C2semidirect
14. #19098623C2semidirect
15. #459×C79C2semidirect
18. C2×Dic316C22semidirect
21. C2×#11929612C22semidirect
22. C2×#11929612C22semidirect
24. #14579160C22semidirect
29. #14579148C22semidirect
39. C4×Dic158C22semidirect
41. C4⋊(C79⋊C8)C22semidirect
42. #14579086C22semidirect
43. #14579084C22semidirect
46. #14579082C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
53. C2×D8×C79C22semidirect
55. C4×D4×C79C22semidirect
56. C4⋊C8×C79C22semidirect
58. #102×C79C22semidirect
197. C79#3224semidirect
207. #459D79semidirect
222. C2×D8C2×D79semidirect
240. C4×D4C2×D79semidirect
243. C4⋊C8C2×D79semidirect
251. #102C2×D79semidirect