Finite Group Databasebeta

← #23774490

Subgroups — #23774490

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#19099180C211yesmaximal, characteristic, complemented
2#19099130C211yesmaximal, characteristic, complemented
3#19098951C211yesmaximal, characteristic, complemented
4#19098946C211yesmaximal, characteristic, complemented
5#19098921C211yesmaximal, characteristic, complemented
6#19098908C211yesmaximal, characteristic, complemented
7#19098784C211yesmaximal, characteristic, complemented
8#19098776C211yesmaximal, characteristic, complemented
9#19098762C211yesmaximal, characteristic, complemented
10#19098756C211yesmaximal, characteristic, complemented
11#19098727C211yesmaximal, characteristic, complemented
12#19098714C211yesmaximal, characteristic, complemented
13#19098706C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#447×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×Dic316C2211yescharacteristic, complemented
18C2×#11929613C2211yescharacteristic, complemented
19C2×#11929612C2211yescharacteristic
20C2×#11929612C2211yescharacteristic
21C2×#11929612C2211yescharacteristic, complemented
22C2×#11929609C2211yescharacteristic, complemented
23#14579160C2211yescharacteristic, complemented
24#14579157C2211yescharacteristic
25#14579157C2211yescharacteristic
26#14579154—21no—
27#14579148—21no—
28#14579148C2211yescharacteristic
29#14579148C2211yescharacteristic
30#14579148C2211yescharacteristic, complemented
31#14579142—21no—
32#14579140C2211yescharacteristic
33#14579138—21no—
34#14579132—21no—
35#14579132—21no—
36#14579130—21no—
37#14579130—21no—
38#14579126C2211yescharacteristic, complemented
39D4×Dic79C2211yescharacteristic, complemented
40#14579120C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C2×D8×C79C2211yescharacteristic
54C2×D8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59#11929624—41no—
60#11929624—41no—
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63C2×Dic158C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C22×Dic79—21no—
71C2×C4×D79—21no—
72Dic316—41no—
73#11929613—41no—
74#11929612—41no—
75#11929612—41no—
76#11929612—41no—
77#11929609—41no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C4⋊Dic79D411yescharacteristic
81C4⋊Dic79D411yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94C22⋊Dic79D411yescharacteristic
95C22⋊Dic79D411yescharacteristic
96C4×Dic79—21no—
97C4×Dic79C2311yescharacteristic
98C4×Dic79C2311yescharacteristic
99C24×C79—21no—
100C2×D4×C79—21no—
101C2×D4×C79—21no—
102C2×D4×C79—41no—
103C2×D4×C79—41no—
104C2×D4×C79C2311yescharacteristic
105C2×D4×C79C2311yescharacteristic
106C2×D4×C79C2311yescharacteristic
107C22×C4×C79C2311yescharacteristic
108D8×C79—41no—
109D8×C79—41no—
110C2×C8×C79C2311yescharacteristic
111C2×C8×C79C2311yescharacteristic
112C4⋊C4×C79C2311yescharacteristic
113C22⋊C4×C79—21no—
114C23×C79—21no—
115C23×C79—21no—
116C23×C79—21no—
117C23×C79—42no—
118C23×C79—81no—
119C23×C79—81no—
120C23×C79C2×D411yescharacteristic
121C22×D79—21no—
122D4×C79—21no—
123D4×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—42no—
129D4×C79—81no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2411yescharacteristic
135C22⋊D79—42no—
136C22⋊D79—81no—
137C22⋊D79—81no—
138C22⋊D79—81no—
139C22⋊D79—81no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—81no—
144C2×Dic79C2×D411yescharacteristic
145C2×Dic79C2×D411yescharacteristic
146C2×Dic79C2×D411yescharacteristic
147C2×Dic79C2×D411yescharacteristic
148D316—21no—
149D316—21no—
150C4×D79—42no—
151Dic158—21no—
152Dic158—21no—
153Dic158—21no—
154Dic158—21no—
155Dic158—81no—
156C8×C79—21no—
157C8×C79—21no—
158C79⋊C8—21no—
159C79⋊C8—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—84no—
173C22×C79C22×D411yescharacteristic
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C4×C79—21no—
178C4×C79—41no—
179C4×C79H(5,𝔽2)11yescharacteristic
180C4×C79H(5,𝔽2)11yescharacteristic
181Dic79—21no—
182Dic79—21no—
183Dic79—21no—
184Dic79—21no—
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188C2×C79—41no—
189C2×C79—81no—
190C2×C79—81no—
191C2×C79—81no—
192C2×C79#53511yescharacteristic
193C2×C79#57611yescharacteristic
194C2×C79#57711yescharacteristic
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#459—791no—
208#452—791no—
209#450—791no—
210#449—791no—
211#447D7911yescharacteristic, complemented
212#433—791no—
213C2×#41—791no—
214C22×D4C2×D7911yescharacteristic
215C2×Q16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×SD16—791no—
219C2×SD16—791no—
220C2×D8—791no—
221C2×D8C2×D7911yescharacteristic
222C2×D8C2×D7911yescharacteristic
223C4⋊Q8—791no—
224#127—791no—
225#127—791no—
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—1581no—
235#121—1581no—
236#121C2×D7911yescharacteristic
237#120—1581no—
238#120—1581no—
239C4×Q8—791no—
240C4×D4—791no—
241#117—791no—
242C4⋊C8—791no—
243C4⋊C8—791no—
244#103—791no—
245#103—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102C2×D7911yescharacteristic
251#102C2×D7911yescharacteristic
252C22⋊C8—791no—
253C22⋊C8C2×D7911yescharacteristic
254#97—791no—
255C4×C8—791no—
256C24—21no—
257#41—3161no—
258#41—3161no—
259C2×Q8—791no—
260C2×Q8—791no—
261C2×Q8—1581no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—41no—
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—1581no—
276C22×C4—1581no—
277C22×C4C22×D7911yescharacteristic
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—791no—
310C42—1581no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—1581no—
318C23D4×D7911yescharacteristic
319Q8—6321no—
320Q8—1581no—
321Q8—1581no—
322Q8—1581no—
323Q8—1581no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—81no—
332D4—3162no—
333D4—6321no—
334D4—6321no—
335D4—6321no—
336D4—6321no—
337D4—1581no—
338D4—1581no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—3162no—
343C2×C4—791no—
344C2×C4—791no—
345C2×C4—791no—
346C2×C4—791no—
347C2×C4—6321no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4D4×D7911yescharacteristic
352C2×C4C23×D7911yescharacteristic
353C8—21no—
354C8—21no—
355C8—1581no—
356C8—1581no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—3161no—
371C22—3161no—
372C22—3161no—
373C22C2×D4×D7911yescharacteristic
374C4—21no—
375C4—41no—
376C4—3161no—
377C4—3161no—
378C4—3161no—
379C4—1581no—
380C4—1581no—
381C4—1581no—
382C4—1581no—
383C4#1457920611yescharacteristic
384C4#1457920611yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—6321no—
390C2#1909912811yescharacteristic
391C2#1909936411yescharacteristic
392C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#447×C79C2
socleC22×C79C22×D4
hypercenter#447D79
hypocenterC79#3224
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #19099180C2semidirect
2. #19099130C2semidirect
3. #19098951C2semidirect
4. #19098946C2semidirect
5. #19098921C2semidirect
6. #19098908C2semidirect
7. #19098784C2semidirect
8. #19098776C2semidirect
9. #19098762C2semidirect
10. #19098756C2semidirect
11. #19098727C2semidirect
12. #19098714C2semidirect
13. #19098706C2semidirect
14. #19098621C2semidirect
15. #447×C79C2semidirect
17. C2×Dic316C22semidirect
18. C2×#11929613C22semidirect
21. C2×#11929612C22semidirect
22. C2×#11929609C22semidirect
23. #14579160C22semidirect
30. #14579148C22semidirect
38. #14579126C22semidirect
39. D4×Dic79C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579084C22semidirect
45. #14579083C22semidirect
48. #14579081C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
197. C79#3224semidirect
211. #447D79semidirect