Finite Group Databasebeta

← #23774470

Subgroups — #23774470

Order 10112.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099173C211yesmaximal, characteristic, complemented
2#19099127C211yesmaximal, characteristic
3#19098956C211yesmaximal, characteristic, complemented
4#19098934C211yesmaximal, characteristic, complemented
5#19098926C211yesmaximal, characteristic, complemented
6#19098919C211yesmaximal, characteristic, complemented
7#19098788C211yesmaximal, characteristic, complemented
8#19098787C211yesmaximal, characteristic, complemented
9#19098762C211yesmaximal, characteristic, complemented
10#19098761C211yesmaximal, characteristic, complemented
11#19098725C211yesmaximal, characteristic, complemented
12#19098716C211yesmaximal, characteristic, complemented
13#19098713C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#452×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C2×#11929614C2211yescharacteristic, complemented
18C2×#11929613C2211yescharacteristic
19C2×#11929613C2211yescharacteristic
20C2×#11929612C2211yescharacteristic, complemented
21C2×#11929611C2211yescharacteristic
22C2×#11929611C2211yescharacteristic
23#14579159C2211yescharacteristic, complemented
24#14579157C2211yescharacteristic
25#14579157C2211yescharacteristic
26#14579154—21no—
27#14579154—21no—
28#14579152—21no—
29#14579152C2211yescharacteristic, complemented
30#14579151—21no—
31#14579150C2211yescharacteristic
32#14579150C2211yescharacteristic
33#14579140C2211yescharacteristic
34#14579135—21no—
35#14579135—21no—
36#14579129—21no—
37#14579129—21no—
38Q8×Dic79C2211yescharacteristic, complemented
39#14579126C2211yescharacteristic, complemented
40#14579120C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C2×#41×C79C2211yescharacteristic
53C2×Q16×C79C2211yescharacteristic, complemented
54C2×SD16×C79C2211yescharacteristic, complemented
55C22⋊Q8×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic
59C23×D79—21no—
60C2×Dic158C2311yescharacteristic
61C2×D316—21no—
62C2×D316—41no—
63C2×D316—41no—
64C2×D316C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70#11929614—41no—
71#11929613—41no—
72#11929613—41no—
73#11929612—41no—
74#11929611—41no—
75#11929611—41no—
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C4⋊Dic79—21no—
79C4⋊Dic79—21no—
80C4⋊Dic79D411yescharacteristic
81C4⋊Dic79D411yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79D411yescharacteristic
90C22⋊Dic79D411yescharacteristic
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95C4×Dic79—21no—
96C4×Dic79—21no—
97C4×Dic79C2311yescharacteristic
98C4×Dic79C2311yescharacteristic
99#41×C79—41no—
100#41×C79—41no—
101C2×Q8×C79C2311yescharacteristic
102C2×Q8×C79C2311yescharacteristic
103C2×D4×C79—21no—
104C2×D4×C79C2311yescharacteristic
105C22×C4×C79—21no—
106C22×C4×C79C2311yescharacteristic
107Q16×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×C79C2×D411yescharacteristic
116C22×D79—21no—
117C22×D79—21no—
118C22×D79—42no—
119C22×D79—81no—
120C22×D79—81no—
121Q8×C79—21no—
122Q8×C79—21no—
123Q8×C79—21no—
124Q8×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—42no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—42no—
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2411yescharacteristic
136C22⋊D79—81no—
137C22⋊D79—81no—
138C22⋊D79—81no—
139C22⋊D79—81no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79C2×D411yescharacteristic
143C2×Dic79C2×D411yescharacteristic
144C2×Dic79C2×D411yescharacteristic
145C2×Dic79C2×D411yescharacteristic
146D316—21no—
147D316—21no—
148D316—21no—
149D316—21no—
150D316—42no—
151Dic158—21no—
152Dic158—21no—
153C8×C79—21no—
154C8×C79—21no—
155C79⋊C8—21no—
156C79⋊C8—21no—
157C22×C79—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79C22×D411yescharacteristic
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—84no—
171C4×C79—21no—
172C4×C79—41no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79H(5,𝔽2)11yescharacteristic
176C4×C79H(5,𝔽2)11yescharacteristic
177Dic79—21no—
178Dic79—21no—
179Dic79—21no—
180Dic79—21no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—41no—
184C2×C79—81no—
185C2×C79#53511yescharacteristic
186C2×C79#57711yescharacteristic
187C2×C79#57711yescharacteristic
188D79—81no—
189D79—81no—
190#3222—791nomaximal, Sylow
191C79#322211yescharacteristic, complemented, Sylow
192#541—791no—
193#535—791no—
194#497—791no—
195#492—791no—
196#490—791no—
197#488—791no—
198#464—791no—
199#464—791no—
200#460—791no—
201#460—791no—
202#452—791no—
203#452D7911yescharacteristic, complemented
204#450—791no—
205#450—791no—
206#433—791no—
207C2×#41C2×D7911yescharacteristic
208C22×D4—791no—
209C2×Q16—791no—
210C2×Q16C2×D7911yescharacteristic, complemented
211C2×SD16—791no—
212C2×SD16—791no—
213C2×SD16—791no—
214C2×SD16—791no—
215C2×SD16—791no—
216C2×SD16C2×D7911yescharacteristic, complemented
217C4⋊Q8—791no—
218#127—791no—
219#127—791no—
220#126—1581no—
221#126—1581no—
222#125—791no—
223#125—1581no—
224#125—1581no—
225#124—791no—
226#124—791no—
227C22⋊Q8—791no—
228C22⋊Q8C2×D7911yescharacteristic
229#121—1581no—
230#121—1581no—
231#120—1581no—
232#120—1581no—
233C4×Q8—791no—
234C4×Q8—791no—
235#117—791no—
236C4⋊C8—791no—
237C4⋊C8—791no—
238#103—791no—
239#103C2×D7911yescharacteristic, complemented
240#102—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102C2×D7911yescharacteristic, complemented
246C22⋊C8—791no—
247C22⋊C8C2×D7911yescharacteristic
248#97—791no—
249C4×C8—791no—
250C24—1581no—
251#41—41no—
252#41—41no—
253C2×Q8—791no—
254C2×Q8C22×D7911yescharacteristic
255C2×Q8C22×D7911yescharacteristic
256C2×D4—21no—
257C2×D4—3161no—
258C2×D4—3161no—
259C2×D4—791no—
260C2×D4—791no—
261C2×D4—1581no—
262C2×D4—1581no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4—1581no—
266C2×D4C22×D7911yescharacteristic
267C22×C4—21no—
268C22×C4C22×D7911yescharacteristic
269Q16—41no—
270Q16—3161no—
271SD16—41no—
272SD16—3161no—
273SD16—3161no—
274SD16—3161no—
275SD16—3161no—
276SD16—3161no—
277C2×C8—791no—
278C2×C8—791no—
279C2×C8C22×D7911yescharacteristic
280C2×C8C22×D7911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—791no—
283C4⋊C4—791no—
284C4⋊C4—791no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4—1581no—
288C4⋊C4—1581no—
289C4⋊C4—1581no—
290C4⋊C4—1581no—
291C4⋊C4—1581no—
292C4⋊C4C22×D7911yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—791no—
295C22⋊C4—791no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C42—791no—
302C42—791no—
303C42—1581no—
304C42—1581no—
305C23—21no—
306C23—3162no—
307C23—6321no—
308C23—6321no—
309C23—1581no—
310C23—1581no—
311C23D4×D7911yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—1581no—
317Q8—1581no—
318D4—21no—
319D4—21no—
320D4—42no—
321D4—3162no—
322D4—6321no—
323D4—6321no—
324D4—6321no—
325D4—6321no—
326D4—1581no—
327D4—1581no—
328D4—1581no—
329D4—1581no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—791no—
337C2×C4—791no—
338C2×C4—791no—
339C2×C4—791no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4D4×D7911yescharacteristic
343C2×C4C23×D7911yescharacteristic
344C8—21no—
345C8—21no—
346C8—1581no—
347C8—1581no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—3161no—
355C22—3161no—
356C22—3161no—
357C22—3161no—
358C22—3161no—
359C22—3161no—
360C22—6324no—
361C22C2×D4×D7911yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—3161no—
367C4—3161no—
368C4—1581no—
369C4—1581no—
370C4—1581no—
371C4—1581no—
372C4#1457920611yescharacteristic
373C4#1457920611yescharacteristic
374C2—41no—
375C2—81no—
376C2—6321no—
377C2—6321no—
378C2#1909912811yescharacteristic
379C2#1909937011yescharacteristic
380C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#452×C79C2
socleC22×C79C22×D4
prime radical#19099127C2
hypercenter#452D79
hypocenterC79#3222
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #19099173C2semidirect
3. #19098956C2semidirect
4. #19098934C2semidirect
5. #19098926C2semidirect
6. #19098919C2semidirect
7. #19098788C2semidirect
8. #19098787C2semidirect
9. #19098762C2semidirect
10. #19098761C2semidirect
11. #19098725C2semidirect
12. #19098716C2semidirect
13. #19098713C2semidirect
14. #19098621C2semidirect
15. #452×C79C2semidirect
17. C2×#11929614C22semidirect
20. C2×#11929612C22semidirect
23. #14579159C22semidirect
29. #14579152C22semidirect
38. Q8×Dic79C22semidirect
39. #14579126C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579085C22semidirect
46. #14579082C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
53. C2×Q16×C79C22semidirect
54. C2×SD16×C79C22semidirect
56. #103×C79C22semidirect
57. #102×C79C22semidirect
191. C79#3222semidirect
203. #452D79semidirect
210. C2×Q16C2×D79semidirect
216. C2×SD16C2×D79semidirect
239. #103C2×D79semidirect
245. #102C2×D79semidirect