Finite Group Databasebeta

← #23774468

Subgroups — #23774468

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#19099130C211yesmaximal, characteristic
3#19098954C211yesmaximal, characteristic, complemented
4#19098934C211yesmaximal, characteristic, complemented
5#19098926C211yesmaximal, characteristic, complemented
6#19098916C211yesmaximal, characteristic, complemented
7#19098784C211yesmaximal, characteristic, complemented
8#19098783C211yesmaximal, characteristic, complemented
9#19098762C211yesmaximal, characteristic, complemented
10#19098761C211yesmaximal, characteristic, complemented
11#19098727C211yesmaximal, characteristic, complemented
12#19098723C211yesmaximal, characteristic, complemented
13#19098714C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#450×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×Dic316C2211yescharacteristic, complemented
18C2×#11929614C2211yescharacteristic, complemented
19C2×#11929613C2211yescharacteristic, complemented
20C2×#11929612C2211yescharacteristic
21C2×#11929612C2211yescharacteristic
22C2×#11929611C2211yescharacteristic, complemented
23#14579159C2211yescharacteristic, complemented
24#14579157C2211yescharacteristic
25#14579157C2211yescharacteristic
26#14579154—21no—
27#14579154—21no—
28#14579152—21no—
29#14579152C2211yescharacteristic, complemented
30#14579151—21no—
31#14579148C2211yescharacteristic
32#14579148C2211yescharacteristic
33#14579140C2211yescharacteristic
34#14579132—21no—
35#14579132—21no—
36#14579130—21no—
37#14579130—21no—
38Q8×Dic79C2211yescharacteristic, complemented
39#14579126C2211yescharacteristic, 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×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59#11929624—41no—
60#11929624—41no—
61C2×Dic158C2311yescharacteristic
62C2×Dic158C2311yescharacteristic
63C2×D316C2311yescharacteristic
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C4×D79—21no—
70Dic316—41no—
71#11929614—41no—
72#11929613—41no—
73#11929612—41no—
74#11929612—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⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79D411yescharacteristic
94C22⋊Dic79D411yescharacteristic
95C4×Dic79—21no—
96C4×Dic79—21no—
97C4×Dic79C2311yescharacteristic
98C4×Dic79C2311yescharacteristic
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—
121Q8×C79—21no—
122Q8×C79—21no—
123D4×C79—21no—
124D4×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×C79C2×D411yescharacteristic
133C2×C4×C79C2411yescharacteristic
134C22⋊D79—42no—
135C22⋊D79—81no—
136C22⋊D79—81no—
137C22⋊D79—81no—
138C22⋊D79—81no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79C2×D411yescharacteristic
143C2×Dic79C2×D411yescharacteristic
144C2×Dic79C2×D411yescharacteristic
145C2×Dic79C2×D411yescharacteristic
146D316—21no—
147D316—21no—
148C4×D79—42no—
149Dic158—21no—
150Dic158—21no—
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×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—84no—
167C22×C79C22×D411yescharacteristic
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C4×C79—21no—
172C4×C79—41no—
173C4×C79—41no—
174C4×C79H(5,𝔽2)11yescharacteristic
175C4×C79H(5,𝔽2)11yescharacteristic
176Dic79—21no—
177Dic79—21no—
178Dic79—21no—
179Dic79—21no—
180Dic79—41no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—41no—
184C2×C79—81no—
185C2×C79—81no—
186C2×C79#53511yescharacteristic
187C2×C79#57711yescharacteristic
188C2×C79#57711yescharacteristic
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#452—791no—
204#450—791no—
205#450D7911yescharacteristic, complemented
206#433—791no—
207C2×#41—791no—
208C22×D4C2×D7911yescharacteristic
209C2×Q16—791no—
210C2×Q16—791no—
211C2×SD16—791no—
212C2×SD16—791no—
213C2×SD16—791no—
214C2×SD16—791no—
215C2×SD16C2×D7911yescharacteristic
216C2×SD16C2×D7911yescharacteristic
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#103—791no—
240#102—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244#102C2×D7911yescharacteristic
245#102C2×D7911yescharacteristic
246C22⋊C8—791no—
247C22⋊C8C2×D7911yescharacteristic
248#97—791no—
249C4×C8—791no—
250C24—21no—
251#41—3161no—
252#41—3161no—
253C2×Q8—791no—
254C2×Q8—791no—
255C2×Q8C22×D7911yescharacteristic
256C2×D4—21no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—791no—
260C2×D4—1581no—
261C2×D4—1581no—
262C2×D4—1581no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4C22×D7911yescharacteristic
266C2×D4C22×D7911yescharacteristic
267C22×C4—1581no—
268C22×C4C22×D7911yescharacteristic
269Q16—3161no—
270Q16—3161no—
271SD16—41no—
272SD16—41no—
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—21no—
307C23—42no—
308C23—81no—
309C23—81no—
310C23—1581no—
311C23D4×D7911yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—1581no—
315Q8—1581no—
316Q8—1581no—
317Q8—1581no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—42no—
323D4—3162no—
324D4—6321no—
325D4—6321no—
326D4—6321no—
327D4—6321no—
328D4—1581no—
329D4—1581no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—3162no—
335C2×C4—791no—
336C2×C4—791no—
337C2×C4—791no—
338C2×C4—791no—
339C2×C4—1581no—
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—41no—
355C22—41no—
356C22—41no—
357C22—84no—
358C22—3161no—
359C22—3161no—
360C22—3161no—
361C22C2×D4×D7911yescharacteristic
362C4—21no—
363C4—41no—
364C4—41no—
365C4—3161no—
366C4—3161no—
367C4—3161no—
368C4—1581no—
369C4—1581no—
370C4—1581no—
371C4—1581no—
372C4#1457920611yescharacteristic
373C4#1457920611yescharacteristic
374C2—41no—
375C2—81no—
376C2—81no—
377C2—6321no—
378C2#1909912811yescharacteristic
379C2#1909936911yescharacteristic
380C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#450×C79C2
socleC22×C79C22×D4
prime radical#19099130C2
hypercenter#450D79
hypocenterC79#3222
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. #19099173C2semidirect
3. #19098954C2semidirect
4. #19098934C2semidirect
5. #19098926C2semidirect
6. #19098916C2semidirect
7. #19098784C2semidirect
8. #19098783C2semidirect
9. #19098762C2semidirect
10. #19098761C2semidirect
11. #19098727C2semidirect
12. #19098723C2semidirect
13. #19098714C2semidirect
14. #19098621C2semidirect
15. #450×C79C2semidirect
17. C2×Dic316C22semidirect
18. C2×#11929614C22semidirect
19. C2×#11929613C22semidirect
22. C2×#11929611C22semidirect
23. #14579159C22semidirect
29. #14579152C22semidirect
38. Q8×Dic79C22semidirect
39. #14579126C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579084C22semidirect
45. #14579083C22semidirect
48. #14579081C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
191. C79#3222semidirect
205. #450D79semidirect