Finite Group Databasebeta

← #23775483

Subgroups — #23775483

Order 10112.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099270C211yesmaximal, characteristic, complemented
2#19099209C211yesmaximal, characteristic
3#19098923C211yesmaximal, characteristic, complemented
4#19098899C211yesmaximal, characteristic, complemented
5#19098877C211yesmaximal, characteristic, complemented
6#19098844C211yesmaximal, characteristic, complemented
7#19098809C211yesmaximal, characteristic, complemented
8#19098804C211yesmaximal, characteristic, complemented
9#19098786C211yesmaximal, characteristic, complemented
10#19098727C211yesmaximal, characteristic, complemented
11#19098716C211yesmaximal, characteristic, complemented
12#19098665C211yesmaximal, characteristic, complemented
13#19098565C211yesmaximal, characteristic, complemented
14C2×#14579083C211yesmaximal, characteristic, complemented
15#435×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×Dic316C2211yescharacteristic, complemented
19C2×#11929613C2211yescharacteristic
20C2×#11929613C2211yescharacteristic
21#14579161C2211yescharacteristic, complemented
22#14579152—21no—
23#14579149C2211yescharacteristic
24#14579146—21no—
25#14579140C2211yescharacteristic
26#14579140C2211yescharacteristic
27#14579140C2211yescharacteristic, complemented
28#14579138—21no—
29#14579138—21no—
30#14579135C2211yescharacteristic
31#14579134—21no—
32#14579129—21no—
33C4×Dic158C2211yescharacteristic, complemented
34C4×D316C2211yescharacteristic
35D4×Dic79—21no—
36C2×C4⋊Dic79C2211yescharacteristic
37C2×C4⋊Dic79C2211yescharacteristic, complemented
38C22⋊C4×D79—21no—
39#14579095C2211yescharacteristic, complemented
40#14579095C2211yescharacteristic, complemented
41#14579095C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579086C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic
51#14579083C2211yescharacteristic
52C2×M16×C79C2211yescharacteristic, complemented
53C22×C8×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic
55C4⋊C8×C79C2211yescharacteristic, complemented
56C22⋊C8×C79C2211yescharacteristic
57C22⋊C8×C79C2211yescharacteristic, complemented
58#97×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—22no—
61#11929624—41no—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64C2×Dic158C2311yescharacteristic
65C2×D316—22no—
66C2×D316—21no—
67C2×D316—41no—
68C2×D316C2311yescharacteristic
69C2×D316C2311yescharacteristic
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C22×Dic79—21no—
73C22×Dic79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76Dic316—41no—
77#11929613—22no—
78#11929613—41no—
79C4⋊Dic79—21no—
80C4⋊Dic79—21no—
81C4⋊Dic79—21no—
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97C4×Dic79—21no—
98C2×D4×C79D411yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101M16×C79—41no—
102C2×C8×C79—41no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C22⋊C4×C79D411yescharacteristic
110C42×C79C2311yescharacteristic
111C23×C79C2×D411yescharacteristic
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79—81no—
118D4×C79—22no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2411yescharacteristic
128C22⋊D79—42no—
129C22⋊D79—81no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—81no—
137C2×Dic79—81no—
138D316—21no—
139D316—21no—
140D316—21no—
141D316—42no—
142D316#4112yes—
143C4×D79—42no—
144C4×D79—81no—
145Dic158—21no—
146Dic158—21no—
147Dic158—21no—
148Dic158—21no—
149Dic158—81no—
150C8×C79—21no—
151C8×C79—21no—
152C8×C79—21no—
153C8×C79—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—21no—
159C22×C79#13712yes—
160C22×C79C22×D411yescharacteristic
161C2×D79—22no—
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—84no—
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—21no—
171C4×C79—21no—
172C4×C79C2×#4111yescharacteristic
173C4×C79H(5,𝔽2)11yescharacteristic
174Dic79—41no—
175Dic79—41no—
176Dic79—41no—
177Dic79—41no—
178Dic79—41no—
179Dic79—41no—
180C2×C79—22no—
181C2×C79—41no—
182C2×C79#54611yescharacteristic
183C2×C79C2×#13711yescharacteristic
184C2×C79#57611yescharacteristic
185D79—42no—
186D79—81no—
187#3314—791nomaximal, Sylow
188C79#331411yescharacteristic, complemented, Sylow
189#554—791no—
190#546—791no—
191#489—791no—
192#484—791no—
193#480—791no—
194#474—791no—
195#468—791no—
196#467—791no—
197#464—791no—
198#452—791no—
199#450—791no—
200#440—791no—
201#435D7911yescharacteristic, complemented
202#417—791no—
203C2×#102—791no—
204C2×#41—791no—
205C22×D4—791no—
206C2×Q16—791no—
207C2×SD16—791no—
208C2×SD16—791no—
209C2×M16C2×D7911yescharacteristic, complemented
210C22×C8C2×D7911yescharacteristic
211C4⋊Q8—791no—
212#125—1581no—
213#124—791no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8—791no—
218C22⋊Q8—1581no—
219C22⋊Q8—1581no—
220#121—791no—
221#121—1581no—
222#120—1581no—
223C4×Q8—791no—
224C4×D4—791no—
225C4×D4—1581no—
226C4×D4C2×D7911yescharacteristic
227C2×C4⋊C4—791no—
228C2×C4⋊C4—791no—
229C2×C22⋊C4—1581no—
230#107—791no—
231#107—791no—
232#107—791no—
233C4⋊C8C2×D7911yescharacteristic, complemented
234#103—791no—
235#103—791no—
236#103—791no—
237#103—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244C22⋊C8C2×D7911yescharacteristic
245C22⋊C8C2×D7911yescharacteristic, complemented
246#97C2×D7911yescharacteristic, complemented
247C24—1581no—
248#41—3161no—
249#41—1582no—
250C2×Q8—791no—
251C2×Q8—791no—
252C2×Q8—1581no—
253C2×D4—3161no—
254C2×D4—791no—
255C2×D4—791no—
256C2×D4—1582no—
257C2×D4—1581no—
258C2×D4—1581no—
259C2×D4—1581no—
260C2×D4D31611yescharacteristic
261C22×C4—1581no—
262C22×C4—1581no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4C22×D7911yescharacteristic
266C22×C4C22×D7911yescharacteristic
267Q16—3161no—
268SD16—3161no—
269SD16—1582no—
270M16—41no—
271C2×C8—41no—
272C2×C8C22×D7911yescharacteristic
273C2×C8C22×D7911yescharacteristic
274C2×C8C22×D7911yescharacteristic
275C2×C8C22×D7911yescharacteristic
276C4⋊C4—791no—
277C4⋊C4—791no—
278C4⋊C4—791no—
279C4⋊C4—791no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4D31611yescharacteristic
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4D31611yescharacteristic
296C22⋊C4D31611yescharacteristic
297C42—1581no—
298C42C22×D7911yescharacteristic
299C23—3162no—
300C23—3162no—
301C23—6321no—
302C23—1581no—
303C23—1581no—
304C23C2×D31611yescharacteristic
305C23C2×D31611yescharacteristic
306Q8—6321no—
307Q8—1581no—
308Q8—1581no—
309Q8—1581no—
310Q8—1581no—
311D4—22no—
312D4—3162no—
313D4—3162no—
314D4—792no—
315D4—6321no—
316D4—1581no—
317D4—1581no—
318D4—1581no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—3162no—
324C2×C4—6321no—
325C2×C4—6321no—
326C2×C4—6321no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4C2×D31611yescharacteristic
334C2×C4C2×D31611yescharacteristic
335C2×C4C2×D31611yescharacteristic
336C2×C4C2×D31611yescharacteristic
337C2×C4C23×D7911yescharacteristic
338C8—21no—
339C8—21no—
340C8—21no—
341C8—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—3161no—
348C22—3161no—
349C22—3161no—
350C22—3161no—
351C22—3161no—
352C22—6324no—
353C22—1582no—
354C22#1457919412yes—
355C22C22×D31611yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—3161no—
361C4—3161no—
362C4—3161no—
363C4—3161no—
364C4—3161no—
365C4—3161no—
366C4#41×D7911yescharacteristic
367C4#1457920611yescharacteristic
368C2—22no—
369C2—41no—
370C2—3162no—
371C2—6321no—
372C2#1909920811yescharacteristic
373C2C2×#1457919411yescharacteristic
374C2#1909936811yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#435×C79C2
socleC22×C79C22×D4
prime radical#19099209C2
hypercenter#435D79
hypocenterC79#3314
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #19099270C2semidirect
3. #19098923C2semidirect
4. #19098899C2semidirect
5. #19098877C2semidirect
6. #19098844C2semidirect
7. #19098809C2semidirect
8. #19098804C2semidirect
9. #19098786C2semidirect
10. #19098727C2semidirect
11. #19098716C2semidirect
12. #19098665C2semidirect
13. #19098565C2semidirect
14. C2×#14579083C2semidirect
15. #435×C79C2semidirect
18. C2×Dic316C22semidirect
21. #14579161C22semidirect
27. #14579140C22semidirect
33. C4×Dic158C22semidirect
37. C2×C4⋊Dic79C22semidirect
39. #14579095C22semidirect
40. #14579095C22semidirect
41. #14579095C22semidirect
42. #14579086C22semidirect
43. #14579086C22semidirect
44. #14579086C22semidirect
45. #14579086C22semidirect
52. C2×M16×C79C22semidirect
55. C4⋊C8×C79C22semidirect
57. C22⋊C8×C79C22semidirect
58. #97×C79C22semidirect
188. C79#3314semidirect
201. #435D79semidirect
209. C2×M16C2×D79semidirect
233. C4⋊C8C2×D79semidirect
245. C22⋊C8C2×D79semidirect
246. #97C2×D79semidirect