Finite Group Databasebeta

← #23775475

Subgroups — #23775475

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#19099209C211yesmaximal, characteristic
2#19098925C211yesmaximal, characteristic, complemented
3#19098898C211yesmaximal, characteristic, complemented
4#19098876C211yesmaximal, characteristic, complemented
5#19098840C211yesmaximal, characteristic, complemented
6#19098811C211yesmaximal, characteristic, complemented
7#19098802C211yesmaximal, characteristic, complemented
8#19098785C211yesmaximal, characteristic, complemented
9#19098723C211yesmaximal, characteristic, complemented
10#19098713C211yesmaximal, characteristic, complemented
11#19098661C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098562C211yesmaximal, characteristic, complemented
14C2×#14579081C211yesmaximal, characteristic, complemented
15#554×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×#11929614C2211yescharacteristic, complemented
19C2×#11929611C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
21C2×#11929608C2211yescharacteristic, complemented
22C22×C79⋊C8C2211yescharacteristic
23#14579149C2211yescharacteristic
24#14579146—21no—
25#14579140C2211yescharacteristic
26#14579135C2211yescharacteristic
27#14579134—21no—
28#14579129—21no—
29C4×D316C2211yescharacteristic
30C22⋊C4×D79—21no—
31#14579094C2211yescharacteristic, complemented
32#14579094C2211yescharacteristic, complemented
33#14579094C2211yescharacteristic, complemented
34C4⋊(C79⋊C8)C2211yescharacteristic, complemented
35#14579085C2211yescharacteristic, complemented
36#14579084C2211yescharacteristic, complemented
37#14579084C2211yescharacteristic, complemented
38#14579084C2211yescharacteristic, complemented
39#14579081C2211yescharacteristic
40#14579081C2211yescharacteristic
41#14579081C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic, complemented
47#14579072C2211yescharacteristic, complemented
48C4⋊Q8×C79C2211yescharacteristic, complemented
49#125×C79—21no—
50C22⋊Q8×C79—21no—
51C22⋊Q8×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53C22⋊Q8×C79C2211yescharacteristic, complemented
54C4×Q8×C79C2211yescharacteristic, complemented
55C4×D4×C79—21no—
56C4×D4×C79C2211yescharacteristic
57C2×C4⋊C4×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—22no—
61#11929624—41no—
62C2×Dic158C2311yescharacteristic
63C2×D316—22no—
64C2×D316—21no—
65C2×D316—41no—
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72#11929614—41no—
73#11929611—22no—
74#11929611—41no—
75#11929608—41no—
76C2×C79⋊C8—41no—
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83C22⋊Dic79—21no—
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88C2×Q8×C79—21no—
89C2×Q8×C79C2311yescharacteristic
90C2×D4×C79D411yescharacteristic
91C22×C4×C79—21no—
92C22×C4×C79—21no—
93C22×C4×C79C2311yescharacteristic
94C22×C4×C79C2311yescharacteristic
95C4⋊C4×C79—21no—
96C4⋊C4×C79—21no—
97C4⋊C4×C79—21no—
98C4⋊C4×C79—21no—
99C4⋊C4×C79—21no—
100C4⋊C4×C79—21no—
101C4⋊C4×C79D411yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79C2×D411yescharacteristic
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79—81no—
118Q8×C79—21no—
119Q8×C79—21no—
120Q8×C79—81no—
121D4×C79—22no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—81no—
131C2×C4×C79—81no—
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2411yescharacteristic
137C22⋊D79—42no—
138C22⋊D79—81no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141D316—21no—
142D316—21no—
143D316—21no—
144D316—42no—
145D316#4112yes—
146C4×D79—42no—
147C4×D79—81no—
148Dic158—21no—
149Dic158—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C79⋊C8—21no—
153C79⋊C8—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×C79—41no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79—41no—
176C4×C79C2×#4111yescharacteristic
177C4×C79H(5,𝔽2)11yescharacteristic
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#554D7911yescharacteristic, complemented
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#435—791no—
202#417—791no—
203C2×#102—791no—
204C2×#41—791no—
205C22×D4—791no—
206C2×Q16—791no—
207C2×SD16—791no—
208C2×SD16—791no—
209C2×M16—791no—
210C22×C8—791no—
211C4⋊Q8C2×D7911yescharacteristic, complemented
212#125—21no—
213#124—791no—
214#123—1581no—
215C22⋊Q8—21no—
216C22⋊Q8—21no—
217C22⋊Q8—791no—
218C22⋊Q8C2×D7911yescharacteristic
219C22⋊Q8C2×D7911yescharacteristic, complemented
220#121—791no—
221#121—1581no—
222#120—1581no—
223C4×Q8C2×D7911yescharacteristic, complemented
224C4×D4—21no—
225C4×D4—791no—
226C4×D4C2×D7911yescharacteristic
227C2×C4⋊C4C2×D7911yescharacteristic
228C2×C4⋊C4C2×D7911yescharacteristic, complemented
229C2×C22⋊C4—1581no—
230#107—791no—
231#107—791no—
232#107—791no—
233C4⋊C8—791no—
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⋊C8—791no—
245C22⋊C8—791no—
246#97—791no—
247C24—1581no—
248#41—3161no—
249#41—1582no—
250C2×Q8—21no—
251C2×Q8—791no—
252C2×Q8C22×D7911yescharacteristic
253C2×D4—3161no—
254C2×D4—791no—
255C2×D4—791no—
256C2×D4—1582no—
257C2×D4—1581no—
258C2×D4—1581no—
259C2×D4—1581no—
260C2×D4C22⋊D7911yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4C22×D7911yescharacteristic
266C22×C4C22×D7911yescharacteristic
267Q16—3161no—
268SD16—3161no—
269SD16—1582no—
270M16—3161no—
271C2×C8—3161no—
272C2×C8—791no—
273C2×C8—791no—
274C2×C8—791no—
275C2×C8—791no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—791no—
283C4⋊C4—1581no—
284C4⋊C4C22⋊D7911yescharacteristic
285C4⋊C4C22×D7911yescharacteristic
286C4⋊C4C22×D7911yescharacteristic
287C4⋊C4C22×D7911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4C22⋊D7911yescharacteristic
296C22⋊C4C22⋊D7911yescharacteristic
297C42—21no—
298C42C22×D7911yescharacteristic
299C23—3162no—
300C23—3162no—
301C23—6321no—
302C23—1581no—
303C23—1581no—
304C23C2×C22⋊D7911yescharacteristic
305C23C2×C22⋊D7911yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—81no—
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—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—3162no—
330C2×C4—6321no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4C2×C22⋊D7911yescharacteristic
334C2×C4C2×C22⋊D7911yescharacteristic
335C2×C4C2×C22⋊D7911yescharacteristic
336C2×C4C2×C22⋊D7911yescharacteristic
337C2×C4C23×D7911yescharacteristic
338C8—1581no—
339C8—1581no—
340C8—1581no—
341C8—1581no—
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#1457919212yes—
355C22C22×C22⋊D7911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—3161no—
365C4—3161no—
366C4#41×D7911yescharacteristic
367C4#1457920711yescharacteristic
368C2—22no—
369C2—41no—
370C2—3162no—
371C2—6321no—
372C2#1909920111yescharacteristic
373C2C2×#1457919211yescharacteristic
374C2#1909936611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#554×C79C2
socleC22×C79C22×D4
prime radical#19099209C2
hypercenter#554D79
hypocenterC79#3314
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #19098925C2semidirect
3. #19098898C2semidirect
4. #19098876C2semidirect
5. #19098840C2semidirect
6. #19098811C2semidirect
7. #19098802C2semidirect
8. #19098785C2semidirect
9. #19098723C2semidirect
10. #19098713C2semidirect
11. #19098661C2semidirect
12. #19098635C2semidirect
13. #19098562C2semidirect
14. C2×#14579081C2semidirect
15. #554×C79C2semidirect
18. C2×#11929614C22semidirect
21. C2×#11929608C22semidirect
31. #14579094C22semidirect
32. #14579094C22semidirect
33. #14579094C22semidirect
34. C4⋊(C79⋊C8)C22semidirect
35. #14579085C22semidirect
36. #14579084C22semidirect
37. #14579084C22semidirect
38. #14579084C22semidirect
46. C22⋊(C79⋊C8)C22semidirect
47. #14579072C22semidirect
48. C4⋊Q8×C79C22semidirect
53. C22⋊Q8×C79C22semidirect
54. C4×Q8×C79C22semidirect
58. C2×C4⋊C4×C79C22semidirect
188. C79#3314semidirect
189. #554D79semidirect
211. C4⋊Q8C2×D79semidirect
219. C22⋊Q8C2×D79semidirect
223. C4×Q8C2×D79semidirect
228. C2×C4⋊C4C2×D79semidirect