Finite Group Databasebeta

← #23774254

Subgroups — #23774254

Order 10112.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099141C211yesmaximal, characteristic, complemented
2#19099127C211yesmaximal, characteristic, complemented
3#19098905C211yesmaximal, characteristic, complemented
4#19098888C211yesmaximal, characteristic, complemented
5#19098882C211yesmaximal, characteristic, complemented
6#19098877C211yesmaximal, characteristic, complemented
7#19098816C211yesmaximal, characteristic, complemented
8#19098809C211yesmaximal, characteristic, complemented
9#19098799C211yesmaximal, characteristic, complemented
10#19098792C211yesmaximal, characteristic, complemented
11#19098716C211yesmaximal, characteristic, complemented
12#19098710C211yesmaximal, characteristic, complemented
13#19098710C211yesmaximal, characteristic, complemented
14#19098699C211yesmaximal, characteristic, complemented
15#408×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic, complemented
17C22×D316C2211yescharacteristic
18C2×#11929613C2211yescharacteristic
19C2×#11929613C2211yescharacteristic
20C2×D632C2211yescharacteristic
21C2×D632C2211yescharacteristic
22#14579157—21no—
23#14579150—21no—
24#14579140C2211yescharacteristic
25#14579140C2211yescharacteristic, complemented
26#14579137—21no—
27#14579135C2211yescharacteristic
28#14579135C2211yescharacteristic
29#14579135C2211yescharacteristic
30#14579135C2211yescharacteristic
31#14579135C2211yescharacteristic
32#14579135C2211yescharacteristic, complemented
33#14579133—21no—
34#14579133—21no—
35#14579132—21no—
36#14579129—21no—
37#14579129—21no—
38#14579120C2211yescharacteristic
39C2×C4⋊Dic79C2211yescharacteristic, complemented
40#14579095C2211yescharacteristic, complemented
41#14579095C2211yescharacteristic, complemented
42#14579093C2211yescharacteristic, complemented
43#14579093C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579086C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic
47#14579083C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic, complemented
51#14579083C2211yescharacteristic, complemented
52C2×#41×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic, complemented
54C22×C8×C79C2211yescharacteristic, complemented
55C22⋊C8×C79C2211yescharacteristic
56C22⋊C8×C79C2211yescharacteristic
57C22⋊C8×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—41no—
61#11929624—41no—
62C2×Dic158C2311yescharacteristic
63C2×D316—21no—
64C2×D316—41no—
65C2×D316—41no—
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×D316C2311yescharacteristic
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79—21no—
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75C2×C22⋊D79—21no—
76C22×Dic79—21no—
77C2×C4×D79—21no—
78#11929613—41no—
79#11929613—41no—
80D632—41no—
81D632—41no—
82C4⋊Dic79—21no—
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86C4⋊Dic79C2311yescharacteristic
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98C4×Dic79—21no—
99#41×C79—41no—
100#41×C79—41no—
101C2×Q8×C79D411yescharacteristic
102C2×D4×C79D411yescharacteristic
103C2×D4×C79D411yescharacteristic
104C2×D4×C79D411yescharacteristic
105C22×C4×C79C2311yescharacteristic
106C22×C4×C79C2311yescharacteristic
107C22×C4×C79C2311yescharacteristic
108M16×C79—41no—
109C2×C8×C79—41no—
110C2×C8×C79C2311yescharacteristic
111C2×C8×C79C2311yescharacteristic
112C2×C8×C79C2311yescharacteristic
113C2×C8×C79C2311yescharacteristic
114C23×C79C2×D411yescharacteristic
115C23×C79C2×D411yescharacteristic
116C23×C79C2×D411yescharacteristic
117C22×D79—21no—
118C22×D79—21no—
119C22×D79—21no—
120C22×D79—42no—
121C22×D79—81no—
122C22×D79—81no—
123Q8×C79—41no—
124D4×C79—41no—
125D4×C79—41no—
126D4×C79—41no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2411yescharacteristic
137C22⋊D79—42no—
138C22⋊D79—81no—
139C22⋊D79—81no—
140C22⋊D79—81no—
141C22⋊D79—81no—
142C22⋊D79—81no—
143C22⋊D79—81no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—81no—
150D316—21no—
151D316—21no—
152D316—21no—
153D316—21no—
154D316—21no—
155D316—21no—
156D316—42no—
157C4×D79—42no—
158Dic158—21no—
159Dic158—21no—
160C8×C79—21no—
161C8×C79—21no—
162C8×C79—21no—
163C8×C79—21no—
164C22×C79—21no—
165C22×C79—21no—
166C22×C79—21no—
167C22×C79—21no—
168C22×C79—21no—
169C22×C79—21no—
170C22×C79—21no—
171C22×C79—21no—
172C22×C79—21no—
173C22×C79C22×D411yescharacteristic
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C2×D79—41no—
178C2×D79—41no—
179C2×D79—41no—
180C2×D79—41no—
181C2×D79—41no—
182C2×D79—41no—
183C2×D79—84no—
184C4×C79—21no—
185C4×C79—21no—
186C4×C79—21no—
187C4×C79H(5,𝔽2)11yescharacteristic
188C4×C79H(5,𝔽2)11yescharacteristic
189Dic79—41no—
190Dic79—41no—
191Dic79—41no—
192Dic79—41no—
193Dic79—41no—
194C2×C79—41no—
195C2×C79—41no—
196C2×C79—41no—
197C2×C79#53411yescharacteristic
198C2×C79#57611yescharacteristic
199C2×C79#57711yescharacteristic
200D79—81no—
201D79—81no—
202D79—81no—
203#3198—791nomaximal, Sylow
204C79#319811yescharacteristic, complemented, Sylow
205#537—791no—
206#535—791no—
207#485—791no—
208#482—791no—
209#481—791no—
210#480—791no—
211#469—791no—
212#468—791no—
213#466—791no—
214#465—791no—
215#450—791no—
216#449—791no—
217#449—791no—
218#447—791no—
219#408D7911yescharacteristic, complemented
220C2×#41—791no—
221C2×#41C2×D7911yescharacteristic
222C22×D4—791no—
223C2×SD16—791no—
224C2×SD16—791no—
225C2×D8—791no—
226C2×D8—791no—
227C2×M16C2×D7911yescharacteristic, complemented
228C22×C8C2×D7911yescharacteristic, complemented
229#127—1581no—
230#124—1581no—
231C22⋊Q8—791no—
232C22⋊Q8—791no—
233C22⋊Q8—1581no—
234#121—791no—
235#121—791no—
236#121—791no—
237#121—791no—
238#121—791no—
239#121—791no—
240#121—1581no—
241#121—1581no—
242#121—1581no—
243#120—1581no—
244#120—1581no—
245#117—791no—
246C2×C4⋊C4—791no—
247#107—791no—
248#107—791no—
249#106—791no—
250#106—791no—
251#103—791no—
252#103—791no—
253#102—791no—
254#102—791no—
255#102—791no—
256#102—791no—
257#102—791no—
258#102—791no—
259C22⋊C8C2×D7911yescharacteristic
260C22⋊C8C2×D7911yescharacteristic
261C22⋊C8C2×D7911yescharacteristic, complemented
262C22⋊C8C2×D7911yescharacteristic, complemented
263C24—1581no—
264#41—41no—
265#41—41no—
266#41—3161no—
267#41—3161no—
268C2×Q8—791no—
269C2×Q8D31611yescharacteristic
270C2×D4—3161no—
271C2×D4—3161no—
272C2×D4—791no—
273C2×D4—791no—
274C2×D4—791no—
275C2×D4—1581no—
276C2×D4—1581no—
277C2×D4—1581no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4—1581no—
281C2×D4—1581no—
282C2×D4—1581no—
283C2×D4D31611yescharacteristic
284C2×D4D31611yescharacteristic
285C2×D4D31611yescharacteristic
286C22×C4—1581no—
287C22×C4—1581no—
288C22×C4C22×D7911yescharacteristic
289C22×C4C22×D7911yescharacteristic
290C22×C4C22×D7911yescharacteristic
291SD16—3161no—
292SD16—3161no—
293D8—3161no—
294D8—3161no—
295M16—41no—
296C2×C8—41no—
297C2×C8C22×D7911yescharacteristic
298C2×C8C22×D7911yescharacteristic
299C2×C8C22×D7911yescharacteristic
300C2×C8C22×D7911yescharacteristic
301C4⋊C4—791no—
302C4⋊C4—791no—
303C4⋊C4—791no—
304C4⋊C4—791no—
305C4⋊C4—1581no—
306C4⋊C4—1581no—
307C4⋊C4—1581no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C22⋊C4—1581no—
311C22⋊C4—1581no—
312C22⋊C4—1581no—
313C22⋊C4—1581no—
314C22⋊C4—1581no—
315C22⋊C4—1581no—
316C22⋊C4—1581no—
317C42—1581no—
318C23—3162no—
319C23—6321no—
320C23—6321no—
321C23—1581no—
322C23—1581no—
323C23—1581no—
324C23C2×D31611yescharacteristic
325C23C2×D31611yescharacteristic
326C23C2×D31611yescharacteristic
327Q8—41no—
328Q8—1581no—
329Q8—1581no—
330D4—41no—
331D4—41no—
332D4—41no—
333D4—3162no—
334D4—3162no—
335D4—6321no—
336D4—6321no—
337D4—6321no—
338D4—6321no—
339D4—6321no—
340D4—6321no—
341D4—1581no—
342D4—1581no—
343D4—1581no—
344D4—1581no—
345D4—1581no—
346D4—1581no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—3162no—
354C2×C4—6321no—
355C2×C4—1581no—
356C2×C4—1581no—
357C2×C4—1581no—
358C2×C4—1581no—
359C2×C4—1581no—
360C2×C4C2×D31611yescharacteristic
361C2×C4C2×D31611yescharacteristic
362C2×C4C2×D31611yescharacteristic
363C2×C4C23×D7911yescharacteristic
364C8—21no—
365C8—21no—
366C8—21no—
367C8—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—3161no—
378C22—3161no—
379C22—3161no—
380C22—3161no—
381C22—3161no—
382C22—3161no—
383C22—3161no—
384C22—3161no—
385C22—3161no—
386C22—6324no—
387C22C22×D31611yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—3161no—
392C4—3161no—
393C4—3161no—
394C4—3161no—
395C4—3161no—
396C4#1457920611yescharacteristic
397C4#1457920611yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—6321no—
402C2—6321no—
403C2—6321no—
404C2#1909912511yescharacteristic
405C2#1909936811yescharacteristic
406C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#408×C79C2
socleC22×C79C22×D4
hypercenter#408D79
hypocenterC79#3198
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #19099141C2semidirect
2. #19099127C2semidirect
3. #19098905C2semidirect
4. #19098888C2semidirect
5. #19098882C2semidirect
6. #19098877C2semidirect
7. #19098816C2semidirect
8. #19098809C2semidirect
9. #19098799C2semidirect
10. #19098792C2semidirect
11. #19098716C2semidirect
12. #19098710C2semidirect
13. #19098710C2semidirect
14. #19098699C2semidirect
15. #408×C79C2semidirect
16. C2×#11929624C22semidirect
25. #14579140C22semidirect
32. #14579135C22semidirect
39. C2×C4⋊Dic79C22semidirect
40. #14579095C22semidirect
41. #14579095C22semidirect
42. #14579093C22semidirect
43. #14579093C22semidirect
44. #14579086C22semidirect
45. #14579086C22semidirect
50. #14579083C22semidirect
51. #14579083C22semidirect
53. C2×M16×C79C22semidirect
54. C22×C8×C79C22semidirect
57. C22⋊C8×C79C22semidirect
58. C22⋊C8×C79C22semidirect
204. C79#3198semidirect
219. #408D79semidirect
227. C2×M16C2×D79semidirect
228. C22×C8C2×D79semidirect
261. C22⋊C8C2×D79semidirect
262. C22⋊C8C2×D79semidirect