Finite Group Databasebeta

← #23775557

Subgroups — #23775557

Order 10112.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099276C211yesmaximal, characteristic, complemented
2#19099207C211yesmaximal, characteristic, complemented
3#19098921C211yesmaximal, characteristic, complemented
4#19098904C211yesmaximal, characteristic, complemented
5#19098885C211yesmaximal, characteristic, complemented
6#19098841C211yesmaximal, characteristic, complemented
7#19098809C211yesmaximal, characteristic, complemented
8#19098798C211yesmaximal, characteristic, complemented
9#19098777C211yesmaximal, characteristic, complemented
10#19098709C211yesmaximal, characteristic, complemented
11#19098697C211yesmaximal, characteristic, complemented
12#19098672C211yesmaximal, characteristic, complemented
13#19098632C211yesmaximal, characteristic, complemented
14#19098556C211yesmaximal, characteristic, complemented
15#418×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×#11929613C2211yescharacteristic, complemented
18C2×#11929609C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×C8×D79C2211yescharacteristic, complemented
21#14579160C2211yescharacteristic, complemented
22#14579149—21no—
23#14579148C2211yescharacteristic
24#14579147—21no—
25#14579142—21no—
26#14579140C2211yescharacteristic
27#14579136C2211yescharacteristic, complemented
28#14579135C2211yescharacteristic
29#14579134—21no—
30#14579133—21no—
31#14579132C2211yescharacteristic
32#14579130—21no—
33D4×Dic79C2211yescharacteristic
34#14579123C2211yescharacteristic, complemented
35C4×C22⋊D79C2211yescharacteristic
36#14579119C2211yescharacteristic, complemented
37#14579118—21no—
38C2×C22⋊Dic79—21no—
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51#14579071C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic
54#117×C79C2211yescharacteristic
55#102×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59#11929623—22no—
60#11929623—41no—
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63C2×D316—21no—
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79D411yescharacteristic
69C22×Dic79—21no—
70C22×Dic79—21no—
71C2×C4×D79—21no—
72C2×C4×D79C2311yescharacteristic
73#11929613—41no—
74#11929609—22no—
75#11929609—41no—
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C8×D79—41no—
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4D411yescharacteristic
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79D411yescharacteristic
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4D411yescharacteristic
95C4×Dic79—21no—
96C4×Dic79C2311yescharacteristic
97C24×C79—21no—
98C2×D4×C79—22no—
99C2×D4×C79—21no—
100C2×D4×C79—41no—
101C2×D4×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104M16×C79—41no—
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C42×C79—21no—
111C23×C79—21no—
112C23×C79—21no—
113C23×C79—42no—
114C23×C79—42no—
115C23×C79—81no—
116C23×C79C2×D411yescharacteristic
117C22×D79—21no—
118C22×D79C2×D411yescharacteristic
119D4×C79—21no—
120D4×C79—21no—
121D4×C79—21no—
122D4×C79—42no—
123D4×C79#4112yes—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—41no—
131C22⋊D79—42no—
132C22⋊D79—81no—
133C22⋊D79—81no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—42no—
138C2×Dic79—81no—
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141C2×Dic79C2×D411yescharacteristic
142D316—21no—
143D316—21no—
144D316—81no—
145C4×D79—21no—
146C4×D79—21no—
147C4×D79—42no—
148Dic158—21no—
149Dic158—21no—
150Dic158—81no—
151C8×C79—21no—
152C8×C79—21no—
153C79⋊C8—21no—
154C79⋊C8—21no—
155C22×C79—22no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—21no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—84no—
165C22×C79C22×D411yescharacteristic
166C2×D79—21no—
167C2×D79—21no—
168C2×D79—21no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C4×C79—21no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79C2×#4111yescharacteristic
176C4×C79H(5,𝔽2)11yescharacteristic
177Dic79—21no—
178Dic79—21no—
179Dic79—21no—
180Dic79—41no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—41no—
184C2×C79—42no—
185C2×C79—81no—
186C2×C79#54611yescharacteristic
187C2×C79#57511yescharacteristic
188C2×C79#57611yescharacteristic
189D79—41no—
190D79—81no—
191#3319—791nomaximal, Sylow
192C79#331911yescharacteristic, complemented, Sylow
193#555—791no—
194#546—791no—
195#489—791no—
196#485—791no—
197#482—791no—
198#474—791no—
199#468—791no—
200#466—791no—
201#463—791no—
202#449—791no—
203#447—791no—
204#442—791no—
205#435—791no—
206#418D7911yescharacteristic, complemented
207#416—791no—
208C2×#41—791no—
209C22×D4C2×D7911yescharacteristic
210C2×SD16—791no—
211C2×D8—791no—
212C2×D8—791no—
213C2×M16C2×D7911yescharacteristic
214C22×C8—791no—
215C4⋊Q8—791no—
216#124—791no—
217#124—1581no—
218#124—1581no—
219#123—1581no—
220C22⋊Q8—791no—
221#121—791no—
222#121—791no—
223#121—791no—
224#121—1581no—
225#121—1581no—
226#120—1581no—
227C4×D4—791no—
228C4×D4—791no—
229C4×D4—791no—
230#117—791no—
231#117—1581no—
232#117C2×D7911yescharacteristic
233C2×C22⋊C4—1581no—
234#107—791no—
235#107—791no—
236#106—791no—
237C4⋊C8—791no—
238#103—791no—
239#103—791no—
240#103—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244#102C2×D7911yescharacteristic
245#102C2×D7911yescharacteristic
246#102C2×D7911yescharacteristic
247#102C2×D7911yescharacteristic
248C22⋊C8—791no—
249C22⋊C8—791no—
250#97—791no—
251C24—21no—
252#41—3161no—
253#41—1582no—
254C2×Q8—791no—
255C2×Q8—1581no—
256C2×D4—22no—
257C2×D4—21no—
258C2×D4—41no—
259C2×D4—791no—
260C2×D4—791no—
261C2×D4—1581no—
262C2×D4—1581no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4C22×D7911yescharacteristic
266C2×D4C22×D7911yescharacteristic
267C22×C4—791no—
268C22×C4—1581no—
269C22×C4—1581no—
270C22×C4—1581no—
271C22×C4C22×D7911yescharacteristic
272SD16—3161no—
273D8—3161no—
274D8—1582no—
275M16—41no—
276C2×C8—3161no—
277C2×C8—791no—
278C2×C8—791no—
279C2×C8C22×D7911yescharacteristic
280C2×C8C22×D7911yescharacteristic
281C4⋊C4—791no—
282C4⋊C4—791no—
283C4⋊C4—791no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4C22×D7911yescharacteristic
287C4⋊C4C22×D7911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—791no—
290C22⋊C4—791no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C42—21no—
301C42—791no—
302C42—1581no—
303C23—21no—
304C23—21no—
305C23—42no—
306C23—42no—
307C23—81no—
308C23—791no—
309C23—1581no—
310C23D4×D7911yescharacteristic
311Q8—6321no—
312Q8—1581no—
313Q8—1581no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—3162no—
319D4—3161no—
320D4—6321no—
321D4—6321no—
322D4—6321no—
323D4—1581no—
324D4—1581no—
325D4#1192962412yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—3162no—
331C2×C4—3162no—
332C2×C4—791no—
333C2×C4—791no—
334C2×C4—791no—
335C2×C4—6321no—
336C2×C4—1581no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4D4×D7911yescharacteristic
342C2×C4C23×D7911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1581no—
346C8—1581no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—84no—
357C22—3161no—
358C22—3161no—
359C22—3161no—
360C22—1581no—
361C22—1581no—
362C22—1581no—
363C22C2×D4×D7911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—3161no—
368C4—3161no—
369C4—3161no—
370C4—1581no—
371C4—1581no—
372C4—1581no—
373C4C2×#1192962411yescharacteristic
374C4#1457920611yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—3161no—
379C2—6321no—
380C2#1909920311yescharacteristic
381C2#1909935911yescharacteristic
382C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#418×C79C2
socleC22×C79C22×D4
hypercenter#418D79
hypocenterC79#3319
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #19099276C2semidirect
2. #19099207C2semidirect
3. #19098921C2semidirect
4. #19098904C2semidirect
5. #19098885C2semidirect
6. #19098841C2semidirect
7. #19098809C2semidirect
8. #19098798C2semidirect
9. #19098777C2semidirect
10. #19098709C2semidirect
11. #19098697C2semidirect
12. #19098672C2semidirect
13. #19098632C2semidirect
14. #19098556C2semidirect
15. #418×C79C2semidirect
17. C2×#11929613C22semidirect
20. C2×C8×D79C22semidirect
21. #14579160C22semidirect
27. #14579136C22semidirect
34. #14579123C22semidirect
36. #14579119C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579092C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579084C22semidirect
45. #14579084C22semidirect
46. #14579083C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. #14579071C22semidirect
192. C79#3319semidirect
206. #418D79semidirect