Finite Group Databasebeta

← #23774239

Subgroups — #23774239

Order 10112.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099073C211yesmaximal, characteristic, complemented
2#19099070C211yesmaximal, characteristic, complemented
3#19098905C211yesmaximal, characteristic, complemented
4#19098902C211yesmaximal, characteristic, complemented
5#19098885C211yesmaximal, characteristic, complemented
6#19098884C211yesmaximal, characteristic, complemented
7#19098820C211yesmaximal, characteristic, complemented
8#19098813C211yesmaximal, characteristic, complemented
9#19098808C211yesmaximal, characteristic, complemented
10#19098806C211yesmaximal, characteristic, complemented
11#19098725C211yesmaximal, characteristic, complemented
12#19098722C211yesmaximal, characteristic, complemented
13#19098705C211yesmaximal, characteristic, complemented
14#19098525C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18C2×#11929614C2211yescharacteristic, complemented
19C2×#11929612C2211yescharacteristic, complemented
20C2×#11929607C2211yescharacteristic
21C2×#11929607C2211yescharacteristic
22#14579143—21no—
23#14579142—21no—
24#14579141C2211yescharacteristic
25#14579140C2211yescharacteristic
26#14579137C2211yescharacteristic
27#14579137C2211yescharacteristic
28#14579132C2211yescharacteristic
29#14579132C2211yescharacteristic
30#14579132C2211yescharacteristic
31#14579129—21no—
32#14579129—21no—
33D4×Dic79—21no—
34C4×C22⋊D79—21no—
35C4×C22⋊D79—21no—
36(C22⋊D79)⋊C4—21no—
37#14579120C2211yescharacteristic
38#14579119C2211yescharacteristic
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579093C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579085C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic, complemented
48#14579082C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52C2×#41×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic, complemented
54C2×D8×C79C2211yescharacteristic, complemented
55#121×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic
59C23×D79D411yescharacteristic
60#11929623—41no—
61#11929623—41no—
62C2×Dic158C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C22×Dic79—21no—
68C22×Dic79D411yescharacteristic
69C2×C4×D79—41no—
70C2×C4×D79—41no—
71C2×C4×D79D411yescharacteristic
72C2×C4×D79D411yescharacteristic
73C2×C4×D79C2311yescharacteristic
74C2×C4×D79C2311yescharacteristic
75#11929614—41no—
76#11929612—41no—
77#11929607—41no—
78#11929607—41no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C4⋊Dic79—21no—
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—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—
98C4×Dic79—21no—
99#41×C79—41no—
100#41×C79—41no—
101C2×Q8×C79C2311yescharacteristic
102C2×D4×C79—21no—
103C2×D4×C79—21no—
104C2×D4×C79C2311yescharacteristic
105C2×D4×C79C2311yescharacteristic
106C22×C4×C79—21no—
107C22×C4×C79C2311yescharacteristic
108SD16×C79—41no—
109D8×C79—41no—
110C2×C8×C79C2311yescharacteristic
111C2×C8×C79C2311yescharacteristic
112C4⋊C4×C79C2311yescharacteristic
113C22⋊C4×C79—21no—
114C23×C79—21no—
115C23×C79—21no—
116C23×C79C2×D411yescharacteristic
117C22×D79—41no—
118C22×D79—41no—
119C22×D79—41no—
120C22×D79C2×D411yescharacteristic
121C22×D79C2×D411yescharacteristic
122Q8×C79—21no—
123Q8×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—42no—
129D4×C79—42no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—42no—
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2411yescharacteristic
137C22⋊D79—42no—
138C22⋊D79—42no—
139C22⋊D79—42no—
140C22⋊D79—42no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—41no—
146C2×Dic79—42no—
147C2×Dic79C2×D411yescharacteristic
148C2×Dic79C2×D411yescharacteristic
149C4×D79—21no—
150C4×D79—21no—
151C4×D79—21no—
152C4×D79—21no—
153C4×D79—41no—
154C4×D79—41no—
155Dic158—21no—
156Dic158—21no—
157C8×C79—21no—
158C8×C79—21no—
159C79⋊C8—21no—
160C79⋊C8—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—21no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79C22×D411yescharacteristic
171C2×D79—21no—
172C2×D79—21no—
173C2×D79—21no—
174C2×D79—21no—
175C2×D79—21no—
176C2×D79—21no—
177C2×D79—44no—
178C4×C79—21no—
179C4×C79—41no—
180C4×C79—41no—
181C4×C79H(5,𝔽2)11yescharacteristic
182C4×C79H(5,𝔽2)11yescharacteristic
183Dic79—21no—
184Dic79—21no—
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188Dic79—41no—
189C2×C79—41no—
190C2×C79—81no—
191C2×C79—81no—
192C2×C79#53411yescharacteristic
193C2×C79#57511yescharacteristic
194C2×C79#57511yescharacteristic
195D79—41no—
196D79—41no—
197#3197—791nomaximal, Sylow
198C79#319711yescharacteristic, complemented, Sylow
199#525—791no—
200#525—791no—
201#485—791no—
202#485—791no—
203#482—791no—
204#482—791no—
205#470—791no—
206#469—791no—
207#468—791no—
208#468—791no—
209#452—791no—
210#452—791no—
211#449—791no—
212#449D7911yescharacteristic, complemented
213#407—791no—
214C2×#41—791no—
215C2×#41C2×D7911yescharacteristic
216C23×C4—791no—
217C2×Q16—791no—
218C2×SD16—791no—
219C2×SD16C2×D7911yescharacteristic, complemented
220C2×D8C2×D7911yescharacteristic, complemented
221C2×M16—791no—
222C2×M16—791no—
223#123—1581no—
224#123—1581no—
225C22⋊Q8—791no—
226C22⋊Q8—791no—
227C22⋊Q8—791no—
228C22⋊Q8—791no—
229#121—791no—
230#121—791no—
231#121—791no—
232#121C2×D7911yescharacteristic
233#120—1581no—
234#120—1581no—
235C4×D4—1581no—
236C4×D4—1581no—
237C4×D4—1581no—
238C4×D4—1581no—
239#117—791no—
240#117—791no—
241#107—791no—
242#107—791no—
243#106—791no—
244#106—791no—
245#103—791no—
246#103—791no—
247#103—791no—
248#103C2×D7911yescharacteristic, complemented
249#102—791no—
250#102—791no—
251#102—791no—
252#102C2×D7911yescharacteristic, complemented
253C22⋊C8—791no—
254C22⋊C8—791no—
255C22⋊C8—791no—
256C22⋊C8C2×D7911yescharacteristic
257C24—791no—
258#41—41no—
259#41—41no—
260#41—3161no—
261#41—3161no—
262C2×Q8—791no—
263C2×Q8C22×D7911yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4C22×D7911yescharacteristic
271C2×D4C22×D7911yescharacteristic
272C22×C4—21no—
273C22×C4—3161no—
274C22×C4—3161no—
275C22×C4—791no—
276C22×C4—791no—
277C22×C4—791no—
278C22×C4—791no—
279C22×C4—791no—
280C22×C4—1581no—
281C22×C4C22×D7911yescharacteristic
282Q16—3161no—
283SD16—41no—
284SD16—3161no—
285D8—41no—
286M16—3161no—
287M16—3161no—
288C2×C8—791no—
289C2×C8—791no—
290C2×C8C22×D7911yescharacteristic
291C2×C8C22×D7911yescharacteristic
292C4⋊C4—791no—
293C4⋊C4—791no—
294C4⋊C4—791no—
295C4⋊C4—1581no—
296C4⋊C4—1581no—
297C4⋊C4—1581no—
298C4⋊C4—1581no—
299C4⋊C4C22×D7911yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C42—1581no—
311C42—1581no—
312C23—21no—
313C23—21no—
314C23—3161no—
315C23—3161no—
316C23—3161no—
317C23—791no—
318C23—791no—
319C23D4×D7911yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—1581no—
323Q8—1581no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—3162no—
331D4—3162no—
332D4—3162no—
333D4—3162no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—3161no—
340C2×C4—3161no—
341C2×C4—3162no—
342C2×C4—3161no—
343C2×C4—791no—
344C2×C4—791no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4—1581no—
352C2×C4—1581no—
353C2×C4D4×D7911yescharacteristic
354C2×C4C23×D7911yescharacteristic
355C8—21no—
356C8—21no—
357C8—1581no—
358C8—1581no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—3164no—
369C22—1581no—
370C22—1581no—
371C22—1581no—
372C22—1581no—
373C22—1581no—
374C22—1581no—
375C22C2×D4×D7911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—3161no—
380C4—3161no—
381C4—3161no—
382C4—3161no—
383C4—1581no—
384C4—1581no—
385C4#1457920611yescharacteristic
386C4#1457920611yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—3161no—
391C2—3161no—
392C2#1909912311yescharacteristic
393C2#1909935911yescharacteristic
394C2#1909936011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3197
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #19099073C2semidirect
2. #19099070C2semidirect
3. #19098905C2semidirect
4. #19098902C2semidirect
5. #19098885C2semidirect
6. #19098884C2semidirect
7. #19098820C2semidirect
8. #19098813C2semidirect
9. #19098808C2semidirect
10. #19098806C2semidirect
11. #19098725C2semidirect
12. #19098722C2semidirect
13. #19098705C2semidirect
14. #19098525C2semidirect
15. #449×C79C2semidirect
18. C2×#11929614C22semidirect
19. C2×#11929612C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579093C22semidirect
42. #14579092C22semidirect
43. #14579086C22semidirect
44. #14579086C22semidirect
45. #14579085C22semidirect
46. #14579082C22semidirect
47. #14579082C22semidirect
48. #14579082C22semidirect
53. C2×SD16×C79C22semidirect
54. C2×D8×C79C22semidirect
56. #103×C79C22semidirect
57. #102×C79C22semidirect
198. C79#3197semidirect
212. #449D79semidirect
219. C2×SD16C2×D79semidirect
220. C2×D8C2×D79semidirect
248. #103C2×D79semidirect
252. #102C2×D79semidirect