Finite Group Databasebeta

← #23775036

Subgroups — #23775036

Order 10112.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579194C211yesmaximal, characteristic, complemented
2C2×#14579189C211yesmaximal, characteristic, complemented
3#19099222C211yesmaximal, characteristic, complemented
4#19099209C211yesmaximal, characteristic, complemented
5#19098947C211yesmaximal, characteristic, complemented
6#19098821C211yesmaximal, characteristic, complemented
7#19098816C211yesmaximal, characteristic, complemented
8#19098786C211yesmaximal, characteristic, complemented
9#19098779C211yesmaximal, characteristic, complemented
10#19098727C211yesmaximal, characteristic, complemented
11#19098716C211yesmaximal, characteristic, complemented
12#19098710C211yesmaximal, characteristic, complemented
13#19098704C211yesmaximal, characteristic, complemented
14C4×#11929613C211yesmaximal, characteristic, complemented
15#436×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929624C2211yescharacteristic
18C22×Dic158C2211yescharacteristic, complemented
19C22×D316C2211yescharacteristic
20#14579194—24no—
21#14579189—24no—
22C2×Dic316C2211yescharacteristic, complemented
23C2×Dic316C2211yescharacteristic, complemented
24C2×#11929613C2211yescharacteristic
25C2×#11929613C2211yescharacteristic
26C2×#11929613C2211yescharacteristic
27C2×#11929613C2211yescharacteristic
28C2×#11929613C2211yescharacteristic, complemented
29C2×D632C2211yescharacteristic
30C2×D632C2211yescharacteristic
31#14579149C2211yescharacteristic
32#14579149C2211yescharacteristic, complemented
33#14579147—21no—
34#14579146—21no—
35#14579140C2211yescharacteristic
36#14579140C2211yescharacteristic
37#14579139—21no—
38#14579135C2211yescharacteristic
39#14579135C2211yescharacteristic, complemented
40#14579134—21no—
41#14579133—21no—
42#14579129—21no—
43C4×Dic158C2211yescharacteristic, complemented
44C4×D316C2211yescharacteristic
45(C22⋊D79)⋊C4—21no—
46C22⋊C4×D79—21no—
47#14579093C2211yescharacteristic, complemented
48#14579086C2211yescharacteristic, complemented
49#14579086C2211yescharacteristic, complemented
50#14579086C2211yescharacteristic, complemented
51#14579083C2211yescharacteristic
52#14579083C2211yescharacteristic
53#14579083C2211yescharacteristic, complemented
54C2×M16×C79C2211yescharacteristic
55C2×M16×C79C2211yescharacteristic, complemented
56C4×D4×C79C2211yescharacteristic
57C4⋊C8×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic
59C22⋊C8×C79C2211yescharacteristic, complemented
60C4×C8×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62#11929624—22no—
63#11929624—22no—
64#11929624—41no—
65#11929624—41no—
66C2×Dic158—22no—
67C2×Dic158—21no—
68C2×Dic158—41no—
69C2×Dic158C2311yescharacteristic
70C2×Dic158C2311yescharacteristic
71C2×Dic158C2311yescharacteristic
72C2×D316—22no—
73C2×D316—21no—
74C2×D316—41no—
75C2×D316C2311yescharacteristic
76C2×D316C2311yescharacteristic
77C2×D316C2311yescharacteristic
78C2×C22⋊D79—21no—
79C2×C22⋊D79—21no—
80C2×C22⋊D79—21no—
81C2×C22⋊D79—21no—
82C22×Dic79—21no—
83C2×C4×D79—21no—
84C2×C4×D79—21no—
85C2×C4×D79—21no—
86Dic316—22no—
87Dic316—22no—
88#11929613—22no—
89#11929613—22no—
90#11929613—41no—
91#11929613—41no—
92#11929613D414yescomplemented
93D632—22no—
94D632—22no—
95C4⋊Dic79C2311yescharacteristic
96C4⋊Dic79C2311yescharacteristic
97Dic79⋊C4—21no—
98Dic79⋊C4—21no—
99Dic79⋊C4—21no—
100C22⋊Dic79—21no—
101C22⋊Dic79—21no—
102(C2×D79)⋊C4—21no—
103(C2×D79)⋊C4—21no—
104(C2×D79)⋊C4—21no—
105(C2×D79)⋊C4—21no—
106(C2×D79)⋊C4—21no—
107(C2×D79)⋊C4—21no—
108(C2×D79)⋊C4—21no—
109C4×Dic79—21no—
110C2×D4×C79D411yescharacteristic
111C22×C4×C79C2311yescharacteristic
112C22×C4×C79C2311yescharacteristic
113M16×C79—22no—
114M16×C79—22no—
115C2×C8×C79C2311yescharacteristic
116C2×C8×C79C2311yescharacteristic
117C2×C8×C79C2311yescharacteristic
118C2×C8×C79C2311yescharacteristic
119C4⋊C4×C79D411yescharacteristic
120C22⋊C4×C79D411yescharacteristic
121C22⋊C4×C79D411yescharacteristic
122C42×C79C2311yescharacteristic
123C23×C79C2×D411yescharacteristic
124C23×C79C2×D411yescharacteristic
125C22×D79—21no—
126C22×D79—21no—
127C22×D79—21no—
128C22×D79—42no—
129C22×D79—42no—
130C22×D79—81no—
131D4×C79—41no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2×D411yescharacteristic
140C2×C4×C79C2411yescharacteristic
141C22⋊D79—42no—
142C22⋊D79—42no—
143C22⋊D79—42no—
144C22⋊D79—81no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79—42no—
151D316—21no—
152D316—21no—
153D316—21no—
154D316—21no—
155D316—21no—
156D316—42no—
157D316C2×D412yes—
158C4×D79—42no—
159C4×D79—42no—
160C4×D79—81no—
161Dic158—21no—
162Dic158—21no—
163Dic158—21no—
164Dic158—21no—
165Dic158—21no—
166Dic158—42no—
167Dic158C2×D412yes—
168C8×C79—21no—
169C8×C79—21no—
170C8×C79—21no—
171C8×C79C2×D412yes—
172C22×C79—21no—
173C22×C79—21no—
174C22×C79—21no—
175C22×C79—21no—
176C22×C79—21no—
177C22×C79—21no—
178C22×C79C22×D411yescharacteristic
179C2×D79—22no—
180C2×D79—41no—
181C2×D79—41no—
182C2×D79—41no—
183C2×D79—41no—
184C2×D79—41no—
185C2×D79—41no—
186C2×D79—41no—
187C2×D79—41no—
188C2×D79—84no—
189C4×C79—21no—
190C4×C79—21no—
191C4×C79—21no—
192C4×C79—21no—
193C4×C79C22×D411yescharacteristic
194C4×C79H(5,𝔽2)11yescharacteristic
195Dic79—22no—
196Dic79—41no—
197Dic79—41no—
198Dic79—41no—
199Dic79—41no—
200C2×C79—41no—
201C2×C79—41no—
202C2×C79D4211yescharacteristic
203C2×C79#57511yescharacteristic
204C2×C79#57711yescharacteristic
205D79—42no—
206D79—81no—
207D79—81no—
208#3275—791nomaximal, Sylow
209C79#327511yescharacteristic, complemented, Sylow
210C2×#137—791no—
211C2×AGL(1,ℤ/8)—791no—
212#548—791no—
213#546—791no—
214#495—791no—
215#470—791no—
216#469—791no—
217#464—791no—
218#463—791no—
219#452—791no—
220#450—791no—
221#449—791no—
222#448—791no—
223C4×SD16—791no—
224#436D7911yescharacteristic, complemented
225C2×#41—791no—
226C2×#41—791no—
227C22×Q8—791no—
228C22×D4—791no—
229#137—1584no—
230AGL(1,ℤ/8)—1584no—
231C2×Q16—791no—
232C2×Q16—791no—
233C2×SD16—791no—
234C2×SD16—791no—
235C2×SD16—791no—
236C2×SD16—791no—
237C2×SD16—791no—
238C2×D8—791no—
239C2×D8—791no—
240C2×M16C2×D7911yescharacteristic
241C2×M16C2×D7911yescharacteristic, complemented
242#124—791no—
243#124—791no—
244#124—1581no—
245#123—1581no—
246C22⋊Q8—791no—
247C22⋊Q8—791no—
248C22⋊Q8—1581no—
249#121—791no—
250#121—791no—
251#121—1581no—
252#121—1581no—
253#120—1581no—
254C4×Q8—791no—
255C4×D4—791no—
256C4×D4—1581no—
257C4×D4C2×D7911yescharacteristic
258C2×C22⋊C4—1581no—
259#106—791no—
260C4⋊C8C2×D7911yescharacteristic, complemented
261#103—791no—
262#103—791no—
263#103—791no—
264#102—791no—
265#102—791no—
266#102—791no—
267C22⋊C8C2×D7911yescharacteristic
268C22⋊C8C2×D7911yescharacteristic, complemented
269C4×C8C2×D7911yescharacteristic, complemented
270C24—1581no—
271#41—3161no—
272#41—3161no—
273#41—1582no—
274#41—1582no—
275C2×Q8—3161no—
276C2×Q8—791no—
277C2×Q8—791no—
278C2×Q8—791no—
279C2×Q8—1582no—
280C2×Q8—1581no—
281C2×D4—3161no—
282C2×D4—791no—
283C2×D4—791no—
284C2×D4—791no—
285C2×D4—1582no—
286C2×D4—1581no—
287C2×D4—1581no—
288C2×D4—1581no—
289C2×D4—1581no—
290C2×D4—1581no—
291C2×D4D31611yescharacteristic
292C22×C4—1581no—
293C22×C4—1581no—
294C22×C4—1581no—
295C22×C4—1581no—
296C22×C4C22×D7911yescharacteristic
297C22×C4C22×D7911yescharacteristic
298Q16—1582no—
299Q16—1582no—
300SD16—3161no—
301SD16—3161no—
302SD16—794no—
303SD16—1582no—
304SD16—1582no—
305D8—1582no—
306D8—1582no—
307M16—22no—
308M16—22no—
309C2×C8C22×D7911yescharacteristic
310C2×C8C22×D7911yescharacteristic
311C2×C8C22×D7911yescharacteristic
312C2×C8C22×D7911yescharacteristic
313C4⋊C4—791no—
314C4⋊C4—791no—
315C4⋊C4—1581no—
316C4⋊C4—1581no—
317C4⋊C4—1581no—
318C4⋊C4D31611yescharacteristic
319C22⋊C4—1581no—
320C22⋊C4—1581no—
321C22⋊C4—1581no—
322C22⋊C4—1581no—
323C22⋊C4—1581no—
324C22⋊C4—1581no—
325C22⋊C4—1581no—
326C22⋊C4—1581no—
327C22⋊C4—1581no—
328C22⋊C4D31611yescharacteristic
329C22⋊C4D31611yescharacteristic
330C42—1581no—
331C42C22×D7911yescharacteristic
332C23—3162no—
333C23—3162no—
334C23—6321no—
335C23—1581no—
336C23—1581no—
337C23—1581no—
338C23C2×D31611yescharacteristic
339C23C2×D31611yescharacteristic
340Q8—3162no—
341Q8—792no—
342Q8—1581no—
343Q8—1581no—
344Q8—1581no—
345Q8—1581no—
346Q8—1581no—
347D4—41no—
348D4—3162no—
349D4—3162no—
350D4—3162no—
351D4—3162no—
352D4—792no—
353D4—6321no—
354D4—1581no—
355D4—1581no—
356D4—1581no—
357D4—1581no—
358D4—1581no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—3162no—
364C2×C4—3162no—
365C2×C4—3162no—
366C2×C4—6321no—
367C2×C4—1581no—
368C2×C4—1581no—
369C2×C4—1581no—
370C2×C4—1581no—
371C2×C4—1581no—
372C2×C4C2×D31611yescharacteristic
373C2×C4C2×D31611yescharacteristic
374C2×C4C2×D31611yescharacteristic
375C2×C4C2×D31611yescharacteristic
376C2×C4C23×D7911yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D7912yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—3161no—
388C22—3161no—
389C22—3161no—
390C22—3161no—
391C22—3161no—
392C22—3161no—
393C22—3161no—
394C22—3161no—
395C22—6324no—
396C22—1582no—
397C22C22×D31611yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—3161no—
403C4—3161no—
404C4—3161no—
405C4—3161no—
406C4—1582no—
407C4C2×D4×D7911yescharacteristic
408C4#1457920711yescharacteristic
409C2—41no—
410C2—41no—
411C2—3162no—
412C2—6321no—
413C2—6321no—
414C2D4×D31611yescharacteristic
415C2#1909936311yescharacteristic
416C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#436×C79C2
socleC22×C79C22×D4
hypercenter#436D79
hypocenterC79#3275
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. C2×#14579194C2semidirect
2. C2×#14579189C2semidirect
3. #19099222C2semidirect
4. #19099209C2semidirect
5. #19098947C2semidirect
6. #19098821C2semidirect
7. #19098816C2semidirect
8. #19098786C2semidirect
9. #19098779C2semidirect
10. #19098727C2semidirect
11. #19098716C2semidirect
12. #19098710C2semidirect
13. #19098704C2semidirect
14. C4×#11929613C2semidirect
15. #436×C79C2semidirect
18. C22×Dic158C22semidirect
22. C2×Dic316C22semidirect
23. C2×Dic316C22semidirect
28. C2×#11929613C22semidirect
32. #14579149C22semidirect
39. #14579135C22semidirect
43. C4×Dic158C22semidirect
47. #14579093C22semidirect
48. #14579086C22semidirect
49. #14579086C22semidirect
50. #14579086C22semidirect
53. #14579083C22semidirect
55. C2×M16×C79C22semidirect
57. C4⋊C8×C79C22semidirect
59. C22⋊C8×C79C22semidirect
60. C4×C8×C79C22semidirect
92. #11929613D4semidirect
209. C79#3275semidirect
224. #436D79semidirect
241. C2×M16C2×D79semidirect
260. C4⋊C8C2×D79semidirect
268. C22⋊C8C2×D79semidirect
269. C4×C8C2×D79semidirect