Finite Group Databasebeta

← #23775031

Subgroups — #23775031

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×#14579190C211yesmaximal, characteristic, complemented
2#19099220C211yesmaximal, characteristic, complemented
3#19099207C211yesmaximal, characteristic, complemented
4#19098946C211yesmaximal, characteristic, complemented
5#19098821C211yesmaximal, characteristic, complemented
6#19098813C211yesmaximal, characteristic, complemented
7#19098783C211yesmaximal, characteristic, complemented
8#19098776C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098714C211yesmaximal, characteristic, complemented
11#19098705C211yesmaximal, characteristic, complemented
12#19098700C211yesmaximal, characteristic, complemented
13SD16×Dic79C211yesmaximal, characteristic, complemented
14#19098639C211yesmaximal, characteristic, complemented
15C2×AGL(1,ℤ/8)×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic, complemented
18#14579190—24no—
19C2×Dic316C2211yescharacteristic, complemented
20C2×#11929614C2211yescharacteristic, complemented
21C2×#11929612C2211yescharacteristic
22C2×#11929612C2211yescharacteristic
23C2×#11929612C2211yescharacteristic, complemented
24C2×#11929607C2211yescharacteristic, complemented
25#14579148—21no—
26#14579148C2211yescharacteristic
27#14579148C2211yescharacteristic, complemented
28#14579142—21no—
29#14579140—21no—
30#14579140C2211yescharacteristic
31#14579140C2211yescharacteristic
32#14579133—21no—
33#14579132—21no—
34#14579132C2211yescharacteristic
35#14579132C2211yescharacteristic, complemented
36#14579130—21no—
37Q8×Dic79C2211yescharacteristic, complemented
38D4×Dic79C2211yescharacteristic
39C4×C22⋊D79—21no—
40C4×C22⋊D79C2211yescharacteristic
41C2×C22⋊Dic79—21no—
42#14579093C2211yescharacteristic, complemented
43Dic79⋊C8C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579086C2211yescharacteristic, complemented
46#14579085C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579082C2211yescharacteristic, complemented
50C22⋊(C79⋊C8)C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52C8×Dic79C2211yescharacteristic, complemented
53C2×#41×C79C2211yescharacteristic
54C22×D4×C79C2211yescharacteristic
55AGL(1,ℤ/8)×C79—24no—
56C2×SD16×C79C2211yescharacteristic
57C2×SD16×C79C2211yescharacteristic
58C2×D8×C79C2211yescharacteristic
59C2×D8×C79C2211yescharacteristic
60C2×M16×C79C2211yescharacteristic
61#11929623—22no—
62#11929623—41no—
63C2×Dic158—21no—
64C2×Dic158C2311yescharacteristic
65C2×Dic158C2311yescharacteristic
66Q8×D79—22no—
67Q8×D79—41no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79D411yescharacteristic
72C22×Dic79—21no—
73C22×Dic79—21no—
74C2×C4×D79—21no—
75C2×C4×D79C2311yescharacteristic
76Dic316—22no—
77#11929614—22no—
78#11929612—22no—
79#11929612—41no—
80#11929612—41no—
81#11929607—22no—
82C2×C79⋊C8C2311yescharacteristic
83C2×C79⋊C8C2311yescharacteristic
84C4⋊Dic79—21no—
85C4⋊Dic79C2311yescharacteristic
86C4⋊Dic79C2311yescharacteristic
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4D411yescharacteristic
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94C22⋊Dic79—21no—
95C22⋊Dic79—21no—
96C22⋊Dic79—21no—
97C22⋊Dic79—21no—
98C22⋊Dic79—21no—
99C22⋊Dic79D411yescharacteristic
100(C2×D79)⋊C4D411yescharacteristic
101C4×Dic79—21no—
102C4×Dic79C2311yescharacteristic
103C24×C79—21no—
104#41×C79—22no—
105#41×C79—41no—
106C2×Q8×C79C2311yescharacteristic
107C2×D4×C79—22no—
108C2×D4×C79—21no—
109C2×D4×C79—21no—
110C2×D4×C79—41no—
111C2×D4×C79C2311yescharacteristic
112C2×D4×C79C2311yescharacteristic
113C2×D4×C79C2311yescharacteristic
114C22×C4×C79—21no—
115C22×C4×C79C2311yescharacteristic
116SD16×C79—22no—
117SD16×C79D414yescomplemented
118D8×C79—22no—
119D8×C79—22no—
120M16×C79—22no—
121C2×C8×C79C2311yescharacteristic
122C2×C8×C79C2311yescharacteristic
123C23×C79—21no—
124C23×C79—21no—
125C23×C79—21no—
126C23×C79—42no—
127C23×C79—42no—
128C23×C79—81no—
129C23×C79C2×D411yescharacteristic
130C22×D79C2×D411yescharacteristic
131Q8×C79—21no—
132Q8×C79C2×D412yes—
133D4×C79—21no—
134D4×C79—21no—
135D4×C79—21no—
136D4×C79—21no—
137D4×C79—21no—
138D4×C79—42no—
139D4×C79—42no—
140D4×C79C2×D412yes—
141C2×C4×C79—21no—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79—42no—
145C2×C4×C79C2×D411yescharacteristic
146C2×C4×C79C2411yescharacteristic
147C22⋊D79—41no—
148C22⋊D79—42no—
149C22⋊D79—42no—
150C22⋊D79—81no—
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—42no—
156C2×Dic79—81no—
157C2×Dic79C2×D411yescharacteristic
158C2×Dic79C2×D411yescharacteristic
159C2×Dic79C2×D411yescharacteristic
160C4×D79—21no—
161C4×D79—21no—
162C4×D79—42no—
163Dic158—21no—
164Dic158—21no—
165Dic158—21no—
166Dic158—21no—
167Dic158—42no—
168C8×C79—21no—
169C8×C79C2×D412yes—
170C79⋊C8—21no—
171C79⋊C8—21no—
172C22×C79—22no—
173C22×C79—21no—
174C22×C79—21no—
175C22×C79—21no—
176C22×C79—41no—
177C22×C79—41no—
178C22×C79—41no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79—41no—
182C22×C79—41no—
183C22×C79—41no—
184C22×C79—84no—
185C22×C79C22×D411yescharacteristic
186C2×D79—21no—
187C2×D79—21no—
188C2×D79—21no—
189C4×C79—21no—
190C4×C79—22no—
191C4×C79C22×D411yescharacteristic
192C4×C79H(5,𝔽2)11yescharacteristic
193Dic79—21no—
194Dic79—21no—
195Dic79—21no—
196Dic79—41no—
197Dic79—41no—
198Dic79—41no—
199Dic79—41no—
200C2×C79—41no—
201C2×C79—42no—
202C2×C79—81no—
203C2×C79—81no—
204C2×C79D4211yescharacteristic
205C2×C79#57511yescharacteristic
206C2×C79#57711yescharacteristic
207D79—41no—
208#3275—791nomaximal, Sylow
209C79#327511yescharacteristic, complemented, Sylow
210C2×#137—791no—
211C2×AGL(1,ℤ/8)D7911yescharacteristic, complemented
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#436—791no—
225C2×#41—791no—
226C2×#41C2×D7911yescharacteristic
227C22×Q8—791no—
228C22×D4C2×D7911yescharacteristic
229#137—1584no—
230AGL(1,ℤ/8)—24no—
231C2×Q16—791no—
232C2×Q16—791no—
233C2×SD16—791no—
234C2×SD16—791no—
235C2×SD16—791no—
236C2×SD16C2×D7911yescharacteristic
237C2×SD16C2×D7911yescharacteristic
238C2×D8C2×D7911yescharacteristic
239C2×D8C2×D7911yescharacteristic
240C2×M16—791no—
241C2×M16C2×D7911yescharacteristic
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—791no—
257C4×D4—1581no—
258C2×C22⋊C4—1581no—
259#106—791no—
260C4⋊C8—791no—
261#103—791no—
262#103—791no—
263#103—791no—
264#102—791no—
265#102—791no—
266#102—791no—
267C22⋊C8—791no—
268C22⋊C8—791no—
269C4×C8—791no—
270C24—21no—
271#41—22no—
272#41—41no—
273#41—3161no—
274#41—1582no—
275C2×Q8—3161no—
276C2×Q8—791no—
277C2×Q8—791no—
278C2×Q8—1581no—
279C2×Q8—1582no—
280C2×Q8C22×D7911yescharacteristic
281C2×D4—22no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—791no—
286C2×D4—1581no—
287C2×D4—1581no—
288C2×D4—1581no—
289C2×D4C22×D7911yescharacteristic
290C2×D4C22×D7911yescharacteristic
291C2×D4C22×D7911yescharacteristic
292C22×C4—21no—
293C22×C4—791no—
294C22×C4—1581no—
295C22×C4—1581no—
296C22×C4—1581no—
297C22×C4C22×D7911yescharacteristic
298Q16—1582no—
299Q16—1582no—
300SD16—22no—
301SD16—3161no—
302SD16—3161no—
303SD16—1582no—
304SD16C22⋊D7914yescomplemented
305D8—22no—
306D8—22no—
307M16—22no—
308M16—1582no—
309C2×C8—791no—
310C2×C8—791no—
311C2×C8C22×D7911yescharacteristic
312C2×C8C22×D7911yescharacteristic
313C4⋊C4—791no—
314C4⋊C4—791no—
315C4⋊C4—791no—
316C4⋊C4—1581no—
317C4⋊C4—1581no—
318C4⋊C4—1581no—
319C22⋊C4—791no—
320C22⋊C4—791no—
321C22⋊C4—1581no—
322C22⋊C4—1581no—
323C22⋊C4—1581no—
324C22⋊C4—1581no—
325C22⋊C4—1581no—
326C22⋊C4—1581no—
327C22⋊C4—1581no—
328C22⋊C4—1581no—
329C22⋊C4—1581no—
330C42—791no—
331C42—1581no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—42no—
336C23—42no—
337C23—81no—
338C23—791no—
339C23D4×D7911yescharacteristic
340Q8—21no—
341Q8—3162no—
342Q8—1581no—
343Q8—1581no—
344Q8—1581no—
345Q8—1581no—
346Q8C2×C22⋊D7912yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—21no—
352D4—42no—
353D4—42no—
354D4—3162no—
355D4—3162no—
356D4—3161no—
357D4—6321no—
358D4C2×C22⋊D7912yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—3162no—
364C2×C4—3162no—
365C2×C4—791no—
366C2×C4—791no—
367C2×C4—791no—
368C2×C4—6321no—
369C2×C4—1581no—
370C2×C4—1581no—
371C2×C4—1581no—
372C2×C4—1581no—
373C2×C4—1581no—
374C2×C4—1581no—
375C2×C4D4×D7911yescharacteristic
376C2×C4C23×D7911yescharacteristic
377C8—21no—
378C8—1581no—
379C8—1581no—
380C8C2×C22⋊D7912yes—
381C22—21no—
382C22—22no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—1581no—
395C22—1581no—
396C22—1581no—
397C22C2×D4×D7911yescharacteristic
398C4—21no—
399C4—22no—
400C4—3161no—
401C4—3161no—
402C4—3161no—
403C4—3161no—
404C4—1581no—
405C4—1581no—
406C4—1581no—
407C4C22×C22⋊D7911yescharacteristic
408C4#1457920611yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—81no—
413C2—3161no—
414C2D4×C22⋊D7911yescharacteristic
415C2#1909935911yescharacteristic
416C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×AGL(1,ℤ/8)×C79C2
socleC22×C79C22×D4
hypercenterC2×AGL(1,ℤ/8)D79
hypocenterC79#3275
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#14579190C2semidirect
2. #19099220C2semidirect
3. #19099207C2semidirect
4. #19098946C2semidirect
5. #19098821C2semidirect
6. #19098813C2semidirect
7. #19098783C2semidirect
8. #19098776C2semidirect
9. #19098725C2semidirect
10. #19098714C2semidirect
11. #19098705C2semidirect
12. #19098700C2semidirect
13. SD16×Dic79C2semidirect
14. #19098639C2semidirect
15. C2×AGL(1,ℤ/8)×C79C2semidirect
17. C2×Q8×D79C22semidirect
19. C2×Dic316C22semidirect
20. C2×#11929614C22semidirect
23. C2×#11929612C22semidirect
24. C2×#11929607C22semidirect
27. #14579148C22semidirect
35. #14579132C22semidirect
37. Q8×Dic79C22semidirect
42. #14579093C22semidirect
43. Dic79⋊C8C22semidirect
44. #14579086C22semidirect
45. #14579086C22semidirect
46. #14579085C22semidirect
49. #14579082C22semidirect
51. (C2×D79)⋊C8C22semidirect
52. C8×Dic79C22semidirect
117. SD16×C79D4semidirect
209. C79#3275semidirect
211. C2×AGL(1,ℤ/8)D79semidirect
304. SD16C22⋊D79semidirect