Finite Group Databasebeta

← #23774925

Subgroups — #23774925

Order 10112.

500 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×#14579185C211yesmaximal, characteristic, complemented
2#19099212C211yesmaximal, characteristic, complemented
3#19099201C211yesmaximal, characteristic, complemented
4#19098956C211yesmaximal, characteristic, complemented
5#19098818C211yesmaximal, characteristic, complemented
6#19098792C211yesmaximal, characteristic, complemented
7#19098780C211yesmaximal, characteristic, complemented
8#19098766C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098722C211yesmaximal, characteristic, complemented
11#19098712C211yesmaximal, characteristic, complemented
12#19098708C211yesmaximal, characteristic, complemented
13#19098675C211yesmaximal, characteristic, complemented
14#19098634C211yesmaximal, characteristic, complemented
15C2×#135×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18#14579185—24no—
19C2×#11929614C2211yescharacteristic, complemented
20C2×#11929613C2211yescharacteristic
21C2×#11929612C2211yescharacteristic
22C2×#11929611C2211yescharacteristic
23C2×#11929609C2211yescharacteristic
24C2×#11929607C2211yescharacteristic
25#14579159C2211yescharacteristic, complemented
26#14579150C2211yescharacteristic
27#14579144—21no—
28#14579144—21no—
29#14579142—21no—
30#14579140C2211yescharacteristic, complemented
31#14579137C2211yescharacteristic
32#14579137C2211yescharacteristic
33#14579135C2211yescharacteristic
34#14579133—21no—
35#14579133—21no—
36#14579129—21no—
37D4×Dic79C2211yescharacteristic
38D4×Dic79C2211yescharacteristic, complemented
39C4×C22⋊D79C2211yescharacteristic
40C2×Dic79⋊C4—21no—
41C2×(C2×D79)⋊C4—21no—
42#14579093C2211yescharacteristic, complemented
43Dic79⋊C8C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579085C2211yescharacteristic, complemented
46#14579085C2211yescharacteristic, complemented
47#14579083C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579082C2211yescharacteristic, complemented
50C22⋊(C79⋊C8)C2211yescharacteristic, complemented
51(C2×D79)⋊C8C2211yescharacteristic
52#14579071C2211yescharacteristic, complemented
53C2×#41×C79C2211yescharacteristic
54C2×#41×C79C2211yescharacteristic, complemented
55#135×C79—24no—
56C2×Q16×C79C2211yescharacteristic, complemented
57C2×SD16×C79C2211yescharacteristic
58C2×SD16×C79C2211yescharacteristic, complemented
59C2×D8×C79C2211yescharacteristic
60C22×C8×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62#11929623—22no—
63#11929623—41no—
64C2×Dic158C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79D411yescharacteristic
70D4×D79—22no—
71D4×D79—41no—
72C22×Dic79—21no—
73C22×Dic79—21no—
74C22×Dic79—21no—
75C2×C4×D79C2311yescharacteristic
76#11929614—41no—
77#11929613—22no—
78#11929612—22no—
79#11929611—41no—
80#11929609—22no—
81#11929607—22no—
82C2×C79⋊C8C2311yescharacteristic
83C2×C79⋊C8C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90Dic79⋊C4—21no—
91Dic79⋊C4D411yescharacteristic
92C22⋊Dic79—21no—
93C22⋊Dic79—21no—
94C22⋊Dic79—21no—
95C22⋊Dic79D411yescharacteristic
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4—21no—
100(C2×D79)⋊C4—21no—
101(C2×D79)⋊C4D411yescharacteristic
102C4×Dic79C2311yescharacteristic
103#41×C79—22no—
104#41×C79—22no—
105#41×C79—41no—
106#41×C79—41no—
107C2×Q8×C79C2311yescharacteristic
108C2×Q8×C79C2311yescharacteristic
109C2×D4×C79—21no—
110C2×D4×C79—21no—
111C2×D4×C79C2311yescharacteristic
112C2×D4×C79C2311yescharacteristic
113C22×C4×C79—21no—
114C22×C4×C79—21no—
115C22×C4×C79C2311yescharacteristic
116Q16×C79—22no—
117SD16×C79—22no—
118SD16×C79—22no—
119D8×C79D414yescomplemented
120C2×C8×C79—22no—
121C2×C8×C79C2311yescharacteristic
122C2×C8×C79C2311yescharacteristic
123C23×C79—21no—
124C23×C79—21no—
125C23×C79C2×D411yescharacteristic
126C22×D79—21no—
127C22×D79—42no—
128C22×D79—42no—
129C22×D79—81no—
130C22×D79C2×D411yescharacteristic
131Q8×C79—21no—
132Q8×C79—21no—
133Q8×C79—21no—
134Q8×C79—21no—
135D4×C79—21no—
136D4×C79—21no—
137D4×C79—42no—
138D4×C79—42no—
139D4×C79C2×D412yes—
140D4×C79C2×D412yes—
141C2×C4×C79—21no—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79—42no—
146C2×C4×C79—42no—
147C2×C4×C79C2×D411yescharacteristic
148C2×C4×C79C2411yescharacteristic
149C22⋊D79—41no—
150C22⋊D79—42no—
151C22⋊D79—42no—
152C22⋊D79—81no—
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—21no—
156C2×Dic79—42no—
157C2×Dic79—42no—
158C2×Dic79—81no—
159C2×Dic79C2×D411yescharacteristic
160C2×Dic79C2×D411yescharacteristic
161C2×Dic79C2×D411yescharacteristic
162D316—21no—
163D316—21no—
164C4×D79—21no—
165C4×D79—21no—
166Dic158—21no—
167Dic158—21no—
168C8×C79—21no—
169C8×C79C2×D412yes—
170C79⋊C8—21no—
171C79⋊C8—21no—
172C22×C79—22no—
173C22×C79—22no—
174C22×C79—21no—
175C22×C79—21no—
176C22×C79—21no—
177C22×C79—41no—
178C22×C79—41no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79C22×D411yescharacteristic
182C2×D79—21no—
183C2×D79—21no—
184C2×D79—21no—
185C2×D79—41no—
186C2×D79—41no—
187C2×D79—41no—
188C2×D79—84no—
189C4×C79—21no—
190C4×C79—41no—
191C4×C79—41no—
192C4×C79C22×D411yescharacteristic
193C4×C79H(5,𝔽2)11yescharacteristic
194Dic79—21no—
195Dic79—21no—
196Dic79—21no—
197Dic79—41no—
198Dic79—41no—
199Dic79—41no—
200C2×C79—42no—
201C2×C79—41no—
202C2×C79—42no—
203C2×C79D4211yescharacteristic
204C2×C79#57511yescharacteristic
205C2×C79#57711yescharacteristic
206D79—41no—
207D79—81no—
208#3267—791nomaximal, Sylow
209C79#326711yescharacteristic, complemented, Sylow
210C2×AGL(1,ℤ/8)—791no—
211C2×#135D7911yescharacteristic, complemented
212#547—791no—
213#546—791no—
214#497—791no—
215#470—791no—
216#465—791no—
217#463—791no—
218#461—791no—
219#452—791no—
220#452—791no—
221#450—791no—
222#449—791no—
223#442—791no—
224#435—791no—
225C2×#41—791no—
226C2×#41C2×D7911yescharacteristic
227C2×#41C2×D7911yescharacteristic, complemented
228C22×D4—791no—
229AGL(1,ℤ/8)—1584no—
230#135—24no—
231C2×Q16—791no—
232C2×Q16C2×D7911yescharacteristic, complemented
233C2×SD16—791no—
234C2×SD16—791no—
235C2×SD16—791no—
236C2×SD16C2×D7911yescharacteristic
237C2×SD16C2×D7911yescharacteristic, complemented
238C2×D8—791no—
239C2×D8C2×D7911yescharacteristic
240C2×M16—791no—
241C22×C8C2×D7911yescharacteristic, complemented
242C4⋊Q8—791no—
243#124—791no—
244#123—1581no—
245#123—1581no—
246#123—1581no—
247C22⋊Q8—791no—
248C22⋊Q8—791no—
249C22⋊Q8—791no—
250#121—791no—
251#121—1581no—
252#121—1581no—
253#120—1581no—
254C4×D4—791no—
255C4×D4—791no—
256C4×D4—791no—
257C2×C4⋊C4—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—
269#97—791no—
270C24—1581no—
271#41—22no—
272#41—22no—
273#41—41no—
274#41—41no—
275#41—3161no—
276#41—1582no—
277C2×Q8—791no—
278C2×Q8C22×D7911yescharacteristic
279C2×Q8C22×D7911yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—3161no—
283C2×D4—791no—
284C2×D4—791no—
285C2×D4—1581no—
286C2×D4—1581no—
287C2×D4—1582no—
288C2×D4—1581no—
289C2×D4C22×D7911yescharacteristic
290C2×D4C22×D7911yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—791no—
294C22×C4—1581no—
295C22×C4—1581no—
296C22×C4—1581no—
297C22×C4C22×D7911yescharacteristic
298Q16—22no—
299Q16—3161no—
300SD16—22no—
301SD16—22no—
302SD16—3161no—
303SD16—1582no—
304SD16—1582no—
305D8—1582no—
306D8C22⋊D7914yescomplemented
307M16—1582no—
308C2×C8—22no—
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—
319C4⋊C4—1581no—
320C4⋊C4—1581no—
321C22⋊C4—791no—
322C22⋊C4—791no—
323C22⋊C4—1581no—
324C22⋊C4—1581no—
325C22⋊C4—1581no—
326C22⋊C4—1581no—
327C22⋊C4—1581no—
328C22⋊C4—1581no—
329C22⋊C4—1581no—
330C22⋊C4—1581no—
331C42—791no—
332C23—21no—
333C23—21no—
334C23—3162no—
335C23—3162no—
336C23—791no—
337C23—6321no—
338C23—1581no—
339C23D4×D7911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—1581no—
345Q8—1581no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—42no—
350D4—3162no—
351D4—3162no—
352D4—3161no—
353D4—6321no—
354D4—1581no—
355D4—1581no—
356D4C2×C22⋊D7912yes—
357D4C2×C22⋊D7912yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—3162no—
365C2×C4—3162no—
366C2×C4—791no—
367C2×C4—791no—
368C2×C4—791no—
369C2×C4—6321no—
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—22no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—3161no—
391C22—3161no—
392C22—3161no—
393C22—6324no—
394C22—1581no—
395C22—1581no—
396C22—1581no—
397C22C2×D4×D7911yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—3161no—
402C4—3161no—
403C4—3161no—
404C4—1581no—
405C4—1581no—
406C4—1581no—
407C4C22×C22⋊D7911yescharacteristic
408C4#1457920611yescharacteristic
409C2—41no—
410C2—42no—
411C2—42no—
412C2—3161no—
413C2—6321no—
414C2D4×C22⋊D7911yescharacteristic
415C2#1909936011yescharacteristic
416C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×#135×C79C2
socleC22×C79C22×D4
hypercenterC2×#135D79
hypocenterC79#3267
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#14579185C2semidirect
2. #19099212C2semidirect
3. #19099201C2semidirect
4. #19098956C2semidirect
5. #19098818C2semidirect
6. #19098792C2semidirect
7. #19098780C2semidirect
8. #19098766C2semidirect
9. #19098725C2semidirect
10. #19098722C2semidirect
11. #19098712C2semidirect
12. #19098708C2semidirect
13. #19098675C2semidirect
14. #19098634C2semidirect
15. C2×#135×C79C2semidirect
19. C2×#11929614C22semidirect
25. #14579159C22semidirect
30. #14579140C22semidirect
38. D4×Dic79C22semidirect
42. #14579093C22semidirect
43. Dic79⋊C8C22semidirect
44. #14579086C22semidirect
45. #14579085C22semidirect
46. #14579085C22semidirect
49. #14579082C22semidirect
50. C22⋊(C79⋊C8)C22semidirect
52. #14579071C22semidirect
54. C2×#41×C79C22semidirect
56. C2×Q16×C79C22semidirect
58. C2×SD16×C79C22semidirect
60. C22×C8×C79C22semidirect
119. D8×C79D4semidirect
209. C79#3267semidirect
211. C2×#135D79semidirect
227. C2×#41C2×D79semidirect
232. C2×Q16C2×D79semidirect
237. C2×SD16C2×D79semidirect
241. C22×C8C2×D79semidirect
306. D8C22⋊D79semidirect