Finite Group Databasebeta

← #23777079

Subgroups — #23777079

Order 10112.

1522 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579209C211yesmaximal, characteristic, complemented
2C2×#41×D79C211yesmaximal, characteristic, complemented
3Q8×D316C211yesmaximal, characteristic, complemented
4Q8×C22⋊D79C211yesmaximal, characteristic, complemented
5#19099220C211yesmaximal, characteristic, complemented
6#19099218C213yesmaximal, complemented
7#19099215C213yesmaximal, complemented
8#19099210C213yesmaximal, complemented
9#19099206C213yesmaximal, complemented
10#19099142C213yesmaximal, complemented
11#19099133C213yesmaximal, complemented
12#19099072C213yesmaximal, complemented
13C22⋊Q8×D79C213yesmaximal, complemented
14#19099045C211yesmaximal, characteristic, complemented
15#548×C79C211yesmaximal, characteristic, complemented
16#14579209—28no—
17C2×#11929625C2211yescharacteristic
18C2×#11929625C2213yescomplemented
19C2×#11929624C2213yes—
20C2×#11929624C2213yescomplemented
21C2×#11929624C2213yescomplemented
22C2×#11929623C2213yes—
23#41×D79—28no—
24C2×Q8×D79C2211yescharacteristic
25C2×Q8×D79C2211yescharacteristic, complemented
26C2×Q8×D79C2213yescomplemented
27C2×D4×D79C2213yes—
28C22×C4×D79C2213yes—
29#14579161C2213yescomplemented
30#14579159C2213yescomplemented
31#14579148C2213yescomplemented
32#14579146C2213yescomplemented
33#14579143C2216yescomplemented
34#14579143C2216yescomplemented
35#14579143C2213yescomplemented
36#14579141C2213yes—
37#14579141C2213yescomplemented
38#14579140C2213yescomplemented
39#14579140C2213yescomplemented
40#14579139C2213yes—
41#14579138C2216yescomplemented
42#14579138C2213yescomplemented
43#14579137C2213yes—
44#14579134C2211yescharacteristic
45#14579134C2216yescomplemented
46#14579133C2213yescomplemented
47#14579132C2213yescomplemented
48#14579132C2216yescomplemented
49#14579131C2213yes—
50#14579129C2213yes—
51Q8×Dic79C2211yescharacteristic, complemented
52C4×D316C2213yes—
53C4×D316C2213yescomplemented
54#14579123C2213yescomplemented
55C4×C22⋊D79C2213yes—
56C4×C22⋊D79C2213yescomplemented
57#14579118C2213yescomplemented
58C4⋊C4×D79C2213yescomplemented
59C4⋊C4×D79C2216yescomplemented
60C22⋊C4×D79C2216yes—
61C2×#41×C79C2211yescharacteristic
62C22×Q8×C79C2211yescharacteristic, complemented
63#124×C79C2213yescomplemented
64C22⋊Q8×C79C2213yescomplemented
65#121×C79C2213yescomplemented
66C4×Q8×C79C2211yescharacteristic, complemented
67C4×D4×C79C2213yescomplemented
68C23×D79C2313yes—
69#11929625—212no—
70#11929625D418yescomplemented
71#11929624—212no—
72#11929624—212no—
73#11929624—212no—
74#11929623—212no—
75C2×Dic158C2313yes—
76C2×Dic158C2313yes—
77C2×Dic158C2313yes—
78Q8×D79—212no—
79Q8×D79—24no—
80Q8×D79—24no—
81C2×D316C2313yes—
82C2×D316C2311yescharacteristic
83C2×D316C2313yes—
84C2×C22⋊D79C2316yes—
85C2×C22⋊D79C2313yes—
86C2×C22⋊D79C2311yescharacteristic
87C2×C22⋊D79C2311yescharacteristic
88C2×C22⋊D79C2313yes—
89D4×D79—212no—
90C22×Dic79C2313yes—
91C2×C4×D79—212no—
92C2×C4×D79C2313yes—
93C2×C4×D79C2316yes—
94C2×C4×D79C2313yes—
95C2×C4×D79C2313yes—
96C2×C4×D79C2311yescharacteristic
97C2×C4×D79C2316yes—
98C2×C4×D79C2313yes—
99C4⋊Dic79C2313yes—
100C4⋊Dic79C2316yes—
101C4⋊Dic79C2313yes—
102Dic79⋊C4C2313yes—
103Dic79⋊C4C2313yes—
104Dic79⋊C4C2316yes—
105Dic79⋊C4C2311yescharacteristic
106Dic79⋊C4C2313yes—
107C22⋊Dic79C2316yes—
108C22⋊Dic79C2313yes—
109C22⋊Dic79C2313yes—
110(C2×D79)⋊C4C2313yes—
111(C2×D79)⋊C4C2313yes—
112(C2×D79)⋊C4C2313yes—
113(C2×D79)⋊C4C2313yes—
114(C2×D79)⋊C4C2311yescharacteristic
115(C2×D79)⋊C4C2313yes—
116C4×Dic79C2313yes—
117#41×C79—24no—
118C2×Q8×C79—24no—
119C2×Q8×C79C2313yes—
120C2×Q8×C79C2311yescharacteristic
121C2×D4×C79C2313yes—
122C2×D4×C79C2313yes—
123C22×C4×C79C2313yes—
124C22×C4×C79C2313yes—
125C4⋊C4×C79C2313yes—
126C4⋊C4×C79C2313yes—
127C22⋊C4×C79C2311yescharacteristic
128C22⋊C4×C79C2313yes—
129C22⋊C4×C79C2316yes—
130C42×C79C2313yes—
131C23×C79C2413yes—
132C23×C79C2411yescharacteristic
133C22×D79—26no—
134C22×D79—26no—
135C22×D79—43no—
136C22×D79C2411yescharacteristic
137C22×D79C2413yes—
138C22×D79C2411yescharacteristic
139Q8×C79—26no—
140Q8×C79C2×D414yes—
141D4×C79—26no—
142D4×C79—43no—
143C2×C4×C79—26no—
144C2×C4×C79—26no—
145C2×C4×C79C2411yescharacteristic
146C2×C4×C79C2413yes—
147C2×C4×C79C2411yescharacteristic
148C2×C4×C79C2413yes—
149C2×C4×C79C2413yes—
150C22⋊D79—212no—
151C22⋊D79—26no—
152C22⋊D79—22no—
153C22⋊D79—22no—
154C22⋊D79—43no—
155C2×Dic79—26no—
156C2×Dic79C2411yescharacteristic
157C2×Dic79C2413yes—
158C2×Dic79C2413yes—
159C2×Dic79C2413yes—
160C2×Dic79C2411yescharacteristic
161D316—26no—
162D316—22no—
163D316C2×D4112yes—
164C4×D79—26no—
165C4×D79—212no—
166C4×D79—26no—
167C4×D79—26no—
168C4×D79—22no—
169C4×D79—46no—
170C4×D79C2×D4112yes—
171Dic158—26no—
172Dic158—26no—
173Dic158—26no—
174C22×C79—21no—
175C22×C79—23no—
176C22×C79—21no—
177C22×C79—23no—
178C22×C79—23no—
179C22×C79—21no—
180C22×C79C2511yescharacteristic
181C2×D79—21no—
182C2×D79—23no—
183C2×D79—21no—
184C2×D79—23no—
185C2×D79—21no—
186C2×D79—21no—
187C2×D79—21no—
188C2×D79—412no—
189C2×D79C22×D416yes—
190C2×D792−1+412yescomplemented
191C4×C79—21no—
192C4×C79—23no—
193C4×C79—21no—
194C4×C79—23no—
195C4×C79C22×D416yes—
196Dic79—23no—
197Dic79—23no—
198Dic79—21no—
199Dic79—23no—
200Dic79C22×D412yes—
201C2×C79—43no—
202C2×C79—41no—
203C2×C79C23×D411yescharacteristic
204C2×C79C2×2−1+411yescharacteristic
205C2×C79#58511yescharacteristic
206D79—22no—
207D79—26no—
208D79—41no—
209#3489—791nomaximal, Sylow
210C79#348911yescharacteristic, complemented, Sylow
211C2×2−1+4—791no—
212C22×#41—791no—
213D4×Q8—791no—
214D4×Q8—791no—
215#548—791no—
216#548D7911yescharacteristic, complemented
217#547—793no—
218#547—793no—
219#546—793no—
220#546—793no—
221#537—793no—
222#536—793no—
223#525—793no—
224C2×C22⋊Q8—793no—
225#520—791no—
2262−1+4—1588no—
227C2×#41—791no—
228C2×#41—793no—
229C2×#41—793no—
230C2×#41—793no—
231C2×#41—793no—
232C2×#41—793no—
233C2×#41—1588no—
234C2×#41C2×D7911yescharacteristic
235C22×Q8—791no—
236C22×Q8—793no—
237C22×Q8—791no—
238C22×Q8C2×D7911yescharacteristic, complemented
239C22×D4—793no—
240C23×C4—793no—
241C4⋊Q8—793no—
242C4⋊Q8—793no—
243#124—793no—
244#124C2×D7913yescomplemented
245#123—793no—
246#123—793no—
247#123—796no—
248#123—796no—
249C22⋊Q8—793no—
250C22⋊Q8—793no—
251C22⋊Q8—793no—
252C22⋊Q8—793no—
253C22⋊Q8—793no—
254C22⋊Q8—793no—
255C22⋊Q8—796no—
256C22⋊Q8—793no—
257C22⋊Q8C2×D7913yescomplemented
258#121—793no—
259#121—796no—
260#121—793no—
261#121—791no—
262#121—796no—
263#121C2×D7913yescomplemented
264#120—793no—
265#120—793no—
266C4×Q8—791no—
267C4×Q8C2×D7911yescharacteristic, complemented
268C4×D4—793no—
269C4×D4—793no—
270C4×D4—793no—
271C4×D4—793no—
272C4×D4—793no—
273C4×D4C2×D7913yescomplemented
274#117—793no—
275C2×C4⋊C4—793no—
276C2×C4⋊C4—796no—
277C2×C22⋊C4—796no—
278C24—793no—
279#41—24no—
280#41—798no—
281#41—15812no—
282#41—15812no—
283#41—15812no—
284#41—15812no—
285#41—15812no—
286C2×Q8—24no—
287C2×Q8—793no—
288C2×Q8—793no—
289C2×Q8—793no—
290C2×Q8—15812no—
291C2×Q8—1584no—
292C2×Q8—1584no—
293C2×Q8C22×D7913yes—
294C2×Q8C22×D7911yescharacteristic
295C2×D4—793no—
296C2×D4—791no—
297C2×D4—793no—
298C2×D4—791no—
299C2×D4—796no—
300C2×D4—793no—
301C2×D4—791no—
302C2×D4—793no—
303C2×D4—15812no—
304C2×D4C22×D7913yes—
305C2×D4C22×D7913yes—
306C22×C4—796no—
307C22×C4—793no—
308C22×C4—793no—
309C22×C4—796no—
310C22×C4—793no—
311C22×C4—793no—
312C22×C4—793no—
313C22×C4—791no—
314C22×C4—15812no—
315C22×C4C22×D7913yes—
316C22×C4C22×D7913yes—
317C4⋊C4—793no—
318C4⋊C4—793no—
319C4⋊C4—796no—
320C4⋊C4—791no—
321C4⋊C4—793no—
322C4⋊C4—793no—
323C4⋊C4—796no—
324C4⋊C4—793no—
325C4⋊C4C22×D7913yes—
326C4⋊C4C22×D7913yes—
327C22⋊C4—796no—
328C22⋊C4—793no—
329C22⋊C4—793no—
330C22⋊C4—793no—
331C22⋊C4—793no—
332C22⋊C4—793no—
333C22⋊C4—793no—
334C22⋊C4—791no—
335C22⋊C4—793no—
336C22⋊C4C22×D7916yes—
337C22⋊C4C22×D7911yescharacteristic
338C22⋊C4C22×D7913yes—
339C42—793no—
340C42C22×D7913yes—
341C23—3163no—
342C23—791no—
343C23—793no—
344C23—791no—
345C23—1586no—
346C23—1586no—
347C23C23×D7913yes—
348C23C23×D7911yescharacteristic
349Q8—26no—
350Q8—1586no—
351Q8—1586no—
352Q8—1586no—
353Q8D4×D7914yes—
354D4—26no—
355D4—43no—
356D4—3163no—
357D4—7912no—
358D4—1586no—
359D4—1582no—
360D4—1582no—
361D4—1582no—
362D4—15812no—
363D4—1586no—
364C2×C4—26no—
365C2×C4—26no—
366C2×C4—3166no—
367C2×C4—791no—
368C2×C4—7912no—
369C2×C4—791no—
370C2×C4—793no—
371C2×C4—793no—
372C2×C4—793no—
373C2×C4—1582no—
374C2×C4—1586no—
375C2×C4—15812no—
376C2×C4—1586no—
377C2×C4—1586no—
378C2×C4—1586no—
379C2×C4C23×D7911yescharacteristic
380C2×C4C23×D7913yes—
381C2×C4C23×D7913yes—
382C2×C4C23×D7911yescharacteristic
383C2×C4C23×D7913yes—
384C22—21no—
385C22—23no—
386C22—21no—
387C22—23no—
388C22—21no—
389C22—23no—
390C22—31612no—
391C22—792no—
392C22—796no—
393C22—1581no—
394C22—1581no—
395C22—1581no—
396C22—1583no—
397C22—1583no—
398C22—1581no—
399C22—1581no—
400C22C24×D7911yescharacteristic
401C4—21no—
402C4—23no—
403C4—21no—
404C4—23no—
405C4—792no—
406C4—1581no—
407C4—1583no—
408C4—1583no—
409C4—1583no—
410C4C2×D4×D7916yes—
411C2—43no—
412C2—41no—
413C2—3161no—
414C2—1582no—
415C2—1586no—
416C2C22×D4×D7911yescharacteristic
417C22−1+4×D7911yescharacteristic
418C2#1909939911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D79
commutator, socle, cosocleC22×C79C25
Fitting#548×C79C2
hypercenter#548D79
hypocenterC79#3489
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14579209C2semidirect
2. C2×#41×D79C2semidirect
3. Q8×D316C2semidirect
4. Q8×C22⋊D79C2semidirect
5. #19099220C2semidirect
6. #19099218C2semidirect
7. #19099215C2semidirect
8. #19099210C2semidirect
9. #19099206C2semidirect
10. #19099142C2semidirect
11. #19099133C2semidirect
12. #19099072C2semidirect
13. C22⋊Q8×D79C2semidirect
14. #19099045C2semidirect
15. #548×C79C2semidirect
18. C2×#11929625C22semidirect
20. C2×#11929624C22semidirect
21. C2×#11929624C22semidirect
25. C2×Q8×D79C22semidirect
26. C2×Q8×D79C22semidirect
29. #14579161C22semidirect
30. #14579159C22semidirect
31. #14579148C22semidirect
32. #14579146C22semidirect
33. #14579143C22semidirect
34. #14579143C22semidirect
35. #14579143C22semidirect
37. #14579141C22semidirect
38. #14579140C22semidirect
39. #14579140C22semidirect
41. #14579138C22semidirect
42. #14579138C22semidirect
45. #14579134C22semidirect
46. #14579133C22semidirect
47. #14579132C22semidirect
48. #14579132C22semidirect
51. Q8×Dic79C22semidirect
53. C4×D316C22semidirect
54. #14579123C22semidirect
56. C4×C22⋊D79C22semidirect
57. #14579118C22semidirect
58. C4⋊C4×D79C22semidirect
59. C4⋊C4×D79C22semidirect
62. C22×Q8×C79C22semidirect
63. #124×C79C22semidirect
64. C22⋊Q8×C79C22semidirect
65. #121×C79C22semidirect
66. C4×Q8×C79C22semidirect
67. C4×D4×C79C22semidirect
70. #11929625D4semidirect
190. C2×D792−1+4semidirect
210. C79#3489semidirect
216. #548D79semidirect
238. C22×Q8C2×D79semidirect
244. #124C2×D79semidirect
257. C22⋊Q8C2×D79semidirect
263. #121C2×D79semidirect
267. C4×Q8C2×D79semidirect
273. C4×D4C2×D79semidirect