Finite Group Databasebeta

← #23777050

Subgroups — #23777050

Order 10112.

1492 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×#14579209C211yesmaximal, characteristic, complemented
2C22×Q8×D79C211yesmaximal, characteristic, complemented
3#19099228C213yesmaximal, complemented
4Q8×C22⋊D79C211yesmaximal, characteristic, complemented
5#19099226C213yesmaximal, complemented
6#19099225C211yesmaximal, characteristic, complemented
7#19099224C211yesmaximal, characteristic, complemented
8#19099223C213yesmaximal, complemented
9#19099222C213yesmaximal, complemented
10#19099138C213yesmaximal, complemented
11#19099136C213yesmaximal, complemented
12#19099076C213yesmaximal, complemented
13#19099072C213yesmaximal, complemented
14#19099039C211yesmaximal, characteristic, complemented
15D4×Q8×C79C211yesmaximal, characteristic, complemented
16#14579209—28no—
17C2×#11929625C2213yes—
18C2×#11929625C2211yescharacteristic, complemented
19C2×#11929624C2213yes—
20C2×#11929624C2213yescomplemented
21C22×Dic158C2213yes—
22C2×Q8×D79—28no—
23C2×Q8×D79C2213yes—
24C2×Q8×D79C2213yes—
25C2×Q8×D79C2211yescharacteristic
26C2×Q8×D79C2211yescharacteristic
27C2×Q8×D79C2213yescomplemented
28C22×C4×D79C2213yes—
29#14579160C2216yescomplemented
30#14579159C2213yescomplemented
31#14579150C2213yescomplemented
32#14579149C2213yescomplemented
33#14579147C2216yescomplemented
34#14579146C2216yes—
35#14579146C2213yes—
36#14579143C2213yes—
37#14579141C2213yescomplemented
38#14579140C2213yescomplemented
39#14579139C2213yes—
40#14579139C2216yescomplemented
41#14579139C2216yescomplemented
42#14579138C2213yes—
43#14579137C2213yes—
44#14579137C2213yescomplemented
45#14579136C2213yes—
46#14579135C2213yes—
47#14579134C2213yes—
48#14579133C2213yes—
49#14579131C2213yes—
50#14579129C2211yescharacteristic
51Q8×Dic79C2211yescharacteristic, complemented
52C4×Dic158C2213yescomplemented
53#14579126C2213yescomplemented
54C4×D316C2213yes—
55#14579123C2216yes—
56C4×C22⋊D79C2213yes—
57C4×C22⋊D79C2213yes—
58(C22⋊D79)⋊C4C2216yes—
59#14579119C2213yes—
60#14579118C2213yes—
61C22×Q8×C79C2211yescharacteristic
62C22×Q8×C79C2211yescharacteristic, complemented
63C4⋊Q8×C79C2213yescomplemented
64C22⋊Q8×C79C2213yes—
65C22⋊Q8×C79C2213yescomplemented
66C4×Q8×C79C2211yescharacteristic, complemented
67C4×D4×C79C2213yes—
68C23×D79C2311yescharacteristic
69#11929625—212no—
70#11929625—24no—
71#11929624—212no—
72#11929624—212no—
73C2×Dic158—212no—
74C2×Dic158C2316yes—
75C2×Dic158C2313yes—
76C2×Dic158C2313yes—
77C2×Dic158C2313yes—
78Q8×D79—212no—
79Q8×D79—212no—
80Q8×D79—212no—
81Q8×D79—24no—
82Q8×D79D418yescomplemented
83C2×D316C2313yes—
84C2×D316C2313yes—
85C2×D316C2313yes—
86C2×C22⋊D79C2311yescharacteristic
87C2×C22⋊D79C2313yes—
88C2×C22⋊D79C2313yes—
89C2×C22⋊D79C2311yescharacteristic
90C22×Dic79C2313yes—
91C2×C4×D79—212no—
92C2×C4×D79C2313yes—
93C2×C4×D79C2313yes—
94C2×C4×D79C2313yes—
95C2×C4×D79C2313yes—
96C2×C4×D79C2316yes—
97C2×C4×D79C2313yes—
98C4⋊Dic79C2313yes—
99C4⋊Dic79C2313yes—
100Dic79⋊C4C2313yes—
101Dic79⋊C4C2313yes—
102Dic79⋊C4C2316yes—
103Dic79⋊C4C2313yes—
104Dic79⋊C4C2313yes—
105C22⋊Dic79C2311yescharacteristic
106C22⋊Dic79C2313yes—
107(C2×D79)⋊C4C2311yescharacteristic
108(C2×D79)⋊C4C2313yes—
109(C2×D79)⋊C4C2316yes—
110(C2×D79)⋊C4C2313yes—
111(C2×D79)⋊C4C2313yes—
112(C2×D79)⋊C4C2316yes—
113(C2×D79)⋊C4C2311yescharacteristic
114(C2×D79)⋊C4C2313yes—
115C4×Dic79C2313yes—
116C4×Dic79C2316yes—
117C2×Q8×C79—24no—
118C2×Q8×C79—24no—
119C2×Q8×C79C2313yes—
120C2×Q8×C79C2313yes—
121C2×Q8×C79C2311yescharacteristic
122C2×D4×C79C2311yescharacteristic
123C22×C4×C79C2313yes—
124C22×C4×C79C2313yes—
125C4⋊C4×C79C2313yes—
126C4⋊C4×C79C2313yes—
127C4⋊C4×C79C2316yes—
128C22⋊C4×C79C2313yes—
129C22⋊C4×C79C2313yes—
130C42×C79C2313yes—
131C23×C79C2411yescharacteristic
132C23×C79C2411yescharacteristic
133C22×D79—22no—
134C22×D79—22no—
135C22×D79—22no—
136C22×D79C2413yes—
137C22×D79C2411yescharacteristic
138C22×D79C2411yescharacteristic
139Q8×C79—26no—
140Q8×C79—26no—
141Q8×C79C2×D414yes—
142D4×C79—22no—
143C2×C4×C79—26no—
144C2×C4×C79—26no—
145C2×C4×C79C2413yes—
146C2×C4×C79C2411yescharacteristic
147C2×C4×C79C2413yes—
148C2×C4×C79C2413yes—
149C2×C4×C79C2413yes—
150C22⋊D79—26no—
151C22⋊D79—22no—
152C22⋊D79—22no—
153C22⋊D79—26no—
154C2×Dic79—26no—
155C2×Dic79C2411yescharacteristic
156C2×Dic79C2413yes—
157C2×Dic79C2413yes—
158C2×Dic79C2411yescharacteristic
159C2×Dic79C2413yes—
160D316—26no—
161D316—26no—
162D316—26no—
163C4×D79—26no—
164C4×D79—26no—
165C4×D79—26no—
166C4×D79—26no—
167C4×D79—212no—
168C4×D79C2×D4112yes—
169Dic158—26no—
170Dic158—212no—
171Dic158—26no—
172Dic158C2×D4112yes—
173C22×C79—21no—
174C22×C79—21no—
175C22×C79—21no—
176C22×C79—21no—
177C22×C79—21no—
178C22×C792−1+412yescomplemented
179C22×C79C2511yescharacteristic
180C2×D79—28no—
181C2×D79—21no—
182C2×D79—21no—
183C2×D79—21no—
184C2×D79—21no—
185C2×D79—23no—
186C2×D79—23no—
187C2×D79—23no—
188C2×D79C22×D412yes—
189C2×D792−1+412yescomplemented
190C4×C79—23no—
191C4×C79—23no—
192C4×C79—21no—
193C4×C79—23no—
194C4×C79C22×D416yes—
195Dic79—21no—
196Dic79—23no—
197Dic79—21no—
198Dic79—23no—
199Dic79C22×D416yes—
200C2×C79—22no—
201C2×C79—41no—
202C2×C79C23×D411yescharacteristic
203C2×C79C2×2−1+411yescharacteristic
204C2×C79C2×2−1+411yescharacteristic
205D79—22no—
206D79—22no—
207D79—43no—
208#3486—791nomaximal, Sylow
209C79#348611yescharacteristic, complemented, Sylow
210C2×2−1+4—791no—
211C23×Q8—791no—
212D4×Q8—791no—
213D4×Q8—793no—
214D4×Q8—793no—
215D4×Q8D7911yescharacteristic, complemented
216#548—791no—
217#548—793no—
218#548—791no—
219#548—793no—
220#536—793no—
221#536—793no—
222#525—793no—
223#525—793no—
224#519—791no—
2252−1+4—1588no—
226C2×#41—793no—
227C2×#41—791no—
228C2×#41—793no—
229C2×#41—793no—
230C22×Q8—791no—
231C22×Q8—793no—
232C22×Q8—793no—
233C22×Q8—791no—
234C22×Q8—793no—
235C22×Q8—793no—
236C22×Q8—1588no—
237C22×Q8C2×D7911yescharacteristic
238C22×Q8C2×D7911yescharacteristic, complemented
239C23×C4—793no—
240C4⋊Q8—793no—
241C4⋊Q8—796no—
242C4⋊Q8C2×D7913yescomplemented
243#124—793no—
244#124—796no—
245#124—793no—
246#123—796no—
247#123—793no—
248#123—793no—
249C22⋊Q8—793no—
250C22⋊Q8—793no—
251C22⋊Q8—793no—
252C22⋊Q8—793no—
253C22⋊Q8—796no—
254C22⋊Q8—796no—
255C22⋊Q8—793no—
256C22⋊Q8—793no—
257C22⋊Q8C2×D7913yes—
258C22⋊Q8C2×D7913yescomplemented
259#121—793no—
260#121—793no—
261#121—793no—
262#121—793no—
263#120—791no—
264#120—793no—
265C4×Q8—791no—
266C4×Q8—793no—
267C4×Q8—793no—
268C4×Q8C2×D7911yescharacteristic, complemented
269C4×D4—793no—
270C4×D4—793no—
271C4×D4—796no—
272C4×D4—796no—
273C4×D4—793no—
274C4×D4C2×D7913yes—
275#117—793no—
276#117—793no—
277C24—791no—
278#41—15812no—
279#41—15812no—
280#41—15812no—
281#41—1584no—
282C2×Q8—24no—
283C2×Q8—24no—
284C2×Q8—798no—
285C2×Q8—793no—
286C2×Q8—796no—
287C2×Q8—793no—
288C2×Q8—793no—
289C2×Q8—15812no—
290C2×Q8—15812no—
291C2×Q8—15812no—
292C2×Q8—15812no—
293C2×Q8—1584no—
294C2×Q8C22×D7913yes—
295C2×Q8C22×D7913yes—
296C2×Q8C22×D7911yescharacteristic
297C2×D4—791no—
298C2×D4—793no—
299C2×D4—791no—
300C2×D4—793no—
301C2×D4—793no—
302C2×D4—793no—
303C2×D4—793no—
304C2×D4C22×D7911yescharacteristic
305C22×C4—793no—
306C22×C4—793no—
307C22×C4—793no—
308C22×C4—793no—
309C22×C4—796no—
310C22×C4—793no—
311C22×C4—793no—
312C22×C4—15812no—
313C22×C4C22×D7913yes—
314C22×C4C22×D7913yes—
315C4⋊C4—793no—
316C4⋊C4—793no—
317C4⋊C4—796no—
318C4⋊C4—793no—
319C4⋊C4—793no—
320C4⋊C4—793no—
321C4⋊C4—793no—
322C4⋊C4C22×D7913yes—
323C4⋊C4C22×D7916yes—
324C4⋊C4C22×D7913yes—
325C22⋊C4—791no—
326C22⋊C4—793no—
327C22⋊C4—793no—
328C22⋊C4—791no—
329C22⋊C4—793no—
330C22⋊C4—791no—
331C22⋊C4—793no—
332C22⋊C4—796no—
333C22⋊C4—796no—
334C22⋊C4—793no—
335C22⋊C4C22×D7913yes—
336C22⋊C4C22×D7913yes—
337C42—796no—
338C42—793no—
339C42C22×D7913yes—
340C23—791no—
341C23—791no—
342C23—793no—
343C23—1582no—
344C23—1582no—
345C23—1582no—
346C23C23×D7911yescharacteristic
347C23C23×D7911yescharacteristic
348Q8—26no—
349Q8—26no—
350Q8—7912no—
351Q8—15812no—
352Q8—1586no—
353Q8—1586no—
354Q8D4×D7914yes—
355D4—22no—
356D4—1586no—
357D4—1586no—
358D4—1586no—
359D4—1582no—
360D4—1582no—
361D4—1586no—
362D4—1586no—
363C2×C4—26no—
364C2×C4—26no—
365C2×C4—793no—
366C2×C4—7912no—
367C2×C4—791no—
368C2×C4—793no—
369C2×C4—793no—
370C2×C4—791no—
371C2×C4—1586no—
372C2×C4—15812no—
373C2×C4—1586no—
374C2×C4—1586no—
375C2×C4—1586no—
376C2×C4—1586no—
377C2×C4C23×D7913yes—
378C2×C4C23×D7911yescharacteristic
379C2×C4C23×D7913yes—
380C2×C4C23×D7913yes—
381C2×C4C23×D7913yes—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—792no—
388C22—792no—
389C22—1588no—
390C22—1583no—
391C22—1583no—
392C22—1583no—
393C22—1581no—
394C22—1581no—
395C22—1581no—
396C22—1581no—
397C22#1457920912yescomplemented
398C22C24×D7911yescharacteristic
399C4—23no—
400C4—21no—
401C4—23no—
402C4—23no—
403C4—796no—
404C4—1581no—
405C4—1583no—
406C4—1581no—
407C4—1583no—
408C4C2×D4×D7916yes—
409C2—22no—
410C2—41no—
411C2—3163no—
412C2—1582no—
413C2—1582no—
414C2C22×D4×D7911yescharacteristic
415C22−1+4×D7911yescharacteristic
416C2C2×#1457920911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D79
commutator, socle, cosocleC22×C79C25
FittingD4×Q8×C79C2
hypercenterD4×Q8D79
hypocenterC79#3486
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14579209C2semidirect
2. C22×Q8×D79C2semidirect
3. #19099228C2semidirect
4. Q8×C22⋊D79C2semidirect
5. #19099226C2semidirect
6. #19099225C2semidirect
7. #19099224C2semidirect
8. #19099223C2semidirect
9. #19099222C2semidirect
10. #19099138C2semidirect
11. #19099136C2semidirect
12. #19099076C2semidirect
13. #19099072C2semidirect
14. #19099039C2semidirect
15. D4×Q8×C79C2semidirect
18. C2×#11929625C22semidirect
20. C2×#11929624C22semidirect
27. C2×Q8×D79C22semidirect
29. #14579160C22semidirect
30. #14579159C22semidirect
31. #14579150C22semidirect
32. #14579149C22semidirect
33. #14579147C22semidirect
37. #14579141C22semidirect
38. #14579140C22semidirect
40. #14579139C22semidirect
41. #14579139C22semidirect
44. #14579137C22semidirect
51. Q8×Dic79C22semidirect
52. C4×Dic158C22semidirect
53. #14579126C22semidirect
62. C22×Q8×C79C22semidirect
63. C4⋊Q8×C79C22semidirect
65. C22⋊Q8×C79C22semidirect
66. C4×Q8×C79C22semidirect
82. Q8×D79D4semidirect
178. C22×C792−1+4semidirect
189. C2×D792−1+4semidirect
209. C79#3486semidirect
215. D4×Q8D79semidirect
238. C22×Q8C2×D79semidirect
242. C4⋊Q8C2×D79semidirect
258. C22⋊Q8C2×D79semidirect
268. C4×Q8C2×D79semidirect
397. C22#14579209semidirect