Finite Group Databasebeta

← #2249×D79 #34443664

Subgroups — #2249×D79 #34443664

Order 20224.

854 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q32×D79C211yesmaximal, characteristic, complemented
2C2×SD32×D79C212yesmaximal, complemented
3C2×D16×D79C211yesmaximal, characteristic
4#495×D79C212yesmaximal, complemented
5#23765662C211yesmaximal, characteristic, complemented
6#23765661C211yesmaximal, characteristic, complemented
7#23765660C212yesmaximal, complemented
8#23765659C212yesmaximal, complemented
9#23765658C211yesmaximal, characteristic, complemented
10C4×C16×D79C211yesmaximal, characteristic, complemented
11C79×#2249C211yesmaximal, characteristic, complemented
12C2×Q16×D79C2212yes—
13C2×SD16×D79—22no—
14C2×D8×D79C2212yes—
15#124×D79—22no—
16C2×Dic632C2211yescharacteristic, complemented
17C2×#14579107C2212yescomplemented
18Q32×D79—24no—
19C2×#14579106C2212yescomplemented
20C2×#14579105C2212yescomplemented
21C2×#14579104C2212yescomplemented
22SD32×D79—28no—
23C2×D1264C2211yescharacteristic
24C2×#14579102C2212yes—
25D16×D79—24no—
26C2×C16×D79C2211yescharacteristic
27C2×C16×D79C2211yescharacteristic
28#19098948C2212yescomplemented
29#19098947C2212yescomplemented
30#19098946C2212yescomplemented
31#19098945—22no—
32#19098944—22no—
33C4×C8×D79C2211yescharacteristic
34C4×C79⋊C16C2211yescharacteristic, complemented
35C16×Dic79C2211yescharacteristic, complemented
36C16×Dic79C2211yescharacteristic, complemented
37C2×Q32×C79C2211yescharacteristic, complemented
38C2×SD32×C79C2212yescomplemented
39C2×D16×C79C2211yescharacteristic
40#495×C79C2212yescomplemented
41C4×C16×C79C2211yescharacteristic, complemented
42C2×Q8×D79—22no—
43C2×D4×D79—22no—
44C2×Dic316C2312yes—
45C2×#11929614—22no—
46Q16×D79—24no—
47Q16×D79—24no—
48C2×#11929613—22no—
49C2×#11929612—22no—
50C2×#11929611—22no—
51SD16×D79—48no—
52C2×D632C2312yes—
53C2×#11929609—22no—
54D8×D79—24no—
55D8×D79—24no—
56C2×C8×D79D411yescharacteristic
57C2×C8×D79C2311yescharacteristic
58#14579150—22no—
59#14579149—22no—
60#14579148—22no—
61#14579147—44no—
62C22⋊C4×D79—44no—
63C42×D79D411yescharacteristic
64Dic632—22no—
65#14579107—24no—
66#14579106—24no—
67#14579105—24no—
68#14579104—24no—
69D1264—22no—
70#14579102—24no—
71C2×C79⋊C16C2311yescharacteristic
72C2×C79⋊C16C2311yescharacteristic
73C16×D79D414yes—
74C16×D79D414yes—
75C4×C79⋊C8D411yescharacteristic
76C8×Dic79D411yescharacteristic
77C8×Dic79C2311yescharacteristic
78C2×Q16×C79C2312yes—
79C2×SD16×C79—22no—
80C2×D8×C79C2312yes—
81#124×C79—22no—
82Q32×C79—22no—
83SD32×C79—24no—
84D16×C79—22no—
85C2×C16×C79C2311yescharacteristic
86C2×C16×C79C2311yescharacteristic
87C4×C8×C79C2311yescharacteristic
88C23×D79—42no—
89C2×Dic158—22no—
90C2×Dic158—42no—
91Q8×D79—44no—
92Q8×D79—44no—
93C2×D316—22no—
94C2×C22⋊D79—42no—
95D4×D79—44no—
96D4×D79—44no—
97C2×C4×D79—42no—
98C2×C4×D79D812yes—
99C2×C4×D79C2×D411yescharacteristic
100Dic316—22no—
101Dic316—22no—
102#11929614—44no—
103#11929613—44no—
104#11929612—44no—
105#11929611—44no—
106D632—22no—
107D632—22no—
108#11929609—44no—
109C2×C79⋊C8C2×D411yescharacteristic
110C2×C79⋊C8C2×D411yescharacteristic
111C8×D79D814yes—
112C8×D79C2×D412yes—
113C8×D79C2×D412yes—
114C22⋊Dic79—44no—
115(C2×D79)⋊C4—44no—
116(C2×D79)⋊C4—44no—
117C4×Dic79D812yes—
118C4×Dic79C2×D411yescharacteristic
119C79⋊C16C2×D412yes—
120C79⋊C16C2×D412yes—
121C2×Q8×C79—22no—
122C2×D4×C79—22no—
123Q16×C79—22no—
124Q16×C79—22no—
125SD16×C79—44no—
126D8×C79—22no—
127D8×C79—22no—
128C2×C8×C79C2×D411yescharacteristic
129C2×C8×C79C2411yescharacteristic
130C22⋊C4×C79—44no—
131C42×C79C2×D411yescharacteristic
132C16×C79C2×D412yes—
133C16×C79C2×D412yes—
134C23×C79—42no—
135C22×D79—42no—
136C22×D79—84no—
137C22×D79—88no—
138C22×D79C2×D811yescharacteristic
139Q8×C79—42no—
140Q8×C79—42no—
141D4×C79—42no—
142D4×C79—42no—
143C2×C4×C79—42no—
144C2×C4×C79C2×D812yes—
145C2×C4×C79C22×D411yescharacteristic
146C22⋊D79—84no—
147C2×Dic79—42no—
148C2×Dic79C2×D812yes—
149C2×Dic79C2×D811yescharacteristic
150D316—42no—
151D316—42no—
152C4×D79—24no—
153C4×D79—84no—
154C4×D79#12712yes—
155C4×D79C2×D812yes—
156Dic158—42no—
157Dic158—42no—
158Dic158—84no—
159C8×C79C2×D812yes—
160C8×C79C22×D411yescharacteristic
161C8×C79C22×D411yescharacteristic
162C79⋊C8#12712yes—
163C79⋊C8C2×D812yes—
164C22×C79—82no—
165C22×C79—84no—
166C22×C79C22×D811yescharacteristic
167C2×D79—82no—
168C2×D79—84no—
169C2×D79—168no—
170C2×D79#49312yes—
171C2×D79#50814yes—
172C4×C79—22no—
173C4×C79—82no—
174C4×C79C2×#12711yescharacteristic
175C4×C79C22×D811yescharacteristic
176Dic79—22no—
177Dic79—82no—
178Dic79#49312yes—
179C2×#2249—791nomaximal, Sylow
180C2×C79—162no—
181C2×C79C2×#49311yescharacteristic
182C2×C79C2×#50812yes—
183D79—162no—
184D79#224914yesdirect product factor
185C22×Q32—791no—
186C22×SD32—792no—
187C22×D16—791no—
188C2×#495—792no—
189#2249—791no—
190#2249—792no—
191#2249—791no—
192#2249—792no—
193#2249—791no—
194#2249D7911yescharacteristic, direct product factor
195C2×C4×C16—791no—
196C79C2×#224911yescharacteristic, complemented, Sylow
197C22×Q16—792no—
198C22×SD16—1582no—
199C22×D8—792no—
200C2×#124—1582no—
201C2×Q32—792no—
202C2×Q32—791no—
203C2×Q32—1584no—
204C2×Q32C2×D7911yescharacteristic, complemented
205C2×SD32—792no—
206C2×SD32—792no—
207C2×SD32—792no—
208C2×SD32—1588no—
209C2×SD32C2×D7912yescomplemented
210C2×D16—792no—
211C2×D16—791no—
212C2×D16—1584no—
213C2×D16C2×D7911yescharacteristic
214C22×C16—791no—
215C22×C16—791no—
216#495—792no—
217#495—792no—
218#495—792no—
219#495—1582no—
220#495—1582no—
221#495C2×D7912yescomplemented
222C2×C4×C8—791no—
223C4×C16—791no—
224C4×C16—791no—
225C4×C16—791no—
226C4×C16C2×D7911yescharacteristic, complemented
227C22×Q8—1582no—
228C22×D4—1582no—
229C2×Q16—792no—
230C2×Q16—1584no—
231C2×Q16—1584no—
232C2×Q16—1582no—
233C2×Q16C22×D7912yes—
234C2×SD16—22no—
235C2×SD16—3168no—
236C2×SD16—1582no—
237C2×SD16—1582no—
238C2×SD16—1582no—
239C2×D8—792no—
240C2×D8—1584no—
241C2×D8—1584no—
242C2×D8—1582no—
243C2×D8C22×D7912yes—
244C22×C8—791no—
245C22×C8—791no—
246#124—22no—
247#124—3164no—
248#124—1582no—
249#124—1582no—
250#124—1582no—
251C2×C22⋊C4—3164no—
252C2×C42—791no—
253Q32—22no—
254Q32—1584no—
255Q32—1582no—
256SD32—24no—
257SD32—1584no—
258SD32—1584no—
259SD32—1584no—
260D16—22no—
261D16—1584no—
262D16—1582no—
263C2×C16—791no—
264C2×C16—791no—
265C2×C16—794no—
266C2×C16—794no—
267C2×C16C22×D7911yescharacteristic
268C2×C16C22×D7911yescharacteristic
269C4×C8—791no—
270C4×C8—791no—
271C4×C8—791no—
272C4×C8C22×D7911yescharacteristic
273C24—3162no—
274C2×Q8—22no—
275C2×Q8—3162no—
276C2×Q8—3164no—
277C2×Q8—3164no—
278C2×Q8—1582no—
279C2×D4—22no—
280C2×D4—3164no—
281C2×D4—3164no—
282C2×D4—3162no—
283C2×D4—1582no—
284C22×C4—3162no—
285C22×C4—791no—
286C22×C4—792no—
287Q16—22no—
288Q16—22no—
289Q16—3164no—
290Q16—1582no—
291Q16—1582no—
292SD16—44no—
293SD16—3164no—
294SD16—3164no—
295SD16—3164no—
296D8—22no—
297D8—22no—
298D8—3164no—
299D8—1582no—
300D8—1582no—
301C2×C8—791no—
302C2×C8—791no—
303C2×C8—794no—
304C2×C8—792no—
305C2×C8—792no—
306C2×C8D4×D7911yescharacteristic
307C2×C8C23×D7911yescharacteristic
308C22⋊C4—44no—
309C22⋊C4—3164no—
310C22⋊C4—3164no—
311C22⋊C4—3164no—
312C42—792no—
313C42—791no—
314C42D4×D7911yescharacteristic
315C16—792no—
316C16—792no—
317C16D4×D7912yes—
318C16D4×D7912yes—
319C23—42no—
320C23—3162no—
321C23—791no—
322C23—6324no—
323C23—6328no—
324Q8—42no—
325Q8—42no—
326Q8—3162no—
327Q8—3162no—
328Q8—6324no—
329D4—42no—
330D4—42no—
331D4—3162no—
332D4—3162no—
333D4—6324no—
334C2×C4—42no—
335C2×C4—3162no—
336C2×C4—791no—
337C2×C4—792no—
338C2×C4—792no—
339C2×C4—792no—
340C2×C4—6324no—
341C2×C4—1584no—
342C2×C4D8×D7912yes—
343C2×C4C2×D4×D7911yescharacteristic
344C8—792no—
345C8—792no—
346C8D8×D7912yes—
347C8C2×D4×D7911yescharacteristic
348C8C2×D4×D7911yescharacteristic
349C22—84no—
350C22—82no—
351C22—794no—
352C22—792no—
353C22—6324no—
354C22—6322no—
355C22—12648no—
356C22C2×D8×D7911yescharacteristic
357C4—22no—
358C4—82no—
359C4—792no—
360C4—6322no—
361C4—1582no—
362C4#127×D7911yescharacteristic
363C4C2×D8×D7911yescharacteristic
364C2—162no—
365C2—794no—
366C2—12642no—
367C2#493×D7911yescharacteristic
368C2#508×D7912yes—
subgroupG/H
centerC22C2×D8×D79
commutator, cosocleC2×C8×C79C24
FrattiniC2×C8C23×D79
FittingC79×#2249C2
socleC22×C79C22×D8
prime radicalC2×D16×D79C2
hypercenter#2249D79
hypocenterC79C2×#2249
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2249

Complements

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

NH ≅ G/Ntype
1. C2×Q32×D79C2semidirect
2. C2×SD32×D79C2semidirect
4. #495×D79C2semidirect
5. #23765662C2semidirect
6. #23765661C2semidirect
7. #23765660C2semidirect
8. #23765659C2semidirect
9. #23765658C2semidirect
10. C4×C16×D79C2semidirect
11. C79×#2249C2semidirect
16. C2×Dic632C22semidirect
17. C2×#14579107C22semidirect
19. C2×#14579106C22semidirect
20. C2×#14579105C22semidirect
21. C2×#14579104C22semidirect
28. #19098948C22semidirect
29. #19098947C22semidirect
30. #19098946C22semidirect
34. C4×C79⋊C16C22semidirect
35. C16×Dic79C22semidirect
36. C16×Dic79C22semidirect
37. C2×Q32×C79C22semidirect
38. C2×SD32×C79C22semidirect
40. #495×C79C22semidirect
41. C4×C16×C79C22semidirect
184. D79#2249direct (N × H)
194. #2249D79direct (N × H)
196. C79C2×#2249semidirect
204. C2×Q32C2×D79semidirect
209. C2×SD32C2×D79semidirect
221. #495C2×D79semidirect
226. C4×C16C2×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×Q32×D792
C2×SD32×D792
C2×D16×D792
#495×D792
#237656622
#237656612
#237656602
#237656592
#237656582
C4×C16×D792
C79×#22492
C2×#224979