Finite Group Databasebeta

← C2×#21437110 #29469627

Subgroups — C2×#21437110 #29469627

Order 15104.

2086 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838138C212yesmaximal, complemented
2#21437110C2116yesmaximal, direct product factor
3C2×#16837785C212yesmaximal, complemented
4C2×#16837599C212yesmaximal, complemented
5C2×#16837615C214yesmaximal, complemented
6C2×C8×Dic118C211yesmaximal, characteristic, complemented
7C2×C4×Dic236C211yesmaximal, characteristic, complemented
8C2×D8×Dic59C212yesmaximal, complemented
9C2×C59×#493C211yesmaximal, characteristic
10C22×Dic236C2211yescharacteristic
11C22×#11745670C2214yes—
12#16838138—28no—
13#16838138C22116yescomplemented
14C2×#14273714—22no—
15C2×#14273714C2214yes—
16C2×#14273708—24no—
17C2×C4×Dic118C2212yes—
18C2×C4×Dic118C2211yescharacteristic
19C2×D4×Dic59—22no—
20C2×D4×Dic59C2214yes—
21#16837785C22116yescomplemented
22#16837615C22132yescomplemented
23#16837599C22116yescomplemented
24C8×Dic118C2218yescomplemented
25C4×Dic236C2218yescomplemented
26D8×Dic59C22116yescomplemented
27C2×#14273661C2211yescharacteristic
28C2×C4⋊(C59⋊C8)C2211yescharacteristic
29C2×Dic59⋊C8C2212yes—
30C2×#14273652C2212yes—
31C2×#14273648C2214yes—
32C2×C8×Dic59C2212yes—
33C22×D8×C59C2212yes—
34C22×D8×C59C2212yes—
35C2×#127×C59C2212yes—
36C59×#493C2218yes—
37C2×C4×C8×C59C2211yescharacteristic
38C22×Dic118D411yescharacteristic
39C22×Dic118C2312yes—
40C23×Dic59—24no—
41C2×Dic236—24no—
42C2×Dic236C2314yes—
43C2×#11745670—48no—
44C2×#11745670C23116yes—
45C22×C59⋊C8C2312yes—
46#14273714—216no—
47#14273714—28no—
48#14273714C23116yes—
49#14273708—232no—
50C4×Dic118—24no—
51C4×Dic118D414yes—
52C4×Dic118C2318yes—
53C4×Dic118C2314yes—
54D4×Dic59—216no—
55D4×Dic59—28no—
56D4×Dic59C23116yes—
57C2×C4⋊Dic59D411yescharacteristic
58C2×C4⋊Dic59C2312yes—
59C2×Dic59⋊C4—22no—
60C2×Dic59⋊C4D412yes—
61C2×C22⋊Dic59—24no—
62C2×C22⋊Dic59—24no—
63C2×C22⋊Dic59—24no—
64C2×C4×Dic59—22no—
65C2×C4×Dic59C2312yes—
66#14273661C2314yes—
67C4⋊(C59⋊C8)C2314yes—
68Dic59⋊C8C2318yes—
69#14273652C2318yes—
70#14273648C23116yes—
71C8×Dic59C2318yes—
72C22×D4×C59—22no—
73C22×D4×C59—22no—
74C22×D4×C59C2314yes—
75C2×D8×C59—28no—
76C2×D8×C59—44no—
77C2×D8×C59C2318yes—
78C2×D8×C59C2318yes—
79C22×C8×C59C2311yescharacteristic
80C22×C8×C59C2311yescharacteristic
81#127×C59—24no—
82#127×C59C2318yes—
83C2×C42×C59C2311yescharacteristic
84C4×C8×C59C2314yes—
85C24×C59—24no—
86C2×D4×C59—24no—
87C2×D4×C59—28no—
88C2×D4×C59—28no—
89C2×D4×C59—28no—
90C2×D4×C59—28no—
91C2×D4×C59—48no—
92C2×D4×C59—84no—
93C2×D4×C59C2418yes—
94C22×C4×C59C2×D411yescharacteristic
95C22×C4×C59C2×D411yescharacteristic
96C22×C4×C59C2411yescharacteristic
97C22×Dic59—22no—
98C22×Dic59—22no—
99C22×Dic59—216no—
100C22×Dic59—88no—
101C22×Dic59C2×D412yes—
102C22×Dic59C2×D412yes—
103C2×Dic118—24no—
104C2×Dic118—24no—
105C2×Dic118—24no—
106C2×Dic118—22no—
107C2×Dic118C2×D414yes—
108C2×Dic118C2414yes—
109D8×C59—216no—
110D8×C59—48no—
111C2×C8×C59—22no—
112C2×C8×C59#4114yes—
113C2×C8×C59C2412yes—
114C2×C8×C59C2412yes—
115C42×C59C2×D412yes—
116C42×C59C2412yes—
117C22⋊Dic59—216no—
118C22⋊Dic59—216no—
119C22⋊Dic59—216no—
120#11745670—416no—
121C4⋊Dic59—22no—
122C4⋊Dic59C2×D414yes—
123C4⋊Dic59C2414yes—
124Dic59⋊C4—28no—
125Dic59⋊C4C2×D418yes—
126C4×Dic59—28no—
127C4×Dic59C2×D414yes—
128C4×Dic59C2414yes—
129C2×C59⋊C8—24no—
130C2×C59⋊C8C2414yes—
131Dic236—28no—
132C23×C59—28no—
133C23×C59—48no—
134C23×C59—48no—
135C23×C59—48no—
136C23×C59C22×D411yescharacteristic
137D4×C59—28no—
138D4×C59—28no—
139D4×C59—48no—
140D4×C59—416no—
141D4×C59—88no—
142C2×C4×C59—22no—
143C2×C4×C59#13514yes—
144C2×C4×C59C22×D412yes—
145C2×C4×C59C22×D411yescharacteristic
146C2×C4×C59C22×D412yes—
147C2×C4×C59C2×#4112yes—
148C2×C4×C59H(5,𝔽2)12yes—
149C2×C4×C59C2511yescharacteristic
150C2×Dic59—24no—
151C2×Dic59—24no—
152C2×Dic59—24no—
153C2×Dic59—24no—
154C2×Dic59—44no—
155C2×Dic59—44no—
156C2×Dic59—816no—
157C2×Dic59C22×D414yes—
158C2×Dic59C22×D414yes—
159Dic118—28no—
160Dic118—24no—
161Dic118—24no—
162Dic118—44no—
163C8×C59—22no—
164C8×C59C2×#4114yes—
165C59⋊C8—24no—
166C2×#3396—591nomaximal, Sylow
167C22×C59—48no—
168C22×C59—48no—
169C22×C59—48no—
170C22×C59—816no—
171C22×C59#55012yes—
172C22×C59C2×#13512yes—
173C22×C59#57612yes—
174C22×C59C23×D411yescharacteristic
175C4×C59—22no—
176C4×C59#55012yes—
177C4×C59C2×#13514yes—
178C4×C59C22×#4111yescharacteristic
179C4×C59C2×H(5,𝔽2)11yescharacteristic
180Dic59—24no—
181Dic59—24no—
182Dic59—44no—
183Dic59—44no—
184C2×#559—592no—
185#3396—5916no—
186C2×#495—592no—
187C2×#493D5911yescharacteristic
188C2×#460—592no—
189C2×#463—594no—
190C2×C8×Q8—591no—
191C2×C4×Q16—591no—
192C2×C4×D8—592no—
193C2×C59—88no—
194C2×C59#339614yescomplemented
195C2×C59C2×#55011yescharacteristic
196C2×C59C22×#13511yescharacteristic
197C2×C59C2×#57611yescharacteristic
198C22×Q16—591no—
199C22×SD16—594no—
200C22×D8C2×D5912yes—
201C22×D8C2×D5912yes—
202#559—5916no—
203#559—1188no—
204C2×#127C2×D5912yes—
205C2×#124—594no—
206C2×#124—1182no—
207C2×#123—1184no—
208C2×C4×Q8—591no—
209C2×C4×Q8—592no—
210C2×C4×D4—594no—
211C2×C4×D4—1182no—
212#495—5916no—
213#493C2×D5918yes—
214#463—5932no—
215#460—5916no—
216C8×Q8—598no—
217C4×Q16—598no—
218C4×D8—5916no—
219C2×#107—591no—
220C2×C4⋊C8—592no—
221C2×C4⋊C8—591no—
222C2×#103—592no—
223C2×#102—594no—
224C2×C4×C8—592no—
225C2×C4×C8C2×D5911yescharacteristic
226C59C2×#339611yescharacteristic, complemented, Sylow
227C22×Q8—591no—
228C22×Q8—592no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4C22×D5914yes—
232C23×C4—1184no—
233C2×Q16—594no—
234C2×Q16—1184no—
235C2×SD16—5916no—
236C2×SD16—2368no—
237C2×D8—28no—
238C2×D8—44no—
239C2×D8C22×D5918yes—
240C2×D8C22×D5918yes—
241C22×C8—592no—
242C22×C8C22×D5911yescharacteristic
243C22×C8C22×D5911yescharacteristic
244#127—24no—
245#127C22×D5918yes—
246#124—5916no—
247#124—1188no—
248#124—11816no—
249#123—11832no—
250C4×Q8—594no—
251C4×Q8—594no—
252C4×Q8—598no—
253C4×Q8—1184no—
254C4×D4—5916no—
255C4×D4—1188no—
256C4×D4—11816no—
257C2×C4⋊C4—591no—
258C2×C4⋊C4—592no—
259C2×C4⋊C4—592no—
260C2×C4⋊C4—1182no—
261C2×C22⋊C4—1184no—
262C2×C22⋊C4—1184no—
263C2×C22⋊C4—1184no—
264C2×C42—592no—
265C2×C42—1182no—
266C2×C42C22×D5911yescharacteristic
267#107—594no—
268C4⋊C8—598no—
269C4⋊C8—594no—
270#103—598no—
271#102—5916no—
272C4×C8—598no—
273C4×C8C22×D5914yes—
274C24—24no—
275C2×Q8—594no—
276C2×Q8—594no—
277C2×Q8—1184no—
278C2×Q8—1182no—
279C2×Q8—1184no—
280C2×Q8—1184no—
281C2×D4—24no—
282C2×D4—28no—
283C2×D4—28no—
284C2×D4—28no—
285C2×D4—28no—
286C2×D4—48no—
287C2×D4—84no—
288C2×D4C23×D5918yes—
289C22×C4—592no—
290C22×C4—592no—
291C22×C4—11816no—
292C22×C4—1182no—
293C22×C4—1182no—
294C22×C4—4728no—
295C22×C4D4×D5911yescharacteristic
296C22×C4D4×D5911yescharacteristic
297C22×C4C23×D5911yescharacteristic
298Q16—1188no—
299SD16—23616no—
300D8—216no—
301D8—48no—
302C2×C8—22no—
303C2×C8—594no—
304C2×C8—1184no—
305C2×C8#1174568714yes—
306C2×C8C23×D5912yes—
307C2×C8C23×D5912yes—
308C4⋊C4—594no—
309C4⋊C4—598no—
310C4⋊C4—594no—
311C4⋊C4—1182no—
312C4⋊C4—1188no—
313C22⋊C4—11816no—
314C22⋊C4—11816no—
315C22⋊C4—11816no—
316C42—594no—
317C42—594no—
318C42—1188no—
319C42D4×D5912yes—
320C42C23×D5912yes—
321C23—28no—
322C23—48no—
323C23—48no—
324C23—48no—
325C23C2×D4×D5911yescharacteristic
326Q8—1188no—
327Q8—1184no—
328Q8—1184no—
329Q8—2364no—
330D4—28no—
331D4—28no—
332D4—416no—
333D4—48no—
334D4—88no—
335C2×C4—22no—
336C2×C4—594no—
337C2×C4—594no—
338C2×C4—1184no—
339C2×C4—1184no—
340C2×C4—1184no—
341C2×C4—1184no—
342C2×C4—47216no—
343C2×C4—2364no—
344C2×C4—2364no—
345C2×C4#1427374614yes—
346C2×C4C2×D4×D5912yes—
347C2×C4C2×D4×D5912yes—
348C2×C4C2×D4×D5911yescharacteristic
349C2×C4C2×#1174568712yes—
350C2×C4#1427377212yes—
351C2×C4C24×D5911yescharacteristic
352C8—22no—
353C8—1184no—
354C8C2×#1174568714yes—
355C22—48no—
356C22—48no—
357C22—48no—
358C22—816no—
359C22#1683807212yes—
360C22C2×#1427374612yes—
361C22#1683820312yes—
362C22C22×D4×D5911yescharacteristic
363C4—22no—
364C4—1184no—
365C4—1184no—
366C4—2364no—
367C4—2364no—
368C4#1683807212yes—
369C4C2×#1427374614yes—
370C4C22×#1174568711yescharacteristic
371C4C2×#1427377211yescharacteristic
372C2—88no—
373C2#2143711014yesdirect product factor
374C2C2×#1683807211yescharacteristic
375C2C22×#1427374611yescharacteristic
376C2C2×#1683820311yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
Fitting, prime radicalC2×C59×#493C2
socleC23×C59C22×D4
hypercenterC2×#493D59
hypocenterC59C2×#3396
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#16838138C2semidirect
2. #21437110C2direct (N × H)
3. C2×#16837785C2semidirect
4. C2×#16837599C2semidirect
5. C2×#16837615C2semidirect
6. C2×C8×Dic118C2semidirect
7. C2×C4×Dic236C2semidirect
8. C2×D8×Dic59C2semidirect
13. #16838138C22semidirect
21. #16837785C22semidirect
22. #16837615C22semidirect
23. #16837599C22semidirect
24. C8×Dic118C22semidirect
25. C4×Dic236C22semidirect
26. D8×Dic59C22semidirect
194. C2×C59#3396semidirect
226. C59C2×#3396semidirect
373. C2#21437110direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381382
#214371102
C2×#168377852
C2×#168375992
C2×#168376152
C2×C8×Dic1182
C2×C4×Dic2362
C2×D8×Dic592
C2×C59×#4932
C2×#339659