Finite Group Databasebeta

← C2×#24920477 #36285342

Subgroups — C2×#24920477 #36285342

Order 21248.

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×#19128437C212yesmaximal, complemented
2#24920477C2116yesmaximal, direct product factor
3C2×#19128084C212yesmaximal, complemented
4C2×#19127898C212yesmaximal, complemented
5C2×#19127914C214yesmaximal, complemented
6C2×C8×Dic166C211yesmaximal, characteristic, complemented
7C2×C4×Dic332C211yesmaximal, characteristic, complemented
8C2×D8×Dic83C212yesmaximal, complemented
9C2×#493×C83C211yesmaximal, characteristic
10C22×Dic332C2211yescharacteristic
11C22×#13050578C2214yes—
12#19128437—28no—
13#19128437C22116yescomplemented
14C2×#14581779—22no—
15C2×#14581779C2214yes—
16C2×#14581773—24no—
17C2×C4×Dic166C2211yescharacteristic
18C2×C4×Dic166C2212yes—
19C2×D4×Dic83—22no—
20C2×D4×Dic83C2214yes—
21#19128084C22116yescomplemented
22#19127914C22132yescomplemented
23#19127898C22116yescomplemented
24C8×Dic166C2218yescomplemented
25C4×Dic332C2218yescomplemented
26D8×Dic83C22116yescomplemented
27C2×#14581726C2211yescharacteristic
28C2×C4⋊(C83⋊C8)C2211yescharacteristic
29C2×Dic83⋊C8C2212yes—
30C2×#14581717C2212yes—
31C2×#14581713C2214yes—
32C2×C8×Dic83C2212yes—
33C22×D8×C83C2212yes—
34C22×D8×C83C2212yes—
35C2×#127×C83C2212yes—
36#493×C83C2218yes—
37C2×C4×C8×C83C2211yescharacteristic
38C22×Dic166D411yescharacteristic
39C22×Dic166C2312yes—
40C23×Dic83—24no—
41C2×Dic332—24no—
42C2×Dic332C2314yes—
43C2×#13050578—48no—
44C2×#13050578C23116yes—
45C22×C83⋊C8C2312yes—
46#14581779—216no—
47#14581779—28no—
48#14581779C23116yes—
49#14581773—232no—
50C4×Dic166—24no—
51C4×Dic166D414yes—
52C4×Dic166C2318yes—
53C4×Dic166C2314yes—
54D4×Dic83—216no—
55D4×Dic83—28no—
56D4×Dic83C23116yes—
57C2×C4⋊Dic83D411yescharacteristic
58C2×C4⋊Dic83C2312yes—
59C2×Dic83⋊C4—22no—
60C2×Dic83⋊C4D412yes—
61C2×C22⋊Dic83—24no—
62C2×C22⋊Dic83—24no—
63C2×C22⋊Dic83—24no—
64C2×C4×Dic83—22no—
65C2×C4×Dic83C2312yes—
66#14581726C2314yes—
67C4⋊(C83⋊C8)C2314yes—
68Dic83⋊C8C2318yes—
69#14581717C2318yes—
70#14581713C23116yes—
71C8×Dic83C2318yes—
72C22×D4×C83—22no—
73C22×D4×C83—22no—
74C22×D4×C83C2314yes—
75C2×D8×C83—28no—
76C2×D8×C83—44no—
77C2×D8×C83C2318yes—
78C2×D8×C83C2318yes—
79C22×C8×C83C2311yescharacteristic
80C22×C8×C83C2311yescharacteristic
81#127×C83—24no—
82#127×C83C2318yes—
83C2×C42×C83C2311yescharacteristic
84C4×C8×C83C2314yes—
85C2×Dic166—24no—
86C2×Dic166—24no—
87C2×Dic166—24no—
88C2×Dic166—22no—
89C2×Dic166C2×D414yes—
90C2×Dic166C2414yes—
91C22×Dic83—22no—
92C22×Dic83—22no—
93C22×Dic83—216no—
94C22×Dic83—88no—
95C22×Dic83C2×D412yes—
96C22×Dic83C2×D412yes—
97Dic332—28no—
98#13050578—416no—
99C2×C83⋊C8—24no—
100C2×C83⋊C8C2414yes—
101C4⋊Dic83—22no—
102C4⋊Dic83C2×D414yes—
103C4⋊Dic83C2414yes—
104Dic83⋊C4—28no—
105Dic83⋊C4C2×D418yes—
106C22⋊Dic83—216no—
107C22⋊Dic83—216no—
108C22⋊Dic83—216no—
109C4×Dic83—28no—
110C4×Dic83C2×D414yes—
111C4×Dic83C2414yes—
112C24×C83—24no—
113C2×D4×C83—24no—
114C2×D4×C83—28no—
115C2×D4×C83—28no—
116C2×D4×C83—28no—
117C2×D4×C83—28no—
118C2×D4×C83—48no—
119C2×D4×C83—84no—
120C2×D4×C83C2418yes—
121C22×C4×C83C2×D411yescharacteristic
122C22×C4×C83C2×D411yescharacteristic
123C22×C4×C83C2411yescharacteristic
124D8×C83—216no—
125D8×C83—48no—
126C2×C8×C83—22no—
127C2×C8×C83#4114yes—
128C2×C8×C83C2412yes—
129C2×C8×C83C2412yes—
130C42×C83C2×D412yes—
131C42×C83C2412yes—
132C23×C83—28no—
133C23×C83—48no—
134C23×C83—48no—
135C23×C83—48no—
136C23×C83C22×D411yescharacteristic
137D4×C83—28no—
138D4×C83—28no—
139D4×C83—48no—
140D4×C83—416no—
141D4×C83—88no—
142C2×C4×C83—22no—
143C2×C4×C83#13514yes—
144C2×C4×C83C22×D412yes—
145C2×C4×C83C22×D411yescharacteristic
146C2×C4×C83C22×D412yes—
147C2×C4×C83C2×#4112yes—
148C2×C4×C83H(5,𝔽2)12yes—
149C2×C4×C83C2511yescharacteristic
150C2×Dic83—24no—
151C2×Dic83—24no—
152C2×Dic83—24no—
153C2×Dic83—24no—
154C2×Dic83—44no—
155C2×Dic83—44no—
156C2×Dic83—816no—
157C2×Dic83C22×D414yes—
158C2×Dic83C22×D414yes—
159Dic166—28no—
160Dic166—24no—
161Dic166—24no—
162Dic166—44no—
163C8×C83—22no—
164C8×C83C2×#4114yes—
165C83⋊C8—24no—
166C22×C83—48no—
167C22×C83—48no—
168C22×C83—48no—
169C22×C83—816no—
170C22×C83#55012yes—
171C22×C83C2×#13512yes—
172C22×C83#57612yes—
173C22×C83C23×D411yescharacteristic
174C4×C83—22no—
175C4×C83#55012yes—
176C4×C83C2×#13514yes—
177C4×C83C22×#4111yescharacteristic
178C4×C83C2×H(5,𝔽2)11yescharacteristic
179Dic83—24no—
180Dic83—24no—
181Dic83—44no—
182Dic83—44no—
183C2×#3396—831nomaximal, Sylow
184C2×C83—88no—
185C2×C83#339614yescomplemented
186C2×C83C2×#55011yescharacteristic
187C2×C83C22×#13511yescharacteristic
188C2×C83C2×#57611yescharacteristic
189C2×#559—832no—
190#3396—8316no—
191C2×#495—832no—
192C2×#493D8311yescharacteristic
193C2×#460—832no—
194C2×#463—834no—
195C2×C8×Q8—831no—
196C2×C4×Q16—831no—
197C2×C4×D8—832no—
198C83C2×#339611yescharacteristic, complemented, Sylow
199C22×Q16—831no—
200C22×SD16—834no—
201C22×D8C2×D8312yes—
202C22×D8C2×D8312yes—
203#559—8316no—
204#559—1668no—
205C2×#127C2×D8312yes—
206C2×#124—834no—
207C2×#124—1662no—
208C2×#123—1664no—
209C2×C4×Q8—831no—
210C2×C4×Q8—832no—
211C2×C4×D4—834no—
212C2×C4×D4—1662no—
213#495—8316no—
214#493C2×D8318yes—
215#463—8332no—
216#460—8316no—
217C8×Q8—838no—
218C4×Q16—838no—
219C4×D8—8316no—
220C2×#107—831no—
221C2×C4⋊C8—832no—
222C2×C4⋊C8—831no—
223C2×#103—832no—
224C2×#102—834no—
225C2×C4×C8—832no—
226C2×C4×C8C2×D8311yescharacteristic
227C22×Q8—831no—
228C22×Q8—832no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4C22×D8314yes—
232C23×C4—1664no—
233C2×Q16—834no—
234C2×Q16—1664no—
235C2×SD16—3328no—
236C2×SD16—8316no—
237C2×D8—28no—
238C2×D8—44no—
239C2×D8C22×D8318yes—
240C2×D8C22×D8318yes—
241C22×C8—832no—
242C22×C8C22×D8311yescharacteristic
243C22×C8C22×D8311yescharacteristic
244#127—24no—
245#127C22×D8318yes—
246#124—8316no—
247#124—1668no—
248#124—16616no—
249#123—16632no—
250C4×Q8—834no—
251C4×Q8—834no—
252C4×Q8—838no—
253C4×Q8—1664no—
254C4×D4—8316no—
255C4×D4—1668no—
256C4×D4—16616no—
257C2×C4⋊C4—831no—
258C2×C4⋊C4—832no—
259C2×C4⋊C4—832no—
260C2×C4⋊C4—1662no—
261C2×C22⋊C4—1664no—
262C2×C22⋊C4—1664no—
263C2×C22⋊C4—1664no—
264C2×C42—832no—
265C2×C42—1662no—
266C2×C42C22×D8311yescharacteristic
267#107—834no—
268C4⋊C8—838no—
269C4⋊C8—834no—
270#103—838no—
271#102—8316no—
272C4×C8—838no—
273C4×C8C22×D8314yes—
274C24—24no—
275C2×Q8—834no—
276C2×Q8—834no—
277C2×Q8—1664no—
278C2×Q8—1664no—
279C2×Q8—1664no—
280C2×Q8—1662no—
281C2×D4—24no—
282C2×D4—28no—
283C2×D4—28no—
284C2×D4—28no—
285C2×D4—28no—
286C2×D4—48no—
287C2×D4—84no—
288C2×D4C23×D8318yes—
289C22×C4—832no—
290C22×C4—832no—
291C22×C4—6648no—
292C22×C4—1662no—
293C22×C4—1662no—
294C22×C4—16616no—
295C22×C4D4×D8311yescharacteristic
296C22×C4D4×D8311yescharacteristic
297C22×C4C23×D8311yescharacteristic
298Q16—1668no—
299SD16—33216no—
300D8—216no—
301D8—48no—
302C2×C8—22no—
303C2×C8—834no—
304C2×C8—1664no—
305C2×C8#1305058914yes—
306C2×C8C23×D8312yes—
307C2×C8C23×D8312yes—
308C4⋊C4—834no—
309C4⋊C4—838no—
310C4⋊C4—834no—
311C4⋊C4—1662no—
312C4⋊C4—1668no—
313C22⋊C4—16616no—
314C22⋊C4—16616no—
315C22⋊C4—16616no—
316C42—834no—
317C42—834no—
318C42—1668no—
319C42D4×D8312yes—
320C42C23×D8312yes—
321C23—28no—
322C23—48no—
323C23—48no—
324C23—48no—
325C23C2×D4×D8311yescharacteristic
326Q8—3324no—
327Q8—1664no—
328Q8—1664no—
329Q8—1668no—
330D4—28no—
331D4—28no—
332D4—48no—
333D4—416no—
334D4—88no—
335C2×C4—22no—
336C2×C4—3324no—
337C2×C4—3324no—
338C2×C4—834no—
339C2×C4—834no—
340C2×C4—66416no—
341C2×C4—1664no—
342C2×C4—1664no—
343C2×C4—1664no—
344C2×C4—1664no—
345C2×C4#1458181114yes—
346C2×C4C2×D4×D8312yes—
347C2×C4C2×D4×D8311yescharacteristic
348C2×C4C2×D4×D8312yes—
349C2×C4C2×#1305058912yes—
350C2×C4#1458183712yes—
351C2×C4C24×D8311yescharacteristic
352C8—22no—
353C8—1664no—
354C8C2×#1305058914yes—
355C22—48no—
356C22—48no—
357C22—48no—
358C22—816no—
359C22#1912837112yes—
360C22C2×#1458181112yes—
361C22#1912850212yes—
362C22C22×D4×D8311yescharacteristic
363C4—22no—
364C4—3324no—
365C4—3324no—
366C4—1664no—
367C4—1664no—
368C4#1912837112yes—
369C4C2×#1458181114yes—
370C4C22×#1305058911yescharacteristic
371C4C2×#1458183711yescharacteristic
372C2—88no—
373C2#2492047714yesdirect product factor
374C2C2×#1912837111yescharacteristic
375C2C22×#1458181111yescharacteristic
376C2C2×#1912850211yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
Fitting, prime radicalC2×#493×C83C2
socleC23×C83C22×D4
hypercenterC2×#493D83
hypocenterC83C2×#3396
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#19128437C2semidirect
2. #24920477C2direct (N × H)
3. C2×#19128084C2semidirect
4. C2×#19127898C2semidirect
5. C2×#19127914C2semidirect
6. C2×C8×Dic166C2semidirect
7. C2×C4×Dic332C2semidirect
8. C2×D8×Dic83C2semidirect
13. #19128437C22semidirect
21. #19128084C22semidirect
22. #19127914C22semidirect
23. #19127898C22semidirect
24. C8×Dic166C22semidirect
25. C4×Dic332C22semidirect
26. D8×Dic83C22semidirect
185. C2×C83#3396semidirect
198. C83C2×#3396semidirect
373. C2#24920477direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284372
#249204772
C2×#191280842
C2×#191278982
C2×#191279142
C2×C8×Dic1662
C2×C4×Dic3322
C2×D8×Dic832
C2×#493×C832
C2×#339683