Finite Group Databasebeta

← C2×#14541798 #17915262

Subgroups — C2×#14541798 #17915262

Order 4352.

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×#11763545C212yesmaximal, complemented
2#14541798C2116yesmaximal, direct product factor
3C2×#11763192C212yesmaximal, complemented
4C2×#11763006C212yesmaximal, complemented
5C2×#11763022C214yesmaximal, complemented
6C2×C8×Dic34C211yesmaximal, characteristic, complemented
7C2×C4×Dic68C211yesmaximal, characteristic, complemented
8C2×D8×Dic17C212yesmaximal, complemented
9C2×C17×#493C211yesmaximal, characteristic
10C22×Dic68C2211yescharacteristic
11C22×#63229C2214yes—
12#11763545—28no—
13#11763545C22116yescomplemented
14C2×#10587622—22no—
15C2×#10587622C2214yes—
16C2×#10587621—24no—
17C2×C4×Dic34C2211yescharacteristic
18C2×C4×Dic34C2212yes—
19C2×D4×Dic17—22no—
20C2×D4×Dic17C2214yes—
21#11763192C22116yescomplemented
22#11763022C22132yescomplemented
23#11763006C22116yescomplemented
24C8×Dic34C2218yescomplemented
25C4×Dic68C2218yescomplemented
26D8×Dic17C22116yescomplemented
27C2×#10587489C2211yescharacteristic
28C2×C4⋊#3622C2211yescharacteristic
29C2×#10587485C2212yes—
30C2×#10587487C2212yes—
31C2×#10587503C2214yes—
32C2×C8×Dic17C2212yes—
33C22×D8×C17C2212yes—
34C22×D8×C17C2212yes—
35C2×C17×#127C2212yes—
36C17×#493C2218yes—
37C2×C4×C8×C17C2211yescharacteristic
38C22×D4×C17—22no—
39C22×D4×C17—22no—
40C22×D4×C17C2314yes—
41C23×Dic17—24no—
42C22×Dic34D411yescharacteristic
43C22×Dic34C2312yes—
44C2×D8×C17—28no—
45C2×D8×C17—44no—
46C2×D8×C17C2318yes—
47C2×D8×C17C2318yes—
48C22×C8×C17C2311yescharacteristic
49C22×C8×C17C2311yescharacteristic
50C17×#127—24no—
51C17×#127C2318yes—
52C2×C42×C17C2311yescharacteristic
53C2×C22⋊Dic17—24no—
54C2×C22⋊Dic17—24no—
55C2×C22⋊Dic17—24no—
56#10587622—28no—
57#10587622—216no—
58#10587622C23116yes—
59#10587621—232no—
60D4×Dic17—216no—
61D4×Dic17—28no—
62D4×Dic17C23116yes—
63C2×#63229—48no—
64C2×#63229C23116yes—
65C2×C4⋊Dic17D411yescharacteristic
66C2×C4⋊Dic17C2312yes—
67C2×#63225—22no—
68C2×#63225D412yes—
69C2×C4×Dic17—22no—
70C2×C4×Dic17C2312yes—
71C22×#3622C2312yes—
72C2×Dic68—24no—
73C2×Dic68C2314yes—
74C4×Dic34—24no—
75C4×Dic34D414yes—
76C4×Dic34C2314yes—
77C4×Dic34C2318yes—
78C4×C8×C17C2314yes—
79#10587503C23116yes—
80#10587489C2314yes—
81#10587487C2318yes—
82#10587485C2318yes—
83C8×Dic17C2318yes—
84C4⋊#3622C2314yes—
85C24×C17—24no—
86C2×D4×C17—24no—
87C2×D4×C17—28no—
88C2×D4×C17—28no—
89C2×D4×C17—28no—
90C2×D4×C17—28no—
91C2×D4×C17—48no—
92C2×D4×C17—84no—
93C2×D4×C17C2418yes—
94C22×C4×C17C2×D411yescharacteristic
95C22×C4×C17C2×D411yescharacteristic
96C22×C4×C17C2411yescharacteristic
97C22×Dic17—22no—
98C22×Dic17—22no—
99C22×Dic17—216no—
100C22×Dic17—88no—
101C22×Dic17C2×D412yes—
102C22×Dic17C2×D412yes—
103C2×Dic34—24no—
104C2×Dic34—24no—
105C2×Dic34—24no—
106C2×Dic34—22no—
107C2×Dic34C2×D414yes—
108C2×Dic34C2414yes—
109D8×C17—216no—
110D8×C17—48no—
111C2×C8×C17—22no—
112C2×C8×C17#4114yes—
113C2×C8×C17C2412yes—
114C2×C8×C17C2412yes—
115C42×C17C2×D412yes—
116C42×C17C2412yes—
117C22⋊Dic17—216no—
118C22⋊Dic17—216no—
119C22⋊Dic17—216no—
120#63229—416no—
121C4⋊Dic17—22no—
122C4⋊Dic17C2×D414yes—
123C4⋊Dic17C2414yes—
124#63225—28no—
125#63225C2×D418yes—
126C4×Dic17—28no—
127C4×Dic17C2×D414yes—
128C4×Dic17C2414yes—
129C2×#3622—24no—
130C2×#3622C2414yes—
131Dic68—28no—
132C2×#3396—171nomaximal, Sylow
133C23×C17—28no—
134C23×C17—48no—
135C23×C17—48no—
136C23×C17—48no—
137C23×C17C22×D411yescharacteristic
138D4×C17—28no—
139D4×C17—28no—
140D4×C17—48no—
141D4×C17—416no—
142D4×C17—88no—
143C2×C4×C17—22no—
144C2×C4×C17#13514yes—
145C2×C4×C17C22×D412yes—
146C2×C4×C17C22×D411yescharacteristic
147C2×C4×C17C22×D412yes—
148C2×C4×C17C2×#4112yes—
149C2×C4×C17H(5,𝔽2)12yes—
150C2×C4×C17C2511yescharacteristic
151C2×Dic17—24no—
152C2×Dic17—24no—
153C2×Dic17—24no—
154C2×Dic17—24no—
155C2×Dic17—44no—
156C2×Dic17—44no—
157C2×Dic17—816no—
158C2×Dic17C22×D414yes—
159C2×Dic17C22×D414yes—
160Dic34—28no—
161Dic34—24no—
162Dic34—24no—
163Dic34—44no—
164C8×C17—22no—
165C8×C17C2×#4114yes—
166#3622—24no—
167C2×#559—172no—
168#3396—1716no—
169C2×#495—172no—
170C2×#493D1711yescharacteristic
171C2×#460—172no—
172C2×#463—174no—
173C2×C8×Q8—171no—
174C2×C4×Q16—171no—
175C2×C4×D8—172no—
176C22×C17—48no—
177C22×C17—48no—
178C22×C17—48no—
179C22×C17—816no—
180C22×C17#55012yes—
181C22×C17C2×#13512yes—
182C22×C17#57612yes—
183C22×C17C23×D411yescharacteristic
184C4×C17—22no—
185C4×C17#55012yes—
186C4×C17C2×#13514yes—
187C4×C17C22×#4111yescharacteristic
188C4×C17C2×H(5,𝔽2)11yescharacteristic
189Dic17—24no—
190Dic17—24no—
191Dic17—44no—
192Dic17—44no—
193C22×Q16—171no—
194C22×SD16—174no—
195C22×D8C2×D1712yes—
196C22×D8C2×D1712yes—
197#559—1716no—
198#559—348no—
199C2×#127C2×D1712yes—
200C2×#124—174no—
201C2×#124—342no—
202C2×#123—344no—
203C2×C4×Q8—171no—
204C2×C4×Q8—172no—
205C2×C4×D4—174no—
206C2×C4×D4—342no—
207#495—1716no—
208#493C2×D1718yes—
209#463—1732no—
210#460—1716no—
211C8×Q8—178no—
212C4×Q16—178no—
213C4×D8—1716no—
214C2×#107—171no—
215C2×C4⋊C8—172no—
216C2×C4⋊C8—171no—
217C2×#103—172no—
218C2×#102—174no—
219C2×C4×C8—172no—
220C2×C4×C8C2×D1711yescharacteristic
221C2×C17—88no—
222C2×C17#339614yescomplemented
223C2×C17C2×#55011yescharacteristic
224C2×C17C22×#13511yescharacteristic
225C2×C17C2×#57611yescharacteristic
226C22×Q8—171no—
227C22×Q8—172no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4C22×D1714yes—
231C23×C4—344no—
232C2×Q16—174no—
233C2×Q16—344no—
234C2×SD16—1716no—
235C2×SD16—688no—
236C2×D8—28no—
237C2×D8—44no—
238C2×D8C22×D1718yes—
239C2×D8C22×D1718yes—
240C22×C8—172no—
241C22×C8C22×D1711yescharacteristic
242C22×C8C22×D1711yescharacteristic
243#127—24no—
244#127C22×D1718yes—
245#124—1716no—
246#124—348no—
247#124—3416no—
248#123—3432no—
249C4×Q8—174no—
250C4×Q8—174no—
251C4×Q8—178no—
252C4×Q8—344no—
253C4×D4—1716no—
254C4×D4—348no—
255C4×D4—3416no—
256C2×C4⋊C4—171no—
257C2×C4⋊C4—172no—
258C2×C4⋊C4—172no—
259C2×C4⋊C4—342no—
260C2×C22⋊C4—344no—
261C2×C22⋊C4—344no—
262C2×C22⋊C4—344no—
263C2×C42—172no—
264C2×C42—342no—
265C2×C42C22×D1711yescharacteristic
266#107—174no—
267C4⋊C8—178no—
268C4⋊C8—174no—
269#103—178no—
270#102—1716no—
271C4×C8—178no—
272C4×C8C22×D1714yes—
273C17C2×#339611yescharacteristic, complemented, Sylow
274C24—24no—
275C2×Q8—174no—
276C2×Q8—174no—
277C2×Q8—342no—
278C2×Q8—344no—
279C2×Q8—344no—
280C2×Q8—344no—
281C2×D4—24no—
282C2×D4—28no—
283C2×D4—28no—
284C2×D4—28no—
285C2×D4—28no—
286C2×D4—48no—
287C2×D4—84no—
288C2×D4C23×D1718yes—
289C22×C4—172no—
290C22×C4—172no—
291C22×C4—3416no—
292C22×C4—342no—
293C22×C4—342no—
294C22×C4—1368no—
295C22×C4D4×D1711yescharacteristic
296C22×C4D4×D1711yescharacteristic
297C22×C4C23×D1711yescharacteristic
298Q16—348no—
299SD16—6816no—
300D8—216no—
301D8—48no—
302C2×C8—22no—
303C2×C8—174no—
304C2×C8—344no—
305C2×C8#6325414yes—
306C2×C8C23×D1712yes—
307C2×C8C23×D1712yes—
308C4⋊C4—174no—
309C4⋊C4—178no—
310C4⋊C4—174no—
311C4⋊C4—342no—
312C4⋊C4—348no—
313C22⋊C4—3416no—
314C22⋊C4—3416no—
315C22⋊C4—3416no—
316C42—174no—
317C42—174no—
318C42—348no—
319C42D4×D1712yes—
320C42C23×D1712yes—
321C23—28no—
322C23—48no—
323C23—48no—
324C23—48no—
325C23C2×D4×D1711yescharacteristic
326Q8—348no—
327Q8—344no—
328Q8—344no—
329Q8—684no—
330D4—28no—
331D4—28no—
332D4—48no—
333D4—416no—
334D4—88no—
335C2×C4—22no—
336C2×C4—174no—
337C2×C4—174no—
338C2×C4—344no—
339C2×C4—344no—
340C2×C4—344no—
341C2×C4—344no—
342C2×C4—684no—
343C2×C4—684no—
344C2×C4—13616no—
345C2×C4#1058759814yes—
346C2×C4C2×D4×D1712yes—
347C2×C4C2×D4×D1711yescharacteristic
348C2×C4C2×D4×D1712yes—
349C2×C4C2×#6325412yes—
350C2×C4#1058769112yes—
351C2×C4C24×D1711yescharacteristic
352C8—22no—
353C8—344no—
354C8C2×#6325414yes—
355C22—48no—
356C22—48no—
357C22—48no—
358C22—816no—
359C22#1176347912yes—
360C22C2×#1058759812yes—
361C22#1176361012yes—
362C22C22×D4×D1711yescharacteristic
363C4—22no—
364C4—344no—
365C4—344no—
366C4—684no—
367C4—684no—
368C4#1176347912yes—
369C4C2×#1058759814yes—
370C4C22×#6325411yescharacteristic
371C4C2×#1058769111yescharacteristic
372C2—88no—
373C2#1454179814yesdirect product factor
374C2C2×#1176347911yescharacteristic
375C2C22×#1058759811yescharacteristic
376C2C2×#1176361011yescharacteristic
subgroupG/H
centerC23C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
Fitting, prime radicalC2×C17×#493C2
socleC23×C17C22×D4
hypercenterC2×#493D17
hypocenterC17C2×#3396
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#11763545C2semidirect
2. #14541798C2direct (N × H)
3. C2×#11763192C2semidirect
4. C2×#11763006C2semidirect
5. C2×#11763022C2semidirect
6. C2×C8×Dic34C2semidirect
7. C2×C4×Dic68C2semidirect
8. C2×D8×Dic17C2semidirect
13. #11763545C22semidirect
21. #11763192C22semidirect
22. #11763022C22semidirect
23. #11763006C22semidirect
24. C8×Dic34C22semidirect
25. C4×Dic68C22semidirect
26. D8×Dic17C22semidirect
222. C2×C17#3396semidirect
273. C17C2×#3396semidirect
373. C2#14541798direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635452
#145417982
C2×#117631922
C2×#117630062
C2×#117630222
C2×C8×Dic342
C2×C4×Dic682
C2×D8×Dic172
C2×C17×#4932
C2×#339617