Finite Group Databasebeta

← C2×#14530092 #17062250

Subgroups — C2×#14530092 #17062250

Order 4352.

1918 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587485C211yesmaximal, characteristic, complemented
2C22×#10587503C212yesmaximal, complemented
3C2×#11762712C212yesmaximal, complemented
4#14530092C218yesmaximal, direct product factor
5C2×#11762572C211yesmaximal, characteristic, complemented
6C23×D8×C17C211yesmaximal, characteristic
7C23×#3622C2211yescharacteristic
8C22×C4⋊Dic17C2212yes—
9C22×C22⋊Dic17—22no—
10C22×C22⋊Dic17—22no—
11C22×C4×Dic17C2211yescharacteristic
12C2×#10587485—24no—
13C2×#10587485C2214yescomplemented
14C2×#10587503—28no—
15C2×#10587503C2218yescomplemented
16#11762712—24no—
17#11762712C2218yescomplemented
18#11762572C2214yescomplemented
19C23×D4×C17C2212yes—
20C22×D8×C17—28no—
21C22×D8×C17—24no—
22C22×D8×C17C2214yes—
23C23×C8×C17C2211yescharacteristic
24C25×C17—22no—
25C22×D4×C17—24no—
26C22×D4×C17—24no—
27C22×D4×C17—22no—
28C22×D4×C17—24no—
29C22×D4×C17—24no—
30C22×D4×C17—24no—
31C22×D4×C17D418yes—
32C22×D4×C17C2314yes—
33C23×C4×C17C2311yescharacteristic
34C23×Dic17—22no—
35C23×Dic17D411yescharacteristic
36C23×Dic17D411yescharacteristic
37C2×D8×C17—232no—
38C2×D8×C17—216no—
39C2×D8×C17—28no—
40C22×C8×C17—24no—
41C22×C8×C17D414yes—
42C22×C8×C17C2312yes—
43C2×C22⋊Dic17—28no—
44C2×C22⋊Dic17—28no—
45C2×C22⋊Dic17—48no—
46C2×C22⋊Dic17—48no—
47C2×C4⋊Dic17—22no—
48C2×C4⋊Dic17—24no—
49C2×C4⋊Dic17—24no—
50C2×C4⋊Dic17C2314yes—
51C2×C4×Dic17—22no—
52C2×C4×Dic17—22no—
53C2×C4×Dic17D412yes—
54C2×C4×Dic17C2312yes—
55C22×#3622—24no—
56C22×#3622—22no—
57C22×#3622C2312yes—
58#10587503—216no—
59#10587485—28no—
60C24×C17—28no—
61C24×C17—24no—
62C24×C17—44no—
63C24×C17—44no—
64C24×C17—44no—
65C24×C17—44no—
66C24×C17—44no—
67C24×C17—44no—
68C24×C17C2×D411yescharacteristic
69C2×D4×C17—216no—
70C2×D4×C17—28no—
71C2×D4×C17—216no—
72C2×D4×C17—24no—
73C2×D4×C17—24no—
74C2×D4×C17—24no—
75C2×D4×C17—24no—
76C2×D4×C17—24no—
77C2×D4×C17—44no—
78C2×D4×C17—44no—
79C2×D4×C17—48no—
80C2×D4×C17—48no—
81C2×D4×C17C2×D418yes—
82C22×C4×C17C2×D411yescharacteristic
83C22×C4×C17C2×D414yes—
84C22×C4×C17C2×D412yes—
85C22×C4×C17#4112yes—
86C22×C4×C17#4114yes—
87C22×C4×C17C2411yescharacteristic
88C22×Dic17—22no—
89C22×Dic17—22no—
90C22×Dic17—22no—
91C22×Dic17—24no—
92C22×Dic17—24no—
93C22×Dic17—44no—
94C22×Dic17—44no—
95C22×Dic17—44no—
96C22×Dic17D814yescomplemented
97C22×Dic17C2×D412yes—
98C22×Dic17C2×D412yes—
99D8×C17—232no—
100C2×C8×C17—28no—
101C2×C8×C17—24no—
102C2×C8×C17C2×D414yes—
103C22⋊Dic17—416no—
104C22⋊Dic17—416no—
105C4⋊Dic17—24no—
106C4⋊Dic17—24no—
107C4⋊Dic17—44no—
108C4×Dic17—24no—
109C4×Dic17—22no—
110C4×Dic17—22no—
111C2×#3622—22no—
112C2×#3622—24no—
113C2×#3622—44no—
114C2×#2054—171nomaximal, Sylow
115C23×C17—28no—
116C23×C17—44no—
117C23×C17—44no—
118C23×C17—44no—
119C23×C17—44no—
120C23×C17—44no—
121C23×C17—44no—
122C23×C17—416no—
123C23×C17—416no—
124C23×C17—416no—
125C23×C17—88no—
126C23×C17—88no—
127C23×C17—88no—
128C23×C17—88no—
129C23×C17#12112yes—
130C23×C17#12114yes—
131C23×C17C2×D812yes—
132C23×C17#13512yes—
133C23×C17AGL(1,ℤ/8)14yes—
134C23×C17C22×D411yescharacteristic
135D4×C17—28no—
136D4×C17—28no—
137D4×C17—44no—
138D4×C17—44no—
139D4×C17—416no—
140C2×C4×C17#12014yes—
141C2×C4×C17#12112yes—
142C2×C4×C17#12114yes—
143C2×C4×C17#12318yes—
144C2×C4×C17#12414yes—
145C2×C4×C17C22×D412yes—
146C2×C4×C17C22×D411yescharacteristic
147C2×C4×C17C2×#4111yescharacteristic
148C2×C4×C17C2×#4112yes—
149C2×Dic17—22no—
150C2×Dic17—22no—
151C2×Dic17—28no—
152C2×Dic17—22no—
153C2×Dic17—24no—
154C2×Dic17—44no—
155C2×Dic17—44no—
156C2×Dic17—44no—
157C2×Dic17—44no—
158C2×Dic17—88no—
159C2×Dic17C2×D814yescomplemented
160C8×C17—24no—
161#3622—42no—
162C23×D8D1711yescharacteristic
163C22×C4⋊C8—171no—
164C22×#102—172no—
165C2×#390—172no—
166#2054—178no—
167C2×#340—171no—
168C22×C17—48no—
169C22×C17—48no—
170C22×C17—48no—
171C22×C17—832no—
172C22×C17—84no—
173C22×C17—84no—
174C22×C17—84no—
175C22×C17—84no—
176C22×C17#39414yes—
177C22×C17#45918yes—
178C22×C17#46318yes—
179C22×C17#46614yes—
180C22×C17#46914yes—
181C22×C17C2×#12111yescharacteristic
182C22×C17C2×#12112yes—
183C22×C17C22×D811yescharacteristic
184C22×C17C2×#13511yescharacteristic
185C22×C17C2×AGL(1,ℤ/8)12yes—
186C4×C17#39414yes—
187C4×C17C2×#12011yescharacteristic
188C4×C17C2×#12312yes—
189C4×C17C2×#12411yescharacteristic
190Dic17—24no—
191Dic17—42no—
192Dic17—84no—
193C23×D4C2×D1712yes—
194C22×D8—28no—
195C22×D8—24no—
196C22×D8C2×D1714yes—
197C23×C8—171no—
198C23×C8C2×D1711yescharacteristic
199C22×C4⋊C4—172no—
200C22×C22⋊C4—342no—
201C22×C22⋊C4—342no—
202C22×C42—171no—
203C2×C4⋊C8—174no—
204C2×C4⋊C8—344no—
205C2×#102—178no—
206C2×#102—348no—
207#390—178no—
208#390—344no—
209#340—174no—
210C2×C17—88no—
211C2×C17#205418yescomplemented
212C2×C17C2×#39411yescharacteristic
213C2×C17C2×#45912yes—
214C2×C17C2×#46312yes—
215C2×C17C2×#46611yescharacteristic
216C2×C17C2×#46911yescharacteristic
217C25—22no—
218C22×D4—22no—
219C22×D4—24no—
220C22×D4—24no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4C22⋊D1718yes—
225C22×D4C22×D1714yes—
226C23×C4—171no—
227C23×C4—171no—
228C23×C4—342no—
229C23×C4C22×D1711yescharacteristic
230C2×D8—232no—
231C2×D8—216no—
232C2×D8—28no—
233C22×C8—24no—
234C22×C8—172no—
235C22×C8—344no—
236C22×C8—342no—
237C22×C8C22⋊D1714yes—
238C22×C8C22×D1712yes—
239C2×C4⋊C4—174no—
240C2×C4⋊C4—344no—
241C2×C4⋊C4—344no—
242C2×C4⋊C4—342no—
243C2×C22⋊C4—348no—
244C2×C22⋊C4—348no—
245C2×C22⋊C4—688no—
246C2×C22⋊C4—688no—
247C2×C42—172no—
248C2×C42—172no—
249C2×C42—342no—
250C2×C42—342no—
251C4⋊C8—348no—
252#102—3416no—
253C17C2×#205411yescharacteristic, complemented, Sylow
254C24—24no—
255C24—28no—
256C24—44no—
257C24—44no—
258C24—44no—
259C24—44no—
260C24—44no—
261C24—44no—
262C24D4×D1711yescharacteristic
263C2×D4—24no—
264C2×D4—24no—
265C2×D4—24no—
266C2×D4—24no—
267C2×D4—24no—
268C2×D4—216no—
269C2×D4—28no—
270C2×D4—216no—
271C2×D4—48no—
272C2×D4—48no—
273C2×D4—44no—
274C2×D4—44no—
275C2×D4C2×C22⋊D1718yes—
276C22×C4—172no—
277C22×C4—174no—
278C22×C4—172no—
279C22×C4—342no—
280C22×C4—342no—
281C22×C4—344no—
282C22×C4—342no—
283C22×C4—344no—
284C22×C4—684no—
285C22×C4—684no—
286C22×C4—684no—
287C22×C4D4×D1711yescharacteristic
288C22×C4#6325412yes—
289C22×C4#6325414yes—
290C22×C4C2×C22⋊D1714yes—
291C22×C4C2×C22⋊D1712yes—
292C22×C4C23×D1711yescharacteristic
293D8—232no—
294C2×C8—24no—
295C2×C8—28no—
296C2×C8—344no—
297C2×C8—342no—
298C2×C8—684no—
299C2×C8C2×C22⋊D1714yes—
300C4⋊C4—344no—
301C4⋊C4—344no—
302C4⋊C4—684no—
303C22⋊C4—6816no—
304C22⋊C4—6816no—
305C42—342no—
306C42—342no—
307C42—344no—
308C23—28no—
309C23—416no—
310C23—416no—
311C23—416no—
312C23—44no—
313C23—44no—
314C23—44no—
315C23—44no—
316C23—44no—
317C23—44no—
318C23—88no—
319C23—88no—
320C23—88no—
321C23—88no—
322C23D8×D1712yes—
323C23#1058759714yes—
324C23#1058759812yes—
325C23#1058762412yes—
326C23#1058762514yes—
327C23C2×D4×D1711yescharacteristic
328D4—28no—
329D4—28no—
330D4—416no—
331D4—44no—
332D4—44no—
333C2×C4—174no—
334C2×C4—348no—
335C2×C4—342no—
336C2×C4—342no—
337C2×C4—342no—
338C2×C4—344no—
339C2×C4—684no—
340C2×C4—684no—
341C2×C4—684no—
342C2×C4—684no—
343C2×C4—1368no—
344C2×C4#1058762118yes—
345C2×C4#1058762214yes—
346C2×C4#1058762412yes—
347C2×C4#1058762514yes—
348C2×C4#1058763914yes—
349C2×C4C2×#6325411yescharacteristic
350C2×C4C2×#6325412yes—
351C2×C4C22×C22⋊D1712yes—
352C2×C4C22×C22⋊D1711yescharacteristic
353C8—24no—
354C8—682no—
355C22—48no—
356C22—48no—
357C22—48no—
358C22—832no—
359C22—84no—
360C22—84no—
361C22—84no—
362C22—84no—
363C22#1176272314yes—
364C22#1176300218yes—
365C22#1176302218yes—
366C22#1176304214yes—
367C22#1176305914yes—
368C22C2×#1058762411yescharacteristic
369C22C2×#1058762512yes—
370C22C2×D8×D1711yescharacteristic
371C22C2×#1058759811yescharacteristic
372C22C2×#1058759712yes—
373C4—344no—
374C4—682no—
375C4—1364no—
376C4#1176272314yes—
377C4C2×#1058763911yescharacteristic
378C4C2×#1058762112yes—
379C4C2×#1058762211yescharacteristic
380C2—88no—
381C2#1453009218yesdirect product factor
382C2C2×#1176272311yescharacteristic
383C2C2×#1176300212yes—
384C2C2×#1176302212yes—
385C2C2×#1176304211yescharacteristic
386C2C2×#1176305911yescharacteristic
subgroupG/H
centerC24D4×D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
Fitting, prime radicalC23×D8×C17C2
socleC24×C17C2×D4
hypercenterC23×D8D17
hypocenterC17C2×#2054
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D8

Complements

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

NH ≅ G/Ntype
1. C22×#10587485C2semidirect
2. C22×#10587503C2semidirect
3. C2×#11762712C2semidirect
4. #14530092C2direct (N × H)
5. C2×#11762572C2semidirect
13. C2×#10587485C22semidirect
15. C2×#10587503C22semidirect
17. #11762712C22semidirect
18. #11762572C22semidirect
96. C22×Dic17D8semidirect
159. C2×Dic17C2×D8semidirect
211. C2×C17#2054semidirect
253. C17C2×#2054semidirect
381. C2#14530092direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105874852
C22×#105875032
C2×#117627122
#145300922
C2×#117625722
C23×D8×C172
C2×#205417