Finite Group Databasebeta

← C2×#14534647 #17201247

Subgroups — C2×#14534647 #17201247

Order 4352.

2806 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587561C211yesmaximal, characteristic
2C22×C4×Dic34C211yesmaximal, characteristic, complemented
3#14534647C2116yesmaximal, direct product factor
4C2×#11762746C212yesmaximal, complemented
5C2×#11762730C212yesmaximal, complemented
6C2×#11762727C212yesmaximal
7C2×#11762722C212yesmaximal, complemented
8C2×#11762701C214yesmaximal, complemented
9C2×C17×#383C211yesmaximal, characteristic, complemented
10C23×Dic34C2211yescharacteristic
11C23×Dic34C2211yescharacteristic
12C23×D68C2211yescharacteristic
13C2×#10587561—28no—
14C2×#10587561C2218yes—
15C2×C4×Dic34—28no—
16C2×C4×Dic34C2218yescomplemented
17C22×C4⋊Dic17C2211yescharacteristic
18C22×C4⋊Dic17C2214yes—
19C22×#63225C2212yes—
20C22×#63227C2212yes—
21C22×#63227C2214yes—
22C22×#63227C2212yes—
23C22×#63227C2214yes—
24C22×C4×Dic17C2212yes—
25#11762746C22116yescomplemented
26#11762730C22116yescomplemented
27#11762727C22116yes—
28#11762722C22116yescomplemented
29#11762701C22132yescomplemented
30C2×#10587502C2214yes—
31C22×C42×C17C2211yescharacteristic
32C17×#383C2218yescomplemented
33C2×C17×#95C2212yes—
34C2×C17×#95C2212yes—
35C2×C17×#95C2212yes—
36C24×D17C2312yes—
37C23×C4×C17C2314yes—
38C23×C4×C17C2311yescharacteristic
39C23×C4×C17C2311yescharacteristic
40C23×C4×C17C2311yescharacteristic
41C23×Dic17C2312yes—
42C23×Dic17C2312yes—
43C23×Dic17C2312yes—
44C22×D68—24no—
45C22×D68—44no—
46C22×D68C2314yes—
47C22×Dic34—24no—
48C22×Dic34—28no—
49C22×Dic34—24no—
50C22×Dic34—44no—
51C22×Dic34C2314yes—
52C22×Dic34C2314yes—
53C2×C42×C17D418yes—
54C2×C42×C17C2314yes—
55C2×#63227—28no—
56C2×#63227—28no—
57C2×#63227—216no—
58C2×#63227—48no—
59C2×#63227C2318yes—
60C2×#63227C23116yes—
61C2×#63227C2318yes—
62C2×#63227C23116yes—
63C2×C4⋊Dic17—24no—
64C2×C4⋊Dic17—48no—
65C2×C4⋊Dic17C2314yes—
66C2×C4⋊Dic17C23116yes—
67C2×#63225—28no—
68C2×#63225C2318yes—
69C2×C4×Dic17—28no—
70C2×C4×Dic17C2318yes—
71#10587561—232no—
72C4×Dic34—232no—
73C17×#95C2318yes—
74C17×#95C2318yes—
75C17×#95C2318yes—
76#10587502C23116yes—
77C24×C17C2411yescharacteristic
78C23×D17—24no—
79C23×D17—28no—
80C23×D17—28no—
81C23×D17—28no—
82C23×D17C2414yes—
83C22×C4×C17—24no—
84C22×C4×C17—24no—
85C22×C4×C17—24no—
86C22×C4×C17—28no—
87C22×C4×C17—28no—
88C22×C4×C17—28no—
89C22×C4×C17C2×D414yes—
90C22×C4×C17C2×D414yes—
91C22×C4×C17C2×D414yes—
92C22×C4×C17C2418yes—
93C22×C4×C17C2412yes—
94C22×C4×C17C2412yes—
95C22×C4×C17C2412yes—
96C22×Dic17—24no—
97C22×Dic17—24no—
98C22×Dic17—24no—
99C22×Dic17—24no—
100C22×Dic17—28no—
101C22×Dic17—28no—
102C22×Dic17#4118yes—
103C22×Dic17C2414yes—
104C22×Dic17C2414yes—
105C22×Dic17C2414yes—
106C2×D68—28no—
107C2×D68—48no—
108C2×D68—416no—
109C2×Dic34—232no—
110C2×Dic34—28no—
111C2×Dic34—216no—
112C2×Dic34—28no—
113C2×Dic34—48no—
114C2×Dic34—416no—
115C42×C17C2×D4116yes—
116#63227—216no—
117#63227—216no—
118#63227—232no—
119#63227—416no—
120C4⋊Dic17—28no—
121C4⋊Dic17—416no—
122#63225—216no—
123C4×Dic17—216no—
124C2×#2632—171nomaximal, Sylow
125C23×C17C22×D412yes—
126C23×C17C2×#4114yes—
127C23×C17H(5,𝔽2)14yes—
128C23×C172−1+414yes—
129C23×C17C2511yescharacteristic
130C22×D17—24no—
131C22×D17—28no—
132C22×D17—28no—
133C22×D17—28no—
134C22×D17—48no—
135C22×D17—48no—
136C22×D17—48no—
137C22×D17—432no—
138C2×C4×C17—28no—
139C2×C4×C17—28no—
140C2×C4×C17—28no—
141C2×C4×C17—24no—
142C2×C4×C17—24no—
143C2×C4×C17—24no—
144C2×C4×C17—28no—
145C2×C4×C17—28no—
146C2×C4×C17—28no—
147C2×C4×C17—416no—
148C2×C4×C17C22×D414yes—
149C2×C4×C17C22×D414yes—
150C2×C4×C17C22×D414yes—
151C2×Dic17—216no—
152C2×Dic17—24no—
153C2×Dic17—24no—
154C2×Dic17—24no—
155C2×Dic17—24no—
156C2×Dic17—28no—
157C2×Dic17—28no—
158C2×Dic17—48no—
159C2×Dic17—48no—
160C2×Dic17C2×#4118yes—
161D68—416no—
162Dic34—232no—
163Dic34—416no—
164C22×#124—171no—
165C22×C4×Q8—171no—
166#2632—1716no—
167C2×#399—172no—
168C2×#395—172no—
169C2×#394—172no—
170C2×#393—172no—
171C2×#388—174no—
172C2×#383D1711yescharacteristic, complemented
173C22×C17#52514yes—
174C22×C17#53514yes—
175C22×C17#53614yes—
176C22×C17#542116yes—
177C22×C17C23×D411yescharacteristic
178C22×C17C22×#4112yes—
179C22×C17C2×H(5,𝔽2)12yes—
180C22×C17C2×2−1+412yes—
181C2×D17—44no—
182C2×D17—44no—
183C2×D17—44no—
184C2×D17—416no—
185C2×D17—816no—
186C4×C17—24no—
187C4×C17—24no—
188C4×C17—24no—
189C4×C17—48no—
190Dic17—28no—
191Dic17—44no—
192Dic17—44no—
193C23×Q8—171no—
194C23×Q8—171no—
195C23×D4—171no—
196C2×#124—178no—
197C2×#124—348no—
198C2×C4×Q8—178no—
199C2×C4×Q8—348no—
200C22×C4⋊C4—172no—
201C22×C4⋊C4—171no—
202C22×C4⋊C4—174no—
203C22×C22⋊C4—174no—
204C22×C22⋊C4—172no—
205C22×C22⋊C4—172no—
206C22×C22⋊C4—174no—
207C22×C42—172no—
208C22×C42C2×D1711yescharacteristic
209#399—1716no—
210#395—1716no—
211#394—1716no—
212#393—1716no—
213#388—1732no—
214#383C2×D1718yescomplemented
215C2×#95—174no—
216C2×#95C2×D1712yes—
217C2×#95C2×D1712yes—
218C2×#95C2×D1712yes—
219C2×C17#263218yescomplemented
220C2×C17C2×#52511yescharacteristic
221C2×C17C2×#53511yescharacteristic
222C2×C17C2×#53611yescharacteristic
223C2×C17C2×#54214yes—
224D17—84no—
225C25—172no—
226C22×Q8—174no—
227C22×Q8—174no—
228C22×Q8—348no—
229C22×Q8—344no—
230C22×Q8—344no—
231C22×Q8—684no—
232C22×D4—174no—
233C22×D4—344no—
234C22×D4—684no—
235C23×C4—172no—
236C23×C4—172no—
237C23×C4—172no—
238C23×C4C22×D1714yes—
239C23×C4C22×D1711yescharacteristic
240C23×C4C22×D1711yescharacteristic
241C23×C4C22×D1711yescharacteristic
242#124—3432no—
243C4×Q8—3432no—
244C2×C4⋊C4—178no—
245C2×C4⋊C4—174no—
246C2×C4⋊C4—1716no—
247C2×C4⋊C4—348no—
248C2×C4⋊C4—344no—
249C2×C4⋊C4—688no—
250C2×C22⋊C4—178no—
251C2×C22⋊C4—178no—
252C2×C22⋊C4—1716no—
253C2×C22⋊C4—1716no—
254C2×C22⋊C4—3416no—
255C2×C22⋊C4—348no—
256C2×C22⋊C4—348no—
257C2×C22⋊C4—688no—
258C2×C42—178no—
259C2×C42—348no—
260C2×C42D6818yes—
261C2×C42C22×D1714yes—
262#95—1716no—
263#95C22×D1718yes—
264#95C22×D1718yes—
265#95C22×D1718yes—
266C17C2×#263211yescharacteristic, complemented, Sylow
267C24—174no—
268C24—344no—
269C24—348no—
270C24—348no—
271C24—348no—
272C24C23×D1711yescharacteristic
273C2×Q8—3416no—
274C2×Q8—3432no—
275C2×Q8—348no—
276C2×Q8—348no—
277C2×Q8—688no—
278C2×Q8—6816no—
279C2×D4—348no—
280C2×D4—688no—
281C2×D4—6816no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—28no—
286C22×C4—28no—
287C22×C4—28no—
288C22×C4—178no—
289C22×C4—174no—
290C22×C4—174no—
291C22×C4—174no—
292C22×C4—344no—
293C22×C4—344no—
294C22×C4—344no—
295C22×C4—344no—
296C22×C4—348no—
297C22×C4—348no—
298C22×C4C2×D6814yes—
299C22×C4C2×D6814yes—
300C22×C4C2×D6814yes—
301C22×C4C23×D1718yes—
302C22×C4C23×D1712yes—
303C22×C4C23×D1712yes—
304C22×C4C23×D1712yes—
305C4⋊C4—3416no—
306C4⋊C4—348no—
307C4⋊C4—6816no—
308C22⋊C4—3432no—
309C22⋊C4—3416no—
310C22⋊C4—3416no—
311C22⋊C4—6816no—
312C42—3416no—
313C42C2×D68116yes—
314C23—344no—
315C23—348no—
316C23—348no—
317C23—348no—
318C23—688no—
319C23—688no—
320C23—688no—
321C23—6832no—
322C23C22×D6812yes—
323C23#41×D1714yes—
324C23#1058769614yes—
325C23#1058769714yes—
326C23C24×D1711yescharacteristic
327Q8—3432no—
328Q8—6816no—
329D4—6816no—
330C2×C4—28no—
331C2×C4—28no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—28no—
335C2×C4—24no—
336C2×C4—28no—
337C2×C4—28no—
338C2×C4—28no—
339C2×C4—416no—
340C2×C4—178no—
341C2×C4—3416no—
342C2×C4—344no—
343C2×C4—344no—
344C2×C4—344no—
345C2×C4—344no—
346C2×C4—348no—
347C2×C4—348no—
348C2×C4—688no—
349C2×C4—688no—
350C2×C4C22×D6814yes—
351C2×C4C22×D6814yes—
352C2×C4C22×D6814yes—
353C22—684no—
354C22—684no—
355C22—6816no—
356C22—684no—
357C22—13616no—
358C22#1176332114yes—
359C22#1176337814yes—
360C22#1176338514yes—
361C22#11763425116yes—
362C22C23×D6811yescharacteristic
363C22C2×#41×D1712yes—
364C22C2×#1058769612yes—
365C22C2×#1058769712yes—
366C4—24no—
367C4—24no—
368C4—24no—
369C4—48no—
370C4—348no—
371C4—684no—
372C4—684no—
373C2—1364no—
374C2#1453464718yesdirect product factor
375C2C2×#1176332111yescharacteristic
376C2C2×#1176337811yescharacteristic
377C2C2×#1176338511yescharacteristic
378C2C2×#1176342514yes—
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C17×#383C2
socleC24×C17C24
prime radicalC23×D68C22
hypercenterC2×#383D17
hypocenterC17C2×#2632
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic34C2semidirect
3. #14534647C2direct (N × H)
4. C2×#11762746C2semidirect
5. C2×#11762730C2semidirect
7. C2×#11762722C2semidirect
8. C2×#11762701C2semidirect
9. C2×C17×#383C2semidirect
16. C2×C4×Dic34C22semidirect
25. #11762746C22semidirect
26. #11762730C22semidirect
28. #11762722C22semidirect
29. #11762701C22semidirect
32. C17×#383C22semidirect
172. C2×#383D17semidirect
214. #383C2×D17semidirect
219. C2×C17#2632semidirect
266. C17C2×#2632semidirect
374. C2#14534647direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875612
C22×C4×Dic342
#145346472
C2×#117627462
C2×#117627302
C2×#117627272
C2×#117627222
C2×#117627012
C2×C17×#3832
C2×#263217