Finite Group Databasebeta

← C2×#14533067 #17204141

Subgroups — C2×#14533067 #17204141

Order 4352.

2918 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#63225C211yesmaximal, characteristic
2#14533067C2116yesmaximal, direct product factor
3C2×#11762747C212yesmaximal, complemented
4C2×#11762740C212yesmaximal, complemented
5C2×#11762693C214yesmaximal, complemented
6C2×#11762681C212yesmaximal
7C2×#11762672C211yesmaximal, characteristic
8C2×#11762670C212yesmaximal
9C22×C17×#117C211yesmaximal, characteristic
10C24×Dic17C2211yescharacteristic
11C24×Dic17C2211yescharacteristic
12C22×#63225—28no—
13C22×#63225C2212yes—
14C22×#63225C2212yes—
15C22×#63225C2218yes—
16C22×#63225C2214yes—
17C22×C22⋊Dic17C2212yes—
18#11762747C22116yescomplemented
19#11762740C22116yescomplemented
20#11762693C22132yescomplemented
21#11762681C22116yes—
22#11762672C2218yes—
23#11762670C22116yes—
24C2×#10587502C2214yes—
25C2×#10587502C2214yes—
26C2×#10587502C2212yes—
27C2×#10587502C2212yes—
28C2×#10587502C2214yes—
29C24×C4×C17C2211yescharacteristic
30C2×C17×#117—28no—
31C2×C17×#117C2218yes—
32C22×C4⋊C4×C17C2211yescharacteristic
33C22×C4⋊C4×C17C2211yescharacteristic
34C22×C22⋊C4×C17C2212yes—
35C22×C42×C17C2212yes—
36C25×C17C2311yescharacteristic
37C23×C4×C17—28no—
38C23×C4×C17D418yes—
39C23×C4×C17C2312yes—
40C23×C4×C17C2312yes—
41C23×C4×C17C2311yescharacteristic
42C23×C4×C17C2311yescharacteristic
43C23×C4×C17C2314yes—
44C23×Dic17—24no—
45C23×Dic17—28no—
46C23×Dic17—24no—
47C23×Dic17—28no—
48C23×Dic17C2314yes—
49C23×Dic17C2312yes—
50C23×Dic17C2314yes—
51C23×Dic17C2314yes—
52C23×Dic17C2312yes—
53C17×#117—232no—
54C2×C4⋊C4×C17—24no—
55C2×C4⋊C4×C17—24no—
56C2×C4⋊C4×C17C2314yes—
57C2×C4⋊C4×C17C2314yes—
58C2×C22⋊C4×C17—28no—
59C2×C22⋊C4×C17C2318yes—
60C2×C42×C17—28no—
61C2×C42×C17C2318yes—
62C2×C22⋊Dic17—28no—
63C2×C22⋊Dic17C2318yes—
64C2×#63225—28no—
65C2×#63225—28no—
66C2×#63225—232no—
67C2×#63225—216no—
68C2×#63225C2318yes—
69C2×#63225C23116yes—
70C2×#63225C2318yes—
71#10587502C2318yes—
72#10587502C23116yes—
73#10587502C23116yes—
74#10587502C23116yes—
75#10587502C2318yes—
76C24×C17—24no—
77C24×C17—24no—
78C24×C17C2×D414yes—
79C24×C17#4118yes—
80C24×C17C2412yes—
81C24×C17C2411yescharacteristic
82C22×C4×C17—232no—
83C22×C4×C17—216no—
84C22×C4×C17—24no—
85C22×C4×C17—24no—
86C22×C4×C17—24no—
87C22×C4×C17—24no—
88C22×C4×C17—28no—
89C22×C4×C17—28no—
90C22×C4×C17C2×D414yes—
91C22×C4×C17C2×D414yes—
92C22×C4×C17C2×D4116yes—
93C22×C4×C17C2414yes—
94C22×C4×C17C2414yes—
95C22×C4×C17C2412yes—
96C22×C4×C17C2412yes—
97C22×Dic17—232no—
98C22×Dic17—28no—
99C22×Dic17—24no—
100C22×Dic17—24no—
101C22×Dic17—216no—
102C22×Dic17—28no—
103C22×Dic17—24no—
104C22×Dic17—216no—
105C22×Dic17—28no—
106C22×Dic17—28no—
107C22×Dic17—28no—
108C22×Dic17—28no—
109C22×Dic17—416no—
110C22×Dic17#4118yes—
111C22×Dic17C2414yes—
112C22×Dic17C2418yes—
113C22×Dic17C2414yes—
114C4⋊C4×C17—28no—
115C4⋊C4×C17—28no—
116C22⋊C4×C17—216no—
117C42×C17—216no—
118C22⋊Dic17—216no—
119#63225—216no—
120#63225—216no—
121#63225—232no—
122C2×#2484—171nomaximal, Sylow
123C23×C17—28no—
124C23×C17—28no—
125C23×C17—232no—
126C23×C17—24no—
127C23×C17—24no—
128C23×C17#123116yes—
129C23×C17C22×D414yes—
130C23×C17C22×D412yes—
131C23×C17C2×#4118yes—
132C23×C17C2×#4114yes—
133C23×C17C2×#4114yes—
134C23×C172−1+414yes—
135C23×C17C2511yescharacteristic
136C2×C4×C17—232no—
137C2×C4×C17—28no—
138C2×C4×C17—28no—
139C2×C4×C17—24no—
140C2×C4×C17—24no—
141C2×C4×C17—24no—
142C2×C4×C17—24no—
143C2×C4×C17—28no—
144C2×C4×C17—28no—
145C2×C4×C17—48no—
146C2×C4×C17—48no—
147C2×C4×C17C22×D414yes—
148C2×C4×C17C22×D414yes—
149C2×Dic17—232no—
150C2×Dic17—216no—
151C2×Dic17—24no—
152C2×Dic17—24no—
153C2×Dic17—24no—
154C2×Dic17—28no—
155C2×Dic17—28no—
156C2×Dic17—28no—
157C2×Dic17—28no—
158C2×Dic17—416no—
159C2×Dic17—48no—
160C2×Dic17—416no—
161C2×Dic17C2×#4118yes—
162C22×#117D1711yescharacteristic
163C23×C4⋊C4—171no—
164#2484—1716no—
165C2×#400—172no—
166C2×#398—172no—
167C2×#387—174no—
168C2×#385—172no—
169C2×#381—171no—
170C2×#381—172no—
171C22×C17—24no—
172C22×C17—24no—
173C22×C17—216no—
174C22×C17—232no—
175C22×C17C2×#12318yes—
176C22×C17C2×#12314yes—
177C22×C17#52514yes—
178C22×C17#53614yes—
179C22×C17#552116yes—
180C22×C17C23×D411yescharacteristic
181C22×C17C22×#4112yes—
182C22×C17C22×#4112yes—
183C22×C17C2×2−1+412yes—
184C4×C17—24no—
185C4×C17—24no—
186C4×C17—44no—
187C4×C17—44no—
188Dic17—28no—
189Dic17—44no—
190Dic17—48no—
191C24×C4—171no—
192C24×C4—171no—
193C24×C4C2×D1711yescharacteristic
194C2×#117—28no—
195C2×#117C2×D1718yes—
196C22×C4⋊C4—172no—
197C22×C4⋊C4—174no—
198C22×C4⋊C4—178no—
199C22×C4⋊C4—172no—
200C22×C4⋊C4—348no—
201C22×C4⋊C4C2×D1711yescharacteristic
202C22×C4⋊C4C2×D1711yescharacteristic
203C22×C22⋊C4—172no—
204C22×C22⋊C4C2×D1712yes—
205C22×C42C2×D1712yes—
206#400—1716no—
207#398—1716no—
208#387—1732no—
209#385—1716no—
210#381—178no—
211#381—1716no—
212C2×#95—172no—
213C2×#95—174no—
214C2×#95—174no—
215C2×#95—174no—
216C2×#95—172no—
217C2×C17—28no—
218C2×C17#248418yescomplemented
219C2×C17C22×#12311yescharacteristic
220C2×C17C2×#52511yescharacteristic
221C2×C17C2×#53611yescharacteristic
222C2×C17C2×#55214yes—
223C25C22×D1711yescharacteristic
224C23×C4—28no—
225C23×C4—172no—
226C23×C4—174no—
227C23×C4—174no—
228C23×C4—174no—
229C23×C4—172no—
230C23×C4—348no—
231C23×C4—344no—
232C23×C4—348no—
233C23×C4—344no—
234C23×C4C22⋊D1718yes—
235C23×C4C22×D1712yes—
236C23×C4C22×D1712yes—
237C23×C4C22×D1714yes—
238C23×C4C22×D1711yescharacteristic
239C23×C4C22×D1711yescharacteristic
240#117—232no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—178no—
244C2×C4⋊C4—178no—
245C2×C4⋊C4—1716no—
246C2×C4⋊C4—3416no—
247C2×C4⋊C4—348no—
248C2×C4⋊C4—348no—
249C2×C4⋊C4—3432no—
250C2×C4⋊C4C22×D1714yes—
251C2×C4⋊C4C22×D1714yes—
252C2×C22⋊C4—28no—
253C2×C22⋊C4—178no—
254C2×C22⋊C4—348no—
255C2×C22⋊C4C22×D1718yes—
256C2×C42—28no—
257C2×C42C22×D1718yes—
258#95—178no—
259#95—1716no—
260#95—1716no—
261#95—178no—
262#95—1716no—
263C17C2×#248411yescharacteristic, complemented, Sylow
264C24—24no—
265C24—24no—
266C24#6325218yes—
267C24C2×C22⋊D1714yes—
268C24C23×D1712yes—
269C24C23×D1711yescharacteristic
270C22×C4—216no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—232no—
274C22×C4—28no—
275C22×C4—28no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—178no—
279C22×C4—174no—
280C22×C4—178no—
281C22×C4—174no—
282C22×C4—3416no—
283C22×C4—3432no—
284C22×C4—344no—
285C22×C4—348no—
286C22×C4—344no—
287C22×C4—348no—
288C22×C4—3416no—
289C22×C4—348no—
290C22×C4—348no—
291C22×C4—348no—
292C22×C4—348no—
293C22×C4—344no—
294C22×C4—6816no—
295C22×C4C2×C22⋊D1714yes—
296C22×C4C2×C22⋊D1714yes—
297C22×C4C2×C22⋊D17116yes—
298C22×C4C23×D1714yes—
299C22×C4C23×D1714yes—
300C22×C4C23×D1712yes—
301C22×C4C23×D1712yes—
302C4⋊C4—28no—
303C4⋊C4—28no—
304C4⋊C4—3432no—
305C4⋊C4—3416no—
306C4⋊C4—3416no—
307C22⋊C4—216no—
308C22⋊C4—3416no—
309C42—216no—
310C23—232no—
311C23—28no—
312C23—24no—
313C23—28no—
314C23—24no—
315C23#10587615116yes—
316C23C2×#6325218yes—
317C23C2×#6325214yes—
318C23#41×D1714yes—
319C23#1058769714yes—
320C23C22×C22⋊D1714yes—
321C23C22×C22⋊D1712yes—
322C23C24×D1711yescharacteristic
323C2×C4—232no—
324C2×C4—28no—
325C2×C4—28no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—24no—
330C2×C4—28no—
331C2×C4—28no—
332C2×C4—48no—
333C2×C4—48no—
334C2×C4—178no—
335C2×C4—3432no—
336C2×C4—3416no—
337C2×C4—344no—
338C2×C4—344no—
339C2×C4—344no—
340C2×C4—348no—
341C2×C4—348no—
342C2×C4—348no—
343C2×C4—348no—
344C2×C4—6816no—
345C2×C4—6816no—
346C2×C4—688no—
347C2×C4C22×C22⋊D1714yes—
348C2×C4C22×C22⋊D1714yes—
349C22—24no—
350C22—24no—
351C22—232no—
352C22—216no—
353C22C2×#1058761518yes—
354C22C2×#1058761514yes—
355C22#1176331614yes—
356C22#1176338014yes—
357C22#11763492116yes—
358C22C23×C22⋊D1711yescharacteristic
359C22C2×#41×D1712yes—
360C22C22×#6325212yes—
361C22C2×#1058769712yes—
362C4—24no—
363C4—24no—
364C4—44no—
365C4—44no—
366C4—348no—
367C4—684no—
368C4—688no—
369C2—28no—
370C2#1453306718yesdirect product factor
371C2C22×#1058761511yescharacteristic
372C2C2×#1176331611yescharacteristic
373C2C2×#1176338011yescharacteristic
374C2C2×#1176349214yes—
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC22×C17×#117C2
socleC24×C17C24
prime radicalC25×C17C23
hypercenterC22×#117D17
hypocenterC17C2×#2484
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. #14533067C2direct (N × H)
3. C2×#11762747C2semidirect
4. C2×#11762740C2semidirect
5. C2×#11762693C2semidirect
18. #11762747C22semidirect
19. #11762740C22semidirect
20. #11762693C22semidirect
218. C2×C17#2484semidirect
263. C17C2×#2484semidirect
370. C2#14533067direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#632252
#145330672
C2×#117627472
C2×#117627402
C2×#117626932
C2×#117626812
C2×#117626722
C2×#117626702
C22×C17×#1172
C2×#248417