Finite Group Databasebeta

← C2×#14529925 #17061606

Subgroups — C2×#14529925 #17061606

Order 4352.

1518 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587555C211yesmaximal, characteristic
2C22×#10587506C212yesmaximal
3#14529925C218yesmaximal, direct product factor
4C2×#11762571C212yesmaximal
5C2×#11762564C211yesmaximal, characteristic
6C2×C17×#391C211yesmaximal, characteristic
7C23×Dic34—21no—
8C23×#3622C2212yes—
9C2×#10587555—22no—
10C2×#10587555—28no—
11C2×#10587555C2214yes—
12C22×C4⋊Dic17—21no—
13C22×C4⋊Dic17C2212yes—
14C2×#10587506—28no—
15C2×#10587506C2218yes—
16#11762571C2218yes—
17#11762564C2214yes—
18C23×Q8×C17C2211yescharacteristic
19C22×C4⋊C4×C17C2211yescharacteristic
20C22×C42×C17C2211yescharacteristic
21C17×#391—22no—
22C17×#391C2214yes—
23C2×C17×#95—21no—
24C2×C17×#95—21no—
25C22×Q8×C17—21no—
26C22×Q8×C17—22no—
27C22×Q8×C17—24no—
28C22×Q8×C17—24no—
29C22×Q8×C17Q814yescomplemented
30C22×Q8×C17C2312yes—
31C23×C4×C17—21no—
32C23×C4×C17—21no—
33C23×C4×C17D411yescharacteristic
34C23×C4×C17D411yescharacteristic
35C23×C4×C17C2311yescharacteristic
36C23×Dic17—22no—
37C22×Dic34—28no—
38C22×Dic34—24no—
39C22×Dic34—44no—
40C22×Dic34—44no—
41C2×C4⋊C4×C17—24no—
42C2×C4⋊C4×C17—21no—
43C2×C4⋊C4×C17C2312yes—
44C2×C42×C17—24no—
45C2×C42×C17D412yes—
46C2×C42×C17C2312yes—
47C2×C4⋊Dic17—28no—
48C2×C4⋊Dic17—24no—
49C2×C4⋊Dic17—24no—
50C2×C4⋊Dic17—22no—
51C2×C4⋊Dic17D418yes—
52C2×C4⋊Dic17C2314yes—
53C22×#3622—24no—
54C22×#3622—24no—
55C22×#3622—24no—
56C22×#3622C2314yes—
57#10587555—216no—
58#10587555—216no—
59C17×#95—24no—
60C17×#95—24no—
61#10587506—216no—
62C24×C17C2×D411yescharacteristic
63C2×Q8×C17—24no—
64C2×Q8×C17—22no—
65C2×Q8×C17—216no—
66C2×Q8×C17—24no—
67C2×Q8×C17—24no—
68C2×Q8×C17—42no—
69C2×Q8×C17—48no—
70C2×Q8×C17—42no—
71C2×Q8×C17C2×Q814yescomplemented
72C22×C4×C17—22no—
73C22×C4×C17—22no—
74C22×C4×C17—22no—
75C22×C4×C17—22no—
76C22×C4×C17—24no—
77C22×C4×C17—22no—
78C22×C4×C17—22no—
79C22×C4×C17—42no—
80C22×C4×C17—42no—
81C22×C4×C17—42no—
82C22×C4×C17—42no—
83C22×C4×C17—42no—
84C22×C4×C17SD1614yes—
85C22×C4×C17Q1614yes—
86C22×C4×C17C2×D414yes—
87C22×C4×C17C2×D412yes—
88C22×C4×C17C2×D412yes—
89C22×C4×C17C2×D411yescharacteristic
90C22×C4×C17C2×Q812yes—
91C22×C4×C17#4112yes—
92C22×C4×C17#4114yes—
93C22×C4×C17C2411yescharacteristic
94C22×Dic17—28no—
95C22×Dic17—24no—
96C22×Dic17—44no—
97C22×Dic17—44no—
98C2×Dic34—216no—
99C2×Dic34—48no—
100C2×Dic34—432no—
101C2×Dic34—48no—
102C4⋊C4×C17—24no—
103C4⋊C4×C17—42no—
104C42×C17—24no—
105C42×C17—24no—
106C4⋊Dic17—216no—
107C4⋊Dic17—28no—
108C4⋊Dic17—24no—
109C4⋊Dic17C2×D418yes—
110C2×#3622—24no—
111C2×#3622—24no—
112C2×#3622—24no—
113C2×#3622—48no—
114C2×#2024—171nomaximal, Sylow
115C23×C17#12012yes—
116C23×C17C22⋊Q812yes—
117C23×C17#12412yes—
118C23×C17C2×SD1612yes—
119C23×C17C2×Q1612yes—
120C23×C17AGL(1,ℤ/8)12yes—
121C23×C17#13712yes—
122C23×C17C22×D411yescharacteristic
123Q8×C17—28no—
124Q8×C17—44no—
125Q8×C17—48no—
126C2×C4×C17—22no—
127C2×C4×C17—22no—
128C2×C4×C17—22no—
129C2×C4×C17—22no—
130C2×C4×C17—28no—
131C2×C4×C17—28no—
132C2×C4×C17—24no—
133C2×C4×C17—42no—
134C2×C4×C17—42no—
135C2×C4×C17—48no—
136C2×C4×C17—42no—
137C2×C4×C17—42no—
138C2×C4×C17—42no—
139C2×C4×C17—84no—
140C2×C4×C17#12012yes—
141C2×C4×C17C22⋊Q818yes—
142C2×C4×C17C22⋊Q812yes—
143C2×C4×C17#12418yes—
144C2×C4×C17#12412yes—
145C2×C4×C17C2×SD1614yes—
146C2×C4×C17C2×Q1614yes—
147C2×C4×C17C22×D412yes—
148C2×C4×C17C22×Q811yescharacteristic
149C2×C4×C17C2×#4111yescharacteristic
150C2×C4×C17C2×#4112yes—
151C2×Dic17—28no—
152C2×Dic17—44no—
153C2×Dic17—44no—
154C2×Dic17—416no—
155Dic34—432no—
156#3622—44no—
157C22×C4⋊Q8—171no—
158C22×#103—172no—
159C2×#391D1711yescharacteristic
160#2024—178no—
161C2×#340—172no—
162C2×#336—171no—
163C22×C17#39314yes—
164C22×C17#45014yes—
165C22×C17#45114yes—
166C22×C17#47514yes—
167C22×C17#47714yes—
168C22×C17#48714yes—
169C22×C17#48914yes—
170C22×C17C2×#12011yescharacteristic
171C22×C17C2×C22⋊Q811yescharacteristic
172C22×C17C2×#12411yescharacteristic
173C22×C17C22×SD1611yescharacteristic
174C22×C17C22×Q1611yescharacteristic
175C22×C17C2×AGL(1,ℤ/8)11yescharacteristic
176C22×C17C2×#13711yescharacteristic
177C4×C17—24no—
178C4×C17—24no—
179C4×C17—44no—
180C4×C17—82no—
181C4×C17#39314yes—
182C4×C17C2×C22⋊Q812yes—
183C4×C17C2×#12412yes—
184Dic17—48no—
185C23×Q8—341no—
186C23×Q8C2×D1711yescharacteristic
187C23×C8—172no—
188C2×C4⋊Q8—174no—
189C2×C4⋊Q8—348no—
190C2×C4⋊Q8—342no—
191C22×C4⋊C4—172no—
192C22×C4⋊C4—341no—
193C22×C4⋊C4C2×D1711yescharacteristic
194C22×C42C2×D1711yescharacteristic
195C2×#103—178no—
196C2×#103—348no—
197#391—22no—
198#391C2×D1714yes—
199C2×#95—21no—
200C2×#95—21no—
201#340—178no—
202#336—174no—
203C2×C17#202418yescomplemented
204C2×C17C2×#39311yescharacteristic
205C2×C17C2×#45011yescharacteristic
206C2×C17C2×#45111yescharacteristic
207C2×C17C2×#47511yescharacteristic
208C2×C17C2×#47711yescharacteristic
209C2×C17C2×#48711yescharacteristic
210C2×C17C2×#48911yescharacteristic
211C22×Q8—22no—
212C22×Q8—21no—
213C22×Q8—24no—
214C22×Q8—24no—
215C22×Q8—348no—
216C22×Q8—344no—
217C22×Q8—684no—
218C22×Q8—684no—
219C22×Q8Dic3414yescomplemented
220C22×Q8C22×D1712yes—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—342no—
224C23×C4C22⋊D1711yescharacteristic
225C23×C4C22⋊D1711yescharacteristic
226C23×C4C22×D1711yescharacteristic
227C22×C8—174no—
228C22×C8—344no—
229C22×C8—344no—
230C22×C8—344no—
231C4⋊Q8—3416no—
232C4⋊Q8—3416no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—178no—
236C2×C4⋊C4—174no—
237C2×C4⋊C4—348no—
238C2×C4⋊C4—344no—
239C2×C4⋊C4—342no—
240C2×C4⋊C4—344no—
241C2×C4⋊C4C22×D1712yes—
242C2×C42—24no—
243C2×C42C22⋊D1712yes—
244C2×C42C22×D1712yes—
245#103—3416no—
246#95—24no—
247#95—24no—
248C17C2×#202411yescharacteristic, complemented, Sylow
249C24C2×C22⋊D1711yescharacteristic
250C2×Q8—22no—
251C2×Q8—24no—
252C2×Q8—24no—
253C2×Q8—24no—
254C2×Q8—216no—
255C2×Q8—48no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—3416no—
259C2×Q8—6832no—
260C2×Q8—688no—
261C2×Q8—688no—
262C2×Q8C2×Dic3414yescomplemented
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—22no—
270C22×C4—42no—
271C22×C4—42no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—344no—
276C22×C4—348no—
277C22×C4—684no—
278C22×C4—684no—
279C22×C4#6323014yes—
280C22×C4#6323114yes—
281C22×C4C2×Dic3412yes—
282C22×C4#6325212yes—
283C22×C4D4×D1714yes—
284C22×C4#6325414yes—
285C22×C4C2×C22⋊D1712yes—
286C22×C4C2×C22⋊D1712yes—
287C22×C4C2×C22⋊D1711yescharacteristic
288C22×C4C23×D1711yescharacteristic
289C2×C8—344no—
290C2×C8—344no—
291C2×C8—344no—
292C2×C8—688no—
293C4⋊C4—24no—
294C4⋊C4—42no—
295C4⋊C4—178no—
296C4⋊C4—3416no—
297C4⋊C4—344no—
298C4⋊C4—348no—
299C42—24no—
300C42—24no—
301C23#1058761012yes—
302C23#1058762212yes—
303C23#1058762312yes—
304C23C2×#6323012yes—
305C23C2×#6323112yes—
306C23#1058763512yes—
307C23#1058763712yes—
308C23C22×C22⋊D1711yescharacteristic
309Q8—28no—
310Q8—48no—
311Q8—44no—
312Q8—6832no—
313C2×C4—28no—
314C2×C4—28no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—48no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—84no—
327C2×C4—348no—
328C2×C4—6816no—
329C2×C4—684no—
330C2×C4—684no—
331C2×C4#1058756418yes—
332C2×C4#1058757118yes—
333C2×C4#1058761012yes—
334C2×C4#1058762212yes—
335C2×C4#1058762312yes—
336C2×C4C2×#6323014yes—
337C2×C4C2×#6323114yes—
338C2×C4C22×Dic3411yescharacteristic
339C2×C4C2×#6325211yescharacteristic
340C2×C4C2×D4×D1712yes—
341C2×C4C2×#6325412yes—
342C8—684no—
343C22#1176272114yes—
344C22#1176295914yes—
345C22#1176296414yes—
346C22#1176309414yes—
347C22#1176310414yes—
348C22#1176315914yes—
349C22#1176316814yes—
350C22C2×#1058762311yescharacteristic
351C22C2×#1058761011yescharacteristic
352C22C2×#1058762211yescharacteristic
353C22C22×#6323011yescharacteristic
354C22C22×#6323111yescharacteristic
355C22C2×#1058763511yescharacteristic
356C22C2×#1058763711yescharacteristic
357C4—24no—
358C4—24no—
359C4—44no—
360C4—82no—
361C4—688no—
362C4#1176272114yes—
363C4C2×#1058756412yes—
364C4C2×#1058757112yes—
365C2#1452992518yesdirect product factor
366C2C2×#1176272111yescharacteristic
367C2C2×#1176295911yescharacteristic
368C2C2×#1176296411yescharacteristic
369C2C2×#1176309411yescharacteristic
370C2C2×#1176310411yescharacteristic
371C2C2×#1176315911yescharacteristic
372C2C2×#1176316811yescharacteristic
subgroupG/H
centerC24C2×C22⋊D17
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC2×C17×#391C2
socle, prime radicalC24×C17C2×D4
hypercenterC2×#391D17
hypocenterC17C2×#2024
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. #14529925C2direct (N × H)
29. C22×Q8×C17Q8semidirect
71. C2×Q8×C17C2×Q8semidirect
203. C2×C17#2024semidirect
219. C22×Q8Dic34semidirect
248. C17C2×#2024semidirect
262. C2×Q8C2×Dic34semidirect
365. C2#14529925direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875552
C22×#105875062
#145299252
C2×#117625712
C2×#117625642
C2×C17×#3912
C2×#202417