Finite Group Databasebeta

← C2×#14541797 #17915261

Subgroups — C2×#14541797 #17915261

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×#11763544C212yesmaximal, complemented
2#14541797C2116yesmaximal, direct product factor
3C2×#11763193C212yesmaximal, complemented
4C2×#11763186C211yesmaximal, characteristic
5C2×#11763010C212yesmaximal, complemented
6C2×#11763025C214yesmaximal, complemented
7C2×C4×Dic68C211yesmaximal, characteristic, complemented
8C2×C4×D136C212yesmaximal, complemented
9C2×C8×Q8×C17C211yesmaximal, characteristic, complemented
10C22×Dic68C2211yescharacteristic
11C22×#63219C2214yes—
12C22×D136C2212yes—
13C22×D136C2212yes—
14#11763544—28no—
15#11763544C22116yescomplemented
16C2×#10587560C2212yes—
17C2×#10587633—22no—
18C2×#10587561C2214yes—
19C2×#10587580—24no—
20C2×C4×Dic34C2212yes—
21C2×C4×D68C2214yes—
22C2×#10587579—22no—
23#11763193C22116yescomplemented
24#11763186C2218yes—
25#11763025C22132yescomplemented
26#11763010C22116yescomplemented
27C4×Dic68C2218yescomplemented
28C4×D136C22116yescomplemented
29C2×#10587489C2211yescharacteristic
30C2×#10587487C2212yes—
31C2×#10587492C2214yes—
32C2×C4×Q8×C17C2211yescharacteristic
33C8×Q8×C17C2218yescomplemented
34C2×C17×C4⋊C8C2212yes—
35C2×C17×C4⋊C8C2211yescharacteristic
36C2×C4×C8×C17C2212yes—
37C2×C4×C8×C17C2211yescharacteristic
38C22×Q8×C17D411yescharacteristic
39C22×D68—22no—
40C22×D68—22no—
41C22×D68C2314yes—
42C22×C4×D17—24no—
43C22×Dic34C2312yes—
44C22×C8×C17C2312yes—
45C22×C8×C17C2311yescharacteristic
46C22×C8×C17C2311yescharacteristic
47C4×Q8×C17D414yes—
48C4×Q8×C17C2314yes—
49C2×C4⋊C4×C17D411yescharacteristic
50C2×C4⋊C4×C17D412yes—
51C2×C42×C17C2312yes—
52C2×C42×C17C2311yescharacteristic
53#10587633—216no—
54C2×#63227—24no—
55C2×#63227—24no—
56C2×#63227—24no—
57C2×C4⋊Dic17C2312yes—
58C2×#63225—22no—
59C2×C4×Dic17—22no—
60C2×Dic68—24no—
61C2×Dic68C2314yes—
62C2×D136—28no—
63C2×D136—44no—
64C2×D136C2318yes—
65C2×D136C2318yes—
66C2×#63219—48no—
67C2×#63219C23116yes—
68#10587580—232no—
69#10587579—216no—
70#10587561—28no—
71#10587561C23116yes—
72#10587560—24no—
73#10587560C2318yes—
74C4×D68—28no—
75C4×D68C23116yes—
76C4×Dic34—24no—
77C4×Dic34C2318yes—
78C17×C4⋊C8C2314yes—
79C17×C4⋊C8C2318yes—
80C4×C8×C17C2318yes—
81C4×C8×C17C2314yes—
82#10587492C23116yes—
83#10587489C2314yes—
84#10587487C2318yes—
85C23×D17—24no—
86C2×Q8×C17—24no—
87C2×Q8×C17C2×D414yes—
88C22×C4×C17C2×D412yes—
89C22×C4×C17C2×D411yescharacteristic
90C22×C4×C17C2×D412yes—
91C22×C4×C17C2×D411yescharacteristic
92C22×C4×C17C2411yescharacteristic
93C22×Dic17—22no—
94C22×Dic17—22no—
95C2×D68—28no—
96C2×D68—28no—
97C2×D68—28no—
98C2×D68—24no—
99C2×D68—28no—
100C2×D68—48no—
101C2×D68—84no—
102C2×D68C2418yes—
103C2×C4×D17—216no—
104C2×C4×D17—88no—
105C2×Dic34—24no—
106C2×Dic34—24no—
107C2×Dic34—22no—
108C2×Dic34C2414yes—
109C2×C8×C17—24no—
110C2×C8×C17—22no—
111C2×C8×C17#4114yes—
112C2×C8×C17C2412yes—
113C2×C8×C17C2414yes—
114C2×C8×C17C2412yes—
115C4⋊C4×C17C2×D414yes—
116C4⋊C4×C17C2×D418yes—
117C42×C17C2×D412yes—
118C42×C17C2×D414yes—
119C42×C17C2412yes—
120C42×C17C2414yes—
121#63227—216no—
122#63227—216no—
123#63227—216no—
124C4⋊Dic17—22no—
125C4⋊Dic17C2414yes—
126#63225—28no—
127C4×Dic17—28no—
128Dic68—28no—
129D136—216no—
130D136—48no—
131#63219—416no—
132C2×#3396—171nomaximal, Sylow
133C23×C17C22×D411yescharacteristic
134C22×D17—28no—
135C22×D17—48no—
136C22×D17—48no—
137C22×D17—48no—
138Q8×C17—28no—
139C2×C4×C17—24no—
140C2×C4×C17—24no—
141C2×C4×C17—22no—
142C2×C4×C17#13514yes—
143C2×C4×C17C22×D414yes—
144C2×C4×C17C22×D412yes—
145C2×C4×C17C22×D414yes—
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—44no—
154C2×Dic17—44no—
155D68—28no—
156D68—28no—
157D68—48no—
158D68—416no—
159D68—88no—
160C4×D17—816no—
161Dic34—24no—
162Dic34—24no—
163Dic34—44no—
164C8×C17—24no—
165C8×C17—22no—
166C8×C17C2×#4114yes—
167C2×#559—172no—
168#3396—1716no—
169C2×#495—172no—
170C2×#493—171no—
171C2×#460—172no—
172C2×#463—174no—
173C2×C8×Q8D1711yescharacteristic, complemented
174C2×C4×Q16—171no—
175C2×C4×D8—172no—
176C22×C17#55012yes—
177C22×C17C2×#13512yes—
178C22×C17#57612yes—
179C22×C17C23×D411yescharacteristic
180C2×D17—48no—
181C2×D17—48no—
182C2×D17—48no—
183C2×D17—816no—
184C4×C17—24no—
185C4×C17—24no—
186C4×C17—22no—
187C4×C17#55012yes—
188C4×C17C2×#13514yes—
189C4×C17C22×#4111yescharacteristic
190C4×C17C2×H(5,𝔽2)11yescharacteristic
191Dic17—44no—
192Dic17—44no—
193C22×Q16—171no—
194C22×SD16—174no—
195C22×D8—172no—
196C22×D8—172no—
197#559—1716no—
198#559—348no—
199C2×#127—172no—
200C2×#124—174no—
201C2×#124—342no—
202C2×#123—344no—
203C2×C4×Q8—172no—
204C2×C4×Q8C2×D1711yescharacteristic
205C2×C4×D4—174no—
206C2×C4×D4—342no—
207#495—1716no—
208#493—178no—
209#463—1732no—
210#460—1716no—
211C8×Q8C2×D1718yescomplemented
212C4×Q16—178no—
213C4×D8—1716no—
214C2×#107—171no—
215C2×C4⋊C8C2×D1712yes—
216C2×C4⋊C8C2×D1711yescharacteristic
217C2×#103—172no—
218C2×#102—174no—
219C2×C4×C8C2×D1711yescharacteristic
220C2×C4×C8C2×D1712yes—
221C2×C17#339614yescomplemented
222C2×C17C2×#55011yescharacteristic
223C2×C17C22×#13511yescharacteristic
224C2×C17C2×#57611yescharacteristic
225D17—88no—
226C22×Q8—172no—
227C22×Q8D6811yescharacteristic
228C22×D4—174no—
229C22×D4—342no—
230C22×D4—342no—
231C23×C4—344no—
232C2×Q16—174no—
233C2×Q16—344no—
234C2×SD16—1716no—
235C2×SD16—688no—
236C2×D8—178no—
237C2×D8—178no—
238C2×D8—348no—
239C2×D8—684no—
240C22×C8C22×D1711yescharacteristic
241C22×C8C22×D1712yes—
242C22×C8C22×D1711yescharacteristic
243#127—178no—
244#127—344no—
245#124—1716no—
246#124—3416no—
247#124—348no—
248#123—3432no—
249C4×Q8—178no—
250C4×Q8—344no—
251C4×Q8D6814yes—
252C4×Q8C22×D1714yes—
253C4×D4—1716no—
254C4×D4—3416no—
255C4×D4—348no—
256C2×C4⋊C4—172no—
257C2×C4⋊C4—342no—
258C2×C4⋊C4D6811yescharacteristic
259C2×C4⋊C4D6812yes—
260C2×C22⋊C4—344no—
261C2×C22⋊C4—344no—
262C2×C22⋊C4—344no—
263C2×C42—342no—
264C2×C42C22×D1712yes—
265C2×C42C22×D1711yescharacteristic
266#107—174no—
267C4⋊C8C22×D1714yes—
268C4⋊C8C22×D1718yes—
269#103—178no—
270#102—1716no—
271C4×C8C22×D1718yes—
272C4×C8C22×D1714yes—
273C17C2×#339611yescharacteristic, complemented, Sylow
274C24—344no—
275C2×Q8—24no—
276C2×Q8—174no—
277C2×Q8—342no—
278C2×Q8—344no—
279C2×Q8—344no—
280C2×Q8C2×D6814yes—
281C2×D4—178no—
282C2×D4—348no—
283C2×D4—344no—
284C2×D4—348no—
285C2×D4—348no—
286C2×D4—348no—
287C2×D4—688no—
288C2×D4—1364no—
289C22×C4—342no—
290C22×C4—342no—
291C22×C4—3416no—
292C22×C4—1368no—
293C22×C4C2×D6812yes—
294C22×C4C2×D6812yes—
295C22×C4C2×D6811yescharacteristic
296C22×C4C2×D6811yescharacteristic
297C22×C4C23×D1711yescharacteristic
298Q16—348no—
299SD16—6816no—
300D8—3416no—
301D8—688no—
302C2×C8—22no—
303C2×C8—24no—
304C2×C8#6325614yes—
305C2×C8C23×D1714yes—
306C2×C8C23×D1712yes—
307C2×C8C23×D1712yes—
308C4⋊C4—174no—
309C4⋊C4—342no—
310C4⋊C4—348no—
311C4⋊C4C2×D6814yes—
312C4⋊C4C2×D6818yes—
313C22⋊C4—3416no—
314C22⋊C4—3416no—
315C22⋊C4—3416no—
316C42—348no—
317C42C2×D6814yes—
318C42C2×D6812yes—
319C42C23×D1714yes—
320C42C23×D1712yes—
321C23—348no—
322C23—688no—
323C23—688no—
324C23—688no—
325C23C22×D6811yescharacteristic
326Q8—28no—
327Q8—344no—
328Q8—344no—
329Q8—684no—
330D4—348no—
331D4—348no—
332D4—688no—
333D4—6816no—
334D4—1368no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—344no—
339C2×C4—344no—
340C2×C4—684no—
341C2×C4—684no—
342C2×C4—13616no—
343C2×C4#1058759014yes—
344C2×C4C22×D6814yes—
345C2×C4C22×D6814yes—
346C2×C4C22×D6812yes—
347C2×C4C22×D6811yescharacteristic
348C2×C4C22×D6812yes—
349C2×C4C2×#6325612yes—
350C2×C4#1058769612yes—
351C2×C4C24×D1711yescharacteristic
352C8—22no—
353C8—24no—
354C8C2×#6325614yes—
355C22—688no—
356C22—688no—
357C22—688no—
358C22—13616no—
359C22#1176348112yes—
360C22C2×#1058759012yes—
361C22#1176361412yes—
362C22C23×D6811yescharacteristic
363C4—24no—
364C4—24no—
365C4—22no—
366C4—684no—
367C4—684no—
368C4#1176348112yes—
369C4C2×#1058759014yes—
370C4C22×#6325611yescharacteristic
371C4C2×#1058769611yescharacteristic
372C2—1368no—
373C2#1454179714yesdirect product factor
374C2C2×#1176348111yescharacteristic
375C2C22×#1058759011yescharacteristic
376C2C2×#1176361411yescharacteristic
subgroupG/H
centerC23C22×D68
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC2×C8×Q8×C17C2
socleC23×C17C22×D4
prime radicalC2×#11763186C2
hypercenterC2×C8×Q8D17
hypocenterC17C2×#3396
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11763544C2semidirect
2. #14541797C2direct (N × H)
3. C2×#11763193C2semidirect
5. C2×#11763010C2semidirect
6. C2×#11763025C2semidirect
7. C2×C4×Dic68C2semidirect
8. C2×C4×D136C2semidirect
9. C2×C8×Q8×C17C2semidirect
15. #11763544C22semidirect
23. #11763193C22semidirect
25. #11763025C22semidirect
26. #11763010C22semidirect
27. C4×Dic68C22semidirect
28. C4×D136C22semidirect
33. C8×Q8×C17C22semidirect
173. C2×C8×Q8D17semidirect
211. C8×Q8C2×D17semidirect
221. C2×C17#3396semidirect
273. C17C2×#3396semidirect
373. C2#14541797direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117635442
#145417972
C2×#117631932
C2×#117631862
C2×#117630102
C2×#117630252
C2×C4×Dic682
C2×C4×D1362
C2×C8×Q8×C172
C2×#339617