Finite Group Databasebeta

← C2×#14528131 #17016643

Subgroups — C2×#14528131 #17016643

Order 4352.

786 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763181C211yesmaximal, characteristic
2C2×#11763095C211yesmaximal, characteristic, complemented
3C2×#11763006C211yesmaximal, characteristic
4C2×#11762933C211yesmaximal, characteristic, complemented
5#14528131C218yesmaximal, direct product factor
6C2×#11762559C211yesmaximal, characteristic, complemented
7C2×#11762556C211yesmaximal, characteristic, complemented
8C2×C17×#331C211yesmaximal, characteristic
9C22×#63229—21no—
10C22×#63229—21no—
11C22×#63229—21no—
12C2×#10587555C2211yescharacteristic
13C2×C4×Dic34C2211yescharacteristic
14#11763181—22no—
15#11763181C2214yes—
16#11763095—22no—
17#11763095C2214yescomplemented
18#11763006—22no—
19#11763006C2214yes—
20#11762933—22no—
21#11762933C2214yescomplemented
22C2×#10587488—21no—
23C2×C4⋊#3622C2211yescharacteristic
24C2×#10587485—21no—
25C2×#10587487—21no—
26C2×#10587503—21no—
27C2×C4×#3622C2211yescharacteristic
28C2×C8×Dic17—21no—
29#11762559C2214yescomplemented
30#11762556C2214yescomplemented
31C2×C17×#127C2211yescharacteristic
32C2×C17×C4⋊C8C2211yescharacteristic
33C2×C17×C4⋊C8C2211yescharacteristic
34C17×#331C2214yes—
35C22×D4×C17—21no—
36C22×D4×C17—21no—
37C22×D4×C17—21no—
38C22×Dic34—21no—
39C22×Dic34D411yescharacteristic
40C22×C8×C17—21no—
41C22×C8×C17—21no—
42C17×#127—21no—
43C17×#127—21no—
44C17×#127—21no—
45C17×#127C2312yes—
46C2×C42×C17C2311yescharacteristic
47C2×#63229—24no—
48C2×#63229—24no—
49C2×#63229—24no—
50C2×#63229—44no—
51C2×#63229—44no—
52C2×#63229—44no—
53C2×C4⋊Dic17—21no—
54C2×C4⋊Dic17—21no—
55C2×C4⋊Dic17D411yescharacteristic
56C2×#63225—21no—
57C2×C4×Dic17—21no—
58C22×#3622—21no—
59C22×#3622D411yescharacteristic
60C22×#3622D411yescharacteristic
61#10587555—21no—
62#10587555—21no—
63#10587555—21no—
64#10587555C2312yes—
65C4×Dic34—21no—
66C4×Dic34—21no—
67C4×Dic34D412yes—
68C4×Dic34C2312yes—
69C17×C4⋊C8—21no—
70C17×C4⋊C8—21no—
71C17×C4⋊C8C2312yes—
72C17×C4⋊C8C2312yes—
73#10587503—24no—
74#10587488—24no—
75#10587487—24no—
76#10587485—24no—
77C8×Dic17—24no—
78C4⋊#3622—21no—
79C4⋊#3622C2312yes—
80C4×#3622D412yes—
81C4×#3622C2312yes—
82C24×C17—41no—
83C2×D4×C17—22no—
84C2×D4×C17—22no—
85C2×D4×C17—22no—
86C2×D4×C17—41no—
87C2×D4×C17—41no—
88C2×D4×C17—41no—
89C2×D4×C17—42no—
90C2×D4×C17—42no—
91C2×D4×C17—42no—
92C2×D4×C17—42no—
93C2×D4×C17—82no—
94C22×C4×C17C2×D411yescharacteristic
95C22×C4×C17C2×D411yescharacteristic
96C22×C4×C17#4111yescharacteristic
97C22×Dic17—21no—
98C22×Dic17—21no—
99C22×Dic17—41no—
100C2×Dic34—21no—
101C2×Dic34—22no—
102C2×Dic34—22no—
103C2×Dic34—42no—
104C2×Dic34—42no—
105C2×Dic34—41no—
106C2×Dic34SD1614yescomplemented
107C2×Dic34C2×D412yes—
108C2×C8×C17—22no—
109C2×C8×C17—22no—
110C2×C8×C17—42no—
111C2×C8×C17—42no—
112C42×C17C2×D411yescharacteristic
113C42×C17C2×D411yescharacteristic
114C42×C17#4111yescharacteristic
115C42×C17C2411yescharacteristic
116#63229—48no—
117#63229—48no—
118#63229—48no—
119C4⋊Dic17—21no—
120C4⋊Dic17—22no—
121C4⋊Dic17—22no—
122C4⋊Dic17—41no—
123C4⋊Dic17—41no—
124C4⋊Dic17C2×D412yes—
125#63225—22no—
126#63225—22no—
127C4×Dic17—22no—
128C4×Dic17—22no—
129C2×#3622—22no—
130C2×#3622—22no—
131C2×#3622—42no—
132C2×#3622SD1614yescomplemented
133C2×#3622C2×D412yes—
134C2×#3622C2×D412yes—
135C2×#1666—171nomaximal, Sylow
136C23×C17—42no—
137C23×C17—82no—
138C23×C17—82no—
139C23×C17—82no—
140C23×C17#12111yescharacteristic
141D4×C17—42no—
142D4×C17—42no—
143D4×C17—42no—
144D4×C17—42no—
145D4×C17—82no—
146D4×C17—82no—
147D4×C17—82no—
148D4×C17—82no—
149C2×C4×C17—22no—
150C2×C4×C17#12111yescharacteristic
151C2×C4×C17#12111yescharacteristic
152C2×C4×C17#12111yescharacteristic
153C2×C4×C17C2×SD1612yes—
154C2×C4×C17C2×SD1612yes—
155C2×C4×C17#13512yes—
156C2×C4×C17AGL(1,ℤ/8)12yes—
157C2×C4×C17C22×D411yescharacteristic
158C2×C4×C17C22×D411yescharacteristic
159C2×C4×C17C2×#4111yescharacteristic
160C2×Dic17—22no—
161C2×Dic17—24no—
162C2×Dic17—22no—
163C2×Dic17—42no—
164C2×Dic17—42no—
165C2×Dic17—82no—
166Dic34—22no—
167Dic34—24no—
168Dic34—42no—
169Dic34—42no—
170Dic34—82no—
171Dic34C2×SD1614yescomplemented
172C8×C17—42no—
173C8×C17—42no—
174#3622—22no—
175#3622—42no—
176#3622C2×SD1614yescomplemented
177C2×#492—171no—
178C2×#475—171no—
179C2×#460—171no—
180C2×C8×Q8—171no—
181#1666—178no—
182C2×#334—171no—
183C2×#332—171no—
184C2×#331D1711yescharacteristic
185C22×C17—82no—
186C22×C17—82no—
187C22×C17—82no—
188C22×C17—164no—
189C22×C17#46012yes—
190C22×C17#46512yes—
191C22×C17#47112yes—
192C22×C17C2×#12111yescharacteristic
193C4×C17—21no—
194C4×C17—21no—
195C4×C17#46012yes—
196C4×C17#46512yes—
197C4×C17C22×SD1611yescharacteristic
198C4×C17C22×SD1611yescharacteristic
199C4×C17C2×#13511yescharacteristic
200C4×C17C2×AGL(1,ℤ/8)11yescharacteristic
201Dic17—24no—
202Dic17—42no—
203Dic17—82no—
204C22×SD16—341no—
205C22×SD16—341no—
206C22×SD16—341no—
207C2×C4⋊Q8—171no—
208C2×#127C2×D1711yescharacteristic
209C2×C4×Q8—171no—
210#492—174no—
211#492—342no—
212#475—174no—
213#475—342no—
214#460—174no—
215#460—342no—
216C8×Q8—174no—
217C8×Q8—342no—
218C2×#106—341no—
219C2×C4⋊C8—171no—
220C2×C4⋊C8—341no—
221C2×C4⋊C8C2×D1711yescharacteristic
222C2×C4⋊C8C2×D1711yescharacteristic
223C2×#103—341no—
224C2×#102—341no—
225C2×C4×C8—171no—
226C2×C4×C8—341no—
227#334—174no—
228#332—174no—
229#331C2×D1714yes—
230C2×C17—162no—
231C2×C17#166614yescomplemented
232C2×C17C2×#46011yescharacteristic
233C2×C17C2×#46511yescharacteristic
234C2×C17C2×#47111yescharacteristic
235C22×Q8—171no—
236C22×Q8—341no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C2×SD16—344no—
241C2×SD16—344no—
242C2×SD16—344no—
243C2×SD16—684no—
244C2×SD16—684no—
245C2×SD16—684no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—171no—
249C22×C8—171no—
250C22×C8—341no—
251C4⋊Q8—172no—
252C4⋊Q8—341no—
253C4⋊Q8—341no—
254C4⋊Q8—341no—
255#127—21no—
256#127—21no—
257#127—21no—
258#127C22×D1712yes—
259C4×Q8—172no—
260C4×Q8—172no—
261C4×Q8—341no—
262C4×Q8—341no—
263C2×C4⋊C4—171no—
264C2×C4⋊C4—341no—
265C2×C4⋊C4—341no—
266C2×C4⋊C4—341no—
267C2×C42—341no—
268C2×C42C22×D1711yescharacteristic
269#106—344no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—172no—
273C4⋊C8—344no—
274C4⋊C8—341no—
275C4⋊C8C22×D1712yes—
276C4⋊C8C22×D1712yes—
277#103—344no—
278#102—344no—
279C4×C8—172no—
280C4×C8—172no—
281C4×C8—344no—
282C17C2×#166611yescharacteristic, complemented, Sylow
283C24—41no—
284C2×Q8—172no—
285C2×Q8—174no—
286C2×Q8—341no—
287C2×Q8—342no—
288C2×Q8—342no—
289C2×Q8—681no—
290C2×Q8—682no—
291C2×Q8—682no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—82no—
303C22×C4—341no—
304C22×C4—341no—
305C22×C4—681no—
306C22×C4#6325211yescharacteristic
307C22×C4D4×D1711yescharacteristic
308C22×C4D4×D1711yescharacteristic
309SD16—688no—
310SD16—688no—
311SD16—688no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—42no—
315C2×C8—42no—
316C2×C8—172no—
317C2×C8—174no—
318C2×C8—172no—
319C2×C8—342no—
320C2×C8—342no—
321C2×C8—682no—
322C4⋊C4—172no—
323C4⋊C4—342no—
324C4⋊C4—341no—
325C4⋊C4—342no—
326C4⋊C4—342no—
327C4⋊C4—342no—
328C4⋊C4—681no—
329C4⋊C4—681no—
330C42—342no—
331C42—342no—
332C42#6325211yescharacteristic
333C42D4×D1711yescharacteristic
334C42D4×D1711yescharacteristic
335C42C23×D1711yescharacteristic
336C23—42no—
337C23—82no—
338C23—82no—
339C23—82no—
340C23#1058757011yescharacteristic
341Q8—174no—
342Q8—344no—
343Q8—342no—
344Q8—682no—
345Q8—682no—
346Q8—1362no—
347D4—42no—
348D4—42no—
349D4—42no—
350D4—42no—
351D4—82no—
352D4—82no—
353D4—82no—
354D4—82no—
355C2×C4—22no—
356C2×C4—344no—
357C2×C4—342no—
358C2×C4—342no—
359C2×C4—682no—
360C2×C4—682no—
361C2×C4—1362no—
362C2×C4#1058757011yescharacteristic
363C2×C4#1058757011yescharacteristic
364C2×C4#1058757011yescharacteristic
365C2×C4#1058759712yes—
366C2×C4#1058759812yes—
367C2×C4SD16×D1712yes—
368C2×C4SD16×D1712yes—
369C2×C4C2×#6325211yescharacteristic
370C2×C4C2×D4×D1711yescharacteristic
371C2×C4C2×D4×D1711yescharacteristic
372C8—42no—
373C8—42no—
374C8—174no—
375C8—342no—
376C8—682no—
377C22—82no—
378C22—82no—
379C22—82no—
380C22—164no—
381C22#1176300812yes—
382C22#1176303712yes—
383C22#1176307112yes—
384C22C2×#1058757011yescharacteristic
385C4—21no—
386C4—21no—
387C4—344no—
388C4—682no—
389C4—1362no—
390C4#1176300812yes—
391C4#1176303712yes—
392C4C2×SD16×D1711yescharacteristic
393C4C2×SD16×D1711yescharacteristic
394C4C2×#1058759811yescharacteristic
395C4C2×#1058759711yescharacteristic
396C2—162no—
397C2#1452813114yesdirect product factor
398C2C2×#1176300811yescharacteristic
399C2C2×#1176303711yescharacteristic
400C2C2×#1176307111yescharacteristic
subgroupG/H
centerC23#10587570
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC2×C17×#331C2
socleC23×C17#121
prime radicalC2×C17×#127C22
hypercenterC2×#331D17
hypocenterC17C2×#1666
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. C2×#11763095C2semidirect
4. C2×#11762933C2semidirect
5. #14528131C2direct (N × H)
6. C2×#11762559C2semidirect
7. C2×#11762556C2semidirect
17. #11763095C22semidirect
21. #11762933C22semidirect
29. #11762559C22semidirect
30. #11762556C22semidirect
106. C2×Dic34SD16semidirect
132. C2×#3622SD16semidirect
171. Dic34C2×SD16semidirect
176. #3622C2×SD16semidirect
231. C2×C17#1666semidirect
282. C17C2×#1666semidirect
397. C2#14528131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117631812
C2×#117630952
C2×#117630062
C2×#117629332
#145281312
C2×#117625592
C2×#117625562
C2×C17×#3312
C2×#166617