Finite Group Databasebeta

← C2×#14528352 #17016988

Subgroups — C2×#14528352 #17016988

Order 4352.

734 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763156C211yesmaximal, characteristic
2C2×#11763019C211yesmaximal, characteristic, complemented
3C2×#11763009C211yesmaximal, characteristic
4#14528352C218yesmaximal, direct product factor
5C2×#11762560C211yesmaximal, characteristic, complemented
6C2×#11762554C211yesmaximal, characteristic, complemented
7C2×#11762552C211yesmaximal, characteristic
8C2×C17×#446C211yesmaximal, characteristic, complemented
9C22×#63231—21no—
10C22×#63230—21no—
11C2×#10587555C2211yescharacteristic
12C2×#10587560C2211yescharacteristic
13#11763156—22no—
14#11763156C2214yes—
15#11763019—22no—
16#11763019C2214yescomplemented
17#11763009—22no—
18#11763009C2214yes—
19C2×C4⋊#3622C2211yescharacteristic
20C2×C4⋊#3622C2211yescharacteristic
21C2×#10587481—21no—
22C2×#10587492—21no—
23C2×#10587492—21no—
24C2×#10587480—21no—
25#11762560C2214yescomplemented
26#11762554C2214yescomplemented
27#11762552C2214yes—
28C2×C4×Q8×C17C2211yescharacteristic
29C17×#446—22no—
30C17×#446C2214yescomplemented
31C2×C17×C4⋊C8—21no—
32C2×C17×C4⋊C8C2211yescharacteristic
33C2×C17×#97—21no—
34C2×C4×C8×C17C2211yescharacteristic
35C22×Q8×C17D411yescharacteristic
36C22×D68—21no—
37C22×D68—21no—
38C22×D68—21no—
39C22×Dic34—21no—
40C22×C8×C17—21no—
41C22×C8×C17D411yescharacteristic
42C22×C8×C17D411yescharacteristic
43C4×Q8×C17—21no—
44C4×Q8×C17—21no—
45C4×Q8×C17D412yes—
46C4×Q8×C17C2312yes—
47C2×C4⋊C4×C17—21no—
48C2×C4⋊C4×C17D411yescharacteristic
49C2×C42×C17—21no—
50C2×C42×C17C2311yescharacteristic
51C2×#63231—24no—
52C2×#63231—44no—
53C2×#63230—24no—
54C2×#63230—44no—
55C2×C4⋊Dic17—21no—
56C2×C4⋊Dic17—21no—
57C22×#3622—21no—
58C22×#3622—21no—
59#10587560—21no—
60#10587560—21no—
61#10587560—21no—
62#10587560C2312yes—
63#10587555—21no—
64#10587555—21no—
65#10587555—21no—
66#10587555C2312yes—
67C17×C4⋊C8—24no—
68C17×C4⋊C8—21no—
69C17×C4⋊C8C2312yes—
70C17×#97—24no—
71C4×C8×C17D412yes—
72C4×C8×C17C2312yes—
73#10587492—24no—
74#10587492—24no—
75#10587481—24no—
76#10587480—24no—
77C4⋊#3622—21no—
78C4⋊#3622—21no—
79C4⋊#3622C2312yes—
80C4⋊#3622C2312yes—
81C23×D17—41no—
82C2×Q8×C17—21no—
83C2×Q8×C17—22no—
84C2×Q8×C17—22no—
85C2×Q8×C17C2×D412yes—
86C22×C4×C17—21no—
87C22×C4×C17—21no—
88C22×C4×C17C2×D411yescharacteristic
89C22×C4×C17C2×D411yescharacteristic
90C22×C4×C17#4111yescharacteristic
91C22×Dic17—41no—
92C2×D68—22no—
93C2×D68—22no—
94C2×D68—22no—
95C2×D68—42no—
96C2×D68—42no—
97C2×D68—42no—
98C2×D68—42no—
99C2×D68—41no—
100C2×D68—41no—
101C2×D68—41no—
102C2×D68—82no—
103C2×Dic34—22no—
104C2×Dic34—42no—
105C2×Dic34—42no—
106C2×Dic34—41no—
107C2×C8×C17—22no—
108C2×C8×C17—22no—
109C2×C8×C17—22no—
110C2×C8×C17—42no—
111C2×C8×C17C2×D412yes—
112C2×C8×C17C2×D412yes—
113C4⋊C4×C17—22no—
114C4⋊C4×C17—21no—
115C4⋊C4×C17—22no—
116C4⋊C4×C17C2×D412yes—
117C42×C17—22no—
118C42×C17—22no—
119C42×C17C2×D411yescharacteristic
120C42×C17C2×D411yescharacteristic
121C42×C17#4111yescharacteristic
122C42×C17C2411yescharacteristic
123#63231—48no—
124#63230—48no—
125C4⋊Dic17—22no—
126C4⋊Dic17—22no—
127C4⋊Dic17—41no—
128C4⋊Dic17—41no—
129C2×#3622—22no—
130C2×#3622—22no—
131C2×#3622—42no—
132C2×#3622—42no—
133C2×#1702—171nomaximal, Sylow
134C23×C17#12111yescharacteristic
135C22×D17—42no—
136C22×D17—82no—
137C22×D17—82no—
138C22×D17—82no—
139Q8×C17—22no—
140Q8×C17—22no—
141Q8×C17—42no—
142C2×C4×C17—22no—
143C2×C4×C17—22no—
144C2×C4×C17—22no—
145C2×C4×C17—42no—
146C2×C4×C17—42no—
147C2×C4×C17#12111yescharacteristic
148C2×C4×C17#12111yescharacteristic
149C2×C4×C17#12111yescharacteristic
150C2×C4×C17#13512yes—
151C2×C4×C17AGL(1,ℤ/8)12yes—
152C2×C4×C17AGL(1,ℤ/8)12yes—
153C2×C4×C17#13712yes—
154C2×C4×C17C22×D411yescharacteristic
155C2×C4×C17C22×D411yescharacteristic
156C2×C4×C17C2×#4111yescharacteristic
157C2×Dic17—42no—
158C2×Dic17—82no—
159D68—42no—
160D68—42no—
161D68—42no—
162D68—42no—
163D68—82no—
164D68—82no—
165D68—82no—
166D68—82no—
167Dic34—42no—
168Dic34—42no—
169Dic34—82no—
170C8×C17—22no—
171C8×C17—22no—
172C8×C17—42no—
173#3622—42no—
174#3622—42no—
175C2×#486—171no—
176C2×#462—171no—
177C2×#460—171no—
178C2×#446D1711yescharacteristic, complemented
179#1702—178no—
180C2×#334—171no—
181C2×#332—171no—
182C2×#331—171no—
183C22×C17#46412yes—
184C22×C17#46912yes—
185C22×C17#47112yes—
186C22×C17C2×#12111yescharacteristic
187C2×D17—82no—
188C2×D17—82no—
189C2×D17—82no—
190C2×D17—164no—
191C4×C17—21no—
192C4×C17—21no—
193C4×C17—42no—
194C4×C17—42no—
195C4×C17#46412yes—
196C4×C17#46912yes—
197C4×C17C2×#13511yescharacteristic
198C4×C17C2×AGL(1,ℤ/8)11yescharacteristic
199C4×C17C2×AGL(1,ℤ/8)11yescharacteristic
200C4×C17C2×#13711yescharacteristic
201Dic17—82no—
202C22×Q16—341no—
203C22×SD16—341no—
204C2×C4⋊Q8—171no—
205C2×#127—171no—
206C2×C4×Q8C2×D1711yescharacteristic
207#486—174no—
208#486—342no—
209#462—174no—
210#462—342no—
211#460—174no—
212#460—342no—
213#446—22no—
214#446C2×D1714yescomplemented
215C2×C4⋊C8—21no—
216C2×C4⋊C8—171no—
217C2×C4⋊C8—171no—
218C2×C4⋊C8C2×D1711yescharacteristic
219C2×#103—341no—
220C2×#102—341no—
221C2×#102—341no—
222C2×#102—341no—
223C2×#97—21no—
224C2×C4×C8C2×D1711yescharacteristic
225#334—174no—
226#332—174no—
227#331—174no—
228C2×C17#170214yescomplemented
229C2×C17C2×#46411yescharacteristic
230C2×C17C2×#46911yescharacteristic
231C2×C17C2×#47111yescharacteristic
232D17—162no—
233C22×Q8—341no—
234C22×Q8D6811yescharacteristic
235C22×D4—341no—
236C22×D4—341no—
237C22×D4—341no—
238C2×Q16—344no—
239C2×Q16—684no—
240C2×SD16—344no—
241C2×SD16—684no—
242C22×C8—21no—
243C22×C8—341no—
244C22×C8—341no—
245C22×C8C22⋊D1711yescharacteristic
246C22×C8C22⋊D1711yescharacteristic
247C4⋊Q8—172no—
248C4⋊Q8—341no—
249C4⋊Q8—341no—
250C4⋊Q8—341no—
251#127—172no—
252#127—341no—
253#127—341no—
254#127—341no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8D6812yes—
258C4×Q8C22×D1712yes—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—341no—
261C2×C4⋊C4—341no—
262C2×C4⋊C4D6811yescharacteristic
263C2×C42—21no—
264C2×C42C22×D1711yescharacteristic
265C4⋊C8—24no—
266C4⋊C8—21no—
267C4⋊C8—172no—
268C4⋊C8—172no—
269C4⋊C8—341no—
270C4⋊C8—341no—
271C4⋊C8C22×D1712yes—
272#103—344no—
273#102—344no—
274#102—344no—
275#102—344no—
276#97—24no—
277C4×C8C22⋊D1712yes—
278C4×C8C22×D1712yes—
279C17C2×#170211yescharacteristic, complemented, Sylow
280C24—681no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—342no—
285C2×Q8—681no—
286C2×Q8—682no—
287C2×Q8—682no—
288C2×Q8C2×D6812yes—
289C2×D4—342no—
290C2×D4—342no—
291C2×D4—342no—
292C2×D4—682no—
293C2×D4—682no—
294C2×D4—681no—
295C2×D4—681no—
296C2×D4—681no—
297C2×D4—682no—
298C2×D4—682no—
299C2×D4—1362no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—681no—
303C22×C4C2×D6811yescharacteristic
304C22×C4#6325211yescharacteristic
305C22×C4C2×C22⋊D1711yescharacteristic
306Q16—688no—
307SD16—688no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—42no—
312C2×C8—342no—
313C2×C8—342no—
314C2×C8—682no—
315C2×C8—682no—
316C2×C8C2×C22⋊D1712yes—
317C2×C8C2×C22⋊D1712yes—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—342no—
322C4⋊C4—342no—
323C4⋊C4—681no—
324C4⋊C4—681no—
325C4⋊C4C2×D6812yes—
326C42—22no—
327C42—22no—
328C42C2×D6811yescharacteristic
329C42#6325211yescharacteristic
330C42C2×C22⋊D1711yescharacteristic
331C42C23×D1711yescharacteristic
332C23—682no—
333C23—1362no—
334C23—1362no—
335C23—1362no—
336C23#1058761611yescharacteristic
337Q8—22no—
338Q8—22no—
339Q8—42no—
340Q8—682no—
341Q8—682no—
342Q8—1362no—
343D4—682no—
344D4—682no—
345D4—682no—
346D4—682no—
347D4—1362no—
348D4—1362no—
349D4—1362no—
350D4—1362no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—682no—
357C2×C4—1362no—
358C2×C4#1058759412yes—
359C2×C4#1058759412yes—
360C2×C4#1058761611yescharacteristic
361C2×C4#1058761611yescharacteristic
362C2×C4#1058761611yescharacteristic
363C2×C4#1058762812yes—
364C2×C4#1058763612yes—
365C2×C4C22×D6811yescharacteristic
366C2×C4C2×#6325211yescharacteristic
367C2×C4C22×C22⋊D1711yescharacteristic
368C8—22no—
369C8—22no—
370C8—42no—
371C8—682no—
372C8—682no—
373C22—2724no—
374C22—1362no—
375C22—1362no—
376C22—1362no—
377C22#1176303112yes—
378C22#1176306212yes—
379C22#1176307212yes—
380C22C2×#1058761611yescharacteristic
381C4—21no—
382C4—21no—
383C4—42no—
384C4—42no—
385C4—1362no—
386C4#1176303112yes—
387C4#1176306212yes—
388C4C2×#1058763611yescharacteristic
389C4C2×#1058759411yescharacteristic
390C4C2×#1058759411yescharacteristic
391C4C2×#1058762811yescharacteristic
392C2—2722no—
393C2#1452835214yesdirect product factor
394C2C2×#1176303111yescharacteristic
395C2C2×#1176306211yescharacteristic
396C2C2×#1176307211yescharacteristic
subgroupG/H
centerC23#10587616
commutator, cosocleC42×C17C24
FrattiniC42C23×D17
FittingC2×C17×#446C2
socleC23×C17#121
prime radicalC2×#10587560C22
hypercenterC2×#446D17
hypocenterC17C2×#1702
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#11763019C2semidirect
4. #14528352C2direct (N × H)
5. C2×#11762560C2semidirect
6. C2×#11762554C2semidirect
8. C2×C17×#446C2semidirect
16. #11763019C22semidirect
25. #11762560C22semidirect
26. #11762554C22semidirect
30. C17×#446C22semidirect
178. C2×#446D17semidirect
214. #446C2×D17semidirect
228. C2×C17#1702semidirect
279. C17C2×#1702semidirect
393. C2#14528352direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117631562
C2×#117630192
C2×#117630092
#145283522
C2×#117625602
C2×#117625542
C2×#117625522
C2×C17×#4462
C2×#170217