Finite Group Databasebeta

← C2×#14544918 #17970545

Subgroups — C2×#14544918 #17970545

Order 4352.

1878 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763813C211yesmaximal, characteristic, complemented
2C22×#10587548C214yesmaximal, complemented
3C2×C42×#595C211yesmaximal, characteristic, complemented
4#14544918C218yesmaximal, direct product factor
5C2×#11763357C211yesmaximal, characteristic
6C22×#63243C2212yes—
7C22×C4×#595—22no—
8C22×C4×#595C2212yes—
9#11763813—22no—
10#11763813C2214yescomplemented
11C2×C4⋊#3624—22no—
12C2×#10587548—216no—
13C2×#10587548C22116yescomplemented
14C42×#595—22no—
15C42×#595C2214yescomplemented
16C22×#63254C2212yes—
17#11763357—22no—
18#11763357—22no—
19#11763357C414yescomplemented
20#11763357C2214yes—
21C2×#10587555C411yescharacteristic, complemented
22C2×#10587622C412yescomplemented
23C2×#10587624—22no—
24C2×D4×Dic17—22no—
25C2×C42×D17C2211yescharacteristic
26C2×C17×#127C411yescharacteristic, complemented
27C23×#595—22no—
28C22×D4×C17—22no—
29C22×D4×C17C2×C412yes—
30C22×C22⋊D17—22no—
31C23×Dic17—22no—
32C2×#63254—28no—
33C2×#63254—22no—
34C2×#63254—22no—
35C2×#63254—28no—
36C2×#63254C2×C414yes—
37C2×#63254C2314yes—
38C22×C4×D17D412yes—
39C22×C4×D17C2311yescharacteristic
40C22×Dic34C2×C412yes—
41C22×#3624—22no—
42C2×C4×#595—216no—
43C2×C4×#595—22no—
44C2×C4×#595—28no—
45C2×C4×#595—24no—
46C2×C4×#595D418yescomplemented
47C2×C4×#595C2314yes—
48C2×#63243—28no—
49C2×#63243—22no—
50C2×#63243C2314yes—
51C17×#127—22no—
52C17×#127C2×C414yescomplemented
53C2×C42×C17C2×C411yescharacteristic
54C2×C22⋊Dic17—24no—
55#10587624—28no—
56#10587624—28no—
57#10587622—24no—
58#10587622C2×C418yescomplemented
59D4×Dic17—28no—
60D4×Dic17—28no—
61C2×C4⋊Dic17—22no—
62C2×C4×Dic17C2×C411yescharacteristic
63C2×C4×Dic17D412yes—
64C42×D17C2×C412yes—
65C42×D17D412yes—
66C42×D17D412yes—
67C42×D17C2312yes—
68#10587555—22no—
69#10587555C2×C414yescomplemented
70#10587548—232no—
71C4⋊#3624—28no—
72C24×C17—22no—
73C23×D17C2×D411yescharacteristic
74C22×#595—216no—
75C22×#595—28no—
76C22×#595—24no—
77C2×D4×C17—22no—
78C2×D4×C17—28no—
79C2×D4×C17—28no—
80C2×D4×C17—48no—
81C2×D4×C17C22×C414yes—
82C22×C4×C17C22⋊C412yes—
83C22×C4×C17C22×C411yescharacteristic
84C2×C22⋊D17—24no—
85C2×C22⋊D17—24no—
86C2×C22⋊D17—48no—
87C22×Dic17—22no—
88C22×Dic17—24no—
89C22×Dic17—24no—
90C22×Dic17—44no—
91C22×Dic17—44no—
92C22×Dic17C22⋊C412yes—
93C22×Dic17C2×D411yescharacteristic
94#63254—216no—
95#63254—28no—
96#63254—28no—
97#63254—48no—
98#63254—44no—
99#63254—44no—
100C2×C4×D17—28no—
101C2×C4×D17C22⋊C414yes—
102C2×C4×D17C22×C411yescharacteristic
103C2×C4×D17C2×D414yes—
104C2×C4×D17C2×D414yes—
105C2×C4×D17C2×D411yescharacteristic
106C2×C4×D17C2×D411yescharacteristic
107C2×C4×D17#4114yes—
108C2×C4×D17C2411yescharacteristic
109C2×Dic34—28no—
110C2×Dic34—22no—
111C2×Dic34C22×C414yes—
112C2×#3624—24no—
113C2×#3624—44no—
114C4×#595—232no—
115C4×#595—28no—
116C4×#595—24no—
117C4×#595C2×D418yescomplemented
118#63243—28no—
119#63243—44no—
120C42×C17C22⋊C412yes—
121C42×C17C22×C412yes—
122C22⋊Dic17—216no—
123C4⋊Dic17—28no—
124C4×Dic17C22⋊C414yes—
125C4×Dic17C22⋊C412yes—
126C4×Dic17C22×C412yes—
127C4×Dic17C2×D414yes—
128C2×#1962—171nomaximal, Sylow
129C23×C17—24no—
130C23×C17—44no—
131C23×C17—48no—
132C23×C17C2×C22⋊C411yescharacteristic
133C22×D17—24no—
134C22×D17C2×C22⋊C411yescharacteristic
135C22×D17#12114yes—
136C22×D17C22×D411yescharacteristic
137C2×#595—216no—
138C2×#595—232no—
139C2×#595—28no—
140D4×C17—28no—
141D4×C17—44no—
142D4×C17—416no—
143C2×C4×C17#10418yescomplemented
144C2×C4×C17C2×C22⋊C411yescharacteristic
145C2×C4×C17C2×C22⋊C414yes—
146C2×C4×C17C4×D414yes—
147C2×C4×C17C23×C411yescharacteristic
148C22⋊D17—48no—
149C22⋊D17—48no—
150C2×Dic17—24no—
151C2×Dic17—24no—
152C2×Dic17—44no—
153C2×Dic17—44no—
154C2×Dic17—44no—
155C2×Dic17—48no—
156C2×Dic17C2×C22⋊C414yes—
157C2×Dic17C2×C22⋊C411yescharacteristic
158C2×Dic17#12412yes—
159C2×Dic17#12712yes—
160C2×Dic17C22×D411yescharacteristic
161C4×D17—28no—
162C4×D17—28no—
163C4×D17C4×D414yes—
164C4×D17#12114yes—
165C4×D17#12412yes—
166C4×D17#12712yes—
167C4×D17C22×D412yes—
168C4×D17C2×#4112yes—
169Dic34—28no—
170Dic34—44no—
171#3624—44no—
172C2×#532—171no—
173C2×#423—171no—
174C22×#104—174no—
175C2×C43—171no—
176#1962—178no—
177C22×C17—48no—
178C22×C17—44no—
179C22×C17—88no—
180C22×C17#39012yes—
181C22×C17C2×#10414yes—
182C22×C17C22×C22⋊C411yescharacteristic
183C2×D17—22no—
184C2×D17—22no—
185C2×D17—28no—
186C2×D17#39012yes—
187C2×D17C2×#12112yes—
188#595—216no—
189C4×C17#39012yes—
190C4×C17C2×#10418yescomplemented
191C4×C17C2×C4×D412yes—
192Dic17—24no—
193Dic17—44no—
194Dic17#39012yes—
195Dic17C2×#12411yescharacteristic
196Dic17C2×#12711yescharacteristic
197C22×#41—172no—
198C22×M16—172no—
199#532—174no—
200#532—174no—
201#532—342no—
202#532—342no—
203C2×C4⋊Q8—171no—
204C2×#127#59511yescharacteristic, complemented
205C2×#124—172no—
206C2×#121—342no—
207C2×C4×D4—342no—
208C22×C42—171no—
209C22×C42—172no—
210C22×C42—342no—
211#423—174no—
212#423—342no—
213C2×C4⋊C8—342no—
214C2×#104—1716no—
215C2×#104—3416no—
216C43—174no—
217C43—342no—
218C2×C17—84no—
219C2×C17#196214yescomplemented
220C2×C17C2×#39011yescharacteristic
221C2×C17C22×#10412yes—
222D17—22no—
223D17—22no—
224C2×#41—174no—
225C2×#41—174no—
226C2×#41—342no—
227C2×#41—342no—
228C2×#41—348no—
229C2×#41—348no—
230C22×Q8—172no—
231C22×D4—22no—
232C22×D4—342no—
233C22×D4C2×#59512yes—
234C23×C4—171no—
235C23×C4—172no—
236C23×C4—342no—
237C23×C4—342no—
238C2×M16—174no—
239C2×M16—342no—
240C2×M16—348no—
241C22×C8—342no—
242C4⋊Q8—174no—
243C4⋊Q8—342no—
244#127—22no—
245#127C2×#59514yescomplemented
246#124—178no—
247#124—344no—
248#121—348no—
249#121—348no—
250C4×D4—348no—
251C4×D4—348no—
252C2×C4⋊C4—342no—
253C2×C22⋊C4—344no—
254C2×C42—172no—
255C2×C42—171no—
256C2×C42—172no—
257C2×C42—172no—
258C2×C42—172no—
259C2×C42—172no—
260C2×C42—178no—
261C2×C42—174no—
262C2×C42—348no—
263C2×C42—342no—
264C2×C42—344no—
265C2×C42—3416no—
266C2×C42C2×#59511yescharacteristic
267C4⋊C8—348no—
268#104—3432no—
269C17C2×#196211yescharacteristic, complemented, Sylow
270C24—22no—
271C24—171no—
272#41—348no—
273#41—348no—
274#41—3416no—
275#41—688no—
276#41—684no—
277#41—684no—
278C2×Q8—174no—
279C2×Q8—342no—
280C2×Q8—348no—
281C2×D4—28no—
282C2×D4—28no—
283C2×D4—22no—
284C2×D4—48no—
285C2×D4—344no—
286C2×D4—344no—
287C2×D4—688no—
288C2×D4C22×#59514yes—
289C22×C4—171no—
290C22×C4—174no—
291C22×C4—174no—
292C22×C4—171no—
293C22×C4—171no—
294C22×C4—171no—
295C22×C4—171no—
296C22×C4—172no—
297C22×C4—174no—
298C22×C4—174no—
299C22×C4—344no—
300C22×C4—344no—
301C22×C4—344no—
302C22×C4—348no—
303C22×C4—3416no—
304C22×C4—348no—
305C22×C4—342no—
306C22×C4—684no—
307C22×C4—684no—
308C22×C4C22⋊#59512yes—
309C22×C4C22×#59511yescharacteristic
310M16—348no—
311M16—684no—
312C2×C8—344no—
313C2×C8—684no—
314C4⋊C4—348no—
315C22⋊C4—3416no—
316C42—174no—
317C42—174no—
318C42—172no—
319C42—172no—
320C42—178no—
321C42—348no—
322C42—344no—
323C42—3432no—
324C42C22⋊#59512yes—
325C42C22×#59512yes—
326C23—24no—
327C23—44no—
328C23—48no—
329C23—174no—
330C23—171no—
331C23—171no—
332C23—344no—
333C23C2×C22⋊#59511yescharacteristic
334Q8—348no—
335Q8—684no—
336D4—28no—
337D4—44no—
338D4—416no—
339D4—688no—
340D4—688no—
341C2×C4—172no—
342C2×C4—172no—
343C2×C4—171no—
344C2×C4—171no—
345C2×C4—174no—
346C2×C4—172no—
347C2×C4—172no—
348C2×C4—172no—
349C2×C4—172no—
350C2×C4—174no—
351C2×C4—174no—
352C2×C4—348no—
353C2×C4—3416no—
354C2×C4—3432no—
355C2×C4—344no—
356C2×C4—348no—
357C2×C4—348no—
358C2×C4—344no—
359C2×C4—684no—
360C2×C4—684no—
361C2×C4—688no—
362C2×C4—684no—
363C2×C4#1058754818yescomplemented
364C2×C4D4×#59514yes—
365C2×C4C2×C22⋊#59511yescharacteristic
366C2×C4C2×C22⋊#59514yes—
367C2×C4C23×#59511yescharacteristic
368C8—684no—
369C22—44no—
370C22—48no—
371C22—88no—
372C22—172no—
373C22—172no—
374C22—348no—
375C22—342no—
376C22—342no—
377C22#1176376112yes—
378C22C2×#1058754814yes—
379C22C22×C22⋊#59511yescharacteristic
380C4—171no—
381C4—171no—
382C4—172no—
383C4—3416no—
384C4—344no—
385C4—684no—
386C4#1176376112yes—
387C4C2×#1058754818yescomplemented
388C4C2×D4×#59512yes—
389C2—84no—
390C2—342no—
391C2—342no—
392C2#1454491814yesdirect product factor
393C2C2×#1176376111yescharacteristic
394C2C22×#1058754812yes—
subgroupG/H
centerC23C2×C22⋊#595
commutatorC2×C4×C17C23×C4
FrattiniC2×C4C23×#595
FittingC2×C17×#127C4
socleC23×C17C2×C22⋊C4
prime radicalC2×#11763357C2
cosocleC2×C4×D17C24
hypercenterC2×#127#595
hypocenterC17C2×#1962
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#11763813C2semidirect
2. C22×#10587548C2semidirect
3. C2×C42×#595C2semidirect
4. #14544918C2direct (N × H)
10. #11763813C22semidirect
13. C2×#10587548C22semidirect
15. C42×#595C22semidirect
19. #11763357C4semidirect
21. C2×#10587555C4semidirect
22. C2×#10587622C4semidirect
26. C2×C17×#127C4semidirect
46. C2×C4×#595D4semidirect
52. C17×#127C2×C4semidirect
58. #10587622C2×C4semidirect
69. #10587555C2×C4semidirect
117. C4×#595C2×D4semidirect
143. C2×C4×C17#104semidirect
190. C4×C17C2×#104semidirect
204. C2×#127#595semidirect
219. C2×C17#1962semidirect
245. #127C2×#595semidirect
269. C17C2×#1962semidirect
363. C2×C4#10587548semidirect
387. C4C2×#10587548semidirect
392. C2#14544918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117638132
C22×#105875482
C2×C42×#5952
#145449182
C2×#117633572
C2×#196217