Finite Group Databasebeta

← C2×#14544599 #17968600

Subgroups — C2×#14544599 #17968600

Order 4352.

1318 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587533C211yesmaximal, characteristic
2C22×#10587532C211yesmaximal, characteristic
3C2×C4⋊C4×#595C212yesmaximal
4#14544599C218yesmaximal, direct product factor
5C2×#11763682C212yesmaximal
6C2×#107×D17C211yesmaximal, characteristic
7C22×#63242C2211yescharacteristic
8C22×C4⋊#595C2212yes—
9C22×C4×#595—22no—
10C22×C4×#595C2211yescharacteristic
11C2×#10587533C418yescomplemented
12C2×#10587533C2214yes—
13C2×#10587532C418yescomplemented
14C2×#10587532C2214yes—
15C4⋊C4×#595—24no—
16C4⋊C4×#595C2218yes—
17C2×(C2×#595)⋊C4—22no—
18#11763682C2218yes—
19C22×C8×D17C2211yescharacteristic
20C2×C4⋊C4×D17C2212yes—
21C2×#10587489C411yescharacteristic, complemented
22C2×#10587478C412yescomplemented
23#107×D17C414yescomplemented
24#107×D17C2214yes—
25C2×C17×#107C411yescharacteristic, complemented
26C23×#595—22no—
27C23×#595D412yes—
28C22×C4×D17—22no—
29C22×C4×D17C2311yescharacteristic
30C22×#3624—21no—
31C2×C4⋊#595—22no—
32C2×C4⋊#595—24no—
33C2×C4⋊#595C2×C418yes—
34C2×C4⋊#595C2314yes—
35C2×C4×#595—28no—
36C2×C4×#595—48no—
37C2×C4×#595C2×C414yes—
38C2×C4×#595D412yes—
39C2×C4×#595Q814yes—
40C2×C4×#595C2312yes—
41C2×#63242—21no—
42C2×#63242—22no—
43C2×#63242C2×C414yes—
44C2×#63242C2312yes—
45C22×C8×C17C2×C411yescharacteristic
46C2×C4⋊C4×C17C2×C412yes—
47C2×C4⋊Dic17C2×C412yes—
48C2×#63225—22no—
49C22×#3622C2×C411yescharacteristic
50C2×C8×D17C2×C414yes—
51C2×C8×D17C2×C414yes—
52C2×C8×D17C2×C412yes—
53C2×C8×D17C2312yes—
54C4⋊C4×D17—22no—
55C4⋊C4×D17—22no—
56C4⋊C4×D17C2×C414yes—
57C4⋊C4×D17C2314yes—
58(C2×#595)⋊C4—28no—
59#10587533C2×C4116yescomplemented
60#10587532C2×C4116yescomplemented
61C17×#107C2×C414yescomplemented
62#10587489C2×C414yescomplemented
63#10587478C2×C418yescomplemented
64C23×D17C2×D411yescharacteristic
65C22×#595—24no—
66C22×#595—24no—
67C22×#595—28no—
68C22×#595—24no—
69C22×#595—44no—
70C22×#595—44no—
71C22×#595C4⋊C418yes—
72C22×#595C2×D414yes—
73C22×C4×C17—22no—
74C22×C4×C17C22×C411yescharacteristic
75C22×Dic17—22no—
76C22×Dic17#4111yescharacteristic
77C2×C4×D17—24no—
78C2×C4×D17—24no—
79C2×C4×D17—44no—
80C2×C4×D17—44no—
81C2×C4×D17C22×C411yescharacteristic
82C2×C4×D17C22×C412yes—
83C2×C4×D17C22×C412yes—
84C2×C4×D17C2×D411yescharacteristic
85C2×C4×D17C2×Q812yes—
86C2×C4×D17#4111yescharacteristic
87C2×C4×D17#4112yes—
88C2×C4×D17C2411yescharacteristic
89C2×#3624—24no—
90C2×#3624—22no—
91C4⋊#595—28no—
92C4⋊#595—24no—
93C4⋊#595C22×C418yes—
94C4×#595—416no—
95C4×#595C4⋊C418yes—
96C4×#595C22×C414yes—
97C4×#595C2×Q814yes—
98#63242—24no—
99#63242—22no—
100#63242C22×C414yes—
101C2×C8×C17C4214yescomplemented
102C2×C8×C17C22×C412yes—
103C4⋊C4×C17—22no—
104C4⋊C4×C17C22×C414yes—
105C4⋊Dic17—22no—
106C4⋊Dic17C22×C414yes—
107#63225—24no—
108#63225—24no—
109C2×#3622C4214yescomplemented
110C2×#3622C22×C412yes—
111C8×D17C4218yescomplemented
112C8×D17C22×C414yes—
113C8×D17C22×C414yes—
114C2×#1776—171nomaximal, Sylow
115C23×C17C4×D411yescharacteristic
116C22×D17C2×C4⋊C412yes—
117C22×D17C4×D412yes—
118C22×D17C4×D411yescharacteristic
119C22×D17AGL(1,ℤ/8)14yes—
120C22×D17#13714yes—
121C22×D17C22×D411yescharacteristic
122C2×#595—24no—
123C2×#595—24no—
124C2×#595—216no—
125C2×#595—28no—
126C2×#595—44no—
127C2×#595—44no—
128C2×#595—416no—
129C2×#595C2×C4⋊C418yes—
130C2×C4×C17—24no—
131C2×C4×C17—44no—
132C2×C4×C17C2×C4212yes—
133C2×C4×C17C4×D411yescharacteristic
134C2×C4×C17C4×Q812yes—
135C2×C4×C17C23×C411yescharacteristic
136C2×Dic17—24no—
137C2×Dic17—44no—
138C2×Dic17#11712yes—
139C2×Dic17C4×D411yescharacteristic
140C2×Dic17C4×Q812yes—
141C2×Dic17C2×#4111yescharacteristic
142C4×D17—44no—
143C4×D17—44no—
144C4×D17—48no—
145C4×D17C2×C4212yes—
146C4×D17C2×C4⋊C412yes—
147C4×D17#11712yes—
148C4×D17C4×D412yes—
149C4×D17C4×Q812yes—
150C4×D17C4×Q812yes—
151C4×D17C23×C411yescharacteristic
152C4×D17C23×C411yescharacteristic
153C4×D17C22×Q811yescharacteristic
154C4×D17C2×#4111yescharacteristic
155#3624—24no—
156C8×C17C2×C4214yescomplemented
157#3622C2×C4214yescomplemented
158C22×#107—171no—
159C22×#106—171no—
160C22×#97—171no—
161C2×C4×C4⋊C4—172no—
162#1776—178no—
163C2×#340—172no—
164C22×C17C4×C4⋊C412yes—
165C22×C17#44112yes—
166C22×C17#44212yes—
167C22×C17C2×C4×D411yescharacteristic
168C2×D17C4×C4⋊C412yes—
169C2×D17#42818yes—
170C2×D17#44018yes—
171C2×D17#44112yes—
172C2×D17#44212yes—
173C2×D17C22×C4⋊C411yescharacteristic
174C2×D17C2×C4×D411yescharacteristic
175C2×D17C2×AGL(1,ℤ/8)12yes—
176C2×D17C2×#13712yes—
177#595—28no—
178#595—48no—
179C4×C17—44no—
180C4×C17C4×C4⋊C412yes—
181C4×C17C22×C4211yescharacteristic
182C4×C17C2×C4×Q811yescharacteristic
183Dic17—44no—
184Dic17C4×C4⋊C412yes—
185Dic17C2×#11711yescharacteristic
186Dic17C2×C4×Q811yescharacteristic
187C23×C8—171no—
188C23×C8—171no—
189C22×C4⋊C4—172no—
190C22×C4⋊C4—172no—
191C22×C42—171no—
192C22×C42—342no—
193C2×#107—171no—
194C2×#107—172no—
195C2×#107—174no—
196C2×#107—174no—
197C2×#107#59511yescharacteristic, complemented
198C2×#106—178no—
199C2×#106—174no—
200C2×#97—178no—
201C2×#97—174no—
202C4×C4⋊C4—178no—
203C4×C4⋊C4—344no—
204C2×#95—342no—
205#340—178no—
206C2×C17#177614yescomplemented
207C2×C17C2×C4×C4⋊C411yescharacteristic
208C2×C17C2×#44111yescharacteristic
209C2×C17C2×#44211yescharacteristic
210D17#177614yescomplemented
211D17C2×#42812yes—
212D17C2×#44012yes—
213C23×C4—171no—
214C23×C4—172no—
215C23×C4—342no—
216C23×C4—342no—
217C22×C8—171no—
218C22×C8—174no—
219C22×C8—174no—
220C22×C8—172no—
221C22×C8—172no—
222C22×C8—174no—
223C22×C8—172no—
224C22×C8—341no—
225C22×C8—342no—
226C22×C8—341no—
227C22×C8C2×#59511yescharacteristic
228C2×C4⋊C4—178no—
229C2×C4⋊C4—174no—
230C2×C4⋊C4—172no—
231C2×C4⋊C4—174no—
232C2×C4⋊C4—174no—
233C2×C4⋊C4—342no—
234C2×C4⋊C4—342no—
235C2×C4⋊C4—342no—
236C2×C4⋊C4—344no—
237C2×C4⋊C4—342no—
238C2×C4⋊C4C2×#59512yes—
239C2×C42—174no—
240C2×C42—172no—
241C2×C42—174no—
242C2×C42—172no—
243C2×C42—348no—
244C2×C42—688no—
245#107—174no—
246#107—178no—
247#107C2×#59514yescomplemented
248#106—1716no—
249#97—1716no—
250#95—348no—
251C17C2×#177611yescharacteristic, complemented, Sylow
252C24—171no—
253C22×C4—22no—
254C22×C4—171no—
255C22×C4—172no—
256C22×C4—172no—
257C22×C4—171no—
258C22×C4—171no—
259C22×C4—172no—
260C22×C4—172no—
261C22×C4—171no—
262C22×C4—171no—
263C22×C4—178no—
264C22×C4—174no—
265C22×C4—344no—
266C22×C4—344no—
267C22×C4—344no—
268C22×C4—344no—
269C22×C4—344no—
270C22×C4—348no—
271C22×C4—342no—
272C22×C4—684no—
273C22×C4—684no—
274C22×C4—684no—
275C22×C4—684no—
276C22×C4C22×#59511yescharacteristic
277C2×C8—174no—
278C2×C8—172no—
279C2×C8—174no—
280C2×C8—174no—
281C2×C8—178no—
282C2×C8—174no—
283C2×C8—344no—
284C2×C8—342no—
285C2×C8—344no—
286C2×C8—342no—
287C2×C8C4×#59514yescomplemented
288C2×C8C22×#59512yes—
289C4⋊C4—22no—
290C4⋊C4—178no—
291C4⋊C4—174no—
292C4⋊C4—344no—
293C4⋊C4—344no—
294C4⋊C4—348no—
295C4⋊C4—344no—
296C4⋊C4—342no—
297C4⋊C4C22×#59514yes—
298C42—178no—
299C42—174no—
300C42—174no—
301C42—6816no—
302C23—172no—
303C23—172no—
304C23—174no—
305C23—174no—
306C23—171no—
307C23—171no—
308C23D4×#59511yescharacteristic
309C2×C4—24no—
310C2×C4—44no—
311C2×C4—172no—
312C2×C4—172no—
313C2×C4—171no—
314C2×C4—171no—
315C2×C4—172no—
316C2×C4—172no—
317C2×C4—172no—
318C2×C4—172no—
319C2×C4—171no—
320C2×C4—171no—
321C2×C4—172no—
322C2×C4—171no—
323C2×C4—171no—
324C2×C4—172no—
325C2×C4—178no—
326C2×C4—344no—
327C2×C4—344no—
328C2×C4—3416no—
329C2×C4—348no—
330C2×C4—344no—
331C2×C4—684no—
332C2×C4—684no—
333C2×C4—688no—
334C2×C4—684no—
335C2×C4—684no—
336C2×C4—6816no—
337C2×C4—684no—
338C2×C4C2×C4×#59512yes—
339C2×C4D4×#59511yescharacteristic
340C2×C4Q8×#59512yes—
341C2×C4C23×#59511yescharacteristic
342C8—174no—
343C8—344no—
344C8C2×C4×#59514yescomplemented
345C22—171no—
346C22—171no—
347C22—172no—
348C22—172no—
349C22—172no—
350C22—172no—
351C22—172no—
352C22—178no—
353C22—178no—
354C22C4⋊C4×#59512yes—
355C22#1176384912yes—
356C22#1176385012yes—
357C22C2×D4×#59511yescharacteristic
358C4—44no—
359C4—171no—
360C4—171no—
361C4—172no—
362C4—348no—
363C4—688no—
364C4—684no—
365C4C4⋊C4×#59512yes—
366C4C22×C4×#59511yescharacteristic
367C4C2×Q8×#59511yescharacteristic
368C2—172no—
369C2—172no—
370C2—174no—
371C2#1454459914yesdirect product factor
372C2C2×C4⋊C4×#59511yescharacteristic
373C2C2×#1176384911yescharacteristic
374C2C2×#1176385011yescharacteristic
subgroupG/H
centerC23D4×#595
commutatorC4×C17C22×C42
FrattiniC2×C4C23×#595
FittingC2×C17×#107C4
socleC23×C17C4×D4
prime radicalC23×D17C2×D4
cosocleC2×C4×D17C24
hypercenterC2×#107#595
hypocenterC17C2×#1776
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
4. #14544599C2direct (N × H)
11. C2×#10587533C4semidirect
13. C2×#10587532C4semidirect
21. C2×#10587489C4semidirect
22. C2×#10587478C4semidirect
23. #107×D17C4semidirect
25. C2×C17×#107C4semidirect
59. #10587533C2×C4semidirect
60. #10587532C2×C4semidirect
61. C17×#107C2×C4semidirect
62. #10587489C2×C4semidirect
63. #10587478C2×C4semidirect
101. C2×C8×C17C42semidirect
109. C2×#3622C42semidirect
111. C8×D17C42semidirect
156. C8×C17C2×C42semidirect
157. #3622C2×C42semidirect
197. C2×#107#595semidirect
206. C2×C17#1776semidirect
210. D17#1776semidirect
247. #107C2×#595semidirect
251. C17C2×#1776semidirect
287. C2×C8C4×#595semidirect
344. C8C2×C4×#595semidirect
371. C2#14544599direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875332
C22×#105875322
C2×C4⋊C4×#5952
#145445992
C2×#117636822
C2×#107×D172
C2×#177617