Finite Group Databasebeta

← C2×#14545330 #17979214

Subgroups — C2×#14545330 #17979214

Order 4352.

2198 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545330C2116yesmaximal, direct product factor
2C2×#11763760C214yesmaximal
3C2×#11763758C214yesmaximal
4C2×#11763758C214yesmaximal
5C2×#11763753C212yesmaximal
6C2×#125×D17C211yesmaximal, characteristic
7C22×C4⋊#595C2212yes—
8C22×C4⋊#595C2212yes—
9C22×C4⋊#595C2214yes—
10C22×C4×#595C2214yes—
11#11763760C22132yes—
12#11763758C22132yes—
13#11763758C22132yes—
14#11763753C22116yes—
15C2×(C2×#595)⋊C4C2214yes—
16C2×(C2×#595)⋊C4C2214yes—
17C2×(C2×#595)⋊C4C2214yes—
18C2×(C2×#595)⋊C4C2214yes—
19C2×#10587556C411yescharacteristic, complemented
20C2×#10587576C412yescomplemented
21C2×#10587575C414yescomplemented
22#125×D17C418yescomplemented
23#125×D17C2218yes—
24C2×C4⋊C4×D17C2212yes—
25C2×C4⋊C4×D17C2214yes—
26C2×C42×D17C2211yescharacteristic
27C2×C17×#125C411yescharacteristic, complemented
28C23×#595C2314yes—
29C23×#595C2314yes—
30C22×C4×D17C2311yescharacteristic
31C22×C4×D17C2312yes—
32C22×C4×D17C2314yes—
33C2×C4⋊#595—48no—
34C2×C4⋊#595—44no—
35C2×C4⋊#595—44no—
36C2×C4⋊#595C2318yes—
37C2×C4⋊#595C2318yes—
38C2×C4⋊#595C23116yes—
39C2×C4×#595—48no—
40C2×C4×#595C23116yes—
41C17×#125C2×C418yescomplemented
42C2×C4⋊C4×C17C2×C414yes—
43C2×C4⋊C4×C17C2×C412yes—
44C2×C42×C17C2×C411yescharacteristic
45C2×C4⋊Dic17C2×C414yes—
46C2×C4⋊Dic17C2×C412yes—
47C2×#63225C2×C414yes—
48C2×#63225C2×C414yes—
49C2×#63225C2×C414yes—
50C2×C4×Dic17C2×C412yes—
51C2×C4×Dic17C2×C411yescharacteristic
52C4⋊C4×D17C2×C4116yes—
53C4⋊C4×D17C2×C418yes—
54C4⋊C4×D17C2318yes—
55C4⋊C4×D17C23116yes—
56#10587576C2×C4116yescomplemented
57#10587575C2×C4132yescomplemented
58C42×D17C2×C414yes—
59C42×D17C2314yes—
60#10587556C2×C418yescomplemented
61(C2×#595)⋊C4C23116yes—
62(C2×#595)⋊C4C23116yes—
63(C2×#595)⋊C4C23116yes—
64(C2×#595)⋊C4C23116yes—
65C23×D17C2411yescharacteristic
66C22×#595—28no—
67C22×#595—28no—
68C22×#595—28no—
69C22×#595—28no—
70C22×#595—28no—
71C22×#595—28no—
72C22×#595C2418yes—
73C22×#595C2418yes—
74C22×C4×C17C22×C412yes—
75C22×C4×C17C22×C411yescharacteristic
76C22×C4×C17C22×C414yes—
77C22×Dic17C22×C411yescharacteristic
78C22×Dic17C22×C412yes—
79C22×Dic17C22×C414yes—
80C2×C4×D17—28no—
81C2×C4×D17—24no—
82C2×C4×D17—22no—
83C2×C4×D17—22no—
84C2×C4×D17—24no—
85C2×C4×D17—28no—
86C2×C4×D17C22×C412yes—
87C2×C4×D17C22×C414yes—
88C2×C4×D17C22×C418yes—
89C2×C4×D17C2418yes—
90C2×C4×D17C2414yes—
91C2×C4×D17C2412yes—
92C4⋊#595—416no—
93C4⋊#595—48no—
94C4⋊#595—48no—
95C4×#595—416no—
96C4⋊C4×C17C22×C4116yes—
97C4⋊C4×C17C22×C418yes—
98C42×C17C22×C414yes—
99C4⋊Dic17C22×C418yes—
100C4⋊Dic17C22×C4116yes—
101#63225C22×C4116yes—
102#63225C22×C4116yes—
103#63225C22×C4116yes—
104C4×Dic17C22×C418yes—
105C4×Dic17C22×C414yes—
106C2×#2382—171nomaximal, Sylow
107C23×C17C23×C411yescharacteristic
108C22×D17C23×C411yescharacteristic
109C22×D17H(5,𝔽2)14yes—
110C22×D172−1+412yes—
111C22×D172−1+412yes—
112C22×D172−1+414yes—
113C22×D17C2511yescharacteristic
114C2×#595—28no—
115C2×#595—28no—
116C2×#595—28no—
117C2×#595—28no—
118C2×#595—28no—
119C2×#595—28no—
120C2×#595—416no—
121C2×#595—416no—
122C2×C4×C17—22no—
123C2×C4×C17—28no—
124C2×C4×C17—24no—
125C2×C4×C17C23×C414yes—
126C2×C4×C17C23×C412yes—
127C2×C4×C17C23×C418yes—
128C2×Dic17—22no—
129C2×Dic17—28no—
130C2×Dic17—24no—
131C2×Dic17C23×C412yes—
132C2×Dic17C23×C414yes—
133C2×Dic17C23×C418yes—
134C4×D17—24no—
135C4×D17—216no—
136C4×D17—28no—
137C4×D17—28no—
138C4×D17—24no—
139C4×D17—22no—
140C4×D17—22no—
141C4×D17—28no—
142C4×D17—24no—
143C22×#125—171no—
144#2382—1716no—
145C2×#389—174no—
146C2×#387—174no—
147C2×#387—174no—
148C2×#382—172no—
149C22×C17#51912yes—
150C22×C17#52014yes—
151C22×C17C24×C411yescharacteristic
152C2×D17#51912yes—
153C2×D17#52014yes—
154C2×D17#56214yes—
155C2×D17#56318yes—
156C2×D17#56414yes—
157C2×D17C2×H(5,𝔽2)12yes—
158C2×D17C2×2−1+411yescharacteristic
159C2×D17C2×2−1+411yescharacteristic
160C2×D17C2×2−1+412yes—
161#595—48no—
162#595—48no—
163C4×C17—22no—
164C4×C17—28no—
165C4×C17—24no—
166Dic17—22no—
167Dic17—28no—
168Dic17—24no—
169C2×#125—178no—
170C2×#125—178no—
171C2×#125—174no—
172C2×#125—172no—
173C2×#125—171no—
174C2×#125#59511yescharacteristic, complemented
175C22×C4⋊C4—172no—
176C22×C4⋊C4—174no—
177C22×C4⋊C4—172no—
178C22×C4⋊C4—172no—
179C22×C4⋊C4—174no—
180C22×C42—171no—
181C22×C42—174no—
182#389—1732no—
183#387—1732no—
184#387—1732no—
185#382—1716no—
186C2×#95—174no—
187C2×#95—174no—
188C2×#95—174no—
189C2×#95—174no—
190C2×C17#238214yescomplemented
191C2×C17C2×#51911yescharacteristic
192C2×C17C2×#52012yes—
193D17#238214yescomplemented
194D17C2×#56211yescharacteristic
195D17C2×#56312yes—
196D17C2×#56411yescharacteristic
197C23×C4—172no—
198C23×C4—174no—
199C23×C4—171no—
200C23×C4—174no—
201C23×C4—174no—
202#125—1732no—
203#125—1716no—
204#125—178no—
205#125C2×#59518yescomplemented
206C2×C4⋊C4—174no—
207C2×C4⋊C4—174no—
208C2×C4⋊C4—174no—
209C2×C4⋊C4—174no—
210C2×C4⋊C4—172no—
211C2×C4⋊C4—178no—
212C2×C4⋊C4—1716no—
213C2×C4⋊C4—178no—
214C2×C4⋊C4—1716no—
215C2×C4⋊C4—178no—
216C2×C4⋊C4—178no—
217C2×C4⋊C4—1716no—
218C2×C4⋊C4—688no—
219C2×C4⋊C4—684no—
220C2×C4⋊C4—684no—
221C2×C4⋊C4C2×#59512yes—
222C2×C4⋊C4C2×#59514yes—
223C2×C42—172no—
224C2×C42—171no—
225C2×C42—174no—
226C2×C42—174no—
227C2×C42—1716no—
228C2×C42—688no—
229C2×C42C2×#59511yescharacteristic
230#95—1716no—
231#95—1716no—
232#95—1716no—
233#95—1716no—
234C17C2×#238211yescharacteristic, complemented, Sylow
235C24—171no—
236C22×C4—171no—
237C22×C4—172no—
238C22×C4—174no—
239C22×C4—174no—
240C22×C4—172no—
241C22×C4—178no—
242C22×C4—172no—
243C22×C4—174no—
244C22×C4—178no—
245C22×C4—178no—
246C22×C4—178no—
247C22×C4—348no—
248C22×C4—344no—
249C22×C4—342no—
250C22×C4—342no—
251C22×C4—348no—
252C22×C4—344no—
253C22×C4—348no—
254C22×C4—348no—
255C22×C4—348no—
256C22×C4—348no—
257C22×C4—348no—
258C22×C4—348no—
259C22×C4C22×#59511yescharacteristic
260C22×C4C22×#59512yes—
261C22×C4C22×#59514yes—
262C4⋊C4—1716no—
263C4⋊C4—1716no—
264C4⋊C4—1716no—
265C4⋊C4—1716no—
266C4⋊C4—178no—
267C4⋊C4—6816no—
268C4⋊C4—688no—
269C4⋊C4—688no—
270C4⋊C4C22×#595116yes—
271C4⋊C4C22×#59518yes—
272C42—178no—
273C42—174no—
274C42—6816no—
275C42C22×#59514yes—
276C23—172no—
277C23—172no—
278C23—174no—
279C23—174no—
280C23—171no—
281C23—171no—
282C23C23×#59511yescharacteristic
283C2×C4—22no—
284C2×C4—28no—
285C2×C4—24no—
286C2×C4—172no—
287C2×C4—174no—
288C2×C4—178no—
289C2×C4—348no—
290C2×C4—344no—
291C2×C4—342no—
292C2×C4—342no—
293C2×C4—344no—
294C2×C4—348no—
295C2×C4—344no—
296C2×C4—348no—
297C2×C4—3416no—
298C2×C4—342no—
299C2×C4—344no—
300C2×C4—348no—
301C2×C4—348no—
302C2×C4—348no—
303C2×C4—348no—
304C2×C4—348no—
305C2×C4—348no—
306C2×C4—348no—
307C2×C4—6816no—
308C2×C4—6816no—
309C2×C4C23×#59512yes—
310C2×C4C23×#59514yes—
311C2×C4C23×#59518yes—
312C22—171no—
313C22—171no—
314C22—172no—
315C22—172no—
316C22—172no—
317C22—174no—
318C22—174no—
319C22—178no—
320C22—174no—
321C22#1176387712yes—
322C22#1176387814yes—
323C22C24×#59511yescharacteristic
324C4—22no—
325C4—28no—
326C4—24no—
327C4—342no—
328C4—344no—
329C4—348no—
330C4—688no—
331C4—688no—
332C2—171no—
333C2—172no—
334C2—174no—
335C2—171no—
336C2#1454533014yesdirect product factor
337C2C2×#1176387711yescharacteristic
338C2C2×#1176387812yes—
subgroupG/H
centerC23C23×#595
commutatorC22×C17C24×C4
FrattiniC22C24×#595
FittingC2×C17×#125C4
socleC23×C17C23×C4
prime radicalC23×D17C24
cosocleC22×D17C25
hypercenterC2×#125#595
hypocenterC17C2×#2382
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #14545330C2direct (N × H)
19. C2×#10587556C4semidirect
20. C2×#10587576C4semidirect
21. C2×#10587575C4semidirect
22. #125×D17C4semidirect
27. C2×C17×#125C4semidirect
41. C17×#125C2×C4semidirect
56. #10587576C2×C4semidirect
57. #10587575C2×C4semidirect
60. #10587556C2×C4semidirect
174. C2×#125#595semidirect
190. C2×C17#2382semidirect
193. D17#2382semidirect
205. #125C2×#595semidirect
234. C17C2×#2382semidirect
336. C2#14545330direct (N × H)

Maximal subgroups

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

subgroupindex
#145453302
C2×#117637602
C2×#117637582
C2×#117637532
C2×#125×D172
C2×#238217