Finite Group Databasebeta

← C2×D17⋊#99 #14545377

Subgroups — C2×D17⋊#99 #14545377

Order 2176.

1112 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊#595C212yesmaximal, complemented
2C2×#10587539C212yesmaximal, complemented
3D17⋊#99C218yesmaximal, direct product factor
4C2×#10587551C212yesmaximal, complemented
5C22×D4×D17C211yesmaximal, characteristic
6C24×D17C411yescharacteristic, complemented
7C24×D17C2211yescharacteristic
8C23×#595—22no—
9C22×D4×C17C411yescharacteristic, complemented
10C22×C22⋊D17C411yescharacteristic, complemented
11C22×C22⋊D17C2211yescharacteristic
12C2×D4×D17—22no—
13C2×D4×D17—22no—
14C2×D4×D17—24no—
15C2×D4×D17C414yescomplemented
16C2×D4×D17C2214yes—
17C22×D68C2211yescharacteristic
18C22×C4×D17C411yescharacteristic, complemented
19C2×C22⋊#595—24no—
20C2×C22⋊#595—22no—
21C2×C22⋊#595C2214yescomplemented
22C2×C22⋊#595C2218yescomplemented
23#10587551C2218yescomplemented
24#10587539C2218yescomplemented
25C24×C17C2×C411yescharacteristic
26C24×C17C2×C411yescharacteristic, complemented
27C23×D17—22no—
28C23×D17—21no—
29C23×D17—21no—
30C23×D17—44no—
31C23×D17—44no—
32C23×D17C2×C411yescharacteristic
33C23×D17C2×C412yes—
34C23×D17C2×C414yescomplemented
35C23×D17C2×C411yescharacteristic, complemented
36C23×D17D412yes—
37C23×D17D414yes—
38C23×D17D412yes—
39C23×D17C2311yescharacteristic
40C23×D17C2312yes—
41C22×#595—24no—
42C22×#595—28no—
43C22×#595—48no—
44C2×D4×C17—22no—
45C2×D4×C17—22no—
46C2×D4×C17C2×C414yescomplemented
47C22×C4×C17C2×C411yescharacteristic, complemented
48C2×C22⋊D17—22no—
49C2×C22⋊D17—22no—
50C2×C22⋊D17—22no—
51C2×C22⋊D17—22no—
52C2×C22⋊D17C2×C412yescomplemented
53C2×C22⋊D17C2×C414yescomplemented
54C2×C22⋊D17C2312yes—
55C22×Dic17C2×C411yescharacteristic, complemented
56D4×D17—28no—
57D4×D17—28no—
58D4×D17—28no—
59D4×D17—28no—
60C2×D68—22no—
61C2×D68—22no—
62C2×D68C2×C412yescomplemented
63C2×D68C2312yes—
64C2×C4×D17—22no—
65C2×C4×D17—21no—
66C2×C4×D17—21no—
67C2×C4×D17C2×C414yescomplemented
68C22⋊#595—24no—
69C22⋊#595—28no—
70C22⋊#595C2318yescomplemented
71C23×C17—21no—
72C23×C17—21no—
73C23×C17—42no—
74C23×C17—42no—
75C23×C17C22⋊C412yes—
76C23×C17C22⋊C412yes—
77C23×C17C22×C411yescharacteristic
78C23×C17C22×C412yes—
79C23×C17C22×C412yescomplemented
80C22×D17—28no—
81C22×D17—24no—
82C22×D17—21no—
83C22×D17—21no—
84C22×D17—24no—
85C22×D17—24no—
86C22×D17—44no—
87C22×D17—48no—
88C22×D17—44no—
89C22×D17—44no—
90C22×D17—42no—
91C22×D17—44no—
92C22×D17—48no—
93C22×D17—48no—
94C22×D17—44no—
95C22×D17—42no—
96C22×D17C22⋊C412yes—
97C22×D17C22⋊C411yescharacteristic
98C22×D17C22⋊C414yes—
99C22×D17C22⋊C414yes—
100C22×D17C22⋊C411yescharacteristic
101C22×D17C22×C412yes—
102C22×D17C22×C411yescharacteristic
103C22×D17C22×C412yescomplemented
104C22×D17C2×D412yes—
105C22×D17C2×D414yes—
106C22×D17C2×D412yes—
107C22×D17C2×D414yes—
108C22×D17C2411yescharacteristic
109C2×#595—28no—
110C2×#595—48no—
111C2×#595—416no—
112D4×C17—28no—
113C2×C4×C17—21no—
114C2×C4×C17—21no—
115C2×C4×C17C22×C412yescomplemented
116C22⋊D17—28no—
117C22⋊D17—24no—
118C22⋊D17—24no—
119C2×Dic17—21no—
120C2×Dic17—21no—
121C2×Dic17C22×C412yescomplemented
122D68—24no—
123D68—24no—
124C4×D17—24no—
125C4×D17—24no—
126C22×#99—171nomaximal, Sylow
127C22×C17—22no—
128C22×C17—24no—
129C22×C17—22no—
130C22×C17—42no—
131C22×C17—42no—
132C22×C17—42no—
133C22×C17—42no—
134C22×C17—42no—
135C22×C17C2×C22⋊C411yescharacteristic
136C22×C17C2×C22⋊C414yes—
137C22×C17C2×C22⋊C411yescharacteristic
138C22×C17C23×C411yescharacteristic
139C2×D17—24no—
140C2×D17—22no—
141C2×D17—28no—
142C2×D17—24no—
143C2×D17—24no—
144C2×D17—28no—
145C2×D17—22no—
146C2×D17—44no—
147C2×D17—41no—
148C2×D17—44no—
149C2×D17—42no—
150C2×D17—41no—
151C2×D17—48no—
152C2×D17—42no—
153C2×D17—42no—
154C2×D17—48no—
155C2×D17—42no—
156C2×D17#9914yescomplemented
157C2×D17C2×C22⋊C412yes—
158C2×D17C2×C22⋊C412yes—
159C2×D17C2×C22⋊C412yes—
160C2×D17C22×D412yes—
161#595—48no—
162C4×C17—22no—
163Dic17—22no—
164C23×D4—171no—
165C22×C22⋊C4—172no—
166C2×#99—172no—
167C2×#99—178no—
168C2×#99—172no—
169C2×C17—21no—
170C2×C17—21no—
171C2×C17—24no—
172C2×C17—42no—
173C2×C17C2×#9912yescomplemented
174C2×C17C22×C22⋊C411yescharacteristic
175D17—22no—
176D17—22no—
177D17—22no—
178D17—42no—
179D17C2×#9914yescomplemented
180C25—171no—
181C25—171no—
182C22×D4—171no—
183C22×D4—171no—
184C22×D4—174no—
185C22×D4—174no—
186C22×D4—171no—
187C22×D4—342no—
188C22×D4—344no—
189C22×D4—342no—
190C22×D4#59511yescharacteristic, complemented
191C23×C4—171no—
192C23×C4—342no—
193C2×C22⋊C4—174no—
194C2×C22⋊C4—178no—
195C2×C22⋊C4—344no—
196C2×C22⋊C4—342no—
197#99—178no—
198#99—178no—
199C17C22×#9911yescharacteristic, complemented, Sylow
200C24—172no—
201C24—171no—
202C24—174no—
203C24—172no—
204C24—172no—
205C24—172no—
206C24—171no—
207C24—171no—
208C24—174no—
209C24—342no—
210C24—341no—
211C24—341no—
212C24—684no—
213C24—684no—
214C24C2×#59511yescharacteristic
215C24C2×#59511yescharacteristic, complemented
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—174no—
219C2×D4—172no—
220C2×D4—172no—
221C2×D4—172no—
222C2×D4—172no—
223C2×D4—342no—
224C2×D4—342no—
225C2×D4—348no—
226C2×D4—348no—
227C2×D4—348no—
228C2×D4—348no—
229C2×D4—342no—
230C2×D4—342no—
231C2×D4—342no—
232C2×D4—342no—
233C2×D4C2×#59514yescomplemented
234C22×C4—171no—
235C22×C4—174no—
236C22×C4—342no—
237C22×C4—341no—
238C22×C4—341no—
239C22×C4—348no—
240C22×C4—344no—
241C22×C4—688no—
242C22×C4C2×#59511yescharacteristic, complemented
243C22⋊C4—178no—
244C22⋊C4—348no—
245C22⋊C4—344no—
246C23—21no—
247C23—21no—
248C23—42no—
249C23—42no—
250C23—171no—
251C23—174no—
252C23—172no—
253C23—174no—
254C23—172no—
255C23—171no—
256C23—172no—
257C23—174no—
258C23—172no—
259C23—174no—
260C23—171no—
261C23—171no—
262C23—172no—
263C23—348no—
264C23—344no—
265C23—344no—
266C23—344no—
267C23—341no—
268C23—341no—
269C23—682no—
270C23—684no—
271C23—682no—
272C23—684no—
273C23—688no—
274C23—684no—
275C23—684no—
276C23—688no—
277C23—688no—
278C23—684no—
279C23C22⋊#59512yes—
280C23C22⋊#59512yes—
281C23C22×#59511yescharacteristic
282C23C22×#59512yes—
283C23C22×#59512yescomplemented
284D4—28no—
285D4—344no—
286D4—344no—
287D4—344no—
288D4—344no—
289D4—348no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—172no—
293C2×C4—344no—
294C2×C4—344no—
295C2×C4—341no—
296C2×C4—341no—
297C2×C4—348no—
298C2×C4—6816no—
299C2×C4—688no—
300C2×C4C22×#59512yescomplemented
301C22—22no—
302C22—24no—
303C22—22no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—174no—
310C22—172no—
311C22—172no—
312C22—172no—
313C22—172no—
314C22—348no—
315C22—344no—
316C22—344no—
317C22—348no—
318C22—344no—
319C22—342no—
320C22—342no—
321C22—682no—
322C22—681no—
323C22—681no—
324C22—684no—
325C22—684no—
326C22—682no—
327C22—682no—
328C22—688no—
329C22—688no—
330C22—682no—
331C22C2×C22⋊#59511yescharacteristic
332C22C2×C22⋊#59514yes—
333C22C2×C22⋊#59511yescharacteristic
334C22C23×#59511yescharacteristic
335C4—22no—
336C4—342no—
337C4—688no—
338C2—21no—
339C2—21no—
340C2—24no—
341C2—42no—
342C2—174no—
343C2—342no—
344C2—342no—
345C2—342no—
346C2—682no—
347C2D17⋊#9912yesdirect product factor
348C2C22×C22⋊#59511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#595
commutatorC22×C17C23×C4
FrattiniC22C23×#595
FittingC22×D4×C17C4
socleC22×C17C2×C22⋊C4
prime radicalC22×D4×D17C2
cosocleC22×D17C24
hypercenterC22×D4#595
hypocenterC17C22×#99
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊#595C2semidirect
2. C2×#10587539C2semidirect
3. D17⋊#99C2direct (N × H)
4. C2×#10587551C2semidirect
6. C24×D17C4semidirect
9. C22×D4×C17C4semidirect
10. C22×C22⋊D17C4semidirect
15. C2×D4×D17C4semidirect
18. C22×C4×D17C4semidirect
21. C2×C22⋊#595C22semidirect
22. C2×C22⋊#595C22semidirect
23. #10587551C22semidirect
24. #10587539C22semidirect
26. C24×C17C2×C4semidirect
34. C23×D17C2×C4semidirect
35. C23×D17C2×C4semidirect
46. C2×D4×C17C2×C4semidirect
47. C22×C4×C17C2×C4semidirect
52. C2×C22⋊D17C2×C4semidirect
53. C2×C22⋊D17C2×C4semidirect
55. C22×Dic17C2×C4semidirect
62. C2×D68C2×C4semidirect
67. C2×C4×D17C2×C4semidirect
70. C22⋊#595C23semidirect
79. C23×C17C22×C4semidirect
103. C22×D17C22×C4semidirect
115. C2×C4×C17C22×C4semidirect
121. C2×Dic17C22×C4semidirect
156. C2×D17#99semidirect
173. C2×C17C2×#99semidirect
179. D17C2×#99semidirect
190. C22×D4#595semidirect
199. C17C22×#99semidirect
215. C24C2×#595semidirect
233. C2×D4C2×#595semidirect
242. C22×C4C2×#595semidirect
283. C23C22×#595semidirect
300. C2×C4C22×#595semidirect
347. C2D17⋊#99direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C22⋊#5952
C2×#105875392
D17⋊#992
C2×#105875512
C22×D4×D172
C22×#9917