Finite Group Databasebeta

← C2×#26019087 #36523939

Subgroups — C2×#26019087 #36523939

Order 22784.

762 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151725C211yesmaximal, characteristic, complemented
2C2×C4×#13083563C211yesmaximal, characteristic
3C2×#19151663C211yesmaximal, characteristic
4#26019087C218yesmaximal, direct product factor
5C2×#19151328C211yesmaximal, characteristic, complemented
6C2×#19151325C211yesmaximal, characteristic
7C2×#19151320C211yesmaximal, characteristic, complemented
8C2×#334×C89C211yesmaximal, characteristic, complemented
9C22×#13083563C411yescharacteristic
10C22×C8×D89—21no—
11C2×C4×Dic178C2211yescharacteristic
12C2×C4×D356C2211yescharacteristic
13#19151725—22no—
14#19151725C2214yescomplemented
15C4×#13083563C414yes—
16C4×#13083563C2214yes—
17#19151663—22no—
18#19151663C2214yes—
19C2×#15667944C411yescharacteristic
20C2×#15667941—21no—
21C2×#15667937C411yescharacteristic
22C2×#15667934C411yescharacteristic
23C2×#15667924—21no—
24C2×#15667922—21no—
25C2×C4×#10623494C2211yescharacteristic
26C2×C4×#10623494C2211yescharacteristic
27#19151328C2214yescomplemented
28#19151325C2214yes—
29#19151320C2214yescomplemented
30C2×C4⋊C8×C89C2211yescharacteristic
31C2×C4⋊C8×C89C2211yescharacteristic
32C2×C4×C8×C89C2211yescharacteristic
33#334×C89C2214yescomplemented
34C22×Dic178C2×C411yescharacteristic
35C22×D356C2×C411yescharacteristic
36C22×C4×D89—21no—
37C2×#13083563—24no—
38C2×#13083563C2×C414yes—
39C22×#10623494—21no—
40C22×#10623494D411yescharacteristic
41C22×#10623494D411yescharacteristic
42C2×C8×D89—24no—
43C2×C8×D89—44no—
44C4×Dic178—21no—
45C4×Dic178—21no—
46C4×Dic178C2×C412yes—
47C4×Dic178C2312yes—
48C4×D356—21no—
49C4×D356—21no—
50C4×D356C2×C412yes—
51C4×D356C2312yes—
52C2×C4⋊Dic89C2×C411yescharacteristic
53C2×C4⋊Dic89C2×C411yescharacteristic
54C2×#13083553—21no—
55C2×#13083551—21no—
56C2×C4×Dic89—21no—
57#15667944C2×C414yes—
58#15667941—24no—
59#15667937C2×C414yes—
60#15667934C2×C414yes—
61#15667924—24no—
62#15667922—24no—
63C4×#10623494—21no—
64C4×#10623494D412yes—
65C4×#10623494C2312yes—
66C4×#10623494C2312yes—
67C22×C8×C89—21no—
68C22×C8×C89—21no—
69C22×C8×C89C2×C411yescharacteristic
70C22×C8×C89C2×C411yescharacteristic
71C2×C42×C89C2311yescharacteristic
72C4⋊C8×C89—21no—
73C4⋊C8×C89—21no—
74C4⋊C8×C89C2312yes—
75C4⋊C8×C89C2312yes—
76C4×C8×C89C2×C412yes—
77C4×C8×C89C2312yes—
78C23×D89—21no—
79C2×Dic178—22no—
80C2×Dic178—22no—
81C2×Dic178—21no—
82C2×Dic178C22×C412yes—
83C2×D356—21no—
84C2×D356—22no—
85C2×D356M1614yes—
86C2×D356C22×C412yes—
87C22×Dic89—21no—
88C22×Dic89—21no—
89C22×Dic89—21no—
90C2×C4×D89—22no—
91C2×C4×D89—22no—
92C2×C4×D89—42no—
93C2×C4×D89—42no—
94#13083563—28no—
95C2×#10623494—22no—
96C2×#10623494—22no—
97C2×#10623494—42no—
98C2×#10623494SD1614yescomplemented
99C2×#10623494C2×D412yes—
100C2×#10623494C2×D412yes—
101C8×D89—48no—
102C4⋊Dic89—21no—
103C4⋊Dic89—21no—
104C4⋊Dic89C22×C412yes—
105C4⋊Dic89C22×C412yes—
106#13083553—22no—
107#13083553—22no—
108#13083551—22no—
109#13083551—22no—
110C4×Dic89—22no—
111C4×Dic89—22no—
112C22×C4×C89C22×C411yescharacteristic
113C22×C4×C89C2×D411yescharacteristic
114C22×C4×C89#4111yescharacteristic
115C2×C8×C89—22no—
116C2×C8×C89—22no—
117C2×C8×C89—22no—
118C2×C8×C89—22no—
119C2×C8×C89—42no—
120C2×C8×C89—42no—
121C2×C8×C89C22×C412yes—
122C2×C8×C89C22×C412yes—
123C42×C89C22×C411yescharacteristic
124C42×C89C2×D411yescharacteristic
125C42×C89#4111yescharacteristic
126C42×C89C2411yescharacteristic
127C23×C89C4×D411yescharacteristic
128C22×D89—22no—
129C22×D89—24no—
130C22×D89—42no—
131C22×D89—42no—
132C2×C4×C89—22no—
133C2×C4×C89C4×D411yescharacteristic
134C2×C4×C89C4×D411yescharacteristic
135C2×C4×C89C4×D411yescharacteristic
136C2×C4×C89C2×M1612yes—
137C2×C4×C89#13112yes—
138C2×C4×C89C2×SD1612yes—
139C2×C4×C89#13512yes—
140C2×C4×C89C23×C411yescharacteristic
141C2×C4×C89C22×D411yescharacteristic
142C2×C4×C89C2×#4111yescharacteristic
143C2×Dic89—22no—
144C2×Dic89—22no—
145C2×Dic89—22no—
146C2×Dic89—42no—
147C2×Dic89—42no—
148C2×Dic89—42no—
149D356—22no—
150D356—24no—
151D356C2×M1614yes—
152C4×D89—42no—
153C4×D89—42no—
154C4×D89—44no—
155Dic178—22no—
156Dic178—22no—
157Dic178—42no—
158C8×C89—22no—
159C8×C89—22no—
160C8×C89—42no—
161C8×C89—42no—
162#10623494—22no—
163#10623494—42no—
164#10623494C2×SD1614yescomplemented
165C22×C89#43512yes—
166C22×C89C4×SD1612yes—
167C22×C89#44412yes—
168C22×C89C2×C4×D411yescharacteristic
169C2×D89—24no—
170C2×D89—48no—
171C2×D89—42no—
172C2×D89—42no—
173C4×C89—21no—
174C4×C89—21no—
175C4×C89#43512yes—
176C4×C89C4×SD1612yes—
177C4×C89C22×M1611yescharacteristic
178C4×C89C2×#13111yescharacteristic
179C4×C89C22×SD1611yescharacteristic
180C4×C89C2×#13511yescharacteristic
181Dic89—42no—
182Dic89—42no—
183Dic89—42no—
184C2×#1582—891nomaximal, Sylow
185C2×C89#158214yescomplemented
186C2×C89C2×#43511yescharacteristic
187C2×C89C2×C4×SD1611yescharacteristic
188C2×C89C2×#44411yescharacteristic
189D89—44no—
190C2×#446—891no—
191C2×C4×SD16—891no—
192C2×C8×D4—891no—
193#1582—898no—
194C2×#334D8911yescharacteristic, complemented
195C2×Q8⋊C8—891no—
196C2×D4⋊C8—891no—
197C2×#322—891no—
198C89C2×#158211yescharacteristic, complemented, Sylow
199C22×SD16—891no—
200C23×C8—1781no—
201C2×C4×Q8—891no—
202C2×C4×D4—891no—
203#446—894no—
204#446—1782no—
205C4×SD16—894no—
206C4×SD16—894no—
207C8×D4—894no—
208C8×D4—1782no—
209C2×#106—891no—
210C2×C4⋊C8—1781no—
211C2×C4⋊C8C2×D8911yescharacteristic
212C2×C4⋊C8C2×D8911yescharacteristic
213C2×#103—891no—
214C2×#102—891no—
215C2×C22⋊C8—1781no—
216C2×#97—1781no—
217C2×C4×C8—891no—
218C2×C4×C8—891no—
219C2×C4×C8C2×D8911yescharacteristic
220#334C2×D8914yescomplemented
221Q8⋊C8—894no—
222D4⋊C8—894no—
223#322—894no—
224C22×Q8—891no—
225C22×D4—891no—
226C23×C4—1781no—
227C2×SD16—894no—
228C2×SD16—1784no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—891no—
232C22×C8—891no—
233C22×C8—3564no—
234C22×C8—1784no—
235C22×C8—1781no—
236C22×C8C4×D8911yescharacteristic
237C22×C8C4×D8911yescharacteristic
238C4×Q8—892no—
239C4×Q8—892no—
240C4×Q8—1781no—
241C4×Q8—1781no—
242C4×D4—892no—
243C4×D4—892no—
244C4×D4—1781no—
245C4×D4—1781no—
246C2×C4⋊C4—891no—
247C2×C4⋊C4—891no—
248C2×C4⋊C4—1781no—
249C2×C22⋊C4—1781no—
250C2×C42—1781no—
251C2×C42C22×D8911yescharacteristic
252#106—894no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—1784no—
256C4⋊C8C22×D8912yes—
257C4⋊C8C22×D8912yes—
258#103—894no—
259#102—894no—
260C22⋊C8—1784no—
261#97—1784no—
262C4×C8—892no—
263C4×C8—892no—
264C4×C8—892no—
265C4×C8—1781no—
266C4×C8C4×D8912yes—
267C4×C8C22×D8912yes—
268C24—1781no—
269C2×Q8—892no—
270C2×Q8—1782no—
271C2×Q8—1782no—
272C2×Q8—1781no—
273C2×D4—894no—
274C2×D4—892no—
275C2×D4—1781no—
276C2×D4—1782no—
277C22×C4—3562no—
278C22×C4—3562no—
279C22×C4—1781no—
280C22×C4—1781no—
281C22×C4—1781no—
282C22×C4—1782no—
283C22×C4—1782no—
284C22×C4C2×C4×D8911yescharacteristic
285C22×C4D4×D8911yescharacteristic
286C22×C4#1308357511yescharacteristic
287SD16—1788no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—894no—
295C2×C8—892no—
296C2×C8—892no—
297C2×C8—3568no—
298C2×C8—3562no—
299C2×C8—1782no—
300C2×C8—1782no—
301C2×C8C2×C4×D8912yes—
302C2×C8C2×C4×D8912yes—
303C4⋊C4—892no—
304C4⋊C4—892no—
305C4⋊C4—1781no—
306C4⋊C4—1781no—
307C4⋊C4—1782no—
308C4⋊C4—1782no—
309C22⋊C4—1782no—
310C22⋊C4—1782no—
311C42—1782no—
312C42—1782no—
313C42C2×C4×D8911yescharacteristic
314C42D4×D8911yescharacteristic
315C42#1308357511yescharacteristic
316C42C23×D8911yescharacteristic
317C23—3562no—
318C23—3562no—
319C23—1784no—
320C23—1782no—
321C23#1566797411yescharacteristic
322Q8—3562no—
323Q8—1782no—
324Q8—1782no—
325D4—894no—
326D4—1784no—
327D4—1782no—
328C2×C4—22no—
329C2×C4—3562no—
330C2×C4—3562no—
331C2×C4—3562no—
332C2×C4—3564no—
333C2×C4—3562no—
334C2×C4—3562no—
335C2×C4—1782no—
336C2×C4—1782no—
337C2×C4—1782no—
338C2×C4#1566797411yescharacteristic
339C2×C4#1566797411yescharacteristic
340C2×C4#1566797411yescharacteristic
341C2×C4M16×D8912yes—
342C2×C4#1566801812yes—
343C2×C4SD16×D8912yes—
344C2×C4#1566803312yes—
345C2×C4C22×C4×D8911yescharacteristic
346C2×C4C2×D4×D8911yescharacteristic
347C2×C4C2×#1308357511yescharacteristic
348C8—22no—
349C8—22no—
350C8—42no—
351C8—42no—
352C8—894no—
353C8—3562no—
354C8—1782no—
355C22—3568no—
356C22—3562no—
357C22—3562no—
358C22—1784no—
359C22#1915166812yes—
360C22#1915168512yes—
361C22#1915171912yes—
362C22C2×#1566797411yescharacteristic
363C4—21no—
364C4—21no—
365C4—3562no—
366C4—3562no—
367C4—3562no—
368C4#1915166812yes—
369C4#1915168512yes—
370C4C2×M16×D8911yescharacteristic
371C4C2×#1566801811yescharacteristic
372C4C2×SD16×D8911yescharacteristic
373C4C2×#1566803311yescharacteristic
374C2—3564no—
375C2#2601908714yesdirect product factor
376C2C2×#1915166811yescharacteristic
377C2C2×#1915168511yescharacteristic
378C2C2×#1915171911yescharacteristic
subgroupG/H
centerC22×C4D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC2×#334×C89C2
socleC23×C89C4×D4
prime radicalC22×D356C2×C4
cosocleC42×C89C24
hypercenterC2×#334D89
hypocenterC89C2×#1582
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
1. C2×#19151725C2semidirect
4. #26019087C2direct (N × H)
5. C2×#19151328C2semidirect
7. C2×#19151320C2semidirect
8. C2×#334×C89C2semidirect
14. #19151725C22semidirect
27. #19151328C22semidirect
29. #19151320C22semidirect
33. #334×C89C22semidirect
98. C2×#10623494SD16semidirect
164. #10623494C2×SD16semidirect
185. C2×C89#1582semidirect
194. C2×#334D89semidirect
198. C89C2×#1582semidirect
220. #334C2×D89semidirect
375. C2#26019087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191517252
C2×C4×#130835632
C2×#191516632
#260190872
C2×#191513282
C2×#191513252
C2×#191513202
C2×#334×C892
C2×#158289