Finite Group Databasebeta

← C2×#26019106 #36523964

Subgroups — C2×#26019106 #36523964

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×#13083562C211yesmaximal, characteristic
3C2×D4×#10623494C211yesmaximal, characteristic
4#26019106C218yesmaximal, direct product factor
5C2×#19151350C211yesmaximal, characteristic, complemented
6C2×#19151330C211yesmaximal, characteristic, complemented
7C2×#19151319C211yesmaximal, characteristic, complemented
8C2×D4⋊C8×C89C211yesmaximal, characteristic
9C22×#13083562C411yescharacteristic
10C23×#10623494—21no—
11C2×C4×Dic178C2211yescharacteristic
12#19151725—22no—
13#19151725C2214yescomplemented
14C4×#13083562C414yes—
15C4×#13083562C2214yes—
16D4×#10623494—22no—
17D4×#10623494C2214yes—
18C2×#15667943C411yescharacteristic
19C2×C4⋊#10623494C2211yescharacteristic
20C2×#15667941—21no—
21C2×#15667935C411yescharacteristic
22C2×#15667933C411yescharacteristic
23C2×C22⋊#10623494—21no—
24C2×#15667922—21no—
25C2×C4×#10623494C2211yescharacteristic
26C2×C4×#10623494C2211yescharacteristic
27#19151350C2214yescomplemented
28#19151330C2214yescomplemented
29#19151319C2214yescomplemented
30C2×C4×D4×C89C2211yescharacteristic
31C2×C4⋊C8×C89C2211yescharacteristic
32C2×C4×C8×C89C2211yescharacteristic
33D4⋊C8×C89C2214yes—
34C22×Dic178C2×C411yescharacteristic
35C2×#13083562—24no—
36C2×#13083562C2×C414yes—
37C22×#10623494—24no—
38C22×#10623494—21no—
39C22×#10623494—44no—
40C22×#10623494C2×C411yescharacteristic
41C22×#10623494C2×C411yescharacteristic
42C22×#10623494D411yescharacteristic
43C22×#10623494D411yescharacteristic
44C4×Dic178—21no—
45C4×Dic178—21no—
46C4×Dic178C2×C412yes—
47C4×Dic178C2312yes—
48C2×C4⋊Dic89C2×C411yescharacteristic
49C2×#13083553—21no—
50C2×C4×Dic89—21no—
51#15667943C2×C414yes—
52C4⋊#10623494—21no—
53C4⋊#10623494C2312yes—
54#15667941—24no—
55#15667935C2×C414yes—
56#15667933C2×C414yes—
57C22⋊#10623494—24no—
58#15667922—24no—
59C4×#10623494C2×C412yes—
60C4×#10623494D412yes—
61C4×#10623494C2312yes—
62C4×#10623494C2312yes—
63C22×D4×C89C2×C411yescharacteristic
64C23×C4×C89—21no—
65C22×C8×C89—21no—
66C22×C8×C89—21no—
67C4×D4×C89—21no—
68C4×D4×C89—21no—
69C4×D4×C89C2×C412yes—
70C4×D4×C89C2312yes—
71C2×C4⋊C4×C89C2×C411yescharacteristic
72C2×C22⋊C4×C89—21no—
73C2×C42×C89C2311yescharacteristic
74C4⋊C8×C89—21no—
75C4⋊C8×C89C2312yes—
76C4×C8×C89—21no—
77C4×C8×C89C2312yes—
78C2×Dic178—22no—
79C2×Dic178—22no—
80C2×Dic178—21no—
81C2×Dic178C22×C412yes—
82C22×Dic89—21no—
83C22×Dic89—21no—
84#13083562—28no—
85C2×#10623494—22no—
86C2×#10623494—22no—
87C2×#10623494—22no—
88C2×#10623494—22no—
89C2×#10623494—22no—
90C2×#10623494—48no—
91C2×#10623494—42no—
92C2×#10623494C22×C412yes—
93C2×#10623494C22×C412yes—
94C2×#10623494C2×D412yes—
95C2×#10623494C2×D412yes—
96C4⋊Dic89—21no—
97C4⋊Dic89C22×C412yes—
98#13083553—22no—
99#13083553—22no—
100C4×Dic89—22no—
101C4×Dic89—22no—
102C24×C89—21no—
103C2×D4×C89—21no—
104C2×D4×C89—22no—
105C2×D4×C89M1614yes—
106C2×D4×C89C22×C412yes—
107C22×C4×C89—21no—
108C22×C4×C89—22no—
109C22×C4×C89—22no—
110C22×C4×C89—42no—
111C22×C4×C89—42no—
112C22×C4×C89C22×C411yescharacteristic
113C22×C4×C89C2×D411yescharacteristic
114C22×C4×C89#4111yescharacteristic
115C2×C8×C89—24no—
116C2×C8×C89—22no—
117C2×C8×C89—22no—
118C2×C8×C89—42no—
119C4⋊C4×C89—21no—
120C4⋊C4×C89C22×C412yes—
121C22⋊C4×C89—22no—
122C22⋊C4×C89—22no—
123C42×C89C22×C411yescharacteristic
124C42×C89C2×D411yescharacteristic
125C42×C89#4111yescharacteristic
126C42×C89C2411yescharacteristic
127C23×C89—22no—
128C23×C89—24no—
129C23×C89—42no—
130C23×C89—42no—
131C23×C89C4×D411yescharacteristic
132D4×C89—22no—
133D4×C89—24no—
134D4×C89C2×M1614yes—
135C2×C4×C89—22no—
136C2×C4×C89—22no—
137C2×C4×C89—42no—
138C2×C4×C89—42no—
139C2×C4×C89—42no—
140C2×C4×C89—44no—
141C2×C4×C89C4×D411yescharacteristic
142C2×C4×C89C4×D411yescharacteristic
143C2×C4×C89C4×D411yescharacteristic
144C2×C4×C89C2×M1612yes—
145C2×C4×C89#13112yes—
146C2×C4×C89AGL(1,ℤ/8)12yes—
147C2×C4×C89#13712yes—
148C2×C4×C89C23×C411yescharacteristic
149C2×C4×C89C22×D411yescharacteristic
150C2×C4×C89C2×#4111yescharacteristic
151C2×Dic89—22no—
152C2×Dic89—22no—
153C2×Dic89—42no—
154C2×Dic89—42no—
155Dic178—22no—
156Dic178—22no—
157Dic178—42no—
158C8×C89—24no—
159C8×C89—42no—
160#10623494—22no—
161#10623494—22no—
162#10623494—22no—
163#10623494—22no—
164#10623494—42no—
165C22×C89—24no—
166C22×C89—48no—
167C22×C89—42no—
168C22×C89—42no—
169C22×C89#43512yes—
170C22×C89#44012yes—
171C22×C89#44312yes—
172C22×C89C2×C4×D411yescharacteristic
173C4×C89—21no—
174C4×C89—21no—
175C4×C89—42no—
176C4×C89#43512yes—
177C4×C89#44012yes—
178C4×C89C22×M1611yescharacteristic
179C4×C89C2×#13111yescharacteristic
180C4×C89C2×AGL(1,ℤ/8)11yescharacteristic
181C4×C89C2×#13711yescharacteristic
182Dic89—42no—
183Dic89—42no—
184C2×#1585—891nomaximal, Sylow
185C2×C89—44no—
186C2×C89#158514yescomplemented
187C2×C89C2×#43511yescharacteristic
188C2×C89C2×#44011yescharacteristic
189C2×C89C2×#44311yescharacteristic
190C2×#446—891no—
191C2×C4×SD16—891no—
192C2×C8×D4—891no—
193#1585—898no—
194C2×#335—891no—
195C2×Q8⋊C8—891no—
196C2×D4⋊C8D8911yescharacteristic
197C2×#322—891no—
198C89C2×#158511yescharacteristic, complemented, Sylow
199C22×SD16—891no—
200C23×C8—1781no—
201C2×C4×Q8—891no—
202C2×C4×D4C2×D8911yescharacteristic
203#446—894no—
204#446—1782no—
205C4×SD16—894no—
206C4×SD16—894no—
207C8×D4—894no—
208C8×D4—1782no—
209C2×#106—891no—
210C2×C4⋊C8—891no—
211C2×C4⋊C8—1781no—
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#335—894no—
221Q8⋊C8—894no—
222D4⋊C8C2×D8914yes—
223#322—894no—
224C22×Q8—891no—
225C22×D4C4×D8911yescharacteristic
226C23×C4—21no—
227C2×SD16—894no—
228C2×SD16—1784no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—891no—
232C22×C8—891no—
233C22×C8—891no—
234C22×C8—891no—
235C22×C8—3564no—
236C22×C8—1784no—
237C22×C8—1781no—
238C4×Q8—892no—
239C4×Q8—892no—
240C4×Q8—1781no—
241C4×Q8—1781no—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4C4×D8912yes—
245C4×D4C22×D8912yes—
246C2×C4⋊C4—891no—
247C2×C4⋊C4—1781no—
248C2×C4⋊C4C4×D8911yescharacteristic
249C2×C22⋊C4—21no—
250C2×C42—1781no—
251C2×C42C22×D8911yescharacteristic
252#106—894no—
253C4⋊C8—21no—
254C4⋊C8—892no—
255C4⋊C8—1784no—
256C4⋊C8—1781no—
257C4⋊C8C22×D8912yes—
258#103—894no—
259#102—894no—
260C22⋊C8—1784no—
261#97—1784no—
262C4×C8—21no—
263C4×C8—892no—
264C4×C8—892no—
265C4×C8—892no—
266C4×C8—892no—
267C4×C8C22×D8912yes—
268C24—21no—
269C2×Q8—892no—
270C2×Q8—1782no—
271C2×Q8—1782no—
272C2×Q8—1781no—
273C2×D4—21no—
274C2×D4—22no—
275C2×D4#1308355714yes—
276C2×D4C2×C4×D8912yes—
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—1781no—
283C22×C4—1781no—
284C22×C4C2×C4×D8911yescharacteristic
285C22×C4D4×D8911yescharacteristic
286C22×C4#1308357311yescharacteristic
287SD16—1788no—
288C2×C8—24no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—42no—
292C2×C8—892no—
293C2×C8—892no—
294C2×C8—892no—
295C2×C8—892no—
296C2×C8—3562no—
297C2×C8—3568no—
298C2×C8—1782no—
299C2×C8—1782no—
300C2×C8—1782no—
301C2×C8—1782no—
302C2×C8—1782no—
303C4⋊C4—21no—
304C4⋊C4—892no—
305C4⋊C4—1781no—
306C4⋊C4—1782no—
307C4⋊C4—1782no—
308C4⋊C4C2×C4×D8912yes—
309C22⋊C4—22no—
310C22⋊C4—22no—
311C42—1782no—
312C42—1782no—
313C42C2×C4×D8911yescharacteristic
314C42D4×D8911yescharacteristic
315C42#1308357311yescharacteristic
316C42C23×D8911yescharacteristic
317C23—24no—
318C23—22no—
319C23—42no—
320C23—42no—
321C23#1566797211yescharacteristic
322Q8—3562no—
323Q8—1782no—
324Q8—1782no—
325D4—24no—
326D4—22no—
327D4C2×#1308355714yes—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—3562no—
335C2×C4—3562no—
336C2×C4—1782no—
337C2×C4—1782no—
338C2×C4#1566797211yescharacteristic
339C2×C4#1566797211yescharacteristic
340C2×C4#1566797211yescharacteristic
341C2×C4C2×#1308355712yes—
342C2×C4#1566802012yes—
343C2×C4#1566803612yes—
344C2×C4#1566804112yes—
345C2×C4C22×C4×D8911yescharacteristic
346C2×C4C2×D4×D8911yescharacteristic
347C2×C4C2×#1308357311yescharacteristic
348C8—24no—
349C8—42no—
350C8—3562no—
351C8—1782no—
352C8—1782no—
353C8—1782no—
354C8—1782no—
355C22—24no—
356C22—48no—
357C22—42no—
358C22—42no—
359C22#1915166612yes—
360C22#1915169512yes—
361C22#1915171212yes—
362C22C2×#1566797211yescharacteristic
363C4—21no—
364C4—21no—
365C4—42no—
366C4—3562no—
367C4—3562no—
368C4#1915166612yes—
369C4#1915169512yes—
370C4C22×#1308355711yescharacteristic
371C4C2×#1566802011yescharacteristic
372C4C2×#1566803611yescharacteristic
373C4C2×#1566804111yescharacteristic
374C2—44no—
375C2#2601910614yesdirect product factor
376C2C2×#1915166611yescharacteristic
377C2C2×#1915169511yescharacteristic
378C2C2×#1915171211yescharacteristic
subgroupG/H
centerC22×C4D4×D89
commutatorC2×C4×C89C23×C4
FrattiniC42C23×D89
FittingC2×D4⋊C8×C89C2
socleC23×C89C4×D4
prime radicalC22×D4×C89C2×C4
cosocleC42×C89C24
hypercenterC2×D4⋊C8D89
hypocenterC89C2×#1585
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#19151725C2semidirect
4. #26019106C2direct (N × H)
5. C2×#19151350C2semidirect
6. C2×#19151330C2semidirect
7. C2×#19151319C2semidirect
13. #19151725C22semidirect
27. #19151350C22semidirect
28. #19151330C22semidirect
29. #19151319C22semidirect
186. C2×C89#1585semidirect
198. C89C2×#1585semidirect
375. C2#26019106direct (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×#130835622
C2×D4×#106234942
#260191062
C2×#191513502
C2×#191513302
C2×#191513192
C2×D4⋊C8×C892
C2×#158589