Finite Group Databasebeta

← C2×#26019625 #36536675

Subgroups — C2×#26019625 #36536675

Order 22784.

758 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19151994C211yesmaximal, characteristic, complemented
2C2×#19151888C211yesmaximal, characteristic
3C2×D4×#10623494C211yesmaximal, characteristic
4#26019625C218yesmaximal, direct product factor
5C2×#19151348C211yesmaximal, characteristic, complemented
6C2×#19151346C211yesmaximal, characteristic, complemented
7C2×#19151344C211yesmaximal, characteristic, complemented
8C2×#461×C89C211yesmaximal, characteristic
9C23×#10623494—21no—
10C2×#15668012C2211yescharacteristic
11#19151994—22no—
12#19151994C2214yescomplemented
13#19151888—22no—
14#19151888C2214yes—
15D4×#10623494—22no—
16D4×#10623494C2214yes—
17C2×#15667943—21no—
18C2×#15667943—21no—
19C2×#15667943—21no—
20C2×C4⋊#10623494C2211yescharacteristic
21C2×C4⋊#10623494C2211yescharacteristic
22C2×#15667933—21no—
23C2×C22⋊#10623494—21no—
24C2×C4×#10623494C2211yescharacteristic
25#19151348C2214yescomplemented
26#19151346C2214yescomplemented
27#19151344C2214yescomplemented
28C22×SD16×C89—21no—
29C2×C4⋊Q8×C89C2211yescharacteristic
30C2×C4×D4×C89C2211yescharacteristic
31#461×C89—22no—
32#461×C89C2214yes—
33C2×C4⋊C8×C89C2211yescharacteristic
34C2×#103×C89—21no—
35C22×Dic178—21no—
36C22×#10623494—24no—
37C22×#10623494—21no—
38C22×#10623494—21no—
39C22×#10623494—44no—
40C22×#10623494D411yescharacteristic
41C22×#10623494D411yescharacteristic
42#15668012—21no—
43#15668012—21no—
44#15668012—21no—
45#15668012C2312yes—
46C2×C4⋊Dic89—21no—
47C2×C4⋊Dic89—21no—
48#15667943—24no—
49#15667943—24no—
50#15667943—24no—
51C4⋊#10623494—21no—
52C4⋊#10623494—21no—
53C4⋊#10623494C2312yes—
54C4⋊#10623494C2312yes—
55#15667933—24no—
56C22⋊#10623494—24no—
57C4×#10623494D412yes—
58C4×#10623494C2312yes—
59C22×Q8×C89—21no—
60C22×D4×C89D411yescharacteristic
61C23×C4×C89—21no—
62C2×SD16×C89—24no—
63C2×SD16×C89—44no—
64C22×C8×C89—21no—
65C4⋊Q8×C89—21no—
66C4⋊Q8×C89—21no—
67C4⋊Q8×C89—21no—
68C4⋊Q8×C89C2312yes—
69C4×D4×C89—21no—
70C4×D4×C89—21no—
71C4×D4×C89D412yes—
72C4×D4×C89C2312yes—
73C2×C4⋊C4×C89—21no—
74C2×C4⋊C4×C89—21no—
75C2×C4⋊C4×C89D411yescharacteristic
76C2×C22⋊C4×C89—21no—
77C2×C42×C89C2311yescharacteristic
78C4⋊C8×C89—21no—
79C4⋊C8×C89C2312yes—
80#103×C89—24no—
81C2×Dic178—22no—
82C2×Dic178—41no—
83C2×Dic178—82no—
84C22×Dic89—41no—
85C2×#10623494—22no—
86C2×#10623494—22no—
87C2×#10623494—22no—
88C2×#10623494—42no—
89C2×#10623494—42no—
90C2×#10623494—48no—
91C2×#10623494SD1614yescomplemented
92C2×#10623494C2×D412yes—
93C2×#10623494C2×D412yes—
94C4⋊Dic89—22no—
95C4⋊Dic89—22no—
96C4⋊Dic89—41no—
97C4⋊Dic89—41no—
98C24×C89—21no—
99C2×Q8×C89—22no—
100C2×Q8×C89—41no—
101C2×Q8×C89—42no—
102C2×Q8×C89—42no—
103C2×D4×C89—21no—
104C2×D4×C89—22no—
105C2×D4×C89SD1614yes—
106C2×D4×C89C2×D412yes—
107C22×C4×C89—21no—
108C22×C4×C89—22no—
109C22×C4×C89—22no—
110C22×C4×C89—42no—
111C22×C4×C89—42no—
112C22×C4×C89—41no—
113C22×C4×C89C2×D411yescharacteristic
114C22×C4×C89C2×D411yescharacteristic
115C22×C4×C89#4111yescharacteristic
116SD16×C89—48no—
117C2×C8×C89—22no—
118C2×C8×C89—42no—
119C4⋊C4×C89—21no—
120C4⋊C4×C89—22no—
121C4⋊C4×C89—22no—
122C4⋊C4×C89—41no—
123C4⋊C4×C89—41no—
124C4⋊C4×C89C2×D412yes—
125C22⋊C4×C89—22no—
126C22⋊C4×C89—22no—
127C42×C89C2×D411yescharacteristic
128C42×C89C2×D411yescharacteristic
129C42×C89#4111yescharacteristic
130C42×C89C2411yescharacteristic
131C23×C89—22no—
132C23×C89—24no—
133C23×C89—42no—
134C23×C89—42no—
135C23×C89#12111yescharacteristic
136Q8×C89—42no—
137Q8×C89—42no—
138Q8×C89—82no—
139D4×C89—22no—
140D4×C89—24no—
141D4×C89C2×SD1614yes—
142C2×C4×C89—22no—
143C2×C4×C89—22no—
144C2×C4×C89—42no—
145C2×C4×C89—42no—
146C2×C4×C89—42no—
147C2×C4×C89—44no—
148C2×C4×C89—42no—
149C2×C4×C89—82no—
150C2×C4×C89#12111yescharacteristic
151C2×C4×C89#12111yescharacteristic
152C2×C4×C89#12111yescharacteristic
153C2×C4×C89C2×SD1612yes—
154C2×C4×C89C2×SD1612yes—
155C2×C4×C89#13512yes—
156C2×C4×C89#13712yes—
157C2×C4×C89C22×D411yescharacteristic
158C2×C4×C89C22×D411yescharacteristic
159C2×C4×C89C2×#4111yescharacteristic
160C2×Dic89—42no—
161C2×Dic89—82no—
162Dic178—82no—
163Dic178—82no—
164C8×C89—42no—
165#10623494—22no—
166#10623494—42no—
167#10623494—42no—
168#10623494C2×SD1614yescomplemented
169C22×C89—24no—
170C22×C89—48no—
171C22×C89—42no—
172C22×C89—42no—
173C22×C89#46112yes—
174C22×C89#46512yes—
175C22×C89#47112yes—
176C22×C89C2×#12111yescharacteristic
177C4×C89—21no—
178C4×C89—21no—
179C4×C89—42no—
180C4×C89—82no—
181C4×C89#46112yes—
182C4×C89#46512yes—
183C4×C89C22×SD1611yescharacteristic
184C4×C89C22×SD1611yescharacteristic
185C4×C89C2×#13511yescharacteristic
186C4×C89C2×#13711yescharacteristic
187Dic89—82no—
188C2×#1671—891nomaximal, Sylow
189C2×C89—44no—
190C2×C89#167114yescomplemented
191C2×C89C2×#46111yescharacteristic
192C2×C89C2×#46511yescharacteristic
193C2×C89C2×#47111yescharacteristic
194C2×#498—891no—
195C2×#476—891no—
196C2×#461D8911yescharacteristic
197C2×C8×D4—891no—
198#1671—898no—
199C2×#334—891no—
200C2×#333—891no—
201C2×#332—891no—
202C89C2×#167111yescharacteristic, complemented, Sylow
203C22×SD16—21no—
204C23×C8—1781no—
205C2×C4⋊Q8—891no—
206C2×C4⋊Q8C2×D8911yescharacteristic
207C2×C4×D4C2×D8911yescharacteristic
208#498—894no—
209#498—1782no—
210#476—894no—
211#476—1782no—
212#461—22no—
213#461C2×D8914yes—
214C8×D4—894no—
215C8×D4—1782no—
216C2×#106—1781no—
217C2×#106—1781no—
218C2×#106—1781no—
219C2×C4⋊C8—891no—
220C2×C4⋊C8—891no—
221C2×C4⋊C8C2×D8911yescharacteristic
222C2×#103—21no—
223C2×#102—1781no—
224C2×C22⋊C8—1781no—
225C2×C4×C8—891no—
226#334—894no—
227#333—894no—
228#332—894no—
229C22×Q8—21no—
230C22×Q8—1781no—
231C22×D4C22⋊D8911yescharacteristic
232C23×C4—21no—
233C2×SD16—24no—
234C2×SD16—44no—
235C22×C8—21no—
236C22×C8—891no—
237C22×C8—891no—
238C22×C8—3564no—
239C22×C8—1784no—
240C22×C8—1781no—
241C22×C8—1781no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—892no—
246C4⋊Q8—1781no—
247C4⋊Q8—1781no—
248C4⋊Q8—1781no—
249C4⋊Q8C22×D8912yes—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4C22⋊D8912yes—
253C4×D4C22×D8912yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—1781no—
257C2×C4⋊C4—1781no—
258C2×C4⋊C4C22⋊D8911yescharacteristic
259C2×C22⋊C4—21no—
260C2×C42C22×D8911yescharacteristic
261#106—1784no—
262#106—1784no—
263#106—1784no—
264C4⋊C8—21no—
265C4⋊C8—892no—
266C4⋊C8—892no—
267C4⋊C8—1781no—
268C4⋊C8—1781no—
269C4⋊C8C22×D8912yes—
270#103—24no—
271#102—1784no—
272C22⋊C8—1784no—
273C4×C8—892no—
274C4×C8—892no—
275C24—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—42no—
279C2×Q8—42no—
280C2×Q8—3561no—
281C2×Q8—1782no—
282C2×Q8—7122no—
283C2×D4—21no—
284C2×D4—22no—
285C2×D4#1308356214yes—
286C2×D4C2×C22⋊D8912yes—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—3561no—
294C22×C4D4×D8911yescharacteristic
295C22×C4C2×C22⋊D8911yescharacteristic
296C22×C4#1308357311yescharacteristic
297SD16—48no—
298C2×C8—22no—
299C2×C8—42no—
300C2×C8—894no—
301C2×C8—892no—
302C2×C8—892no—
303C2×C8—3568no—
304C2×C8—3562no—
305C2×C8—3562no—
306C2×C8—1782no—
307C2×C8—1782no—
308C2×C8—1782no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—3561no—
315C4⋊C4—3561no—
316C4⋊C4—1782no—
317C4⋊C4—1782no—
318C4⋊C4C2×C22⋊D8912yes—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C42D4×D8911yescharacteristic
322C42C2×C22⋊D8911yescharacteristic
323C42#1308357311yescharacteristic
324C42C23×D8911yescharacteristic
325C23—24no—
326C23—22no—
327C23—42no—
328C23—42no—
329C23#1566798411yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—82no—
333Q8—7122no—
334Q8—7122no—
335D4—24no—
336D4—22no—
337D4C2×#1308356214yes—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—44no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—3562no—
347C2×C4—7122no—
348C2×C4#1566798411yescharacteristic
349C2×C4#1566798411yescharacteristic
350C2×C4#1566798411yescharacteristic
351C2×C4SD16×D8912yes—
352C2×C4C2×#1308356212yes—
353C2×C4#1566803212yes—
354C2×C4#1566804112yes—
355C2×C4C2×D4×D8911yescharacteristic
356C2×C4C22×C22⋊D8911yescharacteristic
357C2×C4C2×#1308357311yescharacteristic
358C8—42no—
359C8—894no—
360C8—3562no—
361C8—3562no—
362C8—1782no—
363C22—24no—
364C22—48no—
365C22—42no—
366C22—42no—
367C22#1915180112yes—
368C22#1915182512yes—
369C22#1915186312yes—
370C22C2×#1566798411yescharacteristic
371C4—21no—
372C4—21no—
373C4—42no—
374C4—82no—
375C4—7122no—
376C4#1915180112yes—
377C4#1915182512yes—
378C4C2×SD16×D8911yescharacteristic
379C4C22×#1308356211yescharacteristic
380C4C2×#1566803211yescharacteristic
381C4C2×#1566804111yescharacteristic
382C2—44no—
383C2#2601962514yesdirect product factor
384C2C2×#1915180111yescharacteristic
385C2C2×#1915182511yescharacteristic
386C2C2×#1915186311yescharacteristic
subgroupG/H
centerC23#15667984
commutator, cosocleC42×C89C24
FrattiniC42C23×D89
FittingC2×#461×C89C2
socleC23×C89#121
prime radicalC22×D4×C89D4
hypercenterC2×#461D89
hypocenterC89C2×#1671
LCSG ▷ C42×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#19151994C2semidirect
4. #26019625C2direct (N × H)
5. C2×#19151348C2semidirect
6. C2×#19151346C2semidirect
7. C2×#19151344C2semidirect
12. #19151994C22semidirect
25. #19151348C22semidirect
26. #19151346C22semidirect
27. #19151344C22semidirect
91. C2×#10623494SD16semidirect
168. #10623494C2×SD16semidirect
190. C2×C89#1671semidirect
202. C89C2×#1671semidirect
383. C2#26019625direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191519942
C2×#191518882
C2×D4×#106234942
#260196252
C2×#191513482
C2×#191513462
C2×#191513442
C2×#461×C892
C2×#167189