Finite Group Databasebeta

← C2×#26021963 #36707325

Subgroups — C2×#26021963 #36707325

Order 22784.

1214 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
1C22×#15668035C211yesmaximal, characteristic
2C22×#15667951C211yesmaximal, characteristic, complemented
3C2×#107×D89C211yesmaximal, characteristic, complemented
4#26021963C218yesmaximal, direct product factor
5C2×#19151402C211yesmaximal, characteristic, complemented
6C2×#19151400C211yesmaximal, characteristic, complemented
7C2×#19151398C211yesmaximal, characteristic, complemented
8C2×#358×C89C211yesmaximal, characteristic, complemented
9C22×#13083575—21no—
10C2×#15668035—22no—
11C2×#15668035—24no—
12C2×#15668035C418yescomplemented
13C2×#15668035C2214yes—
14C22×#13083561—21no—
15C22×D712C2211yescharacteristic
16C22×C8×D89C2211yescharacteristic
17C2×C4⋊C4×D89—21no—
18C2×#15667951—24no—
19C2×#15667951C2214yescomplemented
20C22×#13083549C2211yescharacteristic
21C2×#15667946C2211yescharacteristic
22C2×#15667945—21no—
23#107×D89—22no—
24#107×D89C2214yescomplemented
25#19151402C2214yescomplemented
26#19151400C2214yescomplemented
27#19151398C2214yescomplemented
28C22×Q16×C89C2211yescharacteristic
29C22×C16×C89C2211yescharacteristic
30C2×#107×C89C2211yescharacteristic
31#358×C89C2214yescomplemented
32C2×#13083575—28no—
33C2×#13083575—24no—
34C2×#13083575—42no—
35C2×#13083575—44no—
36C22×D356—21no—
37C22×D356—41no—
38C22×C4×D89—41no—
39C22×C4×D89—41no—
40C22×C4×D89D411yescharacteristic
41#15668035—216no—
42#15668035—28no—
43#15668035C2×C4116yescomplemented
44C2×#13083561—28no—
45C2×#13083561—24no—
46C2×D712—21no—
47C2×D712—22no—
48C2×D712C2×C414yescomplemented
49C2×D712C2312yes—
50C22×#10623494D411yescharacteristic
51C2×C8×D89C2×C414yes—
52C2×C8×D89D412yes—
53C2×C8×D89D414yes—
54C2×C8×D89C2312yes—
55C2×C4⋊Dic89—21no—
56C2×#13083553—41no—
57C4⋊C4×D89—24no—
58C4⋊C4×D89—42no—
59#15667951—28no—
60C2×#13083549—22no—
61C2×#13083549C2312yes—
62#15667946—21no—
63#15667946C2312yes—
64#15667945—24no—
65C22×Q8×C89—21no—
66C2×Q16×C89—21no—
67C2×Q16×C89—22no—
68C2×Q16×C89C2×C414yescomplemented
69C2×Q16×C89C2312yes—
70C22×C8×C89C2311yescharacteristic
71C2×C4⋊C4×C89—21no—
72C2×C16×C89—22no—
73C2×C16×C89C2312yes—
74#107×C89—21no—
75#107×C89C2312yes—
76C23×D89—41no—
77C23×D89D811yescharacteristic
78#13083575—216no—
79#13083575—416no—
80#13083575—48no—
81C2×D356—24no—
82C2×D356—22no—
83C2×D356—48no—
84C2×D356—44no—
85C2×D356—41no—
86C2×D356—42no—
87C22×Dic89—41no—
88C22×Dic89D811yescharacteristic
89C2×C4×D89—48no—
90C2×C4×D89—44no—
91C2×C4×D89—44no—
92C2×C4×D89—84no—
93C2×C4×D89C22⋊C414yes—
94C2×C4×D89D812yes—
95C2×C4×D89SD1614yes—
96C2×C4×D89C2×D412yes—
97#13083561—216no—
98D712—24no—
99D712—22no—
100D712C22×C414yescomplemented
101C2×#10623494C22⋊C414yes—
102C2×#10623494C2×D412yes—
103C8×D89C22⋊C418yes—
104C8×D89C22×C414yes—
105C8×D89C2×D414yes—
106C4⋊Dic89—22no—
107C4⋊Dic89—41no—
108#13083553—44no—
109#13083549—22no—
110C2×Q8×C89—24no—
111C2×Q8×C89—22no—
112C2×Q8×C89—41no—
113C2×Q8×C89—42no—
114C22×C4×C89—41no—
115C22×C4×C89—41no—
116C22×C4×C89C2×D411yescharacteristic
117Q16×C89—24no—
118Q16×C89—22no—
119Q16×C89C22×C414yescomplemented
120C2×C8×C89C22×C412yes—
121C2×C8×C89C2×D411yescharacteristic
122C2×C8×C89C2×D412yes—
123C2×C8×C89C2411yescharacteristic
124C4⋊C4×C89—22no—
125C4⋊C4×C89—41no—
126C16×C89—22no—
127C23×C89C2×D811yescharacteristic
128C22×D89—22no—
129C22×D89—22no—
130C22×D89—42no—
131C22×D89—44no—
132C22×D89—82no—
133C22×D89—82no—
134C22×D89#10214yes—
135C22×D89C2×D812yes—
136Q8×C89—24no—
137Q8×C89—42no—
138Q8×C89—44no—
139C2×C4×C89—42no—
140C2×C4×C89—44no—
141C2×C4×C89—42no—
142C2×C4×C89—82no—
143C2×C4×C89C2×C22⋊C412yes—
144C2×C4×C89C2×D811yescharacteristic
145C2×C4×C89C2×SD1612yes—
146C2×C4×C89C22×D411yescharacteristic
147C2×Dic89—42no—
148C2×Dic89—82no—
149C2×Dic89#10214yes—
150C2×Dic89C2×D812yes—
151D356—24no—
152D356—416no—
153D356—42no—
154D356—44no—
155C4×D89—416no—
156C4×D89—88no—
157C4×D89#10218yes—
158C4×D89C2×C22⋊C414yes—
159C4×D89C2×SD1614yes—
160C8×C89C2×C22⋊C412yes—
161C8×C89C23×C411yescharacteristic
162C8×C89C22×D411yescharacteristic
163#10623494C2×C22⋊C414yes—
164C22×C89C2×#10212yes—
165C22×C89#50912yes—
166C22×C89#51012yes—
167C22×C89C22×D811yescharacteristic
168C2×D89—22no—
169C2×D89—22no—
170C2×D89—28no—
171C2×D89—44no—
172C2×D89—82no—
173C2×D89—82no—
174C2×D89—88no—
175C2×D89C2×#10214yes—
176C4×C89—44no—
177C4×C89—82no—
178C4×C89C2×#10212yes—
179C4×C89C22×C22⋊C411yescharacteristic
180C4×C89C22×SD1611yescharacteristic
181Dic89—82no—
182Dic89C2×#10214yes—
183C2×#2139—891nomaximal, Sylow
184C2×C89#213914yescomplemented
185C2×C89C22×#10211yescharacteristic
186C2×C89C2×#50911yescharacteristic
187C2×C89C2×#51011yescharacteristic
188D89—24no—
189D89—84no—
190C22×#135—891no—
191C22×M32—891no—
192C22×#107—891no—
193#2139—898no—
194C2×#358—891no—
195C2×#358D8911yescharacteristic, complemented
196C2×#357—891no—
197C2×#357—891no—
198C89C2×#213911yescharacteristic, complemented, Sylow
199C22×#41—1781no—
200C2×#135—898no—
201C2×#135—894no—
202C2×#135—1782no—
203C2×#135—1784no—
204C22×Q16C2×D8911yescharacteristic
205C22×SD16—1781no—
206C22×D8—891no—
207C23×C8—891no—
208C22×C4⋊C4—1781no—
209C2×M32—894no—
210C2×M32—1784no—
211C22×C16—891no—
212C22×C16C2×D8911yescharacteristic
213C2×#107—891no—
214C2×#107—894no—
215C2×#107—1782no—
216C2×#107—1781no—
217C2×#107C2×D8911yescharacteristic
218#358—894no—
219#358C2×D8914yescomplemented
220#357—894no—
221#357—894no—
222C2×#41—3562no—
223C2×#41—3564no—
224C2×#41—1784no—
225C2×#41—1788no—
226C22×Q8—21no—
227C22×D4—3561no—
228C22×D4—1781no—
229C23×C4—891no—
230C23×C4—3561no—
231C23×C4—3561no—
232#135—8916no—
233#135—1788no—
234#135—17816no—
235C2×Q16—22no—
236C2×Q16—21no—
237C2×Q16C4×D8914yescomplemented
238C2×Q16C22×D8912yes—
239C2×SD16—1784no—
240C2×SD16—1788no—
241C2×D8—894no—
242C2×D8—892no—
243C2×D8—1782no—
244C2×D8—1781no—
245C22×C8—891no—
246C22×C8—894no—
247C22×C8—892no—
248C22×C8—894no—
249C22×C8—892no—
250C22×C8C22×D8911yescharacteristic
251C2×C4⋊C4—21no—
252C2×C4⋊C4—3562no—
253C2×C4⋊C4—3561no—
254C2×C4⋊C4—1784no—
255C2×C4⋊C4—1781no—
256M32—1788no—
257C2×C16—22no—
258C2×C16—892no—
259C2×C16—1782no—
260C2×C16C22×D8912yes—
261#107—21no—
262#107—892no—
263#107—1784no—
264#107—1781no—
265#107C22×D8912yes—
266C24—891no—
267C24—3561no—
268#41—35616no—
269#41—3568no—
270#41—17816no—
271C2×Q8—22no—
272C2×Q8—24no—
273C2×Q8—41no—
274C2×Q8—42no—
275C2×D4—3568no—
276C2×D4—3564no—
277C2×D4—3561no—
278C2×D4—3562no—
279C2×D4—1782no—
280C2×D4—1784no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—891no—
284C22×C4—892no—
285C22×C4—894no—
286C22×C4—892no—
287C22×C4—894no—
288C22×C4—3568no—
289C22×C4—3564no—
290C22×C4—3564no—
291C22×C4—3561no—
292C22×C4—7124no—
293C22×C4D4×D8911yescharacteristic
294Q16—22no—
295Q16—24no—
296Q16C2×C4×D8914yescomplemented
297SD16—17816no—
298D8—894no—
299D8—1782no—
300D8—1784no—
301C2×C8—892no—
302C2×C8—894no—
303C2×C8—894no—
304C2×C8—894no—
305C2×C8—898no—
306C2×C8C2×C4×D8912yes—
307C2×C8D4×D8912yes—
308C2×C8D4×D8911yescharacteristic
309C2×C8C23×D8911yescharacteristic
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—3564no—
313C4⋊C4—3561no—
314C4⋊C4—1782no—
315C16—22no—
316C16—1782no—
317C23—894no—
318C23—892no—
319C23—3564no—
320C23—3562no—
321C23—1782no—
322C23—1782no—
323C23—7122no—
324C23—7122no—
325C23D8×D8911yescharacteristic
326Q8—24no—
327Q8—44no—
328Q8—42no—
329D4—35616no—
330D4—3564no—
331D4—3562no—
332D4—1784no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—894no—
338C2×C4—892no—
339C2×C4—894no—
340C2×C4—898no—
341C2×C4—894no—
342C2×C4—35616no—
343C2×C4—3562no—
344C2×C4—7128no—
345C2×C4—7122no—
346C2×C4C22⋊C4×D8912yes—
347C2×C4D8×D8911yescharacteristic
348C2×C4SD16×D8912yes—
349C2×C4C2×D4×D8911yescharacteristic
350C8—894no—
351C8C22⋊C4×D8912yes—
352C8C22×C4×D8911yescharacteristic
353C8C2×D4×D8911yescharacteristic
354C22—894no—
355C22—3564no—
356C22—1788no—
357C22—1782no—
358C22—1782no—
359C22—7128no—
360C22—7122no—
361C22—7122no—
362C22#102×D8912yes—
363C22#1915203512yes—
364C22#1915204012yes—
365C22C2×D8×D8911yescharacteristic
366C4—44no—
367C4—82no—
368C4—894no—
369C4—7122no—
370C4#102×D8912yes—
371C4C2×C22⋊C4×D8911yescharacteristic
372C4C2×SD16×D8911yescharacteristic
373C2—1784no—
374C2—7124no—
375C2#2602196314yesdirect product factor
376C2C2×#102×D8911yescharacteristic
377C2C2×#1915203511yescharacteristic
378C2C2×#1915204011yescharacteristic
subgroupG/H
centerC23D8×D89
commutatorC8×C89C23×C4
FrattiniC2×C8C23×D89
FittingC2×#358×C89C2
socleC23×C89C2×D8
prime radicalC22×#15668035C2
cosocleC2×C8×C89C24
hypercenterC2×#358D89
hypocenterC89C2×#2139
LCSG ▷ C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C22×#15667951C2semidirect
3. C2×#107×D89C2semidirect
4. #26021963C2direct (N × H)
5. C2×#19151402C2semidirect
6. C2×#19151400C2semidirect
7. C2×#19151398C2semidirect
8. C2×#358×C89C2semidirect
12. C2×#15668035C4semidirect
19. C2×#15667951C22semidirect
24. #107×D89C22semidirect
25. #19151402C22semidirect
26. #19151400C22semidirect
27. #19151398C22semidirect
31. #358×C89C22semidirect
43. #15668035C2×C4semidirect
48. C2×D712C2×C4semidirect
68. C2×Q16×C89C2×C4semidirect
100. D712C22×C4semidirect
119. Q16×C89C22×C4semidirect
184. C2×C89#2139semidirect
195. C2×#358D89semidirect
198. C89C2×#2139semidirect
219. #358C2×D89semidirect
237. C2×Q16C4×D89semidirect
296. Q16C2×C4×D89semidirect
375. C2#26021963direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#156680352
C22×#156679512
C2×#107×D892
#260219632
C2×#191514022
C2×#191514002
C2×#191513982
C2×#358×C892
C2×#213989