Finite Group Databasebeta

← C2×#23782338 #35228030

Subgroups — C2×#23782338 #35228030

Order 20864.

1328 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782338C2116yesmaximal, direct product factor
2C2×#19104730C211yesmaximal, characteristic, complemented
3C2×#19104730C211yesmaximal, characteristic, complemented
4C2×#19104721C211yesmaximal, characteristic, complemented
5C2×#19104719C211yesmaximal, characteristic, complemented
6C2×#19104717C211yesmaximal, characteristic, complemented
7C2×#19104715C211yesmaximal, characteristic, complemented
8C2×#19104712C211yesmaximal, characteristic, complemented
9C2×#19104703C211yesmaximal, characteristic
10C2×D4×Dic163C211yesmaximal, characteristic, complemented
11C2×(C22⋊D163)⋊C4C211yesmaximal, characteristic, complemented
12C2×#19104694C211yesmaximal, characteristic, complemented
13C2×#19104693C211yesmaximal, characteristic, complemented
14C22×(C2×D163)⋊C4C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×D163C211yesmaximal, characteristic, complemented
16C2×#123×C163C211yesmaximal, characteristic, complemented
17C24×D163C2211yescharacteristic
18C22×Dic326C2211yescharacteristic, complemented
19C22×C22⋊D163C2211yescharacteristic
20C22×C22⋊D163C2211yescharacteristic
21C23×Dic163C2211yescharacteristic
22C23×Dic163C2211yescharacteristic, complemented
23C22×C4×D163C2211yescharacteristic
24C22×C4×D163C2211yescharacteristic
25#19104730C2218yescomplemented
26#19104730C2218yescomplemented
27#19104721C2218yescomplemented
28#19104719C2218yescomplemented
29#19104717C2218yescomplemented
30#19104715C2218yescomplemented
31#19104712C2218yescomplemented
32#19104703C2218yes—
33D4×Dic163C2218yescomplemented
34(C22⋊D163)⋊C4C2218yescomplemented
35#19104694C2218yescomplemented
36#19104693C2218yescomplemented
37C2×C4⋊Dic163C2211yescharacteristic, complemented
38C2×C4⋊Dic163C2211yescharacteristic, complemented
39C2×C4⋊Dic163C2211yescharacteristic, complemented
40C2×C4⋊Dic163C2211yescharacteristic, complemented
41C2×Dic163⋊C4C2211yescharacteristic, complemented
42C2×Dic163⋊C4C2211yescharacteristic, complemented
43C2×C22⋊Dic163C2211yescharacteristic
44C2×C22⋊Dic163C2211yescharacteristic
45C2×C22⋊Dic163C2211yescharacteristic, complemented
46C2×(C2×D163)⋊C4C2211yescharacteristic
47C2×(C2×D163)⋊C4C2211yescharacteristic
48C2×(C2×D163)⋊C4C2211yescharacteristic
49C2×(C2×D163)⋊C4C2211yescharacteristic
50C2×(C2×D163)⋊C4C2211yescharacteristic
51C2×(C2×D163)⋊C4C2211yescharacteristic
52C2×(C2×D163)⋊C4C2211yescharacteristic
53C2×(C2×D163)⋊C4C2211yescharacteristic
54C2×(C2×D163)⋊C4C2218yescomplemented
55C22⋊C4×D163C2218yescomplemented
56C2×C4×Dic163C2211yescharacteristic, complemented
57C2×C4×Dic163C2211yescharacteristic, complemented
58C2×C4×Dic163C2211yescharacteristic, complemented
59C22×D4×C163C2211yescharacteristic
60C23×C4×C163C2211yescharacteristic
61#123×C163C2218yescomplemented
62C2×C4⋊C4×C163C2211yescharacteristic, complemented
63C2×C4⋊C4×C163C2211yescharacteristic, complemented
64C2×C22⋊C4×C163C2211yescharacteristic
65C2×C22⋊C4×C163C2211yescharacteristic, complemented
66C2×C22⋊C4×C163C2211yescharacteristic, complemented
67C23×D163—24no—
68C23×D163—24no—
69C23×D163—42no—
70C23×D163C2311yescharacteristic
71C23×D163C2314yes—
72C23×D163C2311yescharacteristic
73C2×Dic326—42no—
74C2×Dic326C2314yescomplemented
75C2×C22⋊D163—24no—
76C2×C22⋊D163—42no—
77C2×C22⋊D163C2314yes—
78C2×C22⋊D163C2314yes—
79C22×Dic163—42no—
80C22×Dic163—42no—
81C22×Dic163C2311yescharacteristic
82C22×Dic163C2311yescharacteristic
83C22×Dic163C2311yescharacteristic
84C22×Dic163C2311yescharacteristic
85C22×Dic163C2311yescharacteristic
86C22×Dic163C2311yescharacteristic
87C22×Dic163C2314yes—
88C22×Dic163C2314yescomplemented
89C2×C4×D163—24no—
90C2×C4×D163—42no—
91C2×C4×D163C2314yes—
92C2×C4×D163C2314yes—
93C4⋊Dic163C2314yescomplemented
94C4⋊Dic163C2314yescomplemented
95C4⋊Dic163C2314yescomplemented
96C4⋊Dic163C2314yescomplemented
97Dic163⋊C4C2314yescomplemented
98Dic163⋊C4C2314yescomplemented
99C22⋊Dic163C2314yes—
100C22⋊Dic163C2314yes—
101C22⋊Dic163C2314yescomplemented
102(C2×D163)⋊C4C2314yes—
103(C2×D163)⋊C4C2314yes—
104(C2×D163)⋊C4C2314yes—
105(C2×D163)⋊C4C2314yes—
106(C2×D163)⋊C4C2314yes—
107(C2×D163)⋊C4C2314yes—
108(C2×D163)⋊C4C2314yes—
109(C2×D163)⋊C4C2314yes—
110C4×Dic163C2314yescomplemented
111C4×Dic163C2314yescomplemented
112C4×Dic163C2314yescomplemented
113C24×C163C2311yescharacteristic
114C24×C163C2311yescharacteristic
115C2×D4×C163—24no—
116C2×D4×C163C2314yes—
117C22×C4×C163—24no—
118C22×C4×C163C2311yescharacteristic
119C22×C4×C163C2311yescharacteristic
120C22×C4×C163C2311yescharacteristic
121C22×C4×C163C2311yescharacteristic
122C22×C4×C163C2311yescharacteristic
123C22×C4×C163C2314yes—
124C4⋊C4×C163C2314yescomplemented
125C4⋊C4×C163C2314yescomplemented
126C22⋊C4×C163C2314yes—
127C22⋊C4×C163C2314yescomplemented
128C22⋊C4×C163C2314yescomplemented
129C22×D163—22no—
130C22×D163—22no—
131C22×D163—22no—
132C22×D163—28no—
133C22×D163—22no—
134C22×D163—22no—
135C22×D163—28no—
136C22×D163—44no—
137C22×D163—416no—
138C22×D163#4114yes—
139C22×D163C2412yes—
140C22×D163C2412yes—
141Dic326—44no—
142C22⋊D163—28no—
143C22⋊D163—44no—
144C2×Dic163—22no—
145C2×Dic163—22no—
146C2×Dic163—22no—
147C2×Dic163—22no—
148C2×Dic163—22no—
149C2×Dic163—22no—
150C2×Dic163—44no—
151C2×Dic163—44no—
152C2×Dic163C2412yes—
153C2×Dic163C2412yes—
154C2×Dic163C2412yes—
155C2×Dic163C2412yes—
156C2×Dic163C2412yes—
157C2×Dic163C2412yes—
158C4×D163—28no—
159C4×D163—44no—
160C23×C163—22no—
161C23×C163—22no—
162C23×C163—22no—
163C23×C163—22no—
164C23×C163—22no—
165C23×C163#4114yes—
166C23×C163C2412yes—
167C23×C163C2412yes—
168C23×C163C2411yescharacteristic
169D4×C163—28no—
170C2×C4×C163—28no—
171C2×C4×C163—22no—
172C2×C4×C163—22no—
173C2×C4×C163—22no—
174C2×C4×C163—22no—
175C2×C4×C163—22no—
176C2×C4×C163C2412yes—
177C2×C4×C163C2412yes—
178C2×C4×C163C2412yes—
179C2×C4×C163C2412yes—
180C2×C4×C163C2412yes—
181C22×C163—28no—
182C22×C163—22no—
183C22×C163—22no—
184C22×C163—22no—
185C22×C163—22no—
186C22×C163—22no—
187C22×C163—44no—
188C22×C163C2×#4112yes—
189C22×C163C2×#4114yes—
190C22×C163C2×#4112yes—
191C22×C163H(5,𝔽2)12yes—
192C22×C163C2511yescharacteristic
193C2×D163—28no—
194C2×D163—22no—
195C2×D163—22no—
196C2×D163—22no—
197C2×D163—22no—
198C2×D163—22no—
199C2×D163—416no—
200C2×D163—44no—
201C2×D163C2×#4114yes—
202C4×C163—22no—
203C4×C163—22no—
204C4×C163—22no—
205C4×C163—22no—
206C4×C163—22no—
207Dic163—22no—
208Dic163—22no—
209Dic163—22no—
210Dic163—22no—
211Dic163—22no—
212Dic163—22no—
213C2×C163—24no—
214C2×C163—42no—
215C2×C163#55114yescomplemented
216C2×C163C22×#4111yescharacteristic
217C2×C163C22×#4111yescharacteristic
218C2×C163C2×H(5,𝔽2)11yescharacteristic
219D163—24no—
220D163—42no—
221C163C2×#55111yescharacteristic, complemented, Sylow
222C2×#551—1631nomaximal, Sylow
223#551—16316no—
224C2×#126—1631no—
225C2×#126—1631no—
226C2×#124—1631no—
227C2×#123—1631no—
228C2×#123—1631no—
229C2×#123D16311yescharacteristic, complemented
230C2×C22⋊Q8—1631no—
231C2×C22⋊Q8—1631no—
232C2×#120—1631no—
233C2×C4×D4—1631no—
234C2×C4×D4—1631no—
235C2×#117—1631no—
236C2×#117—1631no—
237C22×C22⋊C4—1631no—
238C22×C22⋊C4—1631no—
239C25—1631no—
240C22×Q8—1631no—
241C22×D4—1631no—
242C22×D4—1631no—
243C22×D4C2×D16311yescharacteristic
244C23×C4—1631no—
245C23×C4—1631no—
246C23×C4—1631no—
247C23×C4—1631no—
248C23×C4C2×D16311yescharacteristic
249#126—1638no—
250#126—1638no—
251#124—1638no—
252#123—1638no—
253#123—1638no—
254#123C2×D16318yescomplemented
255C22⋊Q8—1638no—
256C22⋊Q8—1638no—
257#120—1638no—
258C4×D4—1638no—
259C4×D4—1638no—
260#117—1638no—
261#117—1638no—
262C2×C4⋊C4—1631no—
263C2×C4⋊C4—1631no—
264C2×C4⋊C4—1631no—
265C2×C4⋊C4—1631no—
266C2×C4⋊C4—1631no—
267C2×C4⋊C4—1631no—
268C2×C4⋊C4C2×D16311yescharacteristic, complemented
269C2×C4⋊C4C2×D16311yescharacteristic, complemented
270C2×C22⋊C4—1631no—
271C2×C22⋊C4—1631no—
272C2×C22⋊C4—1631no—
273C2×C22⋊C4—1631no—
274C2×C22⋊C4—1631no—
275C2×C22⋊C4—1631no—
276C2×C22⋊C4—1631no—
277C2×C22⋊C4—1631no—
278C2×C22⋊C4—1631no—
279C2×C22⋊C4—1638no—
280C2×C22⋊C4—1631no—
281C2×C22⋊C4—1631no—
282C2×C22⋊C4—1638no—
283C2×C22⋊C4C2×D16311yescharacteristic
284C2×C22⋊C4C2×D16311yescharacteristic, complemented
285C2×C22⋊C4C2×D16311yescharacteristic, complemented
286C2×C42—1631no—
287C2×C42—1631no—
288C2×C42—1631no—
289C24—3264no—
290C24—3264no—
291C24—6522no—
292C24—1631no—
293C24—1634no—
294C24—1631no—
295C24C22×D16311yescharacteristic
296C24C22×D16311yescharacteristic
297C2×Q8—6522no—
298C2×Q8—1634no—
299C2×D4—24no—
300C2×D4—3264no—
301C2×D4—6522no—
302C2×D4—1634no—
303C2×D4—1634no—
304C2×D4C22×D16314yes—
305C22×C4—24no—
306C22×C4—3264no—
307C22×C4—6522no—
308C22×C4—6522no—
309C22×C4—6522no—
310C22×C4—1631no—
311C22×C4—1631no—
312C22×C4—1631no—
313C22×C4—1631no—
314C22×C4—1631no—
315C22×C4—1631no—
316C22×C4—1634no—
317C22×C4—1634no—
318C22×C4—1634no—
319C22×C4—1634no—
320C22×C4C22×D16314yes—
321C22×C4C22×D16311yescharacteristic
322C22×C4C22×D16311yescharacteristic
323C22×C4C22×D16311yescharacteristic
324C22×C4C22×D16311yescharacteristic
325C22×C4C22×D16311yescharacteristic
326C4⋊C4—1634no—
327C4⋊C4—1634no—
328C4⋊C4—1634no—
329C4⋊C4—1634no—
330C4⋊C4—1634no—
331C4⋊C4—1634no—
332C4⋊C4C22×D16314yescomplemented
333C4⋊C4C22×D16314yescomplemented
334C22⋊C4—1634no—
335C22⋊C4—1634no—
336C22⋊C4—1634no—
337C22⋊C4—1634no—
338C22⋊C4—1634no—
339C22⋊C4—1634no—
340C22⋊C4—1634no—
341C22⋊C4—1634no—
342C22⋊C4—1634no—
343C22⋊C4—1634no—
344C22⋊C4—1634no—
345C22⋊C4C22×D16314yes—
346C22⋊C4C22×D16314yescomplemented
347C22⋊C4C22×D16314yescomplemented
348C42—1634no—
349C42—1634no—
350C42—1634no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—3268no—
357C23—3262no—
358C23—3262no—
359C23—3262no—
360C23—3268no—
361C23—3262no—
362C23—3262no—
363C23—6524no—
364C23—65216no—
365C23—1632no—
366C23—1634no—
367C23—1632no—
368C23#1457969814yes—
369C23C23×D16312yes—
370C23C23×D16312yes—
371C23C23×D16311yescharacteristic
372Q8—6524no—
373D4—28no—
374D4—3268no—
375D4—6524no—
376C2×C4—22no—
377C2×C4—28no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—3268no—
383C2×C4—3262no—
384C2×C4—3262no—
385C2×C4—3262no—
386C2×C4—3262no—
387C2×C4—3262no—
388C2×C4—3262no—
389C2×C4—6524no—
390C2×C4—6524no—
391C2×C4—6524no—
392C2×C4—1632no—
393C2×C4—1632no—
394C2×C4—1632no—
395C2×C4—1632no—
396C2×C4—1632no—
397C2×C4—1632no—
398C2×C4C23×D16312yes—
399C2×C4C23×D16312yes—
400C2×C4C23×D16312yes—
401C2×C4C23×D16312yes—
402C2×C4C23×D16312yes—
403C22—22no—
404C22—22no—
405C22—28no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—44no—
410C22—3262no—
411C22—3262no—
412C22—3268no—
413C22—3262no—
414C22—3262no—
415C22—3262no—
416C22—65216no—
417C22—6524no—
418C22—1634no—
419C22#41×D16312yes—
420C22C2×#1457969814yes—
421C22C2×#1457969812yes—
422C22#1910478112yes—
423C22C24×D16311yescharacteristic
424C4—22no—
425C4—22no—
426C4—22no—
427C4—22no—
428C4—22no—
429C4—3262no—
430C4—3262no—
431C4—3262no—
432C4—3262no—
433C4—3262no—
434C4—3262no—
435C2—24no—
436C2—42no—
437C2—3264no—
438C2—6522no—
439C2#2378233814yesdirect product factor
440C2C2×#41×D16311yescharacteristic
441C2C22×#1457969811yescharacteristic
442C2C2×#1910478111yescharacteristic
subgroupG/H
centerC23C23×D163
commutator, cosocleC22×C163C25
FrattiniC22C24×D163
FittingC2×#123×C163C2
socleC23×C163C24
prime radicalC2×#19104703C2
hypercenterC2×#123D163
hypocenterC163C2×#551
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #23782338C2direct (N × H)
2. C2×#19104730C2semidirect
3. C2×#19104730C2semidirect
4. C2×#19104721C2semidirect
5. C2×#19104719C2semidirect
6. C2×#19104717C2semidirect
7. C2×#19104715C2semidirect
8. C2×#19104712C2semidirect
10. C2×D4×Dic163C2semidirect
11. C2×(C22⋊D163)⋊C4C2semidirect
12. C2×#19104694C2semidirect
13. C2×#19104693C2semidirect
14. C22×(C2×D163)⋊C4C2semidirect
15. C2×C22⋊C4×D163C2semidirect
16. C2×#123×C163C2semidirect
18. C22×Dic326C22semidirect
22. C23×Dic163C22semidirect
25. #19104730C22semidirect
26. #19104730C22semidirect
27. #19104721C22semidirect
28. #19104719C22semidirect
29. #19104717C22semidirect
30. #19104715C22semidirect
31. #19104712C22semidirect
33. D4×Dic163C22semidirect
34. (C22⋊D163)⋊C4C22semidirect
35. #19104694C22semidirect
36. #19104693C22semidirect
37. C2×C4⋊Dic163C22semidirect
38. C2×C4⋊Dic163C22semidirect
39. C2×C4⋊Dic163C22semidirect
40. C2×C4⋊Dic163C22semidirect
41. C2×Dic163⋊C4C22semidirect
42. C2×Dic163⋊C4C22semidirect
45. C2×C22⋊Dic163C22semidirect
54. C2×(C2×D163)⋊C4C22semidirect
55. C22⋊C4×D163C22semidirect
56. C2×C4×Dic163C22semidirect
57. C2×C4×Dic163C22semidirect
58. C2×C4×Dic163C22semidirect
61. #123×C163C22semidirect
62. C2×C4⋊C4×C163C22semidirect
63. C2×C4⋊C4×C163C22semidirect
65. C2×C22⋊C4×C163C22semidirect
66. C2×C22⋊C4×C163C22semidirect
74. C2×Dic326C23semidirect
88. C22×Dic163C23semidirect
93. C4⋊Dic163C23semidirect
94. C4⋊Dic163C23semidirect
95. C4⋊Dic163C23semidirect
96. C4⋊Dic163C23semidirect
97. Dic163⋊C4C23semidirect
98. Dic163⋊C4C23semidirect
101. C22⋊Dic163C23semidirect
110. C4×Dic163C23semidirect
111. C4×Dic163C23semidirect
112. C4×Dic163C23semidirect
124. C4⋊C4×C163C23semidirect
125. C4⋊C4×C163C23semidirect
127. C22⋊C4×C163C23semidirect
128. C22⋊C4×C163C23semidirect
215. C2×C163#551semidirect
221. C163C2×#551semidirect
229. C2×#123D163semidirect
254. #123C2×D163semidirect
268. C2×C4⋊C4C2×D163semidirect
269. C2×C4⋊C4C2×D163semidirect
284. C2×C22⋊C4C2×D163semidirect
285. C2×C22⋊C4C2×D163semidirect
332. C4⋊C4C22×D163semidirect
333. C4⋊C4C22×D163semidirect
346. C22⋊C4C22×D163semidirect
347. C22⋊C4C22×D163semidirect
439. C2#23782338direct (N × H)

Maximal subgroups

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

subgroupindex
#237823382
C2×#191047302
C2×#191047212
C2×#191047192
C2×#191047172
C2×#191047152
C2×#191047122
C2×#191047032
C2×D4×Dic1632
C2×(C22⋊D163)⋊C42
C2×#191046942
C2×#191046932
C22×(C2×D163)⋊C42
C2×C22⋊C4×D1632
C2×#123×C1632
C2×#551163