Finite Group Databasebeta

← C2×#23782352 #35228045

Subgroups — C2×#23782352 #35228045

Order 20864.

1124 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782352C2116yesmaximal, direct product factor
2C2×#19104728C211yesmaximal, characteristic, complemented
3C2×#19104728C211yesmaximal, characteristic, complemented
4C2×#19104726C211yesmaximal, characteristic, complemented
5C2×#19104725C211yesmaximal, characteristic, complemented
6C2×#19104725C211yesmaximal, characteristic, complemented
7C2×#19104716C211yesmaximal, characteristic
8C2×#19104712C211yesmaximal, characteristic, complemented
9C2×#19104712C211yesmaximal, characteristic, complemented
10C2×#19104700C211yesmaximal, characteristic, complemented
11C2×D4×Dic163C211yesmaximal, characteristic
12C2×#19104694C211yesmaximal, characteristic, complemented
13C2×#19104691C211yesmaximal, characteristic, complemented
14C2×#19104691C211yesmaximal, characteristic, complemented
15C22×Dic163⋊C4C211yesmaximal, characteristic, complemented
16C2×#123×C163C211yesmaximal, characteristic
17C22×Dic326C2211yescharacteristic
18C23×Dic163C2211yescharacteristic
19C23×Dic163C2211yescharacteristic
20C23×Dic163C2211yescharacteristic
21#19104728C2218yescomplemented
22#19104728C2218yescomplemented
23#19104726C2218yescomplemented
24#19104725C2218yescomplemented
25#19104725C2218yescomplemented
26#19104716C2218yes—
27#19104712C2218yescomplemented
28#19104712C2218yescomplemented
29#19104700C2218yescomplemented
30D4×Dic163C2218yes—
31#19104694C2218yescomplemented
32#19104691C2218yescomplemented
33#19104691C2218yescomplemented
34C2×C4⋊Dic163C2211yescharacteristic
35C2×C4⋊Dic163C2211yescharacteristic
36C2×C4⋊Dic163C2211yescharacteristic
37C2×C4⋊Dic163C2211yescharacteristic
38C2×Dic163⋊C4C2211yescharacteristic
39C2×Dic163⋊C4C2211yescharacteristic
40C2×Dic163⋊C4C2211yescharacteristic
41C2×Dic163⋊C4C2211yescharacteristic
42C2×Dic163⋊C4C2211yescharacteristic
43C2×Dic163⋊C4C2211yescharacteristic
44C2×Dic163⋊C4C2211yescharacteristic
45C2×Dic163⋊C4C2211yescharacteristic
46C2×Dic163⋊C4C2211yescharacteristic
47C2×Dic163⋊C4C2211yescharacteristic
48C2×Dic163⋊C4C2218yescomplemented
49C2×C22⋊Dic163C2211yescharacteristic
50C2×C22⋊Dic163C2211yescharacteristic
51C2×C22⋊Dic163C2211yescharacteristic
52C2×C22⋊Dic163C2211yescharacteristic
53C2×C22⋊Dic163C2211yescharacteristic
54C2×C4×Dic163C2211yescharacteristic
55C2×C4×Dic163C2211yescharacteristic
56C2×C4×Dic163C2211yescharacteristic
57C2×C4×Dic163C2211yescharacteristic
58C2×C4×Dic163C2211yescharacteristic
59C22×D4×C163C2211yescharacteristic
60C23×C4×C163C2211yescharacteristic
61#123×C163C2218yes—
62C2×C4⋊C4×C163C2211yescharacteristic
63C2×C4⋊C4×C163C2211yescharacteristic
64C2×C22⋊C4×C163C2211yescharacteristic
65C2×C22⋊C4×C163C2211yescharacteristic
66C2×C22⋊C4×C163C2211yescharacteristic
67C2×Dic326—24no—
68C2×Dic326C2314yes—
69C22×Dic163—24no—
70C22×Dic163—24no—
71C22×Dic163—24no—
72C22×Dic163C2311yescharacteristic
73C22×Dic163C2311yescharacteristic
74C22×Dic163C2311yescharacteristic
75C22×Dic163C2311yescharacteristic
76C22×Dic163C2314yes—
77C22×Dic163C2314yes—
78C22×Dic163C2314yes—
79C22×Dic163C2311yescharacteristic
80C22×Dic163C2311yescharacteristic
81C22×Dic163C2311yescharacteristic
82C22×Dic163C2311yescharacteristic
83C4⋊Dic163C2314yes—
84C4⋊Dic163C2314yes—
85C4⋊Dic163C2314yes—
86C4⋊Dic163C2314yes—
87Dic163⋊C4C2314yes—
88Dic163⋊C4C2314yes—
89Dic163⋊C4C2314yes—
90Dic163⋊C4C2314yes—
91Dic163⋊C4C2314yes—
92Dic163⋊C4C2314yes—
93Dic163⋊C4C2314yes—
94Dic163⋊C4C2314yes—
95Dic163⋊C4C2314yes—
96Dic163⋊C4C2314yes—
97C22⋊Dic163C2314yes—
98C22⋊Dic163C2314yes—
99C22⋊Dic163C2314yes—
100C22⋊Dic163C2314yes—
101C22⋊Dic163C2314yes—
102C4×Dic163C2314yes—
103C4×Dic163C2314yes—
104C4×Dic163C2314yes—
105C4×Dic163C2314yes—
106C4×Dic163C2314yes—
107C24×C163C2311yescharacteristic
108C24×C163C2311yescharacteristic
109C2×D4×C163—24no—
110C2×D4×C163C2314yes—
111C22×C4×C163—24no—
112C22×C4×C163C2311yescharacteristic
113C22×C4×C163C2311yescharacteristic
114C22×C4×C163C2311yescharacteristic
115C22×C4×C163C2311yescharacteristic
116C22×C4×C163C2311yescharacteristic
117C22×C4×C163C2314yes—
118C4⋊C4×C163C2314yes—
119C4⋊C4×C163C2314yes—
120C22⋊C4×C163C2314yes—
121C22⋊C4×C163C2314yes—
122C22⋊C4×C163C2314yes—
123Dic326—28no—
124C2×Dic163—22no—
125C2×Dic163—22no—
126C2×Dic163—28no—
127C2×Dic163—22no—
128C2×Dic163—22no—
129C2×Dic163—22no—
130C2×Dic163—22no—
131C2×Dic163—22no—
132C2×Dic163—28no—
133C2×Dic163—28no—
134C2×Dic163#4114yes—
135C2×Dic163C2412yes—
136C2×Dic163C2412yes—
137C2×Dic163C2412yes—
138C2×Dic163C2412yes—
139C2×Dic163C2412yes—
140C2×Dic163C2412yes—
141C2×Dic163C2412yes—
142C2×Dic163C2412yes—
143C23×C163—22no—
144C23×C163—22no—
145C23×C163—22no—
146C23×C163—22no—
147C23×C163—22no—
148C23×C163#4114yes—
149C23×C163C2412yes—
150C23×C163C2412yes—
151C23×C163C2411yescharacteristic
152D4×C163—28no—
153C2×C4×C163—28no—
154C2×C4×C163—22no—
155C2×C4×C163—22no—
156C2×C4×C163—22no—
157C2×C4×C163—22no—
158C2×C4×C163—22no—
159C2×C4×C163C2412yes—
160C2×C4×C163C2412yes—
161C2×C4×C163C2412yes—
162C2×C4×C163C2412yes—
163C2×C4×C163C2412yes—
164C22×C163—28no—
165C22×C163—22no—
166C22×C163—22no—
167C22×C163—22no—
168C22×C163—22no—
169C22×C163—22no—
170C22×C163—44no—
171C22×C163C2×#4112yes—
172C22×C163C2×#4114yes—
173C22×C163C2×#4112yes—
174C22×C1632−1+412yes—
175C22×C163C2511yescharacteristic
176C4×C163—22no—
177C4×C163—22no—
178C4×C163—22no—
179C4×C163—22no—
180C4×C163—22no—
181Dic163—22no—
182Dic163—22no—
183Dic163—22no—
184Dic163—22no—
185Dic163—22no—
186Dic163—22no—
187Dic163—22no—
188Dic163C2×#4114yes—
189C2×C163—24no—
190C2×C163—42no—
191C2×C163#55214yescomplemented
192C2×C163C22×#4111yescharacteristic
193C2×C163C22×#4111yescharacteristic
194C2×C163C2×2−1+411yescharacteristic
195C163C2×#55211yescharacteristic, complemented, Sylow
196C2×#552—1631nomaximal, Sylow
197#552—16316no—
198C2×#126—1631no—
199C2×#126—1631no—
200C2×#125—1631no—
201C2×#125—1631no—
202C2×#125—1631no—
203C2×#123—1631no—
204C2×#123D16311yescharacteristic
205C2×C22⋊Q8—1631no—
206C2×C22⋊Q8—1631no—
207C2×C4×Q8—1631no—
208C2×C4×D4—1631no—
209C2×#117—1631no—
210C2×#117—1631no—
211C2×#117—1631no—
212C22×C4⋊C4—1631no—
213C22×Q8—1631no—
214C22×D4C2×D16311yescharacteristic
215C23×C4—1631no—
216C23×C4—1631no—
217C23×C4—1631no—
218C23×C4C2×D16311yescharacteristic
219#126—1638no—
220#126—1638no—
221#125—1638no—
222#125—1638no—
223#125—1638no—
224#123—1638no—
225#123C2×D16318yes—
226C22⋊Q8—1638no—
227C22⋊Q8—1638no—
228C4×Q8—1638no—
229C4×D4—1638no—
230#117—1638no—
231#117—1638no—
232#117—1638no—
233C2×C4⋊C4—1631no—
234C2×C4⋊C4—1631no—
235C2×C4⋊C4—1631no—
236C2×C4⋊C4—1631no—
237C2×C4⋊C4—1638no—
238C2×C4⋊C4—1631no—
239C2×C4⋊C4—1631no—
240C2×C4⋊C4—1631no—
241C2×C4⋊C4—1631no—
242C2×C4⋊C4—1631no—
243C2×C4⋊C4—1631no—
244C2×C4⋊C4—1631no—
245C2×C4⋊C4—1631no—
246C2×C4⋊C4—1631no—
247C2×C4⋊C4—1631no—
248C2×C4⋊C4C2×D16311yescharacteristic
249C2×C4⋊C4C2×D16311yescharacteristic
250C2×C22⋊C4—1631no—
251C2×C22⋊C4—1631no—
252C2×C22⋊C4—1631no—
253C2×C22⋊C4—1631no—
254C2×C22⋊C4—1631no—
255C2×C22⋊C4C2×D16311yescharacteristic
256C2×C22⋊C4C2×D16311yescharacteristic
257C2×C22⋊C4C2×D16311yescharacteristic
258C2×C42—1631no—
259C2×C42—1631no—
260C2×C42—1631no—
261C2×C42—1631no—
262C2×C42—1631no—
263C24C22×D16311yescharacteristic
264C24C22×D16311yescharacteristic
265C2×Q8—3264no—
266C2×Q8—1634no—
267C2×D4—24no—
268C2×D4C22×D16314yes—
269C22×C4—24no—
270C22×C4—3264no—
271C22×C4—3264no—
272C22×C4—3264no—
273C22×C4—1634no—
274C22×C4—1634no—
275C22×C4—1634no—
276C22×C4—1631no—
277C22×C4—1631no—
278C22×C4—1631no—
279C22×C4—1631no—
280C22×C4—1631no—
281C22×C4—1631no—
282C22×C4—1631no—
283C22×C4—1631no—
284C22×C4C22×D16314yes—
285C22×C4C22×D16311yescharacteristic
286C22×C4C22×D16311yescharacteristic
287C22×C4C22×D16311yescharacteristic
288C22×C4C22×D16311yescharacteristic
289C22×C4C22×D16311yescharacteristic
290C4⋊C4—1634no—
291C4⋊C4—1634no—
292C4⋊C4—1634no—
293C4⋊C4—1634no—
294C4⋊C4—1634no—
295C4⋊C4—1634no—
296C4⋊C4—1634no—
297C4⋊C4—1634no—
298C4⋊C4—1634no—
299C4⋊C4—1634no—
300C4⋊C4—1634no—
301C4⋊C4—1634no—
302C4⋊C4—1634no—
303C4⋊C4—1634no—
304C4⋊C4C22×D16314yes—
305C4⋊C4C22×D16314yes—
306C22⋊C4—1634no—
307C22⋊C4—1634no—
308C22⋊C4—1634no—
309C22⋊C4—1634no—
310C22⋊C4—1634no—
311C22⋊C4C22×D16314yes—
312C22⋊C4C22×D16314yes—
313C22⋊C4C22×D16314yes—
314C42—1634no—
315C42—1634no—
316C42—1634no—
317C42—1634no—
318C42—1634no—
319C23—22no—
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23#1457969814yes—
325C23C23×D16312yes—
326C23C23×D16312yes—
327C23C23×D16311yescharacteristic
328Q8—3268no—
329D4—28no—
330C2×C4—22no—
331C2×C4—28no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—3262no—
337C2×C4—3262no—
338C2×C4—3262no—
339C2×C4—3268no—
340C2×C4—3262no—
341C2×C4—3262no—
342C2×C4—3262no—
343C2×C4—3262no—
344C2×C4—3268no—
345C2×C4—3268no—
346C2×C4—1632no—
347C2×C4—1632no—
348C2×C4—1632no—
349C2×C4—1632no—
350C2×C4—1632no—
351C2×C4—1632no—
352C2×C4—1632no—
353C2×C4—1634no—
354C2×C4—1632no—
355C2×C4C23×D16312yes—
356C2×C4C23×D16312yes—
357C2×C4C23×D16312yes—
358C2×C4C23×D16312yes—
359C2×C4C23×D16312yes—
360C22—22no—
361C22—22no—
362C22—28no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—44no—
367C22#41×D16312yes—
368C22C2×#1457969814yes—
369C22C2×#1457969812yes—
370C22#1910478212yes—
371C22C24×D16311yescharacteristic
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—22no—
377C4—3262no—
378C4—3262no—
379C4—3262no—
380C4—3262no—
381C4—3262no—
382C4—3262no—
383C4—3262no—
384C4—1634no—
385C2—24no—
386C2—42no—
387C2#2378235214yesdirect product factor
388C2C2×#41×D16311yescharacteristic
389C2C22×#1457969811yescharacteristic
390C2C2×#1910478211yescharacteristic
subgroupG/H
centerC23C23×D163
commutator, cosocleC22×C163C25
FrattiniC22C24×D163
FittingC2×#123×C163C2
socleC23×C163C24
prime radicalC22×D4×C163C22
hypercenterC2×#123D163
hypocenterC163C2×#552
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #23782352C2direct (N × H)
2. C2×#19104728C2semidirect
3. C2×#19104728C2semidirect
4. C2×#19104726C2semidirect
5. C2×#19104725C2semidirect
6. C2×#19104725C2semidirect
8. C2×#19104712C2semidirect
9. C2×#19104712C2semidirect
10. C2×#19104700C2semidirect
12. C2×#19104694C2semidirect
13. C2×#19104691C2semidirect
14. C2×#19104691C2semidirect
15. C22×Dic163⋊C4C2semidirect
21. #19104728C22semidirect
22. #19104728C22semidirect
23. #19104726C22semidirect
24. #19104725C22semidirect
25. #19104725C22semidirect
27. #19104712C22semidirect
28. #19104712C22semidirect
29. #19104700C22semidirect
31. #19104694C22semidirect
32. #19104691C22semidirect
33. #19104691C22semidirect
48. C2×Dic163⋊C4C22semidirect
191. C2×C163#552semidirect
195. C163C2×#552semidirect
387. C2#23782352direct (N × H)

Maximal subgroups

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

subgroupindex
#237823522
C2×#191047282
C2×#191047262
C2×#191047252
C2×#191047162
C2×#191047122
C2×#191047002
C2×D4×Dic1632
C2×#191046942
C2×#191046912
C22×Dic163⋊C42
C2×#123×C1632
C2×#552163