Finite Group Databasebeta

← C2×#23782274 #35227901

Subgroups — C2×#23782274 #35227901

Order 20864.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23782274C2116yesmaximal, direct product factor
2C2×#19104734C211yesmaximal, characteristic, complemented
3C2×#19104730C211yesmaximal, characteristic
4C2×#19104730C211yesmaximal, characteristic
5C2×#19104730C211yesmaximal, characteristic
6C2×#19104729C211yesmaximal, characteristic
7C2×#19104726C211yesmaximal, characteristic, complemented
8C2×#19104725C211yesmaximal, characteristic, complemented
9C2×#19104725C211yesmaximal, characteristic, complemented
10C2×#19104725C211yesmaximal, characteristic, complemented
11C2×#19104713C211yesmaximal, characteristic
12C2×#19104713C211yesmaximal, characteristic
13C2×C4×Dic326C211yesmaximal, characteristic, complemented
14C2×#19104700C211yesmaximal, characteristic, complemented
15C2×#19104693C211yesmaximal, characteristic
16C2×#125×C163C211yesmaximal, characteristic, complemented
17C22×Dic326C2211yescharacteristic
18C22×Dic326C2211yescharacteristic
19C22×C4×D163C2211yescharacteristic
20#19104734C2218yescomplemented
21#19104730C2218yes—
22#19104730C2218yes—
23#19104730C2218yes—
24#19104729C2218yes—
25#19104726C2218yescomplemented
26#19104725C2218yescomplemented
27#19104725C2218yescomplemented
28#19104725C2218yescomplemented
29#19104713C2218yes—
30#19104713C2218yes—
31C4×Dic326C2218yescomplemented
32#19104700C2218yescomplemented
33#19104693C2218yes—
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×(C2×D163)⋊C4C2211yescharacteristic
49C2×(C2×D163)⋊C4C2211yescharacteristic
50C2×(C2×D163)⋊C4C2211yescharacteristic
51C2×(C2×D163)⋊C4C2211yescharacteristic
52C2×(C2×D163)⋊C4C2211yescharacteristic
53C2×(C2×D163)⋊C4C2211yescharacteristic
54C2×C4×Dic163C2211yescharacteristic
55C2×C4×Dic163C2211yescharacteristic
56C2×C4×Dic163C2211yescharacteristic
57C2×C4×Dic163C2211yescharacteristic
58C2×C4×Dic163C2211yescharacteristic
59#125×C163C2218yescomplemented
60C2×C4⋊C4×C163C2211yescharacteristic
61C2×C4⋊C4×C163C2211yescharacteristic
62C2×C4⋊C4×C163C2211yescharacteristic
63C2×C4⋊C4×C163C2211yescharacteristic
64C2×C4⋊C4×C163C2211yescharacteristic
65C2×C4⋊C4×C163C2211yescharacteristic
66C2×C42×C163C2211yescharacteristic
67C23×D163C2311yescharacteristic
68C2×Dic326—24no—
69C2×Dic326—24no—
70C2×Dic326C2314yes—
71C2×Dic326C2314yes—
72C22×Dic163C2311yescharacteristic
73C22×Dic163C2311yescharacteristic
74C22×Dic163C2311yescharacteristic
75C22×Dic163C2311yescharacteristic
76C22×Dic163C2311yescharacteristic
77C22×Dic163C2311yescharacteristic
78C22×Dic163C2311yescharacteristic
79C2×C4×D163—24no—
80C2×C4×D163C2314yes—
81C4⋊Dic163C2314yes—
82C4⋊Dic163C2314yes—
83C4⋊Dic163C2314yes—
84C4⋊Dic163C2314yes—
85Dic163⋊C4C2314yes—
86Dic163⋊C4C2314yes—
87Dic163⋊C4C2314yes—
88Dic163⋊C4C2314yes—
89Dic163⋊C4C2314yes—
90Dic163⋊C4C2314yes—
91Dic163⋊C4C2314yes—
92Dic163⋊C4C2314yes—
93Dic163⋊C4C2314yes—
94Dic163⋊C4C2314yes—
95(C2×D163)⋊C4C2314yes—
96(C2×D163)⋊C4C2314yes—
97(C2×D163)⋊C4C2314yes—
98(C2×D163)⋊C4C2314yes—
99(C2×D163)⋊C4C2314yes—
100(C2×D163)⋊C4C2314yes—
101C4×Dic163C2314yes—
102C4×Dic163C2314yes—
103C4×Dic163C2314yes—
104C4×Dic163C2314yes—
105C4×Dic163C2314yes—
106C22×C4×C163C2311yescharacteristic
107C22×C4×C163C2311yescharacteristic
108C22×C4×C163C2311yescharacteristic
109C22×C4×C163C2311yescharacteristic
110C22×C4×C163C2311yescharacteristic
111C22×C4×C163C2311yescharacteristic
112C22×C4×C163C2311yescharacteristic
113C4⋊C4×C163C2314yes—
114C4⋊C4×C163C2314yes—
115C4⋊C4×C163C2314yes—
116C4⋊C4×C163C2314yes—
117C4⋊C4×C163C2314yes—
118C4⋊C4×C163C2314yes—
119C42×C163C2314yes—
120C22×D163—22no—
121C22×D163—22no—
122C22×D163—22no—
123C22×D163C2412yes—
124Dic326—28no—
125Dic326—28no—
126C2×Dic163—22no—
127C2×Dic163—22no—
128C2×Dic163—22no—
129C2×Dic163—22no—
130C2×Dic163—22no—
131C2×Dic163—22no—
132C2×Dic163#4114yes—
133C2×Dic163C2412yes—
134C2×Dic163C2412yes—
135C2×Dic163C2412yes—
136C2×Dic163C2412yes—
137C2×Dic163C2412yes—
138C2×Dic163C2412yes—
139C2×Dic163C2412yes—
140C4×D163—28no—
141C23×C163C2411yescharacteristic
142C2×C4×C163—22no—
143C2×C4×C163—22no—
144C2×C4×C163—22no—
145C2×C4×C163—22no—
146C2×C4×C163—22no—
147C2×C4×C163—22no—
148C2×C4×C163—22no—
149C2×C4×C163C2412yes—
150C2×C4×C163C2412yes—
151C2×C4×C163C2412yes—
152C2×C4×C163C2412yes—
153C2×C4×C163C2412yes—
154C2×C4×C163C2412yes—
155C2×C4×C163C2412yes—
156C22×C163C2×#4112yes—
157C22×C1632−1+412yes—
158C22×C1632−1+412yes—
159C22×C163C2511yescharacteristic
160C2×D163—22no—
161C2×D163—22no—
162C2×D163—22no—
163C2×D163—44no—
164C4×C163—22no—
165C4×C163—22no—
166C4×C163—22no—
167C4×C163—22no—
168C4×C163—22no—
169C4×C163—22no—
170C4×C163—22no—
171Dic163—22no—
172Dic163—22no—
173Dic163—22no—
174Dic163—22no—
175Dic163—22no—
176Dic163—22no—
177Dic163C2×#4114yes—
178C2×C163#54114yescomplemented
179C2×C163C22×#4111yescharacteristic
180C2×C163C2×2−1+411yescharacteristic
181C2×C163C2×2−1+411yescharacteristic
182D163—42no—
183C163C2×#54111yescharacteristic, complemented, Sylow
184C2×#541—1631nomaximal, Sylow
185#541—16316no—
186C2×C4⋊Q8—1631no—
187C2×#126—1631no—
188C2×#126—1631no—
189C2×#126—1631no—
190C2×#126—1631no—
191C2×#125—1631no—
192C2×#125—1631no—
193C2×#125—1631no—
194C2×#125—1631no—
195C2×#125D16311yescharacteristic, complemented
196C2×C22⋊Q8—1631no—
197C2×C22⋊Q8—1631no—
198C2×C4×Q8—1631no—
199C2×C4×Q8—1631no—
200C2×#117—1631no—
201C22×Q8—1631no—
202C22×Q8—1631no—
203C23×C4—1631no—
204C4⋊Q8—1638no—
205#126—1638no—
206#126—1638no—
207#126—1638no—
208#126—1638no—
209#125—1638no—
210#125—1638no—
211#125—1638no—
212#125—1638no—
213#125C2×D16318yescomplemented
214C22⋊Q8—1638no—
215C22⋊Q8—1638no—
216C4×Q8—1638no—
217C4×Q8—1638no—
218#117—1638no—
219C2×C4⋊C4—1631no—
220C2×C4⋊C4—1631no—
221C2×C4⋊C4—1631no—
222C2×C4⋊C4—1631no—
223C2×C4⋊C4—1631no—
224C2×C4⋊C4—1631no—
225C2×C4⋊C4—1631no—
226C2×C4⋊C4—1631no—
227C2×C4⋊C4—1631no—
228C2×C4⋊C4—1631no—
229C2×C4⋊C4—1631no—
230C2×C4⋊C4—1631no—
231C2×C4⋊C4—1631no—
232C2×C4⋊C4—1631no—
233C2×C4⋊C4C2×D16311yescharacteristic
234C2×C4⋊C4C2×D16311yescharacteristic
235C2×C4⋊C4C2×D16311yescharacteristic
236C2×C4⋊C4C2×D16311yescharacteristic
237C2×C4⋊C4C2×D16311yescharacteristic
238C2×C4⋊C4C2×D16311yescharacteristic
239C2×C22⋊C4—1631no—
240C2×C22⋊C4—1631no—
241C2×C22⋊C4—1631no—
242C2×C22⋊C4—1631no—
243C2×C22⋊C4—1631no—
244C2×C22⋊C4—1631no—
245C2×C42—1631no—
246C2×C42—1631no—
247C2×C42—1631no—
248C2×C42—1631no—
249C2×C42—1631no—
250C2×C42C2×D16311yescharacteristic
251C24—1631no—
252C2×Q8—3264no—
253C2×Q8—3264no—
254C2×Q8—1634no—
255C2×Q8—1634no—
256C22×C4—3264no—
257C22×C4—1631no—
258C22×C4—1631no—
259C22×C4—1631no—
260C22×C4—1631no—
261C22×C4—1631no—
262C22×C4—1631no—
263C22×C4—1634no—
264C22×C4—1631no—
265C22×C4C22×D16311yescharacteristic
266C22×C4C22×D16311yescharacteristic
267C22×C4C22×D16311yescharacteristic
268C22×C4C22×D16311yescharacteristic
269C22×C4C22×D16311yescharacteristic
270C22×C4C22×D16311yescharacteristic
271C22×C4C22×D16311yescharacteristic
272C4⋊C4—1634no—
273C4⋊C4—1634no—
274C4⋊C4—1634no—
275C4⋊C4—1634no—
276C4⋊C4—1634no—
277C4⋊C4—1634no—
278C4⋊C4—1634no—
279C4⋊C4—1634no—
280C4⋊C4—1634no—
281C4⋊C4—1634no—
282C4⋊C4—1634no—
283C4⋊C4—1634no—
284C4⋊C4—1634no—
285C4⋊C4—1634no—
286C4⋊C4C22×D16314yes—
287C4⋊C4C22×D16314yes—
288C4⋊C4C22×D16314yes—
289C4⋊C4C22×D16314yes—
290C4⋊C4C22×D16314yes—
291C4⋊C4C22×D16314yes—
292C22⋊C4—1634no—
293C22⋊C4—1634no—
294C22⋊C4—1634no—
295C22⋊C4—1634no—
296C22⋊C4—1634no—
297C22⋊C4—1634no—
298C42—1634no—
299C42—1634no—
300C42—1634no—
301C42—1634no—
302C42—1634no—
303C42C22×D16314yes—
304C23—3262no—
305C23—3262no—
306C23—3262no—
307C23—1632no—
308C23C23×D16311yescharacteristic
309Q8—3268no—
310Q8—3268no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—3268no—
319C2×C4—3262no—
320C2×C4—3262no—
321C2×C4—3262no—
322C2×C4—3262no—
323C2×C4—3262no—
324C2×C4—3262no—
325C2×C4—1632no—
326C2×C4—1632no—
327C2×C4—1632no—
328C2×C4—1632no—
329C2×C4—1632no—
330C2×C4—1632no—
331C2×C4—1634no—
332C2×C4—1632no—
333C2×C4C23×D16312yes—
334C2×C4C23×D16312yes—
335C2×C4C23×D16312yes—
336C2×C4C23×D16312yes—
337C2×C4C23×D16312yes—
338C2×C4C23×D16312yes—
339C2×C4C23×D16312yes—
340C22—3262no—
341C22—3262no—
342C22—3262no—
343C22—6524no—
344C22#41×D16312yes—
345C22#1910478212yes—
346C22#1910478312yes—
347C22C24×D16311yescharacteristic
348C4—22no—
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—3262no—
356C4—3262no—
357C4—3262no—
358C4—3262no—
359C4—3262no—
360C4—3262no—
361C4—1634no—
362C2—6522no—
363C2#2378227414yesdirect product factor
364C2C2×#41×D16311yescharacteristic
365C2C2×#1910478211yescharacteristic
366C2C2×#1910478311yescharacteristic
subgroupG/H
centerC23C23×D163
commutator, cosocleC22×C163C25
FrattiniC22C24×D163
FittingC2×#125×C163C2
socleC23×C163C24
prime radicalC23×D163C23
hypercenterC2×#125D163
hypocenterC163C2×#541
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. #23782274C2direct (N × H)
2. C2×#19104734C2semidirect
7. C2×#19104726C2semidirect
8. C2×#19104725C2semidirect
9. C2×#19104725C2semidirect
10. C2×#19104725C2semidirect
13. C2×C4×Dic326C2semidirect
14. C2×#19104700C2semidirect
16. C2×#125×C163C2semidirect
20. #19104734C22semidirect
25. #19104726C22semidirect
26. #19104725C22semidirect
27. #19104725C22semidirect
28. #19104725C22semidirect
31. C4×Dic326C22semidirect
32. #19104700C22semidirect
59. #125×C163C22semidirect
178. C2×C163#541semidirect
183. C163C2×#541semidirect
195. C2×#125D163semidirect
213. #125C2×D163semidirect
363. C2#23782274direct (N × H)

Maximal subgroups

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

subgroupindex
#237822742
C2×#191047342
C2×#191047302
C2×#191047292
C2×#191047262
C2×#191047252
C2×#191047132
C2×C4×Dic3262
C2×#191047002
C2×#191046932
C2×#125×C1632
C2×#541163