Finite Group Databasebeta

← C2×#20242961 #26198849

Subgroups — C2×#20242961 #26198849

Order 12032.

694 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689473C211yesmaximal, characteristic, complemented
2C2×#15689413C211yesmaximal, characteristic
3C2×#15689201C211yesmaximal, characteristic
4#20242961C218yesmaximal, direct product factor
5C2×#15688873C211yesmaximal, characteristic, complemented
6C2×#15688871C211yesmaximal, characteristic, complemented
7C2×#15688869C211yesmaximal, characteristic, complemented
8C2×C47×#474C211yesmaximal, characteristic
9C22×#10625329—21no—
10C2×#13094024C2211yescharacteristic
11#15689473—22no—
12#15689473C2214yescomplemented
13#15689413—22no—
14#15689413C2214yes—
15#15689201—22no—
16#15689201C2214yes—
17C2×#13093955—21no—
18C2×C4⋊(C47⋊C8)C2211yescharacteristic
19C2×C4⋊(C47⋊C8)C2211yescharacteristic
20C2×#13093948—21no—
21C2×#13093948—21no—
22C2×#13093945—21no—
23C2×C22⋊(C47⋊C8)—21no—
24C2×C4×C47⋊C8C2211yescharacteristic
25#15688873C2214yescomplemented
26#15688871C2214yescomplemented
27#15688869C2214yescomplemented
28C2×C4⋊Q8×C47C2211yescharacteristic
29C2×C4×D4×C47C2211yescharacteristic
30C47×#474—22no—
31C47×#474C2214yes—
32C2×#107×C47—21no—
33C2×C4⋊C8×C47C2211yescharacteristic
34C2×#102×C47—21no—
35C22×Dic94—21no—
36C2×#10625329—24no—
37C2×#10625329—44no—
38C22×C47⋊C8—21no—
39C22×C47⋊C8—21no—
40C22×C47⋊C8D411yescharacteristic
41C22×C47⋊C8D411yescharacteristic
42#13094024—21no—
43#13094024—21no—
44#13094024—21no—
45#13094024C2312yes—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47—21no—
48#13093955—24no—
49C4⋊(C47⋊C8)—21no—
50C4⋊(C47⋊C8)—21no—
51C4⋊(C47⋊C8)C2312yes—
52C4⋊(C47⋊C8)C2312yes—
53#13093948—24no—
54#13093948—24no—
55#13093945—24no—
56C22⋊(C47⋊C8)—24no—
57C4×C47⋊C8D412yes—
58C4×C47⋊C8C2312yes—
59C22×Q8×C47—21no—
60C22×D4×C47D411yescharacteristic
61C23×C4×C47—21no—
62C22×C8×C47—21no—
63C4⋊Q8×C47—21no—
64C4⋊Q8×C47—21no—
65C4⋊Q8×C47—21no—
66C4⋊Q8×C47C2312yes—
67C4×D4×C47—21no—
68C4×D4×C47—21no—
69C4×D4×C47D412yes—
70C4×D4×C47C2312yes—
71C2×C4⋊C4×C47—21no—
72C2×C4⋊C4×C47—21no—
73C2×C4⋊C4×C47D411yescharacteristic
74C2×C22⋊C4×C47—21no—
75C2×C42×C47C2311yescharacteristic
76#107×C47—24no—
77C4⋊C8×C47—21no—
78C4⋊C8×C47C2312yes—
79#102×C47—24no—
80C24×C47—21no—
81C2×Q8×C47—22no—
82C2×Q8×C47—41no—
83C2×Q8×C47—42no—
84C2×Q8×C47—42no—
85C2×D4×C47—21no—
86C2×D4×C47—22no—
87C2×D4×C47—22no—
88C2×D4×C47C2×D412yes—
89C22×C4×C47—21no—
90C22×C4×C47—22no—
91C22×C4×C47—22no—
92C22×C4×C47—42no—
93C22×C4×C47—42no—
94C22×C4×C47—41no—
95C22×C4×C47C2×D411yescharacteristic
96C22×C4×C47C2×D411yescharacteristic
97C22×C4×C47#4111yescharacteristic
98C22×Dic47—41no—
99C2×Dic94—22no—
100C2×Dic94—41no—
101C2×Dic94—82no—
102C2×C8×C47—22no—
103C2×C8×C47—42no—
104C4⋊C4×C47—21no—
105C4⋊C4×C47—22no—
106C4⋊C4×C47—22no—
107C4⋊C4×C47—41no—
108C4⋊C4×C47—41no—
109C4⋊C4×C47C2×D412yes—
110C22⋊C4×C47—22no—
111C22⋊C4×C47—22no—
112C42×C47C2×D411yescharacteristic
113C42×C47C2×D411yescharacteristic
114C42×C47#4111yescharacteristic
115C42×C47C2411yescharacteristic
116C4⋊Dic47—22no—
117C4⋊Dic47—22no—
118C4⋊Dic47—41no—
119C4⋊Dic47—41no—
120#10625329—48no—
121C2×C47⋊C8—22no—
122C2×C47⋊C8—22no—
123C2×C47⋊C8—22no—
124C2×C47⋊C8—22no—
125C2×C47⋊C8—42no—
126C2×C47⋊C8—42no—
127C2×C47⋊C8C2×D412yes—
128C2×C47⋊C8C2×D412yes—
129C23×C47—22no—
130C23×C47—42no—
131C23×C47—42no—
132C23×C47—42no—
133C23×C47#12111yescharacteristic
134Q8×C47—42no—
135Q8×C47—42no—
136Q8×C47—82no—
137D4×C47—22no—
138D4×C47—22no—
139D4×C47—42no—
140C2×C4×C47—22no—
141C2×C4×C47—22no—
142C2×C4×C47—42no—
143C2×C4×C47—42no—
144C2×C4×C47—42no—
145C2×C4×C47—44no—
146C2×C4×C47—42no—
147C2×C4×C47—82no—
148C2×C4×C47#12111yescharacteristic
149C2×C4×C47#12111yescharacteristic
150C2×C4×C47#12111yescharacteristic
151C2×C4×C47#13512yes—
152C2×C4×C47AGL(1,ℤ/8)12yes—
153C2×C4×C47#13712yes—
154C2×C4×C47#13712yes—
155C2×C4×C47C22×D411yescharacteristic
156C2×C4×C47C22×D411yescharacteristic
157C2×C4×C47C2×#4111yescharacteristic
158C2×Dic47—42no—
159C2×Dic47—82no—
160Dic94—82no—
161Dic94—82no—
162C8×C47—42no—
163C47⋊C8—22no—
164C47⋊C8—22no—
165C47⋊C8—42no—
166C47⋊C8—42no—
167C2×#1703—471nomaximal, Sylow
168C22×C47—42no—
169C22×C47—42no—
170C22×C47—42no—
171C22×C47—84no—
172C22×C47#46312yes—
173C22×C47#47012yes—
174C22×C47#47112yes—
175C22×C47C2×#12111yescharacteristic
176C4×C47—21no—
177C4×C47—21no—
178C4×C47—42no—
179C4×C47—82no—
180C4×C47#46312yes—
181C4×C47#47012yes—
182C4×C47C2×#13511yescharacteristic
183C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
184C4×C47C2×#13711yescharacteristic
185C4×C47C2×#13711yescharacteristic
186Dic47—82no—
187C2×#487—471no—
188C2×#476—471no—
189C2×#474D4711yescharacteristic
190C2×#436—471no—
191#1703—478no—
192C2×#334—471no—
193C2×#333—471no—
194C2×#332—471no—
195C2×C47—82no—
196C2×C47#170314yescomplemented
197C2×C47C2×#46311yescharacteristic
198C2×C47C2×#47011yescharacteristic
199C2×C47C2×#47111yescharacteristic
200C22×M16—941no—
201C2×C4⋊Q8—471no—
202C2×C4⋊Q8C2×D4711yescharacteristic
203C2×C4×D4C2×D4711yescharacteristic
204#487—474no—
205#487—942no—
206#476—474no—
207#476—942no—
208#474—22no—
209#474C2×D4714yes—
210#436—474no—
211#436—942no—
212C2×#107—21no—
213C2×#106—941no—
214C2×C4⋊C8—471no—
215C2×C4⋊C8—471no—
216C2×C4⋊C8C2×D4711yescharacteristic
217C2×#103—941no—
218C2×#103—941no—
219C2×#102—21no—
220C2×#102—941no—
221C2×C22⋊C8—941no—
222C2×C4×C8—471no—
223#334—474no—
224#333—474no—
225#332—474no—
226C47C2×#170311yescharacteristic, complemented, Sylow
227C22×Q8—21no—
228C22×Q8—941no—
229C22×D4C22⋊D4711yescharacteristic
230C23×C4—21no—
231C2×M16—944no—
232C2×M16—1884no—
233C22×C8—21no—
234C22×C8—471no—
235C22×C8—471no—
236C22×C8—941no—
237C22×C8—941no—
238C4⋊Q8—21no—
239C4⋊Q8—21no—
240C4⋊Q8—21no—
241C4⋊Q8—472no—
242C4⋊Q8—941no—
243C4⋊Q8—941no—
244C4⋊Q8—941no—
245C4⋊Q8C22×D4712yes—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4C22⋊D4712yes—
249C4×D4C22×D4712yes—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—941no—
253C2×C4⋊C4—941no—
254C2×C4⋊C4C22⋊D4711yescharacteristic
255C2×C22⋊C4—21no—
256C2×C42C22×D4711yescharacteristic
257#107—24no—
258#106—944no—
259C4⋊C8—21no—
260C4⋊C8—472no—
261C4⋊C8—472no—
262C4⋊C8—941no—
263C4⋊C8—941no—
264C4⋊C8C22×D4712yes—
265#103—944no—
266#103—944no—
267#102—24no—
268#102—944no—
269C22⋊C8—944no—
270C4×C8—472no—
271C4×C8—472no—
272C24—21no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×Q8—942no—
278C2×Q8—3762no—
279C2×Q8—1881no—
280C2×D4—21no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4C2×C22⋊D4712yes—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—41no—
290C22×C4—1881no—
291C22×C4D4×D4711yescharacteristic
292C22×C4#1062535211yescharacteristic
293C22×C4C2×C22⋊D4711yescharacteristic
294M16—1888no—
295C2×C8—22no—
296C2×C8—42no—
297C2×C8—472no—
298C2×C8—472no—
299C2×C8—942no—
300C2×C8—942no—
301C2×C8—942no—
302C2×C8—942no—
303C2×C8—1882no—
304C2×C8—1882no—
305C4⋊C4—21no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—942no—
311C4⋊C4—942no—
312C4⋊C4—1881no—
313C4⋊C4—1881no—
314C4⋊C4C2×C22⋊D4712yes—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C42D4×D4711yescharacteristic
318C42#1062535211yescharacteristic
319C42C2×C22⋊D4711yescharacteristic
320C42C23×D4711yescharacteristic
321C23—22no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23#1309399611yescharacteristic
326Q8—42no—
327Q8—42no—
328Q8—82no—
329Q8—3762no—
330Q8—3762no—
331D4—22no—
332D4—22no—
333D4—42no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—82no—
342C2×C4—3762no—
343C2×C4—1882no—
344C2×C4#1309399611yescharacteristic
345C2×C4#1309399611yescharacteristic
346C2×C4#1309399611yescharacteristic
347C2×C4#1309404312yes—
348C2×C4#1309404812yes—
349C2×C4#1309405412yes—
350C2×C4#1309405512yes—
351C2×C4C2×D4×D4711yescharacteristic
352C2×C4C22×C22⋊D4711yescharacteristic
353C2×C4C2×#1062535211yescharacteristic
354C8—42no—
355C8—942no—
356C8—942no—
357C8—1882no—
358C8—1882no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—84no—
363C22#1568933612yes—
364C22#1568937912yes—
365C22#1568938812yes—
366C22C2×#1309399611yescharacteristic
367C4—21no—
368C4—21no—
369C4—42no—
370C4—82no—
371C4—3762no—
372C4#1568933612yes—
373C4#1568937912yes—
374C4C2×#1309404311yescharacteristic
375C4C2×#1309404811yescharacteristic
376C4C2×#1309405411yescharacteristic
377C4C2×#1309405511yescharacteristic
378C2—82no—
379C2#2024296114yesdirect product factor
380C2C2×#1568933611yescharacteristic
381C2C2×#1568937911yescharacteristic
382C2C2×#1568938811yescharacteristic
subgroupG/H
centerC23#13093996
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC2×C47×#474C2
socleC23×C47#121
prime radicalC22×D4×C47D4
hypercenterC2×#474D47
hypocenterC47C2×#1703
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#15689473C2semidirect
4. #20242961C2direct (N × H)
5. C2×#15688873C2semidirect
6. C2×#15688871C2semidirect
7. C2×#15688869C2semidirect
12. #15689473C22semidirect
25. #15688873C22semidirect
26. #15688871C22semidirect
27. #15688869C22semidirect
196. C2×C47#1703semidirect
226. C47C2×#1703semidirect
379. C2#20242961direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156894732
C2×#156894132
C2×#156892012
#202429612
C2×#156888732
C2×#156888712
C2×#156888692
C2×C47×#4742
C2×#170347