Finite Group Databasebeta

← C2×C47×#1742 #26060055

Subgroups — C2×C47×#1742 #26060055

Order 12032.

2190 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C47C212yesmaximal
2C22×#117×C47C211yesmaximal, characteristic
3C47×#1742C218yesmaximal, direct product factor
4C2×C47×#343C214yesmaximal, complemented
5C24×C4×C47C2211yescharacteristic
6C22×M16×C47—28no—
7C22×M16×C47—22no—
8C22×M16×C47—24no—
9C22×M16×C47C4116yescomplemented
10C22×M16×C47C2214yes—
11C22×M16×C47C2218yes—
12C23×C8×C47—22no—
13C2×#117×C47—22no—
14C2×#117×C47—24no—
15C2×#117×C47—22no—
16C2×#117×C47C414yes—
17C2×#117×C47C2214yes—
18C22×C4⋊C4×C47C2212yes—
19C22×C22⋊C4×C47C412yes—
20C22×C42×C47C412yes—
21C47×#343C22116yescomplemented
22C25×C47C2×C411yescharacteristic
23C23×C4×C47C2×C414yes—
24C23×C4×C47C2×C412yes—
25C23×C4×C47C2×C411yescharacteristic
26C23×C4×C47C2×C418yes—
27C23×C4×C47D414yes—
28C23×C4×C47D412yes—
29C23×C4×C47D414yes—
30C23×C4×C47D412yes—
31C23×C4×C47Q814yes—
32C23×C4×C47C2311yescharacteristic
33C23×C4×C47C2312yes—
34C2×M16×C47—216no—
35C2×M16×C47—232no—
36C2×M16×C47—28no—
37C2×M16×C47—216no—
38C2×M16×C47—24no—
39C2×M16×C47—28no—
40C2×M16×C47C2×C4116yes—
41C2×M16×C47C2×C4132yescomplemented
42C2×M16×C47C2318yes—
43C22×C8×C47—216no—
44C22×C8×C47—24no—
45C22×C8×C47—28no—
46#117×C47—28no—
47#117×C47—28no—
48#117×C47—28no—
49#117×C47—28no—
50C2×C4⋊C4×C47—24no—
51C2×C4⋊C4×C47—24no—
52C2×C4⋊C4×C47C2×C414yes—
53C2×C4⋊C4×C47C2314yes—
54C2×C22⋊C4×C47—24no—
55C2×C22⋊C4×C47—24no—
56C2×C22⋊C4×C47C2×C418yes—
57C2×C42×C47—22no—
58C2×C42×C47—24no—
59C2×C42×C47—22no—
60C2×C42×C47C2×C418yes—
61C24×C47—44no—
62C24×C47C4214yes—
63C24×C47C22⋊C412yes—
64C24×C47C22⋊C412yes—
65C24×C47C4⋊C414yes—
66C24×C47C22×C411yescharacteristic
67C24×C47C22×C412yes—
68C22×C4×C47—24no—
69C22×C4×C47—24no—
70C22×C4×C47—48no—
71C22×C4×C47C4218yes—
72C22×C4×C47C4214yes—
73C22×C4×C47C22⋊C411yescharacteristic
74C22×C4×C47C22⋊C412yes—
75C22×C4×C47C22⋊C414yes—
76C22×C4×C47C22⋊C414yes—
77C22×C4×C47C22⋊C418yes—
78C22×C4×C47C22⋊C418yes—
79C22×C4×C47C22⋊C4116yes—
80C22×C4×C47C22⋊C411yescharacteristic
81C22×C4×C47C4⋊C418yes—
82C22×C4×C47C4⋊C414yes—
83C22×C4×C47C4⋊C418yes—
84C22×C4×C47C4⋊C4116yes—
85C22×C4×C47C4⋊C418yes—
86C22×C4×C47C22×C418yes—
87C22×C4×C47C22×C412yes—
88C22×C4×C47C22×C411yescharacteristic
89C22×C4×C47C22×C414yes—
90C22×C4×C47C22×C418yes—
91C22×C4×C47C2×D412yes—
92C22×C4×C47C2×D414yes—
93C22×C4×C47C2×D412yes—
94C22×C4×C47C2×D412yes—
95C22×C4×C47C2×D414yes—
96C22×C4×C47C2×D414yes—
97C22×C4×C47C2×Q812yes—
98C22×C4×C47C2×Q814yes—
99C22×C4×C47C2411yescharacteristic
100M16×C47—216no—
101M16×C47—232no—
102M16×C47—28no—
103M16×C47C22×C4116yes—
104C2×C8×C47—216no—
105C2×C8×C47—232no—
106C2×C8×C47—28no—
107C4⋊C4×C47—28no—
108C4⋊C4×C47—28no—
109C22⋊C4×C47—216no—
110C42×C47—28no—
111C42×C47—28no—
112C23×C47—24no—
113C23×C47—28no—
114C23×C47—48no—
115C23×C47—44no—
116C23×C47—48no—
117C23×C47—44no—
118C23×C47#9518yes—
119C23×C47#9518yes—
120C23×C47C2×C4212yes—
121C23×C47C2×C4214yes—
122C23×C47C2×C22⋊C414yes—
123C23×C47C2×C22⋊C411yescharacteristic
124C23×C47C2×C22⋊C411yescharacteristic
125C23×C47C2×C4⋊C412yes—
126C23×C47C2×C4⋊C414yes—
127C23×C47C23×C411yescharacteristic
128C2×C4×C47—28no—
129C2×C4×C47—48no—
130C2×C4×C47—48no—
131C2×C4×C47—48no—
132C2×C4×C47#9518yes—
133C2×C4×C47#95116yes—
134C2×C4×C47#95116yes—
135C2×C4×C47#9514yes—
136C2×C4×C47#9514yes—
137C2×C4×C47C2×C4214yes—
138C2×C4×C47C2×C4212yes—
139C2×C4×C47C2×C22⋊C418yes—
140C2×C4×C47C2×C22⋊C414yes—
141C2×C4×C47C2×C22⋊C414yes—
142C2×C4×C47C2×C22⋊C418yes—
143C2×C4×C47C2×C22⋊C412yes—
144C2×C4×C47C2×C22⋊C412yes—
145C2×C4×C47C2×C22⋊C412yes—
146C2×C4×C47C2×C4⋊C414yes—
147C2×C4×C47C2×C4⋊C418yes—
148C2×C4×C47C2×C4⋊C418yes—
149C2×C4×C47C2×C4⋊C414yes—
150C2×C4×C47C2×C4⋊C414yes—
151C2×C4×C47C2×C4⋊C412yes—
152C2×C4×C47C23×C412yes—
153C2×C4×C47C22×D411yescharacteristic
154C2×C4×C47C22×D412yes—
155C2×C4×C47C22×Q811yescharacteristic
156C8×C47—216no—
157C2×#1742C4711yesmaximal, characteristic, direct product factor, Sylow
158C22×C47—22no—
159C22×C47—22no—
160C22×C47—28no—
161C22×C47—216no—
162C22×C47—24no—
163C22×C47—24no—
164C22×C47—48no—
165C22×C47—44no—
166C22×C47—44no—
167C22×C47C2×#9518yes—
168C22×C47C2×#9512yes—
169C22×C47C2×#9512yes—
170C22×C47#41314yes—
171C22×C47C22×C4211yescharacteristic
172C22×C47C22×C22⋊C411yescharacteristic
173C22×C47C22×C4⋊C411yescharacteristic
174C4×C47—48no—
175C4×C47C2×#9514yes—
176C4×C47C2×#9514yes—
177C4×C47C2×#9514yes—
178C4×C47C22×C22⋊C412yes—
179C4×C47C22×C4⋊C412yes—
180C23×M16C2×C4712yes—
181C22×#117C2×C4711yescharacteristic
182#1742C2×C4718yesdirect product factor
183C2×#343C2×C4714yescomplemented
184C2×C47—21no—
185C2×C47—22no—
186C2×C47—28no—
187C2×C47—21no—
188C2×C47#174214yesdirect product factor
189C2×C47C22×#9511yescharacteristic
190C2×C47C2×#41312yes—
191C24×C4C22×C4711yescharacteristic
192C22×M16—28no—
193C22×M16—22no—
194C22×M16—24no—
195C22×M16C4×C47116yescomplemented
196C22×M16C22×C4714yes—
197C22×M16C22×C4718yes—
198C23×C8—22no—
199C2×#117—22no—
200C2×#117—22no—
201C2×#117—24no—
202C2×#117C4×C4714yes—
203C2×#117C22×C4714yes—
204C22×C4⋊C4C22×C4712yes—
205C22×C22⋊C4C4×C4712yes—
206C22×C42C4×C4712yes—
207#343C22×C47116yescomplemented
208C47C2×#174211yescharacteristic, direct product factor, Sylow
209C25C2×C4×C4711yescharacteristic
210C23×C4C2×C4×C4714yes—
211C23×C4C2×C4×C4712yes—
212C23×C4C2×C4×C4711yescharacteristic
213C23×C4C2×C4×C4718yes—
214C23×C4D4×C4714yes—
215C23×C4D4×C4712yes—
216C23×C4D4×C4712yes—
217C23×C4D4×C4714yes—
218C23×C4Q8×C4714yes—
219C23×C4C23×C4711yescharacteristic
220C23×C4C23×C4712yes—
221C2×M16—216no—
222C2×M16—232no—
223C2×M16—28no—
224C2×M16—216no—
225C2×M16—24no—
226C2×M16—28no—
227C2×M16C2×C4×C47116yes—
228C2×M16C2×C4×C47132yescomplemented
229C2×M16C23×C4718yes—
230C22×C8—216no—
231C22×C8—24no—
232C22×C8—28no—
233#117—28no—
234#117—28no—
235#117—28no—
236#117—28no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4C2×C4×C4714yes—
240C2×C4⋊C4C23×C4714yes—
241C2×C22⋊C4—24no—
242C2×C22⋊C4—24no—
243C2×C22⋊C4C2×C4×C4718yes—
244C2×C42—24no—
245C2×C42—22no—
246C2×C42—22no—
247C2×C42C2×C4×C4718yes—
248C24—44no—
249C24C42×C4714yes—
250C24C22⋊C4×C4712yes—
251C24C22⋊C4×C4712yes—
252C24C4⋊C4×C4714yes—
253C24C22×C4×C4711yescharacteristic
254C24C22×C4×C4712yes—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—48no—
258C22×C4C42×C4714yes—
259C22×C4C42×C4718yes—
260C22×C4C22⋊C4×C4718yes—
261C22×C4C22⋊C4×C4718yes—
262C22×C4C22⋊C4×C47116yes—
263C22×C4C22⋊C4×C4712yes—
264C22×C4C22⋊C4×C4711yescharacteristic
265C22×C4C22⋊C4×C4714yes—
266C22×C4C22⋊C4×C4714yes—
267C22×C4C22⋊C4×C4711yescharacteristic
268C22×C4C4⋊C4×C4718yes—
269C22×C4C4⋊C4×C4718yes—
270C22×C4C4⋊C4×C47116yes—
271C22×C4C4⋊C4×C4714yes—
272C22×C4C4⋊C4×C4718yes—
273C22×C4C22×C4×C4718yes—
274C22×C4C22×C4×C4712yes—
275C22×C4C22×C4×C4711yescharacteristic
276C22×C4C22×C4×C4714yes—
277C22×C4C22×C4×C4718yes—
278C22×C4C2×D4×C4712yes—
279C22×C4C2×D4×C4714yes—
280C22×C4C2×D4×C4712yes—
281C22×C4C2×D4×C4712yes—
282C22×C4C2×D4×C4714yes—
283C22×C4C2×D4×C4714yes—
284C22×C4C2×Q8×C4712yes—
285C22×C4C2×Q8×C4714yes—
286C22×C4C24×C4711yescharacteristic
287M16—216no—
288M16—232no—
289M16—28no—
290M16C22×C4×C47116yes—
291C2×C8—216no—
292C2×C8—232no—
293C2×C8—28no—
294C4⋊C4—28no—
295C4⋊C4—28no—
296C22⋊C4—216no—
297C42—28no—
298C42—28no—
299C23—24no—
300C23—28no—
301C23—48no—
302C23—44no—
303C23—48no—
304C23—44no—
305C23#95×C4718yes—
306C23#95×C4718yes—
307C23C2×C42×C4712yes—
308C23C2×C42×C4714yes—
309C23C2×C22⋊C4×C4714yes—
310C23C2×C22⋊C4×C4711yescharacteristic
311C23C2×C22⋊C4×C4711yescharacteristic
312C23C2×C4⋊C4×C4712yes—
313C23C2×C4⋊C4×C4714yes—
314C23C23×C4×C4711yescharacteristic
315C2×C4—28no—
316C2×C4—48no—
317C2×C4—48no—
318C2×C4—48no—
319C2×C4#95×C47116yes—
320C2×C4#95×C4718yes—
321C2×C4#95×C47116yes—
322C2×C4#95×C4714yes—
323C2×C4#95×C4714yes—
324C2×C4C2×C42×C4714yes—
325C2×C4C2×C42×C4712yes—
326C2×C4C2×C22⋊C4×C4718yes—
327C2×C4C2×C22⋊C4×C4714yes—
328C2×C4C2×C22⋊C4×C4714yes—
329C2×C4C2×C22⋊C4×C4718yes—
330C2×C4C2×C22⋊C4×C4712yes—
331C2×C4C2×C22⋊C4×C4712yes—
332C2×C4C2×C22⋊C4×C4712yes—
333C2×C4C2×C4⋊C4×C4714yes—
334C2×C4C2×C4⋊C4×C4718yes—
335C2×C4C2×C4⋊C4×C4718yes—
336C2×C4C2×C4⋊C4×C4714yes—
337C2×C4C2×C4⋊C4×C4714yes—
338C2×C4C2×C4⋊C4×C4712yes—
339C2×C4C23×C4×C4712yes—
340C2×C4C22×D4×C4711yescharacteristic
341C2×C4C22×D4×C4712yes—
342C2×C4C22×Q8×C4711yescharacteristic
343C8—216no—
344C22—22no—
345C22—22no—
346C22—28no—
347C22—24no—
348C22—24no—
349C22—216no—
350C22—44no—
351C22—44no—
352C22—48no—
353C22C2×#95×C4718yes—
354C22C2×#95×C4712yes—
355C22C2×#95×C4712yes—
356C22C47×#41314yes—
357C22C22×C42×C4711yescharacteristic
358C22C22×C22⋊C4×C4711yescharacteristic
359C22C22×C4⋊C4×C4711yescharacteristic
360C4—48no—
361C4C2×#95×C4714yes—
362C4C2×#95×C4714yes—
363C4C2×#95×C4714yes—
364C4C22×C22⋊C4×C4712yes—
365C4C22×C4⋊C4×C4712yes—
366C2—21no—
367C2—21no—
368C2—22no—
369C2—28no—
370C2C47×#174214yesdirect product factor
371C2C22×#95×C4711yescharacteristic
372C2C2×C47×#41312yes—
subgroupG/H
centerC22×C4×C47C22⋊C4
commutatorC22C22×C42×C47
Frattini, cosocleC22×C4C24×C47
socleC23×C47C2×C22⋊C4
prime radicalC25×C47C2×C4
LCSG ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ C24×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1742C2direct (N × H)
4. C2×C47×#343C2semidirect
9. C22×M16×C47C4semidirect
21. C47×#343C22semidirect
41. C2×M16×C47C2×C4semidirect
157. C2×#1742C47direct (N × H)
182. #1742C2×C47direct (N × H)
183. C2×#343C2×C47semidirect
188. C2×C47#1742direct (N × H)
195. C22×M16C4×C47semidirect
207. #343C22×C47semidirect
208. C47C2×#1742direct (N × H)
228. C2×M16C2×C4×C47semidirect
370. C2C47×#1742direct (N × H)

Maximal subgroups

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

subgroupindex
C23×M16×C472
C22×#117×C472
C47×#17422
C2×C47×#3432
C2×#174247