Finite Group Databasebeta

← C47×#10460 #26050158

Subgroups — C47×#10460 #26050158

Order 12032.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3077C211yesmaximal, characteristic
2C47×#1800C211yesmaximal, characteristic
3C47×#1566C211yesmaximal, characteristic, complemented
4C47×#1550C211yesmaximal, characteristic, complemented
5C47×#1493C211yesmaximal, characteristic, complemented
6C2×C47×D4⋊C8C211yesmaximal, characteristic
7C47×#1292C211yesmaximal, characteristic, complemented
8C47×#533C2211yescharacteristic
9C2×C4×D4×C47C2211yescharacteristic
10C47×#478—22no—
11C47×#476—21no—
12C47×#474—21no—
13C47×#428—21no—
14C47×#423C2211yescharacteristic
15C47×#423C2211yescharacteristic
16C47×#423C2211yescharacteristic
17C2×C4⋊C8×C47C2211yescharacteristic
18C47×#418—21no—
19C2×#100×C47—21no—
20C2×C4×C8×C47C2211yescharacteristic
21C47×#343—21no—
22C47×#334—22no—
23C47×#333—21no—
24C47×#332—21no—
25C47×Q8⋊C8—21no—
26C47×Q8⋊C8—21no—
27C47×D4⋊C8—21no—
28C47×D4⋊C8—21no—
29C22×D4×C47D411yescharacteristic
30C23×C4×C47—21no—
31C2×M16×C47—21no—
32C2×M16×C47—21no—
33C2×M16×C47—21no—
34C22×C8×C47—21no—
35C22×C8×C47—21no—
36C4⋊Q8×C47D411yescharacteristic
37C4⋊Q8×C47D411yescharacteristic
38#125×C47—21no—
39C22⋊Q8×C47—21no—
40C22⋊Q8×C47—21no—
41C4×Q8×C47—21no—
42C4×Q8×C47—21no—
43C4×D4×C47—21no—
44C4×D4×C47—21no—
45C4×D4×C47—21no—
46C4×D4×C47—21no—
47#117×C47—21no—
48C2×C4⋊C4×C47D411yescharacteristic
49C2×C22⋊C4×C47—21no—
50C2×C42×C47C2311yescharacteristic
51#107×C47—22no—
52#106×C47—22no—
53C4⋊C8×C47—21no—
54C4⋊C8×C47—21no—
55C4⋊C8×C47—21no—
56C4⋊C8×C47—21no—
57C4⋊C8×C47—21no—
58C4⋊C8×C47—21no—
59C4⋊C8×C47—21no—
60C4⋊C8×C47D412yes—
61#102×C47—22no—
62#102×C47—22no—
63#100×C47—42no—
64C4×C8×C47—21no—
65C4×C8×C47D411yescharacteristic
66C4×C8×C47D411yescharacteristic
67C24×C47—21no—
68C2×Q8×C47—21no—
69C2×Q8×C47—21no—
70C2×D4×C47—21no—
71C2×D4×C47—21no—
72C2×D4×C47—21no—
73C2×D4×C47—21no—
74C2×D4×C47—21no—
75C2×D4×C47SD1612yes—
76C22×C4×C47—21no—
77C22×C4×C47—41no—
78C22×C4×C47—41no—
79C22×C4×C47—81no—
80C22×C4×C47—81no—
81C22×C4×C47C2×D411yescharacteristic
82C22×C4×C47#4111yescharacteristic
83C22×C4×C47#4111yescharacteristic
84M16×C47—41no—
85M16×C47—41no—
86M16×C47—41no—
87M16×C47—41no—
88M16×C47—41no—
89M16×C47—41no—
90C2×C8×C47—21no—
91C2×C8×C47—22no—
92C2×C8×C47—21no—
93C2×C8×C47—42no—
94C2×C8×C47—41no—
95C2×C8×C47—41no—
96C2×C8×C47—41no—
97C2×C8×C47—81no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47—21no—
100C4⋊C4×C47—21no—
101C4⋊C4×C47—21no—
102C4⋊C4×C47—21no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—41no—
105C4⋊C4×C47—41no—
106C22⋊C4×C47—41no—
107C22⋊C4×C47—41no—
108C22⋊C4×C47—41no—
109C42×C47—41no—
110C42×C47C2×D411yescharacteristic
111C42×C47C2×D411yescharacteristic
112C42×C47C2×D411yescharacteristic
113C42×C47#4111yescharacteristic
114C23×C47—22no—
115C23×C47—41no—
116C23×C47—41no—
117C23×C47—81no—
118C23×C47—81no—
119C23×C47#12311yescharacteristic
120Q8×C47—41no—
121Q8×C47—41no—
122Q8×C47—81no—
123D4×C47—22no—
124D4×C47—22no—
125D4×C47—41no—
126D4×C47—41no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—41no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—82no—
134C2×C4×C47—81no—
135C2×C4×C47—81no—
136C2×C4×C47—81no—
137C2×C4×C47#12011yescharacteristic
138C2×C4×C47#12111yescharacteristic
139C2×C4×C47#12111yescharacteristic
140C2×C4×C47#12111yescharacteristic
141C2×C4×C47#12311yescharacteristic
142C2×C4×C47#12411yescharacteristic
143C2×C4×C47C2×SD1611yescharacteristic
144C2×C4×C47#13511yescharacteristic
145C2×C4×C47#13711yescharacteristic
146C2×C4×C47#13711yescharacteristic
147C8×C47—22no—
148C8×C47—41no—
149C8×C47—42no—
150C8×C47—81no—
151C8×C47—81no—
152C8×C47—81no—
153#10460C4711yesmaximal, characteristic, direct product factor, Sylow
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—42no—
157C22×C47—82no—
158C22×C47—82no—
159C22×C47—81no—
160C22×C47—81no—
161C22×C47#39411yescharacteristic
162C22×C47#48311yescharacteristic
163C22×C47#48511yescharacteristic
164C4×C47—21no—
165C4×C47—21no—
166C4×C47—21no—
167C4×C47—81no—
168C4×C47—81no—
169C4×C47—81no—
170C4×C47#44811yescharacteristic
171C4×C47#45211yescharacteristic
172C4×C47#46511yescharacteristic
173C4×C47#47011yescharacteristic
174C4×C47#47111yescharacteristic
175C4×C47#47211yescharacteristic
176#3077C2×C4711yescharacteristic
177#1800C2×C4711yescharacteristic
178#1566C2×C4711yescharacteristic, complemented
179#1550C2×C4711yescharacteristic, complemented
180#1493C2×C4711yescharacteristic, complemented
181C2×D4⋊C8C2×C4711yescharacteristic
182#1292C2×C4711yescharacteristic, complemented
183C2×C47—21no—
184C2×C47—21no—
185C2×C47—82no—
186C2×C47#203511yescharacteristic
187C2×C47#205011yescharacteristic
188C2×C47#205111yescharacteristic
189#533C22×C4711yescharacteristic
190C2×C4×D4C22×C4711yescharacteristic
191#478—22no—
192#476—21no—
193#474—21no—
194#428—21no—
195#423C22×C4711yescharacteristic
196#423C22×C4711yescharacteristic
197#423C22×C4711yescharacteristic
198C2×C4⋊C8C22×C4711yescharacteristic
199#418—21no—
200C2×#100—21no—
201C2×C4×C8C22×C4711yescharacteristic
202#343—21no—
203#334—22no—
204#333—21no—
205#332—21no—
206Q8⋊C8—21no—
207Q8⋊C8—21no—
208D4⋊C8—21no—
209D4⋊C8—21no—
210C47#1046011yescharacteristic, direct product factor, Sylow
211C22×D4D4×C4711yescharacteristic
212C23×C4—21no—
213C2×M16—21no—
214C2×M16—21no—
215C2×M16—21no—
216C22×C8—21no—
217C22×C8—21no—
218C4⋊Q8D4×C4711yescharacteristic
219C4⋊Q8D4×C4711yescharacteristic
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4—21no—
228C4×D4—21no—
229#117—21no—
230C2×C4⋊C4D4×C4711yescharacteristic
231C2×C22⋊C4—21no—
232C2×C42C23×C4711yescharacteristic
233#107—22no—
234#106—22no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8D4×C4712yes—
243#102—22no—
244#102—22no—
245#100—42no—
246C4×C8—21no—
247C4×C8D4×C4711yescharacteristic
248C4×C8D4×C4711yescharacteristic
249C24—21no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4SD16×C4712yes—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4C2×D4×C4711yescharacteristic
264C22×C4#41×C4711yescharacteristic
265C22×C4#41×C4711yescharacteristic
266M16—41no—
267M16—41no—
268M16—41no—
269M16—41no—
270M16—41no—
271M16—41no—
272C2×C8—21no—
273C2×C8—22no—
274C2×C8—21no—
275C2×C8—42no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—81no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C42—41no—
292C42C2×D4×C4711yescharacteristic
293C42C2×D4×C4711yescharacteristic
294C42C2×D4×C4711yescharacteristic
295C42#41×C4711yescharacteristic
296C23—22no—
297C23—41no—
298C23—41no—
299C23—81no—
300C23—81no—
301C23#123×C4711yescharacteristic
302Q8—41no—
303Q8—41no—
304Q8—81no—
305D4—22no—
306D4—22no—
307D4—41no—
308D4—41no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4#120×C4711yescharacteristic
320C2×C4#121×C4711yescharacteristic
321C2×C4#121×C4711yescharacteristic
322C2×C4#121×C4711yescharacteristic
323C2×C4#123×C4711yescharacteristic
324C2×C4#124×C4711yescharacteristic
325C2×C4C2×SD16×C4711yescharacteristic
326C2×C4#135×C4711yescharacteristic
327C2×C4#137×C4711yescharacteristic
328C2×C4#137×C4711yescharacteristic
329C8—22no—
330C8—41no—
331C8—42no—
332C8—81no—
333C8—81no—
334C8—81no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—82no—
339C22—82no—
340C22—81no—
341C22—81no—
342C22C47×#39411yescharacteristic
343C22C47×#48311yescharacteristic
344C22C47×#48511yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4C47×#44811yescharacteristic
352C4C47×#45211yescharacteristic
353C4C47×#46511yescharacteristic
354C4C47×#47011yescharacteristic
355C4C47×#47111yescharacteristic
356C4C47×#47211yescharacteristic
357C2—21no—
358C2—21no—
359C2—82no—
360C2C47×#203511yescharacteristic
361C2C47×#205011yescharacteristic
362C2C47×#205111yescharacteristic
subgroupG/H
center, socleC22×C47#394
commutator, Frattini, cosocleC2×C42C23×C47
prime radicalC22×D4×C47D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1566C2semidirect
4. C47×#1550C2semidirect
5. C47×#1493C2semidirect
7. C47×#1292C2semidirect
153. #10460C47direct (N × H)
178. #1566C2×C47semidirect
179. #1550C2×C47semidirect
180. #1493C2×C47semidirect
182. #1292C2×C47semidirect
210. C47#10460direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30772
C47×#18002
C47×#15662
C47×#15502
C47×#14932
C2×C47×D4⋊C82
C47×#12922
#1046047