Finite Group Databasebeta

← C47×#10445 #26050143

Subgroups — C47×#10445 #26050143

Order 12032.

440 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#461C211yesmaximal, characteristic
2C47×#1800C211yesmaximal, characteristic
3C47×#1570C211yesmaximal, characteristic, complemented
4C47×#1546C211yesmaximal, characteristic, complemented
5C47×#1546C211yesmaximal, characteristic, complemented
6C47×#1478C211yesmaximal, characteristic
7C47×#1301C211yesmaximal, characteristic, complemented
8C22×SD16×C47—21no—
9C2×C4⋊Q8×C47C2211yescharacteristic
10C2×C4×D4×C47C2211yescharacteristic
11C47×#461—22no—
12C47×#461—22no—
13C47×#431C2211yescharacteristic
14C47×#431C2211yescharacteristic
15C47×#423C2211yescharacteristic
16C47×#423C2211yescharacteristic
17C2×C4⋊C8×C47C2211yescharacteristic
18C2×#103×C47—21no—
19C2×#100×C47—21no—
20C47×#343—21no—
21C47×#334—22no—
22C47×#332—22no—
23C47×#332—22no—
24C47×D4⋊C8—22no—
25C22×Q8×C47—21no—
26C22×D4×C47D411yescharacteristic
27C23×C4×C47—21no—
28C2×SD16×C47—24no—
29C2×SD16×C47—42no—
30C2×SD16×C47—42no—
31C2×M16×C47—21no—
32C2×M16×C47—21no—
33C22×C8×C47—21no—
34C4⋊Q8×C47—21no—
35C4⋊Q8×C47—21no—
36C4⋊Q8×C47—21no—
37C4⋊Q8×C47D412yes—
38C4×D4×C47—21no—
39C4×D4×C47—21no—
40C4×D4×C47—21no—
41C4×D4×C47—21no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47—21no—
44C2×C4⋊C4×C47D411yescharacteristic
45C2×C22⋊C4×C47—21no—
46C2×C42×C47C2311yescharacteristic
47C4⋊C8×C47—21no—
48C4⋊C8×C47—21no—
49C4⋊C8×C47—21no—
50C4⋊C8×C47—21no—
51C4⋊C8×C47—21no—
52C4⋊C8×C47—21no—
53C4⋊C8×C47D412yes—
54C4⋊C8×C47D412yes—
55#103×C47—24no—
56#100×C47—42no—
57C22⋊C8×C47—21no—
58C22⋊C8×C47—21no—
59C4×C8×C47—21no—
60C4×C8×C47—21no—
61C24×C47—21no—
62C2×Q8×C47—22no—
63C2×Q8×C47—41no—
64C2×Q8×C47—41no—
65C2×Q8×C47—41no—
66C2×Q8×C47—41no—
67C2×Q8×C47—41no—
68C2×D4×C47—21no—
69C2×D4×C47—21no—
70C2×D4×C47—21no—
71C2×D4×C47—21no—
72C2×D4×C47—21no—
73C2×D4×C47SD1612yes—
74C22×C4×C47—21no—
75C22×C4×C47—41no—
76C22×C4×C47—41no—
77C22×C4×C47—41no—
78C22×C4×C47—82no—
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47#4111yescharacteristic
81C22×C4×C47#4111yescharacteristic
82SD16×C47—48no—
83M16×C47—41no—
84M16×C47—41no—
85M16×C47—41no—
86M16×C47—41no—
87C2×C8×C47—22no—
88C2×C8×C47—22no—
89C2×C8×C47—41no—
90C2×C8×C47—41no—
91C2×C8×C47—41no—
92C2×C8×C47—41no—
93C2×C8×C47—41no—
94C4⋊C4×C47—21no—
95C4⋊C4×C47—22no—
96C4⋊C4×C47—21no—
97C4⋊C4×C47—22no—
98C4⋊C4×C47—41no—
99C4⋊C4×C47—41no—
100C22⋊C4×C47—41no—
101C22⋊C4×C47—41no—
102C42×C47C2×D411yescharacteristic
103C42×C47C2×D411yescharacteristic
104C42×C47C2×D411yescharacteristic
105C42×C47#4111yescharacteristic
106C23×C47—22no—
107C23×C47—41no—
108C23×C47—41no—
109C23×C47—81no—
110C23×C47—81no—
111C23×C47#12311yescharacteristic
112Q8×C47—42no—
113Q8×C47—42no—
114Q8×C47—81no—
115Q8×C47—81no—
116D4×C47—22no—
117D4×C47—22no—
118D4×C47—41no—
119D4×C47—41no—
120C2×C4×C47—22no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47—42no—
124C2×C4×C47—82no—
125C2×C4×C47—81no—
126C2×C4×C47—81no—
127C2×C4×C47—82no—
128C2×C4×C47—81no—
129C2×C4×C47#12011yescharacteristic
130C2×C4×C47#12111yescharacteristic
131C2×C4×C47#12111yescharacteristic
132C2×C4×C47#12111yescharacteristic
133C2×C4×C47#12311yescharacteristic
134C2×C4×C47#12411yescharacteristic
135C2×C4×C47C2×SD1611yescharacteristic
136C2×C4×C47#13511yescharacteristic
137C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
139C8×C47—42no—
140C8×C47—42no—
141C8×C47—81no—
142C8×C47—81no—
143C8×C47—81no—
144#10445C4711yesmaximal, characteristic, direct product factor, Sylow
145C22×C47—21no—
146C22×C47—21no—
147C22×C47—42no—
148C22×C47—82no—
149C22×C47—82no—
150C22×C47—81no—
151C22×C47—81no—
152C22×C47#39411yescharacteristic
153C22×C47#48111yescharacteristic
154C22×C47#48211yescharacteristic
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—82no—
159C4×C47—81no—
160C4×C47#44911yescharacteristic
161C4×C47#45011yescharacteristic
162C4×C47#46511yescharacteristic
163C4×C47#46911yescharacteristic
164C4×C47#47112yes—
165C2×#461C2×C4711yescharacteristic
166#1800C2×C4711yescharacteristic
167#1570C2×C4711yescharacteristic, complemented
168#1546C2×C4711yescharacteristic, complemented
169#1546C2×C4711yescharacteristic, complemented
170#1478C2×C4711yescharacteristic
171#1301C2×C4711yescharacteristic, complemented
172C2×C47—21no—
173C2×C47—21no—
174C2×C47—82no—
175C2×C47#203411yescharacteristic
176C2×C47#204611yescharacteristic
177C2×C47#204911yescharacteristic
178C22×SD16—21no—
179C2×C4⋊Q8C22×C4711yescharacteristic
180C2×C4×D4C22×C4711yescharacteristic
181#461—22no—
182#461—22no—
183#431C22×C4711yescharacteristic
184#431C22×C4711yescharacteristic
185#423C22×C4711yescharacteristic
186#423C22×C4711yescharacteristic
187C2×C4⋊C8C22×C4711yescharacteristic
188C2×#103—21no—
189C2×#100—21no—
190#343—21no—
191#334—22no—
192#332—22no—
193#332—22no—
194D4⋊C8—22no—
195C47#1044511yescharacteristic, direct product factor, Sylow
196C22×Q8—21no—
197C22×D4D4×C4711yescharacteristic
198C23×C4—21no—
199C2×SD16—24no—
200C2×SD16—42no—
201C2×SD16—42no—
202C2×M16—21no—
203C2×M16—21no—
204C22×C8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8D4×C4712yes—
209C4×D4—21no—
210C4×D4—21no—
211C4×D4—21no—
212C4×D4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4D4×C4711yescharacteristic
216C2×C22⋊C4—21no—
217C2×C42C23×C4711yescharacteristic
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8D4×C4712yes—
225C4⋊C8D4×C4712yes—
226#103—24no—
227#100—42no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C4×C8—21no—
231C4×C8—21no—
232C24—21no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4SD16×C4712yes—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—82no—
250C22×C4C2×D4×C4711yescharacteristic
251C22×C4#41×C4711yescharacteristic
252C22×C4#41×C4711yescharacteristic
253SD16—48no—
254M16—41no—
255M16—41no—
256M16—41no—
257M16—41no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C42C2×D4×C4711yescharacteristic
274C42C2×D4×C4711yescharacteristic
275C42C2×D4×C4711yescharacteristic
276C42#41×C4711yescharacteristic
277C23—22no—
278C23—41no—
279C23—41no—
280C23—81no—
281C23—81no—
282C23#123×C4711yescharacteristic
283Q8—42no—
284Q8—42no—
285Q8—81no—
286Q8—81no—
287D4—22no—
288D4—22no—
289D4—41no—
290D4—41no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—82no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—82no—
299C2×C4—81no—
300C2×C4#120×C4711yescharacteristic
301C2×C4#121×C4711yescharacteristic
302C2×C4#121×C4711yescharacteristic
303C2×C4#121×C4711yescharacteristic
304C2×C4#123×C4711yescharacteristic
305C2×C4#124×C4711yescharacteristic
306C2×C4C2×SD16×C4711yescharacteristic
307C2×C4#135×C4711yescharacteristic
308C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
309C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
310C8—42no—
311C8—42no—
312C8—81no—
313C8—81no—
314C8—81no—
315C22—21no—
316C22—21no—
317C22—42no—
318C22—82no—
319C22—82no—
320C22—81no—
321C22—81no—
322C22C47×#39411yescharacteristic
323C22C47×#48111yescharacteristic
324C22C47×#48211yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—82no—
329C4—81no—
330C4C47×#44911yescharacteristic
331C4C47×#45011yescharacteristic
332C4C47×#46511yescharacteristic
333C4C47×#46911yescharacteristic
334C4C47×#47112yes—
335C2—21no—
336C2—21no—
337C2—82no—
338C2C47×#203411yescharacteristic
339C2C47×#204611yescharacteristic
340C2C47×#204911yescharacteristic
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×#1570C2semidirect
4. C47×#1546C2semidirect
5. C47×#1546C2semidirect
7. C47×#1301C2semidirect
144. #10445C47direct (N × H)
167. #1570C2×C47semidirect
168. #1546C2×C47semidirect
169. #1546C2×C47semidirect
171. #1301C2×C47semidirect
195. C47#10445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#4612
C47×#18002
C47×#15702
C47×#15462
C47×#14782
C47×#13012
#1044547