Finite Group Databasebeta

← C47×#10283 #26049981

Subgroups — C47×#10283 #26049981

Order 12032.

626 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3227C211yesmaximal, characteristic
2C47×#3206C211yesmaximal, characteristic
3C47×#2868C211yesmaximal, characteristic, complemented
4C47×#1962C211yesmaximal, characteristic
5C47×#1549C211yesmaximal, characteristic, complemented
6C47×#1548C211yesmaximal, characteristic, complemented
7C47×#1276C211yesmaximal, characteristic, complemented
8C47×#532C2211yescharacteristic
9C2×C4⋊Q8×C47—22no—
10C2×C4⋊Q8×C47C2211yescharacteristic
11C2×C4⋊Q8×C47C2211yescharacteristic
12C47×#498—21no—
13C47×#492—21no—
14C47×#487—21no—
15C47×#486—21no—
16C47×#481—22no—
17C47×#476—22no—
18C47×#461—22no—
19C47×#448—22no—
20C47×#431C2211yescharacteristic
21C47×#431C2211yescharacteristic
22C47×#423C2211yescharacteristic
23C2×#104×C47—22no—
24C47×#384—22no—
25C47×#384—22no—
26C43×C47C2211yescharacteristic
27C47×#333—22no—
28C47×#332—22no—
29C2×#41×C47—21no—
30C22×Q8×C47—21no—
31C22×Q8×C47D412yes—
32C2×SD16×C47—24no—
33C2×M16×C47—21no—
34C4⋊Q8×C47—21no—
35C4⋊Q8×C47—21no—
36C4⋊Q8×C47—21no—
37C4⋊Q8×C47—21no—
38C4⋊Q8×C47—21no—
39C4⋊Q8×C47—21no—
40C4⋊Q8×C47—21no—
41C4⋊Q8×C47—21no—
42C4⋊Q8×C47—48no—
43C4⋊Q8×C47D411yescharacteristic
44#127×C47D411yescharacteristic
45#124×C47—21no—
46#121×C47—21no—
47#121×C47—21no—
48C4×D4×C47—21no—
49C4×D4×C47—21no—
50C2×C4⋊C4×C47—28no—
51C2×C4⋊C4×C47—21no—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47D412yes—
55C2×C42×C47—21no—
56C2×C42×C47—21no—
57C2×C42×C47D412yes—
58C2×C42×C47C2311yescharacteristic
59#106×C47—24no—
60C4⋊C8×C47—21no—
61C4⋊C8×C47—21no—
62C4⋊C8×C47D412yes—
63C4⋊C8×C47D412yes—
64#104×C47—44no—
65#103×C47—24no—
66#102×C47—24no—
67C22⋊C8×C47—21no—
68C22⋊C8×C47—21no—
69C4×C8×C47—21no—
70C4×C8×C47—21no—
71#41×C47—42no—
72#41×C47—42no—
73C2×Q8×C47—22no—
74C2×Q8×C47—21no—
75C2×Q8×C47—22no—
76C2×Q8×C47—44no—
77C2×Q8×C47—44no—
78C2×Q8×C47—41no—
79C2×Q8×C47—41no—
80C2×D4×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—21no—
83C2×D4×C47—41no—
84C22×C4×C47—22no—
85C22×C4×C47—22no—
86C22×C4×C47—22no—
87C22×C4×C47—41no—
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91SD16×C47—84no—
92M16×C47—42no—
93C2×C8×C47—22no—
94C2×C8×C47—22no—
95C2×C8×C47—41no—
96C4⋊C4×C47—21no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—22no—
99C4⋊C4×C47—22no—
100C4⋊C4×C47—416no—
101C4⋊C4×C47—41no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C4⋊C4×C47—41no—
105C4⋊C4×C47—41no—
106C4⋊C4×C47—41no—
107C22⋊C4×C47—41no—
108C22⋊C4×C47—41no—
109C42×C47—24no—
110C42×C47—24no—
111C42×C47—22no—
112C42×C47SD1614yescomplemented
113C42×C47C2×D411yescharacteristic
114C42×C47C2×D411yescharacteristic
115C42×C47C2×D411yescharacteristic
116C42×C47#4111yescharacteristic
117C23×C47—41no—
118C23×C47#12011yescharacteristic
119Q8×C47—44no—
120Q8×C47—42no—
121Q8×C47—82no—
122Q8×C47—82no—
123Q8×C47—82no—
124D4×C47—42no—
125D4×C47—42no—
126D4×C47—42no—
127D4×C47—82no—
128C2×C4×C47—24no—
129C2×C4×C47—24no—
130C2×C4×C47—24no—
131C2×C4×C47—22no—
132C2×C4×C47—22no—
133C2×C4×C47—44no—
134C2×C4×C47—44no—
135C2×C4×C47—41no—
136C2×C4×C47—42no—
137C2×C4×C47—42no—
138C2×C4×C47—81no—
139C2×C4×C47—81no—
140C2×C4×C47#12011yescharacteristic
141C2×C4×C47#12011yescharacteristic
142C2×C4×C47#12111yescharacteristic
143C2×C4×C47#12111yescharacteristic
144C2×C4×C47#12111yescharacteristic
145C2×C4×C47#12711yescharacteristic
146C2×C4×C47C2×SD1612yes—
147C2×C4×C47#13712yes—
148C8×C47—42no—
149C8×C47—42no—
150C8×C47—81no—
151#10283C4711yesmaximal, characteristic, direct product factor, Sylow
152C22×C47—21no—
153C22×C47—21no—
154C22×C47—81no—
155C22×C47—81no—
156C22×C47—81no—
157C22×C47#39211yescharacteristic
158C22×C47#44812yes—
159C4×C47—28no—
160C4×C47—21no—
161C4×C47—21no—
162C4×C47—82no—
163C4×C47—82no—
164C4×C47—81no—
165C4×C47#45312yes—
166C4×C47#45612yes—
167C4×C47#46112yes—
168C4×C47#49211yescharacteristic
169C4×C47#49711yescharacteristic
170#3227C2×C4711yescharacteristic
171#3206C2×C4711yescharacteristic
172#2868C2×C4711yescharacteristic, complemented
173#1962C2×C4711yescharacteristic
174#1549C2×C4711yescharacteristic, complemented
175#1548C2×C4711yescharacteristic, complemented
176#1276C2×C4711yescharacteristic, complemented
177C2×C47—22no—
178C2×C47—161no—
179C2×C47#200211yescharacteristic
180C2×C47#200511yescharacteristic
181C2×C47#201311yescharacteristic
182#532C22×C4711yescharacteristic
183C2×C4⋊Q8—22no—
184C2×C4⋊Q8C22×C4711yescharacteristic
185C2×C4⋊Q8C22×C4711yescharacteristic
186#498—21no—
187#492—21no—
188#487—21no—
189#486—21no—
190#481—22no—
191#476—22no—
192#461—22no—
193#448—22no—
194#431C22×C4711yescharacteristic
195#431C22×C4711yescharacteristic
196#423C22×C4711yescharacteristic
197C2×#104—22no—
198#384—22no—
199#384—22no—
200C43C22×C4711yescharacteristic
201#333—22no—
202#332—22no—
203C47#1028311yescharacteristic, direct product factor, Sylow
204C2×#41—21no—
205C22×Q8—21no—
206C22×Q8D4×C4712yes—
207C2×SD16—24no—
208C2×M16—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—21no—
216C4⋊Q8—21no—
217C4⋊Q8—48no—
218C4⋊Q8D4×C4711yescharacteristic
219#127D4×C4711yescharacteristic
220#124—21no—
221#121—21no—
222#121—21no—
223C4×D4—21no—
224C4×D4—21no—
225C2×C4⋊C4—28no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4D4×C4712yes—
230C2×C42—21no—
231C2×C42—21no—
232C2×C42D4×C4712yes—
233C2×C42C23×C4711yescharacteristic
234#106—24no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8D4×C4712yes—
238C4⋊C8D4×C4712yes—
239#104—44no—
240#103—24no—
241#102—24no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C4×C8—21no—
245C4×C8—21no—
246#41—42no—
247#41—42no—
248C2×Q8—22no—
249C2×Q8—21no—
250C2×Q8—22no—
251C2×Q8—44no—
252C2×Q8—44no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—41no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—41no—
263C22×C4C2×D4×C4711yescharacteristic
264C22×C4C2×D4×C4711yescharacteristic
265C22×C4C2×D4×C4711yescharacteristic
266SD16—84no—
267M16—42no—
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—41no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—416no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C42—24no—
285C42—24no—
286C42—22no—
287C42SD16×C4714yescomplemented
288C42C2×D4×C4711yescharacteristic
289C42C2×D4×C4711yescharacteristic
290C42C2×D4×C4711yescharacteristic
291C42#41×C4711yescharacteristic
292C23—41no—
293C23#120×C4711yescharacteristic
294Q8—44no—
295Q8—42no—
296Q8—82no—
297Q8—82no—
298Q8—82no—
299D4—42no—
300D4—42no—
301D4—42no—
302D4—82no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4#120×C4711yescharacteristic
316C2×C4#120×C4711yescharacteristic
317C2×C4#121×C4711yescharacteristic
318C2×C4#121×C4711yescharacteristic
319C2×C4#121×C4711yescharacteristic
320C2×C4#127×C4711yescharacteristic
321C2×C4C2×SD16×C4712yes—
322C2×C4#137×C4712yes—
323C8—42no—
324C8—42no—
325C8—81no—
326C22—21no—
327C22—21no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22C47×#39211yescharacteristic
332C22C47×#44812yes—
333C4—28no—
334C4—21no—
335C4—21no—
336C4—81no—
337C4—82no—
338C4—82no—
339C4C47×#45312yes—
340C4C47×#45612yes—
341C4C47×#46112yes—
342C4C47×#49211yescharacteristic
343C4C47×#49711yescharacteristic
344C2—22no—
345C2—161no—
346C2C47×#200211yescharacteristic
347C2C47×#200511yescharacteristic
348C2C47×#201311yescharacteristic
subgroupG/H
center, socleC22×C47#392
commutator, Frattini, cosocleC2×C42C23×C47
prime radicalC47×#532C22
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×#2868C2semidirect
5. C47×#1549C2semidirect
6. C47×#1548C2semidirect
7. C47×#1276C2semidirect
112. C42×C47SD16semidirect
151. #10283C47direct (N × H)
172. #2868C2×C47semidirect
174. #1549C2×C47semidirect
175. #1548C2×C47semidirect
176. #1276C2×C47semidirect
203. C47#10283direct (N × H)
287. C42SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#32272
C47×#32062
C47×#28682
C47×#19622
C47×#15492
C47×#15482
C47×#12762
#1028347