Finite Group Databasebeta

← C47×#13443 #26053141

Subgroups — C47×#13443 #26053141

Order 12032.

378 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#510C211yesmaximal, characteristic
2C47×#2153C211yesmaximal, characteristic, complemented
3C47×#2148C211yesmaximal, characteristic
4C47×#2141C211yesmaximal, characteristic, complemented
5C47×#1979C211yesmaximal, characteristic, complemented
6C47×#1976C211yesmaximal, characteristic
7C47×#1389C211yesmaximal, characteristic, complemented
8C2×#135×C47C2211yescharacteristic
9C22×Q16×C47C2211yescharacteristic
10C47×#510—22no—
11C47×#510—22no—
12C2×Q32×C47—21no—
13C2×SD32×C47—21no—
14C2×M32×C47C2211yescharacteristic
15C2×M32×C47C2211yescharacteristic
16C2×#108×C47C2211yescharacteristic
17C47×#427C2211yescharacteristic
18C47×#421—21no—
19C47×#419—21no—
20C2×#101×C47—21no—
21C47×#410—21no—
22C47×#405C2211yescharacteristic
23C47×#364—22no—
24C47×#362—21no—
25C47×#361—21no—
26C47×#358—22no—
27C2×#41×C47—21no—
28C22×Q8×C47—21no—
29#135×C47—21no—
30#135×C47—21no—
31#135×C47—21no—
32#135×C47—21no—
33C2×Q16×C47—21no—
34C2×Q16×C47—21no—
35C2×Q16×C47—21no—
36C2×Q16×C47—21no—
37C2×Q16×C47—21no—
38C2×Q16×C47D411yescharacteristic
39C2×Q16×C47D412yes—
40C2×SD16×C47—21no—
41C2×D8×C47D411yescharacteristic
42C2×M16×C47—21no—
43C2×M16×C47D411yescharacteristic
44C22×C8×C47C2311yescharacteristic
45#117×C47—21no—
46#117×C47D411yescharacteristic
47Q32×C47—24no—
48SD32×C47—24no—
49M32×C47—21no—
50M32×C47—21no—
51M32×C47—21no—
52M32×C47D412yes—
53C2×C16×C47—21no—
54C2×C16×C47—21no—
55#108×C47—21no—
56#108×C47—21no—
57#107×C47—21no—
58#106×C47—21no—
59#104×C47—42no—
60#103×C47—42no—
61#101×C47—42no—
62#99×C47—42no—
63#97×C47—21no—
64C4×C8×C47—21no—
65#41×C47—41no—
66#41×C47—41no—
67#41×C47—41no—
68#41×C47—41no—
69C2×Q8×C47—21no—
70C2×Q8×C47—22no—
71C2×Q8×C47—41no—
72C2×Q8×C47—41no—
73C2×Q8×C47—41no—
74C2×Q8×C47—41no—
75C2×Q8×C47—41no—
76C2×D4×C47—21no—
77C2×D4×C47—41no—
78C22×C4×C47—41no—
79C22×C4×C47—41no—
80C22×C4×C47C2×D411yescharacteristic
81Q16×C47—22no—
82Q16×C47—21no—
83Q16×C47—22no—
84Q16×C47—21no—
85Q16×C47—41no—
86Q16×C47—41no—
87SD16×C47—41no—
88SD16×C47—41no—
89D8×C47—21no—
90D8×C47—21no—
91M16×C47—21no—
92M16×C47—41no—
93M16×C47—41no—
94M16×C47D812yes—
95C2×C8×C47—21no—
96C2×C8×C47—41no—
97C2×C8×C47C2×D411yescharacteristic
98C2×C8×C47C2×D411yescharacteristic
99C2×C8×C47C2×D411yescharacteristic
100C2×C8×C47#4111yescharacteristic
101C2×C8×C47#4111yescharacteristic
102C2×C8×C47#4111yescharacteristic
103C4⋊C4×C47—21no—
104C4⋊C4×C47—41no—
105C22⋊C4×C47—21no—
106C22⋊C4×C47—41no—
107C42×C47—21no—
108C42×C47—41no—
109C16×C47—22no—
110C16×C47—41no—
111C23×C47—41no—
112C23×C47AGL(1,ℤ/8)11yescharacteristic
113Q8×C47—41no—
114Q8×C47—42no—
115Q8×C47—41no—
116Q8×C47—42no—
117Q8×C47—81no—
118Q8×C47—81no—
119D4×C47—41no—
120D4×C47—41no—
121D4×C47—81no—
122D4×C47—81no—
123C2×C4×C47—42no—
124C2×C4×C47—41no—
125C2×C4×C47—41no—
126C2×C4×C47—81no—
127C2×C4×C47—81no—
128C2×C4×C47—81no—
129C2×C4×C47—81no—
130C2×C4×C47—81no—
131C2×C4×C47#12111yescharacteristic
132C2×C4×C47#12111yescharacteristic
133C2×C4×C47#12111yescharacteristic
134C2×C4×C47C2×D811yescharacteristic
135C2×C4×C47#13511yescharacteristic
136C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
137C8×C47—22no—
138C8×C47—81no—
139C8×C47#12011yescharacteristic
140C8×C47#12311yescharacteristic
141C8×C47#12311yescharacteristic
142C8×C47#12411yescharacteristic
143#13443C4711yesmaximal, characteristic, direct product factor, Sylow
144C22×C47—41no—
145C22×C47—81no—
146C22×C47—161no—
147C22×C47#45911yescharacteristic
148C22×C47#46311yescharacteristic
149C22×C47#46911yescharacteristic
150C4×C47—81no—
151C4×C47—81no—
152C4×C47—82no—
153C4×C47—161no—
154C4×C47#39411yescharacteristic
155C4×C47#45911yescharacteristic
156C4×C47#46311yescharacteristic
157C4×C47#46611yescharacteristic
158C2×#510C2×C4711yescharacteristic
159#2153C2×C4711yescharacteristic, complemented
160#2148C2×C4711yescharacteristic
161#2141C2×C4711yescharacteristic, complemented
162#1979C2×C4711yescharacteristic, complemented
163#1976C2×C4711yescharacteristic
164#1389C2×C4711yescharacteristic, complemented
165C2×C47—21no—
166C2×C47—21no—
167C2×C47—21no—
168C2×C47—161no—
169C2×C47#205411yescharacteristic
170C2×#135C22×C4711yescharacteristic
171C22×Q16C22×C4711yescharacteristic
172#510—22no—
173#510—22no—
174C2×Q32—21no—
175C2×SD32—21no—
176C2×M32C22×C4711yescharacteristic
177C2×M32C22×C4711yescharacteristic
178C2×#108C22×C4711yescharacteristic
179#427C22×C4711yescharacteristic
180#421—21no—
181#419—21no—
182C2×#101—21no—
183#410—21no—
184#405C22×C4711yescharacteristic
185#364—22no—
186#362—21no—
187#361—21no—
188#358—22no—
189C47#1344311yescharacteristic, direct product factor, Sylow
190C2×#41—21no—
191C22×Q8—21no—
192#135—21no—
193#135—21no—
194#135—21no—
195#135—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16D4×C4712yes—
202C2×Q16D4×C4711yescharacteristic
203C2×SD16—21no—
204C2×D8D4×C4711yescharacteristic
205C2×M16—21no—
206C2×M16D4×C4711yescharacteristic
207C22×C8C23×C4711yescharacteristic
208#117—21no—
209#117D4×C4711yescharacteristic
210Q32—24no—
211SD32—24no—
212M32—21no—
213M32—21no—
214M32—21no—
215M32D4×C4712yes—
216C2×C16—21no—
217C2×C16—21no—
218#108—21no—
219#108—21no—
220#107—21no—
221#106—21no—
222#104—42no—
223#103—42no—
224#101—42no—
225#99—42no—
226#97—21no—
227C4×C8—21no—
228#41—41no—
229#41—41no—
230#41—41no—
231#41—41no—
232C2×Q8—21no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×D4—21no—
240C2×D4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C2×D4×C4711yescharacteristic
244Q16—22no—
245Q16—21no—
246Q16—22no—
247Q16—21no—
248Q16—41no—
249Q16—41no—
250SD16—41no—
251SD16—41no—
252D8—21no—
253D8—21no—
254M16—21no—
255M16—41no—
256M16—41no—
257M16D8×C4712yes—
258C2×C8—21no—
259C2×C8—41no—
260C2×C8C2×D4×C4711yescharacteristic
261C2×C8C2×D4×C4711yescharacteristic
262C2×C8C2×D4×C4711yescharacteristic
263C2×C8#41×C4711yescharacteristic
264C2×C8#41×C4711yescharacteristic
265C2×C8#41×C4711yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—41no—
268C22⋊C4—21no—
269C22⋊C4—41no—
270C42—21no—
271C42—41no—
272C16—22no—
273C16—41no—
274C23—41no—
275C23AGL(1,ℤ/8)×C4711yescharacteristic
276Q8—41no—
277Q8—42no—
278Q8—41no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282D4—41no—
283D4—41no—
284D4—81no—
285D4—81no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4#121×C4711yescharacteristic
295C2×C4#121×C4711yescharacteristic
296C2×C4#121×C4711yescharacteristic
297C2×C4C2×D8×C4711yescharacteristic
298C2×C4#135×C4711yescharacteristic
299C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
300C8—22no—
301C8—81no—
302C8#120×C4711yescharacteristic
303C8#123×C4711yescharacteristic
304C8#123×C4711yescharacteristic
305C8#124×C4711yescharacteristic
306C22—41no—
307C22—81no—
308C22—161no—
309C22C47×#45911yescharacteristic
310C22C47×#46311yescharacteristic
311C22C47×#46911yescharacteristic
312C4—81no—
313C4—81no—
314C4—82no—
315C4—161no—
316C4C47×#39411yescharacteristic
317C4C47×#45911yescharacteristic
318C4C47×#46311yescharacteristic
319C4C47×#46611yescharacteristic
320C2—21no—
321C2—21no—
322C2—21no—
323C2—161no—
324C2C47×#205411yescharacteristic
subgroupG/H
center, socleC2×C47#2054
commutator, Frattini, cosocleC22×C8C23×C47
prime radicalC2×#135×C47C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C4×C47 ◁ C47×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2153C2semidirect
4. C47×#2141C2semidirect
5. C47×#1979C2semidirect
7. C47×#1389C2semidirect
143. #13443C47direct (N × H)
159. #2153C2×C47semidirect
161. #2141C2×C47semidirect
162. #1979C2×C47semidirect
164. #1389C2×C47semidirect
189. C47#13443direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5102
C47×#21532
C47×#21482
C47×#21412
C47×#19792
C47×#19762
C47×#13892
#1344347