Finite Group Databasebeta

← C47×#13412 #26053110

Subgroups — C47×#13412 #26053110

Order 12032.

430 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3156C211yesmaximal, characteristic
2C2×C47×#362C211yesmaximal, characteristic, complemented
3C2×C47×#359C211yesmaximal, characteristic
4C47×#2139C211yesmaximal, characteristic
5C2×C47×#358C211yesmaximal, characteristic, complemented
6C47×#1952C211yesmaximal, characteristic, complemented
7C47×#1379C211yesmaximal, characteristic, complemented
8C2×#137×C47—21no—
9C2×#135×C47C2211yescharacteristic
10C22×Q16×C47C2211yescharacteristic
11C47×#536—21no—
12C2×M32×C47C2211yescharacteristic
13C22×C16×C47C2211yescharacteristic
14C47×#497—22no—
15C47×#495—21no—
16C47×#494—21no—
17C2×#108×C47C2211yescharacteristic
18C47×#428—21no—
19C2×#107×C47C2211yescharacteristic
20C47×#405C2211yescharacteristic
21C47×#362—22no—
22C47×#359—22no—
23C47×#358—22no—
24C47×#358—21no—
25C47×#357—21no—
26C47×#343—21no—
27C2×#41×C47—21no—
28C22×Q8×C47—21no—
29#137×C47—42no—
30#137×C47—42no—
31#135×C47—21no—
32#135×C47—21no—
33#135×C47—21no—
34#135×C47—21no—
35C2×Q16×C47—22no—
36C2×Q16×C47—21no—
37C2×Q16×C47—21no—
38C2×Q16×C47—21no—
39C2×Q16×C47—21no—
40C2×Q16×C47—21no—
41C2×Q16×C47D411yescharacteristic
42C2×Q16×C47D412yes—
43C2×SD16×C47—22no—
44C2×SD16×C47—21no—
45C2×D8×C47D411yescharacteristic
46C2×M16×C47—21no—
47C2×M16×C47D411yescharacteristic
48C22×C8×C47C2311yescharacteristic
49C4⋊Q8×C47—22no—
50#124×C47—22no—
51#123×C47—42no—
52C22⋊Q8×C47—41no—
53C22⋊Q8×C47—41no—
54#117×C47D411yescharacteristic
55C2×C4⋊C4×C47—21no—
56M32×C47—21no—
57M32×C47—21no—
58C2×C16×C47—21no—
59C2×C16×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62#108×C47—21no—
63#108×C47D412yes—
64#107×C47—21no—
65#107×C47—21no—
66#107×C47—41no—
67#106×C47—41no—
68#97×C47—21no—
69C4×C8×C47—21no—
70#41×C47—41no—
71#41×C47—41no—
72#41×C47—41no—
73#41×C47—41no—
74C2×Q8×C47—22no—
75C2×Q8×C47—21no—
76C2×Q8×C47—41no—
77C2×Q8×C47—41no—
78C2×Q8×C47—41no—
79C2×Q8×C47—41no—
80C2×Q8×C47—41no—
81C2×D4×C47—21no—
82C2×D4×C47—41no—
83C22×C4×C47—41no—
84C22×C4×C47—41no—
85C22×C4×C47—41no—
86C22×C4×C47C2×D411yescharacteristic
87Q16×C47—22no—
88Q16×C47—21no—
89Q16×C47—22no—
90Q16×C47—21no—
91Q16×C47—44no—
92Q16×C47—41no—
93Q16×C47—41no—
94SD16×C47—44no—
95SD16×C47—41no—
96SD16×C47—41no—
97D8×C47—21no—
98D8×C47—21no—
99M16×C47—21no—
100M16×C47—22no—
101M16×C47—41no—
102M16×C47SD1612yes—
103C2×C8×C47—21no—
104C2×C8×C47—41no—
105C2×C8×C47C2×D411yescharacteristic
106C2×C8×C47C2×D411yescharacteristic
107C2×C8×C47C2×D411yescharacteristic
108C2×C8×C47#4111yescharacteristic
109C2×C8×C47#4111yescharacteristic
110C2×C8×C47#4111yescharacteristic
111C4⋊C4×C47—42no—
112C4⋊C4×C47—42no—
113C4⋊C4×C47—41no—
114C4⋊C4×C47—41no—
115C4⋊C4×C47D811yescharacteristic
116C4⋊C4×C47D811yescharacteristic
117C22⋊C4×C47—21no—
118C22⋊C4×C47—42no—
119C22⋊C4×C47—42no—
120C42×C47—21no—
121C16×C47—41no—
122C16×C47—41no—
123C23×C47—41no—
124C23×C47AGL(1,ℤ/8)11yescharacteristic
125Q8×C47—41no—
126Q8×C47—42no—
127Q8×C47—42no—
128Q8×C47—41no—
129Q8×C47—81no—
130Q8×C47—81no—
131D4×C47—41no—
132D4×C47—41no—
133D4×C47—81no—
134D4×C47—81no—
135C2×C4×C47—21no—
136C2×C4×C47—21no—
137C2×C4×C47—42no—
138C2×C4×C47—41no—
139C2×C4×C47—81no—
140C2×C4×C47—81no—
141C2×C4×C47—81no—
142C2×C4×C47—81no—
143C2×C4×C47—81no—
144C2×C4×C47—161no—
145C2×C4×C47#12011yescharacteristic
146C2×C4×C47#12111yescharacteristic
147C2×C4×C47#12411yescharacteristic
148C2×C4×C47C2×D811yescharacteristic
149C2×C4×C47C2×SD1611yescharacteristic
150C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
151C8×C47—22no—
152C8×C47—42no—
153C8×C47#12111yescharacteristic
154C8×C47#12111yescharacteristic
155C8×C47#12311yescharacteristic
156C8×C47#12311yescharacteristic
157#13412C4711yesmaximal, characteristic, direct product factor, Sylow
158C22×C47—21no—
159C22×C47—21no—
160C22×C47—81no—
161C22×C47—81no—
162C22×C47—81no—
163C22×C47#44711yescharacteristic
164C22×C47#46011yescharacteristic
165C22×C47#49011yescharacteristic
166C4×C47—41no—
167C4×C47—41no—
168C4×C47—81no—
169C4×C47—82no—
170C4×C47—161no—
171C4×C47#39411yescharacteristic
172C4×C47#45011yescharacteristic
173C4×C47#45911yescharacteristic
174C4×C47#48611yescharacteristic
175#3156C2×C4711yescharacteristic
176C2×#362C2×C4711yescharacteristic, complemented
177C2×#359C2×C4711yescharacteristic
178#2139C2×C4711yescharacteristic
179C2×#358C2×C4711yescharacteristic, complemented
180#1952C2×C4711yescharacteristic, complemented
181#1379C2×C4711yescharacteristic, complemented
182C2×C47—21no—
183C2×C47—21no—
184C2×C47—161no—
185C2×C47#204111yescharacteristic
186C2×C47#219311yescharacteristic
187C2×C47#219511yescharacteristic
188C2×#137—21no—
189C2×#135C22×C4711yescharacteristic
190C22×Q16C22×C4711yescharacteristic
191#536—21no—
192C2×M32C22×C4711yescharacteristic
193C22×C16C22×C4711yescharacteristic
194#497—22no—
195#495—21no—
196#494—21no—
197C2×#108C22×C4711yescharacteristic
198#428—21no—
199C2×#107C22×C4711yescharacteristic
200#405C22×C4711yescharacteristic
201#362—22no—
202#359—22no—
203#358—22no—
204#358—21no—
205#357—21no—
206#343—21no—
207C47#1341211yescharacteristic, direct product factor, Sylow
208C2×#41—21no—
209C22×Q8—21no—
210#137—42no—
211#137—42no—
212#135—21no—
213#135—21no—
214#135—21no—
215#135—21no—
216C2×Q16—22no—
217C2×Q16—21no—
218C2×Q16—21no—
219C2×Q16—21no—
220C2×Q16—21no—
221C2×Q16—21no—
222C2×Q16D4×C4712yes—
223C2×Q16D4×C4711yescharacteristic
224C2×SD16—22no—
225C2×SD16—21no—
226C2×D8D4×C4711yescharacteristic
227C2×M16—21no—
228C2×M16D4×C4711yescharacteristic
229C22×C8C23×C4711yescharacteristic
230C4⋊Q8—22no—
231#124—22no—
232#123—42no—
233C22⋊Q8—41no—
234C22⋊Q8—41no—
235#117D4×C4711yescharacteristic
236C2×C4⋊C4—21no—
237M32—21no—
238M32—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—21no—
243#108—21no—
244#108D4×C4712yes—
245#107—21no—
246#107—21no—
247#107—41no—
248#106—41no—
249#97—21no—
250C4×C8—21no—
251#41—41no—
252#41—41no—
253#41—41no—
254#41—41no—
255C2×Q8—22no—
256C2×Q8—21no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×D4—21no—
263C2×D4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4C2×D4×C4711yescharacteristic
268Q16—22no—
269Q16—21no—
270Q16—22no—
271Q16—21no—
272Q16—44no—
273Q16—41no—
274Q16—41no—
275SD16—44no—
276SD16—41no—
277SD16—41no—
278D8—21no—
279D8—21no—
280M16—21no—
281M16—22no—
282M16—41no—
283M16SD16×C4712yes—
284C2×C8—21no—
285C2×C8—41no—
286C2×C8C2×D4×C4711yescharacteristic
287C2×C8C2×D4×C4711yescharacteristic
288C2×C8C2×D4×C4711yescharacteristic
289C2×C8#41×C4711yescharacteristic
290C2×C8#41×C4711yescharacteristic
291C2×C8#41×C4711yescharacteristic
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4D8×C4711yescharacteristic
297C4⋊C4D8×C4711yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—42no—
300C22⋊C4—42no—
301C42—21no—
302C16—41no—
303C16—41no—
304C23—41no—
305C23AGL(1,ℤ/8)×C4711yescharacteristic
306Q8—42no—
307Q8—41no—
308Q8—41no—
309Q8—42no—
310Q8—81no—
311Q8—81no—
312D4—41no—
313D4—41no—
314D4—81no—
315D4—81no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—161no—
326C2×C4#120×C4711yescharacteristic
327C2×C4#121×C4711yescharacteristic
328C2×C4#124×C4711yescharacteristic
329C2×C4C2×D8×C4711yescharacteristic
330C2×C4C2×SD16×C4711yescharacteristic
331C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
332C8—22no—
333C8—42no—
334C8#121×C4711yescharacteristic
335C8#121×C4711yescharacteristic
336C8#123×C4711yescharacteristic
337C8#123×C4711yescharacteristic
338C22—21no—
339C22—21no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22C47×#44711yescharacteristic
344C22C47×#46011yescharacteristic
345C22C47×#49011yescharacteristic
346C4—41no—
347C4—41no—
348C4—81no—
349C4—82no—
350C4—161no—
351C4C47×#39411yescharacteristic
352C4C47×#45011yescharacteristic
353C4C47×#45911yescharacteristic
354C4C47×#48611yescharacteristic
355C2—21no—
356C2—21no—
357C2—161no—
358C2C47×#204111yescharacteristic
359C2C47×#219311yescharacteristic
360C2C47×#219511yescharacteristic
subgroupG/H
center, socleC22×C47#447
commutator, Frattini, cosocleC22×C8C23×C47
prime radicalC2×#135×C47C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C47×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C47×#362C2semidirect
5. C2×C47×#358C2semidirect
6. C47×#1952C2semidirect
7. C47×#1379C2semidirect
157. #13412C47direct (N × H)
176. C2×#362C2×C47semidirect
179. C2×#358C2×C47semidirect
180. #1952C2×C47semidirect
181. #1379C2×C47semidirect
207. C47#13412direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#31562
C2×C47×#3622
C2×C47×#3592
C47×#21392
C2×C47×#3582
C47×#19522
C47×#13792
#1341247