Finite Group Databasebeta

← C47×#9285 #26048983

Subgroups — C47×#9285 #26048983

Order 12032.

426 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3210C211yesmaximal, characteristic
2C47×#2981C211yesmaximal, characteristic
3C47×#1531C211yesmaximal, characteristic, complemented
4C47×#1530C211yesmaximal, characteristic
5C47×#1497C211yesmaximal, characteristic, complemented
6C47×#1287C211yesmaximal, characteristic, complemented
7C47×#1275C211yesmaximal, characteristic, complemented
8C47×#533C2211yescharacteristic
9C47×#532C2211yescharacteristic
10C47×#494C411yescharacteristic
11C47×#492C411yescharacteristic
12C47×#487C411yescharacteristic
13C47×#486C411yescharacteristic
14C47×#464—22no—
15C47×#452—22no—
16C47×#436—21no—
17C47×#435—22no—
18C8×D4×C47—21no—
19C47×#432C2211yescharacteristic
20C47×#432C2211yescharacteristic
21C47×#431C2211yescharacteristic
22C47×#431C2211yescharacteristic
23C47×#408—22no—
24C2×#97×C47C2211yescharacteristic
25C47×#330—22no—
26C47×#329—22no—
27C47×Q8⋊C8—21no—
28C47×Q8⋊C8—21no—
29C2×#41×C47D412yes—
30C2×Q16×C47—22no—
31C2×SD16×C47—22no—
32C2×M16×C47—22no—
33C22×C8×C47—21no—
34C22×C8×C47—22no—
35C4⋊Q8×C47C2×C411yescharacteristic
36C4⋊Q8×C47C2×C411yescharacteristic
37C4⋊Q8×C47C2×C411yescharacteristic
38#127×C47C2×C411yescharacteristic
39#125×C47—21no—
40#124×C47D412yes—
41C22⋊Q8×C47—21no—
42C22⋊Q8×C47—21no—
43#121×C47—21no—
44#121×C47—21no—
45C4×Q8×C47—21no—
46C4×Q8×C47—21no—
47C4×D4×C47—21no—
48C4×D4×C47—21no—
49#117×C47—21no—
50C2×C42×C47C2311yescharacteristic
51C4⋊C8×C47—21no—
52C4⋊C8×C47—21no—
53C4⋊C8×C47—21no—
54C4⋊C8×C47—21no—
55#103×C47—22no—
56#102×C47—22no—
57C22⋊C8×C47—22no—
58C22⋊C8×C47—22no—
59C22⋊C8×C47—21no—
60C22⋊C8×C47—21no—
61C22⋊C8×C47—21no—
62C22⋊C8×C47—21no—
63#97×C47—21no—
64#97×C47—21no—
65#97×C47—21no—
66#97×C47D412yes—
67C4×C8×C47C2×C411yescharacteristic
68C4×C8×C47C2×C411yescharacteristic
69C4×C8×C47D411yescharacteristic
70C4×C8×C47D411yescharacteristic
71#41×C47—82no—
72C2×Q8×C47—21no—
73C2×Q8×C47—21no—
74C2×Q8×C47C22⋊C412yes—
75C2×D4×C47—22no—
76C2×D4×C47—21no—
77C2×D4×C47—21no—
78C2×D4×C47C22⋊C412yes—
79C22×C4×C47—22no—
80C22×C4×C47C2×D411yescharacteristic
81C22×C4×C47#4111yescharacteristic
82C22×C4×C47#4111yescharacteristic
83Q16×C47—82no—
84SD16×C47—82no—
85M16×C47—82no—
86C2×C8×C47—22no—
87C2×C8×C47—21no—
88C2×C8×C47—21no—
89C2×C8×C47—21no—
90C2×C8×C47—22no—
91C2×C8×C47—21no—
92C2×C8×C47—41no—
93C2×C8×C47—41no—
94C2×C8×C47—41no—
95C2×C8×C47—82no—
96C4⋊C4×C47—21no—
97C4⋊C4×C47—21no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47—21no—
100C4⋊C4×C47—21no—
101C4⋊C4×C47—21no—
102C4⋊C4×C47—41no—
103C4⋊C4×C47—41no—
104C22⋊C4×C47—22no—
105C22⋊C4×C47—22no—
106C22⋊C4×C47—41no—
107C42×C47—41no—
108C42×C47C22×C411yescharacteristic
109C42×C47C2×D411yescharacteristic
110C42×C47C2×D411yescharacteristic
111C42×C47C2×D411yescharacteristic
112C23×C47—22no—
113C23×C47#12311yescharacteristic
114Q8×C47—42no—
115Q8×C47—42no—
116Q8×C47—41no—
117Q8×C47—41no—
118D4×C47—42no—
119D4×C47—41no—
120D4×C47—41no—
121D4×C47—81no—
122D4×C47—82no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—22no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—42no—
129C2×C4×C47—42no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47C2×C22⋊C411yescharacteristic
133C2×C4×C47C4×D411yescharacteristic
134C2×C4×C47C4×D411yescharacteristic
135C2×C4×C47#12011yescharacteristic
136C2×C4×C47#12111yescharacteristic
137C2×C4×C47#12111yescharacteristic
138C8×C47—42no—
139C8×C47—41no—
140C8×C47—42no—
141C8×C47—41no—
142C8×C47—41no—
143C8×C47—41no—
144C8×C47—81no—
145#9285C4711yesmaximal, characteristic, direct product factor, Sylow
146C22×C47—21no—
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—42no—
150C22×C47—42no—
151C22×C47—42no—
152C22×C47#38611yescharacteristic
153C4×C47—21no—
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—21no—
158C4×C47—42no—
159C4×C47—81no—
160C4×C47—81no—
161C4×C47#44311yescharacteristic
162C4×C47#44411yescharacteristic
163#3210C2×C4711yescharacteristic
164#2981C2×C4711yescharacteristic
165#1531C2×C4711yescharacteristic, complemented
166#1530C2×C4711yescharacteristic
167#1497C2×C4711yescharacteristic, complemented
168#1287C2×C4711yescharacteristic, complemented
169#1275C2×C4711yescharacteristic, complemented
170C2×C47—41no—
171C2×C47—82no—
172C2×C47#187611yescharacteristic
173C2×C47#190211yescharacteristic
174C2×C47#191111yescharacteristic
175#533C22×C4711yescharacteristic
176#532C22×C4711yescharacteristic
177#494C4×C4711yescharacteristic
178#492C4×C4711yescharacteristic
179#487C4×C4711yescharacteristic
180#486C4×C4711yescharacteristic
181#464—22no—
182#452—22no—
183#436—21no—
184#435—22no—
185C8×D4—21no—
186#432C22×C4711yescharacteristic
187#432C22×C4711yescharacteristic
188#431C22×C4711yescharacteristic
189#431C22×C4711yescharacteristic
190#408—22no—
191C2×#97C22×C4711yescharacteristic
192#330—22no—
193#329—22no—
194Q8⋊C8—21no—
195Q8⋊C8—21no—
196C47#928511yescharacteristic, direct product factor, Sylow
197C2×#41D4×C4712yes—
198C2×Q16—22no—
199C2×SD16—22no—
200C2×M16—22no—
201C22×C8—21no—
202C22×C8—22no—
203C4⋊Q8C2×C4×C4711yescharacteristic
204C4⋊Q8C2×C4×C4711yescharacteristic
205C4⋊Q8C2×C4×C4711yescharacteristic
206#127C2×C4×C4711yescharacteristic
207#125—21no—
208#124D4×C4712yes—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211#121—21no—
212#121—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×D4—21no—
216C4×D4—21no—
217#117—21no—
218C2×C42C23×C4711yescharacteristic
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223#103—22no—
224#102—22no—
225C22⋊C8—22no—
226C22⋊C8—22no—
227C22⋊C8—21no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C22⋊C8—21no—
231#97—21no—
232#97—21no—
233#97—21no—
234#97D4×C4712yes—
235C4×C8C2×C4×C4711yescharacteristic
236C4×C8C2×C4×C4711yescharacteristic
237C4×C8D4×C4711yescharacteristic
238C4×C8D4×C4711yescharacteristic
239#41—82no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8C22⋊C4×C4712yes—
243C2×D4—22no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4C22⋊C4×C4712yes—
247C22×C4—22no—
248C22×C4C2×D4×C4711yescharacteristic
249C22×C4#41×C4711yescharacteristic
250C22×C4#41×C4711yescharacteristic
251Q16—82no—
252SD16—82no—
253M16—82no—
254C2×C8—22no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—82no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—41no—
275C42—41no—
276C42C22×C4×C4711yescharacteristic
277C42C2×D4×C4711yescharacteristic
278C42C2×D4×C4711yescharacteristic
279C42C2×D4×C4711yescharacteristic
280C23—22no—
281C23#123×C4711yescharacteristic
282Q8—42no—
283Q8—42no—
284Q8—41no—
285Q8—41no—
286D4—42no—
287D4—41no—
288D4—41no—
289D4—81no—
290D4—82no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4C2×C22⋊C4×C4711yescharacteristic
301C2×C4C4×D4×C4711yescharacteristic
302C2×C4C4×D4×C4711yescharacteristic
303C2×C4#120×C4711yescharacteristic
304C2×C4#121×C4711yescharacteristic
305C2×C4#121×C4711yescharacteristic
306C8—42no—
307C8—41no—
308C8—42no—
309C8—41no—
310C8—41no—
311C8—41no—
312C8—81no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—42no—
317C22—42no—
318C22—42no—
319C22C47×#38611yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—81no—
327C4—81no—
328C4C47×#44311yescharacteristic
329C4C47×#44411yescharacteristic
330C2—41no—
331C2—82no—
332C2C47×#187611yescharacteristic
333C2C47×#190211yescharacteristic
334C2C47×#191111yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC47×#532C22
LCSG ▷ 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×#1531C2semidirect
5. C47×#1497C2semidirect
6. C47×#1287C2semidirect
7. C47×#1275C2semidirect
145. #9285C47direct (N × H)
165. #1531C2×C47semidirect
167. #1497C2×C47semidirect
168. #1287C2×C47semidirect
169. #1275C2×C47semidirect
196. C47#9285direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32102
C47×#29812
C47×#15312
C47×#15302
C47×#14972
C47×#12872
C47×#12752
#928547