Finite Group Databasebeta

← C47×#9521 #26049219

Subgroups — C47×#9521 #26049219

Order 12032.

472 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3092C211yesmaximal, characteristic
2C47×#2976C211yesmaximal, characteristic
3C47×#1824C211yesmaximal, characteristic, complemented
4C47×#1821C211yesmaximal, characteristic, complemented
5C47×#1513C211yesmaximal, characteristic
6C47×#1305C211yesmaximal, characteristic, complemented
7C47×#1293C211yesmaximal, characteristic, complemented
8C47×#525C2211yescharacteristic
9C22×C4⋊C4×C47C2211yescharacteristic
10C47×#484—21no—
11C47×#483C412yescomplemented
12C47×#481—21no—
13C47×#480C412yescomplemented
14C47×#436—21no—
15C47×#435—21no—
16C47×#435—21no—
17C8×D4×C47—21no—
18C47×#433—21no—
19C47×#428—21no—
20C47×#417—21no—
21C47×#408—21no—
22C47×#407C2211yescharacteristic
23C47×#407C2211yescharacteristic
24C47×#407C2211yescharacteristic
25C2×C22⋊C8×C47C2211yescharacteristic
26C47×#380C2211yescharacteristic
27C47×#343—21no—
28C47×#343—21no—
29C47×#340—21no—
30C47×#340—21no—
31C47×#328—21no—
32C47×#327—21no—
33C2×#41×C47D411yescharacteristic
34C23×C4×C47—21no—
35C23×C4×C47C2311yescharacteristic
36C2×M16×C47—21no—
37C2×M16×C47—21no—
38C2×M16×C47—21no—
39C2×M16×C47D411yescharacteristic
40C2×M16×C47D411yescharacteristic
41C22×C8×C47—21no—
42C22×C8×C47D411yescharacteristic
43C22×C8×C47D411yescharacteristic
44#123×C47—21no—
45C22⋊Q8×C47C2×C411yescharacteristic
46C22⋊Q8×C47D411yescharacteristic
47#121×C47C2×C411yescharacteristic
48#121×C47D411yescharacteristic
49#120×C47—21no—
50C4×D4×C47—21no—
51C4×D4×C47—21no—
52#117×C47D411yescharacteristic
53C2×C4⋊C4×C47—21no—
54C2×C4⋊C4×C47—21no—
55C2×C4⋊C4×C47—21no—
56C2×C4⋊C4×C47—21no—
57C2×C4⋊C4×C47—21no—
58C2×C4⋊C4×C47—21no—
59C2×C4⋊C4×C47C2×C412yes—
60C2×C22⋊C4×C47—21no—
61#107×C47—22no—
62#106×C47—22no—
63C4⋊C8×C47—21no—
64C4⋊C8×C47—21no—
65#103×C47—22no—
66#102×C47—22no—
67C22⋊C8×C47—21no—
68C22⋊C8×C47—21no—
69C22⋊C8×C47—21no—
70C22⋊C8×C47—21no—
71C22⋊C8×C47—21no—
72C22⋊C8×C47—21no—
73C22⋊C8×C47—21no—
74C22⋊C8×C47—21no—
75C22⋊C8×C47—21no—
76C22⋊C8×C47C2×C412yes—
77#97×C47—21no—
78C4×C8×C47—21no—
79#95×C47—21no—
80C24×C47#4111yescharacteristic
81#41×C47—41no—
82#41×C47—41no—
83C2×Q8×C47C22⋊C411yescharacteristic
84C2×D4×C47—21no—
85C2×D4×C47—21no—
86C2×D4×C47—21no—
87C2×D4×C47C22⋊C411yescharacteristic
88C22×C4×C47—21no—
89C22×C4×C47—22no—
90C22×C4×C47—41no—
91C22×C4×C47—41no—
92C22×C4×C47—41no—
93C22×C4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—82no—
96C22×C4×C47C22×C411yescharacteristic
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47#4111yescharacteristic
102M16×C47—41no—
103M16×C47—41no—
104M16×C47—41no—
105M16×C47—41no—
106M16×C47—41no—
107M16×C47—41no—
108M16×C47—81no—
109C2×C8×C47—22no—
110C2×C8×C47—21no—
111C2×C8×C47—21no—
112C2×C8×C47—21no—
113C2×C8×C47—21no—
114C2×C8×C47—41no—
115C2×C8×C47—41no—
116C2×C8×C47—41no—
117C2×C8×C47—81no—
118C4⋊C4×C47—21no—
119C4⋊C4×C47—21no—
120C4⋊C4×C47—22no—
121C4⋊C4×C47—22no—
122C4⋊C4×C47—41no—
123C4⋊C4×C47—41no—
124C4⋊C4×C47—41no—
125C4⋊C4×C47—41no—
126C4⋊C4×C47C22⋊C411yescharacteristic
127C4⋊C4×C47C22⋊C411yescharacteristic
128C22⋊C4×C47—21no—
129C22⋊C4×C47—21no—
130C22⋊C4×C47—21no—
131C22⋊C4×C47—21no—
132C22⋊C4×C47—21no—
133C22⋊C4×C47—81no—
134C42×C47—21no—
135C23×C47—21no—
136C23×C47—21no—
137C23×C47—21no—
138C23×C47—41no—
139C23×C47—41no—
140C23×C47C4×D411yescharacteristic
141C23×C47#12111yescharacteristic
142C23×C47#12311yescharacteristic
143Q8×C47—41no—
144D4×C47—41no—
145D4×C47—41no—
146D4×C47—41no—
147D4×C47—81no—
148D4×C47—81no—
149C2×C4×C47—21no—
150C2×C4×C47—21no—
151C2×C4×C47—21no—
152C2×C4×C47—21no—
153C2×C4×C47—21no—
154C2×C4×C47—21no—
155C2×C4×C47—21no—
156C2×C4×C47—21no—
157C2×C4×C47—21no—
158C2×C4×C47—41no—
159C2×C4×C47—41no—
160C2×C4×C47—41no—
161C2×C4×C47—41no—
162C2×C4×C47—41no—
163C2×C4×C47—42no—
164C2×C4×C47—82no—
165C2×C4×C47—82no—
166C2×C4×C47—82no—
167C2×C4×C47—81no—
168C2×C4×C47—81no—
169C2×C4×C47—81no—
170C2×C4×C47C2×C22⋊C411yescharacteristic
171C2×C4×C47C4×D411yescharacteristic
172C2×C4×C47#12011yescharacteristic
173C2×C4×C47#12111yescharacteristic
174C8×C47—42no—
175C8×C47—41no—
176C8×C47—41no—
177C8×C47—41no—
178C8×C47—41no—
179C8×C47—81no—
180#9521C4711yesmaximal, characteristic, direct product factor, Sylow
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—21no—
186C22×C47—21no—
187C22×C47—21no—
188C22×C47—21no—
189C22×C47—42no—
190C22×C47—42no—
191C22×C47—41no—
192C22×C47—41no—
193C22×C47—41no—
194C22×C47#38611yescharacteristic
195C22×C47#47111yescharacteristic
196C22×C47#47311yescharacteristic
197C4×C47—21no—
198C4×C47—21no—
199C4×C47—21no—
200C4×C47—41no—
201C4×C47—41no—
202C4×C47—41no—
203C4×C47—82no—
204C4×C47—161no—
205C4×C47#45811yescharacteristic
206C4×C47#45811yescharacteristic
207#3092C2×C4711yescharacteristic
208#2976C2×C4711yescharacteristic
209#1824C2×C4711yescharacteristic, complemented
210#1821C2×C4711yescharacteristic, complemented
211#1513C2×C4711yescharacteristic
212#1305C2×C4711yescharacteristic, complemented
213#1293C2×C4711yescharacteristic, complemented
214C2×C47—21no—
215C2×C47—21no—
216C2×C47—41no—
217C2×C47—41no—
218C2×C47—81no—
219C2×C47#189011yescharacteristic
220C2×C47#190311yescharacteristic
221C2×C47#190811yescharacteristic
222#525C22×C4711yescharacteristic
223C22×C4⋊C4C22×C4711yescharacteristic
224#484—21no—
225#483C4×C4712yescomplemented
226#481—21no—
227#480C4×C4712yescomplemented
228#436—21no—
229#435—21no—
230#435—21no—
231C8×D4—21no—
232#433—21no—
233#428—21no—
234#417—21no—
235#408—21no—
236#407C22×C4711yescharacteristic
237#407C22×C4711yescharacteristic
238#407C22×C4711yescharacteristic
239C2×C22⋊C8C22×C4711yescharacteristic
240#380C22×C4711yescharacteristic
241#343—21no—
242#343—21no—
243#340—21no—
244#340—21no—
245#328—21no—
246#327—21no—
247C47#952111yescharacteristic, direct product factor, Sylow
248C2×#41D4×C4711yescharacteristic
249C23×C4—21no—
250C23×C4C23×C4711yescharacteristic
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16D4×C4711yescharacteristic
255C2×M16D4×C4711yescharacteristic
256C22×C8—21no—
257C22×C8D4×C4711yescharacteristic
258C22×C8D4×C4711yescharacteristic
259#123—21no—
260C22⋊Q8C2×C4×C4711yescharacteristic
261C22⋊Q8D4×C4711yescharacteristic
262#121C2×C4×C4711yescharacteristic
263#121D4×C4711yescharacteristic
264#120—21no—
265C4×D4—21no—
266C4×D4—21no—
267#117D4×C4711yescharacteristic
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4C2×C4×C4712yes—
275C2×C22⋊C4—21no—
276#107—22no—
277#106—22no—
278C4⋊C8—21no—
279C4⋊C8—21no—
280#103—22no—
281#102—22no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C22⋊C8C2×C4×C4712yes—
292#97—21no—
293C4×C8—21no—
294#95—21no—
295C24#41×C4711yescharacteristic
296#41—41no—
297#41—41no—
298C2×Q8C22⋊C4×C4711yescharacteristic
299C2×D4—21no—
300C2×D4—21no—
301C2×D4—21no—
302C2×D4C22⋊C4×C4711yescharacteristic
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—82no—
311C22×C4C22×C4×C4711yescharacteristic
312C22×C4C2×D4×C4711yescharacteristic
313C22×C4C2×D4×C4711yescharacteristic
314C22×C4C2×D4×C4711yescharacteristic
315C22×C4C2×D4×C4711yescharacteristic
316C22×C4#41×C4711yescharacteristic
317M16—41no—
318M16—41no—
319M16—41no—
320M16—41no—
321M16—41no—
322M16—41no—
323M16—81no—
324C2×C8—22no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—21no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—81no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—22no—
336C4⋊C4—22no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4C22⋊C4×C4711yescharacteristic
342C4⋊C4C22⋊C4×C4711yescharacteristic
343C22⋊C4—21no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—81no—
349C42—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23C4×D4×C4711yescharacteristic
356C23#121×C4711yescharacteristic
357C23#123×C4711yescharacteristic
358Q8—41no—
359D4—41no—
360D4—41no—
361D4—41no—
362D4—81no—
363D4—81no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—82no—
380C2×C4—82no—
381C2×C4—82no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4C2×C22⋊C4×C4711yescharacteristic
386C2×C4C4×D4×C4711yescharacteristic
387C2×C4#120×C4711yescharacteristic
388C2×C4#121×C4711yescharacteristic
389C8—42no—
390C8—41no—
391C8—41no—
392C8—41no—
393C8—41no—
394C8—81no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—42no—
404C22—42no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22C47×#38611yescharacteristic
409C22C47×#47111yescharacteristic
410C22C47×#47311yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—82no—
418C4—161no—
419C4C47×#45811yescharacteristic
420C4C47×#45811yescharacteristic
421C2—21no—
422C2—21no—
423C2—41no—
424C2—41no—
425C2—81no—
426C2C47×#189011yescharacteristic
427C2C47×#190311yescharacteristic
428C2C47×#190811yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC22×C4C22×C4×C47
Frattini, cosocleC23×C4C23×C47
prime radicalC47×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
3. C47×#1824C2semidirect
4. C47×#1821C2semidirect
6. C47×#1305C2semidirect
7. C47×#1293C2semidirect
11. C47×#483C4semidirect
13. C47×#480C4semidirect
180. #9521C47direct (N × H)
209. #1824C2×C47semidirect
210. #1821C2×C47semidirect
212. #1305C2×C47semidirect
213. #1293C2×C47semidirect
225. #483C4×C47semidirect
227. #480C4×C47semidirect
247. C47#9521direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30922
C47×#29762
C47×#18242
C47×#18212
C47×#15132
C47×#13052
C47×#12932
#952147