Finite Group Databasebeta

← C47×#18632 #26058330

Subgroups — C47×#18632 #26058330

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3503C211yesmaximal, characteristic
2C47×#3229C211yesmaximal, characteristic, complemented
3C2×C47×#487C211yesmaximal, characteristic, complemented
4C47×#3039C211yesmaximal, characteristic
5C47×#1645C214yesmaximal, complemented
6C47×#1643C214yesmaximal, complemented
7C47×#1548C211yesmaximal, characteristic, complemented
8C47×#1493C211yesmaximal, characteristic, complemented
9C47×#1476C211yesmaximal, characteristic
10C2×#137×C47—21no—
11Q82×C47C2212yes—
12C47×#557—21no—
13C47×#554—22no—
14C47×#554C2212yes—
15D4×Q8×C47—22no—
16D4×Q8×C47—21no—
17C47×#544—22no—
18C47×#544—21no—
19C47×#533—21no—
20C47×#533C2211yescharacteristic
21C2×C4⋊Q8×C47—21no—
22C2×C4⋊Q8×C47C2211yescharacteristic
23C2×C4⋊Q8×C47C2211yescharacteristic
24C47×#520—21no—
25C4×#41×C47C2211yescharacteristic
26C47×#498—21no—
27C47×#487—22no—
28C47×#487—21no—
29C47×#487C2214yes—
30C47×#483—22no—
31C47×#475C2214yes—
32C47×#462—21no—
33C47×#462C2212yes—
34C47×#461—21no—
35C47×#461C2212yes—
36C47×#431C2211yescharacteristic
37C47×#423C2211yescharacteristic
38C47×#419—21no—
39C2×#103×C47—22no—
40C2×C4×C8×C47C2211yescharacteristic
41C47×#333C2214yes—
42C47×Q8⋊C8C2214yes—
43C47×Q8⋊C8C2212yes—
44C47×D4⋊C8C2212yes—
45C2×#41×C47D411yescharacteristic
46C22×Q8×C47—22no—
47C22×Q8×C47—21no—
48C22×Q8×C47D412yes—
49#137×C47—44no—
50C2×Q16×C47—22no—
51C2×SD16×C47—22no—
52C2×M16×C47—21no—
53C22×C8×C47—21no—
54C4⋊Q8×C47—22no—
55C4⋊Q8×C47—22no—
56C4⋊Q8×C47—24no—
57C4⋊Q8×C47—22no—
58C4⋊Q8×C47—22no—
59C4⋊Q8×C47—21no—
60C4⋊Q8×C47—21no—
61C4⋊Q8×C47—21no—
62C4⋊Q8×C47—21no—
63C4⋊Q8×C47—21no—
64C4⋊Q8×C47D412yes—
65C4⋊Q8×C47D411yescharacteristic
66C4⋊Q8×C47D411yescharacteristic
67C4⋊Q8×C47C2312yes—
68C4⋊Q8×C47C2312yes—
69#125×C47—22no—
70#125×C47—24no—
71#125×C47—22no—
72#125×C47—21no—
73C22⋊Q8×C47—22no—
74C22⋊Q8×C47—24no—
75C22⋊Q8×C47—24no—
76C22⋊Q8×C47—22no—
77C22⋊Q8×C47—24no—
78C22⋊Q8×C47—21no—
79C22⋊Q8×C47D412yes—
80C4×Q8×C47—22no—
81C4×Q8×C47—22no—
82C4×Q8×C47—22no—
83C4×Q8×C47—21no—
84C4×Q8×C47D411yescharacteristic
85C4×Q8×C47C2311yescharacteristic
86C4×Q8×C47C2312yes—
87C4×D4×C47—24no—
88C4×D4×C47—22no—
89C4×D4×C47—21no—
90C4×D4×C47—21no—
91C4×D4×C47D411yescharacteristic
92C4×D4×C47C2311yescharacteristic
93#117×C47—22no—
94#117×C47—21no—
95#117×C47—21no—
96#117×C47D411yescharacteristic
97C2×C4⋊C4×C47—22no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—21no—
103C2×C42×C47—21no—
104C2×C42×C47C2311yescharacteristic
105#106×C47—24no—
106C4⋊C8×C47—21no—
107C4⋊C8×C47C2312yes—
108C4⋊C8×C47C2312yes—
109#103×C47—24no—
110#103×C47—28no—
111#103×C47—22no—
112#103×C47—22no—
113C22⋊C8×C47—21no—
114C4×C8×C47—21no—
115C4×C8×C47—21no—
116C4×C8×C47C2312yes—
117#41×C47—22no—
118#41×C47SD1614yes—
119C2×Q8×C47—24no—
120C2×Q8×C47—22no—
121C2×Q8×C47—21no—
122C2×Q8×C47—22no—
123C2×Q8×C47—44no—
124C2×Q8×C47—41no—
125C2×Q8×C47—42no—
126C2×Q8×C47—42no—
127C2×Q8×C47—84no—
128C2×Q8×C47C2×D412yes—
129C2×Q8×C47C2×D411yescharacteristic
130C2×Q8×C47C2×D414yes—
131C2×D4×C47—21no—
132C2×D4×C47C2×D411yescharacteristic
133C22×C4×C47—21no—
134C22×C4×C47—24no—
135C22×C4×C47—22no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—41no—
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142Q16×C47—44no—
143SD16×C47—44no—
144M16×C47—42no—
145C2×C8×C47—22no—
146C2×C8×C47—22no—
147C2×C8×C47—22no—
148C2×C8×C47—42no—
149C4⋊C4×C47—24no—
150C4⋊C4×C47—24no—
151C4⋊C4×C47—24no—
152C4⋊C4×C47—24no—
153C4⋊C4×C47—22no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—22no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—22no—
160C4⋊C4×C47—22no—
161C4⋊C4×C47—22no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—41no—
167C4⋊C4×C47—41no—
168C4⋊C4×C47C2×D411yescharacteristic
169C4⋊C4×C47C2×D411yescharacteristic
170C4⋊C4×C47C2×D412yes—
171C22⋊C4×C47—24no—
172C22⋊C4×C47—22no—
173C22⋊C4×C47—21no—
174C22⋊C4×C47—21no—
175C22⋊C4×C47—21no—
176C42×C47—24no—
177C42×C47—21no—
178C42×C47—21no—
179C42×C47—21no—
180C42×C47—22no—
181C42×C47C2×D411yescharacteristic
182C42×C47C2×D411yescharacteristic
183C42×C47C2×D411yescharacteristic
184C42×C47C2411yescharacteristic
185C23×C47—21no—
186C23×C47#12011yescharacteristic
187Q8×C47—21no—
188Q8×C47—24no—
189Q8×C47—44no—
190Q8×C47—44no—
191Q8×C47—42no—
192Q8×C47—42no—
193Q8×C47—42no—
194Q8×C47—84no—
195Q8×C47—82no—
196Q8×C47C2×SD1612yes—
197D4×C47—24no—
198D4×C47—21no—
199D4×C47C2×SD1612yes—
200C2×C4×C47—21no—
201C2×C4×C47—22no—
202C2×C4×C47—24no—
203C2×C4×C47—22no—
204C2×C4×C47—22no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—24no—
208C2×C4×C47—22no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—82no—
213C2×C4×C47—84no—
214C2×C4×C47—82no—
215C2×C4×C47#12011yescharacteristic
216C2×C4×C47#12011yescharacteristic
217C2×C4×C47#12011yescharacteristic
218C2×C4×C47C2×SD1612yes—
219C2×C4×C47#13712yes—
220C2×C4×C47C22×D411yescharacteristic
221C2×C4×C47C22×D411yescharacteristic
222C2×C4×C47C22×D411yescharacteristic
223C8×C47—42no—
224C8×C47—42no—
225C8×C47—42no—
226#18632C4711yesmaximal, characteristic, direct product factor, Sylow
227C22×C47—21no—
228C22×C47—21no—
229C22×C47—22no—
230C22×C47—41no—
231C22×C47—41no—
232C22×C47#44812yes—
233C22×C47C2×#12011yescharacteristic
234C4×C47—22no—
235C4×C47—21no—
236C4×C47—21no—
237C4×C47—41no—
238C4×C47—42no—
239C4×C47—41no—
240C4×C47—44no—
241C4×C47—42no—
242C4×C47—82no—
243C4×C47#44812yes—
244C4×C47#45512yes—
245C4×C47C22×SD1611yescharacteristic
246C4×C47C2×#13711yescharacteristic
247C4×C47#57812yes—
248#3503C2×C4711yescharacteristic
249#3229C2×C4711yescharacteristic, complemented
250C2×#487C2×C4711yescharacteristic, complemented
251#3039C2×C4711yescharacteristic
252#1645C2×C4714yescomplemented
253#1643C2×C4714yescomplemented
254#1548C2×C4711yescharacteristic, complemented
255#1493C2×C4711yescharacteristic, complemented
256#1476C2×C4711yescharacteristic
257C2×C47—22no—
258C2×C47—42no—
259C2×C47C2×#44811yescharacteristic
260C2×C47#301111yescharacteristic
261C2×C47C2×#45511yescharacteristic
262C2×#137—21no—
263Q82C22×C4712yes—
264#557—21no—
265#554—22no—
266#554C22×C4712yes—
267D4×Q8—22no—
268D4×Q8—21no—
269#544—22no—
270#544—21no—
271#533—21no—
272#533C22×C4711yescharacteristic
273C2×C4⋊Q8—21no—
274C2×C4⋊Q8C22×C4711yescharacteristic
275C2×C4⋊Q8C22×C4711yescharacteristic
276#520—21no—
277C4×#41C22×C4711yescharacteristic
278#498—21no—
279#487—22no—
280#487—21no—
281#487C22×C4714yes—
282#483—22no—
283#475C22×C4714yes—
284#462—21no—
285#462C22×C4712yes—
286#461—21no—
287#461C22×C4712yes—
288#431C22×C4711yescharacteristic
289#423C22×C4711yescharacteristic
290#419—21no—
291C2×#103—22no—
292C2×C4×C8C22×C4711yescharacteristic
293#333C22×C4714yes—
294Q8⋊C8C22×C4714yes—
295Q8⋊C8C22×C4712yes—
296D4⋊C8C22×C4712yes—
297C47#1863211yescharacteristic, direct product factor, Sylow
298C2×#41D4×C4711yescharacteristic
299C22×Q8—22no—
300C22×Q8—21no—
301C22×Q8D4×C4712yes—
302#137—44no—
303C2×Q16—22no—
304C2×SD16—22no—
305C2×M16—21no—
306C22×C8—21no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—24no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8D4×C4712yes—
318C4⋊Q8D4×C4711yescharacteristic
319C4⋊Q8D4×C4711yescharacteristic
320C4⋊Q8C23×C4712yes—
321C4⋊Q8C23×C4712yes—
322#125—22no—
323#125—24no—
324#125—22no—
325#125—21no—
326C22⋊Q8—22no—
327C22⋊Q8—24no—
328C22⋊Q8—24no—
329C22⋊Q8—22no—
330C22⋊Q8—24no—
331C22⋊Q8—21no—
332C22⋊Q8D4×C4712yes—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—21no—
337C4×Q8D4×C4711yescharacteristic
338C4×Q8C23×C4711yescharacteristic
339C4×Q8C23×C4712yes—
340C4×D4—24no—
341C4×D4—22no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4D4×C4711yescharacteristic
345C4×D4C23×C4711yescharacteristic
346#117—22no—
347#117—21no—
348#117—21no—
349#117D4×C4711yescharacteristic
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C42—21no—
357C2×C42C23×C4711yescharacteristic
358#106—24no—
359C4⋊C8—21no—
360C4⋊C8C23×C4712yes—
361C4⋊C8C23×C4712yes—
362#103—28no—
363#103—24no—
364#103—22no—
365#103—22no—
366C22⋊C8—21no—
367C4×C8—21no—
368C4×C8—21no—
369C4×C8C23×C4712yes—
370#41—22no—
371#41SD16×C4714yes—
372C2×Q8—24no—
373C2×Q8—22no—
374C2×Q8—21no—
375C2×Q8—22no—
376C2×Q8—44no—
377C2×Q8—41no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8—84no—
381C2×Q8C2×D4×C4712yes—
382C2×Q8C2×D4×C4711yescharacteristic
383C2×Q8C2×D4×C4714yes—
384C2×D4—21no—
385C2×D4C2×D4×C4711yescharacteristic
386C22×C4—21no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—41no—
392C22×C4C2×D4×C4711yescharacteristic
393C22×C4C2×D4×C4711yescharacteristic
394C22×C4C2×D4×C4711yescharacteristic
395Q16—44no—
396SD16—44no—
397M16—42no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—42no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4C2×D4×C4711yescharacteristic
422C4⋊C4C2×D4×C4711yescharacteristic
423C4⋊C4C2×D4×C4712yes—
424C22⋊C4—24no—
425C22⋊C4—22no—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C22⋊C4—21no—
429C42—24no—
430C42—21no—
431C42—21no—
432C42—21no—
433C42—22no—
434C42C2×D4×C4711yescharacteristic
435C42C2×D4×C4711yescharacteristic
436C42C2×D4×C4711yescharacteristic
437C42C24×C4711yescharacteristic
438C23—21no—
439C23#120×C4711yescharacteristic
440Q8—21no—
441Q8—24no—
442Q8—44no—
443Q8—44no—
444Q8—42no—
445Q8—42no—
446Q8—42no—
447Q8—84no—
448Q8—82no—
449Q8C2×SD16×C4712yes—
450D4—24no—
451D4—21no—
452D4C2×SD16×C4712yes—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—82no—
466C2×C4—84no—
467C2×C4—82no—
468C2×C4#120×C4711yescharacteristic
469C2×C4#120×C4711yescharacteristic
470C2×C4#120×C4711yescharacteristic
471C2×C4C2×SD16×C4712yes—
472C2×C4#137×C4712yes—
473C2×C4C22×D4×C4711yescharacteristic
474C2×C4C22×D4×C4711yescharacteristic
475C2×C4C22×D4×C4711yescharacteristic
476C8—42no—
477C8—42no—
478C8—42no—
479C22—21no—
480C22—21no—
481C22—22no—
482C22—41no—
483C22—41no—
484C22C47×#44812yes—
485C22C2×#120×C4711yescharacteristic
486C4—22no—
487C4—21no—
488C4—21no—
489C4—41no—
490C4—42no—
491C4—41no—
492C4—44no—
493C4—42no—
494C4—82no—
495C4C47×#44812yes—
496C4C47×#45512yes—
497C4C22×SD16×C4711yescharacteristic
498C4C2×#137×C4711yescharacteristic
499C4C47×#57812yes—
500C2—22no—
501C2—42no—
502C2C2×C47×#44811yescharacteristic
503C2C47×#301111yescharacteristic
504C2C2×C47×#45511yescharacteristic
subgroupG/H
center, socleC22×C47C2×#120
commutator, Frattini, cosocleC42C24×C47
prime radicalC2×#41×C47D4
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
2. C47×#3229C2semidirect
3. C2×C47×#487C2semidirect
5. C47×#1645C2semidirect
6. C47×#1643C2semidirect
7. C47×#1548C2semidirect
8. C47×#1493C2semidirect
226. #18632C47direct (N × H)
249. #3229C2×C47semidirect
250. C2×#487C2×C47semidirect
252. #1645C2×C47semidirect
253. #1643C2×C47semidirect
254. #1548C2×C47semidirect
255. #1493C2×C47semidirect
297. C47#18632direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35032
C47×#32292
C2×C47×#4872
C47×#30392
C47×#16452
C47×#16432
C47×#15482
C47×#14932
C47×#14762
#1863247