Finite Group Databasebeta

← C47×#18654 #26058352

Subgroups — C47×#18654 #26058352

Order 12032.

904 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3509C211yesmaximal, characteristic
2C47×#3229C211yesmaximal, characteristic, complemented
3C2×C47×#500C211yesmaximal, characteristic, complemented
4C47×#3039C211yesmaximal, characteristic
5C47×#1650C214yesmaximal, complemented
6C47×#1648C214yesmaximal, complemented
7C47×#1546C211yesmaximal, characteristic, complemented
8C47×#1493C211yesmaximal, characteristic, complemented
9C47×#1476C211yesmaximal, characteristic
10C2×#137×C47—21no—
11C47×#557—21no—
12C47×#557C2212yes—
13C47×#556—21no—
14C47×#556C2212yes—
15C47×#552—22no—
16C47×#552—22no—
17C47×#541—22no—
18C47×#536—21no—
19C47×#533—21no—
20C47×#533—21no—
21C47×#533C2211yescharacteristic
22C2×C4⋊Q8×C47C2211yescharacteristic
23C2×C4⋊Q8×C47C2211yescharacteristic
24C47×#519—21no—
25C4×#41×C47C2211yescharacteristic
26C47×#500—22no—
27C47×#500C2214yes—
28C47×#498—21no—
29C47×#487—21no—
30C47×#483—22no—
31C47×#475C2214yes—
32C47×#462—21no—
33C47×#462C2212yes—
34C47×#461—21no—
35C47×#461C2212yes—
36C47×#431C2211yescharacteristic
37C2×#107×C47—22no—
38C47×#423C2211yescharacteristic
39C47×#419—21no—
40C2×C4×C8×C47C2211yescharacteristic
41C47×#332C2214yes—
42C47×Q8⋊C8C2212yes—
43C47×Q8⋊C8C2214yes—
44C47×D4⋊C8C2212yes—
45C2×#41×C47D411yescharacteristic
46C22×Q8×C47—21no—
47C22×Q8×C47—21no—
48#137×C47—44no—
49C2×Q16×C47—22no—
50C2×SD16×C47—22no—
51C2×M16×C47—21no—
52C22×C8×C47—21no—
53C4⋊Q8×C47—22no—
54C4⋊Q8×C47—21no—
55C4⋊Q8×C47—21no—
56C4⋊Q8×C47—21no—
57C4⋊Q8×C47—21no—
58C4⋊Q8×C47—21no—
59C4⋊Q8×C47D411yescharacteristic
60C4⋊Q8×C47D411yescharacteristic
61C4⋊Q8×C47D412yes—
62C4⋊Q8×C47C2312yes—
63C4⋊Q8×C47C2312yes—
64#126×C47—24no—
65#126×C47—24no—
66#125×C47—22no—
67#125×C47—24no—
68#125×C47—22no—
69#125×C47—24no—
70#125×C47—21no—
71#124×C47—22no—
72#123×C47—24no—
73C22⋊Q8×C47—22no—
74C22⋊Q8×C47—22no—
75C22⋊Q8×C47—22no—
76C22⋊Q8×C47—22no—
77C22⋊Q8×C47—21no—
78C22⋊Q8×C47D412yes—
79C4×Q8×C47—22no—
80C4×Q8×C47—22no—
81C4×Q8×C47—22no—
82C4×Q8×C47—22no—
83C4×Q8×C47—22no—
84C4×Q8×C47—22no—
85C4×Q8×C47—21no—
86C4×Q8×C47D411yescharacteristic
87C4×Q8×C47C2311yescharacteristic
88C4×Q8×C47C2312yes—
89C4×D4×C47—21no—
90C4×D4×C47—21no—
91C4×D4×C47D411yescharacteristic
92C4×D4×C47C2311yescharacteristic
93#117×C47—24no—
94#117×C47—22no—
95#117×C47—21no—
96#117×C47—22no—
97#117×C47—21no—
98#117×C47D411yescharacteristic
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47D412yes—
103C2×C42×C47—21no—
104C2×C42×C47C2311yescharacteristic
105#107×C47—28no—
106#106×C47—24no—
107C4⋊C8×C47—21no—
108C4⋊C8×C47C2312yes—
109C4⋊C8×C47C2312yes—
110#103×C47—24no—
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×C47—22no—
119C2×Q8×C47—21no—
120C2×Q8×C47—22no—
121C2×Q8×C47—22no—
122C2×Q8×C47—22no—
123C2×Q8×C47—41no—
124C2×Q8×C47—42no—
125C2×Q8×C47—42no—
126C2×Q8×C47—42no—
127C2×Q8×C47—42no—
128C2×Q8×C47C2×D412yes—
129C2×Q8×C47C2×D411yescharacteristic
130C2×D4×C47—21no—
131C2×D4×C47C2×D411yescharacteristic
132C22×C4×C47—22no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—41no—
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140Q16×C47—44no—
141SD16×C47—44no—
142M16×C47—42no—
143C2×C8×C47—24no—
144C2×C8×C47—22no—
145C2×C8×C47—22no—
146C2×C8×C47—22no—
147C4⋊C4×C47—24no—
148C4⋊C4×C47—24no—
149C4⋊C4×C47—24no—
150C4⋊C4×C47—24no—
151C4⋊C4×C47—22no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47—21no—
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—22no—
158C4⋊C4×C47—22no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—22no—
161C4⋊C4×C47—22no—
162C4⋊C4×C47—22no—
163C4⋊C4×C47—41no—
164C4⋊C4×C47—41no—
165C4⋊C4×C47C2×D411yescharacteristic
166C4⋊C4×C47C2×D411yescharacteristic
167C4⋊C4×C47C2×D412yes—
168C4⋊C4×C47C2×D414yes—
169C22⋊C4×C47—24no—
170C22⋊C4×C47—24no—
171C22⋊C4×C47—21no—
172C22⋊C4×C47—22no—
173C22⋊C4×C47—21no—
174C22⋊C4×C47—21no—
175C42×C47—24no—
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—21no—
189Q8×C47—24no—
190Q8×C47—42no—
191Q8×C47—42no—
192Q8×C47—44no—
193Q8×C47—42no—
194Q8×C47—42no—
195Q8×C47—42no—
196Q8×C47—82no—
197D4×C47—21no—
198D4×C47—21no—
199D4×C47—42no—
200C2×C4×C47—22no—
201C2×C4×C47—22no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—22no—
205C2×C4×C47—22no—
206C2×C4×C47—24no—
207C2×C4×C47—21no—
208C2×C4×C47—44no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47—82no—
214C2×C4×C47#12011yescharacteristic
215C2×C4×C47#12011yescharacteristic
216C2×C4×C47#12011yescharacteristic
217C2×C4×C47#13512yes—
218C2×C4×C47AGL(1,ℤ/8)12yes—
219C2×C4×C47C22×D411yescharacteristic
220C2×C4×C47C22×D411yescharacteristic
221C2×C4×C47C22×D411yescharacteristic
222C8×C47—24no—
223C8×C47—42no—
224C8×C47—42no—
225#18654C4711yesmaximal, characteristic, direct product factor, Sylow
226C22×C47—21no—
227C22×C47—21no—
228C22×C47—41no—
229C22×C47—41no—
230C22×C47—41no—
231C22×C47#44912yes—
232C22×C47C2×#12011yescharacteristic
233C4×C47—21no—
234C4×C47—21no—
235C4×C47—41no—
236C4×C47—44no—
237C4×C47—41no—
238C4×C47—42no—
239C4×C47—41no—
240C4×C47—42no—
241C4×C47—82no—
242C4×C47#44912yes—
243C4×C47#45612yes—
244C4×C47C2×#13511yescharacteristic
245C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
246C4×C47#57812yes—
247#3509C2×C4711yescharacteristic
248#3229C2×C4711yescharacteristic, complemented
249C2×#500C2×C4711yescharacteristic, complemented
250#3039C2×C4711yescharacteristic
251#1650C2×C4714yescomplemented
252#1648C2×C4714yescomplemented
253#1546C2×C4711yescharacteristic, complemented
254#1493C2×C4711yescharacteristic, complemented
255#1476C2×C4711yescharacteristic
256C2×C47—22no—
257C2×C47—81no—
258C2×C47C2×#44911yescharacteristic
259C2×C47#301111yescharacteristic
260C2×C47C2×#45611yescharacteristic
261C2×#137—21no—
262#557—21no—
263#557C22×C4712yes—
264#556—21no—
265#556C22×C4712yes—
266#552—22no—
267#552—22no—
268#541—22no—
269#536—21no—
270#533—21no—
271#533—21no—
272#533C22×C4711yescharacteristic
273C2×C4⋊Q8C22×C4711yescharacteristic
274C2×C4⋊Q8C22×C4711yescharacteristic
275#519—21no—
276C4×#41C22×C4711yescharacteristic
277#500—22no—
278#500C22×C4714yes—
279#498—21no—
280#487—21no—
281#483—22no—
282#475C22×C4714yes—
283#462—21no—
284#462C22×C4712yes—
285#461—21no—
286#461C22×C4712yes—
287#431C22×C4711yescharacteristic
288C2×#107—22no—
289#423C22×C4711yescharacteristic
290#419—21no—
291C2×C4×C8C22×C4711yescharacteristic
292#332C22×C4714yes—
293Q8⋊C8C22×C4712yes—
294Q8⋊C8C22×C4714yes—
295D4⋊C8C22×C4712yes—
296C47#1865411yescharacteristic, direct product factor, Sylow
297C2×#41D4×C4711yescharacteristic
298C22×Q8—21no—
299C22×Q8—21no—
300#137—44no—
301C2×Q16—22no—
302C2×SD16—22no—
303C2×M16—21no—
304C22×C8—21no—
305C4⋊Q8—22no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8D4×C4711yescharacteristic
312C4⋊Q8D4×C4712yes—
313C4⋊Q8D4×C4711yescharacteristic
314C4⋊Q8C23×C4712yes—
315C4⋊Q8C23×C4712yes—
316#126—24no—
317#126—24no—
318#125—22no—
319#125—24no—
320#125—22no—
321#125—24no—
322#125—21no—
323#124—22no—
324#123—24no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—21no—
330C22⋊Q8D4×C4712yes—
331C4×Q8—22no—
332C4×Q8—22no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—21no—
338C4×Q8D4×C4711yescharacteristic
339C4×Q8C23×C4711yescharacteristic
340C4×Q8C23×C4712yes—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4D4×C4711yescharacteristic
344C4×D4C23×C4711yescharacteristic
345#117—24no—
346#117—22no—
347#117—21no—
348#117—22no—
349#117—21no—
350#117D4×C4711yescharacteristic
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4D4×C4712yes—
355C2×C42—21no—
356C2×C42C23×C4711yescharacteristic
357#107—28no—
358#106—24no—
359C4⋊C8—21no—
360C4⋊C8C23×C4712yes—
361C4⋊C8C23×C4712yes—
362#103—24no—
363#103—22no—
364#103—22no—
365C22⋊C8—21no—
366C4×C8—21no—
367C4×C8—21no—
368C4×C8C23×C4712yes—
369#41—22no—
370#41—22no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—41no—
376C2×Q8—42no—
377C2×Q8—42no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8C2×D4×C4712yes—
381C2×Q8C2×D4×C4711yescharacteristic
382C2×D4—21no—
383C2×D4C2×D4×C4711yescharacteristic
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—41no—
389C22×C4C2×D4×C4711yescharacteristic
390C22×C4C2×D4×C4711yescharacteristic
391C22×C4C2×D4×C4711yescharacteristic
392Q16—44no—
393SD16—44no—
394M16—42no—
395C2×C8—24no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—22no—
399C4⋊C4—24no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4C2×D4×C4711yescharacteristic
418C4⋊C4C2×D4×C4711yescharacteristic
419C4⋊C4C2×D4×C4712yes—
420C4⋊C4C2×D4×C4714yes—
421C22⋊C4—24no—
422C22⋊C4—24no—
423C22⋊C4—21no—
424C22⋊C4—22no—
425C22⋊C4—21no—
426C22⋊C4—21no—
427C42—24no—
428C42—24no—
429C42—21no—
430C42—21no—
431C42—21no—
432C42—22no—
433C42C2×D4×C4711yescharacteristic
434C42C2×D4×C4711yescharacteristic
435C42C2×D4×C4711yescharacteristic
436C42C24×C4711yescharacteristic
437C23—21no—
438C23#120×C4711yescharacteristic
439Q8—21no—
440Q8—21no—
441Q8—24no—
442Q8—44no—
443Q8—42no—
444Q8—42no—
445Q8—42no—
446Q8—42no—
447Q8—42no—
448Q8—82no—
449D4—21no—
450D4—21no—
451D4—42no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—21no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—82no—
466C2×C4#120×C4711yescharacteristic
467C2×C4#120×C4711yescharacteristic
468C2×C4#120×C4711yescharacteristic
469C2×C4#135×C4712yes—
470C2×C4AGL(1,ℤ/8)×C4712yes—
471C2×C4C22×D4×C4711yescharacteristic
472C2×C4C22×D4×C4711yescharacteristic
473C2×C4C22×D4×C4711yescharacteristic
474C8—24no—
475C8—42no—
476C8—42no—
477C22—21no—
478C22—21no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22C47×#44912yes—
483C22C2×#120×C4711yescharacteristic
484C4—21no—
485C4—21no—
486C4—41no—
487C4—44no—
488C4—41no—
489C4—42no—
490C4—41no—
491C4—42no—
492C4—82no—
493C4C47×#44912yes—
494C4C47×#45612yes—
495C4C2×#135×C4711yescharacteristic
496C4C2×AGL(1,ℤ/8)×C4711yescharacteristic
497C4C47×#57812yes—
498C2—22no—
499C2—81no—
500C2C2×C47×#44911yescharacteristic
501C2C47×#301111yescharacteristic
502C2C2×C47×#45611yescharacteristic
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×#500C2semidirect
5. C47×#1650C2semidirect
6. C47×#1648C2semidirect
7. C47×#1546C2semidirect
8. C47×#1493C2semidirect
225. #18654C47direct (N × H)
248. #3229C2×C47semidirect
249. C2×#500C2×C47semidirect
251. #1650C2×C47semidirect
252. #1648C2×C47semidirect
253. #1546C2×C47semidirect
254. #1493C2×C47semidirect
296. C47#18654direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35092
C47×#32292
C2×C47×#5002
C47×#30392
C47×#16502
C47×#16482
C47×#15462
C47×#14932
C47×#14762
#1865447