Finite Group Databasebeta

← C47×#33882 #26073580

Subgroups — C47×#33882 #26073580

Order 12032.

542 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3336C211yesmaximal, characteristic, complemented
2C47×#3283C211yesmaximal, characteristic
3C47×#2245C211yesmaximal, characteristic, complemented
4C47×#2237C211yesmaximal, characteristic, complemented
5C47×#2236C211yesmaximal, characteristic, complemented
6C47×#2228C211yesmaximal, characteristic, complemented
7C47×#2219C211yesmaximal, characteristic, complemented
8C47×#2216C211yesmaximal, characteristic, complemented
9C47×#2209C211yesmaximal, characteristic, complemented
10C47×#2189C211yesmaximal, characteristic, complemented
11C47×#2189C211yesmaximal, characteristic, complemented
12C47×#2175C211yesmaximal, characteristic, complemented
13C47×#2168C211yesmaximal, characteristic, complemented
14C47×#2139C211yesmaximal, characteristic, complemented
15C47×#2138C211yesmaximal, characteristic, complemented
16C2×#135×C47C2211yescharacteristic
17C2×#135×C47C2211yescharacteristic
18C47×#552—21no—
19C47×#547—21no—
20C2×Q32×C47C2211yescharacteristic
21C2×Q32×C47C2211yescharacteristic
22C2×SD32×C47C2211yescharacteristic
23C2×M32×C47C2211yescharacteristic
24C22×C16×C47C2211yescharacteristic
25C47×#499C2211yescharacteristic
26C47×#494C2211yescharacteristic
27C47×#485—21no—
28C47×#483—21no—
29C47×#479—21no—
30C47×#467C2211yescharacteristic
31C47×#467C2211yescharacteristic
32C47×#467C2211yescharacteristic
33C47×#467C2211yescharacteristic
34C47×#461—21no—
35C47×#452—21no—
36C47×#452—21no—
37C4×Q16×C47C2211yescharacteristic
38C4×D8×C47C2211yescharacteristic
39C8×D4×C47C2211yescharacteristic
40C47×#427C2211yescharacteristic
41C2×#107×C47C2211yescharacteristic
42C47×#367C2211yescharacteristic
43C47×#366C2211yescharacteristic
44C47×#366C2211yescharacteristic
45C47×C4⋊C16C2211yescharacteristic
46C47×#358C2211yescharacteristic
47C47×#358C2211yescharacteristic
48C47×#358C2211yescharacteristic
49C47×#358C2211yescharacteristic
50C47×#358C2211yescharacteristic
51C47×#358C2211yescharacteristic
52C47×#358C2211yescharacteristic
53C47×#357C2211yescharacteristic
54C47×#357C2211yescharacteristic
55C47×#357C2211yescharacteristic
56C47×C22⋊C16C2211yescharacteristic
57C47×C22⋊C16C2211yescharacteristic
58C47×#346C2211yescharacteristic
59C2×#41×C47—21no—
60C2×#41×C47—21no—
61#135×C47—22no—
62#135×C47—22no—
63#135×C47—41no—
64#135×C47—41no—
65C2×Q16×C47—21no—
66C2×Q16×C47C2311yescharacteristic
67C2×Q16×C47C2311yescharacteristic
68C2×Q16×C47C2311yescharacteristic
69C2×SD16×C47—21no—
70C2×SD16×C47—21no—
71C2×D8×C47C2311yescharacteristic
72C22×C8×C47C2311yescharacteristic
73C22×C8×C47C2311yescharacteristic
74C4⋊Q8×C47—21no—
75#126×C47—41no—
76#125×C47—21no—
77#125×C47—41no—
78#123×C47—41no—
79#123×C47—41no—
80#123×C47—41no—
81C22⋊Q8×C47—21no—
82C22⋊Q8×C47—21no—
83C22⋊Q8×C47—21no—
84C22⋊Q8×C47—21no—
85#121×C47—41no—
86C4×Q8×C47—21no—
87C4×D4×C47—21no—
88C4×D4×C47D411yescharacteristic
89#117×C47—21no—
90#117×C47—41no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—41no—
93Q32×C47—41no—
94Q32×C47—41no—
95SD32×C47—22no—
96M32×C47—41no—
97C2×C16×C47—41no—
98C2×C16×C47C2311yescharacteristic
99C2×C16×C47C2311yescharacteristic
100C2×C16×C47C2311yescharacteristic
101C2×C16×C47C2311yescharacteristic
102#107×C47—21no—
103#107×C47C2311yescharacteristic
104#107×C47C2311yescharacteristic
105#107×C47C2311yescharacteristic
106#107×C47C2311yescharacteristic
107#106×C47—21no—
108#106×C47—21no—
109C4⋊C8×C47D411yescharacteristic
110#103×C47—21no—
111#103×C47—21no—
112#103×C47—21no—
113#103×C47—21no—
114#103×C47—21no—
115#102×C47—21no—
116C22⋊C8×C47D411yescharacteristic
117C22⋊C8×C47D411yescharacteristic
118C4×C8×C47C2311yescharacteristic
119#41×C47—42no—
120#41×C47—42no—
121#41×C47—81no—
122#41×C47—81no—
123C2×Q8×C47—21no—
124C2×Q8×C47—21no—
125C2×Q8×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47—41no—
128C2×D4×C47—41no—
129C2×D4×C47D811yescharacteristic
130C22×C4×C47—41no—
131C22×C4×C47—41no—
132C22×C4×C47—41no—
133C22×C4×C47—41no—
134C22×C4×C47C2×D411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136Q16×C47—21no—
137Q16×C47—21no—
138Q16×C47—21no—
139Q16×C47—21no—
140Q16×C47—21no—
141Q16×C47—21no—
142Q16×C47—81no—
143SD16×C47—42no—
144SD16×C47—42no—
145D8×C47—21no—
146D8×C47#4112yes—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C2×C8×C47C2×D411yescharacteristic
152C2×C8×C47C2×D411yescharacteristic
153C2×C8×C47C2×D411yescharacteristic
154C2×C8×C47C2411yescharacteristic
155C4⋊C4×C47—21no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—41no—
160C4⋊C4×C47—41no—
161C4⋊C4×C47—41no—
162C4⋊C4×C47—41no—
163C4⋊C4×C47—41no—
164C4⋊C4×C47—41no—
165C4⋊C4×C47—41no—
166C4⋊C4×C47—41no—
167C4⋊C4×C47—41no—
168C4⋊C4×C47—41no—
169C4⋊C4×C47D811yescharacteristic
170C22⋊C4×C47—41no—
171C22⋊C4×C47—41no—
172C22⋊C4×C47—41no—
173C22⋊C4×C47—41no—
174C22⋊C4×C47—41no—
175C22⋊C4×C47—41no—
176C22⋊C4×C47D811yescharacteristic
177C22⋊C4×C47D811yescharacteristic
178C42×C47—41no—
179C42×C47—41no—
180C42×C47C2×D411yescharacteristic
181C16×C47—21no—
182C16×C47—21no—
183C16×C47—21no—
184C16×C47—21no—
185C23×C47—41no—
186C23×C47C2×D811yescharacteristic
187C23×C47C2×D811yescharacteristic
188Q8×C47—41no—
189Q8×C47—41no—
190Q8×C47—41no—
191Q8×C47—41no—
192Q8×C47—41no—
193Q8×C47—41no—
194D4×C47—22no—
195D4×C47—41no—
196D4×C47—41no—
197D4×C47—82no—
198D4×C47—82no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—41no—
204C2×C4×C47—41no—
205C2×C4×C47—41no—
206C2×C4×C47—41no—
207C2×C4×C47—41no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—82no—
211C2×C4×C47—82no—
212C2×C4×C47—82no—
213C2×C4×C47—82no—
214C2×C4×C47C2×D811yescharacteristic
215C2×C4×C47C2×D811yescharacteristic
216C2×C4×C47C2×D811yescharacteristic
217C2×C4×C47C2×D811yescharacteristic
218C2×C4×C47C22×D411yescharacteristic
219C8×C47—21no—
220C8×C47—21no—
221C8×C47—21no—
222C8×C47C2×#4111yescharacteristic
223C8×C47H(5,𝔽2)11yescharacteristic
224#33882C4711yesmaximal, characteristic, direct product factor, Sylow
225C22×C47—21no—
226C22×C47—21no—
227C22×C47—21no—
228C22×C47—21no—
229C22×C47—21no—
230C22×C47—21no—
231C22×C47—42no—
232C22×C47—81no—
233C22×C47—81no—
234C22×C47C22×D811yescharacteristic
235C4×C47—21no—
236C4×C47—21no—
237C4×C47—21no—
238C4×C47—21no—
239C4×C47—81no—
240C4×C47—81no—
241C4×C47—81no—
242C4×C47—81no—
243C4×C47—81no—
244C4×C47—81no—
245C4×C47—81no—
246C4×C47#54611yescharacteristic
247C4×C47#57711yescharacteristic
248#3336C2×C4711yescharacteristic, complemented
249#3283C2×C4711yescharacteristic
250#2245C2×C4711yescharacteristic, complemented
251#2237C2×C4711yescharacteristic, complemented
252#2236C2×C4711yescharacteristic, complemented
253#2228C2×C4711yescharacteristic, complemented
254#2219C2×C4711yescharacteristic, complemented
255#2216C2×C4711yescharacteristic, complemented
256#2209C2×C4711yescharacteristic, complemented
257#2189C2×C4711yescharacteristic, complemented
258#2189C2×C4711yescharacteristic, complemented
259#2175C2×C4711yescharacteristic, complemented
260#2168C2×C4711yescharacteristic, complemented
261#2139C2×C4711yescharacteristic, complemented
262#2138C2×C4711yescharacteristic, complemented
263C2×C47—41no—
264C2×C47—41no—
265C2×C47—82no—
266C2×C47#329411yescharacteristic
267C2×C47#341411yescharacteristic
268C2×C47#341711yescharacteristic
269C2×#135C22×C4711yescharacteristic
270C2×#135C22×C4711yescharacteristic
271#552—21no—
272#547—21no—
273C2×Q32C22×C4711yescharacteristic
274C2×Q32C22×C4711yescharacteristic
275C2×SD32C22×C4711yescharacteristic
276C2×M32C22×C4711yescharacteristic
277C22×C16C22×C4711yescharacteristic
278#499C22×C4711yescharacteristic
279#494C22×C4711yescharacteristic
280#485—21no—
281#483—21no—
282#479—21no—
283#467C22×C4711yescharacteristic
284#467C22×C4711yescharacteristic
285#467C22×C4711yescharacteristic
286#467C22×C4711yescharacteristic
287#461—21no—
288#452—21no—
289#452—21no—
290C4×Q16C22×C4711yescharacteristic
291C4×D8C22×C4711yescharacteristic
292C8×D4C22×C4711yescharacteristic
293#427C22×C4711yescharacteristic
294C2×#107C22×C4711yescharacteristic
295#367C22×C4711yescharacteristic
296#366C22×C4711yescharacteristic
297#366C22×C4711yescharacteristic
298C4⋊C16C22×C4711yescharacteristic
299#358C22×C4711yescharacteristic
300#358C22×C4711yescharacteristic
301#358C22×C4711yescharacteristic
302#358C22×C4711yescharacteristic
303#358C22×C4711yescharacteristic
304#358C22×C4711yescharacteristic
305#358C22×C4711yescharacteristic
306#357C22×C4711yescharacteristic
307#357C22×C4711yescharacteristic
308#357C22×C4711yescharacteristic
309C22⋊C16C22×C4711yescharacteristic
310C22⋊C16C22×C4711yescharacteristic
311#346C22×C4711yescharacteristic
312C47#3388211yescharacteristic, direct product factor, Sylow
313C2×#41—21no—
314C2×#41—21no—
315#135—22no—
316#135—22no—
317#135—41no—
318#135—41no—
319C2×Q16—21no—
320C2×Q16C23×C4711yescharacteristic
321C2×Q16C23×C4711yescharacteristic
322C2×Q16C23×C4711yescharacteristic
323C2×SD16—21no—
324C2×SD16—21no—
325C2×D8C23×C4711yescharacteristic
326C22×C8C23×C4711yescharacteristic
327C22×C8C23×C4711yescharacteristic
328C4⋊Q8—21no—
329#126—41no—
330#125—21no—
331#125—41no—
332#123—41no—
333#123—41no—
334#123—41no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—21no—
338C22⋊Q8—21no—
339#121—41no—
340C4×Q8—21no—
341C4×D4—21no—
342C4×D4D4×C4711yescharacteristic
343#117—21no—
344#117—41no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—41no—
347Q32—41no—
348Q32—41no—
349SD32—22no—
350M32—41no—
351C2×C16—41no—
352C2×C16C23×C4711yescharacteristic
353C2×C16C23×C4711yescharacteristic
354C2×C16C23×C4711yescharacteristic
355C2×C16C23×C4711yescharacteristic
356#107—21no—
357#107C23×C4711yescharacteristic
358#107C23×C4711yescharacteristic
359#107C23×C4711yescharacteristic
360#107C23×C4711yescharacteristic
361#106—21no—
362#106—21no—
363C4⋊C8D4×C4711yescharacteristic
364#103—21no—
365#103—21no—
366#103—21no—
367#103—21no—
368#103—21no—
369#102—21no—
370C22⋊C8D4×C4711yescharacteristic
371C22⋊C8D4×C4711yescharacteristic
372C4×C8C23×C4711yescharacteristic
373#41—42no—
374#41—42no—
375#41—81no—
376#41—81no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×D4—21no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4D8×C4711yescharacteristic
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4C2×D4×C4711yescharacteristic
389C22×C4C2×D4×C4711yescharacteristic
390Q16—21no—
391Q16—21no—
392Q16—21no—
393Q16—21no—
394Q16—21no—
395Q16—21no—
396Q16—81no—
397SD16—42no—
398SD16—42no—
399D8—21no—
400D8#41×C4712yes—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8C2×D4×C4711yescharacteristic
406C2×C8C2×D4×C4711yescharacteristic
407C2×C8C2×D4×C4711yescharacteristic
408C2×C8C24×C4711yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4D8×C4711yescharacteristic
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4D8×C4711yescharacteristic
431C22⋊C4D8×C4711yescharacteristic
432C42—41no—
433C42—41no—
434C42C2×D4×C4711yescharacteristic
435C16—21no—
436C16—21no—
437C16—21no—
438C16—21no—
439C23—41no—
440C23C2×D8×C4711yescharacteristic
441C23C2×D8×C4711yescharacteristic
442Q8—41no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446Q8—41no—
447Q8—41no—
448D4—22no—
449D4—41no—
450D4—41no—
451D4—82no—
452D4—82no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—82no—
465C2×C4—82no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4C2×D8×C4711yescharacteristic
469C2×C4C2×D8×C4711yescharacteristic
470C2×C4C2×D8×C4711yescharacteristic
471C2×C4C2×D8×C4711yescharacteristic
472C2×C4C22×D4×C4711yescharacteristic
473C8—21no—
474C8—21no—
475C8—21no—
476C8C2×#41×C4711yescharacteristic
477C8H(5,𝔽2)×C4711yescharacteristic
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—81no—
486C22—81no—
487C22C22×D8×C4711yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—81no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—81no—
499C4C47×#54611yescharacteristic
500C4C47×#57711yescharacteristic
501C2—41no—
502C2—41no—
503C2—82no—
504C2C47×#329411yescharacteristic
505C2C47×#341411yescharacteristic
506C2C47×#341711yescharacteristic
subgroupG/H
center, socleC22×C47C22×D8
commutator, Frattini, cosocleC2×C8C24×C47
prime radicalC47×#3283C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C4×D4×C47 ◁ C8×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3336C2semidirect
3. C47×#2245C2semidirect
4. C47×#2237C2semidirect
5. C47×#2236C2semidirect
6. C47×#2228C2semidirect
7. C47×#2219C2semidirect
8. C47×#2216C2semidirect
9. C47×#2209C2semidirect
10. C47×#2189C2semidirect
11. C47×#2189C2semidirect
12. C47×#2175C2semidirect
13. C47×#2168C2semidirect
14. C47×#2139C2semidirect
15. C47×#2138C2semidirect
224. #33882C47direct (N × H)
248. #3336C2×C47semidirect
250. #2245C2×C47semidirect
251. #2237C2×C47semidirect
252. #2236C2×C47semidirect
253. #2228C2×C47semidirect
254. #2219C2×C47semidirect
255. #2216C2×C47semidirect
256. #2209C2×C47semidirect
257. #2189C2×C47semidirect
258. #2189C2×C47semidirect
259. #2175C2×C47semidirect
260. #2168C2×C47semidirect
261. #2139C2×C47semidirect
262. #2138C2×C47semidirect
312. C47#33882direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#33362
C47×#32832
C47×#22452
C47×#22372
C47×#22362
C47×#22282
C47×#22192
C47×#22162
C47×#22092
C47×#21892
C47×#21752
C47×#21682
C47×#21392
C47×#21382
#3388247