Finite Group Databasebeta

← C47×#60345 #26100043

Subgroups — C47×#60345 #26100043

Order 12032.

1744 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3482C211yesmaximal, characteristic
2C47×#2993C216yesmaximal, complemented
3C47×#2991C211yesmaximal, characteristic, complemented
4C47×#2991C213yesmaximal, complemented
5C47×#2986C213yesmaximal, complemented
6C47×#2982C212yesmaximal, complemented
7C47×#2969C216yesmaximal, complemented
8C47×#2965C213yesmaximal, complemented
9C8×#41×C47C211yesmaximal, characteristic, complemented
10Q8×M16×C47C212yesmaximal, complemented
11C47×#2960C213yesmaximal, complemented
12C47×#557C411yescharacteristic
13C47×#556C413yes—
14C47×#552C416yes—
15D4×Q8×C47C411yescharacteristic
16C47×#548C412yes—
17C47×#547C413yes—
18C47×#533C2213yes—
19C47×#529C2216yes—
20C4×#41×C47C2211yescharacteristic
21C4×#41×C47C2213yes—
22C2×C4×Q8×C47C2212yes—
23C47×#446C2213yes—
24C47×#446C2216yes—
25C47×#446C2216yes—
26C47×#446C2213yes—
27C8×Q8×C47C2216yes—
28C8×Q8×C47C2216yes—
29C8×Q8×C47C2211yescharacteristic
30C8×Q8×C47C2212yes—
31C8×Q8×C47C2211yescharacteristic
32C8×Q8×C47C2216yes—
33C47×#436C2211yescharacteristic
34C47×#436C2213yes—
35C47×#436C2216yes—
36C47×#436C22112yes—
37C47×#435C2216yes—
38C47×#435C2216yes—
39C8×D4×C47C2213yes—
40C8×D4×C47C2213yes—
41C47×#433C22112yes—
42C47×#431C2213yes—
43C47×#431C2216yes—
44C47×#431C2213yes—
45C47×#431C2216yes—
46C47×#424C2216yes—
47C47×#423C2213yes—
48C47×#423C2216yes—
49C47×#405C2216yes—
50C4×M16×C47C2216yes—
51C2×C4×C8×C47C2213yes—
52C2×#41×C47C2×C411yescharacteristic
53C2×#41×C47C2×C413yes—
54C22×Q8×C47C2×C412yes—
55C2×M16×C47C2312yes—
56C2×M16×C47C2316yes—
57C2×M16×C47C2316yes—
58C22×C8×C47C2313yes—
59C22×C8×C47C2313yes—
60C4⋊Q8×C47C2×C413yes—
61C4⋊Q8×C47C2×C413yes—
62#126×C47C2×C4112yes—
63#125×C47C2×C416yes—
64#125×C47C2×C416yes—
65#124×C47C2×C416yes—
66#123×C47C2×C4112yes—
67C22⋊Q8×C47C2×C416yes—
68C22⋊Q8×C47C2×C416yes—
69C22⋊Q8×C47C2×C416yes—
70#121×C47C2×C416yes—
71C4×Q8×C47C2×C412yes—
72C4×Q8×C47C2×C416yes—
73C4×Q8×C47C2×C411yescharacteristic
74C4×Q8×C47C2×C413yes—
75C4×Q8×C47C2311yescharacteristic
76C4×Q8×C47C2316yes—
77C4×Q8×C47C2313yes—
78C4×D4×C47C2×C413yes—
79C4×D4×C47C2×C413yes—
80C4×D4×C47C2×C416yes—
81C4×D4×C47C2311yescharacteristic
82C4×D4×C47C2313yes—
83C4×D4×C47C2316yes—
84#117×C47C2×C413yes—
85#117×C47C2×C416yes—
86#117×C47C2×C413yes—
87#117×C47C2316yes—
88C2×C4⋊C4×C47C2×C416yes—
89C2×C42×C47C2316yes—
90C2×C42×C47C2313yes—
91C4⋊C8×C47C2313yes—
92C4⋊C8×C47C2313yes—
93C4⋊C8×C47C2316yes—
94C4⋊C8×C47C23112yes—
95C4⋊C8×C47C2316yes—
96C4⋊C8×C47C2313yes—
97C4⋊C8×C47C2311yescharacteristic
98C4⋊C8×C47C2316yes—
99C22⋊C8×C47C2312yes—
100C22⋊C8×C47C2316yes—
101C22⋊C8×C47C2316yes—
102C22⋊C8×C47C2316yes—
103#97×C47C2316yes—
104#97×C47C2316yes—
105C4×C8×C47C2311yescharacteristic
106C4×C8×C47C2313yes—
107C4×C8×C47C2313yes—
108C4×C8×C47C2313yes—
109C4×C8×C47C2316yes—
110C4×C8×C47C23112yes—
111#41×C47—24no—
112#41×C47—46no—
113C2×Q8×C47—28no—
114C2×Q8×C47C22×C416yes—
115C2×Q8×C47C22×C413yes—
116C2×Q8×C47C22×C411yescharacteristic
117C2×D4×C47C22×C411yescharacteristic
118C2×D4×C47C22×C413yes—
119C2×D4×C47C22×C416yes—
120C22×C4×C47C22×C416yes—
121C22×C4×C47C22×C413yes—
122C22×C4×C47C22×C413yes—
123C22×C4×C47C22×C416yes—
124C22×C4×C47C2412yes—
125C22×C4×C47C2413yes—
126M16×C47—24no—
127M16×C47—46no—
128M16×C47—46no—
129C2×C8×C47—26no—
130C2×C8×C47—43no—
131C2×C8×C47C2411yescharacteristic
132C2×C8×C47C2413yes—
133C2×C8×C47C2416yes—
134C2×C8×C47C2413yes—
135C2×C8×C47C2412yes—
136C2×C8×C47C2411yescharacteristic
137C4⋊C4×C47C22×C413yes—
138C4⋊C4×C47C22×C416yes—
139C4⋊C4×C47C22×C4112yes—
140C4⋊C4×C47C22×C411yescharacteristic
141C4⋊C4×C47C22×C416yes—
142C4⋊C4×C47C22×C413yes—
143C4⋊C4×C47C22×C413yes—
144C4⋊C4×C47C22×C416yes—
145C4⋊C4×C47C22×C416yes—
146C4⋊C4×C47C22×C416yes—
147C22⋊C4×C47C22×C412yes—
148C22⋊C4×C47C22×C416yes—
149C22⋊C4×C47C22×C416yes—
150C22⋊C4×C47C22×C416yes—
151C22⋊C4×C47C22×C4112yes—
152C42×C47C22×C413yes—
153C42×C47C22×C416yes—
154C42×C47C22×C413yes—
155C42×C47C22×C416yes—
156C42×C47C2413yes—
157C42×C47C2411yescharacteristic
158C42×C47C2416yes—
159C23×C47C23×C413yes—
160C23×C47C23×C412yes—
161Q8×C47—212no—
162Q8×C47—26no—
163Q8×C47#13114yes—
164D4×C47—26no—
165D4×C47—22no—
166D4×C47—46no—
167C2×C4×C47—212no—
168C2×C4×C47—26no—
169C2×C4×C47—26no—
170C2×C4×C47—23no—
171C2×C4×C47—22no—
172C2×C4×C47—23no—
173C2×C4×C47—22no—
174C2×C4×C47—46no—
175C2×C4×C47C23×C412yes—
176C2×C4×C47C23×C411yescharacteristic
177C2×C4×C47C23×C413yes—
178C2×C4×C47C23×C413yes—
179C2×C4×C47C23×C416yes—
180C2×C4×C47C23×C416yes—
181C2×C4×C47C23×C413yes—
182C2×C4×C47C23×C411yescharacteristic
183C2×C4×C47C2511yescharacteristic
184C8×C47—23no—
185C8×C47—22no—
186C8×C47—21no—
187C8×C47—23no—
188C8×C47—26no—
189C8×C472−1+412yes—
190#60345C4711yesmaximal, characteristic, direct product factor, Sylow
191C22×C47—23no—
192C22×C47—22no—
193C22×C47—22no—
194C22×C47—23no—
195C22×C47—23no—
196C22×C47—22no—
197C22×C47C24×C411yescharacteristic
198C4×C47—23no—
199C4×C47—22no—
200C4×C47—21no—
201C4×C47—26no—
202C4×C47—23no—
203C4×C47—26no—
204C4×C47C2×#13116yes—
205C4×C47#56812yes—
206C4×C47C2×2−1+411yescharacteristic
207C4×C47#58511yescharacteristic
208#3482C2×C4711yescharacteristic
209#2993C2×C4716yescomplemented
210#2991C2×C4711yescharacteristic, complemented
211#2991C2×C4713yescomplemented
212#2986C2×C4713yescomplemented
213#2982C2×C4712yescomplemented
214#2969C2×C4716yescomplemented
215#2965C2×C4713yescomplemented
216C8×#41C2×C4711yescharacteristic, complemented
217Q8×M16C2×C4712yescomplemented
218#2960C2×C4713yescomplemented
219C2×C47—42no—
220C2×C47—43no—
221C2×C47C4×2−1+411yescharacteristic
222C2×C47C22×#13111yescharacteristic
223C2×C47C2×#56811yescharacteristic
224#557C4×C4711yescharacteristic
225#556C4×C4713yes—
226#552C4×C4716yes—
227D4×Q8C4×C4711yescharacteristic
228#548C4×C4712yes—
229#547C4×C4713yes—
230#533C22×C4713yes—
231#529C22×C4716yes—
232C4×#41C22×C4711yescharacteristic
233C4×#41C22×C4713yes—
234C2×C4×Q8C22×C4712yes—
235#446C22×C4713yes—
236#446C22×C4716yes—
237#446C22×C4716yes—
238#446C22×C4713yes—
239C8×Q8C22×C4716yes—
240C8×Q8C22×C4716yes—
241C8×Q8C22×C4711yescharacteristic
242C8×Q8C22×C4712yes—
243C8×Q8C22×C4711yescharacteristic
244C8×Q8C22×C4716yes—
245#436C22×C4711yescharacteristic
246#436C22×C4713yes—
247#436C22×C4716yes—
248#436C22×C47112yes—
249#435C22×C4716yes—
250#435C22×C4716yes—
251C8×D4C22×C4713yes—
252C8×D4C22×C4713yes—
253#433C22×C47112yes—
254#431C22×C4713yes—
255#431C22×C4716yes—
256#431C22×C4713yes—
257#431C22×C4716yes—
258#424C22×C4716yes—
259#423C22×C4713yes—
260#423C22×C4716yes—
261#405C22×C4716yes—
262C4×M16C22×C4716yes—
263C2×C4×C8C22×C4713yes—
264C47#6034511yescharacteristic, direct product factor, Sylow
265C2×#41C2×C4×C4711yescharacteristic
266C2×#41C2×C4×C4713yes—
267C22×Q8C2×C4×C4712yes—
268C2×M16C23×C4712yes—
269C2×M16C23×C4716yes—
270C2×M16C23×C4716yes—
271C22×C8C23×C4713yes—
272C22×C8C23×C4713yes—
273C4⋊Q8C2×C4×C4713yes—
274C4⋊Q8C2×C4×C4713yes—
275#126C2×C4×C47112yes—
276#125C2×C4×C4716yes—
277#125C2×C4×C4716yes—
278#124C2×C4×C4716yes—
279#123C2×C4×C47112yes—
280C22⋊Q8C2×C4×C4716yes—
281C22⋊Q8C2×C4×C4716yes—
282C22⋊Q8C2×C4×C4716yes—
283#121C2×C4×C4716yes—
284C4×Q8C2×C4×C4712yes—
285C4×Q8C2×C4×C4716yes—
286C4×Q8C2×C4×C4711yescharacteristic
287C4×Q8C2×C4×C4713yes—
288C4×Q8C23×C4711yescharacteristic
289C4×Q8C23×C4716yes—
290C4×Q8C23×C4713yes—
291C4×D4C2×C4×C4713yes—
292C4×D4C2×C4×C4713yes—
293C4×D4C2×C4×C4716yes—
294C4×D4C23×C4711yescharacteristic
295C4×D4C23×C4713yes—
296C4×D4C23×C4716yes—
297#117C2×C4×C4713yes—
298#117C2×C4×C4716yes—
299#117C2×C4×C4713yes—
300#117C23×C4716yes—
301C2×C4⋊C4C2×C4×C4716yes—
302C2×C42C23×C4716yes—
303C2×C42C23×C4713yes—
304C4⋊C8C23×C4713yes—
305C4⋊C8C23×C4713yes—
306C4⋊C8C23×C4716yes—
307C4⋊C8C23×C47112yes—
308C4⋊C8C23×C4716yes—
309C4⋊C8C23×C4713yes—
310C4⋊C8C23×C4711yescharacteristic
311C4⋊C8C23×C4716yes—
312C22⋊C8C23×C4712yes—
313C22⋊C8C23×C4716yes—
314C22⋊C8C23×C4716yes—
315C22⋊C8C23×C4716yes—
316#97C23×C4716yes—
317#97C23×C4716yes—
318C4×C8C23×C4711yescharacteristic
319C4×C8C23×C4713yes—
320C4×C8C23×C4713yes—
321C4×C8C23×C4713yes—
322C4×C8C23×C4716yes—
323C4×C8C23×C47112yes—
324#41—24no—
325#41—46no—
326C2×Q8—28no—
327C2×Q8C22×C4×C4716yes—
328C2×Q8C22×C4×C4713yes—
329C2×Q8C22×C4×C4711yescharacteristic
330C2×D4C22×C4×C4711yescharacteristic
331C2×D4C22×C4×C4713yes—
332C2×D4C22×C4×C4716yes—
333C22×C4C22×C4×C4716yes—
334C22×C4C22×C4×C4713yes—
335C22×C4C22×C4×C4713yes—
336C22×C4C22×C4×C4716yes—
337C22×C4C24×C4712yes—
338C22×C4C24×C4713yes—
339M16—24no—
340M16—46no—
341M16—46no—
342C2×C8—26no—
343C2×C8—43no—
344C2×C8C24×C4713yes—
345C2×C8C24×C4711yescharacteristic
346C2×C8C24×C4712yes—
347C2×C8C24×C4716yes—
348C2×C8C24×C4713yes—
349C2×C8C24×C4711yescharacteristic
350C4⋊C4C22×C4×C4713yes—
351C4⋊C4C22×C4×C4716yes—
352C4⋊C4C22×C4×C47112yes—
353C4⋊C4C22×C4×C4711yescharacteristic
354C4⋊C4C22×C4×C4716yes—
355C4⋊C4C22×C4×C4713yes—
356C4⋊C4C22×C4×C4713yes—
357C4⋊C4C22×C4×C4716yes—
358C4⋊C4C22×C4×C4716yes—
359C4⋊C4C22×C4×C4716yes—
360C22⋊C4C22×C4×C4712yes—
361C22⋊C4C22×C4×C4716yes—
362C22⋊C4C22×C4×C4716yes—
363C22⋊C4C22×C4×C4716yes—
364C22⋊C4C22×C4×C47112yes—
365C42C22×C4×C4713yes—
366C42C22×C4×C4716yes—
367C42C22×C4×C4713yes—
368C42C22×C4×C4716yes—
369C42C24×C4713yes—
370C42C24×C4711yescharacteristic
371C42C24×C4716yes—
372C23C23×C4×C4713yes—
373C23C23×C4×C4712yes—
374Q8—212no—
375Q8—26no—
376Q8#131×C4714yes—
377D4—26no—
378D4—22no—
379D4—46no—
380C2×C4—212no—
381C2×C4—26no—
382C2×C4—26no—
383C2×C4—23no—
384C2×C4—22no—
385C2×C4—23no—
386C2×C4—22no—
387C2×C4—46no—
388C2×C4C23×C4×C4712yes—
389C2×C4C23×C4×C4711yescharacteristic
390C2×C4C23×C4×C4713yes—
391C2×C4C23×C4×C4713yes—
392C2×C4C23×C4×C4716yes—
393C2×C4C23×C4×C4716yes—
394C2×C4C23×C4×C4713yes—
395C2×C4C23×C4×C4711yescharacteristic
396C2×C4C25×C4711yescharacteristic
397C8—23no—
398C8—22no—
399C8—21no—
400C8—23no—
401C8—26no—
402C82−1+4×C4712yes—
403C22—22no—
404C22—23no—
405C22—23no—
406C22—22no—
407C22—23no—
408C22—22no—
409C22C24×C4×C4711yescharacteristic
410C4—21no—
411C4—26no—
412C4—23no—
413C4—26no—
414C4—23no—
415C4—22no—
416C4C2×#131×C4716yes—
417C4C47×#56812yes—
418C4C2×2−1+4×C4711yescharacteristic
419C4C47×#58511yescharacteristic
420C2—42no—
421C2—43no—
422C2C4×2−1+4×C4711yescharacteristic
423C2C22×#131×C4711yescharacteristic
424C2C2×C47×#56811yescharacteristic
subgroupG/H
centerC2×C4×C47C25
commutatorC22C24×C4×C47
Frattini, cosocleC2×C4C25×C47
socleC22×C47C24×C4
prime radicalC47×#3482C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2993C2semidirect
3. C47×#2991C2semidirect
4. C47×#2991C2semidirect
5. C47×#2986C2semidirect
6. C47×#2982C2semidirect
7. C47×#2969C2semidirect
8. C47×#2965C2semidirect
9. C8×#41×C47C2semidirect
10. Q8×M16×C47C2semidirect
11. C47×#2960C2semidirect
190. #60345C47direct (N × H)
209. #2993C2×C47semidirect
210. #2991C2×C47semidirect
211. #2991C2×C47semidirect
212. #2986C2×C47semidirect
213. #2982C2×C47semidirect
214. #2969C2×C47semidirect
215. #2965C2×C47semidirect
216. C8×#41C2×C47semidirect
217. Q8×M16C2×C47semidirect
218. #2960C2×C47semidirect
264. C47#60345direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#34822
C47×#29932
C47×#29912
C47×#29862
C47×#29822
C47×#29692
C47×#29652
C8×#41×C472
Q8×M16×C472
C47×#29602
#6034547