Finite Group Databasebeta

← C2×C47×#3482 #26102413

Subgroups — C2×C47×#3482 #26102413

Order 12032.

7706 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3482C2132yesmaximal, direct product factor
2C2×C47×#557C211yesmaximal, characteristic, complemented
3C2×C47×#556C213yesmaximal, complemented
4C2×C47×#552C216yesmaximal, complemented
5C2×D4×Q8×C47C211yesmaximal, characteristic, complemented
6C2×C47×#548C212yesmaximal, complemented
7C2×C47×#547C213yesmaximal, complemented
8C2×C47×#533C213yesmaximal, complemented
9C2×C47×#529C216yesmaximal, complemented
10C2×C4×#41×C47C213yesmaximal, complemented
11C2×C4×#41×C47C211yesmaximal, characteristic, complemented
12C22×C4×Q8×C47C212yesmaximal, complemented
13C22×#41×C47C2213yes—
14C22×#41×C47C2211yescharacteristic
15C23×Q8×C47C2212yes—
16C47×#557C22116yescomplemented
17C47×#556C22148yescomplemented
18C47×#552C22196yescomplemented
19D4×Q8×C47C22116yescomplemented
20C47×#548C22132yescomplemented
21C47×#547C22148yescomplemented
22C47×#533C22148yescomplemented
23C2×C4⋊Q8×C47C2213yes—
24C2×C4⋊Q8×C47C2213yes—
25C47×#529C22196yescomplemented
26C2×#126×C47C22112yes—
27C2×#125×C47C2216yes—
28C2×#125×C47C2216yes—
29C2×#124×C47C2216yes—
30C2×#123×C47C22112yes—
31C2×C22⋊Q8×C47C2216yes—
32C2×C22⋊Q8×C47C2216yes—
33C2×C22⋊Q8×C47C2216yes—
34C2×#121×C47C2216yes—
35C4×#41×C47C22148yescomplemented
36C4×#41×C47C22116yescomplemented
37C2×C4×Q8×C47C2211yescharacteristic
38C2×C4×Q8×C47C2216yes—
39C2×C4×Q8×C47C2212yes—
40C2×C4×Q8×C47C2216yes—
41C2×C4×Q8×C47C2213yes—
42C2×C4×Q8×C47C2211yescharacteristic
43C2×C4×Q8×C47C2213yes—
44C2×C4×Q8×C47C22132yescomplemented
45C2×C4×D4×C47C2211yescharacteristic
46C2×C4×D4×C47C2213yes—
47C2×C4×D4×C47C2216yes—
48C2×C4×D4×C47C2213yes—
49C2×C4×D4×C47C2213yes—
50C2×C4×D4×C47C2216yes—
51C2×#117×C47C2213yes—
52C2×#117×C47C2216yes—
53C2×#117×C47C2213yes—
54C2×#117×C47C2216yes—
55C22×C4⋊C4×C47C2216yes—
56C22×C42×C47C2216yes—
57C22×C42×C47C2213yes—
58C2×#41×C47—28no—
59C2×#41×C47—224no—
60C2×#41×C47C23124yes—
61C2×#41×C47C2318yes—
62C22×Q8×C47—216no—
63C22×Q8×C47C2316yes—
64C22×Q8×C47C2313yes—
65C22×Q8×C47C23116yes—
66C22×Q8×C47C2311yescharacteristic
67C22×D4×C47C2316yes—
68C22×D4×C47C2313yes—
69C22×D4×C47C2311yescharacteristic
70C23×C4×C47C2316yes—
71C23×C4×C47C2316yes—
72C23×C4×C47C2313yes—
73C23×C4×C47C2313yes—
74C23×C4×C47C2312yes—
75C23×C4×C47C2313yes—
76C4⋊Q8×C47C23124yes—
77C4⋊Q8×C47C23124yes—
78#126×C47C23196yes—
79#125×C47C23148yes—
80#125×C47C23148yes—
81#124×C47C23148yes—
82#123×C47C23196yes—
83C22⋊Q8×C47C23148yes—
84C22⋊Q8×C47C23148yes—
85C22⋊Q8×C47C23148yes—
86#121×C47C23148yes—
87C4×Q8×C47C2318yes—
88C4×Q8×C47C23148yes—
89C4×Q8×C47C23116yes—
90C4×Q8×C47C23148yes—
91C4×Q8×C47C23124yes—
92C4×Q8×C47C2318yes—
93C4×Q8×C47C23124yes—
94C4×D4×C47C2318yes—
95C4×D4×C47C23124yes—
96C4×D4×C47C23148yes—
97C4×D4×C47C23124yes—
98C4×D4×C47C23124yes—
99C4×D4×C47C23148yes—
100#117×C47C23124yes—
101#117×C47C23148yes—
102#117×C47C23124yes—
103#117×C47C23148yes—
104C2×C4⋊C4×C47C2313yes—
105C2×C4⋊C4×C47C2316yes—
106C2×C4⋊C4×C47C23112yes—
107C2×C4⋊C4×C47C23148yes—
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2316yes—
110C2×C4⋊C4×C47C2313yes—
111C2×C4⋊C4×C47C2313yes—
112C2×C4⋊C4×C47C2316yes—
113C2×C4⋊C4×C47C2316yes—
114C2×C4⋊C4×C47C2316yes—
115C2×C22⋊C4×C47C2312yes—
116C2×C22⋊C4×C47C2316yes—
117C2×C22⋊C4×C47C2316yes—
118C2×C22⋊C4×C47C2316yes—
119C2×C22⋊C4×C47C23112yes—
120C2×C42×C47C2313yes—
121C2×C42×C47C2316yes—
122C2×C42×C47C2313yes—
123C2×C42×C47C2316yes—
124C2×C42×C47C23148yes—
125C2×C42×C47C23124yes—
126C2×C42×C47C2313yes—
127C2×C42×C47C2311yescharacteristic
128C2×C42×C47C2316yes—
129C24×C47C2413yes—
130C24×C47C2412yes—
131#41×C47—232no—
132#41×C47—296no—
133C2×Q8×C47—264no—
134C2×Q8×C47—224no—
135C2×Q8×C47—212no—
136C2×Q8×C47#4118yescomplemented
137C2×Q8×C47C24124yes—
138C2×Q8×C47C24112yes—
139C2×Q8×C47C2414yes—
140C2×D4×C47—224no—
141C2×D4×C47—212no—
142C2×D4×C47#4118yescomplemented
143C2×D4×C47C24124yes—
144C2×D4×C47C24112yes—
145C2×D4×C47C2414yes—
146C22×C4×C47—224no—
147C22×C4×C47—224no—
148C22×C4×C47—212no—
149C22×C4×C47—212no—
150C22×C4×C47—28no—
151C22×C4×C47—212no—
152C22×C4×C47C2412yes—
153C22×C4×C47C2418yes—
154C22×C4×C47C2411yescharacteristic
155C22×C4×C47C2413yes—
156C22×C4×C47C2413yes—
157C22×C4×C47C2416yes—
158C22×C4×C47C2416yes—
159C22×C4×C47C24124yes—
160C22×C4×C47C24124yes—
161C22×C4×C47C24112yes—
162C22×C4×C47C24112yes—
163C22×C4×C47C24112yes—
164C22×C4×C47C2413yes—
165C22×C4×C47C2411yescharacteristic
166C22×C4×C47C2411yescharacteristic
167C4⋊C4×C47C24112yes—
168C4⋊C4×C47C24124yes—
169C4⋊C4×C47C24148yes—
170C4⋊C4×C47C2414yes—
171C4⋊C4×C47C24124yes—
172C4⋊C4×C47C24112yes—
173C4⋊C4×C47C24112yes—
174C4⋊C4×C47C24124yes—
175C4⋊C4×C47C24124yes—
176C4⋊C4×C47C24124yes—
177C22⋊C4×C47C2418yes—
178C22⋊C4×C47C24124yes—
179C22⋊C4×C47C24124yes—
180C22⋊C4×C47C24124yes—
181C22⋊C4×C47C24148yes—
182C42×C47C24112yes—
183C42×C47C2414yes—
184C42×C47C24112yes—
185C42×C47C24124yes—
186C42×C47C24124yes—
187C42×C47C24112yes—
188C42×C47C24124yes—
189C23×C47—24no—
190C23×C47—24no—
191C23×C47—26no—
192C23×C47—26no—
193C23×C47—26no—
194C23×C47C2×#4118yes—
195C23×C47C2516yes—
196C23×C47C2514yes—
197C23×C47C2511yescharacteristic
198Q8×C47—248no—
199Q8×C47—224no—
200Q8×C47C2×#41116yescomplemented
201D4×C47—248no—
202D4×C47—224no—
203D4×C47C2×#41116yescomplemented
204C2×C4×C47—26no—
205C2×C4×C47—22no—
206C2×C4×C47—212no—
207C2×C4×C47—212no—
208C2×C4×C47—248no—
209C2×C4×C47—24no—
210C2×C4×C47—26no—
211C2×C4×C47—248no—
212C2×C4×C47—224no—
213C2×C4×C47—224no—
214C2×C4×C47—216no—
215C2×C4×C47—224no—
216C2×C4×C47C2×#41112yes—
217C2×C4×C47C2×#4114yes—
218C2×C4×C472−1+414yes—
219C2×C4×C47C2514yes—
220C2×C4×C47C2512yes—
221C2×C4×C47C2516yes—
222C2×C4×C47C2516yes—
223C2×C4×C47C25112yes—
224C2×C4×C47C25112yes—
225C2×C4×C47C2516yes—
226C2×C4×C47C2512yes—
227C2×C4×C47C2512yes—
228C2×#3482C4711yesmaximal, characteristic, direct product factor, Sylow
229C22×C47—24no—
230C22×C47—24no—
231C22×C47—216no—
232C22×C47—26no—
233C22×C47—26no—
234C22×C47—26no—
235C22×C47—412no—
236C22×C47C22×#4118yes—
237C22×C47C22×#4112yes—
238C22×C47C22×#4112yes—
239C22×C47C2×2−1+412yes—
240C22×C47C2611yescharacteristic
241C4×C47—26no—
242C4×C47—22no—
243C4×C47—212no—
244C4×C47—212no—
245C4×C47—24no—
246C4×C47—26no—
247C4×C47C22×#41112yes—
248C4×C47C22×#4114yes—
249C4×C47C2×2−1+414yes—
250#3482C2×C47132yesdirect product factor
251C2×#557C2×C4711yescharacteristic, complemented
252C2×#556C2×C4713yescomplemented
253C2×#552C2×C4716yescomplemented
254C2×D4×Q8C2×C4711yescharacteristic, complemented
255C2×#548C2×C4712yescomplemented
256C2×#547C2×C4713yescomplemented
257C2×#533C2×C4713yescomplemented
258C2×#529C2×C4716yescomplemented
259C2×C4×#41C2×C4711yescharacteristic, complemented
260C2×C4×#41C2×C4713yescomplemented
261C22×C4×Q8C2×C4712yescomplemented
262C2×C47—28no—
263C2×C47—46no—
264C2×C47#348214yesdirect product factor
265C2×C47C23×#4111yescharacteristic
266C2×C47C23×#4111yescharacteristic
267C2×C47C22×2−1+411yescharacteristic
268C22×#41C22×C4713yes—
269C22×#41C22×C4711yescharacteristic
270C23×Q8C22×C4712yes—
271#557C22×C47116yescomplemented
272#556C22×C47148yescomplemented
273#552C22×C47196yescomplemented
274D4×Q8C22×C47116yescomplemented
275#548C22×C47132yescomplemented
276#547C22×C47148yescomplemented
277#533C22×C47148yescomplemented
278C2×C4⋊Q8C22×C4713yes—
279C2×C4⋊Q8C22×C4713yes—
280#529C22×C47196yescomplemented
281C2×#126C22×C47112yes—
282C2×#125C22×C4716yes—
283C2×#125C22×C4716yes—
284C2×#124C22×C4716yes—
285C2×#123C22×C47112yes—
286C2×C22⋊Q8C22×C4716yes—
287C2×C22⋊Q8C22×C4716yes—
288C2×C22⋊Q8C22×C4716yes—
289C2×#121C22×C4716yes—
290C4×#41C22×C47148yescomplemented
291C4×#41C22×C47116yescomplemented
292C2×C4×Q8C22×C4711yescharacteristic
293C2×C4×Q8C22×C4716yes—
294C2×C4×Q8C22×C4712yes—
295C2×C4×Q8C22×C4716yes—
296C2×C4×Q8C22×C4713yes—
297C2×C4×Q8C22×C4711yescharacteristic
298C2×C4×Q8C22×C4713yes—
299C2×C4×Q8C22×C47132yescomplemented
300C2×C4×D4C22×C4711yescharacteristic
301C2×C4×D4C22×C4716yes—
302C2×C4×D4C22×C4713yes—
303C2×C4×D4C22×C4713yes—
304C2×C4×D4C22×C4713yes—
305C2×C4×D4C22×C4716yes—
306C2×#117C22×C4713yes—
307C2×#117C22×C4716yes—
308C2×#117C22×C4713yes—
309C2×#117C22×C4716yes—
310C22×C4⋊C4C22×C4716yes—
311C22×C42C22×C4716yes—
312C22×C42C22×C4713yes—
313C47C2×#348211yescharacteristic, direct product factor, Sylow
314C2×#41—28no—
315C2×#41—224no—
316C2×#41C23×C47124yes—
317C2×#41C23×C4718yes—
318C22×Q8—216no—
319C22×Q8C23×C4716yes—
320C22×Q8C23×C4713yes—
321C22×Q8C23×C47116yes—
322C22×Q8C23×C4711yescharacteristic
323C22×D4C23×C4716yes—
324C22×D4C23×C4713yes—
325C22×D4C23×C4711yescharacteristic
326C23×C4C23×C4716yes—
327C23×C4C23×C4716yes—
328C23×C4C23×C4713yes—
329C23×C4C23×C4713yes—
330C23×C4C23×C4713yes—
331C23×C4C23×C4712yes—
332C4⋊Q8C23×C47124yes—
333C4⋊Q8C23×C47124yes—
334#126C23×C47196yes—
335#125C23×C47148yes—
336#125C23×C47148yes—
337#124C23×C47148yes—
338#123C23×C47196yes—
339C22⋊Q8C23×C47148yes—
340C22⋊Q8C23×C47148yes—
341C22⋊Q8C23×C47148yes—
342#121C23×C47148yes—
343C4×Q8C23×C4718yes—
344C4×Q8C23×C47148yes—
345C4×Q8C23×C47116yes—
346C4×Q8C23×C47148yes—
347C4×Q8C23×C47124yes—
348C4×Q8C23×C4718yes—
349C4×Q8C23×C47124yes—
350C4×D4C23×C4718yes—
351C4×D4C23×C47124yes—
352C4×D4C23×C47148yes—
353C4×D4C23×C47124yes—
354C4×D4C23×C47124yes—
355C4×D4C23×C47148yes—
356#117C23×C47124yes—
357#117C23×C47148yes—
358#117C23×C47124yes—
359#117C23×C47148yes—
360C2×C4⋊C4C23×C4713yes—
361C2×C4⋊C4C23×C4716yes—
362C2×C4⋊C4C23×C47112yes—
363C2×C4⋊C4C23×C47148yes—
364C2×C4⋊C4C23×C4711yescharacteristic
365C2×C4⋊C4C23×C4716yes—
366C2×C4⋊C4C23×C4713yes—
367C2×C4⋊C4C23×C4713yes—
368C2×C4⋊C4C23×C4716yes—
369C2×C4⋊C4C23×C4716yes—
370C2×C4⋊C4C23×C4716yes—
371C2×C22⋊C4C23×C4712yes—
372C2×C22⋊C4C23×C4716yes—
373C2×C22⋊C4C23×C4716yes—
374C2×C22⋊C4C23×C4716yes—
375C2×C22⋊C4C23×C47112yes—
376C2×C42C23×C4713yes—
377C2×C42C23×C4716yes—
378C2×C42C23×C4716yes—
379C2×C42C23×C4713yes—
380C2×C42C23×C4716yes—
381C2×C42C23×C4711yescharacteristic
382C2×C42C23×C4713yes—
383C2×C42C23×C47148yes—
384C2×C42C23×C47124yes—
385C24C24×C4713yes—
386C24C24×C4712yes—
387#41—232no—
388#41—296no—
389C2×Q8—264no—
390C2×Q8—224no—
391C2×Q8—212no—
392C2×Q8#41×C4718yescomplemented
393C2×Q8C24×C47124yes—
394C2×Q8C24×C47112yes—
395C2×Q8C24×C4714yes—
396C2×D4—224no—
397C2×D4—212no—
398C2×D4#41×C4718yescomplemented
399C2×D4C24×C47124yes—
400C2×D4C24×C47112yes—
401C2×D4C24×C4714yes—
402C22×C4—224no—
403C22×C4—224no—
404C22×C4—212no—
405C22×C4—212no—
406C22×C4—28no—
407C22×C4—212no—
408C22×C4C24×C4712yes—
409C22×C4C24×C4718yes—
410C22×C4C24×C4711yescharacteristic
411C22×C4C24×C4713yes—
412C22×C4C24×C4713yes—
413C22×C4C24×C4716yes—
414C22×C4C24×C4716yes—
415C22×C4C24×C47124yes—
416C22×C4C24×C47124yes—
417C22×C4C24×C47112yes—
418C22×C4C24×C47112yes—
419C22×C4C24×C47112yes—
420C22×C4C24×C4713yes—
421C22×C4C24×C4711yescharacteristic
422C22×C4C24×C4711yescharacteristic
423C4⋊C4C24×C47112yes—
424C4⋊C4C24×C47124yes—
425C4⋊C4C24×C47148yes—
426C4⋊C4C24×C4714yes—
427C4⋊C4C24×C47124yes—
428C4⋊C4C24×C47112yes—
429C4⋊C4C24×C47112yes—
430C4⋊C4C24×C47124yes—
431C4⋊C4C24×C47124yes—
432C4⋊C4C24×C47124yes—
433C22⋊C4C24×C4718yes—
434C22⋊C4C24×C47124yes—
435C22⋊C4C24×C47124yes—
436C22⋊C4C24×C47124yes—
437C22⋊C4C24×C47148yes—
438C42C24×C47112yes—
439C42C24×C4714yes—
440C42C24×C47112yes—
441C42C24×C47124yes—
442C42C24×C47124yes—
443C42C24×C47112yes—
444C42C24×C47124yes—
445C23—24no—
446C23—24no—
447C23—26no—
448C23—26no—
449C23—26no—
450C23C2×#41×C4718yes—
451C23C25×C4716yes—
452C23C25×C4714yes—
453C23C25×C4711yescharacteristic
454Q8—248no—
455Q8—224no—
456Q8C2×#41×C47116yescomplemented
457D4—248no—
458D4—224no—
459D4C2×#41×C47116yescomplemented
460C2×C4—26no—
461C2×C4—22no—
462C2×C4—212no—
463C2×C4—212no—
464C2×C4—248no—
465C2×C4—24no—
466C2×C4—26no—
467C2×C4—248no—
468C2×C4—224no—
469C2×C4—224no—
470C2×C4—216no—
471C2×C4—224no—
472C2×C4C2×#41×C47112yes—
473C2×C4C2×#41×C4714yes—
474C2×C42−1+4×C4714yes—
475C2×C4C25×C4714yes—
476C2×C4C25×C4712yes—
477C2×C4C25×C4716yes—
478C2×C4C25×C4716yes—
479C2×C4C25×C47112yes—
480C2×C4C25×C47112yes—
481C2×C4C25×C4716yes—
482C2×C4C25×C4712yes—
483C2×C4C25×C4712yes—
484C22—24no—
485C22—24no—
486C22—216no—
487C22—26no—
488C22—26no—
489C22—26no—
490C22—412no—
491C22C22×#41×C4718yes—
492C22C22×#41×C4712yes—
493C22C22×#41×C4712yes—
494C22C2×2−1+4×C4712yes—
495C22C26×C4711yescharacteristic
496C4—26no—
497C4—22no—
498C4—212no—
499C4—212no—
500C4—24no—
501C4—26no—
502C4C22×#41×C47112yes—
503C4C22×#41×C4714yes—
504C4C2×2−1+4×C4714yes—
505C2—28no—
506C2—46no—
507C2C47×#348214yesdirect product factor
508C2C23×#41×C4711yescharacteristic
509C2C23×#41×C4711yescharacteristic
510C2C22×2−1+4×C4711yescharacteristic
subgroupG/H
centerC22×C4×C47C24
commutator, Frattini, cosocleC22C26×C47
socleC23×C47C25
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3482C2direct (N × H)
2. C2×C47×#557C2semidirect
3. C2×C47×#556C2semidirect
4. C2×C47×#552C2semidirect
5. C2×D4×Q8×C47C2semidirect
6. C2×C47×#548C2semidirect
7. C2×C47×#547C2semidirect
8. C2×C47×#533C2semidirect
9. C2×C47×#529C2semidirect
10. C2×C4×#41×C47C2semidirect
11. C2×C4×#41×C47C2semidirect
12. C22×C4×Q8×C47C2semidirect
16. C47×#557C22semidirect
17. C47×#556C22semidirect
18. C47×#552C22semidirect
19. D4×Q8×C47C22semidirect
20. C47×#548C22semidirect
21. C47×#547C22semidirect
22. C47×#533C22semidirect
25. C47×#529C22semidirect
35. C4×#41×C47C22semidirect
36. C4×#41×C47C22semidirect
44. C2×C4×Q8×C47C22semidirect
136. C2×Q8×C47#41semidirect
142. C2×D4×C47#41semidirect
200. Q8×C47C2×#41semidirect
203. D4×C47C2×#41semidirect
228. C2×#3482C47direct (N × H)
250. #3482C2×C47direct (N × H)
251. C2×#557C2×C47semidirect
252. C2×#556C2×C47semidirect
253. C2×#552C2×C47semidirect
254. C2×D4×Q8C2×C47semidirect
255. C2×#548C2×C47semidirect
256. C2×#547C2×C47semidirect
257. C2×#533C2×C47semidirect
258. C2×#529C2×C47semidirect
259. C2×C4×#41C2×C47semidirect
260. C2×C4×#41C2×C47semidirect
261. C22×C4×Q8C2×C47semidirect
264. C2×C47#3482direct (N × H)
271. #557C22×C47semidirect
272. #556C22×C47semidirect
273. #552C22×C47semidirect
274. D4×Q8C22×C47semidirect
275. #548C22×C47semidirect
276. #547C22×C47semidirect
277. #533C22×C47semidirect
280. #529C22×C47semidirect
290. C4×#41C22×C47semidirect
291. C4×#41C22×C47semidirect
299. C2×C4×Q8C22×C47semidirect
313. C47C2×#3482direct (N × H)
392. C2×Q8#41×C47semidirect
398. C2×D4#41×C47semidirect
456. Q8C2×#41×C47semidirect
459. D4C2×#41×C47semidirect
507. C2C47×#3482direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#34822
C2×C47×#5572
C2×C47×#5562
C2×C47×#5522
C2×D4×Q8×C472
C2×C47×#5482
C2×C47×#5472
C2×C47×#5332
C2×C47×#5292
C2×C4×#41×C472
C22×C4×Q8×C472
C2×#348247