Finite Group Databasebeta

← #26124535

Subgroups — #26124535

Order 12032.

886 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688992C211yesmaximal, characteristic
2C2×#15688886C211yesmaximal, characteristic
3C2×#15688885C211yesmaximal, characteristic
4C2×#15688885C211yesmaximal, characteristic
5C2×#15688877C211yesmaximal, characteristic
6#20241617C211yesmaximal, characteristic
7C2×C47×#340C211yesmaximal, characteristic
8C23×C47⋊C8C2211yescharacteristic
9C22×C4⋊Dic47C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×Dic47⋊C4—21no—
12C22×Dic47⋊C4—21no—
13C22×C4×Dic47C2211yescharacteristic
14#15688992—22no—
15#15688992—22no—
16C2×C47⋊#95—21no—
17C2×C47⋊#95—21no—
18#15688886—22no—
19#15688885—22no—
20#15688885—22no—
21#15688877C414yescomplemented
22C23×C8×C47C2211yescharacteristic
23C22×C4⋊C4×C47C2211yescharacteristic
24C22×C4⋊C4×C47C2211yescharacteristic
25C47×#340—22no—
26C23×Dic47—21no—
27C23×Dic47—21no—
28C23×Dic47D411yescharacteristic
29C23×Dic47D411yescharacteristic
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32C22×C47⋊C8—21no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C22×C47⋊C8C2×C412yes—
37C2×C4⋊Dic47—21no—
38C2×C4⋊Dic47—21no—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47—21no—
42C2×C4⋊Dic47—21no—
43C2×C4⋊Dic47—21no—
44C2×C4⋊Dic47—21no—
45C2×C4⋊Dic47—21no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47D412yes—
48C2×C4⋊Dic47Q812yes—
49C2×Dic47⋊C4—24no—
50C2×Dic47⋊C4—24no—
51C2×Dic47⋊C4—42no—
52C2×Dic47⋊C4—42no—
53C2×Dic47⋊C4—42no—
54C2×Dic47⋊C4—42no—
55C2×C4×Dic47—21no—
56C2×C4×Dic47—21no—
57C2×C4×Dic47—21no—
58C2×C4×Dic47—21no—
59C2×C4×Dic47C2×C412yes—
60C2×C4×Dic47Q812yes—
61C47⋊#95—42no—
62C47⋊#95—42no—
63C23×C4×C47—21no—
64C23×C4×C47—21no—
65C23×C4×C47C2311yescharacteristic
66C22×C8×C47—21no—
67C22×C8×C47—21no—
68C22×C8×C47—21no—
69C22×C8×C47—21no—
70C22×C8×C47—21no—
71C22×C8×C47—21no—
72C22×C8×C47C2×C412yes—
73C2×C4⋊C4×C47—21no—
74C2×C4⋊C4×C47—21no—
75C2×C4⋊C4×C47—21no—
76C2×C4⋊C4×C47—21no—
77C2×C4⋊C4×C47—21no—
78C2×C4⋊C4×C47—21no—
79C2×C4⋊C4×C47—21no—
80C2×C4⋊C4×C47—21no—
81C2×C4⋊C4×C47—21no—
82C2×C4⋊C4×C47—21no—
83C2×C4⋊C4×C47D412yes—
84C2×C4⋊C4×C47D412yes—
85C24×C47C2×D411yescharacteristic
86C22×C4×C47—22no—
87C22×C4×C47—22no—
88C22×C4×C47—41no—
89C22×C4×C47—41no—
90C22×C4×C47—41no—
91C22×C4×C47—41no—
92C22×C4×C47—41no—
93C22×C4×C47—41no—
94C22×C4×C47—41no—
95C22×C4×C47—41no—
96C22×C4×C47—41no—
97C22×C4×C47—41no—
98C22×C4×C47—41no—
99C22×C4×C47—41no—
100C22×C4×C47C22×C411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47C2×Q811yescharacteristic
105C22×C4×C47C2×Q811yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×Dic47—21no—
115C22×Dic47—21no—
116C22×Dic47—21no—
117C22×Dic47—21no—
118C22×Dic47—21no—
119C22×Dic47—21no—
120C22×Dic47—21no—
121C22×Dic47—21no—
122C22×Dic47—22no—
123C22×Dic47—22no—
124C22×Dic47—41no—
125C22×Dic47—41no—
126C22×Dic47—41no—
127C22×Dic47—41no—
128C22×Dic47—41no—
129C22×Dic47—41no—
130C22×Dic47—41no—
131C22×Dic47—41no—
132C22×Dic47—41no—
133C22×Dic47—41no—
134C22×Dic47—41no—
135C22×Dic47—41no—
136C22×Dic47C4⋊C412yes—
137C22×Dic47C4⋊C412yes—
138C22×Dic47D812yes—
139C22×Dic47SD1612yes—
140C22×Dic47SD1612yes—
141C22×Dic47Q1612yes—
142C2×C8×C47—22no—
143C2×C8×C47—22no—
144C2×C8×C47—22no—
145C2×C8×C47—41no—
146C2×C8×C47—41no—
147C2×C8×C47—41no—
148C2×C8×C47—41no—
149C4⋊C4×C47—22no—
150C4⋊C4×C47—22no—
151C4⋊C4×C47—22no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—41no—
154C4⋊C4×C47—41no—
155C4⋊C4×C47—41no—
156C4⋊C4×C47—41no—
157C4⋊Dic47—22no—
158C4⋊Dic47—22no—
159C4⋊Dic47—22no—
160C4⋊Dic47—22no—
161C4⋊Dic47—41no—
162C4⋊Dic47—41no—
163C4⋊Dic47—41no—
164C4⋊Dic47—41no—
165Dic47⋊C4—48no—
166Dic47⋊C4—48no—
167C4×Dic47—22no—
168C4×Dic47—22no—
169C4×Dic47—22no—
170C4×Dic47—22no—
171C2×C47⋊C8—22no—
172C2×C47⋊C8—22no—
173C2×C47⋊C8—22no—
174C2×C47⋊C8—41no—
175C2×C47⋊C8—41no—
176C2×C47⋊C8—41no—
177C2×C47⋊C8—41no—
178C23×C47C2×C4⋊C411yescharacteristic
179C23×C47#12011yescharacteristic
180C23×C47#12111yescharacteristic
181C23×C47C22⋊Q811yescharacteristic
182C23×C47#12311yescharacteristic
183C23×C47#12411yescharacteristic
184C23×C47#12411yescharacteristic
185C23×C47C2×D811yescharacteristic
186C23×C47C2×SD1611yescharacteristic
187C23×C47C2×SD1611yescharacteristic
188C23×C47C2×Q1611yescharacteristic
189C23×C47AGL(1,ℤ/8)11yescharacteristic
190C23×C47AGL(1,ℤ/8)11yescharacteristic
191C23×C47#13711yescharacteristic
192C23×C47#13711yescharacteristic
193C2×C4×C47—42no—
194C2×C4×C47—42no—
195C2×C4×C47—42no—
196C2×C4×C47—42no—
197C2×C4×C47—42no—
198C2×C4×C47—42no—
199C2×C4×C47—81no—
200C2×C4×C47—81no—
201C2×C4×C47—81no—
202C2×C4×C47—81no—
203C2×C4×C47—81no—
204C2×C4×C47—81no—
205C2×C4×C47—81no—
206C2×C4×C47—81no—
207C2×C4×C47#11711yescharacteristic
208C2×C4×C47#11711yescharacteristic
209C2×C4×C47C4×D411yescharacteristic
210C2×C4×C47C4×D411yescharacteristic
211C2×C4×C47C4×D411yescharacteristic
212C2×C4×C47C4×Q811yescharacteristic
213C2×C4×C47#12111yescharacteristic
214C2×C4×C47#12111yescharacteristic
215C2×C4×C47C22⋊Q811yescharacteristic
216C2×C4×C47C22⋊Q811yescharacteristic
217C2×C4×C47C22⋊Q811yescharacteristic
218C2×C4×C47C22⋊Q811yescharacteristic
219C2×C4×C47#12311yescharacteristic
220C2×C4×C47#12311yescharacteristic
221C2×C4×C47#12311yescharacteristic
222C2×C4×C47#12311yescharacteristic
223C2×C4×C47#12411yescharacteristic
224C2×C4×C47#12411yescharacteristic
225C2×C4×C47#12511yescharacteristic
226C2×C4×C47#12511yescharacteristic
227C2×C4×C47#12511yescharacteristic
228C2×C4×C47#12511yescharacteristic
229C2×C4×C47#12511yescharacteristic
230C2×C4×C47#12611yescharacteristic
231C2×C4×C47#12611yescharacteristic
232C2×C4×C47#12611yescharacteristic
233C2×C4×C47#12611yescharacteristic
234C2×C4×C47C4⋊Q811yescharacteristic
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—81no—
254C2×Dic47—81no—
255C2×Dic47—81no—
256C2×Dic47—81no—
257C2×Dic47—81no—
258C2×Dic47—81no—
259C2×Dic47—81no—
260C2×Dic47—81no—
261C2×Dic47#10614yes—
262C2×Dic47#10714yes—
263C8×C47—42no—
264C47⋊C8—42no—
265#11267—471nomaximal, Sylow
266C22×C47#38211yescharacteristic
267C22×C47#38511yescharacteristic
268C22×C47#38911yescharacteristic
269C22×C47#39311yescharacteristic
270C22×C47#39411yescharacteristic
271C22×C47#39711yescharacteristic
272C22×C47#40011yescharacteristic
273C22×C47C2×#10611yescharacteristic
274C22×C47C2×#10711yescharacteristic
275C22×C47#42811yescharacteristic
276C22×C47#42811yescharacteristic
277C22×C47#44711yescharacteristic
278C22×C47#44811yescharacteristic
279C22×C47#45011yescharacteristic
280C22×C47#45111yescharacteristic
281C22×C47#45911yescharacteristic
282C22×C47#46011yescharacteristic
283C22×C47#46111yescharacteristic
284C22×C47#46211yescharacteristic
285C22×C47#47411yescharacteristic
286C22×C47#47511yescharacteristic
287C22×C47#47611yescharacteristic
288C22×C47#47711yescharacteristic
289C22×C47#48011yescharacteristic
290C22×C47#48111yescharacteristic
291C22×C47#48311yescharacteristic
292C22×C47#48411yescharacteristic
293C22×C47#48611yescharacteristic
294C22×C47#48611yescharacteristic
295C22×C47#48711yescharacteristic
296C22×C47#48711yescharacteristic
297C22×C47#48911yescharacteristic
298C22×C47#48911yescharacteristic
299C22×C47#49011yescharacteristic
300C22×C47#49111yescharacteristic
301C4×C47—82no—
302C4×C47—82no—
303C4×C47#38711yescharacteristic
304C4×C47#38711yescharacteristic
305C4×C47#38811yescharacteristic
306C4×C47#38811yescharacteristic
307C4×C47#39811yescharacteristic
308C4×C47#39811yescharacteristic
309C4×C47#40011yescharacteristic
310C4×C47#40011yescharacteristic
311Dic47—24no—
312Dic47—24no—
313Dic47—82no—
314Dic47—82no—
315C2×#384—471no—
316C2×#340—471no—
317C2×#340—471no—
318C2×#340—471no—
319C2×#340D4711yescharacteristic
320C2×#336—471no—
321C4⋊#95—471no—
322C2×C47#144211yescharacteristic
323C2×C47#183411yescharacteristic
324C2×C47#183611yescharacteristic
325C2×C47#185211yescharacteristic
326C2×C47#185311yescharacteristic
327C2×C47#194711yescharacteristic
328C2×C47#194811yescharacteristic
329C2×C47#202311yescharacteristic
330C2×C47#202411yescharacteristic
331C2×C47#204111yescharacteristic
332C2×C47#204311yescharacteristic
333C2×C47#207111yescharacteristic
334C2×C47#207211yescharacteristic
335C2×C47#209911yescharacteristic
336C2×C47#210011yescharacteristic
337C23×C8—471no—
338C23×C8C2×D4711yescharacteristic
339C22×C4⋊C4—471no—
340C22×C4⋊C4—471no—
341C22×C4⋊C4—941no—
342C22×C4⋊C4—941no—
343C22×C4⋊C4C2×D4711yescharacteristic
344C22×C4⋊C4C2×D4711yescharacteristic
345C22×C42—471no—
346#384—942no—
347#384—942no—
348C2×#95—941no—
349C2×#95—941no—
350#340—22no—
351#340—942no—
352#340—942no—
353#340—942no—
354#336—474no—
355C47#1126711yescharacteristic, complemented, Sylow
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—471no—
359C23×C4—471no—
360C23×C4—941no—
361C23×C4—941no—
362C23×C4C22×D4711yescharacteristic
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—472no—
370C22×C8—941no—
371C22×C8—941no—
372C22×C8—941no—
373C22×C8—941no—
374C22×C8—941no—
375C22×C8—941no—
376C22×C8C4×D4712yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—472no—
388C2×C4⋊C4—472no—
389C2×C4⋊C4—941no—
390C2×C4⋊C4—941no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4—941no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4—941no—
396C2×C4⋊C4—941no—
397C2×C4⋊C4—944no—
398C2×C4⋊C4—944no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—1882no—
402C2×C4⋊C4—1882no—
403C2×C4⋊C4—1882no—
404C2×C4⋊C4—1882no—
405C2×C4⋊C4D18812yes—
406C2×C4⋊C4C22⋊D4712yes—
407C2×C42—472no—
408C2×C42—472no—
409C2×C42—941no—
410C2×C42—941no—
411C2×C42—941no—
412C2×C42—941no—
413#95—1882no—
414#95—1882no—
415C24D4×D4711yescharacteristic
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—472no—
431C22×C4—472no—
432C22×C4—472no—
433C22×C4—472no—
434C22×C4—472no—
435C22×C4—472no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—941no—
443C22×C4—941no—
444C22×C4—942no—
445C22×C4—942no—
446C22×C4—1881no—
447C22×C4—1881no—
448C22×C4—1881no—
449C22×C4—1881no—
450C22×C4—1881no—
451C22×C4—1881no—
452C22×C4—1881no—
453C22×C4—1881no—
454C22×C4—1881no—
455C22×C4—1881no—
456C22×C4—1881no—
457C22×C4—1881no—
458C22×C4C2×C4×D4711yescharacteristic
459C22×C4C2×D18811yescharacteristic
460C22×C4#1062535011yescharacteristic
461C22×C4#1062535011yescharacteristic
462C22×C4#1062535011yescharacteristic
463C22×C4#1062535011yescharacteristic
464C22×C4D4×D4711yescharacteristic
465C22×C4#1062535211yescharacteristic
466C22×C4#1062535211yescharacteristic
467C22×C4#1062535211yescharacteristic
468C22×C4#1062535211yescharacteristic
469C22×C4Q8×D4711yescharacteristic
470C22×C4Q8×D4711yescharacteristic
471C22×C4C2×C22⋊D4711yescharacteristic
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—942no—
480C2×C8—942no—
481C2×C8—942no—
482C2×C8—1881no—
483C2×C8—1881no—
484C2×C8—1881no—
485C2×C8—1881no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—942no—
495C4⋊C4—942no—
496C4⋊C4—942no—
497C4⋊C4—942no—
498C4⋊C4—1888no—
499C4⋊C4—1888no—
500C4⋊C4—1881no—
501C4⋊C4—1881no—
502C4⋊C4—1881no—
503C4⋊C4—1881no—
504C42—942no—
505C42—942no—
506C42—942no—
507C42—942no—
508C23C4⋊C4×D4711yescharacteristic
509C23#1309399411yescharacteristic
510C23#1309399611yescharacteristic
511C23#1309400211yescharacteristic
512C23#1309400611yescharacteristic
513C23#1309401011yescharacteristic
514C23#1309401011yescharacteristic
515C23D8×D4711yescharacteristic
516C23SD16×D4711yescharacteristic
517C23SD16×D4711yescharacteristic
518C23Q16×D4711yescharacteristic
519C23#1309404811yescharacteristic
520C23#1309405111yescharacteristic
521C23#1309405311yescharacteristic
522C23#1309405611yescharacteristic
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—81no—
534C2×C4—81no—
535C2×C4—81no—
536C2×C4—81no—
537C2×C4—474no—
538C2×C4—474no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—942no—
549C2×C4—942no—
550C2×C4—942no—
551C2×C4—3761no—
552C2×C4—3761no—
553C2×C4—3761no—
554C2×C4—3761no—
555C2×C4—3761no—
556C2×C4—3761no—
557C2×C4—3761no—
558C2×C4—3761no—
559C2×C4—1882no—
560C2×C4—1882no—
561C2×C4—1882no—
562C2×C4—1882no—
563C2×C4—1882no—
564C2×C4—1882no—
565C2×C4#1309398011yescharacteristic
566C2×C4#1309398111yescharacteristic
567C2×C4(C22⋊D47)⋊C411yescharacteristic
568C2×C4C4×C22⋊D4711yescharacteristic
569C2×C4C4×D18811yescharacteristic
570C2×C4#1309398911yescharacteristic
571C2×C4#1309399511yescharacteristic
572C2×C4#1309399811yescharacteristic
573C2×C4#1309400211yescharacteristic
574C2×C4#1309400211yescharacteristic
575C2×C4#1309400411yescharacteristic
576C2×C4#1309400411yescharacteristic
577C2×C4#1309400511yescharacteristic
578C2×C4#1309400611yescharacteristic
579C2×C4#1309400711yescharacteristic
580C2×C4#1309400811yescharacteristic
581C2×C4#1309401011yescharacteristic
582C2×C4#1309401211yescharacteristic
583C2×C4#1309401411yescharacteristic
584C2×C4#1309401411yescharacteristic
585C2×C4#1309401411yescharacteristic
586C2×C4#1309401411yescharacteristic
587C2×C4#1309401411yescharacteristic
588C2×C4#1309401711yescharacteristic
589C2×C4#1309401711yescharacteristic
590C2×C4#1309401711yescharacteristic
591C2×C4#1309401811yescharacteristic
592C2×C4#1309402211yescharacteristic
593C8—42no—
594C8—1882no—
595C22#1568898711yescharacteristic
596C22#1568899711yescharacteristic
597C22#1568901811yescharacteristic
598C22#1568903611yescharacteristic
599C22#1568903911yescharacteristic
600C22#1568905111yescharacteristic
601C22#1568906411yescharacteristic
602C22#106×D4711yescharacteristic
603C22#107×D4711yescharacteristic
604C22#1568916211yescharacteristic
605C22#1568916411yescharacteristic
606C22#1568925811yescharacteristic
607C22#1568926311yescharacteristic
608C22#1568927511yescharacteristic
609C22#1568928011yescharacteristic
610C22#1568931611yescharacteristic
611C22#1568932111yescharacteristic
612C22#1568932611yescharacteristic
613C22#1568933111yescharacteristic
614C22#1568940211yescharacteristic
615C22#1568940711yescharacteristic
616C22#1568941211yescharacteristic
617C22#1568941711yescharacteristic
618C22#1568943511yescharacteristic
619C22#1568944011yescharacteristic
620C22#1568945211yescharacteristic
621C22#1568945711yescharacteristic
622C22#1568946811yescharacteristic
623C22#1568946811yescharacteristic
624C22#1568947211yescharacteristic
625C22#1568947211yescharacteristic
626C22#1568948111yescharacteristic
627C22#1568948411yescharacteristic
628C22#1568948611yescharacteristic
629C22#1568949011yescharacteristic
630C4—82no—
631C4—82no—
632C4—944no—
633C4—944no—
634C4—3762no—
635C4—3762no—
636C4#1568900511yescharacteristic
637C4#1568900811yescharacteristic
638C4#1568901111yescharacteristic
639C4#1568901411yescharacteristic
640C4#1568905311yescharacteristic
641C4#1568905411yescharacteristic
642C4#1568906311yescharacteristic
643C4#1568906411yescharacteristic
644C2#2024164311yescharacteristic
645C2#2024351411yescharacteristic
646C2#2024352011yescharacteristic
647C2#2024357711yescharacteristic
648C2#2024358211yescharacteristic
649C2#2024414311yescharacteristic
650C2#2024414811yescharacteristic
651C2#2024452311yescharacteristic
652C2#2024452811yescharacteristic
653C2#2024462111yescharacteristic
654C2#2024463311yescharacteristic
655C2#2024479411yescharacteristic
656C2#2024479911yescharacteristic
657C2#2024494811yescharacteristic
658C2#2024495311yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#340C2
socle, prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×#340D47
hypocenterC47#11267
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
21. #15688877C4semidirect
355. C47#11267semidirect

Maximal subgroups

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

subgroupindex
C2×#156889922
C2×#156888862
C2×#156888852
C2×#156888772
#202416172
C2×C47×#3402
#1126747