Finite Group Databasebeta

← #26122446

Subgroups — #26122446

Order 12032.

958 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
1C22×#13093956C211yesmaximal, characteristic
2C2×C4×C4⋊Dic47C211yesmaximal, characteristic
3C2×#15688886C211yesmaximal, characteristic
4C2×#15688886C211yesmaximal, characteristic
5C2×#15688886C211yesmaximal, characteristic
6#20241618C211yesmaximal, characteristic
7C2×C47×#336C211yesmaximal, characteristic
8C22×C4⋊Dic47C2211yescharacteristic
9C22×C4⋊Dic47C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×C4⋊Dic47C2211yescharacteristic
12C22×C4×Dic47—21no—
13C2×#13093956—22no—
14C2×#13093956—22no—
15C2×#13093956C414yescomplemented
16C4×C4⋊Dic47—22no—
17C4×C4⋊Dic47—22no—
18C2×C47⋊#95—21no—
19C2×C47⋊#95—21no—
20C2×C47⋊#95—21no—
21#15688886—22no—
22#15688886—22no—
23#15688886C414yescomplemented
24C23×C8×C47C2211yescharacteristic
25C23×C8×C47C2211yescharacteristic
26C22×C42×C47C2211yescharacteristic
27C47×#336C414yescomplemented
28C23×Dic47—21no—
29C23×Dic47—21no—
30C23×Dic47—21no—
31C23×Dic47—21no—
32C2×C4⋊Dic47—21no—
33C2×C4⋊Dic47—21no—
34C2×C4⋊Dic47—21no—
35C2×C4⋊Dic47—21no—
36C2×C4⋊Dic47—21no—
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⋊Dic47—21no—
48C2×C4⋊Dic47C2×C412yes—
49C2×C4⋊Dic47C2×C412yes—
50C2×C4⋊Dic47C2×C412yes—
51C2×C4⋊Dic47C2×C412yes—
52C2×C4⋊Dic47D412yes—
53C2×C4⋊Dic47D412yes—
54C2×C4⋊Dic47D412yes—
55C2×C4⋊Dic47Q812yes—
56C2×C4×Dic47—24no—
57C2×C4×Dic47—42no—
58C2×C4×Dic47—42no—
59#13093956—28no—
60C47⋊#95—24no—
61C47⋊#95—42no—
62C47⋊#95—42no—
63C23×C4×C47D411yescharacteristic
64C23×C4×C47D411yescharacteristic
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×C47—21no—
73C22×C8×C47—21no—
74C22×C8×C47—21no—
75C22×C8×C47—21no—
76C22×C8×C47C2×C412yes—
77C22×C8×C47C2×C412yes—
78C22×C8×C47C2×C412yes—
79C22×C8×C47C2×C412yes—
80C2×C42×C47—21no—
81C2×C42×C47—21no—
82C2×C42×C47—21no—
83C2×C42×C47—21no—
84C2×C42×C47C2×C412yes—
85C2×C42×C47Q812yes—
86C24×C47C2×D411yescharacteristic
87C22×C4×C47—21no—
88C22×C4×C47—21no—
89C22×C4×C47—21no—
90C22×C4×C47—21no—
91C22×C4×C47—21no—
92C22×C4×C47—21no—
93C22×C4×C47—21no—
94C22×C4×C47—21no—
95C22×C4×C47—21no—
96C22×C4×C47—21no—
97C22×C4×C47C4⋊C412yes—
98C22×C4×C47C4⋊C412yes—
99C22×C4×C47SD1612yes—
100C22×C4×C47SD1612yes—
101C22×C4×C47C22×C411yescharacteristic
102C22×C4×C47C22×C411yescharacteristic
103C22×C4×C47C22×C411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47C2×Q811yescharacteristic
108C22×C4×C47C2×Q811yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47#4111yescharacteristic
115C22×Dic47—22no—
116C22×Dic47—22no—
117C22×Dic47—22no—
118C22×Dic47—22no—
119C22×Dic47—22no—
120C22×Dic47—22no—
121C22×Dic47—22no—
122C22×Dic47—22no—
123C22×Dic47—41no—
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×Dic47—41no—
137C22×Dic47—41no—
138C22×Dic47—41no—
139C22×Dic47—41no—
140C22×Dic47—41no—
141C22×Dic47—41no—
142C22×Dic47—41no—
143C2×C8×C47—22no—
144C2×C8×C47—22no—
145C2×C8×C47—22no—
146C2×C8×C47—22no—
147C2×C8×C47—22no—
148C2×C8×C47—22no—
149C2×C8×C47—22no—
150C2×C8×C47—22no—
151C2×C8×C47—22no—
152C2×C8×C47—41no—
153C2×C8×C47—41no—
154C2×C8×C47—41no—
155C2×C8×C47—41no—
156C2×C8×C47C4214yescomplemented
157C42×C47—22no—
158C42×C47—22no—
159C42×C47—22no—
160C42×C47—22no—
161C4⋊Dic47—22no—
162C4⋊Dic47—22no—
163C4⋊Dic47—22no—
164C4⋊Dic47—22no—
165C4⋊Dic47—22no—
166C4⋊Dic47—22no—
167C4⋊Dic47—22no—
168C4⋊Dic47—22no—
169C4⋊Dic47—22no—
170C4⋊Dic47—22no—
171C4⋊Dic47—41no—
172C4⋊Dic47—41no—
173C4⋊Dic47—41no—
174C4⋊Dic47—41no—
175C4⋊Dic47C22⋊C414yes—
176C4⋊Dic47C4⋊C414yes—
177C4×Dic47—48no—
178C23×C47C2×C4⋊C411yescharacteristic
179C23×C47C4×D411yescharacteristic
180C23×C47C4×D411yescharacteristic
181C23×C47#12011yescharacteristic
182C23×C47#12111yescharacteristic
183C23×C47C22⋊Q811yescharacteristic
184C23×C47#12311yescharacteristic
185C23×C47C2×SD1611yescharacteristic
186C23×C47C2×SD1611yescharacteristic
187C23×C47#13511yescharacteristic
188C23×C47#13511yescharacteristic
189C23×C47AGL(1,ℤ/8)11yescharacteristic
190C23×C47AGL(1,ℤ/8)11yescharacteristic
191C23×C47#13711yescharacteristic
192C23×C47#13711yescharacteristic
193C2×C4×C47—22no—
194C2×C4×C47—22no—
195C2×C4×C47—22no—
196C2×C4×C47—22no—
197C2×C4×C47—22no—
198C2×C4×C47—22no—
199C2×C4×C47—22no—
200C2×C4×C47—22no—
201C2×C4×C47—22no—
202C2×C4×C47—41no—
203C2×C4×C47—41no—
204C2×C4×C47—41no—
205C2×C4×C47—41no—
206C2×C4×C47#10614yescomplemented
207C2×C4×C47C2×C4211yescharacteristic
208C2×C4×C47C2×C22⋊C411yescharacteristic
209C2×C4×C47C2×C4⋊C411yescharacteristic
210C2×C4×C47#11711yescharacteristic
211C2×C4×C47#11711yescharacteristic
212C2×C4×C47#11711yescharacteristic
213C2×C4×C47C4×D411yescharacteristic
214C2×C4×C47C4×D411yescharacteristic
215C2×C4×C47C4×D411yescharacteristic
216C2×C4×C47C4×D411yescharacteristic
217C2×C4×C47C4×D411yescharacteristic
218C2×C4×C47C4×D411yescharacteristic
219C2×C4×C47C4×Q811yescharacteristic
220C2×C4×C47C4×Q811yescharacteristic
221C2×C4×C47C4×Q811yescharacteristic
222C2×C4×C47C4×Q811yescharacteristic
223C2×C4×C47#12111yescharacteristic
224C2×C4×C47C22⋊Q811yescharacteristic
225C2×C4×C47C22⋊Q811yescharacteristic
226C2×C4×C47C22⋊Q811yescharacteristic
227C2×C4×C47#12311yescharacteristic
228C2×C4×C47#12311yescharacteristic
229C2×C4×C47#12411yescharacteristic
230C2×C4×C47#12511yescharacteristic
231C2×C4×C47#12511yescharacteristic
232C2×C4×C47#12611yescharacteristic
233C2×C4×C47#12611yescharacteristic
234C2×C4×C47C4⋊Q811yescharacteristic
235C2×Dic47—24no—
236C2×Dic47—24no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47—42no—
245C2×Dic47—42no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—81no—
256C2×Dic47—81no—
257C2×Dic47—81no—
258C2×Dic47—81no—
259C2×Dic47—81no—
260C2×Dic47—81no—
261C2×Dic47—81no—
262C2×Dic47—81no—
263C8×C47—24no—
264C8×C47—42no—
265#10908—471nomaximal, Sylow
266C22×C47C4×C4⋊C411yescharacteristic
267C22×C47#38511yescharacteristic
268C22×C47#38511yescharacteristic
269C22×C47#38611yescharacteristic
270C22×C47#38711yescharacteristic
271C22×C47#38811yescharacteristic
272C22×C47#38911yescharacteristic
273C22×C47C2×#10611yescharacteristic
274C22×C47#42711yescharacteristic
275C22×C47#42811yescharacteristic
276C22×C47#42811yescharacteristic
277C22×C47C4×SD1611yescharacteristic
278C22×C47C4×SD1611yescharacteristic
279C22×C47C4×SD1611yescharacteristic
280C22×C47C4×SD1611yescharacteristic
281C22×C47#44011yescharacteristic
282C22×C47#44011yescharacteristic
283C22×C47#44111yescharacteristic
284C22×C47#44211yescharacteristic
285C22×C47#44811yescharacteristic
286C22×C47#44911yescharacteristic
287C22×C47#45011yescharacteristic
288C22×C47#45211yescharacteristic
289C22×C47#46011yescharacteristic
290C22×C47#46111yescharacteristic
291C22×C47#46311yescharacteristic
292C22×C47#46411yescharacteristic
293C22×C47#47511yescharacteristic
294C22×C47#47611yescharacteristic
295C22×C47#47811yescharacteristic
296C22×C47#47911yescharacteristic
297C22×C47#48111yescharacteristic
298C22×C47#48211yescharacteristic
299C22×C47#48311yescharacteristic
300C22×C47#48511yescharacteristic
301C4×C47—24no—
302C4×C47—42no—
303C4×C47C4×C22⋊C411yescharacteristic
304C4×C47C4×C4⋊C411yescharacteristic
305C4×C47#38711yescharacteristic
306C4×C47#38711yescharacteristic
307C4×C47#38711yescharacteristic
308C4×C47#38811yescharacteristic
309C4×C47#38911yescharacteristic
310C4×C47#39111yescharacteristic
311Dic47—44no—
312Dic47—44no—
313Dic47—82no—
314Dic47—82no—
315C22×#106—471no—
316C2×C4×C4⋊C4—471no—
317C2×#340—471no—
318C2×#340—471no—
319C2×#340—471no—
320C2×#336D4711yescharacteristic
321C4⋊#95—471no—
322C2×C47#143611yescharacteristic
323C2×C47C4×#10611yescharacteristic
324C2×C47#177611yescharacteristic
325C2×C47#185311yescharacteristic
326C2×C47#185411yescharacteristic
327C2×C47#186411yescharacteristic
328C2×C47#186511yescharacteristic
329C2×C47#187711yescharacteristic
330C2×C47#188011yescharacteristic
331C2×C47#191911yescharacteristic
332C2×C47#192011yescharacteristic
333C2×C47#192611yescharacteristic
334C2×C47#192711yescharacteristic
335C2×C47#194811yescharacteristic
336C2×C47#194911yescharacteristic
337C23×C8C2×D4711yescharacteristic
338C23×C8C2×D4711yescharacteristic
339C22×C4⋊C4—471no—
340C22×C4⋊C4—471no—
341C22×C4⋊C4—471no—
342C22×C4⋊C4—471no—
343C22×C42—941no—
344C22×C42C2×D4711yescharacteristic
345C2×#106—474no—
346C2×#106—942no—
347C2×#106—942no—
348C4×C4⋊C4—942no—
349C4×C4⋊C4—942no—
350C2×#95—941no—
351C2×#95—941no—
352C2×#95—941no—
353#340—474no—
354#340—942no—
355#340—942no—
356#336Dic4714yescomplemented
357C47#1090811yescharacteristic, complemented, Sylow
358C23×C4—941no—
359C23×C4—941no—
360C23×C4—941no—
361C23×C4—941no—
362C23×C4D18811yescharacteristic
363C23×C4D18811yescharacteristic
364C23×C4C22×D4711yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8C4×D4712yes—
376C22×C8C4×D4712yes—
377C22×C8C2×Dic4712yes—
378C22×C8C2×Dic4712yes—
379C2×C4⋊C4—472no—
380C2×C4⋊C4—472no—
381C2×C4⋊C4—472no—
382C2×C4⋊C4—472no—
383C2×C4⋊C4—472no—
384C2×C4⋊C4—472no—
385C2×C4⋊C4—472no—
386C2×C4⋊C4—472no—
387C2×C4⋊C4—941no—
388C2×C4⋊C4—941no—
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—941no—
398C2×C4⋊C4—941no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—941no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—944no—
408C2×C42—1882no—
409C2×C42—1882no—
410C2×C42Dic9412yes—
411C2×C42C2×Dic4712yes—
412#106—948no—
413#95—944no—
414#95—1882no—
415#95—1882no—
416C24C2×D18811yescharacteristic
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—942no—
428C22×C4—942no—
429C22×C4—942no—
430C22×C4—942no—
431C22×C4—942no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—1881no—
436C22×C4—1881no—
437C22×C4—1881no—
438C22×C4—1881no—
439C22×C4—1881no—
440C22×C4—1881no—
441C22×C4—1881no—
442C22×C4—1881no—
443C22×C4—1881no—
444C22×C4—1881no—
445C22×C4—1881no—
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#1062532512yes—
456C22×C4#1062532512yes—
457C22×C4C4⋊Dic4712yes—
458C22×C4C4⋊Dic4712yes—
459C22×C4C2×Dic9411yescharacteristic
460C22×C4C2×C4×D4711yescharacteristic
461C22×C4C2×C4×D4711yescharacteristic
462C22×C4#1062535011yescharacteristic
463C22×C4#1062535011yescharacteristic
464C22×C4D4×D4711yescharacteristic
465C22×C4D4×D4711yescharacteristic
466C22×C4D4×D4711yescharacteristic
467C22×C4#1062535211yescharacteristic
468C22×C4#1062535211yescharacteristic
469C22×C4#1062535211yescharacteristic
470C22×C4Q8×D4711yescharacteristic
471C22×C4#1062535411yescharacteristic
472C22×C4C22×Dic4711yescharacteristic
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8C4×Dic4714yescomplemented
487C4⋊C4—474no—
488C4⋊C4—474no—
489C4⋊C4—942no—
490C4⋊C4—942no—
491C4⋊C4—942no—
492C4⋊C4—942no—
493C4⋊C4—942no—
494C4⋊C4—942no—
495C4⋊C4—942no—
496C4⋊C4—942no—
497C4⋊C4—942no—
498C4⋊C4—942no—
499C4⋊C4—1881no—
500C4⋊C4—1881no—
501C4⋊C4—1881no—
502C4⋊C4—1881no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—1888no—
508C23C2×C4⋊Dic4711yescharacteristic
509C23C4×D18811yescharacteristic
510C23C4×D18811yescharacteristic
511C23#1309399411yescharacteristic
512C23#1309399911yescharacteristic
513C23#1309400411yescharacteristic
514C23#1309400811yescharacteristic
515C23C2×#1062532511yescharacteristic
516C23C2×#1062532511yescharacteristic
517C23#1309404611yescharacteristic
518C23#1309404611yescharacteristic
519C23#1309405211yescharacteristic
520C23#1309405211yescharacteristic
521C23#1309405711yescharacteristic
522C23#1309405711yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—944no—
537C2×C4—944no—
538C2×C4—3761no—
539C2×C4—3761no—
540C2×C4—3761no—
541C2×C4—3761no—
542C2×C4—3761no—
543C2×C4—3761no—
544C2×C4—3761no—
545C2×C4—3761no—
546C2×C4—1882no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4—1882no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4—1882no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4—1882no—
560C2×C4—1882no—
561C2×C4—1882no—
562C2×C4—1882no—
563C2×C4—1882no—
564C2×C4#1309395614yescomplemented
565C2×C4C2×C4×Dic4711yescharacteristic
566C2×C4C22⋊C4×D4711yescharacteristic
567C2×C4C4⋊C4×D4711yescharacteristic
568C2×C4#1309398011yescharacteristic
569C2×C4#1309398211yescharacteristic
570C2×C4#1309398311yescharacteristic
571C2×C4(C22⋊D47)⋊C411yescharacteristic
572C2×C4(C22⋊D47)⋊C411yescharacteristic
573C2×C4#1309398611yescharacteristic
574C2×C4D4×Dic4711yescharacteristic
575C2×C4D4×Dic4711yescharacteristic
576C2×C4D4×Dic4711yescharacteristic
577C2×C4#1309398911yescharacteristic
578C2×C4C4×Dic9411yescharacteristic
579C2×C4C4×Dic9411yescharacteristic
580C2×C4Q8×Dic4711yescharacteristic
581C2×C4#1309399711yescharacteristic
582C2×C4#1309400111yescharacteristic
583C2×C4#1309400111yescharacteristic
584C2×C4#1309400211yescharacteristic
585C2×C4#1309400611yescharacteristic
586C2×C4#1309400911yescharacteristic
587C2×C4#1309401011yescharacteristic
588C2×C4#1309401411yescharacteristic
589C2×C4#1309401511yescharacteristic
590C2×C4#1309401711yescharacteristic
591C2×C4#1309401911yescharacteristic
592C2×C4#1309402311yescharacteristic
593C8—24no—
594C8—42no—
595C22C4×C4⋊Dic4711yescharacteristic
596C22#1568899711yescharacteristic
597C22#1568899811yescharacteristic
598C22#1568900111yescharacteristic
599C22#1568900811yescharacteristic
600C22#1568901511yescharacteristic
601C22#1568902211yescharacteristic
602C22C2×#1309395611yescharacteristic
603C22#1568916111yescharacteristic
604C22#1568916511yescharacteristic
605C22#1568916511yescharacteristic
606C22C4×#1062532511yescharacteristic
607C22C4×#1062532511yescharacteristic
608C22C4×#1062532511yescharacteristic
609C22C4×#1062532511yescharacteristic
610C22#1568922511yescharacteristic
611C22#1568922511yescharacteristic
612C22#1568923111yescharacteristic
613C22#1568923611yescharacteristic
614C22#1568926411yescharacteristic
615C22#1568927011yescharacteristic
616C22#1568927611yescharacteristic
617C22#1568928711yescharacteristic
618C22#1568932411yescharacteristic
619C22#1568932911yescharacteristic
620C22#1568933911yescharacteristic
621C22#1568934611yescharacteristic
622C22#1568940911yescharacteristic
623C22#1568941411yescharacteristic
624C22#1568942411yescharacteristic
625C22#1568943111yescharacteristic
626C22#1568944211yescharacteristic
627C22#1568944811yescharacteristic
628C22#1568945411yescharacteristic
629C22#1568946511yescharacteristic
630C4—24no—
631C4—42no—
632C4—3762no—
633C4—3762no—
634C4—1884no—
635C4—1884no—
636C4C22⋊C4×Dic4711yescharacteristic
637C4C4⋊C4×Dic4711yescharacteristic
638C4#1568900611yescharacteristic
639C4#1568900911yescharacteristic
640C4#1568901011yescharacteristic
641C4#1568901611yescharacteristic
642C4#1568902011yescharacteristic
643C4#1568902711yescharacteristic
644C2#2024162211yescharacteristic
645C2C4×#1309395611yescharacteristic
646C2#2024328511yescharacteristic
647C2#2024358311yescharacteristic
648C2#2024358911yescharacteristic
649C2#2024365211yescharacteristic
650C2#2024365911yescharacteristic
651C2#2024372111yescharacteristic
652C2#2024374211yescharacteristic
653C2#2024396711yescharacteristic
654C2#2024397411yescharacteristic
655C2#2024401611yescharacteristic
656C2#2024402311yescharacteristic
657C2#2024415211yescharacteristic
658C2#2024415811yescharacteristic
subgroupG/H
centerC24C2×D188
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#336C2
socle, prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×#336D47
hypocenterC47#10908
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
15. C2×#13093956C4semidirect
23. #15688886C4semidirect
27. C47×#336C4semidirect
156. C2×C8×C47C42semidirect
206. C2×C4×C47#106semidirect
356. #336Dic47semidirect
357. C47#10908semidirect
486. C2×C8C4×Dic47semidirect
564. C2×C4#13093956semidirect

Maximal subgroups

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

subgroupindex
C22×#130939562
C2×C4×C4⋊Dic472
C2×#156888862
#202416182
C2×C47×#3362
#1090847