Finite Group Databasebeta

← #26122288

Subgroups — #26122288

Order 12032.

986 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689019C211yesmaximal, characteristic
2C2×C4⋊C4×Dic47C211yesmaximal, characteristic
3C2×#15688886C211yesmaximal, characteristic
4C2×#15688885C211yesmaximal, characteristic
5C2×#15688885C211yesmaximal, characteristic
6C2×#15688877C211yesmaximal, characteristic
7C2×C47×#340C211yesmaximal, characteristic
8C23×C47⋊C8C2211yescharacteristic
9C22×C4⋊Dic47C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×Dic47⋊C4—21no—
12C22×C4×Dic47—21no—
13C22×C4×Dic47C2211yescharacteristic
14#15689019—22no—
15#15689019C414yescomplemented
16C4⋊C4×Dic47—22no—
17C4⋊C4×Dic47—22no—
18C2×C47⋊#95—21no—
19C2×C47⋊#95—21no—
20#15688886C414yescomplemented
21#15688885—22no—
22#15688885C414yescomplemented
23#15688877—22no—
24C23×C8×C47C2211yescharacteristic
25C22×C4⋊C4×C47C2211yescharacteristic
26C22×C4⋊C4×C47C2211yescharacteristic
27C47×#340—22no—
28C23×Dic47—21no—
29C23×Dic47—21no—
30C23×Dic47D411yescharacteristic
31C23×Dic47D411yescharacteristic
32C22×C47⋊C8—21no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C22×C47⋊C8—21no—
37C22×C47⋊C8—21no—
38C22×C47⋊C8C2×C412yes—
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⋊Dic47C2×C412yes—
46C2×C4⋊Dic47C2×C412yes—
47C2×C4⋊Dic47C2×C412yes—
48C2×C4⋊Dic47C2×C412yes—
49C2×C4⋊Dic47D412yes—
50C2×C4⋊Dic47Q812yes—
51C2×Dic47⋊C4—24no—
52C2×Dic47⋊C4—42no—
53C2×Dic47⋊C4—42no—
54C2×C4×Dic47—21no—
55C2×C4×Dic47—21no—
56C2×C4×Dic47—21no—
57C2×C4×Dic47—21no—
58C2×C4×Dic47—24no—
59C2×C4×Dic47—42no—
60C2×C4×Dic47—42no—
61C2×C4×Dic47C2×C412yes—
62C2×C4×Dic47D412yes—
63C47⋊#95—24no—
64C47⋊#95—24no—
65C23×C4×C47—21no—
66C23×C4×C47—21no—
67C23×C4×C47C2311yescharacteristic
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×C47C2×C412yes—
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×C47C2×C412yes—
84C2×C4⋊C4×C47C2×C412yes—
85C2×C4⋊C4×C47D412yes—
86C2×C4⋊C4×C47Q812yes—
87C24×C47C2×D411yescharacteristic
88C22×C4×C47—22no—
89C22×C4×C47—22no—
90C22×C4×C47—22no—
91C22×C4×C47—22no—
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×C47—41no—
101C22×C4×C47—41no—
102C22×C4×C47C22×C411yescharacteristic
103C22×C4×C47C22×C411yescharacteristic
104C22×C4×C47C22×C411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47C2×D411yescharacteristic
108C22×C4×C47C2×Q811yescharacteristic
109C22×C4×C47C2×Q811yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47#4111yescharacteristic
115C22×C4×C47#4111yescharacteristic
116C22×Dic47—21no—
117C22×Dic47—21no—
118C22×Dic47—21no—
119C22×Dic47—21no—
120C22×Dic47—22no—
121C22×Dic47—22no—
122C22×Dic47—22no—
123C22×Dic47—22no—
124C22×Dic47—21no—
125C22×Dic47—22no—
126C22×Dic47—22no—
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47—21no—
131C22×Dic47—21no—
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×Dic47C22⋊C412yes—
141C22×Dic47C22⋊C412yes—
142C22×Dic47D812yes—
143C22×Dic47SD1612yes—
144C2×C8×C47—22no—
145C2×C8×C47—22no—
146C2×C8×C47—22no—
147C2×C8×C47—41no—
148C2×C8×C47—41no—
149C2×C8×C47—41no—
150C2×C8×C47—41no—
151C4⋊C4×C47—22no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—22no—
154C4⋊C4×C47—22no—
155C4⋊C4×C47—22no—
156C4⋊C4×C47—41no—
157C4⋊C4×C47—41no—
158C4⋊C4×C47C4⋊C414yescomplemented
159C4⋊Dic47—22no—
160C4⋊Dic47—22no—
161C4⋊Dic47—22no—
162C4⋊Dic47—22no—
163C4⋊Dic47—22no—
164C4⋊Dic47—22no—
165C4⋊Dic47C4214yescomplemented
166C4⋊Dic47C4⋊C414yescomplemented
167Dic47⋊C4—48no—
168C4×Dic47—22no—
169C4×Dic47—22no—
170C4×Dic47—22no—
171C4×Dic47—22no—
172C4×Dic47—48no—
173C2×C47⋊C8—22no—
174C2×C47⋊C8—22no—
175C2×C47⋊C8—22no—
176C2×C47⋊C8—41no—
177C2×C47⋊C8—41no—
178C2×C47⋊C8—41no—
179C2×C47⋊C8—41no—
180C23×C47C2×C22⋊C411yescharacteristic
181C23×C47C4×D411yescharacteristic
182C23×C47C4×D411yescharacteristic
183C23×C47#12011yescharacteristic
184C23×C47C22⋊Q811yescharacteristic
185C23×C47C22⋊Q811yescharacteristic
186C23×C47#12311yescharacteristic
187C23×C47C2×D811yescharacteristic
188C23×C47C2×SD1611yescharacteristic
189C23×C47#13511yescharacteristic
190C23×C47#13511yescharacteristic
191C23×C47AGL(1,ℤ/8)11yescharacteristic
192C23×C47#13711yescharacteristic
193C23×C47#13711yescharacteristic
194C23×C47#13711yescharacteristic
195C2×C4×C47—24no—
196C2×C4×C47—42no—
197C2×C4×C47—42no—
198C2×C4×C47—42no—
199C2×C4×C47—42no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—42no—
204C2×C4×C47—42no—
205C2×C4×C47—81no—
206C2×C4×C47—81no—
207C2×C4×C47—81no—
208C2×C4×C47—81no—
209C2×C4×C47C2×C4211yescharacteristic
210C2×C4×C47C2×C4⋊C411yescharacteristic
211C2×C4×C47C2×C4⋊C411yescharacteristic
212C2×C4×C47#11711yescharacteristic
213C2×C4×C47#11711yescharacteristic
214C2×C4×C47#11711yescharacteristic
215C2×C4×C47C4×D411yescharacteristic
216C2×C4×C47C4×D411yescharacteristic
217C2×C4×C47C4×D411yescharacteristic
218C2×C4×C47C4×D411yescharacteristic
219C2×C4×C47C4×D411yescharacteristic
220C2×C4×C47C4×D411yescharacteristic
221C2×C4×C47C4×Q811yescharacteristic
222C2×C4×C47C4×Q811yescharacteristic
223C2×C4×C47C4×Q811yescharacteristic
224C2×C4×C47C4×Q811yescharacteristic
225C2×C4×C47#12111yescharacteristic
226C2×C4×C47#12111yescharacteristic
227C2×C4×C47C22⋊Q811yescharacteristic
228C2×C4×C47C22⋊Q811yescharacteristic
229C2×C4×C47#12311yescharacteristic
230C2×C4×C47#12311yescharacteristic
231C2×C4×C47#12411yescharacteristic
232C2×C4×C47#12511yescharacteristic
233C2×C4×C47#12511yescharacteristic
234C2×C4×C47#12611yescharacteristic
235C2×C4×C47#12611yescharacteristic
236C2×C4×C47C4⋊Q811yescharacteristic
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—24no—
244C2×Dic47—24no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—42no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—42no—
260C2×Dic47—42no—
261C2×Dic47—42no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47#10214yes—
265C8×C47—42no—
266C47⋊C8—42no—
267#10884—471nomaximal, Sylow
268C22×C47C4×C22⋊C411yescharacteristic
269C22×C47#38511yescharacteristic
270C22×C47#38511yescharacteristic
271C22×C47#38611yescharacteristic
272C22×C47#38711yescharacteristic
273C22×C47#38711yescharacteristic
274C22×C47#39111yescharacteristic
275C22×C47C2×#10211yescharacteristic
276C22×C47#41611yescharacteristic
277C22×C47#41711yescharacteristic
278C22×C47#41911yescharacteristic
279C22×C47C4×D811yescharacteristic
280C22×C47C4×D811yescharacteristic
281C22×C47C4×SD1611yescharacteristic
282C22×C47C4×SD1611yescharacteristic
283C22×C47#44011yescharacteristic
284C22×C47#44011yescharacteristic
285C22×C47#44111yescharacteristic
286C22×C47#44111yescharacteristic
287C22×C47#44711yescharacteristic
288C22×C47#44811yescharacteristic
289C22×C47#45211yescharacteristic
290C22×C47#45211yescharacteristic
291C22×C47#47411yescharacteristic
292C22×C47#47411yescharacteristic
293C22×C47#47511yescharacteristic
294C22×C47#47511yescharacteristic
295C22×C47#47811yescharacteristic
296C22×C47#47811yescharacteristic
297C22×C47#47911yescharacteristic
298C22×C47#47911yescharacteristic
299C22×C47#48011yescharacteristic
300C22×C47#48111yescharacteristic
301C22×C47#48511yescharacteristic
302C22×C47#48511yescharacteristic
303C4×C47—44no—
304C4×C47—82no—
305C4×C47C4×C4⋊C411yescharacteristic
306C4×C47C4×C4⋊C411yescharacteristic
307C4×C47#38711yescharacteristic
308C4×C47#38711yescharacteristic
309C4×C47#38811yescharacteristic
310C4×C47#38811yescharacteristic
311C4×C47#38911yescharacteristic
312C4×C47#38911yescharacteristic
313Dic47—24no—
314Dic47—44no—
315Dic47—42no—
316Dic47—44no—
317C2×#389—471no—
318C2×C4×C4⋊C4—471no—
319C2×#340—471no—
320C2×#340—471no—
321C2×#340—471no—
322C2×#340D4711yescharacteristic
323C2×#336—471no—
324C2×C47#143611yescharacteristic
325C2×C47C4×#10211yescharacteristic
326C2×C47#176311yescharacteristic
327C2×C47#186211yescharacteristic
328C2×C47#186211yescharacteristic
329C2×C47#186511yescharacteristic
330C2×C47#186511yescharacteristic
331C2×C47#187311yescharacteristic
332C2×C47#187411yescharacteristic
333C2×C47#191811yescharacteristic
334C2×C47#191811yescharacteristic
335C2×C47#191911yescharacteristic
336C2×C47#191911yescharacteristic
337C2×C47#198811yescharacteristic
338C2×C47#198911yescharacteristic
339C23×C8—471no—
340C23×C8C2×D4711yescharacteristic
341C22×C4⋊C4—471no—
342C22×C4⋊C4—471no—
343C22×C4⋊C4—941no—
344C22×C4⋊C4C2×D4711yescharacteristic
345C22×C4⋊C4C2×D4711yescharacteristic
346C22×C42—471no—
347C22×C42—941no—
348#389—474no—
349#389—942no—
350C4×C4⋊C4—942no—
351C4×C4⋊C4—942no—
352C2×#95—941no—
353C2×#95—941no—
354#340—22no—
355#340—474no—
356#340—474no—
357#340—942no—
358#336—942no—
359C47#1088411yescharacteristic, complemented, Sylow
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—471no—
363C23×C4—471no—
364C23×C4—941no—
365C23×C4—941no—
366C23×C4C22×D4711yescharacteristic
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—472no—
374C22×C8—941no—
375C22×C8—941no—
376C22×C8—941no—
377C22×C8—941no—
378C22×C8—941no—
379C22×C8—941no—
380C22×C8C4×D4712yes—
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—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—472no—
390C2×C4⋊C4—472no—
391C2×C4⋊C4—472no—
392C2×C4⋊C4—472no—
393C2×C4⋊C4—472no—
394C2×C4⋊C4—472no—
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—944no—
402C2×C4⋊C4—1882no—
403C2×C4⋊C4—1882no—
404C2×C4⋊C4Dic9412yes—
405C2×C4⋊C4C4×D4712yes—
406C2×C4⋊C4C4×D4712yes—
407C2×C4⋊C4C22⋊D4712yes—
408C2×C42—472no—
409C2×C42—472no—
410C2×C42—941no—
411C2×C42—941no—
412C2×C42—941no—
413C2×C42—941no—
414C2×C42—944no—
415C2×C42—1882no—
416C2×C42—1882no—
417#95—944no—
418#95—944no—
419C24D4×D4711yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—472no—
435C22×C4—472no—
436C22×C4—472no—
437C22×C4—472no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—942no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—942no—
446C22×C4—941no—
447C22×C4—942no—
448C22×C4—942no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—941no—
454C22×C4—1881no—
455C22×C4—1881no—
456C22×C4—1881no—
457C22×C4—1881no—
458C22×C4—1881no—
459C22×C4—1881no—
460C22×C4—1881no—
461C22×C4—1881no—
462C22×C4C2×Dic9411yescharacteristic
463C22×C4C2×C4×D4711yescharacteristic
464C22×C4C2×C4×D4711yescharacteristic
465C22×C4C2×C4×D4711yescharacteristic
466C22×C4#1062535011yescharacteristic
467C22×C4#1062535011yescharacteristic
468C22×C4D4×D4711yescharacteristic
469C22×C4D4×D4711yescharacteristic
470C22×C4#1062535211yescharacteristic
471C22×C4#1062535211yescharacteristic
472C22×C4#1062535211yescharacteristic
473C22×C4Q8×D4711yescharacteristic
474C22×C4#1062535411yescharacteristic
475C22×C4C2×C22⋊D4711yescharacteristic
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—942no—
484C2×C8—942no—
485C2×C8—942no—
486C2×C8—1881no—
487C2×C8—1881no—
488C2×C8—1881no—
489C2×C8—1881no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—474no—
498C4⋊C4—474no—
499C4⋊C4—942no—
500C4⋊C4—942no—
501C4⋊C4—942no—
502C4⋊C4—942no—
503C4⋊C4—942no—
504C4⋊C4—942no—
505C4⋊C4—1888no—
506C4⋊C4Dic47⋊C414yescomplemented
507C42—942no—
508C42—942no—
509C42—942no—
510C42—942no—
511C42—1888no—
512C23C22⋊C4×D4711yescharacteristic
513C23(C22⋊D47)⋊C411yescharacteristic
514C23#1309398611yescharacteristic
515C23#1309399211yescharacteristic
516C23#1309400111yescharacteristic
517C23#1309400211yescharacteristic
518C23#1309400611yescharacteristic
519C23D8×D4711yescharacteristic
520C23SD16×D4711yescharacteristic
521C23#1309404511yescharacteristic
522C23#1309404711yescharacteristic
523C23#1309404811yescharacteristic
524C23#1309405311yescharacteristic
525C23#1309405311yescharacteristic
526C23#1309405611yescharacteristic
527C2×C4—24no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—81no—
541C2×C4—474no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—944no—
549C2×C4—944no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—942no—
553C2×C4—1882no—
554C2×C4—1882no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1882no—
558C2×C4—1882no—
559C2×C4—1882no—
560C2×C4—1882no—
561C2×C4—1882no—
562C2×C4—1882no—
563C2×C4—1882no—
564C2×C4—1882no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1882no—
568C2×C4—1882no—
569C2×C4C42×D4711yescharacteristic
570C2×C4C4⋊C4×D4711yescharacteristic
571C2×C4C2×Dic47⋊C411yescharacteristic
572C2×C4#1309398011yescharacteristic
573C2×C4#1309398111yescharacteristic
574C2×C4#1309398211yescharacteristic
575C2×C4(C22⋊D47)⋊C411yescharacteristic
576C2×C4(C22⋊D47)⋊C411yescharacteristic
577C2×C4(C22⋊D47)⋊C411yescharacteristic
578C2×C4C4×C22⋊D4711yescharacteristic
579C2×C4C4×C22⋊D4711yescharacteristic
580C2×C4#1309398611yescharacteristic
581C2×C4#1309398911yescharacteristic
582C2×C4#1309398911yescharacteristic
583C2×C4C4×Dic9411yescharacteristic
584C2×C4C4×Dic9411yescharacteristic
585C2×C4#1309399511yescharacteristic
586C2×C4#1309399711yescharacteristic
587C2×C4#1309400011yescharacteristic
588C2×C4#1309400111yescharacteristic
589C2×C4#1309400511yescharacteristic
590C2×C4#1309400911yescharacteristic
591C2×C4#1309401011yescharacteristic
592C2×C4#1309401411yescharacteristic
593C2×C4#1309401511yescharacteristic
594C2×C4#1309401711yescharacteristic
595C2×C4#1309401911yescharacteristic
596C2×C4#1309402311yescharacteristic
597C8—42no—
598C8—1882no—
599C22#1568897011yescharacteristic
600C22#1568899411yescharacteristic
601C22#1568899511yescharacteristic
602C22#1568899911yescharacteristic
603C22#1568900511yescharacteristic
604C22#1568900611yescharacteristic
605C22#1568902711yescharacteristic
606C22#102×D4711yescharacteristic
607C22#1568911811yescharacteristic
608C22#1568912111yescharacteristic
609C22#1568913011yescharacteristic
610C22#1568920311yescharacteristic
611C22#1568920511yescharacteristic
612C22#1568920811yescharacteristic
613C22#1568921011yescharacteristic
614C22#1568922011yescharacteristic
615C22#1568922211yescharacteristic
616C22#1568922711yescharacteristic
617C22#1568922911yescharacteristic
618C22#1568925511yescharacteristic
619C22#1568926011yescharacteristic
620C22#1568928211yescharacteristic
621C22#1568928411yescharacteristic
622C22#1568940111yescharacteristic
623C22#1568940211yescharacteristic
624C22#1568940611yescharacteristic
625C22#1568940711yescharacteristic
626C22#1568942511yescharacteristic
627C22#1568942611yescharacteristic
628C22#1568943211yescharacteristic
629C22#1568943311yescharacteristic
630C22#1568943511yescharacteristic
631C22#1568944011yescharacteristic
632C22#1568946211yescharacteristic
633C22#1568946311yescharacteristic
634C4—44no—
635C4—82no—
636C4—944no—
637C4—1884no—
638C4—1884no—
639C4—1882no—
640C4#1568897411yescharacteristic
641C4C4×Dic47⋊C411yescharacteristic
642C4#1568900411yescharacteristic
643C4#1568901011yescharacteristic
644C4#1568901111yescharacteristic
645C4#1568901211yescharacteristic
646C4#1568901911yescharacteristic
647C4#1568902011yescharacteristic
648C2#2024161911yescharacteristic
649C2#2024320211yescharacteristic
650C2#2024321711yescharacteristic
651C2#2024363211yescharacteristic
652C2#2024363311yescharacteristic
653C2#2024365311yescharacteristic
654C2#2024365411yescharacteristic
655C2#2024369711yescharacteristic
656C2#2024370211yescharacteristic
657C2#2024395711yescharacteristic
658C2#2024395811yescharacteristic
659C2#2024396411yescharacteristic
660C2#2024396511yescharacteristic
661C2#2024433811yescharacteristic
662C2#2024434211yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#340C2
socle, prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×#340D47
hypocenterC47#10884
LCSG ▷ C2×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
15. #15689019C4semidirect
20. #15688886C4semidirect
22. #15688885C4semidirect
158. C4⋊C4×C47C4⋊C4semidirect
165. C4⋊Dic47C42semidirect
166. C4⋊Dic47C4⋊C4semidirect
359. C47#10884semidirect
506. C4⋊C4Dic47⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156890192
C2×C4⋊C4×Dic472
C2×#156888862
C2×#156888852
C2×#156888772
C2×C47×#3402
#1088447