Finite Group Databasebeta

← C4×#15688997 #26137446

Subgroups — C4×#15688997 #26137446

Order 12032.

2782 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D47C211yesmaximal, characteristic
2C2×#15688997C212yesmaximal
3C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
6C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic
7#20241623C212yesmaximal, complemented
8#20241622C212yesmaximal, complemented
9(C2×D47)⋊#95C212yesmaximal
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C4×#95×C47C211yesmaximal, characteristic, complemented
12C23×C4×D47C2212yes—
13C23×C4×D47C2211yescharacteristic
14C22×C4⋊Dic47C2212yes—
15C22×Dic47⋊C4C2212yes—
16C22×(C2×D47)⋊C4C2212yes—
17C22×(C2×D47)⋊C4C2211yescharacteristic
18C22×(C2×D47)⋊C4C2211yescharacteristic
19C22×C4×Dic47C2212yes—
20C22×C4×Dic47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C2×C42×D47—24no—
24C2×C42×D47—24no—
25C2×C42×D47—24no—
26#15688997C4116yesdirect product factor
27C4×Dic47⋊C4—24no—
28C4×C4⋊Dic47—24no—
29C4×(C2×D47)⋊C4—24no—
30C4×(C2×D47)⋊C4C418yescomplemented
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2211yescharacteristic
37C2×C47⋊#95C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C22×C42×C47C2211yescharacteristic
40C22×C42×C47C2211yescharacteristic
41C2×#95×C47C2212yes—
42C2×#95×C47C2212yes—
43C24×D47C2311yescharacteristic
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C23×Dic47C2311yescharacteristic
48C23×Dic47C2312yes—
49C22×C4×D47—24no—
50C22×C4×D47—24no—
51C22×C4×D47—24no—
52C22×C4×D47—22no—
53C22×C4×D47—22no—
54C22×C4×D47—24no—
55C22×C4×D47—22no—
56C22×C4×D47—22no—
57C22×C4×D47—24no—
58C22×C4×D47—24no—
59C22×C4×D47C2×C418yes—
60C22×C4×D47C2×C414yes—
61C22×C4×D47D414yes—
62C22×C4×D47Q814yes—
63C2×C4⋊Dic47—24no—
64C2×C4⋊Dic47—24no—
65C2×C4⋊Dic47C2×C418yescomplemented
66C2×Dic47⋊C4—24no—
67C2×Dic47⋊C4—24no—
68C2×Dic47⋊C4C2×C418yescomplemented
69C2×(C2×D47)⋊C4—24no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—24no—
72C2×(C2×D47)⋊C4C2×C414yes—
73C2×(C2×D47)⋊C4C2×C418yes—
74C2×(C2×D47)⋊C4C2×C414yes—
75C2×(C2×D47)⋊C4C2×C418yes—
76C2×C4×Dic47—22no—
77C2×C4×Dic47—24no—
78C2×C4×Dic47—22no—
79C2×C4×Dic47—22no—
80C2×C4×Dic47—22no—
81C2×C4×Dic47—24no—
82C2×C4×Dic47—24no—
83C2×C4×Dic47—22no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—22no—
86C2×C4×Dic47C2×C414yescomplemented
87C2×C4×Dic47D414yes—
88C42×D47—232no—
89C47⋊#95—24no—
90C47⋊#95—24no—
91C47⋊#95—24no—
92C47⋊#95—24no—
93C47⋊#95C2×C414yescomplemented
94C47⋊#95C2×C414yescomplemented
95C47⋊#95C2×C418yescomplemented
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2312yes—
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2312yes—
100C23×C4×C47C2311yescharacteristic
101C2×C42×C47—22no—
102C2×C42×C47—22no—
103C2×C42×C47—22no—
104C2×C42×C47—22no—
105C2×C42×C47—22no—
106C2×C42×C47—22no—
107C2×C42×C47—22no—
108C2×C42×C47C2×C414yescomplemented
109C2×C42×C47D414yes—
110#95×C47—24no—
111#95×C47C2×C418yescomplemented
112C24×C47C2411yescharacteristic
113C23×D47—21no—
114C23×D47—21no—
115C23×D47—21no—
116C23×D47—21no—
117C23×D47—22no—
118C23×D47—22no—
119C23×D47C22×C412yes—
120C23×D47C22×C414yes—
121C23×D47C2×D412yes—
122C23×D47C2×Q812yes—
123C23×D47#4114yes—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—21no—
132C22×C4×C47—22no—
133C22×C4×C47—21no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47C22×C412yes—
142C22×C4×C47C22×C414yes—
143C22×C4×C47C22×C412yes—
144C22×C4×C47C22×C414yes—
145C22×C4×C47C22×C414yes—
146C22×C4×C47C22×C412yes—
147C22×C4×C47C2×D414yes—
148C22×C4×C47C2×D412yes—
149C22×C4×C47C2×D412yes—
150C22×C4×C47C2×D412yes—
151C22×C4×C47C2×Q812yes—
152C22×C4×C47#4114yes—
153C22×C4×C47#4112yes—
154C22×C4×C47#4112yes—
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—21no—
160C22×Dic47—21no—
161C22×Dic47—22no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—21no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—21no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47C22×C412yes—
177C22×Dic47C22×C414yes—
178C22×Dic47C22×C412yes—
179C22×Dic47C22×C414yes—
180C22×Dic47C22×C412yes—
181C22×Dic47C22×C414yes—
182C22×Dic47C2×D412yes—
183C22×Dic47C2×D414yes—
184C22×Dic47C2×Q812yes—
185C22×Dic47#4114yes—
186C2×C4×D47—216no—
187C2×C4×D47—216no—
188C2×C4×D47—216no—
189C2×C4×D47—216no—
190C2×C4×D47—216no—
191C2×C4×D47—216no—
192C2×C4×D47—28no—
193C2×C4×D47—28no—
194C2×C4×D47—28no—
195C2×C4×D47—28no—
196C2×C4×D47—28no—
197C2×C4×D47—28no—
198C2×C4×D47—216no—
199C2×C4×D47C4⋊C4116yescomplemented
200C42×C47—28no—
201C42×C47—28no—
202C42×C47—44no—
203(C2×D47)⋊C4—28no—
204(C2×D47)⋊C4—216no—
205(C2×D47)⋊C4C42116yescomplemented
206C4⋊Dic47—216no—
207Dic47⋊C4—216no—
208C4×Dic47—216no—
209C4×Dic47—28no—
210C4×Dic47—28no—
211C4×Dic47—44no—
212C23×C47C23×C411yescharacteristic
213C23×C47C23×C412yes—
214C23×C47C22×D411yescharacteristic
215C23×C47C22×D411yescharacteristic
216C23×C47C22×D411yescharacteristic
217C23×C47C22×Q811yescharacteristic
218C23×C47C2×#4112yes—
219C23×C47C2×#4112yes—
220C23×C47C2×#4111yescharacteristic
221C23×C47C2×#4111yescharacteristic
222C23×C47C2×#4112yes—
223C22×D47—24no—
224C22×D47—22no—
225C22×D47—22no—
226C22×D47—24no—
227C22×D47—24no—
228C22×D47—22no—
229C22×D47—22no—
230C22×D47—24no—
231C22×D47—22no—
232C22×D47—22no—
233C22×D47—22no—
234C22×D47—22no—
235C22×D47—24no—
236C22×D47—24no—
237C22×D47—24no—
238C22×D47—24no—
239C22×D47—24no—
240C22×D47—24no—
241C22×D47C2×C4214yes—
242C22×D47C2×C4⋊C414yes—
243C22×D47#11714yes—
244C22×D47C4×D418yes—
245C22×D47C4×Q818yes—
246C2×C4×C47—24no—
247C2×C4×C47—22no—
248C2×C4×C47—24no—
249C2×C4×C47—24no—
250C2×C4×C47—24no—
251C2×C4×C47—22no—
252C2×C4×C47—24no—
253C2×C4×C47—24no—
254C2×C4×C47—24no—
255C2×C4×C47—24no—
256C2×C4×C47—22no—
257C2×C4×C47—24no—
258C2×C4×C47—22no—
259C2×C4×C47—24no—
260C2×C4×C47—22no—
261C2×C4×C47—24no—
262C2×C4×C47—42no—
263C2×C4×C47—42no—
264C2×C4×C47—42no—
265C2×C4×C47—42no—
266C2×C4×C47—42no—
267C2×C4×C47—42no—
268C2×C4×C47C2×C4214yescomplemented
269C2×C4×C47C2×C4⋊C414yes—
270C2×C4×C47C4×D414yes—
271C2×C4×C47C4×D418yes—
272C2×C4×C47C4×D414yes—
273C2×C4×C47#12014yes—
274C2×C4×C47C22⋊Q814yes—
275C2×C4×C47C22⋊Q814yes—
276C2×C4×C47#12314yes—
277C2×Dic47—22no—
278C2×Dic47—24no—
279C2×Dic47—24no—
280C2×Dic47—22no—
281C2×Dic47—22no—
282C2×Dic47—24no—
283C2×Dic47—22no—
284C2×Dic47—24no—
285C2×Dic47—22no—
286C2×Dic47—24no—
287C2×Dic47—22no—
288C2×Dic47—22no—
289C2×Dic47—22no—
290C2×Dic47—24no—
291C2×Dic47—24no—
292C2×Dic47—24no—
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—24no—
296C2×Dic47—24no—
297C2×Dic47—24no—
298C2×Dic47—22no—
299C2×Dic47—42no—
300C2×Dic47—42no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47C2×C4214yescomplemented
306C2×Dic47C2×C4⋊C414yes—
307C2×Dic47C4×D418yes—
308C4×D47—264no—
309C4×D47—232no—
310C4×#385—471nomaximal, Sylow
311C22×C47C22×C4211yescharacteristic
312C22×C47C22×C4⋊C411yescharacteristic
313C22×C47C2×#11711yescharacteristic
314C22×C47C2×C4×D412yes—
315C22×C47C2×C4×D412yes—
316C22×C47C2×C4×D411yescharacteristic
317C22×C47C2×C4×D411yescharacteristic
318C22×C47C2×C4×D412yes—
319C22×C47C2×C4×Q812yes—
320C22×C47C4×#4112yes—
321C22×C47C4×#4111yescharacteristic
322C22×C47C4×#4111yescharacteristic
323C22×C47C4×#4112yes—
324C22×C47C2×#12011yescharacteristic
325C22×C47C2×C22⋊Q811yescharacteristic
326C22×C47C2×C22⋊Q811yescharacteristic
327C22×C47C2×#12311yescharacteristic
328C22×C47#52512yes—
329C22×C47#52512yes—
330C22×C47#52512yes—
331C22×C47#52912yes—
332C22×C47#52912yes—
333C22×C47#53312yes—
334C2×D47—24no—
335C2×D47—24no—
336C2×D47—24no—
337C2×D47—24no—
338C2×D47—24no—
339C2×D47—24no—
340C2×D47—28no—
341C2×D47—28no—
342C2×D47—28no—
343C2×D47—28no—
344C2×D47C4×C4⋊C418yescomplemented
345C4×C47—24no—
346C4×C47—28no—
347C4×C47—42no—
348C4×C47—44no—
349C4×C47#38518yescomplemented
350Dic47—24no—
351Dic47—24no—
352Dic47—28no—
353Dic47—42no—
354Dic47—44no—
355C23×C42—471no—
356C2×#385—472no—
357C2×C4×C4⋊C4—471no—
358C2×C4×C4⋊C4—471no—
359C2×C4×C22⋊C4—471no—
360C2×C4×C22⋊C4—471no—
361#1436—472no—
362#1436—472no—
363C22⋊#95—472no—
364C4×#95—471no—
365C4×#95D4711yescharacteristic, complemented
366C2×C47C2×C4×C4⋊C411yescharacteristic
367C2×C47C42×D411yescharacteristic
368C2×C47C42×D411yescharacteristic
369C2×C47C2×#38511yescharacteristic
370C2×C47#229011yescharacteristic
371C2×C47#229011yescharacteristic
372C2×C47#229611yescharacteristic
373C2×C47C4×#12012yes—
374C2×C47C4×#12312yes—
375C2×C47C4×C22⋊Q812yes—
376C2×C47C4×C22⋊Q812yes—
377D47—28no—
378C24×C4—471no—
379C24×C4—472no—
380C22×C4⋊C4—472no—
381C22×C4⋊C4—472no—
382C22×C22⋊C4—471no—
383C22×C22⋊C4—471no—
384C22×C22⋊C4—472no—
385C22×C42—471no—
386C22×C42—471no—
387C22×C42—472no—
388C22×C42—471no—
389C22×C42—944no—
390C22×C42—944no—
391C22×C42—944no—
392C22×C42C2×D4711yescharacteristic
393C22×C42C2×D4711yescharacteristic
394C22×C42C2×D4711yescharacteristic
395#385—4716no—
396C4×C4⋊C4—944no—
397C4×C4⋊C4—944no—
398C4×C22⋊C4—478no—
399C4×C22⋊C4—944no—
400C2×#95—472no—
401C2×#95—471no—
402C2×#95—471no—
403C2×#95—472no—
404C2×#95—472no—
405C2×#95—472no—
406C2×#95—472no—
407C2×#95C2×D4712yes—
408C2×#95C2×D4712yes—
409C47C4×#38511yescharacteristic, complemented, Sylow
410C25—471no—
411C23×C4—471no—
412C23×C4—472no—
413C23×C4—471no—
414C23×C4—474no—
415C23×C4—474no—
416C23×C4—474no—
417C23×C4—472no—
418C23×C4—471no—
419C23×C4—478no—
420C23×C4—944no—
421C23×C4—944no—
422C23×C4—944no—
423C23×C4—944no—
424C23×C4—944no—
425C23×C4—942no—
426C23×C4—944no—
427C23×C4—942no—
428C23×C4—942no—
429C23×C4—942no—
430C23×C4C22×D4711yescharacteristic
431C23×C4C22×D4712yes—
432C23×C4C22×D4711yescharacteristic
433C23×C4C22×D4712yes—
434C23×C4C22×D4711yescharacteristic
435C2×C4⋊C4—478no—
436C2×C4⋊C4—478no—
437C2×C4⋊C4—944no—
438C2×C4⋊C4—944no—
439C2×C4⋊C4—944no—
440C2×C4⋊C4—944no—
441C2×C22⋊C4—474no—
442C2×C22⋊C4—478no—
443C2×C22⋊C4—474no—
444C2×C22⋊C4—478no—
445C2×C22⋊C4—944no—
446C2×C22⋊C4—944no—
447C2×C22⋊C4—944no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—474no—
456C2×C42—474no—
457C2×C42—9432no—
458C2×C42—944no—
459C2×C42—944no—
460C2×C42—942no—
461C2×C42—944no—
462C2×C42—942no—
463C2×C42—942no—
464C2×C42—942no—
465C2×C42—942no—
466C2×C42—942no—
467C2×C42—942no—
468C2×C42C4×D4714yescomplemented
469C2×C42D18814yes—
470#95—24no—
471#95—474no—
472#95—474no—
473#95—478no—
474#95—944no—
475#95—944no—
476#95—944no—
477#95—944no—
478#95C4×D4718yescomplemented
479C24—472no—
480C24—474no—
481C24—472no—
482C24—472no—
483C24—474no—
484C24—941no—
485C24—941no—
486C24—942no—
487C24—941no—
488C24—941no—
489C24—942no—
490C24C23×D4711yescharacteristic
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—472no—
509C22×C4—472no—
510C22×C4—474no—
511C22×C4—474no—
512C22×C4—472no—
513C22×C4—474no—
514C22×C4—472no—
515C22×C4—474no—
516C22×C4—4716no—
517C22×C4—472no—
518C22×C4—474no—
519C22×C4—9416no—
520C22×C4—9416no—
521C22×C4—9416no—
522C22×C4—9416no—
523C22×C4—9416no—
524C22×C4—9416no—
525C22×C4—942no—
526C22×C4—941no—
527C22×C4—941no—
528C22×C4—942no—
529C22×C4—941no—
530C22×C4—942no—
531C22×C4—941no—
532C22×C4—941no—
533C22×C4—942no—
534C22×C4—941no—
535C22×C4—942no—
536C22×C4—948no—
537C22×C4—9416no—
538C22×C4—948no—
539C22×C4—948no—
540C22×C4—948no—
541C22×C4—948no—
542C22×C4—948no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—941no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—941no—
552C22×C4—942no—
553C22×C4C2×C4×D4714yes—
554C22×C4C2×C4×D4712yes—
555C22×C4C2×C4×D4712yes—
556C22×C4C2×C4×D4714yes—
557C22×C4C2×C4×D4714yes—
558C22×C4C2×C4×D4712yes—
559C22×C4C2×D18814yes—
560C22×C4C2×D18812yes—
561C22×C4#1062535014yes—
562C22×C4#1062535012yes—
563C22×C4D4×D4712yes—
564C22×C4D4×D4712yes—
565C22×C4#1062535212yes—
566C22×C4Q8×D4712yes—
567C4⋊C4—9416no—
568C4⋊C4—9416no—
569C22⋊C4—4716no—
570C22⋊C4—948no—
571C22⋊C4—9416no—
572C42—28no—
573C42—28no—
574C42—44no—
575C42—9416no—
576C42—948no—
577C42—948no—
578C42—1884no—
579C23—474no—
580C23—474no—
581C23—474no—
582C23—478no—
583C23—478no—
584C23—944no—
585C23—942no—
586C23—942no—
587C23—944no—
588C23—944no—
589C23—942no—
590C23—942no—
591C23—944no—
592C23—942no—
593C23—942no—
594C23—942no—
595C23—942no—
596C23—944no—
597C23—944no—
598C23—944no—
599C23—944no—
600C23—944no—
601C23—944no—
602C23C22×C4×D4711yescharacteristic
603C23C22×C4×D4712yes—
604C23C2×D4×D4711yescharacteristic
605C23C2×D4×D4711yescharacteristic
606C23C22×D18811yescharacteristic
607C23C2×Q8×D4711yescharacteristic
608C23#41×D4712yes—
609C23#41×D4712yes—
610C23C2×#1062535211yescharacteristic
611C23C2×#1062535011yescharacteristic
612C23C2×#1062535012yes—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—22no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—474no—
636C2×C4—474no—
637C2×C4—478no—
638C2×C4—9464no—
639C2×C4—944no—
640C2×C4—942no—
641C2×C4—942no—
642C2×C4—944no—
643C2×C4—942no—
644C2×C4—944no—
645C2×C4—942no—
646C2×C4—944no—
647C2×C4—942no—
648C2×C4—944no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—944no—
653C2×C4—944no—
654C2×C4—944no—
655C2×C4—9432no—
656C2×C4—942no—
657C2×C4—944no—
658C2×C4—944no—
659C2×C4—942no—
660C2×C4—944no—
661C2×C4—942no—
662C2×C4—1882no—
663C2×C4—1882no—
664C2×C4—1882no—
665C2×C4—1882no—
666C2×C4—1882no—
667C2×C4—1882no—
668C2×C4C42×D4714yescomplemented
669C2×C4C4⋊C4×D4714yes—
670C2×C4(C22⋊D47)⋊C414yes—
671C2×C4C4×D18818yes—
672C2×C4C4×D18814yes—
673C2×C4#1309399414yes—
674C2×C4#1309400214yes—
675C2×C4#1309400414yes—
676C2×C4#1309400614yes—
677C22—478no—
678C22—944no—
679C22—944no—
680C22—944no—
681C22—944no—
682C22—948no—
683C22—948no—
684C22—948no—
685C22—948no—
686C22—944no—
687C22—944no—
688C22C2×C42×D4711yescharacteristic
689C22C2×C4⋊C4×D4711yescharacteristic
690C22#117×D4711yescharacteristic
691C22C4×D4×D4712yes—
692C22C4×D4×D4712yes—
693C22C2×(C22⋊D47)⋊C411yescharacteristic
694C22C2×C4×D18811yescharacteristic
695C22C2×C4×D18812yes—
696C22C4×Q8×D4712yes—
697C22C4×#1062535212yes—
698C22#1568959111yescharacteristic
699C22C4×#1062535011yescharacteristic
700C22C4×#1062535012yes—
701C22C2×#1309399411yescharacteristic
702C22C2×#1309400211yescharacteristic
703C22C2×#1309400411yescharacteristic
704C22C2×#1309400611yescharacteristic
705C22#1568963212yes—
706C22#1568963212yes—
707C22#1568963512yes—
708C22#1568965112yes—
709C22#1568965512yes—
710C22#1568967712yes—
711C4—28no—
712C4—24no—
713C4—42no—
714C4—44no—
715C4—944no—
716C4—948no—
717C4—944no—
718C4—1882no—
719C4—1884no—
720C4#1568899718yesdirect product factor
721C2—948no—
722C2C4×C4⋊C4×D4711yescharacteristic
723C2C4×(C22⋊D47)⋊C411yescharacteristic
724C2C42×D18811yescharacteristic
725C2C2×#1568899711yescharacteristic
726C2#2024583211yescharacteristic
727C2#2024583411yescharacteristic
728C2#2024586811yescharacteristic
729C2C4×#1309399412yes—
730C2C4×#1309400612yes—
731C2C4×#1309400212yes—
732C2C4×#1309400412yes—
subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC4×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC24×D47C23
hypercenterC4×#95D47
hypocenterC47C4×#385
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic47⋊C4C2semidirect
4. C2×C4×C4⋊Dic47C2semidirect
7. #20241623C2semidirect
8. #20241622C2semidirect
10. C4×C47⋊#95C2semidirect
11. C4×#95×C47C2semidirect
26. #15688997C4direct (N × H)
30. C4×(C2×D47)⋊C4C4semidirect
65. C2×C4⋊Dic47C2×C4semidirect
68. C2×Dic47⋊C4C2×C4semidirect
86. C2×C4×Dic47C2×C4semidirect
93. C47⋊#95C2×C4semidirect
94. C47⋊#95C2×C4semidirect
95. C47⋊#95C2×C4semidirect
108. C2×C42×C47C2×C4semidirect
111. #95×C47C2×C4semidirect
199. C2×C4×D47C4⋊C4semidirect
205. (C2×D47)⋊C4C42semidirect
268. C2×C4×C47C2×C42semidirect
305. C2×Dic47C2×C42semidirect
344. C2×D47C4×C4⋊C4semidirect
349. C4×C47#385semidirect
365. C4×#95D47semidirect
409. C47C4×#385semidirect
468. C2×C42C4×D47semidirect
478. #95C4×D47semidirect
668. C2×C4C42×D47semidirect
720. C4#15688997direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C42×D472
C2×#156889972
C2×C4×Dic47⋊C42
C2×C4×C4⋊Dic472
C2×C4×(C2×D47)⋊C42
#202416232
#202416222
(C2×D47)⋊#952
C4×C47⋊#952
C4×#95×C472
C4×#38547