Finite Group Databasebeta

← C4×#15689032 #26138064

Subgroups — C4×#15689032 #26138064

Order 12032.

3502 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D188C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D47C212yesmaximal, complemented
3C2×#15689032C211yesmaximal, characteristic
4C2×C4×(C2×D47)⋊C4C212yesmaximal, complemented
5#20241652C211yesmaximal, characteristic, complemented
6#20241633C211yesmaximal, characteristic, complemented
7#20241632C212yesmaximal, complemented
8#20241628C211yesmaximal, characteristic, complemented
9#20241627C212yesmaximal, complemented
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C23×C22⋊D47C2212yes—
14C23×C4×D47C2212yes—
15C2×C4×D188—28no—
16C2×C4×D188—24no—
17C2×C4×C22⋊D47—28no—
18C2×C4×C22⋊D47—28no—
19C2×C4×C22⋊D47—28no—
20C22×C4⋊Dic47C2211yescharacteristic
21C22×Dic47⋊C4C2212yes—
22C22×C22⋊Dic47C2212yes—
23C22×(C2×D47)⋊C4C2212yes—
24C22×(C2×D47)⋊C4C2212yes—
25C22×(C2×D47)⋊C4C2212yes—
26C22×(C2×D47)⋊C4C2212yes—
27C22×C4×Dic47C2212yes—
28#15689032C418yesdirect product factor
29C4×(C2×D47)⋊C4—28no—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2211yescharacteristic
35C24×C4×C47C2211yescharacteristic
36C22×C22⋊C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C22×C42×C47C2211yescharacteristic
40C4×C22⋊C4×C47—24no—
41C2×#95×C47C2211yescharacteristic
42C2×#95×C47C2211yescharacteristic
43C24×D47C2312yes—
44C22×D188—24no—
45C22×D188—24no—
46C22×D188—22no—
47C22×D188—22no—
48C22×D188C2×C414yescomplemented
49C22×C22⋊D47—24no—
50C22×C22⋊D47—24no—
51C22×C22⋊D47—24no—
52C22×C22⋊D47—24no—
53C22×C22⋊D47—24no—
54C22×C22⋊D47—24no—
55C22×C22⋊D47C2×C418yescomplemented
56C23×Dic47C2312yes—
57C23×Dic47C2312yes—
58C23×Dic47C2312yes—
59C22×C4×D47—24no—
60C22×C4×D47—24no—
61C22×C4×D47—24no—
62C22×C4×D47—24no—
63C22×C4×D47—24no—
64C22×C4×D47—24no—
65C22×C4×D47D418yescomplemented
66C4×D188—232no—
67C4×C22⋊D47—264no—
68C2×C4⋊Dic47—22no—
69C2×C4⋊Dic47—24no—
70C2×Dic47⋊C4—24no—
71C2×Dic47⋊C4—24no—
72C2×Dic47⋊C4—24no—
73C2×C22⋊Dic47—24no—
74C2×C22⋊Dic47—24no—
75C2×C22⋊Dic47—24no—
76C2×(C2×D47)⋊C4—24no—
77C2×(C2×D47)⋊C4—24no—
78C2×(C2×D47)⋊C4—24no—
79C2×(C2×D47)⋊C4—24no—
80C2×(C2×D47)⋊C4—24no—
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4—24no—
83C2×(C2×D47)⋊C4—24no—
84C2×(C2×D47)⋊C4—24no—
85C2×(C2×D47)⋊C4—24no—
86C2×(C2×D47)⋊C4—24no—
87C2×(C2×D47)⋊C4C2×C418yescomplemented
88C2×C4×Dic47—24no—
89C2×C4×Dic47—24no—
90C2×C4×Dic47D418yescomplemented
91C47⋊#95—22no—
92C47⋊#95—24no—
93C47⋊#95—24no—
94C47⋊#95—24no—
95C47⋊#95C2×C414yescomplemented
96C25×C47C2311yescharacteristic
97C23×C4×C47—24no—
98C23×C4×C47—24no—
99C23×C4×C47—22no—
100C23×C4×C47—22no—
101C23×C4×C47D414yescomplemented
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2311yescharacteristic
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2311yescharacteristic
106C23×C4×C47C2311yescharacteristic
107C23×C4×C47C2311yescharacteristic
108C2×C22⋊C4×C47—22no—
109C2×C22⋊C4×C47—22no—
110C2×C22⋊C4×C47—22no—
111C2×C22⋊C4×C47—22no—
112C2×C22⋊C4×C47—22no—
113C2×C22⋊C4×C47C2×C414yescomplemented
114C2×C42×C47—24no—
115C2×C42×C47—24no—
116C2×C42×C47—22no—
117C2×C42×C47D414yescomplemented
118#95×C47—22no—
119#95×C47—22no—
120C24×C47—21no—
121C24×C47—22no—
122C24×C47—22no—
123C24×C47—21no—
124C24×C47—21no—
125C24×C47—21no—
126C24×C47—22no—
127C24×C47—22no—
128C24×C47C22×C412yes—
129C24×C47C2×D412yes—
130C24×C47#4112yes—
131C24×C47C2411yescharacteristic
132C23×D47—22no—
133C23×D47—22no—
134C23×D47—22no—
135C23×D47—22no—
136C23×D47—22no—
137C23×D47—22no—
138C23×D47—22no—
139C23×D47—22no—
140C23×D47—22no—
141C23×D47—22no—
142C23×D47—22no—
143C23×D47—22no—
144C23×D47C22×C414yes—
145C23×D47C2×D414yes—
146C23×D47#4114yes—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—216no—
166C22×C4×C47—28no—
167C22×C4×C47—44no—
168C22×C4×C47—48no—
169C22×C4×C47—44no—
170C22×C4×C47C22×C412yes—
171C22×C4×C47C22×C412yes—
172C22×C4×C47C2×D412yes—
173C22×C4×C47C2×D412yes—
174C22×C4×C47C2×D412yes—
175C22×C4×C47C2×D412yes—
176C22×C4×C47C2×D414yes—
177C22×C4×C47C2×D414yes—
178C22×C4×C47C2×D412yes—
179C22×C4×C47#4112yes—
180C22×C4×C47#4112yes—
181C22×C4×C47#4112yes—
182C2×C22⋊D47—216no—
183C2×C22⋊D47—216no—
184C2×C22⋊D47—216no—
185C2×C22⋊D47—216no—
186C2×C22⋊D47—216no—
187C2×C22⋊D47—216no—
188C2×C22⋊D47—216no—
189C22×Dic47—22no—
190C22×Dic47—22no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47C22×C414yes—
206C22×Dic47C2×D414yes—
207C22×Dic47C2×D414yes—
208C22×Dic47C2×D414yes—
209C22×Dic47#4114yes—
210C2×D188—28no—
211C2×D188—28no—
212C2×D188—216no—
213C2×D188—216no—
214C2×D188—28no—
215C2×C4×D47—216no—
216C2×C4×D47—216no—
217C2×C4×D47—216no—
218C2×C4×D47—48no—
219C2×C4×D47—48no—
220C2×C4×D47—48no—
221C2×C4×D47—48no—
222C22⋊C4×C47—28no—
223C22⋊C4×C47—28no—
224C42×C47—28no—
225C42×C47—44no—
226C22⋊Dic47—216no—
227(C2×D47)⋊C4—216no—
228(C2×D47)⋊C4—216no—
229(C2×D47)⋊C4—216no—
230(C2×D47)⋊C4—216no—
231C4⋊Dic47—28no—
232Dic47⋊C4—216no—
233C4×Dic47—216no—
234C23×C47—22no—
235C23×C47—24no—
236C23×C47—24no—
237C23×C47—22no—
238C23×C47—24no—
239C23×C47—22no—
240C23×C47—22no—
241C23×C47—24no—
242C23×C47—24no—
243C23×C47—24no—
244C23×C47—22no—
245C23×C47—22no—
246C23×C47—41no—
247C23×C47—42no—
248C23×C47—41no—
249C23×C47—42no—
250C23×C47—42no—
251C23×C47—42no—
252C23×C47—41no—
253C23×C47—41no—
254C23×C47—42no—
255C23×C47—42no—
256C23×C47C4×D414yescomplemented
257C23×C47C23×C411yescharacteristic
258C23×C47C22×D412yes—
259C23×C47C22×D412yes—
260C23×C47C22×D411yescharacteristic
261C23×C47C22×D411yescharacteristic
262C23×C47C2×#4112yes—
263C23×C47C2×#4112yes—
264C23×C47C2×#4111yescharacteristic
265C23×C47C2×#4111yescharacteristic
266C23×C47C2×#4111yescharacteristic
267C23×C47C2×#4111yescharacteristic
268C22×D47—24no—
269C22×D47—24no—
270C22×D47—24no—
271C22×D47—24no—
272C22×D47—24no—
273C22×D47—24no—
274C22×D47—24no—
275C22×D47—24no—
276C22×D47—24no—
277C22×D47—24no—
278C22×D47—24no—
279C22×D47—24no—
280C22×D47—24no—
281C22×D47—24no—
282C22×D47—24no—
283C22×D47—24no—
284C22×D47—24no—
285C22×D47—24no—
286C22×D47—42no—
287C22×D47—42no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47—42no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47—42no—
297C22×D47—42no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47—42no—
301C22×D47—42no—
302C22×D47C4×D418yescomplemented
303C2×C4×C47—24no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—24no—
307C2×C4×C47—24no—
308C2×C4×C47—22no—
309C2×C4×C47—24no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—24no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—41no—
317C2×C4×C47—42no—
318C2×C4×C47—41no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—41no—
322C2×C4×C47—41no—
323C2×C4×C47—41no—
324C2×C4×C47—41no—
325C2×C4×C47—42no—
326C2×C4×C47—42no—
327C2×C4×C47—416no—
328C2×C4×C47C4×D414yescomplemented
329C2×C4×C47#12014yes—
330C2×C4×C47#12018yes—
331C2×C4×C47#12118yes—
332C2×C4×C47#12114yes—
333C2×C4×C47#12714yes—
334C22⋊D47—264no—
335C2×Dic47—24no—
336C2×Dic47—24no—
337C2×Dic47—24no—
338C2×Dic47—24no—
339C2×Dic47—24no—
340C2×Dic47—24no—
341C2×Dic47—24no—
342C2×Dic47—24no—
343C2×Dic47—24no—
344C2×Dic47—24no—
345C2×Dic47—24no—
346C2×Dic47—24no—
347C2×Dic47—42no—
348C2×Dic47—42no—
349C2×Dic47—42no—
350C2×Dic47—42no—
351C2×Dic47—42no—
352C2×Dic47—42no—
353C2×Dic47—42no—
354C2×Dic47—42no—
355C2×Dic47C4×D418yescomplemented
356D188—232no—
357C4×D47—432no—
358C4×#392—471nomaximal, Sylow
359C22×C47—28no—
360C22×C47—24no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—42no—
364C22×C47—44no—
365C22×C47—42no—
366C22×C47—44no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47—44no—
370C22×C47C2×C4×D412yes—
371C22×C47C2×C4×D412yes—
372C22×C47C2×C4×D411yescharacteristic
373C22×C47C2×C4×D411yescharacteristic
374C22×C47C4×#4111yescharacteristic
375C22×C47C2×#12011yescharacteristic
376C22×C47C2×#12012yes—
377C22×C47C2×#12112yes—
378C22×C47C2×#12111yescharacteristic
379C22×C47#52511yescharacteristic
380C22×C47#52512yes—
381C22×C47#52512yes—
382C22×C47#52512yes—
383C22×C47#52512yes—
384C22×C47#52511yescharacteristic
385C22×C47#52512yes—
386C22×C47#52912yes—
387C22×C47#52911yescharacteristic
388C22×C47C2×#12711yescharacteristic
389C22×C47#53211yescharacteristic
390C22×C47#53212yes—
391C22×C47#53212yes—
392C22×C47#53211yescharacteristic
393C2×D47—28no—
394C2×D47—28no—
395C2×D47—28no—
396C2×D47—44no—
397C2×D47—44no—
398C2×D47—44no—
399C2×D47—44no—
400C2×D47—44no—
401C2×D47—44no—
402C2×D47—44no—
403C2×D47—44no—
404C2×D47—44no—
405C2×D47—44no—
406C2×D47—44no—
407C2×D47—44no—
408C4×C47—24no—
409C4×C47—42no—
410C4×C47—42no—
411C4×C47—42no—
412C4×C47—42no—
413C4×C47#39218yescomplemented
414Dic47—28no—
415Dic47—44no—
416Dic47—44no—
417C22×C4×D4—471no—
418C22×C4×D4—472no—
419C2×#392—471no—
420C2×C4×C22⋊C4—472no—
421C2×C4×C22⋊C4D4711yescharacteristic, complemented
422#1444—471no—
423#1439—472no—
424#1439—471no—
425#1438—471no—
426#1438—472no—
427C4×#95—471no—
428C2×C47—44no—
429C2×C47C4×#12011yescharacteristic
430C2×C47C4×#12012yes—
431C2×C47C4×#12112yes—
432C2×C47C4×#12111yescharacteristic
433C2×C47C4×#12711yescharacteristic
434C2×C47C2×#39211yescharacteristic
435C2×C47#238811yescharacteristic
436C2×C47#238812yes—
437C2×C47#239211yescharacteristic
438C2×C47#239212yes—
439C2×C47#239711yescharacteristic
440D47—48no—
441C23×D4—472no—
442C23×D4—471no—
443C24×C4—472no—
444C24×C4C2×D4711yescharacteristic
445C2×C4×D4—948no—
446C2×C4×D4—948no—
447C2×C4×D4—948no—
448C2×C4×D4—948no—
449C2×C4×D4—944no—
450C22×C4⋊C4—472no—
451C22×C4⋊C4—471no—
452C22×C22⋊C4—472no—
453C22×C22⋊C4—472no—
454C22×C22⋊C4—472no—
455C22×C22⋊C4—472no—
456C22×C22⋊C4—472no—
457C22×C22⋊C4C2×D4711yescharacteristic
458C22×C22⋊C4C2×D4711yescharacteristic
459C22×C42—472no—
460C22×C42C2×D4711yescharacteristic
461C22×C42C2×D4711yescharacteristic
462#392—478no—
463C4×C22⋊C4—24no—
464C4×C22⋊C4—948no—
465C2×#95—471no—
466C2×#95—472no—
467C2×#95—471no—
468C2×#95—472no—
469C2×#95—472no—
470C2×#95C2×D4711yescharacteristic
471C2×#95C2×D4711yescharacteristic
472C47C4×#39211yescharacteristic, complemented, Sylow
473C25—472no—
474C25C22×D4711yescharacteristic
475C22×D4—478no—
476C22×D4—474no—
477C22×D4—944no—
478C22×D4—944no—
479C22×D4—944no—
480C22×D4—944no—
481C22×D4—944no—
482C22×D4—944no—
483C22×D4—944no—
484C22×D4—944no—
485C22×D4—942no—
486C22×D4—942no—
487C23×C4—22no—
488C23×C4—24no—
489C23×C4—24no—
490C23×C4—22no—
491C23×C4—472no—
492C23×C4—472no—
493C23×C4—472no—
494C23×C4—478no—
495C23×C4—944no—
496C23×C4—944no—
497C23×C4—944no—
498C23×C4—944no—
499C23×C4—944no—
500C23×C4—944no—
501C23×C4D18814yescomplemented
502C23×C4C22×D4711yescharacteristic
503C23×C4C22×D4711yescharacteristic
504C23×C4C22×D4711yescharacteristic
505C23×C4C22×D4711yescharacteristic
506C23×C4C22×D4711yescharacteristic
507C23×C4C22×D4711yescharacteristic
508C4×D4—9432no—
509C4×D4—9464no—
510C2×C4⋊C4—944no—
511C2×C4⋊C4—944no—
512C2×C4⋊C4—944no—
513C2×C4⋊C4—944no—
514C2×C4⋊C4—942no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—478no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—944no—
524C2×C22⋊C4—944no—
525C2×C22⋊C4—944no—
526C2×C22⋊C4—944no—
527C2×C22⋊C4—944no—
528C2×C22⋊C4—944no—
529C2×C22⋊C4—944no—
530C2×C22⋊C4—944no—
531C2×C22⋊C4—944no—
532C2×C22⋊C4—944no—
533C2×C22⋊C4—944no—
534C2×C22⋊C4—944no—
535C2×C22⋊C4C4×D4714yescomplemented
536C2×C42—24no—
537C2×C42—24no—
538C2×C42—22no—
539C2×C42—478no—
540C2×C42—944no—
541C2×C42—944no—
542C2×C42C22⋊D4714yescomplemented
543#95—22no—
544#95—22no—
545#95—474no—
546#95—944no—
547#95—944no—
548#95—944no—
549#95—942no—
550C24—22no—
551C24—22no—
552C24—21no—
553C24—22no—
554C24—22no—
555C24—21no—
556C24—21no—
557C24—21no—
558C24—474no—
559C24—474no—
560C24—474no—
561C24—942no—
562C24—942no—
563C24—942no—
564C24—942no—
565C24—942no—
566C24—942no—
567C24—942no—
568C24—942no—
569C24—942no—
570C24—942no—
571C24—942no—
572C24—942no—
573C24C2×C4×D4712yes—
574C24C2×D18812yes—
575C24#1062535012yes—
576C24C23×D4711yescharacteristic
577C2×D4—9416no—
578C2×D4—948no—
579C2×D4—948no—
580C2×D4—9416no—
581C2×D4—9416no—
582C2×D4—9416no—
583C2×D4—9416no—
584C2×D4—9416no—
585C2×D4—9416no—
586C2×D4—9416no—
587C2×D4—9416no—
588C2×D4—948no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—216no—
608C22×C4—28no—
609C22×C4—44no—
610C22×C4—48no—
611C22×C4—44no—
612C22×C4—474no—
613C22×C4—474no—
614C22×C4—474no—
615C22×C4—474no—
616C22×C4—474no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—942no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—9416no—
634C22×C4—9416no—
635C22×C4—9416no—
636C22×C4—1888no—
637C22×C4—1888no—
638C22×C4—1888no—
639C22×C4—1888no—
640C22×C4C2×C4×D4712yes—
641C22×C4C2×C4×D4712yes—
642C22×C4C2×D18812yes—
643C22×C4C2×D18812yes—
644C22×C4#1062535012yes—
645C22×C4#1062535012yes—
646C22×C4#1062535012yes—
647C22×C4D4×D4714yes—
648C22×C4D4×D4714yes—
649C22×C4C2×C22⋊D4712yes—
650C22×C4C2×C22⋊D4712yes—
651C22×C4C2×C22⋊D4712yes—
652C4⋊C4—9416no—
653C4⋊C4—948no—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—9416no—
657C22⋊C4—9416no—
658C22⋊C4—9416no—
659C22⋊C4—9416no—
660C22⋊C4—9416no—
661C42—28no—
662C42—44no—
663C42—9416no—
664C23—24no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—24no—
671C23—24no—
672C23—22no—
673C23—24no—
674C23—22no—
675C23—22no—
676C23—41no—
677C23—42no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—478no—
687C23—944no—
688C23—944no—
689C23—944no—
690C23—944no—
691C23—944no—
692C23—944no—
693C23—944no—
694C23—944no—
695C23—944no—
696C23—944no—
697C23—944no—
698C23—944no—
699C23—944no—
700C23—944no—
701C23—944no—
702C23—944no—
703C23—944no—
704C23—944no—
705C23—1882no—
706C23—1882no—
707C23—1882no—
708C23—1882no—
709C23—1882no—
710C23—1882no—
711C23—1882no—
712C23—1882no—
713C23—1882no—
714C23—1882no—
715C23—1882no—
716C23—1882no—
717C23—1882no—
718C23—1882no—
719C23—1882no—
720C23—1882no—
721C23C4×D18814yescomplemented
722C23C22×C4×D4711yescharacteristic
723C23C2×D4×D4712yes—
724C23C2×D4×D4712yes—
725C23C22×C22⋊D4711yescharacteristic
726C23C22×D18811yescharacteristic
727C23#41×D4712yes—
728C23#41×D4712yes—
729C23C2×#1062535011yescharacteristic
730C23C2×#1062535011yescharacteristic
731C23C2×#1062535011yescharacteristic
732C23C2×#1062535011yescharacteristic
733D4—9432no—
734D4—9464no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—416no—
760C2×C4—478no—
761C2×C4—944no—
762C2×C4—944no—
763C2×C4—944no—
764C2×C4—944no—
765C2×C4—944no—
766C2×C4—944no—
767C2×C4—944no—
768C2×C4—944no—
769C2×C4—944no—
770C2×C4—944no—
771C2×C4—944no—
772C2×C4—944no—
773C2×C4—1882no—
774C2×C4—1882no—
775C2×C4—1882no—
776C2×C4—1882no—
777C2×C4—1882no—
778C2×C4—1882no—
779C2×C4—1882no—
780C2×C4—1882no—
781C2×C4—18832no—
782C2×C4C4×C22⋊D4714yescomplemented
783C2×C4#1309399214yes—
784C2×C4#1309399418yes—
785C2×C4#1309399718yes—
786C2×C4#1309399814yes—
787C2×C4#1309402014yes—
788C22—28no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—44no—
793C22—42no—
794C22—44no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—948no—
800C22—948no—
801C22—948no—
802C22—1884no—
803C22—1884no—
804C22—1884no—
805C22—1884no—
806C22—1884no—
807C22—1884no—
808C22—1884no—
809C22—1884no—
810C22—1884no—
811C22—1884no—
812C22—1884no—
813C22—1884no—
814C22C4×D4×D4712yes—
815C22C4×D4×D4712yes—
816C22C2×C4×C22⋊D4711yescharacteristic
817C22C2×C4×D18811yescharacteristic
818C22C4×#1062535011yescharacteristic
819C22C2×#1309399211yescharacteristic
820C22C2×#1309399412yes—
821C22C2×#1309399712yes—
822C22C2×#1309399811yescharacteristic
823C22#1568963011yescharacteristic
824C22#1568963212yes—
825C22#1568963212yes—
826C22#1568963212yes—
827C22#1568963212yes—
828C22#1568963411yescharacteristic
829C22#1568963512yes—
830C22#1568965112yes—
831C22#1568965711yescharacteristic
832C22C2×#1309402011yescharacteristic
833C22#1568966911yescharacteristic
834C22#1568967012yes—
835C22#1568967012yes—
836C22#1568967311yescharacteristic
837C4—24no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—948no—
843C4—1884no—
844C4—1884no—
845C4#1568903218yesdirect product factor
846C2—44no—
847C2—1888no—
848C2C4×#1309399211yescharacteristic
849C2C4×#1309399412yes—
850C2C4×#1309399712yes—
851C2C4×#1309399811yescharacteristic
852C2C4×#1309402011yescharacteristic
853C2C2×#1568903211yescharacteristic
854C2#2024660311yescharacteristic
855C2#2024660412yes—
856C2#2024662411yescharacteristic
857C2#2024663212yes—
858C2#2024666711yescharacteristic
subgroupG/H
centerC23×C4C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC2×#15689032C2
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C4×#392
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×D188C2semidirect
2. C22×C4×C22⋊D47C2semidirect
4. C2×C4×(C2×D47)⋊C4C2semidirect
5. #20241652C2semidirect
6. #20241633C2semidirect
7. #20241632C2semidirect
8. #20241628C2semidirect
9. #20241627C2semidirect
10. C4×C47⋊#95C2semidirect
11. C2×C4×C22⋊C4×C47C2semidirect
28. #15689032C4direct (N × H)
48. C22×D188C2×C4semidirect
55. C22×C22⋊D47C2×C4semidirect
65. C22×C4×D47D4semidirect
87. C2×(C2×D47)⋊C4C2×C4semidirect
90. C2×C4×Dic47D4semidirect
95. C47⋊#95C2×C4semidirect
101. C23×C4×C47D4semidirect
113. C2×C22⋊C4×C47C2×C4semidirect
117. C2×C42×C47D4semidirect
256. C23×C47C4×D4semidirect
302. C22×D47C4×D4semidirect
328. C2×C4×C47C4×D4semidirect
355. C2×Dic47C4×D4semidirect
413. C4×C47#392semidirect
421. C2×C4×C22⋊C4D47semidirect
472. C47C4×#392semidirect
501. C23×C4D188semidirect
535. C2×C22⋊C4C4×D47semidirect
542. C2×C42C22⋊D47semidirect
721. C23C4×D188semidirect
782. C2×C4C4×C22⋊D47semidirect
845. C4#15689032direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D1882
C22×C4×C22⋊D472
C2×#156890322
C2×C4×(C2×D47)⋊C42
#202416522
#202416332
#202416322
#202416282
#202416272
C4×C47⋊#952
C2×C4×C22⋊C4×C472
C4×#39247