Finite Group Databasebeta

← C4×#15689001 #26137428

Subgroups — C4×#15689001 #26137428

Order 12032.

3366 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D188C211yesmaximal, characteristic
2C22×C42×D47C211yesmaximal, characteristic, complemented
3C2×#15689001C212yesmaximal
4C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
7#20241624C212yesmaximal, complemented
8#20241622C212yesmaximal, complemented
9(C2×D47)⋊#95C212yesmaximal, complemented
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C4×#95×C47C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C23×C4×D47C2212yes—
14C23×C4×D47C2211yescharacteristic
15C23×C4×D47C2211yescharacteristic
16C2×C4×D188—24no—
17C2×C4×D188—24no—
18C2×C4×D188C418yescomplemented
19C22×C4⋊Dic47C2211yescharacteristic
20C22×(C2×D47)⋊C4C2211yescharacteristic
21C22×(C2×D47)⋊C4C2212yes—
22C22×(C2×D47)⋊C4C2212yes—
23C22×(C2×D47)⋊C4C2212yes—
24C22×(C2×D47)⋊C4C2211yescharacteristic
25C22×C4×Dic47C2212yes—
26C22×C4×Dic47C2211yescharacteristic
27C22×C4×Dic47C2211yescharacteristic
28C2×C42×D47—24no—
29C2×C42×D47—24no—
30C2×C42×D47—24no—
31#15689001C4116yesdirect product factor
32C4×(C2×D47)⋊C4—24no—
33C4×(C2×D47)⋊C4—24no—
34C4×(C2×D47)⋊C4—24no—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C2×C47⋊#95C2212yes—
38C2×C47⋊#95C2212yes—
39C2×C47⋊#95C2212yes—
40C22×C42×C47C2211yescharacteristic
41C22×C42×C47C2211yescharacteristic
42C22×C42×C47C2211yescharacteristic
43C2×#95×C47C2212yes—
44C2×#95×C47C2212yes—
45C24×D47C2311yescharacteristic
46C24×D47C2311yescharacteristic
47C22×D188—22no—
48C22×D188—22no—
49C22×D188—24no—
50C22×D188C2×C418yes—
51C22×D188C2×C414yes—
52C23×Dic47C2312yes—
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2311yescharacteristic
55C23×Dic47C2312yes—
56C22×C4×D47—24no—
57C22×C4×D47—24no—
58C22×C4×D47—24no—
59C22×C4×D47—22no—
60C22×C4×D47—22no—
61C22×C4×D47—24no—
62C22×C4×D47—22no—
63C22×C4×D47—22no—
64C22×C4×D47—24no—
65C22×C4×D47—24no—
66C22×C4×D47—22no—
67C22×C4×D47—22no—
68C22×C4×D47—22no—
69C22×C4×D47—22no—
70C22×C4×D47—22no—
71C22×C4×D47—22no—
72C22×C4×D47C2×C414yes—
73C22×C4×D47C2×C418yescomplemented
74C22×C4×D47C2×C414yescomplemented
75C22×C4×D47D414yes—
76C22×C4×D47D414yes—
77C4×D188—232no—
78C2×C4⋊Dic47—22no—
79C2×C4⋊Dic47—22no—
80C2×C4⋊Dic47C2×C414yescomplemented
81C2×(C2×D47)⋊C4—24no—
82C2×(C2×D47)⋊C4—22no—
83C2×(C2×D47)⋊C4—22no—
84C2×(C2×D47)⋊C4—24no—
85C2×(C2×D47)⋊C4—24no—
86C2×(C2×D47)⋊C4—24no—
87C2×(C2×D47)⋊C4—24no—
88C2×(C2×D47)⋊C4—22no—
89C2×(C2×D47)⋊C4—22no—
90C2×(C2×D47)⋊C4—24no—
91C2×(C2×D47)⋊C4C2×C414yes—
92C2×(C2×D47)⋊C4C2×C418yescomplemented
93C2×(C2×D47)⋊C4C2×C418yescomplemented
94C2×(C2×D47)⋊C4C2×C418yescomplemented
95C2×(C2×D47)⋊C4C2×C414yescomplemented
96C2×C4×Dic47—24no—
97C2×C4×Dic47—22no—
98C2×C4×Dic47—22no—
99C2×C4×Dic47—24no—
100C2×C4×Dic47—24no—
101C2×C4×Dic47—22no—
102C2×C4×Dic47—22no—
103C2×C4×Dic47—22no—
104C2×C4×Dic47D414yescomplemented
105C42×D47—232no—
106C47⋊#95—24no—
107C47⋊#95—24no—
108C47⋊#95—24no—
109C47⋊#95—24no—
110C47⋊#95C2×C418yescomplemented
111C23×C4×C47C2312yes—
112C23×C4×C47C2311yescharacteristic
113C23×C4×C47C2311yescharacteristic
114C23×C4×C47C2312yes—
115C23×C4×C47C2311yescharacteristic
116C2×C42×C47—22no—
117C2×C42×C47—22no—
118C2×C42×C47—22no—
119C2×C42×C47—22no—
120C2×C42×C47—22no—
121C2×C42×C47—22no—
122C2×C42×C47—22no—
123C2×C42×C47C2×C414yescomplemented
124C2×C42×C47D414yescomplemented
125#95×C47—24no—
126#95×C47C2×C418yescomplemented
127C24×C47C2411yescharacteristic
128C23×D47—21no—
129C23×D47—21no—
130C23×D47—21no—
131C23×D47—21no—
132C23×D47—22no—
133C23×D47—22no—
134C23×D47—21no—
135C23×D47—21no—
136C23×D47—21no—
137C23×D47—21no—
138C23×D47—22no—
139C23×D47—22no—
140C23×D47—21no—
141C23×D47—21no—
142C23×D47—22no—
143C23×D47C22×C414yes—
144C23×D47C22×C412yes—
145C23×D47C22×C412yes—
146C23×D47C22×C414yes—
147C23×D47C2×D412yes—
148C23×D47C2×D412yes—
149C23×D47#4114yes—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—22no—
162C22×C4×C47—22no—
163C22×C4×C47—22no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47C22×C412yes—
168C22×C4×C47C22×C414yes—
169C22×C4×C47C22×C412yes—
170C22×C4×C47C22×C414yes—
171C22×C4×C47C22×C414yes—
172C22×C4×C47C22×C412yes—
173C22×C4×C47C2×D414yes—
174C22×C4×C47C2×D412yes—
175C22×C4×C47C2×D412yes—
176C22×C4×C47C2×D412yes—
177C22×C4×C47C2×D412yes—
178C22×C4×C47#4114yes—
179C22×C4×C47#4112yes—
180C22×C4×C47#4112yes—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—22no—
188C22×Dic47—22no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47C22×C414yes—
202C22×Dic47C22×C412yes—
203C22×Dic47C22×C412yes—
204C22×Dic47C22×C414yes—
205C22×Dic47C2×D412yes—
206C22×Dic47C2×D412yes—
207C22×Dic47C2×D414yes—
208C22×Dic47#4114yes—
209C2×D188—28no—
210C2×D188—28no—
211C2×D188—216no—
212C2×D188—216no—
213C2×D188C42116yescomplemented
214C2×C4×D47—216no—
215C2×C4×D47—216no—
216C2×C4×D47—216no—
217C2×C4×D47—216no—
218C2×C4×D47—216no—
219C2×C4×D47—28no—
220C2×C4×D47—28no—
221C2×C4×D47—216no—
222C2×C4×D47—28no—
223C2×C4×D47—28no—
224C2×C4×D47—28no—
225C2×C4×D47—28no—
226C2×C4×D47—216no—
227C2×C4×D47—28no—
228C2×C4×D47—28no—
229C2×C4×D47—28no—
230C2×C4×D47—44no—
231C2×C4×D47—44no—
232C2×C4×D47—44no—
233C2×C4×D47—44no—
234C2×C4×D47C22⋊C4116yescomplemented
235C42×C47—28no—
236C42×C47—28no—
237C42×C47—44no—
238(C2×D47)⋊C4—28no—
239(C2×D47)⋊C4—216no—
240(C2×D47)⋊C4—216no—
241(C2×D47)⋊C4—28no—
242(C2×D47)⋊C4—216no—
243C4⋊Dic47—28no—
244C4×Dic47—216no—
245C4×Dic47—28no—
246C4×Dic47—44no—
247C23×C47C23×C411yescharacteristic
248C23×C47C23×C412yes—
249C23×C47C22×D411yescharacteristic
250C23×C47C22×D411yescharacteristic
251C23×C47C22×D411yescharacteristic
252C23×C47C22×D411yescharacteristic
253C23×C47C2×#4112yes—
254C23×C47C2×#4112yes—
255C23×C47C2×#4111yescharacteristic
256C23×C47C2×#4112yes—
257C23×C47C2×#4111yescharacteristic
258C22×D47—24no—
259C22×D47—22no—
260C22×D47—22no—
261C22×D47—24no—
262C22×D47—22no—
263C22×D47—22no—
264C22×D47—24no—
265C22×D47—24no—
266C22×D47—22no—
267C22×D47—22no—
268C22×D47—22no—
269C22×D47—22no—
270C22×D47—24no—
271C22×D47—24no—
272C22×D47—24no—
273C22×D47—24no—
274C22×D47—24no—
275C22×D47—24no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—24no—
279C22×D47—24no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—24no—
283C22×D47—24no—
284C22×D47—22no—
285C22×D47—22no—
286C22×D47—24no—
287C22×D47—24no—
288C22×D47—41no—
289C22×D47—41no—
290C22×D47—41no—
291C22×D47—41no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—42no—
295C22×D47—42no—
296C22×D47—42no—
297C22×D47—42no—
298C22×D47C2×C4214yes—
299C22×D47C2×C4214yescomplemented
300C22×D47C2×C22⋊C414yes—
301C22×D47#11714yes—
302C22×D47C4×D418yes—
303C22×D47C4×D418yes—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—24no—
307C2×C4×C47—24no—
308C2×C4×C47—24no—
309C2×C4×C47—24no—
310C2×C4×C47—24no—
311C2×C4×C47—24no—
312C2×C4×C47—24no—
313C2×C4×C47—24no—
314C2×C4×C47—22no—
315C2×C4×C47—24no—
316C2×C4×C47—24no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—24no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47—42no—
325C2×C4×C47—42no—
326C2×C4×C47C2×C4214yescomplemented
327C2×C4×C47C2×C22⋊C414yes—
328C2×C4×C47C4×D414yes—
329C2×C4×C47C4×D414yes—
330C2×C4×C47C4×D418yescomplemented
331C2×C4×C47#12014yes—
332C2×C4×C47#12114yes—
333C2×C4×C47#12114yes—
334C2×C4×C47#12314yes—
335C2×Dic47—24no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—24no—
339C2×Dic47—22no—
340C2×Dic47—24no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—24no—
345C2×Dic47—24no—
346C2×Dic47—24no—
347C2×Dic47—22no—
348C2×Dic47—24no—
349C2×Dic47—24no—
350C2×Dic47—22no—
351C2×Dic47—22no—
352C2×Dic47—24no—
353C2×Dic47—41no—
354C2×Dic47—42no—
355C2×Dic47—41no—
356C2×Dic47—41no—
357C2×Dic47—41no—
358C2×Dic47—42no—
359C2×Dic47—42no—
360C2×Dic47—42no—
361C2×Dic47C2×C22⋊C414yes—
362C2×Dic47C4×D418yescomplemented
363D188—232no—
364C4×D47—264no—
365C4×D47—232no—
366C4×D47—416no—
367C4×#386—471nomaximal, Sylow
368C22×C47C22×C4211yescharacteristic
369C22×C47C22×C22⋊C411yescharacteristic
370C22×C47C2×#11711yescharacteristic
371C22×C47C2×C4×D412yes—
372C22×C47C2×C4×D412yes—
373C22×C47C2×C4×D412yes—
374C22×C47C2×C4×D411yescharacteristic
375C22×C47C2×C4×D411yescharacteristic
376C22×C47C2×C4×D412yes—
377C22×C47C4×#4111yescharacteristic
378C22×C47C4×#4111yescharacteristic
379C22×C47C4×#4112yes—
380C22×C47C4×#4112yes—
381C22×C47C2×#12011yescharacteristic
382C22×C47C2×#12111yescharacteristic
383C22×C47C2×#12111yescharacteristic
384C22×C47C2×#12311yescharacteristic
385C22×C47#52512yes—
386C22×C47#52512yes—
387C22×C47#52512yes—
388C22×C47#52912yes—
389C22×C47#52912yes—
390C22×C47#53212yes—
391C2×D47—24no—
392C2×D47—24no—
393C2×D47—24no—
394C2×D47—24no—
395C2×D47—24no—
396C2×D47—24no—
397C2×D47—28no—
398C2×D47—28no—
399C2×D47—28no—
400C2×D47—28no—
401C2×D47—24no—
402C2×D47—24no—
403C2×D47—24no—
404C2×D47—42no—
405C2×D47—42no—
406C2×D47—42no—
407C2×D47—42no—
408C2×D47—44no—
409C2×D47—44no—
410C2×D47—44no—
411C2×D47—44no—
412C2×D47C4×C22⋊C418yescomplemented
413C4×C47—24no—
414C4×C47—28no—
415C4×C47—42no—
416C4×C47—44no—
417C4×C47#38618yescomplemented
418Dic47—24no—
419Dic47—28no—
420Dic47—42no—
421Dic47—44no—
422C22×C4×D4—471no—
423C23×C42—471no—
424C2×#386—472no—
425C2×C4×C22⋊C4—471no—
426C2×C4×C22⋊C4—471no—
427C2×C4×C22⋊C4—471no—
428#1437—472no—
429#1436—472no—
430C22⋊#95—472no—
431C4×#95—471no—
432C4×#95D4711yescharacteristic, complemented
433C2×C47C2×C4×C22⋊C411yescharacteristic
434C2×C47C42×D411yescharacteristic
435C2×C47C42×D411yescharacteristic
436C2×C47C2×#38611yescharacteristic
437C2×C47#229011yescharacteristic
438C2×C47#229011yescharacteristic
439C2×C47#229711yescharacteristic
440C2×C47C4×#12012yes—
441C2×C47C4×#12112yes—
442C2×C47C4×#12112yes—
443C2×C47C4×#12312yes—
444D47—28no—
445D47—44no—
446C23×D4—471no—
447C24×C4—471no—
448C24×C4—472no—
449C24×C4—471no—
450C2×C4×D4—478no—
451C2×C4×D4—944no—
452C2×C4×D4—944no—
453C22×C4⋊C4—471no—
454C22×C22⋊C4—471no—
455C22×C22⋊C4—471no—
456C22×C22⋊C4—472no—
457C22×C22⋊C4—472no—
458C22×C22⋊C4—472no—
459C22×C42—471no—
460C22×C42—472no—
461C22×C42—471no—
462C22×C42—944no—
463C22×C42—944no—
464C22×C42—944no—
465C22×C42C2×D4711yescharacteristic
466C22×C42C2×D4711yescharacteristic
467C22×C42C2×D4711yescharacteristic
468#386—4716no—
469C4×C22⋊C4—944no—
470C4×C22⋊C4—944no—
471C4×C22⋊C4—944no—
472C2×#95—472no—
473C2×#95—472no—
474C2×#95—472no—
475C2×#95—472no—
476C2×#95—472no—
477C2×#95C2×D4712yes—
478C2×#95C2×D4712yes—
479C47C4×#38611yescharacteristic, complemented, Sylow
480C25—471no—
481C25—471no—
482C22×D4—474no—
483C22×D4—478no—
484C22×D4—942no—
485C22×D4—942no—
486C22×D4—944no—
487C23×C4—471no—
488C23×C4—472no—
489C23×C4—474no—
490C23×C4—474no—
491C23×C4—474no—
492C23×C4—472no—
493C23×C4—471no—
494C23×C4—474no—
495C23×C4—478no—
496C23×C4—944no—
497C23×C4—944no—
498C23×C4—944no—
499C23×C4—944no—
500C23×C4—944no—
501C23×C4—942no—
502C23×C4—944no—
503C23×C4—942no—
504C23×C4—942no—
505C23×C4—942no—
506C23×C4—942no—
507C23×C4—942no—
508C23×C4—942no—
509C23×C4—942no—
510C23×C4—942no—
511C23×C4—942no—
512C23×C4C22×D4712yes—
513C23×C4C22×D4711yescharacteristic
514C23×C4C22×D4711yescharacteristic
515C23×C4C22×D4712yes—
516C23×C4C22×D4711yescharacteristic
517C4×D4—9432no—
518C2×C4⋊C4—474no—
519C2×C4⋊C4—942no—
520C2×C4⋊C4—942no—
521C2×C22⋊C4—474no—
522C2×C22⋊C4—474no—
523C2×C22⋊C4—478no—
524C2×C22⋊C4—478no—
525C2×C22⋊C4—478no—
526C2×C22⋊C4—942no—
527C2×C22⋊C4—942no—
528C2×C22⋊C4—944no—
529C2×C22⋊C4—944no—
530C2×C22⋊C4—942no—
531C2×C22⋊C4—942no—
532C2×C22⋊C4—944no—
533C2×C22⋊C4—944no—
534C2×C22⋊C4—944no—
535C2×C22⋊C4—944no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—474no—
544C2×C42—9432no—
545C2×C42—944no—
546C2×C42—944no—
547C2×C42—944no—
548C2×C42—942no—
549C2×C42—942no—
550C2×C42—942no—
551C2×C42—942no—
552C2×C42—942no—
553C2×C42C4×D4714yescomplemented
554C2×C42D18814yescomplemented
555#95—24no—
556#95—478no—
557#95—944no—
558#95—944no—
559#95—944no—
560#95—944no—
561#95C4×D4718yescomplemented
562C24—472no—
563C24—474no—
564C24—472no—
565C24—472no—
566C24—474no—
567C24—474no—
568C24—472no—
569C24—941no—
570C24—941no—
571C24—942no—
572C24—941no—
573C24—942no—
574C24—941no—
575C24—941no—
576C24—941no—
577C24—941no—
578C24—941no—
579C24—942no—
580C24—942no—
581C24—942no—
582C24—941no—
583C24—941no—
584C24C23×D4711yescharacteristic
585C2×D4—4716no—
586C2×D4—948no—
587C2×D4—948no—
588C2×D4—9416no—
589C2×D4—9416no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—474no—
608C22×C4—472no—
609C22×C4—472no—
610C22×C4—474no—
611C22×C4—472no—
612C22×C4—474no—
613C22×C4—4716no—
614C22×C4—474no—
615C22×C4—472no—
616C22×C4—9416no—
617C22×C4—9416no—
618C22×C4—9416no—
619C22×C4—9416no—
620C22×C4—9416no—
621C22×C4—9416no—
622C22×C4—942no—
623C22×C4—941no—
624C22×C4—941no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—941no—
628C22×C4—942no—
629C22×C4—941no—
630C22×C4—948no—
631C22×C4—948no—
632C22×C4—9416no—
633C22×C4—948no—
634C22×C4—948no—
635C22×C4—948no—
636C22×C4—948no—
637C22×C4—941no—
638C22×C4—942no—
639C22×C4—941no—
640C22×C4—941no—
641C22×C4—941no—
642C22×C4—942no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4—942no—
646C22×C4—941no—
647C22×C4—942no—
648C22×C4—941no—
649C22×C4—948no—
650C22×C4—948no—
651C22×C4—948no—
652C22×C4—1884no—
653C22×C4—1884no—
654C22×C4—1884no—
655C22×C4—1884no—
656C22×C4C2×C4×D4714yes—
657C22×C4C2×C4×D4712yes—
658C22×C4C2×C4×D4714yes—
659C22×C4C2×C4×D4712yes—
660C22×C4C2×C4×D4714yes—
661C22×C4C2×C4×D4712yes—
662C22×C4C2×D18814yes—
663C22×C4C2×D18812yes—
664C22×C4#1062535014yes—
665C22×C4#1062535012yes—
666C22×C4D4×D4712yes—
667C22×C4D4×D4712yes—
668C22×C4D4×D4712yes—
669C22×C4#1062535412yes—
670C4⋊C4—948no—
671C22⋊C4—9416no—
672C22⋊C4—948no—
673C22⋊C4—9416no—
674C22⋊C4—948no—
675C22⋊C4—9416no—
676C42—28no—
677C42—28no—
678C42—44no—
679C42—9416no—
680C42—948no—
681C42—1884no—
682C23—474no—
683C23—474no—
684C23—474no—
685C23—478no—
686C23—478no—
687C23—474no—
688C23—944no—
689C23—942no—
690C23—942no—
691C23—944no—
692C23—942no—
693C23—942no—
694C23—944no—
695C23—944no—
696C23—942no—
697C23—942no—
698C23—942no—
699C23—942no—
700C23—944no—
701C23—944no—
702C23—944no—
703C23—944no—
704C23—944no—
705C23—944no—
706C23—942no—
707C23—942no—
708C23—944no—
709C23—944no—
710C23—944no—
711C23—942no—
712C23—944no—
713C23—942no—
714C23—942no—
715C23—942no—
716C23—944no—
717C23—944no—
718C23—1881no—
719C23—1881no—
720C23—1881no—
721C23—1881no—
722C23—1882no—
723C23—1882no—
724C23—1882no—
725C23—1882no—
726C23—1882no—
727C23—1882no—
728C23C22×C4×D4711yescharacteristic
729C23C22×C4×D4712yes—
730C23C2×D4×D4711yescharacteristic
731C23C2×D4×D4711yescharacteristic
732C23C2×D4×D4711yescharacteristic
733C23C22×D18811yescharacteristic
734C23#41×D4712yes—
735C23#41×D4712yes—
736C23C2×#1062535011yescharacteristic
737C23C2×#1062535012yes—
738C23C2×#1062535411yescharacteristic
739D4—9432no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—474no—
763C2×C4—478no—
764C2×C4—9464no—
765C2×C4—944no—
766C2×C4—942no—
767C2×C4—942no—
768C2×C4—944no—
769C2×C4—942no—
770C2×C4—944no—
771C2×C4—942no—
772C2×C4—942no—
773C2×C4—942no—
774C2×C4—944no—
775C2×C4—944no—
776C2×C4—944no—
777C2×C4—9432no—
778C2×C4—942no—
779C2×C4—944no—
780C2×C4—942no—
781C2×C4—944no—
782C2×C4—942no—
783C2×C4—944no—
784C2×C4—1881no—
785C2×C4—1881no—
786C2×C4—1882no—
787C2×C4—1881no—
788C2×C4—1881no—
789C2×C4—1882no—
790C2×C4—1882no—
791C2×C4—1882no—
792C2×C4—18816no—
793C2×C4C42×D4714yescomplemented
794C2×C4C22⋊C4×D4714yes—
795C2×C4#1309398614yes—
796C2×C4C4×D18814yes—
797C2×C4C4×D18818yescomplemented
798C2×C4#1309399414yes—
799C2×C4#1309399714yes—
800C2×C4#1309399914yes—
801C2×C4#1309400914yes—
802C22—478no—
803C22—944no—
804C22—944no—
805C22—944no—
806C22—944no—
807C22—948no—
808C22—948no—
809C22—948no—
810C22—948no—
811C22—944no—
812C22—944no—
813C22—944no—
814C22—944no—
815C22—944no—
816C22—1882no—
817C22—1882no—
818C22—1882no—
819C22—1882no—
820C22—1884no—
821C22—1884no—
822C22—1884no—
823C22—1884no—
824C22C2×C42×D4711yescharacteristic
825C22C2×C22⋊C4×D4711yescharacteristic
826C22#117×D4711yescharacteristic
827C22C4×D4×D4712yes—
828C22C4×D4×D4712yes—
829C22C4×D4×D4712yes—
830C22C2×#1309398611yescharacteristic
831C22C2×C4×D18811yescharacteristic
832C22C2×C4×D18812yes—
833C22#1568959111yescharacteristic
834C22C4×#1062535011yescharacteristic
835C22C4×#1062535012yes—
836C22C4×#1062535412yes—
837C22C2×#1309399411yescharacteristic
838C22C2×#1309399711yescharacteristic
839C22C2×#1309399911yescharacteristic
840C22C2×#1309400911yescharacteristic
841C22#1568963212yes—
842C22#1568963212yes—
843C22#1568963512yes—
844C22#1568965112yes—
845C22#1568966012yes—
846C22#1568967012yes—
847C4—28no—
848C4—24no—
849C4—42no—
850C4—44no—
851C4—944no—
852C4—948no—
853C4—1882no—
854C4—1884no—
855C4#1568900118yesdirect product factor
856C2—948no—
857C2—1884no—
858C2C4×C22⋊C4×D4711yescharacteristic
859C2C4×#1309398611yescharacteristic
860C2C42×D18811yescharacteristic
861C2C2×#1568900111yescharacteristic
862C2#2024582911yescharacteristic
863C2#2024583211yescharacteristic
864C2#2024587411yescharacteristic
865C2C4×#1309399412yes—
866C2C4×#1309399712yes—
867C2C4×#1309399912yes—
868C2C4×#1309400912yes—
subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC4×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenterC4×#95D47
hypocenterC47C4×#386
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. C22×C42×D47C2semidirect
4. C2×C4×(C2×D47)⋊C4C2semidirect
5. C2×C4×(C2×D47)⋊C4C2semidirect
6. C2×C4×(C2×D47)⋊C4C2semidirect
7. #20241624C2semidirect
8. #20241622C2semidirect
9. (C2×D47)⋊#95C2semidirect
10. C4×C47⋊#95C2semidirect
11. C4×#95×C47C2semidirect
18. C2×C4×D188C4semidirect
31. #15689001C4direct (N × H)
73. C22×C4×D47C2×C4semidirect
74. C22×C4×D47C2×C4semidirect
80. C2×C4⋊Dic47C2×C4semidirect
92. C2×(C2×D47)⋊C4C2×C4semidirect
93. C2×(C2×D47)⋊C4C2×C4semidirect
94. C2×(C2×D47)⋊C4C2×C4semidirect
95. C2×(C2×D47)⋊C4C2×C4semidirect
104. C2×C4×Dic47D4semidirect
110. C47⋊#95C2×C4semidirect
123. C2×C42×C47C2×C4semidirect
124. C2×C42×C47D4semidirect
126. #95×C47C2×C4semidirect
213. C2×D188C42semidirect
234. C2×C4×D47C22⋊C4semidirect
299. C22×D47C2×C42semidirect
326. C2×C4×C47C2×C42semidirect
330. C2×C4×C47C4×D4semidirect
362. C2×Dic47C4×D4semidirect
412. C2×D47C4×C22⋊C4semidirect
417. C4×C47#386semidirect
432. C4×#95D47semidirect
479. C47C4×#386semidirect
553. C2×C42C4×D47semidirect
554. C2×C42D188semidirect
561. #95C4×D47semidirect
793. C2×C4C42×D47semidirect
797. C2×C4C4×D188semidirect
855. C4#15689001direct (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×C42×D472
C2×#156890012
C2×C4×(C2×D47)⋊C42
#202416242
#202416222
(C2×D47)⋊#952
C4×C47⋊#952
C4×#95×C472
C4×#38647