Finite Group Databasebeta

← #26121590

Subgroups — #26121590

Order 12032.

1406 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D47C211yesmaximal, characteristic
2C2×#15689086C211yesmaximal, characteristic
3C2×#15688980C211yesmaximal, characteristic
4C2×#15688892C211yesmaximal, characteristic, complemented
5C2×#15688891C211yesmaximal, characteristic, complemented
6C2×#15688891C211yesmaximal, characteristic, complemented
7C2×C47×#343C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C22×#10625324—21no—
12C2×M16×D47—22no—
13C2×M16×D47—22no—
14C2×M16×D47—22no—
15C2×M16×D47—22no—
16C2×M16×D47—22no—
17C2×M16×D47C414yescomplemented
18C22×C8×D47—21no—
19C22×C4⋊Dic47C2211yescharacteristic
20C22×(C2×D47)⋊C4C412yes—
21#15689086—22no—
22#15689086C414yescomplemented
23C2×(C2×D47)⋊C8—21no—
24C2×(C2×D47)⋊C8—21no—
25#15688980—21no—
26#15688980—21no—
27#15688980—21no—
28#15688980—21no—
29C2×C47⋊#95C412yes—
30#15688892—22no—
31#15688891—22no—
32#15688891—22no—
33C22×M16×C47C2211yescharacteristic
34C22×M16×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2211yescharacteristic
36C47×#343—22no—
37C24×D47C2×C411yescharacteristic
38C23×Dic47C2×C411yescharacteristic
39C23×Dic47C2×C412yes—
40C22×C4×D47—21no—
41C22×C4×D47—21no—
42C22×C4×D47—21no—
43C22×C4×D47—21no—
44C22×C4×D47—21no—
45C22×C4×D47—21no—
46C22×C4×D47—21no—
47C22×C4×D47—21no—
48C22×C4×D47C2×C412yes—
49C22×C4×D47C2×C412yes—
50C22×C4×D47D412yes—
51C22×C4×D47D411yescharacteristic
52C22×C4×D47D411yescharacteristic
53C22×C4×D47D411yescharacteristic
54C22×C4×D47D411yescharacteristic
55C22×C4×D47Q812yes—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C2×#10625329—21no—
63C2×#10625329—21no—
64C2×#10625329C2×C412yes—
65C2×#10625329C2×C412yes—
66C2×#10625329D412yes—
67C2×#10625329D412yes—
68C2×#10625324—24no—
69C2×#10625324—24no—
70C2×#10625324—24no—
71M16×D47—28no—
72M16×D47—28no—
73M16×D47—28no—
74M16×D47—28no—
75C22×C47⋊C8—21no—
76C22×C47⋊C8—21no—
77C2×C8×D47—24no—
78C2×C8×D47—24no—
79C2×C8×D47—24no—
80C2×C4⋊Dic47—21no—
81C2×C4⋊Dic47—21no—
82C2×C4⋊Dic47—21no—
83C2×C4⋊Dic47—21no—
84C2×C4⋊Dic47—21no—
85C2×C4⋊Dic47—21no—
86C2×(C2×D47)⋊C4—22no—
87C2×(C2×D47)⋊C4—22no—
88C2×(C2×D47)⋊C4—44no—
89(C2×D47)⋊C8—24no—
90(C2×D47)⋊C8—24no—
91C47⋊#95—22no—
92C47⋊#95—22no—
93C23×C4×C47C2×C412yes—
94C23×C4×C47C2311yescharacteristic
95C2×M16×C47—21no—
96C2×M16×C47—21no—
97C2×M16×C47—21no—
98C2×M16×C47—21no—
99C2×M16×C47—21no—
100C2×M16×C47—21no—
101C2×M16×C47—21no—
102C2×M16×C47—21no—
103C2×M16×C47C2×C412yes—
104C2×M16×C47C2×C412yes—
105C2×M16×C47D412yes—
106C2×M16×C47D412yes—
107C22×C8×C47—21no—
108C22×C8×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47—21no—
115C24×C47C22×C411yescharacteristic
116C23×D47—21no—
117C23×D47—21no—
118C23×D47—21no—
119C23×D47—21no—
120C23×D47—22no—
121C23×D47—22no—
122C23×D47—41no—
123C23×D47—41no—
124C23×D47C4212yes—
125C23×D47C22⋊C411yescharacteristic
126C23×D47C22⋊C411yescharacteristic
127C23×D47C4⋊C412yes—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—42no—
132C22×C4×C47—42no—
133C22×C4×C47C22×C411yescharacteristic
134C22×C4×C47C22×C411yescharacteristic
135C22×C4×C47C2×D411yescharacteristic
136C22×C4×C47C2×D411yescharacteristic
137C22×C4×C47C2×D411yescharacteristic
138C22×C4×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×Q811yescharacteristic
143C22×C4×C47#4111yescharacteristic
144C22×C4×C47#4111yescharacteristic
145C22×C4×C47#4111yescharacteristic
146C22×C4×C47#4111yescharacteristic
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—42no—
155C22×Dic47—42no—
156C22×Dic47C4212yes—
157C22×Dic47C22⋊C411yescharacteristic
158C22×Dic47C22⋊C411yescharacteristic
159C22×Dic47C4⋊C412yes—
160C2×C4×D47—22no—
161C2×C4×D47—22no—
162C2×C4×D47—22no—
163C2×C4×D47—22no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—21no—
169C2×C4×D47—21no—
170C2×C4×D47—22no—
171C2×C4×D47—22no—
172C2×C4×D47—21no—
173C2×C4×D47—21no—
174C2×C4×D47—21no—
175C2×C4×D47—21no—
176C2×C4×D47—21no—
177C2×C4×D47—21no—
178C2×C4×D47—21no—
179C2×C4×D47—21no—
180C2×C4×D47—21no—
181C2×C4×D47—21no—
182C2×C4×D47—22no—
183C2×C4×D47—22no—
184C2×C4×D47—22no—
185C2×C4×D47—22no—
186C2×C4×D47—21no—
187C2×C4×D47—21no—
188C2×C4×D47—21no—
189C2×C4×D47—21no—
190C2×C4×D47—22no—
191C2×C4×D47—22no—
192C2×C4×D47C22⋊C412yes—
193C2×C4×D47C22⋊C412yes—
194C2×C4×D47C22⋊C412yes—
195C2×C4×D47C22⋊C412yes—
196C2×C4×D47C4⋊C412yes—
197C2×C4×D47C4⋊C412yes—
198C2×C4×D47C4⋊C412yes—
199C2×C4×D47C4⋊C412yes—
200M16×C47—22no—
201M16×C47—22no—
202M16×C47—22no—
203M16×C47—22no—
204M16×C47—22no—
205M16×C47—41no—
206M16×C47—41no—
207M16×C47C22⋊C414yescomplemented
208C2×C8×C47—22no—
209C2×C8×C47—22no—
210C2×C8×C47—22no—
211C2×C8×C47—22no—
212C2×C8×C47—41no—
213C2×C8×C47—41no—
214C4⋊C4×C47—41no—
215C4⋊C4×C47—41no—
216C4⋊C4×C47—41no—
217C4⋊C4×C47—41no—
218(C2×D47)⋊C4—44no—
219(C2×D47)⋊C4—44no—
220C4⋊Dic47—41no—
221C4⋊Dic47—41no—
222C4⋊Dic47—41no—
223C4⋊Dic47—41no—
224#10625329—22no—
225#10625329—22no—
226#10625329—22no—
227#10625329—22no—
228#10625329—22no—
229#10625329—41no—
230#10625329—41no—
231#10625329C22⋊C414yescomplemented
232C2×C47⋊C8—22no—
233C2×C47⋊C8—22no—
234C2×C47⋊C8—22no—
235C2×C47⋊C8—22no—
236C2×C47⋊C8—41no—
237C2×C47⋊C8—41no—
238#10625324—216no—
239C8×D47—216no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47C2×C4211yescharacteristic
245C23×C47C2×C22⋊C411yescharacteristic
246C23×C47C2×C4⋊C411yescharacteristic
247C23×C47C4×D411yescharacteristic
248C23×C47C4×D411yescharacteristic
249C23×C47C4×D411yescharacteristic
250C23×C47C4×D411yescharacteristic
251C22×D47—21no—
252C22×D47—21no—
253C22×D47—21no—
254C22×D47—21no—
255C22×D47—22no—
256C22×D47—22no—
257C22×D47—22no—
258C22×D47—22no—
259C22×D47—21no—
260C22×D47—21no—
261C22×D47—21no—
262C22×D47—21no—
263C22×D47—21no—
264C22×D47—21no—
265C22×D47—24no—
266C22×D47—24no—
267C22×D47—42no—
268C22×D47—42no—
269C22×D47—42no—
270C22×D47—42no—
271C22×D47—42no—
272C22×D47—42no—
273C22×D47—42no—
274C22×D47—42no—
275C22×D47—42no—
276C22×D47—42no—
277C22×D47#9512yes—
278C22×D47#9512yes—
279C22×D47#10012yes—
280C22×D47#10112yes—
281C2×C4×C47—42no—
282C2×C4×C47—42no—
283C2×C4×C47—42no—
284C2×C4×C47—82no—
285C2×C4×C47—82no—
286C2×C4×C47C2×C22⋊C411yescharacteristic
287C2×C4×C47C2×C22⋊C411yescharacteristic
288C2×C4×C47C2×C22⋊C411yescharacteristic
289C2×C4×C47C2×C22⋊C411yescharacteristic
290C2×C4×C47C2×C4⋊C411yescharacteristic
291C2×C4×C47C2×C4⋊C411yescharacteristic
292C2×C4×C47#11711yescharacteristic
293C2×C4×C47#11711yescharacteristic
294C2×C4×C47C4×D411yescharacteristic
295C2×C4×C47C4×D411yescharacteristic
296C2×C4×C47C4×D411yescharacteristic
297C2×C4×C47C4×D411yescharacteristic
298C2×C4×C47#12011yescharacteristic
299C2×C4×C47#12011yescharacteristic
300C2×C4×C47#12011yescharacteristic
301C2×C4×C47#12011yescharacteristic
302C2×C4×C47#12111yescharacteristic
303C2×C4×C47#12111yescharacteristic
304C2×C4×C47#12111yescharacteristic
305C2×C4×C47#12111yescharacteristic
306C2×C4×C47C22⋊Q811yescharacteristic
307C2×C4×C47C22⋊Q811yescharacteristic
308C2×C4×C47C22⋊Q811yescharacteristic
309C2×C4×C47C22⋊Q811yescharacteristic
310C2×C4×C47#12311yescharacteristic
311C2×C4×C47#12311yescharacteristic
312C2×C4×C47#12311yescharacteristic
313C2×C4×C47#12311yescharacteristic
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—21no—
319C2×Dic47—21no—
320C2×Dic47—21no—
321C2×Dic47—21no—
322C2×Dic47—42no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—82no—
326C2×Dic47—82no—
327C2×Dic47#9512yes—
328C2×Dic47#9512yes—
329C4×D47—22no—
330C4×D47—22no—
331C4×D47—22no—
332C4×D47—22no—
333C4×D47—22no—
334C4×D47—22no—
335C4×D47—22no—
336C4×D47—22no—
337C4×D47—22no—
338C4×D47—22no—
339C4×D47—22no—
340C4×D47—22no—
341C4×D47—22no—
342C4×D47—22no—
343C4×D47—22no—
344C4×D47—22no—
345C8×C47—24no—
346C8×C47—42no—
347C47⋊C8—24no—
348C47⋊C8—42no—
349#10739—471nomaximal, Sylow
350C22×C47—21no—
351C22×C47—21no—
352C22×C47—21no—
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—21no—
357C22×C47—21no—
358C22×C47—21no—
359C22×C47—21no—
360C22×C47—21no—
361C22×C47—21no—
362C22×C47C2×#9511yescharacteristic
363C22×C47C4×C22⋊C411yescharacteristic
364C22×C47C4×C22⋊C411yescharacteristic
365C22×C47#38511yescharacteristic
366C22×C47#38511yescharacteristic
367C22×C47#38611yescharacteristic
368C22×C47#38611yescharacteristic
369C22×C47C2×#10011yescharacteristic
370C22×C47C2×#10111yescharacteristic
371C22×C47#41311yescharacteristic
372C22×C47#41311yescharacteristic
373C2×D47—22no—
374C2×D47—22no—
375C2×D47—22no—
376C2×D47—22no—
377C2×D47—22no—
378C2×D47—22no—
379C2×D47—22no—
380C2×D47—22no—
381C2×D47—22no—
382C2×D47—44no—
383C2×D47—44no—
384C2×D47—44no—
385C2×D47—44no—
386C2×D47—41no—
387C2×D47—41no—
388C2×D47—41no—
389C2×D47—41no—
390C2×D47#34314yescomplemented
391C4×C47—82no—
392C4×C47#37911yescharacteristic
393C4×C47#38011yescharacteristic
394C4×C47#38011yescharacteristic
395C4×C47#38111yescharacteristic
396C4×C47#38511yescharacteristic
397C4×C47#38511yescharacteristic
398C4×C47#38611yescharacteristic
399C4×C47#38611yescharacteristic
400Dic47—22no—
401Dic47—22no—
402Dic47—82no—
403C23×M16—471no—
404C2×#407—471no—
405C2×#380—471no—
406C2×#343—471no—
407C2×#343—471no—
408C2×#343—471no—
409C2×#343D4711yescharacteristic, complemented
410C2×C47—21no—
411C2×C47—21no—
412C2×C47—21no—
413C2×C47—21no—
414C2×C47C22⋊#9511yescharacteristic
415C2×C47C2×#34311yescharacteristic
416C2×C47#174211yescharacteristic
417C2×C47#190011yescharacteristic
418C2×C47#190011yescharacteristic
419C2×C47#190111yescharacteristic
420C2×C47#190111yescharacteristic
421D47—24no—
422D47—42no—
423C24×C4—471no—
424C22×M16—471no—
425C22×M16—471no—
426C22×M16—474no—
427C22×M16—941no—
428C22×M16—942no—
429C22×M16—942no—
430C22×M16—942no—
431C22×M16—942no—
432C22×M16—942no—
433C22×M16C2×D4711yescharacteristic
434C22×M16C2×D4711yescharacteristic
435C23×C8—941no—
436C22×C4⋊C4—471no—
437C22×C4⋊C4C2×D4711yescharacteristic
438C22×C22⋊C4—472no—
439#407—474no—
440#407—942no—
441C2×C22⋊C8—941no—
442C2×C22⋊C8—941no—
443#380—941no—
444#380—941no—
445#380—941no—
446#380—941no—
447C2×#95—472no—
448#343—22no—
449#343—942no—
450#343—942no—
451#343—942no—
452C47#1073911yescharacteristic, complemented, Sylow
453C25—471no—
454C23×C4—471no—
455C23×C4—472no—
456C23×C4—472no—
457C23×C4—471no—
458C23×C4—471no—
459C23×C4—472no—
460C23×C4—471no—
461C23×C4—471no—
462C23×C4—472no—
463C23×C4—472no—
464C23×C4—941no—
465C23×C4—941no—
466C23×C4—941no—
467C23×C4—941no—
468C23×C4—941no—
469C23×C4—941no—
470C23×C4—941no—
471C23×C4—941no—
472C23×C4C4×D4712yes—
473C23×C4C22×D4711yescharacteristic
474C2×M16—21no—
475C2×M16—21no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16—21no—
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—472no—
483C2×M16—472no—
484C2×M16—472no—
485C2×M16—472no—
486C2×M16—944no—
487C2×M16—944no—
488C2×M16—944no—
489C2×M16—948no—
490C2×M16—948no—
491C2×M16—948no—
492C2×M16—941no—
493C2×M16—941no—
494C2×M16—941no—
495C2×M16—948no—
496C2×M16—941no—
497C2×M16—941no—
498C2×M16—941no—
499C2×M16—941no—
500C2×M16—941no—
501C2×M16C4×D4712yes—
502C2×M16C4×D4712yes—
503C2×M16D18812yes—
504C2×M16C22⋊D4712yes—
505C22×C8—21no—
506C22×C8—21no—
507C22×C8—944no—
508C22×C8—944no—
509C22×C8—944no—
510C22×C8—941no—
511C22×C8—941no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—941no—
519C2×C4⋊C4—941no—
520C2×C4⋊C4—941no—
521C2×C4⋊C4—941no—
522C2×C4⋊C4—941no—
523C2×C4⋊C4—941no—
524C2×C22⋊C4—942no—
525C2×C22⋊C4—942no—
526C2×C22⋊C4—1884no—
527C22⋊C8—944no—
528C22⋊C8—944no—
529#95—942no—
530#95—942no—
531C24—471no—
532C24—471no—
533C24—472no—
534C24—472no—
535C24—942no—
536C24—942no—
537C24—941no—
538C24—941no—
539C24—941no—
540C24—941no—
541C24—1881no—
542C24—1881no—
543C24C2×C4×D4711yescharacteristic
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—472no—
550C22×C4—471no—
551C22×C4—471no—
552C22×C4—472no—
553C22×C4—472no—
554C22×C4—472no—
555C22×C4—472no—
556C22×C4—472no—
557C22×C4—472no—
558C22×C4—472no—
559C22×C4—472no—
560C22×C4—472no—
561C22×C4—941no—
562C22×C4—941no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—942no—
572C22×C4—942no—
573C22×C4—941no—
574C22×C4—942no—
575C22×C4—941no—
576C22×C4—941no—
577C22×C4—942no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—941no—
585C22×C4—941no—
586C22×C4—941no—
587C22×C4—942no—
588C22×C4—942no—
589C22×C4—942no—
590C22×C4—942no—
591C22×C4—942no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—942no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—1882no—
601C22×C4—1882no—
602C22×C4C2×C4×D4711yescharacteristic
603C22×C4C2×C4×D4711yescharacteristic
604C22×C4C2×D18811yescharacteristic
605C22×C4#1062535011yescharacteristic
606C22×C4#1062535011yescharacteristic
607C22×C4D4×D4711yescharacteristic
608C22×C4D4×D4711yescharacteristic
609C22×C4D4×D4711yescharacteristic
610C22×C4D4×D4711yescharacteristic
611C22×C4D4×D4711yescharacteristic
612C22×C4#1062535211yescharacteristic
613C22×C4Q8×D4711yescharacteristic
614C22×C4#1062535411yescharacteristic
615C22×C4C2×C22⋊D4711yescharacteristic
616M16—22no—
617M16—22no—
618M16—22no—
619M16—22no—
620M16—22no—
621M16—41no—
622M16—41no—
623M16—474no—
624M16—9416no—
625M16—942no—
626M16—942no—
627M16—942no—
628M16—942no—
629M16—942no—
630M16—1881no—
631M16—1881no—
632M16(C2×D47)⋊C414yescomplemented
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—9416no—
640C2×C8—942no—
641C2×C8—942no—
642C2×C8—942no—
643C2×C8—942no—
644C2×C8—1881no—
645C2×C8—1881no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—1881no—
651C4⋊C4—1881no—
652C4⋊C4—1881no—
653C4⋊C4—1881no—
654C22⋊C4—1884no—
655C22⋊C4—1884no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—472no—
661C23—472no—
662C23—472no—
663C23—472no—
664C23—944no—
665C23—944no—
666C23—941no—
667C23—941no—
668C23—941no—
669C23—941no—
670C23—942no—
671C23—942no—
672C23—942no—
673C23—942no—
674C23—941no—
675C23—941no—
676C23—941no—
677C23—941no—
678C23—941no—
679C23—941no—
680C23—1882no—
681C23—1882no—
682C23—1882no—
683C23—1882no—
684C23—1882no—
685C23—1882no—
686C23—1882no—
687C23—1882no—
688C23—1882no—
689C23—1882no—
690C23C42×D4711yescharacteristic
691C23C22⋊C4×D4711yescharacteristic
692C23C4⋊C4×D4711yescharacteristic
693C23(C22⋊D47)⋊C411yescharacteristic
694C23C4×C22⋊D4711yescharacteristic
695C23#1309398611yescharacteristic
696C23C4×D18811yescharacteristic
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—472no—
703C2×C4—472no—
704C2×C4—942no—
705C2×C4—942no—
706C2×C4—942no—
707C2×C4—942no—
708C2×C4—941no—
709C2×C4—941no—
710C2×C4—941no—
711C2×C4—941no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—3762no—
729C2×C4—3762no—
730C2×C4—1882no—
731C2×C4—1882no—
732C2×C4—1882no—
733C2×C4C22⋊C4×D4711yescharacteristic
734C2×C4C22⋊C4×D4711yescharacteristic
735C2×C4C22⋊C4×D4711yescharacteristic
736C2×C4C2×(C2×D47)⋊C411yescharacteristic
737C2×C4C4⋊C4×D4711yescharacteristic
738C2×C4C4⋊C4×D4711yescharacteristic
739C2×C4#1309398111yescharacteristic
740C2×C4#1309398211yescharacteristic
741C2×C4(C22⋊D47)⋊C411yescharacteristic
742C2×C4C4×C22⋊D4711yescharacteristic
743C2×C4#1309398611yescharacteristic
744C2×C4C4×D18811yescharacteristic
745C2×C4#1309399211yescharacteristic
746C2×C4#1309399211yescharacteristic
747C2×C4#1309399411yescharacteristic
748C2×C4#1309399411yescharacteristic
749C2×C4#1309399511yescharacteristic
750C2×C4#1309399711yescharacteristic
751C2×C4#1309399711yescharacteristic
752C2×C4#1309399911yescharacteristic
753C2×C4#1309400011yescharacteristic
754C2×C4#1309400211yescharacteristic
755C2×C4#1309400211yescharacteristic
756C2×C4#1309400411yescharacteristic
757C2×C4#1309400611yescharacteristic
758C2×C4#1309400611yescharacteristic
759C2×C4#1309400911yescharacteristic
760C2×C4#1309400911yescharacteristic
761C8—24no—
762C8—42no—
763C8—944no—
764C8—1882no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—474no—
778C22—942no—
779C22—942no—
780C22—942no—
781C22—942no—
782C22—942no—
783C22—942no—
784C22—942no—
785C22—942no—
786C22—942no—
787C22—1884no—
788C22—1884no—
789C22—1884no—
790C22—1884no—
791C22—1881no—
792C22—1881no—
793C22—1881no—
794C22—1881no—
795C22#95×D4711yescharacteristic
796C22#1568897011yescharacteristic
797C22C4×(C2×D47)⋊C411yescharacteristic
798C22#1568899411yescharacteristic
799C22#1568899711yescharacteristic
800C22#1568899911yescharacteristic
801C22#1568900111yescharacteristic
802C22#100×D4711yescharacteristic
803C22#101×D4711yescharacteristic
804C22#1568910411yescharacteristic
805C22#1568910611yescharacteristic
806C4—82no—
807C4—942no—
808C4—942no—
809C4—3762no—
810C4#1568897811yescharacteristic
811C4#1568898011yescharacteristic
812C4#1568898211yescharacteristic
813C4#1568898511yescharacteristic
814C4#1568899411yescharacteristic
815C4#1568899711yescharacteristic
816C4#1568899911yescharacteristic
817C4#1568900111yescharacteristic
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—944no—
823C2—1882no—
824C2(C2×D47)⋊#9511yescharacteristic
825C2#343×D4711yescharacteristic
826C2#2024312511yescharacteristic
827C2#2024384811yescharacteristic
828C2#2024385011yescharacteristic
829C2#2024385311yescharacteristic
830C2#2024385511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC23×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#343C2
socleC23×C47C2×C22⋊C4
prime radicalC24×D47C2×C4
cosocleC23×C4×C47C23
hypercenterC2×#343D47
hypocenterC47#10739
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. C2×#15688892C2semidirect
5. C2×#15688891C2semidirect
6. C2×#15688891C2semidirect
7. C2×C47×#343C2semidirect
17. C2×M16×D47C4semidirect
22. #15689086C4semidirect
207. M16×C47C22⋊C4semidirect
231. #10625329C22⋊C4semidirect
390. C2×D47#343semidirect
409. C2×#343D47semidirect
452. C47#10739semidirect
632. M16(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D472
C2×#156890862
C2×#156889802
C2×#156888922
C2×#156888912
C2×C47×#3432
#1073947