Finite Group Databasebeta

← #26123082

Subgroups — #26123082

Order 12032.

1606 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093948C211yesmaximal, characteristic, complemented
2C22×#13093945C211yesmaximal, characteristic
3C2×#15689030C211yesmaximal, characteristic, complemented
4C2×#15689026C211yesmaximal, characteristic
5C2×#15688886C211yesmaximal, characteristic, complemented
6C2×#15688877C211yesmaximal, characteristic, complemented
7C23×SD16×C47C211yesmaximal, characteristic
8C23×C47⋊C8C2211yescharacteristic
9C22×C4⋊Dic47C2211yescharacteristic
10C22×C4⋊Dic47C2211yescharacteristic
11C22×C22⋊Dic47—22no—
12C22×C4×Dic47C2211yescharacteristic
13C2×#13093948—22no—
14C2×#13093948—22no—
15C2×#13093948—22no—
16C2×#13093945—22no—
17C2×#13093945—22no—
18C2×#13093945—22no—
19#15689030—22no—
20#15689030—22no—
21#15689026—22no—
22#15689026—22no—
23C2×C47⋊#95—22no—
24#15688886—22no—
25#15688877—22no—
26C23×Q8×C47C2211yescharacteristic
27C23×D4×C47C2211yescharacteristic
28C22×SD16×C47—22no—
29C22×SD16×C47—22no—
30C22×SD16×C47—22no—
31C22×SD16×C47—22no—
32C22×SD16×C47—22no—
33C22×SD16×C47—22no—
34C22×SD16×C47C414yescomplemented
35C23×C8×C47C2211yescharacteristic
36C23×Dic47—21no—
37C23×Dic47—21no—
38C23×Dic47D412yes—
39C22×C47⋊C8—21no—
40C22×C47⋊C8—21no—
41C22×C47⋊C8—21no—
42C22×C47⋊C8—21no—
43C22×C47⋊C8—21no—
44C22×C47⋊C8—21no—
45C22×C47⋊C8D412yes—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47—21no—
48C2×C4⋊Dic47—21no—
49C2×C4⋊Dic47—21no—
50C2×C4⋊Dic47—21no—
51C2×C4⋊Dic47—21no—
52C2×C4⋊Dic47—21no—
53C2×C4⋊Dic47—21no—
54C2×C4⋊Dic47—21no—
55C2×C4⋊Dic47—21no—
56C2×C4⋊Dic47D412yes—
57C2×C4⋊Dic47D412yes—
58C2×C22⋊Dic47—28no—
59C2×C22⋊Dic47—44no—
60C2×C22⋊Dic47—44no—
61C2×C4×Dic47—21no—
62C2×C4×Dic47—21no—
63C2×C4×Dic47—21no—
64C2×C4×Dic47—21no—
65C2×C4×Dic47—21no—
66C2×C4×Dic47—21no—
67#13093948—28no—
68#13093945—28no—
69C47⋊#95—28no—
70C25×C47—21no—
71C22×Q8×C47—21no—
72C22×Q8×C47—21no—
73C22×Q8×C47—21no—
74C22×Q8×C47—21no—
75C22×Q8×C47—21no—
76C22×Q8×C47—21no—
77C22×Q8×C47—21no—
78C22×Q8×C47—21no—
79C22×Q8×C47—21no—
80C22×Q8×C47—21no—
81C22×Q8×C47—21no—
82C22×Q8×C47C2×C412yes—
83C22×Q8×C47D412yes—
84C22×Q8×C47D412yes—
85C22×D4×C47—21no—
86C22×D4×C47—21no—
87C22×D4×C47—21no—
88C22×D4×C47—21no—
89C22×D4×C47—21no—
90C22×D4×C47—21no—
91C22×D4×C47—21no—
92C22×D4×C47—21no—
93C22×D4×C47—21no—
94C22×D4×C47—21no—
95C22×D4×C47—21no—
96C22×D4×C47C2×C412yes—
97C22×D4×C47D412yes—
98C22×D4×C47D412yes—
99C23×C4×C47—21no—
100C23×C4×C47C2311yescharacteristic
101C2×SD16×C47—28no—
102C2×SD16×C47—28no—
103C2×SD16×C47—28no—
104C2×SD16×C47—28no—
105C2×SD16×C47—28no—
106C2×SD16×C47—28no—
107C2×SD16×C47—28no—
108C22×C8×C47—21no—
109C22×C8×C47—21no—
110C22×C8×C47—21no—
111C22×C8×C47—21no—
112C22×C8×C47C2×C412yes—
113C22×C8×C47D412yes—
114C22×C8×C47D412yes—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47—22no—
118C24×C47—41no—
119C24×C47—41no—
120C24×C47—41no—
121C24×C47—41no—
122C24×C47—42no—
123C24×C47—42no—
124C24×C47—42no—
125C24×C47—42no—
126C24×C47C2×D411yescharacteristic
127C2×Q8×C47—22no—
128C2×Q8×C47—22no—
129C2×Q8×C47—22no—
130C2×Q8×C47—22no—
131C2×Q8×C47—22no—
132C2×Q8×C47—22no—
133C2×Q8×C47—22no—
134C2×Q8×C47—22no—
135C2×Q8×C47—22no—
136C2×Q8×C47—22no—
137C2×Q8×C47—22no—
138C2×Q8×C47—22no—
139C2×Q8×C47—22no—
140C2×Q8×C47—22no—
141C2×Q8×C47—22no—
142C2×Q8×C47—41no—
143C2×Q8×C47—41no—
144C2×Q8×C47—41no—
145C2×Q8×C47—41no—
146C2×Q8×C47—41no—
147C2×Q8×C47—41no—
148C2×Q8×C47—41no—
149C2×Q8×C47—41no—
150C2×Q8×C47—41no—
151C2×Q8×C47—41no—
152C2×Q8×C47—41no—
153C2×Q8×C47—41no—
154C2×Q8×C47C22⋊C414yescomplemented
155C2×D4×C47—22no—
156C2×D4×C47—22no—
157C2×D4×C47—22no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—22no—
161C2×D4×C47—22no—
162C2×D4×C47—22no—
163C2×D4×C47—22no—
164C2×D4×C47—22no—
165C2×D4×C47—22no—
166C2×D4×C47—22no—
167C2×D4×C47—22no—
168C2×D4×C47—22no—
169C2×D4×C47—22no—
170C2×D4×C47—41no—
171C2×D4×C47—41no—
172C2×D4×C47—41no—
173C2×D4×C47—41no—
174C2×D4×C47—41no—
175C2×D4×C47—41no—
176C2×D4×C47—41no—
177C2×D4×C47—41no—
178C2×D4×C47—41no—
179C2×D4×C47—41no—
180C2×D4×C47—41no—
181C2×D4×C47—41no—
182C2×D4×C47C22⋊C414yes—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—41no—
187C22×C4×C47—41no—
188C22×C4×C47—41no—
189C22×C4×C47—41no—
190C22×C4×C47C22×C411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47#4111yescharacteristic
201C22×C4×C47#4111yescharacteristic
202C22×C4×C47#4111yescharacteristic
203C22×C4×C47#4111yescharacteristic
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—41no—
213C22×Dic47—41no—
214C22×Dic47—41no—
215C22×Dic47—41no—
216C22×Dic47—42no—
217C22×Dic47—42no—
218C22×Dic47—42no—
219C22×Dic47—42no—
220C22×Dic47SD1614yescomplemented
221SD16×C47—232no—
222C2×C8×C47—22no—
223C2×C8×C47—22no—
224C2×C8×C47—22no—
225C2×C8×C47—22no—
226C2×C8×C47—22no—
227C2×C8×C47—22no—
228C2×C8×C47C22⋊C414yescomplemented
229C22⋊Dic47—416no—
230C4⋊Dic47—22no—
231C4⋊Dic47—22no—
232C4⋊Dic47—22no—
233C4⋊Dic47—22no—
234C4⋊Dic47—41no—
235C4⋊Dic47—41no—
236C4⋊Dic47—41no—
237C4⋊Dic47—41no—
238C4×Dic47—41no—
239C4×Dic47—41no—
240C4×Dic47—41no—
241C4×Dic47—41no—
242C2×C47⋊C8—22no—
243C2×C47⋊C8—22no—
244C2×C47⋊C8—22no—
245C2×C47⋊C8—41no—
246C2×C47⋊C8—41no—
247C2×C47⋊C8—41no—
248C2×C47⋊C8—41no—
249C23×C47—24no—
250C23×C47—42no—
251C23×C47—42no—
252C23×C47—42no—
253C23×C47—42no—
254C23×C47—42no—
255C23×C47—42no—
256C23×C47—44no—
257C23×C47—44no—
258C23×C47—44no—
259C23×C47—44no—
260C23×C47—44no—
261C23×C47—44no—
262C23×C47—82no—
263C23×C47—82no—
264C23×C47—82no—
265C23×C47—82no—
266C23×C47—82no—
267C23×C47—82no—
268C23×C47—81no—
269C23×C47—81no—
270C23×C47—81no—
271C23×C47—81no—
272C23×C47C4×D411yescharacteristic
273C23×C47#12011yescharacteristic
274C23×C47#12011yescharacteristic
275C23×C47#12111yescharacteristic
276C23×C47#12111yescharacteristic
277C23×C47#12111yescharacteristic
278C23×C47#12711yescharacteristic
279C23×C47C2×SD1612yes—
280C23×C47#13512yes—
281C23×C47AGL(1,ℤ/8)12yes—
282C23×C47#13712yes—
283Q8×C47—24no—
284Q8×C47—24no—
285Q8×C47—42no—
286Q8×C47—42no—
287Q8×C47—42no—
288Q8×C47—42no—
289Q8×C47—42no—
290Q8×C47—42no—
291D4×C47—24no—
292D4×C47—24no—
293D4×C47—42no—
294D4×C47—42no—
295D4×C47—42no—
296D4×C47—42no—
297D4×C47—42no—
298D4×C47—42no—
299C2×C4×C47—24no—
300C2×C4×C47—42no—
301C2×C4×C47—42no—
302C2×C4×C47—42no—
303C2×C4×C47—42no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47C2×C22⋊C411yescharacteristic
307C2×C4×C47C2×C22⋊C411yescharacteristic
308C2×C4×C47C2×C22⋊C411yescharacteristic
309C2×C4×C47C4×D411yescharacteristic
310C2×C4×C47C4×D411yescharacteristic
311C2×C4×C47C4×D411yescharacteristic
312C2×C4×C47#12011yescharacteristic
313C2×C4×C47#12011yescharacteristic
314C2×C4×C47#12011yescharacteristic
315C2×C4×C47#12011yescharacteristic
316C2×C4×C47#12011yescharacteristic
317C2×C4×C47#12011yescharacteristic
318C2×C4×C47#12111yescharacteristic
319C2×C4×C47#12111yescharacteristic
320C2×C4×C47#12111yescharacteristic
321C2×C4×C47#12111yescharacteristic
322C2×C4×C47#12111yescharacteristic
323C2×C4×C47#12111yescharacteristic
324C2×C4×C47#12111yescharacteristic
325C2×C4×C47#12111yescharacteristic
326C2×C4×C47#12111yescharacteristic
327C2×C4×C47#12311yescharacteristic
328C2×C4×C47#12311yescharacteristic
329C2×C4×C47#12311yescharacteristic
330C2×C4×C47#12311yescharacteristic
331C2×C4×C47#12411yescharacteristic
332C2×C4×C47#12411yescharacteristic
333C2×C4×C47#12711yescharacteristic
334C2×Dic47—24no—
335C2×Dic47—24no—
336C2×Dic47—24no—
337C2×Dic47—42no—
338C2×Dic47—42no—
339C2×Dic47—42no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47—44no—
344C2×Dic47—44no—
345C2×Dic47—82no—
346C2×Dic47—82no—
347C2×Dic47—81no—
348C2×Dic47—81no—
349C2×Dic47—81no—
350C2×Dic47—81no—
351C8×C47—24no—
352C47⋊C8—42no—
353#11023—471nomaximal, Sylow
354C22×C47—48no—
355C22×C47—44no—
356C22×C47—84no—
357C22×C47—84no—
358C22×C47—82no—
359C22×C47—82no—
360C22×C47—84no—
361C22×C47—82no—
362C22×C47—82no—
363C22×C47—82no—
364C22×C47—82no—
365C22×C47#38611yescharacteristic
366C22×C47#38611yescharacteristic
367C22×C47#39011yescharacteristic
368C22×C47#39211yescharacteristic
369C22×C47#39211yescharacteristic
370C22×C47#39211yescharacteristic
371C22×C47#39411yescharacteristic
372C22×C47C4×SD1612yes—
373C22×C47#44012yes—
374C22×C47#44812yes—
375C22×C47#44912yes—
376C22×C47#45012yes—
377C22×C47#45212yes—
378C22×C47#46012yes—
379C22×C47#46112yes—
380C22×C47#46312yes—
381C22×C47#46412yes—
382C22×C47#46512yes—
383C22×C47#46812yes—
384C22×C47#49211yescharacteristic
385C22×C47#49511yescharacteristic
386C22×C47#49611yescharacteristic
387C22×C47#49711yescharacteristic
388C4×C47—44no—
389C4×C47#37911yescharacteristic
390C4×C47#38611yescharacteristic
391C4×C47#38611yescharacteristic
392C4×C47#39011yescharacteristic
393C4×C47#39211yescharacteristic
394C4×C47#39411yescharacteristic
395C4×C47#39411yescharacteristic
396C4×C47#39411yescharacteristic
397Dic47—44no—
398Dic47—82no—
399Dic47—82no—
400C23×SD16D4711yescharacteristic
401C22×#103—471no—
402C22×#102—471no—
403C2×#391—471no—
404C2×#390—471no—
405C2×#340—471no—
406C2×#336—471no—
407C2×C47—84no—
408C2×C47#143811yescharacteristic
409C2×C47#187712yes—
410C2×C47#188012yes—
411C2×C47#196811yescharacteristic
412C2×C47#197311yescharacteristic
413C2×C47#200012yes—
414C2×C47#201211yescharacteristic
415C2×C47#201311yescharacteristic
416C2×C47#201411yescharacteristic
417C2×C47#201511yescharacteristic
418C2×C47#205512yes—
419C23×Q8C2×D4711yescharacteristic
420C23×D4C2×D4711yescharacteristic
421C22×SD16—22no—
422C22×SD16—22no—
423C22×SD16—22no—
424C22×SD16—22no—
425C22×SD16—22no—
426C22×SD16—22no—
427C22×SD16Dic4714yescomplemented
428C23×C8—471no—
429C23×C8C2×D4711yescharacteristic
430C22×C4⋊C4—471no—
431C22×C4⋊C4—471no—
432C22×C22⋊C4—942no—
433C22×C42—471no—
434C2×#103—942no—
435C2×#103—942no—
436C2×#103—942no—
437C2×#102—942no—
438C2×#102—942no—
439C2×#102—942no—
440#391—942no—
441#391—942no—
442#390—942no—
443#390—942no—
444C2×#95—942no—
445#340—942no—
446#336—942no—
447C47#1102311yescharacteristic, complemented, Sylow
448C25—21no—
449C22×Q8—21no—
450C22×Q8—21no—
451C22×Q8—21no—
452C22×Q8—21no—
453C22×Q8—21no—
454C22×Q8—21no—
455C22×Q8—21no—
456C22×Q8—21no—
457C22×Q8—21no—
458C22×Q8—21no—
459C22×Q8—21no—
460C22×Q8C2×Dic4712yes—
461C22×Q8C22⋊D4712yes—
462C22×Q8C22⋊D4712yes—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4C2×Dic4712yes—
475C22×D4C22⋊D4712yes—
476C22×D4C22⋊D4712yes—
477C23×C4—21no—
478C23×C4—472no—
479C23×C4—941no—
480C23×C4—941no—
481C23×C4C22×D4711yescharacteristic
482C2×SD16—28no—
483C2×SD16—28no—
484C2×SD16—28no—
485C2×SD16—28no—
486C2×SD16—28no—
487C2×SD16—28no—
488C2×SD16—28no—
489C22×C8—21no—
490C22×C8—21no—
491C22×C8—21no—
492C22×C8—21no—
493C22×C8—472no—
494C22×C8—941no—
495C22×C8—941no—
496C22×C8—941no—
497C22×C8—941no—
498C22×C8—941no—
499C22×C8—941no—
500C22×C8C2×Dic4712yes—
501C22×C8C22⋊D4712yes—
502C22×C8C22⋊D4712yes—
503C2×C4⋊C4—472no—
504C2×C4⋊C4—472no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4—941no—
508C2×C4⋊C4—941no—
509C2×C4⋊C4—941no—
510C2×C4⋊C4—941no—
511C2×C4⋊C4—941no—
512C2×C4⋊C4—941no—
513C2×C4⋊C4—941no—
514C2×C4⋊C4—941no—
515C2×C22⋊C4—948no—
516C2×C22⋊C4—1884no—
517C2×C22⋊C4—1884no—
518C2×C42—941no—
519C2×C42—941no—
520C2×C42—941no—
521C2×C42—941no—
522C2×C42—941no—
523C2×C42—941no—
524#103—948no—
525#102—948no—
526#95—948no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—41no—
531C24—41no—
532C24—41no—
533C24—41no—
534C24—42no—
535C24—42no—
536C24—42no—
537C24—42no—
538C24D4×D4711yescharacteristic
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×Q8—41no—
561C2×Q8—41no—
562C2×Q8—41no—
563C2×Q8—41no—
564C2×Q8—41no—
565C2×Q8—41no—
566C2×Q8C22⋊Dic4714yescomplemented
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C2×D4—41no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4C22⋊Dic4714yes—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—474no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—1881no—
612C22×C4—1881no—
613C22×C4—1881no—
614C22×C4—1881no—
615C22×C4—1882no—
616C22×C4—1882no—
617C22×C4—1882no—
618C22×C4—1882no—
619C22×C4D4×D4711yescharacteristic
620C22×C4D4×D4711yescharacteristic
621C22×C4D4×D4711yescharacteristic
622C22×C4#1062535211yescharacteristic
623C22×C4#1062535211yescharacteristic
624C22×C4#1062535211yescharacteristic
625C22×C4#1062535211yescharacteristic
626C22×C4C22×Dic4711yescharacteristic
627C22×C4C2×C22⋊D4711yescharacteristic
628C22×C4C2×C22⋊D4711yescharacteristic
629C22×C4C2×C22⋊D4711yescharacteristic
630C22×C4C2×C22⋊D4711yescharacteristic
631C22×C4C2×C22⋊D4711yescharacteristic
632C22×C4C2×C22⋊D4711yescharacteristic
633SD16—232no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—942no—
641C2×C8—942no—
642C2×C8—942no—
643C2×C8—1881no—
644C2×C8—1881no—
645C2×C8—1881no—
646C2×C8—1881no—
647C2×C8C22⋊Dic4714yescomplemented
648C4⋊C4—942no—
649C4⋊C4—942no—
650C4⋊C4—942no—
651C4⋊C4—942no—
652C4⋊C4—1881no—
653C4⋊C4—1881no—
654C4⋊C4—1881no—
655C4⋊C4—1881no—
656C22⋊C4—18816no—
657C42—1881no—
658C42—1881no—
659C42—1881no—
660C42—1881no—
661C23—24no—
662C23—44no—
663C23—42no—
664C23—44no—
665C23—42no—
666C23—44no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—81no—
675C23—81no—
676C23—81no—
677C23—81no—
678C23—82no—
679C23—82no—
680C23—82no—
681C23—82no—
682C23—82no—
683C23—82no—
684C23D4×Dic4711yescharacteristic
685C23#1309399211yescharacteristic
686C23#1309399211yescharacteristic
687C23#1309399511yescharacteristic
688C23#1309399611yescharacteristic
689C23#1309399611yescharacteristic
690C23#1309402011yescharacteristic
691C23SD16×D4712yes—
692C23#1309404512yes—
693C23#1309405112yes—
694C23#1309405312yes—
695Q8—24no—
696Q8—24no—
697Q8—42no—
698Q8—42no—
699Q8—42no—
700Q8—42no—
701Q8—42no—
702Q8—42no—
703D4—24no—
704D4—24no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—42no—
709D4—42no—
710D4—42no—
711C2×C4—24no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—944no—
719C2×C4—944no—
720C2×C4—944no—
721C2×C4—3761no—
722C2×C4—3761no—
723C2×C4—3761no—
724C2×C4—3761no—
725C2×C4—3762no—
726C2×C4—3762no—
727C2×C4—1884no—
728C2×C4—1884no—
729C2×C4—1882no—
730C2×C4—1882no—
731C2×C4—1882no—
732C2×C4—1882no—
733C2×C4—1882no—
734C2×C4—1882no—
735C2×C4C2×C22⋊Dic4711yescharacteristic
736C2×C4C2×C22⋊Dic4711yescharacteristic
737C2×C4C2×C22⋊Dic4711yescharacteristic
738C2×C4D4×Dic4711yescharacteristic
739C2×C4D4×Dic4711yescharacteristic
740C2×C4D4×Dic4711yescharacteristic
741C2×C4#1309399211yescharacteristic
742C2×C4#1309399211yescharacteristic
743C2×C4#1309399311yescharacteristic
744C2×C4#1309399311yescharacteristic
745C2×C4#1309399311yescharacteristic
746C2×C4#1309399311yescharacteristic
747C2×C4#1309399511yescharacteristic
748C2×C4#1309399511yescharacteristic
749C2×C4#1309399511yescharacteristic
750C2×C4#1309399611yescharacteristic
751C2×C4#1309399611yescharacteristic
752C2×C4#1309399611yescharacteristic
753C2×C4#1309399611yescharacteristic
754C2×C4#1309399611yescharacteristic
755C2×C4#1309399611yescharacteristic
756C2×C4#1309400511yescharacteristic
757C2×C4#1309400511yescharacteristic
758C2×C4#1309400511yescharacteristic
759C2×C4#1309400511yescharacteristic
760C2×C4#1309401111yescharacteristic
761C2×C4#1309401111yescharacteristic
762C2×C4#1309402011yescharacteristic
763C8—24no—
764C8—1882no—
765C22—48no—
766C22—44no—
767C22—82no—
768C22—82no—
769C22—84no—
770C22—82no—
771C22—84no—
772C22—84no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22#1568900311yescharacteristic
777C22#1568900311yescharacteristic
778C22#1568902611yescharacteristic
779C22#1568903111yescharacteristic
780C22#1568903111yescharacteristic
781C22#1568903111yescharacteristic
782C22#1568903711yescharacteristic
783C22SD16×Dic4712yes—
784C22#1568922412yes—
785C22#1568926012yes—
786C22#1568926712yes—
787C22#1568927212yes—
788C22#1568928212yes—
789C22#1568932112yes—
790C22#1568932612yes—
791C22#1568934012yes—
792C22#1568934312yes—
793C22#1568934912yes—
794C22#1568936612yes—
795C22#1568949411yescharacteristic
796C22#1568950411yescharacteristic
797C22#1568950911yescharacteristic
798C22#1568951411yescharacteristic
799C4—44no—
800C4—3762no—
801C4—3762no—
802C4—1884no—
803C4#1568897911yescharacteristic
804C4#1568900311yescharacteristic
805C4#1568900311yescharacteristic
806C4#1568902611yescharacteristic
807C4#1568903111yescharacteristic
808C4#1568903711yescharacteristic
809C4#1568903711yescharacteristic
810C4#1568903711yescharacteristic
811C2—84no—
812C2#2024162911yescharacteristic
813C2#2024372412yes—
814C2#2024374512yes—
815C2#2024424411yescharacteristic
816C2#2024427111yescharacteristic
817C2#2024438812yes—
818C2#2024446211yescharacteristic
819C2#2024446911yescharacteristic
820C2#2024447411yescharacteristic
821C2#2024448011yescharacteristic
822C2#2024470112yes—
subgroupG/H
centerC24D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC23×SD16×C47C2
socleC24×C47C2×D4
prime radicalC23×D4×C47C22
cosocleC23×C4×C47C23
hypercenterC23×SD16D47
hypocenterC47#11023
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#13093948C2semidirect
3. C2×#15689030C2semidirect
5. C2×#15688886C2semidirect
6. C2×#15688877C2semidirect
34. C22×SD16×C47C4semidirect
154. C2×Q8×C47C22⋊C4semidirect
220. C22×Dic47SD16semidirect
228. C2×C8×C47C22⋊C4semidirect
427. C22×SD16Dic47semidirect
447. C47#11023semidirect
566. C2×Q8C22⋊Dic47semidirect
647. C2×C8C22⋊Dic47semidirect

Maximal subgroups

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

subgroupindex
C22×#130939482
C22×#130939452
C2×#156890302
C2×#156890262
C2×#156888862
C2×#156888772
C23×SD16×C472
#1102347