Finite Group Databasebeta

← #26123086

Subgroups — #26123086

Order 12032.

1390 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#10625337C211yesmaximal, characteristic
2C22×#13093949C211yesmaximal, characteristic
3C2×#15689030C211yesmaximal, characteristic
4C2×#15689028C211yesmaximal, characteristic
5C2×#15688885C211yesmaximal, characteristic
6C2×#15688877C211yesmaximal, characteristic
7C22×#103×C47C211yesmaximal, characteristic
8C23×Dic94C2211yescharacteristic
9C22×#10625337—22no—
10C22×#10625337—22no—
11C22×#10625337—22no—
12C22×#10625337—22no—
13C22×#10625337—22no—
14C22×#10625337—22no—
15C22×#10625337C414yescomplemented
16C23×C47⋊C8C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4×Dic47C2211yescharacteristic
19C2×#13093949—22no—
20C2×#13093949—22no—
21C2×#13093949—22no—
22#15689030—22no—
23#15689030—22no—
24#15689028—22no—
25#15689028—22no—
26C2×C47⋊#95—22no—
27C2×C47⋊#95—22no—
28#15688885—22no—
29#15688877—22no—
30C23×Q8×C47C2211yescharacteristic
31C23×C8×C47C2211yescharacteristic
32C22×C4⋊C4×C47C2211yescharacteristic
33C2×#103×C47—22no—
34C2×#103×C47—22no—
35C2×#103×C47—22no—
36C22×Dic94—21no—
37C22×Dic94—21no—
38C22×Dic94—21no—
39C22×Dic94—21no—
40C22×Dic94—21no—
41C22×Dic94—21no—
42C22×Dic94—21no—
43C22×Dic94—21no—
44C22×Dic94—21no—
45C22×Dic94—21no—
46C22×Dic94—21no—
47C22×Dic94C2×C412yes—
48C22×Dic94D412yes—
49C22×Dic94D412yes—
50C23×Dic47—21no—
51C23×Dic47—21no—
52C23×Dic47D412yes—
53C2×#10625337—28no—
54C2×#10625337—28no—
55C2×#10625337—28no—
56C2×#10625337—28no—
57C2×#10625337—28no—
58C2×#10625337—28no—
59C2×#10625337—28no—
60C22×C47⋊C8—21no—
61C22×C47⋊C8—21no—
62C22×C47⋊C8—21no—
63C22×C47⋊C8—21no—
64C22×C47⋊C8C2×C412yes—
65C22×C47⋊C8D412yes—
66C22×C47⋊C8D412yes—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47D412yes—
73C2×C4×Dic47—21no—
74C2×C4×Dic47—21no—
75C2×C4×Dic47—21no—
76C2×C4×Dic47—21no—
77C2×C4×Dic47—21no—
78C2×C4×Dic47—21no—
79#13093949—28no—
80C47⋊#95—28no—
81C47⋊#95—28no—
82C22×Q8×C47—21no—
83C22×Q8×C47—21no—
84C22×Q8×C47—21no—
85C22×Q8×C47—21no—
86C22×Q8×C47—21no—
87C22×Q8×C47—21no—
88C22×Q8×C47—21no—
89C22×Q8×C47—21no—
90C22×Q8×C47—21no—
91C22×Q8×C47—21no—
92C22×Q8×C47—21no—
93C22×Q8×C47C2×C412yes—
94C22×Q8×C47D412yes—
95C22×Q8×C47D412yes—
96C23×C4×C47—21no—
97C23×C4×C47—21no—
98C23×C4×C47C2311yescharacteristic
99C22×C8×C47—21no—
100C22×C8×C47—21no—
101C22×C8×C47—21no—
102C22×C8×C47—21no—
103C22×C8×C47—21no—
104C22×C8×C47—21no—
105C22×C8×C47D412yes—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47D412yes—
112#103×C47—28no—
113C24×C47C2×D411yescharacteristic
114C2×Q8×C47—22no—
115C2×Q8×C47—22no—
116C2×Q8×C47—22no—
117C2×Q8×C47—22no—
118C2×Q8×C47—22no—
119C2×Q8×C47—22no—
120C2×Q8×C47—22no—
121C2×Q8×C47—22no—
122C2×Q8×C47—22no—
123C2×Q8×C47—22no—
124C2×Q8×C47—22no—
125C2×Q8×C47—22no—
126C2×Q8×C47—22no—
127C2×Q8×C47—22no—
128C2×Q8×C47—22no—
129C2×Q8×C47—41no—
130C2×Q8×C47—41no—
131C2×Q8×C47—41no—
132C2×Q8×C47—41no—
133C2×Q8×C47—41no—
134C2×Q8×C47—41no—
135C2×Q8×C47—41no—
136C2×Q8×C47—41no—
137C2×Q8×C47—41no—
138C2×Q8×C47—41no—
139C2×Q8×C47—41no—
140C2×Q8×C47—41no—
141C2×Q8×C47C22⋊C414yes—
142C22×C4×C47—22no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—22no—
146C22×C4×C47—41no—
147C22×C4×C47—41no—
148C22×C4×C47—41no—
149C22×C4×C47—41no—
150C22×C4×C47—41no—
151C22×C4×C47—41no—
152C22×C4×C47—42no—
153C22×C4×C47—42no—
154C22×C4×C47C22×C411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D411yescharacteristic
164C22×C4×C47#4111yescharacteristic
165C22×C4×C47#4111yescharacteristic
166C22×C4×C47#4111yescharacteristic
167C22×C4×C47#4111yescharacteristic
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—22no—
176C22×Dic47—22no—
177C22×Dic47—22no—
178C22×Dic47—41no—
179C22×Dic47—41no—
180C22×Dic47—41no—
181C22×Dic47—41no—
182C22×Dic47—41no—
183C22×Dic47—41no—
184C22×Dic47—42no—
185C22×Dic47—42no—
186C22×Dic47Q1614yescomplemented
187C2×Dic94—22no—
188C2×Dic94—22no—
189C2×Dic94—22no—
190C2×Dic94—22no—
191C2×Dic94—22no—
192C2×Dic94—22no—
193C2×Dic94—22no—
194C2×Dic94—22no—
195C2×Dic94—22no—
196C2×Dic94—22no—
197C2×Dic94—22no—
198C2×Dic94—22no—
199C2×Dic94—22no—
200C2×Dic94—22no—
201C2×Dic94—22no—
202C2×Dic94—41no—
203C2×Dic94—41no—
204C2×Dic94—41no—
205C2×Dic94—41no—
206C2×Dic94—41no—
207C2×Dic94—41no—
208C2×Dic94—41no—
209C2×Dic94—41no—
210C2×Dic94—41no—
211C2×Dic94—41no—
212C2×Dic94—41no—
213C2×Dic94—41no—
214C2×Dic94C22⋊C414yes—
215C2×C8×C47—22no—
216C2×C8×C47—22no—
217C2×C8×C47—22no—
218C2×C8×C47—41no—
219C2×C8×C47—41no—
220C2×C8×C47—41no—
221C2×C8×C47—41no—
222C4⋊C4×C47—22no—
223C4⋊C4×C47—22no—
224C4⋊C4×C47—41no—
225C4⋊C4×C47—41no—
226#10625337—232no—
227C4⋊Dic47—22no—
228C4⋊Dic47—22no—
229C4⋊Dic47—41no—
230C4⋊Dic47—41no—
231C4×Dic47—41no—
232C4×Dic47—41no—
233C4×Dic47—41no—
234C4×Dic47—41no—
235C2×C47⋊C8—22no—
236C2×C47⋊C8—22no—
237C2×C47⋊C8—22no—
238C2×C47⋊C8—22no—
239C2×C47⋊C8—22no—
240C2×C47⋊C8—22no—
241C2×C47⋊C8C22⋊C414yes—
242C23×C47C4×D411yescharacteristic
243C23×C47#12011yescharacteristic
244C23×C47#12011yescharacteristic
245C23×C47#12111yescharacteristic
246C23×C47#12111yescharacteristic
247C23×C47#12111yescharacteristic
248C23×C47#12711yescharacteristic
249C23×C47C2×Q1612yes—
250C23×C47#13512yes—
251C23×C47#13712yes—
252C23×C47#13712yes—
253Q8×C47—24no—
254Q8×C47—24no—
255Q8×C47—42no—
256Q8×C47—42no—
257Q8×C47—42no—
258Q8×C47—42no—
259Q8×C47—42no—
260Q8×C47—42no—
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×C47—42no—
269C2×C4×C47—44no—
270C2×C4×C47—82no—
271C2×C4×C47—81no—
272C2×C4×C47—81no—
273C2×C4×C47C2×C22⋊C411yescharacteristic
274C2×C4×C47C2×C22⋊C411yescharacteristic
275C2×C4×C47C2×C22⋊C411yescharacteristic
276C2×C4×C47C4×D411yescharacteristic
277C2×C4×C47C4×D411yescharacteristic
278C2×C4×C47C4×D411yescharacteristic
279C2×C4×C47#12011yescharacteristic
280C2×C4×C47#12011yescharacteristic
281C2×C4×C47#12011yescharacteristic
282C2×C4×C47#12011yescharacteristic
283C2×C4×C47#12011yescharacteristic
284C2×C4×C47#12011yescharacteristic
285C2×C4×C47#12111yescharacteristic
286C2×C4×C47#12111yescharacteristic
287C2×C4×C47#12111yescharacteristic
288C2×C4×C47#12111yescharacteristic
289C2×C4×C47#12111yescharacteristic
290C2×C4×C47#12111yescharacteristic
291C2×C4×C47#12111yescharacteristic
292C2×C4×C47#12111yescharacteristic
293C2×C4×C47#12111yescharacteristic
294C2×C4×C47#12311yescharacteristic
295C2×C4×C47#12311yescharacteristic
296C2×C4×C47#12311yescharacteristic
297C2×C4×C47#12311yescharacteristic
298C2×C4×C47#12411yescharacteristic
299C2×C4×C47#12411yescharacteristic
300C2×C4×C47#12711yescharacteristic
301C2×Dic47—24no—
302C2×Dic47—24no—
303C2×Dic47—24no—
304C2×Dic47—24no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—42no—
314C2×Dic47—42no—
315C2×Dic47—42no—
316C2×Dic47—44no—
317C2×Dic47—82no—
318C2×Dic47—81no—
319C2×Dic47—81no—
320Dic94—24no—
321Dic94—24no—
322Dic94—42no—
323Dic94—42no—
324Dic94—42no—
325Dic94—42no—
326Dic94—42no—
327Dic94—42no—
328C8×C47—42no—
329C47⋊C8—24no—
330#11024—471nomaximal, Sylow
331C22×C47#38611yescharacteristic
332C22×C47#38611yescharacteristic
333C22×C47#39011yescharacteristic
334C22×C47#39211yescharacteristic
335C22×C47#39211yescharacteristic
336C22×C47#39211yescharacteristic
337C22×C47#39411yescharacteristic
338C22×C47C4×Q1612yes—
339C22×C47#44112yes—
340C22×C47#45112yes—
341C22×C47#45112yes—
342C22×C47#45212yes—
343C22×C47#45212yes—
344C22×C47#46212yes—
345C22×C47#46212yes—
346C22×C47#46412yes—
347C22×C47#46412yes—
348C22×C47#46712yes—
349C22×C47#47012yes—
350C22×C47#49411yescharacteristic
351C22×C47#49511yescharacteristic
352C22×C47#49711yescharacteristic
353C22×C47#49711yescharacteristic
354C4×C47—44no—
355C4×C47—82no—
356C4×C47#37911yescharacteristic
357C4×C47#38611yescharacteristic
358C4×C47#38611yescharacteristic
359C4×C47#39011yescharacteristic
360C4×C47#39211yescharacteristic
361C4×C47#39411yescharacteristic
362C4×C47#39411yescharacteristic
363C4×C47#39411yescharacteristic
364Dic47—44no—
365Dic47—44no—
366Dic47—82no—
367C23×Q16—471no—
368C22×#103—471no—
369C22×#103D4711yescharacteristic
370C2×#391—471no—
371C2×#391—471no—
372C2×#340—471no—
373C2×#336—471no—
374C2×C47#143811yescharacteristic
375C2×C47#187812yes—
376C2×C47#187812yes—
377C2×C47#196911yescharacteristic
378C2×C47#197111yescharacteristic
379C2×C47#200112yes—
380C2×C47#201511yescharacteristic
381C2×C47#201511yescharacteristic
382C2×C47#201611yescharacteristic
383C2×C47#201611yescharacteristic
384C2×C47#205612yes—
385C23×Q8—471no—
386C23×Q8C2×D4711yescharacteristic
387C22×Q16—474no—
388C22×Q16—942no—
389C22×Q16—942no—
390C22×Q16—942no—
391C22×Q16—942no—
392C22×Q16—942no—
393C22×Q16—942no—
394C23×C8—471no—
395C23×C8C2×D4711yescharacteristic
396C22×C4⋊C4—471no—
397C22×C4⋊C4C2×D4711yescharacteristic
398C22×C42—471no—
399C2×#103—22no—
400C2×#103—22no—
401C2×#103—22no—
402C2×#103—942no—
403C2×#103—942no—
404C2×#103—942no—
405#391—942no—
406#391—942no—
407#391—942no—
408#391—942no—
409C2×#95—942no—
410C2×#95—942no—
411#340—942no—
412#336—942no—
413C47#1102411yescharacteristic, complemented, Sylow
414C22×Q8—21no—
415C22×Q8—21no—
416C22×Q8—21no—
417C22×Q8—21no—
418C22×Q8—21no—
419C22×Q8—21no—
420C22×Q8—21no—
421C22×Q8—21no—
422C22×Q8—21no—
423C22×Q8—21no—
424C22×Q8—21no—
425C22×Q8—472no—
426C22×Q8—472no—
427C22×Q8—472no—
428C22×Q8—941no—
429C22×Q8—941no—
430C22×Q8—941no—
431C22×Q8—941no—
432C22×Q8—941no—
433C22×Q8—941no—
434C22×Q8—941no—
435C22×Q8—941no—
436C22×Q8—941no—
437C22×Q8—941no—
438C22×Q8—941no—
439C22×Q8C4×D4712yes—
440C22×Q8D18812yes—
441C22×Q8C22⋊D4712yes—
442C23×C4—21no—
443C23×C4—21no—
444C23×C4—472no—
445C23×C4—941no—
446C23×C4—941no—
447C23×C4C22×D4711yescharacteristic
448C2×Q16—948no—
449C2×Q16—948no—
450C2×Q16—948no—
451C2×Q16—948no—
452C2×Q16—948no—
453C2×Q16—948no—
454C2×Q16—948no—
455C22×C8—21no—
456C22×C8—21no—
457C22×C8—21no—
458C22×C8—21no—
459C22×C8—21no—
460C22×C8—21no—
461C22×C8—472no—
462C22×C8—472no—
463C22×C8—472no—
464C22×C8—941no—
465C22×C8—941no—
466C22×C8—941no—
467C22×C8—941no—
468C22×C8C22⋊D4712yes—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—472no—
475C2×C4⋊C4—941no—
476C2×C4⋊C4—941no—
477C2×C4⋊C4—941no—
478C2×C4⋊C4—941no—
479C2×C4⋊C4—941no—
480C2×C4⋊C4C22⋊D4712yes—
481C2×C42—941no—
482C2×C42—941no—
483C2×C42—941no—
484C2×C42—941no—
485C2×C42—941no—
486C2×C42—941no—
487#103—28no—
488#103—948no—
489#95—948no—
490#95—948no—
491C24D4×D4711yescharacteristic
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—41no—
508C2×Q8—41no—
509C2×Q8—41no—
510C2×Q8—41no—
511C2×Q8—41no—
512C2×Q8—41no—
513C2×Q8—41no—
514C2×Q8—41no—
515C2×Q8—41no—
516C2×Q8—41no—
517C2×Q8—41no—
518C2×Q8—41no—
519C2×Q8—474no—
520C2×Q8—942no—
521C2×Q8—942no—
522C2×Q8—942no—
523C2×Q8—942no—
524C2×Q8—942no—
525C2×Q8—942no—
526C2×Q8—942no—
527C2×Q8—942no—
528C2×Q8—942no—
529C2×Q8—942no—
530C2×Q8—942no—
531C2×Q8—942no—
532C2×Q8—942no—
533C2×Q8—942no—
534C2×Q8—942no—
535C2×Q8—1881no—
536C2×Q8—1881no—
537C2×Q8—1881no—
538C2×Q8—1881no—
539C2×Q8—1881no—
540C2×Q8—1881no—
541C2×Q8—1881no—
542C2×Q8—1881no—
543C2×Q8—1881no—
544C2×Q8—1881no—
545C2×Q8—1881no—
546C2×Q8—1881no—
547C2×Q8(C2×D47)⋊C414yes—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—474no—
561C22×C4—942no—
562C22×C4—942no—
563C22×C4—942no—
564C22×C4—942no—
565C22×C4—942no—
566C22×C4—942no—
567C22×C4—942no—
568C22×C4—942no—
569C22×C4—942no—
570C22×C4—942no—
571C22×C4—1881no—
572C22×C4—1881no—
573C22×C4—1882no—
574C22×C4—1882no—
575C22×C4—1881no—
576C22×C4—1881no—
577C22×C4—1881no—
578C22×C4—1881no—
579C22×C4C2×C4×D4711yescharacteristic
580C22×C4C2×D18811yescharacteristic
581C22×C4#1062535011yescharacteristic
582C22×C4#1062535011yescharacteristic
583C22×C4D4×D4711yescharacteristic
584C22×C4D4×D4711yescharacteristic
585C22×C4D4×D4711yescharacteristic
586C22×C4D4×D4711yescharacteristic
587C22×C4D4×D4711yescharacteristic
588C22×C4#1062535211yescharacteristic
589C22×C4#1062535211yescharacteristic
590C22×C4C2×C22⋊D4711yescharacteristic
591C22×C4C2×C22⋊D4711yescharacteristic
592C22×C4C2×C22⋊D4711yescharacteristic
593Q16—9432no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—41no—
598C2×C8—41no—
599C2×C8—41no—
600C2×C8—41no—
601C2×C8—474no—
602C2×C8—942no—
603C2×C8—942no—
604C2×C8—942no—
605C2×C8—942no—
606C2×C8—942no—
607C2×C8—942no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—942no—
613C4⋊C4—942no—
614C4⋊C4—1881no—
615C4⋊C4—1881no—
616C42—1881no—
617C42—1881no—
618C42—1881no—
619C42—1881no—
620C23(C22⋊D47)⋊C411yescharacteristic
621C23#1309399211yescharacteristic
622C23#1309399411yescharacteristic
623C23#1309399611yescharacteristic
624C23#1309399711yescharacteristic
625C23#1309399711yescharacteristic
626C23#1309402011yescharacteristic
627C23Q16×D4712yes—
628C23#1309404512yes—
629C23#1309405312yes—
630C23#1309405612yes—
631Q8—24no—
632Q8—24no—
633Q8—42no—
634Q8—42no—
635Q8—42no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—944no—
640Q8—944no—
641Q8—1882no—
642Q8—1882no—
643Q8—1882no—
644Q8—1882no—
645Q8—1882no—
646Q8—1882no—
647C2×C4—24no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—44no—
655C2×C4—42no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—82no—
659C2×C4—944no—
660C2×C4—944no—
661C2×C4—944no—
662C2×C4—944no—
663C2×C4—3761no—
664C2×C4—3761no—
665C2×C4—3762no—
666C2×C4—1882no—
667C2×C4—1884no—
668C2×C4—1882no—
669C2×C4—1882no—
670C2×C4—1882no—
671C2×C4—1882no—
672C2×C4—1882no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4—1882no—
676C2×C4—1882no—
677C2×C4—1882no—
678C2×C4C22⋊C4×D4711yescharacteristic
679C2×C4C22⋊C4×D4711yescharacteristic
680C2×C4C2×(C2×D47)⋊C411yescharacteristic
681C2×C4(C22⋊D47)⋊C411yescharacteristic
682C2×C4C4×C22⋊D4711yescharacteristic
683C2×C4C4×C22⋊D4711yescharacteristic
684C2×C4#1309399211yescharacteristic
685C2×C4#1309399211yescharacteristic
686C2×C4#1309399211yescharacteristic
687C2×C4#1309399311yescharacteristic
688C2×C4#1309399411yescharacteristic
689C2×C4#1309399411yescharacteristic
690C2×C4#1309399511yescharacteristic
691C2×C4#1309399511yescharacteristic
692C2×C4#1309399611yescharacteristic
693C2×C4#1309399611yescharacteristic
694C2×C4#1309399611yescharacteristic
695C2×C4#1309399711yescharacteristic
696C2×C4#1309399711yescharacteristic
697C2×C4#1309399811yescharacteristic
698C2×C4#1309399811yescharacteristic
699C2×C4#1309400611yescharacteristic
700C2×C4#1309400611yescharacteristic
701C2×C4#1309400711yescharacteristic
702C2×C4#1309400811yescharacteristic
703C2×C4#1309401011yescharacteristic
704C2×C4#1309401011yescharacteristic
705C2×C4#1309402011yescharacteristic
706C8—42no—
707C8—944no—
708C22#1568899911yescharacteristic
709C22#1568900011yescharacteristic
710C22#1568902311yescharacteristic
711C22#1568903111yescharacteristic
712C22#1568903211yescharacteristic
713C22#1568903211yescharacteristic
714C22#1568903811yescharacteristic
715C22#1568921512yes—
716C22#1568922712yes—
717C22#1568927712yes—
718C22#1568928012yes—
719C22#1568928212yes—
720C22#1568928812yes—
721C22#1568933112yes—
722C22#1568933212yes—
723C22#1568934312yes—
724C22#1568934812yes—
725C22#1568936312yes—
726C22#1568938012yes—
727C22#1568950111yescharacteristic
728C22#1568950411yescharacteristic
729C22#1568951411yescharacteristic
730C22#1568951611yescharacteristic
731C4—44no—
732C4—82no—
733C4—3762no—
734C4—1884no—
735C4—1884no—
736C4#1568897811yescharacteristic
737C4#1568899911yescharacteristic
738C4#1568900211yescharacteristic
739C4#1568902311yescharacteristic
740C4#1568903111yescharacteristic
741C4#1568903811yescharacteristic
742C4#1568903911yescharacteristic
743C4#1568903911yescharacteristic
744C2#2024162711yescharacteristic
745C2#2024372612yes—
746C2#2024372712yes—
747C2#2024424611yescharacteristic
748C2#2024425611yescharacteristic
749C2#2024439712yes—
750C2#2024448011yescharacteristic
751C2#2024448311yescharacteristic
752C2#2024448611yescharacteristic
753C2#2024448911yescharacteristic
754C2#2024470912yes—
subgroupG/H
centerC24D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC22×#103×C47C2
socle, prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC22×#103D47
hypocenterC47#11024
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
15. C22×#10625337C4semidirect
186. C22×Dic47Q16semidirect
413. C47#11024semidirect

Maximal subgroups

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

subgroupindex
C23×#106253372
C22×#130939492
C2×#156890302
C2×#156890282
C2×#156888852
C2×#156888772
C22×#103×C472
#1102447