Finite Group Databasebeta

← #26122788

Subgroups — #26122788

Order 12032.

1578 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094000C211yesmaximal, characteristic
2C22×#13093948C211yesmaximal, characteristic, complemented
3C22×(C2×D47)⋊C8C211yesmaximal, characteristic
4C2×#15688980C211yesmaximal, characteristic
5C2×#15688886C211yesmaximal, characteristic, complemented
6C2×#15688885C211yesmaximal, characteristic, complemented
7C22×#103×C47C211yesmaximal, characteristic, complemented
8C23×C4×D47C2211yescharacteristic
9C23×C47⋊C8C2211yescharacteristic
10C2×#13094000—22no—
11C2×#13094000—22no—
12C2×#13094000—22no—
13C2×#13094000—22no—
14C2×#13094000—22no—
15C2×#13094000C414yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×Dic47⋊C4—21no—
19C22×(C2×D47)⋊C4—21no—
20C22×(C2×D47)⋊C4—21no—
21C2×#13093948—22no—
22C2×#13093948—22no—
23C2×#13093948—22no—
24C2×(C2×D47)⋊C8—22no—
25C2×(C2×D47)⋊C8—22no—
26C2×(C2×D47)⋊C8—22no—
27#15688980—22no—
28#15688980—22no—
29C2×C47⋊#95—21no—
30#15688886—22no—
31#15688885—22no—
32C23×Q8×C47C2211yescharacteristic
33C23×C8×C47C2211yescharacteristic
34C22×C4⋊C4×C47C2211yescharacteristic
35C2×#103×C47—22no—
36C2×#103×C47—22no—
37C2×#103×C47—22no—
38C24×D47D411yescharacteristic
39C23×Dic47—21no—
40C23×Dic47—21no—
41C23×Dic47D411yescharacteristic
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×D47—21no—
49C22×C4×D47—21no—
50C22×C4×D47—21no—
51C22×C4×D47—21no—
52C22×C4×D47—21no—
53C22×C4×D47—21no—
54C22×C4×D47C2×C412yes—
55C22×C4×D47D412yes—
56C22×C47⋊C8—21no—
57C22×C47⋊C8—21no—
58C22×C47⋊C8—21no—
59C22×C47⋊C8—21no—
60C22×C47⋊C8—21no—
61C22×C47⋊C8—21no—
62C22×C47⋊C8D412yes—
63#13094000—28no—
64#13094000—28no—
65#13094000—28no—
66#13094000—28no—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47—21no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47C2×C412yes—
76C2×C4⋊Dic47D412yes—
77C2×C4⋊Dic47D412yes—
78C2×C4⋊Dic47D412yes—
79C2×Dic47⋊C4—24no—
80C2×Dic47⋊C4—24no—
81C2×Dic47⋊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—42no—
87C2×(C2×D47)⋊C4—42no—
88#13093948—28no—
89(C2×D47)⋊C8—28no—
90C47⋊#95—24no—
91C22×Q8×C47—21no—
92C22×Q8×C47—21no—
93C22×Q8×C47—21no—
94C22×Q8×C47—21no—
95C22×Q8×C47—21no—
96C22×Q8×C47—21no—
97C22×Q8×C47—21no—
98C22×Q8×C47—21no—
99C22×Q8×C47—21no—
100C22×Q8×C47—21no—
101C22×Q8×C47—21no—
102C22×Q8×C47C2×C412yes—
103C22×Q8×C47D412yes—
104C22×Q8×C47D412yes—
105C23×C4×C47—21no—
106C23×C4×C47—21no—
107C23×C4×C47C2311yescharacteristic
108C22×C8×C47—21no—
109C22×C8×C47—21no—
110C22×C8×C47—21no—
111C22×C8×C47—21no—
112C22×C8×C47—21no—
113C22×C8×C47—21no—
114C22×C8×C47D412yes—
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47—21no—
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47—21no—
120C2×C4⋊C4×C47D412yes—
121#103×C47—28no—
122C24×C47C2×D411yescharacteristic
123C23×D47—21no—
124C23×D47—21no—
125C23×D47—21no—
126C23×D47—21no—
127C23×D47—21no—
128C23×D47—21no—
129C23×D47—21no—
130C23×D47—21no—
131C23×D47—21no—
132C23×D47—21no—
133C23×D47—21no—
134C23×D47—21no—
135C23×D47C22⋊C412yes—
136C23×D47SD1612yes—
137C23×D47Q1612yes—
138C2×Q8×C47—22no—
139C2×Q8×C47—22no—
140C2×Q8×C47—22no—
141C2×Q8×C47—22no—
142C2×Q8×C47—22no—
143C2×Q8×C47—22no—
144C2×Q8×C47—22no—
145C2×Q8×C47—22no—
146C2×Q8×C47—22no—
147C2×Q8×C47—22no—
148C2×Q8×C47—22no—
149C2×Q8×C47—22no—
150C2×Q8×C47—22no—
151C2×Q8×C47—22no—
152C2×Q8×C47—22no—
153C2×Q8×C47—41no—
154C2×Q8×C47—41no—
155C2×Q8×C47—41no—
156C2×Q8×C47—41no—
157C2×Q8×C47—41no—
158C2×Q8×C47—41no—
159C2×Q8×C47—41no—
160C2×Q8×C47—41no—
161C2×Q8×C47—41no—
162C2×Q8×C47—41no—
163C2×Q8×C47—41no—
164C2×Q8×C47—41no—
165C2×Q8×C47C22⋊C414yescomplemented
166C22×C4×C47—22no—
167C22×C4×C47—22no—
168C22×C4×C47—22no—
169C22×C4×C47—22no—
170C22×C4×C47—41no—
171C22×C4×C47—41no—
172C22×C4×C47—41no—
173C22×C4×C47—41no—
174C22×C4×C47—41no—
175C22×C4×C47—41no—
176C22×C4×C47—41no—
177C22×C4×C47—41no—
178C22×C4×C47—41no—
179C22×C4×C47—41no—
180C22×C4×C47C22×C411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47#4111yescharacteristic
191C22×C4×C47#4111yescharacteristic
192C22×C4×C47#4111yescharacteristic
193C22×C4×C47#4111yescharacteristic
194C22×Dic47—22no—
195C22×Dic47—21no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—22no—
204C22×Dic47—41no—
205C22×Dic47—41no—
206C22×Dic47—41no—
207C22×Dic47—41no—
208C22×Dic47—41no—
209C22×Dic47—41no—
210C22×Dic47—41no—
211C22×Dic47—41no—
212C22×Dic47—41no—
213C22×Dic47—41no—
214C22×Dic47C22⋊C412yes—
215C2×C4×D47—22no—
216C2×C4×D47—22no—
217C2×C4×D47—22no—
218C2×C4×D47—22no—
219C2×C4×D47—22no—
220C2×C4×D47—22no—
221C2×C4×D47—22no—
222C2×C4×D47—22no—
223C2×C4×D47—22no—
224C2×C4×D47—22no—
225C2×C4×D47—22no—
226C2×C4×D47—22no—
227C2×C4×D47—41no—
228C2×C4×D47—41no—
229C2×C4×D47—41no—
230C2×C4×D47—41no—
231C2×C4×D47—41no—
232C2×C4×D47—41no—
233C2×C4×D47—41no—
234C2×C4×D47—41no—
235C2×C4×D47—41no—
236C2×C4×D47—41no—
237C2×C4×D47—41no—
238C2×C4×D47—41no—
239C2×C4×D47—41no—
240C2×C4×D47—41no—
241C2×C4×D47—41no—
242C2×C4×D47—41no—
243C2×C8×C47—22no—
244C2×C8×C47—22no—
245C2×C8×C47—22no—
246C2×C8×C47—41no—
247C2×C8×C47—41no—
248C2×C8×C47—41no—
249C2×C8×C47—41no—
250C4⋊C4×C47—22no—
251C4⋊C4×C47—22no—
252C4⋊C4×C47—41no—
253C4⋊C4×C47—41no—
254(C2×D47)⋊C4—216no—
255(C2×D47)⋊C4—48no—
256C4⋊Dic47—22no—
257C4⋊Dic47—22no—
258C4⋊Dic47—22no—
259C4⋊Dic47—22no—
260C4⋊Dic47—22no—
261C4⋊Dic47—41no—
262C4⋊Dic47—41no—
263C4⋊Dic47C22⋊C414yescomplemented
264Dic47⋊C4—216no—
265C2×C47⋊C8—22no—
266C2×C47⋊C8—22no—
267C2×C47⋊C8—22no—
268C2×C47⋊C8—41no—
269C2×C47⋊C8—41no—
270C2×C47⋊C8—41no—
271C2×C47⋊C8—41no—
272C23×C47C2×C22⋊C411yescharacteristic
273C23×C47#12011yescharacteristic
274C23×C47#12011yescharacteristic
275C23×C47#12011yescharacteristic
276C23×C47#12111yescharacteristic
277C23×C47#12111yescharacteristic
278C23×C47#12311yescharacteristic
279C23×C47C2×SD1611yescharacteristic
280C23×C47C2×Q1611yescharacteristic
281C23×C47#13511yescharacteristic
282C23×C47#13511yescharacteristic
283C23×C47AGL(1,ℤ/8)11yescharacteristic
284C23×C47#13711yescharacteristic
285C23×C47#13711yescharacteristic
286C23×C47#13711yescharacteristic
287C22×D47—22no—
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—22no—
301C22×D47—22no—
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—41no—
306C22×D47—41no—
307C22×D47—41no—
308C22×D47—41no—
309C22×D47—41no—
310C22×D47—41no—
311C22×D47—41no—
312C22×D47—41no—
313C22×D47—41no—
314C22×D47—41no—
315C22×D47—41no—
316C22×D47—41no—
317C22×D47—41no—
318C22×D47—41no—
319C22×D47—41no—
320C22×D47—41no—
321C22×D47#10314yescomplemented
322Q8×C47—24no—
323Q8×C47—24no—
324Q8×C47—42no—
325Q8×C47—42no—
326Q8×C47—42no—
327Q8×C47—42no—
328Q8×C47—42no—
329Q8×C47—42no—
330C2×C4×C47—24no—
331C2×C4×C47—42no—
332C2×C4×C47—42no—
333C2×C4×C47—42no—
334C2×C4×C47—42no—
335C2×C4×C47—42no—
336C2×C4×C47—42no—
337C2×C4×C47—42no—
338C2×C4×C47—42no—
339C2×C4×C47—42no—
340C2×C4×C47—81no—
341C2×C4×C47—81no—
342C2×C4×C47—81no—
343C2×C4×C47—81no—
344C2×C4×C47C2×C22⋊C411yescharacteristic
345C2×C4×C47C2×C22⋊C411yescharacteristic
346C2×C4×C47C4×D411yescharacteristic
347C2×C4×C47C4×D411yescharacteristic
348C2×C4×C47C4×D411yescharacteristic
349C2×C4×C47C4×D411yescharacteristic
350C2×C4×C47#12011yescharacteristic
351C2×C4×C47#12011yescharacteristic
352C2×C4×C47#12011yescharacteristic
353C2×C4×C47#12011yescharacteristic
354C2×C4×C47#12011yescharacteristic
355C2×C4×C47#12111yescharacteristic
356C2×C4×C47#12111yescharacteristic
357C2×C4×C47#12111yescharacteristic
358C2×C4×C47#12111yescharacteristic
359C2×C4×C47#12111yescharacteristic
360C2×C4×C47#12111yescharacteristic
361C2×C4×C47#12111yescharacteristic
362C2×C4×C47#12111yescharacteristic
363C2×C4×C47#12111yescharacteristic
364C2×C4×C47#12111yescharacteristic
365C2×C4×C47#12311yescharacteristic
366C2×C4×C47#12311yescharacteristic
367C2×C4×C47#12311yescharacteristic
368C2×C4×C47#12411yescharacteristic
369C2×C4×C47#12411yescharacteristic
370C2×C4×C47#12711yescharacteristic
371C2×C4×C47#12711yescharacteristic
372C2×Dic47—22no—
373C2×Dic47—24no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—41no—
377C2×Dic47—41no—
378C2×Dic47—41no—
379C2×Dic47—41no—
380C2×Dic47—42no—
381C2×Dic47—42no—
382C2×Dic47—42no—
383C2×Dic47—42no—
384C2×Dic47—42no—
385C2×Dic47—42no—
386C2×Dic47—42no—
387C2×Dic47—42no—
388C2×Dic47—42no—
389C2×Dic47—81no—
390C2×Dic47—81no—
391C2×Dic47—81no—
392C2×Dic47—81no—
393C4×D47—42no—
394C4×D47—42no—
395C4×D47—42no—
396C4×D47—42no—
397C4×D47—42no—
398C4×D47—42no—
399C4×D47—42no—
400C4×D47—42no—
401C8×C47—42no—
402C47⋊C8—42no—
403#10970—471nomaximal, Sylow
404C22×C47#37911yescharacteristic
405C22×C47#38611yescharacteristic
406C22×C47#38611yescharacteristic
407C22×C47#39211yescharacteristic
408C22×C47#39211yescharacteristic
409C22×C47#39411yescharacteristic
410C22×C47#39411yescharacteristic
411C22×C47C2×#10311yescharacteristic
412C22×C47#41611yescharacteristic
413C22×C47#41711yescharacteristic
414C22×C47#41911yescharacteristic
415C22×C47#44811yescharacteristic
416C22×C47#44811yescharacteristic
417C22×C47#44911yescharacteristic
418C22×C47#44911yescharacteristic
419C22×C47#45011yescharacteristic
420C22×C47#45111yescharacteristic
421C22×C47#45111yescharacteristic
422C22×C47#45111yescharacteristic
423C22×C47#45211yescharacteristic
424C22×C47#45211yescharacteristic
425C22×C47#45211yescharacteristic
426C22×C47#45211yescharacteristic
427C22×C47#46511yescharacteristic
428C22×C47#46511yescharacteristic
429C22×C47#46711yescharacteristic
430C22×C47#46711yescharacteristic
431C22×C47#46811yescharacteristic
432C22×C47#46811yescharacteristic
433C22×C47#47011yescharacteristic
434C22×C47#47011yescharacteristic
435C22×C47#48311yescharacteristic
436C22×C47#48411yescharacteristic
437C22×C47#48511yescharacteristic
438C22×C47#48511yescharacteristic
439C2×D47—24no—
440C2×D47—24no—
441C2×D47—24no—
442C2×D47—42no—
443C2×D47—42no—
444C2×D47—42no—
445C2×D47—42no—
446C2×D47—42no—
447C2×D47—42no—
448C2×D47—42no—
449C2×D47—42no—
450C2×D47—42no—
451C2×D47—42no—
452C2×D47—42no—
453C2×D47—42no—
454C4×C47—44no—
455C4×C47—82no—
456C4×C47#38611yescharacteristic
457C4×C47#38611yescharacteristic
458C4×C47#39011yescharacteristic
459C4×C47#39011yescharacteristic
460C4×C47#39211yescharacteristic
461C4×C47#39211yescharacteristic
462C4×C47#39411yescharacteristic
463C4×C47#39411yescharacteristic
464Dic47—42no—
465Dic47—44no—
466Dic47—82no—
467C22×C22⋊Q8—471no—
468C22×#103—471no—
469C22×#103D4711yescharacteristic, complemented
470C22×C22⋊C8—471no—
471C2×#380—471no—
472C2×#340—471no—
473C2×#340—471no—
474C2×C47#143811yescharacteristic
475C2×C47#178711yescharacteristic
476C2×C47#178811yescharacteristic
477C2×C47#187211yescharacteristic
478C2×C47#187311yescharacteristic
479C2×C47#189211yescharacteristic
480C2×C47#189411yescharacteristic
481C2×C47#200011yescharacteristic
482C2×C47#200011yescharacteristic
483C2×C47#200111yescharacteristic
484C2×C47#200111yescharacteristic
485C2×C47#203511yescharacteristic
486C2×C47#203511yescharacteristic
487C2×C47#203611yescharacteristic
488C2×C47#203611yescharacteristic
489D47—44no—
490C23×Q8C2×D4711yescharacteristic
491C24×C4—471no—
492C23×C8—471no—
493C23×C8C2×D4711yescharacteristic
494C2×C22⋊Q8—474no—
495C2×C22⋊Q8—942no—
496C2×C22⋊Q8—942no—
497C2×C22⋊Q8—942no—
498C2×C22⋊Q8—942no—
499C2×C22⋊Q8—942no—
500C22×C4⋊C4—471no—
501C22×C4⋊C4—471no—
502C22×C4⋊C4—941no—
503C22×C4⋊C4C2×D4711yescharacteristic
504C22×C22⋊C4—941no—
505C22×C22⋊C4—941no—
506C2×#103—22no—
507C2×#103—22no—
508C2×#103—22no—
509C2×#103—942no—
510C2×#103—942no—
511C2×#103—942no—
512C2×C22⋊C8—942no—
513C2×C22⋊C8—942no—
514C2×C22⋊C8—942no—
515#380—942no—
516#380—942no—
517C2×#95—941no—
518#340—942no—
519#340—942no—
520C47#1097011yescharacteristic, complemented, Sylow
521C25—471no—
522C22×Q8—21no—
523C22×Q8—21no—
524C22×Q8—21no—
525C22×Q8—21no—
526C22×Q8—21no—
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8—21no—
531C22×Q8—21no—
532C22×Q8—21no—
533C22×Q8C4×D4712yes—
534C22×Q8D18812yes—
535C22×Q8C22⋊D4712yes—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—471no—
539C23×C4—472no—
540C23×C4—472no—
541C23×C4—941no—
542C23×C4—941no—
543C23×C4—941no—
544C23×C4—941no—
545C23×C4—941no—
546C23×C4—941no—
547C23×C4—941no—
548C23×C4—941no—
549C23×C4—941no—
550C23×C4—941no—
551C23×C4—941no—
552C23×C4—941no—
553C23×C4—941no—
554C23×C4—941no—
555C23×C4C22×D4711yescharacteristic
556C22×C8—21no—
557C22×C8—21no—
558C22×C8—21no—
559C22×C8—21no—
560C22×C8—21no—
561C22×C8—21no—
562C22×C8—472no—
563C22×C8—941no—
564C22×C8—941no—
565C22×C8—941no—
566C22×C8—941no—
567C22×C8—941no—
568C22×C8—941no—
569C22×C8C22⋊D4712yes—
570C22⋊Q8—948no—
571C22⋊Q8—948no—
572C22⋊Q8—948no—
573C22⋊Q8—948no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—472no—
580C2×C4⋊C4—472no—
581C2×C4⋊C4—472no—
582C2×C4⋊C4—472no—
583C2×C4⋊C4—944no—
584C2×C4⋊C4—944no—
585C2×C4⋊C4—944no—
586C2×C4⋊C4—941no—
587C2×C4⋊C4—941no—
588C2×C4⋊C4—941no—
589C2×C4⋊C4—941no—
590C2×C4⋊C4—941no—
591C2×C4⋊C4—941no—
592C2×C4⋊C4—941no—
593C2×C4⋊C4—941no—
594C2×C4⋊C4C22⋊D4712yes—
595C2×C22⋊C4—944no—
596C2×C22⋊C4—944no—
597C2×C22⋊C4—944no—
598C2×C22⋊C4—944no—
599C2×C22⋊C4—1882no—
600C2×C22⋊C4—1882no—
601#103—28no—
602#103—948no—
603C22⋊C8—948no—
604#95—944no—
605C24—472no—
606C24—472no—
607C24—472no—
608C24—941no—
609C24—941no—
610C24—941no—
611C24—941no—
612C24—941no—
613C24—941no—
614C24—941no—
615C24—941no—
616C24—941no—
617C24—941no—
618C24—941no—
619C24—941no—
620C24D4×D4711yescharacteristic
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—41no—
637C2×Q8—41no—
638C2×Q8—41no—
639C2×Q8—41no—
640C2×Q8—41no—
641C2×Q8—41no—
642C2×Q8—41no—
643C2×Q8—41no—
644C2×Q8—41no—
645C2×Q8—41no—
646C2×Q8—41no—
647C2×Q8—41no—
648C2×Q8(C2×D47)⋊C414yescomplemented
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—41no—
663C22×C4—472no—
664C22×C4—942no—
665C22×C4—941no—
666C22×C4—942no—
667C22×C4—941no—
668C22×C4—942no—
669C22×C4—941no—
670C22×C4—941no—
671C22×C4—941no—
672C22×C4—941no—
673C22×C4—942no—
674C22×C4—942no—
675C22×C4—942no—
676C22×C4—942no—
677C22×C4—942no—
678C22×C4—942no—
679C22×C4—942no—
680C22×C4—942no—
681C22×C4—942no—
682C22×C4—942no—
683C22×C4—942no—
684C22×C4—942no—
685C22×C4—942no—
686C22×C4—1881no—
687C22×C4—1881no—
688C22×C4—1881no—
689C22×C4—1881no—
690C22×C4—1881no—
691C22×C4—1881no—
692C22×C4—1881no—
693C22×C4—1881no—
694C22×C4—1881no—
695C22×C4—1881no—
696C22×C4—1881no—
697C22×C4—1881no—
698C22×C4—1881no—
699C22×C4—1881no—
700C22×C4—1881no—
701C22×C4—1881no—
702C22×C4—1881no—
703C22×C4—1881no—
704C22×C4—1881no—
705C22×C4—1881no—
706C22×C4—1881no—
707C22×C4—1881no—
708C22×C4—1881no—
709C22×C4—1881no—
710C22×C4—1881no—
711C22×C4—1881no—
712C22×C4C2×C4×D4711yescharacteristic
713C22×C4C2×D18811yescharacteristic
714C22×C4#1062535011yescharacteristic
715C22×C4#1062535011yescharacteristic
716C22×C4D4×D4711yescharacteristic
717C22×C4D4×D4711yescharacteristic
718C22×C4D4×D4711yescharacteristic
719C22×C4D4×D4711yescharacteristic
720C22×C4D4×D4711yescharacteristic
721C22×C4#1062535211yescharacteristic
722C22×C4#1062535211yescharacteristic
723C22×C4C2×C22⋊D4711yescharacteristic
724C22×C4C2×C22⋊D4711yescharacteristic
725C22×C4C2×C22⋊D4711yescharacteristic
726C2×C8—22no—
727C2×C8—22no—
728C2×C8—22no—
729C2×C8—41no—
730C2×C8—41no—
731C2×C8—41no—
732C2×C8—41no—
733C2×C8—942no—
734C2×C8—942no—
735C2×C8—942no—
736C2×C8—1881no—
737C2×C8—1881no—
738C2×C8—1881no—
739C2×C8—1881no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—41no—
743C4⋊C4—41no—
744C4⋊C4—474no—
745C4⋊C4—9416no—
746C4⋊C4—942no—
747C4⋊C4—942no—
748C4⋊C4—942no—
749C4⋊C4—942no—
750C4⋊C4—942no—
751C4⋊C4—1881no—
752C4⋊C4—1881no—
753C22⋊C4—9416no—
754C22⋊C4—1888no—
755C23—474no—
756C23—942no—
757C23—942no—
758C23—942no—
759C23—942no—
760C23—942no—
761C23—942no—
762C23—942no—
763C23—942no—
764C23—942no—
765C23—942no—
766C23—942no—
767C23—942no—
768C23—942no—
769C23—942no—
770C23—942no—
771C23—942no—
772C23—942no—
773C23—942no—
774C23—1881no—
775C23—1881no—
776C23—1881no—
777C23—1881no—
778C23—1881no—
779C23—1881no—
780C23—1881no—
781C23—1881no—
782C23—1881no—
783C23—1881no—
784C23—1881no—
785C23—1881no—
786C23—1881no—
787C23—1881no—
788C23—1881no—
789C23—1881no—
790C23C22⋊C4×D4711yescharacteristic
791C23#1309399211yescharacteristic
792C23#1309399211yescharacteristic
793C23#1309399411yescharacteristic
794C23#1309399511yescharacteristic
795C23#1309399711yescharacteristic
796C23#1309400611yescharacteristic
797C23SD16×D4711yescharacteristic
798C23Q16×D4711yescharacteristic
799C23#1309404511yescharacteristic
800C23#1309404711yescharacteristic
801C23#1309405111yescharacteristic
802C23#1309405311yescharacteristic
803C23#1309405611yescharacteristic
804C23#1309405611yescharacteristic
805Q8—24no—
806Q8—24no—
807Q8—42no—
808Q8—42no—
809Q8—42no—
810Q8—42no—
811Q8—42no—
812Q8—42no—
813C2×C4—24no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—944no—
828C2×C4—942no—
829C2×C4—942no—
830C2×C4—942no—
831C2×C4—3761no—
832C2×C4—3761no—
833C2×C4—3761no—
834C2×C4—3761no—
835C2×C4—1882no—
836C2×C4—1882no—
837C2×C4—1882no—
838C2×C4—1882no—
839C2×C4—1882no—
840C2×C4—1882no—
841C2×C4—1881no—
842C2×C4—1881no—
843C2×C4—1882no—
844C2×C4—1881no—
845C2×C4—1881no—
846C2×C4—1882no—
847C2×C4—1882no—
848C2×C4—1882no—
849C2×C4—1882no—
850C2×C4—1882no—
851C2×C4—1882no—
852C2×C4—1882no—
853C2×C4—1882no—
854C2×C4—1882no—
855C2×C4—1882no—
856C2×C4C22⋊C4×D4711yescharacteristic
857C2×C4C2×(C2×D47)⋊C411yescharacteristic
858C2×C4(C22⋊D47)⋊C411yescharacteristic
859C2×C4(C22⋊D47)⋊C411yescharacteristic
860C2×C4C4×C22⋊D4711yescharacteristic
861C2×C4C4×C22⋊D4711yescharacteristic
862C2×C4#1309399211yescharacteristic
863C2×C4#1309399211yescharacteristic
864C2×C4#1309399311yescharacteristic
865C2×C4#1309399411yescharacteristic
866C2×C4#1309399411yescharacteristic
867C2×C4#1309399511yescharacteristic
868C2×C4#1309399611yescharacteristic
869C2×C4#1309399611yescharacteristic
870C2×C4#1309399611yescharacteristic
871C2×C4#1309399611yescharacteristic
872C2×C4#1309399711yescharacteristic
873C2×C4#1309399711yescharacteristic
874C2×C4#1309399711yescharacteristic
875C2×C4#1309399811yescharacteristic
876C2×C4#1309399811yescharacteristic
877C2×C4#1309400611yescharacteristic
878C2×C4#1309400711yescharacteristic
879C2×C4#1309400811yescharacteristic
880C2×C4#1309401011yescharacteristic
881C2×C4#1309401011yescharacteristic
882C2×C4#1309402011yescharacteristic
883C2×C4#1309402011yescharacteristic
884C8—42no—
885C8—1882no—
886C22—944no—
887C22—944no—
888C22—944no—
889C22—1882no—
890C22—1882no—
891C22—1882no—
892C22—1882no—
893C22—1882no—
894C22—1882no—
895C22—1882no—
896C22—1882no—
897C22—1882no—
898C22—1882no—
899C22—1882no—
900C22—1882no—
901C22#1568897811yescharacteristic
902C22#1568899911yescharacteristic
903C22#1568899911yescharacteristic
904C22#1568903111yescharacteristic
905C22#1568903211yescharacteristic
906C22#1568903811yescharacteristic
907C22#1568903911yescharacteristic
908C22#103×D4711yescharacteristic
909C22#1568911811yescharacteristic
910C22#1568912311yescharacteristic
911C22#1568913011yescharacteristic
912C22#1568926011yescharacteristic
913C22#1568926311yescharacteristic
914C22#1568926711yescharacteristic
915C22#1568927111yescharacteristic
916C22#1568927211yescharacteristic
917C22#1568927711yescharacteristic
918C22#1568927711yescharacteristic
919C22#1568928011yescharacteristic
920C22#1568928211yescharacteristic
921C22#1568928411yescharacteristic
922C22#1568928411yescharacteristic
923C22#1568928811yescharacteristic
924C22#1568934911yescharacteristic
925C22#1568935511yescharacteristic
926C22#1568936111yescharacteristic
927C22#1568936311yescharacteristic
928C22#1568936611yescharacteristic
929C22#1568937211yescharacteristic
930C22#1568937811yescharacteristic
931C22#1568938011yescharacteristic
932C22#1568945211yescharacteristic
933C22#1568945711yescharacteristic
934C22#1568946211yescharacteristic
935C22#1568946311yescharacteristic
936C4—44no—
937C4—82no—
938C4—3762no—
939C4—1884no—
940C4—1882no—
941C4#1568900011yescharacteristic
942C4#1568900211yescharacteristic
943C4#1568902311yescharacteristic
944C4#1568902311yescharacteristic
945C4#1568903111yescharacteristic
946C4#1568903211yescharacteristic
947C4#1568903811yescharacteristic
948C4#1568903911yescharacteristic
949C2—1884no—
950C2#2024162711yescharacteristic
951C2#2024332111yescharacteristic
952C2#2024332711yescharacteristic
953C2#2024369211yescharacteristic
954C2#2024369711yescharacteristic
955C2#2024380811yescharacteristic
956C2#2024381811yescharacteristic
957C2#2024438811yescharacteristic
958C2#2024439011yescharacteristic
959C2#2024439511yescharacteristic
960C2#2024439711yescharacteristic
961C2#2024458211yescharacteristic
962C2#2024458311yescharacteristic
963C2#2024458911yescharacteristic
964C2#2024459011yescharacteristic
subgroupG/H
centerC24D4×D47
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC22×#103×C47C2
socleC24×C47C2×D4
prime radicalC24×D47D4
cosocleC23×C4×C47C23
hypercenterC22×#103D47
hypocenterC47#10970
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
2. C22×#13093948C2semidirect
5. C2×#15688886C2semidirect
6. C2×#15688885C2semidirect
7. C22×#103×C47C2semidirect
15. C2×#13094000C4semidirect
165. C2×Q8×C47C22⋊C4semidirect
263. C4⋊Dic47C22⋊C4semidirect
321. C22×D47#103semidirect
469. C22×#103D47semidirect
520. C47#10970semidirect
648. C2×Q8(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130940002
C22×#130939482
C22×(C2×D47)⋊C82
C2×#156889802
C2×#156888862
C2×#156888852
C22×#103×C472
#1097047