Finite Group Databasebeta

← #26138174

Subgroups — #26138174

Order 12032.

2590 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C22×#13093982C211yesmaximal, characteristic, complemented
3C2×#15688983C211yesmaximal, characteristic, complemented
4C2×#15688980C211yesmaximal, characteristic, complemented
5#20241636C212yesmaximal, complemented
6#20241627C212yesmaximal
7#20241625C212yesmaximal, complemented
8#20241619C212yesmaximal, complemented
9#20241617C211yesmaximal, characteristic, complemented
10#20241617C211yesmaximal, characteristic, complemented
11C2×C47×#380C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C23×C4×D47C2211yescharacteristic
14C2×C4×C22⋊D47—24no—
15C2×C4×C22⋊D47—24no—
16C2×C4×C22⋊D47C418yescomplemented
17C2×#13093982—24no—
18C2×#13093982—24no—
19C2×#13093982—24no—
20C22×C4⋊Dic47C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22C22×Dic47⋊C4C2211yescharacteristic
23C22×C22⋊Dic47C2212yes—
24C22×C22⋊Dic47C2211yescharacteristic
25C22×(C2×D47)⋊C4C2212yes—
26C22×(C2×D47)⋊C4C2211yescharacteristic
27C22×(C2×D47)⋊C4C2212yes—
28C22×C4×Dic47C2212yes—
29C22×C4×Dic47C2211yescharacteristic
30#15688983—24no—
31#15688980—24no—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C2×C47⋊#95C2212yes—
38C24×C4×C47C2211yescharacteristic
39C22×C4⋊C4×C47C2211yescharacteristic
40C22×C4⋊C4×C47C2211yescharacteristic
41C22×C22⋊C4×C47C2212yes—
42C47×#380—24no—
43C2×#95×C47C2212yes—
44C24×D47C2311yescharacteristic
45C22×C22⋊D47—22no—
46C22×C22⋊D47—22no—
47C22×C22⋊D47—22no—
48C22×C22⋊D47—22no—
49C22×C22⋊D47—22no—
50C22×C22⋊D47—22no—
51C22×C22⋊D47C2×C414yes—
52C23×Dic47C2312yes—
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2312yes—
55C23×Dic47C2311yescharacteristic
56C23×Dic47C2311yescharacteristic
57C22×C4×D47—22no—
58C22×C4×D47—22no—
59C22×C4×D47—22no—
60C22×C4×D47—22no—
61C22×C4×D47C2×C414yes—
62C22×C4×D47D414yes—
63C22×C4×D47D414yes—
64C4×C22⋊D47—232no—
65#13093982—232no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47—22no—
69C2×C4⋊Dic47—22no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47D414yescomplemented
72C2×Dic47⋊C4—22no—
73C2×Dic47⋊C4—22no—
74C2×Dic47⋊C4C2×C414yes—
75C2×C22⋊Dic47—22no—
76C2×C22⋊Dic47—22no—
77C2×C22⋊Dic47—24no—
78C2×C22⋊Dic47—24no—
79C2×C22⋊Dic47—42no—
80C2×C22⋊Dic47C2×C414yes—
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—42no—
88C2×(C2×D47)⋊C4—42no—
89C2×(C2×D47)⋊C4C2×C414yes—
90C2×C4×Dic47—24no—
91C2×C4×Dic47—22no—
92C2×C4×Dic47—22no—
93C2×C4×Dic47—24no—
94C2×C4×Dic47—24no—
95C2×C4×Dic47C2×C414yes—
96C47⋊#95—24no—
97C47⋊#95—24no—
98C47⋊#95—24no—
99C47⋊#95—24no—
100C47⋊#95—42no—
101C47⋊#95—42no—
102C25×C47C2311yescharacteristic
103C23×C4×C47—22no—
104C23×C4×C47—22no—
105C23×C4×C47—22no—
106C23×C4×C47—22no—
107C23×C4×C47—22no—
108C23×C4×C47—22no—
109C23×C4×C47C2×C414yes—
110C23×C4×C47C2312yes—
111C23×C4×C47C2311yescharacteristic
112C23×C4×C47C2312yes—
113C23×C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47—22no—
115C2×C4⋊C4×C47—22no—
116C2×C4⋊C4×C47—22no—
117C2×C4⋊C4×C47—22no—
118C2×C4⋊C4×C47—22no—
119C2×C4⋊C4×C47D414yescomplemented
120C2×C22⋊C4×C47—24no—
121C2×C22⋊C4×C47—24no—
122C2×C22⋊C4×C47—42no—
123#95×C47—24no—
124C24×C47—21no—
125C24×C47—21no—
126C24×C47—21no—
127C24×C47—21no—
128C24×C47—21no—
129C24×C47—21no—
130C24×C47—21no—
131C24×C47—21no—
132C24×C47—21no—
133C24×C47—21no—
134C24×C47—21no—
135C24×C47—21no—
136C24×C47C22×C412yes—
137C24×C47#4112yes—
138C24×C47#4112yes—
139C24×C47C2411yescharacteristic
140C23×D47—21no—
141C23×D47—21no—
142C23×D47—21no—
143C23×D47—21no—
144C23×D47—21no—
145C23×D47—21no—
146C23×D47—21no—
147C23×D47—21no—
148C23×D47—21no—
149C23×D47—21no—
150C23×D47—21no—
151C23×D47—21no—
152C23×D47C22×C412yes—
153C23×D47C2×D412yes—
154C23×D47C2×D412yes—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—21no—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—22no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—22no—
165C22×C4×C47—22no—
166C22×C4×C47—22no—
167C22×C4×C47—28no—
168C22×C4×C47—28no—
169C22×C4×C47—28no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—44no—
178C22×C4×C47—44no—
179C22×C4×C47—44no—
180C22×C4×C47—44no—
181C22×C4×C47C22×C412yes—
182C22×C4×C47C22×C412yes—
183C22×C4×C47C2×D414yes—
184C22×C4×C47C2×D412yes—
185C22×C4×C47C2×D412yes—
186C22×C4×C47C2×D412yes—
187C22×C4×C47C2×D412yes—
188C22×C4×C47#4112yes—
189C22×C4×C47#4112yes—
190C2×C22⋊D47—28no—
191C2×C22⋊D47—28no—
192C2×C22⋊D47—28no—
193C2×C22⋊D47—28no—
194C2×C22⋊D47—28no—
195C2×C22⋊D47—28no—
196C2×C22⋊D47—28no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—21no—
206C22×Dic47—21no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—21no—
212C22×Dic47—21no—
213C22×Dic47—22no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—22no—
220C22×Dic47—22no—
221C22×Dic47—22no—
222C22×Dic47—22no—
223C22×Dic47—22no—
224C22×Dic47C22×C412yes—
225C22×Dic47C22×C412yes—
226C22×Dic47C22×C412yes—
227C22×Dic47C2×D414yes—
228C22×Dic47C2×D412yes—
229C22×Dic47C2×D412yes—
230C22×Dic47#4112yes—
231C22×Dic47#4112yes—
232C2×C4×D47—28no—
233C2×C4×D47—28no—
234C2×C4×D47—28no—
235C2×C4×D47—28no—
236C2×C4×D47—28no—
237C2×C4×D47—28no—
238C2×C4×D47C22⋊C4116yescomplemented
239C4⋊C4×C47—28no—
240C4⋊C4×C47—44no—
241C22⋊C4×C47—48no—
242C22⋊Dic47—28no—
243C22⋊Dic47—48no—
244(C2×D47)⋊C4—216no—
245(C2×D47)⋊C4—28no—
246(C2×D47)⋊C4—48no—
247C4⋊Dic47—28no—
248C4⋊Dic47—44no—
249Dic47⋊C4—28no—
250C4×Dic47—216no—
251C4×Dic47—28no—
252C23×C47—22no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—22no—
261C23×C47—22no—
262C23×C47—22no—
263C23×C47—22no—
264C23×C47—22no—
265C23×C47—22no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—41no—
271C23×C47—41no—
272C23×C47—41no—
273C23×C47—41no—
274C23×C47—41no—
275C23×C47—41no—
276C23×C47—41no—
277C23×C47—41no—
278C23×C47—41no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—41no—
282C23×C47—41no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—41no—
286C23×C47#11714yescomplemented
287C23×C47C23×C411yescharacteristic
288C23×C47C22×D411yescharacteristic
289C23×C47C22×D411yescharacteristic
290C23×C47C22×D411yescharacteristic
291C23×C47C22×D411yescharacteristic
292C23×C47C2×#4111yescharacteristic
293C23×C47C2×#4111yescharacteristic
294C23×C47C2×#4111yescharacteristic
295C23×C47C2×#4111yescharacteristic
296C23×C47C2×#4111yescharacteristic
297C23×C47C2×#4111yescharacteristic
298C23×C47H(5,𝔽2)11yescharacteristic
299C23×C47H(5,𝔽2)11yescharacteristic
300C23×C472−1+411yescharacteristic
301C23×C472−1+411yescharacteristic
302C22×D47—22no—
303C22×D47—22no—
304C22×D47—22no—
305C22×D47—22no—
306C22×D47—22no—
307C22×D47—22no—
308C22×D47—22no—
309C22×D47—22no—
310C22×D47—22no—
311C22×D47—22no—
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—22no—
320C22×D47—41no—
321C22×D47—41no—
322C22×D47—41no—
323C22×D47—41no—
324C22×D47—41no—
325C22×D47—41no—
326C22×D47—41no—
327C22×D47—41no—
328C22×D47—41no—
329C22×D47—41no—
330C22×D47—41no—
331C22×D47—41no—
332C22×D47—41no—
333C22×D47—41no—
334C22×D47—41no—
335C22×D47—41no—
336C22×D47C2×C22⋊C414yes—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—24no—
341C2×C4×C47—24no—
342C2×C4×C47—24no—
343C2×C4×C47—41no—
344C2×C4×C47—41no—
345C2×C4×C47—41no—
346C2×C4×C47—41no—
347C2×C4×C47—42no—
348C2×C4×C47—42no—
349C2×C4×C47—42no—
350C2×C4×C47—42no—
351C2×C4×C47—416no—
352C2×C4×C47—42no—
353C2×C4×C47—42no—
354C2×C4×C47—42no—
355C2×C4×C47—42no—
356C2×C4×C47—42no—
357C2×C4×C47—42no—
358C2×C4×C47—42no—
359C2×C4×C47C2×C22⋊C414yes—
360C2×C4×C47C4×D414yes—
361C2×C4×C47C4×D414yes—
362C2×C4×C47#12014yes—
363C2×C4×C47#12114yes—
364C2×C4×C47#12114yes—
365C2×C4×C47#12314yes—
366C22⋊D47—232no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—22no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—22no—
378C2×Dic47—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—22no—
382C2×Dic47—24no—
383C2×Dic47—24no—
384C2×Dic47—24no—
385C2×Dic47—42no—
386C2×Dic47—41no—
387C2×Dic47—41no—
388C2×Dic47—41no—
389C2×Dic47—41no—
390C2×Dic47—42no—
391C2×Dic47—42no—
392C2×Dic47—42no—
393C2×Dic47—42no—
394C2×Dic47—42no—
395C2×Dic47—42no—
396C2×Dic47—42no—
397C2×Dic47—42no—
398C2×Dic47—42no—
399C2×Dic47—42no—
400C2×Dic47C2×C22⋊C414yes—
401C2×Dic47#11714yescomplemented
402C4×D47—232no—
403#13871—471nomaximal, Sylow
404C22×C47—24no—
405C22×C47—24no—
406C22×C47—24no—
407C22×C47—42no—
408C22×C47—42no—
409C22×C47—42no—
410C22×C47—42no—
411C22×C47—42no—
412C22×C47—42no—
413C22×C47—42no—
414C22×C47—42no—
415C22×C47—42no—
416C22×C47—42no—
417C22×C47—42no—
418C22×C47—42no—
419C22×C47C22×C22⋊C411yescharacteristic
420C22×C47C2×#11711yescharacteristic
421C22×C47C2×#11711yescharacteristic
422C22×C47C2×C4×D411yescharacteristic
423C22×C47C2×C4×D411yescharacteristic
424C22×C47#52011yescharacteristic
425C22×C47#52011yescharacteristic
426C22×C47C2×#12011yescharacteristic
427C22×C47C2×#12111yescharacteristic
428C22×C47C2×#12111yescharacteristic
429C22×C47C2×#12311yescharacteristic
430C22×C47#52511yescharacteristic
431C22×C47#52511yescharacteristic
432C22×C47#52511yescharacteristic
433C22×C47#52511yescharacteristic
434C22×C47#53511yescharacteristic
435C22×C47#53611yescharacteristic
436C22×C47#53711yescharacteristic
437C22×C47#53711yescharacteristic
438C22×C47#54611yescharacteristic
439C22×C47#54611yescharacteristic
440C22×C47#54711yescharacteristic
441C22×C47#54711yescharacteristic
442C22×C47#54811yescharacteristic
443C22×C47#54811yescharacteristic
444C22×C47#55011yescharacteristic
445C22×C47#55011yescharacteristic
446C22×C47#55211yescharacteristic
447C22×C47#55211yescharacteristic
448C22×C47#55311yescharacteristic
449C22×C47#55311yescharacteristic
450C22×C47#55511yescharacteristic
451C22×C47#55511yescharacteristic
452C22×C47#55611yescharacteristic
453C22×C47#55611yescharacteristic
454C2×D47—24no—
455C2×D47—24no—
456C2×D47—24no—
457C2×D47—42no—
458C2×D47—42no—
459C2×D47—42no—
460C2×D47—42no—
461C2×D47—42no—
462C2×D47—42no—
463C2×D47—42no—
464C2×D47—42no—
465C2×D47—42no—
466C2×D47—42no—
467C2×D47—42no—
468C2×D47—42no—
469C4×C47—44no—
470C4×C47—42no—
471C4×C47—82no—
472C4×C47#38618yes—
473Dic47—24no—
474Dic47—24no—
475Dic47—42no—
476Dic47—44no—
477Dic47—82no—
478C22×C4×D4—471no—
479C22×#117—471no—
480C2×#380—471no—
481C2×#380—471no—
482C2×#380D4711yescharacteristic, complemented
483#1440—472no—
484#1438—472no—
485#1437—472no—
486#1436—472no—
487C4⋊#95—471no—
488C4⋊#95—471no—
489C2×C47—44no—
490C2×C47#228011yescharacteristic
491C2×C47C2×#38611yescharacteristic
492C2×C47#231111yescharacteristic
493C2×C47#235211yescharacteristic
494C2×C47#235211yescharacteristic
495C2×C47#235411yescharacteristic
496C2×C47#235411yescharacteristic
497C2×C47#240711yescharacteristic
498C2×C47#240711yescharacteristic
499C2×C47#241411yescharacteristic
500C2×C47#241411yescharacteristic
501C2×C47#241511yescharacteristic
502C2×C47#241511yescharacteristic
503C2×C47#248511yescharacteristic
504C2×C47#248511yescharacteristic
505D47—44no—
506C23×D4—471no—
507C24×C4—471no—
508C24×C4C2×D4711yescharacteristic
509C2×C4×D4—478no—
510C2×C4×D4—944no—
511C2×C4×D4—944no—
512C2×#117—944no—
513C2×#117—944no—
514C2×#117—944no—
515C22×C4⋊C4—471no—
516C22×C4⋊C4—471no—
517C22×C4⋊C4—471no—
518C22×C4⋊C4C2×D4711yescharacteristic
519C22×C4⋊C4C2×D4711yescharacteristic
520C22×C22⋊C4—471no—
521C22×C22⋊C4—471no—
522C22×C22⋊C4—472no—
523C22×C22⋊C4—472no—
524C22×C22⋊C4—472no—
525C22×C22⋊C4C2×D4712yes—
526C22×C42—471no—
527C22×C42—472no—
528#380—24no—
529#380—944no—
530#380—944no—
531C2×#95—472no—
532C2×#95—472no—
533C2×#95—472no—
534C2×#95—472no—
535C2×#95—472no—
536C2×#95—472no—
537C2×#95C2×D4712yes—
538C47#1387111yescharacteristic, complemented, Sylow
539C25—471no—
540C25C22×D4711yescharacteristic
541C22×D4—474no—
542C22×D4—942no—
543C22×D4—942no—
544C22×D4—942no—
545C22×D4—942no—
546C22×D4—942no—
547C22×D4—942no—
548C23×C4—22no—
549C23×C4—22no—
550C23×C4—22no—
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—471no—
555C23×C4—471no—
556C23×C4—474no—
557C23×C4—474no—
558C23×C4—474no—
559C23×C4—472no—
560C23×C4—471no—
561C23×C4—472no—
562C23×C4—942no—
563C23×C4—942no—
564C23×C4—942no—
565C23×C4—942no—
566C23×C4C4×D4714yes—
567C23×C4C22×D4712yes—
568C23×C4C22×D4711yescharacteristic
569C23×C4C22×D4712yes—
570C23×C4C22×D4711yescharacteristic
571C4×D4—9432no—
572#117—9432no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—474no—
579C2×C4⋊C4—474no—
580C2×C4⋊C4—942no—
581C2×C4⋊C4—942no—
582C2×C4⋊C4—942no—
583C2×C4⋊C4—942no—
584C2×C4⋊C4—942no—
585C2×C4⋊C4—942no—
586C2×C4⋊C4—942no—
587C2×C4⋊C4C22⋊D4714yescomplemented
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—474no—
592C2×C22⋊C4—474no—
593C2×C22⋊C4—944no—
594C2×C22⋊C4—944no—
595C2×C22⋊C4—942no—
596C2×C22⋊C4—942no—
597C2×C22⋊C4—942no—
598C2×C22⋊C4—942no—
599C2×C22⋊C4—944no—
600C2×C22⋊C4—944no—
601C2×C22⋊C4—944no—
602C2×C22⋊C4—944no—
603C2×C22⋊C4—1882no—
604C2×C22⋊C4—1882no—
605C2×C22⋊C4—1882no—
606C2×C42—474no—
607C2×C42—944no—
608C2×C42—944no—
609C2×C42—942no—
610C2×C42—942no—
611C2×C42—944no—
612#95—24no—
613#95—944no—
614#95—944no—
615#95—944no—
616#95—944no—
617#95—1882no—
618#95—1882no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—472no—
632C24—472no—
633C24—472no—
634C24—941no—
635C24—941no—
636C24—941no—
637C24—941no—
638C24—941no—
639C24—941no—
640C24—941no—
641C24—941no—
642C24—941no—
643C24—941no—
644C24—941no—
645C24—941no—
646C24C2×C4×D4712yes—
647C24#1062535212yes—
648C24#1062535412yes—
649C24C23×D4711yescharacteristic
650C2×D4—948no—
651C2×D4—948no—
652C2×D4—948no—
653C2×D4—948no—
654C2×D4—948no—
655C2×D4—948no—
656C2×D4—948no—
657C22×C4—21no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—28no—
670C22×C4—28no—
671C22×C4—28no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—472no—
684C22×C4—472no—
685C22×C4—472no—
686C22×C4—472no—
687C22×C4—472no—
688C22×C4—472no—
689C22×C4—4716no—
690C22×C4—472no—
691C22×C4—474no—
692C22×C4—941no—
693C22×C4—941no—
694C22×C4—941no—
695C22×C4—941no—
696C22×C4—941no—
697C22×C4—941no—
698C22×C4—941no—
699C22×C4—941no—
700C22×C4—948no—
701C22×C4—948no—
702C22×C4—948no—
703C22×C4—948no—
704C22×C4—948no—
705C22×C4—948no—
706C22×C4—941no—
707C22×C4—941no—
708C22×C4—942no—
709C22×C4—942no—
710C22×C4—942no—
711C22×C4—942no—
712C22×C4—941no—
713C22×C4—941no—
714C22×C4—942no—
715C22×C4—941no—
716C22×C4—942no—
717C22×C4—941no—
718C22×C4—942no—
719C22×C4—942no—
720C22×C4—942no—
721C22×C4—942no—
722C22×C4—942no—
723C22×C4—942no—
724C22×C4—942no—
725C22×C4C2×C4×D4712yes—
726C22×C4C2×C4×D4712yes—
727C22×C4#1062535012yes—
728C22×C4D4×D4712yes—
729C22×C4D4×D4712yes—
730C22×C4D4×D4712yes—
731C22×C4#1062535212yes—
732C22×C4C2×C22⋊D4714yes—
733C22×C4C2×C22⋊D4712yes—
734C4⋊C4—28no—
735C4⋊C4—44no—
736C4⋊C4—948no—
737C4⋊C4—948no—
738C4⋊C4—1884no—
739C22⋊C4—48no—
740C22⋊C4—948no—
741C22⋊C4—9416no—
742C22⋊C4—948no—
743C22⋊C4—1888no—
744C22⋊C4—1888no—
745C42—9416no—
746C42—948no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—474no—
782C23—942no—
783C23—942no—
784C23—942no—
785C23—942no—
786C23—942no—
787C23—942no—
788C23—942no—
789C23—942no—
790C23—942no—
791C23—942no—
792C23—942no—
793C23—942no—
794C23—942no—
795C23—942no—
796C23—942no—
797C23—942no—
798C23—942no—
799C23—942no—
800C23—1881no—
801C23—1881no—
802C23—1881no—
803C23—1881no—
804C23—1881no—
805C23—1881no—
806C23—1881no—
807C23—1881no—
808C23—1881no—
809C23—1881no—
810C23—1881no—
811C23—1881no—
812C23—1881no—
813C23—1881no—
814C23—1881no—
815C23—1881no—
816C23#1309398214yescomplemented
817C23C22×C4×D4711yescharacteristic
818C23C2×D4×D4711yescharacteristic
819C23C2×D4×D4711yescharacteristic
820C23C2×D4×D4711yescharacteristic
821C23C22×C22⋊D4711yescharacteristic
822C23#41×D4711yescharacteristic
823C23#41×D4711yescharacteristic
824C23C2×#1062535211yescharacteristic
825C23C2×#1062535211yescharacteristic
826C23C2×#1062535011yescharacteristic
827C23C2×#1062535411yescharacteristic
828C23#1309406911yescharacteristic
829C23#1309407011yescharacteristic
830C23#1309407111yescharacteristic
831C23#1309407211yescharacteristic
832D4—9432no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—24no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—416no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—474no—
856C2×C4—474no—
857C2×C4—942no—
858C2×C4—942no—
859C2×C4—942no—
860C2×C4—942no—
861C2×C4—942no—
862C2×C4—942no—
863C2×C4—942no—
864C2×C4—942no—
865C2×C4—942no—
866C2×C4—942no—
867C2×C4—942no—
868C2×C4—942no—
869C2×C4—9432no—
870C2×C4—944no—
871C2×C4—944no—
872C2×C4—942no—
873C2×C4—942no—
874C2×C4—942no—
875C2×C4—944no—
876C2×C4—1882no—
877C2×C4—1882no—
878C2×C4—1882no—
879C2×C4—1882no—
880C2×C4—1882no—
881C2×C4—1882no—
882C2×C4—1882no—
883C2×C4—1882no—
884C2×C4—1882no—
885C2×C4—1882no—
886C2×C4—1881no—
887C2×C4—1881no—
888C2×C4—1881no—
889C2×C4—1882no—
890C2×C4—1881no—
891C2×C4C22⋊C4×D4714yes—
892C2×C4(C22⋊D47)⋊C414yes—
893C2×C4C4×C22⋊D4714yes—
894C2×C4#1309399214yes—
895C2×C4#1309399514yes—
896C2×C4#1309399714yes—
897C2×C4#1309400614yes—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—944no—
914C22—944no—
915C22—944no—
916C22—1882no—
917C22—1882no—
918C22—1882no—
919C22—1882no—
920C22—1882no—
921C22—1882no—
922C22—1882no—
923C22—1882no—
924C22—1882no—
925C22—1882no—
926C22—1882no—
927C22—1882no—
928C22C2×C22⋊C4×D4711yescharacteristic
929C22#117×D4711yescharacteristic
930C22C2×#1309398211yescharacteristic
931C22C2×(C22⋊D47)⋊C411yescharacteristic
932C22C2×C4×C22⋊D4711yescharacteristic
933C22#1568960311yescharacteristic
934C22#1568960411yescharacteristic
935C22C2×#1309399211yescharacteristic
936C22C2×#1309399511yescharacteristic
937C22C2×#1309399711yescharacteristic
938C22C2×#1309400611yescharacteristic
939C22#1568963311yescharacteristic
940C22#1568963311yescharacteristic
941C22#1568963611yescharacteristic
942C22#1568963611yescharacteristic
943C22#1568968911yescharacteristic
944C22#1568969611yescharacteristic
945C22#1568970211yescharacteristic
946C22#1568970311yescharacteristic
947C22#1568976411yescharacteristic
948C22#1568976711yescharacteristic
949C22#1568977211yescharacteristic
950C22#1568977511yescharacteristic
951C22#1568977911yescharacteristic
952C22#1568978411yescharacteristic
953C22#1568979111yescharacteristic
954C22#1568979211yescharacteristic
955C22#1568980811yescharacteristic
956C22#1568981511yescharacteristic
957C22#1568982111yescharacteristic
958C22#1568982511yescharacteristic
959C22#1568983611yescharacteristic
960C22#1568983711yescharacteristic
961C22#1568984111yescharacteristic
962C22#1568984411yescharacteristic
963C4—42no—
964C4—44no—
965C4—82no—
966C4—944no—
967C4—944no—
968C4—3762no—
969C4—1884no—
970C4—1882no—
971C4#1568899918yes—
972C2—44no—
973C2—1884no—
974C2#2024577011yescharacteristic
975C2C2×#1568899911yescharacteristic
976C2#2024597711yescharacteristic
977C2#2024631311yescharacteristic
978C2#2024631911yescharacteristic
979C2#2024633211yescharacteristic
980C2#2024633811yescharacteristic
981C2#2024672911yescharacteristic
982C2#2024673511yescharacteristic
983C2#2024680211yescharacteristic
984C2#2024680811yescharacteristic
985C2#2024681311yescharacteristic
986C2#2024681911yescharacteristic
987C2#2024768111yescharacteristic
988C2#2024768711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#380C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC2×#380D47
hypocenterC47#13871
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#13093982C2semidirect
3. C2×#15688983C2semidirect
4. C2×#15688980C2semidirect
5. #20241636C2semidirect
7. #20241625C2semidirect
8. #20241619C2semidirect
9. #20241617C2semidirect
10. #20241617C2semidirect
11. C2×C47×#380C2semidirect
16. C2×C4×C22⋊D47C4semidirect
71. C2×C4⋊Dic47D4semidirect
119. C2×C4⋊C4×C47D4semidirect
238. C2×C4×D47C22⋊C4semidirect
286. C23×C47#117semidirect
401. C2×Dic47#117semidirect
482. C2×#380D47semidirect
538. C47#13871semidirect
587. C2×C4⋊C4C22⋊D47semidirect
816. C23#13093982semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C22×#130939822
C2×#156889832
C2×#156889802
#202416362
#202416272
#202416252
#202416192
#202416172
C2×C47×#3802
#1387147