Finite Group Databasebeta

← #26139423

Subgroups — #26139423

Order 12032.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093998C211yesmaximal, characteristic
2C2×#15689025C211yesmaximal, characteristic, complemented
3C2×#15689025C211yesmaximal, characteristic, complemented
4C2×#15689023C212yesmaximal, complemented
5C2×#15689021C211yesmaximal, characteristic, complemented
6C2×#15688983C211yesmaximal, characteristic, complemented
7C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
8#20241632C212yesmaximal, complemented
9#20241627C212yesmaximal, complemented
10#20241624C212yesmaximal, complemented
11C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
12C23×D188C2211yescharacteristic
13C23×C22⋊D47C2212yes—
14C2×#13093998—24no—
15C2×#13093998—24no—
16C2×#13093998C418yescomplemented
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C4⋊Dic47C2211yescharacteristic
19C22×C4⋊Dic47C2211yescharacteristic
20C22×Dic47⋊C4C2212yes—
21C22×C22⋊Dic47C2212yes—
22C22×(C2×D47)⋊C4C2212yes—
23C22×(C2×D47)⋊C4C2212yes—
24C22×(C2×D47)⋊C4C2212yes—
25C22×(C2×D47)⋊C4C2212yes—
26C22×(C2×D47)⋊C4C2212yes—
27C22×C4×Dic47C2212yes—
28#15689025—24no—
29#15689025—24no—
30#15689023—28no—
31#15689021—24no—
32#15688983—24no—
33C4×C4⋊Dic47—24no—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C2×C47⋊#95C2212yes—
37C24×C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2211yescharacteristic
39C22×C22⋊C4×C47C2211yescharacteristic
40C22×C42×C47C2211yescharacteristic
41C22×C42×C47C2211yescharacteristic
42C4×C22⋊C4×C47—24no—
43C2×#95×C47C2211yescharacteristic
44C2×#95×C47C2211yescharacteristic
45C24×D47C2312yes—
46C22×D188—22no—
47C22×D188—22no—
48C22×D188—22no—
49C22×D188—22no—
50C22×D188—22no—
51C22×D188—22no—
52C22×D188C2×C414yes—
53C22×C22⋊D47—24no—
54C22×C22⋊D47—24no—
55C22×C22⋊D47—24no—
56C22×C22⋊D47—24no—
57C22×C22⋊D47—42no—
58C22×C22⋊D47—42no—
59C22×C22⋊D47C2×C418yes—
60C23×Dic47C2312yes—
61C23×Dic47C2312yes—
62C23×Dic47C2312yes—
63#13093998—232no—
64C2×C4⋊Dic47—22no—
65C2×C4⋊Dic47—22no—
66C2×C4⋊Dic47—22no—
67C2×C4⋊Dic47—22no—
68C2×C4⋊Dic47—22no—
69C2×C4⋊Dic47C2×C414yes—
70C2×C4⋊Dic47D414yes—
71C2×C4⋊Dic47D414yes—
72C2×C4⋊Dic47D414yescomplemented
73C2×Dic47⋊C4—24no—
74C2×Dic47⋊C4—24no—
75C2×Dic47⋊C4—42no—
76C2×C22⋊Dic47—24no—
77C2×C22⋊Dic47—24no—
78C2×C22⋊Dic47—42no—
79C2×(C2×D47)⋊C4—24no—
80C2×(C2×D47)⋊C4—24no—
81C2×(C2×D47)⋊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—24no—
87C2×(C2×D47)⋊C4—24no—
88C2×(C2×D47)⋊C4—24no—
89C2×(C2×D47)⋊C4—42no—
90C2×(C2×D47)⋊C4—42no—
91C2×(C2×D47)⋊C4—42no—
92C2×(C2×D47)⋊C4—42no—
93C2×(C2×D47)⋊C4C2×C418yes—
94C2×C4×Dic47—24no—
95C2×C4×Dic47—24no—
96C2×C4×Dic47—42no—
97C47⋊#95—24no—
98C47⋊#95—24no—
99C47⋊#95—24no—
100C25×C47C2311yescharacteristic
101C23×C4×C47—22no—
102C23×C4×C47—22no—
103C23×C4×C47—22no—
104C23×C4×C47—22no—
105C23×C4×C47—22no—
106C23×C4×C47—22no—
107C23×C4×C47C2×C414yes—
108C23×C4×C47C2311yescharacteristic
109C23×C4×C47C2311yescharacteristic
110C23×C4×C47C2311yescharacteristic
111C23×C4×C47C2311yescharacteristic
112C23×C4×C47C2311yescharacteristic
113C23×C4×C47C2311yescharacteristic
114C2×C22⋊C4×C47—22no—
115C2×C22⋊C4×C47—22no—
116C2×C22⋊C4×C47—22no—
117C2×C22⋊C4×C47—22no—
118C2×C22⋊C4×C47—22no—
119C2×C22⋊C4×C47D414yescomplemented
120C2×C42×C47—22no—
121C2×C42×C47—22no—
122C2×C42×C47—22no—
123C2×C42×C47—22no—
124C2×C42×C47—22no—
125C2×C42×C47D414yescomplemented
126#95×C47—22no—
127#95×C47—22no—
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×C47—21no—
137C24×C47—21no—
138C24×C47—21no—
139C24×C47—21no—
140C24×C47C22×C412yes—
141C24×C47C2×D412yes—
142C24×C47#4112yes—
143C24×C47C2411yescharacteristic
144C23×D47—22no—
145C23×D47—22no—
146C23×D47—22no—
147C23×D47—22no—
148C23×D47—22no—
149C23×D47—22no—
150C23×D47—22no—
151C23×D47—22no—
152C23×D47—22no—
153C23×D47—22no—
154C23×D47—22no—
155C23×D47—22no—
156C23×D47—22no—
157C23×D47—22no—
158C23×D47C22×C414yes—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—28no—
188C22×C4×C47—28no—
189C22×C4×C47—28no—
190C22×C4×C47—44no—
191C22×C4×C47—44no—
192C22×C4×C47—44no—
193C22×C4×C47—44no—
194C22×C4×C47C22×C412yes—
195C22×C4×C47C22×C412yes—
196C22×C4×C47C2×D412yes—
197C22×C4×C47C2×D412yes—
198C22×C4×C47C2×D412yes—
199C22×C4×C47C2×D412yes—
200C22×C4×C47C2×D412yes—
201C22×C4×C47C2×D412yes—
202C22×C4×C47C2×D412yes—
203C22×C4×C47C2×D412yes—
204C22×C4×C47#4112yes—
205C22×C4×C47#4112yes—
206C22×C4×C47#4112yes—
207C22×C4×C47#4112yes—
208C2×C22⋊D47—216no—
209C2×C22⋊D47—216no—
210C2×C22⋊D47—48no—
211C2×C22⋊D47—48no—
212C2×C22⋊D47—48no—
213C2×C22⋊D47—48no—
214C2×C22⋊D47—48no—
215C22×Dic47—22no—
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×Dic47—22no—
225C22×Dic47—22no—
226C22×Dic47—22no—
227C22×Dic47—22no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—22no—
231C22×Dic47—22no—
232C22×Dic47C22×C414yes—
233C22×Dic47C2×D414yes—
234C22×Dic47C2×D414yes—
235C22×Dic47C2×D414yes—
236C2×D188—28no—
237C2×D188—28no—
238C2×D188—28no—
239C2×D188—44no—
240C2×D188—44no—
241C2×D188—44no—
242C2×D188—44no—
243C22⋊C4×C47—28no—
244C22⋊C4×C47—28no—
245C42×C47—28no—
246C42×C47—44no—
247C22⋊Dic47—48no—
248(C2×D47)⋊C4—216no—
249(C2×D47)⋊C4—48no—
250(C2×D47)⋊C4—48no—
251(C2×D47)⋊C4—48no—
252(C2×D47)⋊C4—48no—
253C4⋊Dic47—28no—
254C4⋊Dic47—44no—
255C4⋊Dic47C22⋊C4116yescomplemented
256Dic47⋊C4—48no—
257C4×Dic47—48no—
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—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
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—41no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47—41no—
291C23×C47—41no—
292C23×C47C4×D414yes—
293C23×C47C23×C411yescharacteristic
294C23×C47C22×D411yescharacteristic
295C23×C47C22×D411yescharacteristic
296C23×C47C22×D411yescharacteristic
297C23×C47C22×D411yescharacteristic
298C23×C47C22×D411yescharacteristic
299C23×C47C2×#4111yescharacteristic
300C23×C47C2×#4111yescharacteristic
301C23×C47C2×#4111yescharacteristic
302C23×C47C2×#4111yescharacteristic
303C23×C47C2×#4111yescharacteristic
304C23×C47H(5,𝔽2)11yescharacteristic
305C23×C47H(5,𝔽2)11yescharacteristic
306C23×C47H(5,𝔽2)11yescharacteristic
307C23×C472−1+411yescharacteristic
308C22×D47—24no—
309C22×D47—24no—
310C22×D47—24no—
311C22×D47—24no—
312C22×D47—24no—
313C22×D47—24no—
314C22×D47—24no—
315C22×D47—42no—
316C22×D47—42no—
317C22×D47—42no—
318C22×D47—42no—
319C22×D47—42no—
320C22×D47—42no—
321C22×D47—42no—
322C22×D47—42no—
323C22×D47—42no—
324C22×D47—42no—
325C22×D47—42no—
326C22×D47—42no—
327C22×D47—42no—
328C22×D47—42no—
329C22×D47—42no—
330C22×D47—42no—
331C22×D47—42no—
332C22×D47—42no—
333C22×D47—42no—
334C22×D47—42no—
335C22×D47—42no—
336C22×D47—42no—
337C22×D47—42no—
338C22×D47—42no—
339C22×D47—42no—
340C22×D47—42no—
341C22×D47—42no—
342C22×D47—42no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—22no—
351C2×C4×C47—22no—
352C2×C4×C47—22no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—41no—
362C2×C4×C47—41no—
363C2×C4×C47—41no—
364C2×C4×C47—41no—
365C2×C4×C47—41no—
366C2×C4×C47—41no—
367C2×C4×C47—41no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—416no—
378C2×C4×C47C2×C22⋊C414yes—
379C2×C4×C47C4×D414yes—
380C2×C4×C47C4×D414yes—
381C2×C4×C47#12114yes—
382C2×C4×C47#12114yes—
383C2×C4×C47#12114yescomplemented
384C2×C4×C47#12414yes—
385C2×C4×C47#12714yes—
386C22⋊D47—432no—
387C2×Dic47—24no—
388C2×Dic47—24no—
389C2×Dic47—24no—
390C2×Dic47—24no—
391C2×Dic47—24no—
392C2×Dic47—24no—
393C2×Dic47—24no—
394C2×Dic47—24no—
395C2×Dic47—24no—
396C2×Dic47—42no—
397C2×Dic47—42no—
398C2×Dic47—42no—
399C2×Dic47—42no—
400C2×Dic47—42no—
401C2×Dic47—42no—
402C2×Dic47—42no—
403C2×Dic47—42no—
404C2×Dic47—42no—
405C2×Dic47—42no—
406C2×Dic47—42no—
407C2×Dic47C2×C22⋊C418yes—
408D188—416no—
409#13998—471nomaximal, Sylow
410C22×C47—24no—
411C22×C47—24no—
412C22×C47—24no—
413C22×C47—42no—
414C22×C47—42no—
415C22×C47—42no—
416C22×C47—42no—
417C22×C47—42no—
418C22×C47—42no—
419C22×C47—42no—
420C22×C47—42no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47—42no—
425C22×C47C22×C22⋊C411yescharacteristic
426C22×C47C2×C4×D411yescharacteristic
427C22×C47C2×C4×D411yescharacteristic
428C22×C47C2×C4×D411yescharacteristic
429C22×C47C4×#4111yescharacteristic
430C22×C47#51811yescharacteristic
431C22×C47#52011yescharacteristic
432C22×C47C2×#12111yescharacteristic
433C22×C47C2×#12111yescharacteristic
434C22×C47C2×#12111yescharacteristic
435C22×C47#52511yescharacteristic
436C22×C47C2×#12411yescharacteristic
437C22×C47#52911yescharacteristic
438C22×C47C2×#12711yescharacteristic
439C22×C47#53211yescharacteristic
440C22×C47#53511yescharacteristic
441C22×C47#53711yescharacteristic
442C22×C47#54011yescharacteristic
443C22×C47#54211yescharacteristic
444C22×C47D4211yescharacteristic
445C22×C47D4211yescharacteristic
446C22×C47D4211yescharacteristic
447C22×C47#54611yescharacteristic
448C22×C47#54611yescharacteristic
449C22×C47#54611yescharacteristic
450C22×C47#54711yescharacteristic
451C22×C47#54811yescharacteristic
452C22×C47#54811yescharacteristic
453C22×C47#54811yescharacteristic
454C22×C47#55011yescharacteristic
455C22×C47#55011yescharacteristic
456C22×C47#55011yescharacteristic
457C22×C47#55311yescharacteristic
458C22×C47#55311yescharacteristic
459C22×C47#55511yescharacteristic
460C2×D47—44no—
461C2×D47—44no—
462C2×D47—44no—
463C2×D47—44no—
464C2×D47—44no—
465C2×D47—44no—
466C2×D47—44no—
467C2×D47—82no—
468C2×D47—82no—
469C2×D47—82no—
470C2×D47—82no—
471C2×D47—82no—
472C2×D47—82no—
473C2×D47—82no—
474C2×D47—82no—
475C4×C47—24no—
476C4×C47—42no—
477C4×C47—42no—
478C4×C47—42no—
479C4×C47—42no—
480C4×C47#39018yescomplemented
481Dic47—28no—
482Dic47—44no—
483Dic47—82no—
484C22×#121—471no—
485C2×#390—471no—
486C2×#390—471no—
487C2×#390—472no—
488C2×#389—471no—
489C2×#380—471no—
490C2×C4×C4⋊C4—471no—
491C2×C4×C22⋊C4D4711yescharacteristic, complemented
492#1439—472no—
493#1438—472no—
494#1437—472no—
495C2×C47—44no—
496C2×C47C2×#39011yescharacteristic
497C2×C47C4×#12111yescharacteristic
498C2×C47#232411yescharacteristic
499C2×C47D4×C22⋊C411yescharacteristic
500C2×C47#234111yescharacteristic
501C2×C47#236111yescharacteristic
502C2×C47#236311yescharacteristic
503C2×C47#241411yescharacteristic
504C2×C47#241611yescharacteristic
505C2×C47#242611yescharacteristic
506C2×C47#242811yescharacteristic
507C2×C47#249011yescharacteristic
508C2×C47#249111yescharacteristic
509C2×C47#254011yescharacteristic
510C2×C47#254111yescharacteristic
511D47—84no—
512C23×D4—472no—
513C23×D4—471no—
514C24×C4C2×D4711yescharacteristic
515C2×#121—478no—
516C2×#121—944no—
517C2×#121—944no—
518C22×C4⋊C4—471no—
519C22×C4⋊C4—471no—
520C22×C4⋊C4—471no—
521C22×C4⋊C4—472no—
522C22×C22⋊C4—472no—
523C22×C22⋊C4—472no—
524C22×C22⋊C4—472no—
525C22×C22⋊C4—472no—
526C22×C22⋊C4—472no—
527C22×C22⋊C4—472no—
528C22×C22⋊C4C2×D4711yescharacteristic
529C22×C22⋊C4C2×D4711yescharacteristic
530C22×C42—472no—
531C22×C42C2×D4711yescharacteristic
532C22×C42C2×D4711yescharacteristic
533#390—944no—
534#390—948no—
535#390—944no—
536#389—944no—
537#380—944no—
538C4×C4⋊C4—944no—
539C4×C22⋊C4—24no—
540C2×#95—472no—
541C2×#95—472no—
542C2×#95—472no—
543C2×#95C2×D4711yescharacteristic
544C2×#95C2×D4711yescharacteristic
545C47#1399811yescharacteristic, complemented, Sylow
546C25—472no—
547C25C22×D4711yescharacteristic
548C22×D4—478no—
549C22×D4—474no—
550C22×D4—944no—
551C22×D4—944no—
552C22×D4—944no—
553C22×D4—944no—
554C22×D4—942no—
555C22×D4—942no—
556C22×D4—942no—
557C22×D4—942no—
558C22×D4—942no—
559C22×D4—942no—
560C22×D4—1882no—
561C22×D4—1882no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—472no—
569C23×C4—472no—
570C23×C4—472no—
571C23×C4C4×D4714yes—
572C23×C4C22×D4711yescharacteristic
573C23×C4C22×D4711yescharacteristic
574C23×C4C22×D4711yescharacteristic
575C23×C4C22×D4711yescharacteristic
576C23×C4C22×D4711yescharacteristic
577C23×C4C22×D4711yescharacteristic
578#121—9432no—
579C2×C4⋊C4—474no—
580C2×C4⋊C4—474no—
581C2×C4⋊C4—474no—
582C2×C4⋊C4—474no—
583C2×C4⋊C4—942no—
584C2×C4⋊C4—942no—
585C2×C4⋊C4—944no—
586C2×C4⋊C4—944no—
587C2×C4⋊C4—942no—
588C2×C4⋊C4—942no—
589C2×C4⋊C4—942no—
590C2×C4⋊C4—1882no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—478no—
597C2×C22⋊C4—944no—
598C2×C22⋊C4—944no—
599C2×C22⋊C4—944no—
600C2×C22⋊C4—944no—
601C2×C22⋊C4—944no—
602C2×C22⋊C4—944no—
603C2×C22⋊C4—944no—
604C2×C22⋊C4—944no—
605C2×C22⋊C4—944no—
606C2×C22⋊C4—944no—
607C2×C22⋊C4—944no—
608C2×C22⋊C4—944no—
609C2×C22⋊C4—1882no—
610C2×C22⋊C4—1882no—
611C2×C22⋊C4—1882no—
612C2×C22⋊C4—1882no—
613C2×C22⋊C4—1882no—
614C2×C22⋊C4D18814yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618C2×C42—22no—
619C2×C42—22no—
620C2×C42—944no—
621C2×C42—944no—
622C2×C42—1882no—
623C2×C42C22⋊D4714yescomplemented
624#95—22no—
625#95—22no—
626#95—944no—
627#95—944no—
628#95—944no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—474no—
642C24—942no—
643C24—942no—
644C24—942no—
645C24—942no—
646C24—942no—
647C24—942no—
648C24—942no—
649C24—942no—
650C24—942no—
651C24—942no—
652C24—942no—
653C24—942no—
654C24—942no—
655C24—942no—
656C24C2×C4×D4712yes—
657C24C2×D18812yes—
658C24#1062535012yes—
659C24C23×D4711yescharacteristic
660C2×D4—9416no—
661C2×D4—9416no—
662C2×D4—948no—
663C2×D4—948no—
664C2×D4—948no—
665C2×D4—1888no—
666C2×D4—1888no—
667C2×D4—1888no—
668C2×D4—1888no—
669C2×D4—1888no—
670C2×D4—1884no—
671C2×D4—1884no—
672C2×D4—1884no—
673C2×D4—1884no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—474no—
710C22×C4—474no—
711C22×C4—474no—
712C22×C4—474no—
713C22×C4—942no—
714C22×C4—942no—
715C22×C4—942no—
716C22×C4—942no—
717C22×C4—942no—
718C22×C4—942no—
719C22×C4—942no—
720C22×C4—942no—
721C22×C4—942no—
722C22×C4—942no—
723C22×C4—942no—
724C22×C4—942no—
725C22×C4—942no—
726C22×C4—942no—
727C22×C4—942no—
728C22×C4—942no—
729C22×C4—942no—
730C22×C4C2×C4×D4712yes—
731C22×C4C2×C4×D4712yes—
732C22×C4C2×D18812yes—
733C22×C4C2×D18812yes—
734C22×C4#1062535012yes—
735C22×C4#1062535012yes—
736C22×C4#1062535012yes—
737C22×C4D4×D4712yes—
738C22×C4D4×D4712yes—
739C22×C4D4×D4712yes—
740C22×C4#1062535212yes—
741C22×C4C2×C22⋊D4712yes—
742C22×C4C2×C22⋊D4712yes—
743C22×C4C2×C22⋊D4712yes—
744C4⋊C4—4716no—
745C4⋊C4—948no—
746C4⋊C4—1888no—
747C4⋊C4—1884no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—9416no—
751C22⋊C4—1888no—
752C22⋊C4—1888no—
753C22⋊C4—1888no—
754C22⋊C4—1888no—
755C22⋊C4—1888no—
756C42—28no—
757C42—44no—
758C42—1888no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—944no—
794C23—944no—
795C23—944no—
796C23—944no—
797C23—944no—
798C23—944no—
799C23—944no—
800C23—1882no—
801C23—1882no—
802C23—1882no—
803C23—1882no—
804C23—1882no—
805C23—1882no—
806C23—1882no—
807C23—1882no—
808C23—1882no—
809C23—1882no—
810C23—1882no—
811C23—1882no—
812C23—1882no—
813C23—1882no—
814C23—1882no—
815C23—1882no—
816C23—1882no—
817C23—1882no—
818C23—1882no—
819C23—1882no—
820C23—1882no—
821C23—1882no—
822C23—1882no—
823C23—1882no—
824C23—1882no—
825C23—1882no—
826C23—1882no—
827C23—1882no—
828C23C4×D18814yes—
829C23C22×C4×D4711yescharacteristic
830C23C2×D4×D4711yescharacteristic
831C23C2×D4×D4711yescharacteristic
832C23C2×D4×D4711yescharacteristic
833C23C22×C22⋊D4711yescharacteristic
834C23C22×D18811yescharacteristic
835C23C2×#1062535211yescharacteristic
836C23C2×#1062535011yescharacteristic
837C23C2×#1062535011yescharacteristic
838C23C2×#1062535011yescharacteristic
839C23C2×#1062535011yescharacteristic
840C23#1309407011yescharacteristic
841C23#1309407011yescharacteristic
842C23#1309407011yescharacteristic
843C23#1309407111yescharacteristic
844D4—18832no—
845D4—18816no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—416no—
881C2×C4—478no—
882C2×C4—944no—
883C2×C4—944no—
884C2×C4—944no—
885C2×C4—944no—
886C2×C4—944no—
887C2×C4—944no—
888C2×C4—944no—
889C2×C4—944no—
890C2×C4—944no—
891C2×C4—1882no—
892C2×C4—1882no—
893C2×C4—1882no—
894C2×C4—1882no—
895C2×C4—1882no—
896C2×C4—1882no—
897C2×C4—1882no—
898C2×C4—1882no—
899C2×C4—1882no—
900C2×C4—1882no—
901C2×C4—1882no—
902C2×C4C22⋊C4×D4714yes—
903C2×C4(C22⋊D47)⋊C414yes—
904C2×C4C4×C22⋊D4714yes—
905C2×C4#1309399614yes—
906C2×C4#1309399714yes—
907C2×C4#1309399814yescomplemented
908C2×C4#1309401014yes—
909C2×C4#1309402014yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—3762no—
926C22—3762no—
927C22—3762no—
928C22—3762no—
929C22—3762no—
930C22—3762no—
931C22—3762no—
932C22—3762no—
933C22—1884no—
934C22—1884no—
935C22—1884no—
936C22—1884no—
937C22—1884no—
938C22—1884no—
939C22—1884no—
940C22C2×C22⋊C4×D4711yescharacteristic
941C22C2×(C22⋊D47)⋊C411yescharacteristic
942C22C2×C4×C22⋊D4711yescharacteristic
943C22C2×C4×D18811yescharacteristic
944C22C4×#1062535011yescharacteristic
945C22#1568959711yescharacteristic
946C22#1568960311yescharacteristic
947C22C2×#1309399611yescharacteristic
948C22C2×#1309399711yescharacteristic
949C22C2×#1309399811yescharacteristic
950C22#1568963411yescharacteristic
951C22C2×#1309401011yescharacteristic
952C22#1568965711yescharacteristic
953C22C2×#1309402011yescharacteristic
954C22#1568967311yescharacteristic
955C22#1568968711yescharacteristic
956C22#1568970111yescharacteristic
957C22#1568972811yescharacteristic
958C22#1568974411yescharacteristic
959C22D4×D18811yescharacteristic
960C22D4×D18811yescharacteristic
961C22D4×D18811yescharacteristic
962C22#1568976911yescharacteristic
963C22#1568976911yescharacteristic
964C22#1568976911yescharacteristic
965C22#1568977711yescharacteristic
966C22#1568978211yescharacteristic
967C22#1568978211yescharacteristic
968C22#1568978211yescharacteristic
969C22#1568979411yescharacteristic
970C22#1568979411yescharacteristic
971C22#1568979411yescharacteristic
972C22#1568981911yescharacteristic
973C22#1568981911yescharacteristic
974C22#1568983811yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—948no—
981C4—3762no—
982C4—1884no—
983C4#1568902318yescomplemented
984C2—44no—
985C2—3764no—
986C2C2×#1568902311yescharacteristic
987C2C4×#1309399811yescharacteristic
988C2#2024608111yescharacteristic
989C2C22⋊C4×D18811yescharacteristic
990C2#2024622811yescharacteristic
991C2#2024640211yescharacteristic
992C2#2024642411yescharacteristic
993C2#2024680611yescharacteristic
994C2#2024682811yescharacteristic
995C2#2024695411yescharacteristic
996C2#2024697611yescharacteristic
997C2#2024774011yescharacteristic
998C2#2024775111yescharacteristic
999C2#2024832711yescharacteristic
1000C2#2024833411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C4×C22⋊C4×C47C2
socle, cosocleC24×C47C24
prime radicalC22×#13093998C2
hypercenterC2×C4×C22⋊C4D47
hypocenterC47#13998
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15689025C2semidirect
3. C2×#15689025C2semidirect
4. C2×#15689023C2semidirect
5. C2×#15689021C2semidirect
6. C2×#15688983C2semidirect
7. C2×C4×C4⋊Dic47C2semidirect
8. #20241632C2semidirect
9. #20241627C2semidirect
10. #20241624C2semidirect
11. C2×C4×C22⋊C4×C47C2semidirect
16. C2×#13093998C4semidirect
72. C2×C4⋊Dic47D4semidirect
119. C2×C22⋊C4×C47D4semidirect
125. C2×C42×C47D4semidirect
255. C4⋊Dic47C22⋊C4semidirect
383. C2×C4×C47#121semidirect
480. C4×C47#390semidirect
491. C2×C4×C22⋊C4D47semidirect
545. C47#13998semidirect
614. C2×C22⋊C4D188semidirect
623. C2×C42C22⋊D47semidirect
907. C2×C4#13093998semidirect
983. C4#15689023semidirect

Maximal subgroups

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

subgroupindex
C22×#130939982
C2×#156890252
C2×#156890232
C2×#156890212
C2×#156889832
C2×C4×C4⋊Dic472
#202416322
#202416272
#202416242
C2×C4×C22⋊C4×C472
#1399847