Finite Group Databasebeta

← C2×#20247636 #26383892

Subgroups — C2×#20247636 #26383892

Order 12032.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094019C211yesmaximal, characteristic, complemented
2C23×(C2×D47)⋊C4C211yesmaximal, characteristic
3#20247636C2116yesmaximal, direct product factor
4C2×#15689052C211yesmaximal, characteristic, complemented
5C2×#15689050C211yesmaximal, characteristic, complemented
6C2×#15689049C211yesmaximal, characteristic, complemented
7C2×#15689045C211yesmaximal, characteristic, complemented
8C2×#15689015C211yesmaximal, characteristic, complemented
9C2×#15689013C211yesmaximal, characteristic, complemented
10C2×#15689012C211yesmaximal, characteristic, complemented
11C2×#15688998C211yesmaximal, characteristic, complemented
12C2×#15688981C211yesmaximal, characteristic, complemented
13C2×#15688978C211yesmaximal, characteristic
14C2×#15688978C211yesmaximal, characteristic
15C2×C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C2×#13094019—28no—
20C2×#13094019C2218yescomplemented
21C22×C4⋊Dic47C2211yescharacteristic, complemented
22C22×C4⋊Dic47C2211yescharacteristic, complemented
23C22×Dic47⋊C4C2211yescharacteristic, complemented
24C22×Dic47⋊C4C2211yescharacteristic, complemented
25C22×C22⋊Dic47C2211yescharacteristic
26C22×C22⋊Dic47C2211yescharacteristic
27C22×(C2×D47)⋊C4—28no—
28C22×(C2×D47)⋊C4C2211yescharacteristic
29C22×(C2×D47)⋊C4C2211yescharacteristic
30C22×(C2×D47)⋊C4C2218yes—
31C22×(C2×D47)⋊C4C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic, complemented
42C22×C4×Dic47C2211yescharacteristic, complemented
43#15689052C2218yescomplemented
44#15689050C2218yescomplemented
45#15689049C2218yescomplemented
46#15689045C2218yescomplemented
47#15689015C2218yescomplemented
48#15689013C2218yescomplemented
49#15689012C2218yescomplemented
50#15688998C2218yescomplemented
51#15688981C2218yescomplemented
52#15688978C2218yes—
53#15688978C2218yes—
54C4×C22⋊Dic47C2218yescomplemented
55C2×C47⋊#95C2211yescharacteristic, complemented
56C2×C47⋊#95C2211yescharacteristic, complemented
57C2×C47⋊#95C2211yescharacteristic, complemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C24×C4×C47C2211yescharacteristic
62C22×C4⋊C4×C47C2211yescharacteristic, complemented
63C22×C4⋊C4×C47C2211yescharacteristic, complemented
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C47×#385C2218yescomplemented
67C2×#95×C47C2211yescharacteristic, complemented
68C2×#95×C47C2211yescharacteristic, complemented
69C24×D47—24no—
70C24×D47—24no—
71C24×D47—24no—
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—42no—
75C24×D47—42no—
76C24×D47C2311yescharacteristic
77C24×D47C2311yescharacteristic
78C24×D47C2314yes—
79C23×Dic47—24no—
80C23×Dic47—24no—
81C23×Dic47—42no—
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2314yes—
88C23×Dic47C2311yescharacteristic
89#13094019—232no—
90C2×C4⋊Dic47—24no—
91C2×C4⋊Dic47—42no—
92C2×C4⋊Dic47C2314yescomplemented
93C2×C4⋊Dic47C2314yescomplemented
94C2×Dic47⋊C4—24no—
95C2×Dic47⋊C4—42no—
96C2×Dic47⋊C4C2314yescomplemented
97C2×Dic47⋊C4C2314yescomplemented
98C2×C22⋊Dic47—24no—
99C2×C22⋊Dic47—24no—
100C2×C22⋊Dic47C2314yes—
101C2×C22⋊Dic47C2314yes—
102C2×(C2×D47)⋊C4—24no—
103C2×(C2×D47)⋊C4—24no—
104C2×(C2×D47)⋊C4—24no—
105C2×(C2×D47)⋊C4—24no—
106C2×(C2×D47)⋊C4—24no—
107C2×(C2×D47)⋊C4—24no—
108C2×(C2×D47)⋊C4—24no—
109C2×(C2×D47)⋊C4—232no—
110C2×(C2×D47)⋊C4—42no—
111C2×(C2×D47)⋊C4—42no—
112C2×(C2×D47)⋊C4—42no—
113C2×(C2×D47)⋊C4—42no—
114C2×(C2×D47)⋊C4D418yes—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×(C2×D47)⋊C4C2314yes—
127C2×C4×Dic47—24no—
128C2×C4×Dic47—42no—
129C2×C4×Dic47C2314yescomplemented
130C2×C4×Dic47C2314yescomplemented
131C47⋊#95C2314yescomplemented
132C47⋊#95C2314yescomplemented
133C47⋊#95C2314yescomplemented
134C47⋊#95C2314yescomplemented
135C47⋊#95C2314yescomplemented
136C47⋊#95C2314yescomplemented
137C25×C47C2311yescharacteristic
138C23×C4×C47—24no—
139C23×C4×C47—24no—
140C23×C4×C47—42no—
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C23×C4×C47C2314yes—
147C23×C4×C47C2311yescharacteristic
148C2×C4⋊C4×C47—24no—
149C2×C4⋊C4×C47—42no—
150C2×C4⋊C4×C47C2314yescomplemented
151C2×C4⋊C4×C47C2314yescomplemented
152C2×C22⋊C4×C47—24no—
153C2×C22⋊C4×C47—24no—
154C2×C22⋊C4×C47C2314yes—
155C2×C22⋊C4×C47C2314yes—
156#95×C47C2314yescomplemented
157#95×C47C2314yescomplemented
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47#4114yes—
163C24×C47#4114yes—
164C24×C47#4114yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C23×D47—232no—
168C23×D47—22no—
169C23×D47—28no—
170C23×D47—22no—
171C23×D47—22no—
172C23×D47—22no—
173C23×D47—22no—
174C23×D47—22no—
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—28no—
182C23×D47—28no—
183C23×D47—28no—
184C23×D47—28no—
185C23×D47—44no—
186C23×D47—44no—
187C23×D47—416no—
188C23×D47—416no—
189C23×D47—416no—
190C23×D47—416no—
191C23×D47—416no—
192C23×D47—416no—
193C23×D47C2×D414yes—
194C23×D47#4114yes—
195C23×D47C2412yes—
196C23×D47C2412yes—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—22no—
203C22×C4×C47—22no—
204C22×C4×C47—22no—
205C22×C4×C47—22no—
206C22×C4×C47—28no—
207C22×C4×C47—22no—
208C22×C4×C47—22no—
209C22×C4×C47—22no—
210C22×C4×C47—22no—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—28no—
216C22×C4×C47—44no—
217C22×C4×C47—416no—
218C22×C4×C47C2×D414yes—
219C22×C4×C47C2412yes—
220C22×C4×C47C2412yes—
221C22×C4×C47C2412yes—
222C22×C4×C47C2412yes—
223C22×C4×C47C2412yes—
224C22×C4×C47C2412yes—
225C22×Dic47—22no—
226C22×Dic47—22no—
227C22×Dic47—22no—
228C22×Dic47—22no—
229C22×Dic47—22no—
230C22×Dic47—22no—
231C22×Dic47—22no—
232C22×Dic47—22no—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—28no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—28no—
244C22×Dic47—44no—
245C22×Dic47—416no—
246C22×Dic47C2×D414yes—
247C22×Dic47C2412yes—
248C22×Dic47C2412yes—
249C22×Dic47C2412yes—
250C22×Dic47C2412yes—
251C22×Dic47C2412yes—
252C22×Dic47C2412yes—
253C4⋊C4×C47—28no—
254C4⋊C4×C47—44no—
255C22⋊C4×C47—28no—
256C22⋊C4×C47—28no—
257C22⋊Dic47—28no—
258C22⋊Dic47—28no—
259(C2×D47)⋊C4—28no—
260(C2×D47)⋊C4—28no—
261(C2×D47)⋊C4—28no—
262(C2×D47)⋊C4—28no—
263(C2×D47)⋊C4—28no—
264(C2×D47)⋊C4—28no—
265(C2×D47)⋊C4—28no—
266(C2×D47)⋊C4—44no—
267(C2×D47)⋊C4—44no—
268(C2×D47)⋊C4—44no—
269(C2×D47)⋊C4—44no—
270(C2×D47)⋊C4C2×D4116yes—
271C4⋊Dic47—28no—
272C4⋊Dic47—44no—
273Dic47⋊C4—28no—
274Dic47⋊C4—44no—
275C4×Dic47—28no—
276C4×Dic47—44no—
277C23×C47—28no—
278C23×C47—28no—
279C23×C47—28no—
280C23×C47—28no—
281C23×C47—28no—
282C23×C47—28no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—22no—
287C23×C47#126116yescomplemented
288C23×C47C22×D412yes—
289C23×C47C2×#4112yes—
290C23×C47C2×#4114yes—
291C23×C47C2×#4112yes—
292C23×C47C2×#4114yes—
293C23×C47C2×#4112yes—
294C23×C47C2×#4114yes—
295C23×C47C2×#4112yes—
296C23×C47H(5,𝔽2)12yes—
297C23×C47H(5,𝔽2)12yes—
298C23×C47C2511yescharacteristic
299C22×D47—232no—
300C22×D47—28no—
301C22×D47—28no—
302C22×D47—28no—
303C22×D47—28no—
304C22×D47—28no—
305C22×D47—28no—
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—416no—
319C22×D47—416no—
320C22×D47—416no—
321C22×D47—416no—
322C22×D47—416no—
323C22×D47—4128no—
324C22×D47—44no—
325C22×D47—44no—
326C22×D47—416no—
327C22×D47—44no—
328C22×D47—44no—
329C22×D47—44no—
330C22×D47—44no—
331C22×D47—44no—
332C22×D47—44no—
333C22×D47C22×D414yes—
334C22×D47C2×#4114yes—
335C2×C4×C47—28no—
336C2×C4×C47—22no—
337C2×C4×C47—22no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—22no—
341C2×C4×C47—22no—
342C2×C4×C47—22no—
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—416no—
354C2×C4×C47—44no—
355C2×C4×C47—44no—
356C2×C4×C47—44no—
357C2×C4×C47—44no—
358C2×C4×C47—44no—
359C2×C4×C47C22×D414yes—
360C2×Dic47—28no—
361C2×Dic47—22no—
362C2×Dic47—22no—
363C2×Dic47—22no—
364C2×Dic47—22no—
365C2×Dic47—22no—
366C2×Dic47—22no—
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—416no—
379C2×Dic47—44no—
380C2×Dic47—44no—
381C2×Dic47—44no—
382C2×Dic47—44no—
383C2×Dic47—44no—
384C2×Dic47C22×D414yes—
385C2×#2480—471nomaximal, Sylow
386C22×C47—24no—
387C22×C47—24no—
388C22×C47—24no—
389C22×C47—24no—
390C22×C47—24no—
391C22×C47—24no—
392C22×C47—232no—
393C22×C47#52514yes—
394C22×C47C2×#12614yes—
395C22×C47C2×#12618yescomplemented
396C22×C47#53814yes—
397C22×C47#54614yes—
398C22×C47#54614yes—
399C22×C47#55114yes—
400C22×C47#55114yes—
401C22×C47C23×D411yescharacteristic
402C22×C47C22×#4111yescharacteristic
403C22×C47C22×#4111yescharacteristic
404C22×C47C22×#4111yescharacteristic
405C22×C47C22×#4111yescharacteristic
406C22×C47C2×H(5,𝔽2)11yescharacteristic
407C22×C47C2×H(5,𝔽2)11yescharacteristic
408C2×D47—24no—
409C2×D47—24no—
410C2×D47—24no—
411C2×D47—24no—
412C2×D47—24no—
413C2×D47—24no—
414C2×D47—464no—
415C2×D47—42no—
416C2×D47—42no—
417C2×D47—42no—
418C2×D47—42no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—42no—
423C2×D47—416no—
424C2×D47—416no—
425C4×C47—24no—
426C4×C47—42no—
427C4×C47—42no—
428C4×C47—42no—
429C4×C47—42no—
430C4×C47—42no—
431Dic47—24no—
432Dic47—42no—
433Dic47—42no—
434Dic47—42no—
435Dic47—42no—
436Dic47—42no—
437C22×#126—471no—
438C23×C22⋊C4—471no—
439#2480—4716no—
440C2×#397—471no—
441C2×#397—471no—
442C2×#397—471no—
443C2×#396—471no—
444C2×#388—471no—
445C2×#388—471no—
446C2×#388—471no—
447C2×#385—471no—
448C2×#385D4711yescharacteristic, complemented
449C2×#380—471no—
450C2×#379—471no—
451C2×#379—471no—
452C2×C4×C22⋊C4—471no—
453C2×C47—28no—
454C2×C47#248018yescomplemented
455C2×C47C2×#52511yescharacteristic
456C2×C47C22×#12611yescharacteristic
457C2×C47C2×#53811yescharacteristic
458C2×C47C2×#54611yescharacteristic
459C2×C47C2×#54611yescharacteristic
460C2×C47C2×#55111yescharacteristic
461C2×C47C2×#55111yescharacteristic
462D47—44no—
463D47—44no—
464C26—471no—
465C24×C4—471no—
466C24×C4C2×D4711yescharacteristic
467C2×#126—478no—
468C2×#126—948no—
469C22×C4⋊C4—471no—
470C22×C4⋊C4—471no—
471C22×C4⋊C4—471no—
472C22×C4⋊C4—471no—
473C22×C4⋊C4C2×D4711yescharacteristic, complemented
474C22×C4⋊C4C2×D4711yescharacteristic, complemented
475C22×C22⋊C4—471no—
476C22×C22⋊C4—471no—
477C22×C22⋊C4—471no—
478C22×C22⋊C4—471no—
479C22×C22⋊C4—471no—
480C22×C22⋊C4—471no—
481C22×C22⋊C4—471no—
482C22×C22⋊C4—471no—
483C22×C22⋊C4—471no—
484C22×C22⋊C4—478no—
485C22×C22⋊C4—471no—
486C22×C22⋊C4—471no—
487C22×C22⋊C4—471no—
488C22×C22⋊C4—471no—
489C22×C22⋊C4—471no—
490C22×C22⋊C4—948no—
491C22×C22⋊C4C2×D4711yescharacteristic
492C22×C22⋊C4C2×D4711yescharacteristic
493C22×C42—471no—
494C22×C42—471no—
495#397—478no—
496#397—478no—
497#397—478no—
498#396—478no—
499#388—478no—
500#388—478no—
501#388—478no—
502#385—478no—
503#385C2×D4718yescomplemented
504#380—478no—
505#379—478no—
506#379—478no—
507C4×C22⋊C4—478no—
508C2×#95—471no—
509C2×#95—471no—
510C2×#95—471no—
511C2×#95—471no—
512C2×#95—471no—
513C2×#95—471no—
514C2×#95C2×D4711yescharacteristic, complemented
515C2×#95C2×D4711yescharacteristic, complemented
516C47C2×#248011yescharacteristic, complemented, Sylow
517C25—471no—
518C25—471no—
519C25—474no—
520C25—944no—
521C25—944no—
522C25—944no—
523C25—944no—
524C25—944no—
525C25—1882no—
526C25—1882no—
527C25C22×D4711yescharacteristic
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—42no—
531C23×C4—471no—
532C23×C4—471no—
533C23×C4—471no—
534C23×C4—471no—
535C23×C4—471no—
536C23×C4—471no—
537C23×C4—474no—
538C23×C4—944no—
539C23×C4—944no—
540C23×C4—1882no—
541C23×C4C22×D4711yescharacteristic
542C23×C4C22×D4711yescharacteristic
543C23×C4C22×D4711yescharacteristic
544C23×C4C22×D4711yescharacteristic
545C23×C4C22×D4711yescharacteristic
546C23×C4C22×D4714yes—
547C23×C4C22×D4711yescharacteristic
548#126—9432no—
549C2×C4⋊C4—24no—
550C2×C4⋊C4—42no—
551C2×C4⋊C4—474no—
552C2×C4⋊C4—474no—
553C2×C4⋊C4—474no—
554C2×C4⋊C4—474no—
555C2×C4⋊C4—944no—
556C2×C4⋊C4—944no—
557C2×C4⋊C4—1882no—
558C2×C4⋊C4—1882no—
559C2×C4⋊C4C22×D4714yescomplemented
560C2×C4⋊C4C22×D4714yescomplemented
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—478no—
564C2×C22⋊C4—474no—
565C2×C22⋊C4—474no—
566C2×C22⋊C4—474no—
567C2×C22⋊C4—474no—
568C2×C22⋊C4—474no—
569C2×C22⋊C4—474no—
570C2×C22⋊C4—474no—
571C2×C22⋊C4—474no—
572C2×C22⋊C4—474no—
573C2×C22⋊C4—474no—
574C2×C22⋊C4—474no—
575C2×C22⋊C4—474no—
576C2×C22⋊C4—474no—
577C2×C22⋊C4—474no—
578C2×C22⋊C4—9432no—
579C2×C22⋊C4—944no—
580C2×C22⋊C4—944no—
581C2×C22⋊C4—944no—
582C2×C22⋊C4—944no—
583C2×C22⋊C4—944no—
584C2×C22⋊C4—944no—
585C2×C22⋊C4—944no—
586C2×C22⋊C4—944no—
587C2×C22⋊C4—944no—
588C2×C22⋊C4—1882no—
589C2×C22⋊C4—1882no—
590C2×C22⋊C4—1882no—
591C2×C22⋊C4—1882no—
592C2×C22⋊C4C22×D4714yes—
593C2×C22⋊C4C22×D4714yes—
594C2×C42—474no—
595C2×C42—474no—
596C2×C42—944no—
597C2×C42—1882no—
598#95—474no—
599#95—474no—
600#95—474no—
601#95—474no—
602#95—474no—
603#95—474no—
604#95C22×D4714yescomplemented
605#95C22×D4714yescomplemented
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—474no—
611C24—474no—
612C24—472no—
613C24—472no—
614C24—948no—
615C24—948no—
616C24—9432no—
617C24—942no—
618C24—942no—
619C24—942no—
620C24—942no—
621C24—948no—
622C24—942no—
623C24—942no—
624C24—942no—
625C24—942no—
626C24—942no—
627C24—942no—
628C24—942no—
629C24—942no—
630C24—948no—
631C24—948no—
632C24—1884no—
633C24—1884no—
634C24—18816no—
635C24—18816no—
636C24—18816no—
637C24—18816no—
638C24—18816no—
639C24—18816no—
640C24#1062535014yes—
641C24#1062535214yes—
642C24#1062535414yes—
643C24C23×D4712yes—
644C24C23×D4711yescharacteristic
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—28no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—28no—
664C22×C4—44no—
665C22×C4—416no—
666C22×C4—474no—
667C22×C4—472no—
668C22×C4—472no—
669C22×C4—472no—
670C22×C4—472no—
671C22×C4—472no—
672C22×C4—472no—
673C22×C4—948no—
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—948no—
686C22×C4—942no—
687C22×C4—942no—
688C22×C4—942no—
689C22×C4—942no—
690C22×C4—942no—
691C22×C4—942no—
692C22×C4—1884no—
693C22×C4—18816no—
694C22×C4D4×D4714yes—
695C22×C4C23×D4712yes—
696C22×C4C23×D4712yes—
697C22×C4C23×D4712yes—
698C22×C4C23×D4712yes—
699C22×C4C23×D4712yes—
700C22×C4C23×D4712yes—
701C4⋊C4—28no—
702C4⋊C4—44no—
703C4⋊C4—948no—
704C4⋊C4—948no—
705C4⋊C4—1884no—
706C4⋊C4—1884no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—4716no—
710C22⋊C4—948no—
711C22⋊C4—948no—
712C22⋊C4—948no—
713C22⋊C4—948no—
714C22⋊C4—948no—
715C22⋊C4—948no—
716C22⋊C4—948no—
717C22⋊C4—948no—
718C22⋊C4—948no—
719C22⋊C4—1884no—
720C22⋊C4—1884no—
721C22⋊C4—1884no—
722C22⋊C4—1884no—
723C42—948no—
724C42—1884no—
725C23—28no—
726C23—28no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—28no—
735C23—474no—
736C23—474no—
737C23—9432no—
738C23—948no—
739C23—948no—
740C23—948no—
741C23—948no—
742C23—948no—
743C23—948no—
744C23—942no—
745C23—942no—
746C23—942no—
747C23—942no—
748C23—942no—
749C23—942no—
750C23—942no—
751C23—942no—
752C23—942no—
753C23—942no—
754C23—942no—
755C23—942no—
756C23—18816no—
757C23—18816no—
758C23—18816no—
759C23—18816no—
760C23—188128no—
761C23—18816no—
762C23—1884no—
763C23—1884no—
764C23—1884no—
765C23—1884no—
766C23—1884no—
767C23—1884no—
768C23—18816no—
769C23—1884no—
770C23—1884no—
771C23#13094019116yescomplemented
772C23C2×D4×D4712yes—
773C23#41×D4712yes—
774C23C2×#1062535214yes—
775C23C2×#1062535212yes—
776C23C2×#1062535014yes—
777C23C2×#1062535012yes—
778C23C2×#1062535414yes—
779C23C2×#1062535412yes—
780C23#1309406912yes—
781C23#1309407012yes—
782C23C24×D4711yescharacteristic
783C2×C4—28no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—416no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—474no—
808C2×C4—948no—
809C2×C4—942no—
810C2×C4—942no—
811C2×C4—942no—
812C2×C4—942no—
813C2×C4—942no—
814C2×C4—942no—
815C2×C4—942no—
816C2×C4—942no—
817C2×C4—942no—
818C2×C4—942no—
819C2×C4—942no—
820C2×C4—942no—
821C2×C4—942no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—18816no—
827C2×C4—1884no—
828C2×C4—1884no—
829C2×C4—1884no—
830C2×C4—1884no—
831C2×C4—1884no—
832C2×C4C2×D4×D4714yes—
833C22—24no—
834C22—24no—
835C22—232no—
836C22—24no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—944no—
841C22—944no—
842C22—944no—
843C22—944no—
844C22—944no—
845C22—944no—
846C22—18864no—
847C22—1882no—
848C22—1882no—
849C22—18816no—
850C22—18816no—
851C22—1882no—
852C22—1882no—
853C22—1882no—
854C22—1882no—
855C22—1882no—
856C22—1882no—
857C22#1568963214yes—
858C22C2×#1309401914yes—
859C22C2×#1309401918yescomplemented
860C22#1568970614yes—
861C22#1568976014yes—
862C22#1568976414yes—
863C22#1568979614yes—
864C22#1568980014yes—
865C22C22×D4×D4711yescharacteristic
866C22C2×#41×D4711yescharacteristic
867C22C22×#1062535211yescharacteristic
868C22C22×#1062535011yescharacteristic
869C22C22×#1062535411yescharacteristic
870C22C2×#1309406911yescharacteristic
871C22C2×#1309407011yescharacteristic
872C4—24no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—944no—
879C4—1882no—
880C4—1882no—
881C4—1882no—
882C4—1882no—
883C4—1882no—
884C2—28no—
885C2—1884no—
886C2—1884no—
887C2#2024763618yesdirect product factor
888C2C2×#1568963211yescharacteristic
889C2C22×#1309401911yescharacteristic
890C2C2×#1568970611yescharacteristic
891C2C2×#1568976011yescharacteristic
892C2C2×#1568976411yescharacteristic
893C2C2×#1568979611yescharacteristic
894C2C2×#1568980011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
prime radicalC25×D47C22
hypercenterC2×#385D47
hypocenterC47C2×#2480
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13094019C2semidirect
3. #20247636C2direct (N × H)
4. C2×#15689052C2semidirect
5. C2×#15689050C2semidirect
6. C2×#15689049C2semidirect
7. C2×#15689045C2semidirect
8. C2×#15689015C2semidirect
9. C2×#15689013C2semidirect
10. C2×#15689012C2semidirect
11. C2×#15688998C2semidirect
12. C2×#15688981C2semidirect
15. C2×C4×C22⋊Dic47C2semidirect
16. C2×C47×#385C2semidirect
20. C2×#13094019C22semidirect
21. C22×C4⋊Dic47C22semidirect
22. C22×C4⋊Dic47C22semidirect
23. C22×Dic47⋊C4C22semidirect
24. C22×Dic47⋊C4C22semidirect
41. C22×C4×Dic47C22semidirect
42. C22×C4×Dic47C22semidirect
43. #15689052C22semidirect
44. #15689050C22semidirect
45. #15689049C22semidirect
46. #15689045C22semidirect
47. #15689015C22semidirect
48. #15689013C22semidirect
49. #15689012C22semidirect
50. #15688998C22semidirect
51. #15688981C22semidirect
54. C4×C22⋊Dic47C22semidirect
55. C2×C47⋊#95C22semidirect
56. C2×C47⋊#95C22semidirect
57. C2×C47⋊#95C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
62. C22×C4⋊C4×C47C22semidirect
63. C22×C4⋊C4×C47C22semidirect
66. C47×#385C22semidirect
67. C2×#95×C47C22semidirect
68. C2×#95×C47C22semidirect
92. C2×C4⋊Dic47C23semidirect
93. C2×C4⋊Dic47C23semidirect
96. C2×Dic47⋊C4C23semidirect
97. C2×Dic47⋊C4C23semidirect
129. C2×C4×Dic47C23semidirect
130. C2×C4×Dic47C23semidirect
131. C47⋊#95C23semidirect
132. C47⋊#95C23semidirect
133. C47⋊#95C23semidirect
134. C47⋊#95C23semidirect
135. C47⋊#95C23semidirect
136. C47⋊#95C23semidirect
150. C2×C4⋊C4×C47C23semidirect
151. C2×C4⋊C4×C47C23semidirect
156. #95×C47C23semidirect
157. #95×C47C23semidirect
287. C23×C47#126semidirect
395. C22×C47C2×#126semidirect
448. C2×#385D47semidirect
454. C2×C47#2480semidirect
473. C22×C4⋊C4C2×D47semidirect
474. C22×C4⋊C4C2×D47semidirect
503. #385C2×D47semidirect
514. C2×#95C2×D47semidirect
515. C2×#95C2×D47semidirect
516. C47C2×#2480semidirect
559. C2×C4⋊C4C22×D47semidirect
560. C2×C4⋊C4C22×D47semidirect
604. #95C22×D47semidirect
605. #95C22×D47semidirect
771. C23#13094019semidirect
859. C22C2×#13094019semidirect
887. C2#20247636direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940192
C23×(C2×D47)⋊C42
#202476362
C2×#156890522
C2×#156890502
C2×#156890492
C2×#156890452
C2×#156890152
C2×#156890132
C2×#156890122
C2×#156889982
C2×#156889812
C2×#156889782
C2×C4×C22⋊Dic472
C2×C47×#3852
C2×#248047