Finite Group Databasebeta

← C2×#20246781 #26383838

Subgroups — C2×#20246781 #26383838

Order 12032.

5162 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094009C211yesmaximal, characteristic, complemented
2C22×#13093994C211yesmaximal, characteristic
3C23×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#20246781C2116yesmaximal, direct product factor
6C2×#15689052C211yesmaximal, characteristic, complemented
7C2×#15689049C211yesmaximal, characteristic, complemented
8C2×#15689041C211yesmaximal, characteristic, complemented
9C2×#15689040C211yesmaximal, characteristic, complemented
10C2×#15689002C211yesmaximal, characteristic, complemented
11C2×#15689001C211yesmaximal, characteristic, complemented
12C2×#15689000C211yesmaximal, characteristic, complemented
13C2×#15688994C211yesmaximal, characteristic, complemented
14C2×#15688985C211yesmaximal, characteristic, complemented
15C2×#15688981C211yesmaximal, characteristic, complemented
16C2×C47×#380C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C24×Dic47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic
24C2×#13094009—28no—
25C2×#13094009C2218yescomplemented
26C2×#13093994—28no—
27C2×#13093994C2218yes—
28C22×Dic47⋊C4C2211yescharacteristic, complemented
29C22×Dic47⋊C4C2211yescharacteristic, complemented
30C22×C22⋊Dic47C2211yescharacteristic
31C22×(C2×D47)⋊C4—28no—
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)⋊C4C2218yescomplemented
41C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
42C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
43C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
45C2×C22⋊C4×D47—28no—
46C2×C22⋊C4×D47C2218yescomplemented
47#15689052C2218yescomplemented
48#15689049C2218yescomplemented
49#15689041C2218yescomplemented
50#15689040C2218yescomplemented
51#15689002C2218yescomplemented
52#15689001C2218yescomplemented
53#15689000C2218yescomplemented
54#15688994C2218yescomplemented
55#15688985C2218yescomplemented
56#15688981C2218yescomplemented
57C2×C47⋊#95C2211yescharacteristic, complemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C2×C47⋊#95C2211yescharacteristic, complemented
63C24×C4×C47C2211yescharacteristic
64C22×C4⋊C4×C47C2211yescharacteristic, complemented
65C22×C4⋊C4×C47C2211yescharacteristic, complemented
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C47×#380C2218yescomplemented
69C2×#95×C47C2211yescharacteristic, complemented
70C2×#95×C47C2211yescharacteristic, complemented
71C24×D47—24no—
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—42no—
76C24×D47—42no—
77C24×D47D418yes—
78C24×D47C2311yescharacteristic
79C24×D47C2311yescharacteristic
80C24×D47C2314yes—
81C24×D47C2311yescharacteristic
82C22×D188—24no—
83C22×D188—24no—
84C22×D188—24no—
85C22×D188—24no—
86C22×D188—42no—
87C22×D188—42no—
88C22×D188C2314yes—
89C22×D188C2314yes—
90C22×C22⋊D47—24no—
91C22×C22⋊D47—24no—
92C22×C22⋊D47—24no—
93C22×C22⋊D47C2314yes—
94C23×Dic47—24no—
95C23×Dic47—24no—
96C23×Dic47—42no—
97C23×Dic47C2311yescharacteristic
98C23×Dic47C2311yescharacteristic
99C23×Dic47C2311yescharacteristic
100C23×Dic47C2311yescharacteristic
101C23×Dic47C2314yes—
102C23×Dic47C2311yescharacteristic
103C22×C4×D47—24no—
104C22×C4×D47—24no—
105C22×C4×D47—24no—
106C22×C4×D47—24no—
107C22×C4×D47—42no—
108C22×C4×D47—42no—
109C22×C4×D47C2314yes—
110C22×C4×D47C2314yes—
111#13094009—232no—
112#13093994—232no—
113C2×Dic47⋊C4—24no—
114C2×Dic47⋊C4—42no—
115C2×Dic47⋊C4C2314yescomplemented
116C2×Dic47⋊C4C2314yescomplemented
117C2×C22⋊Dic47—24no—
118C2×C22⋊Dic47C2314yes—
119C2×(C2×D47)⋊C4—24no—
120C2×(C2×D47)⋊C4—24no—
121C2×(C2×D47)⋊C4—24no—
122C2×(C2×D47)⋊C4—24no—
123C2×(C2×D47)⋊C4—24no—
124C2×(C2×D47)⋊C4—24no—
125C2×(C2×D47)⋊C4—24no—
126C2×(C2×D47)⋊C4—24no—
127C2×(C2×D47)⋊C4—24no—
128C2×(C2×D47)⋊C4—232no—
129C2×(C2×D47)⋊C4—42no—
130C2×(C2×D47)⋊C4—42no—
131C2×(C2×D47)⋊C4D418yescomplemented
132C2×(C2×D47)⋊C4C2314yes—
133C2×(C2×D47)⋊C4C2314yes—
134C2×(C2×D47)⋊C4C2314yes—
135C2×(C2×D47)⋊C4C2314yes—
136C2×(C2×D47)⋊C4C2314yes—
137C2×(C2×D47)⋊C4C2314yes—
138C2×(C2×D47)⋊C4C2314yes—
139C2×(C2×D47)⋊C4C2314yes—
140C2×(C2×D47)⋊C4C2314yescomplemented
141C2×(C2×D47)⋊C4C2314yescomplemented
142C2×(C2×D47)⋊C4C2314yescomplemented
143C2×(C2×D47)⋊C4C2314yescomplemented
144C22⋊C4×D47—232no—
145C47⋊#95C2314yescomplemented
146C47⋊#95C2314yescomplemented
147C47⋊#95C2314yescomplemented
148C47⋊#95C2314yescomplemented
149C47⋊#95C2314yescomplemented
150C47⋊#95C2314yescomplemented
151C25×C47C2311yescharacteristic
152C23×C4×C47—24no—
153C23×C4×C47—24no—
154C23×C4×C47—42no—
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2314yes—
161C23×C4×C47C2311yescharacteristic
162C2×C4⋊C4×C47—24no—
163C2×C4⋊C4×C47—42no—
164C2×C4⋊C4×C47C2314yescomplemented
165C2×C4⋊C4×C47C2314yescomplemented
166C2×C22⋊C4×C47—24no—
167C2×C22⋊C4×C47—24no—
168C2×C22⋊C4×C47C2314yes—
169C2×C22⋊C4×C47C2314yes—
170#95×C47C2314yescomplemented
171#95×C47C2314yescomplemented
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47C2×D414yes—
177C24×C47#4114yes—
178C24×C47#4114yes—
179C24×C47C2412yes—
180C24×C47C2411yescharacteristic
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—232no—
186C23×D47—22no—
187C23×D47—28no—
188C23×D47—28no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47—22no—
192C23×D47—22no—
193C23×D47—22no—
194C23×D47—232no—
195C23×D47—28no—
196C23×D47—28no—
197C23×D47—22no—
198C23×D47—22no—
199C23×D47—22no—
200C23×D47—22no—
201C23×D47—22no—
202C23×D47—22no—
203C23×D47—22no—
204C23×D47—416no—
205C23×D47—44no—
206C23×D47—44no—
207C23×D47—416no—
208C23×D47—416no—
209C23×D47—416no—
210C23×D47—416no—
211C23×D47C2×D414yes—
212C23×D47C2×D4116yes—
213C23×D47C2×D414yes—
214C23×D47C2×D414yes—
215C23×D47#4114yes—
216C23×D47C2412yes—
217C23×D47C2412yes—
218C23×D47C2412yes—
219C22×C4×C47—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47—22no—
226C22×C4×C47—22no—
227C22×C4×C47—22no—
228C22×C4×C47—28no—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—22no—
233C22×C4×C47—22no—
234C22×C4×C47—22no—
235C22×C4×C47—22no—
236C22×C4×C47—22no—
237C22×C4×C47—28no—
238C22×C4×C47—44no—
239C22×C4×C47—416no—
240C22×C4×C47C2×D414yes—
241C22×C4×C47C2412yes—
242C22×C4×C47C2412yes—
243C22×C4×C47C2412yes—
244C22×C4×C47C2412yes—
245C22×C4×C47C2412yes—
246C22×C4×C47C2412yes—
247C2×C22⋊D47—28no—
248C2×C22⋊D47—28no—
249C2×C22⋊D47—28no—
250C2×C22⋊D47—416no—
251C22×Dic47—22no—
252C22×Dic47—22no—
253C22×Dic47—22no—
254C22×Dic47—22no—
255C22×Dic47—22no—
256C22×Dic47—22no—
257C22×Dic47—22no—
258C22×Dic47—22no—
259C22×Dic47—28no—
260C22×Dic47—22no—
261C22×Dic47—22no—
262C22×Dic47—22no—
263C22×Dic47—22no—
264C22×Dic47—22no—
265C22×Dic47—22no—
266C22×Dic47—28no—
267C22×Dic47—44no—
268C22×Dic47—416no—
269C22×Dic47C2×D414yes—
270C22×Dic47C2412yes—
271C22×Dic47C2412yes—
272C22×Dic47C2412yes—
273C22×Dic47C2412yes—
274C22×Dic47C2412yes—
275C2×D188—28no—
276C2×D188—28no—
277C2×D188—28no—
278C2×D188—28no—
279C2×D188—44no—
280C2×D188—44no—
281C2×D188—416no—
282C2×D188—416no—
283C2×C4×D47—28no—
284C2×C4×D47—28no—
285C2×C4×D47—28no—
286C2×C4×D47—28no—
287C2×C4×D47—44no—
288C2×C4×D47—44no—
289C2×C4×D47—416no—
290C2×C4×D47—416no—
291C4⋊C4×C47—28no—
292C4⋊C4×C47—44no—
293C22⋊C4×C47—28no—
294C22⋊C4×C47—28no—
295C22⋊Dic47—28no—
296(C2×D47)⋊C4—28no—
297(C2×D47)⋊C4—28no—
298(C2×D47)⋊C4—28no—
299(C2×D47)⋊C4—28no—
300(C2×D47)⋊C4—28no—
301(C2×D47)⋊C4—28no—
302(C2×D47)⋊C4—28no—
303(C2×D47)⋊C4—28no—
304(C2×D47)⋊C4—28no—
305(C2×D47)⋊C4—44no—
306(C2×D47)⋊C4—44no—
307(C2×D47)⋊C4C2×D4116yescomplemented
308Dic47⋊C4—28no—
309Dic47⋊C4—44no—
310C23×C47—28no—
311C23×C47—28no—
312C23×C47—28no—
313C23×C47—28no—
314C23×C47—28no—
315C23×C47—28no—
316C23×C47—22no—
317C23×C47—22no—
318C23×C47—22no—
319C23×C47—22no—
320C23×C47#123116yescomplemented
321C23×C47C22×D414yes—
322C23×C47C22×D412yes—
323C23×C47C22×D412yes—
324C23×C47C2×#4112yes—
325C23×C47C2×#4114yes—
326C23×C47C2×#4112yes—
327C23×C47C2×#4114yes—
328C23×C47C2×#4112yes—
329C23×C47H(5,𝔽2)12yes—
330C23×C47H(5,𝔽2)12yes—
331C23×C47C2511yescharacteristic
332C22×D47—28no—
333C22×D47—28no—
334C22×D47—28no—
335C22×D47—28no—
336C22×D47—28no—
337C22×D47—28no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—28no—
343C22×D47—28no—
344C22×D47—232no—
345C22×D47—28no—
346C22×D47—22no—
347C22×D47—22no—
348C22×D47—22no—
349C22×D47—22no—
350C22×D47—22no—
351C22×D47—22no—
352C22×D47—232no—
353C22×D47—22no—
354C22×D47—22no—
355C22×D47—22no—
356C22×D47—22no—
357C22×D47—22no—
358C22×D47—22no—
359C22×D47—22no—
360C22×D47—416no—
361C22×D47—4128no—
362C22×D47—416no—
363C22×D47—416no—
364C22×D47—416no—
365C22×D47—416no—
366C22×D47—44no—
367C22×D47—44no—
368C22×D47—44no—
369C22×D47—44no—
370C22×D47—44no—
371C22×D47—44no—
372C22×D47—44no—
373C22×D47—44no—
374C22×D47—44no—
375C22×D47—44no—
376C22×D47—44no—
377C22×D47#121116yes—
378C22×D47C22×D414yes—
379C22×D47C22×D414yes—
380C22×D47C22×D414yes—
381C22×D47C2×#4114yes—
382C2×C4×C47—28no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—22no—
387C2×C4×C47—22no—
388C2×C4×C47—22no—
389C2×C4×C47—22no—
390C2×C4×C47—22no—
391C2×C4×C47—22no—
392C2×C4×C47—22no—
393C2×C4×C47—22no—
394C2×C4×C47—22no—
395C2×C4×C47—22no—
396C2×C4×C47—22no—
397C2×C4×C47—22no—
398C2×C4×C47—22no—
399C2×C4×C47—22no—
400C2×C4×C47—416no—
401C2×C4×C47—44no—
402C2×C4×C47—44no—
403C2×C4×C47—44no—
404C2×C4×C47—44no—
405C2×C4×C47—44no—
406C2×C4×C47C22×D414yes—
407C22⋊D47—416no—
408C2×Dic47—28no—
409C2×Dic47—22no—
410C2×Dic47—22no—
411C2×Dic47—22no—
412C2×Dic47—22no—
413C2×Dic47—22no—
414C2×Dic47—22no—
415C2×Dic47—22no—
416C2×Dic47—22no—
417C2×Dic47—22no—
418C2×Dic47—22no—
419C2×Dic47—22no—
420C2×Dic47—22no—
421C2×Dic47—22no—
422C2×Dic47—22no—
423C2×Dic47—416no—
424C2×Dic47—44no—
425C2×Dic47—44no—
426C2×Dic47—44no—
427C2×Dic47—44no—
428C2×Dic47C22×D414yes—
429D188—416no—
430D188—416no—
431C4×D47—416no—
432C4×D47—416no—
433C2×#2412—471nomaximal, Sylow
434C22×C47—24no—
435C22×C47—232no—
436C22×C47—24no—
437C22×C47—24no—
438C22×C47—24no—
439C22×C47—24no—
440C22×C47—24no—
441C22×C47C2×#12114yes—
442C22×C47C2×#12314yes—
443C22×C47C2×#12318yescomplemented
444C22×C47#53414yes—
445C22×C47#54614yes—
446C22×C47#54614yes—
447C22×C47#55114yes—
448C22×C47#55114yes—
449C22×C47C23×D411yescharacteristic
450C22×C47C23×D411yescharacteristic
451C22×C47C22×#4111yescharacteristic
452C22×C47C22×#4111yescharacteristic
453C22×C47C22×#4111yescharacteristic
454C22×C47C2×H(5,𝔽2)11yescharacteristic
455C22×C47C2×H(5,𝔽2)11yescharacteristic
456C2×D47—24no—
457C2×D47—232no—
458C2×D47—24no—
459C2×D47—24no—
460C2×D47—24no—
461C2×D47—24no—
462C2×D47—24no—
463C2×D47—24no—
464C2×D47—24no—
465C2×D47—24no—
466C2×D47—464no—
467C2×D47—416no—
468C2×D47—42no—
469C2×D47—42no—
470C2×D47—42no—
471C2×D47—42no—
472C2×D47—42no—
473C2×D47—42no—
474C2×D47—42no—
475C2×D47—42no—
476C2×D47—42no—
477C2×D47—42no—
478C2×D47—42no—
479C2×D47—88no—
480C2×D47C2×#12118yes—
481C4×C47—24no—
482C4×C47—42no—
483C4×C47—42no—
484C4×C47—42no—
485C4×C47—42no—
486C4×C47—42no—
487Dic47—24no—
488Dic47—42no—
489Dic47—42no—
490Dic47—42no—
491Dic47—42no—
492C22×#123—471no—
493C22×#120—471no—
494C23×C22⋊C4—471no—
495C23×C22⋊C4—471no—
496#2412—4716no—
497C2×#397—471no—
498C2×#397—471no—
499C2×#394—471no—
500C2×#394—471no—
501C2×#386—471no—
502C2×#386—471no—
503C2×#386—471no—
504C2×#385—471no—
505C2×#381—471no—
506C2×#380—471no—
507C2×#380D4711yescharacteristic, complemented
508C2×C47—28no—
509C2×C47#241218yescomplemented
510C2×C47C22×#12111yescharacteristic
511C2×C47C22×#12311yescharacteristic
512C2×C47C2×#53411yescharacteristic
513C2×C47C2×#54611yescharacteristic
514C2×C47C2×#54611yescharacteristic
515C2×C47C2×#55111yescharacteristic
516C2×C47C2×#55111yescharacteristic
517D47—28no—
518D47—44no—
519D47—82no—
520C26—471no—
521C23×D4—471no—
522C23×D4—471no—
523C23×D4—471no—
524C24×C4—471no—
525C24×C4—471no—
526C24×C4—471no—
527C24×C4C2×D4711yescharacteristic
528C2×#123—478no—
529C2×#123—948no—
530C2×#120—478no—
531C2×#120—948no—
532C22×C4⋊C4—471no—
533C22×C4⋊C4—471no—
534C22×C4⋊C4C2×D4711yescharacteristic, complemented
535C22×C4⋊C4C2×D4711yescharacteristic, complemented
536C22×C22⋊C4—471no—
537C22×C22⋊C4—471no—
538C22×C22⋊C4—471no—
539C22×C22⋊C4—471no—
540C22×C22⋊C4—471no—
541C22×C22⋊C4—471no—
542C22×C22⋊C4—471no—
543C22×C22⋊C4—471no—
544C22×C22⋊C4—471no—
545C22×C22⋊C4—471no—
546C22×C22⋊C4—478no—
547C22×C22⋊C4—471no—
548C22×C22⋊C4—471no—
549C22×C22⋊C4—471no—
550C22×C22⋊C4—478no—
551C22×C22⋊C4—948no—
552C22×C22⋊C4—948no—
553C22×C22⋊C4C2×D4711yescharacteristic
554C22×C22⋊C4C2×D4711yescharacteristic
555#397—478no—
556#397—478no—
557#394—478no—
558#394—478no—
559#386—478no—
560#386—478no—
561#386—478no—
562#385—478no—
563#381—478no—
564#380—478no—
565#380C2×D4718yescomplemented
566C2×#95—471no—
567C2×#95—471no—
568C2×#95—471no—
569C2×#95—471no—
570C2×#95—471no—
571C2×#95—471no—
572C2×#95C2×D4711yescharacteristic, complemented
573C2×#95C2×D4711yescharacteristic, complemented
574C47C2×#241211yescharacteristic, complemented, Sylow
575C25—471no—
576C25—471no—
577C25—478no—
578C25—474no—
579C25—471no—
580C25—944no—
581C25—944no—
582C25—944no—
583C25—944no—
584C25—1882no—
585C25—1882no—
586C25C22×D4711yescharacteristic
587C22×D4—474no—
588C22×D4—474no—
589C22×D4—474no—
590C22×D4—944no—
591C22×D4—944no—
592C22×D4—944no—
593C22×D4—944no—
594C22×D4—944no—
595C22×D4—944no—
596C22×D4—944no—
597C22×D4—1882no—
598C22×D4—1882no—
599C23×C4—24no—
600C23×C4—24no—
601C23×C4—42no—
602C23×C4—471no—
603C23×C4—471no—
604C23×C4—471no—
605C23×C4—471no—
606C23×C4—471no—
607C23×C4—474no—
608C23×C4—474no—
609C23×C4—474no—
610C23×C4—944no—
611C23×C4—944no—
612C23×C4—944no—
613C23×C4—944no—
614C23×C4—944no—
615C23×C4—944no—
616C23×C4—1882no—
617C23×C4—1882no—
618C23×C4—1882no—
619C23×C4C22×D4711yescharacteristic
620C23×C4C22×D4711yescharacteristic
621C23×C4C22×D4711yescharacteristic
622C23×C4C22×D4711yescharacteristic
623C23×C4C22×D4711yescharacteristic
624C23×C4C22×D4714yes—
625C23×C4C22×D4711yescharacteristic
626#123—9432no—
627#120—9432no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—42no—
630C2×C4⋊C4—474no—
631C2×C4⋊C4—474no—
632C2×C4⋊C4—944no—
633C2×C4⋊C4—1882no—
634C2×C4⋊C4C22×D4714yescomplemented
635C2×C4⋊C4C22×D4714yescomplemented
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—478no—
639C2×C22⋊C4—474no—
640C2×C22⋊C4—474no—
641C2×C22⋊C4—474no—
642C2×C22⋊C4—474no—
643C2×C22⋊C4—474no—
644C2×C22⋊C4—474no—
645C2×C22⋊C4—474no—
646C2×C22⋊C4—474no—
647C2×C22⋊C4—474no—
648C2×C22⋊C4—474no—
649C2×C22⋊C4—474no—
650C2×C22⋊C4—474no—
651C2×C22⋊C4—474no—
652C2×C22⋊C4—9432no—
653C2×C22⋊C4—9432no—
654C2×C22⋊C4—944no—
655C2×C22⋊C4—944no—
656C2×C22⋊C4—944no—
657C2×C22⋊C4—944no—
658C2×C22⋊C4—944no—
659C2×C22⋊C4—944no—
660C2×C22⋊C4—944no—
661C2×C22⋊C4—944no—
662C2×C22⋊C4—944no—
663C2×C22⋊C4—944no—
664C2×C22⋊C4—1882no—
665C2×C22⋊C4—1882no—
666C2×C22⋊C4C22×D4714yes—
667C2×C22⋊C4C22×D4714yes—
668#95—474no—
669#95—474no—
670#95—474no—
671#95—474no—
672#95—474no—
673#95—474no—
674#95C22×D4714yescomplemented
675#95C22×D4714yescomplemented
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—474no—
681C24—474no—
682C24—474no—
683C24—472no—
684C24—474no—
685C24—472no—
686C24—4716no—
687C24—472no—
688C24—948no—
689C24—9432no—
690C24—948no—
691C24—942no—
692C24—942no—
693C24—942no—
694C24—942no—
695C24—9432no—
696C24—942no—
697C24—942no—
698C24—948no—
699C24—942no—
700C24—948no—
701C24—942no—
702C24—942no—
703C24—942no—
704C24—942no—
705C24—942no—
706C24—942no—
707C24—942no—
708C24—942no—
709C24—942no—
710C24—942no—
711C24—18816no—
712C24—1884no—
713C24—1884no—
714C24—18816no—
715C24—18816no—
716C24—18816no—
717C24—18816no—
718C24#1062535014yes—
719C24D4×D4714yes—
720C24#1062535414yes—
721C24C23×D4712yes—
722C24C23×D4711yescharacteristic
723C2×D4—948no—
724C2×D4—948no—
725C2×D4—948no—
726C2×D4—948no—
727C2×D4—948no—
728C2×D4—948no—
729C2×D4—948no—
730C2×D4—1884no—
731C2×D4—1884no—
732C2×D4—18816no—
733C2×D4—18816no—
734C2×D4—18816no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—28no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—28no—
754C22×C4—44no—
755C22×C4—416no—
756C22×C4—474no—
757C22×C4—472no—
758C22×C4—472no—
759C22×C4—472no—
760C22×C4—472no—
761C22×C4—472no—
762C22×C4—948no—
763C22×C4—948no—
764C22×C4—948no—
765C22×C4—948no—
766C22×C4—948no—
767C22×C4—942no—
768C22×C4—942no—
769C22×C4—942no—
770C22×C4—942no—
771C22×C4—942no—
772C22×C4—942no—
773C22×C4—942no—
774C22×C4—942no—
775C22×C4—942no—
776C22×C4—948no—
777C22×C4—942no—
778C22×C4—942no—
779C22×C4—942no—
780C22×C4—942no—
781C22×C4—942no—
782C22×C4—1884no—
783C22×C4—1884no—
784C22×C4—18816no—
785C22×C4—18816no—
786C22×C4—1884no—
787C22×C4—18816no—
788C22×C4D4×D4714yes—
789C22×C4C23×D4712yes—
790C22×C4C23×D4712yes—
791C22×C4C23×D4712yes—
792C22×C4C23×D4712yes—
793C22×C4C23×D4712yes—
794C22×C4C23×D4712yes—
795C4⋊C4—28no—
796C4⋊C4—44no—
797C4⋊C4—948no—
798C4⋊C4—1884no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—4716no—
802C22⋊C4—948no—
803C22⋊C4—948no—
804C22⋊C4—948no—
805C22⋊C4—948no—
806C22⋊C4—948no—
807C22⋊C4—948no—
808C22⋊C4—948no—
809C22⋊C4—948no—
810C22⋊C4—948no—
811C22⋊C4—948no—
812C22⋊C4—1884no—
813C22⋊C4—1884no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—28no—
818C23—28no—
819C23—28no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—4716no—
825C23—474no—
826C23—474no—
827C23—474no—
828C23—474no—
829C23—9432no—
830C23—948no—
831C23—948no—
832C23—948no—
833C23—948no—
834C23—948no—
835C23—948no—
836C23—942no—
837C23—942no—
838C23—942no—
839C23—942no—
840C23—948no—
841C23—948no—
842C23—9432no—
843C23—948no—
844C23—942no—
845C23—942no—
846C23—942no—
847C23—942no—
848C23—942no—
849C23—942no—
850C23—942no—
851C23—942no—
852C23—942no—
853C23—942no—
854C23—942no—
855C23—942no—
856C23—942no—
857C23—18816no—
858C23—18816no—
859C23—18816no—
860C23—18816no—
861C23—18816no—
862C23—188128no—
863C23—1884no—
864C23—1884no—
865C23—1884no—
866C23—1884no—
867C23—1884no—
868C23—1884no—
869C23—1884no—
870C23—1884no—
871C23—1884no—
872C23—1884no—
873C23—1884no—
874C23#13094009116yescomplemented
875C23C2×D4×D4714yes—
876C23C2×D4×D4712yes—
877C23C2×D4×D4712yes—
878C23#41×D4712yes—
879C23C2×#1062535014yes—
880C23C2×#1062535012yes—
881C23C2×#1062535414yes—
882C23C2×#1062535412yes—
883C23#1309406912yes—
884C23#1309407012yes—
885C23C24×D4711yescharacteristic
886D4—18816no—
887D4—18816no—
888D4—18816no—
889C2×C4—28no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—416no—
908C2×C4—44no—
909C2×C4—44no—
910C2×C4—44no—
911C2×C4—44no—
912C2×C4—44no—
913C2×C4—474no—
914C2×C4—948no—
915C2×C4—942no—
916C2×C4—942no—
917C2×C4—942no—
918C2×C4—942no—
919C2×C4—942no—
920C2×C4—942no—
921C2×C4—942no—
922C2×C4—942no—
923C2×C4—942no—
924C2×C4—942no—
925C2×C4—942no—
926C2×C4—942no—
927C2×C4—942no—
928C2×C4—942no—
929C2×C4—18816no—
930C2×C4—18816no—
931C2×C4—18816no—
932C2×C4—1884no—
933C2×C4—1884no—
934C2×C4—1884no—
935C2×C4—1884no—
936C2×C4C2×D4×D4714yes—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—232no—
944C22—478no—
945C22—944no—
946C22—944no—
947C22—944no—
948C22—944no—
949C22—944no—
950C22—944no—
951C22—9432no—
952C22—944no—
953C22—944no—
954C22—944no—
955C22—3768no—
956C22—18864no—
957C22—1882no—
958C22—1882no—
959C22—1882no—
960C22—1882no—
961C22—1882no—
962C22—1882no—
963C22—1882no—
964C22—1882no—
965C22—1882no—
966C22—1882no—
967C22—1882no—
968C22—18816no—
969C22#121×D4714yes—
970C22C2×#1309400914yes—
971C22C2×#1309400918yescomplemented
972C22#1568968114yes—
973C22#1568976314yes—
974C22#1568976414yes—
975C22#1568979714yes—
976C22#1568980014yes—
977C22C22×D4×D4711yescharacteristic
978C22C22×D4×D4711yescharacteristic
979C22C2×#41×D4711yescharacteristic
980C22C22×#1062535011yescharacteristic
981C22C22×#1062535411yescharacteristic
982C22C2×#1309406911yescharacteristic
983C22C2×#1309407011yescharacteristic
984C4—24no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—944no—
991C4—1882no—
992C4—1882no—
993C4—1882no—
994C4—1882no—
995C2—28no—
996C2—948no—
997C2—3762no—
998C2—1884no—
999C2#2024678118yesdirect product factor
1000C2C2×#121×D4711yescharacteristic
1001C2C22×#1309400911yescharacteristic
1002C2C2×#1568968111yescharacteristic
1003C2C2×#1568976311yescharacteristic
1004C2C2×#1568976411yescharacteristic
1005C2C2×#1568979711yescharacteristic
1006C2C2×#1568980011yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#380C2
socleC24×C47C24
prime radicalC22×#13093994C2
hypercenterC2×#380D47
hypocenterC47C2×#2412
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#13094009C2semidirect
3. C23×(C2×D47)⋊C4C2semidirect
4. C22×C22⋊C4×D47C2semidirect
5. #20246781C2direct (N × H)
6. C2×#15689052C2semidirect
7. C2×#15689049C2semidirect
8. C2×#15689041C2semidirect
9. C2×#15689040C2semidirect
10. C2×#15689002C2semidirect
11. C2×#15689001C2semidirect
12. C2×#15689000C2semidirect
13. C2×#15688994C2semidirect
14. C2×#15688985C2semidirect
15. C2×#15688981C2semidirect
16. C2×C47×#380C2semidirect
25. C2×#13094009C22semidirect
28. C22×Dic47⋊C4C22semidirect
29. C22×Dic47⋊C4C22semidirect
40. C22×(C2×D47)⋊C4C22semidirect
41. C22×(C2×D47)⋊C4C22semidirect
42. C22×(C2×D47)⋊C4C22semidirect
43. C22×(C2×D47)⋊C4C22semidirect
44. C22×(C2×D47)⋊C4C22semidirect
46. C2×C22⋊C4×D47C22semidirect
47. #15689052C22semidirect
48. #15689049C22semidirect
49. #15689041C22semidirect
50. #15689040C22semidirect
51. #15689002C22semidirect
52. #15689001C22semidirect
53. #15689000C22semidirect
54. #15688994C22semidirect
55. #15688985C22semidirect
56. #15688981C22semidirect
57. C2×C47⋊#95C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
62. C2×C47⋊#95C22semidirect
64. C22×C4⋊C4×C47C22semidirect
65. C22×C4⋊C4×C47C22semidirect
68. C47×#380C22semidirect
69. C2×#95×C47C22semidirect
70. C2×#95×C47C22semidirect
115. C2×Dic47⋊C4C23semidirect
116. C2×Dic47⋊C4C23semidirect
131. C2×(C2×D47)⋊C4D4semidirect
140. C2×(C2×D47)⋊C4C23semidirect
141. C2×(C2×D47)⋊C4C23semidirect
142. C2×(C2×D47)⋊C4C23semidirect
143. C2×(C2×D47)⋊C4C23semidirect
145. C47⋊#95C23semidirect
146. C47⋊#95C23semidirect
147. C47⋊#95C23semidirect
148. C47⋊#95C23semidirect
149. C47⋊#95C23semidirect
150. C47⋊#95C23semidirect
164. C2×C4⋊C4×C47C23semidirect
165. C2×C4⋊C4×C47C23semidirect
170. #95×C47C23semidirect
171. #95×C47C23semidirect
307. (C2×D47)⋊C4C2×D4semidirect
320. C23×C47#123semidirect
443. C22×C47C2×#123semidirect
507. C2×#380D47semidirect
509. C2×C47#2412semidirect
534. C22×C4⋊C4C2×D47semidirect
535. C22×C4⋊C4C2×D47semidirect
565. #380C2×D47semidirect
572. C2×#95C2×D47semidirect
573. C2×#95C2×D47semidirect
574. C47C2×#2412semidirect
634. C2×C4⋊C4C22×D47semidirect
635. C2×C4⋊C4C22×D47semidirect
674. #95C22×D47semidirect
675. #95C22×D47semidirect
874. C23#13094009semidirect
971. C22C2×#13094009semidirect
999. C2#20246781direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940092
C22×#130939942
C23×(C2×D47)⋊C42
C22×C22⋊C4×D472
#202467812
C2×#156890522
C2×#156890492
C2×#156890412
C2×#156890402
C2×#156890022
C2×#156890012
C2×#156890002
C2×#156889942
C2×#156889852
C2×#156889812
C2×C47×#3802
C2×#241247