Finite Group Databasebeta

← C2×#20246944 #26384002

Subgroups — C2×#20246944 #26384002

Order 12032.

3938 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094009C211yesmaximal, characteristic, complemented
2C22×#13094006C211yesmaximal, characteristic, complemented
3C22×#13093997C211yesmaximal, characteristic
4C22×C4×D188C211yesmaximal, characteristic, complemented
5#20246944C2116yesmaximal, direct product factor
6C2×#15689056C211yesmaximal, characteristic, complemented
7C2×#15689050C211yesmaximal, characteristic, complemented
8C2×#15689046C211yesmaximal, characteristic, complemented
9C2×#15689039C211yesmaximal, characteristic, complemented
10C2×#15689021C211yesmaximal, characteristic, complemented
11C2×#15688999C211yesmaximal, characteristic, complemented
12C2×#15688999C211yesmaximal, characteristic, complemented
13C2×#15688997C211yesmaximal, characteristic, complemented
14C2×#15688982C211yesmaximal, characteristic, complemented
15C2×#95×D47C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C22⋊D47C2211yescharacteristic
19C23×C22⋊D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic
24C2×#13094009—28no—
25C2×#13094009C2218yescomplemented
26C2×#13094006—28no—
27C2×#13094006C2218yescomplemented
28C2×#13093997—28no—
29C2×#13093997C2218yes—
30C2×C4×D188—28no—
31C2×C4×D188C2218yescomplemented
32C22×C4⋊Dic47C2211yescharacteristic
33C22×C4⋊Dic47C2211yescharacteristic
34C22×C4⋊Dic47C2211yescharacteristic
35C22×Dic47⋊C4C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C22×Dic47⋊C4C2211yescharacteristic
38C22×Dic47⋊C4C2211yescharacteristic
39C22×C22⋊Dic47C2211yescharacteristic
40C22×C22⋊Dic47C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47#15689056C2218yescomplemented
48#15689050C2218yescomplemented
49#15689046C2218yescomplemented
50#15689039C2218yescomplemented
51#15689021C2218yescomplemented
52#15688999C2218yescomplemented
53#15688999C2218yescomplemented
54#15688997C2218yescomplemented
55#15688982C2218yescomplemented
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62#95×D47C2218yescomplemented
63C22×C4⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C42×C47C2211yescharacteristic
68C47×#388C2218yescomplemented
69C2×#95×C47C2211yescharacteristic
70C2×#95×C47C2211yescharacteristic
71C24×D47C2311yescharacteristic
72C24×D47C2311yescharacteristic
73C22×D188—24no—
74C22×D188—24no—
75C22×D188D418yes—
76C22×D188C2314yes—
77C22×C22⋊D47—24no—
78C22×C22⋊D47—24no—
79C22×C22⋊D47—24no—
80C22×C22⋊D47—24no—
81C22×C22⋊D47—24no—
82C22×C22⋊D47—42no—
83C22×C22⋊D47C2314yes—
84C22×C22⋊D47C2314yes—
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C23×Dic47C2311yescharacteristic
89C23×Dic47C2311yescharacteristic
90C23×Dic47C2311yescharacteristic
91C22×C4×D47—24no—
92C22×C4×D47—24no—
93C22×C4×D47—24no—
94C22×C4×D47—24no—
95C22×C4×D47—24no—
96C22×C4×D47—24no—
97C22×C4×D47—24no—
98C22×C4×D47—24no—
99C22×C4×D47—24no—
100C22×C4×D47—42no—
101C22×C4×D47—42no—
102C22×C4×D47—42no—
103C22×C4×D47C2314yes—
104C22×C4×D47C2314yes—
105C22×C4×D47C2314yes—
106C22×C4×D47C2314yes—
107#13094009—232no—
108#13094006—232no—
109#13093997—232no—
110C4×D188—232no—
111C2×C4⋊Dic47—24no—
112C2×C4⋊Dic47—24no—
113C2×C4⋊Dic47—24no—
114C2×C4⋊Dic47C2314yes—
115C2×C4⋊Dic47C2314yes—
116C2×C4⋊Dic47C2314yes—
117C2×Dic47⋊C4—24no—
118C2×Dic47⋊C4—24no—
119C2×Dic47⋊C4—24no—
120C2×Dic47⋊C4—42no—
121C2×Dic47⋊C4C2314yes—
122C2×Dic47⋊C4C2314yes—
123C2×Dic47⋊C4C2314yes—
124C2×Dic47⋊C4C2314yes—
125C2×C22⋊Dic47—24no—
126C2×C22⋊Dic47—42no—
127C2×C22⋊Dic47C2314yes—
128C2×C22⋊Dic47C2314yes—
129C2×(C2×D47)⋊C4—24no—
130C2×(C2×D47)⋊C4—24no—
131C2×(C2×D47)⋊C4—24no—
132C2×(C2×D47)⋊C4—24no—
133C2×(C2×D47)⋊C4—24no—
134C2×(C2×D47)⋊C4D418yescomplemented
135C2×(C2×D47)⋊C4C2314yes—
136C2×(C2×D47)⋊C4C2314yes—
137C2×(C2×D47)⋊C4C2314yes—
138C2×(C2×D47)⋊C4C2314yes—
139C2×(C2×D47)⋊C4C2314yes—
140C2×(C2×D47)⋊C4C2314yes—
141C47⋊#95C2314yes—
142C47⋊#95C2314yes—
143C47⋊#95C2314yes—
144C47⋊#95C2314yes—
145C47⋊#95C2314yes—
146C47⋊#95C2314yes—
147C25×C47C2311yescharacteristic
148C23×C4×C47C2311yescharacteristic
149C23×C4×C47C2311yescharacteristic
150C23×C4×C47C2311yescharacteristic
151C23×C4×C47C2311yescharacteristic
152C23×C4×C47C2311yescharacteristic
153C23×C4×C47C2311yescharacteristic
154C2×C4⋊C4×C47—24no—
155C2×C4⋊C4×C47C2314yes—
156C2×C22⋊C4×C47—24no—
157C2×C22⋊C4×C47—24no—
158C2×C22⋊C4×C47—24no—
159C2×C22⋊C4×C47C2314yes—
160C2×C22⋊C4×C47C2314yes—
161C2×C22⋊C4×C47C2314yes—
162C2×C42×C47—24no—
163C2×C42×C47C2314yes—
164#95×C47C2314yes—
165#95×C47C2314yes—
166C24×C47—22no—
167C24×C47—22no—
168C24×C47—22no—
169C24×C47—22no—
170C24×C47—22no—
171C24×C47—22no—
172C24×C47—22no—
173C24×C47C2412yes—
174C24×C47C2411yescharacteristic
175C23×D47—22no—
176C23×D47—22no—
177C23×D47—22no—
178C23×D47—22no—
179C23×D47—22no—
180C23×D47—22no—
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47C2×D414yes—
186C23×D47C2×D414yes—
187C23×D47C2×D414yes—
188C23×D47#4114yes—
189C23×D47C2412yes—
190C23×D47C2412yes—
191C22×C4×C47—22no—
192C22×C4×C47—22no—
193C22×C4×C47—22no—
194C22×C4×C47—22no—
195C22×C4×C47—22no—
196C22×C4×C47—22no—
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×C47C2×D414yes—
207C22×C4×C47C2×D414yes—
208C22×C4×C47#4114yes—
209C22×C4×C47C2412yes—
210C22×C4×C47C2412yes—
211C22×C4×C47C2412yes—
212C22×C4×C47C2412yes—
213C22×C4×C47C2412yes—
214C22×C4×C47C2412yes—
215C2×C22⋊D47—28no—
216C2×C22⋊D47—28no—
217C2×C22⋊D47—28no—
218C2×C22⋊D47—28no—
219C2×C22⋊D47—28no—
220C2×C22⋊D47—44no—
221C2×C22⋊D47—416no—
222C2×C22⋊D47—416no—
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×Dic47—22no—
233C22×Dic47—22no—
234C22×Dic47—22no—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47C2×D414yes—
240C22×Dic47#4114yes—
241C22×Dic47C2412yes—
242C22×Dic47C2412yes—
243C22×Dic47C2412yes—
244C22×Dic47C2412yes—
245C22×Dic47C2412yes—
246C22×Dic47C2412yes—
247C2×D188—232no—
248C2×D188—28no—
249C2×D188—28no—
250C2×D188C2×D4116yes—
251C2×C4×D47—28no—
252C2×C4×D47—28no—
253C2×C4×D47—28no—
254C2×C4×D47—28no—
255C2×C4×D47—28no—
256C2×C4×D47—28no—
257C2×C4×D47—28no—
258C2×C4×D47—28no—
259C2×C4×D47—28no—
260C2×C4×D47—44no—
261C2×C4×D47—44no—
262C2×C4×D47—44no—
263C2×C4×D47—416no—
264C2×C4×D47—416no—
265C2×C4×D47—416no—
266C2×C4×D47—416no—
267C4⋊C4×C47—28no—
268C22⋊C4×C47—28no—
269C22⋊C4×C47—28no—
270C22⋊C4×C47—28no—
271C42×C47—28no—
272C22⋊Dic47—28no—
273C22⋊Dic47—44no—
274(C2×D47)⋊C4—28no—
275(C2×D47)⋊C4—28no—
276(C2×D47)⋊C4—28no—
277(C2×D47)⋊C4—28no—
278(C2×D47)⋊C4—28no—
279(C2×D47)⋊C4C2×D4116yescomplemented
280C4⋊Dic47—28no—
281C4⋊Dic47—28no—
282C4⋊Dic47—28no—
283Dic47⋊C4—28no—
284Dic47⋊C4—28no—
285Dic47⋊C4—28no—
286Dic47⋊C4—44no—
287C23×C47—22no—
288C23×C47—22no—
289C23×C47—22no—
290C23×C47—22no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—44no—
295C23×C47—44no—
296C23×C47—44no—
297C23×C47—44no—
298C23×C47—44no—
299C23×C47—44no—
300C23×C47—44no—
301C23×C47C22×D412yes—
302C23×C47C22×D412yes—
303C23×C47C2×#4112yes—
304C23×C47C2×#4112yes—
305C23×C47C2×#4112yes—
306C23×C47H(5,𝔽2)12yes—
307C23×C472−1+412yes—
308C23×C47C2511yescharacteristic
309C22×D47—28no—
310C22×D47—28no—
311C22×D47—28no—
312C22×D47—28no—
313C22×D47—28no—
314C22×D47—28no—
315C22×D47—22no—
316C22×D47—22no—
317C22×D47—22no—
318C22×D47—22no—
319C22×D47—28no—
320C22×D47—28no—
321C22×D47—28no—
322C22×D47—22no—
323C22×D47—22no—
324C22×D47—22no—
325C22×D47—22no—
326C22×D47—22no—
327C22×D47—22no—
328C22×D47—44no—
329C22×D47—44no—
330C22×D47—44no—
331C22×D47—44no—
332C22×D47#121116yes—
333C22×D47C22×D414yes—
334C22×D47C22×D414yes—
335C22×D47C22×D414yes—
336C22×D47C2×#4114yes—
337C2×C4×C47—28no—
338C2×C4×C47—28no—
339C2×C4×C47—28no—
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—22no—
354C2×C4×C47—22no—
355C2×C4×C47—44no—
356C2×C4×C47—44no—
357C2×C4×C47—44no—
358C2×C4×C47C22×D414yes—
359C2×C4×C47C22×D414yes—
360C2×C4×C47C2×#4114yes—
361C22⋊D47—416no—
362C22⋊D47—416no—
363C2×Dic47—28no—
364C2×Dic47—28no—
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—22no—
379C2×Dic47—22no—
380C2×Dic47—22no—
381C2×Dic47—44no—
382C2×Dic47—44no—
383C2×Dic47—44no—
384C2×Dic47—44no—
385C2×Dic47C22×D414yes—
386C2×Dic47C2×#4114yes—
387D188—232no—
388C4×D47—416no—
389C4×D47—416no—
390C4×D47—416no—
391C4×D47—416no—
392C2×#2425—471nomaximal, Sylow
393C22×C47—42no—
394C22×C47—42no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—88no—
401C22×C47C2×#12114yes—
402C22×C47#52914yes—
403C22×C47#53914yes—
404C22×C47#54614yes—
405C22×C47#54614yes—
406C22×C47#54714yes—
407C22×C47#54714yes—
408C22×C47C23×D411yescharacteristic
409C22×C47C23×D411yescharacteristic
410C22×C47C22×#4111yescharacteristic
411C22×C47C22×#4111yescharacteristic
412C22×C47C22×#4111yescharacteristic
413C22×C47C2×H(5,𝔽2)11yescharacteristic
414C22×C47C2×2−1+411yescharacteristic
415C2×D47—24no—
416C2×D47—232no—
417C2×D47—24no—
418C2×D47—24no—
419C2×D47—24no—
420C2×D47—24no—
421C2×D47—24no—
422C2×D47—24no—
423C2×D47—24no—
424C2×D47—24no—
425C2×D47—42no—
426C2×D47—416no—
427C2×D47—42no—
428C2×D47—42no—
429C2×D47—42no—
430C2×D47C2×#12118yes—
431C4×C47—24no—
432C4×C47—24no—
433C4×C47—24no—
434C4×C47—42no—
435C4×C47—42no—
436C4×C47—42no—
437Dic47—24no—
438Dic47—24no—
439Dic47—42no—
440Dic47—42no—
441Dic47—42no—
442Dic47—42no—
443C22×#123—471no—
444C22×#123—471no—
445C22×#121—471no—
446C22×C4×D4—471no—
447#2425—4716no—
448C2×#398—471no—
449C2×#397—471no—
450C2×#396—471no—
451C2×#394—471no—
452C2×#389—471no—
453C2×#388D4711yescharacteristic, complemented
454C2×#386—471no—
455C2×#386—471no—
456C2×#385—471no—
457C2×#380—471no—
458C22×#95—471no—
459C2×C47—82no—
460C2×C47#242518yescomplemented
461C2×C47C22×#12111yescharacteristic
462C2×C47C2×#52911yescharacteristic
463C2×C47C2×#53911yescharacteristic
464C2×C47C2×#54611yescharacteristic
465C2×C47C2×#54611yescharacteristic
466C2×C47C2×#54711yescharacteristic
467C2×C47C2×#54711yescharacteristic
468D47—28no—
469D47—44no—
470C23×D4—471no—
471C23×D4—471no—
472C23×D4—471no—
473C24×C4—471no—
474C24×C4—471no—
475C24×C4—471no—
476C24×C4—471no—
477C2×#123—478no—
478C2×#123—478no—
479C2×#123—948no—
480C2×#123—948no—
481C2×#121—478no—
482C2×#121—948no—
483C2×C4×D4—478no—
484C2×C4×D4—948no—
485C22×C4⋊C4—471no—
486C22×C4⋊C4—471no—
487C22×C4⋊C4—471no—
488C22×C4⋊C4—471no—
489C22×C4⋊C4—471no—
490C22×C4⋊C4—471no—
491C22×C4⋊C4—471no—
492C22×C4⋊C4C2×D4711yescharacteristic
493C22×C22⋊C4—471no—
494C22×C22⋊C4—471no—
495C22×C22⋊C4—471no—
496C22×C22⋊C4—471no—
497C22×C22⋊C4—471no—
498C22×C22⋊C4—471no—
499C22×C22⋊C4—471no—
500C22×C22⋊C4—471no—
501C22×C22⋊C4C2×D4711yescharacteristic
502C22×C22⋊C4C2×D4711yescharacteristic
503C22×C22⋊C4C2×D4711yescharacteristic
504C22×C42C2×D4711yescharacteristic
505#398—478no—
506#397—478no—
507#396—478no—
508#394—478no—
509#389—478no—
510#388C2×D4718yescomplemented
511#386—478no—
512#386—478no—
513#385—478no—
514#380—478no—
515C2×#95—471no—
516C2×#95—471no—
517C2×#95—471no—
518C2×#95—471no—
519C2×#95—471no—
520C2×#95—471no—
521C2×#95—478no—
522C2×#95C2×D4711yescharacteristic
523C2×#95C2×D4711yescharacteristic
524C47C2×#242511yescharacteristic, complemented, Sylow
525C25—471no—
526C25—471no—
527C25C22×D4711yescharacteristic
528C22×D4—474no—
529C22×D4—474no—
530C22×D4—478no—
531C22×D4—474no—
532C22×D4—944no—
533C22×D4—944no—
534C22×D4—944no—
535C22×D4—944no—
536C22×D4—944no—
537C22×D4—944no—
538C22×D4—944no—
539C22×D4—1882no—
540C23×C4—471no—
541C23×C4—471no—
542C23×C4—471no—
543C23×C4—471no—
544C23×C4—471no—
545C23×C4—471no—
546C23×C4—474no—
547C23×C4—474no—
548C23×C4—474no—
549C23×C4—474no—
550C23×C4—944no—
551C23×C4—944no—
552C23×C4—944no—
553C23×C4—944no—
554C23×C4—944no—
555C23×C4—944no—
556C23×C4—944no—
557C23×C4—944no—
558C23×C4—944no—
559C23×C4—1882no—
560C23×C4—1882no—
561C23×C4—1882no—
562C23×C4C22×D4711yescharacteristic
563C23×C4C22×D4711yescharacteristic
564C23×C4C22×D4711yescharacteristic
565C23×C4C22×D4711yescharacteristic
566C23×C4C22×D4711yescharacteristic
567C23×C4C22×D4711yescharacteristic
568#123—9432no—
569#123—9432no—
570#121—9432no—
571C4×D4—9432no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—474no—
574C2×C4⋊C4—474no—
575C2×C4⋊C4—474no—
576C2×C4⋊C4—474no—
577C2×C4⋊C4—474no—
578C2×C4⋊C4—474no—
579C2×C4⋊C4—474no—
580C2×C4⋊C4—944no—
581C2×C4⋊C4—944no—
582C2×C4⋊C4—944no—
583C2×C4⋊C4—944no—
584C2×C4⋊C4—944no—
585C2×C4⋊C4—944no—
586C2×C4⋊C4—1882no—
587C2×C4⋊C4C22×D4714yes—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—478no—
592C2×C22⋊C4—474no—
593C2×C22⋊C4—474no—
594C2×C22⋊C4—474no—
595C2×C22⋊C4—474no—
596C2×C22⋊C4—474no—
597C2×C22⋊C4—474no—
598C2×C22⋊C4—474no—
599C2×C22⋊C4—474no—
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—1882no—
607C2×C22⋊C4C22×D4714yes—
608C2×C22⋊C4C22×D4714yes—
609C2×C22⋊C4C22×D4714yes—
610C2×C42—24no—
611C2×C42C22×D4714yes—
612#95—474no—
613#95—474no—
614#95—474no—
615#95—474no—
616#95—474no—
617#95—474no—
618#95C22×D4714yes—
619#95C22×D4714yes—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—474no—
628C24—474no—
629C24—474no—
630C24—472no—
631C24—474no—
632C24—472no—
633C24—942no—
634C24—942no—
635C24—942no—
636C24—942no—
637C24—942no—
638C24—942no—
639C24—942no—
640C24—942no—
641C24—942no—
642C24—942no—
643C24C23×D4712yes—
644C24C23×D4711yescharacteristic
645C2×D4—4716no—
646C2×D4—948no—
647C2×D4—9432no—
648C2×D4—948no—
649C2×D4—948no—
650C2×D4—948no—
651C2×D4—948no—
652C2×D4—948no—
653C2×D4—948no—
654C2×D4—1884no—
655C2×D4—18816no—
656C2×D4—18816no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—474no—
673C22×C4—474no—
674C22×C4—472no—
675C22×C4—472no—
676C22×C4—472no—
677C22×C4—472no—
678C22×C4—472no—
679C22×C4—472no—
680C22×C4—948no—
681C22×C4—948no—
682C22×C4—948no—
683C22×C4—948no—
684C22×C4—948no—
685C22×C4—948no—
686C22×C4—948no—
687C22×C4—942no—
688C22×C4—942no—
689C22×C4—942no—
690C22×C4—942no—
691C22×C4—942no—
692C22×C4—942no—
693C22×C4—942no—
694C22×C4—942no—
695C22×C4—942no—
696C22×C4—942no—
697C22×C4—942no—
698C22×C4—942no—
699C22×C4—942no—
700C22×C4—942no—
701C22×C4—942no—
702C22×C4—942no—
703C22×C4—948no—
704C22×C4—948no—
705C22×C4—1884no—
706C22×C4—1884no—
707C22×C4—1884no—
708C22×C4—18816no—
709C22×C4—18816no—
710C22×C4—18816no—
711C22×C4—18816no—
712C22×C4#1062535014yes—
713C22×C4D4×D4714yes—
714C22×C4D4×D4714yes—
715C22×C4C23×D4712yes—
716C22×C4C23×D4712yes—
717C22×C4C23×D4712yes—
718C22×C4C23×D4712yes—
719C22×C4C23×D4712yes—
720C22×C4C23×D4712yes—
721C4⋊C4—28no—
722C4⋊C4—948no—
723C4⋊C4—948no—
724C4⋊C4—948no—
725C4⋊C4—948no—
726C4⋊C4—948no—
727C4⋊C4—948no—
728C4⋊C4—1884no—
729C22⋊C4—28no—
730C22⋊C4—28no—
731C22⋊C4—28no—
732C22⋊C4—4716no—
733C22⋊C4—948no—
734C22⋊C4—948no—
735C22⋊C4—948no—
736C22⋊C4—948no—
737C22⋊C4—948no—
738C22⋊C4—948no—
739C22⋊C4—1884no—
740C42—28no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—4716no—
756C23—474no—
757C23—474no—
758C23—474no—
759C23—474no—
760C23—948no—
761C23—948no—
762C23—948no—
763C23—948no—
764C23—948no—
765C23—942no—
766C23—942no—
767C23—942no—
768C23—942no—
769C23—948no—
770C23—948no—
771C23—948no—
772C23—948no—
773C23—942no—
774C23—942no—
775C23—942no—
776C23—942no—
777C23—942no—
778C23—942no—
779C23—1884no—
780C23—1884no—
781C23—1884no—
782C23—1884no—
783C23C2×D4×D4712yes—
784C23C2×D4×D4712yes—
785C23#41×D4712yes—
786C23#41×D4712yes—
787C23C2×#1062535012yes—
788C23#1309407012yes—
789C23#1309407112yes—
790C23C24×D4711yescharacteristic
791D4—9432no—
792D4—18816no—
793D4—18816no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—474no—
816C2×C4—474no—
817C2×C4—948no—
818C2×C4—948no—
819C2×C4—942no—
820C2×C4—942no—
821C2×C4—942no—
822C2×C4—942no—
823C2×C4—942no—
824C2×C4—942no—
825C2×C4—942no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—942no—
829C2×C4—942no—
830C2×C4—942no—
831C2×C4—942no—
832C2×C4—942no—
833C2×C4—942no—
834C2×C4—942no—
835C2×C4—18816no—
836C2×C4—18816no—
837C2×C4—18816no—
838C2×C4—18816no—
839C2×C4—1884no—
840C2×C4—1884no—
841C2×C4—1884no—
842C2×C4—1884no—
843C2×C4C2×D4×D4714yes—
844C2×C4C2×D4×D4714yes—
845C2×C4C2×#1062535014yes—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—88no—
854C22—478no—
855C22—944no—
856C22—944no—
857C22—944no—
858C22—944no—
859C22—944no—
860C22—9432no—
861C22—944no—
862C22—944no—
863C22—944no—
864C22—944no—
865C22—1882no—
866C22—1882no—
867C22—1882no—
868C22—18816no—
869C22—1882no—
870C22#121×D4714yes—
871C22#1568965114yes—
872C22#1568971414yes—
873C22#1568976614yes—
874C22#1568976914yes—
875C22#1568977114yes—
876C22#1568977814yes—
877C22C22×D4×D4711yescharacteristic
878C22C22×D4×D4711yescharacteristic
879C22C2×#41×D4711yescharacteristic
880C22C2×#41×D4711yescharacteristic
881C22C22×#1062535011yescharacteristic
882C22C2×#1309407011yescharacteristic
883C22C2×#1309407111yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—944no—
891C4—944no—
892C4—1882no—
893C4—1882no—
894C4—1882no—
895C4—1882no—
896C2—82no—
897C2—948no—
898C2—1884no—
899C2#2024694418yesdirect product factor
900C2C2×#121×D4711yescharacteristic
901C2C2×#1568965111yescharacteristic
902C2C2×#1568971411yescharacteristic
903C2C2×#1568976611yescharacteristic
904C2C2×#1568976911yescharacteristic
905C2C2×#1568977111yescharacteristic
906C2C2×#1568977811yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC22×#13093997C2
hypercenterC2×#388D47
hypocenterC47C2×#2425
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#13094009C2semidirect
2. C22×#13094006C2semidirect
4. C22×C4×D188C2semidirect
5. #20246944C2direct (N × H)
6. C2×#15689056C2semidirect
7. C2×#15689050C2semidirect
8. C2×#15689046C2semidirect
9. C2×#15689039C2semidirect
10. C2×#15689021C2semidirect
11. C2×#15688999C2semidirect
12. C2×#15688999C2semidirect
13. C2×#15688997C2semidirect
14. C2×#15688982C2semidirect
15. C2×#95×D47C2semidirect
16. C2×C47×#388C2semidirect
25. C2×#13094009C22semidirect
27. C2×#13094006C22semidirect
31. C2×C4×D188C22semidirect
47. #15689056C22semidirect
48. #15689050C22semidirect
49. #15689046C22semidirect
50. #15689039C22semidirect
51. #15689021C22semidirect
52. #15688999C22semidirect
53. #15688999C22semidirect
54. #15688997C22semidirect
55. #15688982C22semidirect
62. #95×D47C22semidirect
68. C47×#388C22semidirect
134. C2×(C2×D47)⋊C4D4semidirect
279. (C2×D47)⋊C4C2×D4semidirect
453. C2×#388D47semidirect
460. C2×C47#2425semidirect
510. #388C2×D47semidirect
524. C47C2×#2425semidirect
899. C2#20246944direct (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×#130940062
C22×#130939972
C22×C4×D1882
#202469442
C2×#156890562
C2×#156890502
C2×#156890462
C2×#156890392
C2×#156890212
C2×#156889992
C2×#156889972
C2×#156889822
C2×#95×D472
C2×C47×#3882
C2×#242547