Finite Group Databasebeta

← C2×#20247394 #26384121

Subgroups — C2×#20247394 #26384121

Order 12032.

4218 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094006C211yesmaximal, characteristic, complemented
2C22×#13093998C211yesmaximal, characteristic, complemented
3C22×#13093997C211yesmaximal, characteristic, complemented
4C22×C4×D188C211yesmaximal, characteristic, complemented
5#20247394C2116yesmaximal, direct product factor
6C2×#15689055C211yesmaximal, characteristic, complemented
7C2×#15689039C211yesmaximal, characteristic, complemented
8C2×#15689033C211yesmaximal, characteristic, complemented
9C2×#15689032C211yesmaximal, characteristic, complemented
10C2×#15689025C211yesmaximal, characteristic, complemented
11C2×#15689014C211yesmaximal, characteristic, complemented
12C2×#15689014C211yesmaximal, characteristic, complemented
13C2×#15689002C211yesmaximal, characteristic, complemented
14C2×#15689001C211yesmaximal, characteristic, complemented
15C2×#15688997C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C22⋊D47C2211yescharacteristic
22C23×C22⋊D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic
24C23×C4×D47C2211yescharacteristic
25C2×#13094006—28no—
26C2×#13094006C2218yescomplemented
27C2×#13093998—28no—
28C2×#13093998C2218yescomplemented
29C2×#13093997—28no—
30C2×#13093997C2218yescomplemented
31C2×C4×D188—28no—
32C2×C4×D188C2218yescomplemented
33C22×C4⋊Dic47C2211yescharacteristic
34C22×C4⋊Dic47C2211yescharacteristic
35C22×C4⋊Dic47C2211yescharacteristic
36C22×Dic47⋊C4C2211yescharacteristic
37C22×Dic47⋊C4C2211yescharacteristic
38C22×C22⋊Dic47C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47C22×(C2×D47)⋊C4C2211yescharacteristic
48C22×(C2×D47)⋊C4C2211yescharacteristic
49#15689055C2218yescomplemented
50#15689039C2218yescomplemented
51#15689033C2218yescomplemented
52#15689032C2218yescomplemented
53#15689025C2218yescomplemented
54#15689014C2218yescomplemented
55#15689014C2218yescomplemented
56#15689002C2218yescomplemented
57#15689001C2218yescomplemented
58#15688997C2218yescomplemented
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C2×C47⋊#95C2211yescharacteristic
62C2×C47⋊#95C2211yescharacteristic
63C24×C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C22×C42×C47C2211yescharacteristic
68C4×C22⋊C4×C47C2218yescomplemented
69C2×#95×C47C2211yescharacteristic
70C2×#95×C47C2211yescharacteristic
71C24×D47C2311yescharacteristic
72C24×D47C2311yescharacteristic
73C24×D47C2311yescharacteristic
74C22×D188—24no—
75C22×D188—24no—
76C22×D188—24no—
77C22×D188—24no—
78C22×D188—24no—
79C22×D188—24no—
80C22×D188—24no—
81C22×D188—42no—
82C22×D188—42no—
83C22×D188C2314yes—
84C22×D188C2314yes—
85C22×D188C2314yes—
86C22×C22⋊D47—24no—
87C22×C22⋊D47—24no—
88C22×C22⋊D47—24no—
89C22×C22⋊D47—24no—
90C22×C22⋊D47—24no—
91C22×C22⋊D47—24no—
92C22×C22⋊D47—42no—
93C22×C22⋊D47—42no—
94C22×C22⋊D47—42no—
95C22×C22⋊D47C2314yes—
96C22×C22⋊D47C2314yes—
97C22×C22⋊D47C2314yes—
98C23×Dic47C2311yescharacteristic
99C23×Dic47C2311yescharacteristic
100C23×Dic47C2311yescharacteristic
101C23×Dic47C2311yescharacteristic
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#13094006—232no—
112#13093998—232no—
113#13093997—232no—
114C4×D188—232no—
115C2×C4⋊Dic47—24no—
116C2×C4⋊Dic47—24no—
117C2×C4⋊Dic47—24no—
118C2×C4⋊Dic47C2314yes—
119C2×C4⋊Dic47C2314yes—
120C2×C4⋊Dic47C2314yes—
121C2×Dic47⋊C4—24no—
122C2×Dic47⋊C4—24no—
123C2×Dic47⋊C4C2314yes—
124C2×Dic47⋊C4C2314yes—
125C2×C22⋊Dic47—24no—
126C2×C22⋊Dic47C2314yes—
127C2×(C2×D47)⋊C4—24no—
128C2×(C2×D47)⋊C4—24no—
129C2×(C2×D47)⋊C4—24no—
130C2×(C2×D47)⋊C4—24no—
131C2×(C2×D47)⋊C4—24no—
132C2×(C2×D47)⋊C4—24no—
133C2×(C2×D47)⋊C4—42no—
134C2×(C2×D47)⋊C4—42no—
135C2×(C2×D47)⋊C4—42no—
136C2×(C2×D47)⋊C4D418yescomplemented
137C2×(C2×D47)⋊C4C2314yes—
138C2×(C2×D47)⋊C4C2314yes—
139C2×(C2×D47)⋊C4C2314yes—
140C2×(C2×D47)⋊C4C2314yes—
141C2×(C2×D47)⋊C4C2314yes—
142C2×(C2×D47)⋊C4C2314yes—
143C2×(C2×D47)⋊C4C2314yes—
144C2×(C2×D47)⋊C4C2314yes—
145C2×(C2×D47)⋊C4C2314yes—
146C2×(C2×D47)⋊C4C2314yes—
147C47⋊#95C2314yes—
148C47⋊#95C2314yes—
149C47⋊#95C2314yes—
150C47⋊#95C2314yes—
151C25×C47C2311yescharacteristic
152C23×C4×C47—24no—
153C23×C4×C47—24no—
154C23×C4×C47—42no—
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2314yes—
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C23×C4×C47C2311yescharacteristic
162C2×C22⋊C4×C47—24no—
163C2×C22⋊C4×C47D418yescomplemented
164C2×C22⋊C4×C47C2314yes—
165C2×C22⋊C4×C47C2314yes—
166C2×C42×C47—24no—
167C2×C42×C47—42no—
168C2×C42×C47C2314yes—
169C2×C42×C47C2314yes—
170#95×C47C2314yes—
171#95×C47C2314yes—
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47C2×D414yes—
179C24×C47C2412yes—
180C24×C47C2411yescharacteristic
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—22no—
188C23×D47—22no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47—22no—
192C23×D47—22no—
193C23×D47—22no—
194C23×D47—22no—
195C23×D47—22no—
196C23×D47—22no—
197C23×D47—22no—
198C23×D47—22no—
199C23×D47—22no—
200C23×D47C2×D414yes—
201C23×D47#4114yes—
202C23×D47C2412yes—
203C23×D47C2412yes—
204C23×D47C2412yes—
205C22×C4×C47—22no—
206C22×C4×C47—22no—
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—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—28no—
219C22×C4×C47—28no—
220C22×C4×C47—44no—
221C22×C4×C47—416no—
222C22×C4×C47C2×D414yes—
223C22×C4×C47C2×D414yes—
224C22×C4×C47C2×D414yes—
225C22×C4×C47#4114yes—
226C22×C4×C47#4114yes—
227C22×C4×C47C2412yes—
228C22×C4×C47C2412yes—
229C22×C4×C47C2412yes—
230C22×C4×C47C2412yes—
231C22×C4×C47C2412yes—
232C22×C4×C47C2412yes—
233C2×C22⋊D47—28no—
234C2×C22⋊D47—28no—
235C2×C22⋊D47—28no—
236C2×C22⋊D47—28no—
237C2×C22⋊D47—28no—
238C2×C22⋊D47—28no—
239C2×C22⋊D47—44no—
240C2×C22⋊D47—44no—
241C2×C22⋊D47—44no—
242C2×C22⋊D47—416no—
243C2×C22⋊D47—416no—
244C2×C22⋊D47—416no—
245C22×Dic47—22no—
246C22×Dic47—22no—
247C22×Dic47—22no—
248C22×Dic47—22no—
249C22×Dic47—22no—
250C22×Dic47—22no—
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×Dic47C2×D414yes—
260C22×Dic47C2412yes—
261C22×Dic47C2412yes—
262C22×Dic47C2412yes—
263C22×Dic47C2412yes—
264C22×Dic47C2412yes—
265C2×D188—232no—
266C2×D188—28no—
267C2×D188—28no—
268C2×D188—28no—
269C2×D188—28no—
270C2×D188—28no—
271C2×D188—28no—
272C2×D188—28no—
273C2×D188—44no—
274C2×D188—44no—
275C2×D188—416no—
276C2×D188—416no—
277C2×C4×D47—28no—
278C2×C4×D47—28no—
279C2×C4×D47—28no—
280C2×C4×D47—28no—
281C2×C4×D47—44no—
282C2×C4×D47—44no—
283C2×C4×D47—416no—
284C2×C4×D47—416no—
285C22⋊C4×C47—28no—
286C22⋊C4×C47C2×D4116yescomplemented
287C42×C47—28no—
288C42×C47—44no—
289C22⋊Dic47—28no—
290(C2×D47)⋊C4—28no—
291(C2×D47)⋊C4—28no—
292(C2×D47)⋊C4—28no—
293(C2×D47)⋊C4—28no—
294(C2×D47)⋊C4—28no—
295(C2×D47)⋊C4—28no—
296(C2×D47)⋊C4—44no—
297(C2×D47)⋊C4—44no—
298(C2×D47)⋊C4—44no—
299(C2×D47)⋊C4C2×D4116yescomplemented
300C4⋊Dic47—28no—
301C4⋊Dic47—28no—
302C4⋊Dic47—28no—
303Dic47⋊C4—28no—
304Dic47⋊C4—28no—
305C23×C47—28no—
306C23×C47—28no—
307C23×C47—28no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—44no—
315C23×C47—44no—
316C23×C47—44no—
317C23×C47—44no—
318C23×C47C22×D412yes—
319C23×C47C22×D414yes—
320C23×C47C22×D412yes—
321C23×C47C2×#4112yes—
322C23×C47C2×#4112yes—
323C23×C47C2×#4112yes—
324C23×C47H(5,𝔽2)12yes—
325C23×C47H(5,𝔽2)12yes—
326C23×C47C2511yescharacteristic
327C22×D47—28no—
328C22×D47—28no—
329C22×D47—28no—
330C22×D47—28no—
331C22×D47—28no—
332C22×D47—28no—
333C22×D47—22no—
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—22no—
341C22×D47—22no—
342C22×D47—22no—
343C22×D47—22no—
344C22×D47—22no—
345C22×D47—22no—
346C22×D47—22no—
347C22×D47—22no—
348C22×D47—22no—
349C22×D47—22no—
350C22×D47—22no—
351C22×D47—22no—
352C22×D47—44no—
353C22×D47—44no—
354C22×D47—44no—
355C22×D47—44no—
356C22×D47—44no—
357C22×D47—44no—
358C22×D47—44no—
359C22×D47—44no—
360C22×D47—44no—
361C22×D47—44no—
362C22×D47—44no—
363C22×D47—44no—
364C22×D47—44no—
365C22×D47—44no—
366C22×D47—44no—
367C22×D47C22×D414yes—
368C22×D47C2×#4114yes—
369C2×C4×C47—28no—
370C2×C4×C47—28no—
371C2×C4×C47—28no—
372C2×C4×C47—28no—
373C2×C4×C47—28no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—22no—
380C2×C4×C47—22no—
381C2×C4×C47—22no—
382C2×C4×C47—22no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—22no—
386C2×C4×C47—22no—
387C2×C4×C47—416no—
388C2×C4×C47—44no—
389C2×C4×C47C22×D414yes—
390C2×C4×C47C22×D414yes—
391C2×C4×C47C22×D414yes—
392C2×C4×C47C2×#4114yes—
393C2×C4×C47C2×#4114yes—
394C22⋊D47—416no—
395C22⋊D47—416no—
396C22⋊D47—416no—
397C2×Dic47—28no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
402C2×Dic47—22no—
403C2×Dic47—22no—
404C2×Dic47—22no—
405C2×Dic47—22no—
406C2×Dic47—22no—
407C2×Dic47—22no—
408C2×Dic47—22no—
409C2×Dic47—22no—
410C2×Dic47—22no—
411C2×Dic47—22no—
412C2×Dic47—44no—
413C2×Dic47—44no—
414C2×Dic47—44no—
415C2×Dic47—44no—
416C2×Dic47C22×D414yes—
417D188—232no—
418D188—416no—
419D188—416no—
420C4×D47—416no—
421C4×D47—416no—
422C2×#2464—471nomaximal, Sylow
423C22×C47—24no—
424C22×C47—24no—
425C22×C47—24no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—42no—
429C22×C47—42no—
430C22×C47—416no—
431C22×C47#52514yes—
432C22×C47#53214yes—
433C22×C47#54014yes—
434C22×C47D4214yes—
435C22×C47#54614yes—
436C22×C47#54614yes—
437C22×C47#55314yes—
438C22×C47C23×D411yescharacteristic
439C22×C47C23×D411yescharacteristic
440C22×C47C22×#4111yescharacteristic
441C22×C47C22×#4111yescharacteristic
442C22×C47C22×#4111yescharacteristic
443C22×C47C2×H(5,𝔽2)11yescharacteristic
444C22×C47C2×H(5,𝔽2)11yescharacteristic
445C2×D47—24no—
446C2×D47—24no—
447C2×D47—24no—
448C2×D47—24no—
449C2×D47—24no—
450C2×D47—24no—
451C2×D47—42no—
452C2×D47—42no—
453C2×D47—42no—
454C2×D47—42no—
455C2×D47—42no—
456C2×D47—42no—
457C2×D47—42no—
458C2×D47—42no—
459C2×D47—416no—
460C2×D47—416no—
461C2×D47—42no—
462C2×D47—42no—
463C2×D47—42no—
464C2×D47—42no—
465C2×D47—42no—
466C2×D47—42no—
467C2×D47—42no—
468C2×D47—88no—
469C4×C47—24no—
470C4×C47—24no—
471C4×C47—24no—
472C4×C47—24no—
473C4×C47—24no—
474C4×C47—42no—
475Dic47—24no—
476Dic47—42no—
477Dic47—42no—
478Dic47—42no—
479Dic47—42no—
480C22×#123—471no—
481C22×#121—471no—
482C22×#121—471no—
483C22×C4×D4—471no—
484#2464—4716no—
485C2×#398—471no—
486C2×#394—471no—
487C2×#392—471no—
488C2×#392—471no—
489C2×#390—471no—
490C2×#388—471no—
491C2×#388—471no—
492C2×#386—471no—
493C2×#386—471no—
494C2×#385—471no—
495C2×C4×C22⋊C4D4711yescharacteristic, complemented
496C2×C47—44no—
497C2×C47#246418yescomplemented
498C2×C47C2×#52511yescharacteristic
499C2×C47C2×#53211yescharacteristic
500C2×C47C2×#54011yescharacteristic
501C2×C47C2×D4211yescharacteristic
502C2×C47C2×#54611yescharacteristic
503C2×C47C2×#54611yescharacteristic
504C2×C47C2×#55311yescharacteristic
505D47—44no—
506D47—44no—
507D47—82no—
508C23×D4—471no—
509C23×D4—471no—
510C23×D4—471no—
511C23×D4—471no—
512C23×D4—471no—
513C23×D4—471no—
514C24×C4—471no—
515C24×C4—471no—
516C24×C4C2×D4711yescharacteristic
517C2×#123—478no—
518C2×#123—948no—
519C2×#121—478no—
520C2×#121—478no—
521C2×#121—948no—
522C2×#121—948no—
523C2×C4×D4—478no—
524C2×C4×D4—948no—
525C22×C4⋊C4—471no—
526C22×C4⋊C4—471no—
527C22×C4⋊C4—471no—
528C22×C4⋊C4—471no—
529C22×C4⋊C4—471no—
530C22×C22⋊C4—471no—
531C22×C22⋊C4—471no—
532C22×C22⋊C4—471no—
533C22×C22⋊C4—471no—
534C22×C22⋊C4—471no—
535C22×C22⋊C4—471no—
536C22×C22⋊C4—471no—
537C22×C22⋊C4—471no—
538C22×C22⋊C4—471no—
539C22×C22⋊C4—471no—
540C22×C22⋊C4—471no—
541C22×C22⋊C4C2×D4711yescharacteristic
542C22×C22⋊C4C2×D4711yescharacteristic
543C22×C42C2×D4711yescharacteristic
544C22×C42C2×D4711yescharacteristic
545#398—478no—
546#394—478no—
547#392—478no—
548#392—478no—
549#390—478no—
550#388—478no—
551#388—478no—
552#386—478no—
553#386—478no—
554#385—478no—
555C4×C22⋊C4C2×D4718yescomplemented
556C2×#95—471no—
557C2×#95—471no—
558C2×#95—471no—
559C2×#95—471no—
560C2×#95C2×D4711yescharacteristic
561C2×#95C2×D4711yescharacteristic
562C47C2×#246411yescharacteristic, complemented, Sylow
563C25—471no—
564C25—471no—
565C25—471no—
566C25C22×D4711yescharacteristic
567C22×D4—474no—
568C22×D4—474no—
569C22×D4—474no—
570C22×D4—474no—
571C22×D4—474no—
572C22×D4—474no—
573C22×D4—944no—
574C22×D4—944no—
575C22×D4—944no—
576C22×D4—944no—
577C22×D4—944no—
578C22×D4—944no—
579C22×D4—944no—
580C22×D4—944no—
581C22×D4—944no—
582C22×D4—944no—
583C22×D4—944no—
584C22×D4—944no—
585C22×D4—944no—
586C22×D4—1882no—
587C22×D4—1882no—
588C22×D4—1882no—
589C22×D4—1882no—
590C22×D4—1882no—
591C23×C4—24no—
592C23×C4—24no—
593C23×C4—42no—
594C23×C4—471no—
595C23×C4—471no—
596C23×C4—471no—
597C23×C4—471no—
598C23×C4—471no—
599C23×C4—474no—
600C23×C4—474no—
601C23×C4—944no—
602C23×C4—944no—
603C23×C4—944no—
604C23×C4—944no—
605C23×C4—1882no—
606C23×C4—1882no—
607C23×C4C22×D4711yescharacteristic
608C23×C4C22×D4714yes—
609C23×C4C22×D4711yescharacteristic
610C23×C4C22×D4711yescharacteristic
611C23×C4C22×D4711yescharacteristic
612C23×C4C22×D4711yescharacteristic
613C23×C4C22×D4711yescharacteristic
614#123—9432no—
615#121—9432no—
616#121—9432no—
617C4×D4—9432no—
618C2×C4⋊C4—474no—
619C2×C4⋊C4—474no—
620C2×C4⋊C4—474no—
621C2×C4⋊C4—474no—
622C2×C4⋊C4—474no—
623C2×C4⋊C4—944no—
624C2×C4⋊C4—944no—
625C2×C4⋊C4—944no—
626C2×C4⋊C4—944no—
627C2×C4⋊C4—944no—
628C2×C22⋊C4—24no—
629C2×C22⋊C4—478no—
630C2×C22⋊C4—474no—
631C2×C22⋊C4—474no—
632C2×C22⋊C4—474no—
633C2×C22⋊C4—474no—
634C2×C22⋊C4—474no—
635C2×C22⋊C4—474no—
636C2×C22⋊C4—474no—
637C2×C22⋊C4—474no—
638C2×C22⋊C4—474no—
639C2×C22⋊C4—474no—
640C2×C22⋊C4—474no—
641C2×C22⋊C4—944no—
642C2×C22⋊C4—944no—
643C2×C22⋊C4—944no—
644C2×C22⋊C4—944no—
645C2×C22⋊C4—944no—
646C2×C22⋊C4—944no—
647C2×C22⋊C4—944no—
648C2×C22⋊C4—1882no—
649C2×C22⋊C4—1882no—
650C2×C22⋊C4—1882no—
651C2×C22⋊C4D18818yescomplemented
652C2×C22⋊C4C22×D4714yes—
653C2×C22⋊C4C22×D4714yes—
654C2×C42—24no—
655C2×C42—42no—
656C2×C42C22×D4714yes—
657C2×C42C22×D4714yes—
658#95—474no—
659#95—474no—
660#95—474no—
661#95—474no—
662#95C22×D4714yes—
663#95C22×D4714yes—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—474no—
671C24—474no—
672C24—472no—
673C24—472no—
674C24—472no—
675C24—942no—
676C24—942no—
677C24—942no—
678C24—942no—
679C24—942no—
680C24—942no—
681C24—942no—
682C24—942no—
683C24—942no—
684C24—942no—
685C24—942no—
686C24—942no—
687C24—942no—
688C24—942no—
689C24—942no—
690C24—942no—
691C24—942no—
692C24—942no—
693C24—942no—
694C24C2×D18814yes—
695C24C23×D4712yes—
696C24C23×D4711yescharacteristic
697C2×D4—948no—
698C2×D4—948no—
699C2×D4—9432no—
700C2×D4—948no—
701C2×D4—948no—
702C2×D4—948no—
703C2×D4—948no—
704C2×D4—948no—
705C2×D4—948no—
706C2×D4—948no—
707C2×D4—948no—
708C2×D4—948no—
709C2×D4—948no—
710C2×D4—948no—
711C2×D4—1884no—
712C2×D4—1884no—
713C2×D4—18816no—
714C2×D4—18816no—
715C2×D4—1884no—
716C2×D4—1884no—
717C2×D4—1884no—
718C2×D4—18816no—
719C2×D4—18816no—
720C2×D4—18816no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—44no—
737C22×C4—416no—
738C22×C4—474no—
739C22×C4—472no—
740C22×C4—472no—
741C22×C4—472no—
742C22×C4—472no—
743C22×C4—472no—
744C22×C4—948no—
745C22×C4—948no—
746C22×C4—942no—
747C22×C4—942no—
748C22×C4—942no—
749C22×C4—942no—
750C22×C4—942no—
751C22×C4—942no—
752C22×C4—942no—
753C22×C4—942no—
754C22×C4—942no—
755C22×C4—942no—
756C22×C4—942no—
757C22×C4—942no—
758C22×C4—942no—
759C22×C4—942no—
760C22×C4—948no—
761C22×C4—948no—
762C22×C4—1884no—
763C22×C4—1884no—
764C22×C4—18816no—
765C22×C4—18816no—
766C22×C4C2×D18814yes—
767C22×C4C2×D18814yes—
768C22×C4#1062535014yes—
769C22×C4#1062535014yes—
770C22×C4D4×D4714yes—
771C22×C4C23×D4712yes—
772C22×C4C23×D4712yes—
773C22×C4C23×D4712yes—
774C22×C4C23×D4712yes—
775C22×C4C23×D4712yes—
776C22×C4C23×D4712yes—
777C4⋊C4—948no—
778C4⋊C4—948no—
779C4⋊C4—948no—
780C4⋊C4—948no—
781C4⋊C4—948no—
782C22⋊C4—28no—
783C22⋊C4—4716no—
784C22⋊C4—948no—
785C22⋊C4—948no—
786C22⋊C4—948no—
787C22⋊C4—948no—
788C22⋊C4—948no—
789C22⋊C4—948no—
790C22⋊C4—948no—
791C22⋊C4—1884no—
792C22⋊C4—1884no—
793C22⋊C4—1884no—
794C22⋊C4C2×D188116yescomplemented
795C42—28no—
796C42—44no—
797C23—28no—
798C23—28no—
799C23—28no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—474no—
811C23—474no—
812C23—948no—
813C23—948no—
814C23—948no—
815C23—948no—
816C23—948no—
817C23—948no—
818C23—942no—
819C23—942no—
820C23—942no—
821C23—942no—
822C23—942no—
823C23—942no—
824C23—942no—
825C23—942no—
826C23—942no—
827C23—942no—
828C23—942no—
829C23—942no—
830C23—942no—
831C23—942no—
832C23—942no—
833C23—942no—
834C23—942no—
835C23—942no—
836C23—942no—
837C23—1884no—
838C23—1884no—
839C23—1884no—
840C23—1884no—
841C23—1884no—
842C23—1884no—
843C23—1884no—
844C23—1884no—
845C23—1884no—
846C23—1884no—
847C23—1884no—
848C23—1884no—
849C23—1884no—
850C23—1884no—
851C23—1884no—
852C23C2×D4×D4712yes—
853C23C22×D18814yes—
854C23C22×D18812yes—
855C23#41×D4712yes—
856C23C2×#1062535012yes—
857C23C2×#1062535012yes—
858C23#1309406912yes—
859C23#1309407012yes—
860C23C24×D4711yescharacteristic
861D4—9432no—
862D4—18816no—
863D4—18816no—
864D4—18816no—
865D4—18816no—
866D4—18816no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—28no—
870C2×C4—28no—
871C2×C4—28no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—416no—
886C2×C4—44no—
887C2×C4—474no—
888C2×C4—948no—
889C2×C4—942no—
890C2×C4—942no—
891C2×C4—942no—
892C2×C4—942no—
893C2×C4—942no—
894C2×C4—942no—
895C2×C4—942no—
896C2×C4—942no—
897C2×C4—942no—
898C2×C4—942no—
899C2×C4—942no—
900C2×C4—942no—
901C2×C4—942no—
902C2×C4—942no—
903C2×C4—18816no—
904C2×C4—18816no—
905C2×C4—1884no—
906C2×C4—1884no—
907C2×C4—1884no—
908C2×C4—1884no—
909C2×C4C2×D4×D4714yes—
910C2×C4C22×D18814yes—
911C2×C4C22×D18814yes—
912C2×C4C2×#1062535014yes—
913C2×C4C2×#1062535014yes—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—42no—
918C22—416no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—944no—
923C22—944no—
924C22—944no—
925C22—944no—
926C22—944no—
927C22—944no—
928C22—3768no—
929C22—1882no—
930C22—1882no—
931C22—1882no—
932C22—1882no—
933C22—1882no—
934C22—1882no—
935C22—1882no—
936C22—1882no—
937C22—1882no—
938C22—1882no—
939C22—18816no—
940C22—18816no—
941C22—1882no—
942C22—1882no—
943C22—1882no—
944C22—1882no—
945C22—1882no—
946C22#1568963214yes—
947C22#1568967314yes—
948C22#1568972414yes—
949C22D4×D18814yes—
950C22#1568976314yes—
951C22#1568976814yes—
952C22#1568981714yes—
953C22C22×D4×D4711yescharacteristic
954C22C23×D18811yescharacteristic
955C22C2×#41×D4711yescharacteristic
956C22C22×#1062535011yescharacteristic
957C22C22×#1062535011yescharacteristic
958C22C2×#1309406911yescharacteristic
959C22C2×#1309407011yescharacteristic
960C4—24no—
961C4—24no—
962C4—24no—
963C4—24no—
964C4—24no—
965C4—42no—
966C4—944no—
967C4—1882no—
968C4—1882no—
969C4—1882no—
970C4—1882no—
971C2—44no—
972C2—3762no—
973C2—1884no—
974C2—1884no—
975C2#2024739418yesdirect product factor
976C2C2×#1568963211yescharacteristic
977C2C2×#1568967311yescharacteristic
978C2C2×#1568972411yescharacteristic
979C2C2×D4×D18811yescharacteristic
980C2C2×#1568976311yescharacteristic
981C2C2×#1568976811yescharacteristic
982C2C2×#1568981711yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C4×C22⋊C4×C47C2
socleC24×C47C24
hypercenterC2×C4×C22⋊C4D47
hypocenterC47C2×#2464
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#13094006C2semidirect
2. C22×#13093998C2semidirect
3. C22×#13093997C2semidirect
4. C22×C4×D188C2semidirect
5. #20247394C2direct (N × H)
6. C2×#15689055C2semidirect
7. C2×#15689039C2semidirect
8. C2×#15689033C2semidirect
9. C2×#15689032C2semidirect
10. C2×#15689025C2semidirect
11. C2×#15689014C2semidirect
12. C2×#15689014C2semidirect
13. C2×#15689002C2semidirect
14. C2×#15689001C2semidirect
15. C2×#15688997C2semidirect
16. C2×C4×C22⋊C4×C47C2semidirect
26. C2×#13094006C22semidirect
28. C2×#13093998C22semidirect
30. C2×#13093997C22semidirect
32. C2×C4×D188C22semidirect
49. #15689055C22semidirect
50. #15689039C22semidirect
51. #15689033C22semidirect
52. #15689032C22semidirect
53. #15689025C22semidirect
54. #15689014C22semidirect
55. #15689014C22semidirect
56. #15689002C22semidirect
57. #15689001C22semidirect
58. #15688997C22semidirect
68. C4×C22⋊C4×C47C22semidirect
136. C2×(C2×D47)⋊C4D4semidirect
163. C2×C22⋊C4×C47D4semidirect
286. C22⋊C4×C47C2×D4semidirect
299. (C2×D47)⋊C4C2×D4semidirect
495. C2×C4×C22⋊C4D47semidirect
497. C2×C47#2464semidirect
555. C4×C22⋊C4C2×D47semidirect
562. C47C2×#2464semidirect
651. C2×C22⋊C4D188semidirect
794. C22⋊C4C2×D188semidirect
975. C2#20247394direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940062
C22×#130939982
C22×#130939972
C22×C4×D1882
#202473942
C2×#156890552
C2×#156890392
C2×#156890332
C2×#156890322
C2×#156890252
C2×#156890142
C2×#156890022
C2×#156890012
C2×#156889972
C2×C4×C22⋊C4×C472
C2×#246447