Finite Group Databasebeta

← C2×#20246772 #26384898

Subgroups — C2×#20246772 #26384898

Order 12032.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094009C211yesmaximal, characteristic, complemented
2C22×#13093994C211yesmaximal, characteristic
3C22×#13093981C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D47C211yesmaximal, characteristic, complemented
5#20246772C2116yesmaximal, direct product factor
6C2×#15689047C211yesmaximal, characteristic, complemented
7C2×#15689046C211yesmaximal, characteristic, complemented
8C2×#15689041C211yesmaximal, characteristic, complemented
9C2×#15689038C211yesmaximal, characteristic, complemented
10C2×#15689025C211yesmaximal, characteristic, complemented
11C2×#15689023C211yesmaximal, characteristic, complemented
12C2×#15689013C211yesmaximal, characteristic, complemented
13C2×#15689001C211yesmaximal, characteristic, complemented
14C2×#15688997C211yesmaximal, characteristic, complemented
15C2×#15688978C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C2×#13094009—28no—
24C2×#13094009C2218yescomplemented
25C2×#13093994—28no—
26C2×#13093994C2218yes—
27C2×#13093981—28no—
28C2×#13093981C2218yescomplemented
29C22×C4⋊Dic47C2211yescharacteristic, complemented
30C22×Dic47⋊C4C2211yescharacteristic, complemented
31C22×Dic47⋊C4C2211yescharacteristic, complemented
32C22×Dic47⋊C4C2211yescharacteristic, complemented
33C22×Dic47⋊C4C2211yescharacteristic, complemented
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×(C2×D47)⋊C4C2211yescharacteristic
42C22×(C2×D47)⋊C4C2211yescharacteristic
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
47C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
48C2×C22⋊C4×D47—28no—
49C2×C22⋊C4×D47C2218yescomplemented
50C22×C4×Dic47C2211yescharacteristic, complemented
51#15689047C2218yescomplemented
52#15689046C2218yescomplemented
53#15689041C2218yescomplemented
54#15689038C2218yescomplemented
55#15689025C2218yescomplemented
56#15689023C2218yescomplemented
57#15689013C2218yescomplemented
58#15689001C2218yescomplemented
59#15688997C2218yescomplemented
60#15688978C2218yescomplemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C2×C47⋊#95C2211yescharacteristic, complemented
63C22×C4⋊C4×C47C2211yescharacteristic, complemented
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C42×C47C2211yescharacteristic, complemented
68C47×#388C2218yescomplemented
69C2×#95×C47C2211yescharacteristic, complemented
70C2×#95×C47C2211yescharacteristic, complemented
71C24×D47—24no—
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—24no—
76C24×D47—42no—
77C24×D47—42no—
78C24×D47C2311yescharacteristic
79C24×D47C2311yescharacteristic
80C24×D47C2314yes—
81C24×D47C2311yescharacteristic
82C22×D188—24no—
83C22×D188—24no—
84C22×D188—24no—
85C22×D188—24no—
86C22×D188—24no—
87C22×D188—42no—
88C22×D188C2314yes—
89C22×D188C2314yes—
90C22×C22⋊D47—24no—
91C22×C22⋊D47—24no—
92C22×C22⋊D47—42no—
93C22×C22⋊D47C2314yes—
94C23×Dic47C2311yescharacteristic
95C23×Dic47C2311yescharacteristic
96C23×Dic47C2311yescharacteristic
97C23×Dic47C2311yescharacteristic
98C23×Dic47C2311yescharacteristic
99C22×C4×D47—24no—
100C22×C4×D47—24no—
101C22×C4×D47—24no—
102C22×C4×D47—42no—
103C22×C4×D47—42no—
104C22×C4×D47D418yescomplemented
105C22×C4×D47C2314yes—
106C22×C4×D47C2314yes—
107#13094009—232no—
108#13093994—232no—
109#13093981—232no—
110C2×C4⋊Dic47—42no—
111C2×C4⋊Dic47C2314yescomplemented
112C2×Dic47⋊C4—24no—
113C2×Dic47⋊C4—24no—
114C2×Dic47⋊C4—24no—
115C2×Dic47⋊C4—42no—
116C2×Dic47⋊C4C2314yescomplemented
117C2×Dic47⋊C4C2314yescomplemented
118C2×Dic47⋊C4C2314yescomplemented
119C2×Dic47⋊C4C2314yescomplemented
120C2×C22⋊Dic47—24no—
121C2×C22⋊Dic47—42no—
122C2×C22⋊Dic47C2314yes—
123C2×C22⋊Dic47C2314yes—
124C2×(C2×D47)⋊C4—24no—
125C2×(C2×D47)⋊C4—24no—
126C2×(C2×D47)⋊C4—24no—
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—42no—
133C2×(C2×D47)⋊C4—42no—
134C2×(C2×D47)⋊C4—42no—
135C2×(C2×D47)⋊C4D418yes—
136C2×(C2×D47)⋊C4C2314yes—
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)⋊C4C2314yescomplemented
145C2×(C2×D47)⋊C4C2314yescomplemented
146C2×(C2×D47)⋊C4C2314yescomplemented
147C2×(C2×D47)⋊C4C2314yescomplemented
148C22⋊C4×D47—232no—
149C2×C4×Dic47—24no—
150C2×C4×Dic47C2314yescomplemented
151C47⋊#95C2314yescomplemented
152C47⋊#95C2314yescomplemented
153C25×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C2×C4⋊C4×C47—24no—
161C2×C4⋊C4×C47C2314yescomplemented
162C2×C22⋊C4×C47—24no—
163C2×C22⋊C4×C47—24no—
164C2×C22⋊C4×C47—24no—
165C2×C22⋊C4×C47C2314yes—
166C2×C22⋊C4×C47C2314yes—
167C2×C22⋊C4×C47C2314yes—
168C2×C42×C47—24no—
169C2×C42×C47C2314yescomplemented
170#95×C47C2314yescomplemented
171#95×C47C2314yescomplemented
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
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—22no—
188C23×D47—28no—
189C23×D47—22no—
190C23×D47—22no—
191C23×D47—22no—
192C23×D47—22no—
193C23×D47—28no—
194C23×D47—28no—
195C23×D47—22no—
196C23×D47—22no—
197C23×D47—22no—
198C23×D47—22no—
199C23×D47—22no—
200C23×D47—22no—
201C23×D47—22no—
202C23×D47—28no—
203C23×D47—28no—
204C23×D47—44no—
205C23×D47—44no—
206C23×D47—416no—
207C23×D47—416no—
208C23×D47—416no—
209C23×D47—416no—
210C23×D47—416no—
211C23×D47—416no—
212C23×D47C2×D414yes—
213C23×D47C2×D414yes—
214C23×D47#4114yes—
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—22no—
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×C47C2×D414yes—
236C22×C4×C47C2×D414yes—
237C22×C4×C47C2412yes—
238C22×C4×C47C2412yes—
239C22×C4×C47C2412yes—
240C22×C4×C47C2412yes—
241C22×C4×C47C2412yes—
242C22×C4×C47C2412yes—
243C2×C22⋊D47—28no—
244C2×C22⋊D47—28no—
245C2×C22⋊D47—44no—
246C2×C22⋊D47—416no—
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×Dic47—22no—
260C22×Dic47C2×D414yes—
261C22×Dic47C2×D414yes—
262C22×Dic47C2412yes—
263C22×Dic47C2412yes—
264C22×Dic47C2412yes—
265C22×Dic47C2412yes—
266C22×Dic47C2412yes—
267C2×D188—28no—
268C2×D188—28no—
269C2×D188—28no—
270C2×D188—28no—
271C2×D188—28no—
272C2×D188—44no—
273C2×D188—416no—
274C2×D188—416no—
275C2×C4×D47—232no—
276C2×C4×D47—28no—
277C2×C4×D47—28no—
278C2×C4×D47—28no—
279C2×C4×D47—44no—
280C2×C4×D47—44no—
281C2×C4×D47—416no—
282C2×C4×D47C2×D4116yescomplemented
283C4⋊C4×C47—28no—
284C22⋊C4×C47—28no—
285C22⋊C4×C47—28no—
286C22⋊C4×C47—28no—
287C42×C47—28no—
288C22⋊Dic47—28no—
289C22⋊Dic47—44no—
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—28no—
297(C2×D47)⋊C4—28no—
298(C2×D47)⋊C4—44no—
299(C2×D47)⋊C4—44no—
300(C2×D47)⋊C4—44no—
301(C2×D47)⋊C4C2×D4116yes—
302C4⋊Dic47—44no—
303Dic47⋊C4—28no—
304Dic47⋊C4—28no—
305Dic47⋊C4—28no—
306Dic47⋊C4—44no—
307C4×Dic47—28no—
308C23×C47—28no—
309C23×C47—28no—
310C23×C47—28no—
311C23×C47—22no—
312C23×C47—22no—
313C23×C47—22no—
314C23×C47—22no—
315C23×C47—22no—
316C23×C47—22no—
317C23×C47—44no—
318C23×C47—44no—
319C23×C47—44no—
320C23×C47—44no—
321C23×C47C22×D412yes—
322C23×C47C22×D412yes—
323C23×C47C2×#4112yes—
324C23×C47C2×#4112yes—
325C23×C47C2×#4114yes—
326C23×C47C2×#4112yes—
327C23×C47H(5,𝔽2)12yes—
328C23×C47H(5,𝔽2)12yes—
329C23×C47C2511yescharacteristic
330C22×D47—28no—
331C22×D47—28no—
332C22×D47—28no—
333C22×D47—28no—
334C22×D47—28no—
335C22×D47—28no—
336C22×D47—22no—
337C22×D47—22no—
338C22×D47—22no—
339C22×D47—22no—
340C22×D47—232no—
341C22×D47—28no—
342C22×D47—28no—
343C22×D47—28no—
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—22no—
353C22×D47—22no—
354C22×D47—22no—
355C22×D47—22no—
356C22×D47—22no—
357C22×D47—416no—
358C22×D47—416no—
359C22×D47—416no—
360C22×D47—416no—
361C22×D47—4128no—
362C22×D47—416no—
363C22×D47—44no—
364C22×D47—44no—
365C22×D47—44no—
366C22×D47—44no—
367C22×D47—416no—
368C22×D47—44no—
369C22×D47—44no—
370C22×D47—44no—
371C22×D47—44no—
372C22×D47—44no—
373C22×D47—44no—
374C22×D47—44no—
375C22×D47#121116yes—
376C22×D47C22×D414yes—
377C22×D47C22×D414yes—
378C22×D47C2×#4114yes—
379C22×D47C2×#4114yes—
380C2×C4×C47—28no—
381C2×C4×C47—28no—
382C2×C4×C47—22no—
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—44no—
399C2×C4×C47—44no—
400C2×C4×C47—44no—
401C2×C4×C47—44no—
402C2×C4×C47C22×D414yes—
403C2×C4×C47C22×D414yes—
404C22⋊D47—416no—
405C2×Dic47—28no—
406C2×Dic47—28no—
407C2×Dic47—22no—
408C2×Dic47—22no—
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—44no—
421C2×Dic47—44no—
422C2×Dic47—44no—
423C2×Dic47C22×D414yes—
424C2×Dic47C22×D414yes—
425D188—416no—
426D188—416no—
427C4×D47—232no—
428C4×D47—416no—
429C2×#2411—471nomaximal, Sylow
430C22×C47—24no—
431C22×C47—24no—
432C22×C47—24no—
433C22×C47—42no—
434C22×C47—416no—
435C22×C47—42no—
436C22×C47—42no—
437C22×C47—42no—
438C22×C47C2×#12114yes—
439C22×C47#52514yes—
440C22×C47#53514yes—
441C22×C47#54614yes—
442C22×C47#54614yes—
443C22×C47#55114yes—
444C22×C47#55114yes—
445C22×C47C23×D411yescharacteristic
446C22×C47C23×D411yescharacteristic
447C22×C47C22×#4111yescharacteristic
448C22×C47C22×#4111yescharacteristic
449C22×C47C22×#4111yescharacteristic
450C22×C47C2×H(5,𝔽2)11yescharacteristic
451C22×C47C2×H(5,𝔽2)11yescharacteristic
452C2×D47—232no—
453C2×D47—24no—
454C2×D47—24no—
455C2×D47—24no—
456C2×D47—24no—
457C2×D47—24no—
458C2×D47—24no—
459C2×D47—24no—
460C2×D47—24no—
461C2×D47—24no—
462C2×D47—464no—
463C2×D47—42no—
464C2×D47—416no—
465C2×D47—42no—
466C2×D47—42no—
467C2×D47—42no—
468C2×D47—42no—
469C2×D47—42no—
470C2×D47—42no—
471C2×D47—42no—
472C2×D47—42no—
473C2×D47—42no—
474C2×D47—42no—
475C2×D47—88no—
476C2×D47C2×#12118yes—
477C4×C47—24no—
478C4×C47—24no—
479C4×C47—42no—
480C4×C47—42no—
481C4×C47—42no—
482C4×C47—42no—
483Dic47—24no—
484Dic47—24no—
485Dic47—42no—
486Dic47—42no—
487Dic47—42no—
488C22×#123—471no—
489C22×#120—471no—
490C22×#117—471no—
491C23×C22⋊C4—471no—
492#2411—4716no—
493C2×#396—471no—
494C2×#396—471no—
495C2×#394—471no—
496C2×#394—471no—
497C2×#390—471no—
498C2×#390—471no—
499C2×#388—471no—
500C2×#388D4711yescharacteristic, complemented
501C2×#386—471no—
502C2×#385—471no—
503C2×#379—471no—
504C2×C47—44no—
505C2×C47#241118yescomplemented
506C2×C47C22×#12111yescharacteristic
507C2×C47C2×#52511yescharacteristic
508C2×C47C2×#53511yescharacteristic
509C2×C47C2×#54611yescharacteristic
510C2×C47C2×#54611yescharacteristic
511C2×C47C2×#55111yescharacteristic
512C2×C47C2×#55111yescharacteristic
513D47—28no—
514D47—44no—
515D47—82no—
516C26—471no—
517C23×D4—471no—
518C23×D4—471no—
519C23×D4—471no—
520C24×C4—471no—
521C24×C4—471no—
522C2×#123—478no—
523C2×#123—948no—
524C2×#120—478no—
525C2×#120—948no—
526C2×#117—478no—
527C2×#117—948no—
528C22×C4⋊C4—471no—
529C22×C4⋊C4—471no—
530C22×C4⋊C4—471no—
531C22×C4⋊C4—471no—
532C22×C4⋊C4—471no—
533C22×C4⋊C4C2×D4711yescharacteristic, complemented
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⋊C4—471no—
542C22×C22⋊C4—471no—
543C22×C22⋊C4—471no—
544C22×C22⋊C4—471no—
545C22×C22⋊C4—471no—
546C22×C22⋊C4—471no—
547C22×C22⋊C4—471no—
548C22×C22⋊C4—478no—
549C22×C22⋊C4—948no—
550C22×C22⋊C4C2×D4711yescharacteristic
551C22×C22⋊C4C2×D4711yescharacteristic
552C22×C22⋊C4C2×D4711yescharacteristic
553C22×C42—471no—
554C22×C42C2×D4711yescharacteristic, complemented
555#396—478no—
556#396—478no—
557#394—478no—
558#394—478no—
559#390—478no—
560#390—478no—
561#388—478no—
562#388C2×D4718yescomplemented
563#386—478no—
564#385—478no—
565#379—478no—
566C2×#95—471no—
567C2×#95—471no—
568C2×#95C2×D4711yescharacteristic, complemented
569C2×#95C2×D4711yescharacteristic, complemented
570C47C2×#241111yescharacteristic, complemented, Sylow
571C25—471no—
572C25—471no—
573C25—471no—
574C25—474no—
575C25—944no—
576C25—944no—
577C25—944no—
578C25—944no—
579C25—944no—
580C25—1882no—
581C25—1882no—
582C25C22×D4711yescharacteristic
583C22×D4—474no—
584C22×D4—474no—
585C22×D4—474no—
586C22×D4—944no—
587C22×D4—944no—
588C22×D4—944no—
589C22×D4—944no—
590C22×D4—944no—
591C22×D4—944no—
592C22×D4—944no—
593C22×D4—1882no—
594C22×D4—1882no—
595C23×C4—471no—
596C23×C4—471no—
597C23×C4—478no—
598C23×C4—474no—
599C23×C4—471no—
600C23×C4—471no—
601C23×C4—471no—
602C23×C4—474no—
603C23×C4—944no—
604C23×C4—944no—
605C23×C4—944no—
606C23×C4—1882no—
607C23×C4—1882no—
608C23×C4C22×D4711yescharacteristic
609C23×C4C22×D4711yescharacteristic
610C23×C4C22×D4711yescharacteristic
611C23×C4C22×D4711yescharacteristic
612C23×C4C22×D4711yescharacteristic
613C23×C4C22×D4711yescharacteristic
614#123—9432no—
615#120—9432no—
616#117—9432no—
617C2×C4⋊C4—24no—
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—1882no—
627C2×C4⋊C4—1882no—
628C2×C4⋊C4C22×D4714yescomplemented
629C2×C22⋊C4—24no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—478no—
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—474no—
642C2×C22⋊C4—474no—
643C2×C22⋊C4—474no—
644C2×C22⋊C4—474no—
645C2×C22⋊C4—474no—
646C2×C22⋊C4—474no—
647C2×C22⋊C4—9432no—
648C2×C22⋊C4—944no—
649C2×C22⋊C4—944no—
650C2×C22⋊C4—944no—
651C2×C22⋊C4—944no—
652C2×C22⋊C4—944no—
653C2×C22⋊C4—944no—
654C2×C22⋊C4—944no—
655C2×C22⋊C4—944no—
656C2×C22⋊C4—944no—
657C2×C22⋊C4—1882no—
658C2×C22⋊C4—1882no—
659C2×C22⋊C4—1882no—
660C2×C22⋊C4—1882no—
661C2×C22⋊C4C22×D4714yes—
662C2×C22⋊C4C22×D4714yes—
663C2×C22⋊C4C22×D4714yes—
664C2×C42—24no—
665C2×C42—474no—
666C2×C42—944no—
667C2×C42C22×D4714yescomplemented
668#95—474no—
669#95—474no—
670#95C22×D4714yescomplemented
671#95C22×D4714yescomplemented
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—474no—
679C24—474no—
680C24—474no—
681C24—472no—
682C24—474no—
683C24—472no—
684C24—472no—
685C24—948no—
686C24—948no—
687C24—948no—
688C24—948no—
689C24—9432no—
690C24—942no—
691C24—942no—
692C24—942no—
693C24—942no—
694C24—942no—
695C24—942no—
696C24—942no—
697C24—948no—
698C24—942no—
699C24—942no—
700C24—942no—
701C24—942no—
702C24—942no—
703C24—942no—
704C24—942no—
705C24—942no—
706C24—942no—
707C24—942no—
708C24—1884no—
709C24—1884no—
710C24—18816no—
711C24—18816no—
712C24—18816no—
713C24—18816no—
714C24—18816no—
715C24—18816no—
716C24#1062535014yes—
717C24C23×D4712yes—
718C24C23×D4711yescharacteristic
719C2×D4—948no—
720C2×D4—948no—
721C2×D4—948no—
722C2×D4—948no—
723C2×D4—948no—
724C2×D4—948no—
725C2×D4—948no—
726C2×D4—1884no—
727C2×D4—18816no—
728C2×D4—18816no—
729C2×D4—1884no—
730C2×D4—18816no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
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—22no—
747C22×C4—474no—
748C22×C4—474no—
749C22×C4—472no—
750C22×C4—472no—
751C22×C4—4716no—
752C22×C4—472no—
753C22×C4—472no—
754C22×C4—472no—
755C22×C4—948no—
756C22×C4—9432no—
757C22×C4—948no—
758C22×C4—948no—
759C22×C4—942no—
760C22×C4—942no—
761C22×C4—942no—
762C22×C4—942no—
763C22×C4—942no—
764C22×C4—942no—
765C22×C4—942no—
766C22×C4—942no—
767C22×C4—942no—
768C22×C4—942no—
769C22×C4—942no—
770C22×C4—942no—
771C22×C4—942no—
772C22×C4—1884no—
773C22×C4—1884no—
774C22×C4—18816no—
775C22×C4D4×D4714yes—
776C22×C4D4×D4714yes—
777C22×C4C23×D4712yes—
778C22×C4C23×D4712yes—
779C22×C4C23×D4712yes—
780C22×C4C23×D4712yes—
781C22×C4C23×D4712yes—
782C22×C4C23×D4712yes—
783C4⋊C4—28no—
784C4⋊C4—948no—
785C4⋊C4—948no—
786C4⋊C4—948no—
787C4⋊C4—1884no—
788C4⋊C4—1884no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—28no—
792C22⋊C4—4716no—
793C22⋊C4—948no—
794C22⋊C4—948no—
795C22⋊C4—948no—
796C22⋊C4—948no—
797C22⋊C4—948no—
798C22⋊C4—948no—
799C22⋊C4—948no—
800C22⋊C4—948no—
801C22⋊C4—948no—
802C22⋊C4—1884no—
803C22⋊C4—1884no—
804C22⋊C4—1884no—
805C22⋊C4—1884no—
806C42—28no—
807C42—948no—
808C23—28no—
809C23—28no—
810C23—28no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—44no—
818C23—44no—
819C23—44no—
820C23—44no—
821C23—4716no—
822C23—474no—
823C23—474no—
824C23—474no—
825C23—474no—
826C23—9432no—
827C23—948no—
828C23—948no—
829C23—948no—
830C23—948no—
831C23—948no—
832C23—948no—
833C23—942no—
834C23—942no—
835C23—942no—
836C23—942no—
837C23—948no—
838C23—948no—
839C23—948no—
840C23—942no—
841C23—942no—
842C23—942no—
843C23—942no—
844C23—942no—
845C23—942no—
846C23—942no—
847C23—942no—
848C23—942no—
849C23—942no—
850C23—942no—
851C23—942no—
852C23—942no—
853C23—18816no—
854C23—18816no—
855C23—18816no—
856C23—18816no—
857C23—18816no—
858C23—18816no—
859C23—188128no—
860C23—1884no—
861C23—1884no—
862C23—1884no—
863C23—1884no—
864C23—1884no—
865C23—1884no—
866C23—1884no—
867C23—1884no—
868C23—1884no—
869C23—1884no—
870C23—1884no—
871C23C2×D4×D4712yes—
872C23C2×D4×D4712yes—
873C23#41×D4712yes—
874C23#41×D4712yes—
875C23C2×#1062535014yes—
876C23C2×#1062535012yes—
877C23#1309407012yes—
878C23#1309407012yes—
879C23C24×D4711yescharacteristic
880D4—18816no—
881D4—18816no—
882D4—18816no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
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—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—474no—
906C2×C4—474no—
907C2×C4—9432no—
908C2×C4—948no—
909C2×C4—948no—
910C2×C4—942no—
911C2×C4—942no—
912C2×C4—942no—
913C2×C4—942no—
914C2×C4—942no—
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—18816no—
924C2×C4—1884no—
925C2×C4—1884no—
926C2×C4—1884no—
927C2×C4C2×D4×D4714yes—
928C2×C4C2×D4×D4714yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—416no—
937C22—478no—
938C22—944no—
939C22—944no—
940C22—944no—
941C22—944no—
942C22—944no—
943C22—944no—
944C22—9432no—
945C22—944no—
946C22—944no—
947C22—944no—
948C22—3768no—
949C22—18864no—
950C22—1882no—
951C22—1882no—
952C22—1882no—
953C22—1882no—
954C22—1882no—
955C22—1882no—
956C22—1882no—
957C22—1882no—
958C22—1882no—
959C22—1882no—
960C22—1882no—
961C22—18816no—
962C22#121×D4714yes—
963C22#1568963214yes—
964C22#1568969114yes—
965C22#1568976514yes—
966C22#1568976914yes—
967C22#1568979714yes—
968C22#1568979814yes—
969C22C22×D4×D4711yescharacteristic
970C22C22×D4×D4711yescharacteristic
971C22C2×#41×D4711yescharacteristic
972C22C2×#41×D4711yescharacteristic
973C22C22×#1062535011yescharacteristic
974C22C2×#1309407011yescharacteristic
975C22C2×#1309407011yescharacteristic
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—944no—
983C4—944no—
984C4—1882no—
985C4—1882no—
986C4—1882no—
987C2—44no—
988C2—948no—
989C2—3762no—
990C2—1884no—
991C2#2024677218yesdirect product factor
992C2C2×#121×D4711yescharacteristic
993C2C2×#1568963211yescharacteristic
994C2C2×#1568969111yescharacteristic
995C2C2×#1568976511yescharacteristic
996C2C2×#1568976911yescharacteristic
997C2C2×#1568979711yescharacteristic
998C2C2×#1568979811yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC22×#13093994C2
hypercenterC2×#388D47
hypocenterC47C2×#2411
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
3. C22×#13093981C2semidirect
4. C22×C22⋊C4×D47C2semidirect
5. #20246772C2direct (N × H)
6. C2×#15689047C2semidirect
7. C2×#15689046C2semidirect
8. C2×#15689041C2semidirect
9. C2×#15689038C2semidirect
10. C2×#15689025C2semidirect
11. C2×#15689023C2semidirect
12. C2×#15689013C2semidirect
13. C2×#15689001C2semidirect
14. C2×#15688997C2semidirect
15. C2×#15688978C2semidirect
16. C2×C47×#388C2semidirect
24. C2×#13094009C22semidirect
28. C2×#13093981C22semidirect
29. C22×C4⋊Dic47C22semidirect
30. C22×Dic47⋊C4C22semidirect
31. C22×Dic47⋊C4C22semidirect
32. C22×Dic47⋊C4C22semidirect
33. C22×Dic47⋊C4C22semidirect
44. C22×(C2×D47)⋊C4C22semidirect
45. C22×(C2×D47)⋊C4C22semidirect
46. C22×(C2×D47)⋊C4C22semidirect
47. C22×(C2×D47)⋊C4C22semidirect
49. C2×C22⋊C4×D47C22semidirect
50. C22×C4×Dic47C22semidirect
51. #15689047C22semidirect
52. #15689046C22semidirect
53. #15689041C22semidirect
54. #15689038C22semidirect
55. #15689025C22semidirect
56. #15689023C22semidirect
57. #15689013C22semidirect
58. #15689001C22semidirect
59. #15688997C22semidirect
60. #15688978C22semidirect
61. C2×C47⋊#95C22semidirect
62. C2×C47⋊#95C22semidirect
63. C22×C4⋊C4×C47C22semidirect
67. C22×C42×C47C22semidirect
68. C47×#388C22semidirect
69. C2×#95×C47C22semidirect
70. C2×#95×C47C22semidirect
104. C22×C4×D47D4semidirect
111. C2×C4⋊Dic47C23semidirect
116. C2×Dic47⋊C4C23semidirect
117. C2×Dic47⋊C4C23semidirect
118. C2×Dic47⋊C4C23semidirect
119. C2×Dic47⋊C4C23semidirect
144. C2×(C2×D47)⋊C4C23semidirect
145. C2×(C2×D47)⋊C4C23semidirect
146. C2×(C2×D47)⋊C4C23semidirect
147. C2×(C2×D47)⋊C4C23semidirect
150. C2×C4×Dic47C23semidirect
151. C47⋊#95C23semidirect
152. C47⋊#95C23semidirect
161. C2×C4⋊C4×C47C23semidirect
169. C2×C42×C47C23semidirect
170. #95×C47C23semidirect
171. #95×C47C23semidirect
282. C2×C4×D47C2×D4semidirect
500. C2×#388D47semidirect
505. C2×C47#2411semidirect
533. C22×C4⋊C4C2×D47semidirect
554. C22×C42C2×D47semidirect
562. #388C2×D47semidirect
568. C2×#95C2×D47semidirect
569. C2×#95C2×D47semidirect
570. C47C2×#2411semidirect
628. C2×C4⋊C4C22×D47semidirect
667. C2×C42C22×D47semidirect
670. #95C22×D47semidirect
671. #95C22×D47semidirect
991. C2#20246772direct (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
C22×#130939812
C22×C22⋊C4×D472
#202467722
C2×#156890472
C2×#156890462
C2×#156890412
C2×#156890382
C2×#156890252
C2×#156890232
C2×#156890132
C2×#156890012
C2×#156889972
C2×#156889782
C2×C47×#3882
C2×#241147