Finite Group Databasebeta

← C2×#20246918 #26383748

Subgroups — C2×#20246918 #26383748

Order 12032.

5898 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093998C211yesmaximal, characteristic, complemented
2C22×#13093996C211yesmaximal, characteristic, complemented
3C22×#13093994C211yesmaximal, characteristic, complemented
4C22×#13093992C211yesmaximal, characteristic, complemented
5C23×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
6#20246918C2116yesmaximal, direct product factor
7C2×#15689045C211yesmaximal, characteristic, complemented
8C2×#15689040C211yesmaximal, characteristic, complemented
9C2×#15689039C211yesmaximal, characteristic, complemented
10C2×#15689032C211yesmaximal, characteristic, complemented
11C2×#15689025C211yesmaximal, characteristic, complemented
12C2×#15689014C211yesmaximal, characteristic, complemented
13C2×#15689002C211yesmaximal, characteristic, complemented
14C2×#15689002C211yesmaximal, characteristic, complemented
15C2×#15688998C211yesmaximal, characteristic, complemented
16C22×C4×D4×C47C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C22⋊D47C2211yescharacteristic
22C23×C22⋊D47C2211yescharacteristic
23C23×C22⋊D47C2211yescharacteristic, complemented
24C24×Dic47C2211yescharacteristic
25C2×#13093998—28no—
26C2×#13093998C2218yescomplemented
27C2×#13093996—28no—
28C2×#13093996C2218yescomplemented
29C2×#13093994—28no—
30C2×#13093994C2218yescomplemented
31C2×#13093992—28no—
32C2×#13093992C2218yescomplemented
33C22×C4⋊Dic47C2211yescharacteristic, complemented
34C22×C4⋊Dic47C2211yescharacteristic, complemented
35C22×Dic47⋊C4C2211yescharacteristic, complemented
36C22×C22⋊Dic47C2211yescharacteristic
37C22×C22⋊Dic47C2211yescharacteristic, complemented
38C22×(C2×D47)⋊C4—28no—
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)⋊C4C2218yescomplemented
48C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
50C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
51#15689045C2218yescomplemented
52#15689040C2218yescomplemented
53#15689039C2218yescomplemented
54#15689032C2218yescomplemented
55#15689025C2218yescomplemented
56#15689014C2218yescomplemented
57#15689002C2218yescomplemented
58#15689002C2218yescomplemented
59#15688998C2218yescomplemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62C2×C47⋊#95C2211yescharacteristic, complemented
63C2×C47⋊#95C2211yescharacteristic, complemented
64C23×D4×C47C2211yescharacteristic
65C24×C4×C47C2211yescharacteristic
66C24×C4×C47C2211yescharacteristic, complemented
67C2×C4×D4×C47—28no—
68C2×C4×D4×C47C2218yescomplemented
69C22×C4⋊C4×C47C2211yescharacteristic, complemented
70C22×C22⋊C4×C47C2211yescharacteristic
71C22×C22⋊C4×C47C2211yescharacteristic, complemented
72C22×C42×C47C2211yescharacteristic, complemented
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—24no—
76C24×D47—24no—
77C24×D47—24no—
78C24×D47—42no—
79C24×D47—42no—
80C24×D47C2311yescharacteristic
81C24×D47C2311yescharacteristic
82C24×D47C2311yescharacteristic
83C24×D47C2314yes—
84C22×D188—24no—
85C22×D188—24no—
86C22×D188—24no—
87C22×D188—24no—
88C22×D188—42no—
89C22×D188—42no—
90C22×D188C2314yes—
91C22×D188C2314yes—
92C22×C22⋊D47—24no—
93C22×C22⋊D47—24no—
94C22×C22⋊D47—24no—
95C22×C22⋊D47—24no—
96C22×C22⋊D47—24no—
97C22×C22⋊D47—24no—
98C22×C22⋊D47—24no—
99C22×C22⋊D47—24no—
100C22×C22⋊D47—24no—
101C22×C22⋊D47—42no—
102C22×C22⋊D47—42no—
103C22×C22⋊D47—42no—
104C22×C22⋊D47C2314yes—
105C22×C22⋊D47C2314yes—
106C22×C22⋊D47C2314yes—
107C22×C22⋊D47C2314yescomplemented
108C23×Dic47—24no—
109C23×Dic47—24no—
110C23×Dic47—42no—
111C23×Dic47C2311yescharacteristic
112C23×Dic47C2311yescharacteristic
113C23×Dic47C2311yescharacteristic
114C23×Dic47C2311yescharacteristic
115C23×Dic47C2314yes—
116C23×Dic47C2311yescharacteristic
117#13093998—232no—
118#13093996—232no—
119#13093994—232no—
120#13093992—232no—
121C2×C4⋊Dic47—24no—
122C2×C4⋊Dic47—42no—
123C2×C4⋊Dic47C2314yescomplemented
124C2×C4⋊Dic47C2314yescomplemented
125C2×Dic47⋊C4—24no—
126C2×Dic47⋊C4C2314yescomplemented
127C2×C22⋊Dic47—24no—
128C2×C22⋊Dic47—24no—
129C2×C22⋊Dic47C2314yes—
130C2×C22⋊Dic47C2314yescomplemented
131C2×(C2×D47)⋊C4—24no—
132C2×(C2×D47)⋊C4—24no—
133C2×(C2×D47)⋊C4—24no—
134C2×(C2×D47)⋊C4—24no—
135C2×(C2×D47)⋊C4—24no—
136C2×(C2×D47)⋊C4—24no—
137C2×(C2×D47)⋊C4—24no—
138C2×(C2×D47)⋊C4—24no—
139C2×(C2×D47)⋊C4—24no—
140C2×(C2×D47)⋊C4—232no—
141C2×(C2×D47)⋊C4—42no—
142C2×(C2×D47)⋊C4D418yescomplemented
143C2×(C2×D47)⋊C4C2314yes—
144C2×(C2×D47)⋊C4C2314yes—
145C2×(C2×D47)⋊C4C2314yes—
146C2×(C2×D47)⋊C4C2314yes—
147C2×(C2×D47)⋊C4C2314yes—
148C2×(C2×D47)⋊C4C2314yes—
149C2×(C2×D47)⋊C4C2314yes—
150C2×(C2×D47)⋊C4C2314yes—
151C2×(C2×D47)⋊C4C2314yescomplemented
152C2×(C2×D47)⋊C4C2314yescomplemented
153C2×(C2×D47)⋊C4C2314yescomplemented
154C47⋊#95C2314yescomplemented
155C47⋊#95C2314yescomplemented
156C47⋊#95C2314yescomplemented
157C47⋊#95C2314yescomplemented
158C25×C47C2311yescharacteristic
159C25×C47C2311yescharacteristic
160C22×D4×C47—24no—
161C22×D4×C47—24no—
162C22×D4×C47D418yescomplemented
163C22×D4×C47C2314yes—
164C23×C4×C47—24no—
165C23×C4×C47—24no—
166C23×C4×C47—24no—
167C23×C4×C47—24no—
168C23×C4×C47—42no—
169C23×C4×C47—42no—
170C23×C4×C47C2311yescharacteristic
171C23×C4×C47C2314yes—
172C23×C4×C47C2311yescharacteristic
173C23×C4×C47C2311yescharacteristic
174C23×C4×C47C2311yescharacteristic
175C23×C4×C47C2311yescharacteristic
176C23×C4×C47C2314yescomplemented
177C4×D4×C47—232no—
178C2×C4⋊C4×C47—24no—
179C2×C4⋊C4×C47C2314yescomplemented
180C2×C22⋊C4×C47—24no—
181C2×C22⋊C4×C47D418yescomplemented
182C2×C22⋊C4×C47C2314yes—
183C2×C22⋊C4×C47C2314yescomplemented
184C2×C42×C47—24no—
185C2×C42×C47C2314yescomplemented
186C24×C47—22no—
187C24×C47—22no—
188C24×C47—22no—
189C24×C47—22no—
190C24×C47—22no—
191C24×C47—22no—
192C24×C47—22no—
193C24×C47—22no—
194C24×C47—22no—
195C24×C47—22no—
196C24×C47C2×D414yes—
197C24×C47C2×D414yes—
198C24×C47C2×D414yes—
199C24×C47#4114yes—
200C24×C47C2412yes—
201C24×C47C2412yes—
202C24×C47C2411yescharacteristic
203C23×D47—232no—
204C23×D47—22no—
205C23×D47—22no—
206C23×D47—22no—
207C23×D47—22no—
208C23×D47—22no—
209C23×D47—28no—
210C23×D47—22no—
211C23×D47—22no—
212C23×D47—22no—
213C23×D47—22no—
214C23×D47—22no—
215C23×D47—22no—
216C23×D47—22no—
217C23×D47—28no—
218C23×D47—28no—
219C23×D47—22no—
220C23×D47—22no—
221C23×D47—28no—
222C23×D47—28no—
223C23×D47—22no—
224C23×D47—22no—
225C23×D47—22no—
226C23×D47—22no—
227C23×D47—22no—
228C23×D47—44no—
229C23×D47—44no—
230C23×D47—416no—
231C23×D47—416no—
232C23×D47—416no—
233C23×D47—416no—
234C23×D47—416no—
235C23×D47—416no—
236C23×D47C2×D414yes—
237C23×D47#4114yes—
238C23×D47C2412yes—
239C23×D47C2412yes—
240C23×D47C2412yes—
241C2×D4×C47—232no—
242C2×D4×C47—28no—
243C2×D4×C47—28no—
244C2×D4×C47C2×D4116yescomplemented
245C22×C4×C47—22no—
246C22×C4×C47—22no—
247C22×C4×C47—22no—
248C22×C4×C47—22no—
249C22×C4×C47—22no—
250C22×C4×C47—22no—
251C22×C4×C47—22no—
252C22×C4×C47—22no—
253C22×C4×C47—22no—
254C22×C4×C47—28no—
255C22×C4×C47—22no—
256C22×C4×C47—22no—
257C22×C4×C47—28no—
258C22×C4×C47—28no—
259C22×C4×C47—28no—
260C22×C4×C47—44no—
261C22×C4×C47—44no—
262C22×C4×C47—416no—
263C22×C4×C47—416no—
264C22×C4×C47C2×D414yes—
265C22×C4×C47C2×D414yes—
266C22×C4×C47C2×D414yes—
267C22×C4×C47C2×D414yes—
268C22×C4×C47C2412yes—
269C22×C4×C47C2412yes—
270C22×C4×C47C2412yes—
271C22×C4×C47C2412yes—
272C22×C4×C47C2412yes—
273C2×C22⋊D47—28no—
274C2×C22⋊D47—28no—
275C2×C22⋊D47—28no—
276C2×C22⋊D47—28no—
277C2×C22⋊D47—28no—
278C2×C22⋊D47—28no—
279C2×C22⋊D47—28no—
280C2×C22⋊D47—28no—
281C2×C22⋊D47—28no—
282C2×C22⋊D47—44no—
283C2×C22⋊D47—44no—
284C2×C22⋊D47—44no—
285C2×C22⋊D47—416no—
286C2×C22⋊D47—416no—
287C2×C22⋊D47—416no—
288C2×C22⋊D47—416no—
289C22×Dic47—22no—
290C22×Dic47—22no—
291C22×Dic47—22no—
292C22×Dic47—22no—
293C22×Dic47—22no—
294C22×Dic47—22no—
295C22×Dic47—22no—
296C22×Dic47—22no—
297C22×Dic47—22no—
298C22×Dic47—28no—
299C22×Dic47—22no—
300C22×Dic47—22no—
301C22×Dic47—22no—
302C22×Dic47—22no—
303C22×Dic47—22no—
304C22×Dic47—28no—
305C22×Dic47—44no—
306C22×Dic47—416no—
307C22×Dic47C2×D414yes—
308C22×Dic47C2412yes—
309C22×Dic47C2412yes—
310C22×Dic47C2412yes—
311C22×Dic47C2412yes—
312C22×Dic47C2412yes—
313C2×D188—28no—
314C2×D188—28no—
315C2×D188—28no—
316C2×D188—28no—
317C2×D188—44no—
318C2×D188—44no—
319C2×D188—416no—
320C2×D188—416no—
321C4⋊C4×C47—28no—
322C22⋊C4×C47—28no—
323C22⋊C4×C47C2×D4116yescomplemented
324C42×C47—28no—
325C22⋊Dic47—28no—
326C22⋊Dic47—28no—
327(C2×D47)⋊C4—28no—
328(C2×D47)⋊C4—28no—
329(C2×D47)⋊C4—28no—
330(C2×D47)⋊C4—28no—
331(C2×D47)⋊C4—28no—
332(C2×D47)⋊C4—28no—
333(C2×D47)⋊C4—28no—
334(C2×D47)⋊C4—28no—
335(C2×D47)⋊C4—28no—
336(C2×D47)⋊C4—44no—
337(C2×D47)⋊C4C2×D4116yescomplemented
338C4⋊Dic47—28no—
339C4⋊Dic47—44no—
340Dic47⋊C4—28no—
341C23×C47—28no—
342C23×C47—28no—
343C23×C47—28no—
344C23×C47—28no—
345C23×C47—28no—
346C23×C47—28no—
347C23×C47—22no—
348C23×C47—22no—
349C23×C47—22no—
350C23×C47—22no—
351C23×C47—28no—
352C23×C47—28no—
353C23×C47—28no—
354C23×C47—22no—
355C23×C47—22no—
356C23×C47—22no—
357C23×C47—22no—
358C23×C47—22no—
359C23×C47—22no—
360C23×C47—44no—
361C23×C47—44no—
362C23×C47—44no—
363C23×C47—44no—
364C23×C47#121116yescomplemented
365C23×C47C22×D412yes—
366C23×C47C22×D414yes—
367C23×C47C22×D412yes—
368C23×C47C22×D414yes—
369C23×C47C22×D414yes—
370C23×C47C22×D412yes—
371C23×C47C2×#4112yes—
372C23×C47C2×#4114yes—
373C23×C47C2×#4112yes—
374C23×C47H(5,𝔽2)12yes—
375C23×C47H(5,𝔽2)12yes—
376C23×C47C2511yescharacteristic
377C22×D47—232no—
378C22×D47—28no—
379C22×D47—28no—
380C22×D47—28no—
381C22×D47—28no—
382C22×D47—28no—
383C22×D47—28no—
384C22×D47—22no—
385C22×D47—22no—
386C22×D47—22no—
387C22×D47—22no—
388C22×D47—22no—
389C22×D47—22no—
390C22×D47—22no—
391C22×D47—22no—
392C22×D47—22no—
393C22×D47—22no—
394C22×D47—22no—
395C22×D47—22no—
396C22×D47—22no—
397C22×D47—22no—
398C22×D47—22no—
399C22×D47—22no—
400C22×D47—22no—
401C22×D47—22no—
402C22×D47—22no—
403C22×D47—416no—
404C22×D47—416no—
405C22×D47—416no—
406C22×D47—416no—
407C22×D47—4128no—
408C22×D47—416no—
409C22×D47—44no—
410C22×D47—44no—
411C22×D47—416no—
412C22×D47—44no—
413C22×D47—44no—
414C22×D47—44no—
415C22×D47—44no—
416C22×D47—44no—
417C22×D47—44no—
418C22×D47—44no—
419C22×D47—44no—
420C22×D47—44no—
421C22×D47—44no—
422C22×D47—44no—
423C22×D47—44no—
424C22×D47—44no—
425C22×D47C22×D414yes—
426C22×D47C2×#4114yes—
427D4×C47—232no—
428C2×C4×C47—28no—
429C2×C4×C47—28no—
430C2×C4×C47—28no—
431C2×C4×C47—28no—
432C2×C4×C47—22no—
433C2×C4×C47—22no—
434C2×C4×C47—22no—
435C2×C4×C47—22no—
436C2×C4×C47—22no—
437C2×C4×C47—22no—
438C2×C4×C47—22no—
439C2×C4×C47—22no—
440C2×C4×C47—22no—
441C2×C4×C47—22no—
442C2×C4×C47—22no—
443C2×C4×C47—416no—
444C2×C4×C47—416no—
445C2×C4×C47—44no—
446C2×C4×C47C22×D414yes—
447C2×C4×C47C22×D414yes—
448C2×C4×C47C22×D414yes—
449C2×C4×C47C22×D414yes—
450C22⋊D47—416no—
451C22⋊D47—416no—
452C22⋊D47—416no—
453C22⋊D47—416no—
454C2×Dic47—28no—
455C2×Dic47—22no—
456C2×Dic47—22no—
457C2×Dic47—22no—
458C2×Dic47—22no—
459C2×Dic47—22no—
460C2×Dic47—22no—
461C2×Dic47—22no—
462C2×Dic47—22no—
463C2×Dic47—22no—
464C2×Dic47—22no—
465C2×Dic47—22no—
466C2×Dic47—22no—
467C2×Dic47—22no—
468C2×Dic47—22no—
469C2×Dic47—416no—
470C2×Dic47—44no—
471C2×Dic47—44no—
472C2×Dic47—44no—
473C2×Dic47—44no—
474C2×Dic47C22×D414yes—
475D188—416no—
476D188—416no—
477C2×#2424—471nomaximal, Sylow
478C22×C47—24no—
479C22×C47—232no—
480C22×C47—24no—
481C22×C47—24no—
482C22×C47—24no—
483C22×C47—24no—
484C22×C47—24no—
485C22×C47—24no—
486C22×C47—24no—
487C22×C47—24no—
488C22×C47—42no—
489C22×C47—416no—
490C22×C47—42no—
491C22×C47—42no—
492C22×C47—42no—
493C22×C47C2×#12114yes—
494C22×C47C2×#12118yescomplemented
495C22×C47#52514yes—
496C22×C47#53814yes—
497C22×C47D4214yes—
498C22×C47D4214yes—
499C22×C47#54614yes—
500C22×C47#54614yes—
501C22×C47C23×D411yescharacteristic
502C22×C47C23×D411yescharacteristic
503C22×C47C23×D411yescharacteristic
504C22×C47C22×#4111yescharacteristic
505C22×C47C22×#4111yescharacteristic
506C22×C47C2×H(5,𝔽2)11yescharacteristic
507C22×C47C2×H(5,𝔽2)11yescharacteristic
508C2×D47—24no—
509C2×D47—24no—
510C2×D47—24no—
511C2×D47—24no—
512C2×D47—24no—
513C2×D47—24no—
514C2×D47—464no—
515C2×D47—42no—
516C2×D47—42no—
517C2×D47—416no—
518C2×D47—416no—
519C2×D47—42no—
520C2×D47—42no—
521C2×D47—42no—
522C2×D47—42no—
523C2×D47—42no—
524C2×D47—42no—
525C2×D47—42no—
526C2×D47—42no—
527C2×D47—42no—
528C2×D47—42no—
529C2×D47—42no—
530C2×D47—42no—
531C2×D47—42no—
532C2×D47—88no—
533C4×C47—24no—
534C4×C47—24no—
535C4×C47—24no—
536C4×C47—24no—
537C4×C47—42no—
538Dic47—24no—
539Dic47—42no—
540Dic47—42no—
541Dic47—42no—
542Dic47—42no—
543C22×#121—471no—
544C22×#121—471no—
545C22×#120—471no—
546C22×#120—471no—
547C22×C4×D4D4711yescharacteristic, complemented
548C23×C22⋊C4—471no—
549#2424—4716no—
550C2×#396—471no—
551C2×#394—471no—
552C2×#394—471no—
553C2×#392—471no—
554C2×#390—471no—
555C2×#388—471no—
556C2×#386—471no—
557C2×#386—471no—
558C2×#385—471no—
559C2×C47—28no—
560C2×C47—44no—
561C2×C47#242418yescomplemented
562C2×C47C22×#12111yescharacteristic
563C2×C47C2×#52511yescharacteristic
564C2×C47C2×#53811yescharacteristic
565C2×C47C2×D4211yescharacteristic
566C2×C47C2×D4211yescharacteristic
567C2×C47C2×#54611yescharacteristic
568C2×C47C2×#54611yescharacteristic
569D47—44no—
570D47—44no—
571D47—82no—
572C26—471no—
573C23×D4—471no—
574C23×D4—471no—
575C23×D4—471no—
576C23×D4—471no—
577C23×D4—471no—
578C23×D4—471no—
579C23×D4C2×D4711yescharacteristic
580C24×C4—471no—
581C24×C4C2×D4711yescharacteristic
582C24×C4C2×D4711yescharacteristic, complemented
583C2×#121—478no—
584C2×#121—478no—
585C2×#121—948no—
586C2×#121—948no—
587C2×#120—478no—
588C2×#120—478no—
589C2×#120—948no—
590C2×#120—948no—
591C2×C4×D4—28no—
592C2×C4×D4C2×D4718yescomplemented
593C22×C4⋊C4—471no—
594C22×C4⋊C4—471no—
595C22×C4⋊C4—471no—
596C22×C4⋊C4C2×D4711yescharacteristic, complemented
597C22×C22⋊C4—471no—
598C22×C22⋊C4—471no—
599C22×C22⋊C4—471no—
600C22×C22⋊C4—471no—
601C22×C22⋊C4—471no—
602C22×C22⋊C4—471no—
603C22×C22⋊C4—471no—
604C22×C22⋊C4—471no—
605C22×C22⋊C4—471no—
606C22×C22⋊C4—471no—
607C22×C22⋊C4—471no—
608C22×C22⋊C4—478no—
609C22×C22⋊C4—471no—
610C22×C22⋊C4—471no—
611C22×C22⋊C4—948no—
612C22×C22⋊C4C2×D4711yescharacteristic
613C22×C22⋊C4C2×D4711yescharacteristic, complemented
614C22×C42C2×D4711yescharacteristic, complemented
615#396—478no—
616#394—478no—
617#394—478no—
618#392—478no—
619#390—478no—
620#388—478no—
621#386—478no—
622#386—478no—
623#385—478no—
624C2×#95—471no—
625C2×#95—471no—
626C2×#95—471no—
627C2×#95—471no—
628C47C2×#242411yescharacteristic, complemented, Sylow
629C25—471no—
630C25—471no—
631C25—471no—
632C25—474no—
633C25—944no—
634C25—944no—
635C25—944no—
636C25—944no—
637C25—944no—
638C25—1882no—
639C25—1882no—
640C25C22×D4711yescharacteristic
641C25C22×D4711yescharacteristic
642C22×D4—24no—
643C22×D4—24no—
644C22×D4—474no—
645C22×D4—474no—
646C22×D4—474no—
647C22×D4—474no—
648C22×D4—474no—
649C22×D4—474no—
650C22×D4—944no—
651C22×D4—944no—
652C22×D4—944no—
653C22×D4—944no—
654C22×D4—944no—
655C22×D4—944no—
656C22×D4—944no—
657C22×D4—944no—
658C22×D4—944no—
659C22×D4—944no—
660C22×D4—944no—
661C22×D4—944no—
662C22×D4—944no—
663C22×D4—1882no—
664C22×D4—1882no—
665C22×D4—1882no—
666C22×D4—1882no—
667C22×D4—1882no—
668C22×D4D18818yescomplemented
669C22×D4C22×D4714yes—
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—24no—
673C23×C4—24no—
674C23×C4—42no—
675C23×C4—42no—
676C23×C4—471no—
677C23×C4—471no—
678C23×C4—471no—
679C23×C4—471no—
680C23×C4—471no—
681C23×C4—474no—
682C23×C4—944no—
683C23×C4—944no—
684C23×C4—1882no—
685C23×C4C22×D4711yescharacteristic
686C23×C4C22×D4714yes—
687C23×C4C22×D4711yescharacteristic
688C23×C4C22×D4711yescharacteristic
689C23×C4C22×D4711yescharacteristic
690C23×C4C22×D4711yescharacteristic
691C23×C4C22×D4714yescomplemented
692#121—9432no—
693#121—9432no—
694#120—9432no—
695#120—9432no—
696C4×D4—232no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—474no—
699C2×C4⋊C4—474no—
700C2×C4⋊C4—474no—
701C2×C4⋊C4—944no—
702C2×C4⋊C4—944no—
703C2×C4⋊C4—1882no—
704C2×C4⋊C4C22×D4714yescomplemented
705C2×C22⋊C4—24no—
706C2×C22⋊C4—478no—
707C2×C22⋊C4—474no—
708C2×C22⋊C4—474no—
709C2×C22⋊C4—474no—
710C2×C22⋊C4—474no—
711C2×C22⋊C4—474no—
712C2×C22⋊C4—474no—
713C2×C22⋊C4—474no—
714C2×C22⋊C4—474no—
715C2×C22⋊C4—474no—
716C2×C22⋊C4—474no—
717C2×C22⋊C4—474no—
718C2×C22⋊C4—474no—
719C2×C22⋊C4—474no—
720C2×C22⋊C4—9432no—
721C2×C22⋊C4—944no—
722C2×C22⋊C4—944no—
723C2×C22⋊C4—944no—
724C2×C22⋊C4—944no—
725C2×C22⋊C4—944no—
726C2×C22⋊C4—944no—
727C2×C22⋊C4—944no—
728C2×C22⋊C4—944no—
729C2×C22⋊C4—944no—
730C2×C22⋊C4—944no—
731C2×C22⋊C4—944no—
732C2×C22⋊C4—1882no—
733C2×C22⋊C4C22⋊D4718yescomplemented
734C2×C22⋊C4C22×D4714yes—
735C2×C22⋊C4C22×D4714yescomplemented
736C2×C42—24no—
737C2×C42C22×D4714yescomplemented
738#95—474no—
739#95—474no—
740#95—474no—
741#95—474no—
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—22no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—474no—
753C24—474no—
754C24—472no—
755C24—472no—
756C24—472no—
757C24—948no—
758C24—948no—
759C24—9432no—
760C24—942no—
761C24—942no—
762C24—942no—
763C24—942no—
764C24—942no—
765C24—942no—
766C24—948no—
767C24—942no—
768C24—942no—
769C24—942no—
770C24—942no—
771C24—942no—
772C24—942no—
773C24—942no—
774C24—948no—
775C24—942no—
776C24—942no—
777C24—948no—
778C24—942no—
779C24—942no—
780C24—942no—
781C24—942no—
782C24—1884no—
783C24—1884no—
784C24—18816no—
785C24—18816no—
786C24—18816no—
787C24—18816no—
788C24—18816no—
789C24—18816no—
790C24C2×D18814yes—
791C24C2×D18814yes—
792C24#1062535014yes—
793C24C2×C22⋊D4714yes—
794C24C23×D4712yes—
795C24C23×D4712yes—
796C24C23×D4711yescharacteristic
797C2×D4—232no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—948no—
801C2×D4—948no—
802C2×D4—948no—
803C2×D4—948no—
804C2×D4—948no—
805C2×D4—948no—
806C2×D4—948no—
807C2×D4—948no—
808C2×D4—948no—
809C2×D4—948no—
810C2×D4—948no—
811C2×D4—948no—
812C2×D4—948no—
813C2×D4—1884no—
814C2×D4—1884no—
815C2×D4—18816no—
816C2×D4—18816no—
817C2×D4—1884no—
818C2×D4—1884no—
819C2×D4—1884no—
820C2×D4—18816no—
821C2×D4—18816no—
822C2×D4—18816no—
823C2×D4—18816no—
824C2×D4C2×D188116yescomplemented
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—28no—
836C22×C4—22no—
837C22×C4—28no—
838C22×C4—28no—
839C22×C4—28no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—416no—
843C22×C4—416no—
844C22×C4—474no—
845C22×C4—472no—
846C22×C4—472no—
847C22×C4—472no—
848C22×C4—472no—
849C22×C4—472no—
850C22×C4—948no—
851C22×C4—942no—
852C22×C4—942no—
853C22×C4—942no—
854C22×C4—942no—
855C22×C4—942no—
856C22×C4—942no—
857C22×C4—942no—
858C22×C4—942no—
859C22×C4—942no—
860C22×C4—948no—
861C22×C4—942no—
862C22×C4—942no—
863C22×C4—942no—
864C22×C4—942no—
865C22×C4—942no—
866C22×C4—1884no—
867C22×C4—18816no—
868C22×C4C2×D18814yes—
869C22×C4D4×D4714yes—
870C22×C4C2×C22⋊D4714yes—
871C22×C4C2×C22⋊D4714yes—
872C22×C4C23×D4712yes—
873C22×C4C23×D4712yes—
874C22×C4C23×D4712yes—
875C22×C4C23×D4712yes—
876C22×C4C23×D4712yes—
877C4⋊C4—28no—
878C4⋊C4—948no—
879C4⋊C4—948no—
880C4⋊C4—1884no—
881C22⋊C4—28no—
882C22⋊C4—4716no—
883C22⋊C4—948no—
884C22⋊C4—948no—
885C22⋊C4—948no—
886C22⋊C4—948no—
887C22⋊C4—948no—
888C22⋊C4—948no—
889C22⋊C4—948no—
890C22⋊C4—948no—
891C22⋊C4—948no—
892C22⋊C4—948no—
893C22⋊C4—948no—
894C22⋊C4—1884no—
895C22⋊C4C2×C22⋊D47116yescomplemented
896C42—28no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—28no—
907C23—28no—
908C23—28no—
909C23—28no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—44no—
917C23—44no—
918C23—44no—
919C23—44no—
920C23—474no—
921C23—474no—
922C23—9432no—
923C23—948no—
924C23—948no—
925C23—948no—
926C23—948no—
927C23—948no—
928C23—948no—
929C23—942no—
930C23—942no—
931C23—942no—
932C23—942no—
933C23—942no—
934C23—942no—
935C23—942no—
936C23—942no—
937C23—942no—
938C23—942no—
939C23—942no—
940C23—942no—
941C23—942no—
942C23—942no—
943C23—942no—
944C23—942no—
945C23—942no—
946C23—942no—
947C23—942no—
948C23—18816no—
949C23—18816no—
950C23—18816no—
951C23—18816no—
952C23—188128no—
953C23—18816no—
954C23—1884no—
955C23—1884no—
956C23—1884no—
957C23—1884no—
958C23—1884no—
959C23—1884no—
960C23—1884no—
961C23—1884no—
962C23—1884no—
963C23—1884no—
964C23—1884no—
965C23—1884no—
966C23—1884no—
967C23—18816no—
968C23—1884no—
969C23—1884no—
970C23#13093998116yescomplemented
971C23C2×D4×D4712yes—
972C23C22×C22⋊D4714yes—
973C23C22×C22⋊D4712yes—
974C23C22×D18814yes—
975C23C22×D18814yes—
976C23C22×D18812yes—
977C23#41×D4712yes—
978C23C2×#1062535014yes—
979C23C2×#1062535012yes—
980C23#1309406912yes—
981C23#1309407012yes—
982C23C24×D4711yescharacteristic
983D4—232no—
984D4—18816no—
985D4—18816no—
986D4—18816no—
987D4—18816no—
988D4—18816no—
989D4—18816no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—28no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—416no—
1006C2×C4—416no—
1007C2×C4—44no—
1008C2×C4—474no—
1009C2×C4—948no—
1010C2×C4—942no—
1011C2×C4—942no—
1012C2×C4—942no—
1013C2×C4—942no—
1014C2×C4—942no—
1015C2×C4—942no—
1016C2×C4—942no—
1017C2×C4—942no—
1018C2×C4—942no—
1019C2×C4—942no—
1020C2×C4—942no—
1021C2×C4—942no—
1022C2×C4—942no—
1023C2×C4—942no—
1024C2×C4—18816no—
1025C2×C4—1884no—
1026C2×C4—1884no—
1027C2×C4—1884no—
1028C2×C4—1884no—
1029C2×C4C2×D4×D4714yes—
1030C2×C4C22×C22⋊D4714yes—
1031C2×C4C22×C22⋊D4714yes—
1032C2×C4C22×D18814yes—
1033C22—24no—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—232no—
1039C22—24no—
1040C22—24no—
1041C22—24no—
1042C22—24no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—416no—
1047C22—42no—
1048C22—944no—
1049C22—944no—
1050C22—944no—
1051C22—944no—
1052C22—944no—
1053C22—944no—
1054C22—3768no—
1055C22—18864no—
1056C22—1882no—
1057C22—1882no—
1058C22—1882no—
1059C22—1882no—
1060C22—1882no—
1061C22—1882no—
1062C22—1882no—
1063C22—1882no—
1064C22—1882no—
1065C22—1882no—
1066C22—1882no—
1067C22—1882no—
1068C22—1882no—
1069C22—18816no—
1070C22—18816no—
1071C22—1882no—
1072C22—1882no—
1073C22C2×#1309399814yes—
1074C22C2×#1309399818yescomplemented
1075C22#1568963214yes—
1076C22#1568970614yes—
1077C22D4×C22⋊D4714yes—
1078C22D4×D18814yes—
1079C22#1568976114yes—
1080C22#1568976814yes—
1081C22C22×D4×D4711yescharacteristic
1082C22C23×C22⋊D4711yescharacteristic
1083C22C23×D18811yescharacteristic
1084C22C2×#41×D4711yescharacteristic
1085C22C22×#1062535011yescharacteristic
1086C22C2×#1309406911yescharacteristic
1087C22C2×#1309407011yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—24no—
1092C4—42no—
1093C4—944no—
1094C4—1882no—
1095C4—1882no—
1096C4—1882no—
1097C4—1882no—
1098C2—28no—
1099C2—44no—
1100C2—3762no—
1101C2—1884no—
1102C2—1884no—
1103C2#2024691818yesdirect product factor
1104C2C22×#1309399811yescharacteristic
1105C2C2×#1568963211yescharacteristic
1106C2C2×#1568970611yescharacteristic
1107C2C2×D4×C22⋊D4711yescharacteristic
1108C2C2×D4×D18811yescharacteristic
1109C2C2×#1568976111yescharacteristic
1110C2C2×#1568976811yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC22×C4×D4×C47C2
socleC24×C47C24
hypercenterC22×C4×D4D47
hypocenterC47C2×#2424
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#13093998C2semidirect
2. C22×#13093996C2semidirect
3. C22×#13093994C2semidirect
4. C22×#13093992C2semidirect
5. C23×(C2×D47)⋊C4C2semidirect
6. #20246918C2direct (N × H)
7. C2×#15689045C2semidirect
8. C2×#15689040C2semidirect
9. C2×#15689039C2semidirect
10. C2×#15689032C2semidirect
11. C2×#15689025C2semidirect
12. C2×#15689014C2semidirect
13. C2×#15689002C2semidirect
14. C2×#15689002C2semidirect
15. C2×#15688998C2semidirect
16. C22×C4×D4×C47C2semidirect
23. C23×C22⋊D47C22semidirect
26. C2×#13093998C22semidirect
28. C2×#13093996C22semidirect
30. C2×#13093994C22semidirect
32. C2×#13093992C22semidirect
33. C22×C4⋊Dic47C22semidirect
34. C22×C4⋊Dic47C22semidirect
35. C22×Dic47⋊C4C22semidirect
37. C22×C22⋊Dic47C22semidirect
47. C22×(C2×D47)⋊C4C22semidirect
48. C22×(C2×D47)⋊C4C22semidirect
49. C22×(C2×D47)⋊C4C22semidirect
50. C22×(C2×D47)⋊C4C22semidirect
51. #15689045C22semidirect
52. #15689040C22semidirect
53. #15689039C22semidirect
54. #15689032C22semidirect
55. #15689025C22semidirect
56. #15689014C22semidirect
57. #15689002C22semidirect
58. #15689002C22semidirect
59. #15688998C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
62. C2×C47⋊#95C22semidirect
63. C2×C47⋊#95C22semidirect
66. C24×C4×C47C22semidirect
68. C2×C4×D4×C47C22semidirect
69. C22×C4⋊C4×C47C22semidirect
71. C22×C22⋊C4×C47C22semidirect
72. C22×C42×C47C22semidirect
107. C22×C22⋊D47C23semidirect
123. C2×C4⋊Dic47C23semidirect
124. C2×C4⋊Dic47C23semidirect
126. C2×Dic47⋊C4C23semidirect
130. C2×C22⋊Dic47C23semidirect
142. C2×(C2×D47)⋊C4D4semidirect
151. C2×(C2×D47)⋊C4C23semidirect
152. C2×(C2×D47)⋊C4C23semidirect
153. C2×(C2×D47)⋊C4C23semidirect
154. C47⋊#95C23semidirect
155. C47⋊#95C23semidirect
156. C47⋊#95C23semidirect
157. C47⋊#95C23semidirect
162. C22×D4×C47D4semidirect
176. C23×C4×C47C23semidirect
179. C2×C4⋊C4×C47C23semidirect
181. C2×C22⋊C4×C47D4semidirect
183. C2×C22⋊C4×C47C23semidirect
185. C2×C42×C47C23semidirect
244. C2×D4×C47C2×D4semidirect
323. C22⋊C4×C47C2×D4semidirect
337. (C2×D47)⋊C4C2×D4semidirect
364. C23×C47#121semidirect
494. C22×C47C2×#121semidirect
547. C22×C4×D4D47semidirect
561. C2×C47#2424semidirect
582. C24×C4C2×D47semidirect
592. C2×C4×D4C2×D47semidirect
596. C22×C4⋊C4C2×D47semidirect
613. C22×C22⋊C4C2×D47semidirect
614. C22×C42C2×D47semidirect
628. C47C2×#2424semidirect
668. C22×D4D188semidirect
691. C23×C4C22×D47semidirect
704. C2×C4⋊C4C22×D47semidirect
733. C2×C22⋊C4C22⋊D47semidirect
735. C2×C22⋊C4C22×D47semidirect
737. C2×C42C22×D47semidirect
824. C2×D4C2×D188semidirect
895. C22⋊C4C2×C22⋊D47semidirect
970. C23#13093998semidirect
1074. C22C2×#13093998semidirect
1103. C2#20246918direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939982
C22×#130939962
C22×#130939942
C22×#130939922
C23×(C2×D47)⋊C42
#202469182
C2×#156890452
C2×#156890402
C2×#156890392
C2×#156890322
C2×#156890252
C2×#156890142
C2×#156890022
C2×#156889982
C22×C4×D4×C472
C2×#242447