Finite Group Databasebeta

← C2×#20246922 #26383750

Subgroups — C2×#20246922 #26383750

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×#13093999C211yesmaximal, characteristic, complemented
2C22×#13093998C211yesmaximal, characteristic, complemented
3C22×#13093994C211yesmaximal, characteristic, complemented
4C22×#13093994C211yesmaximal, characteristic, complemented
5C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic, complemented
6C23×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
7#20246922C2116yesmaximal, direct product factor
8C2×#15689045C211yesmaximal, characteristic, complemented
9C2×#15689041C211yesmaximal, characteristic, complemented
10C2×#15689040C211yesmaximal, characteristic, complemented
11C2×#15689033C211yesmaximal, characteristic, complemented
12C2×#15689024C211yesmaximal, characteristic, complemented
13C2×#15689015C211yesmaximal, characteristic, complemented
14C2×#15689001C211yesmaximal, characteristic, complemented
15C2×#15689000C211yesmaximal, characteristic, complemented
16C2×C47×#385C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×D188C2211yescharacteristic
21C23×D188C2211yescharacteristic
22C23×D188C2211yescharacteristic, complemented
23C23×C22⋊D47C2211yescharacteristic
24C23×C22⋊D47C2211yescharacteristic
25C24×Dic47C2211yescharacteristic
26C23×C4×D47C2211yescharacteristic, complemented
27C2×#13093999—28no—
28C2×#13093999C2218yescomplemented
29C2×#13093998—28no—
30C2×#13093998C2218yescomplemented
31C2×#13093994—28no—
32C2×#13093994—28no—
33C2×#13093994C2218yescomplemented
34C2×#13093994C2218yescomplemented
35C2×(C22⋊D47)⋊C4—28no—
36C2×(C22⋊D47)⋊C4C2218yescomplemented
37C22×C4⋊Dic47C2211yescharacteristic, complemented
38C22×Dic47⋊C4C2211yescharacteristic, complemented
39C22×(C2×D47)⋊C4—28no—
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)⋊C4C2218yescomplemented
49C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
50C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
51C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
52C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
53C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
54C22×C4×Dic47C2211yescharacteristic, complemented
55#15689045C2218yescomplemented
56#15689041C2218yescomplemented
57#15689040C2218yescomplemented
58#15689033C2218yescomplemented
59#15689024C2218yescomplemented
60#15689015C2218yescomplemented
61#15689001C2218yescomplemented
62#15689000C2218yescomplemented
63C2×C47⋊#95C2211yescharacteristic, complemented
64C2×C47⋊#95C2211yescharacteristic, complemented
65C24×C4×C47C2211yescharacteristic
66C22×C4⋊C4×C47C2211yescharacteristic, complemented
67C22×C4⋊C4×C47C2211yescharacteristic, complemented
68C22×C22⋊C4×C47C2211yescharacteristic
69C22×C22⋊C4×C47C2211yescharacteristic
70C47×#385C2218yescomplemented
71C2×#95×C47C2211yescharacteristic, complemented
72C2×#95×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×D47C2311yescharacteristic
84C24×D47C2314yes—
85C22×D188—24no—
86C22×D188—24no—
87C22×D188—24no—
88C22×D188—24no—
89C22×D188—24no—
90C22×D188—24no—
91C22×D188—24no—
92C22×D188—24no—
93C22×D188—24no—
94C22×D188—24no—
95C22×D188—42no—
96C22×D188—42no—
97C22×D188—42no—
98C22×D188—42no—
99C22×D188—42no—
100C22×D188C2314yes—
101C22×D188C2314yes—
102C22×D188C2314yes—
103C22×D188C2314yes—
104C22×D188C2314yescomplemented
105C22×C22⋊D47—24no—
106C22×C22⋊D47—24no—
107C22×C22⋊D47—24no—
108C22×C22⋊D47—24no—
109C22×C22⋊D47—24no—
110C22×C22⋊D47D418yescomplemented
111C22×C22⋊D47C2314yes—
112C22×C22⋊D47C2314yes—
113C23×Dic47—24no—
114C23×Dic47—24no—
115C23×Dic47—42no—
116C23×Dic47C2311yescharacteristic
117C23×Dic47C2311yescharacteristic
118C23×Dic47C2314yes—
119C23×Dic47C2311yescharacteristic
120C23×Dic47C2311yescharacteristic
121C22×C4×D47—24no—
122C22×C4×D47—24no—
123C22×C4×D47—42no—
124C22×C4×D47C2314yescomplemented
125#13093999—232no—
126#13093998—232no—
127#13093994—232no—
128#13093994—232no—
129(C22⋊D47)⋊C4—232no—
130C2×C4⋊Dic47—24no—
131C2×C4⋊Dic47C2314yescomplemented
132C2×Dic47⋊C4—24no—
133C2×Dic47⋊C4C2314yescomplemented
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—24no—
141C2×(C2×D47)⋊C4—24no—
142C2×(C2×D47)⋊C4—24no—
143C2×(C2×D47)⋊C4—24no—
144C2×(C2×D47)⋊C4—24no—
145C2×(C2×D47)⋊C4—232no—
146C2×(C2×D47)⋊C4—42no—
147C2×(C2×D47)⋊C4D418yescomplemented
148C2×(C2×D47)⋊C4C2314yes—
149C2×(C2×D47)⋊C4C2314yes—
150C2×(C2×D47)⋊C4C2314yes—
151C2×(C2×D47)⋊C4C2314yes—
152C2×(C2×D47)⋊C4C2314yes—
153C2×(C2×D47)⋊C4C2314yes—
154C2×(C2×D47)⋊C4C2314yes—
155C2×(C2×D47)⋊C4C2314yes—
156C2×(C2×D47)⋊C4C2314yescomplemented
157C2×(C2×D47)⋊C4C2314yescomplemented
158C2×(C2×D47)⋊C4C2314yescomplemented
159C2×(C2×D47)⋊C4C2314yescomplemented
160C2×(C2×D47)⋊C4C2314yescomplemented
161C2×C4×Dic47—24no—
162C2×C4×Dic47C2314yescomplemented
163C47⋊#95C2314yescomplemented
164C47⋊#95C2314yescomplemented
165C25×C47C2311yescharacteristic
166C23×C4×C47—24no—
167C23×C4×C47—24no—
168C23×C4×C47—42no—
169C23×C4×C47C2311yescharacteristic
170C23×C4×C47C2311yescharacteristic
171C23×C4×C47C2311yescharacteristic
172C23×C4×C47C2314yes—
173C23×C4×C47C2311yescharacteristic
174C23×C4×C47C2311yescharacteristic
175C23×C4×C47C2311yescharacteristic
176C2×C4⋊C4×C47—24no—
177C2×C4⋊C4×C47—42no—
178C2×C4⋊C4×C47C2314yescomplemented
179C2×C4⋊C4×C47C2314yescomplemented
180C2×C22⋊C4×C47—24no—
181C2×C22⋊C4×C47D418yescomplemented
182C2×C22⋊C4×C47C2314yes—
183C2×C22⋊C4×C47C2314yes—
184#95×C47C2314yescomplemented
185#95×C47C2314yescomplemented
186C24×C47—22no—
187C24×C47—22no—
188C24×C47—22no—
189C24×C47—22no—
190C24×C47C2×D414yes—
191C24×C47C2×D414yes—
192C24×C47#4114yes—
193C24×C47C2412yes—
194C24×C47C2411yescharacteristic
195C23×D47—232no—
196C23×D47—22no—
197C23×D47—22no—
198C23×D47—22no—
199C23×D47—22no—
200C23×D47—22no—
201C23×D47—22no—
202C23×D47—22no—
203C23×D47—22no—
204C23×D47—22no—
205C23×D47—28no—
206C23×D47—22no—
207C23×D47—22no—
208C23×D47—22no—
209C23×D47—22no—
210C23×D47—22no—
211C23×D47—22no—
212C23×D47—22no—
213C23×D47—22no—
214C23×D47—22no—
215C23×D47—28no—
216C23×D47—28no—
217C23×D47—22no—
218C23×D47—22no—
219C23×D47—28no—
220C23×D47—28no—
221C23×D47—22no—
222C23×D47—22no—
223C23×D47—22no—
224C23×D47—22no—
225C23×D47—22no—
226C23×D47—44no—
227C23×D47—44no—
228C23×D47—416no—
229C23×D47—416no—
230C23×D47—416no—
231C23×D47—416no—
232C23×D47—416no—
233C23×D47—416no—
234C23×D47C2×D414yes—
235C23×D47C2×D414yes—
236C23×D47#4114yes—
237C23×D47C2412yes—
238C23×D47C2412yes—
239C23×D47C2412yes—
240C23×D47C2412yes—
241C22×C4×C47—22no—
242C22×C4×C47—22no—
243C22×C4×C47—22no—
244C22×C4×C47—22no—
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—28no—
253C22×C4×C47—22no—
254C22×C4×C47—22no—
255C22×C4×C47—22no—
256C22×C4×C47—22no—
257C22×C4×C47—28no—
258C22×C4×C47—44no—
259C22×C4×C47—416no—
260C22×C4×C47C2×D414yes—
261C22×C4×C47C2×D414yes—
262C22×C4×C47C2×D414yes—
263C22×C4×C47C2412yes—
264C22×C4×C47C2412yes—
265C22×C4×C47C2412yes—
266C22×C4×C47C2412yes—
267C22×C4×C47C2412yes—
268C22×C4×C47C2412yes—
269C2×C22⋊D47—232no—
270C2×C22⋊D47—28no—
271C2×C22⋊D47—28no—
272C2×C22⋊D47—28no—
273C2×C22⋊D47—28no—
274C2×C22⋊D47—28no—
275C2×C22⋊D47—416no—
276C2×C22⋊D47C2×D4116yescomplemented
277C22×Dic47—22no—
278C22×Dic47—22no—
279C22×Dic47—22no—
280C22×Dic47—22no—
281C22×Dic47—22no—
282C22×Dic47—22no—
283C22×Dic47—22no—
284C22×Dic47—22no—
285C22×Dic47—28no—
286C22×Dic47—22no—
287C22×Dic47—22no—
288C22×Dic47—28no—
289C22×Dic47—44no—
290C22×Dic47—416no—
291C22×Dic47C2×D414yes—
292C22×Dic47C2×D414yes—
293C22×Dic47C2412yes—
294C22×Dic47C2412yes—
295C22×Dic47C2412yes—
296C22×Dic47C2412yes—
297C2×D188—28no—
298C2×D188—28no—
299C2×D188—28no—
300C2×D188—28no—
301C2×D188—28no—
302C2×D188—28no—
303C2×D188—28no—
304C2×D188—28no—
305C2×D188—28no—
306C2×D188—28no—
307C2×D188—44no—
308C2×D188—44no—
309C2×D188—44no—
310C2×D188—44no—
311C2×D188—44no—
312C2×D188—416no—
313C2×D188—416no—
314C2×D188—416no—
315C2×D188—416no—
316C2×D188—416no—
317C2×C4×D47—28no—
318C2×C4×D47—28no—
319C2×C4×D47—44no—
320C2×C4×D47—416no—
321C4⋊C4×C47—28no—
322C4⋊C4×C47—44no—
323C22⋊C4×C47—28no—
324C22⋊C4×C47C2×D4116yescomplemented
325(C2×D47)⋊C4—28no—
326(C2×D47)⋊C4—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—
339Dic47⋊C4—28no—
340C4×Dic47—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#121116yescomplemented
352C23×C47C22×D414yes—
353C23×C47C22×D412yes—
354C23×C47C22×D412yes—
355C23×C47C22×D414yes—
356C23×C47C22×D412yes—
357C23×C47C2×#4112yes—
358C23×C47C2×#4114yes—
359C23×C47C2×#4112yes—
360C23×C47H(5,𝔽2)12yes—
361C23×C47H(5,𝔽2)12yes—
362C23×C47C2511yescharacteristic
363C22×D47—232no—
364C22×D47—28no—
365C22×D47—28no—
366C22×D47—28no—
367C22×D47—28no—
368C22×D47—28no—
369C22×D47—28no—
370C22×D47—28no—
371C22×D47—28no—
372C22×D47—28no—
373C22×D47—22no—
374C22×D47—22no—
375C22×D47—22no—
376C22×D47—22no—
377C22×D47—22no—
378C22×D47—22no—
379C22×D47—22no—
380C22×D47—22no—
381C22×D47—22no—
382C22×D47—22no—
383C22×D47—22no—
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—416no—
399C22×D47—416no—
400C22×D47—416no—
401C22×D47—416no—
402C22×D47—4128no—
403C22×D47—416no—
404C22×D47—44no—
405C22×D47—44no—
406C22×D47—416no—
407C22×D47—44no—
408C22×D47—44no—
409C22×D47—44no—
410C22×D47—44no—
411C22×D47—44no—
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×D47C22×D414yes—
425C22×D47C22×D414yes—
426C22×D47C2×#4114yes—
427C2×C4×C47—28no—
428C2×C4×C47—28no—
429C2×C4×C47—28no—
430C2×C4×C47—22no—
431C2×C4×C47—22no—
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—22no—
444C2×C4×C47—22no—
445C2×C4×C47—416no—
446C2×C4×C47—44no—
447C2×C4×C47—44no—
448C2×C4×C47—44no—
449C2×C4×C47C22×D414yes—
450C2×C4×C47C22×D414yes—
451C2×C4×C47C22×D414yes—
452C22⋊D47—232no—
453C22⋊D47—416no—
454C2×Dic47—28no—
455C2×Dic47—28no—
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—416no—
467C2×Dic47—44no—
468C2×Dic47—44no—
469C2×Dic47C22×D414yes—
470C2×Dic47C22×D414yes—
471D188—416no—
472D188—416no—
473D188—416no—
474D188—416no—
475D188—416no—
476C4×D47—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×C47C2×#12114yes—
486C22×C47C2×#12118yescomplemented
487C22×C47#52514yes—
488C22×C47#53814yes—
489C22×C47D4214yes—
490C22×C47D4214yes—
491C22×C47#54614yes—
492C22×C47#54614yes—
493C22×C47C23×D411yescharacteristic
494C22×C47C23×D411yescharacteristic
495C22×C47C23×D411yescharacteristic
496C22×C47C22×#4111yescharacteristic
497C22×C47C22×#4111yescharacteristic
498C22×C47C2×H(5,𝔽2)11yescharacteristic
499C22×C47C2×H(5,𝔽2)11yescharacteristic
500C2×D47—24no—
501C2×D47—24no—
502C2×D47—24no—
503C2×D47—24no—
504C2×D47—24no—
505C2×D47—24no—
506C2×D47—24no—
507C2×D47—24no—
508C2×D47—24no—
509C2×D47—464no—
510C2×D47—42no—
511C2×D47—42no—
512C2×D47—42no—
513C2×D47—416no—
514C2×D47—416no—
515C2×D47—416no—
516C2×D47—42no—
517C2×D47—42no—
518C2×D47—42no—
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—42no—
537C4×C47—42no—
538C4×C47—42no—
539Dic47—24no—
540Dic47—24no—
541Dic47—42no—
542Dic47—42no—
543C22×#121—471no—
544C22×#121—471no—
545C22×#120—471no—
546C22×#120—471no—
547C22×C4×D4—471no—
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×#385D4711yescharacteristic, complemented
559C2×C47—28no—
560C2×C47#242418yescomplemented
561C2×C47C22×#12111yescharacteristic
562C2×C47C2×#52511yescharacteristic
563C2×C47C2×#53811yescharacteristic
564C2×C47C2×D4211yescharacteristic
565C2×C47C2×D4211yescharacteristic
566C2×C47C2×#54611yescharacteristic
567C2×C47C2×#54611yescharacteristic
568D47—44no—
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×D4—471no—
580C24×C4—471no—
581C24×C4—471no—
582C24×C4C2×D4711yescharacteristic
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—478no—
592C2×C4×D4—948no—
593C22×C4⋊C4—471no—
594C22×C4⋊C4—471no—
595C22×C4⋊C4C2×D4711yescharacteristic, complemented
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
614C22×C42—471no—
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#385C2×D4718yescomplemented
624C2×#95—471no—
625C2×#95—471no—
626C2×#95C2×D4711yescharacteristic, complemented
627C2×#95C2×D4711yescharacteristic, complemented
628C47C2×#242411yescharacteristic, complemented, Sylow
629C25—471no—
630C25—471no—
631C25—471no—
632C25—471no—
633C25—474no—
634C25—944no—
635C25—944no—
636C25—944no—
637C25—944no—
638C25—944no—
639C25—1882no—
640C25—1882no—
641C25C22×D4711yescharacteristic
642C22×D4—478no—
643C22×D4—474no—
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—944no—
664C22×D4—944no—
665C22×D4—1882no—
666C22×D4—1882no—
667C22×D4—1882no—
668C22×D4—1882no—
669C22×D4—1882no—
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—42no—
673C23×C4—471no—
674C23×C4—471no—
675C23×C4—471no—
676C23×C4—471no—
677C23×C4—474no—
678C23×C4—474no—
679C23×C4—944no—
680C23×C4—944no—
681C23×C4—944no—
682C23×C4—944no—
683C23×C4—1882no—
684C23×C4—1882no—
685C23×C4C22×D4711yescharacteristic
686C23×C4C22×D4711yescharacteristic
687C23×C4C22×D4711yescharacteristic
688C23×C4C22×D4714yes—
689C23×C4C22×D4711yescharacteristic
690C23×C4C22×D4711yescharacteristic
691C23×C4C22×D4711yescharacteristic
692#121—9432no—
693#121—9432no—
694#120—9432no—
695#120—9432no—
696C4×D4—9432no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—42no—
699C2×C4⋊C4—474no—
700C2×C4⋊C4—474no—
701C2×C4⋊C4—944no—
702C2×C4⋊C4—944no—
703C2×C4⋊C4C22×D4714yescomplemented
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⋊C4D18818yescomplemented
734C2×C22⋊C4C22×D4714yes—
735C2×C22⋊C4C22×D4714yes—
736C2×C42—474no—
737C2×C42—944no—
738#95—474no—
739#95—474no—
740#95C22×D4714yescomplemented
741#95C22×D4714yescomplemented
742C24—22no—
743C24—22no—
744C24—22no—
745C24—22no—
746C24—474no—
747C24—474no—
748C24—474no—
749C24—472no—
750C24—472no—
751C24—472no—
752C24—472no—
753C24—948no—
754C24—948no—
755C24—9432no—
756C24—942no—
757C24—942no—
758C24—942no—
759C24—942no—
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—942no—
775C24—942no—
776C24—942no—
777C24—948no—
778C24—948no—
779C24—942no—
780C24—942no—
781C24—942no—
782C24—942no—
783C24—942no—
784C24—1884no—
785C24—1884no—
786C24—18816no—
787C24—18816no—
788C24—18816no—
789C24—18816no—
790C24—18816no—
791C24—18816no—
792C24C2×D18814yes—
793C24D4×D4714yes—
794C24#1062535414yes—
795C24C23×D4712yes—
796C24C23×D4711yescharacteristic
797C2×D4—4716no—
798C2×D4—948no—
799C2×D4—948no—
800C2×D4—948no—
801C2×D4—948no—
802C2×D4—948no—
803C2×D4—948no—
804C2×D4—948no—
805C2×D4—9432no—
806C2×D4—948no—
807C2×D4—948no—
808C2×D4—948no—
809C2×D4—948no—
810C2×D4—948no—
811C2×D4—948no—
812C2×D4—948no—
813C2×D4—948no—
814C2×D4—1884no—
815C2×D4—1884no—
816C2×D4—1884no—
817C2×D4—1884no—
818C2×D4—1884no—
819C2×D4—18816no—
820C2×D4—18816no—
821C2×D4—18816no—
822C2×D4—18816no—
823C2×D4—18816no—
824C2×D4—18816no—
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—22no—
836C22×C4—28no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—28no—
842C22×C4—44no—
843C22×C4—416no—
844C22×C4—474no—
845C22×C4—474no—
846C22×C4—472no—
847C22×C4—472no—
848C22×C4—472no—
849C22×C4—472no—
850C22×C4—948no—
851C22×C4—948no—
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—948no—
864C22×C4—1884no—
865C22×C4—18816no—
866C22×C4—1884no—
867C22×C4—18816no—
868C22×C4C2×D18814yes—
869C22×C4C2×D18814yes—
870C22×C4D4×D4714yes—
871C22×C4C23×D4712yes—
872C22×C4C23×D4712yes—
873C22×C4C23×D4712yes—
874C22×C4C23×D4712yes—
875C22×C4C23×D4712yes—
876C22×C4C23×D4712yes—
877C4⋊C4—28no—
878C4⋊C4—44no—
879C4⋊C4—948no—
880C4⋊C4—948no—
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×D188116yescomplemented
896C42—948no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—28no—
907C23—474no—
908C23—474no—
909C23—474no—
910C23—9432no—
911C23—948no—
912C23—948no—
913C23—948no—
914C23—948no—
915C23—948no—
916C23—948no—
917C23—948no—
918C23—948no—
919C23—948no—
920C23—942no—
921C23—942no—
922C23—942no—
923C23—942no—
924C23—942no—
925C23—942no—
926C23—942no—
927C23—942no—
928C23—942no—
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—18816no—
946C23—18816no—
947C23—18816no—
948C23—18816no—
949C23—188128no—
950C23—18816no—
951C23—1884no—
952C23—1884no—
953C23—1884no—
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—18816no—
967C23—1884no—
968C23—1884no—
969C23—1884no—
970C23—1884no—
971C23#13093999116yescomplemented
972C23C2×D4×D4714yes—
973C23C2×D4×D4712yes—
974C23C2×D4×D4712yes—
975C23C22×D18814yes—
976C23C22×D18812yes—
977C23#41×D4712yes—
978C23C2×#1062535414yes—
979C23C2×#1062535412yes—
980C23#1309406912yes—
981C23#1309407012yes—
982C23C24×D4711yescharacteristic
983D4—9432no—
984D4—18816no—
985D4—18816no—
986D4—18816no—
987D4—18816no—
988D4—18816no—
989D4—18816no—
990C2×C4—28no—
991C2×C4—28no—
992C2×C4—28no—
993C2×C4—22no—
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—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—416no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—44no—
1012C2×C4—474no—
1013C2×C4—474no—
1014C2×C4—948no—
1015C2×C4—948no—
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—942no—
1025C2×C4—942no—
1026C2×C4—18816no—
1027C2×C4—18816no—
1028C2×C4—1884no—
1029C2×C4—1884no—
1030C2×C4C2×D4×D4714yes—
1031C2×C4C22×D18814yes—
1032C2×C4C22×D18814yes—
1033C22—24no—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—232no—
1039C22—24no—
1040C22—944no—
1041C22—944no—
1042C22—944no—
1043C22—944no—
1044C22—944no—
1045C22—944no—
1046C22—944no—
1047C22—944no—
1048C22—944no—
1049C22—3768no—
1050C22—18864no—
1051C22—1882no—
1052C22—1882no—
1053C22—1882no—
1054C22—1882no—
1055C22—1882no—
1056C22—1882no—
1057C22—1882no—
1058C22—1882no—
1059C22—1882no—
1060C22—1882no—
1061C22—1882no—
1062C22—1882no—
1063C22—1882no—
1064C22—1882no—
1065C22—1882no—
1066C22—1882no—
1067C22—18816no—
1068C22—18816no—
1069C22—18816no—
1070C22—1882no—
1071C22—1882no—
1072C22—1882no—
1073C22C2×#1309399914yes—
1074C22C2×#1309399918yescomplemented
1075C22#1568963614yes—
1076C22#1568971314yes—
1077C22#1568975514yes—
1078C22D4×D18814yes—
1079C22#1568976514yes—
1080C22#1568976814yes—
1081C22C22×D4×D4711yescharacteristic
1082C22C22×D4×D4711yescharacteristic
1083C22C23×D18811yescharacteristic
1084C22C2×#41×D4711yescharacteristic
1085C22C22×#1062535411yescharacteristic
1086C22C2×#1309406911yescharacteristic
1087C22C2×#1309407011yescharacteristic
1088C4—24no—
1089C4—24no—
1090C4—24no—
1091C4—42no—
1092C4—42no—
1093C4—42no—
1094C4—944no—
1095C4—944no—
1096C4—1882no—
1097C4—1882no—
1098C2—28no—
1099C2—3762no—
1100C2—1884no—
1101C2—1884no—
1102C2—1884no—
1103C2#2024692218yesdirect product factor
1104C2C22×#1309399911yescharacteristic
1105C2C2×#1568963611yescharacteristic
1106C2C2×#1568971311yescharacteristic
1107C2C2×#1568975511yescharacteristic
1108C2C2×D4×D18811yescharacteristic
1109C2C2×#1568976511yescharacteristic
1110C2C2×#1568976811yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#385C2
socleC24×C47C24
hypercenterC2×#385D47
hypocenterC47C2×#2424
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13093999C2semidirect
2. C22×#13093998C2semidirect
3. C22×#13093994C2semidirect
4. C22×#13093994C2semidirect
5. C22×(C22⋊D47)⋊C4C2semidirect
6. C23×(C2×D47)⋊C4C2semidirect
7. #20246922C2direct (N × H)
8. C2×#15689045C2semidirect
9. C2×#15689041C2semidirect
10. C2×#15689040C2semidirect
11. C2×#15689033C2semidirect
12. C2×#15689024C2semidirect
13. C2×#15689015C2semidirect
14. C2×#15689001C2semidirect
15. C2×#15689000C2semidirect
16. C2×C47×#385C2semidirect
22. C23×D188C22semidirect
26. C23×C4×D47C22semidirect
28. C2×#13093999C22semidirect
30. C2×#13093998C22semidirect
33. C2×#13093994C22semidirect
34. C2×#13093994C22semidirect
36. C2×(C22⋊D47)⋊C4C22semidirect
37. C22×C4⋊Dic47C22semidirect
38. C22×Dic47⋊C4C22semidirect
48. C22×(C2×D47)⋊C4C22semidirect
49. C22×(C2×D47)⋊C4C22semidirect
50. C22×(C2×D47)⋊C4C22semidirect
51. C22×(C2×D47)⋊C4C22semidirect
52. C22×(C2×D47)⋊C4C22semidirect
53. C22×(C2×D47)⋊C4C22semidirect
54. C22×C4×Dic47C22semidirect
55. #15689045C22semidirect
56. #15689041C22semidirect
57. #15689040C22semidirect
58. #15689033C22semidirect
59. #15689024C22semidirect
60. #15689015C22semidirect
61. #15689001C22semidirect
62. #15689000C22semidirect
63. C2×C47⋊#95C22semidirect
64. C2×C47⋊#95C22semidirect
66. C22×C4⋊C4×C47C22semidirect
67. C22×C4⋊C4×C47C22semidirect
70. C47×#385C22semidirect
71. C2×#95×C47C22semidirect
72. C2×#95×C47C22semidirect
104. C22×D188C23semidirect
110. C22×C22⋊D47D4semidirect
124. C22×C4×D47C23semidirect
131. C2×C4⋊Dic47C23semidirect
133. C2×Dic47⋊C4C23semidirect
147. C2×(C2×D47)⋊C4D4semidirect
156. C2×(C2×D47)⋊C4C23semidirect
157. C2×(C2×D47)⋊C4C23semidirect
158. C2×(C2×D47)⋊C4C23semidirect
159. C2×(C2×D47)⋊C4C23semidirect
160. C2×(C2×D47)⋊C4C23semidirect
162. C2×C4×Dic47C23semidirect
163. C47⋊#95C23semidirect
164. C47⋊#95C23semidirect
178. C2×C4⋊C4×C47C23semidirect
179. C2×C4⋊C4×C47C23semidirect
181. C2×C22⋊C4×C47D4semidirect
184. #95×C47C23semidirect
185. #95×C47C23semidirect
276. C2×C22⋊D47C2×D4semidirect
324. C22⋊C4×C47C2×D4semidirect
337. (C2×D47)⋊C4C2×D4semidirect
351. C23×C47#121semidirect
486. C22×C47C2×#121semidirect
558. C2×#385D47semidirect
560. C2×C47#2424semidirect
595. C22×C4⋊C4C2×D47semidirect
596. C22×C4⋊C4C2×D47semidirect
623. #385C2×D47semidirect
626. C2×#95C2×D47semidirect
627. C2×#95C2×D47semidirect
628. C47C2×#2424semidirect
703. C2×C4⋊C4C22×D47semidirect
704. C2×C4⋊C4C22×D47semidirect
733. C2×C22⋊C4D188semidirect
740. #95C22×D47semidirect
741. #95C22×D47semidirect
895. C22⋊C4C2×D188semidirect
971. C23#13093999semidirect
1074. C22C2×#13093999semidirect
1103. C2#20246922direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939992
C22×#130939982
C22×#130939942
C22×(C22⋊D47)⋊C42
C23×(C2×D47)⋊C42
#202469222
C2×#156890452
C2×#156890412
C2×#156890402
C2×#156890332
C2×#156890242
C2×#156890152
C2×#156890012
C2×#156890002
C2×C47×#3852
C2×#242447