Finite Group Databasebeta

← C2×#20246926 #26383752

Subgroups — C2×#20246926 #26383752

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×#13093997C211yesmaximal, characteristic, complemented
2C22×#13093996C211yesmaximal, characteristic, complemented
3C22×#13093994C211yesmaximal, characteristic, complemented
4C22×#13093992C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊D47C211yesmaximal, characteristic, complemented
6C23×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
7#20246926C2116yesmaximal, direct product factor
8C2×#15689047C211yesmaximal, characteristic, complemented
9C2×#15689041C211yesmaximal, characteristic, complemented
10C2×#15689038C211yesmaximal, characteristic, complemented
11C2×#15689032C211yesmaximal, characteristic, complemented
12C2×#15689023C211yesmaximal, characteristic, complemented
13C2×#15689012C211yesmaximal, characteristic, complemented
14C2×#15689001C211yesmaximal, characteristic, complemented
15C2×#15688995C211yesmaximal, characteristic, complemented
16C2×C47×#386C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×D188C2211yescharacteristic
19C23×D188C2211yescharacteristic
20C23×C22⋊D47C2211yescharacteristic
21C23×C22⋊D47C2211yescharacteristic
22C23×C22⋊D47C2211yescharacteristic
23C23×C22⋊D47C2211yescharacteristic, complemented
24C24×Dic47C2211yescharacteristic
25C23×C4×D47C2211yescharacteristic, complemented
26C2×#13093997—28no—
27C2×#13093997C2218yescomplemented
28C2×#13093996—28no—
29C2×#13093996C2218yescomplemented
30C2×#13093994—28no—
31C2×#13093994C2218yescomplemented
32C2×#13093992—28no—
33C2×#13093992C2218yescomplemented
34C2×C4×C22⋊D47—28no—
35C2×C4×C22⋊D47C2218yescomplemented
36C22×Dic47⋊C4C2211yescharacteristic, complemented
37C22×Dic47⋊C4C2211yescharacteristic, complemented
38C22×Dic47⋊C4C2211yescharacteristic, complemented
39C22×Dic47⋊C4C2211yescharacteristic, complemented
40C22×C22⋊Dic47C2211yescharacteristic
41C22×C22⋊Dic47C2211yescharacteristic, complemented
42C22×(C2×D47)⋊C4—28no—
43C22×(C2×D47)⋊C4C2211yescharacteristic
44C22×(C2×D47)⋊C4C2211yescharacteristic
45C22×(C2×D47)⋊C4C2211yescharacteristic
46C22×(C2×D47)⋊C4C2211yescharacteristic
47C22×(C2×D47)⋊C4C2211yescharacteristic
48C22×(C2×D47)⋊C4C2211yescharacteristic
49C22×(C2×D47)⋊C4C2211yescharacteristic
50C22×(C2×D47)⋊C4C2211yescharacteristic
51C22×(C2×D47)⋊C4C2218yescomplemented
52C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
53C22×(C2×D47)⋊C4C2211yescharacteristic, complemented
54C22×C4×Dic47C2211yescharacteristic, complemented
55#15689047C2218yescomplemented
56#15689041C2218yescomplemented
57#15689038C2218yescomplemented
58#15689032C2218yescomplemented
59#15689023C2218yescomplemented
60#15689012C2218yescomplemented
61#15689001C2218yescomplemented
62#15688995C2218yescomplemented
63C2×C47⋊#95C2211yescharacteristic, complemented
64C2×C47⋊#95C2211yescharacteristic, complemented
65C23×D4×C47C2211yescharacteristic
66C24×C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C22⋊C4×C47C2211yescharacteristic, complemented
69C22×C22⋊C4×C47C2211yescharacteristic, complemented
70C47×#386C2218yescomplemented
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×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—42no—
101C22×C22⋊D47—42no—
102C22×C22⋊D47—42no—
103C22×C22⋊D47D418yescomplemented
104C22×C22⋊D47C2314yes—
105C22×C22⋊D47C2314yes—
106C22×C22⋊D47C2314yes—
107C22×C22⋊D47C2314yescomplemented
108C23×Dic47—24no—
109C23×Dic47—24no—
110C23×Dic47—42no—
111C23×Dic47C2311yescharacteristic
112C23×Dic47C2314yes—
113C23×Dic47C2311yescharacteristic
114C23×Dic47C2311yescharacteristic
115C23×Dic47C2311yescharacteristic
116C23×Dic47C2311yescharacteristic
117C22×C4×D47—24no—
118C22×C4×D47—24no—
119C22×C4×D47—42no—
120C22×C4×D47C2314yescomplemented
121#13093997—232no—
122#13093996—232no—
123#13093994—232no—
124#13093992—232no—
125C4×C22⋊D47—232no—
126C2×Dic47⋊C4—24no—
127C2×Dic47⋊C4—24no—
128C2×Dic47⋊C4—24no—
129C2×Dic47⋊C4—42no—
130C2×Dic47⋊C4C2314yescomplemented
131C2×Dic47⋊C4C2314yescomplemented
132C2×Dic47⋊C4C2314yescomplemented
133C2×Dic47⋊C4C2314yescomplemented
134C2×C22⋊Dic47—24no—
135C2×C22⋊Dic47D418yescomplemented
136C2×C22⋊Dic47C2314yes—
137C2×C22⋊Dic47C2314yescomplemented
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—24no—
146C2×(C2×D47)⋊C4—24no—
147C2×(C2×D47)⋊C4—232no—
148C2×(C2×D47)⋊C4D418yescomplemented
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)⋊C4C2314yes—
157C2×(C2×D47)⋊C4C2314yescomplemented
158C2×(C2×D47)⋊C4C2314yescomplemented
159C2×C4×Dic47—24no—
160C2×C4×Dic47C2314yescomplemented
161C47⋊#95C2314yescomplemented
162C47⋊#95C2314yescomplemented
163C25×C47C2311yescharacteristic
164C25×C47C2311yescharacteristic
165C22×D4×C47—24no—
166C22×D4×C47—24no—
167C22×D4×C47—24no—
168C22×D4×C47C2314yes—
169C23×C4×C47—24no—
170C23×C4×C47—24no—
171C23×C4×C47—42no—
172C23×C4×C47C2311yescharacteristic
173C23×C4×C47C2311yescharacteristic
174C23×C4×C47C2311yescharacteristic
175C23×C4×C47C2311yescharacteristic
176C23×C4×C47C2314yes—
177C23×C4×C47C2311yescharacteristic
178C2×C22⋊C4×C47—24no—
179C2×C22⋊C4×C47—24no—
180C2×C22⋊C4×C47—42no—
181C2×C22⋊C4×C47C2314yes—
182C2×C22⋊C4×C47C2314yescomplemented
183C2×C22⋊C4×C47C2314yescomplemented
184#95×C47C2314yescomplemented
185#95×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×C47—22no—
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—22no—
210C23×D47—22no—
211C23×D47—22no—
212C23×D47—22no—
213C23×D47—28no—
214C23×D47—22no—
215C23×D47—22no—
216C23×D47—22no—
217C23×D47—22no—
218C23×D47—22no—
219C23×D47—22no—
220C23×D47—22no—
221C23×D47—22no—
222C23×D47—22no—
223C23×D47—28no—
224C23×D47—28no—
225C23×D47—28no—
226C23×D47—28no—
227C23×D47—44no—
228C23×D47—44no—
229C23×D47—416no—
230C23×D47—416no—
231C23×D47—416no—
232C23×D47—416no—
233C23×D47—416no—
234C23×D47—416no—
235C23×D47C2×D414yes—
236C23×D47C2×D414yes—
237C23×D47#4114yes—
238C23×D47C2412yes—
239C23×D47C2412yes—
240C23×D47C2412yes—
241C2×D4×C47—28no—
242C2×D4×C47—28no—
243C2×D4×C47—28no—
244C2×D4×C47—416no—
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—22no—
258C22×C4×C47—22no—
259C22×C4×C47—22no—
260C22×C4×C47—28no—
261C22×C4×C47—44no—
262C22×C4×C47—416no—
263C22×C4×C47C2×D414yes—
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—28no—
276C2×C22⋊D47—28no—
277C2×C22⋊D47—28no—
278C2×C22⋊D47—44no—
279C2×C22⋊D47—44no—
280C2×C22⋊D47—44no—
281C2×C22⋊D47—416no—
282C2×C22⋊D47—416no—
283C2×C22⋊D47—416no—
284C2×C22⋊D47C2×D4116yescomplemented
285C22×Dic47—22no—
286C22×Dic47—22no—
287C22×Dic47—22no—
288C22×Dic47—22no—
289C22×Dic47—22no—
290C22×Dic47—22no—
291C22×Dic47—22no—
292C22×Dic47—22no—
293C22×Dic47—22no—
294C22×Dic47—22no—
295C22×Dic47—28no—
296C22×Dic47—22no—
297C22×Dic47—28no—
298C22×Dic47—44no—
299C22×Dic47—416no—
300C22×Dic47C2×D414yes—
301C22×Dic47C2×D414yes—
302C22×Dic47C2×D414yes—
303C22×Dic47C2×D414yes—
304C22×Dic47C2412yes—
305C22×Dic47C2412yes—
306C22×Dic47C2412yes—
307C22×Dic47C2412yes—
308C22×Dic47C2412yes—
309C2×D188—28no—
310C2×D188—28no—
311C2×D188—28no—
312C2×D188—28no—
313C2×D188—44no—
314C2×D188—44no—
315C2×D188—416no—
316C2×D188—416no—
317C2×C4×D47—28no—
318C2×C4×D47—28no—
319C2×C4×D47—44no—
320C2×C4×D47—416no—
321C22⋊C4×C47—28no—
322C22⋊C4×C47—28no—
323C22⋊C4×C47—44no—
324C22⋊Dic47—28no—
325C22⋊Dic47C2×D4116yescomplemented
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)⋊C4C2×D4116yescomplemented
336Dic47⋊C4—28no—
337Dic47⋊C4—28no—
338Dic47⋊C4—28no—
339Dic47⋊C4—44no—
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—22no—
352C23×C47—22no—
353C23×C47—22no—
354C23×C47—22no—
355C23×C47—22no—
356C23×C47—22no—
357C23×C47—22no—
358C23×C47—44no—
359C23×C47—44no—
360C23×C47—44no—
361C23×C47—44no—
362C23×C47—44no—
363C23×C47—44no—
364C23×C47—44no—
365C23×C47#121116yescomplemented
366C23×C47C22×D414yes—
367C23×C47C22×D414yes—
368C23×C47C22×D412yes—
369C23×C47C22×D412yes—
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—28no—
385C22×D47—28no—
386C22×D47—28no—
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—22no—
404C22×D47—22no—
405C22×D47—416no—
406C22×D47—416no—
407C22×D47—416no—
408C22×D47—416no—
409C22×D47—4128no—
410C22×D47—416no—
411C22×D47—44no—
412C22×D47—44no—
413C22×D47—416no—
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—
427D4×C47—416no—
428C2×C4×C47—28no—
429C2×C4×C47—22no—
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—416no—
444C2×C4×C47—44no—
445C2×C4×C47—44no—
446C2×C4×C47—44no—
447C2×C4×C47—44no—
448C2×C4×C47C22×D414yes—
449C22⋊D47—232no—
450C22⋊D47—416no—
451C22⋊D47—416no—
452C22⋊D47—416no—
453C2×Dic47—28no—
454C2×Dic47—28no—
455C2×Dic47—28no—
456C2×Dic47—28no—
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—416no—
469C2×Dic47—44no—
470C2×Dic47C22×D414yes—
471C2×Dic47C22×D414yes—
472C2×Dic47C22×D414yes—
473C2×Dic47C22×D414yes—
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×C47—42no—
486C22×C47—42no—
487C22×C47—42no—
488C22×C47—42no—
489C22×C47—42no—
490C22×C47—42no—
491C22×C47—42no—
492C22×C47—88no—
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—24no—
515C2×D47—24no—
516C2×D47—24no—
517C2×D47—464no—
518C2×D47—42no—
519C2×D47—42no—
520C2×D47—42no—
521C2×D47—416no—
522C2×D47—416no—
523C2×D47—416no—
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—42no—
533C4×C47—24no—
534C4×C47—42no—
535C4×C47—42no—
536C4×C47—42no—
537C4×C47—42no—
538Dic47—24no—
539Dic47—24no—
540Dic47—24no—
541Dic47—24no—
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×#386D4711yescharacteristic, complemented
558C2×#385—471no—
559C2×C47—28no—
560C2×C47—82no—
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—44no—
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×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⋊C4—471no—
596C22×C4⋊C4—471no—
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—471no—
609C22×C22⋊C4—478no—
610C22×C22⋊C4—948no—
611C22×C22⋊C4C2×D4711yescharacteristic
612C22×C22⋊C4C2×D4711yescharacteristic, complemented
613C22×C22⋊C4C2×D4711yescharacteristic, complemented
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#386C2×D4718yescomplemented
623#385—478no—
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—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—24no—
645C22×D4—478no—
646C22×D4—474no—
647C22×D4—474no—
648C22×D4—474no—
649C22×D4—474no—
650C22×D4—474no—
651C22×D4—474no—
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—1882no—
665C22×D4—1882no—
666C22×D4—1882no—
667C22×D4—1882no—
668C22×D4—1882no—
669C22×D4C22×D4714yes—
670C23×C4—24no—
671C23×C4—24no—
672C23×C4—42no—
673C23×C4—471no—
674C23×C4—471no—
675C23×C4—471no—
676C23×C4—471no—
677C23×C4—471no—
678C23×C4—474no—
679C23×C4—474no—
680C23×C4—944no—
681C23×C4—944no—
682C23×C4—944no—
683C23×C4—944no—
684C23×C4—1882no—
685C23×C4—1882no—
686C23×C4C22×D4711yescharacteristic
687C23×C4C22×D4711yescharacteristic
688C23×C4C22×D4711yescharacteristic
689C23×C4C22×D4711yescharacteristic
690C23×C4C22×D4714yes—
691C23×C4C22×D4711yescharacteristic
692#121—9432no—
693#121—9432no—
694#120—9432no—
695#120—9432no—
696C4×D4—9432no—
697C2×C4⋊C4—474no—
698C2×C4⋊C4—474no—
699C2×C4⋊C4—474no—
700C2×C4⋊C4—474no—
701C2×C4⋊C4—944no—
702C2×C4⋊C4—944no—
703C2×C4⋊C4—944no—
704C2×C4⋊C4—1882no—
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—42no—
708C2×C22⋊C4—478no—
709C2×C22⋊C4—474no—
710C2×C22⋊C4—478no—
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—474no—
721C2×C22⋊C4—474no—
722C2×C22⋊C4—9432no—
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—944no—
733C2×C22⋊C4C22×D4714yes—
734C2×C22⋊C4C22×D4714yescomplemented
735C2×C22⋊C4C22×D4714yescomplemented
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—22no—
747C24—22no—
748C24—22no—
749C24—22no—
750C24—22no—
751C24—22no—
752C24—22no—
753C24—474no—
754C24—474no—
755C24—474no—
756C24—472no—
757C24—472no—
758C24—472no—
759C24—948no—
760C24—948no—
761C24—9432no—
762C24—942no—
763C24—942no—
764C24—942no—
765C24—942no—
766C24—942no—
767C24—942no—
768C24—942no—
769C24—942no—
770C24—942no—
771C24—942no—
772C24—948no—
773C24—942no—
774C24—942no—
775C24—942no—
776C24—942no—
777C24—942no—
778C24—942no—
779C24—942no—
780C24—942no—
781C24—948no—
782C24—948no—
783C24—1884no—
784C24—1884no—
785C24—18816no—
786C24—18816no—
787C24—18816no—
788C24—18816no—
789C24—18816no—
790C24—18816no—
791C24#1062535014yes—
792C24D4×D4714yes—
793C24D4×D4714yes—
794C24C23×D4712yes—
795C24C23×D4712yes—
796C24C23×D4711yescharacteristic
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—416no—
801C2×D4—4716no—
802C2×D4—948no—
803C2×D4—948no—
804C2×D4—948no—
805C2×D4—948no—
806C2×D4—948no—
807C2×D4—948no—
808C2×D4—948no—
809C2×D4—9432no—
810C2×D4—948no—
811C2×D4—948no—
812C2×D4—948no—
813C2×D4—948no—
814C2×D4—948no—
815C2×D4—1884no—
816C2×D4—1884no—
817C2×D4—18816no—
818C2×D4—18816no—
819C2×D4—1884no—
820C2×D4—1884no—
821C2×D4—1884no—
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—28no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—28no—
841C22×C4—44no—
842C22×C4—416no—
843C22×C4—474no—
844C22×C4—474no—
845C22×C4—474no—
846C22×C4—474no—
847C22×C4—472no—
848C22×C4—472no—
849C22×C4—472no—
850C22×C4—472no—
851C22×C4—472no—
852C22×C4—948no—
853C22×C4—948no—
854C22×C4—942no—
855C22×C4—942no—
856C22×C4—942no—
857C22×C4—942no—
858C22×C4—942no—
859C22×C4—942no—
860C22×C4—942no—
861C22×C4—942no—
862C22×C4—942no—
863C22×C4—942no—
864C22×C4—948no—
865C22×C4—942no—
866C22×C4—948no—
867C22×C4—1884no—
868C22×C4—18816no—
869C22×C4—1884no—
870C22×C4—18816no—
871C22×C4D4×D4714yes—
872C22×C4C23×D4712yes—
873C22×C4C23×D4712yes—
874C22×C4C23×D4712yes—
875C22×C4C23×D4712yes—
876C22×C4C23×D4712yes—
877C4⋊C4—948no—
878C4⋊C4—948no—
879C4⋊C4—948no—
880C4⋊C4—1884no—
881C22⋊C4—28no—
882C22⋊C4—28no—
883C22⋊C4—44no—
884C22⋊C4—4716no—
885C22⋊C4—4716no—
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—948no—
895C22⋊C4—948no—
896C42—948no—
897C23—28no—
898C23—28no—
899C23—28no—
900C23—28no—
901C23—28no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—28no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—44no—
915C23—44no—
916C23—44no—
917C23—44no—
918C23—44no—
919C23—44no—
920C23—44no—
921C23—474no—
922C23—474no—
923C23—474no—
924C23—9432no—
925C23—948no—
926C23—948no—
927C23—948no—
928C23—948no—
929C23—948no—
930C23—948no—
931C23—948no—
932C23—948no—
933C23—948no—
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—942no—
949C23—942no—
950C23—942no—
951C23—942no—
952C23—18816no—
953C23—18816no—
954C23—18816no—
955C23—18816no—
956C23—188128no—
957C23—18816no—
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#13093997116yescomplemented
972C23C2×D4×D4714yes—
973C23C2×D4×D4714yes—
974C23C2×D4×D4712yes—
975C23C2×D4×D4712yes—
976C23C2×D4×D4712yes—
977C23#41×D4712yes—
978C23C2×#1062535014yes—
979C23C2×#1062535012yes—
980C23#1309406912yes—
981C23#1309407012yes—
982C23C24×D4711yescharacteristic
983D4—416no—
984D4—9432no—
985D4—18816no—
986D4—18816no—
987D4—18816no—
988D4—18816no—
989D4—18816no—
990C2×C4—28no—
991C2×C4—22no—
992C2×C4—22no—
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—416no—
1006C2×C4—44no—
1007C2×C4—44no—
1008C2×C4—44no—
1009C2×C4—44no—
1010C2×C4—474no—
1011C2×C4—474no—
1012C2×C4—474no—
1013C2×C4—474no—
1014C2×C4—948no—
1015C2×C4—948no—
1016C2×C4—948no—
1017C2×C4—948no—
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—942no—
1027C2×C4—942no—
1028C2×C4—942no—
1029C2×C4—18816no—
1030C2×C4—18816no—
1031C2×C4—1884no—
1032C2×C4C2×D4×D4714yes—
1033C22—24no—
1034C22—24no—
1035C22—24no—
1036C22—24no—
1037C22—24no—
1038C22—232no—
1039C22—24no—
1040C22—42no—
1041C22—42no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—88no—
1048C22—944no—
1049C22—944no—
1050C22—944no—
1051C22—944no—
1052C22—944no—
1053C22—944no—
1054C22—944no—
1055C22—944no—
1056C22—944no—
1057C22—18864no—
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×#1309399714yes—
1074C22C2×#1309399718yescomplemented
1075C22#1568963214yes—
1076C22#1568970614yes—
1077C22#1568975514yes—
1078C22#1568975714yes—
1079C22#1568976214yes—
1080C22#1568976514yes—
1081C22C22×D4×D4711yescharacteristic
1082C22C22×D4×D4711yescharacteristic
1083C22C22×D4×D4711yescharacteristic
1084C22C2×#41×D4711yescharacteristic
1085C22C22×#1062535011yescharacteristic
1086C22C2×#1309406911yescharacteristic
1087C22C2×#1309407011yescharacteristic
1088C4—24no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—42no—
1093C4—944no—
1094C4—944no—
1095C4—944no—
1096C4—944no—
1097C4—1882no—
1098C2—28no—
1099C2—82no—
1100C2—1884no—
1101C2—1884no—
1102C2—1884no—
1103C2#2024692618yesdirect product factor
1104C2C22×#1309399711yescharacteristic
1105C2C2×#1568963211yescharacteristic
1106C2C2×#1568970611yescharacteristic
1107C2C2×#1568975511yescharacteristic
1108C2C2×#1568975711yescharacteristic
1109C2C2×#1568976211yescharacteristic
1110C2C2×#1568976511yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#386C2
socleC24×C47C24
hypercenterC2×#386D47
hypocenterC47C2×#2424
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C22×#13093997C2semidirect
2. C22×#13093996C2semidirect
3. C22×#13093994C2semidirect
4. C22×#13093992C2semidirect
5. C22×C4×C22⋊D47C2semidirect
6. C23×(C2×D47)⋊C4C2semidirect
7. #20246926C2direct (N × H)
8. C2×#15689047C2semidirect
9. C2×#15689041C2semidirect
10. C2×#15689038C2semidirect
11. C2×#15689032C2semidirect
12. C2×#15689023C2semidirect
13. C2×#15689012C2semidirect
14. C2×#15689001C2semidirect
15. C2×#15688995C2semidirect
16. C2×C47×#386C2semidirect
23. C23×C22⋊D47C22semidirect
25. C23×C4×D47C22semidirect
27. C2×#13093997C22semidirect
29. C2×#13093996C22semidirect
31. C2×#13093994C22semidirect
33. C2×#13093992C22semidirect
35. C2×C4×C22⋊D47C22semidirect
36. C22×Dic47⋊C4C22semidirect
37. C22×Dic47⋊C4C22semidirect
38. C22×Dic47⋊C4C22semidirect
39. C22×Dic47⋊C4C22semidirect
41. C22×C22⋊Dic47C22semidirect
51. C22×(C2×D47)⋊C4C22semidirect
52. C22×(C2×D47)⋊C4C22semidirect
53. C22×(C2×D47)⋊C4C22semidirect
54. C22×C4×Dic47C22semidirect
55. #15689047C22semidirect
56. #15689041C22semidirect
57. #15689038C22semidirect
58. #15689032C22semidirect
59. #15689023C22semidirect
60. #15689012C22semidirect
61. #15689001C22semidirect
62. #15688995C22semidirect
63. C2×C47⋊#95C22semidirect
64. C2×C47⋊#95C22semidirect
68. C22×C22⋊C4×C47C22semidirect
69. C22×C22⋊C4×C47C22semidirect
70. C47×#386C22semidirect
71. C2×#95×C47C22semidirect
72. C2×#95×C47C22semidirect
103. C22×C22⋊D47D4semidirect
107. C22×C22⋊D47C23semidirect
120. C22×C4×D47C23semidirect
130. C2×Dic47⋊C4C23semidirect
131. C2×Dic47⋊C4C23semidirect
132. C2×Dic47⋊C4C23semidirect
133. C2×Dic47⋊C4C23semidirect
135. C2×C22⋊Dic47D4semidirect
137. C2×C22⋊Dic47C23semidirect
148. C2×(C2×D47)⋊C4D4semidirect
157. C2×(C2×D47)⋊C4C23semidirect
158. C2×(C2×D47)⋊C4C23semidirect
160. C2×C4×Dic47C23semidirect
161. C47⋊#95C23semidirect
162. C47⋊#95C23semidirect
182. C2×C22⋊C4×C47C23semidirect
183. C2×C22⋊C4×C47C23semidirect
184. #95×C47C23semidirect
185. #95×C47C23semidirect
284. C2×C22⋊D47C2×D4semidirect
325. C22⋊Dic47C2×D4semidirect
335. (C2×D47)⋊C4C2×D4semidirect
365. C23×C47#121semidirect
494. C22×C47C2×#121semidirect
557. C2×#386D47semidirect
561. C2×C47#2424semidirect
612. C22×C22⋊C4C2×D47semidirect
613. C22×C22⋊C4C2×D47semidirect
622. #386C2×D47semidirect
626. C2×#95C2×D47semidirect
627. C2×#95C2×D47semidirect
628. C47C2×#2424semidirect
734. C2×C22⋊C4C22×D47semidirect
735. C2×C22⋊C4C22×D47semidirect
740. #95C22×D47semidirect
741. #95C22×D47semidirect
971. C23#13093997semidirect
1074. C22C2×#13093997semidirect
1103. C2#20246926direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939972
C22×#130939962
C22×#130939942
C22×#130939922
C22×C4×C22⋊D472
C23×(C2×D47)⋊C42
#202469262
C2×#156890472
C2×#156890412
C2×#156890382
C2×#156890322
C2×#156890232
C2×#156890122
C2×#156890012
C2×#156889952
C2×C47×#3862
C2×#242447