Finite Group Databasebeta

← C2×#20247971 #26385415

Subgroups — C2×#20247971 #26385415

Order 12032.

2726 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094018C211yesmaximal, characteristic, complemented
2C22×#13094017C211yesmaximal, characteristic, complemented
3#20247971C2116yesmaximal, direct product factor
4C2×#15689052C211yesmaximal, characteristic, complemented
5C2×#15689051C211yesmaximal, characteristic, complemented
6C2×#15689046C211yesmaximal, characteristic, complemented
7C2×#15689045C211yesmaximal, characteristic, complemented
8C2×#15689023C211yesmaximal, characteristic
9C2×#15689023C211yesmaximal, characteristic
10C2×#15689023C211yesmaximal, characteristic
11C2×#15689020C211yesmaximal, characteristic, complemented
12C2×#15689015C211yesmaximal, characteristic, complemented
13C2×#15688992C211yesmaximal, characteristic, complemented
14C2×C4×Dic47⋊C4C211yesmaximal, characteristic, complemented
15C2×#15688974C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C2×#13094018—28no—
19C2×#13094018C2218yescomplemented
20C2×#13094017—28no—
21C2×#13094017C2218yescomplemented
22C22×C4⋊Dic47C2211yescharacteristic
23C22×C4⋊Dic47C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2211yescharacteristic
27C22×Dic47⋊C4C2211yescharacteristic
28C22×Dic47⋊C4C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×C22⋊Dic47C2211yescharacteristic
33C22×C22⋊Dic47C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×(C2×D47)⋊C4C2211yescharacteristic
40C22×(C2×D47)⋊C4C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43C22×C4×Dic47C2211yescharacteristic
44C22×C4×Dic47C2211yescharacteristic
45#15689052C2218yescomplemented
46#15689051C2218yescomplemented
47#15689046C2218yescomplemented
48#15689045C2218yescomplemented
49#15689023C2218yes—
50#15689023C2218yes—
51#15689023C2218yes—
52#15689020C2218yescomplemented
53#15689015C2218yescomplemented
54#15688992C2218yescomplemented
55C4×Dic47⋊C4C2218yescomplemented
56#15688974C2218yescomplemented
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61C22×C4⋊C4×C47C2211yescharacteristic
62C22×C22⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C42×C47C2211yescharacteristic
66C47×#388C2218yescomplemented
67C2×#95×C47C2211yescharacteristic
68C2×#95×C47C2211yescharacteristic
69C24×D47C2311yescharacteristic
70C22×C22⋊D47—24no—
71C22×C22⋊D47—24no—
72C22×C22⋊D47—24no—
73C22×C22⋊D47C2314yes—
74C23×Dic47C2311yescharacteristic
75C23×Dic47C2311yescharacteristic
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81#13094018—232no—
82#13094017—232no—
83C2×C4⋊Dic47—24no—
84C2×C4⋊Dic47—42no—
85C2×C4⋊Dic47C2314yes—
86C2×C4⋊Dic47C2314yes—
87C2×Dic47⋊C4—24no—
88C2×Dic47⋊C4—24no—
89C2×Dic47⋊C4—24no—
90C2×Dic47⋊C4—24no—
91C2×Dic47⋊C4—24no—
92C2×Dic47⋊C4—24no—
93C2×Dic47⋊C4—24no—
94C2×Dic47⋊C4D418yescomplemented
95C2×Dic47⋊C4C2314yes—
96C2×Dic47⋊C4C2314yes—
97C2×Dic47⋊C4C2314yes—
98C2×Dic47⋊C4C2314yes—
99C2×Dic47⋊C4C2314yes—
100C2×Dic47⋊C4C2314yes—
101C2×Dic47⋊C4C2314yes—
102C2×Dic47⋊C4C2314yes—
103C2×C22⋊Dic47—24no—
104C2×C22⋊Dic47—24no—
105C2×C22⋊Dic47—42no—
106C2×C22⋊Dic47C2314yes—
107C2×C22⋊Dic47C2314yes—
108C2×C22⋊Dic47C2314yes—
109C2×(C2×D47)⋊C4—24no—
110C2×(C2×D47)⋊C4—24no—
111C2×(C2×D47)⋊C4—24no—
112C2×(C2×D47)⋊C4—24no—
113C2×(C2×D47)⋊C4—42no—
114C2×(C2×D47)⋊C4—42no—
115C2×(C2×D47)⋊C4C2314yes—
116C2×(C2×D47)⋊C4C2314yes—
117C2×(C2×D47)⋊C4C2314yes—
118C2×(C2×D47)⋊C4C2314yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×C4×Dic47—24no—
122C2×C4×Dic47—24no—
123C2×C4×Dic47—24no—
124C2×C4×Dic47—24no—
125C2×C4×Dic47C2314yes—
126C2×C4×Dic47C2314yes—
127C2×C4×Dic47C2314yes—
128C2×C4×Dic47C2314yes—
129C47⋊#95C2314yes—
130C47⋊#95C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C25×C47C2311yescharacteristic
134C23×C4×C47C2311yescharacteristic
135C23×C4×C47C2311yescharacteristic
136C23×C4×C47C2311yescharacteristic
137C23×C4×C47C2311yescharacteristic
138C23×C4×C47C2311yescharacteristic
139C23×C4×C47C2311yescharacteristic
140C2×C4⋊C4×C47—42no—
141C2×C4⋊C4×C47C2314yes—
142C2×C22⋊C4×C47—24no—
143C2×C22⋊C4×C47—24no—
144C2×C22⋊C4×C47—42no—
145C2×C22⋊C4×C47C2314yes—
146C2×C22⋊C4×C47C2314yes—
147C2×C22⋊C4×C47C2314yes—
148C2×C42×C47—24no—
149C2×C42×C47C2314yes—
150#95×C47C2314yes—
151#95×C47C2314yes—
152C24×C47—22no—
153C24×C47—22no—
154C24×C47—22no—
155C24×C47—22no—
156C24×C47—22no—
157C24×C47—22no—
158C24×C47—22no—
159C24×C47C2412yes—
160C24×C47C2411yescharacteristic
161C23×D47—22no—
162C23×D47—22no—
163C23×D47—22no—
164C23×D47—22no—
165C23×D47—22no—
166C23×D47—22no—
167C23×D47—22no—
168C23×D47C2412yes—
169C22×C4×C47—22no—
170C22×C4×C47—22no—
171C22×C4×C47—22no—
172C22×C4×C47—22no—
173C22×C4×C47—22no—
174C22×C4×C47—22no—
175C22×C4×C47—22no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47C2×D414yes—
186C22×C4×C47#4114yes—
187C22×C4×C47C2412yes—
188C22×C4×C47C2412yes—
189C22×C4×C47C2412yes—
190C22×C4×C47C2412yes—
191C22×C4×C47C2412yes—
192C22×C4×C47C2412yes—
193C2×C22⋊D47—28no—
194C2×C22⋊D47—28no—
195C2×C22⋊D47—28no—
196C2×C22⋊D47—416no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47—22no—
213C22×Dic47C2×D414yes—
214C22×Dic47C2×D414yes—
215C22×Dic47#4114yes—
216C22×Dic47#4114yes—
217C22×Dic47#4114yes—
218C22×Dic47C2412yes—
219C22×Dic47C2412yes—
220C22×Dic47C2412yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C4⋊C4×C47—44no—
226C22⋊C4×C47—28no—
227C22⋊C4×C47—28no—
228C22⋊C4×C47—44no—
229C42×C47—28no—
230C22⋊Dic47—28no—
231C22⋊Dic47—28no—
232C22⋊Dic47—44no—
233(C2×D47)⋊C4—28no—
234(C2×D47)⋊C4—28no—
235(C2×D47)⋊C4—28no—
236(C2×D47)⋊C4—28no—
237(C2×D47)⋊C4—44no—
238(C2×D47)⋊C4—44no—
239C4⋊Dic47—28no—
240C4⋊Dic47—44no—
241Dic47⋊C4—28no—
242Dic47⋊C4—28no—
243Dic47⋊C4—28no—
244Dic47⋊C4—28no—
245Dic47⋊C4—28no—
246Dic47⋊C4—28no—
247Dic47⋊C4—28no—
248Dic47⋊C4C2×D4116yescomplemented
249C4×Dic47—28no—
250C4×Dic47—28no—
251C4×Dic47—28no—
252C4×Dic47—28no—
253C23×C47—22no—
254C23×C47—22no—
255C23×C47—22no—
256C23×C47—22no—
257C23×C47—22no—
258C23×C47—22no—
259C23×C47—22no—
260C23×C47—44no—
261C23×C47—44no—
262C23×C47—44no—
263C23×C47—44no—
264C23×C47—44no—
265C23×C47—44no—
266C23×C47—44no—
267C23×C47C22×D412yes—
268C23×C47C2×#4112yes—
269C23×C47C2×#4112yes—
270C23×C47C2×#4112yes—
271C23×C47C2×#4112yes—
272C23×C47H(5,𝔽2)12yes—
273C23×C472−1+412yes—
274C23×C47C2511yescharacteristic
275C22×D47—22no—
276C22×D47—22no—
277C22×D47—22no—
278C22×D47—22no—
279C22×D47—22no—
280C22×D47—22no—
281C22×D47—22no—
282C22×D47—44no—
283C22×D47—44no—
284C22×D47—44no—
285C22×D47—44no—
286C22×D47—44no—
287C22×D47—44no—
288C22×D47—44no—
289C2×C4×C47—28no—
290C2×C4×C47—28no—
291C2×C4×C47—22no—
292C2×C4×C47—22no—
293C2×C4×C47—22no—
294C2×C4×C47—22no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—22no—
298C2×C4×C47—22no—
299C2×C4×C47—22no—
300C2×C4×C47—22no—
301C2×C4×C47—22no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—44no—
308C2×C4×C47—44no—
309C2×C4×C47—44no—
310C2×C4×C47—44no—
311C2×C4×C47C22×D414yes—
312C2×C4×C47C2×#4114yes—
313C22⋊D47—416no—
314C2×Dic47—28no—
315C2×Dic47—28no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—22no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—22no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—44no—
333C2×Dic47—44no—
334C2×Dic47—44no—
335C2×Dic47—44no—
336C2×Dic47#126116yescomplemented
337C2×Dic47C22×D414yes—
338C2×Dic47C22×D414yes—
339C2×Dic47C2×#4114yes—
340C2×Dic47C2×#4114yes—
341C2×Dic47C2×#4114yes—
342C2×#2512—471nomaximal, Sylow
343C22×C47—42no—
344C22×C47—42no—
345C22×C47—42no—
346C22×C47—42no—
347C22×C47—42no—
348C22×C47—42no—
349C22×C47—42no—
350C22×C47—88no—
351C22×C47C2×#12614yes—
352C22×C47#53214yes—
353C22×C47#54214yes—
354C22×C47#54714yes—
355C22×C47#55014yes—
356C22×C47#55314yes—
357C22×C47#55614yes—
358C22×C47C23×D411yescharacteristic
359C22×C47C22×#4111yescharacteristic
360C22×C47C22×#4111yescharacteristic
361C22×C47C22×#4111yescharacteristic
362C22×C47C22×#4111yescharacteristic
363C22×C47C2×H(5,𝔽2)11yescharacteristic
364C22×C47C2×2−1+411yescharacteristic
365C2×D47—42no—
366C2×D47—42no—
367C2×D47—42no—
368C2×D47—42no—
369C2×D47—42no—
370C2×D47—42no—
371C2×D47—42no—
372C2×D47—88no—
373C4×C47—24no—
374C4×C47—24no—
375C4×C47—42no—
376C4×C47—42no—
377C4×C47—42no—
378C4×C47—42no—
379Dic47—24no—
380Dic47—24no—
381Dic47—42no—
382Dic47—42no—
383Dic47—42no—
384Dic47—42no—
385Dic47C2×#12618yescomplemented
386C22×#126—471no—
387C22×#126—471no—
388#2512—4716no—
389C2×#397—471no—
390C2×#397—471no—
391C2×#396—471no—
392C2×#396—471no—
393C2×#390—471no—
394C2×#390—471no—
395C2×#390—471no—
396C2×#389—471no—
397C2×#388—471no—
398C2×#388D4711yescharacteristic, complemented
399C2×#384—471no—
400C2×C4×C4⋊C4—471no—
401C2×C4×C4⋊C4—471no—
402C2×C47—82no—
403C2×C47#251218yescomplemented
404C2×C47C22×#12611yescharacteristic
405C2×C47C2×#53211yescharacteristic
406C2×C47C2×#54211yescharacteristic
407C2×C47C2×#54711yescharacteristic
408C2×C47C2×#55011yescharacteristic
409C2×C47C2×#55311yescharacteristic
410C2×C47C2×#55611yescharacteristic
411D47—82no—
412C23×D4—471no—
413C2×#126—478no—
414C2×#126—478no—
415C2×#126—948no—
416C2×#126—948no—
417C22×C4⋊C4—471no—
418C22×C4⋊C4—471no—
419C22×C4⋊C4—471no—
420C22×C4⋊C4—471no—
421C22×C4⋊C4—471no—
422C22×C4⋊C4—471no—
423C22×C4⋊C4—471no—
424C22×C4⋊C4—471no—
425C22×C4⋊C4—471no—
426C22×C4⋊C4—471no—
427C22×C4⋊C4C2×D4711yescharacteristic
428C22×C22⋊C4—471no—
429C22×C22⋊C4—471no—
430C22×C22⋊C4—471no—
431C22×C22⋊C4—471no—
432C22×C22⋊C4—471no—
433C22×C22⋊C4—471no—
434C22×C22⋊C4—471no—
435C22×C22⋊C4—471no—
436C22×C22⋊C4—471no—
437C22×C22⋊C4C2×D4711yescharacteristic
438C22×C22⋊C4C2×D4711yescharacteristic
439C22×C22⋊C4C2×D4711yescharacteristic
440C22×C42—471no—
441C22×C42—471no—
442C22×C42—471no—
443C22×C42—471no—
444C22×C42C2×D4711yescharacteristic
445#397—478no—
446#397—478no—
447#396—478no—
448#396—478no—
449#390—478no—
450#390—478no—
451#390—478no—
452#389—478no—
453#388—478no—
454#388C2×D4718yescomplemented
455#384—478no—
456C4×C4⋊C4—478no—
457C4×C4⋊C4—478no—
458C2×#95—471no—
459C2×#95—471no—
460C2×#95—471no—
461C2×#95—471no—
462C2×#95C2×D4711yescharacteristic
463C2×#95C2×D4711yescharacteristic
464C47C2×#251211yescharacteristic, complemented, Sylow
465C25—471no—
466C25C22×D4711yescharacteristic
467C22×D4—474no—
468C22×D4—944no—
469C22×D4—944no—
470C22×D4—944no—
471C23×C4—471no—
472C23×C4—471no—
473C23×C4—471no—
474C23×C4—471no—
475C23×C4—471no—
476C23×C4—471no—
477C23×C4—471no—
478C23×C4C22×D4711yescharacteristic
479C23×C4C22×D4711yescharacteristic
480C23×C4C22×D4711yescharacteristic
481C23×C4C22×D4711yescharacteristic
482C23×C4C22×D4711yescharacteristic
483C23×C4C22×D4711yescharacteristic
484#126—9432no—
485#126—9432no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—478no—
488C2×C4⋊C4—474no—
489C2×C4⋊C4—474no—
490C2×C4⋊C4—474no—
491C2×C4⋊C4—474no—
492C2×C4⋊C4—474no—
493C2×C4⋊C4—474no—
494C2×C4⋊C4—474no—
495C2×C4⋊C4—474no—
496C2×C4⋊C4—474no—
497C2×C4⋊C4—474no—
498C2×C4⋊C4—944no—
499C2×C4⋊C4—944no—
500C2×C4⋊C4—944no—
501C2×C4⋊C4—944no—
502C2×C4⋊C4—944no—
503C2×C4⋊C4—944no—
504C2×C4⋊C4—944no—
505C2×C4⋊C4—944no—
506C2×C4⋊C4—1882no—
507C2×C4⋊C4C22×D4714yes—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—474no—
512C2×C22⋊C4—474no—
513C2×C22⋊C4—474no—
514C2×C22⋊C4—474no—
515C2×C22⋊C4—474no—
516C2×C22⋊C4—474no—
517C2×C22⋊C4—474no—
518C2×C22⋊C4—474no—
519C2×C22⋊C4—474no—
520C2×C22⋊C4—944no—
521C2×C22⋊C4—944no—
522C2×C22⋊C4—944no—
523C2×C22⋊C4—944no—
524C2×C22⋊C4—944no—
525C2×C22⋊C4—944no—
526C2×C22⋊C4—1882no—
527C2×C22⋊C4—1882no—
528C2×C22⋊C4—1882no—
529C2×C22⋊C4C22×D4714yes—
530C2×C22⋊C4C22×D4714yes—
531C2×C22⋊C4C22×D4714yes—
532C2×C42—24no—
533C2×C42—474no—
534C2×C42—474no—
535C2×C42—474no—
536C2×C42—474no—
537C2×C42—944no—
538C2×C42—944no—
539C2×C42—944no—
540C2×C42—944no—
541C2×C42C22×D4714yes—
542#95—474no—
543#95—474no—
544#95—474no—
545#95—474no—
546#95C22×D4714yes—
547#95C22×D4714yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—472no—
556C24—942no—
557C24—942no—
558C24—942no—
559C24—942no—
560C24—942no—
561C24—942no—
562C24—942no—
563C24C23×D4712yes—
564C24C23×D4711yescharacteristic
565C2×D4—948no—
566C2×D4—948no—
567C2×D4—948no—
568C2×D4—18816no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—474no—
586C22×C4—474no—
587C22×C4—474no—
588C22×C4—472no—
589C22×C4—474no—
590C22×C4—474no—
591C22×C4—472no—
592C22×C4—472no—
593C22×C4—472no—
594C22×C4—472no—
595C22×C4—472no—
596C22×C4—472no—
597C22×C4—942no—
598C22×C4—942no—
599C22×C4—942no—
600C22×C4—942no—
601C22×C4—942no—
602C22×C4—942no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—942no—
606C22×C4—942no—
607C22×C4—942no—
608C22×C4—942no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4#1062535014yes—
614C22×C4D4×D4714yes—
615C22×C4C23×D4712yes—
616C22×C4C23×D4712yes—
617C22×C4C23×D4712yes—
618C22×C4C23×D4712yes—
619C22×C4C23×D4712yes—
620C22×C4C23×D4712yes—
621C4⋊C4—44no—
622C4⋊C4—4716no—
623C4⋊C4—948no—
624C4⋊C4—948no—
625C4⋊C4—948no—
626C4⋊C4—948no—
627C4⋊C4—948no—
628C4⋊C4—948no—
629C4⋊C4—948no—
630C4⋊C4—948no—
631C4⋊C4—1884no—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—44no—
635C22⋊C4—948no—
636C22⋊C4—948no—
637C22⋊C4—948no—
638C22⋊C4—948no—
639C22⋊C4—948no—
640C22⋊C4—948no—
641C22⋊C4—1884no—
642C22⋊C4—1884no—
643C22⋊C4—1884no—
644C42—28no—
645C42—948no—
646C42—948no—
647C42—948no—
648C42—948no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—942no—
664C23—942no—
665C23—942no—
666C23—942no—
667C23—942no—
668C23—942no—
669C23—942no—
670C23—1884no—
671C23—1884no—
672C23—1884no—
673C23—1884no—
674C23—1884no—
675C23—1884no—
676C23—1884no—
677C23C2×D4×D4712yes—
678C23#41×D4712yes—
679C23#41×D4712yes—
680C23#41×D4712yes—
681C23C2×#1062535012yes—
682C23#1309406912yes—
683C23#1309407112yes—
684C23C24×D4711yescharacteristic
685D4—18816no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—4716no—
709C2×C4—474no—
710C2×C4—474no—
711C2×C4—474no—
712C2×C4—474no—
713C2×C4—474no—
714C2×C4—948no—
715C2×C4—948no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—1884no—
733C2×C4—1884no—
734C2×C4—1884no—
735C2×C4—1884no—
736C2×C4C2×D4×D4714yes—
737C2×C4C2×#1062535014yes—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—88no—
746C22—3768no—
747C22—1882no—
748C22—1882no—
749C22—1882no—
750C22—1882no—
751C22—1882no—
752C22—1882no—
753C22—1882no—
754C22#126×D4714yes—
755C22#1568967014yes—
756C22#1568973714yes—
757C22#1568977114yes—
758C22#1568979114yes—
759C22#1568982214yes—
760C22#1568984114yes—
761C22C22×D4×D4711yescharacteristic
762C22C2×#41×D4711yescharacteristic
763C22C2×#41×D4711yescharacteristic
764C22C2×#41×D4711yescharacteristic
765C22C22×#1062535011yescharacteristic
766C22C2×#1309406911yescharacteristic
767C22C2×#1309407111yescharacteristic
768C4—24no—
769C4—24no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—478no—
775C4—944no—
776C4—944no—
777C4—1882no—
778C4—1882no—
779C4—1882no—
780C4—1882no—
781C2—82no—
782C2—3762no—
783C2#2024797118yesdirect product factor
784C2C2×#126×D4711yescharacteristic
785C2C2×#1568967011yescharacteristic
786C2C2×#1568973711yescharacteristic
787C2C2×#1568977111yescharacteristic
788C2C2×#1568979111yescharacteristic
789C2C2×#1568982211yescharacteristic
790C2C2×#1568984111yescharacteristic
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC2×#388D47
hypocenterC47C2×#2512
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#13094018C2semidirect
2. C22×#13094017C2semidirect
3. #20247971C2direct (N × H)
4. C2×#15689052C2semidirect
5. C2×#15689051C2semidirect
6. C2×#15689046C2semidirect
7. C2×#15689045C2semidirect
11. C2×#15689020C2semidirect
12. C2×#15689015C2semidirect
13. C2×#15688992C2semidirect
14. C2×C4×Dic47⋊C4C2semidirect
15. C2×#15688974C2semidirect
16. C2×C47×#388C2semidirect
19. C2×#13094018C22semidirect
21. C2×#13094017C22semidirect
45. #15689052C22semidirect
46. #15689051C22semidirect
47. #15689046C22semidirect
48. #15689045C22semidirect
52. #15689020C22semidirect
53. #15689015C22semidirect
54. #15688992C22semidirect
55. C4×Dic47⋊C4C22semidirect
56. #15688974C22semidirect
66. C47×#388C22semidirect
94. C2×Dic47⋊C4D4semidirect
248. Dic47⋊C4C2×D4semidirect
336. C2×Dic47#126semidirect
385. Dic47C2×#126semidirect
398. C2×#388D47semidirect
403. C2×C47#2512semidirect
454. #388C2×D47semidirect
464. C47C2×#2512semidirect
783. C2#20247971direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940182
C22×#130940172
#202479712
C2×#156890522
C2×#156890512
C2×#156890462
C2×#156890452
C2×#156890232
C2×#156890202
C2×#156890152
C2×#156889922
C2×C4×Dic47⋊C42
C2×#156889742
C2×C47×#3882
C2×#251247