Finite Group Databasebeta

← C2×#20246379 #26375780

Subgroups — C2×#20246379 #26375780

Order 12032.

3830 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094006C211yesmaximal, characteristic
2C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
3C22×#13093982C211yesmaximal, characteristic, complemented
4#20246379C2116yesmaximal, direct product factor
5C2×#15689020C211yesmaximal, characteristic, complemented
6C2×#15689011C211yesmaximal, characteristic, complemented
7C2×#15689006C211yesmaximal, characteristic, complemented
8C2×#15689004C211yesmaximal, characteristic, complemented
9C2×#15688999C211yesmaximal, characteristic
10C2×#15688998C211yesmaximal, characteristic, complemented
11C2×#15688997C211yesmaximal, characteristic, complemented
12C2×C4×C4⋊Dic47C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic47C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
15C2×#95×D47C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D47C2211yescharacteristic
18C24×Dic47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C2×#13094006C4116yescomplemented
23C2×#13094006C2218yes—
24C2×(C22⋊D47)⋊C4—28no—
25C2×(C22⋊D47)⋊C4C2218yes—
26C2×#13093982—28no—
27C2×#13093982C2218yescomplemented
28C22×C4⋊Dic47C2211yescharacteristic
29C22×C4⋊Dic47C2211yescharacteristic
30C22×C4⋊Dic47C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×Dic47⋊C4C2211yescharacteristic
34C22×C22⋊Dic47C2211yescharacteristic
35C22×C22⋊Dic47C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C22×(C2×D47)⋊C4C2211yescharacteristic
39C22×C4×Dic47C2211yescharacteristic
40C22×C4×Dic47C2211yescharacteristic
41C22×C4×Dic47C2211yescharacteristic
42C22×C4×Dic47C2211yescharacteristic
43#15689020C2218yescomplemented
44#15689011C2218yescomplemented
45#15689006C2218yescomplemented
46#15689004C2218yescomplemented
47#15688999C2218yes—
48#15688998C2218yescomplemented
49#15688997C2218yescomplemented
50C4×C4⋊Dic47C2218yescomplemented
51C22⋊C4×Dic47C2218yescomplemented
52C4×(C2×D47)⋊C4C2218yescomplemented
53C2×C47⋊#95C2211yescharacteristic
54C2×C47⋊#95C2211yescharacteristic
55C2×C47⋊#95C2211yescharacteristic
56C2×C47⋊#95C2211yescharacteristic
57C2×C47⋊#95C2211yescharacteristic
58C2×C47⋊#95C2211yescharacteristic
59C2×C47⋊#95C2211yescharacteristic
60C2×C47⋊#95C2211yescharacteristic
61#95×D47C2218yescomplemented
62C22×C4⋊C4×C47C2211yescharacteristic
63C22×C22⋊C4×C47C2211yescharacteristic
64C22×C22⋊C4×C47C2211yescharacteristic
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C47×#388C2218yescomplemented
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C22×C22⋊D47—24no—
72C22×C22⋊D47—24no—
73C22×C22⋊D47C2×C418yes—
74C22×C22⋊D47C2314yes—
75C23×Dic47—24no—
76C23×Dic47—24no—
77C23×Dic47—42no—
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2314yes—
81C23×Dic47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—24no—
90C22×C4×D47—24no—
91C22×C4×D47—24no—
92C22×C4×D47—42no—
93C22×C4×D47—42no—
94C22×C4×D47C2×C418yescomplemented
95C22×C4×D47C2314yes—
96C22×C4×D47C2314yes—
97C22×C4×D47C2314yes—
98#13094006C2×C4164yescomplemented
99(C22⋊D47)⋊C4—232no—
100#13093982—232no—
101C2×C4⋊Dic47—24no—
102C2×C4⋊Dic47—24no—
103C2×C4⋊Dic47C2×C418yescomplemented
104C2×C4⋊Dic47C2314yes—
105C2×C4⋊Dic47C2314yes—
106C2×C4⋊Dic47C2314yes—
107C2×Dic47⋊C4—24no—
108C2×Dic47⋊C4—42no—
109C2×Dic47⋊C4C2×C418yescomplemented
110C2×Dic47⋊C4C2314yes—
111C2×Dic47⋊C4C2314yes—
112C2×Dic47⋊C4C2314yes—
113C2×C22⋊Dic47—42no—
114C2×C22⋊Dic47C2×C418yescomplemented
115C2×C22⋊Dic47C2314yes—
116C2×C22⋊Dic47C2314yes—
117C2×(C2×D47)⋊C4—24no—
118C2×(C2×D47)⋊C4C2×C418yescomplemented
119C2×(C2×D47)⋊C4D418yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×C4×Dic47—24no—
124C2×C4×Dic47—24no—
125C2×C4×Dic47—24no—
126C2×C4×Dic47—42no—
127C2×C4×Dic47C2314yes—
128C2×C4×Dic47C2314yes—
129C2×C4×Dic47C2314yes—
130C2×C4×Dic47C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C25×C47C2311yescharacteristic
140C23×C4×C47C2311yescharacteristic
141C23×C4×C47C2311yescharacteristic
142C23×C4×C47C2311yescharacteristic
143C23×C4×C47C2311yescharacteristic
144C23×C4×C47C2311yescharacteristic
145C23×C4×C47C2311yescharacteristic
146C2×C4⋊C4×C47—24no—
147C2×C4⋊C4×C47C2314yes—
148C2×C22⋊C4×C47—24no—
149C2×C22⋊C4×C47—24no—
150C2×C22⋊C4×C47C2×C418yescomplemented
151C2×C22⋊C4×C47C2314yes—
152C2×C22⋊C4×C47C2314yes—
153C2×C22⋊C4×C47C2314yes—
154C2×C42×C47—24no—
155C2×C42×C47C2314yes—
156#95×C47C2314yes—
157#95×C47C2314yes—
158C24×C47—22no—
159C24×C47—22no—
160C24×C47—22no—
161C24×C47—22no—
162C24×C47—22no—
163C24×C47—22no—
164C24×C47C22×C414yes—
165C24×C47C2412yes—
166C24×C47C2411yescharacteristic
167C23×D47—22no—
168C23×D47—22no—
169C23×D47—22no—
170C23×D47—22no—
171C23×D47C22×C414yes—
172C23×D47C2×D414yes—
173C23×D47#4114yes—
174C23×D47C2412yes—
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×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47—22no—
188C22×C4×C47—22no—
189C22×C4×C47C22×C414yes—
190C22×C4×C47C22×C414yes—
191C22×C4×C47C2×D414yes—
192C22×C4×C47#4114yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2412yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C2×C22⋊D47—232no—
200C2×C22⋊D47—28no—
201C2×C22⋊D47—28no—
202C2×C22⋊D47C22×C4116yes—
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×Dic47—22no—
214C22×Dic47—22no—
215C22×Dic47—22no—
216C22×Dic47—22no—
217C22×Dic47—22no—
218C22×Dic47—22no—
219C22×Dic47—28no—
220C22×Dic47—28no—
221C22×Dic47—44no—
222C22×Dic47—416no—
223C22×Dic47C22×C414yes—
224C22×Dic47C22×C414yes—
225C22×Dic47C22×C414yes—
226C22×Dic47C2×D414yes—
227C22×Dic47#4114yes—
228C22×Dic47C2412yes—
229C22×Dic47C2412yes—
230C22×Dic47C2412yes—
231C22×Dic47C2412yes—
232C22×Dic47C2412yes—
233C22×Dic47C2412yes—
234C22×Dic47C2412yes—
235C2×C4×D47—232no—
236C2×C4×D47—28no—
237C2×C4×D47—28no—
238C2×C4×D47—28no—
239C2×C4×D47—28no—
240C2×C4×D47—28no—
241C2×C4×D47—28no—
242C2×C4×D47—44no—
243C2×C4×D47—44no—
244C2×C4×D47—416no—
245C2×C4×D47—416no—
246C2×C4×D47C22×C4116yescomplemented
247C4⋊C4×C47—28no—
248C22⋊C4×C47—28no—
249C22⋊C4×C47—28no—
250C22⋊C4×C47C22×C4116yescomplemented
251C42×C47—28no—
252C22⋊Dic47—44no—
253C22⋊Dic47C22×C4116yescomplemented
254(C2×D47)⋊C4—28no—
255(C2×D47)⋊C4C22×C4116yescomplemented
256(C2×D47)⋊C4C2×D4116yes—
257C4⋊Dic47—28no—
258C4⋊Dic47—28no—
259C4⋊Dic47C22×C4116yescomplemented
260Dic47⋊C4—28no—
261Dic47⋊C4—44no—
262Dic47⋊C4C22×C4116yescomplemented
263C4×Dic47—28no—
264C4×Dic47—28no—
265C4×Dic47—28no—
266C4×Dic47—44no—
267C23×C47—28no—
268C23×C47—28no—
269C23×C47—28no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47—22no—
273C23×C47—22no—
274C23×C47—22no—
275C23×C47—22no—
276C23×C47—44no—
277C23×C47—44no—
278C23×C47—44no—
279C23×C47—44no—
280C23×C47C23×C414yes—
281C23×C47C23×C412yes—
282C23×C47C22×D412yes—
283C23×C47C2×#4112yes—
284C23×C47C2×#4112yes—
285C23×C47C2×#4112yes—
286C23×C47H(5,𝔽2)12yes—
287C23×C472−1+412yes—
288C23×C47C2511yescharacteristic
289C22×D47—28no—
290C22×D47—28no—
291C22×D47—28no—
292C22×D47—28no—
293C22×D47—28no—
294C22×D47—28no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—22no—
298C22×D47—22no—
299C22×D47C4×D4116yes—
300C22×D47C23×C414yes—
301C22×D47C22×D414yes—
302C22×D47C2×#4114yes—
303C2×C4×C47—28no—
304C2×C4×C47—28no—
305C2×C4×C47—28no—
306C2×C4×C47—28no—
307C2×C4×C47—22no—
308C2×C4×C47—22no—
309C2×C4×C47—22no—
310C2×C4×C47—22no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—22no—
318C2×C4×C47—22no—
319C2×C4×C47—22no—
320C2×C4×C47—22no—
321C2×C4×C47—44no—
322C2×C4×C47—44no—
323C2×C4×C47C23×C414yes—
324C2×C4×C47C23×C414yes—
325C2×C4×C47C22×D414yes—
326C2×C4×C47C2×#4114yes—
327C22⋊D47—232no—
328C2×Dic47—28no—
329C2×Dic47—28no—
330C2×Dic47—28no—
331C2×Dic47—28no—
332C2×Dic47—28no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—22no—
336C2×Dic47—22no—
337C2×Dic47—22no—
338C2×Dic47—22no—
339C2×Dic47—22no—
340C2×Dic47—22no—
341C2×Dic47—22no—
342C2×Dic47—22no—
343C2×Dic47—22no—
344C2×Dic47—22no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—416no—
350C2×Dic47—44no—
351C2×Dic47—44no—
352C2×Dic47C23×C414yes—
353C2×Dic47C23×C414yes—
354C2×Dic47C23×C414yes—
355C2×Dic47C22×D414yes—
356C2×Dic47C2×#4114yes—
357C4×D47—232no—
358C4×D47—416no—
359C4×D47—416no—
360C2×#2359—471nomaximal, Sylow
361C22×C47—24no—
362C22×C47—24no—
363C22×C47—24no—
364C22×C47—416no—
365C22×C47—42no—
366C22×C47—42no—
367C22×C47—42no—
368C22×C47—42no—
369C22×C47C2×C4×D414yes—
370C22×C47C4×#4114yes—
371C22×C47#52014yes—
372C22×C47#54614yes—
373C22×C47#54714yes—
374C22×C47#55114yes—
375C22×C47#55214yes—
376C22×C47C24×C411yescharacteristic
377C22×C47C23×D411yescharacteristic
378C22×C47C22×#4111yescharacteristic
379C22×C47C22×#4111yescharacteristic
380C22×C47C22×#4111yescharacteristic
381C22×C47C2×H(5,𝔽2)11yescharacteristic
382C22×C47C2×2−1+411yescharacteristic
383C2×D47—232no—
384C2×D47—24no—
385C2×D47—24no—
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—24no—
389C2×D47—24no—
390C2×D47C2×C4×D418yes—
391C4×C47—24no—
392C4×C47—24no—
393C4×C47—24no—
394C4×C47—24no—
395C4×C47—42no—
396C4×C47—42no—
397Dic47—24no—
398Dic47—24no—
399Dic47—24no—
400Dic47—24no—
401Dic47—24no—
402Dic47—42no—
403Dic47—42no—
404C22×#123—471no—
405C22×C4×D4—471no—
406C22×#117—471no—
407#2359—4716no—
408C2×#389—471no—
409C2×#388—471no—
410C2×#388D4711yescharacteristic, complemented
411C2×#387—471no—
412C2×#387—471no—
413C2×#386—471no—
414C2×#385—471no—
415C2×#385—471no—
416C2×C4×C4⋊C4—471no—
417C2×C4×C22⋊C4—471no—
418C2×C4×C22⋊C4—471no—
419C22×#95—471no—
420C2×C47—44no—
421C2×C47#235918yescomplemented
422C2×C47C22×C4×D411yescharacteristic
423C2×C47C2×C4×#4111yescharacteristic
424C2×C47C2×#52011yescharacteristic
425C2×C47C2×#54611yescharacteristic
426C2×C47C2×#54711yescharacteristic
427C2×C47C2×#55111yescharacteristic
428C2×C47C2×#55211yescharacteristic
429D47—28no—
430C23×D4—471no—
431C24×C4—471no—
432C24×C4—471no—
433C24×C4—471no—
434C24×C4—471no—
435C2×#123—4716no—
436C2×#123—478no—
437C2×C4×D4—478no—
438C2×C4×D4—948no—
439C2×#117—478no—
440C2×#117—948no—
441C22×C4⋊C4—471no—
442C22×C4⋊C4—471no—
443C22×C4⋊C4—471no—
444C22×C4⋊C4—471no—
445C22×C4⋊C4—471no—
446C22×C4⋊C4—471no—
447C22×C4⋊C4C2×D4711yescharacteristic
448C22×C22⋊C4—471no—
449C22×C22⋊C4—471no—
450C22×C22⋊C4—471no—
451C22×C22⋊C4—471no—
452C22×C22⋊C4—471no—
453C22×C22⋊C4C2×D4711yescharacteristic
454C22×C22⋊C4C2×D4711yescharacteristic
455C22×C22⋊C4C2×D4711yescharacteristic
456C22×C42—471no—
457C22×C42—471no—
458C22×C42—471no—
459C22×C42—471no—
460C22×C42C2×D4711yescharacteristic
461#389—478no—
462#388—478no—
463#388C2×D4718yescomplemented
464#387—478no—
465#387—478no—
466#386—478no—
467#385—478no—
468#385—478no—
469C4×C4⋊C4—478no—
470C4×C22⋊C4—478no—
471C4×C22⋊C4—478no—
472C2×#95—471no—
473C2×#95—471no—
474C2×#95—471no—
475C2×#95—471no—
476C2×#95—471no—
477C2×#95—471no—
478C2×#95—471no—
479C2×#95—471no—
480C2×#95—478no—
481C2×#95C2×D4711yescharacteristic
482C2×#95C2×D4711yescharacteristic
483C47C2×#235911yescharacteristic, complemented, Sylow
484C25—471no—
485C25C22×D4711yescharacteristic
486C22×D4—478no—
487C22×D4—474no—
488C22×D4—944no—
489C22×D4—944no—
490C23×C4—471no—
491C23×C4—471no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—478no—
496C23×C4—474no—
497C23×C4—471no—
498C23×C4—471no—
499C23×C4—474no—
500C23×C4—474no—
501C23×C4—474no—
502C23×C4—944no—
503C23×C4—944no—
504C23×C4—944no—
505C23×C4—944no—
506C23×C4—944no—
507C23×C4—944no—
508C23×C4—944no—
509C23×C4—944no—
510C23×C4—1882no—
511C23×C4—1882no—
512C23×C4—1882no—
513C23×C4C22×D4711yescharacteristic
514C23×C4C22×D4711yescharacteristic
515C23×C4C22×D4711yescharacteristic
516C23×C4C22×D4711yescharacteristic
517C23×C4C22×D4711yescharacteristic
518C23×C4C22×D4711yescharacteristic
519#123—4764no—
520C4×D4—9432no—
521#117—9432no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—478no—
524C2×C4⋊C4—478no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4—474no—
527C2×C4⋊C4—474no—
528C2×C4⋊C4—474no—
529C2×C4⋊C4—474no—
530C2×C4⋊C4—474no—
531C2×C4⋊C4—944no—
532C2×C4⋊C4—944no—
533C2×C4⋊C4—944no—
534C2×C4⋊C4—1882no—
535C2×C4⋊C4C22×D4714yes—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—478no—
539C2×C22⋊C4—474no—
540C2×C22⋊C4—478no—
541C2×C22⋊C4—478no—
542C2×C22⋊C4—474no—
543C2×C22⋊C4—474no—
544C2×C22⋊C4—474no—
545C2×C22⋊C4—474no—
546C2×C22⋊C4—944no—
547C2×C22⋊C4—1882no—
548C2×C22⋊C4C4×D4718yescomplemented
549C2×C22⋊C4C22×D4714yes—
550C2×C22⋊C4C22×D4714yes—
551C2×C22⋊C4C22×D4714yes—
552C2×C42—24no—
553C2×C42—474no—
554C2×C42—474no—
555C2×C42—474no—
556C2×C42—474no—
557C2×C42—944no—
558C2×C42—944no—
559C2×C42—944no—
560C2×C42—1882no—
561C2×C42C22×D4714yes—
562#95—474no—
563#95—474no—
564#95—474no—
565#95—474no—
566#95—474no—
567#95—474no—
568#95—474no—
569#95—474no—
570#95C22×D4714yes—
571#95C22×D4714yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—474no—
579C24—474no—
580C24—474no—
581C24—472no—
582C24—942no—
583C24—942no—
584C24—942no—
585C24—942no—
586C24C2×C4×D4714yes—
587C24C23×D4712yes—
588C24C23×D4711yescharacteristic
589C2×D4—4716no—
590C2×D4—948no—
591C2×D4—9432no—
592C2×D4—948no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—474no—
608C22×C4—474no—
609C22×C4—474no—
610C22×C4—474no—
611C22×C4—474no—
612C22×C4—472no—
613C22×C4—472no—
614C22×C4—472no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—4716no—
618C22×C4—472no—
619C22×C4—472no—
620C22×C4—948no—
621C22×C4—948no—
622C22×C4—9432no—
623C22×C4—948no—
624C22×C4—948no—
625C22×C4—948no—
626C22×C4—948no—
627C22×C4—948no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4—942no—
635C22×C4—942no—
636C22×C4—942no—
637C22×C4—942no—
638C22×C4—942no—
639C22×C4—942no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—942no—
644C22×C4—948no—
645C22×C4—1884no—
646C22×C4—1884no—
647C22×C4—18816no—
648C22×C4—18816no—
649C22×C4—1884no—
650C22×C4—18816no—
651C22×C4C2×C4×D4714yes—
652C22×C4C2×C4×D4714yes—
653C22×C4D4×D4714yes—
654C22×C4#1062535214yes—
655C22×C4C23×D4712yes—
656C22×C4C23×D4712yes—
657C22×C4C23×D4712yes—
658C22×C4C23×D4712yes—
659C22×C4C23×D4712yes—
660C22×C4C23×D4712yes—
661C4⋊C4—28no—
662C4⋊C4—4716no—
663C4⋊C4—4716no—
664C4⋊C4—948no—
665C4⋊C4—948no—
666C4⋊C4—948no—
667C4⋊C4—1884no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—4716no—
671C22⋊C4—4716no—
672C22⋊C4—4716no—
673C22⋊C4—948no—
674C22⋊C4—1884no—
675C22⋊C4C2×C4×D47116yescomplemented
676C42—28no—
677C42—948no—
678C42—948no—
679C42—948no—
680C42—1884no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—4716no—
695C23—474no—
696C23—474no—
697C23—474no—
698C23—948no—
699C23—948no—
700C23—948no—
701C23—948no—
702C23—948no—
703C23—948no—
704C23—942no—
705C23—942no—
706C23—942no—
707C23—942no—
708C23C22×C4×D4714yes—
709C23C22×C4×D4712yes—
710C23C2×D4×D4712yes—
711C23#41×D4712yes—
712C23#41×D4712yes—
713C23C2×#1062535212yes—
714C23#1309407012yes—
715C23#1309407112yes—
716C23C24×D4711yescharacteristic
717D4—9432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—474no—
739C2×C4—474no—
740C2×C4—474no—
741C2×C4—474no—
742C2×C4—474no—
743C2×C4—9432no—
744C2×C4—948no—
745C2×C4—948no—
746C2×C4—948no—
747C2×C4—948no—
748C2×C4—948no—
749C2×C4—942no—
750C2×C4—942no—
751C2×C4—942no—
752C2×C4—942no—
753C2×C4—942no—
754C2×C4—942no—
755C2×C4—942no—
756C2×C4—942no—
757C2×C4—942no—
758C2×C4—942no—
759C2×C4—942no—
760C2×C4—942no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—942no—
765C2×C4—18816no—
766C2×C4—18816no—
767C2×C4—18816no—
768C2×C4—1884no—
769C2×C4—1884no—
770C2×C4C22×C4×D4714yes—
771C2×C4C22×C4×D4714yes—
772C2×C4C2×D4×D4714yes—
773C2×C4C2×#1062535214yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—416no—
780C22—42no—
781C22—42no—
782C22—478no—
783C22—944no—
784C22—944no—
785C22—944no—
786C22—944no—
787C22—9432no—
788C22—944no—
789C22—944no—
790C22C4×D4×D4714yes—
791C22C4×#1062535214yes—
792C22#1568960314yes—
793C22#1568976614yes—
794C22#1568977314yes—
795C22#1568979614yes—
796C22#1568980914yes—
797C22C23×C4×D4711yescharacteristic
798C22C22×D4×D4711yescharacteristic
799C22C2×#41×D4711yescharacteristic
800C22C2×#41×D4711yescharacteristic
801C22C22×#1062535211yescharacteristic
802C22C2×#1309407011yescharacteristic
803C22C2×#1309407111yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—944no—
811C4—944no—
812C4—944no—
813C4—944no—
814C4—944no—
815C4—1882no—
816C4—1882no—
817C2—44no—
818C2—948no—
819C2#2024637918yesdirect product factor
820C2C2×C4×D4×D4711yescharacteristic
821C2C2×C4×#1062535211yescharacteristic
822C2C2×#1568960311yescharacteristic
823C2C2×#1568976611yescharacteristic
824C2C2×#1568977311yescharacteristic
825C2C2×#1568979611yescharacteristic
826C2C2×#1568980911yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC23×C22⋊D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C2×#2359
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C22×#13093982C2semidirect
4. #20246379C2direct (N × H)
5. C2×#15689020C2semidirect
6. C2×#15689011C2semidirect
7. C2×#15689006C2semidirect
8. C2×#15689004C2semidirect
10. C2×#15688998C2semidirect
11. C2×#15688997C2semidirect
12. C2×C4×C4⋊Dic47C2semidirect
13. C2×C22⋊C4×Dic47C2semidirect
14. C2×C4×(C2×D47)⋊C4C2semidirect
15. C2×#95×D47C2semidirect
16. C2×C47×#388C2semidirect
22. C2×#13094006C4semidirect
27. C2×#13093982C22semidirect
43. #15689020C22semidirect
44. #15689011C22semidirect
45. #15689006C22semidirect
46. #15689004C22semidirect
48. #15688998C22semidirect
49. #15688997C22semidirect
50. C4×C4⋊Dic47C22semidirect
51. C22⋊C4×Dic47C22semidirect
52. C4×(C2×D47)⋊C4C22semidirect
61. #95×D47C22semidirect
67. C47×#388C22semidirect
94. C22×C4×D47C2×C4semidirect
98. #13094006C2×C4semidirect
103. C2×C4⋊Dic47C2×C4semidirect
109. C2×Dic47⋊C4C2×C4semidirect
114. C2×C22⋊Dic47C2×C4semidirect
118. C2×(C2×D47)⋊C4C2×C4semidirect
150. C2×C22⋊C4×C47C2×C4semidirect
246. C2×C4×D47C22×C4semidirect
250. C22⋊C4×C47C22×C4semidirect
253. C22⋊Dic47C22×C4semidirect
255. (C2×D47)⋊C4C22×C4semidirect
259. C4⋊Dic47C22×C4semidirect
262. Dic47⋊C4C22×C4semidirect
410. C2×#388D47semidirect
421. C2×C47#2359semidirect
463. #388C2×D47semidirect
483. C47C2×#2359semidirect
548. C2×C22⋊C4C4×D47semidirect
675. C22⋊C4C2×C4×D47semidirect
819. C2#20246379direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940062
C22×(C22⋊D47)⋊C42
C22×#130939822
#202463792
C2×#156890202
C2×#156890112
C2×#156890062
C2×#156890042
C2×#156889992
C2×#156889982
C2×#156889972
C2×C4×C4⋊Dic472
C2×C22⋊C4×Dic472
C2×C4×(C2×D47)⋊C42
C2×#95×D472
C2×C47×#3882
C2×#235947