Finite Group Databasebeta

← C2×#20246385 #26375786

Subgroups — C2×#20246385 #26375786

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×#13094009C211yesmaximal, characteristic
2C22×C4×D188C211yesmaximal, characteristic
3C22×#13093981C211yesmaximal, characteristic, complemented
4#20246385C2116yesmaximal, direct product factor
5C2×#15689020C211yesmaximal, characteristic, complemented
6C2×#15689014C211yesmaximal, characteristic, complemented
7C2×#15689014C211yesmaximal, characteristic, complemented
8C2×#15689009C211yesmaximal, characteristic, complemented
9C2×#15689007C211yesmaximal, characteristic, complemented
10C2×#15689001C211yesmaximal, characteristic
11C2×#15688994C211yesmaximal, characteristic, complemented
12C2×#15688994C211yesmaximal, characteristic, complemented
13C2×C4×(C2×D47)⋊C4C211yesmaximal, characteristic, complemented
14C2×#15688970C211yesmaximal, characteristic, complemented
15C2×#95×D47C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊C4×C47C211yesmaximal, characteristic, complemented
17C23×D188C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C2×#13094009C4116yescomplemented
23C2×#13094009C2218yes—
24C2×C4×D188—28no—
25C2×C4×D188C2218yes—
26C2×#13093981—28no—
27C2×#13093981C2218yescomplemented
28C22×C4⋊Dic47C2211yescharacteristic
29C22×Dic47⋊C4C2211yescharacteristic
30C22×Dic47⋊C4C2211yescharacteristic
31C22×Dic47⋊C4C2211yescharacteristic
32C22×Dic47⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
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
43#15689020C2218yescomplemented
44#15689014C2218yescomplemented
45#15689014C2218yescomplemented
46#15689009C2218yescomplemented
47#15689007C2218yescomplemented
48#15689001C2218yes—
49#15688994C2218yescomplemented
50#15688994C2218yescomplemented
51C4×(C2×D47)⋊C4C2218yescomplemented
52#15688970C2218yescomplemented
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×C4⋊C4×C47C2211yescharacteristic
64C22×C42×C47C2211yescharacteristic
65C22×C42×C47C2211yescharacteristic
66C22×C42×C47C2211yescharacteristic
67C4×C4⋊C4×C47C2218yescomplemented
68C2×#95×C47C2211yescharacteristic
69C2×#95×C47C2211yescharacteristic
70C24×D47C2311yescharacteristic
71C24×D47C2311yescharacteristic
72C22×D188—24no—
73C22×D188—24no—
74C22×D188C2×C418yes—
75C22×D188C2314yes—
76C23×Dic47C2311yescharacteristic
77C23×Dic47C2311yescharacteristic
78C23×Dic47C2311yescharacteristic
79C23×Dic47C2311yescharacteristic
80C23×Dic47C2311yescharacteristic
81C23×Dic47C2311yescharacteristic
82C22×C4×D47—24no—
83C22×C4×D47—24no—
84C22×C4×D47—24no—
85C22×C4×D47—24no—
86C22×C4×D47—24no—
87C22×C4×D47—24no—
88C22×C4×D47—24no—
89C22×C4×D47—24no—
90C22×C4×D47—42no—
91C22×C4×D47—42no—
92C22×C4×D47—42no—
93C22×C4×D47C2×C418yescomplemented
94C22×C4×D47C2314yes—
95C22×C4×D47C2314yes—
96C22×C4×D47C2314yes—
97C22×C4×D47C2314yes—
98#13094009C2×C4164yescomplemented
99C4×D188—232no—
100#13093981—232no—
101C2×C4⋊Dic47—24no—
102C2×C4⋊Dic47C2314yes—
103C2×Dic47⋊C4—24no—
104C2×Dic47⋊C4—24no—
105C2×Dic47⋊C4—42no—
106C2×Dic47⋊C4C2×C418yescomplemented
107C2×Dic47⋊C4C2314yes—
108C2×Dic47⋊C4C2314yes—
109C2×Dic47⋊C4C2314yes—
110C2×Dic47⋊C4C2314yes—
111C2×(C2×D47)⋊C4—24no—
112C2×(C2×D47)⋊C4—24no—
113C2×(C2×D47)⋊C4—24no—
114C2×(C2×D47)⋊C4—42no—
115C2×(C2×D47)⋊C4C2×C418yescomplemented
116C2×(C2×D47)⋊C4C2×C418yescomplemented
117C2×(C2×D47)⋊C4C2×C418yescomplemented
118C2×(C2×D47)⋊C4D418yes—
119C2×(C2×D47)⋊C4C2314yes—
120C2×(C2×D47)⋊C4C2314yes—
121C2×(C2×D47)⋊C4C2314yes—
122C2×(C2×D47)⋊C4C2314yes—
123C2×(C2×D47)⋊C4C2314yes—
124C2×(C2×D47)⋊C4C2314yes—
125C2×(C2×D47)⋊C4C2314yes—
126C2×(C2×D47)⋊C4C2314yes—
127C2×C4×Dic47—24no—
128C2×C4×Dic47—42no—
129C2×C4×Dic47C2314yes—
130C2×C4×Dic47C2314yes—
131C47⋊#95C2314yes—
132C47⋊#95C2314yes—
133C47⋊#95C2314yes—
134C47⋊#95C2314yes—
135C47⋊#95C2314yes—
136C47⋊#95C2314yes—
137C47⋊#95C2314yes—
138C47⋊#95C2314yes—
139C23×C4×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×C47C2×C418yescomplemented
148C2×C4⋊C4×C47C2314yes—
149C2×C4⋊C4×C47C2314yes—
150C2×C42×C47—24no—
151C2×C42×C47—24no—
152C2×C42×C47—24no—
153C2×C42×C47C2314yes—
154C2×C42×C47C2314yes—
155C2×C42×C47C2314yes—
156#95×C47C2314yes—
157#95×C47C2314yes—
158C24×C47C2411yescharacteristic
159C23×D47—22no—
160C23×D47—22no—
161C23×D47—22no—
162C23×D47—22no—
163C23×D47—22no—
164C23×D47—22no—
165C23×D47—22no—
166C23×D47—22no—
167C23×D47—22no—
168C23×D47—22no—
169C23×D47C22×C414yes—
170C23×D47C22×C414yes—
171C23×D47C2×D414yes—
172C23×D47#4114yes—
173C23×D47C2412yes—
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×C47—22no—
190C22×C4×C47C22×C414yes—
191C22×C4×C47C22×C414yes—
192C22×C4×C47C22×C414yes—
193C22×C4×C47C2×D414yes—
194C22×C4×C47#4114yes—
195C22×C4×C47#4114yes—
196C22×C4×C47C2412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2412yes—
199C22×C4×C47C2412yes—
200C22×C4×C47C2412yes—
201C22×C4×C47C2412yes—
202C22×C4×C47C2412yes—
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×Dic47C22×C414yes—
219C22×Dic47C22×C414yes—
220C22×Dic47C2×D414yes—
221C22×Dic47C2412yes—
222C22×Dic47C2412yes—
223C22×Dic47C2412yes—
224C22×Dic47C2412yes—
225C22×Dic47C2412yes—
226C22×Dic47C2412yes—
227C2×D188—232no—
228C2×D188—28no—
229C2×D188—28no—
230C2×D188C22×C4116yes—
231C2×C4×D47—232no—
232C2×C4×D47—28no—
233C2×C4×D47—28no—
234C2×C4×D47—28no—
235C2×C4×D47—28no—
236C2×C4×D47—28no—
237C2×C4×D47—28no—
238C2×C4×D47—28no—
239C2×C4×D47—28no—
240C2×C4×D47—44no—
241C2×C4×D47—44no—
242C2×C4×D47—44no—
243C2×C4×D47—416no—
244C2×C4×D47—416no—
245C2×C4×D47—416no—
246C2×C4×D47C22×C4116yescomplemented
247C4⋊C4×C47—28no—
248C4⋊C4×C47C22×C4116yescomplemented
249C42×C47—28no—
250C42×C47—28no—
251C42×C47—28no—
252(C2×D47)⋊C4—28no—
253(C2×D47)⋊C4—28no—
254(C2×D47)⋊C4—28no—
255(C2×D47)⋊C4—44no—
256(C2×D47)⋊C4C22×C4116yescomplemented
257(C2×D47)⋊C4C22×C4116yescomplemented
258(C2×D47)⋊C4C22×C4116yescomplemented
259(C2×D47)⋊C4C2×D4116yes—
260C4⋊Dic47—28no—
261Dic47⋊C4—28no—
262Dic47⋊C4—28no—
263Dic47⋊C4—44no—
264Dic47⋊C4C22×C4116yescomplemented
265C4×Dic47—28no—
266C4×Dic47—44no—
267C23×C47C23×C412yes—
268C23×C47C22×D412yes—
269C23×C47C2×#4112yes—
270C23×C47C2×#4112yes—
271C23×C47C2×#4112yes—
272C23×C47H(5,𝔽2)12yes—
273C23×C472−1+412yes—
274C23×C47C2511yescharacteristic
275C22×D47—28no—
276C22×D47—28no—
277C22×D47—28no—
278C22×D47—28no—
279C22×D47—28no—
280C22×D47—28no—
281C22×D47—22no—
282C22×D47—22no—
283C22×D47—22no—
284C22×D47—22no—
285C22×D47—28no—
286C22×D47—28no—
287C22×D47—28no—
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—22no—
294C22×D47—44no—
295C22×D47—44no—
296C22×D47—44no—
297C22×D47—44no—
298C22×D47C4×D4116yes—
299C22×D47C23×C414yes—
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—28no—
308C2×C4×C47—28no—
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—22no—
322C2×C4×C47—22no—
323C2×C4×C47—22no—
324C2×C4×C47—44no—
325C2×C4×C47C23×C414yes—
326C2×C4×C47C23×C414yes—
327C2×C4×C47C23×C414yes—
328C2×C4×C47C22×D414yes—
329C2×C4×C47C2×#4114yes—
330C2×C4×C47C2×#4114yes—
331C2×Dic47—28no—
332C2×Dic47—28no—
333C2×Dic47—28no—
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—44no—
350C2×Dic47—44no—
351C2×Dic47—44no—
352C2×Dic47C23×C414yes—
353C2×Dic47C23×C414yes—
354C2×Dic47C22×D414yes—
355D188—232no—
356C4×D47—232no—
357C4×D47—416no—
358C4×D47—416no—
359C4×D47—416no—
360C2×#2359—471nomaximal, Sylow
361C22×C47C2×C4×D414yes—
362C22×C47C4×#4114yes—
363C22×C47#52014yes—
364C22×C47#54614yes—
365C22×C47#54714yes—
366C22×C47#55114yes—
367C22×C47#55214yes—
368C22×C47C24×C411yescharacteristic
369C22×C47C23×D411yescharacteristic
370C22×C47C22×#4111yescharacteristic
371C22×C47C22×#4111yescharacteristic
372C22×C47C22×#4111yescharacteristic
373C22×C47C2×H(5,𝔽2)11yescharacteristic
374C22×C47C2×2−1+411yescharacteristic
375C2×D47—232no—
376C2×D47—24no—
377C2×D47—24no—
378C2×D47—24no—
379C2×D47—24no—
380C2×D47—24no—
381C2×D47—24no—
382C2×D47—24no—
383C2×D47—24no—
384C2×D47—24no—
385C2×D47—416no—
386C2×D47—42no—
387C2×D47—42no—
388C2×D47—42no—
389C2×D47—42no—
390C2×D47C2×C4×D418yes—
391C4×C47—24no—
392C4×C47—24no—
393C4×C47—24no—
394C4×C47—24no—
395C4×C47—24no—
396C4×C47—24no—
397C4×C47—42no—
398Dic47—24no—
399Dic47—24no—
400Dic47—24no—
401Dic47—42no—
402Dic47—42no—
403Dic47—42no—
404C22×#123—471no—
405C22×C4×D4—471no—
406C22×#117—471no—
407#2359—4716no—
408C2×#389—471no—
409C2×#388—471no—
410C2×#388—471no—
411C2×#387—471no—
412C2×#387—471no—
413C2×#386—471no—
414C2×#385—471no—
415C2×#385—471no—
416C2×C4×C4⋊C4D4711yescharacteristic, complemented
417C2×C4×C22⋊C4—471no—
418C2×C4×C22⋊C4—471no—
419C22×#95—471no—
420C2×C47#235918yescomplemented
421C2×C47C22×C4×D411yescharacteristic
422C2×C47C2×C4×#4111yescharacteristic
423C2×C47C2×#52011yescharacteristic
424C2×C47C2×#54611yescharacteristic
425C2×C47C2×#54711yescharacteristic
426C2×C47C2×#55111yescharacteristic
427C2×C47C2×#55211yescharacteristic
428D47—28no—
429D47—44no—
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⋊C4C2×D4711yescharacteristic
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⋊C4—471no—
454C22×C22⋊C4—471no—
455C22×C22⋊C4—471no—
456C22×C42—471no—
457C22×C42—471no—
458C22×C42C2×D4711yescharacteristic
459C22×C42C2×D4711yescharacteristic
460C22×C42C2×D4711yescharacteristic
461#389—478no—
462#388—478no—
463#388—478no—
464#387—478no—
465#387—478no—
466#386—478no—
467#385—478no—
468#385—478no—
469C4×C4⋊C4C2×D4718yescomplemented
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—
485C25—471no—
486C22×D4—478no—
487C22×D4—474no—
488C22×D4—944no—
489C22×D4—944no—
490C23×C4—471no—
491C23×C4—471no—
492C23×C4—471no—
493C23×C4—478no—
494C23×C4—474no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—471no—
498C23×C4—474no—
499C23×C4—474no—
500C23×C4—474no—
501C23×C4—944no—
502C23×C4—944no—
503C23×C4—944no—
504C23×C4—944no—
505C23×C4—944no—
506C23×C4—944no—
507C23×C4—944no—
508C23×C4—944no—
509C23×C4—1882no—
510C23×C4—1882no—
511C23×C4—1882no—
512C23×C4C22×D4711yescharacteristic
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—474no—
525C2×C4⋊C4—474no—
526C2×C4⋊C4—474no—
527C2×C4⋊C4—474no—
528C2×C4⋊C4—474no—
529C2×C4⋊C4—944no—
530C2×C4⋊C4—944no—
531C2×C4⋊C4—944no—
532C2×C4⋊C4—1882no—
533C2×C4⋊C4C4×D4718yescomplemented
534C2×C4⋊C4C22×D4714yes—
535C2×C4⋊C4C22×D4714yes—
536C2×C22⋊C4—478no—
537C2×C22⋊C4—478no—
538C2×C22⋊C4—478no—
539C2×C22⋊C4—478no—
540C2×C22⋊C4—474no—
541C2×C22⋊C4—474no—
542C2×C22⋊C4—474no—
543C2×C22⋊C4—474no—
544C2×C22⋊C4—474no—
545C2×C22⋊C4—474no—
546C2×C22⋊C4—474no—
547C2×C22⋊C4—474no—
548C2×C22⋊C4—944no—
549C2×C22⋊C4—944no—
550C2×C22⋊C4—944no—
551C2×C22⋊C4—1882no—
552C2×C42—24no—
553C2×C42—24no—
554C2×C42—24no—
555C2×C42—474no—
556C2×C42—474no—
557C2×C42—944no—
558C2×C42—1882no—
559C2×C42C22×D4714yes—
560C2×C42C22×D4714yes—
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—474no—
573C24—474no—
574C24—474no—
575C24—472no—
576C24—474no—
577C24—472no—
578C24—942no—
579C24—942no—
580C24—942no—
581C24—942no—
582C24—942no—
583C24—942no—
584C24—942no—
585C24—942no—
586C24—942no—
587C24—942no—
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—22no—
608C22×C4—474no—
609C22×C4—474no—
610C22×C4—474no—
611C22×C4—472no—
612C22×C4—472no—
613C22×C4—472no—
614C22×C4—4716no—
615C22×C4—472no—
616C22×C4—472no—
617C22×C4—472no—
618C22×C4—948no—
619C22×C4—948no—
620C22×C4—9432no—
621C22×C4—948no—
622C22×C4—948no—
623C22×C4—948no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—942no—
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—948no—
640C22×C4—948no—
641C22×C4—948no—
642C22×C4—1884no—
643C22×C4—1884no—
644C22×C4—1884no—
645C22×C4—18816no—
646C22×C4—18816no—
647C22×C4—18816no—
648C22×C4C2×C4×D4714yes—
649C22×C4C2×C4×D4714yes—
650C22×C4C2×C4×D4714yes—
651C22×C4#1062535014yes—
652C22×C4#1062535014yes—
653C22×C4D4×D4714yes—
654C22×C4C23×D4712yes—
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—948no—
664C4⋊C4—948no—
665C4⋊C4—948no—
666C4⋊C4—1884no—
667C4⋊C4C2×C4×D47116yescomplemented
668C22⋊C4—4716no—
669C22⋊C4—4716no—
670C22⋊C4—4716no—
671C22⋊C4—4716no—
672C22⋊C4—948no—
673C22⋊C4—948no—
674C22⋊C4—948no—
675C22⋊C4—1884no—
676C42—28no—
677C42—28no—
678C42—28no—
679C42—948no—
680C42—1884no—
681C23—4716no—
682C23—474no—
683C23—474no—
684C23—474no—
685C23—474no—
686C23—948no—
687C23—948no—
688C23—948no—
689C23—948no—
690C23—948no—
691C23—948no—
692C23—942no—
693C23—942no—
694C23—942no—
695C23—942no—
696C23—948no—
697C23—948no—
698C23—948no—
699C23—942no—
700C23—942no—
701C23—942no—
702C23—942no—
703C23—942no—
704C23—942no—
705C23—1884no—
706C23—1884no—
707C23—1884no—
708C23—1884no—
709C23C22×C4×D4712yes—
710C23C2×D4×D4712yes—
711C23#41×D4712yes—
712C23C2×#1062535012yes—
713C23C2×#1062535012yes—
714C23#1309407012yes—
715C23#1309407212yes—
716C23C24×D4711yescharacteristic
717D4—9432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—28no—
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—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—44no—
740C2×C4—474no—
741C2×C4—474no—
742C2×C4—474no—
743C2×C4—9432no—
744C2×C4—948no—
745C2×C4—948no—
746C2×C4—948no—
747C2×C4—942no—
748C2×C4—942no—
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—18816no—
763C2×C4—18816no—
764C2×C4—18816no—
765C2×C4—1884no—
766C2×C4—1884no—
767C2×C4—1884no—
768C2×C4C22×C4×D4714yes—
769C2×C4C22×C4×D4714yes—
770C2×C4C22×C4×D4714yes—
771C2×C4C2×D4×D4714yes—
772C2×C4C2×#1062535014yes—
773C2×C4C2×#1062535014yes—
774C22—478no—
775C22—944no—
776C22—944no—
777C22—944no—
778C22—944no—
779C22—9432no—
780C22—944no—
781C22—944no—
782C22—944no—
783C22—944no—
784C22—944no—
785C22—1882no—
786C22—1882no—
787C22—18816no—
788C22—1882no—
789C22—1882no—
790C22C4×D4×D4714yes—
791C22C4×#1062535014yes—
792C22#1568960514yes—
793C22#1568976914yes—
794C22#1568977414yes—
795C22#1568979714yes—
796C22#1568981414yes—
797C22C23×C4×D4711yescharacteristic
798C22C22×D4×D4711yescharacteristic
799C22C2×#41×D4711yescharacteristic
800C22C22×#1062535011yescharacteristic
801C22C22×#1062535011yescharacteristic
802C22C2×#1309407011yescharacteristic
803C22C2×#1309407211yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—24no—
809C4—24no—
810C4—42no—
811C4—944no—
812C4—944no—
813C4—944no—
814C4—1882no—
815C4—1882no—
816C4—1882no—
817C2—948no—
818C2—1884no—
819C2#2024638518yesdirect product factor
820C2C2×C4×D4×D4711yescharacteristic
821C2C2×C4×#1062535011yescharacteristic
822C2C2×#1568960511yescharacteristic
823C2C2×#1568976911yescharacteristic
824C2C2×#1568977411yescharacteristic
825C2C2×#1568979711yescharacteristic
826C2C2×#1568981411yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C4×C4⋊C4×C47C2
socleC24×C47C24
prime radicalC23×D188C22
cosocleC23×C47C25
hypercenterC2×C4×C4⋊C4D47
hypocenterC47C2×#2359
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×#13093981C2semidirect
4. #20246385C2direct (N × H)
5. C2×#15689020C2semidirect
6. C2×#15689014C2semidirect
7. C2×#15689014C2semidirect
8. C2×#15689009C2semidirect
9. C2×#15689007C2semidirect
11. C2×#15688994C2semidirect
12. C2×#15688994C2semidirect
13. C2×C4×(C2×D47)⋊C4C2semidirect
14. C2×#15688970C2semidirect
15. C2×#95×D47C2semidirect
16. C2×C4×C4⋊C4×C47C2semidirect
22. C2×#13094009C4semidirect
27. C2×#13093981C22semidirect
43. #15689020C22semidirect
44. #15689014C22semidirect
45. #15689014C22semidirect
46. #15689009C22semidirect
47. #15689007C22semidirect
49. #15688994C22semidirect
50. #15688994C22semidirect
51. C4×(C2×D47)⋊C4C22semidirect
52. #15688970C22semidirect
61. #95×D47C22semidirect
67. C4×C4⋊C4×C47C22semidirect
93. C22×C4×D47C2×C4semidirect
98. #13094009C2×C4semidirect
106. C2×Dic47⋊C4C2×C4semidirect
115. C2×(C2×D47)⋊C4C2×C4semidirect
116. C2×(C2×D47)⋊C4C2×C4semidirect
117. C2×(C2×D47)⋊C4C2×C4semidirect
147. C2×C4⋊C4×C47C2×C4semidirect
246. C2×C4×D47C22×C4semidirect
248. C4⋊C4×C47C22×C4semidirect
256. (C2×D47)⋊C4C22×C4semidirect
257. (C2×D47)⋊C4C22×C4semidirect
258. (C2×D47)⋊C4C22×C4semidirect
264. Dic47⋊C4C22×C4semidirect
416. C2×C4×C4⋊C4D47semidirect
420. C2×C47#2359semidirect
469. C4×C4⋊C4C2×D47semidirect
483. C47C2×#2359semidirect
533. C2×C4⋊C4C4×D47semidirect
667. C4⋊C4C2×C4×D47semidirect
819. C2#20246385direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940092
C22×C4×D1882
C22×#130939812
#202463852
C2×#156890202
C2×#156890142
C2×#156890092
C2×#156890072
C2×#156890012
C2×#156889942
C2×C4×(C2×D47)⋊C42
C2×#156889702
C2×#95×D472
C2×C4×C4⋊C4×C472
C2×#235947