Finite Group Databasebeta

← C2×#388×D47 #26374601

Subgroups — C2×#388×D47 #26374601

Order 12032.

5966 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D47C211yesmaximal, characteristic
3C22×C22⋊C4×D47C211yesmaximal, characteristic
4C22×C22⋊C4×D47C211yesmaximal, characteristic
5C22×C42×D47C211yesmaximal, characteristic, complemented
6C2×#15689017C211yesmaximal, characteristic, complemented
7C2×#15689016C211yesmaximal, characteristic, complemented
8C2×#15689015C211yesmaximal, characteristic, complemented
9C2×#15689014C211yesmaximal, characteristic, complemented
10C2×#15689013C211yesmaximal, characteristic, complemented
11C2×#15689012C211yesmaximal, characteristic, complemented
12C2×#15689011C211yesmaximal, characteristic, complemented
13#388×D47C2116yesmaximal, direct product factor
14C2×#95×D47C211yesmaximal, characteristic, complemented
15C2×#95×D47C211yesmaximal, characteristic, complemented
16C2×C47×#388C211yesmaximal, characteristic, complemented
17C25×D47C2211yescharacteristic
18C23×C4×D47C2211yescharacteristic
19C23×C4×D47C2211yescharacteristic
20C23×C4×D47C2211yescharacteristic
21C23×C4×D47C2211yescharacteristic
22C23×C4×D47C2211yescharacteristic
23C23×C4×D47C2211yescharacteristic
24C22×C4⋊Dic47C2211yescharacteristic, complemented
25C22×Dic47⋊C4C2211yescharacteristic, complemented
26C22×Dic47⋊C4C2211yescharacteristic, complemented
27C2×C4⋊C4×D47—28no—
28C2×C4⋊C4×D47C2218yescomplemented
29C22×C22⋊Dic47C2211yescharacteristic
30C22×C22⋊Dic47C2211yescharacteristic
31C22×C22⋊Dic47C2211yescharacteristic
32C22×(C2×D47)⋊C4C2211yescharacteristic
33C22×(C2×D47)⋊C4C2211yescharacteristic
34C22×(C2×D47)⋊C4C2211yescharacteristic
35C22×(C2×D47)⋊C4C2211yescharacteristic
36C22×(C2×D47)⋊C4C2211yescharacteristic
37C22×(C2×D47)⋊C4C2211yescharacteristic
38C2×C22⋊C4×D47—28no—
39C2×C22⋊C4×D47—28no—
40C2×C22⋊C4×D47C4116yescomplemented
41C2×C22⋊C4×D47C2218yes—
42C2×C22⋊C4×D47C2218yes—
43C2×C22⋊C4×D47C2218yes—
44C22×C4×Dic47C2211yescharacteristic, complemented
45C22×C4×Dic47C2211yescharacteristic, complemented
46C22×C4×Dic47C2211yescharacteristic, complemented
47C2×C42×D47—28no—
48C2×C42×D47C2218yescomplemented
49#15689017C2218yescomplemented
50#15689016C2218yescomplemented
51#15689015C2218yescomplemented
52#15689014C2218yescomplemented
53#15689013C2218yescomplemented
54#15689012C2218yescomplemented
55#15689011C2218yescomplemented
56C2×C47⋊#95C2211yescharacteristic, complemented
57C2×C47⋊#95C2211yescharacteristic, complemented
58C2×C47⋊#95C2211yescharacteristic, complemented
59C2×C47⋊#95C2211yescharacteristic, complemented
60C2×C47⋊#95C2211yescharacteristic, complemented
61C2×C47⋊#95C2211yescharacteristic, complemented
62#95×D47C2218yescomplemented
63#95×D47C2218yescomplemented
64C22×C4⋊C4×C47C2211yescharacteristic, complemented
65C22×C22⋊C4×C47C2211yescharacteristic
66C22×C22⋊C4×C47C2211yescharacteristic
67C22×C22⋊C4×C47C2211yescharacteristic
68C22×C42×C47C2211yescharacteristic, complemented
69C47×#388C2218yescomplemented
70C2×#95×C47C2211yescharacteristic, complemented
71C2×#95×C47C2211yescharacteristic, complemented
72C24×D47—24no—
73C24×D47—24no—
74C24×D47—24no—
75C24×D47—24no—
76C24×D47—24no—
77C24×D47—24no—
78C24×D47C2×C418yes—
79C24×D47C2314yes—
80C24×D47C2311yescharacteristic
81C24×D47C2311yescharacteristic
82C23×Dic47C2311yescharacteristic
83C23×Dic47C2311yescharacteristic
84C23×Dic47C2311yescharacteristic
85C23×Dic47C2311yescharacteristic
86C23×Dic47C2311yescharacteristic
87C23×Dic47C2311yescharacteristic
88C22×C4×D47—24no—
89C22×C4×D47—24no—
90C22×C4×D47—24no—
91C22×C4×D47—24no—
92C22×C4×D47—24no—
93C22×C4×D47—24no—
94C22×C4×D47—24no—
95C22×C4×D47—24no—
96C22×C4×D47—24no—
97C22×C4×D47—24no—
98C22×C4×D47—24no—
99C22×C4×D47—24no—
100C22×C4×D47—24no—
101C22×C4×D47—24no—
102C22×C4×D47C2×C418yes—
103C22×C4×D47C2×C418yes—
104C22×C4×D47D418yes—
105C22×C4×D47D418yes—
106C22×C4×D47C2314yes—
107C22×C4×D47C2314yes—
108C22×C4×D47C2314yes—
109C22×C4×D47C2314yes—
110C22×C4×D47C2314yes—
111C22×C4×D47C2314yes—
112C2×C4⋊Dic47—24no—
113C2×C4⋊Dic47C2314yescomplemented
114C2×Dic47⋊C4—24no—
115C2×Dic47⋊C4—24no—
116C2×Dic47⋊C4C2314yescomplemented
117C2×Dic47⋊C4C2314yescomplemented
118C4⋊C4×D47—232no—
119C2×C22⋊Dic47—24no—
120C2×C22⋊Dic47—24no—
121C2×C22⋊Dic47C2×C418yescomplemented
122C2×C22⋊Dic47C2314yes—
123C2×C22⋊Dic47C2314yes—
124C2×C22⋊Dic47C2314yes—
125C2×(C2×D47)⋊C4—24no—
126C2×(C2×D47)⋊C4—24no—
127C2×(C2×D47)⋊C4—24no—
128C2×(C2×D47)⋊C4—24no—
129C2×(C2×D47)⋊C4C2×C418yescomplemented
130C2×(C2×D47)⋊C4C2×C418yescomplemented
131C2×(C2×D47)⋊C4C2314yes—
132C2×(C2×D47)⋊C4C2314yes—
133C2×(C2×D47)⋊C4C2314yes—
134C2×(C2×D47)⋊C4C2314yes—
135C2×(C2×D47)⋊C4C2314yes—
136C2×(C2×D47)⋊C4C2314yes—
137C22⋊C4×D47—232no—
138C22⋊C4×D47—232no—
139C22⋊C4×D47C2×C4164yescomplemented
140C2×C4×Dic47—24no—
141C2×C4×Dic47—24no—
142C2×C4×Dic47—24no—
143C2×C4×Dic47C2314yescomplemented
144C2×C4×Dic47C2314yescomplemented
145C2×C4×Dic47C2314yescomplemented
146C42×D47—232no—
147C47⋊#95C2314yescomplemented
148C47⋊#95C2314yescomplemented
149C47⋊#95C2314yescomplemented
150C47⋊#95C2314yescomplemented
151C47⋊#95C2314yescomplemented
152C47⋊#95C2314yescomplemented
153C25×C47C2311yescharacteristic
154C23×C4×C47C2311yescharacteristic
155C23×C4×C47C2311yescharacteristic
156C23×C4×C47C2311yescharacteristic
157C23×C4×C47C2311yescharacteristic
158C23×C4×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C2×C4⋊C4×C47—24no—
161C2×C4⋊C4×C47C2314yescomplemented
162C2×C22⋊C4×C47—24no—
163C2×C22⋊C4×C47—24no—
164C2×C22⋊C4×C47C2×C418yescomplemented
165C2×C22⋊C4×C47C2314yes—
166C2×C22⋊C4×C47C2314yes—
167C2×C22⋊C4×C47C2314yes—
168C2×C42×C47—24no—
169C2×C42×C47C2314yescomplemented
170#95×C47C2314yescomplemented
171#95×C47C2314yescomplemented
172C24×C47—22no—
173C24×C47—22no—
174C24×C47—22no—
175C24×C47—22no—
176C24×C47—22no—
177C24×C47—22no—
178C24×C47C22×C414yes—
179C24×C47C2412yes—
180C24×C47C2411yescharacteristic
181C23×D47—22no—
182C23×D47—22no—
183C23×D47—22no—
184C23×D47—22no—
185C23×D47—22no—
186C23×D47—22no—
187C23×D47—232no—
188C23×D47—232no—
189C23×D47—232no—
190C23×D47—28no—
191C23×D47—28no—
192C23×D47—28no—
193C23×D47—28no—
194C23×D47—28no—
195C23×D47—28no—
196C23×D47—416no—
197C23×D47—416no—
198C23×D47—416no—
199C23×D47—416no—
200C23×D47C22×C4116yes—
201C23×D47C22×C414yes—
202C23×D47C22×C414yes—
203C23×D47C2×D414yes—
204C23×D47C2×D414yes—
205C23×D47#4114yes—
206C23×D47#4114yes—
207C23×D47#4114yes—
208C23×D47#4114yes—
209C23×D47C2412yes—
210C23×D47C2412yes—
211C22×C4×C47—22no—
212C22×C4×C47—22no—
213C22×C4×C47—22no—
214C22×C4×C47—22no—
215C22×C4×C47—22no—
216C22×C4×C47—22no—
217C22×C4×C47—22no—
218C22×C4×C47—22no—
219C22×C4×C47—22no—
220C22×C4×C47—22no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—22no—
224C22×C4×C47—22no—
225C22×C4×C47C22×C414yes—
226C22×C4×C47C22×C414yes—
227C22×C4×C47C2×D414yes—
228C22×C4×C47C2×D414yes—
229C22×C4×C47C2412yes—
230C22×C4×C47C2412yes—
231C22×C4×C47C2412yes—
232C22×C4×C47C2412yes—
233C22×C4×C47C2412yes—
234C22×C4×C47C2412yes—
235C22×Dic47—22no—
236C22×Dic47—22no—
237C22×Dic47—22no—
238C22×Dic47—22no—
239C22×Dic47—22no—
240C22×Dic47—22no—
241C22×Dic47—22no—
242C22×Dic47—22no—
243C22×Dic47—22no—
244C22×Dic47—22no—
245C22×Dic47—22no—
246C22×Dic47—22no—
247C22×Dic47—22no—
248C22×Dic47—22no—
249C22×Dic47C22×C414yes—
250C22×Dic47C22×C414yes—
251C22×Dic47C2×D414yes—
252C22×Dic47C2×D414yes—
253C22×Dic47C2412yes—
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C22×Dic47C2412yes—
258C22×Dic47C2412yes—
259C2×C4×D47—232no—
260C2×C4×D47—232no—
261C2×C4×D47—232no—
262C2×C4×D47—232no—
263C2×C4×D47—28no—
264C2×C4×D47—28no—
265C2×C4×D47—28no—
266C2×C4×D47—28no—
267C2×C4×D47—28no—
268C2×C4×D47—28no—
269C2×C4×D47—28no—
270C2×C4×D47—28no—
271C2×C4×D47—28no—
272C2×C4×D47—28no—
273C2×C4×D47—28no—
274C2×C4×D47—28no—
275C2×C4×D47—28no—
276C2×C4×D47—28no—
277C2×C4×D47—416no—
278C2×C4×D47—416no—
279C2×C4×D47C22×C4116yes—
280C2×C4×D47C22×C4116yes—
281C2×C4×D47C2×D4116yes—
282C2×C4×D47C2×D4116yes—
283C4⋊C4×C47—28no—
284C22⋊C4×C47—28no—
285C22⋊C4×C47—28no—
286C22⋊C4×C47C22×C4116yescomplemented
287C42×C47—28no—
288C22⋊Dic47—28no—
289C22⋊Dic47—28no—
290C22⋊Dic47C22×C4116yescomplemented
291(C2×D47)⋊C4—28no—
292(C2×D47)⋊C4—28no—
293(C2×D47)⋊C4—28no—
294(C2×D47)⋊C4—28no—
295(C2×D47)⋊C4C22×C4116yescomplemented
296(C2×D47)⋊C4C22×C4116yescomplemented
297C4⋊Dic47—28no—
298Dic47⋊C4—28no—
299Dic47⋊C4—28no—
300C4×Dic47—28no—
301C4×Dic47—28no—
302C4×Dic47—28no—
303C23×C47—28no—
304C23×C47—28no—
305C23×C47—28no—
306C23×C47—22no—
307C23×C47—22no—
308C23×C47—22no—
309C23×C47—22no—
310C23×C47—22no—
311C23×C47—22no—
312C23×C47—44no—
313C23×C47—44no—
314C23×C47—44no—
315C23×C47—44no—
316C23×C47C23×C414yes—
317C23×C47C23×C412yes—
318C23×C47C22×D412yes—
319C23×C47C22×D412yes—
320C23×C47C2×#4112yes—
321C23×C47C2×#4112yes—
322C23×C47C2×#4112yes—
323C23×C47C2×#4112yes—
324C23×C47C2511yescharacteristic
325C22×D47—28no—
326C22×D47—28no—
327C22×D47—28no—
328C22×D47—22no—
329C22×D47—22no—
330C22×D47—22no—
331C22×D47—22no—
332C22×D47—22no—
333C22×D47—22no—
334C22×D47—232no—
335C22×D47—232no—
336C22×D47—232no—
337C22×D47—44no—
338C22×D47—44no—
339C22×D47—44no—
340C22×D47—44no—
341C22×D47—416no—
342C22×D47—416no—
343C22×D47—416no—
344C22×D47—416no—
345C22×D47—4128no—
346C22×D47#117116yes—
347C22×D47C4×D4116yes—
348C22×D47C4×D4116yes—
349C22×D47#121116yes—
350C22×D47#123116yes—
351C22×D47#124116yes—
352C22×D47#126116yes—
353C22×D47C23×C414yes—
354C22×D47C23×C414yes—
355C22×D47C22×D414yes—
356C22×D47C22×D414yes—
357C22×D47C2×#4114yes—
358C22×D47C2×#4114yes—
359C22×D47C2×#4114yes—
360C22×D47C2×#4114yes—
361C2×C4×C47—28no—
362C2×C4×C47—28no—
363C2×C4×C47—28no—
364C2×C4×C47—28no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—22no—
373C2×C4×C47—22no—
374C2×C4×C47—22no—
375C2×C4×C47—22no—
376C2×C4×C47—22no—
377C2×C4×C47—22no—
378C2×C4×C47—22no—
379C2×C4×C47—44no—
380C2×C4×C47—44no—
381C2×C4×C47C23×C414yes—
382C2×C4×C47C23×C414yes—
383C2×C4×C47C22×D414yes—
384C2×C4×C47C22×D414yes—
385C2×Dic47—28no—
386C2×Dic47—28no—
387C2×Dic47—28no—
388C2×Dic47—28no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—22no—
393C2×Dic47—22no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—22no—
397C2×Dic47—22no—
398C2×Dic47—22no—
399C2×Dic47—22no—
400C2×Dic47—22no—
401C2×Dic47—22no—
402C2×Dic47—22no—
403C2×Dic47—44no—
404C2×Dic47—44no—
405C2×Dic47C23×C414yes—
406C2×Dic47C23×C414yes—
407C2×Dic47C22×D414yes—
408C2×Dic47C22×D414yes—
409C4×D47—232no—
410C4×D47—232no—
411C4×D47—232no—
412C4×D47—232no—
413C4×D47—416no—
414C4×D47—416no—
415C22×#388—471nomaximal, Sylow
416C22×C47—24no—
417C22×C47—24no—
418C22×C47—24no—
419C22×C47—42no—
420C22×C47—42no—
421C22×C47—42no—
422C22×C47—42no—
423C22×C47—416no—
424C22×C47C2×#11714yes—
425C22×C47C2×C4×D414yes—
426C22×C47C2×C4×D414yes—
427C22×C47C2×#12114yes—
428C22×C47C2×#12314yes—
429C22×C47C2×#12414yes—
430C22×C47C2×#12614yes—
431C22×C47C24×C411yescharacteristic
432C22×C47C23×D411yescharacteristic
433C22×C47C23×D411yescharacteristic
434C22×C47C22×#4111yescharacteristic
435C22×C47C22×#4111yescharacteristic
436C22×C47C22×#4111yescharacteristic
437C22×C47C22×#4111yescharacteristic
438C2×D47—24no—
439C2×D47—24no—
440C2×D47—24no—
441C2×D47—42no—
442C2×D47—42no—
443C2×D47—42no—
444C2×D47—42no—
445C2×D47—416no—
446C2×D47—464no—
447C2×D47#388164yesdirect product factor
448C2×D47C2×#11718yes—
449C2×D47C2×C4×D418yes—
450C2×D47C2×C4×D418yes—
451C2×D47C2×#12118yes—
452C2×D47C2×#12318yes—
453C2×D47C2×#12418yes—
454C2×D47C2×#12618yes—
455C4×C47—24no—
456C4×C47—24no—
457C4×C47—24no—
458C4×C47—24no—
459C4×C47—42no—
460C4×C47—42no—
461Dic47—24no—
462Dic47—24no—
463Dic47—24no—
464Dic47—24no—
465Dic47—42no—
466Dic47—42no—
467C23×C4⋊C4—471no—
468C23×C22⋊C4—471no—
469C23×C22⋊C4—471no—
470C23×C22⋊C4—471no—
471C23×C42—471no—
472C2×#388—471no—
473C2×#388—4716no—
474C2×#388—471no—
475C2×#388—471no—
476C2×#388—471no—
477C2×#388—471no—
478C2×#388—471no—
479C2×#388—471no—
480C2×#388D4711yescharacteristic, direct product factor
481C22×#95—471no—
482C22×#95—471no—
483C2×C47—44no—
484C2×C47C2×#38818yescomplemented
485C2×C47C22×#11711yescharacteristic
486C2×C47C22×C4×D411yescharacteristic
487C2×C47C22×C4×D411yescharacteristic
488C2×C47C22×#12111yescharacteristic
489C2×C47C22×#12311yescharacteristic
490C2×C47C22×#12411yescharacteristic
491C2×C47C22×#12611yescharacteristic
492D47—44no—
493D47C2×#388116yesdirect product factor
494C26—471no—
495C24×C4—471no—
496C24×C4—471no—
497C24×C4—471no—
498C24×C4—471no—
499C24×C4—471no—
500C24×C4—471no—
501C22×C4⋊C4—471no—
502C22×C4⋊C4—471no—
503C22×C4⋊C4—471no—
504C22×C4⋊C4—478no—
505C22×C4⋊C4—948no—
506C22×C4⋊C4C2×D4711yescharacteristic, complemented
507C22×C22⋊C4—471no—
508C22×C22⋊C4—471no—
509C22×C22⋊C4—471no—
510C22×C22⋊C4—4716no—
511C22×C22⋊C4—478no—
512C22×C22⋊C4—471no—
513C22×C22⋊C4—471no—
514C22×C22⋊C4—471no—
515C22×C22⋊C4—471no—
516C22×C22⋊C4—471no—
517C22×C22⋊C4—471no—
518C22×C22⋊C4—478no—
519C22×C22⋊C4—478no—
520C22×C22⋊C4—948no—
521C22×C22⋊C4—948no—
522C22×C22⋊C4C2×D4711yescharacteristic
523C22×C22⋊C4C2×D4711yescharacteristic
524C22×C22⋊C4C2×D4711yescharacteristic
525C22×C42—471no—
526C22×C42—471no—
527C22×C42—471no—
528C22×C42—478no—
529C22×C42—948no—
530C22×C42C2×D4711yescharacteristic, complemented
531#388—478no—
532#388—478no—
533#388—478no—
534#388—478no—
535#388—478no—
536#388—478no—
537#388—478no—
538#388C2×D4718yesdirect product factor
539C2×#95—471no—
540C2×#95—471no—
541C2×#95—471no—
542C2×#95—471no—
543C2×#95—471no—
544C2×#95—471no—
545C2×#95—478no—
546C2×#95—478no—
547C2×#95C2×D4711yescharacteristic, complemented
548C2×#95C2×D4711yescharacteristic, complemented
549C47C22×#38811yescharacteristic, complemented, Sylow
550C25—471no—
551C25—478no—
552C25—474no—
553C25—471no—
554C25—944no—
555C25—944no—
556C25—944no—
557C25—944no—
558C25—944no—
559C25—944no—
560C25C22×D4711yescharacteristic
561C23×C4—471no—
562C23×C4—471no—
563C23×C4—471no—
564C23×C4—471no—
565C23×C4—478no—
566C23×C4—478no—
567C23×C4—478no—
568C23×C4—478no—
569C23×C4—474no—
570C23×C4—474no—
571C23×C4—474no—
572C23×C4—474no—
573C23×C4—471no—
574C23×C4—471no—
575C23×C4—474no—
576C23×C4—474no—
577C23×C4—944no—
578C23×C4—944no—
579C23×C4—944no—
580C23×C4—944no—
581C23×C4—944no—
582C23×C4—944no—
583C23×C4—944no—
584C23×C4—944no—
585C23×C4—944no—
586C23×C4—944no—
587C23×C4—944no—
588C23×C4—944no—
589C23×C4—944no—
590C23×C4—944no—
591C23×C4C22×D4711yescharacteristic
592C23×C4C22×D4711yescharacteristic
593C23×C4C22×D4711yescharacteristic
594C23×C4C22×D4711yescharacteristic
595C23×C4C22×D4711yescharacteristic
596C23×C4C22×D4711yescharacteristic
597C2×C4⋊C4—24no—
598C2×C4⋊C4—474no—
599C2×C4⋊C4—474no—
600C2×C4⋊C4—474no—
601C2×C4⋊C4—9432no—
602C2×C4⋊C4—944no—
603C2×C4⋊C4—944no—
604C2×C4⋊C4—944no—
605C2×C4⋊C4C22×D4714yescomplemented
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—478no—
609C2×C22⋊C4—474no—
610C2×C22⋊C4—478no—
611C2×C22⋊C4—478no—
612C2×C22⋊C4—474no—
613C2×C22⋊C4—474no—
614C2×C22⋊C4—4764no—
615C2×C22⋊C4—474no—
616C2×C22⋊C4—474no—
617C2×C22⋊C4—474no—
618C2×C22⋊C4—474no—
619C2×C22⋊C4—474no—
620C2×C22⋊C4—474no—
621C2×C22⋊C4—9432no—
622C2×C22⋊C4—9432no—
623C2×C22⋊C4—944no—
624C2×C22⋊C4—944no—
625C2×C22⋊C4—944no—
626C2×C22⋊C4—944no—
627C2×C22⋊C4—944no—
628C2×C22⋊C4—944no—
629C2×C22⋊C4C4×D4718yescomplemented
630C2×C22⋊C4C22×D4714yes—
631C2×C22⋊C4C22×D4714yes—
632C2×C22⋊C4C22×D4714yes—
633C2×C42—24no—
634C2×C42—474no—
635C2×C42—474no—
636C2×C42—474no—
637C2×C42—9432no—
638C2×C42—944no—
639C2×C42—944no—
640C2×C42—944no—
641C2×C42C22×D4714yescomplemented
642#95—474no—
643#95—474no—
644#95—474no—
645#95—474no—
646#95—474no—
647#95—474no—
648#95C22×D4714yescomplemented
649#95C22×D4714yescomplemented
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—474no—
657C24—474no—
658C24—474no—
659C24—474no—
660C24—474no—
661C24—474no—
662C24—474no—
663C24—472no—
664C24—4716no—
665C24—474no—
666C24—472no—
667C24—948no—
668C24—948no—
669C24—9432no—
670C24—9432no—
671C24—9432no—
672C24—948no—
673C24—948no—
674C24—948no—
675C24—948no—
676C24—942no—
677C24—942no—
678C24—942no—
679C24—942no—
680C24—942no—
681C24—942no—
682C24—18816no—
683C24—18816no—
684C24—18816no—
685C24—18816no—
686C24C2×C4×D4714yes—
687C24C23×D4712yes—
688C24C23×D4711yescharacteristic
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—474no—
704C22×C4—474no—
705C22×C4—474no—
706C22×C4—474no—
707C22×C4—472no—
708C22×C4—472no—
709C22×C4—472no—
710C22×C4—472no—
711C22×C4—4716no—
712C22×C4—4716no—
713C22×C4—4716no—
714C22×C4—4716no—
715C22×C4—472no—
716C22×C4—472no—
717C22×C4—948no—
718C22×C4—948no—
719C22×C4—948no—
720C22×C4—9432no—
721C22×C4—9432no—
722C22×C4—9432no—
723C22×C4—9432no—
724C22×C4—948no—
725C22×C4—948no—
726C22×C4—948no—
727C22×C4—948no—
728C22×C4—948no—
729C22×C4—948no—
730C22×C4—948no—
731C22×C4—948no—
732C22×C4—948no—
733C22×C4—948no—
734C22×C4—948no—
735C22×C4—942no—
736C22×C4—942no—
737C22×C4—942no—
738C22×C4—942no—
739C22×C4—942no—
740C22×C4—942no—
741C22×C4—942no—
742C22×C4—942no—
743C22×C4—942no—
744C22×C4—942no—
745C22×C4—942no—
746C22×C4—942no—
747C22×C4—942no—
748C22×C4—942no—
749C22×C4—18816no—
750C22×C4—18816no—
751C22×C4C2×C4×D4714yes—
752C22×C4C2×C4×D4714yes—
753C22×C4D4×D4714yes—
754C22×C4D4×D4714yes—
755C22×C4C23×D4712yes—
756C22×C4C23×D4712yes—
757C22×C4C23×D4712yes—
758C22×C4C23×D4712yes—
759C22×C4C23×D4712yes—
760C22×C4C23×D4712yes—
761C4⋊C4—28no—
762C4⋊C4—948no—
763C4⋊C4—948no—
764C4⋊C4—948no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—4716no—
768C22⋊C4—4716no—
769C22⋊C4—4716no—
770C22⋊C4—948no—
771C22⋊C4—948no—
772C22⋊C4—948no—
773C22⋊C4—948no—
774C22⋊C4—948no—
775C22⋊C4—948no—
776C22⋊C4C2×C4×D47116yescomplemented
777C42—28no—
778C42—948no—
779C42—948no—
780C42—948no—
781C23—28no—
782C23—28no—
783C23—28no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—4716no—
795C23—4716no—
796C23—4716no—
797C23—4716no—
798C23—4716no—
799C23—4716no—
800C23—4716no—
801C23—474no—
802C23—474no—
803C23—474no—
804C23—474no—
805C23—474no—
806C23—474no—
807C23—474no—
808C23—474no—
809C23—9432no—
810C23—9432no—
811C23—9432no—
812C23—948no—
813C23—948no—
814C23—948no—
815C23—942no—
816C23—942no—
817C23—942no—
818C23—942no—
819C23—942no—
820C23—942no—
821C23—188128no—
822C23—18816no—
823C23—18816no—
824C23—18816no—
825C23—18816no—
826C23—1884no—
827C23—1884no—
828C23—1884no—
829C23—1884no—
830C23C22×C4×D4714yes—
831C23C22×C4×D4712yes—
832C23C2×D4×D4712yes—
833C23C2×D4×D4712yes—
834C23#41×D4712yes—
835C23#41×D4712yes—
836C23#41×D4712yes—
837C23#41×D4712yes—
838C23C24×D4711yescharacteristic
839C2×C4—28no—
840C2×C4—28no—
841C2×C4—28no—
842C2×C4—28no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—44no—
858C2×C4—44no—
859C2×C4—474no—
860C2×C4—474no—
861C2×C4—474no—
862C2×C4—474no—
863C2×C4—9432no—
864C2×C4—9432no—
865C2×C4—9432no—
866C2×C4—9432no—
867C2×C4—948no—
868C2×C4—948no—
869C2×C4—948no—
870C2×C4—948no—
871C2×C4—942no—
872C2×C4—942no—
873C2×C4—942no—
874C2×C4—942no—
875C2×C4—942no—
876C2×C4—942no—
877C2×C4—942no—
878C2×C4—942no—
879C2×C4—942no—
880C2×C4—942no—
881C2×C4—942no—
882C2×C4—942no—
883C2×C4—942no—
884C2×C4—942no—
885C2×C4—18816no—
886C2×C4—18816no—
887C2×C4—1884no—
888C2×C4—1884no—
889C2×C4C22×C4×D4714yes—
890C2×C4C22×C4×D4714yes—
891C2×C4C2×D4×D4714yes—
892C2×C4C2×D4×D4714yes—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—416no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—478no—
902C22—478no—
903C22—478no—
904C22—4764no—
905C22—478no—
906C22—478no—
907C22—478no—
908C22—478no—
909C22—944no—
910C22—944no—
911C22—944no—
912C22—18864no—
913C22—18816no—
914C22—1882no—
915C22—1882no—
916C22—1882no—
917C22—1882no—
918C22#117×D4714yes—
919C22C4×D4×D4714yes—
920C22C4×D4×D4714yes—
921C22#121×D4714yes—
922C22#123×D4714yes—
923C22#124×D4714yes—
924C22#126×D4714yes—
925C22C23×C4×D4711yescharacteristic
926C22C22×D4×D4711yescharacteristic
927C22C22×D4×D4711yescharacteristic
928C22C2×#41×D4711yescharacteristic
929C22C2×#41×D4711yescharacteristic
930C22C2×#41×D4711yescharacteristic
931C22C2×#41×D4711yescharacteristic
932C4—24no—
933C4—24no—
934C4—24no—
935C4—24no—
936C4—42no—
937C4—42no—
938C4—944no—
939C4—944no—
940C4—944no—
941C4—944no—
942C4—1882no—
943C4—1882no—
944C2—44no—
945C2—4716no—
946C2—1884no—
947C2#388×D4718yesdirect product factor
948C2C2×#117×D4711yescharacteristic
949C2C2×C4×D4×D4711yescharacteristic
950C2C2×C4×D4×D4711yescharacteristic
951C2C2×#121×D4711yescharacteristic
952C2C2×#123×D4711yescharacteristic
953C2C2×#124×D4711yescharacteristic
954C2C2×#126×D4711yescharacteristic
subgroupG/H
centerC24C23×D47
commutatorC22×C47C24×C4
FrattiniC23C24×D47
FittingC2×C47×#388C2
socleC24×C47C24
prime radicalC25×D47C22
cosocleC23×C47C25
hypercenterC2×#388D47
hypocenterC47C22×#388
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊C4×D47C2semidirect
5. C22×C42×D47C2semidirect
6. C2×#15689017C2semidirect
7. C2×#15689016C2semidirect
8. C2×#15689015C2semidirect
9. C2×#15689014C2semidirect
10. C2×#15689013C2semidirect
11. C2×#15689012C2semidirect
12. C2×#15689011C2semidirect
13. #388×D47C2direct (N × H)
14. C2×#95×D47C2semidirect
15. C2×#95×D47C2semidirect
16. C2×C47×#388C2semidirect
24. C22×C4⋊Dic47C22semidirect
25. C22×Dic47⋊C4C22semidirect
26. C22×Dic47⋊C4C22semidirect
28. C2×C4⋊C4×D47C22semidirect
40. C2×C22⋊C4×D47C4semidirect
44. C22×C4×Dic47C22semidirect
45. C22×C4×Dic47C22semidirect
46. C22×C4×Dic47C22semidirect
48. C2×C42×D47C22semidirect
49. #15689017C22semidirect
50. #15689016C22semidirect
51. #15689015C22semidirect
52. #15689014C22semidirect
53. #15689013C22semidirect
54. #15689012C22semidirect
55. #15689011C22semidirect
56. C2×C47⋊#95C22semidirect
57. C2×C47⋊#95C22semidirect
58. C2×C47⋊#95C22semidirect
59. C2×C47⋊#95C22semidirect
60. C2×C47⋊#95C22semidirect
61. C2×C47⋊#95C22semidirect
62. #95×D47C22semidirect
63. #95×D47C22semidirect
64. C22×C4⋊C4×C47C22semidirect
68. C22×C42×C47C22semidirect
69. C47×#388C22semidirect
70. C2×#95×C47C22semidirect
71. C2×#95×C47C22semidirect
113. C2×C4⋊Dic47C23semidirect
116. C2×Dic47⋊C4C23semidirect
117. C2×Dic47⋊C4C23semidirect
121. C2×C22⋊Dic47C2×C4semidirect
129. C2×(C2×D47)⋊C4C2×C4semidirect
130. C2×(C2×D47)⋊C4C2×C4semidirect
139. C22⋊C4×D47C2×C4semidirect
143. C2×C4×Dic47C23semidirect
144. C2×C4×Dic47C23semidirect
145. C2×C4×Dic47C23semidirect
147. C47⋊#95C23semidirect
148. C47⋊#95C23semidirect
149. C47⋊#95C23semidirect
150. C47⋊#95C23semidirect
151. C47⋊#95C23semidirect
152. C47⋊#95C23semidirect
161. C2×C4⋊C4×C47C23semidirect
164. C2×C22⋊C4×C47C2×C4semidirect
169. C2×C42×C47C23semidirect
170. #95×C47C23semidirect
171. #95×C47C23semidirect
286. C22⋊C4×C47C22×C4semidirect
290. C22⋊Dic47C22×C4semidirect
295. (C2×D47)⋊C4C22×C4semidirect
296. (C2×D47)⋊C4C22×C4semidirect
447. C2×D47#388direct (N × H)
480. C2×#388D47direct (N × H)
484. C2×C47C2×#388semidirect
493. D47C2×#388direct (N × H)
506. C22×C4⋊C4C2×D47semidirect
530. C22×C42C2×D47semidirect
538. #388C2×D47direct (N × H)
547. C2×#95C2×D47semidirect
548. C2×#95C2×D47semidirect
549. C47C22×#388semidirect
605. C2×C4⋊C4C22×D47semidirect
629. C2×C22⋊C4C4×D47semidirect
641. C2×C42C22×D47semidirect
648. #95C22×D47semidirect
649. #95C22×D47semidirect
776. C22⋊C4C2×C4×D47semidirect
947. C2#388×D47direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D472
C22×C22⋊C4×D472
C22×C42×D472
C2×#156890172
C2×#156890162
C2×#156890152
C2×#156890142
C2×#156890132
C2×#156890122
C2×#156890112
#388×D472
C2×#95×D472
C2×C47×#3882
C22×#38847