Finite Group Databasebeta

← C4×#99×D47 #26213922

Subgroups — C4×#99×D47 #26213922

Order 12032.

2242 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D47C211yesmaximal, characteristic
2C2×#99×D47C212yesmaximal
3C4×C22⋊C4×D47C212yesmaximal, complemented
4#99×Dic47C212yesmaximal, complemented
5C4×#13093938C212yesmaximal, complemented
6C4×#13093939C211yesmaximal, characteristic, complemented
7#20243175C212yesmaximal, complemented
8#342×D47C212yesmaximal, complemented
9C4×#99×C47C211yesmaximal, characteristic, complemented
10C22×D4×D47C2211yescharacteristic
11C23×C4×D47C411yescharacteristic, complemented
12C23×C4×D47C2211yescharacteristic
13C2×C4×D188C411yescharacteristic, complemented
14C2×D4×Dic47C2211yescharacteristic
15C2×#13093986C411yescharacteristic, complemented
16C2×C4×C22⋊D47C411yescharacteristic, complemented
17C2×C4×C22⋊D47C2211yescharacteristic
18C2×(C22⋊D47)⋊C4C411yescharacteristic, complemented
19C2×(C22⋊D47)⋊C4C2211yescharacteristic
20C4×D4×D47—22no—
21C4×D4×D47—22no—
22C4×D4×D47—22no—
23C4×D4×D47—22no—
24C2×C4⋊C4×D47C411yescharacteristic, complemented
25C2×C22⋊C4×D47C411yescharacteristic, complemented
26C2×C22⋊C4×D47C2211yescharacteristic
27C2×C22⋊C4×D47C2214yes—
28C2×C42×D47—22no—
29C2×C42×D47C411yescharacteristic, complemented
30C2×#13093939C2212yes—
31C2×#13093938C2214yes—
32#99×D47C4116yesdirect product factor
33C22⋊C4×Dic47C2214yescomplemented
34C4×(C2×D47)⋊C4—22no—
35C4×C22⋊Dic47C2212yescomplemented
36#15688970—22no—
37#95×D47—22no—
38#15688890C2212yescomplemented
39#15688889C2214yescomplemented
40C2×C4×D4×C47C2211yescharacteristic
41C2×#99×C47C2212yes—
42C4×C22⋊C4×C47C2212yescomplemented
43C47×#342C2212yescomplemented
44C24×D47C2×C411yescharacteristic
45C24×D47C2311yescharacteristic
46C22×D188C2×C411yescharacteristic
47C22×C22⋊D47C2×C411yescharacteristic
48C22×C22⋊D47C2311yescharacteristic
49C2×D4×D47—22no—
50C2×D4×D47—22no—
51C2×D4×D47—24no—
52C2×D4×D47C2×C418yes—
53C23×Dic47C2×C411yescharacteristic, complemented
54C23×Dic47C2311yescharacteristic
55C22×C4×D47—24no—
56C22×C4×D47—21no—
57C22×C4×D47—21no—
58C22×C4×D47—21no—
59C22×C4×D47—21no—
60C22×C4×D47—44no—
61C22×C4×D47—44no—
62C22×C4×D47C2×C411yescharacteristic
63C22×C4×D47C2×C411yescharacteristic
64C22×C4×D47C2×C411yescharacteristic
65C22×C4×D47C2×C411yescharacteristic
66C22×C4×D47C2×C411yescharacteristic
67C22×C4×D47C2×C411yescharacteristic
68C22×C4×D47C2×C411yescharacteristic
69C22×C4×D47C2×C411yescharacteristic, complemented
70C22×C4×D47C2×C411yescharacteristic, complemented
71C22×C4×D47D412yes—
72C22×C4×D47D412yes—
73C22×C4×D47D412yes—
74C22×C4×D47D412yes—
75C4×D188—22no—
76C4×D188—22no—
77D4×Dic47—22no—
78D4×Dic47—22no—
79#13093986—22no—
80#13093986—22no—
81C4×C22⋊D47—22no—
82C4×C22⋊D47—22no—
83C4×C22⋊D47—22no—
84C4×C22⋊D47—22no—
85(C22⋊D47)⋊C4—22no—
86(C22⋊D47)⋊C4—22no—
87(C22⋊D47)⋊C4—22no—
88(C22⋊D47)⋊C4—22no—
89C2×C4⋊Dic47C2×C411yescharacteristic, complemented
90C2×Dic47⋊C4C2×C411yescharacteristic, complemented
91C2×Dic47⋊C4C2×C411yescharacteristic, complemented
92C4⋊C4×D47—22no—
93C4⋊C4×D47—22no—
94C2×C22⋊Dic47C2×C411yescharacteristic, complemented
95C2×C22⋊Dic47C2311yescharacteristic
96C2×C22⋊Dic47C2314yes—
97C2×(C2×D47)⋊C4—24no—
98C2×(C2×D47)⋊C4C2×C411yescharacteristic
99C2×(C2×D47)⋊C4C2×C411yescharacteristic
100C2×(C2×D47)⋊C4C2×C411yescharacteristic, complemented
101C2×(C2×D47)⋊C4C2×C411yescharacteristic, complemented
102C22⋊C4×D47—22no—
103C22⋊C4×D47—22no—
104C22⋊C4×D47—28no—
105C22⋊C4×D47—22no—
106C22⋊C4×D47—22no—
107C22⋊C4×D47C2×C4116yescomplemented
108C2×C4×Dic47—22no—
109C2×C4×Dic47—24no—
110C2×C4×Dic47C2×C411yescharacteristic, complemented
111C2×C4×Dic47C2×C411yescharacteristic, complemented
112C2×C4×Dic47C2×C411yescharacteristic, complemented
113C42×D47—21no—
114C42×D47—21no—
115C42×D47—21no—
116C42×D47—21no—
117C42×D47—48no—
118#13093939C2×C418yescomplemented
119#13093938C2×C4116yescomplemented
120C47⋊#95—22no—
121C47⋊#95—24no—
122C22×D4×C47C2311yescharacteristic
123C23×C4×C47C2×C411yescharacteristic, complemented
124C23×C4×C47C2311yescharacteristic
125C4×D4×C47—22no—
126C4×D4×C47—22no—
127C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
128C2×C22⋊C4×C47C2×C411yescharacteristic, complemented
129C2×C22⋊C4×C47C2311yescharacteristic
130C2×C22⋊C4×C47C2314yes—
131C2×C42×C47—22no—
132C2×C42×C47C2×C411yescharacteristic, complemented
133#99×C47C2×C418yescomplemented
134#95×C47—22no—
135C24×C47C22×C411yescharacteristic
136C24×C47C2411yescharacteristic
137C23×D47—21no—
138C23×D47—21no—
139C23×D47—22no—
140C23×D47—42no—
141C23×D47—42no—
142C23×D47—42no—
143C23×D47—42no—
144C23×D47C4214yescomplemented
145C23×D47C22×C411yescharacteristic
146C23×D47C22×C411yescharacteristic
147C23×D47C22×C411yescharacteristic
148C23×D47C22×C414yes—
149C23×D47C2×D412yes—
150C23×D47C2×D412yes—
151C23×D47#4114yes—
152C2×D4×C47—22no—
153C2×D4×C47—22no—
154C2×D4×C47C22×C414yes—
155C22×C4×C47—24no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47—42no—
159C22×C4×C47—42no—
160C22×C4×C47C22×C411yescharacteristic
161C22×C4×C47C22×C411yescharacteristic
162C22×C4×C47C22×C411yescharacteristic
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C22×C411yescharacteristic
165C22×C4×C47C2×D412yes—
166C22×C4×C47C2×D412yes—
167C2×C22⋊D47—22no—
168C2×C22⋊D47—22no—
169C2×C22⋊D47—22no—
170C2×C22⋊D47—22no—
171C2×C22⋊D47C4214yescomplemented
172C2×C22⋊D47C22×C414yes—
173C22×Dic47—24no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—42no—
177C22×Dic47—42no—
178C22×Dic47C22×C411yescharacteristic
179C22×Dic47C22×C411yescharacteristic
180C22×Dic47C22×C411yescharacteristic
181C22×Dic47C22×C411yescharacteristic
182C22×Dic47C22×C411yescharacteristic
183C22×Dic47C2×D412yes—
184C22×Dic47C2×D412yes—
185D4×D47—216no—
186D4×D47—216no—
187C2×D188—22no—
188C2×D188—22no—
189C2×D188C4214yescomplemented
190C2×C4×D47—21no—
191C2×C4×D47—21no—
192C2×C4×D47—22no—
193C2×C4×D47—28no—
194C2×C4×D47—24no—
195C2×C4×D47—21no—
196C2×C4×D47—21no—
197C2×C4×D47—21no—
198C2×C4×D47—21no—
199C2×C4×D47—216no—
200C2×C4×D47—21no—
201C2×C4×D47—21no—
202C2×C4×D47—21no—
203C2×C4×D47—21no—
204C2×C4×D47—42no—
205C2×C4×D47—44no—
206C2×C4×D47—42no—
207C2×C4×D47—44no—
208C2×C4×D47—42no—
209C2×C4×D47—44no—
210C2×C4×D47—44no—
211C2×C4×D47—44no—
212C2×C4×D47—44no—
213C2×C4×D47—48no—
214C2×C4×D47—48no—
215C2×C4×D47—44no—
216C2×C4×D47—42no—
217C2×C4×D47—42no—
218C2×C4×D47—42no—
219C2×C4×D47—42no—
220C2×C4×D47C4214yescomplemented
221C2×C4×D47C22⋊C411yescharacteristic
222C2×C4×D47C22⋊C411yescharacteristic
223C2×C4×D47C22⋊C411yescharacteristic
224C2×C4×D47C22⋊C412yes—
225C2×C4×D47C22⋊C412yes—
226C2×C4×D47C22⋊C412yes—
227C2×C4×D47C22⋊C412yes—
228C2×C4×D47C22⋊C412yes—
229C2×C4×D47C22⋊C412yes—
230C2×C4×D47C22⋊C411yescharacteristic
231C4⋊C4×C47—22no—
232C22⋊C4×C47—22no—
233C22⋊C4×C47—24no—
234C22⋊C4×C47—22no—
235C22⋊C4×C47C22×C418yescomplemented
236C42×C47—21no—
237C42×C47—21no—
238C42×C47—44no—
239C22⋊Dic47—22no—
240C22⋊Dic47—24no—
241C22⋊Dic47—22no—
242C22⋊Dic47C22×C418yescomplemented
243(C2×D47)⋊C4—22no—
244(C2×D47)⋊C4—22no—
245(C2×D47)⋊C4—216no—
246(C2×D47)⋊C4—22no—
247(C2×D47)⋊C4—22no—
248C4⋊Dic47—22no—
249Dic47⋊C4—22no—
250Dic47⋊C4—22no—
251C4×Dic47—21no—
252C4×Dic47—21no—
253C4×Dic47—21no—
254C4×Dic47—21no—
255C4×Dic47—21no—
256C4×Dic47—21no—
257C4×Dic47—48no—
258C4×Dic47—44no—
259C23×C47—21no—
260C23×C47—21no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47C2×C4212yescomplemented
266C23×C47C23×C411yescharacteristic
267C23×C47C23×C412yes—
268C23×C47C22×D412yes—
269C23×C47C2×#4112yes—
270C22×D47—24no—
271C22×D47—22no—
272C22×D47—24no—
273C22×D47—22no—
274C22×D47—21no—
275C22×D47—21no—
276C22×D47—24no—
277C22×D47—24no—
278C22×D47—48no—
279C22×D47—48no—
280C22×D47—41no—
281C22×D47—42no—
282C22×D47—41no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47—42no—
286C22×D47—48no—
287C22×D47—48no—
288C22×D47—42no—
289C22×D47—42no—
290C22×D47—41no—
291C22×D47—41no—
292C22×D47C2×C4212yes—
293C22×D47C2×C4212yes—
294C22×D47C2×C4212yescomplemented
295C22×D47C2×C22⋊C412yes—
296C22×D47C2×C22⋊C411yescharacteristic
297C22×D47C2×C22⋊C411yescharacteristic
298C22×D47#11712yes—
299C22×D47#11712yes—
300C22×D47C4×D418yes—
301C22×D47C4×D418yes—
302D4×C47—28no—
303C2×C4×C47—21no—
304C2×C4×C47—21no—
305C2×C4×C47—24no—
306C2×C4×C47—22no—
307C2×C4×C47—21no—
308C2×C4×C47—21no—
309C2×C4×C47—28no—
310C2×C4×C47—41no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—44no—
314C2×C4×C47—44no—
315C2×C4×C47—42no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47C2×C4212yescomplemented
319C2×C4×C47C2×C22⋊C411yescharacteristic
320C2×C4×C47C2×C22⋊C412yes—
321C2×C4×C47C2×C22⋊C411yescharacteristic
322C22⋊D47—28no—
323C22⋊D47—28no—
324C2×Dic47—21no—
325C2×Dic47—21no—
326C2×Dic47—24no—
327C2×Dic47—22no—
328C2×Dic47—21no—
329C2×Dic47—21no—
330C2×Dic47—28no—
331C2×Dic47—41no—
332C2×Dic47—42no—
333C2×Dic47—42no—
334C2×Dic47—44no—
335C2×Dic47—44no—
336C2×Dic47—42no—
337C2×Dic47—41no—
338C2×Dic47—41no—
339C2×Dic47C2×C4212yescomplemented
340C2×Dic47C2×C22⋊C411yescharacteristic
341C2×Dic47C2×C22⋊C412yes—
342C2×Dic47C2×C22⋊C411yescharacteristic
343D188—28no—
344C4×D47—24no—
345C4×D47—24no—
346C4×D47—22no—
347C4×D47—24no—
348C4×D47—22no—
349C4×D47—24no—
350C4×D47—22no—
351C4×D47—24no—
352C4×D47—42no—
353C4×D47—42no—
354C4×D47—42no—
355C4×D47—42no—
356C4×D47—42no—
357C4×D47—432no—
358C4×D47—42no—
359C4×D47—42no—
360C4×D47—42no—
361C4×D47—42no—
362C4×D47—42no—
363C4×D47—42no—
364C4×D47#9914yesdirect product factor
365C2×C4×#99—471nomaximal, Sylow
366C22×C47—22no—
367C22×C47—21no—
368C22×C47—22no—
369C22×C47—21no—
370C22×C47—22no—
371C22×C47—42no—
372C22×C47—42no—
373C22×C47—42no—
374C22×C47—42no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47C22×C4211yescharacteristic
378C22×C47C22×C22⋊C411yescharacteristic
379C22×C47C2×#11711yescharacteristic
380C22×C47C2×C4×D414yes—
381C2×D47—21no—
382C2×D47—22no—
383C2×D47—21no—
384C2×D47—22no—
385C2×D47—216no—
386C2×D47—24no—
387C2×D47—24no—
388C2×D47—22no—
389C2×D47—42no—
390C2×D47—42no—
391C2×D47—48no—
392C2×D47—48no—
393C2×D47—42no—
394C2×D47—41no—
395C2×D47—41no—
396C2×D47—48no—
397C2×D47—42no—
398C2×D47C4×C22⋊C412yes—
399C2×D47C4×C22⋊C414yes—
400C2×D47C4×C22⋊C412yes—
401C2×D47C2×#9912yes—
402C2×D47#41012yes—
403C4×C47—21no—
404C4×C47—22no—
405C4×C47—22no—
406C4×C47—48no—
407C4×C47—41no—
408C4×C47—41no—
409C4×C47C2×#9912yescomplemented
410Dic47—21no—
411Dic47—22no—
412Dic47—22no—
413Dic47—48no—
414Dic47—41no—
415Dic47—41no—
416Dic47C2×#9912yescomplemented
417C22×C4×D4—471no—
418C22×#99—472no—
419C2×C4×C22⋊C4—472no—
420C4×#99—472no—
421C4×#99—472no—
422C4×#99—472no—
423C4×#99—471no—
424C4×#99D4711yescharacteristic, direct product factor
425C2×#342—472no—
426C2×C47—24no—
427C2×C47—21no—
428C2×C47—21no—
429C2×C47—42no—
430C2×C47C2×C4×C22⋊C411yescharacteristic
431C2×C47C22×#9911yescharacteristic
432C2×C47C2×#41011yescharacteristic
433D47—22no—
434D47—24no—
435D47—42no—
436D47C4×#9914yesdirect product factor
437C23×D4—471no—
438C24×C4—471no—
439C24×C4—471no—
440C2×C4×D4—471no—
441C2×C4×D4—471no—
442C2×C4×D4—471no—
443C2×C4×D4—471no—
444C2×C4×D4—471no—
445C2×C4×D4—471no—
446C2×C4×D4—471no—
447C2×C4×D4—942no—
448C2×C4×D4—942no—
449C2×C4×D4—942no—
450C2×C4×D4—942no—
451C2×C4×D4C2×D4711yescharacteristic
452C22×C4⋊C4—471no—
453C22×C22⋊C4—474no—
454C22×C22⋊C4—471no—
455C22×C22⋊C4—471no—
456C22×C42—471no—
457C22×C42—942no—
458C2×#99—472no—
459C2×#99—474no—
460C2×#99—4716no—
461C2×#99C2×D4712yes—
462C4×C22⋊C4—472no—
463C4×C22⋊C4—474no—
464C4×C22⋊C4—942no—
465C4×C22⋊C4—942no—
466C4×C22⋊C4C2×D4712yescomplemented
467C2×#95—942no—
468#342—474no—
469#342—472no—
470#342C2×D4712yescomplemented
471C47C2×C4×#9911yescharacteristic, complemented, Sylow
472C25—471no—
473C25—471no—
474C22×D4—471no—
475C22×D4—471no—
476C22×D4—478no—
477C22×D4—471no—
478C22×D4—942no—
479C22×D4—942no—
480C22×D4—944no—
481C22×D4C22×D4711yescharacteristic
482C23×C4—471no—
483C23×C4—471no—
484C23×C4—471no—
485C23×C4—472no—
486C23×C4—471no—
487C23×C4—471no—
488C23×C4—471no—
489C23×C4—472no—
490C23×C4—472no—
491C23×C4—472no—
492C23×C4—471no—
493C23×C4—471no—
494C23×C4—471no—
495C23×C4—471no—
496C23×C4—471no—
497C23×C4—941no—
498C23×C4—941no—
499C23×C4—941no—
500C23×C4—941no—
501C23×C4—944no—
502C23×C4—1884no—
503C23×C4—1884no—
504C23×C4C4×D4711yescharacteristic, complemented
505C23×C4C22×D4711yescharacteristic
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—942no—
509C4×D4—942no—
510C4×D4—942no—
511C4×D4—942no—
512C4×D4—942no—
513C4×D4—942no—
514C4×D4—942no—
515C4×D4—942no—
516C4×D4—942no—
517C4×D4—942no—
518C4×D4—942no—
519C4×D4—942no—
520C4×D4—942no—
521C4×D4—942no—
522C2×C4⋊C4—471no—
523C2×C4⋊C4—471no—
524C2×C4⋊C4—471no—
525C2×C4⋊C4—942no—
526C2×C4⋊C4—942no—
527C2×C4⋊C4C4×D4711yescharacteristic, complemented
528C2×C22⋊C4—474no—
529C2×C22⋊C4—4716no—
530C2×C22⋊C4—471no—
531C2×C22⋊C4—471no—
532C2×C22⋊C4—471no—
533C2×C22⋊C4—471no—
534C2×C22⋊C4—471no—
535C2×C22⋊C4—471no—
536C2×C22⋊C4—942no—
537C2×C22⋊C4—942no—
538C2×C22⋊C4—942no—
539C2×C22⋊C4—942no—
540C2×C22⋊C4—948no—
541C2×C22⋊C4—944no—
542C2×C22⋊C4C4×D4711yescharacteristic, complemented
543C2×C22⋊C4C22×D4711yescharacteristic
544C2×C22⋊C4C22×D4714yes—
545C2×C42—22no—
546C2×C42—471no—
547C2×C42—471no—
548C2×C42—471no—
549C2×C42—941no—
550C2×C42—941no—
551C2×C42—941no—
552C2×C42—941no—
553C2×C42—944no—
554C2×C42—942no—
555C2×C42—1888no—
556C2×C42C4×D4711yescharacteristic, complemented
557#99—478no—
558#99—4716no—
559#99C4×D4718yesdirect product factor
560#95—22no—
561#95—944no—
562#95—942no—
563C24—471no—
564C24—472no—
565C24—474no—
566C24—471no—
567C24—472no—
568C24—474no—
569C24—474no—
570C24—471no—
571C24—941no—
572C24—941no—
573C24—942no—
574C24—1882no—
575C24—1882no—
576C24—1882no—
577C24—1882no—
578C24C2×C4×D4711yescharacteristic
579C24C23×D4711yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—474no—
583C2×D4—474no—
584C2×D4—474no—
585C2×D4—942no—
586C2×D4—942no—
587C2×D4—9416no—
588C2×D4—9416no—
589C2×D4—942no—
590C2×D4—942no—
591C2×D4—942no—
592C2×D4—942no—
593C2×D4C2×C4×D4714yes—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—471no—
600C22×C4—471no—
601C22×C4—471no—
602C22×C4—472no—
603C22×C4—471no—
604C22×C4—472no—
605C22×C4—474no—
606C22×C4—471no—
607C22×C4—471no—
608C22×C4—472no—
609C22×C4—472no—
610C22×C4—471no—
611C22×C4—472no—
612C22×C4—472no—
613C22×C4—472no—
614C22×C4—472no—
615C22×C4—471no—
616C22×C4—471no—
617C22×C4—948no—
618C22×C4—944no—
619C22×C4—941no—
620C22×C4—941no—
621C22×C4—941no—
622C22×C4—941no—
623C22×C4—942no—
624C22×C4—941no—
625C22×C4—941no—
626C22×C4—9416no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—941no—
631C22×C4—944no—
632C22×C4—941no—
633C22×C4—941no—
634C22×C4—1884no—
635C22×C4—1882no—
636C22×C4—1882no—
637C22×C4—1884no—
638C22×C4—1882no—
639C22×C4—1884no—
640C22×C4—1882no—
641C22×C4—1884no—
642C22×C4—1884no—
643C22×C4—1884no—
644C22×C4—1884no—
645C22×C4—1882no—
646C22×C4—1888no—
647C22×C4—1888no—
648C22×C4—1882no—
649C22×C4—1882no—
650C22×C4—1882no—
651C22×C4—1882no—
652C22×C4C2×C4×D4711yescharacteristic
653C22×C4C2×C4×D4711yescharacteristic
654C22×C4C2×C4×D4711yescharacteristic
655C22×C4C2×C4×D4711yescharacteristic
656C22×C4C2×C4×D4711yescharacteristic
657C22×C4D4×D4712yes—
658C22×C4D4×D4712yes—
659C4⋊C4—22no—
660C4⋊C4—942no—
661C4⋊C4—942no—
662C4⋊C4—942no—
663C22⋊C4—22no—
664C22⋊C4—24no—
665C22⋊C4—22no—
666C22⋊C4—478no—
667C22⋊C4—942no—
668C22⋊C4—9416no—
669C22⋊C4—942no—
670C22⋊C4—942no—
671C22⋊C4—942no—
672C22⋊C4—942no—
673C22⋊C4—944no—
674C22⋊C4—942no—
675C22⋊C4C2×C4×D4718yescomplemented
676C42—21no—
677C42—21no—
678C42—44no—
679C42—941no—
680C42—941no—
681C42—941no—
682C42—941no—
683C42—941no—
684C42—941no—
685C42—1884no—
686C42—1888no—
687C23—21no—
688C23—21no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—471no—
694C23—472no—
695C23—472no—
696C23—471no—
697C23—472no—
698C23—478no—
699C23—472no—
700C23—472no—
701C23—478no—
702C23—472no—
703C23—944no—
704C23—942no—
705C23—944no—
706C23—942no—
707C23—944no—
708C23—944no—
709C23—941no—
710C23—941no—
711C23—1882no—
712C23—1881no—
713C23—1882no—
714C23—1881no—
715C23—1881no—
716C23—1881no—
717C23—1882no—
718C23—1882no—
719C23—1888no—
720C23—1888no—
721C23—1888no—
722C23—1882no—
723C23—1888no—
724C23—1882no—
725C23C42×D4712yescomplemented
726C23C22×C4×D4711yescharacteristic
727C23C22×C4×D4712yes—
728C23C2×D4×D4712yes—
729C23#41×D4712yes—
730D4—28no—
731D4—948no—
732D4—948no—
733D4—948no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—28no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—471no—
750C2×C4—474no—
751C2×C4—472no—
752C2×C4—471no—
753C2×C4—472no—
754C2×C4—944no—
755C2×C4—942no—
756C2×C4—944no—
757C2×C4—942no—
758C2×C4—944no—
759C2×C4—944no—
760C2×C4—944no—
761C2×C4—942no—
762C2×C4—941no—
763C2×C4—941no—
764C2×C4—944no—
765C2×C4—942no—
766C2×C4—941no—
767C2×C4—941no—
768C2×C4—948no—
769C2×C4—1882no—
770C2×C4—1882no—
771C2×C4—1882no—
772C2×C4—1882no—
773C2×C4—1882no—
774C2×C4—1882no—
775C2×C4—1882no—
776C2×C4—1882no—
777C2×C4—18832no—
778C2×C4—1882no—
779C2×C4—1882no—
780C2×C4—1882no—
781C2×C4—1882no—
782C2×C4—1881no—
783C2×C4—1882no—
784C2×C4—1884no—
785C2×C4—1884no—
786C2×C4—1882no—
787C2×C4—1881no—
788C2×C4—1881no—
789C2×C4C42×D4712yescomplemented
790C2×C4C22⋊C4×D4711yescharacteristic
791C2×C4C22⋊C4×D4712yes—
792C2×C4C22⋊C4×D4711yescharacteristic
793C22—22no—
794C22—21no—
795C22—22no—
796C22—21no—
797C22—22no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—472no—
805C22—472no—
806C22—472no—
807C22—472no—
808C22—474no—
809C22—9416no—
810C22—944no—
811C22—944no—
812C22—941no—
813C22—942no—
814C22—941no—
815C22—942no—
816C22—942no—
817C22—1888no—
818C22—1882no—
819C22—1882no—
820C22—1882no—
821C22—1882no—
822C22—1888no—
823C22—1888no—
824C22—1881no—
825C22—1881no—
826C22C2×C42×D4711yescharacteristic
827C22C2×C22⋊C4×D4711yescharacteristic
828C22#117×D4711yescharacteristic
829C22C4×D4×D4714yes—
830C4—21no—
831C4—22no—
832C4—22no—
833C4—48no—
834C4—41no—
835C4—41no—
836C4—472no—
837C4—941no—
838C4—942no—
839C4—942no—
840C4—1888no—
841C4—1881no—
842C4—1881no—
843C4#99×D4712yesdirect product factor
844C2—24no—
845C2—21no—
846C2—21no—
847C2—42no—
848C2—474no—
849C2—942no—
850C2—944no—
851C2—1882no—
852C2C4×C22⋊C4×D4711yescharacteristic
853C2C2×#99×D4711yescharacteristic
854C2#410×D4711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC4×#99×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC22×D4×D47C22
cosocleC24×C47C24
hypercenterC4×#99D47
hypocenterC47C2×C4×#99
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. C4×C22⋊C4×D47C2semidirect
4. #99×Dic47C2semidirect
5. C4×#13093938C2semidirect
6. C4×#13093939C2semidirect
7. #20243175C2semidirect
8. #342×D47C2semidirect
9. C4×#99×C47C2semidirect
11. C23×C4×D47C4semidirect
13. C2×C4×D188C4semidirect
15. C2×#13093986C4semidirect
16. C2×C4×C22⋊D47C4semidirect
18. C2×(C22⋊D47)⋊C4C4semidirect
24. C2×C4⋊C4×D47C4semidirect
25. C2×C22⋊C4×D47C4semidirect
29. C2×C42×D47C4semidirect
32. #99×D47C4direct (N × H)
33. C22⋊C4×Dic47C22semidirect
35. C4×C22⋊Dic47C22semidirect
38. #15688890C22semidirect
39. #15688889C22semidirect
42. C4×C22⋊C4×C47C22semidirect
43. C47×#342C22semidirect
53. C23×Dic47C2×C4semidirect
69. C22×C4×D47C2×C4semidirect
70. C22×C4×D47C2×C4semidirect
89. C2×C4⋊Dic47C2×C4semidirect
90. C2×Dic47⋊C4C2×C4semidirect
91. C2×Dic47⋊C4C2×C4semidirect
94. C2×C22⋊Dic47C2×C4semidirect
100. C2×(C2×D47)⋊C4C2×C4semidirect
101. C2×(C2×D47)⋊C4C2×C4semidirect
107. C22⋊C4×D47C2×C4semidirect
110. C2×C4×Dic47C2×C4semidirect
111. C2×C4×Dic47C2×C4semidirect
112. C2×C4×Dic47C2×C4semidirect
118. #13093939C2×C4semidirect
119. #13093938C2×C4semidirect
123. C23×C4×C47C2×C4semidirect
127. C2×C4⋊C4×C47C2×C4semidirect
128. C2×C22⋊C4×C47C2×C4semidirect
132. C2×C42×C47C2×C4semidirect
133. #99×C47C2×C4semidirect
144. C23×D47C42semidirect
171. C2×C22⋊D47C42semidirect
189. C2×D188C42semidirect
220. C2×C4×D47C42semidirect
235. C22⋊C4×C47C22×C4semidirect
242. C22⋊Dic47C22×C4semidirect
265. C23×C47C2×C42semidirect
294. C22×D47C2×C42semidirect
318. C2×C4×C47C2×C42semidirect
339. C2×Dic47C2×C42semidirect
364. C4×D47#99direct (N × H)
409. C4×C47C2×#99semidirect
416. Dic47C2×#99semidirect
424. C4×#99D47direct (N × H)
436. D47C4×#99direct (N × H)
466. C4×C22⋊C4C2×D47semidirect
470. #342C2×D47semidirect
471. C47C2×C4×#99semidirect
504. C23×C4C4×D47semidirect
527. C2×C4⋊C4C4×D47semidirect
542. C2×C22⋊C4C4×D47semidirect
556. C2×C42C4×D47semidirect
559. #99C4×D47direct (N × H)
675. C22⋊C4C2×C4×D47semidirect
725. C23C42×D47semidirect
789. C2×C4C42×D47semidirect
843. C4#99×D47direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×D472
C2×#99×D472
C4×C22⋊C4×D472
#99×Dic472
C4×#130939382
C4×#130939392
#202431752
#342×D472
C4×#99×C472
C2×C4×#9947