Finite Group Databasebeta

← D47×#1799 #26215669

Subgroups — D47×#1799 #26215669

Order 12032.

2066 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D47C211yesmaximal, characteristic
2C2×#99×D47C212yesmaximal
3#380×D47C212yesmaximal, complemented
4#20243376C211yesmaximal, characteristic, complemented
5#20243375C212yesmaximal, complemented
6#20243374C212yesmaximal, complemented
7#20243373C212yesmaximal, complemented
8#342×D47C212yesmaximal, complemented
9C47×#1799C211yesmaximal, 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×D47—22no—
25C2×C4⋊C4×D47C411yescharacteristic, complemented
26C2×C22⋊C4×D47C411yescharacteristic, complemented
27C2×C22⋊C4×D47C2214yes—
28C2×C22⋊C4×D47C2211yescharacteristic
29C2×C42×D47C411yescharacteristic, complemented
30C2×#13093939C2212yes—
31C2×#13093938C2214yes—
32#99×D47—28no—
33#15688983C2212yescomplemented
34#15688982—22no—
35#15688981C2214yescomplemented
36#15688980—22no—
37#95×D47—22no—
38#15688890C2212yescomplemented
39#15688889C2214yescomplemented
40C2×C4×D4×C47C2211yescharacteristic
41C2×#99×C47C2212yes—
42C47×#380C2212yescomplemented
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×D47D414yes—
53C2×D4×D47Q814yes—
54C23×Dic47C2×C411yescharacteristic, complemented
55C23×Dic47C2311yescharacteristic
56C22×C4×D47—21no—
57C22×C4×D47—21no—
58C22×C4×D47—21no—
59C22×C4×D47—21no—
60C22×C4×D47—24no—
61C22×C4×D47—44no—
62C22×C4×D47—44no—
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
70C22×C4×D47C2×C411yescharacteristic, complemented
71C22×C4×D47C2×C411yescharacteristic, complemented
72C22×C4×D47D412yes—
73C22×C4×D47D412yes—
74C22×C4×D47D412yes—
75C22×C4×D47D412yes—
76C4×D188—22no—
77C4×D188—22no—
78D4×Dic47—22no—
79D4×Dic47—22no—
80#13093986—22no—
81#13093986—22no—
82C4×C22⋊D47—22no—
83C4×C22⋊D47—22no—
84C4×C22⋊D47—22no—
85C4×C22⋊D47—22no—
86(C22⋊D47)⋊C4—22no—
87(C22⋊D47)⋊C4—22no—
88(C22⋊D47)⋊C4—22no—
89(C22⋊D47)⋊C4—22no—
90C2×C4⋊Dic47—22no—
91C2×C4⋊Dic47C2×C411yescharacteristic, complemented
92C2×Dic47⋊C4—24no—
93C2×Dic47⋊C4C2×C411yescharacteristic, complemented
94C2×Dic47⋊C4C2×C411yescharacteristic, complemented
95C4⋊C4×D47—22no—
96C4⋊C4×D47—22no—
97C4⋊C4×D47—48no—
98C2×C22⋊Dic47C2×C411yescharacteristic, complemented
99C2×C22⋊Dic47C2314yes—
100C2×C22⋊Dic47C2311yescharacteristic
101C2×(C2×D47)⋊C4—24no—
102C2×(C2×D47)⋊C4C2×C411yescharacteristic
103C2×(C2×D47)⋊C4C2×C411yescharacteristic
104C2×(C2×D47)⋊C4C2×C411yescharacteristic, complemented
105C2×(C2×D47)⋊C4C2×C411yescharacteristic, complemented
106C22⋊C4×D47—22no—
107C22⋊C4×D47—22no—
108C22⋊C4×D47—22no—
109C22⋊C4×D47—22no—
110C22⋊C4×D47—28no—
111C22⋊C4×D47—28no—
112C2×C4×Dic47C2×C411yescharacteristic, complemented
113C2×C4×Dic47C2×C411yescharacteristic, complemented
114C2×C4×Dic47C2×C411yescharacteristic, complemented
115C42×D47—21no—
116C42×D47—21no—
117C42×D47—21no—
118C42×D47—21no—
119#13093939—24no—
120#13093938—28no—
121C47⋊#95—22no—
122C47⋊#95—24no—
123C22×D4×C47C2311yescharacteristic
124C23×C4×C47C2×C411yescharacteristic, complemented
125C23×C4×C47C2311yescharacteristic
126C4×D4×C47—22no—
127C4×D4×C47—22no—
128C2×C4⋊C4×C47—22no—
129C2×C4⋊C4×C47C2×C411yescharacteristic, complemented
130C2×C22⋊C4×C47C2×C411yescharacteristic, complemented
131C2×C22⋊C4×C47C2314yes—
132C2×C22⋊C4×C47C2311yescharacteristic
133C2×C42×C47C2×C411yescharacteristic, complemented
134#99×C47—24no—
135#95×C47—22no—
136C24×C47C22×C411yescharacteristic
137C24×C47C2411yescharacteristic
138C23×D47—21no—
139C23×D47—21no—
140C23×D47—22no—
141C23×D47—42no—
142C23×D47—42no—
143C23×D47—42no—
144C23×D47—42no—
145C23×D47C4⋊C414yescomplemented
146C23×D47C22×C411yescharacteristic
147C23×D47C22×C411yescharacteristic
148C23×D47C22×C411yescharacteristic
149C23×D47C2×D412yes—
150C23×D47C2×D412yes—
151C23×D47C2×D412yes—
152C23×D47C2×Q812yes—
153C23×D47#4114yes—
154C2×D4×C47—22no—
155C2×D4×C47—22no—
156C2×D4×C47C2×D412yes—
157C2×D4×C47C2×Q812yes—
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—24no—
161C22×C4×C47—42no—
162C22×C4×C47—42no—
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C22×C411yescharacteristic
165C22×C4×C47C22×C411yescharacteristic
166C22×C4×C47C22×C411yescharacteristic
167C22×C4×C47C22×C411yescharacteristic
168C22×C4×C47C2×D412yes—
169C22×C4×C47C2×D412yes—
170C2×C22⋊D47—22no—
171C2×C22⋊D47—22no—
172C2×C22⋊D47—22no—
173C2×C22⋊D47—22no—
174C2×C22⋊D47C4⋊C414yescomplemented
175C2×C22⋊D47C2×D412yes—
176C2×C22⋊D47C2×Q812yes—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—24no—
180C22×Dic47—42no—
181C22×Dic47—42no—
182C22×Dic47C22×C411yescharacteristic
183C22×Dic47C22×C411yescharacteristic
184C22×Dic47C22×C411yescharacteristic
185C22×Dic47C22×C411yescharacteristic
186C22×Dic47C22×C411yescharacteristic
187C22×Dic47C2×D412yes—
188C22×Dic47C2×D412yes—
189D4×D47—28no—
190D4×D47—28no—
191D4×D47—28no—
192D4×D47—28no—
193C2×D188—22no—
194C2×D188—22no—
195C2×D188C4⋊C414yescomplemented
196C2×C4×D47—21no—
197C2×C4×D47—21no—
198C2×C4×D47—22no—
199C2×C4×D47—28no—
200C2×C4×D47—24no—
201C2×C4×D47—21no—
202C2×C4×D47—21no—
203C2×C4×D47—21no—
204C2×C4×D47—21no—
205C2×C4×D47—21no—
206C2×C4×D47—21no—
207C2×C4×D47—21no—
208C2×C4×D47—21no—
209C2×C4×D47—42no—
210C2×C4×D47—44no—
211C2×C4×D47—42no—
212C2×C4×D47—44no—
213C2×C4×D47—42no—
214C2×C4×D47—44no—
215C2×C4×D47—44no—
216C2×C4×D47—44no—
217C2×C4×D47—44no—
218C2×C4×D47—44no—
219C2×C4×D47—42no—
220C2×C4×D47—42no—
221C2×C4×D47—42no—
222C2×C4×D47—42no—
223C2×C4×D47—48no—
224C2×C4×D47—48no—
225C2×C4×D47—48no—
226C2×C4×D47C22⋊C411yescharacteristic
227C2×C4×D47C22⋊C411yescharacteristic
228C2×C4×D47C22⋊C411yescharacteristic
229C2×C4×D47C22⋊C412yes—
230C2×C4×D47C22⋊C412yes—
231C2×C4×D47C22⋊C412yes—
232C2×C4×D47C22⋊C412yes—
233C2×C4×D47C22⋊C412yes—
234C2×C4×D47C22⋊C412yes—
235C2×C4×D47C22⋊C411yescharacteristic
236C2×C4×D47C4⋊C414yescomplemented
237C4⋊C4×C47—22no—
238C4⋊C4×C47—44no—
239C22⋊C4×C47—22no—
240C22⋊C4×C47—22no—
241C22⋊C4×C47—24no—
242C22⋊C4×C47—24no—
243C42×C47—21no—
244C42×C47—21no—
245C22⋊Dic47—22no—
246C22⋊Dic47—22no—
247C22⋊Dic47—24no—
248C22⋊Dic47—24no—
249(C2×D47)⋊C4—22no—
250(C2×D47)⋊C4—22no—
251(C2×D47)⋊C4—22no—
252(C2×D47)⋊C4—22no—
253(C2×D47)⋊C4—48no—
254C4⋊Dic47—22no—
255C4⋊Dic47—44no—
256Dic47⋊C4—22no—
257Dic47⋊C4—22no—
258Dic47⋊C4—48no—
259C4×Dic47—21no—
260C4×Dic47—21no—
261C4×Dic47—21no—
262C4×Dic47—21no—
263C4×Dic47—21no—
264C4×Dic47—21no—
265C23×C47—21no—
266C23×C47—21no—
267C23×C47—41no—
268C23×C47—41no—
269C23×C47—41no—
270C23×C47—41no—
271C23×C47C2×C4⋊C412yescomplemented
272C23×C47C23×C411yescharacteristic
273C23×C47C22×D412yes—
274C23×C47C22×D411yescharacteristic
275C23×C47C22×Q811yescharacteristic
276C23×C47C2×#4112yes—
277C22×D47—24no—
278C22×D47—22no—
279C22×D47—24no—
280C22×D47—22no—
281C22×D47—21no—
282C22×D47—21no—
283C22×D47—24no—
284C22×D47—24no—
285C22×D47—44no—
286C22×D47—44no—
287C22×D47—48no—
288C22×D47—41no—
289C22×D47—42no—
290C22×D47—41no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—42no—
294C22×D47—48no—
295C22×D47—48no—
296C22×D47—42no—
297C22×D47—42no—
298C22×D47—41no—
299C22×D47—41no—
300C22×D47C2×C22⋊C412yes—
301C22×D47C2×C22⋊C411yescharacteristic
302C22×D47C2×C22⋊C411yescharacteristic
303C22×D47C2×C4⋊C412yes—
304C22×D47C2×C4⋊C412yes—
305C22×D47C2×C4⋊C412yescomplemented
306C22×D47#11712yes—
307C22×D47#11712yes—
308C22×D47#12114yes—
309C22×D47#12114yes—
310C22×D47C22⋊Q814yes—
311C22×D47C22⋊Q814yes—
312D4×C47—24no—
313D4×C47—24no—
314C2×C4×C47—21no—
315C2×C4×C47—21no—
316C2×C4×C47—24no—
317C2×C4×C47—22no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—41no—
321C2×C4×C47—42no—
322C2×C4×C47—42no—
323C2×C4×C47—42no—
324C2×C4×C47—41no—
325C2×C4×C47—41no—
326C2×C4×C47—44no—
327C2×C4×C47—44no—
328C2×C4×C47—44no—
329C2×C4×C47C2×C22⋊C411yescharacteristic
330C2×C4×C47C2×C22⋊C412yes—
331C2×C4×C47C2×C22⋊C411yescharacteristic
332C2×C4×C47C2×C4⋊C412yescomplemented
333C22⋊D47—24no—
334C22⋊D47—24no—
335C22⋊D47—28no—
336C2×Dic47—21no—
337C2×Dic47—21no—
338C2×Dic47—24no—
339C2×Dic47—22no—
340C2×Dic47—21no—
341C2×Dic47—21no—
342C2×Dic47—41no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47—41no—
347C2×Dic47—41no—
348C2×Dic47—44no—
349C2×Dic47—44no—
350C2×Dic47—44no—
351C2×Dic47C2×C22⋊C411yescharacteristic
352C2×Dic47C2×C22⋊C412yes—
353C2×Dic47C2×C22⋊C411yescharacteristic
354C2×Dic47C2×C4⋊C412yescomplemented
355D188—28no—
356C4×D47—24no—
357C4×D47—24no—
358C4×D47—22no—
359C4×D47—24no—
360C4×D47—22no—
361C4×D47—24no—
362C4×D47—22no—
363C4×D47—24no—
364C4×D47—42no—
365C4×D47—42no—
366C4×D47—42no—
367C4×D47—42no—
368C4×D47—42no—
369C4×D47—42no—
370C4×D47—42no—
371C4×D47—42no—
372C4×D47—42no—
373C4×D47—42no—
374C4×D47—42no—
375C4×D47—816no—
376C4×D47#9914yescomplemented
377C2×#1799—471nomaximal, Sylow
378C22×C47—22no—
379C22×C47—21no—
380C22×C47—22no—
381C22×C47—21no—
382C22×C47—22no—
383C22×C47—41no—
384C22×C47—41no—
385C22×C47—42no—
386C22×C47—42no—
387C22×C47—42no—
388C22×C47—41no—
389C22×C47—41no—
390C22×C47C22×C22⋊C411yescharacteristic
391C22×C47C22×C4⋊C411yescharacteristic
392C22×C47C2×#11711yescharacteristic
393C22×C47C2×#12112yes—
394C22×C47C2×C22⋊Q812yes—
395C2×D47—21no—
396C2×D47—22no—
397C2×D47—21no—
398C2×D47—22no—
399C2×D47—28no—
400C2×D47—24no—
401C2×D47—24no—
402C2×D47—28no—
403C2×D47—22no—
404C2×D47—42no—
405C2×D47—42no—
406C2×D47—44no—
407C2×D47—44no—
408C2×D47—48no—
409C2×D47—42no—
410C2×D47—41no—
411C2×D47—41no—
412C2×D47—48no—
413C2×D47—42no—
414C2×D47#38012yes—
415C2×D47#38014yes—
416C2×D47#38012yes—
417C2×D47C2×#9912yes—
418C2×D47#41012yes—
419C4×C47—21no—
420C4×C47—22no—
421C4×C47—22no—
422C4×C47—41no—
423C4×C47—41no—
424C4×C47—84no—
425C4×C47C2×#9912yescomplemented
426Dic47—21no—
427Dic47—22no—
428Dic47—22no—
429Dic47—41no—
430Dic47—41no—
431Dic47—84no—
432Dic47C2×#9912yescomplemented
433C22×C4×D4—471no—
434C22×#99—472no—
435C2×#380—472no—
436#1799—472no—
437#1799—472no—
438#1799—472no—
439#1799—471no—
440#1799D4711yescharacteristic, direct product factor
441C2×#342—472no—
442C2×C47—22no—
443C2×C47—21no—
444C2×C47—21no—
445C2×C47—22no—
446C2×C47—42no—
447C2×C47C2×#38011yescharacteristic
448C2×C47C22×#9911yescharacteristic
449C2×C47C2×#41011yescharacteristic
450D47—22no—
451D47—24no—
452D47—42no—
453D47#179914yesdirect product factor
454C23×D4—471no—
455C24×C4—471no—
456C24×C4—471no—
457C2×C4×D4—471no—
458C2×C4×D4—471no—
459C2×C4×D4—471no—
460C2×C4×D4—471no—
461C2×C4×D4—471no—
462C2×C4×D4—471no—
463C2×C4×D4—471no—
464C2×C4×D4—942no—
465C2×C4×D4—942no—
466C2×C4×D4—942no—
467C2×C4×D4—942no—
468C2×C4×D4C2×D4711yescharacteristic
469C22×C4⋊C4—471no—
470C22×C4⋊C4—942no—
471C22×C22⋊C4—471no—
472C22×C22⋊C4—471no—
473C22×C22⋊C4—474no—
474C22×C42—471no—
475C2×#99—472no—
476C2×#99—474no—
477C2×#99—948no—
478C2×#99C2×D4712yes—
479#380—472no—
480#380—474no—
481#380—942no—
482#380—942no—
483#380C2×D4712yescomplemented
484C2×#95—942no—
485#342—474no—
486#342—472no—
487#342C2×D4712yescomplemented
488C47C2×#179911yescharacteristic, complemented, Sylow
489C25—471no—
490C25—471no—
491C22×D4—471no—
492C22×D4—471no—
493C22×D4—474no—
494C22×D4—474no—
495C22×D4—471no—
496C22×D4—942no—
497C22×D4—942no—
498C22×D4—944no—
499C22×D4C22×D4711yescharacteristic
500C23×C4—471no—
501C23×C4—471no—
502C23×C4—471no—
503C23×C4—472no—
504C23×C4—471no—
505C23×C4—471no—
506C23×C4—471no—
507C23×C4—472no—
508C23×C4—472no—
509C23×C4—472no—
510C23×C4—471no—
511C23×C4—471no—
512C23×C4—471no—
513C23×C4—471no—
514C23×C4—471no—
515C23×C4—941no—
516C23×C4—941no—
517C23×C4—941no—
518C23×C4—941no—
519C23×C4—944no—
520C23×C4—1884no—
521C23×C4—1884no—
522C23×C4C4×D4711yescharacteristic, complemented
523C23×C4C22×D4711yescharacteristic
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—942no—
527C4×D4—942no—
528C4×D4—942no—
529C4×D4—942no—
530C4×D4—942no—
531C4×D4—942no—
532C4×D4—942no—
533C4×D4—942no—
534C4×D4—942no—
535C4×D4—942no—
536C4×D4—942no—
537C4×D4—942no—
538C4×D4—942no—
539C4×D4—942no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—471no—
542C2×C4⋊C4—471no—
543C2×C4⋊C4—471no—
544C2×C4⋊C4—942no—
545C2×C4⋊C4—942no—
546C2×C4⋊C4—944no—
547C2×C4⋊C4—942no—
548C2×C4⋊C4—1888no—
549C2×C4⋊C4C4×D4711yescharacteristic, complemented
550C2×C22⋊C4—471no—
551C2×C22⋊C4—471no—
552C2×C22⋊C4—471no—
553C2×C22⋊C4—471no—
554C2×C22⋊C4—471no—
555C2×C22⋊C4—471no—
556C2×C22⋊C4—474no—
557C2×C22⋊C4—942no—
558C2×C22⋊C4—942no—
559C2×C22⋊C4—942no—
560C2×C22⋊C4—942no—
561C2×C22⋊C4—948no—
562C2×C22⋊C4—948no—
563C2×C22⋊C4—944no—
564C2×C22⋊C4C4×D4711yescharacteristic, complemented
565C2×C22⋊C4C22×D4714yes—
566C2×C22⋊C4C22×D4711yescharacteristic
567C2×C42—471no—
568C2×C42—471no—
569C2×C42—471no—
570C2×C42—941no—
571C2×C42—941no—
572C2×C42—941no—
573C2×C42—941no—
574C2×C42C4×D4711yescharacteristic, complemented
575#99—24no—
576#99—948no—
577#99—944no—
578#95—22no—
579#95—944no—
580#95—942no—
581C24—471no—
582C24—472no—
583C24—471no—
584C24—472no—
585C24—472no—
586C24—472no—
587C24—474no—
588C24—474no—
589C24—471no—
590C24—941no—
591C24—941no—
592C24—942no—
593C24—1882no—
594C24—1882no—
595C24—1882no—
596C24—1882no—
597C24C2×C4×D4711yescharacteristic
598C24C23×D4711yescharacteristic
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—474no—
602C2×D4—472no—
603C2×D4—472no—
604C2×D4—474no—
605C2×D4—942no—
606C2×D4—942no—
607C2×D4—948no—
608C2×D4—948no—
609C2×D4—948no—
610C2×D4—948no—
611C2×D4—942no—
612C2×D4—942no—
613C2×D4—942no—
614C2×D4—942no—
615C2×D4D4×D4712yes—
616C2×D4Q8×D4712yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—471no—
623C22×C4—471no—
624C22×C4—471no—
625C22×C4—472no—
626C22×C4—471no—
627C22×C4—472no—
628C22×C4—471no—
629C22×C4—471no—
630C22×C4—471no—
631C22×C4—472no—
632C22×C4—472no—
633C22×C4—472no—
634C22×C4—474no—
635C22×C4—472no—
636C22×C4—472no—
637C22×C4—472no—
638C22×C4—471no—
639C22×C4—471no—
640C22×C4—948no—
641C22×C4—944no—
642C22×C4—941no—
643C22×C4—941no—
644C22×C4—941no—
645C22×C4—941no—
646C22×C4—942no—
647C22×C4—941no—
648C22×C4—941no—
649C22×C4—941no—
650C22×C4—941no—
651C22×C4—941no—
652C22×C4—941no—
653C22×C4—941no—
654C22×C4—941no—
655C22×C4—944no—
656C22×C4—1884no—
657C22×C4—1882no—
658C22×C4—1882no—
659C22×C4—1884no—
660C22×C4—1882no—
661C22×C4—1884no—
662C22×C4—1882no—
663C22×C4—1884no—
664C22×C4—1884no—
665C22×C4—1884no—
666C22×C4—1884no—
667C22×C4—1882no—
668C22×C4—1888no—
669C22×C4—1888no—
670C22×C4—1888no—
671C22×C4—1882no—
672C22×C4—1882no—
673C22×C4—1882no—
674C22×C4—1882no—
675C22×C4C2×C4×D4711yescharacteristic
676C22×C4C2×C4×D4711yescharacteristic
677C22×C4C2×C4×D4711yescharacteristic
678C22×C4C2×C4×D4711yescharacteristic
679C22×C4C2×C4×D4711yescharacteristic
680C22×C4D4×D4712yes—
681C22×C4D4×D4712yes—
682C4⋊C4—22no—
683C4⋊C4—44no—
684C4⋊C4—942no—
685C4⋊C4—942no—
686C4⋊C4—942no—
687C4⋊C4—1884no—
688C4⋊C4—1888no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—942no—
694C22⋊C4—942no—
695C22⋊C4—942no—
696C22⋊C4—942no—
697C22⋊C4—942no—
698C22⋊C4—942no—
699C22⋊C4—944no—
700C22⋊C4—944no—
701C22⋊C4—1888no—
702C42—21no—
703C42—21no—
704C42—941no—
705C42—941no—
706C42—941no—
707C42—941no—
708C42—941no—
709C42—941no—
710C23—21no—
711C23—21no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—471no—
717C23—472no—
718C23—471no—
719C23—472no—
720C23—472no—
721C23—474no—
722C23—474no—
723C23—472no—
724C23—472no—
725C23—474no—
726C23—474no—
727C23—472no—
728C23—944no—
729C23—942no—
730C23—944no—
731C23—942no—
732C23—944no—
733C23—944no—
734C23—941no—
735C23—941no—
736C23—1882no—
737C23—1881no—
738C23—1882no—
739C23—1881no—
740C23—1881no—
741C23—1881no—
742C23—1882no—
743C23—1882no—
744C23—1884no—
745C23—1884no—
746C23—1888no—
747C23—1888no—
748C23—1882no—
749C23—1888no—
750C23—1882no—
751C23C4⋊C4×D4712yescomplemented
752C23C22×C4×D4711yescharacteristic
753C23C2×D4×D4712yes—
754C23C2×D4×D4711yescharacteristic
755C23C2×Q8×D4711yescharacteristic
756C23#41×D4712yes—
757D4—24no—
758D4—24no—
759D4—948no—
760D4—948no—
761D4—944no—
762D4—944no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—471no—
779C2×C4—474no—
780C2×C4—471no—
781C2×C4—472no—
782C2×C4—472no—
783C2×C4—944no—
784C2×C4—942no—
785C2×C4—944no—
786C2×C4—942no—
787C2×C4—944no—
788C2×C4—944no—
789C2×C4—944no—
790C2×C4—942no—
791C2×C4—941no—
792C2×C4—941no—
793C2×C4—944no—
794C2×C4—942no—
795C2×C4—941no—
796C2×C4—941no—
797C2×C4—37616no—
798C2×C4—1882no—
799C2×C4—1882no—
800C2×C4—1882no—
801C2×C4—1882no—
802C2×C4—1882no—
803C2×C4—1882no—
804C2×C4—1882no—
805C2×C4—1882no—
806C2×C4—1882no—
807C2×C4—1882no—
808C2×C4—1882no—
809C2×C4—1882no—
810C2×C4—1881no—
811C2×C4—1882no—
812C2×C4—1884no—
813C2×C4—1884no—
814C2×C4—1884no—
815C2×C4—1882no—
816C2×C4—1881no—
817C2×C4—1881no—
818C2×C4C22⋊C4×D4711yescharacteristic
819C2×C4C22⋊C4×D4712yes—
820C2×C4C22⋊C4×D4711yescharacteristic
821C2×C4C4⋊C4×D4712yescomplemented
822C22—22no—
823C22—21no—
824C22—22no—
825C22—21no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—472no—
835C22—472no—
836C22—472no—
837C22—472no—
838C22—474no—
839C22—948no—
840C22—944no—
841C22—944no—
842C22—948no—
843C22—941no—
844C22—942no—
845C22—941no—
846C22—942no—
847C22—942no—
848C22—1884no—
849C22—1882no—
850C22—1882no—
851C22—1884no—
852C22—1882no—
853C22—1882no—
854C22—1888no—
855C22—1888no—
856C22—1881no—
857C22—1881no—
858C22C2×C22⋊C4×D4711yescharacteristic
859C22C2×C4⋊C4×D4711yescharacteristic
860C22#117×D4711yescharacteristic
861C22#121×D4712yes—
862C22C22⋊Q8×D4712yes—
863C4—21no—
864C4—22no—
865C4—22no—
866C4—41no—
867C4—41no—
868C4—84no—
869C4—472no—
870C4—941no—
871C4—942no—
872C4—942no—
873C4—3764no—
874C4—1881no—
875C4—1881no—
876C4#99×D4712yescomplemented
877C2—22no—
878C2—21no—
879C2—21no—
880C2—22no—
881C2—42no—
882C2—474no—
883C2—942no—
884C2—944no—
885C2—1882no—
886C2#380×D4711yescharacteristic
887C2C2×#99×D4711yescharacteristic
888C2#410×D4711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#1799C2
socleC22×C47C22×C22⋊C4
prime radicalC22×D4×D47C22
cosocleC24×C47C24
hypercenter#1799D47
hypocenterC47C2×#1799
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #380×D47C2semidirect
4. #20243376C2semidirect
5. #20243375C2semidirect
6. #20243374C2semidirect
7. #20243373C2semidirect
8. #342×D47C2semidirect
9. C47×#1799C2semidirect
11. C23×C4×D47C4semidirect
13. C2×C4×D188C4semidirect
15. C2×#13093986C4semidirect
16. C2×C4×C22⋊D47C4semidirect
18. C2×(C22⋊D47)⋊C4C4semidirect
25. C2×C4⋊C4×D47C4semidirect
26. C2×C22⋊C4×D47C4semidirect
29. C2×C42×D47C4semidirect
33. #15688983C22semidirect
35. #15688981C22semidirect
38. #15688890C22semidirect
39. #15688889C22semidirect
42. C47×#380C22semidirect
43. C47×#342C22semidirect
54. C23×Dic47C2×C4semidirect
70. C22×C4×D47C2×C4semidirect
71. C22×C4×D47C2×C4semidirect
91. C2×C4⋊Dic47C2×C4semidirect
93. C2×Dic47⋊C4C2×C4semidirect
94. C2×Dic47⋊C4C2×C4semidirect
98. C2×C22⋊Dic47C2×C4semidirect
104. C2×(C2×D47)⋊C4C2×C4semidirect
105. C2×(C2×D47)⋊C4C2×C4semidirect
112. C2×C4×Dic47C2×C4semidirect
113. C2×C4×Dic47C2×C4semidirect
114. C2×C4×Dic47C2×C4semidirect
124. C23×C4×C47C2×C4semidirect
129. C2×C4⋊C4×C47C2×C4semidirect
130. C2×C22⋊C4×C47C2×C4semidirect
133. C2×C42×C47C2×C4semidirect
145. C23×D47C4⋊C4semidirect
174. C2×C22⋊D47C4⋊C4semidirect
195. C2×D188C4⋊C4semidirect
236. C2×C4×D47C4⋊C4semidirect
271. C23×C47C2×C4⋊C4semidirect
305. C22×D47C2×C4⋊C4semidirect
332. C2×C4×C47C2×C4⋊C4semidirect
354. C2×Dic47C2×C4⋊C4semidirect
376. C4×D47#99semidirect
425. C4×C47C2×#99semidirect
432. Dic47C2×#99semidirect
440. #1799D47direct (N × H)
453. D47#1799direct (N × H)
483. #380C2×D47semidirect
487. #342C2×D47semidirect
488. C47C2×#1799semidirect
522. C23×C4C4×D47semidirect
549. C2×C4⋊C4C4×D47semidirect
564. C2×C22⋊C4C4×D47semidirect
574. C2×C42C4×D47semidirect
751. C23C4⋊C4×D47semidirect
821. C2×C4C4⋊C4×D47semidirect
876. C4#99×D47semidirect

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
#380×D472
#202433762
#202433752
#202433742
#202433732
#342×D472
C47×#17992
C2×#179947