Finite Group Databasebeta

← C2×#20253569 #27084506

Subgroups — C2×#20253569 #27084506

Order 12032.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689742C211yesmaximal, characteristic, complemented
2C2×#15689595C211yesmaximal, characteristic, complemented
3#20253569C2116yesmaximal, direct product factor
4C2×#15689463C211yesmaximal, characteristic, complemented
5C2×#15689445C211yesmaximal, characteristic, complemented
6C2×#15689413C211yesmaximal, characteristic, complemented
7C2×#15689404C211yesmaximal, characteristic, complemented
8C2×#15689335C211yesmaximal, characteristic, complemented
9C2×#15689272C211yesmaximal, characteristic, complemented
10C2×#15689255C211yesmaximal, characteristic
11C2×#15689232C211yesmaximal, characteristic, complemented
12C2×#15689224C211yesmaximal, characteristic, complemented
13C2×#15689208C211yesmaximal, characteristic, complemented
14C2×D8×Dic47C211yesmaximal, characteristic, complemented
15C2×#15689183C211yesmaximal, characteristic, complemented
16C2×C47×#463C211yesmaximal, characteristic, complemented
17C22×D4×D47C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20#15689742—24no—
21#15689742C2218yescomplemented
22C2×#13094024C2211yescharacteristic, complemented
23C2×#13094017—21no—
24C2×#13094010—21no—
25C2×#13094008—21no—
26C2×#13094001—21no—
27C2×#13094000C2211yescharacteristic
28C2×#13093995C2211yescharacteristic
29#15689595—24no—
30#15689595C2218yescomplemented
31C2×Q8×Dic47C2211yescharacteristic, complemented
32C2×C4×D188C2211yescharacteristic
33C2×D4×Dic47C2211yescharacteristic
34C2×D4×Dic47C2211yescharacteristic, complemented
35C2×#13093986C2211yescharacteristic
36C2×C4×C22⋊D47—21no—
37C2×(C22⋊D47)⋊C4—21no—
38C2×#13093982C2211yescharacteristic
39C2×#13093981C2211yescharacteristic
40C22×(C2×D47)⋊C4—21no—
41C2×C22⋊C4×D47—21no—
42#15689463C2218yescomplemented
43#15689445C2218yescomplemented
44#15689413C2218yescomplemented
45#15689404C2218yescomplemented
46#15689335C2218yescomplemented
47#15689272C2218yescomplemented
48#15689255C2218yes—
49#15689232C2218yescomplemented
50#15689224C2218yescomplemented
51#15689208C2218yescomplemented
52D8×Dic47C2218yescomplemented
53#15689183C2218yescomplemented
54C2×#13093958C2211yescharacteristic, complemented
55C2×#13093958C2211yescharacteristic, complemented
56C2×#13093955C2211yescharacteristic, complemented
57C2×#13093955C2211yescharacteristic, complemented
58C2×C4⋊(C47⋊C8)C2211yescharacteristic, complemented
59C2×#13093948C2211yescharacteristic, complemented
60C2×#13093946C2211yescharacteristic
61C2×#13093946C2211yescharacteristic
62C2×#13093945C2211yescharacteristic
63C2×#13093945C2211yescharacteristic
64C2×#13093945C2211yescharacteristic, complemented
65C2×(C2×D47)⋊C8C2211yescharacteristic
66C2×(C2×D47)⋊C8C2211yescharacteristic
67C2×#13093934C2211yescharacteristic, complemented
68C2×C8×Dic47C2211yescharacteristic, complemented
69C22×SD16×C47C2211yescharacteristic
70C22×D8×C47C2211yescharacteristic
71C2×#124×C47C2211yescharacteristic, complemented
72C2×C4×D4×C47C2211yescharacteristic
73C47×#463C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic, complemented
75C2×#103×C47C2211yescharacteristic, complemented
76C2×#102×C47C2211yescharacteristic, complemented
77C24×D47—21no—
78C22×Dic94—21no—
79C22×D188C2311yescharacteristic
80C22×C22⋊D47—21no—
81C22×C22⋊D47—21no—
82C2×D4×D47—24no—
83C2×D4×D47—24no—
84C2×D4×D47—22no—
85C2×D4×D47C2314yes—
86C23×Dic47—21no—
87C23×Dic47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47C2311yescharacteristic
91C2×#10625336—24no—
92C2×#10625336C2314yes—
93C2×#10625334—24no—
94C2×#10625334C2314yes—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97#13094024—22no—
98#13094024C2314yescomplemented
99#13094017—28no—
100#13094010—28no—
101#13094008—28no—
102#13094001—28no—
103#13094000—22no—
104#13094000C2314yes—
105#13093995—22no—
106#13093995C2314yes—
107Q8×Dic47—22no—
108Q8×Dic47C2314yescomplemented
109C4×D188—22no—
110C4×D188C2314yes—
111D4×Dic47—22no—
112D4×Dic47—22no—
113D4×Dic47C2314yes—
114D4×Dic47C2314yescomplemented
115#13093986—22no—
116#13093986C2314yes—
117C4×C22⋊D47—28no—
118(C22⋊D47)⋊C4—28no—
119#13093982—22no—
120#13093982C2314yes—
121#13093981D414yes—
122#13093981C2314yes—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47—21no—
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×C4⋊Dic47C2311yescharacteristic
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4D411yescharacteristic
130C2×Dic47⋊C4D411yescharacteristic
131C2×C22⋊Dic47—21no—
132C2×C22⋊Dic47—21no—
133C2×C22⋊Dic47—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×(C2×D47)⋊C4—28no—
139C2×(C2×D47)⋊C4D411yescharacteristic
140C2×(C2×D47)⋊C4D411yescharacteristic
141C22⋊C4×D47—28no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47—21no—
144C2×C4×Dic47C2311yescharacteristic
145#13093958C2314yescomplemented
146#13093958C2314yescomplemented
147#13093955C2314yescomplemented
148#13093955C2314yescomplemented
149C4⋊(C47⋊C8)C2314yescomplemented
150#13093948C2314yescomplemented
151#13093946C2314yes—
152#13093946C2314yes—
153#13093945C2314yes—
154#13093945C2314yes—
155#13093945C2314yescomplemented
156(C2×D47)⋊C8C2314yes—
157(C2×D47)⋊C8C2314yes—
158#13093934C2314yescomplemented
159C8×Dic47C2314yescomplemented
160C22×Q8×C47C2311yescharacteristic
161C22×D4×C47C2311yescharacteristic
162C22×D4×C47C2311yescharacteristic
163C23×C4×C47—21no—
164C2×SD16×C47—24no—
165C2×SD16×C47C2314yes—
166C2×D8×C47—24no—
167C2×D8×C47C2314yes—
168C22×C8×C47C2311yescharacteristic
169C22×C8×C47C2311yescharacteristic
170#124×C47—22no—
171#124×C47C2314yescomplemented
172C4×D4×C47—22no—
173C4×D4×C47C2314yes—
174C2×C4⋊C4×C47C2311yescharacteristic
175C2×C22⋊C4×C47—21no—
176C2×C22⋊C4×C47—21no—
177C2×C22⋊C4×C47—21no—
178C2×C42×C47C2311yescharacteristic
179C4⋊C8×C47C2314yescomplemented
180#103×C47C2314yescomplemented
181#102×C47C2314yescomplemented
182C24×C47—21no—
183C24×C47—21no—
184C23×D47—21no—
185C23×D47—28no—
186C23×D47—24no—
187C23×D47—82no—
188C23×D47—82no—
189C23×D47C2×D411yescharacteristic
190C2×Q8×C47—21no—
191C2×Q8×C47—22no—
192C2×Q8×C47—22no—
193C2×Q8×C47C2412yes—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—22no—
197C2×D4×C47—22no—
198C2×D4×C47—22no—
199C2×D4×C47#4114yes—
200C2×D4×C47C2412yes—
201C2×D4×C47C2412yes—
202C22×C4×C47—21no—
203C22×C4×C47—21no—
204C22×C4×C47—24no—
205C22×C4×C47—82no—
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2411yescharacteristic
209C2×C22⋊D47—28no—
210C2×C22⋊D47—24no—
211C2×C22⋊D47—24no—
212C2×C22⋊D47—82no—
213C22×Dic47—21no—
214C22×Dic47—21no—
215C22×Dic47—21no—
216C22×Dic47—24no—
217C22×Dic47—24no—
218C22×Dic47—82no—
219C22×Dic47—82no—
220C22×Dic47C2×D411yescharacteristic
221C22×Dic47C2×D411yescharacteristic
222C22×Dic47C2×D411yescharacteristic
223D4×D47—216no—
224D4×D47—28no—
225D4×D47—28no—
226C2×D188—21no—
227C2×D188—22no—
228C2×D188#4114yes—
229C2×D188C2412yes—
230C2×C4×D47—22no—
231C2×C4×D47—22no—
232C2×C4×D47—24no—
233C2×C4×D47—24no—
234C2×C4×D47—82no—
235C2×C4×D47—82no—
236C2×C4×D47C2×D412yes—
237C2×C4×D47C2412yes—
238C2×Dic94—24no—
239C2×Dic94—82no—
240SD16×C47—28no—
241D8×C47—28no—
242C2×C8×C47—22no—
243C2×C8×C47—22no—
244C2×C8×C47C2412yes—
245C2×C8×C47C2412yes—
246C4⋊C4×C47—21no—
247C4⋊C4×C47C2412yes—
248C22⋊C4×C47—24no—
249C22⋊C4×C47—24no—
250C22⋊C4×C47—24no—
251C42×C47C2×D412yes—
252C42×C47C2412yes—
253C22⋊Dic47—24no—
254C22⋊Dic47—24no—
255C22⋊Dic47—24no—
256#10625336—28no—
257#10625334—28no—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—24no—
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4C2×D414yes—
263(C2×D47)⋊C4C2×D414yes—
264C4⋊Dic47—24no—
265C4⋊Dic47—21no—
266C4⋊Dic47—21no—
267C4⋊Dic47—21no—
268C4⋊Dic47—24no—
269C4⋊Dic47C2412yes—
270C4⋊Dic47C2412yes—
271C4⋊Dic47C2412yes—
272Dic47⋊C4—24no—
273Dic47⋊C4C2×D414yes—
274Dic47⋊C4C2×D414yes—
275C4×Dic47—24no—
276C4×Dic47—24no—
277C4×Dic47C2×D412yes—
278C4×Dic47C2412yes—
279C2×C47⋊C8—22no—
280C2×C47⋊C8—22no—
281C2×C47⋊C8C2412yes—
282C2×C47⋊C8C2412yes—
283C23×C47—24no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—42no—
287C23×C47—42no—
288C23×C47—42no—
289C23×C47—42no—
290C23×C47—42no—
291C23×C47C22×D411yescharacteristic
292C22×D47—22no—
293C22×D47—24no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—216no—
298C22×D47—42no—
299C22×D47—42no—
300C22×D47—84no—
301C22×D47—84no—
302C22×D47—816no—
303C22×D47C22×D412yes—
304Q8×C47—22no—
305Q8×C47—22no—
306Q8×C47—42no—
307D4×C47—24no—
308D4×C47—22no—
309D4×C47—22no—
310D4×C47—22no—
311D4×C47—42no—
312D4×C47C2×#4114yes—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—22no—
316C2×C4×C47—22no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—84no—
320C2×C4×C47C22×D412yes—
321C2×C4×C47C22×D412yes—
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C2×#4112yes—
324C2×C4×C47C2×#4112yes—
325C2×C4×C47C2511yescharacteristic
326C22⋊D47—216no—
327C22⋊D47—84no—
328C2×Dic47—22no—
329C2×Dic47—22no—
330C2×Dic47—22no—
331C2×Dic47—22no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—84no—
338C2×Dic47—84no—
339C2×Dic47C22×D412yes—
340C2×Dic47C22×D412yes—
341C2×Dic47C22×D412yes—
342D188—24no—
343D188—22no—
344D188C2×#4114yes—
345C4×D47—24no—
346C4×D47—22no—
347C4×D47—22no—
348C4×D47—84no—
349C4×D47—84no—
350Dic94—84no—
351C8×C47—22no—
352C8×C47—22no—
353C47⋊C8—22no—
354C47⋊C8—22no—
355C2×#3118—471nomaximal, Sylow
356C22×C47—24no—
357C22×C47—48no—
358C22×C47—42no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47—42no—
362C22×C47—42no—
363C22×C47—84no—
364C22×C47#52512yes—
365C22×C47#57612yes—
366C22×C47#57712yes—
367C22×C47C23×D411yescharacteristic
368C2×D47—22no—
369C2×D47—24no—
370C2×D47—22no—
371C2×D47—22no—
372C2×D47—44no—
373C2×D47—48no—
374C2×D47—42no—
375C2×D47—42no—
376C2×D47—816no—
377C4×C47—22no—
378C4×C47—22no—
379C4×C47—42no—
380C4×C47—42no—
381C4×C47#52512yes—
382C4×C47C22×#4111yescharacteristic
383C4×C47C22×#4111yescharacteristic
384Dic47—22no—
385Dic47—22no—
386Dic47—22no—
387Dic47—42no—
388Dic47—42no—
389Dic47—42no—
390C2×#542—471no—
391C2×#518—471no—
392#3118—4716no—
393C2×#485—471no—
394C2×#482—471no—
395C2×#476—471no—
396C2×#474—471no—
397C2×#463—471no—
398C2×#463D4711yescharacteristic, complemented
399C2×#450—471no—
400C2×#447—471no—
401C2×#442—471no—
402C2×#440—471no—
403C2×C4×SD16—471no—
404C2×C4×D8—471no—
405C2×#433—471no—
406C2×C47—44no—
407C2×C47—82no—
408C2×C47#311814yescomplemented
409C2×C47C2×#52511yescharacteristic
410C2×C47C2×#57611yescharacteristic
411C2×C47C2×#57711yescharacteristic
412D47—42no—
413D47—44no—
414C23×D4—471no—
415C22×SD16—471no—
416C22×SD16C2×D4711yescharacteristic
417C22×D8—471no—
418C22×D8C2×D4711yescharacteristic
419#542—478no—
420#542—944no—
421C2×C4⋊Q8—471no—
422C2×#126—941no—
423C2×#124—941no—
424C2×#124C2×D4711yescharacteristic, complemented
425C2×#123—941no—
426C2×C22⋊Q8—471no—
427C2×C22⋊Q8—941no—
428C2×#121—471no—
429#518—478no—
430#518—944no—
431C2×C4×Q8—471no—
432C2×C4×D4—471no—
433C2×C4×D4—471no—
434C2×C4×D4—471no—
435C2×C4×D4—471no—
436C2×C4×D4—941no—
437C2×C4×D4—941no—
438C2×C4×D4C2×D4711yescharacteristic
439C2×#117—471no—
440C2×#117—471no—
441C22×C22⋊C4—941no—
442C22×C22⋊C4—941no—
443#485—478no—
444#482—478no—
445#476—478no—
446#474—478no—
447#463—478no—
448#463C2×D4718yescomplemented
449#450—478no—
450#447—478no—
451#442—478no—
452#440—478no—
453C4×SD16—478no—
454C4×D8—478no—
455#433—478no—
456C2×#107—471no—
457C2×#107—471no—
458C2×#106—471no—
459C2×#106—471no—
460C2×C4⋊C8—471no—
461C2×C4⋊C8C2×D4711yescharacteristic, complemented
462C2×#103—471no—
463C2×#103C2×D4711yescharacteristic, complemented
464C2×#102—471no—
465C2×#102—471no—
466C2×#102—471no—
467C2×#102—471no—
468C2×#102—471no—
469C2×#102C2×D4711yescharacteristic, complemented
470C2×C22⋊C8—471no—
471C2×C22⋊C8—471no—
472C2×#97—471no—
473C2×C4×C8—471no—
474C47C2×#311811yescharacteristic, complemented, Sylow
475C25—941no—
476C22×Q8—941no—
477C22×Q8C22×D4711yescharacteristic
478C22×D4—474no—
479C22×D4—471no—
480C22×D4—942no—
481C22×D4—941no—
482C22×D4—944no—
483C22×D4—944no—
484C22×D4—941no—
485C22×D4C22×D4711yescharacteristic
486C22×D4C22×D4711yescharacteristic
487C23×C4—21no—
488C23×C4—471no—
489C23×C4—941no—
490C23×C4—941no—
491C23×C4—941no—
492C23×C4—941no—
493C2×SD16—24no—
494C2×SD16—474no—
495C2×SD16—944no—
496C2×SD16C22×D4714yes—
497C2×D8—24no—
498C2×D8—474no—
499C2×D8—944no—
500C2×D8C22×D4714yes—
501C22×C8—471no—
502C22×C8—471no—
503C22×C8C22×D4711yescharacteristic
504C22×C8C22×D4711yescharacteristic
505C4⋊Q8—474no—
506C4⋊Q8—942no—
507#126—948no—
508#124—22no—
509#124—948no—
510#124C22×D4714yescomplemented
511#123—948no—
512C22⋊Q8—474no—
513C22⋊Q8—948no—
514C22⋊Q8—942no—
515#121—474no—
516#121—942no—
517C4×Q8—474no—
518C4×Q8—942no—
519C4×D4—22no—
520C4×D4—474no—
521C4×D4—474no—
522C4×D4—474no—
523C4×D4—474no—
524C4×D4—942no—
525C4×D4—942no—
526C4×D4—942no—
527C4×D4—948no—
528C4×D4—948no—
529C4×D4—942no—
530C4×D4C22×D4714yes—
531#117—474no—
532#117—474no—
533#117—474no—
534#117—942no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—471no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—471no—
540C2×C4⋊C4—941no—
541C2×C4⋊C4—941no—
542C2×C4⋊C4—941no—
543C2×C4⋊C4C22×D4711yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—471no—
548C2×C22⋊C4—471no—
549C2×C22⋊C4—948no—
550C2×C22⋊C4—948no—
551C2×C22⋊C4—941no—
552C2×C22⋊C4—941no—
553C2×C22⋊C4—941no—
554C2×C22⋊C4—941no—
555C2×C22⋊C4—941no—
556C2×C22⋊C4—941no—
557C2×C22⋊C4—941no—
558C2×C42—471no—
559C2×C42—941no—
560C2×C42—941no—
561C2×C42C22×D4711yescharacteristic
562#107—474no—
563#107—474no—
564#106—474no—
565#106—474no—
566C4⋊C8—474no—
567C4⋊C8C22×D4714yescomplemented
568#103—474no—
569#103C22×D4714yescomplemented
570#102—474no—
571#102—474no—
572#102—474no—
573#102—474no—
574#102—474no—
575#102C22×D4714yescomplemented
576C22⋊C8—474no—
577C22⋊C8—474no—
578#97—474no—
579C4×C8—474no—
580C24—21no—
581C24—21no—
582C24—471no—
583C24—944no—
584C24—948no—
585C24—941no—
586C24—3762no—
587C24—3762no—
588C2×Q8—21no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—944no—
592C2×Q8—3762no—
593C2×Q8C23×D4712yes—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—474no—
600C2×D4—472no—
601C2×D4—944no—
602C2×D4—948no—
603C2×D4—9416no—
604C2×D4—948no—
605C2×D4—948no—
606C2×D4—944no—
607C2×D4—941no—
608C2×D4—942no—
609C2×D4—3762no—
610C2×D4#1062535214yes—
611C2×D4C23×D4712yes—
612C2×D4C23×D4712yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—82no—
617C22×C4—471no—
618C22×C4—471no—
619C22×C4—471no—
620C22×C4—472no—
621C22×C4—472no—
622C22×C4—944no—
623C22×C4—944no—
624C22×C4—944no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—941no—
628C22×C4—941no—
629C22×C4—941no—
630C22×C4—944no—
631C22×C4—3762no—
632C22×C4—3762no—
633C22×C4—3762no—
634C22×C4—3762no—
635C22×C4D4×D4711yescharacteristic
636C22×C4D4×D4711yescharacteristic
637C22×C4C23×D4711yescharacteristic
638SD16—28no—
639SD16—948no—
640D8—28no—
641D8—948no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—472no—
645C2×C8—472no—
646C2×C8—942no—
647C2×C8—942no—
648C2×C8C23×D4712yes—
649C2×C8C23×D4712yes—
650C4⋊C4—21no—
651C4⋊C4—474no—
652C4⋊C4—474no—
653C4⋊C4—472no—
654C4⋊C4—472no—
655C4⋊C4—472no—
656C4⋊C4—944no—
657C4⋊C4—944no—
658C4⋊C4—941no—
659C4⋊C4—941no—
660C4⋊C4—941no—
661C4⋊C4—944no—
662C4⋊C4C23×D4712yes—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—474no—
667C22⋊C4—474no—
668C22⋊C4—944no—
669C22⋊C4—944no—
670C22⋊C4—944no—
671C22⋊C4—944no—
672C22⋊C4—944no—
673C22⋊C4—944no—
674C22⋊C4—944no—
675C42—472no—
676C42—472no—
677C42—944no—
678C42—944no—
679C42D4×D4712yes—
680C42C23×D4712yes—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—472no—
690C23—9416no—
691C23—942no—
692C23—944no—
693C23—942no—
694C23—942no—
695C23—942no—
696C23—3764no—
697C23—3764no—
698C23—37616no—
699C23—1882no—
700C23—1882no—
701C23C2×D4×D4711yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—42no—
705Q8—3764no—
706D4—24no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—42no—
711D4—474no—
712D4—9416no—
713D4—944no—
714D4—942no—
715D4—3764no—
716D4C2×#1062535214yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—84no—
724C2×C4—472no—
725C2×C4—472no—
726C2×C4—472no—
727C2×C4—942no—
728C2×C4—942no—
729C2×C4—942no—
730C2×C4—944no—
731C2×C4—942no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—3764no—
737C2×C4—3764no—
738C2×C4—3764no—
739C2×C4—3764no—
740C2×C4—1882no—
741C2×C4—1882no—
742C2×C4—1882no—
743C2×C4C2×D4×D4712yes—
744C2×C4C2×D4×D4712yes—
745C2×C4C2×D4×D4711yescharacteristic
746C2×C4#41×D4712yes—
747C2×C4C2×#1062535212yes—
748C2×C4C24×D4711yescharacteristic
749C8—22no—
750C8—22no—
751C8—942no—
752C8—942no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—48no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—942no—
762C22—942no—
763C22—942no—
764C22—944no—
765C22—37616no—
766C22—1882no—
767C22—1882no—
768C22—1884no—
769C22—1888no—
770C22#1568963312yes—
771C22#1568992512yes—
772C22#1568993312yes—
773C22C22×D4×D4711yescharacteristic
774C4—22no—
775C4—22no—
776C4—42no—
777C4—42no—
778C4—942no—
779C4—942no—
780C4—942no—
781C4—1882no—
782C4—1882no—
783C4—1882no—
784C4#1568963312yes—
785C4C2×#41×D4711yescharacteristic
786C4C22×#1062535211yescharacteristic
787C2—44no—
788C2—82no—
789C2—1882no—
790C2—1884no—
791C2#2025356914yesdirect product factor
792C2C2×#1568963311yescharacteristic
793C2C2×#1568992511yescharacteristic
794C2C2×#1568993311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#463C2
socleC23×C47C22×D4
prime radicalC2×#15689255C2
hypercenterC2×#463D47
hypocenterC47C2×#3118
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#15689742C2semidirect
2. C2×#15689595C2semidirect
3. #20253569C2direct (N × H)
4. C2×#15689463C2semidirect
5. C2×#15689445C2semidirect
6. C2×#15689413C2semidirect
7. C2×#15689404C2semidirect
8. C2×#15689335C2semidirect
9. C2×#15689272C2semidirect
11. C2×#15689232C2semidirect
12. C2×#15689224C2semidirect
13. C2×#15689208C2semidirect
14. C2×D8×Dic47C2semidirect
15. C2×#15689183C2semidirect
16. C2×C47×#463C2semidirect
21. #15689742C22semidirect
22. C2×#13094024C22semidirect
30. #15689595C22semidirect
31. C2×Q8×Dic47C22semidirect
34. C2×D4×Dic47C22semidirect
42. #15689463C22semidirect
43. #15689445C22semidirect
44. #15689413C22semidirect
45. #15689404C22semidirect
46. #15689335C22semidirect
47. #15689272C22semidirect
49. #15689232C22semidirect
50. #15689224C22semidirect
51. #15689208C22semidirect
52. D8×Dic47C22semidirect
53. #15689183C22semidirect
54. C2×#13093958C22semidirect
55. C2×#13093958C22semidirect
56. C2×#13093955C22semidirect
57. C2×#13093955C22semidirect
58. C2×C4⋊(C47⋊C8)C22semidirect
59. C2×#13093948C22semidirect
64. C2×#13093945C22semidirect
67. C2×#13093934C22semidirect
68. C2×C8×Dic47C22semidirect
71. C2×#124×C47C22semidirect
73. C47×#463C22semidirect
74. C2×C4⋊C8×C47C22semidirect
75. C2×#103×C47C22semidirect
76. C2×#102×C47C22semidirect
98. #13094024C23semidirect
108. Q8×Dic47C23semidirect
114. D4×Dic47C23semidirect
145. #13093958C23semidirect
146. #13093958C23semidirect
147. #13093955C23semidirect
148. #13093955C23semidirect
149. C4⋊(C47⋊C8)C23semidirect
150. #13093948C23semidirect
155. #13093945C23semidirect
158. #13093934C23semidirect
159. C8×Dic47C23semidirect
171. #124×C47C23semidirect
179. C4⋊C8×C47C23semidirect
180. #103×C47C23semidirect
181. #102×C47C23semidirect
398. C2×#463D47semidirect
408. C2×C47#3118semidirect
424. C2×#124C2×D47semidirect
448. #463C2×D47semidirect
461. C2×C4⋊C8C2×D47semidirect
463. C2×#103C2×D47semidirect
469. C2×#102C2×D47semidirect
474. C47C2×#3118semidirect
510. #124C22×D47semidirect
567. C4⋊C8C22×D47semidirect
569. #103C22×D47semidirect
575. #102C22×D47semidirect
791. C2#20253569direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897422
C2×#156895952
#202535692
C2×#156894632
C2×#156894452
C2×#156894132
C2×#156894042
C2×#156893352
C2×#156892722
C2×#156892552
C2×#156892322
C2×#156892242
C2×#156892082
C2×D8×Dic472
C2×#156891832
C2×C47×#4632
C2×#311847