Finite Group Databasebeta

← #26236546

Subgroups — #26236546

Order 12032.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689262C211yesmaximal, characteristic
2C2×#15689221C211yesmaximal, characteristic, complemented
3C22×#13093948C211yesmaximal, characteristic, complemented
4#20246402C211yesmaximal, characteristic
5#20244272C211yesmaximal, characteristic, complemented
6#20244081C211yesmaximal, characteristic, complemented
7#20244026C211yesmaximal, characteristic, complemented
8#20243814C211yesmaximal, characteristic
9#20243743C211yesmaximal, characteristic, complemented
10#20243725C211yesmaximal, characteristic, complemented
11#20243642C211yesmaximal, characteristic, complemented
12#20243575C211yesmaximal, characteristic, complemented
13#20243218C211yesmaximal, characteristic, complemented
14#20243166C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C47C211yesmaximal, characteristic, complemented
16C22×#10625336C2211yescharacteristic
17C22×#10625336C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19C2×#13093998C2211yescharacteristic
20C2×C4×D188C2211yescharacteristic
21C2×(C22⋊D47)⋊C4—21no—
22C22×C4⋊Dic47C2211yescharacteristic
23#15689262C418yescomplemented
24#15689221—24no—
25C2×#13093957C2211yescharacteristic
26C2×#13093957C2211yescharacteristic
27C2×#13093948—24no—
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093948C2211yescharacteristic
31C2×#13093948C2211yescharacteristic
32C2×#13093948C2211yescharacteristic
33C2×#13093948C2211yescharacteristic
34C2×#13093944C2211yescharacteristic
35C2×#13093944C2211yescharacteristic
36C2×C22⋊(C47⋊C8)C2211yescharacteristic
37C2×#13093935C2211yescharacteristic
38C2×#13093935C2211yescharacteristic
39#15689025C2211yescharacteristic
40#15689021C2211yescharacteristic
41#15689015—21no—
42#15689000—21no—
43#15688997—21no—
44C4×C4⋊Dic47C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51C23×Q8×C47C2211yescharacteristic
52C2×C4×Q8×C47C2211yescharacteristic
53C2×C4×Q8×C47C2211yescharacteristic
54C47×#391—21no—
55C47×#391—21no—
56C47×#391C2211yescharacteristic
57C47×#391C2211yescharacteristic
58C47×#380—21no—
59C47×#380C2211yescharacteristic
60C4×C22⋊C4×C47—21no—
61C4×C22⋊C4×C47C2211yescharacteristic
62C22×D188C2311yescharacteristic
63C22×C22⋊D47—21no—
64C23×Dic47—21no—
65C22×C4×D47—21no—
66C2×#10625336—22no—
67C2×#10625336—22no—
68C2×#10625336—41no—
69C2×#10625336—41no—
70C2×#10625336C2×C414yescomplemented
71C2×#10625336C2×C414yescomplemented
72C22×C47⋊C8—22no—
73C22×C47⋊C8—22no—
74C22×C47⋊C8—41no—
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79#13093998—22no—
80#13093998C2×C414yes—
81C4×D188—22no—
82C4×D188—41no—
83(C22⋊D47)⋊C4—44no—
84C2×C4⋊Dic47—22no—
85C2×C4⋊Dic47—21no—
86C2×C4⋊Dic47—41no—
87C2×C4⋊Dic47C2311yescharacteristic
88C2×C4⋊Dic47C2311yescharacteristic
89C2×C4⋊Dic47C2311yescharacteristic
90C2×Dic47⋊C4—21no—
91C2×(C2×D47)⋊C4—21no—
92C2×(C2×D47)⋊C4—21no—
93C2×(C2×D47)⋊C4—21no—
94C2×(C2×D47)⋊C4—21no—
95C2×C4×Dic47—21no—
96#13093957—22no—
97#13093957—41no—
98#13093948—22no—
99#13093948—22no—
100#13093948—22no—
101#13093948C2×C414yescomplemented
102#13093948C2×C414yescomplemented
103#13093948D414yescomplemented
104#13093944—22no—
105#13093944—41no—
106C22⋊(C47⋊C8)C2×C414yescomplemented
107#13093935—22no—
108#13093935—41no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C22×Q8×C47—21no—
112C22×Q8×C47—22no—
113C22×Q8×C47—22no—
114C22×Q8×C47—22no—
115C22×Q8×C47—41no—
116C22×Q8×C47—41no—
117C22×Q8×C47C2×C414yescomplemented
118C22×Q8×C47C2311yescharacteristic
119C22×Q8×C47C2311yescharacteristic
120C23×C4×C47—21no—
121C23×C4×C47C2311yescharacteristic
122C4×Q8×C47—22no—
123C4×Q8×C47—22no—
124C4×Q8×C47—41no—
125C4×Q8×C47—41no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C22⋊C4×C47—21no—
131C2×C22⋊C4×C47D411yescharacteristic
132C2×C22⋊C4×C47D411yescharacteristic
133C2×C42×C47—21no—
134C2×C42×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C2×C42×C47C2311yescharacteristic
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47D411yescharacteristic
143#95×C47D411yescharacteristic
144C24×C47C2×D411yescharacteristic
145C23×D47—21no—
146C2×Q8×C47—24no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—28no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—42no—
157C2×Q8×C47—42no—
158C2×Q8×C47—44no—
159C2×Q8×C47—44no—
160C2×Q8×C47—44no—
161C2×Q8×C47C22×C412yes—
162C2×Q8×C47C22×C412yes—
163C2×Q8×C47C2×D412yes—
164C2×Q8×C47#4112yes—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—24no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—42no—
175C22×C4×C47—42no—
176C22×C4×C47C22×C412yes—
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47#4112yes—
183C22×C4×C47C2411yescharacteristic
184C2×C22⋊D47—24no—
185C2×C22⋊D47—42no—
186C2×C22⋊D47—42no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—42no—
191C22×Dic47—42no—
192C22×Dic47—81no—
193C2×D188—21no—
194C2×D188—21no—
195C2×D188—21no—
196C2×D188—21no—
197C2×D188—21no—
198C2×D188C22×C412yes—
199C2×C4×D47—42no—
200C2×C4×D47—42no—
201C2×C4×D47—81no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—42no—
207C4⋊C4×C47—42no—
208C22⋊C4×C47—22no—
209C22⋊C4×C47—22no—
210C22⋊C4×C47—42no—
211C42×C47—21no—
212C42×C47—21no—
213C42×C47—21no—
214C42×C47—21no—
215C42×C47—42no—
216C42×C47—42no—
217#10625336—28no—
218#10625336—44no—
219(C2×D47)⋊C4—24no—
220(C2×D47)⋊C4—42no—
221(C2×D47)⋊C4—42no—
222(C2×D47)⋊C4—81no—
223C4⋊Dic47—21no—
224C4⋊Dic47—21no—
225C4⋊Dic47—21no—
226C4⋊Dic47—21no—
227C4⋊Dic47—42no—
228C4⋊Dic47C22×C412yes—
229C4⋊Dic47C2×D412yes—
230Dic47⋊C4—42no—
231C4×Dic47—42no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—21no—
237C2×C47⋊C8—21no—
238C2×C47⋊C8—21no—
239C2×C47⋊C8—21no—
240C2×C47⋊C8—21no—
241C2×C47⋊C8—44no—
242C2×C47⋊C8C22×C412yes—
243C2×C47⋊C8C22×C412yes—
244C2×C47⋊C8C2×D412yes—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47C4×D412yes—
250C23×C47AGL(1,ℤ/8)12yes—
251C23×C47#13712yes—
252C23×C47C22×D411yescharacteristic
253C22×D47—22no—
254C22×D47—41no—
255C22×D47—41no—
256C22×D47—41no—
257C22×D47—41no—
258C22×D47—41no—
259C22×D47—41no—
260Q8×C47—22no—
261Q8×C47—22no—
262Q8×C47—22no—
263Q8×C47—22no—
264Q8×C47—22no—
265Q8×C47—48no—
266Q8×C47—41no—
267Q8×C47—41no—
268Q8×C47C4×D414yescomplemented
269C2×C4×C47—22no—
270C2×C4×C47—21no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—21no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—21no—
291C2×C4×C47—48no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47C4×D412yes—
301C2×C4×C47C23×C411yescharacteristic
302C2×C4×C47C22×D411yescharacteristic
303C2×C4×C47C2×#4111yescharacteristic
304C2×C4×C47C2×#4111yescharacteristic
305C2×C4×C47H(5,𝔽2)11yescharacteristic
306C2×C4×C47H(5,𝔽2)11yescharacteristic
307C22⋊D47—48no—
308C2×Dic47—22no—
309C2×Dic47—22no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C2×Dic47—41no—
313C2×Dic47—41no—
314C2×Dic47—41no—
315C2×Dic47—41no—
316C2×Dic47—41no—
317C2×Dic47—84no—
318D188—22no—
319D188—22no—
320D188—41no—
321D188—41no—
322C4×D47—84no—
323C47⋊C8—22no—
324C47⋊C8—22no—
325C47⋊C8—22no—
326C47⋊C8—41no—
327#22855—471nomaximal, Sylow
328C22×C47—22no—
329C22×C47—22no—
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—22no—
333C22×C47—22no—
334C22×C47#44014yescomplemented
335C22×C47C2×C4×D411yescharacteristic
336C22×C47D4211yescharacteristic
337C22×C47#54611yescharacteristic
338C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C47C2×#13711yescharacteristic
340C22×C47#57711yescharacteristic
341C22×C47#57811yescharacteristic
342C2×D47—42no—
343C2×D47—42no—
344C2×D47—42no—
345C2×D47—81no—
346C2×D47—81no—
347C2×D47—81no—
348C2×D47—81no—
349C4×C47—22no—
350C4×C47—24no—
351C4×C47—42no—
352C4×C47—41no—
353C4×C47—41no—
354C4×C47—41no—
355C4×C47—41no—
356C4×C47—81no—
357C4×C47—81no—
358C4×C47C2×C4×D411yescharacteristic
359C4×C47#51811yescharacteristic
360C4×C47#54611yescharacteristic
361C4×C47#55111yescharacteristic
362Dic47—42no—
363Dic47—42no—
364Dic47—81no—
365C2×#448—471no—
366C2×#440—471no—
367C22×#103—471no—
368#2361—471no—
369Q8×C22⋊C4D4711yescharacteristic, complemented
370#1973—471no—
371#1935—471no—
372#1928—471no—
373#1893—471no—
374#1880—471no—
375#1877—471no—
376#1863—471no—
377#1852—471no—
378#1763—471no—
379#1752—471no—
380C2×C47—24no—
381C2×C47#235811yescharacteristic
382C2×C47C2×#44011yescharacteristic
383C2×C47#294711yescharacteristic
384C2×C47#326511yescharacteristic
385C2×C47#327011yescharacteristic
386C2×C47#330811yescharacteristic
387C2×C47#332011yescharacteristic
388D47—82no—
389C23×Q8C2×D4711yescharacteristic
390C22×SD16—471no—
391C22×SD16—471no—
392C23×C8—471no—
393C2×#121—471no—
394C2×C4×Q8C2×D4711yescharacteristic
395C2×C4×Q8C2×D4711yescharacteristic
396C2×C4×D4—471no—
397C2×C4×D4—941no—
398C22×C4⋊C4—471no—
399#448—478no—
400#440—944no—
401C2×#107—471no—
402C2×#107—471no—
403C2×#103—471no—
404C2×#103—471no—
405C2×#103—471no—
406C2×#103—471no—
407C2×#103—471no—
408C2×#103—471no—
409C2×#103—944no—
410C2×#102—471no—
411C2×#102—471no—
412C2×C22⋊C8—471no—
413C2×#97—471no—
414C2×#97—471no—
415#391—21no—
416#391—21no—
417#391C2×D4711yescharacteristic
418#391C2×D4711yescharacteristic
419#390—471no—
420#389—471no—
421#388—941no—
422#386—941no—
423#385—941no—
424#380—21no—
425#380C2×D4711yescharacteristic
426C4×C4⋊C4—471no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4C2×D4711yescharacteristic
429#340—471no—
430#340—471no—
431#340—471no—
432#340—471no—
433#336—471no—
434#336—471no—
435C47#2285511yescharacteristic, complemented, Sylow
436C22×Q8—22no—
437C22×Q8—21no—
438C22×Q8—22no—
439C22×Q8—22no—
440C22×Q8—41no—
441C22×Q8—41no—
442C22×Q8C4×D4714yescomplemented
443C22×Q8C22×D4711yescharacteristic
444C22×Q8C22×D4711yescharacteristic
445C22×D4—471no—
446C22×D4—941no—
447C23×C4—21no—
448C23×C4—941no—
449C23×C4—941no—
450C23×C4C22×D4711yescharacteristic
451C2×SD16—474no—
452C2×SD16—474no—
453C2×SD16—942no—
454C2×SD16—942no—
455C2×SD16—1881no—
456C2×SD16—1881no—
457C22×C8—471no—
458C22×C8—471no—
459C22×C8—471no—
460C22×C8—471no—
461C22×C8—942no—
462C22×C8—942no—
463C22×C8—1881no—
464#121—474no—
465#121—942no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—41no—
469C4×Q8—41no—
470C4×D4—942no—
471C4×D4—1881no—
472C4×D4—1884no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—471no—
476C2×C4⋊C4—471no—
477C2×C4⋊C4—471no—
478C2×C4⋊C4—942no—
479C2×C4⋊C4—941no—
480C2×C4⋊C4—941no—
481C2×C4⋊C4—1881no—
482C2×C4⋊C4C22×D4711yescharacteristic
483C2×C4⋊C4C22×D4711yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—941no—
486C2×C22⋊C4—941no—
487C2×C22⋊C4—941no—
488C2×C22⋊C4—941no—
489C2×C22⋊C4C22⋊D4711yescharacteristic
490C2×C22⋊C4C22⋊D4711yescharacteristic
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—941no—
494C2×C42C22×D4711yescharacteristic
495C2×C42C22×D4711yescharacteristic
496#107—942no—
497#107—1881no—
498#103—474no—
499#103—474no—
500#103—474no—
501#103—942no—
502#103—942no—
503#103—942no—
504#102—942no—
505#102—1881no—
506C22⋊C8—474no—
507#97—942no—
508#97—1881no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—941no—
515#95—941no—
516#95C22⋊D4711yescharacteristic
517#95C22⋊D4711yescharacteristic
518C24—941no—
519C24C2×C22⋊D4711yescharacteristic
520C2×Q8—24no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—28no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—42no—
531C2×Q8—42no—
532C2×Q8—44no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8C2×C4×D4712yes—
536C2×Q8C2×C4×D4712yes—
537C2×Q8D4×D4712yes—
538C2×Q8#1062535212yes—
539C2×D4—472no—
540C2×D4—944no—
541C2×D4—941no—
542C2×D4—941no—
543C2×D4—941no—
544C2×D4—941no—
545C2×D4—941no—
546C2×D4—1882no—
547C2×D4—1882no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—3761no—
563C22×C4—3761no—
564C22×C4—1882no—
565C22×C4—1882no—
566C22×C4—1882no—
567C22×C4—1882no—
568C22×C4C2×C4×D4712yes—
569C22×C4#1062535012yes—
570C22×C4C2×C22⋊D4711yescharacteristic
571C22×C4C2×C22⋊D4711yescharacteristic
572C22×C4C2×C22⋊D4711yescharacteristic
573C22×C4C2×C22⋊D4711yescharacteristic
574C22×C4C2×C22⋊D4711yescharacteristic
575C22×C4C23×D4711yescharacteristic
576SD16—948no—
577SD16—1884no—
578C2×C8—472no—
579C2×C8—472no—
580C2×C8—472no—
581C2×C8—941no—
582C2×C8—941no—
583C2×C8—941no—
584C2×C8—941no—
585C2×C8—941no—
586C2×C8—941no—
587C2×C8—941no—
588C2×C8—941no—
589C2×C8—941no—
590C2×C8—1884no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—472no—
598C4⋊C4—472no—
599C4⋊C4—941no—
600C4⋊C4—941no—
601C4⋊C4—941no—
602C4⋊C4—941no—
603C4⋊C4—1882no—
604C4⋊C4—1882no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—42no—
608C22⋊C4—944no—
609C22⋊C4—3761no—
610C22⋊C4—1882no—
611C22⋊C4—1882no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—42no—
617C42—42no—
618C42—1882no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—942no—
624C23—1881no—
625C23—1881no—
626C23—1881no—
627C23—1881no—
628C23—1881no—
629C23—1881no—
630C23C4×C22⋊D4712yes—
631C23#1309404912yes—
632C23#1309405512yes—
633C23C22×C22⋊D4711yescharacteristic
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—22no—
638Q8—22no—
639Q8—48no—
640Q8—41no—
641Q8—41no—
642Q8(C22⋊D47)⋊C414yescomplemented
643D4—942no—
644D4—942no—
645D4—1888no—
646D4—1881no—
647D4—1881no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—48no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—942no—
680C2×C4—942no—
681C2×C4—3764no—
682C2×C4—3764no—
683C2×C4—1881no—
684C2×C4—1881no—
685C2×C4—1881no—
686C2×C4—1881no—
687C2×C4—1881no—
688C2×C4—1881no—
689C2×C4—1881no—
690C2×C4C4×C22⋊D4712yes—
691C2×C4C22×C4×D4711yescharacteristic
692C2×C4C2×D4×D4711yescharacteristic
693C2×C4C2×#1062535211yescharacteristic
694C2×C4C2×#1062535011yescharacteristic
695C2×C4#1309406911yescharacteristic
696C2×C4#1309406911yescharacteristic
697C8—942no—
698C8—942no—
699C8—942no—
700C8—1881no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—3761no—
708C22—3761no—
709C22—3761no—
710C22—3761no—
711C22—1882no—
712C22—1882no—
713C22—1882no—
714C22#1568922114yescomplemented
715C22C2×C4×C22⋊D4711yescharacteristic
716C22D4×C22⋊D4711yescharacteristic
717C22#1568976711yescharacteristic
718C22C2×#1309404911yescharacteristic
719C22C2×#1309405511yescharacteristic
720C22#1568993111yescharacteristic
721C22#1568993811yescharacteristic
722C4—22no—
723C4—24no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—81no—
730C4—81no—
731C4—3761no—
732C4—1882no—
733C4—1882no—
734C4C2×(C22⋊D47)⋊C411yescharacteristic
735C4#1568959611yescharacteristic
736C4#1568976311yescharacteristic
737C4#1568979911yescharacteristic
738C2—24no—
739C2—3762no—
740C2#2024636711yescharacteristic
741C2C2×#1568922111yescharacteristic
742C2#2025223111yescharacteristic
743C2#2025488411yescharacteristic
744C2#2025495911yescharacteristic
745C2#2025537911yescharacteristic
746C2#2025555911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingQ8×C22⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
cosocleC22×C4×C47C24
hypercenterQ8×C22⋊C4D47
hypocenterC47#22855
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15689221C2semidirect
3. C22×#13093948C2semidirect
5. #20244272C2semidirect
6. #20244081C2semidirect
7. #20244026C2semidirect
9. #20243743C2semidirect
10. #20243725C2semidirect
11. #20243642C2semidirect
12. #20243575C2semidirect
13. #20243218C2semidirect
14. #20243166C2semidirect
15. Q8×C22⋊C4×C47C2semidirect
23. #15689262C4semidirect
70. C2×#10625336C2×C4semidirect
71. C2×#10625336C2×C4semidirect
101. #13093948C2×C4semidirect
102. #13093948C2×C4semidirect
103. #13093948D4semidirect
106. C22⋊(C47⋊C8)C2×C4semidirect
117. C22×Q8×C47C2×C4semidirect
268. Q8×C47C4×D4semidirect
334. C22×C47#440semidirect
369. Q8×C22⋊C4D47semidirect
435. C47#22855semidirect
442. C22×Q8C4×D47semidirect
642. Q8(C22⋊D47)⋊C4semidirect
714. C22#15689221semidirect

Maximal subgroups

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

subgroupindex
C2×#156892622
C2×#156892212
C22×#130939482
#202464022
#202442722
#202440812
#202440262
#202438142
#202437432
#202437252
#202436422
#202435752
#202432182
#202431662
Q8×C22⋊C4×C472
#2285547