Finite Group Databasebeta

← #27080605

Subgroups — #27080605

Order 12032.

2628 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689921C211yesmaximal, characteristic
2C2×#15689889C211yesmaximal, characteristic, complemented
3#20252303C218yesmaximal, complemented
4#20252295C218yesmaximal, complemented
5#20252289C218yesmaximal, complemented
6C2×#15689171C211yesmaximal, characteristic, complemented
7C2×#15689140C211yesmaximal, characteristic, complemented
8C2×#15689139C211yesmaximal, characteristic, complemented
9#20251806C211yesmaximal, characteristic, complemented
10C2×C47×#568C211yesmaximal, characteristic, complemented
11C22×#10625350C2211yescharacteristic
12#15689921C414yescomplemented
13#15689921C414yescomplemented
14#15689921C2214yes—
15#15689921C2214yes—
16C2×#13094055C412yescomplemented
17C2×#13094054C412yescomplemented
18C2×#13094050C412yescomplemented
19C2×#13094049C412yescomplemented
20C2×#13094044C2214yes—
21#15689889—22no—
22#15689889—22no—
23#15689889C2214yescomplemented
24#15689889C2214yescomplemented
25C2×#13094032—22no—
26C2×#13094030C2214yescomplemented
27C22×#10625329C2211yescharacteristic
28C22×#10625329C2211yescharacteristic
29C2×M16×D47—22no—
30C2×#13093983C2211yescharacteristic
31#15689243C22132yescomplemented
32#15689238C22132yescomplemented
33#15689171C2214yescomplemented
34#15689171C2214yescomplemented
35C2×#13093959C2214yescomplemented
36#15689140C2214yescomplemented
37#15689140C2214yescomplemented
38#15689139C2214yescomplemented
39#15689139C2214yescomplemented
40C2×#13093951C2214yescomplemented
41C2×#13093950C2214yescomplemented
42#15689081C2214yescomplemented
43#15689078C2214yescomplemented
44M16×Dic47C2214yescomplemented
45C22×#41×C47C2211yescharacteristic
46C47×#568—22no—
47C47×#568—22no—
48C47×#568C2214yescomplemented
49C47×#568C2214yescomplemented
50C2×#131×C47—22no—
51C2×#131×C47C2214yescomplemented
52C22×M16×C47—22no—
53C22×M16×C47C2211yescharacteristic
54C22×M16×C47C2211yescharacteristic
55C2×#10625350—21no—
56C2×#10625350—21no—
57C2×#10625350—21no—
58C2×#10625350—21no—
59C2×#10625350—21no—
60C2×#10625350—21no—
61C2×#10625350C2×C412yes—
62C2×#10625350C2×C412yes—
63C2×#10625350C2×C412yes—
64C2×#10625350C2312yes—
65C2×#10625350C2312yes—
66C2×#10625350C2312yes—
67C22×Dic94C2×C411yescharacteristic
68C22×D188C2×C411yescharacteristic
69C22×C22⋊D47—21no—
70C22×C4×D47—21no—
71#13094055C2×C418yes—
72#13094055C2×C418yescomplemented
73#13094054C2×C418yes—
74#13094054C2×C418yescomplemented
75#13094050C2×C418yes—
76#13094050C2×C418yescomplemented
77#13094049C2×C418yes—
78#13094049C2×C418yescomplemented
79#13094044C2×C4116yescomplemented
80#13094044C23116yes—
81C2×#10625337C2×C414yescomplemented
82C2×#10625335C2×C414yescomplemented
83C2×#10625336C2×C414yescomplemented
84C2×#10625334C2×C414yescomplemented
85#13094032—28no—
86#13094032—28no—
87#13094030—28no—
88#13094030C23116yescomplemented
89C2×#10625329—21no—
90C2×#10625329—21no—
91C2×#10625329—21no—
92C2×#10625329C2×C412yes—
93C2×#10625329C2×C412yes—
94C2×#10625329C2×C412yes—
95C2×#10625329C2×C412yes—
96C2×#10625329C2312yes—
97C2×#10625329C2312yes—
98C2×#10625329C2312yes—
99C2×#10625329C2312yes—
100C2×#10625329C2312yes—
101C2×#10625324—24no—
102M16×D47—28no—
103M16×D47—28no—
104C22×C47⋊C8—21no—
105C22×C47⋊C8C2312yes—
106C2×C8×D47—24no—
107#13093983—21no—
108#13093983—21no—
109#13093983C2312yes—
110#13093983C2312yes—
111C2×C4⋊Dic47—21no—
112C2×C22⋊Dic47—21no—
113C2×C4×Dic47C2312yes—
114#13093959C23116yescomplemented
115#13093951C23116yescomplemented
116#13093950C23116yescomplemented
117#13093934C2318yescomplemented
118C8×Dic47C2318yescomplemented
119C2×#41×C47—21no—
120C2×#41×C47—21no—
121C2×#41×C47—21no—
122C2×#41×C47—21no—
123C2×#41×C47—21no—
124C2×#41×C47—21no—
125C2×#41×C47C2×C412yes—
126C2×#41×C47C2×C412yes—
127C2×#41×C47C2×C412yes—
128C2×#41×C47C2312yes—
129C2×#41×C47C2312yes—
130C2×#41×C47C2312yes—
131C22×Q8×C47C2×C411yescharacteristic
132C22×D4×C47—21no—
133C22×D4×C47C2×C411yescharacteristic
134C23×C4×C47—21no—
135C23×C4×C47C2311yescharacteristic
136#131×C47—28no—
137#131×C47—28no—
138#131×C47—28no—
139#131×C47C23116yescomplemented
140C2×M16×C47—21no—
141C2×M16×C47—21no—
142C2×M16×C47—21no—
143C2×M16×C47—28no—
144C2×M16×C47—28no—
145C2×M16×C47—24no—
146C2×M16×C47D412yes—
147C2×M16×C47D412yes—
148C2×M16×C47D412yes—
149C2×M16×C47D412yes—
150C2×M16×C47C2312yes—
151C2×M16×C47C2312yes—
152C2×M16×C47C2312yes—
153C2×M16×C47C2312yes—
154C2×M16×C47C2312yes—
155C22×C8×C47—21no—
156C22×C8×C47—24no—
157C22×C8×C47C2312yes—
158C24×C47—21no—
159C24×C47#4111yescharacteristic
160C23×D47—21no—
161#41×C47—22no—
162#41×C47—22no—
163#41×C47—22no—
164#41×C47—22no—
165#41×C47—22no—
166#41×C47—22no—
167#41×C47—22no—
168#41×C47—22no—
169#41×C47—22no—
170#41×C47—22no—
171#41×C47—22no—
172#41×C47—22no—
173#41×C47C22×C414yes—
174#41×C47C22×C414yes—
175#41×C47C22×C414yes—
176#41×C47C2414yes—
177C2×Q8×C47—21no—
178C2×Q8×C47—21no—
179C2×Q8×C47—21no—
180C2×Q8×C47C22×C412yes—
181C2×Q8×C47C22×C412yes—
182C2×Q8×C47C22×C412yes—
183C2×D4×C47—22no—
184C2×D4×C47—22no—
185C2×D4×C47—22no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47—22no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47C22×C412yes—
193C2×D4×C47C22×C412yes—
194C2×D4×C47C22×C412yes—
195C22×C4×C47—21no—
196C22×C4×C47—22no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47C22×C411yescharacteristic
203C22×C4×C47C22×C411yescharacteristic
204C22×C4×C47C22×C411yescharacteristic
205C22×C4×C47C22×C411yescharacteristic
206C22×C4×C47C2×D411yescharacteristic
207C22×C4×C47C2×D411yescharacteristic
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47#4111yescharacteristic
211C22×C4×C47#4111yescharacteristic
212C22×C4×C47#4111yescharacteristic
213C22×C4×C47C2411yescharacteristic
214C22×C4×C47C2411yescharacteristic
215C22×C4×C47C2411yescharacteristic
216C2×C22⋊D47—22no—
217C2×C22⋊D47—22no—
218C2×C22⋊D47—22no—
219C2×C22⋊D47—22no—
220C2×C22⋊D47—22no—
221C2×C22⋊D47—22no—
222C22×Dic47—21no—
223C22×Dic47—22no—
224#10625350—22no—
225#10625350—22no—
226#10625350—22no—
227#10625350—22no—
228#10625350—22no—
229#10625350—22no—
230#10625350—22no—
231#10625350—22no—
232#10625350—22no—
233#10625350—22no—
234#10625350—22no—
235#10625350—22no—
236#10625350C22×C414yes—
237#10625350C22×C414yes—
238#10625350C22×C414yes—
239#10625350C2414yes—
240C2×D188—21no—
241C2×D188—21no—
242C2×D188—21no—
243C2×D188C22×C412yes—
244C2×D188C22×C412yes—
245C2×D188C22×C412yes—
246C2×C4×D47—22no—
247C2×C4×D47—22no—
248C2×C4×D47—22no—
249C2×C4×D47—22no—
250C2×C4×D47—22no—
251C2×C4×D47—22no—
252C2×Dic94—21no—
253C2×Dic94—21no—
254C2×Dic94—21no—
255C2×Dic94C22×C412yes—
256C2×Dic94C22×C412yes—
257C2×Dic94C22×C412yes—
258M16×C47—22no—
259M16×C47—22no—
260M16×C47—22no—
261M16×C47—216no—
262M16×C47C2×D414yes—
263M16×C47C2×D414yes—
264M16×C47C2×D414yes—
265M16×C47C2×D414yes—
266M16×C47C2414yes—
267C2×C8×C47—22no—
268C2×C8×C47—22no—
269C2×C8×C47—22no—
270C2×C8×C47—216no—
271C2×C8×C47C2×D414yes—
272C2×C8×C47C2×D414yes—
273C2×C8×C47C2414yes—
274C22⋊Dic47—22no—
275C22⋊Dic47—22no—
276#10625337C22×C4116yes—
277#10625336C22×C4116yes—
278#10625335C22×C4116yes—
279#10625334C22×C4116yes—
280C4⋊Dic47—22no—
281C4⋊Dic47—22no—
282C4×Dic47—22no—
283C4×Dic47C2414yes—
284#10625329—22no—
285#10625329—22no—
286#10625329—22no—
287#10625329C22×C414yes—
288#10625329C22×C414yes—
289#10625329C22×C414yes—
290#10625329C22×C414yes—
291#10625329C2414yes—
292C2×C47⋊C8—22no—
293C2×C47⋊C8—22no—
294C2×C47⋊C8—22no—
295C2×C47⋊C8C22×C414yes—
296C2×C47⋊C8C22×C414yes—
297C2×C47⋊C8C2414yes—
298#10625324—216no—
299C8×D47—216no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—81no—
304C23×C47—82no—
305C23×C47C4×D411yescharacteristic
306C23×C47C4×D411yescharacteristic
307C23×C47C4×D411yescharacteristic
308C23×C47C4×D411yescharacteristic
309C23×C47C2×#4111yescharacteristic
310C23×C47C2×#4111yescharacteristic
311C23×C47C2×#4111yescharacteristic
312C22×D47—22no—
313C22×D47—22no—
314C22×D47—22no—
315C22×D47—82no—
316Q8×C47—22no—
317Q8×C47—22no—
318Q8×C47—22no—
319Q8×C47C23×C414yes—
320D4×C47—24no—
321D4×C47—24no—
322D4×C47—24no—
323D4×C47—24no—
324D4×C47—22no—
325D4×C47—22no—
326D4×C47—22no—
327D4×C47C23×C414yes—
328C2×C4×C47—22no—
329C2×C4×C47—22no—
330C2×C4×C47—22no—
331C2×C4×C47—24no—
332C2×C4×C47—24no—
333C2×C4×C47—24no—
334C2×C4×C47—24no—
335C2×C4×C47C4×D411yescharacteristic
336C2×C4×C47C4×D411yescharacteristic
337C2×C4×C47C4×D411yescharacteristic
338C2×C4×C47C4×D411yescharacteristic
339C2×C4×C47C4×D411yescharacteristic
340C2×C4×C47C4×D411yescharacteristic
341C2×C4×C47C4×D411yescharacteristic
342C2×C4×C47C4×D411yescharacteristic
343C2×C4×C47C4×D411yescharacteristic
344C2×C4×C47C4×D411yescharacteristic
345C2×C4×C47C4×D411yescharacteristic
346C2×C4×C47C4×D411yescharacteristic
347C2×C4×C47C23×C411yescharacteristic
348C2×C4×C47C23×C411yescharacteristic
349C2×C4×C47C23×C411yescharacteristic
350C2×C4×C47C23×C411yescharacteristic
351C2×C4×C47C23×C411yescharacteristic
352C2×C4×C47C23×C411yescharacteristic
353C2×C4×C47C22×D411yescharacteristic
354C2×C4×C47C22×D411yescharacteristic
355C2×C4×C47C22×D411yescharacteristic
356C2×C4×C47C22×D411yescharacteristic
357C2×C4×C47C22×D411yescharacteristic
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C2×#4111yescharacteristic
360C2×C4×C47C2×#4111yescharacteristic
361C2×C4×C47C2×#4111yescharacteristic
362C2×C4×C47C2511yescharacteristic
363C22⋊D47—24no—
364C22⋊D47—24no—
365C22⋊D47—24no—
366C22⋊D47—24no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—24no—
371C2×Dic47—82no—
372D188—22no—
373D188—22no—
374D188—22no—
375D188C23×C414yes—
376C4×D47—24no—
377C4×D47—24no—
378C4×D47—24no—
379C4×D47—24no—
380Dic94—22no—
381Dic94—22no—
382Dic94—22no—
383Dic94C23×C414yes—
384C8×C47—24no—
385C8×C47C22×D418yes—
386C47⋊C8—24no—
387C47⋊C8C23×C418yes—
388#60182—471nomaximal, Sylow
389C22×C47—24no—
390C22×C47—41no—
391C22×C47—41no—
392C22×C47—41no—
393C22×C47—41no—
394C22×C47—41no—
395C22×C47—41no—
396C22×C47—41no—
397C22×C47—44no—
398C22×C47—82no—
399C22×C47—82no—
400C22×C47C2×C4×D411yescharacteristic
401C22×C47C2×C4×D411yescharacteristic
402C22×C47C2×C4×D411yescharacteristic
403C22×C47C2×C4×D411yescharacteristic
404C22×C47C2×C4×D411yescharacteristic
405C22×C47C2×C4×D411yescharacteristic
406C22×C47C22×#4111yescharacteristic
407C2×D47—24no—
408C2×D47—44no—
409C2×D47—82no—
410C2×D47—82no—
411C4×C47—24no—
412C4×C47C2×C4×D411yescharacteristic
413C4×C47C2×C4×D411yescharacteristic
414C4×C47C2×C4×D411yescharacteristic
415C4×C47C2×C4×D411yescharacteristic
416C4×C47C2×C4×D411yescharacteristic
417C4×C47C2×C4×D411yescharacteristic
418C4×C47C24×C411yescharacteristic
419C4×C47C23×D411yescharacteristic
420Dic47—24no—
421Dic47—44no—
422C2×#575—471no—
423C2×#568—471no—
424C2×#568D4711yescharacteristic, complemented
425#2957—478no—
426#2956—478no—
427#2955—478no—
428C2×#430—471no—
429C2×#421—471no—
430C2×#421—471no—
431#2873—471no—
432C2×C47—21no—
433C2×C47—21no—
434C2×C47—21no—
435C2×C47—21no—
436C2×C47—21no—
437C2×C47—21no—
438C2×C47—21no—
439C2×C47—44no—
440C2×C47C22×C4×D411yescharacteristic
441D47—44no—
442C22×#41—471no—
443C22×#41C2×D4711yescharacteristic
444#575—474no—
445#575—474no—
446#575—474no—
447#575—474no—
448C2×#137—472no—
449C2×#137—472no—
450C2×AGL(1,ℤ/8)—472no—
451C2×AGL(1,ℤ/8)—472no—
452C2×#135—474no—
453#568—22no—
454#568—22no—
455#568—474no—
456#568—474no—
457#568—942no—
458#568—942no—
459#568C2×D4714yescomplemented
460#568C2×D4714yescomplemented
461C2×#131—22no—
462C2×#131—474no—
463C2×#131—942no—
464C2×#131C2×D4714yescomplemented
465C22×M16—22no—
466C22×M16—471no—
467C22×M16—471no—
468C22×M16—942no—
469C22×M16C2×D4711yescharacteristic
470C22×M16C2×D4711yescharacteristic
471C2×#117—471no—
472#444—4732no—
473#443—4732no—
474#430—474no—
475#430—474no—
476C2×#108—474no—
477#421—474no—
478#421—474no—
479#421—474no—
480#421—474no—
481C2×#104—474no—
482C2×#104—474no—
483#405—474no—
484#405—474no—
485C4×M16—474no—
486C47#6018211yescharacteristic, complemented, Sylow
487C2×#41—21no—
488C2×#41—21no—
489C2×#41—21no—
490C2×#41—21no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—472no—
494C2×#41—472no—
495C2×#41—472no—
496C2×#41—472no—
497C2×#41—472no—
498C2×#41—472no—
499C2×#41—941no—
500C2×#41—941no—
501C2×#41—941no—
502C2×#41—941no—
503C2×#41—941no—
504C2×#41—941no—
505C2×#41C4×D4712yes—
506C2×#41C4×D4712yes—
507C2×#41C4×D4712yes—
508C2×#41C22×D4712yes—
509C2×#41C22×D4712yes—
510C2×#41C22×D4712yes—
511C22×Q8—471no—
512C22×Q8C4×D4711yescharacteristic
513C22×D4—21no—
514C22×D4—471no—
515C22×D4—941no—
516C22×D4C4×D4711yescharacteristic
517C23×C4—21no—
518C23×C4—941no—
519C23×C4C22×D4711yescharacteristic
520#137—478no—
521#137—478no—
522#137—478no—
523#137—478no—
524AGL(1,ℤ/8)—478no—
525AGL(1,ℤ/8)—478no—
526AGL(1,ℤ/8)—478no—
527AGL(1,ℤ/8)—478no—
528#135—4716no—
529#135—4716no—
530C2×Q16—474no—
531C2×SD16—474no—
532C2×SD16—474no—
533C2×D8—474no—
534#131—28no—
535#131—28no—
536#131—28no—
537#131—4716no—
538#131—948no—
539#131—948no—
540#131—948no—
541#131C22×D47116yescomplemented
542C2×M16—21no—
543C2×M16—21no—
544C2×M16—21no—
545C2×M16—28no—
546C2×M16—28no—
547C2×M16—24no—
548C2×M16—472no—
549C2×M16—472no—
550C2×M16—472no—
551C2×M16—472no—
552C2×M16—472no—
553C2×M16—472no—
554C2×M16—472no—
555C2×M16—472no—
556C2×M16—472no—
557C2×M16—941no—
558C2×M16—941no—
559C2×M16—941no—
560C2×M16—948no—
561C2×M16—948no—
562C2×M16—944no—
563C2×M16C22⋊D4712yes—
564C2×M16C22⋊D4712yes—
565C2×M16C22⋊D4712yes—
566C2×M16C22⋊D4712yes—
567C2×M16C22×D4712yes—
568C2×M16C22×D4712yes—
569C2×M16C22×D4712yes—
570C2×M16C22×D4712yes—
571C2×M16C22×D4712yes—
572C22×C8—21no—
573C22×C8—24no—
574C22×C8—472no—
575C22×C8—941no—
576C22×C8—944no—
577C22×C8C22×D4712yes—
578#117—472no—
579#117—472no—
580#117—941no—
581#117—941no—
582C2×C4⋊C4—941no—
583C2×C22⋊C4—941no—
584C2×C42—472no—
585#108—4716no—
586#104—4716no—
587#104—4716no—
588#97—478no—
589C4×C8—478no—
590C24—21no—
591C24—941no—
592C24#1062535011yescharacteristic
593#41—22no—
594#41—22no—
595#41—22no—
596#41—22no—
597#41—22no—
598#41—22no—
599#41—22no—
600#41—22no—
601#41—22no—
602#41—22no—
603#41—22no—
604#41—22no—
605#41—474no—
606#41—474no—
607#41—474no—
608#41—474no—
609#41—942no—
610#41—942no—
611#41—942no—
612#41—942no—
613#41—942no—
614#41—942no—
615#41—942no—
616#41—942no—
617#41—942no—
618#41—942no—
619#41—942no—
620#41—942no—
621#41C2×C4×D4714yes—
622#41C2×C4×D4714yes—
623#41C2×C4×D4714yes—
624#41C23×D4714yes—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—472no—
629C2×Q8—472no—
630C2×Q8—472no—
631C2×Q8—941no—
632C2×Q8—941no—
633C2×Q8—941no—
634C2×Q8C2×C4×D4712yes—
635C2×Q8C2×C4×D4712yes—
636C2×Q8C2×C4×D4712yes—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—472no—
647C2×D4—472no—
648C2×D4—472no—
649C2×D4—942no—
650C2×D4—942no—
651C2×D4—942no—
652C2×D4—942no—
653C2×D4—942no—
654C2×D4—942no—
655C2×D4—941no—
656C2×D4—941no—
657C2×D4—941no—
658C2×D4C2×C4×D4712yes—
659C2×D4C2×C4×D4712yes—
660C2×D4C2×C4×D4712yes—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—941no—
669C22×C4—942no—
670C22×C4—942no—
671C22×C4—942no—
672C22×C4—942no—
673C22×C4—942no—
674C22×C4—942no—
675C22×C4—942no—
676C22×C4C2×C4×D4711yescharacteristic
677C22×C4C2×C4×D4711yescharacteristic
678C22×C4C2×C4×D4711yescharacteristic
679C22×C4C2×C4×D4711yescharacteristic
680C22×C4#1062535011yescharacteristic
681C22×C4#1062535011yescharacteristic
682C22×C4#1062535011yescharacteristic
683C22×C4C2×C22⋊D4711yescharacteristic
684C22×C4C2×C22⋊D4711yescharacteristic
685C22×C4C2×C22⋊D4711yescharacteristic
686C22×C4C2×C22⋊D4711yescharacteristic
687C22×C4C23×D4711yescharacteristic
688C22×C4C23×D4711yescharacteristic
689C22×C4C23×D4711yescharacteristic
690Q16—4716no—
691SD16—4716no—
692SD16—4716no—
693D8—4716no—
694M16—22no—
695M16—22no—
696M16—22no—
697M16—216no—
698M16—474no—
699M16—474no—
700M16—474no—
701M16—474no—
702M16—474no—
703M16—942no—
704M16—942no—
705M16—942no—
706M16—9416no—
707M16C2×C22⋊D4714yes—
708M16C2×C22⋊D4714yes—
709M16C2×C22⋊D4714yes—
710M16C2×C22⋊D4714yes—
711M16C23×D4714yes—
712C2×C8—22no—
713C2×C8—22no—
714C2×C8—22no—
715C2×C8—216no—
716C2×C8—474no—
717C2×C8—474no—
718C2×C8—474no—
719C2×C8—942no—
720C2×C8—942no—
721C2×C8—942no—
722C2×C8—9416no—
723C2×C8C2×C22⋊D4714yes—
724C2×C8C2×C22⋊D4714yes—
725C2×C8C23×D4714yes—
726C4⋊C4—942no—
727C4⋊C4—942no—
728C22⋊C4—942no—
729C22⋊C4—942no—
730C42—474no—
731C42—942no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—81no—
736C23—82no—
737C23—942no—
738C23—942no—
739C23—942no—
740C23—3762no—
741C23C4×C22⋊D4711yescharacteristic
742C23C4×C22⋊D4711yescharacteristic
743C23C4×C22⋊D4711yescharacteristic
744C23C4×C22⋊D4711yescharacteristic
745C23C2×#1062535011yescharacteristic
746C23C2×#1062535011yescharacteristic
747C23C2×#1062535011yescharacteristic
748Q8—22no—
749Q8—22no—
750Q8—22no—
751Q8—474no—
752Q8—942no—
753Q8—942no—
754Q8—942no—
755Q8C22×C4×D4714yes—
756D4—24no—
757D4—24no—
758D4—24no—
759D4—24no—
760D4—22no—
761D4—22no—
762D4—22no—
763D4—474no—
764D4—944no—
765D4—944no—
766D4—944no—
767D4—944no—
768D4—942no—
769D4—942no—
770D4—942no—
771D4C22×C4×D4714yes—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—942no—
780C2×C4—942no—
781C2×C4—942no—
782C2×C4—944no—
783C2×C4—944no—
784C2×C4—944no—
785C2×C4—944no—
786C2×C4—944no—
787C2×C4—3762no—
788C2×C4C4×C22⋊D4711yescharacteristic
789C2×C4C4×C22⋊D4711yescharacteristic
790C2×C4C4×C22⋊D4711yescharacteristic
791C2×C4C4×C22⋊D4711yescharacteristic
792C2×C4C4×C22⋊D4711yescharacteristic
793C2×C4C4×C22⋊D4711yescharacteristic
794C2×C4C4×C22⋊D4711yescharacteristic
795C2×C4C4×C22⋊D4711yescharacteristic
796C2×C4C4×C22⋊D4711yescharacteristic
797C2×C4C4×C22⋊D4711yescharacteristic
798C2×C4C4×C22⋊D4711yescharacteristic
799C2×C4C4×C22⋊D4711yescharacteristic
800C2×C4C22×C4×D4711yescharacteristic
801C2×C4C22×C4×D4711yescharacteristic
802C2×C4C22×C4×D4711yescharacteristic
803C2×C4C22×C4×D4711yescharacteristic
804C2×C4C22×C4×D4711yescharacteristic
805C2×C4C22×C4×D4711yescharacteristic
806C2×C4C22×C22⋊D4711yescharacteristic
807C2×C4C22×C22⋊D4711yescharacteristic
808C2×C4C22×C22⋊D4711yescharacteristic
809C2×C4C22×C22⋊D4711yescharacteristic
810C2×C4C22×C22⋊D4711yescharacteristic
811C2×C4C22×C22⋊D4711yescharacteristic
812C2×C4C2×#1062535011yescharacteristic
813C2×C4C2×#1062535011yescharacteristic
814C2×C4C2×#1062535011yescharacteristic
815C2×C4C24×D4711yescharacteristic
816C8—24no—
817C8—478no—
818C8—944no—
819C8C22×C22⋊D4718yes—
820C22—24no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—44no—
829C22—82no—
830C22—82no—
831C22—944no—
832C22—3762no—
833C22—3762no—
834C22—1884no—
835C22C2×C4×C22⋊D4711yescharacteristic
836C22C2×C4×C22⋊D4711yescharacteristic
837C22C2×C4×C22⋊D4711yescharacteristic
838C22C2×C4×C22⋊D4711yescharacteristic
839C22C2×C4×C22⋊D4711yescharacteristic
840C22C2×C4×C22⋊D4711yescharacteristic
841C22C22×#1062535011yescharacteristic
842C4—24no—
843C4—944no—
844C4—1884no—
845C4C2×C4×C22⋊D4711yescharacteristic
846C4C2×C4×C22⋊D4711yescharacteristic
847C4C2×C4×C22⋊D4711yescharacteristic
848C4C2×C4×C22⋊D4711yescharacteristic
849C4C2×C4×C22⋊D4711yescharacteristic
850C4C2×C4×C22⋊D4711yescharacteristic
851C4C23×C4×D4711yescharacteristic
852C4C23×C22⋊D4711yescharacteristic
853C2—21no—
854C2—21no—
855C2—21no—
856C2—21no—
857C2—21no—
858C2—21no—
859C2—21no—
860C2—44no—
861C2—1884no—
862C2C22×C4×C22⋊D4711yescharacteristic
subgroupG/H
centerC4C23×C22⋊D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#568C2
socleC2×C47C22×C4×D4
prime radicalC2×#15689921C2
cosocleC2×C4×C47C25
hypercenterC2×#568D47
hypocenterC47#60182
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×M16 ◁ C2×#568

Complements

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

NH ≅ G/Ntype
2. C2×#15689889C2semidirect
3. #20252303C2semidirect
4. #20252295C2semidirect
5. #20252289C2semidirect
6. C2×#15689171C2semidirect
7. C2×#15689140C2semidirect
8. C2×#15689139C2semidirect
9. #20251806C2semidirect
10. C2×C47×#568C2semidirect
12. #15689921C4semidirect
13. #15689921C4semidirect
16. C2×#13094055C4semidirect
17. C2×#13094054C4semidirect
18. C2×#13094050C4semidirect
19. C2×#13094049C4semidirect
23. #15689889C22semidirect
24. #15689889C22semidirect
26. C2×#13094030C22semidirect
31. #15689243C22semidirect
32. #15689238C22semidirect
33. #15689171C22semidirect
34. #15689171C22semidirect
35. C2×#13093959C22semidirect
36. #15689140C22semidirect
37. #15689140C22semidirect
38. #15689139C22semidirect
39. #15689139C22semidirect
40. C2×#13093951C22semidirect
41. C2×#13093950C22semidirect
42. #15689081C22semidirect
43. #15689078C22semidirect
44. M16×Dic47C22semidirect
48. C47×#568C22semidirect
49. C47×#568C22semidirect
51. C2×#131×C47C22semidirect
72. #13094055C2×C4semidirect
74. #13094054C2×C4semidirect
76. #13094050C2×C4semidirect
78. #13094049C2×C4semidirect
79. #13094044C2×C4semidirect
81. C2×#10625337C2×C4semidirect
82. C2×#10625335C2×C4semidirect
83. C2×#10625336C2×C4semidirect
84. C2×#10625334C2×C4semidirect
88. #13094030C23semidirect
114. #13093959C23semidirect
115. #13093951C23semidirect
116. #13093950C23semidirect
117. #13093934C23semidirect
118. C8×Dic47C23semidirect
139. #131×C47C23semidirect
424. C2×#568D47semidirect
459. #568C2×D47semidirect
460. #568C2×D47semidirect
464. C2×#131C2×D47semidirect
486. C47#60182semidirect
541. #131C22×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156899212
C2×#156898892
#202523032
#202522952
#202522892
C2×#156891712
C2×#156891402
C2×#156891392
#202518062
C2×C47×#5682
#6018247