Finite Group Databasebeta

← #27083701

Subgroups — #27083701

Order 12032.

2628 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689923C211yesmaximal, characteristic, complemented
2C2×#15689921C211yesmaximal, characteristic, complemented
3C2×#15689921C211yesmaximal, characteristic, complemented
4C2×#15689889C211yesmaximal, characteristic, complemented
5#20253128C214yesmaximal, complemented
6#20253124C214yesmaximal, complemented
7#20253119C214yesmaximal, complemented
8#20253115C214yesmaximal, complemented
9#20253107C218yesmaximal, complemented
10C2×#15689171C211yesmaximal, characteristic, complemented
11C2×#15689105C211yesmaximal, characteristic, complemented
12C2×C47×#413C211yesmaximal, characteristic, complemented
13C22×#10625350C2211yescharacteristic
14C22×#10625350C2211yescharacteristic
15#15689923—22no—
16#15689923—22no—
17#15689923C2214yes—
18#15689923C2214yescomplemented
19#15689921—22no—
20#15689921—22no—
21#15689921—22no—
22#15689921—22no—
23#15689921—22no—
24#15689921—22no—
25#15689921C2214yes—
26#15689921C2214yescomplemented
27C2×#13094057—21no—
28C2×#13094057C2212yescomplemented
29C2×#13094055C2212yescomplemented
30C2×#13094055C2212yescomplemented
31C2×#13094054—21no—
32C2×#13094054C2212yescomplemented
33C2×#13094052—21no—
34C2×#13094052C2212yescomplemented
35C2×#13094050C2212yescomplemented
36C2×#13094050C2212yescomplemented
37C2×#13094049—21no—
38C2×#13094049C2212yescomplemented
39C2×#13094046—22no—
40C2×#13094044—22no—
41C2×#13094044C2214yescomplemented
42#15689889—22no—
43#15689889—22no—
44#15689889C2214yescomplemented
45#15689889C2214yescomplemented
46C2×#13094032C2214yescomplemented
47C2×#13094030—22no—
48C22×#10625329C2211yescharacteristic
49C22×#10625329C2211yescharacteristic
50C2×M16×D47—22no—
51#15689397C22116yescomplemented
52#15689392C22116yescomplemented
53#15689389C22116yescomplemented
54#15689385C22116yescomplemented
55#15689171C2214yescomplemented
56#15689171C2214yescomplemented
57C2×#13093959C2214yescomplemented
58#15689105C2214yescomplemented
59#15689105C2214yescomplemented
60C2×#13093942C2212yescomplemented
61C2×#13093940C2212yescomplemented
62C22×#41×C47C2211yescharacteristic
63C22×M16×C47C2211yescharacteristic
64C22×M16×C47C2211yescharacteristic
65C47×#413C2214yescomplemented
66C47×#413C2214yescomplemented
67C2×#101×C47C2212yescomplemented
68C2×#100×C47C2212yescomplemented
69C2×#10625350—21no—
70C2×#10625350—21no—
71C2×#10625350—21no—
72C2×#10625350—21no—
73C2×#10625350—21no—
74C2×#10625350—21no—
75C2×#10625350—21no—
76C2×#10625350—21no—
77C2×#10625350—21no—
78C2×#10625350—21no—
79C2×#10625350—21no—
80C2×#10625350—21no—
81C2×#10625350—21no—
82C2×#10625350—21no—
83C2×#10625350—21no—
84C2×#10625350—21no—
85C2×#10625350D412yes—
86C2×#10625350D412yes—
87C2×#10625350D412yes—
88C2×#10625350C2312yes—
89C2×#10625350C2312yes—
90C2×#10625350C2312yes—
91C2×#10625350C2312yes—
92C2×#10625350C2312yes—
93C22×Dic94D411yescharacteristic
94C22×Dic94C2311yescharacteristic
95C22×D188D411yescharacteristic
96C22×D188C2311yescharacteristic
97C22×C22⋊D47—21no—
98C22×C22⋊D47—21no—
99C22×C4×D47—21no—
100C22×C4×D47—21no—
101#13094057—24no—
102#13094057—24no—
103#13094057—24no—
104#13094057C2318yes—
105#13094055—24no—
106#13094055—24no—
107#13094055—24no—
108#13094055C2318yes—
109#13094054—24no—
110#13094054—24no—
111#13094054—24no—
112#13094054—24no—
113#13094052—24no—
114#13094052—24no—
115#13094052—24no—
116#13094052C2318yes—
117#13094050—24no—
118#13094050—24no—
119#13094050—24no—
120#13094050C2318yes—
121#13094049—24no—
122#13094049—24no—
123#13094049—24no—
124#13094049—24no—
125#13094046—28no—
126#13094046—28no—
127#13094044—28no—
128#13094044—28no—
129#13094044—28no—
130#13094044—28no—
131C2×Dic188—22no—
132C2×#10625337—22no—
133C2×#10625337C2314yescomplemented
134C2×#10625325—22no—
135C2×#10625325—22no—
136C2×#10625335—22no—
137C2×#10625335C2314yescomplemented
138C2×#10625336—22no—
139C2×#10625336C2314yescomplemented
140C2×D376—22no—
141C2×#10625334—22no—
142C2×#10625334C2314yescomplemented
143#13094032—28no—
144#13094032C23116yes—
145#13094030—28no—
146#13094030—28no—
147C2×#10625329—21no—
148C2×#10625329—21no—
149C2×#10625329—21no—
150C2×#10625329D412yes—
151C2×#10625329D412yes—
152C2×#10625329D412yes—
153C2×#10625329D412yes—
154C2×#10625329C2312yes—
155C2×#10625329C2312yes—
156C2×#10625329C2312yes—
157C2×#10625329C2312yes—
158C2×#10625329C2312yes—
159C2×#10625324—24no—
160M16×D47—28no—
161M16×D47—28no—
162C22×C47⋊C8—21no—
163C22×C47⋊C8C2312yes—
164C2×C8×D47—24no—
165#13093959C23116yescomplemented
166#13093942C2318yescomplemented
167#13093940C2318yescomplemented
168C2×#41×C47—21no—
169C2×#41×C47—21no—
170C2×#41×C47—21no—
171C2×#41×C47—21no—
172C2×#41×C47—21no—
173C2×#41×C47—21no—
174C2×#41×C47—21no—
175C2×#41×C47—21no—
176C2×#41×C47—21no—
177C2×#41×C47—21no—
178C2×#41×C47C2312yes—
179C2×#41×C47C2312yes—
180C22×Q8×C47C2311yescharacteristic
181C22×D4×C47—21no—
182C22×D4×C47C2311yescharacteristic
183C23×C4×C47—21no—
184C23×C4×C47C2311yescharacteristic
185C2×M16×C47—21no—
186C2×M16×C47—21no—
187C2×M16×C47—21no—
188C2×M16×C47—21no—
189C2×M16×C47—21no—
190C2×M16×C47—21no—
191C2×M16×C47C2312yes—
192C2×M16×C47C2312yes—
193C2×M16×C47C2312yes—
194C2×M16×C47C2312yes—
195C2×M16×C47C2312yes—
196C2×M16×C47C2312yes—
197C22×C8×C47—21no—
198C22×C8×C47—21no—
199#101×C47C2318yescomplemented
200#100×C47C2318yescomplemented
201C24×C47—21no—
202C24×C47#4111yescharacteristic
203C23×D47—21no—
204C23×D47—21no—
205#41×C47—22no—
206#41×C47—22no—
207#41×C47—22no—
208#41×C47—22no—
209#41×C47—22no—
210#41×C47—22no—
211#41×C47—22no—
212#41×C47—22no—
213#41×C47—41no—
214#41×C47—41no—
215#41×C47—41no—
216#41×C47—41no—
217#41×C47—41no—
218#41×C47—41no—
219#41×C47—41no—
220#41×C47—41no—
221C2×Q8×C47—21no—
222C2×Q8×C47—21no—
223C2×Q8×C47—21no—
224C2×Q8×C47—21no—
225C2×Q8×C47—21no—
226C2×Q8×C47C2412yes—
227C2×D4×C47—22no—
228C2×D4×C47—22no—
229C2×D4×C47—21no—
230C2×D4×C47—21no—
231C2×D4×C47—21no—
232C2×D4×C47—21no—
233C2×D4×C47—21no—
234C2×D4×C47—41no—
235C2×D4×C47—41no—
236C2×D4×C47—41no—
237C2×D4×C47—41no—
238C2×D4×C47C2412yes—
239C22×C4×C47—21no—
240C22×C4×C47—22no—
241C22×C4×C47—22no—
242C22×C4×C47—41no—
243C22×C4×C47—41no—
244C22×C4×C47—41no—
245C22×C4×C47—41no—
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×C4×C47C2×D411yescharacteristic
249C22×C4×C47C2×D411yescharacteristic
250C22×C4×C47C2×D411yescharacteristic
251C22×C4×C47C2×D411yescharacteristic
252C22×C4×C47C2×D411yescharacteristic
253C22×C4×C47C2×D411yescharacteristic
254C22×C4×C47#4111yescharacteristic
255C22×C4×C47#4111yescharacteristic
256C22×C4×C47#4111yescharacteristic
257C22×C4×C47C2411yescharacteristic
258C22×C4×C47C2411yescharacteristic
259C22×C4×C47C2411yescharacteristic
260C2×C22⋊D47—22no—
261C2×C22⋊D47—22no—
262C2×C22⋊D47—22no—
263C2×C22⋊D47—22no—
264C2×C22⋊D47—22no—
265C2×C22⋊D47—22no—
266C2×C22⋊D47—22no—
267C2×C22⋊D47—22no—
268C2×C22⋊D47—41no—
269C2×C22⋊D47—41no—
270C2×C22⋊D47—41no—
271C2×C22⋊D47—41no—
272C22×Dic47—21no—
273C22×Dic47—21no—
274#10625350—22no—
275#10625350—22no—
276#10625350—22no—
277#10625350—22no—
278#10625350—22no—
279#10625350—22no—
280#10625350—22no—
281#10625350—22no—
282#10625350—22no—
283#10625350—22no—
284#10625350—22no—
285#10625350—22no—
286#10625350—22no—
287#10625350—22no—
288#10625350—22no—
289#10625350—22no—
290#10625350—22no—
291#10625350—22no—
292#10625350—22no—
293#10625350—22no—
294#10625350—41no—
295#10625350—41no—
296#10625350—41no—
297#10625350—41no—
298#10625350—41no—
299#10625350—41no—
300#10625350—41no—
301#10625350—41no—
302#10625350C2×D414yes—
303#10625350C2×D414yes—
304#10625350C2×D414yes—
305#10625350C2414yes—
306C2×D188—21no—
307C2×D188—21no—
308C2×D188—21no—
309C2×D188—21no—
310C2×D188—21no—
311C2×D188—21no—
312C2×D188—21no—
313C2×D188—21no—
314C2×D188C2×D412yes—
315C2×D188C2×D412yes—
316C2×D188C2×D412yes—
317C2×D188C2412yes—
318C2×C4×D47—22no—
319C2×C4×D47—22no—
320C2×C4×D47—22no—
321C2×C4×D47—22no—
322C2×C4×D47—22no—
323C2×C4×D47—22no—
324C2×C4×D47—22no—
325C2×C4×D47—22no—
326C2×C4×D47—41no—
327C2×C4×D47—41no—
328C2×C4×D47—41no—
329C2×C4×D47—41no—
330C2×Dic94—21no—
331C2×Dic94—21no—
332C2×Dic94—21no—
333C2×Dic94—21no—
334C2×Dic94—21no—
335C2×Dic94—21no—
336C2×Dic94—21no—
337C2×Dic94—21no—
338C2×Dic94C2×D412yes—
339C2×Dic94C2×D412yes—
340C2×Dic94C2×D412yes—
341C2×Dic94C2412yes—
342M16×C47—22no—
343M16×C47—22no—
344M16×C47—22no—
345M16×C47—22no—
346M16×C47—22no—
347M16×C47—22no—
348M16×C47C2414yes—
349M16×C47C2414yes—
350C2×C8×C47—22no—
351C2×C8×C47—22no—
352C2×C8×C47—22no—
353C2×C8×C47—22no—
354C2×C8×C47—22no—
355C2×C8×C47—22no—
356#10625337—28no—
357#10625337—28no—
358#10625336—28no—
359#10625336—28no—
360#10625335—28no—
361#10625335—28no—
362#10625334—28no—
363#10625334—28no—
364#10625329—22no—
365#10625329—22no—
366#10625329—22no—
367#10625329C2×D414yes—
368#10625329C2×D414yes—
369#10625329C2×D414yes—
370#10625329C2×D414yes—
371#10625329C2414yes—
372C2×C47⋊C8—22no—
373C2×C47⋊C8—22no—
374C2×C47⋊C8—22no—
375C2×C47⋊C8C2×D414yes—
376C2×C47⋊C8C2×D414yes—
377C2×C47⋊C8C2414yes—
378Dic188—28no—
379D376—28no—
380#10625325—28no—
381#10625325—28no—
382#10625324—216no—
383C8×D47—216no—
384C23×C47—22no—
385C23×C47—41no—
386C23×C47—41no—
387C23×C47—81no—
388C23×C47—82no—
389C23×C47#12111yescharacteristic
390C23×C47#12111yescharacteristic
391C23×C47#12111yescharacteristic
392C23×C47#12111yescharacteristic
393C23×C47C2×#4111yescharacteristic
394C23×C47C2×#4111yescharacteristic
395C23×C47C2×#4111yescharacteristic
396C22×D47—22no—
397C22×D47—22no—
398C22×D47—22no—
399C22×D47—22no—
400C22×D47—41no—
401C22×D47—41no—
402C22×D47—82no—
403C22×D47—82no—
404Q8×C47—22no—
405Q8×C47—22no—
406Q8×C47—41no—
407Q8×C47—41no—
408D4×C47—22no—
409D4×C47—22no—
410D4×C47—42no—
411D4×C47—42no—
412D4×C47—42no—
413D4×C47—42no—
414D4×C47—41no—
415D4×C47—41no—
416C2×C4×C47—22no—
417C2×C4×C47—41no—
418C2×C4×C47—41no—
419C2×C4×C47—42no—
420C2×C4×C47—42no—
421C2×C4×C47—42no—
422C2×C4×C47—42no—
423C2×C4×C47#12111yescharacteristic
424C2×C4×C47#12111yescharacteristic
425C2×C4×C47#12111yescharacteristic
426C2×C4×C47#12111yescharacteristic
427C2×C4×C47#12111yescharacteristic
428C2×C4×C47#12111yescharacteristic
429C2×C4×C47#12111yescharacteristic
430C2×C4×C47#12111yescharacteristic
431C2×C4×C47#12111yescharacteristic
432C2×C4×C47#12111yescharacteristic
433C2×C4×C47#12111yescharacteristic
434C2×C4×C47#12111yescharacteristic
435C2×C4×C47C22×D411yescharacteristic
436C2×C4×C47C22×D411yescharacteristic
437C2×C4×C47C22×D411yescharacteristic
438C2×C4×C47C22×D411yescharacteristic
439C2×C4×C47C22×D411yescharacteristic
440C2×C4×C47C22×D411yescharacteristic
441C2×C4×C47C22×D411yescharacteristic
442C2×C4×C47C22×D411yescharacteristic
443C2×C4×C47C22×D411yescharacteristic
444C2×C4×C47C22×D411yescharacteristic
445C2×C4×C47C22×D411yescharacteristic
446C2×C4×C47C22×D411yescharacteristic
447C2×C4×C47C2×#4111yescharacteristic
448C2×C4×C47C2×#4111yescharacteristic
449C2×C4×C47C2×#4111yescharacteristic
450C2×C4×C47C2511yescharacteristic
451C22⋊D47—24no—
452C22⋊D47—24no—
453C22⋊D47—24no—
454C22⋊D47—24no—
455C22⋊D47—42no—
456C22⋊D47—42no—
457C22⋊D47—42no—
458C22⋊D47—42no—
459C2×Dic47—22no—
460C2×Dic47—22no—
461C2×Dic47—22no—
462C2×Dic47—22no—
463C2×Dic47—41no—
464C2×Dic47—41no—
465D188—22no—
466D188—22no—
467D188—22no—
468D188—22no—
469D188—22no—
470D188—41no—
471D188—41no—
472D188C22×D414yes—
473C4×D47—24no—
474C4×D47—24no—
475C4×D47—24no—
476C4×D47—24no—
477C4×D47—42no—
478C4×D47—42no—
479C4×D47—42no—
480C4×D47—42no—
481Dic94—22no—
482Dic94—22no—
483Dic94—22no—
484Dic94—22no—
485Dic94—22no—
486Dic94—41no—
487Dic94—41no—
488Dic94C22×D414yes—
489C8×C47—24no—
490C8×C47—24no—
491C47⋊C8—24no—
492C47⋊C8C22×D418yes—
493#60469—471nomaximal, Sylow
494C22×C47—41no—
495C22×C47—41no—
496C22×C47—41no—
497C22×C47—41no—
498C22×C47—41no—
499C22×C47—41no—
500C22×C47—41no—
501C22×C47—42no—
502C22×C47—82no—
503C22×C47—82no—
504C22×C47—82no—
505C22×C47C2×#12111yescharacteristic
506C22×C47C2×#12111yescharacteristic
507C22×C47C2×#12111yescharacteristic
508C22×C47C2×#12111yescharacteristic
509C22×C47C2×#12111yescharacteristic
510C22×C47C2×#12111yescharacteristic
511C22×C47C22×#4111yescharacteristic
512C2×D47—24no—
513C2×D47—44no—
514C2×D47—42no—
515C2×D47—82no—
516C2×D47—82no—
517C2×D47—82no—
518C2×D47—82no—
519C2×D47—82no—
520C4×C47—42no—
521C4×C47C2×#12111yescharacteristic
522C4×C47C2×#12111yescharacteristic
523C4×C47C2×#12111yescharacteristic
524C4×C47C2×#12111yescharacteristic
525C4×C47C2×#12111yescharacteristic
526C4×C47C2×#12111yescharacteristic
527C4×C47C23×D411yescharacteristic
528C4×C47C23×D411yescharacteristic
529Dic47—24no—
530Dic47—42no—
531C2×#575—471no—
532C2×#575—471no—
533C2×#575—471no—
534C2×#568—471no—
535#3069—474no—
536#3069—474no—
537#3068—474no—
538#3068—474no—
539#3067—478no—
540C2×#430—471no—
541C2×#413—471no—
542C2×#413D4711yescharacteristic, complemented
543C2×C47—21no—
544C2×C47—21no—
545C2×C47—21no—
546C2×C47—21no—
547C2×C47—21no—
548C2×C47—21no—
549C2×C47—21no—
550C2×C47—82no—
551C2×C47C22×#12111yescharacteristic
552D47—44no—
553D47—82no—
554C22×#41—471no—
555C22×#41—471no—
556C22×#41C2×D4711yescharacteristic
557#575—474no—
558#575—474no—
559#575—474no—
560#575—474no—
561#575—942no—
562#575—942no—
563#575—942no—
564#575—942no—
565#575—942no—
566#575—942no—
567#575—942no—
568#575—942no—
569C2×#137—472no—
570C2×#137—472no—
571C2×#137—472no—
572C2×#137—472no—
573C2×#137—941no—
574C2×#137—941no—
575C2×AGL(1,ℤ/8)—472no—
576C2×AGL(1,ℤ/8)—472no—
577C2×AGL(1,ℤ/8)—472no—
578C2×AGL(1,ℤ/8)—472no—
579C2×AGL(1,ℤ/8)—941no—
580C2×AGL(1,ℤ/8)—941no—
581C2×#135—474no—
582C2×#135—942no—
583C2×#135—942no—
584#568—474no—
585#568—474no—
586#568—942no—
587#568—942no—
588C2×#131—474no—
589C2×#131—942no—
590C22×M16—471no—
591C22×M16—471no—
592C22×M16—942no—
593C22×M16C2×D4711yescharacteristic
594C22×M16C2×D4711yescharacteristic
595#473—4716no—
596#472—4716no—
597#471—4716no—
598#471—4716no—
599#430—474no—
600#430—474no—
601C2×#108—474no—
602#413—474no—
603#413—474no—
604#413C2×D4714yescomplemented
605#413C2×D4714yescomplemented
606C2×#101—472no—
607C2×#101C2×D4712yescomplemented
608C2×#100—472no—
609C2×#100C2×D4712yescomplemented
610C47#6046911yescharacteristic, complemented, Sylow
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—21no—
616C2×#41—21no—
617C2×#41—21no—
618C2×#41—21no—
619C2×#41—21no—
620C2×#41—21no—
621C2×#41—472no—
622C2×#41—472no—
623C2×#41—472no—
624C2×#41—472no—
625C2×#41—472no—
626C2×#41—472no—
627C2×#41—472no—
628C2×#41—472no—
629C2×#41—941no—
630C2×#41—941no—
631C2×#41—941no—
632C2×#41—941no—
633C2×#41—941no—
634C2×#41—941no—
635C2×#41—941no—
636C2×#41—941no—
637C2×#41—941no—
638C2×#41—941no—
639C2×#41—941no—
640C2×#41—941no—
641C2×#41—941no—
642C2×#41—941no—
643C2×#41—941no—
644C2×#41—941no—
645C2×#41C22×D4712yes—
646C2×#41C22×D4712yes—
647C22×Q8—471no—
648C22×Q8—471no—
649C22×Q8C22×D4711yescharacteristic
650C22×D4—21no—
651C22×D4—471no—
652C22×D4—471no—
653C22×D4—941no—
654C22×D4—941no—
655C22×D4C22×D4711yescharacteristic
656C23×C4—21no—
657C23×C4—941no—
658C23×C4—941no—
659C23×C4C22×D4711yescharacteristic
660#137—478no—
661#137—478no—
662#137—944no—
663#137—944no—
664#137—944no—
665#137—944no—
666#137—944no—
667#137—944no—
668#137—944no—
669#137—944no—
670#137—944no—
671#137—944no—
672AGL(1,ℤ/8)—478no—
673AGL(1,ℤ/8)—478no—
674AGL(1,ℤ/8)—944no—
675AGL(1,ℤ/8)—944no—
676AGL(1,ℤ/8)—944no—
677AGL(1,ℤ/8)—944no—
678AGL(1,ℤ/8)—944no—
679AGL(1,ℤ/8)—944no—
680AGL(1,ℤ/8)—944no—
681AGL(1,ℤ/8)—944no—
682AGL(1,ℤ/8)—944no—
683AGL(1,ℤ/8)—944no—
684#135—948no—
685#135—948no—
686#135—948no—
687#135—948no—
688#135—948no—
689#135—948no—
690C2×Q16—474no—
691C2×Q16—942no—
692C2×Q16—942no—
693C2×SD16—474no—
694C2×SD16—474no—
695C2×SD16—942no—
696C2×SD16—942no—
697C2×SD16—942no—
698C2×SD16—942no—
699C2×D8—474no—
700C2×D8—942no—
701C2×D8—942no—
702#131—4716no—
703#131—948no—
704#131—948no—
705#131—948no—
706C2×M16—21no—
707C2×M16—21no—
708C2×M16—21no—
709C2×M16—21no—
710C2×M16—21no—
711C2×M16—21no—
712C2×M16—472no—
713C2×M16—472no—
714C2×M16—472no—
715C2×M16—472no—
716C2×M16—472no—
717C2×M16—472no—
718C2×M16—472no—
719C2×M16—472no—
720C2×M16—472no—
721C2×M16—944no—
722C2×M16—948no—
723C2×M16—948no—
724C2×M16—941no—
725C2×M16—941no—
726C2×M16—941no—
727C2×M16C22×D4712yes—
728C2×M16C22×D4712yes—
729C2×M16C22×D4712yes—
730C2×M16C22×D4712yes—
731C2×M16C22×D4712yes—
732C2×M16C22×D4712yes—
733C22×C8—21no—
734C22×C8—21no—
735C22×C8—472no—
736C22×C8—944no—
737C22×C8—941no—
738#108—4716no—
739#101—478no—
740#101C22×D4718yescomplemented
741#100—478no—
742#100C22×D4718yescomplemented
743C24—21no—
744C24—941no—
745C24—941no—
746C24#1062535011yescharacteristic
747#41—22no—
748#41—22no—
749#41—22no—
750#41—22no—
751#41—22no—
752#41—22no—
753#41—22no—
754#41—22no—
755#41—41no—
756#41—41no—
757#41—41no—
758#41—41no—
759#41—41no—
760#41—41no—
761#41—41no—
762#41—41no—
763#41—474no—
764#41—474no—
765#41—474no—
766#41—474no—
767#41—942no—
768#41—942no—
769#41—942no—
770#41—942no—
771#41—942no—
772#41—942no—
773#41—942no—
774#41—942no—
775#41—942no—
776#41—942no—
777#41—942no—
778#41—942no—
779#41—942no—
780#41—942no—
781#41—942no—
782#41—942no—
783#41—942no—
784#41—942no—
785#41—942no—
786#41—942no—
787#41—1881no—
788#41—1881no—
789#41—1881no—
790#41—1881no—
791#41—1881no—
792#41—1881no—
793#41—1881no—
794#41—1881no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—472no—
801C2×Q8—472no—
802C2×Q8—472no—
803C2×Q8—472no—
804C2×Q8—941no—
805C2×Q8—941no—
806C2×Q8—941no—
807C2×Q8—941no—
808C2×Q8—941no—
809C2×Q8—941no—
810C2×Q8—941no—
811C2×Q8—941no—
812C2×Q8C23×D4712yes—
813C2×D4—22no—
814C2×D4—22no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—472no—
825C2×D4—472no—
826C2×D4—472no—
827C2×D4—472no—
828C2×D4—942no—
829C2×D4—942no—
830C2×D4—942no—
831C2×D4—942no—
832C2×D4—942no—
833C2×D4—942no—
834C2×D4—942no—
835C2×D4—942no—
836C2×D4—941no—
837C2×D4—941no—
838C2×D4—941no—
839C2×D4—941no—
840C2×D4—941no—
841C2×D4—941no—
842C2×D4—941no—
843C2×D4—941no—
844C2×D4—1881no—
845C2×D4—1881no—
846C2×D4—1881no—
847C2×D4—1881no—
848C2×D4C23×D4712yes—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—41no—
853C22×C4—41no—
854C22×C4—41no—
855C22×C4—41no—
856C22×C4—941no—
857C22×C4—942no—
858C22×C4—942no—
859C22×C4—942no—
860C22×C4—942no—
861C22×C4—942no—
862C22×C4—942no—
863C22×C4—941no—
864C22×C4—942no—
865C22×C4—942no—
866C22×C4—1881no—
867C22×C4—1881no—
868C22×C4—1881no—
869C22×C4—1881no—
870C22×C4#1062535011yescharacteristic
871C22×C4#1062535011yescharacteristic
872C22×C4#1062535011yescharacteristic
873C22×C4D4×D4711yescharacteristic
874C22×C4D4×D4711yescharacteristic
875C22×C4D4×D4711yescharacteristic
876C22×C4D4×D4711yescharacteristic
877C22×C4D4×D4711yescharacteristic
878C22×C4D4×D4711yescharacteristic
879C22×C4D4×D4711yescharacteristic
880C22×C4D4×D4711yescharacteristic
881C22×C4C23×D4711yescharacteristic
882C22×C4C23×D4711yescharacteristic
883C22×C4C23×D4711yescharacteristic
884Q16—948no—
885Q16—948no—
886Q16—948no—
887SD16—948no—
888SD16—948no—
889SD16—948no—
890SD16—948no—
891SD16—948no—
892SD16—948no—
893D8—948no—
894D8—948no—
895D8—948no—
896M16—22no—
897M16—22no—
898M16—22no—
899M16—22no—
900M16—22no—
901M16—22no—
902M16—474no—
903M16—474no—
904M16—474no—
905M16—474no—
906M16—474no—
907M16—9416no—
908M16—942no—
909M16—942no—
910M16—942no—
911M16C23×D4714yes—
912M16C23×D4714yes—
913C2×C8—22no—
914C2×C8—22no—
915C2×C8—22no—
916C2×C8—22no—
917C2×C8—22no—
918C2×C8—22no—
919C2×C8—474no—
920C2×C8—474no—
921C2×C8—474no—
922C2×C8—9416no—
923C2×C8—942no—
924C2×C8—942no—
925C2×C8—942no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—81no—
930C23—82no—
931C23—942no—
932C23—942no—
933C23—942no—
934C23—942no—
935C23—3762no—
936C23—3762no—
937C23—1881no—
938C23—1881no—
939C23#1309399711yescharacteristic
940C23#1309399711yescharacteristic
941C23#1309399711yescharacteristic
942C23#1309399711yescharacteristic
943C23C2×#1062535011yescharacteristic
944C23C2×#1062535011yescharacteristic
945C23C2×#1062535011yescharacteristic
946Q8—22no—
947Q8—22no—
948Q8—41no—
949Q8—41no—
950Q8—474no—
951Q8—942no—
952Q8—942no—
953Q8—942no—
954Q8—942no—
955Q8—942no—
956Q8—1881no—
957Q8—1881no—
958D4—22no—
959D4—22no—
960D4—42no—
961D4—42no—
962D4—42no—
963D4—42no—
964D4—41no—
965D4—41no—
966D4—474no—
967D4—944no—
968D4—944no—
969D4—944no—
970D4—944no—
971D4—942no—
972D4—942no—
973D4—942no—
974D4—942no—
975D4—942no—
976D4—1882no—
977D4—1882no—
978D4—1882no—
979D4—1882no—
980D4—1881no—
981D4—1881no—
982C2×C4—22no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—942no—
990C2×C4—942no—
991C2×C4—942no—
992C2×C4—944no—
993C2×C4—944no—
994C2×C4—944no—
995C2×C4—944no—
996C2×C4—942no—
997C2×C4—1881no—
998C2×C4—1881no—
999C2×C4—1882no—
1000C2×C4—1882no—
1001C2×C4—1882no—
1002C2×C4—1882no—
1003C2×C4#1309399711yescharacteristic
1004C2×C4#1309399711yescharacteristic
1005C2×C4#1309399711yescharacteristic
1006C2×C4#1309399711yescharacteristic
1007C2×C4#1309399711yescharacteristic
1008C2×C4#1309399711yescharacteristic
1009C2×C4#1309399711yescharacteristic
1010C2×C4#1309399711yescharacteristic
1011C2×C4#1309399711yescharacteristic
1012C2×C4#1309399711yescharacteristic
1013C2×C4#1309399711yescharacteristic
1014C2×C4#1309399711yescharacteristic
1015C2×C4C2×D4×D4711yescharacteristic
1016C2×C4C2×D4×D4711yescharacteristic
1017C2×C4C2×D4×D4711yescharacteristic
1018C2×C4C2×D4×D4711yescharacteristic
1019C2×C4C2×D4×D4711yescharacteristic
1020C2×C4C2×D4×D4711yescharacteristic
1021C2×C4C2×D4×D4711yescharacteristic
1022C2×C4C2×D4×D4711yescharacteristic
1023C2×C4C2×D4×D4711yescharacteristic
1024C2×C4C2×D4×D4711yescharacteristic
1025C2×C4C2×D4×D4711yescharacteristic
1026C2×C4C2×D4×D4711yescharacteristic
1027C2×C4C2×#1062535011yescharacteristic
1028C2×C4C2×#1062535011yescharacteristic
1029C2×C4C2×#1062535011yescharacteristic
1030C2×C4C24×D4711yescharacteristic
1031C8—24no—
1032C8—24no—
1033C8—478no—
1034C8—944no—
1035C22—41no—
1036C22—41no—
1037C22—41no—
1038C22—41no—
1039C22—41no—
1040C22—41no—
1041C22—41no—
1042C22—42no—
1043C22—82no—
1044C22—82no—
1045C22—82no—
1046C22—944no—
1047C22—3762no—
1048C22—3762no—
1049C22—3762no—
1050C22—3762no—
1051C22—3762no—
1052C22—1884no—
1053C22—1882no—
1054C22C2×#1309399711yescharacteristic
1055C22C2×#1309399711yescharacteristic
1056C22C2×#1309399711yescharacteristic
1057C22C2×#1309399711yescharacteristic
1058C22C2×#1309399711yescharacteristic
1059C22C2×#1309399711yescharacteristic
1060C22C22×#1062535011yescharacteristic
1061C4—42no—
1062C4—944no—
1063C4—1882no—
1064C4C2×#1309399711yescharacteristic
1065C4C2×#1309399711yescharacteristic
1066C4C2×#1309399711yescharacteristic
1067C4C2×#1309399711yescharacteristic
1068C4C2×#1309399711yescharacteristic
1069C4C2×#1309399711yescharacteristic
1070C4C22×D4×D4711yescharacteristic
1071C4C22×D4×D4711yescharacteristic
1072C2—21no—
1073C2—21no—
1074C2—21no—
1075C2—21no—
1076C2—21no—
1077C2—21no—
1078C2—21no—
1079C2—82no—
1080C2—3762no—
1081C2—1884no—
1082C2C22×#1309399711yescharacteristic
subgroupG/H
centerC4C2×#13093997
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#413C2
socleC2×C47C22×#121
hypercenterC2×#413D47
hypocenterC47#60469
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
1. C2×#15689923C2semidirect
2. C2×#15689921C2semidirect
3. C2×#15689921C2semidirect
4. C2×#15689889C2semidirect
5. #20253128C2semidirect
6. #20253124C2semidirect
7. #20253119C2semidirect
8. #20253115C2semidirect
9. #20253107C2semidirect
10. C2×#15689171C2semidirect
11. C2×#15689105C2semidirect
12. C2×C47×#413C2semidirect
18. #15689923C22semidirect
26. #15689921C22semidirect
28. C2×#13094057C22semidirect
29. C2×#13094055C22semidirect
30. C2×#13094055C22semidirect
32. C2×#13094054C22semidirect
34. C2×#13094052C22semidirect
35. C2×#13094050C22semidirect
36. C2×#13094050C22semidirect
38. C2×#13094049C22semidirect
41. C2×#13094044C22semidirect
44. #15689889C22semidirect
45. #15689889C22semidirect
46. C2×#13094032C22semidirect
51. #15689397C22semidirect
52. #15689392C22semidirect
53. #15689389C22semidirect
54. #15689385C22semidirect
55. #15689171C22semidirect
56. #15689171C22semidirect
57. C2×#13093959C22semidirect
58. #15689105C22semidirect
59. #15689105C22semidirect
60. C2×#13093942C22semidirect
61. C2×#13093940C22semidirect
65. C47×#413C22semidirect
66. C47×#413C22semidirect
67. C2×#101×C47C22semidirect
68. C2×#100×C47C22semidirect
133. C2×#10625337C23semidirect
137. C2×#10625335C23semidirect
139. C2×#10625336C23semidirect
142. C2×#10625334C23semidirect
165. #13093959C23semidirect
166. #13093942C23semidirect
167. #13093940C23semidirect
199. #101×C47C23semidirect
200. #100×C47C23semidirect
542. C2×#413D47semidirect
604. #413C2×D47semidirect
605. #413C2×D47semidirect
607. C2×#101C2×D47semidirect
609. C2×#100C2×D47semidirect
610. C47#60469semidirect
740. #101C22×D47semidirect
742. #100C22×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156899232
C2×#156899212
C2×#156898892
#202531282
#202531242
#202531192
#202531152
#202531072
C2×#156891712
C2×#156891052
C2×C47×#4132
#6046947