Finite Group Databasebeta

← C2×#20291488 #28329558

Subgroups — C2×#20291488 #28329558

Order 13568.

2666 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133305C211yesmaximal, characteristic, complemented
2C2×D53⋊#131C211yesmaximal, characteristic, complemented
3#20291488C2116yesmaximal, direct product factor
4C2×#16811669C212yesmaximal, complemented
5C2×#16811668C212yesmaximal, complemented
6C2×#16811667C212yesmaximal, complemented
7C2×#16811666C212yesmaximal, complemented
8C2×#16811638C211yesmaximal, characteristic, complemented
9C2×#16811622C211yesmaximal, characteristic, complemented
10C2×#16811620C211yesmaximal, characteristic, complemented
11C2×#16811589C211yesmaximal, characteristic, complemented
12C2×#16811422C211yesmaximal, characteristic
13C2×#13133305—21no—
14C2×#13133305—21no—
15C2×#13133305—24no—
16C2×#13133305C2211yescharacteristic, complemented
17C2×#13133305C2211yescharacteristic, complemented
18C2×#13133305C2212yescomplemented
19C2×#13133305C2212yescomplemented
20C2×#13133305C2218yescomplemented
21D53⋊#131—24no—
22D53⋊#131C2218yescomplemented
23C2×#13133304—21no—
24C2×#13133304—21no—
25C2×#13133304C2211yescharacteristic, complemented
26C2×#13133304C2211yescharacteristic, complemented
27C22×#11719936—21no—
28C22×#11719936C2211yescharacteristic
29C2×D53⋊M16—21no—
30C2×D53⋊M16C2211yescharacteristic
31C22×D53⋊C8—21no—
32C22×D53⋊C8—21no—
33C22×D53⋊C8C2211yescharacteristic
34C2×#13133296C2211yescharacteristic
35#16811669C22116yescomplemented
36#16811668C22116yescomplemented
37#16811667C22116yescomplemented
38#16811666C22116yescomplemented
39#16811638C2218yescomplemented
40C2×#13133288C2212yescomplemented
41C2×#13133287C2212yescomplemented
42#16811622C2218yescomplemented
43#16811620C2218yescomplemented
44C2×#13133282C2212yescomplemented
45C2×#13133282C2212yescomplemented
46C2×#13133282C2212yescomplemented
47C2×#13133281C2212yescomplemented
48#16811589C2218yescomplemented
49C2×#13133271C2212yescomplemented
50C2×C8×#6157C2212yescomplemented
51C22×#11719949C2211yescharacteristic
52C2×#41×D53C2211yescharacteristic
53#16811422C418yescomplemented
54#16811422C2218yes—
55C2×#13133249C412yescomplemented
56C2×#13133248C411yescharacteristic, complemented
57C2×#13133245C411yescharacteristic, complemented
58C2×#13133244C412yescomplemented
59C2×#13133242C411yescharacteristic, complemented
60C2×#13133240C2212yes—
61C2×#13133238C2212yes—
62C2×M16×D53C2211yescharacteristic
63C2×#137×C53C411yescharacteristic, complemented
64#13133305—22no—
65#13133305—22no—
66#13133305—28no—
67#13133305—28no—
68#13133305—24no—
69#13133305—24no—
70#13133305C2318yescomplemented
71#13133305C2314yescomplemented
72#13133305C2318yescomplemented
73#13133305C2314yescomplemented
74#13133304—22no—
75#13133304—22no—
76#13133304—28no—
77#13133304—28no—
78#13133304C2314yescomplemented
79#13133304C2314yescomplemented
80C2×#11719936—21no—
81C2×#11719936—22no—
82C2×#11719936—21no—
83C2×#11719936—21no—
84C2×#11719936—22no—
85C2×#11719936—22no—
86C2×#11719936—28no—
87C2×#11719936C2312yes—
88C2×#11719936C2311yescharacteristic
89C2×#11719936C2311yescharacteristic
90C2×#11719936C2314yes—
91D53⋊M16—28no—
92D53⋊M16—22no—
93D53⋊M16C2314yes—
94C2×#11719940—21no—
95C2×#11719940—21no—
96C2×#11719940—21no—
97C2×D53⋊C8—28no—
98C2×D53⋊C8—21no—
99C2×D53⋊C8—21no—
100C2×D53⋊C8—21no—
101C2×D53⋊C8—22no—
102C2×D53⋊C8—22no—
103C2×D53⋊C8—28no—
104C2×D53⋊C8D411yescharacteristic
105C2×D53⋊C8D411yescharacteristic
106C2×D53⋊C8D414yes—
107C2×D53⋊C8C2311yescharacteristic
108C2×D53⋊C8C2311yescharacteristic
109C2×D53⋊C8C2314yes—
110C22×#88324—21no—
111C22×#88324—21no—
112C22×#88324—21no—
113C22×#88324D411yescharacteristic
114C22×#88324D411yescharacteristic
115#13133296—22no—
116#13133296C2314yes—
117C2×C4⋊#6157—21no—
118C2×C22⋊#6157—21no—
119C2×C4×#6157C2312yes—
120#13133288C2318yescomplemented
121#13133287C2318yescomplemented
122#13133282C2318yescomplemented
123#13133282C2318yescomplemented
124#13133282C2318yescomplemented
125#13133281C2318yescomplemented
126#13133271C2318yescomplemented
127C8×#6157C2318yescomplemented
128C2×#11719949—21no—
129C2×#11719949—22no—
130C2×#11719949—22no—
131C2×#11719949—21no—
132C2×#11719949C2×C412yes—
133C2×#11719949C2×C414yes—
134C2×#11719949C2312yes—
135C2×#11719949C2311yescharacteristic
136C2×#11719949C2314yes—
137C2×#11719945—21no—
138C2×#11719945C2×C411yescharacteristic
139C2×#11719947—21no—
140C2×#11719947C2311yescharacteristic
141#41×D53—22no—
142#41×D53—22no—
143#41×D53C2×C414yes—
144#41×D53C2314yes—
145C2×Q8×D53C2×C411yescharacteristic
146C22×D212—21no—
147C22×D212C2×C411yescharacteristic
148C2×D4×D53—21no—
149C2×D4×D53C2×C411yescharacteristic
150C22×C4×D53—21no—
151C22×C4×D53—21no—
152C22×C4×D53C2311yescharacteristic
153#13133249C2×C4116yescomplemented
154#13133248C2×C418yescomplemented
155#13133245C2×C418yescomplemented
156#13133244C2×C4116yescomplemented
157#13133242C2×C418yescomplemented
158#13133240C2×C418yes—
159#13133240C2318yes—
160#13133238C2×C418yes—
161#13133238C2318yes—
162C2×#11719925C2×C412yes—
163C2×#11719913C2×C412yes—
164C2×#11719924C2×C412yes—
165C2×#11719924C2×C412yes—
166C2×D424C2×C412yes—
167C2×#11719922C2×C412yes—
168C2×#11719917C2×C411yescharacteristic
169C2×#11719912C2×C412yes—
170M16×D53C2×C414yes—
171M16×D53C2314yes—
172C2×C8×D53C2312yes—
173C2×#41×C53C2×C411yescharacteristic
174C22×Q8×C53C2×C411yescharacteristic
175#137×C53C2×C418yescomplemented
176C2×Q16×C53C2×C412yes—
177C2×SD16×C53C2×C412yes—
178C2×M16×C53C2×C411yescharacteristic
179C23×D53—21no—
180C23×D53—21no—
181C23×D53#4111yescharacteristic
182C22×#6157—22no—
183#41×C53—22no—
184#41×C53C22×C414yes—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53C22×C412yes—
188C2×Q8×C53C22×C411yescharacteristic
189C2×Q8×C53C22×C414yes—
190C2×D4×C53—21no—
191C2×D4×C53C22×C411yescharacteristic
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53C22×C411yescharacteristic
195C2×C22⋊D53—21no—
196C2×C22⋊D53—21no—
197C2×C22⋊D53—21no—
198C22×Dic53—21no—
199C22×Dic53C2×D411yescharacteristic
200#11719949—24no—
201#11719949—24no—
202#11719949—24no—
203#11719949—21no—
204#11719949—22no—
205#11719949—24no—
206#11719949—21no—
207#11719949—22no—
208#11719949—24no—
209#11719949C22×C414yes—
210#11719949C22×C412yes—
211#11719949C22×C418yes—
212#11719949C2414yes—
213#11719949C2412yes—
214Q8×D53—22no—
215Q8×D53C22×C414yes—
216#11719947—24no—
217#11719947—24no—
218#11719947—21no—
219#11719947—21no—
220#11719947C22×C412yes—
221#11719947C2412yes—
222D4×D53—24no—
223D4×D53—24no—
224D4×D53—22no—
225D4×D53C22×C414yes—
226#11719945—22no—
227#11719945—24no—
228#11719945—24no—
229#11719945C22×C414yes—
230C2×D212—22no—
231C2×D212—24no—
232C2×D212—21no—
233C2×D212—22no—
234C2×D212—24no—
235C2×D212—21no—
236C2×D212—22no—
237C2×D212C22×C412yes—
238C2×D212C22×C411yescharacteristic
239C2×D212C22×C414yes—
240C2×C4×D53—21no—
241C2×C4×D53—21no—
242C2×C4×D53—22no—
243C2×C4×D53—24no—
244C2×C4×D53—21no—
245C2×C4×D53—22no—
246C2×C4×D53—24no—
247C2×C4×D53—24no—
248C2×C4×D53—24no—
249C2×C4×D53C22×C412yes—
250C2×C4×D53C22×C411yescharacteristic
251C2×C4×D53C2×D411yescharacteristic
252C2×C4×D53C2×D412yes—
253C2×C4×D53#4112yes—
254C2×C4×D53#4111yescharacteristic
255C2×C4×D53C2411yescharacteristic
256C2×C4×D53C2412yes—
257C2×Dic106—21no—
258C2×Dic106C22×C411yescharacteristic
259C22⋊#6157—24no—
260#11719940—24no—
261#11719940—24no—
262#11719940—24no—
263C2×#88324—21no—
264C2×#88324—21no—
265C2×#88324—22no—
266C2×#88324—24no—
267C2×#88324—24no—
268C2×#88324—24no—
269C2×#88324C2×D411yescharacteristic
270C2×#88324C2×D411yescharacteristic
271C2×#88324C2×D411yescharacteristic
272C2×#88324C2×D414yes—
273C2×#88324C2×D411yescharacteristic
274C2×#88324C2×D414yes—
275C4⋊#6157—24no—
276C4×#6157—22no—
277C4×#6157C2414yes—
278#11719936—21no—
279#11719936—21no—
280#11719936—22no—
281#11719936—24no—
282#11719936—24no—
283#11719936—24no—
284#11719936—28no—
285#11719936—28no—
286#11719936C2414yes—
287#11719936C2412yes—
288#11719936C2412yes—
289D53⋊C8—24no—
290D53⋊C8—24no—
291D53⋊C8—24no—
292D53⋊C8—28no—
293D53⋊C8—28no—
294D53⋊C8C2×D414yes—
295D53⋊C8C2×D414yes—
296D53⋊C8C2×D412yes—
297D53⋊C8C2×D412yes—
298D53⋊C8C2412yes—
299D53⋊C8C2412yes—
300Q16×C53C22×C418yes—
301SD16×C53C22×C418yes—
302M16×C53C22×C414yes—
303C2×C8×C53C22×C412yes—
304#11719925C22×C418yes—
305#11719924C22×C418yes—
306#11719924C22×C418yes—
307#11719922C22×C418yes—
308#11719917C22×C414yes—
309C2×#88322C22×C412yes—
310D424C22×C418yes—
311#11719913C22×C418yes—
312#11719912C22×C418yes—
313C8×D53C22×C414yes—
314C8×D53C2414yes—
315C23×C53—21no—
316C23×C53C4×D411yescharacteristic
317C22×D53—24no—
318C22×D53—22no—
319C22×D53—21no—
320C22×D53—24no—
321C22×D53—42no—
322C22×D53—44no—
323C22×D53—44no—
324C22×D53C4×D411yescharacteristic
325C22×D53C4×D412yes—
326C22×D53C2×#4111yescharacteristic
327C22×D53C2×#4112yes—
328C2×#6157—24no—
329C2×#6157—44no—
330Q8×C53—21no—
331Q8×C53—22no—
332Q8×C53—24no—
333Q8×C53C23×C412yes—
334Q8×C53C23×C414yes—
335D4×C53—24no—
336D4×C53—21no—
337D4×C53C23×C412yes—
338C2×C4×C53—21no—
339C2×C4×C53—24no—
340C2×C4×C53—22no—
341C2×C4×C53—24no—
342C2×C4×C53C4×D411yescharacteristic
343C2×C4×C53C4×D412yes—
344C2×C4×C53C23×C411yescharacteristic
345C2×C4×C53C23×C412yes—
346C22⋊D53—24no—
347C22⋊D53—22no—
348C22⋊D53—22no—
349C22⋊D53—24no—
350C2×Dic53—21no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53C4×D411yescharacteristic
354C2×Dic53C4×D412yes—
355C2×Dic53C22×D411yescharacteristic
356C2×Dic53C22×D412yes—
357D212—28no—
358D212—24no—
359D212—22no—
360D212—24no—
361D212—22no—
362D212—22no—
363D212—24no—
364D212—21no—
365D212C23×C414yes—
366D212C23×C412yes—
367C4×D53—24no—
368C4×D53—24no—
369C4×D53—22no—
370C4×D53—28no—
371C4×D53—24no—
372C4×D53—22no—
373C4×D53—24no—
374C4×D53C4×D412yes—
375C4×D53C4×D412yes—
376C4×D53C4×D412yes—
377C4×D53C23×C412yes—
378C4×D53C23×C411yescharacteristic
379C4×D53C22×D411yescharacteristic
380C4×D53C22×D412yes—
381C4×D53C2×#4111yescharacteristic
382C4×D53C2×#4112yes—
383C4×D53C2511yescharacteristic
384Dic106—21no—
385Dic106—24no—
386Dic106C23×C412yes—
387#88324—24no—
388#88324—22no—
389#88324—22no—
390#88324C22×D412yes—
391#88324C22×D412yes—
392#88324C22×D412yes—
393#88324C22×D412yes—
394C8×C53C23×C414yes—
395#88322C23×C414yes—
396C2×#2955—531nomaximal, Sylow
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—42no—
400C22×C53C2×C4×D412yes—
401C22×C53C2×C4×D411yescharacteristic
402C2×D53—22no—
403C2×D53—22no—
404C2×D53—24no—
405C2×D53—22no—
406C2×D53—42no—
407C2×D53—42no—
408C2×D53—48no—
409C2×D53—48no—
410C2×D53—44no—
411C2×D53—42no—
412C2×D53C2×C4×D412yes—
413C2×D53C2×C4×D411yescharacteristic
414C2×D53C22×#4111yescharacteristic
415#6157—44no—
416C4×C53—22no—
417C4×C53—24no—
418C4×C53C2×C4×D411yescharacteristic
419C4×C53C2×C4×D412yes—
420C4×C53C24×C411yescharacteristic
421Dic53—22no—
422Dic53C2×C4×D412yes—
423Dic53C2×C4×D411yescharacteristic
424Dic53C23×D411yescharacteristic
425C2×#575—531no—
426C22×#131—531no—
427C22×#131—531no—
428#2955—5316no—
429C2×#444—532no—
430C2×#444—532no—
431C2×#443—532no—
432C2×#443—532no—
433C2×#430—531no—
434C2×#421—531no—
435C2×#421—531no—
436C2×#405—531no—
437C2×C53—22no—
438C2×C53—42no—
439C2×C53#295512yescomplemented
440C2×C53C22×C4×D411yescharacteristic
441D53—21no—
442D53—22no—
443D53—21no—
444D53—44no—
445D53—42no—
446C22×#41—531no—
447C22×#41—531no—
448#575—538no—
449#575—538no—
450C2×#137—531no—
451C2×#137—532no—
452C2×#137#615711yescharacteristic, complemented
453C2×AGL(1,ℤ/8)—531no—
454C2×AGL(1,ℤ/8)—532no—
455C2×AGL(1,ℤ/8)—531no—
456C2×#135—532no—
457C2×#135—532no—
458C2×#131—531no—
459C2×#131—532no—
460C2×#131—531no—
461C2×#131—531no—
462C2×#131—532no—
463C2×#131—531no—
464C2×#131—538no—
465C2×#131—538no—
466C2×#131—1061no—
467C2×#131—1061no—
468C2×#131—1064no—
469C2×#131—1061no—
470C2×#131—1061no—
471C2×#131—1064no—
472C22×M16—531no—
473C22×M16—531no—
474C22×M16—531no—
475C22×M16—1061no—
476C22×M16—1061no—
477C23×C8—531no—
478C23×C8—1061no—
479C23×C8—1061no—
480C2×#117—531no—
481#444—5316no—
482#444—5316no—
483#443—5316no—
484#443—5316no—
485#430—538no—
486C2×#108—532no—
487C2×#108—532no—
488#421—538no—
489#421—538no—
490C2×#104—532no—
491C2×#104—532no—
492C2×#104—532no—
493C2×#104—532no—
494#405—538no—
495C2×#97—532no—
496C2×C4×C8—532no—
497C53C2×#295511yescharacteristic, complemented, Sylow
498C2×#41—534no—
499C2×#41—534no—
500C2×#41—531no—
501C2×#41—532no—
502C2×#41—534no—
503C2×#41—532no—
504C2×#41—534no—
505C2×#41—531no—
506C2×#41—531no—
507C2×#41—1061no—
508C2×#41—1061no—
509C2×#41—1061no—
510C2×#41—1062no—
511C2×#41—1061no—
512C2×#41—1062no—
513C2×#41—1062no—
514C2×#41—1062no—
515C2×#41C2×#615711yescharacteristic
516C22×Q8—531no—
517C22×Q8C2×#615711yescharacteristic
518C22×D4—531no—
519C22×D4—531no—
520C22×D4—1061no—
521C22×D4—1061no—
522C23×C4—531no—
523C23×C4—1061no—
524C23×C4—1061no—
525#137—538no—
526#137—5316no—
527#137C2×#615718yescomplemented
528AGL(1,ℤ/8)—538no—
529AGL(1,ℤ/8)—5316no—
530AGL(1,ℤ/8)—538no—
531#135—538no—
532#135—538no—
533#135—538no—
534#135—538no—
535C2×Q16—532no—
536C2×Q16C2×#615712yes—
537C2×SD16—532no—
538C2×SD16—532no—
539C2×SD16—532no—
540C2×SD16C2×#615712yes—
541C2×D8—532no—
542C2×D8—532no—
543#131—534no—
544#131—534no—
545#131—538no—
546#131—534no—
547#131—534no—
548#131—538no—
549#131—1068no—
550#131—1068no—
551#131—1062no—
552#131—1062no—
553#131—1068no—
554#131—1068no—
555#131—1062no—
556#131—1064no—
557#131—1062no—
558#131—1064no—
559C2×M16—531no—
560C2×M16—534no—
561C2×M16—534no—
562C2×M16—532no—
563C2×M16—531no—
564C2×M16—531no—
565C2×M16—532no—
566C2×M16—534no—
567C2×M16—534no—
568C2×M16—1061no—
569C2×M16—1061no—
570C2×M16—1068no—
571C2×M16—1061no—
572C2×M16—1062no—
573C2×M16—1061no—
574C2×M16—1062no—
575C2×M16—1068no—
576C2×M16—1061no—
577C2×M16—1062no—
578C2×M16—1061no—
579C2×M16—1062no—
580C2×M16C2×#615711yescharacteristic
581C22×C8—531no—
582C22×C8—531no—
583C22×C8—531no—
584C22×C8—531no—
585C22×C8—531no—
586C22×C8—531no—
587C22×C8—534no—
588C22×C8—534no—
589C22×C8—532no—
590C22×C8—1061no—
591C22×C8—1061no—
592C22×C8—1061no—
593C22×C8—1062no—
594C22×C8—1061no—
595C22×C8—1062no—
596C22×C8—1068no—
597C22×C8—1068no—
598C22×C8—1061no—
599C22×C8—1061no—
600#117—534no—
601#117—1062no—
602C2×C4⋊C4—1061no—
603C2×C22⋊C4—1061no—
604C2×C42—532no—
605#108—538no—
606#108—538no—
607#104—538no—
608#104—538no—
609#104—538no—
610#104—538no—
611#97—538no—
612C4×C8—538no—
613C24—531no—
614C24—1061no—
615C24—1061no—
616#41—22no—
617#41—532no—
618#41—534no—
619#41—538no—
620#41—532no—
621#41—534no—
622#41—532no—
623#41—532no—
624#41—534no—
625#41—1064no—
626#41—1064no—
627#41—1064no—
628#41—1061no—
629#41—1064no—
630#41—1061no—
631#41—1064no—
632#41—1062no—
633#41—1061no—
634#41—1064no—
635#41—1064no—
636#41—1064no—
637#41—1062no—
638#41—1061no—
639#41—1064no—
640#41—1062no—
641#41C22×#615714yes—
642C2×Q8—22no—
643C2×Q8—21no—
644C2×Q8—534no—
645C2×Q8—531no—
646C2×Q8—1061no—
647C2×Q8—1062no—
648C2×Q8C22×#615711yescharacteristic
649C2×Q8C22×#615712yes—
650C2×Q8C22×#615714yes—
651C2×D4—21no—
652C2×D4—534no—
653C2×D4—532no—
654C2×D4—531no—
655C2×D4—534no—
656C2×D4—1064no—
657C2×D4—1064no—
658C2×D4—1061no—
659C2×D4—1062no—
660C2×D4—1062no—
661C2×D4—1062no—
662C2×D4—1061no—
663C2×D4—1064no—
664C2×D4—1064no—
665C2×D4—1061no—
666C2×D4—1061no—
667C2×D4—1062no—
668C2×D4—1061no—
669C2×D4C22×#615711yescharacteristic
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—531no—
673C22×C4—531no—
674C22×C4—532no—
675C22×C4—531no—
676C22×C4—532no—
677C22×C4—531no—
678C22×C4—532no—
679C22×C4—531no—
680C22×C4—532no—
681C22×C4—1064no—
682C22×C4—1061no—
683C22×C4—1062no—
684C22×C4—1064no—
685C22×C4—1064no—
686C22×C4—1062no—
687C22×C4—1064no—
688C22×C4—1061no—
689C22×C4—1061no—
690C22×C4—1061no—
691C22×C4—1062no—
692C22×C4C22×#615711yescharacteristic
693Q16—538no—
694Q16C22×#615718yes—
695SD16—538no—
696SD16—538no—
697SD16—538no—
698SD16C22×#615718yes—
699D8—538no—
700D8—538no—
701M16—534no—
702M16—538no—
703M16—534no—
704M16—532no—
705M16—532no—
706M16—1064no—
707M16—1068no—
708M16—1064no—
709M16—1068no—
710M16—1064no—
711M16—1064no—
712M16—1064no—
713M16—1061no—
714M16—1061no—
715M16—1062no—
716M16—1064no—
717M16C22×#615714yes—
718C2×C8—531no—
719C2×C8—531no—
720C2×C8—531no—
721C2×C8—534no—
722C2×C8—531no—
723C2×C8—534no—
724C2×C8—532no—
725C2×C8—532no—
726C2×C8—534no—
727C2×C8—534no—
728C2×C8—532no—
729C2×C8—532no—
730C2×C8—532no—
731C2×C8—534no—
732C2×C8—534no—
733C2×C8—1064no—
734C2×C8—1064no—
735C2×C8—1064no—
736C2×C8—1068no—
737C2×C8—1064no—
738C2×C8—1068no—
739C2×C8—1064no—
740C2×C8—1061no—
741C2×C8—1061no—
742C2×C8—1062no—
743C2×C8—1064no—
744C2×C8C22×#615712yes—
745C4⋊C4—1064no—
746C22⋊C4—1064no—
747C42—534no—
748C42—1062no—
749C23—21no—
750C23—531no—
751C23—531no—
752C23—532no—
753C23—532no—
754C23—1064no—
755C23—1064no—
756C23—1062no—
757C23—1061no—
758C23—2122no—
759C23—2124no—
760C23—2124no—
761C23D4×#615711yescharacteristic
762Q8—24no—
763Q8—22no—
764Q8—21no—
765Q8—532no—
766Q8—1064no—
767Q8—1061no—
768Q8C23×#615712yes—
769Q8C23×#615714yes—
770D4—24no—
771D4—21no—
772D4—534no—
773D4—532no—
774D4—1062no—
775D4—1062no—
776D4—1064no—
777D4—1068no—
778D4—1064no—
779D4—1064no—
780D4—1062no—
781D4—1062no—
782D4—1064no—
783D4—1064no—
784D4—1062no—
785D4—1061no—
786D4C23×#615712yes—
787C2×C4—24no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—532no—
792C2×C4—532no—
793C2×C4—531no—
794C2×C4—531no—
795C2×C4—532no—
796C2×C4—532no—
797C2×C4—532no—
798C2×C4—532no—
799C2×C4—531no—
800C2×C4—531no—
801C2×C4—532no—
802C2×C4—531no—
803C2×C4—532no—
804C2×C4—531no—
805C2×C4—1062no—
806C2×C4—1064no—
807C2×C4—1062no—
808C2×C4—1064no—
809C2×C4—1068no—
810C2×C4—1064no—
811C2×C4—1062no—
812C2×C4—1062no—
813C2×C4—1061no—
814C2×C4—1064no—
815C2×C4—1064no—
816C2×C4—2124no—
817C2×C4D4×#615712yes—
818C2×C4D4×#615711yescharacteristic
819C2×C4C23×#615712yes—
820C2×C4C23×#615711yescharacteristic
821C8—532no—
822C8—532no—
823C8—532no—
824C8—532no—
825C8—534no—
826C8—1064no—
827C8—1062no—
828C8—1062no—
829C8C23×#615714yes—
830C22—22no—
831C22—22no—
832C22—42no—
833C22—531no—
834C22—532no—
835C22—531no—
836C22—1062no—
837C22—1062no—
838C22—1064no—
839C22—1062no—
840C22—2122no—
841C22—2122no—
842C22—2128no—
843C22—2128no—
844C22—2124no—
845C22—2122no—
846C22C2×D4×#615712yes—
847C22C2×D4×#615711yescharacteristic
848C4—22no—
849C4—24no—
850C4—531no—
851C4—531no—
852C4—532no—
853C4—1062no—
854C4—2124no—
855C4C2×D4×#615712yes—
856C4C2×D4×#615711yescharacteristic
857C4C24×#615711yescharacteristic
858C2—22no—
859C2—42no—
860C2—1061no—
861C2—1062no—
862C2—1061no—
863C2—2124no—
864C2—2122no—
865C2#2029148812yesdirect product factor
866C2C22×D4×#615711yescharacteristic
subgroupG/H
centerC22C2×D4×#6157
commutatorC4×C53C24×C4
FrattiniC4C24×#6157
FittingC2×#137×C53C4
socleC22×C53C2×C4×D4
prime radicalC2×#16811422C2
cosocleC4×D53C25
hypercenterC2×#137#6157
hypocenterC53C2×#2955
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#13133305C2semidirect
2. C2×D53⋊#131C2semidirect
3. #20291488C2direct (N × H)
4. C2×#16811669C2semidirect
5. C2×#16811668C2semidirect
6. C2×#16811667C2semidirect
7. C2×#16811666C2semidirect
8. C2×#16811638C2semidirect
9. C2×#16811622C2semidirect
10. C2×#16811620C2semidirect
11. C2×#16811589C2semidirect
16. C2×#13133305C22semidirect
17. C2×#13133305C22semidirect
18. C2×#13133305C22semidirect
19. C2×#13133305C22semidirect
20. C2×#13133305C22semidirect
22. D53⋊#131C22semidirect
25. C2×#13133304C22semidirect
26. C2×#13133304C22semidirect
35. #16811669C22semidirect
36. #16811668C22semidirect
37. #16811667C22semidirect
38. #16811666C22semidirect
39. #16811638C22semidirect
40. C2×#13133288C22semidirect
41. C2×#13133287C22semidirect
42. #16811622C22semidirect
43. #16811620C22semidirect
44. C2×#13133282C22semidirect
45. C2×#13133282C22semidirect
46. C2×#13133282C22semidirect
47. C2×#13133281C22semidirect
48. #16811589C22semidirect
49. C2×#13133271C22semidirect
50. C2×C8×#6157C22semidirect
53. #16811422C4semidirect
55. C2×#13133249C4semidirect
56. C2×#13133248C4semidirect
57. C2×#13133245C4semidirect
58. C2×#13133244C4semidirect
59. C2×#13133242C4semidirect
63. C2×#137×C53C4semidirect
70. #13133305C23semidirect
71. #13133305C23semidirect
72. #13133305C23semidirect
73. #13133305C23semidirect
78. #13133304C23semidirect
79. #13133304C23semidirect
120. #13133288C23semidirect
121. #13133287C23semidirect
122. #13133282C23semidirect
123. #13133282C23semidirect
124. #13133282C23semidirect
125. #13133281C23semidirect
126. #13133271C23semidirect
127. C8×#6157C23semidirect
153. #13133249C2×C4semidirect
154. #13133248C2×C4semidirect
155. #13133245C2×C4semidirect
156. #13133244C2×C4semidirect
157. #13133242C2×C4semidirect
175. #137×C53C2×C4semidirect
439. C2×C53#2955semidirect
452. C2×#137#6157semidirect
497. C53C2×#2955semidirect
527. #137C2×#6157semidirect
865. C2#20291488direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131333052
C2×D53⋊#1312
#202914882
C2×#168116692
C2×#168116682
C2×#168116672
C2×#168116662
C2×#168116382
C2×#168116222
C2×#168116202
C2×#168115892
C2×#168114222
C2×#295553