Finite Group Databasebeta

← C2×#20286287 #28259139

Subgroups — C2×#20286287 #28259139

Order 13568.

2742 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133249C211yesmaximal, characteristic, complemented
2C22×Q16×D53C211yesmaximal, characteristic, complemented
3C2×Q8×D212C211yesmaximal, characteristic, complemented
4C2×#16811285C211yesmaximal, characteristic
5#20286287C2116yesmaximal, direct product factor
6C2×#16811017C211yesmaximal, characteristic, complemented
7C2×#16810882C211yesmaximal, characteristic, complemented
8C2×#16810853C211yesmaximal, characteristic, complemented
9C2×#16810845C211yesmaximal, characteristic, complemented
10C2×#16810833C211yesmaximal, characteristic, complemented
11C2×#16810788C211yesmaximal, characteristic, complemented
12C2×#16810780C211yesmaximal, characteristic, complemented
13C2×#16810780C211yesmaximal, characteristic, complemented
14C2×#16810763C211yesmaximal, characteristic, complemented
15C2×#16810696C211yesmaximal, characteristic, complemented
16C2×C53×#441C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic
20C22×Q8×D53C2211yescharacteristic
21C2×#13133249—28no—
22C2×#13133249C2218yescomplemented
23C22×Dic212C2211yescharacteristic
24C22×Dic212C2211yescharacteristic
25C22×#11719925C2211yescharacteristic
26C22×#11719925C2211yescharacteristic
27C22×#11719925C2211yescharacteristic
28C2×Q16×D53—28no—
29C2×Q16×D53C2218yescomplemented
30C22×#11719913C2211yescharacteristic
31C22×#11719913C2211yescharacteristic
32C22×#11719924C2211yescharacteristic
33C22×#11719912C2211yescharacteristic
34C22×C8×D53C2211yescharacteristic
35Q8×D212—24no—
36Q8×D212C2218yescomplemented
37#16811285—24no—
38#16811285C2218yes—
39C2×#13133217—21no—
40C2×#13133217C2211yescharacteristic
41C2×#13133205—21no—
42C2×#13133205C2211yescharacteristic
43C2×#13133197—21no—
44C2×#13133197—21no—
45C2×#13133197—21no—
46C2×#13133197C2211yescharacteristic
47C2×#13133197C2211yescharacteristic
48C2×#13133197C2211yescharacteristic
49C2×#13133192—21no—
50C2×#13133192C2211yescharacteristic
51C2×C4×D212—21no—
52C2×C4×D212—21no—
53C2×C4×D212C2211yescharacteristic
54#16811017C2218yescomplemented
55#16810882C2218yescomplemented
56#16810853C2218yescomplemented
57#16810845C2218yescomplemented
58#16810833C2218yescomplemented
59#16810788C2218yescomplemented
60#16810780C2218yescomplemented
61#16810780C2218yescomplemented
62#16810763C2218yescomplemented
63#16810696C2218yescomplemented
64C2×C4⋊#88322C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133140C2211yescharacteristic
67C2×#13133140C2211yescharacteristic
68C2×#13133137C2211yescharacteristic
69C2×#13133129C2211yescharacteristic
70C2×#13133129C2211yescharacteristic
71C22×Q16×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×Q8×C53C2211yescharacteristic
74C53×#441C2218yescomplemented
75C2×#106×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C2×#103×C53C2211yescharacteristic
78C2×#97×C53C2211yescharacteristic
79C2×#11719949—22no—
80C2×#11719949—24no—
81C2×#11719949—42no—
82C2×#11719949C2314yes—
83C22×Dic106—21no—
84C22×Dic106—21no—
85C22×Dic106—21no—
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2311yescharacteristic
88C22×Dic106C2311yescharacteristic
89C2×Q8×D53—22no—
90C2×Q8×D53—22no—
91C2×Q8×D53—22no—
92C2×Q8×D53—24no—
93C2×Q8×D53—24no—
94C2×Q8×D53—24no—
95C2×Q8×D53—42no—
96C2×Q8×D53—42no—
97C2×Q8×D53—42no—
98C2×Q8×D53C2314yes—
99C2×Q8×D53C2314yes—
100C2×Q8×D53C2314yes—
101C22×D212—21no—
102C22×D212—21no—
103C22×D212D411yescharacteristic
104C22×D212C2311yescharacteristic
105C22×C4×D53—21no—
106C22×C4×D53—21no—
107C22×C4×D53—21no—
108C22×C4×D53—21no—
109C22×C4×D53C2311yescharacteristic
110C22×C4×D53C2311yescharacteristic
111#13133249—232no—
112C2×Dic212—24no—
113C2×Dic212—42no—
114C2×Dic212C2314yes—
115C2×Dic212C2314yes—
116C2×#11719925—24no—
117C2×#11719925—24no—
118C2×#11719925—24no—
119C2×#11719925C2314yes—
120C2×#11719925C2314yes—
121C2×#11719925C2314yes—
122Q16×D53—232no—
123C2×#11719913—24no—
124C2×#11719913—42no—
125C2×#11719913C2314yes—
126C2×#11719913C2314yes—
127C2×#11719924—24no—
128C2×#11719924C2314yes—
129C2×#11719912—24no—
130C2×#11719912C2314yes—
131C22×#88322C2311yescharacteristic
132C22×#88322C2311yescharacteristic
133C2×C8×D53—24no—
134C2×C8×D53C2314yes—
135#13133217—22no—
136#13133217—28no—
137#13133217C2314yes—
138#13133205—22no—
139#13133205—28no—
140#13133205C2314yes—
141#13133197—28no—
142#13133197—28no—
143#13133197—28no—
144#13133197—22no—
145#13133197—22no—
146#13133197—22no—
147#13133197C2314yes—
148#13133197C2314yes—
149#13133197C2314yes—
150#13133192—28no—
151#13133192—22no—
152#13133192C2314yes—
153C4×D212—28no—
154C4×D212—28no—
155C4×D212D414yes—
156C4×D212C2314yes—
157C2×C4⋊Dic53—21no—
158C2×C4⋊Dic53—21no—
159C2×C4⋊Dic53—21no—
160C2×C4⋊Dic53—21no—
161C2×C4⋊Dic53—21no—
162C2×C4⋊Dic53D411yescharacteristic
163C2×#11719921—21no—
164C2×#11719921—21no—
165C2×#11719921—21no—
166C2×#11719921—21no—
167C2×#11719921—21no—
168C2×#11719921—21no—
169C2×#11719921D411yescharacteristic
170C2×#11719921D411yescharacteristic
171C4⋊#88322C2314yes—
172#13133140C2314yes—
173#13133140C2314yes—
174#13133140C2314yes—
175#13133137C2314yes—
176#13133129C2314yes—
177#13133129C2314yes—
178C22×Q8×C53C2311yescharacteristic
179C22×Q8×C53C2311yescharacteristic
180C2×Q16×C53D418yescomplemented
181C2×Q16×C53C2314yes—
182C22×C8×C53C2311yescharacteristic
183C22×C8×C53C2311yescharacteristic
184C4×Q8×C53—22no—
185C4×Q8×C53—22no—
186C4×Q8×C53C2314yes—
187C4×Q8×C53C2314yes—
188C2×C4⋊C4×C53—21no—
189C2×C4⋊C4×C53—21no—
190C2×C4⋊C4×C53C2311yescharacteristic
191C2×C4⋊C4×C53C2311yescharacteristic
192C2×C42×C53—21no—
193C2×C42×C53—21no—
194C2×C42×C53C2311yescharacteristic
195#106×C53C2314yes—
196#103×C53C2314yes—
197#103×C53C2314yes—
198#97×C53C2314yes—
199C23×D53—21no—
200C23×D53C2×D411yescharacteristic
201C23×D53C2×D411yescharacteristic
202C2×Q8×C53—21no—
203C2×Q8×C53—21no—
204C2×Q8×C53—22no—
205C2×Q8×C53—22no—
206C2×Q8×C53C2×D414yes—
207C2×Q8×C53C2×D414yes—
208C2×Q8×C53C2412yes—
209C2×Q8×C53C2412yes—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2411yescharacteristic
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222#11719949—28no—
223#11719949—44no—
224#11719949—48no—
225Q8×D53—28no—
226Q8×D53—28no—
227Q8×D53—28no—
228Q8×D53—44no—
229Q8×D53—44no—
230Q8×D53—44no—
231Q8×D53—48no—
232Q8×D53—48no—
233Q8×D53—48no—
234C2×D212—24no—
235C2×D212—22no—
236C2×D212—22no—
237C2×D212—24no—
238C2×D212—24no—
239C2×D212—21no—
240C2×D212—44no—
241C2×D212—44no—
242C2×D212C2×D414yes—
243C2×D212C2412yes—
244C2×C4×D53—22no—
245C2×C4×D53—22no—
246C2×C4×D53—22no—
247C2×C4×D53—22no—
248C2×C4×D53—24no—
249C2×C4×D53—24no—
250C2×C4×D53—24no—
251C2×C4×D53—24no—
252C2×C4×D53—44no—
253C2×C4×D53—44no—
254C2×C4×D53—44no—
255C2×C4×D53—44no—
256C2×C4×D53C2×D412yes—
257C2×C4×D53C2×D412yes—
258C2×C4×D53C2412yes—
259C2×C4×D53C2412yes—
260C2×Dic106—22no—
261C2×Dic106—22no—
262C2×Dic106—22no—
263C2×Dic106—22no—
264C2×Dic106—22no—
265C2×Dic106—22no—
266C2×Dic106—21no—
267C2×Dic106—21no—
268C2×Dic106—21no—
269C2×Dic106—24no—
270C2×Dic106—24no—
271C2×Dic106—24no—
272C2×Dic106—44no—
273C2×Dic106—44no—
274C2×Dic106—44no—
275C2×Dic106C2412yes—
276C2×Dic106C2412yes—
277C2×Dic106C2412yes—
278Q16×C53C2×D4116yescomplemented
279C2×C8×C53—22no—
280C2×C8×C53C2×D414yes—
281C2×C8×C53C2412yes—
282C2×C8×C53C2412yes—
283C4⋊C4×C53—24no—
284C4⋊C4×C53—24no—
285C4⋊C4×C53—21no—
286C4⋊C4×C53—21no—
287C4⋊C4×C53C2412yes—
288C4⋊C4×C53C2412yes—
289C42×C53—24no—
290C42×C53—24no—
291C42×C53C2×D412yes—
292C42×C53C2412yes—
293#11719925—28no—
294#11719925—28no—
295#11719925—28no—
296#11719924—28no—
297#11719921—24no—
298#11719921—24no—
299#11719921—24no—
300#11719921—24no—
301#11719921—24no—
302#11719921—24no—
303#11719921C2×D414yes—
304#11719921C2×D414yes—
305C4⋊Dic53—24no—
306C4⋊Dic53—24no—
307C4⋊Dic53—24no—
308C4⋊Dic53—24no—
309C4⋊Dic53—24no—
310C4⋊Dic53C2×D414yes—
311C2×#88322—22no—
312C2×#88322—22no—
313C2×#88322C2412yes—
314C2×#88322C2412yes—
315Dic212—28no—
316Dic212—44no—
317#11719913—28no—
318#11719913—44no—
319#11719912—28no—
320C8×D53—28no—
321C23×C53C22×D411yescharacteristic
322C22×D53—22no—
323C22×D53—22no—
324C22×D53—22no—
325C22×D53—22no—
326C22×D53—22no—
327C22×D53—22no—
328C22×D53—42no—
329C22×D53—42no—
330C22×D53—42no—
331C22×D53#13714yescomplemented
332C22×D53C22×D412yes—
333C22×D53C22×D412yes—
334Q8×C53—24no—
335Q8×C53—24no—
336Q8×C53—22no—
337Q8×C53—22no—
338Q8×C53C22×D414yes—
339Q8×C53C22×D414yes—
340C2×C4×C53—24no—
341C2×C4×C53—24no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—42no—
349C2×C4×C53—42no—
350C2×C4×C53C22×D412yes—
351C2×C4×C53C22×D412yes—
352C2×C4×C53C22×D411yescharacteristic
353C2×C4×C53C22×D412yes—
354C2×C4×C53H(5,𝔽2)12yes—
355C2×C4×C53C2511yescharacteristic
356C2×Dic53—22no—
357C2×Dic53—22no—
358C2×Dic53—22no—
359C2×Dic53—22no—
360C2×Dic53—22no—
361C2×Dic53—42no—
362C2×Dic53—42no—
363C2×Dic53—42no—
364C2×Dic53C22×D412yes—
365C2×Dic53C22×D412yes—
366D212—28no—
367D212—22no—
368D212—22no—
369D212—48no—
370D212—48no—
371D212—42no—
372C4×D53—24no—
373C4×D53—24no—
374C4×D53—22no—
375C4×D53—22no—
376C4×D53—22no—
377C4×D53—22no—
378C4×D53—48no—
379C4×D53—48no—
380C4×D53—48no—
381C4×D53—48no—
382Dic106—22no—
383Dic106—22no—
384Dic106—22no—
385Dic106—22no—
386Dic106—22no—
387Dic106—22no—
388Dic106—48no—
389Dic106—48no—
390Dic106—48no—
391Dic106—42no—
392Dic106—42no—
393Dic106—42no—
394C8×C53—22no—
395C8×C53C22×D414yes—
396#88322—22no—
397#88322—22no—
398C2×#3270—531nomaximal, Sylow
399C22×C53D4212yes—
400C22×C53C2×#13712yes—
401C22×C53#57812yes—
402C22×C53C23×D411yescharacteristic
403C2×D53—22no—
404C2×D53—28no—
405C2×D53—22no—
406C2×D53—22no—
407C2×D53—22no—
408C2×D53—22no—
409C2×D53—44no—
410C2×D53—42no—
411C2×D53—42no—
412C2×D53—42no—
413C2×D53—84no—
414C2×D53C2×#13714yescomplemented
415C4×C53—24no—
416C4×C53—24no—
417C4×C53—22no—
418C4×C53—22no—
419C4×C53—42no—
420C4×C53—42no—
421C4×C53D4212yes—
422C4×C53C23×D411yescharacteristic
423C4×C53C2×H(5,𝔽2)11yescharacteristic
424Dic53—22no—
425Dic53—22no—
426Dic53—42no—
427Dic53—42no—
428Dic53—42no—
429C22×#137—531no—
430C23×Q16—531no—
431C2×D4×Q8—531no—
432C2×#548—531no—
433#3270—5316no—
434C2×#497—531no—
435C2×#470—531no—
436C2×#465—531no—
437C2×#464—531no—
438C2×#462—531no—
439C2×#452—531no—
440C2×#451—531no—
441C2×#451—531no—
442C2×#448—531no—
443C2×#441D5311yescharacteristic, complemented
444C2×#435—531no—
445C2×C53#327014yescomplemented
446C2×C53C2×D4211yescharacteristic
447C2×C53C22×#13711yescharacteristic
448C2×C53C2×#57811yescharacteristic
449D53—24no—
450D53—42no—
451D53—82no—
452C22×#41—531no—
453C23×Q8—531no—
454C23×Q8—531no—
455C23×Q8—531no—
456C2×#137—538no—
457C2×#137—1068no—
458C22×Q16—531no—
459C22×Q16—531no—
460C22×Q16—531no—
461C22×Q16—538no—
462C22×Q16—531no—
463C22×Q16—531no—
464C22×Q16—1068no—
465C22×Q16C2×D5311yescharacteristic
466C22×SD16—531no—
467C22×SD16—531no—
468C22×SD16—531no—
469C22×M16—531no—
470C23×C8—531no—
471D4×Q8—538no—
472D4×Q8—1064no—
473#548—538no—
474#548—1064no—
475C2×C4⋊Q8—531no—
476C2×C4⋊Q8—1061no—
477C2×#124—531no—
478C2×#124—1061no—
479C2×C22⋊Q8—531no—
480C2×C22⋊Q8—531no—
481C2×C22⋊Q8—531no—
482C2×C22⋊Q8—1061no—
483C2×C22⋊Q8—1061no—
484C2×C22⋊Q8—1061no—
485C2×#121—531no—
486C2×#121—1061no—
487C2×C4×Q8C2×D5311yescharacteristic
488C2×C4×Q8C2×D5311yescharacteristic
489C2×C4×D4—531no—
490C2×C4×D4—1061no—
491C2×C4×D4—1061no—
492#497—538no—
493#470—538no—
494#465—538no—
495#464—538no—
496#462—538no—
497#452—538no—
498#451—538no—
499#451—538no—
500#448—538no—
501#441C2×D5318yescomplemented
502#435—538no—
503C2×#106C2×D5311yescharacteristic
504C2×C4⋊C8—531no—
505C2×#103—531no—
506C2×#103—531no—
507C2×#103—531no—
508C2×#103C2×D5311yescharacteristic
509C2×#103C2×D5311yescharacteristic
510C2×#102—531no—
511C2×C22⋊C8—531no—
512C2×C22⋊C8—531no—
513C2×#97C2×D5311yescharacteristic
514C53C2×#327011yescharacteristic, complemented, Sylow
515C2×#41—534no—
516C2×#41—1062no—
517C2×#41—1064no—
518C2×#41—2122no—
519C22×Q8—534no—
520C22×Q8—534no—
521C22×Q8—534no—
522C22×Q8—531no—
523C22×Q8—531no—
524C22×Q8—531no—
525C22×Q8—1061no—
526C22×Q8—1061no—
527C22×Q8—1061no—
528C22×Q8—1062no—
529C22×Q8—1062no—
530C22×Q8—1062no—
531C22×Q8—1064no—
532C22×Q8—1064no—
533C22×Q8—1064no—
534C22×Q8—2122no—
535C22×Q8—2122no—
536C22×Q8—2122no—
537C22×Q8C22×D5311yescharacteristic
538C22×Q8C22×D5311yescharacteristic
539C22×D4—531no—
540C22×D4—531no—
541C22×D4—1061no—
542C22×D4—1061no—
543C23×C4—531no—
544C23×C4—531no—
545C23×C4—1061no—
546C23×C4—1061no—
547C23×C4—1061no—
548C23×C4—1061no—
549#137—10632no—
550C2×Q16—534no—
551C2×Q16—534no—
552C2×Q16—534no—
553C2×Q16—534no—
554C2×Q16—534no—
555C2×Q16—1064no—
556C2×Q16—1064no—
557C2×Q16—1064no—
558C2×Q16—10632no—
559C2×Q16—1064no—
560C2×Q16—2122no—
561C2×Q16D21218yescomplemented
562C2×Q16C22×D5314yes—
563C2×SD16—534no—
564C2×SD16—534no—
565C2×SD16—534no—
566C2×SD16—1064no—
567C2×SD16—1064no—
568C2×SD16—2122no—
569C2×M16—534no—
570C2×M16—1064no—
571C22×C8—531no—
572C22×C8—531no—
573C22×C8—534no—
574C22×C8—1064no—
575C22×C8C22×D5311yescharacteristic
576C22×C8C22×D5311yescharacteristic
577C4⋊Q8—534no—
578C4⋊Q8—1068no—
579C4⋊Q8—1062no—
580#124—534no—
581#124—1068no—
582#124—1062no—
583C22⋊Q8—534no—
584C22⋊Q8—534no—
585C22⋊Q8—534no—
586C22⋊Q8—1068no—
587C22⋊Q8—1068no—
588C22⋊Q8—1068no—
589C22⋊Q8—1062no—
590C22⋊Q8—1062no—
591C22⋊Q8—1062no—
592#121—534no—
593#121—1062no—
594#121—1068no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8C22×D5314yes—
598C4×Q8C22×D5314yes—
599C4×D4—534no—
600C4×D4—534no—
601C4×D4—1068no—
602C4×D4—1068no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—531no—
606C2×C4⋊C4—1061no—
607C2×C4⋊C4—1061no—
608C2×C4⋊C4—1061no—
609C2×C4⋊C4—1061no—
610C2×C4⋊C4—1061no—
611C2×C4⋊C4C22×D5311yescharacteristic
612C2×C4⋊C4C22×D5311yescharacteristic
613C2×C22⋊C4—531no—
614C2×C22⋊C4—531no—
615C2×C22⋊C4—1061no—
616C2×C22⋊C4—1061no—
617C2×C22⋊C4—1061no—
618C2×C22⋊C4—1061no—
619C2×C22⋊C4—1061no—
620C2×C22⋊C4—1061no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42C22×D5311yescharacteristic
624#106C22×D5314yes—
625C4⋊C8—534no—
626#103—534no—
627#103—534no—
628#103—534no—
629#103C22×D5314yes—
630#103C22×D5314yes—
631#102—534no—
632C22⋊C8—534no—
633C22⋊C8—534no—
634#97C22×D5314yes—
635C24—531no—
636C24—531no—
637C24—1061no—
638#41—1068no—
639#41—2124no—
640#41—2128no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8—532no—
646C2×Q8—532no—
647C2×Q8—532no—
648C2×Q8—1064no—
649C2×Q8—1064no—
650C2×Q8—1064no—
651C2×Q8—1061no—
652C2×Q8—1061no—
653C2×Q8—1061no—
654C2×Q8—1068no—
655C2×Q8—1068no—
656C2×Q8—1068no—
657C2×Q8—1062no—
658C2×Q8—1062no—
659C2×Q8—1062no—
660C2×Q8—1062no—
661C2×Q8—1062no—
662C2×Q8—1062no—
663C2×Q8—2124no—
664C2×Q8—2124no—
665C2×Q8—2124no—
666C2×Q8—2124no—
667C2×Q8—2124no—
668C2×Q8—2124no—
669C2×Q8—2128no—
670C2×Q8—2128no—
671C2×Q8—2128no—
672C2×Q8C2×D21214yes—
673C2×Q8C2×D21214yes—
674C2×Q8C23×D5312yes—
675C2×Q8C23×D5312yes—
676C2×D4—534no—
677C2×D4—532no—
678C2×D4—1064no—
679C2×D4—1064no—
680C2×D4—1064no—
681C2×D4—1061no—
682C2×D4—1062no—
683C2×D4—1062no—
684C2×D4—2124no—
685C2×D4—2124no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—531no—
691C22×C4—531no—
692C22×C4—532no—
693C22×C4—532no—
694C22×C4—532no—
695C22×C4—532no—
696C22×C4—1064no—
697C22×C4—1064no—
698C22×C4—1064no—
699C22×C4—1064no—
700C22×C4—1062no—
701C22×C4—1062no—
702C22×C4—1062no—
703C22×C4—1062no—
704C22×C4—1061no—
705C22×C4—1061no—
706C22×C4—1061no—
707C22×C4—2124no—
708C22×C4—2124no—
709C22×C4—2124no—
710C22×C4—2124no—
711C22×C4D4×D5311yescharacteristic
712C22×C4D4×D5311yescharacteristic
713C22×C4C23×D5311yescharacteristic
714Q16—1068no—
715Q16—1068no—
716Q16—1068no—
717Q16—1068no—
718Q16—2124no—
719Q16C2×D212116yescomplemented
720SD16—1068no—
721SD16—1068no—
722SD16—2124no—
723M16—1068no—
724C2×C8—22no—
725C2×C8—532no—
726C2×C8—532no—
727C2×C8—1062no—
728C2×C8—1062no—
729C2×C8—1068no—
730C2×C8C2×D21214yes—
731C2×C8C23×D5312yes—
732C2×C8C23×D5312yes—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—534no—
738C4⋊C4—1064no—
739C4⋊C4—1064no—
740C4⋊C4—1064no—
741C4⋊C4—1064no—
742C4⋊C4—1064no—
743C4⋊C4C23×D5312yes—
744C4⋊C4C23×D5312yes—
745C22⋊C4—534no—
746C22⋊C4—534no—
747C22⋊C4—1064no—
748C22⋊C4—1064no—
749C22⋊C4—1064no—
750C22⋊C4—1064no—
751C22⋊C4—1064no—
752C22⋊C4—1064no—
753C42—24no—
754C42—24no—
755C42D4×D5312yes—
756C42C23×D5312yes—
757C23—534no—
758C23—532no—
759C23—532no—
760C23—1062no—
761C23—1062no—
762C23—1062no—
763C23—1062no—
764C23—1062no—
765C23—1062no—
766C23—2122no—
767C23—2122no—
768C23—2122no—
769C23C2×D4×D5311yescharacteristic
770Q8—22no—
771Q8—22no—
772Q8—24no—
773Q8—24no—
774Q8—1062no—
775Q8—1062no—
776Q8—1062no—
777Q8—1062no—
778Q8—1062no—
779Q8—1062no—
780Q8—2128no—
781Q8—2128no—
782Q8—2128no—
783Q8—2122no—
784Q8—2122no—
785Q8—2122no—
786Q8C22×D21214yes—
787Q8C22×D21214yes—
788D4—1068no—
789D4—1062no—
790D4—1062no—
791D4—2128no—
792D4—2128no—
793D4—2122no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—532no—
805C2×C4—532no—
806C2×C4—1062no—
807C2×C4—1062no—
808C2×C4—1062no—
809C2×C4—1062no—
810C2×C4—1062no—
811C2×C4—1062no—
812C2×C4—1064no—
813C2×C4—1064no—
814C2×C4—1062no—
815C2×C4—1062no—
816C2×C4—1062no—
817C2×C4—2128no—
818C2×C4—2128no—
819C2×C4—2128no—
820C2×C4—2128no—
821C2×C4—2122no—
822C2×C4—2122no—
823C2×C4—2122no—
824C2×C4C2×D4×D5312yes—
825C2×C4C2×D4×D5312yes—
826C2×C4C2×D4×D5311yescharacteristic
827C2×C4C22×D21212yes—
828C2×C4#1313326312yes—
829C2×C4C24×D5311yescharacteristic
830C8—22no—
831C8—1062no—
832C8—1062no—
833C8C22×D21214yes—
834C22—534no—
835C22—1068no—
836C22—1062no—
837C22—1062no—
838C22—1062no—
839C22—1062no—
840C22—1062no—
841C22—4244no—
842C22—2122no—
843C22—2122no—
844C22—2122no—
845C22—2124no—
846C22D4×D21212yes—
847C22#137×D5312yes—
848C22#1681143912yes—
849C22C22×D4×D5311yescharacteristic
850C4—24no—
851C4—24no—
852C4—22no—
853C4—22no—
854C4—42no—
855C4—42no—
856C4—1062no—
857C4—1062no—
858C4—2122no—
859C4—2122no—
860C4—2122no—
861C4D4×D21212yes—
862C4C23×D21211yescharacteristic
863C4C2×#1313326311yescharacteristic
864C2—1064no—
865C2—4242no—
866C2—2122no—
867C2#2028628714yesdirect product factor
868C2C2×D4×D21211yescharacteristic
869C2C2×#137×D5311yescharacteristic
870C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#441C2
socleC23×C53C22×D4
prime radicalC2×#16811285C2
hypercenterC2×#441D53
hypocenterC53C2×#3270
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
1. C22×#13133249C2semidirect
2. C22×Q16×D53C2semidirect
3. C2×Q8×D212C2semidirect
5. #20286287C2direct (N × H)
6. C2×#16811017C2semidirect
7. C2×#16810882C2semidirect
8. C2×#16810853C2semidirect
9. C2×#16810845C2semidirect
10. C2×#16810833C2semidirect
11. C2×#16810788C2semidirect
12. C2×#16810780C2semidirect
13. C2×#16810780C2semidirect
14. C2×#16810763C2semidirect
15. C2×#16810696C2semidirect
16. C2×C53×#441C2semidirect
22. C2×#13133249C22semidirect
29. C2×Q16×D53C22semidirect
36. Q8×D212C22semidirect
54. #16811017C22semidirect
55. #16810882C22semidirect
56. #16810853C22semidirect
57. #16810845C22semidirect
58. #16810833C22semidirect
59. #16810788C22semidirect
60. #16810780C22semidirect
61. #16810780C22semidirect
62. #16810763C22semidirect
63. #16810696C22semidirect
74. C53×#441C22semidirect
180. C2×Q16×C53D4semidirect
278. Q16×C53C2×D4semidirect
331. C22×D53#137semidirect
414. C2×D53C2×#137semidirect
443. C2×#441D53semidirect
445. C2×C53#3270semidirect
501. #441C2×D53semidirect
514. C53C2×#3270semidirect
561. C2×Q16D212semidirect
719. Q16C2×D212semidirect
867. C2#20286287direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332492
C22×Q16×D532
C2×Q8×D2122
C2×#168112852
#202862872
C2×#168110172
C2×#168108822
C2×#168108532
C2×#168108452
C2×#168108332
C2×#168107882
C2×#168107802
C2×#168107632
C2×#168106962
C2×C53×#4412
C2×#327053