Finite Group Databasebeta

← C2×#20286224 #28259072

Subgroups — C2×#20286224 #28259072

Order 13568.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133249C211yesmaximal, characteristic, complemented
2C22×SD16×D53C211yesmaximal, characteristic, complemented
3C2×#16811288C211yesmaximal, characteristic, complemented
4C2×#16811266C211yesmaximal, characteristic
5#20286224C2116yesmaximal, direct product factor
6C2×#16810866C211yesmaximal, characteristic, complemented
7C2×#16810861C211yesmaximal, characteristic, complemented
8C2×#16810842C211yesmaximal, characteristic, complemented
9C2×#16810825C211yesmaximal, characteristic, complemented
10C2×#16810784C211yesmaximal, characteristic, complemented
11C2×#16810777C211yesmaximal, characteristic, complemented
12C2×#16810760C211yesmaximal, characteristic, complemented
13C2×#16810772C211yesmaximal, characteristic, complemented
14C2×#16810725C211yesmaximal, characteristic, complemented
15C2×#16810696C211yesmaximal, characteristic, complemented
16C2×C53×#497C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic, complemented
20C22×D4×D53C2211yescharacteristic
21C2×#13133249—28no—
22C2×#13133249C2218yescomplemented
23C22×#11719925C2211yescharacteristic, complemented
24C22×#11719913C2211yescharacteristic
25C22×#11719923C2211yescharacteristic
26C22×#11719924C2211yescharacteristic
27C22×#11719924C2211yescharacteristic
28C2×SD16×D53—28no—
29C2×SD16×D53C2218yescomplemented
30C22×#11719912C2211yescharacteristic, complemented
31C22×C8×D53C2211yescharacteristic
32#16811288—24no—
33#16811288C2218yescomplemented
34#16811266—24no—
35#16811266C2218yes—
36C2×#13133216—21no—
37C2×#13133199—21no—
38C2×#13133195—21no—
39C2×#13133195—21no—
40C2×#13133193C2211yescharacteristic
41C2×#13133193C2211yescharacteristic
42C2×#13133193C2211yescharacteristic, complemented
43C2×#13133190—21no—
44C2×#13133188C2211yescharacteristic
45C2×#13133187—21no—
46C2×C4×Dic106C2211yescharacteristic, complemented
47C2×C4×D212C2211yescharacteristic
48C2×C4×D212C2211yescharacteristic
49C2×#13133179—21no—
50C2×C22⋊C4×D53—21no—
51#16810866C2218yescomplemented
52#16810861C2218yescomplemented
53#16810842C2218yescomplemented
54#16810825C2218yescomplemented
55#16810784C2218yescomplemented
56#16810777C2218yescomplemented
57#16810772C2218yescomplemented
58#16810760C2218yescomplemented
59#16810725C2218yescomplemented
60#16810696C2218yescomplemented
61C2×#13133151C2211yescharacteristic, complemented
62C2×C4⋊#88322C2211yescharacteristic, complemented
63C2×#13133142C2211yescharacteristic, complemented
64C2×#13133141C2211yescharacteristic, complemented
65C2×#13133141C2211yescharacteristic, complemented
66C2×#13133141C2211yescharacteristic, complemented
67C2×#13133139C2211yescharacteristic
68C2×#13133138C2211yescharacteristic
69C2×#13133129C2211yescharacteristic
70C2×#13133129C2211yescharacteristic, complemented
71C22×Q16×C53C2211yescharacteristic, complemented
72C22×Q16×C53C2211yescharacteristic, complemented
73C22×SD16×C53C2211yescharacteristic
74C22×SD16×C53C2211yescharacteristic
75C2×C4⋊Q8×C53C2211yescharacteristic, complemented
76C2×#124×C53C2211yescharacteristic
77C53×#497C2218yescomplemented
78C2×#97×C53C2211yescharacteristic, complemented
79C24×D53—21no—
80C2×#11719949—22no—
81C2×#11719949—24no—
82C2×#11719949—42no—
83C2×#11719949C2314yes—
84C22×Dic106—21no—
85C22×Dic106—21no—
86C22×Dic106C2311yescharacteristic
87C2×Q8×D53—22no—
88C2×Q8×D53—22no—
89C2×Q8×D53—24no—
90C2×Q8×D53—24no—
91C2×Q8×D53—42no—
92C2×Q8×D53—42no—
93C2×Q8×D53C2314yes—
94C2×Q8×D53C2314yescomplemented
95C22×D212—21no—
96C22×D212D411yescharacteristic
97C22×D212C2311yescharacteristic
98C22×C22⋊D53—21no—
99C22×C22⋊D53—21no—
100C2×D4×D53—24no—
101C2×D4×D53—22no—
102C2×D4×D53—42no—
103C2×D4×D53C2314yes—
104C22×C4×D53—21no—
105C22×C4×D53—21no—
106C22×C4×D53—21no—
107C22×C4×D53—21no—
108C22×C4×D53C2311yescharacteristic
109C22×C4×D53C2311yescharacteristic
110#13133249—232no—
111C2×#11719925—24no—
112C2×#11719925C2314yescomplemented
113C2×#11719913D418yescomplemented
114C2×#11719913C2314yes—
115C2×#11719923—24no—
116C2×#11719923C2314yes—
117C2×#11719924—24no—
118C2×#11719924—24no—
119C2×#11719924C2314yes—
120C2×#11719924C2314yes—
121SD16×D53—232no—
122C2×#11719912—24no—
123C2×#11719912C2314yescomplemented
124C22×#88322C2311yescharacteristic
125C22×#88322C2311yescharacteristic
126C2×C8×D53—24no—
127C2×C8×D53C2314yes—
128#13133216—28no—
129#13133199—28no—
130#13133195—28no—
131#13133195—28no—
132#13133193—22no—
133#13133193—22no—
134#13133193—22no—
135#13133193C2314yes—
136#13133193C2314yes—
137#13133193C2314yescomplemented
138#13133190—28no—
139#13133188—22no—
140#13133188C2314yes—
141#13133187—28no—
142C4×Dic106—22no—
143C4×Dic106C2314yescomplemented
144C4×D212—22no—
145C4×D212D414yes—
146C4×D212C2314yes—
147C4×D212C2314yes—
148#13133179—28no—
149C2×C4⋊Dic53D411yescharacteristic
150C2×C4⋊Dic53C2311yescharacteristic
151C2×C4⋊Dic53C2311yescharacteristic
152C2×#11719919—21no—
153C2×#11719919—21no—
154C2×#11719919—21no—
155C2×#11719919—21no—
156C2×C22⋊Dic53—21no—
157C2×#11719921—21no—
158C2×#11719921—21no—
159C2×#11719921—21no—
160C2×#11719921—21no—
161C2×#11719921D411yescharacteristic
162C2×#11719921D411yescharacteristic
163C22⋊C4×D53—28no—
164C2×C4×Dic53—21no—
165#13133151C2314yescomplemented
166C4⋊#88322C2314yescomplemented
167#13133142C2314yescomplemented
168#13133141C2314yescomplemented
169#13133141C2314yescomplemented
170#13133141C2314yescomplemented
171#13133139C2314yes—
172#13133138C2314yes—
173#13133129C2314yes—
174#13133129C2314yescomplemented
175C22×Q8×C53C2311yescharacteristic
176C22×Q8×C53C2311yescharacteristic
177C22×Q8×C53C2311yescharacteristic
178C22×D4×C53C2311yescharacteristic
179C2×Q16×C53—24no—
180C2×Q16×C53—42no—
181C2×Q16×C53C2314yescomplemented
182C2×Q16×C53C2314yescomplemented
183C2×SD16×C53—24no—
184C2×SD16×C53—42no—
185C2×SD16×C53C2314yes—
186C2×SD16×C53C2314yes—
187C22×C8×C53C2311yescharacteristic
188C22×C8×C53C2311yescharacteristic
189C4⋊Q8×C53—22no—
190C4⋊Q8×C53C2314yescomplemented
191#124×C53—22no—
192#124×C53C2314yes—
193C2×C4⋊C4×C53—21no—
194C2×C4⋊C4×C53—21no—
195C2×C22⋊C4×C53—21no—
196C2×C22⋊C4×C53—21no—
197C2×C42×C53C2311yescharacteristic
198#97×C53C2314yescomplemented
199C24×C53—21no—
200C23×D53—21no—
201C23×D53—24no—
202C23×D53—44no—
203C23×D53—44no—
204C23×D53—82no—
205C23×D53C2×D411yescharacteristic
206C23×D53C2×D411yescharacteristic
207C2×Q8×C53—21no—
208C2×Q8×C53—21no—
209C2×Q8×C53—21no—
210C2×Q8×C53—22no—
211C2×Q8×C53—22no—
212C2×Q8×C53—22no—
213C2×Q8×C53—22no—
214C2×Q8×C53—22no—
215C2×Q8×C53—22no—
216C2×Q8×C53C2412yes—
217C2×Q8×C53C2412yes—
218C2×Q8×C53C2412yes—
219C2×D4×C53—22no—
220C2×D4×C53—21no—
221C2×D4×C53—22no—
222C2×D4×C53C2412yes—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2411yescharacteristic
229C2×C22⋊D53—24no—
230C2×C22⋊D53—24no—
231C2×C22⋊D53—44no—
232C2×C22⋊D53—82no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53C2×D411yescharacteristic
237C22×Dic53C2×D411yescharacteristic
238#11719949—28no—
239#11719949—44no—
240#11719949—48no—
241Q8×D53—28no—
242Q8×D53—28no—
243Q8×D53—44no—
244Q8×D53—44no—
245Q8×D53—48no—
246Q8×D53—48no—
247D4×D53—28no—
248D4×D53—44no—
249D4×D53—48no—
250C2×D212—24no—
251C2×D212—21no—
252C2×D212—22no—
253C2×D212—24no—
254C2×D212—44no—
255C2×D212C2×D414yes—
256C2×D212C2×D414yes—
257C2×D212C2412yes—
258C2×C4×D53—22no—
259C2×C4×D53—22no—
260C2×C4×D53—22no—
261C2×C4×D53—22no—
262C2×C4×D53—24no—
263C2×C4×D53—24no—
264C2×C4×D53—24no—
265C2×C4×D53—24no—
266C2×C4×D53—44no—
267C2×C4×D53—44no—
268C2×C4×D53—44no—
269C2×C4×D53—82no—
270C2×C4×D53C2×D412yes—
271C2×C4×D53C2×D412yes—
272C2×C4×D53C2412yes—
273C2×C4×D53C2412yes—
274C2×Dic106—21no—
275C2×Dic106—22no—
276C2×Dic106—24no—
277C2×Dic106—24no—
278C2×Dic106—44no—
279C2×Dic106—44no—
280C2×Dic106C2×D414yes—
281C2×Dic106C2412yes—
282Q16×C53—28no—
283Q16×C53—44no—
284SD16×C53—28no—
285SD16×C53—44no—
286C2×C8×C53—22no—
287C2×C8×C53C2×D414yes—
288C2×C8×C53C2412yes—
289C2×C8×C53C2412yes—
290C4⋊C4×C53—24no—
291C4⋊C4×C53—24no—
292C22⋊C4×C53—24no—
293C22⋊C4×C53—24no—
294C42×C53C2×D412yes—
295C42×C53C2412yes—
296C22⋊Dic53—24no—
297#11719925—28no—
298#11719924—28no—
299#11719924—28no—
300#11719923—28no—
301#11719921—24no—
302#11719921—24no—
303#11719921—24no—
304#11719921—24no—
305#11719921C2×D414yes—
306#11719921C2×D414yes—
307C4⋊Dic53—21no—
308C4⋊Dic53—21no—
309C4⋊Dic53C2×D414yes—
310C4⋊Dic53C2412yes—
311C4⋊Dic53C2412yes—
312#11719919—24no—
313#11719919—24no—
314#11719919—24no—
315#11719919—24no—
316C4×Dic53—24no—
317C2×#88322—22no—
318C2×#88322—22no—
319C2×#88322C2412yes—
320C2×#88322C2412yes—
321#11719913C2×D4116yescomplemented
322#11719912—28no—
323C8×D53—28no—
324C23×C53—22no—
325C23×C53—42no—
326C23×C53—42no—
327C23×C53—42no—
328C23×C53C22×D411yescharacteristic
329C22×D53—22no—
330C22×D53—22no—
331C22×D53—22no—
332C22×D53—24no—
333C22×D53—22no—
334C22×D53—22no—
335C22×D53—22no—
336C22×D53—48no—
337C22×D53—42no—
338C22×D53—42no—
339C22×D53—48no—
340C22×D53—84no—
341C22×D53—816no—
342C22×D53#13714yescomplemented
343C22×D53C22×D412yes—
344C22×D53C22×D412yes—
345Q8×C53—22no—
346Q8×C53—22no—
347Q8×C53—22no—
348Q8×C53—22no—
349Q8×C53—22no—
350Q8×C53—22no—
351Q8×C53—42no—
352Q8×C53—42no—
353Q8×C53—42no—
354D4×C53—22no—
355D4×C53—22no—
356D4×C53—42no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—42no—
363C2×C4×C53—42no—
364C2×C4×C53—42no—
365C2×C4×C53C22×D412yes—
366C2×C4×C53C22×D412yes—
367C2×C4×C53C22×D411yescharacteristic
368C2×C4×C53C22×D412yes—
369C2×C4×C53H(5,𝔽2)12yes—
370C2×C4×C53C2511yescharacteristic
371C22⋊D53—48no—
372C22⋊D53—84no—
373C2×Dic53—24no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—42no—
380C2×Dic53—42no—
381C2×Dic53C22×D412yes—
382C2×Dic53C22×D412yes—
383D212—28no—
384D212—24no—
385D212—22no—
386D212—48no—
387D212C22×D414yes—
388C4×D53—24no—
389C4×D53—24no—
390C4×D53—22no—
391C4×D53—22no—
392C4×D53—22no—
393C4×D53—22no—
394C4×D53—48no—
395C4×D53—48no—
396C4×D53—48no—
397C4×D53—84no—
398Dic106—24no—
399Dic106—22no—
400Dic106—48no—
401Dic106—48no—
402Dic106C22×D414yes—
403C8×C53—22no—
404C8×C53C22×D414yes—
405#88322—22no—
406#88322—22no—
407C2×#3266—531nomaximal, Sylow
408C22×C53—42no—
409C22×C53—42no—
410C22×C53—42no—
411C22×C53—84no—
412C22×C53D4212yes—
413C22×C53C2×#13712yes—
414C22×C53#57712yes—
415C22×C53C23×D411yescharacteristic
416C2×D53—22no—
417C2×D53—28no—
418C2×D53—22no—
419C2×D53—22no—
420C2×D53—24no—
421C2×D53—22no—
422C2×D53—22no—
423C2×D53—44no—
424C2×D53—48no—
425C2×D53—42no—
426C2×D53—42no—
427C2×D53—816no—
428C2×D53C2×#13714yescomplemented
429C4×C53—22no—
430C4×C53—22no—
431C4×C53—42no—
432C4×C53—42no—
433C4×C53—42no—
434C4×C53D4212yes—
435C4×C53C23×D411yescharacteristic
436C4×C53C2×H(5,𝔽2)11yescharacteristic
437Dic53—24no—
438Dic53—22no—
439Dic53—22no—
440Dic53—42no—
441Dic53—42no—
442C22×#137—531no—
443C23×SD16—531no—
444C2×D4×Q8—531no—
445C2×#546—531no—
446#3266—5316no—
447C2×#497D5311yescharacteristic, complemented
448C2×#468—531no—
449C2×#467—531no—
450C2×#464—531no—
451C2×#461—531no—
452C2×#452—531no—
453C2×#451—531no—
454C2×#448—531no—
455C2×#450—531no—
456C2×#440—531no—
457C2×#435—531no—
458C2×C53—82no—
459C2×C53#326614yescomplemented
460C2×C53C2×D4211yescharacteristic
461C2×C53C22×#13711yescharacteristic
462C2×C53C2×#57711yescharacteristic
463D53—24no—
464D53—42no—
465D53—44no—
466C22×#41—531no—
467C23×Q8—531no—
468C23×Q8—531no—
469C23×D4—531no—
470C2×#137—538no—
471C2×#137—1068no—
472C22×Q16—531no—
473C22×Q16C2×D5311yescharacteristic, complemented
474C22×Q16C2×D5311yescharacteristic, complemented
475C22×SD16—531no—
476C22×SD16—531no—
477C22×SD16—531no—
478C22×SD16—538no—
479C22×SD16—531no—
480C22×SD16—1068no—
481C22×SD16C2×D5311yescharacteristic
482C22×SD16C2×D5311yescharacteristic
483C22×M16—531no—
484C23×C8—531no—
485D4×Q8—538no—
486D4×Q8—1064no—
487#546—538no—
488#546—1064no—
489C2×C4⋊Q8—1061no—
490C2×C4⋊Q8C2×D5311yescharacteristic, complemented
491C2×#124C2×D5311yescharacteristic
492C2×#123—1061no—
493C2×C22⋊Q8—531no—
494C2×C22⋊Q8—531no—
495C2×C22⋊Q8—531no—
496C2×C22⋊Q8—1061no—
497C2×C22⋊Q8—1061no—
498C2×#121—531no—
499C2×#121—1061no—
500C2×#120—1061no—
501C2×C4×Q8—531no—
502C2×C4×D4—531no—
503C2×C4×D4—531no—
504C2×C4×D4—1061no—
505C22×C22⋊C4—1061no—
506#497C2×D5318yescomplemented
507#468—538no—
508#467—538no—
509#464—538no—
510#461—538no—
511#452—538no—
512#451—538no—
513#450—538no—
514#448—538no—
515#440—538no—
516#435—538no—
517C2×#107—531no—
518C2×C4⋊C8—531no—
519C2×#103—531no—
520C2×#103—531no—
521C2×#103—531no—
522C2×#103—531no—
523C2×#102—531no—
524C2×#102—531no—
525C2×C22⋊C8—531no—
526C2×C22⋊C8—531no—
527C2×#97C2×D5311yescharacteristic, complemented
528C53C2×#326611yescharacteristic, complemented, Sylow
529C25—1061no—
530C2×#41—534no—
531C2×#41—1062no—
532C2×#41—1064no—
533C2×#41—2122no—
534C22×Q8—534no—
535C22×Q8—534no—
536C22×Q8—531no—
537C22×Q8—1061no—
538C22×Q8—1061no—
539C22×Q8—1062no—
540C22×Q8—1062no—
541C22×Q8—1064no—
542C22×Q8—1064no—
543C22×Q8—2122no—
544C22×Q8—2122no—
545C22×Q8C22×D5311yescharacteristic
546C22×Q8C22×D5311yescharacteristic
547C22×Q8C22×D5311yescharacteristic
548C22×D4—534no—
549C22×D4—531no—
550C22×D4—531no—
551C22×D4—1061no—
552C22×D4—1062no—
553C22×D4—1061no—
554C22×D4—1064no—
555C22×D4—1061no—
556C22×D4—2122no—
557C22×D4C22×D5311yescharacteristic
558C23×C4—531no—
559C23×C4—531no—
560C23×C4—1061no—
561C23×C4—1061no—
562C23×C4—1061no—
563C23×C4—1061no—
564#137—10632no—
565C2×Q16—24no—
566C2×Q16—42no—
567C2×Q16—534no—
568C2×Q16—1064no—
569C2×Q16C22×D5314yescomplemented
570C2×Q16C22×D5314yescomplemented
571C2×SD16—24no—
572C2×SD16—42no—
573C2×SD16—534no—
574C2×SD16—534no—
575C2×SD16—534no—
576C2×SD16—538no—
577C2×SD16—534no—
578C2×SD16—10632no—
579C2×SD16—1064no—
580C2×SD16—1064no—
581C2×SD16—1064no—
582C2×SD16C22×D5314yes—
583C2×SD16C22×D5314yes—
584C2×M16—534no—
585C2×M16—1064no—
586C22×C8—531no—
587C22×C8—531no—
588C22×C8—534no—
589C22×C8—1064no—
590C22×C8C22×D5311yescharacteristic
591C22×C8C22×D5311yescharacteristic
592C4⋊Q8—22no—
593C4⋊Q8—1068no—
594C4⋊Q8C22×D5314yescomplemented
595#124—22no—
596#124C22×D5314yes—
597#123—1068no—
598C22⋊Q8—534no—
599C22⋊Q8—534no—
600C22⋊Q8—534no—
601C22⋊Q8—1068no—
602C22⋊Q8—1068no—
603C22⋊Q8—1062no—
604C22⋊Q8—1062no—
605C22⋊Q8—1062no—
606#121—534no—
607#121—1068no—
608#121—1062no—
609#120—1068no—
610C4×Q8—534no—
611C4×Q8—1062no—
612C4×D4—534no—
613C4×D4—534no—
614C4×D4—534no—
615C4×D4—1068no—
616C4×D4—1062no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—531no—
620C2×C4⋊C4—531no—
621C2×C4⋊C4—531no—
622C2×C4⋊C4—1061no—
623C2×C4⋊C4—1061no—
624C2×C4⋊C4—1061no—
625C2×C4⋊C4—1061no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—531no—
629C2×C22⋊C4—531no—
630C2×C22⋊C4—1068no—
631C2×C22⋊C4—1061no—
632C2×C22⋊C4—1061no—
633C2×C22⋊C4—1061no—
634C2×C22⋊C4—1061no—
635C2×C22⋊C4—1061no—
636C2×C42—1061no—
637C2×C42C22×D5311yescharacteristic
638#107—534no—
639C4⋊C8—534no—
640#103—534no—
641#103—534no—
642#103—534no—
643#103—534no—
644#102—534no—
645#102—534no—
646C22⋊C8—534no—
647C22⋊C8—534no—
648#97C22×D5314yescomplemented
649C24—21no—
650C24—531no—
651C24—531no—
652C24—1064no—
653C24—1061no—
654C24—4242no—
655C24—2124no—
656C24—2124no—
657#41—1068no—
658#41—2124no—
659#41—2128no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—22no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—22no—
667C2×Q8—22no—
668C2×Q8—22no—
669C2×Q8—534no—
670C2×Q8—532no—
671C2×Q8—1064no—
672C2×Q8—1064no—
673C2×Q8—1061no—
674C2×Q8—1062no—
675C2×Q8—1068no—
676C2×Q8—1068no—
677C2×Q8—2124no—
678C2×Q8—2124no—
679C2×Q8—2124no—
680C2×Q8—2124no—
681C2×Q8—2128no—
682C2×Q8—2128no—
683C2×Q8C23×D5312yes—
684C2×Q8C23×D5312yes—
685C2×Q8C23×D5312yes—
686C2×D4—22no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—534no—
690C2×D4—534no—
691C2×D4—532no—
692C2×D4—1064no—
693C2×D4—1064no—
694C2×D4—1064no—
695C2×D4—1068no—
696C2×D4—1064no—
697C2×D4—1061no—
698C2×D4—1062no—
699C2×D4—4242no—
700C2×D4—2124no—
701C2×D4—2124no—
702C2×D4—2128no—
703C2×D4—2124no—
704C2×D4C23×D5312yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—531no—
709C22×C4—531no—
710C22×C4—532no—
711C22×C4—532no—
712C22×C4—532no—
713C22×C4—532no—
714C22×C4—1064no—
715C22×C4—1064no—
716C22×C4—1064no—
717C22×C4—1061no—
718C22×C4—1062no—
719C22×C4—1062no—
720C22×C4—1062no—
721C22×C4—1062no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1064no—
725C22×C4—4242no—
726C22×C4—2124no—
727C22×C4—2124no—
728C22×C4—2124no—
729C22×C4D4×D5311yescharacteristic
730C22×C4D4×D5311yescharacteristic
731C22×C4C23×D5311yescharacteristic
732Q16—28no—
733Q16—44no—
734Q16—1068no—
735SD16—28no—
736SD16—44no—
737SD16—5316no—
738SD16—1068no—
739SD16—1068no—
740SD16—1068no—
741M16—1068no—
742C2×C8—22no—
743C2×C8—532no—
744C2×C8—532no—
745C2×C8—1062no—
746C2×C8—1062no—
747C2×C8—1068no—
748C2×C8D4×D5314yes—
749C2×C8C23×D5312yes—
750C2×C8C23×D5312yes—
751C4⋊C4—24no—
752C4⋊C4—24no—
753C4⋊C4—534no—
754C4⋊C4—532no—
755C4⋊C4—532no—
756C4⋊C4—1064no—
757C4⋊C4—1064no—
758C4⋊C4—1064no—
759C4⋊C4—1061no—
760C4⋊C4—1061no—
761C4⋊C4—1064no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—534no—
765C22⋊C4—534no—
766C22⋊C4—1064no—
767C22⋊C4—1064no—
768C22⋊C4—1064no—
769C22⋊C4—1064no—
770C22⋊C4—1064no—
771C42—1064no—
772C42D4×D5312yes—
773C42C23×D5312yes—
774C23—22no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—534no—
779C23—532no—
780C23—532no—
781C23—1062no—
782C23—1062no—
783C23—1062no—
784C23—1062no—
785C23—1062no—
786C23—1062no—
787C23—1064no—
788C23—4244no—
789C23—42416no—
790C23—2128no—
791C23—2128no—
792C23—2122no—
793C23—2122no—
794C23C2×D4×D5311yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—22no—
798Q8—22no—
799Q8—22no—
800Q8—22no—
801Q8—42no—
802Q8—42no—
803Q8—42no—
804Q8—534no—
805Q8—1062no—
806Q8—1064no—
807Q8—2128no—
808Q8—2128no—
809D4—22no—
810D4—22no—
811D4—42no—
812D4—534no—
813D4—1068no—
814D4—1062no—
815D4—1064no—
816D4—4244no—
817D4—2128no—
818D4—2128no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—532no—
828C2×C4—532no—
829C2×C4—1062no—
830C2×C4—1062no—
831C2×C4—1062no—
832C2×C4—1064no—
833C2×C4—1062no—
834C2×C4—1062no—
835C2×C4—1062no—
836C2×C4—1062no—
837C2×C4—1064no—
838C2×C4—1064no—
839C2×C4—1062no—
840C2×C4—1062no—
841C2×C4—4244no—
842C2×C4—2128no—
843C2×C4—2128no—
844C2×C4—2128no—
845C2×C4—2122no—
846C2×C4—2122no—
847C2×C4C2×D4×D5312yes—
848C2×C4C2×D4×D5312yes—
849C2×C4C2×D4×D5312yes—
850C2×C4C2×D4×D5311yescharacteristic
851C2×C4#1313326212yes—
852C2×C4C24×D5311yescharacteristic
853C8—22no—
854C8—1062no—
855C8—1062no—
856C8C2×D4×D5314yes—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—84no—
861C22—534no—
862C22—1068no—
863C22—1062no—
864C22—1062no—
865C22—1062no—
866C22—1064no—
867C22—1062no—
868C22—1062no—
869C22—42416no—
870C22—2124no—
871C22—2128no—
872C22—2122no—
873C22—2122no—
874C22#1681125812yes—
875C22#137×D5312yes—
876C22#1681143212yes—
877C22C22×D4×D5311yescharacteristic
878C4—22no—
879C4—22no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—1062no—
884C4—1062no—
885C4—1064no—
886C4—2122no—
887C4—2122no—
888C4#1681125812yes—
889C4C22×D4×D5311yescharacteristic
890C4C2×#1313326211yescharacteristic
891C2—82no—
892C2—1064no—
893C2—2122no—
894C2—2124no—
895C2#2028622414yesdirect product factor
896C2C2×#1681125811yescharacteristic
897C2C2×#137×D5311yescharacteristic
898C2C2×#1681143211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#497C2
socleC23×C53C22×D4
prime radicalC2×#16811266C2
hypercenterC2×#497D53
hypocenterC53C2×#3266
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C22×#13133249C2semidirect
2. C22×SD16×D53C2semidirect
3. C2×#16811288C2semidirect
5. #20286224C2direct (N × H)
6. C2×#16810866C2semidirect
7. C2×#16810861C2semidirect
8. C2×#16810842C2semidirect
9. C2×#16810825C2semidirect
10. C2×#16810784C2semidirect
11. C2×#16810777C2semidirect
12. C2×#16810760C2semidirect
13. C2×#16810772C2semidirect
14. C2×#16810725C2semidirect
15. C2×#16810696C2semidirect
16. C2×C53×#497C2semidirect
19. C22×Q8×D53C22semidirect
22. C2×#13133249C22semidirect
23. C22×#11719925C22semidirect
29. C2×SD16×D53C22semidirect
30. C22×#11719912C22semidirect
33. #16811288C22semidirect
42. C2×#13133193C22semidirect
46. C2×C4×Dic106C22semidirect
51. #16810866C22semidirect
52. #16810861C22semidirect
53. #16810842C22semidirect
54. #16810825C22semidirect
55. #16810784C22semidirect
56. #16810777C22semidirect
57. #16810772C22semidirect
58. #16810760C22semidirect
59. #16810725C22semidirect
60. #16810696C22semidirect
61. C2×#13133151C22semidirect
62. C2×C4⋊#88322C22semidirect
63. C2×#13133142C22semidirect
64. C2×#13133141C22semidirect
65. C2×#13133141C22semidirect
66. C2×#13133141C22semidirect
70. C2×#13133129C22semidirect
71. C22×Q16×C53C22semidirect
72. C22×Q16×C53C22semidirect
75. C2×C4⋊Q8×C53C22semidirect
77. C53×#497C22semidirect
78. C2×#97×C53C22semidirect
94. C2×Q8×D53C23semidirect
112. C2×#11719925C23semidirect
113. C2×#11719913D4semidirect
123. C2×#11719912C23semidirect
137. #13133193C23semidirect
143. C4×Dic106C23semidirect
165. #13133151C23semidirect
166. C4⋊#88322C23semidirect
167. #13133142C23semidirect
168. #13133141C23semidirect
169. #13133141C23semidirect
170. #13133141C23semidirect
174. #13133129C23semidirect
181. C2×Q16×C53C23semidirect
182. C2×Q16×C53C23semidirect
190. C4⋊Q8×C53C23semidirect
198. #97×C53C23semidirect
321. #11719913C2×D4semidirect
342. C22×D53#137semidirect
428. C2×D53C2×#137semidirect
447. C2×#497D53semidirect
459. C2×C53#3266semidirect
473. C22×Q16C2×D53semidirect
474. C22×Q16C2×D53semidirect
490. C2×C4⋊Q8C2×D53semidirect
506. #497C2×D53semidirect
527. C2×#97C2×D53semidirect
528. C53C2×#3266semidirect
569. C2×Q16C22×D53semidirect
570. C2×Q16C22×D53semidirect
594. C4⋊Q8C22×D53semidirect
648. #97C22×D53semidirect
895. C2#20286224direct (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×SD16×D532
C2×#168112882
C2×#168112662
#202862242
C2×#168108662
C2×#168108612
C2×#168108422
C2×#168108252
C2×#168107842
C2×#168107772
C2×#168107602
C2×#168107722
C2×#168107252
C2×#168106962
C2×C53×#4972
C2×#326653