Finite Group Databasebeta

← C2×#20286257 #28259107

Subgroups — C2×#20286257 #28259107

Order 13568.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133244C211yesmaximal, characteristic, complemented
2C22×#13133238C211yesmaximal, characteristic, complemented
3C2×#16811295C211yesmaximal, characteristic, complemented
4C2×#16811268C211yesmaximal, characteristic, complemented
5#20286257C2116yesmaximal, direct product factor
6C2×#16811012C211yesmaximal, characteristic, complemented
7C2×#16810870C211yesmaximal, characteristic, complemented
8C2×#16810860C211yesmaximal, characteristic, complemented
9C2×#16810845C211yesmaximal, characteristic, complemented
10C2×#16810818C211yesmaximal, characteristic, complemented
11C2×#16810788C211yesmaximal, characteristic, complemented
12C2×#16810771C211yesmaximal, characteristic, complemented
13C2×#16810769C211yesmaximal, characteristic, complemented
14C2×#16810758C211yesmaximal, characteristic, complemented
15C2×#16810696C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719949C2211yescharacteristic, complemented
19C22×#11719947C2211yescharacteristic
20C22×D4×D53C2211yescharacteristic
21C2×#13133244—28no—
22C2×#13133244C2218yescomplemented
23C2×#13133238—28no—
24C2×#13133238C2218yescomplemented
25C22×#11719925C2211yescharacteristic, complemented
26C22×#11719913C2211yescharacteristic, complemented
27C22×#11719913C2211yescharacteristic, complemented
28C22×#11719924C2211yescharacteristic
29C22×D424C2211yescharacteristic
30C22×D424C2211yescharacteristic
31C22×#11719922C2211yescharacteristic
32C22×#11719922C2211yescharacteristic
33C22×#11719912C2211yescharacteristic
34C22×C8×D53C2211yescharacteristic, complemented
35#16811295—24no—
36#16811295C2218yescomplemented
37#16811268—24no—
38#16811268C2218yescomplemented
39C2×#13133214—21no—
40C2×#13133214C2211yescharacteristic, complemented
41C2×#13133205C2211yescharacteristic
42C2×#13133201—21no—
43C2×#13133197C2211yescharacteristic
44C2×#13133192—21no—
45C2×#13133192—21no—
46C2×#13133192C2211yescharacteristic
47C2×#13133192C2211yescharacteristic
48C2×#13133192C2211yescharacteristic, complemented
49C2×#13133191—21no—
50C2×#13133187—21no—
51C2×C4×D212—21no—
52C2×C4×D212C2211yescharacteristic
53C22×#11719921—21no—
54#16811012C2218yescomplemented
55#16810870C2218yescomplemented
56#16810860C2218yescomplemented
57#16810845C2218yescomplemented
58#16810818C2218yescomplemented
59#16810788C2218yescomplemented
60#16810771C2218yescomplemented
61#16810769C2218yescomplemented
62#16810758C2218yescomplemented
63#16810696C2218yescomplemented
64C2×C4⋊#88322C2211yescharacteristic, complemented
65C2×#13133140C2211yescharacteristic, complemented
66C2×#13133137C2211yescharacteristic
67C2×#13133137C2211yescharacteristic, complemented
68C2×#13133137C2211yescharacteristic, complemented
69C2×#13133129C2211yescharacteristic
70C2×#13133129C2211yescharacteristic, complemented
71C22×SD16×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic, complemented
73C2×C4×D4×C53C2211yescharacteristic
74C53×#440C2218yescomplemented
75C2×#107×C53C2211yescharacteristic, complemented
76C2×#103×C53C2211yescharacteristic, complemented
77C2×#102×C53C2211yescharacteristic
78C2×#97×C53C2211yescharacteristic, complemented
79C24×D53—21no—
80C2×#11719949—22no—
81C2×#11719949—22no—
82C2×#11719949—24no—
83C2×#11719949—24no—
84C2×#11719949—42no—
85C2×#11719949—42no—
86C2×#11719949C2314yes—
87C2×#11719949C2314yescomplemented
88C2×#11719947—24no—
89C2×#11719947—22no—
90C2×#11719947—42no—
91C2×#11719947C2314yes—
92C22×Dic106C2311yescharacteristic
93C22×D212—21no—
94C22×D212—21no—
95C22×D212—21no—
96C22×D212—21no—
97C22×D212—21no—
98C22×D212—21no—
99C22×D212—21no—
100C22×D212D411yescharacteristic
101C22×D212C2311yescharacteristic
102C22×D212C2311yescharacteristic
103C22×D212C2311yescharacteristic
104C22×C22⋊D53—21no—
105C22×C22⋊D53—21no—
106C2×D4×D53—24no—
107C2×D4×D53—22no—
108C2×D4×D53—42no—
109C2×D4×D53C2314yes—
110C23×Dic53—21no—
111C22×C4×D53—21no—
112C22×C4×D53—21no—
113C22×C4×D53C2311yescharacteristic
114C22×C4×D53C2311yescharacteristic
115#13133244—232no—
116#13133238—232no—
117C2×#11719925—24no—
118C2×#11719925C2314yescomplemented
119C2×#11719913—24no—
120C2×#11719913—42no—
121C2×#11719913C2314yescomplemented
122C2×#11719913C2314yescomplemented
123C2×#11719924—24no—
124C2×#11719924C2314yes—
125C2×D424—24no—
126C2×D424—42no—
127C2×D424C2314yes—
128C2×D424C2314yes—
129C2×#11719922—24no—
130C2×#11719922—24no—
131C2×#11719922C2314yes—
132C2×#11719922C2314yes—
133C2×#11719912—24no—
134C2×#11719912C2314yes—
135C22×#88322C2311yescharacteristic
136C22×#88322C2311yescharacteristic
137C2×C8×D53—24no—
138C2×C8×D53C2314yescomplemented
139#13133214—22no—
140#13133214—28no—
141#13133214C2314yescomplemented
142#13133205—22no—
143#13133205C2314yes—
144#13133201—28no—
145#13133197—22no—
146#13133197C2314yes—
147#13133192—28no—
148#13133192—28no—
149#13133192—22no—
150#13133192—22no—
151#13133192—22no—
152#13133192C2314yes—
153#13133192C2314yes—
154#13133192C2314yescomplemented
155#13133191—28no—
156#13133187—28no—
157C4×D212—28no—
158C4×D212D414yes—
159C4×D212C2314yes—
160C2×C4⋊Dic53—21no—
161C2×C4⋊Dic53D411yescharacteristic
162C2×#11719921—28no—
163C2×#11719921—21no—
164C2×#11719921—21no—
165C2×#11719921—21no—
166C2×#11719921—21no—
167C2×#11719921—21no—
168C2×#11719921—21no—
169C2×#11719921D411yescharacteristic
170C2×#11719921D411yescharacteristic
171C4⋊#88322C2314yescomplemented
172#13133140C2314yescomplemented
173#13133137C2314yes—
174#13133137C2314yescomplemented
175#13133137C2314yescomplemented
176#13133129C2314yes—
177#13133129C2314yescomplemented
178C22×Q8×C53C2311yescharacteristic
179C22×D4×C53C2311yescharacteristic
180C23×C4×C53—21no—
181C2×SD16×C53D418yescomplemented
182C2×SD16×C53C2314yes—
183C22×C8×C53C2311yescharacteristic
184C22×C8×C53C2311yescharacteristic
185C4×Q8×C53—22no—
186C4×Q8×C53C2314yescomplemented
187C4×D4×C53—22no—
188C4×D4×C53C2314yes—
189C2×C4⋊C4×C53—21no—
190C2×C4⋊C4×C53C2311yescharacteristic
191C2×C4⋊C4×C53C2311yescharacteristic
192C2×C22⋊C4×C53—21no—
193C2×C42×C53—21no—
194C2×C42×C53C2311yescharacteristic
195#107×C53C2314yescomplemented
196#103×C53C2314yescomplemented
197#102×C53C2314yes—
198#97×C53C2314yescomplemented
199C24×C53—21no—
200C23×D53—21no—
201C23×D53—21no—
202C23×D53—21no—
203C23×D53—24no—
204C23×D53—44no—
205C23×D53—44no—
206C23×D53—82no—
207C23×D53C2×D411yescharacteristic
208C23×D53C2×D411yescharacteristic
209C2×Q8×C53—21no—
210C2×Q8×C53—22no—
211C2×Q8×C53C2×D414yes—
212C2×Q8×C53C2412yes—
213C2×D4×C53—21no—
214C2×D4×C53—22no—
215C2×D4×C53C2×D414yes—
216C2×D4×C53C2412yes—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—24no—
221C22×C4×C53—82no—
222C22×C4×C53C2×D411yescharacteristic
223C22×C4×C53C2×D411yescharacteristic
224C22×C4×C53C2411yescharacteristic
225C2×C22⋊D53—24no—
226C2×C22⋊D53—24no—
227C2×C22⋊D53—44no—
228C2×C22⋊D53—44no—
229C22×Dic53—21no—
230C22×Dic53—24no—
231C22×Dic53—44no—
232C22×Dic53C2×D411yescharacteristic
233C22×Dic53C2×D411yescharacteristic
234#11719949—28no—
235#11719949—28no—
236#11719949—44no—
237#11719949—44no—
238#11719949—48no—
239#11719949—48no—
240#11719947—28no—
241#11719947—44no—
242#11719947—48no—
243D4×D53—28no—
244D4×D53—44no—
245D4×D53—48no—
246C2×D212—22no—
247C2×D212—22no—
248C2×D212—22no—
249C2×D212—22no—
250C2×D212—22no—
251C2×D212—22no—
252C2×D212—24no—
253C2×D212—24no—
254C2×D212—24no—
255C2×D212—21no—
256C2×D212—21no—
257C2×D212—21no—
258C2×D212—24no—
259C2×D212—24no—
260C2×D212—24no—
261C2×D212—24no—
262C2×D212—42no—
263C2×D212—44no—
264C2×D212—44no—
265C2×D212—44no—
266C2×D212—82no—
267C2×D212—82no—
268C2×D212—82no—
269C2×D212—82no—
270C2×D212C2×D414yes—
271C2×D212C2412yes—
272C2×D212C2412yes—
273C2×D212C2412yes—
274C2×C4×D53—22no—
275C2×C4×D53—22no—
276C2×C4×D53—22no—
277C2×C4×D53—22no—
278C2×C4×D53—24no—
279C2×C4×D53—24no—
280C2×C4×D53—44no—
281C2×C4×D53—44no—
282C2×C4×D53C2×D412yes—
283C2×C4×D53C2×D412yes—
284C2×C4×D53C2412yes—
285C2×C4×D53C2412yes—
286C2×Dic106—22no—
287C2×Dic106—22no—
288C2×Dic106—21no—
289C2×Dic106C2412yes—
290SD16×C53C2×D4116yescomplemented
291C2×C8×C53—22no—
292C2×C8×C53C2×D414yes—
293C2×C8×C53C2412yes—
294C2×C8×C53C2412yes—
295C4⋊C4×C53—24no—
296C4⋊C4×C53—21no—
297C4⋊C4×C53—21no—
298C4⋊C4×C53C2412yes—
299C4⋊C4×C53C2412yes—
300C22⋊C4×C53—24no—
301C42×C53—24no—
302C42×C53C2×D412yes—
303C42×C53C2412yes—
304#11719925—28no—
305#11719924—28no—
306#11719922—28no—
307#11719922—28no—
308#11719921—24no—
309#11719921—24no—
310#11719921—24no—
311#11719921—24no—
312#11719921—24no—
313#11719921—24no—
314#11719921C2×D414yes—
315#11719921C2×D414yes—
316C4⋊Dic53—24no—
317C4⋊Dic53C2×D414yes—
318C2×#88322—22no—
319C2×#88322—22no—
320C2×#88322C2412yes—
321C2×#88322C2412yes—
322D424—28no—
323D424—44no—
324#11719913—28no—
325#11719913—44no—
326#11719912—28no—
327C8×D53—28no—
328C23×C53—24no—
329C23×C53—22no—
330C23×C53—42no—
331C23×C53—42no—
332C23×C53C22×D411yescharacteristic
333C22×D53—22no—
334C22×D53—22no—
335C22×D53—22no—
336C22×D53—22no—
337C22×D53—22no—
338C22×D53—22no—
339C22×D53—22no—
340C22×D53—22no—
341C22×D53—22no—
342C22×D53—48no—
343C22×D53—48no—
344C22×D53—42no—
345C22×D53—42no—
346C22×D53—42no—
347C22×D53—42no—
348C22×D53—42no—
349C22×D53—42no—
350C22×D53—42no—
351C22×D53—42no—
352C22×D53—42no—
353C22×D53—84no—
354C22×D53—816no—
355C22×D53C22×D412yes—
356C22×D53C22×D412yes—
357Q8×C53—24no—
358Q8×C53—22no—
359Q8×C53C22×D414yes—
360D4×C53—24no—
361D4×C53—22no—
362D4×C53C22×D414yes—
363C2×C4×C53—24no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—22no—
367C2×C4×C53—22no—
368C2×C4×C53—22no—
369C2×C4×C53—42no—
370C2×C4×C53—42no—
371C2×C4×C53—84no—
372C2×C4×C53C22×D412yes—
373C2×C4×C53C22×D412yes—
374C2×C4×C53C22×D411yescharacteristic
375C2×C4×C53C22×D412yes—
376C2×C4×C53H(5,𝔽2)12yes—
377C2×C4×C53C2511yescharacteristic
378C22⋊D53—48no—
379C22⋊D53—48no—
380C2×Dic53—22no—
381C2×Dic53—22no—
382C2×Dic53—22no—
383C2×Dic53—48no—
384C2×Dic53—42no—
385C2×Dic53C22×D412yes—
386C2×Dic53C22×D412yes—
387D212—22no—
388D212—22no—
389D212—22no—
390D212—22no—
391D212—22no—
392D212—22no—
393D212—44no—
394D212—48no—
395D212—48no—
396D212—48no—
397D212—42no—
398D212—42no—
399D212—42no—
400D212—84no—
401D212—84no—
402D212—84no—
403D212—84no—
404C4×D53—24no—
405C4×D53—24no—
406C4×D53—22no—
407C4×D53—22no—
408C4×D53—22no—
409C4×D53—22no—
410C4×D53—48no—
411C4×D53—48no—
412Dic106—22no—
413Dic106—22no—
414Dic106—42no—
415C8×C53—22no—
416C8×C53C22×D414yes—
417#88322—22no—
418#88322—22no—
419C2×#3268—531nomaximal, Sylow
420C22×C53—24no—
421C22×C53—48no—
422C22×C53—42no—
423C22×C53—42no—
424C22×C53D4212yes—
425C22×C53#57512yes—
426C22×C53#57612yes—
427C22×C53C23×D411yescharacteristic
428C2×D53—22no—
429C2×D53—22no—
430C2×D53—22no—
431C2×D53—22no—
432C2×D53—22no—
433C2×D53—22no—
434C2×D53—44no—
435C2×D53—44no—
436C2×D53—42no—
437C2×D53—42no—
438C2×D53—42no—
439C2×D53—42no—
440C2×D53—42no—
441C2×D53—42no—
442C2×D53—42no—
443C2×D53—42no—
444C2×D53—42no—
445C2×D53—816no—
446C2×D53—84no—
447C2×D53—84no—
448C2×D53—84no—
449C4×C53—24no—
450C4×C53—22no—
451C4×C53—22no—
452C4×C53—42no—
453C4×C53—42no—
454C4×C53D4212yes—
455C4×C53C23×D411yescharacteristic
456C4×C53C2×H(5,𝔽2)11yescharacteristic
457Dic53—22no—
458Dic53—22no—
459Dic53—42no—
460C22×AGL(1,ℤ/8)—531no—
461C22×#135—531no—
462C2×#550—531no—
463C2×#546—531no—
464#3268—5316no—
465C2×#496—531no—
466C2×#468—531no—
467C2×#466—531no—
468C2×#464—531no—
469C2×#459—531no—
470C2×#452—531no—
471C2×#449—531no—
472C2×#449—531no—
473C2×#447—531no—
474C2×#440D5311yescharacteristic, complemented
475C2×#435—531no—
476C2×C53—44no—
477C2×C53#326814yescomplemented
478C2×C53C2×D4211yescharacteristic
479C2×C53C2×#57511yescharacteristic
480C2×C53C2×#57611yescharacteristic
481D53—42no—
482D53—42no—
483D53—82no—
484D53—82no—
485D53—82no—
486C22×#41—531no—
487C22×#41—531no—
488C22×#41—531no—
489C23×D4—531no—
490C2×AGL(1,ℤ/8)—538no—
491C2×AGL(1,ℤ/8)—1068no—
492C2×#135—538no—
493C2×#135—1068no—
494C22×Q16—531no—
495C22×SD16—531no—
496C22×SD16—531no—
497C22×SD16—531no—
498C22×SD16C2×D5311yescharacteristic
499C22×D8—531no—
500C22×D8—531no—
501C22×D8—531no—
502C22×D8—531no—
503C22×M16—531no—
504C23×C8—531no—
505#550—538no—
506#550—1064no—
507#546—538no—
508#546—1064no—
509C2×#127—531no—
510C2×#127—1061no—
511C2×#124—531no—
512C2×#123—1061no—
513C2×C22⋊Q8—531no—
514C2×#121—531no—
515C2×#121—531no—
516C2×#121—531no—
517C2×#121—1061no—
518C2×#121—1061no—
519C2×#121—1061no—
520C2×#120—1061no—
521C2×C4×Q8C2×D5311yescharacteristic, complemented
522C2×C4×D4—531no—
523C2×C4×D4—1061no—
524C2×C4×D4C2×D5311yescharacteristic
525C22×C22⋊C4—1061no—
526#496—538no—
527#468—538no—
528#466—538no—
529#464—538no—
530#459—538no—
531#452—538no—
532#449—538no—
533#449—538no—
534#447—538no—
535#440C2×D5318yescomplemented
536#435—538no—
537C2×#107C2×D5311yescharacteristic, complemented
538C2×C4⋊C8—531no—
539C2×#103—531no—
540C2×#103C2×D5311yescharacteristic, complemented
541C2×#102—531no—
542C2×#102—531no—
543C2×#102—531no—
544C2×#102C2×D5311yescharacteristic
545C2×C22⋊C8—531no—
546C2×C22⋊C8—531no—
547C2×#97C2×D5311yescharacteristic, complemented
548C53C2×#326811yescharacteristic, complemented, Sylow
549C25—1061no—
550C2×#41—534no—
551C2×#41—534no—
552C2×#41—534no—
553C2×#41—1062no—
554C2×#41—1062no—
555C2×#41—1062no—
556C2×#41—1064no—
557C2×#41—1064no—
558C2×#41—1064no—
559C2×#41—2122no—
560C2×#41—2122no—
561C2×#41—2122no—
562C22×Q8—531no—
563C22×Q8C22×D5311yescharacteristic
564C22×D4—534no—
565C22×D4—531no—
566C22×D4—531no—
567C22×D4—531no—
568C22×D4—531no—
569C22×D4—1061no—
570C22×D4—1061no—
571C22×D4—1061no—
572C22×D4—1061no—
573C22×D4—1061no—
574C22×D4—1062no—
575C22×D4—1061no—
576C22×D4—1064no—
577C22×D4—1061no—
578C22×D4—1061no—
579C22×D4—1061no—
580C22×D4—2122no—
581C22×D4C22×D5311yescharacteristic
582C23×C4—21no—
583C23×C4—531no—
584C23×C4—531no—
585C23×C4—1061no—
586C23×C4—1061no—
587C23×C4—1061no—
588AGL(1,ℤ/8)—10632no—
589#135—10632no—
590C2×Q16—534no—
591C2×Q16—1064no—
592C2×SD16—534no—
593C2×SD16—534no—
594C2×SD16—534no—
595C2×SD16—1064no—
596C2×SD16—1064no—
597C2×SD16—2122no—
598C2×SD16D21218yescomplemented
599C2×SD16C22×D5314yes—
600C2×D8—534no—
601C2×D8—534no—
602C2×D8—534no—
603C2×D8—534no—
604C2×D8—1064no—
605C2×D8—1064no—
606C2×D8—1064no—
607C2×D8—2122no—
608C2×M16—534no—
609C2×M16—1064no—
610C22×C8—531no—
611C22×C8—531no—
612C22×C8—534no—
613C22×C8—1064no—
614C22×C8C22×D5311yescharacteristic
615C22×C8C22×D5311yescharacteristic
616#127—534no—
617#127—1068no—
618#127—1062no—
619#124—534no—
620#124—1062no—
621#123—1068no—
622C22⋊Q8—534no—
623C22⋊Q8—1062no—
624#121—534no—
625#121—534no—
626#121—534no—
627#121—1068no—
628#121—1068no—
629#121—1068no—
630#121—1062no—
631#121—1062no—
632#121—1062no—
633#120—1068no—
634C4×Q8—22no—
635C4×Q8C22×D5314yescomplemented
636C4×D4—22no—
637C4×D4—534no—
638C4×D4—534no—
639C4×D4—1068no—
640C4×D4C22×D5314yes—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—531no—
643C2×C4⋊C4—1061no—
644C2×C4⋊C4C22×D5311yescharacteristic
645C2×C4⋊C4C22×D5311yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—531no—
648C2×C22⋊C4—531no—
649C2×C22⋊C4—1068no—
650C2×C22⋊C4—1061no—
651C2×C22⋊C4—1061no—
652C2×C22⋊C4—1061no—
653C2×C22⋊C4—1061no—
654C2×C22⋊C4—1061no—
655C2×C22⋊C4—1061no—
656C2×C42—21no—
657C2×C42C22×D5311yescharacteristic
658#107C22×D5314yescomplemented
659C4⋊C8—534no—
660#103—534no—
661#103C22×D5314yescomplemented
662#102—534no—
663#102—534no—
664#102—534no—
665#102C22×D5314yes—
666C22⋊C8—534no—
667C22⋊C8—534no—
668#97C22×D5314yescomplemented
669C24—21no—
670C24—531no—
671C24—531no—
672C24—1064no—
673C24—1061no—
674C24—1061no—
675C24—1061no—
676C24—4242no—
677C24—2124no—
678C24—2124no—
679#41—1068no—
680#41—1068no—
681#41—1068no—
682#41—2124no—
683#41—2128no—
684#41—2124no—
685#41—2124no—
686#41—2128no—
687#41—2128no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—532no—
691C2×Q8—1061no—
692C2×Q8—1062no—
693C2×Q8—1062no—
694C2×Q8C2×D21214yes—
695C2×Q8C23×D5312yes—
696C2×D4—21no—
697C2×D4—22no—
698C2×D4—534no—
699C2×D4—532no—
700C2×D4—532no—
701C2×D4—532no—
702C2×D4—1064no—
703C2×D4—1064no—
704C2×D4—1064no—
705C2×D4—1064no—
706C2×D4—1064no—
707C2×D4—1064no—
708C2×D4—1068no—
709C2×D4—1064no—
710C2×D4—1064no—
711C2×D4—1064no—
712C2×D4—1061no—
713C2×D4—1061no—
714C2×D4—1061no—
715C2×D4—1062no—
716C2×D4—1062no—
717C2×D4—1062no—
718C2×D4—1062no—
719C2×D4—1062no—
720C2×D4—1062no—
721C2×D4—4242no—
722C2×D4—4242no—
723C2×D4—4242no—
724C2×D4—4242no—
725C2×D4—2122no—
726C2×D4—2124no—
727C2×D4—2124no—
728C2×D4—2124no—
729C2×D4—2124no—
730C2×D4—2128no—
731C2×D4—2124no—
732C2×D4—2124no—
733C2×D4C2×D21214yes—
734C2×D4C23×D5312yes—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—24no—
739C22×C4—82no—
740C22×C4—531no—
741C22×C4—531no—
742C22×C4—532no—
743C22×C4—532no—
744C22×C4—532no—
745C22×C4—532no—
746C22×C4—1064no—
747C22×C4—1064no—
748C22×C4—1064no—
749C22×C4—1062no—
750C22×C4—1062no—
751C22×C4—1062no—
752C22×C4—1062no—
753C22×C4—1061no—
754C22×C4—2124no—
755C22×C4—2124no—
756C22×C4—2124no—
757C22×C4D4×D5311yescharacteristic
758C22×C4D4×D5311yescharacteristic
759C22×C4C23×D5311yescharacteristic
760Q16—1068no—
761SD16—1068no—
762SD16—1068no—
763SD16—2124no—
764SD16C2×D212116yescomplemented
765D8—1068no—
766D8—1068no—
767D8—1068no—
768D8—2124no—
769M16—1068no—
770C2×C8—22no—
771C2×C8—532no—
772C2×C8—532no—
773C2×C8—1062no—
774C2×C8—1062no—
775C2×C8—1068no—
776C2×C8C2×D21214yes—
777C2×C8C23×D5312yes—
778C2×C8C23×D5312yes—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—534no—
783C4⋊C4—1064no—
784C4⋊C4C23×D5312yes—
785C4⋊C4C23×D5312yes—
786C22⋊C4—24no—
787C22⋊C4—534no—
788C22⋊C4—534no—
789C22⋊C4—1064no—
790C22⋊C4—1064no—
791C22⋊C4—1064no—
792C22⋊C4—1064no—
793C22⋊C4—1064no—
794C22⋊C4—1064no—
795C42—24no—
796C42D4×D5312yes—
797C42C23×D5312yes—
798C23—22no—
799C23—24no—
800C23—42no—
801C23—42no—
802C23—532no—
803C23—532no—
804C23—1062no—
805C23—1062no—
806C23—1062no—
807C23—1062no—
808C23—1062no—
809C23—1062no—
810C23—1062no—
811C23—1062no—
812C23—1062no—
813C23—4244no—
814C23—42416no—
815C23—2128no—
816C23—2128no—
817C23—2122no—
818C23—2122no—
819C23—2122no—
820C23—2122no—
821C23—2122no—
822C23—2122no—
823C23—2122no—
824C23—2122no—
825C23—2122no—
826C23C2×D4×D5311yescharacteristic
827Q8—22no—
828Q8—24no—
829Q8—1062no—
830Q8—1062no—
831Q8—2122no—
832Q8C22×D21214yes—
833D4—22no—
834D4—24no—
835D4—1062no—
836D4—1062no—
837D4—1062no—
838D4—1062no—
839D4—1062no—
840D4—1062no—
841D4—4244no—
842D4—4244no—
843D4—4244no—
844D4—4244no—
845D4—2124no—
846D4—2128no—
847D4—2128no—
848D4—2128no—
849D4—2128no—
850D4—2128no—
851D4—2122no—
852D4—2122no—
853D4—2122no—
854D4C22×D21214yes—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—84no—
864C2×C4—532no—
865C2×C4—532no—
866C2×C4—1062no—
867C2×C4—1062no—
868C2×C4—1062no—
869C2×C4—1062no—
870C2×C4—1062no—
871C2×C4—1062no—
872C2×C4—1064no—
873C2×C4—1064no—
874C2×C4—1062no—
875C2×C4—2128no—
876C2×C4—2128no—
877C2×C4—2128no—
878C2×C4—2122no—
879C2×C4C2×D4×D5312yes—
880C2×C4C2×D4×D5312yes—
881C2×C4C2×D4×D5311yescharacteristic
882C2×C4C22×D21212yes—
883C2×C4#1313326312yes—
884C2×C4C24×D5311yescharacteristic
885C8—22no—
886C8—1062no—
887C8—1062no—
888C8C22×D21214yes—
889C22—24no—
890C22—48no—
891C22—42no—
892C22—42no—
893C22—1062no—
894C22—1062no—
895C22—1062no—
896C22—1062no—
897C22—1062no—
898C22—1062no—
899C22—42416no—
900C22—4244no—
901C22—4244no—
902C22—4244no—
903C22—2122no—
904C22—2122no—
905C22—2122no—
906C22—2122no—
907C22—2122no—
908C22—2122no—
909C22—2122no—
910C22—2122no—
911C22—2122no—
912C22—2124no—
913C22—2124no—
914C22D4×D21212yes—
915C22#1681142212yes—
916C22#1681142712yes—
917C22C22×D4×D5311yescharacteristic
918C4—24no—
919C4—22no—
920C4—22no—
921C4—42no—
922C4—42no—
923C4—1062no—
924C4—1062no—
925C4—2122no—
926C4D4×D21212yes—
927C4C23×D21211yescharacteristic
928C4C2×#1313326311yescharacteristic
929C2—44no—
930C2—4242no—
931C2—4242no—
932C2—4242no—
933C2—2122no—
934C2—2122no—
935C2#2028625714yesdirect product factor
936C2C2×D4×D21211yescharacteristic
937C2C2×#1681142211yescharacteristic
938C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
hypercenterC2×#440D53
hypocenterC53C2×#3268
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C22×#13133244C2semidirect
2. C22×#13133238C2semidirect
3. C2×#16811295C2semidirect
4. C2×#16811268C2semidirect
5. #20286257C2direct (N × H)
6. C2×#16811012C2semidirect
7. C2×#16810870C2semidirect
8. C2×#16810860C2semidirect
9. C2×#16810845C2semidirect
10. C2×#16810818C2semidirect
11. C2×#16810788C2semidirect
12. C2×#16810771C2semidirect
13. C2×#16810769C2semidirect
14. C2×#16810758C2semidirect
15. C2×#16810696C2semidirect
16. C2×C53×#440C2semidirect
18. C22×#11719949C22semidirect
22. C2×#13133244C22semidirect
24. C2×#13133238C22semidirect
25. C22×#11719925C22semidirect
26. C22×#11719913C22semidirect
27. C22×#11719913C22semidirect
34. C22×C8×D53C22semidirect
36. #16811295C22semidirect
38. #16811268C22semidirect
40. C2×#13133214C22semidirect
48. C2×#13133192C22semidirect
54. #16811012C22semidirect
55. #16810870C22semidirect
56. #16810860C22semidirect
57. #16810845C22semidirect
58. #16810818C22semidirect
59. #16810788C22semidirect
60. #16810771C22semidirect
61. #16810769C22semidirect
62. #16810758C22semidirect
63. #16810696C22semidirect
64. C2×C4⋊#88322C22semidirect
65. C2×#13133140C22semidirect
67. C2×#13133137C22semidirect
68. C2×#13133137C22semidirect
70. C2×#13133129C22semidirect
72. C2×C4×Q8×C53C22semidirect
74. C53×#440C22semidirect
75. C2×#107×C53C22semidirect
76. C2×#103×C53C22semidirect
78. C2×#97×C53C22semidirect
87. C2×#11719949C23semidirect
118. C2×#11719925C23semidirect
121. C2×#11719913C23semidirect
122. C2×#11719913C23semidirect
138. C2×C8×D53C23semidirect
141. #13133214C23semidirect
154. #13133192C23semidirect
171. C4⋊#88322C23semidirect
172. #13133140C23semidirect
174. #13133137C23semidirect
175. #13133137C23semidirect
177. #13133129C23semidirect
181. C2×SD16×C53D4semidirect
186. C4×Q8×C53C23semidirect
195. #107×C53C23semidirect
196. #103×C53C23semidirect
198. #97×C53C23semidirect
290. SD16×C53C2×D4semidirect
474. C2×#440D53semidirect
477. C2×C53#3268semidirect
521. C2×C4×Q8C2×D53semidirect
535. #440C2×D53semidirect
537. C2×#107C2×D53semidirect
540. C2×#103C2×D53semidirect
547. C2×#97C2×D53semidirect
548. C53C2×#3268semidirect
598. C2×SD16D212semidirect
635. C4×Q8C22×D53semidirect
658. #107C22×D53semidirect
661. #103C22×D53semidirect
668. #97C22×D53semidirect
764. SD16C2×D212semidirect
935. C2#20286257direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332442
C22×#131332382
C2×#168112952
C2×#168112682
#202862572
C2×#168110122
C2×#168108702
C2×#168108602
C2×#168108452
C2×#168108182
C2×#168107882
C2×#168107712
C2×#168107692
C2×#168107582
C2×#168106962
C2×C53×#4402
C2×#326853