Finite Group Databasebeta

← #27404409

Subgroups — #27404409

Order 13568.

1386 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810757C211yesmaximal, characteristic
2C2×#16810732C211yesmaximal, characteristic, complemented
3#20277731C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic53C211yesmaximal, characteristic, complemented
5#20275588C211yesmaximal, characteristic, complemented
6#20275409C211yesmaximal, characteristic, complemented
7#20275345C211yesmaximal, characteristic, complemented
8#20275143C211yesmaximal, characteristic, complemented
9#20275061C211yesmaximal, characteristic, complemented
10#20275060C211yesmaximal, characteristic, complemented
11#20274974C211yesmaximal, characteristic, complemented
12#20274908C211yesmaximal, characteristic, complemented
13#20274542C211yesmaximal, characteristic, complemented
14#20274491C211yesmaximal, characteristic, complemented
15C22×#102×C53C211yesmaximal, characteristic, complemented
16C22×#11719922C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C2×#13133191C2211yescharacteristic
19C2×D4×Dic53C2211yescharacteristic
20C2×D4×Dic53C2211yescharacteristic
21C2×#13133179C2211yescharacteristic, complemented
22C2×C4×C22⋊D53—21no—
23C22×C22⋊Dic53—21no—
24#16810757C418yescomplemented
25#16810732—24no—
26C2×#13133148C2211yescharacteristic, complemented
27C2×#13133148C2211yescharacteristic, complemented
28C2×#13133139C2211yescharacteristic, complemented
29C2×#13133139C2211yescharacteristic, complemented
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×C22⋊#88322C2211yescharacteristic
33C2×#13133127C2211yescharacteristic, complemented
34C2×#13133127C2211yescharacteristic, complemented
35#16810526C2211yescharacteristic
36#16810526C2211yescharacteristic
37#16810524C2211yescharacteristic, complemented
38#16810519C2211yescharacteristic, complemented
39#16810513—21no—
40#16810503—21no—
41#16810503—21no—
42#16810502—21no—
43#16810494—21no—
44#16810483C2211yescharacteristic
45#16810479—21no—
46C4⋊C4×Dic53C2211yescharacteristic, complemented
47C4×C22⋊Dic53C2211yescharacteristic
48#16810386C2211yescharacteristic, complemented
49#16810386C2211yescharacteristic, complemented
50#16810385C2211yescharacteristic, complemented
51#16810385C2211yescharacteristic, complemented
52#16810377C2211yescharacteristic, complemented
53#16810377C2211yescharacteristic, complemented
54C23×D4×C53C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C22×C4⋊C4×C53C2211yescharacteristic
57C2×#102×C53—24no—
58C2×#102×C53C2211yescharacteristic
59C2×#102×C53C2211yescharacteristic
60C2×#102×C53C2211yescharacteristic
61C2×#102×C53C2211yescharacteristic
62C22×D212C2311yescharacteristic
63C22×C22⋊D53—21no—
64C23×Dic53—21no—
65C23×Dic53—21no—
66C22×C4×D53—21no—
67C2×#11719922—22no—
68C2×#11719922—22no—
69C2×#11719922—41no—
70C2×#11719922—41no—
71C2×#11719922C2×C414yescomplemented
72C2×#11719922C2×C414yescomplemented
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133191—22no—
76#13133191C2×C414yescomplemented
77D4×Dic53—22no—
78D4×Dic53—22no—
79D4×Dic53—41no—
80D4×Dic53—41no—
81#13133179—22no—
82#13133179—41no—
83C4×C22⋊D53—44no—
84C2×C4⋊Dic53C2311yescharacteristic
85C2×C4⋊Dic53C2311yescharacteristic
86C2×C4⋊Dic53C2311yescharacteristic
87C2×#11719919—21no—
88C2×C22⋊Dic53—21no—
89C2×C22⋊Dic53—21no—
90C2×C22⋊Dic53—21no—
91C2×C22⋊Dic53—21no—
92C2×C22⋊Dic53—21no—
93C2×C22⋊Dic53—21no—
94C2×C22⋊Dic53—21no—
95C2×C22⋊Dic53—44no—
96C2×C22⋊Dic53D411yescharacteristic
97C2×C22⋊Dic53D411yescharacteristic
98C2×#11719921—21no—
99C2×#11719921—21no—
100C2×#11719921—21no—
101C2×#11719921—21no—
102C2×C4×Dic53—21no—
103C2×C4×Dic53C2311yescharacteristic
104C2×C4×Dic53C2311yescharacteristic
105#13133148—22no—
106#13133148—41no—
107#13133139—22no—
108#13133139—41no—
109#13133138C2×C414yescomplemented
110#13133138C2×C414yescomplemented
111C22⋊#88322C2×C414yescomplemented
112#13133127—22no—
113#13133127—41no—
114#13133124—21no—
115#13133124—21no—
116#13133124—21no—
117#13133124D411yescharacteristic
118#13133124D411yescharacteristic
119C25×C53—21no—
120C22×D4×C53—22no—
121C22×D4×C53—22no—
122C22×D4×C53—21no—
123C22×D4×C53—22no—
124C22×D4×C53—41no—
125C22×D4×C53—41no—
126C22×D4×C53C2×C414yescomplemented
127C22×D4×C53C2311yescharacteristic
128C22×D4×C53C2311yescharacteristic
129C23×C4×C53—21no—
130C23×C4×C53C2311yescharacteristic
131C22×C8×C53—22no—
132C22×C8×C53—22no—
133C22×C8×C53—41no—
134C22×C8×C53C2311yescharacteristic
135C22×C8×C53C2311yescharacteristic
136C2×C4⋊C4×C53—21no—
137C2×C4⋊C4×C53—22no—
138C2×C4⋊C4×C53—41no—
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C4⋊C4×C53C2311yescharacteristic
141#102×C53—22no—
142#102×C53—22no—
143#102×C53—22no—
144#102×C53D414yescomplemented
145C24×C53—21no—
146C24×C53—21no—
147C24×C53—24no—
148C24×C53—42no—
149C24×C53—42no—
150C24×C53—42no—
151C24×C53—42no—
152C24×C53—81no—
153C24×C53—81no—
154C24×C53C2×D411yescharacteristic
155C23×D53—21no—
156C2×D4×C53—28no—
157C2×D4×C53—24no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53—21no—
165C2×D4×C53—21no—
166C2×D4×C53—44no—
167C2×D4×C53—44no—
168C2×D4×C53—44no—
169C2×D4×C53—42no—
170C2×D4×C53—42no—
171C2×D4×C53C22×C412yes—
172C2×D4×C53C22×C412yes—
173C2×D4×C53C2×D412yes—
174C2×D4×C53#4112yes—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—42no—
182C22×C4×C53—42no—
183C22×C4×C53—81no—
184C22×C4×C53C22×C412yes—
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53#4112yes—
187C22×C4×C53C2411yescharacteristic
188C2×C22⋊D53—24no—
189C2×C22⋊D53—42no—
190C2×C22⋊D53—42no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—42no—
195C22×Dic53—42no—
196C22×Dic53—42no—
197C22×Dic53—42no—
198C22×Dic53—81no—
199C22×Dic53—81no—
200C22×Dic53C2×D411yescharacteristic
201C22×Dic53C2×D411yescharacteristic
202C22×Dic53C2×D411yescharacteristic
203C22×Dic53C2×D411yescharacteristic
204C2×D212—21no—
205C2×D212—21no—
206C2×D212—21no—
207C2×D212—21no—
208C2×D212—21no—
209C2×D212C22×C412yes—
210C2×C4×D53—42no—
211C2×C4×D53—42no—
212C2×C4×D53—81no—
213C2×C8×C53—21no—
214C2×C8×C53—21no—
215C2×C8×C53—21no—
216C2×C8×C53—21no—
217C2×C8×C53—21no—
218C2×C8×C53—44no—
219C2×C8×C53C2×D412yes—
220C4⋊C4×C53—21no—
221C4⋊C4×C53—21no—
222C4⋊C4×C53—21no—
223C4⋊C4×C53—42no—
224C4⋊C4×C53C2×D412yes—
225C22⋊Dic53—22no—
226C22⋊Dic53—22no—
227C22⋊Dic53—42no—
228C22⋊Dic53—42no—
229C22⋊Dic53—42no—
230C22⋊Dic53—42no—
231C22⋊Dic53—42no—
232C22⋊Dic53—81no—
233C22⋊Dic53—81no—
234#11719922—28no—
235#11719922—44no—
236#11719921—24no—
237#11719921—42no—
238#11719921—42no—
239#11719921—81no—
240C4⋊Dic53—21no—
241C4⋊Dic53—21no—
242C4⋊Dic53—21no—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53C22×C412yes—
246#11719919—42no—
247C4×Dic53—21no—
248C4×Dic53—21no—
249C4×Dic53—21no—
250C4×Dic53—21no—
251C4×Dic53—42no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322C22×C412yes—
257C2×#88322C22×C412yes—
258C23×C53—21no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—22no—
263C23×C53—22no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—48no—
267C23×C53—41no—
268C23×C53—41no—
269C23×C53—41no—
270C23×C53—41no—
271C23×C53—41no—
272C23×C53—41no—
273C23×C53—41no—
274C23×C53—41no—
275C23×C53—41no—
276C23×C53—41no—
277C23×C53—48no—
278C23×C53—84no—
279C23×C53—84no—
280C23×C53—84no—
281C23×C53—84no—
282C23×C53—84no—
283C23×C53C4×D412yes—
284C23×C53AGL(1,ℤ/8)12yes—
285C23×C53AGL(1,ℤ/8)12yes—
286C23×C53C22×D411yescharacteristic
287C22×D53—22no—
288C22×D53—41no—
289C22×D53—41no—
290C22×D53—41no—
291C22×D53—41no—
292C22×D53—41no—
293C22×D53—41no—
294D4×C53—22no—
295D4×C53—22no—
296D4×C53—22no—
297D4×C53—22no—
298D4×C53—22no—
299D4×C53—48no—
300D4×C53—41no—
301D4×C53—41no—
302D4×C53C4×D414yescomplemented
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53—84no—
316C2×C4×C53C4×D412yes—
317C2×C4×C53C23×C411yescharacteristic
318C2×C4×C53C22×D411yescharacteristic
319C2×C4×C53C2×#4111yescharacteristic
320C2×C4×C53C2×#4111yescharacteristic
321C2×C4×C53H(5,𝔽2)11yescharacteristic
322C2×C4×C53H(5,𝔽2)11yescharacteristic
323C22⋊D53—48no—
324C2×Dic53—22no—
325C2×Dic53—21no—
326C2×Dic53—21no—
327C2×Dic53—21no—
328C2×Dic53—21no—
329C2×Dic53—21no—
330C2×Dic53—21no—
331C2×Dic53—21no—
332C2×Dic53—21no—
333C2×Dic53—21no—
334C2×Dic53—21no—
335C2×Dic53—21no—
336C2×Dic53—21no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—41no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—84no—
346C2×Dic53—84no—
347D212—22no—
348D212—22no—
349D212—41no—
350D212—41no—
351C4×D53—84no—
352C8×C53—22no—
353C8×C53—41no—
354#88322—22no—
355#88322—22no—
356#22858—531nomaximal, Sylow
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—22no—
360C22×C53—22no—
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—24no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—42no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53—42no—
371C22×C53—42no—
372C22×C53—42no—
373C22×C53—816no—
374C22×C53—81no—
375C22×C53—81no—
376C22×C53—81no—
377C22×C53—81no—
378C22×C53#44214yescomplemented
379C22×C53C2×C4×D411yescharacteristic
380C22×C53D4211yescharacteristic
381C22×C53#54611yescharacteristic
382C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
384C22×C53#57611yescharacteristic
385C22×C53#57711yescharacteristic
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—81no—
390C2×D53—81no—
391C2×D53—81no—
392C2×D53—81no—
393C4×C53—22no—
394C4×C53—42no—
395C4×C53—81no—
396C4×C53C2×C4×D411yescharacteristic
397C4×C53#51811yescharacteristic
398C4×C53#54611yescharacteristic
399C4×C53#55111yescharacteristic
400Dic53—42no—
401Dic53—41no—
402Dic53—41no—
403Dic53—41no—
404Dic53—41no—
405Dic53—81no—
406Dic53—81no—
407C2×#447—531no—
408C2×#442—531no—
409C22×#102D5311yescharacteristic, complemented
410#2361—531no—
411D4×C22⋊C4—531no—
412#1972—531no—
413#1936—531no—
414#1926—531no—
415#1893—531no—
416#1879—531no—
417#1879—531no—
418#1864—531no—
419#1853—531no—
420#1762—531no—
421#1752—531no—
422C2×C53—24no—
423C2×C53—44no—
424C2×C53—82no—
425C2×C53#235811yescharacteristic
426C2×C53C2×#44211yescharacteristic
427C2×C53#294611yescharacteristic
428C2×C53#326411yescharacteristic
429C2×C53#326511yescharacteristic
430C2×C53#330611yescharacteristic
431C2×C53#331811yescharacteristic
432D53—82no—
433C23×D4C2×D5311yescharacteristic
434C22×D8—531no—
435C22×D8—531no—
436C23×C8C2×D5311yescharacteristic
437C2×#121—531no—
438C2×C4×D4—531no—
439C2×C4×D4—531no—
440C2×C4×D4—531no—
441C2×C4×D4—1061no—
442C22×C4⋊C4C2×D5311yescharacteristic
443C22×C22⋊C4—1061no—
444#447—538no—
445#442—1064no—
446C2×#106—531no—
447C2×#106—531no—
448C2×#102—24no—
449C2×#102—531no—
450C2×#102—531no—
451C2×#102—531no—
452C2×#102—531no—
453C2×#102C2×D5311yescharacteristic
454C2×#102C2×D5311yescharacteristic
455C2×#102C2×D5311yescharacteristic
456C2×#102C2×D5311yescharacteristic
457C2×C22⋊C8—531no—
458C2×#97—531no—
459C2×#97—531no—
460#390—531no—
461#390—531no—
462#390—531no—
463#389—531no—
464#388—1061no—
465#386—1061no—
466#386—1061no—
467#386—1061no—
468#385—1061no—
469#380—531no—
470#379—1061no—
471C4×C4⋊C4—531no—
472C4×C22⋊C4—531no—
473#340—531no—
474#340—531no—
475#340—531no—
476#340—531no—
477#336—531no—
478#336—531no—
479C53#2285811yescharacteristic, complemented, Sylow
480C25—21no—
481C22×D4—22no—
482C22×D4—22no—
483C22×D4—21no—
484C22×D4—22no—
485C22×D4—41no—
486C22×D4—41no—
487C22×D4—531no—
488C22×D4—1061no—
489C22×D4C4×D5314yescomplemented
490C22×D4C22×D5311yescharacteristic
491C22×D4C22×D5311yescharacteristic
492C23×C4—21no—
493C23×C4—1061no—
494C23×C4—1061no—
495C23×C4—1061no—
496C23×C4C22×D5311yescharacteristic
497C2×D8—534no—
498C2×D8—534no—
499C2×D8—1062no—
500C2×D8—1062no—
501C2×D8—2121no—
502C2×D8—2121no—
503C22×C8—22no—
504C22×C8—22no—
505C22×C8—41no—
506C22×C8—531no—
507C22×C8—531no—
508C22×C8C22×D5311yescharacteristic
509C22×C8C22×D5311yescharacteristic
510#121—534no—
511#121—1062no—
512C4×D4—1062no—
513C4×D4—1062no—
514C4×D4—1062no—
515C4×D4—2121no—
516C4×D4—2121no—
517C4×D4—2121no—
518C4×D4—2124no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—41no—
522C2×C4⋊C4—531no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4C22×D5311yescharacteristic
527C2×C4⋊C4C22×D5311yescharacteristic
528C2×C22⋊C4—531no—
529C2×C22⋊C4—531no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C22⋊C4—1061no—
533C2×C22⋊C4—1061no—
534C2×C22⋊C4—1061no—
535C2×C22⋊C4—1061no—
536C2×C22⋊C4—1061no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4—2124no—
542C2×C42—531no—
543C2×C42—531no—
544C2×C42—1061no—
545#106—1062no—
546#106—2121no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—534no—
551#102—534no—
552#102—1062no—
553#102—2121no—
554#102C22⋊D5314yescomplemented
555C22⋊C8—534no—
556#97—1062no—
557#97—2121no—
558#95—531no—
559#95—531no—
560#95—1061no—
561#95—1061no—
562#95—1061no—
563C24—21no—
564C24—21no—
565C24—24no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24—1061no—
573C24D4×D5311yescharacteristic
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—44no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—532no—
590C2×D4—1064no—
591C2×D4—1061no—
592C2×D4—1061no—
593C2×D4—1061no—
594C2×D4—1061no—
595C2×D4—1061no—
596C2×D4—2122no—
597C2×D4—2122no—
598C2×D4C2×C4×D5312yes—
599C2×D4C2×C4×D5312yes—
600C2×D4#1171994512yes—
601C2×D4C2×C22⋊D5312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—81no—
611C22×C4—531no—
612C22×C4—531no—
613C22×C4—531no—
614C22×C4—531no—
615C22×C4—1061no—
616C22×C4—1061no—
617C22×C4—1061no—
618C22×C4—4241no—
619C22×C4—4241no—
620C22×C4—4241no—
621C22×C4—2122no—
622C22×C4—2122no—
623C22×C4—2122no—
624C22×C4—2122no—
625C22×C4—2122no—
626C22×C4—2122no—
627C22×C4C2×C4×D5312yes—
628C22×C4D4×D5311yescharacteristic
629C22×C4#1171994712yes—
630C22×C4C23×D5311yescharacteristic
631D8—1068no—
632D8—2124no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—44no—
639C2×C8—532no—
640C2×C8—532no—
641C2×C8—1061no—
642C2×C8—1061no—
643C2×C8—1061no—
644C2×C8—1061no—
645C2×C8C2×C22⋊D5312yes—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—532no—
651C4⋊C4—1061no—
652C4⋊C4—1061no—
653C4⋊C4—1061no—
654C4⋊C4—1061no—
655C4⋊C4—1061no—
656C4⋊C4—2122no—
657C4⋊C4C2×C22⋊D5312yes—
658C22⋊C4—1062no—
659C22⋊C4—1062no—
660C22⋊C4—1064no—
661C22⋊C4—4241no—
662C22⋊C4—4241no—
663C22⋊C4—4241no—
664C22⋊C4—2122no—
665C22⋊C4—2122no—
666C22⋊C4—2122no—
667C22⋊C4—2122no—
668C22⋊C4—2122no—
669C22⋊C4—2122no—
670C22⋊C4—2122no—
671C42—1061no—
672C42—1061no—
673C42—1061no—
674C42—1061no—
675C42—2122no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—48no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—48no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—1062no—
702C23—2121no—
703C23—2121no—
704C23—2121no—
705C23—2121no—
706C23—2121no—
707C23—2121no—
708C23#1313317712yes—
709C23#1313324112yes—
710C23#1313324412yes—
711C23C2×D4×D5311yescharacteristic
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—41no—
719D4—41no—
720D4—1062no—
721D4—1062no—
722D4—2128no—
723D4—2121no—
724D4—2121no—
725D4C4×C22⋊D5314yescomplemented
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—1062no—
740C2×C4—1061no—
741C2×C4—1061no—
742C2×C4—1061no—
743C2×C4—1061no—
744C2×C4—1061no—
745C2×C4—1061no—
746C2×C4—1061no—
747C2×C4—1061no—
748C2×C4—1061no—
749C2×C4—1061no—
750C2×C4—1061no—
751C2×C4—1061no—
752C2×C4—4244no—
753C2×C4—4244no—
754C2×C4—4244no—
755C2×C4—2121no—
756C2×C4—2121no—
757C2×C4—2121no—
758C2×C4—2121no—
759C2×C4—2121no—
760C2×C4—2121no—
761C2×C4—2121no—
762C2×C4—2121no—
763C2×C4#1313317712yes—
764C2×C4C22×C4×D5311yescharacteristic
765C2×C4C22×C22⋊D5311yescharacteristic
766C2×C4C2×#1171994711yescharacteristic
767C2×C4C2×#1171994511yescharacteristic
768C2×C4#1313326211yescharacteristic
769C2×C4#1313326211yescharacteristic
770C8—22no—
771C8—41no—
772C8—1062no—
773C8—1062no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—24no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—816no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—4241no—
796C22—4241no—
797C22—4241no—
798C22—4241no—
799C22—2122no—
800C22—2122no—
801C22—2122no—
802C22#1681073214yescomplemented
803C22C2×#1313317711yescharacteristic
804C22D4×C22⋊D5311yescharacteristic
805C22#1681126311yescharacteristic
806C22C2×#1313324111yescharacteristic
807C22C2×#1313324411yescharacteristic
808C22#1681142411yescharacteristic
809C22#1681142911yescharacteristic
810C4—22no—
811C4—42no—
812C4—81no—
813C4—4241no—
814C4—4241no—
815C4—2121no—
816C4—2122no—
817C4—2121no—
818C4—2121no—
819C4—2121no—
820C4C2×C4×C22⋊D5311yescharacteristic
821C4#1681109611yescharacteristic
822C4#1681126711yescharacteristic
823C4#1681129911yescharacteristic
824C2—24no—
825C2—44no—
826C2—82no—
827C2—4242no—
828C2#2027769411yescharacteristic
829C2C2×#1681073211yescharacteristic
830C2#2028354111yescharacteristic
831C2#2028619511yescharacteristic
832C2#2028621011yescharacteristic
833C2#2028667211yescharacteristic
834C2#2028685211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC22×#102×C53C2
socleC23×C53C22×D4
prime radicalC2×#16810757C2
cosocleC22×C4×C53C24
hypercenterC22×#102D53
hypocenterC53#22858
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C2×#16810732C2semidirect
3. #20277731C2semidirect
4. D4×C22⋊Dic53C2semidirect
5. #20275588C2semidirect
6. #20275409C2semidirect
7. #20275345C2semidirect
8. #20275143C2semidirect
9. #20275061C2semidirect
10. #20275060C2semidirect
11. #20274974C2semidirect
12. #20274908C2semidirect
13. #20274542C2semidirect
14. #20274491C2semidirect
15. C22×#102×C53C2semidirect
21. C2×#13133179C22semidirect
24. #16810757C4semidirect
26. C2×#13133148C22semidirect
27. C2×#13133148C22semidirect
28. C2×#13133139C22semidirect
29. C2×#13133139C22semidirect
33. C2×#13133127C22semidirect
34. C2×#13133127C22semidirect
37. #16810524C22semidirect
38. #16810519C22semidirect
46. C4⋊C4×Dic53C22semidirect
48. #16810386C22semidirect
49. #16810386C22semidirect
50. #16810385C22semidirect
51. #16810385C22semidirect
52. #16810377C22semidirect
53. #16810377C22semidirect
71. C2×#11719922C2×C4semidirect
72. C2×#11719922C2×C4semidirect
76. #13133191C2×C4semidirect
109. #13133138C2×C4semidirect
110. #13133138C2×C4semidirect
111. C22⋊#88322C2×C4semidirect
126. C22×D4×C53C2×C4semidirect
144. #102×C53D4semidirect
302. D4×C53C4×D4semidirect
378. C22×C53#442semidirect
409. C22×#102D53semidirect
479. C53#22858semidirect
489. C22×D4C4×D53semidirect
554. #102C22⋊D53semidirect
725. D4C4×C22⋊D53semidirect
802. C22#16810732semidirect

Maximal subgroups

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

subgroupindex
C2×#168107572
C2×#168107322
#202777312
D4×C22⋊Dic532
#202755882
#202754092
#202753452
#202751432
#202750612
#202750602
#202749742
#202749082
#202745422
#202744912
C22×#102×C532
#2285853