Finite Group Databasebeta

← C2×#20275716 #27410880

Subgroups — C2×#20275716 #27410880

Order 13568.

2526 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11719924C211yesmaximal, characteristic, complemented
2C22×#13133191C211yesmaximal, characteristic
3C22×#13133141C211yesmaximal, characteristic, complemented
4C22×#13133137C211yesmaximal, characteristic, complemented
5C22×C22⋊#88322C211yesmaximal, characteristic, complemented
6#20275716C218yesmaximal, direct product factor
7C2×#16810385C211yesmaximal, characteristic, complemented
8C22×C22⋊Q8×C53C211yesmaximal, characteristic, complemented
9C23×D212C2211yescharacteristic
10C23×C22⋊D53—21no—
11C22×#11719924—24no—
12C22×#11719924—24no—
13C22×#11719924—24no—
14C22×#11719924C2214yescomplemented
15C23×#88322C2211yescharacteristic
16C23×#88322C2211yescharacteristic
17C2×#13133191—24no—
18C2×#13133191—24no—
19C2×#13133191—22no—
20C2×#13133191C2214yes—
21C22×C4⋊Dic53C2211yescharacteristic
22C22×#11719921—21no—
23C2×#13133141—24no—
24C2×#13133141C2214yescomplemented
25C2×#13133137—24no—
26C2×#13133137C2214yescomplemented
27C2×C22⋊#88322—24no—
28C2×C22⋊#88322C2214yescomplemented
29#16810385C2214yescomplemented
30C23×Q8×C53C2211yescharacteristic
31C24×C4×C53C2211yescharacteristic
32C2×C22⋊Q8×C53—24no—
33C2×C22⋊Q8×C53—22no—
34C2×C22⋊Q8×C53—24no—
35C2×C22⋊Q8×C53C2214yescomplemented
36C22×C4⋊C4×C53—21no—
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C22⋊C4×C53—21no—
39C24×D53—21no—
40C22×D212—22no—
41C22×D212—22no—
42C22×D212—22no—
43C22×D212—22no—
44C22×D212—21no—
45C22×D212—22no—
46C22×D212D414yes—
47C22×D212C2312yes—
48C22×C22⋊D53—28no—
49C22×C22⋊D53—24no—
50C22×C22⋊D53—44no—
51C22×C22⋊D53—44no—
52C23×Dic53—21no—
53C2×#11719924—232no—
54C2×#11719924—28no—
55C2×#11719924—28no—
56C2×#11719924—28no—
57C22×#88322—22no—
58C22×#88322—22no—
59C22×#88322—22no—
60C22×#88322—22no—
61C22×#88322—22no—
62C22×#88322D414yescomplemented
63C22×#88322C2312yes—
64C22×#88322C2312yes—
65#13133191—216no—
66#13133191—28no—
67#13133191—28no—
68C2×C4⋊Dic53—22no—
69C2×C4⋊Dic53—21no—
70C2×C4⋊Dic53D414yes—
71C2×C4⋊Dic53C2312yes—
72C2×#11719921—28no—
73C2×#11719921—24no—
74#13133141—28no—
75#13133137—28no—
76C22⋊#88322—28no—
77C25×C53D411yescharacteristic
78C22×Q8×C53—22no—
79C22×Q8×C53—21no—
80C22×Q8×C53—22no—
81C22×Q8×C53—22no—
82C22×Q8×C53—22no—
83C22×Q8×C53—22no—
84C22×Q8×C53D414yescomplemented
85C22×Q8×C53C2312yes—
86C23×C4×C53—21no—
87C23×C4×C53—21no—
88C23×C4×C53—22no—
89C23×C4×C53—22no—
90C23×C4×C53—22no—
91C23×C4×C53—22no—
92C23×C4×C53—22no—
93C23×C4×C53—22no—
94C23×C4×C53D411yescharacteristic
95C23×C4×C53D412yes—
96C23×C4×C53C2312yes—
97C23×C4×C53C2311yescharacteristic
98C22⋊Q8×C53—216no—
99C22⋊Q8×C53—28no—
100C22⋊Q8×C53—28no—
101C2×C4⋊C4×C53—28no—
102C2×C4⋊C4×C53—24no—
103C2×C4⋊C4×C53—22no—
104C2×C4⋊C4×C53—21no—
105C2×C4⋊C4×C53D414yescomplemented
106C2×C4⋊C4×C53C2312yes—
107C2×C22⋊C4×C53—28no—
108C2×C22⋊C4×C53—24no—
109C24×C53—22no—
110C24×C53—22no—
111C24×C53—22no—
112C24×C53—22no—
113C24×C53—22no—
114C24×C53—22no—
115C24×C53SD1614yescomplemented
116C24×C53C2×D412yes—
117C24×C53C2×D411yescharacteristic
118C23×D53—24no—
119C23×D53—22no—
120C23×D53—42no—
121C23×D53—42no—
122C23×D53—42no—
123C23×D53—42no—
124C23×D53—42no—
125C23×D53—42no—
126C2×Q8×C53—24no—
127C2×Q8×C53—22no—
128C2×Q8×C53—28no—
129C2×Q8×C53—28no—
130C2×Q8×C53—22no—
131C2×Q8×C53—22no—
132C2×Q8×C53—22no—
133C2×Q8×C53—22no—
134C2×Q8×C53—42no—
135C2×Q8×C53—42no—
136C2×Q8×C53—44no—
137C2×Q8×C53—44no—
138C2×Q8×C53C2×D414yescomplemented
139C22×C4×C53—24no—
140C22×C4×C53—24no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—24no—
147C22×C4×C53—24no—
148C22×C4×C53—24no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—42no—
156C22×C4×C53—42no—
157C22×C4×C53—42no—
158C22×C4×C53—42no—
159C22×C4×C53—44no—
160C22×C4×C53—44no—
161C22×C4×C53—44no—
162C22×C4×C53—44no—
163C22×C4×C53C2×D412yes—
164C22×C4×C53C2×D411yescharacteristic
165C22×C4×C53C2×D412yes—
166C22×C4×C53C2×D412yes—
167C22×C4×C53C2×D412yes—
168C22×C4×C53C2×D412yes—
169C22×C4×C53C2×D412yes—
170C22×C4×C53#4112yes—
171C22×C4×C53C2411yescharacteristic
172C2×C22⋊D53—216no—
173C2×C22⋊D53—48no—
174C2×C22⋊D53—432no—
175C2×C22⋊D53—48no—
176C22×Dic53—24no—
177C22×Dic53—22no—
178C22×Dic53—42no—
179C22×Dic53—42no—
180C2×D212—28no—
181C2×D212—28no—
182C2×D212—22no—
183C2×D212—22no—
184C2×D212—22no—
185C2×D212—22no—
186C2×D212—24no—
187C2×D212—22no—
188C2×D212—42no—
189C2×D212—44no—
190C2×D212—42no—
191C2×D212—44no—
192C2×D212C2×D414yes—
193C4⋊C4×C53—216no—
194C4⋊C4×C53—24no—
195C4⋊C4×C53—22no—
196C4⋊C4×C53C2×D414yescomplemented
197C22⋊C4×C53—216no—
198#11719924—232no—
199#11719921—216no—
200C4⋊Dic53—24no—
201C4⋊Dic53—22no—
202C4⋊Dic53C2×D414yes—
203C2×#88322—28no—
204C2×#88322—22no—
205C2×#88322—22no—
206C2×#88322—22no—
207C2×#88322—22no—
208C2×#88322—22no—
209C2×#88322—44no—
210C2×#88322C2×D414yescomplemented
211C23×C53—22no—
212C23×C53—22no—
213C23×C53—22no—
214C23×C53—22no—
215C23×C53—22no—
216C23×C53—22no—
217C23×C53—28no—
218C23×C53—28no—
219C23×C53—28no—
220C23×C53—44no—
221C23×C53—44no—
222C23×C53—44no—
223C23×C53—44no—
224C23×C53#12012yes—
225C23×C53#12012yes—
226C23×C53#12112yes—
227C23×C53C2×SD1612yes—
228C23×C53C2×SD1614yescomplemented
229C23×C53#13512yes—
230C23×C53AGL(1,ℤ/8)12yes—
231C23×C53#13712yes—
232C23×C53C22×D411yescharacteristic
233C22×D53—24no—
234C22×D53—42no—
235C22×D53—42no—
236C22×D53—42no—
237C22×D53—42no—
238C22×D53—42no—
239C22×D53—42no—
240C22×D53—48no—
241C22×D53—48no—
242C22×D53—48no—
243C22×D53—84no—
244C22×D53—84no—
245C22×D53—84no—
246C22×D53—84no—
247Q8×C53—24no—
248Q8×C53—24no—
249Q8×C53—42no—
250Q8×C53—42no—
251Q8×C53—48no—
252C2×C4×C53—22no—
253C2×C4×C53—22no—
254C2×C4×C53—24no—
255C2×C4×C53—24no—
256C2×C4×C53—22no—
257C2×C4×C53—42no—
258C2×C4×C53—42no—
259C2×C4×C53—42no—
260C2×C4×C53—42no—
261C2×C4×C53—44no—
262C2×C4×C53—48no—
263C2×C4×C53—48no—
264C2×C4×C53—42no—
265C2×C4×C53—42no—
266C2×C4×C53—42no—
267C2×C4×C53—42no—
268C2×C4×C53—48no—
269C2×C4×C53#12014yes—
270C2×C4×C53#12012yes—
271C2×C4×C53#12012yes—
272C2×C4×C53#12114yes—
273C2×C4×C53#12114yes—
274C2×C4×C53#12112yes—
275C2×C4×C53#12714yes—
276C2×C4×C53C22×D411yescharacteristic
277C2×C4×C53C22×D411yescharacteristic
278C2×C4×C53C22×D411yescharacteristic
279C2×C4×C53C22×D411yescharacteristic
280C2×C4×C53C22×D411yescharacteristic
281C2×C4×C53C2×#4111yescharacteristic
282C22⋊D53—432no—
283C2×Dic53—24no—
284C2×Dic53—42no—
285C2×Dic53—42no—
286C2×Dic53—48no—
287D212—24no—
288D212—24no—
289D212—42no—
290D212—42no—
291D212—48no—
292#88322—24no—
293#88322—42no—
294C2×#2000—531nomaximal, Sylow
295C22×C53—24no—
296C22×C53—24no—
297C22×C53—24no—
298C22×C53—42no—
299C22×C53—42no—
300C22×C53—42no—
301C22×C53—416no—
302C22×C53—42no—
303C22×C53#39214yes—
304C22×C53#44814yes—
305C22×C53#44914yes—
306C22×C53#45014yes—
307C22×C53#45214yes—
308C22×C53#46514yes—
309C22×C53#46814yes—
310C22×C53C2×#12011yescharacteristic
311C22×C53C2×#12011yescharacteristic
312C22×C53C2×#12111yescharacteristic
313C22×C53C22×SD1611yescharacteristic
314C22×C53C2×#13511yescharacteristic
315C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C53C2×#13711yescharacteristic
317C2×D53—44no—
318C2×D53—44no—
319C2×D53—44no—
320C2×D53—82no—
321C2×D53—82no—
322C2×D53—816no—
323C2×D53—82no—
324C2×D53—82no—
325C4×C53—42no—
326C4×C53—44no—
327C4×C53—44no—
328C4×C53#39214yes—
329C4×C53C2×#12011yescharacteristic
330C4×C53C2×#12111yescharacteristic
331C4×C53C2×#12111yescharacteristic
332C4×C53C2×#12711yescharacteristic
333Dic53—44no—
334C23×SD16—531no—
335C22×C22⋊Q8D5311yescharacteristic, complemented
336C22×#121—531no—
337C22×#103—531no—
338C22×#102—531no—
339C22×C22⋊C8—531no—
340#2000—538no—
341C2×#340—531no—
342C2×C53—44no—
343C2×C53#200018yescomplemented
344C2×C53C2×#39211yescharacteristic
345C2×C53C2×#45011yescharacteristic
346C2×C53C2×#44811yescharacteristic
347C2×C53C2×#44911yescharacteristic
348C2×C53C2×#45211yescharacteristic
349C2×C53C2×#46511yescharacteristic
350C2×C53C2×#46811yescharacteristic
351D53—84no—
352C23×Q8C2×D5311yescharacteristic
353C23×D4—531no—
354C23×D4—1061no—
355C24×C4C2×D5311yescharacteristic
356C22×SD16—534no—
357C22×SD16—1064no—
358C22×SD16—1064no—
359C22×SD16—1064no—
360C23×C8—531no—
361C23×C8—531no—
362C2×C22⋊Q8—24no—
363C2×C22⋊Q8—22no—
364C2×C22⋊Q8—24no—
365C2×C22⋊Q8C2×D5314yescomplemented
366C2×#121—534no—
367C2×#121—1064no—
368C2×#121—1064no—
369C2×#121—1062no—
370C22×C4⋊C4—21no—
371C22×C4⋊C4—531no—
372C22×C4⋊C4C2×D5311yescharacteristic
373C22×C22⋊C4—21no—
374C22×C22⋊C4—1061no—
375C2×#103—534no—
376C2×#103—1064no—
377C2×#102—534no—
378C2×#102—1064no—
379C2×C22⋊C8—534no—
380C2×C22⋊C8—1064no—
381#340—534no—
382C53C2×#200011yescharacteristic, complemented, Sylow
383C25—1061no—
384C25C22⋊D5311yescharacteristic
385C22×Q8—22no—
386C22×Q8—21no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8C22⋊D5314yescomplemented
392C22×Q8C22×D5312yes—
393C22×D4—534no—
394C22×D4—532no—
395C22×D4—1068no—
396C22×D4—1064no—
397C22×D4—1062no—
398C22×D4—1062no—
399C22×D4—1062no—
400C22×D4—1062no—
401C22×D4—1062no—
402C22×D4—1061no—
403C22×D4—2124no—
404C22×D4—2124no—
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—1061no—
414C23×C4C22⋊D5312yes—
415C23×C4C22⋊D5311yescharacteristic
416C23×C4C22×D5312yes—
417C23×C4C22×D5311yescharacteristic
418C2×SD16—1068no—
419C2×SD16—1068no—
420C2×SD16—10632no—
421C2×SD16—1068no—
422C22×C8—534no—
423C22×C8—532no—
424C22×C8—532no—
425C22×C8—1062no—
426C22×C8—1062no—
427C22×C8—1062no—
428C22×C8—1062no—
429C22×C8—1062no—
430C22⋊Q8—216no—
431C22⋊Q8—28no—
432C22⋊Q8—28no—
433#121—1068no—
434#121—1068no—
435#121—10616no—
436C2×C4⋊C4—28no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—534no—
441C2×C4⋊C4—532no—
442C2×C4⋊C4—1062no—
443C2×C4⋊C4—1061no—
444C2×C4⋊C4C22⋊D5314yescomplemented
445C2×C4⋊C4C22×D5312yes—
446C2×C22⋊C4—28no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—1068no—
449C2×C22⋊C4—1064no—
450#103—1068no—
451#102—1068no—
452C22⋊C8—1068no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—1064no—
460C24—1062no—
461C24—2122no—
462C24—2122no—
463C24—2122no—
464C24—2122no—
465C24—2122no—
466C24—2122no—
467C24#1171992414yescomplemented
468C24C2×C22⋊D5312yes—
469C24C2×C22⋊D5311yescharacteristic
470C2×Q8—24no—
471C2×Q8—22no—
472C2×Q8—28no—
473C2×Q8—28no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—42no—
479C2×Q8—44no—
480C2×Q8—42no—
481C2×Q8—44no—
482C2×Q8C2×C22⋊D5314yescomplemented
483C2×D4—534no—
484C2×D4—10616no—
485C2×D4—1068no—
486C2×D4—1064no—
487C2×D4—1068no—
488C2×D4—1062no—
489C2×D4—1062no—
490C2×D4—1062no—
491C2×D4—1062no—
492C2×D4—1062no—
493C2×D4—21232no—
494C2×D4—2128no—
495C2×D4—2128no—
496C2×D4—2122no—
497C2×D4—2122no—
498C2×D4—2124no—
499C2×D4—2124no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—1064no—
525C22×C4—1062no—
526C22×C4—2122no—
527C22×C4—2122no—
528C22×C4D4×D5312yes—
529C22×C4D4×D5312yes—
530C22×C4D4×D5312yes—
531C22×C4#1171994712yes—
532C22×C4C2×C22⋊D5312yes—
533C22×C4C2×C22⋊D5311yescharacteristic
534C22×C4C2×C22⋊D5312yes—
535C22×C4C2×C22⋊D5312yes—
536C22×C4C23×D5311yescharacteristic
537SD16—10632no—
538C2×C8—534no—
539C2×C8—1068no—
540C2×C8—1062no—
541C2×C8—1062no—
542C2×C8—1062no—
543C2×C8—1062no—
544C2×C8—1062no—
545C2×C8—2124no—
546C4⋊C4—216no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—534no—
550C4⋊C4—1064no—
551C4⋊C4—1062no—
552C4⋊C4C2×C22⋊D5314yescomplemented
553C22⋊C4—216no—
554C22⋊C4—10616no—
555C23—28no—
556C23—28no—
557C23—22no—
558C23—22no—
559C23—28no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—44no—
565C23—44no—
566C23—44no—
567C23—44no—
568C23—1064no—
569C23—4244no—
570C23—4244no—
571C23—4244no—
572C23—4244no—
573C23—2128no—
574C23—2128no—
575C23—2128no—
576C23—2122no—
577C23—2122no—
578C23—2122no—
579C23—2122no—
580C23—2122no—
581C23—2122no—
582C23#1313318512yes—
583C23#1313318612yes—
584C23#1313318912yes—
585C23C2×#1171992412yes—
586C23C2×#1171992414yescomplemented
587C23#1313323712yes—
588C23#1313324212yes—
589C23#1313324812yes—
590C23C22×C22⋊D5311yescharacteristic
591Q8—24no—
592Q8—24no—
593Q8—48no—
594Q8—42no—
595Q8—42no—
596D4—1064no—
597D4—1064no—
598D4—21232no—
599D4—2128no—
600D4—2122no—
601D4—2122no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—48no—
608C2×C4—44no—
609C2×C4—48no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—48no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—1064no—
620C2×C4—2128no—
621C2×C4—2122no—
622C2×C4—2122no—
623C2×C4#1313318512yes—
624C2×C4#1313318514yes—
625C2×C4#1313318612yes—
626C2×C4#1313318814yes—
627C2×C4#1313318912yes—
628C2×C4#1313318914yes—
629C2×C4#1313321314yes—
630C2×C4C2×D4×D5311yescharacteristic
631C2×C4C2×D4×D5311yescharacteristic
632C2×C4C2×D4×D5311yescharacteristic
633C2×C4C22×C22⋊D5311yescharacteristic
634C2×C4C22×C22⋊D5311yescharacteristic
635C2×C4C2×#1171994711yescharacteristic
636C8—1064no—
637C8—2122no—
638C22—24no—
639C22—24no—
640C22—24no—
641C22—416no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42416no—
647C22—4242no—
648C22—4242no—
649C22—4242no—
650C22—4242no—
651C22—2124no—
652C22—2124no—
653C22—2124no—
654C22#1681053114yes—
655C22#1681076214yes—
656C22#1681076814yes—
657C22#1681077314yes—
658C22#1681078314yes—
659C22#1681085414yes—
660C22#1681087114yes—
661C22C2×#1313318511yescharacteristic
662C22C2×#1313318611yescharacteristic
663C22C2×#1313318911yescharacteristic
664C22C22×#1171992411yescharacteristic
665C22C2×#1313323711yescharacteristic
666C22C2×#1313324211yescharacteristic
667C22C2×#1313324811yescharacteristic
668C4—44no—
669C4—42no—
670C4—44no—
671C4—2124no—
672C4#1681053114yes—
673C4C2×#1313318511yescharacteristic
674C4C2×#1313318811yescharacteristic
675C4C2×#1313318911yescharacteristic
676C4C2×#1313321311yescharacteristic
677C2—44no—
678C2—4244no—
679C2#2027571618yesdirect product factor
680C2C2×#1681053111yescharacteristic
681C2C2×#1681077311yescharacteristic
682C2C2×#1681076211yescharacteristic
683C2C2×#1681076811yescharacteristic
684C2C2×#1681078311yescharacteristic
685C2C2×#1681085411yescharacteristic
686C2C2×#1681087111yescharacteristic
subgroupG/H
centerC24C2×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC22×C22⋊Q8×C53C2
socleC24×C53C2×D4
prime radicalC22×#13133191C2
hypercenterC22×C22⋊Q8D53
hypocenterC53C2×#2000
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C23×#11719924C2semidirect
3. C22×#13133141C2semidirect
4. C22×#13133137C2semidirect
5. C22×C22⋊#88322C2semidirect
6. #20275716C2direct (N × H)
7. C2×#16810385C2semidirect
8. C22×C22⋊Q8×C53C2semidirect
14. C22×#11719924C22semidirect
24. C2×#13133141C22semidirect
26. C2×#13133137C22semidirect
28. C2×C22⋊#88322C22semidirect
29. #16810385C22semidirect
35. C2×C22⋊Q8×C53C22semidirect
62. C22×#88322D4semidirect
84. C22×Q8×C53D4semidirect
105. C2×C4⋊C4×C53D4semidirect
115. C24×C53SD16semidirect
138. C2×Q8×C53C2×D4semidirect
196. C4⋊C4×C53C2×D4semidirect
210. C2×#88322C2×D4semidirect
228. C23×C53C2×SD16semidirect
335. C22×C22⋊Q8D53semidirect
343. C2×C53#2000semidirect
365. C2×C22⋊Q8C2×D53semidirect
382. C53C2×#2000semidirect
391. C22×Q8C22⋊D53semidirect
444. C2×C4⋊C4C22⋊D53semidirect
467. C24#11719924semidirect
482. C2×Q8C2×C22⋊D53semidirect
552. C4⋊C4C2×C22⋊D53semidirect
586. C23C2×#11719924semidirect
679. C2#20275716direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117199242
C22×#131331912
C22×#131331412
C22×#131331372
C22×C22⋊#883222
#202757162
C2×#168103852
C22×C22⋊Q8×C532
C2×#200053