Finite Group Databasebeta

← #72271364

Subgroups — #72271364

Order 1536.

8596 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11658639C211yesmaximal, characteristic, complemented
2C2×#72090C214yesmaximal, complemented
3#10794436C211yesmaximal, characteristic, complemented
4#10794390C211yesmaximal, characteristic, complemented
5C2×#72129C211yesmaximal, characteristic, complemented
6#10701930C214yesmaximal, complemented
7#10700461C211yesmaximal, characteristic, complemented
8#10700426C211yesmaximal, characteristic, complemented
9C23×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic
10#359476—31nomaximal, Sylow
11C23×C3×#41C2211yescharacteristic
12C24×C3×D4C2211yescharacteristic
13C22×C3×AGL(1,ℤ/8)—24no—
14C22×C3×AGL(1,ℤ/8)—24no—
15C22×C3×AGL(1,ℤ/8)—216no—
16C22×C3×AGL(1,ℤ/8)C412yescomplemented
17C22×C3×AGL(1,ℤ/8)C412yescomplemented
18C22×C3×AGL(1,ℤ/8)C2212yes—
19C22×C3×AGL(1,ℤ/8)C2212yes—
20C23×C3×SD16C412yescomplemented
21C23×C3×D8C412yescomplemented
22C23×C3×M16C2211yescharacteristic
23C2×#5819C2212yescomplemented
24C2×#5236C2212yescomplemented
25C2×#5236C2212yescomplemented
26#84075—24no—
27#84075—24no—
28#84074—22no—
29#84074C2212yescomplemented
30C22×#833C2214yescomplemented
31C2×#5215C2214yescomplemented
32#84027C2211yescharacteristic
33C2×#5207—22no—
34C2×#5207C2211yescharacteristic
35C2×#5207C2211yescharacteristic
36C2×#5207C2211yescharacteristic
37#72138—24no—
38#72129—22no—
39#72129—22no—
40#72128—24no—
41#72090—216no—
42C2×C3⋊#338C2214yescomplemented
43C2×#4556C2214yescomplemented
44C23×AGL(1,ℤ/8)D311yescharacteristic
45#60064—31no—
46C2×#1903—34no—
47#20605—31no—
48#20598—31no—
49C2×#1783—31no—
50#11014—34no—
51#10729—31no—
52C22⋊#338—31no—
53C26×C3—21no—
54C22×C3×#41—21no—
55C22×C3×#41—22no—
56C22×C3×#41—21no—
57C22×C3×#41—22no—
58C22×C3×#41—28no—
59C22×C3×#41—44no—
60C22×C3×#41C2×C411yescharacteristic
61C22×C3×#41C2×C411yescharacteristic
62C22×C3×#41D414yes—
63C22×C3×#41D414yes—
64C22×C3×#41C2311yescharacteristic
65C22×C3×#41C2311yescharacteristic
66C23×C3×Q8C2×C411yescharacteristic
67C23×C3×D4—21no—
68C23×C3×D4—21no—
69C23×C3×D4—21no—
70C23×C3×D4—21no—
71C23×C3×D4—28no—
72C23×C3×D4—22no—
73C23×C3×D4—22no—
74C23×C3×D4—22no—
75C23×C3×D4—22no—
76C23×C3×D4—44no—
77C23×C3×D4C2×C412yes—
78C23×C3×D4C2×C412yes—
79C23×C3×D4C2×C411yescharacteristic
80C23×C3×D4C2312yes—
81C24×C3×C4—21no—
82C24×C3×C4C2311yescharacteristic
83C2×C3×AGL(1,ℤ/8)—264no—
84C2×C3×AGL(1,ℤ/8)—264no—
85C2×C3×AGL(1,ℤ/8)—28no—
86C2×C3×AGL(1,ℤ/8)—28no—
87C2×C3×AGL(1,ℤ/8)—24no—
88C2×C3×AGL(1,ℤ/8)—24no—
89C2×C3×AGL(1,ℤ/8)—24no—
90C2×C3×AGL(1,ℤ/8)—24no—
91C2×C3×AGL(1,ℤ/8)—28no—
92C2×C3×AGL(1,ℤ/8)—28no—
93C2×C3×AGL(1,ℤ/8)—216no—
94C2×C3×AGL(1,ℤ/8)—216no—
95C2×C3×AGL(1,ℤ/8)—28no—
96C2×C3×AGL(1,ℤ/8)D4116yes—
97C22×C3×SD16—28no—
98C22×C3×SD16—216no—
99C22×C3×SD16C2×C414yes—
100C22×C3×SD16C2×C414yes—
101C22×C3×D8—28no—
102C22×C3×D8—216no—
103C22×C3×D8C2×C414yes—
104C22×C3×D8C2×C414yes—
105C22×C3×M16—22no—
106C22×C3×M16—22no—
107C22×C3×M16—28no—
108C22×C3×M16C2×C412yes—
109C22×C3×M16C2312yes—
110C23×C3×C8C2×C412yes—
111#5819—28no—
112#5819—44no—
113C2×#948—24no—
114C2×#948—24no—
115C2×#926C2312yes—
116C22×#208—24no—
117C22×#208C2312yes—
118C22×#208C2312yes—
119C22×#208C2312yes—
120#5247—21no—
121#5236—28no—
122#5236—44no—
123C2×#837—24no—
124C2×#837—24no—
125#5234—216no—
126#5234—24no—
127#5234—24no—
128C2×#833—28no—
129C2×#833—28no—
130C2×#833—44no—
131#5215—28no—
132#5215—44no—
133C2×#832—28no—
134#5212—22no—
135#5211—21no—
136C4×#217—22no—
137#5207—28no—
138#5207—21no—
139#5207—21no—
140#5207—22no—
141#5207—22no—
142#5207—24no—
143#5207—21no—
144#5207—21no—
145#5207—22no—
146#5207D412yes—
147#5207D412yes—
148C2×#830—28no—
149C2×#830—22no—
150C2×#830—22no—
151C2×#830D414yes—
152C3⋊#338—28no—
153#4556—28no—
154C23×#41C2×D311yescharacteristic
155C24×D4C2×D311yescharacteristic
156C22×AGL(1,ℤ/8)—24no—
157C22×AGL(1,ℤ/8)—24no—
158C22×AGL(1,ℤ/8)—216no—
159C22×AGL(1,ℤ/8)Dic312yescomplemented
160C22×AGL(1,ℤ/8)Dic312yescomplemented
161C22×AGL(1,ℤ/8)C2×D312yes—
162C22×AGL(1,ℤ/8)C2×D312yes—
163C23×SD16Dic312yescomplemented
164C23×D8Dic312yescomplemented
165C2×#568—32no—
166C23×M16C2×D311yescharacteristic
167C2×#421—32no—
168C2×#421—32no—
169C2×#418—34no—
170C22×#100—34no—
171#2880—64no—
172#2880—64no—
173#2879—32no—
174#2879—62no—
175C2×#407—31no—
176C2×#407—31no—
177C2×#407—31no—
178C2×#407—62no—
179#2280—31no—
180#1903—616no—
181#1789—64no—
182#1786—64no—
183#1783—62no—
184#1783—62no—
185C2×#344—34no—
186C2×#338—34no—
187C25×C3—21no—
188C25×C3—22no—
189C25×C3—22no—
190C25×C3—22no—
191C25×C3—48no—
192C25×C3—42no—
193C25×C3—42no—
194C25×C3—88no—
195C25×C3#4111yescharacteristic
196C2×C3×#41—22no—
197C2×C3×#41—22no—
198C2×C3×#41—24no—
199C2×C3×#41—24no—
200C2×C3×#41—24no—
201C2×C3×#41—24no—
202C2×C3×#41—21no—
203C2×C3×#41—21no—
204C2×C3×#41—21no—
205C2×C3×#41—21no—
206C2×C3×#41—24no—
207C2×C3×#41—216no—
208C2×C3×#41—216no—
209C2×C3×#41—24no—
210C2×C3×#41—24no—
211C2×C3×#41—24no—
212C2×C3×#41—24no—
213C2×C3×#41—48no—
214C2×C3×#41—42no—
215C2×C3×#41—42no—
216C2×C3×#41—48no—
217C2×C3×#41—48no—
218C2×C3×#41—48no—
219C2×C3×#41—416no—
220C2×C3×#41—416no—
221C2×C3×#41C22⋊C414yes—
222C2×C3×#41C22⋊C414yes—
223C2×C3×#41C2×D412yes—
224C2×C3×#41C2×D412yes—
225C2×C3×#41C2×D412yes—
226C2×C3×#41C2×D412yes—
227C2×C3×#41C2×D418yes—
228C22×C3×Q8—21no—
229C22×C3×Q8—22no—
230C22×C3×Q8—24no—
231C22×C3×Q8—42no—
232C22×C3×Q8C22⋊C414yes—
233C22×C3×Q8C22×C411yescharacteristic
234C22×C3×Q8C22×C411yescharacteristic
235C22×C3×D4—21no—
236C22×C3×D4—216no—
237C22×C3×D4—216no—
238C22×C3×D4—24no—
239C22×C3×D4—28no—
240C22×C3×D4—28no—
241C22×C3×D4—21no—
242C22×C3×D4—21no—
243C22×C3×D4—24no—
244C22×C3×D4—24no—
245C22×C3×D4—21no—
246C22×C3×D4—24no—
247C22×C3×D4—24no—
248C22×C3×D4—22no—
249C22×C3×D4—21no—
250C22×C3×D4—24no—
251C22×C3×D4—24no—
252C22×C3×D4—22no—
253C22×C3×D4—22no—
254C22×C3×D4—22no—
255C22×C3×D4—22no—
256C22×C3×D4—24no—
257C22×C3×D4—22no—
258C22×C3×D4—22no—
259C22×C3×D4—22no—
260C22×C3×D4—24no—
261C22×C3×D4—24no—
262C22×C3×D4—44no—
263C22×C3×D4—44no—
264C22×C3×D4—42no—
265C22×C3×D4—48no—
266C22×C3×D4—416no—
267C22×C3×D4—48no—
268C22×C3×D4—416no—
269C22×C3×D4—48no—
270C22×C3×D4—48no—
271C22×C3×D4—48no—
272C22×C3×D4—48no—
273C22×C3×D4—42no—
274C22×C3×D4—42no—
275C22×C3×D4—42no—
276C22×C3×D4—42no—
277C22×C3×D4—42no—
278C22×C3×D4—42no—
279C22×C3×D4C22⋊C414yes—
280C22×C3×D4C22×C411yescharacteristic
281C22×C3×D4C22×C414yes—
282C22×C3×D4C22×C411yescharacteristic
283C22×C3×D4C2×D418yes—
284C23×C3×C4—24no—
285C23×C3×C4—21no—
286C23×C3×C4—24no—
287C23×C3×C4—21no—
288C23×C3×C4—21no—
289C23×C3×C4—21no—
290C23×C3×C4—24no—
291C23×C3×C4—24no—
292C23×C3×C4—21no—
293C23×C3×C4—48no—
294C23×C3×C4C22×C411yescharacteristic
295C23×C3×C4C22×C411yescharacteristic
296C23×C3×C4C2×D412yes—
297C23×C3×C4C2×D411yescharacteristic
298C23×C3×C4C2×D411yescharacteristic
299C23×C3×C4C2×D412yes—
300C23×C3×C4C2×D412yes—
301C23×C3×C4#4111yescharacteristic
302C23×C3×C4#4112yes—
303C23×C3×C4C2411yescharacteristic
304C3×AGL(1,ℤ/8)—264no—
305C3×AGL(1,ℤ/8)—264no—
306C3×AGL(1,ℤ/8)—232no—
307C3×AGL(1,ℤ/8)—232no—
308C3×AGL(1,ℤ/8)—232no—
309C3×AGL(1,ℤ/8)—232no—
310C2×C3×SD16—264no—
311C2×C3×SD16—28no—
312C2×C3×SD16—28no—
313C2×C3×SD16—28no—
314C2×C3×SD16—28no—
315C2×C3×SD16—28no—
316C2×C3×SD16C22⋊C4116yescomplemented
317C2×C3×D8—264no—
318C2×C3×D8—28no—
319C2×C3×D8—28no—
320C2×C3×D8—28no—
321C2×C3×D8—28no—
322C2×C3×D8—28no—
323C2×C3×D8C22⋊C4116yescomplemented
324C2×C3×M16—216no—
325C2×C3×M16—216no—
326C2×C3×M16—24no—
327C2×C3×M16—22no—
328C2×C3×M16—22no—
329C2×C3×M16—24no—
330C2×C3×M16—28no—
331C2×C3×M16C2×D418yes—
332C22×C3×C8—24no—
333C22×C3×C8—28no—
334C22×C3×C8C22×C414yes—
335C2×#217—22no—
336C2×#217—42no—
337#948—416no—
338#948—48no—
339#948—48no—
340#926—24no—
341#926—24no—
342C2×C4⋊Dic3—22no—
343C2×C4×Dic3—22no—
344C2×#208—28no—
345C2×#208—22no—
346C2×#208—22no—
347C2×#208—22no—
348C2×#208—24no—
349C2×#208—24no—
350C2×#208—24no—
351C2×#208—24no—
352C2×#208—22no—
353C2×#208—22no—
354C2×#208—24no—
355C2×#208—24no—
356C2×#208—416no—
357C2×#208C2×D414yes—
358C22×C3⋊C8—28no—
359C22×C3⋊C8—22no—
360C22×C3⋊C8—22no—
361C22×C3⋊C8C2×D414yes—
362#837—48no—
363#837—48no—
364#833—416no—
365#832—416no—
366C3⋊#95—42no—
367#830—216no—
368#830—24no—
369#830—24no—
370#830—24no—
371#830—24no—
372#830—42no—
373#830—42no—
374C26—21no—
375C22×#41—21no—
376C22×#41—22no—
377C22×#41—21no—
378C22×#41—22no—
379C22×#41—28no—
380C22×#41—44no—
381C22×#41C2×Dic311yescharacteristic
382C22×#41C2×Dic311yescharacteristic
383C22×#41#6714yes—
384C22×#41#6714yes—
385C22×#41C22×D311yescharacteristic
386C22×#41C22×D311yescharacteristic
387C23×Q8C2×Dic311yescharacteristic
388C23×D4—28no—
389C23×D4—21no—
390C23×D4—22no—
391C23×D4—21no—
392C23×D4—21no—
393C23×D4—22no—
394C23×D4—21no—
395C23×D4—22no—
396C23×D4—22no—
397C23×D4—44no—
398C23×D4C2×Dic312yes—
399C23×D4C2×Dic312yes—
400C23×D4C2×Dic311yescharacteristic
401C23×D4C22×D312yes—
402C24×C4—21no—
403C24×C4C22×D311yescharacteristic
404C2×AGL(1,ℤ/8)—264no—
405C2×AGL(1,ℤ/8)—264no—
406C2×AGL(1,ℤ/8)—28no—
407C2×AGL(1,ℤ/8)—28no—
408C2×AGL(1,ℤ/8)—24no—
409C2×AGL(1,ℤ/8)—24no—
410C2×AGL(1,ℤ/8)—24no—
411C2×AGL(1,ℤ/8)—28no—
412C2×AGL(1,ℤ/8)—24no—
413C2×AGL(1,ℤ/8)—28no—
414C2×AGL(1,ℤ/8)—216no—
415C2×AGL(1,ℤ/8)—216no—
416C2×AGL(1,ℤ/8)—28no—
417C2×AGL(1,ℤ/8)#67116yes—
418C22×SD16—28no—
419C22×SD16—216no—
420C22×SD16C2×Dic314yes—
421C22×SD16C2×Dic314yes—
422C22×D8—28no—
423C22×D8—216no—
424C22×D8C2×Dic314yes—
425C22×D8C2×Dic314yes—
426#568—68no—
427#568—124no—
428C2×#131—64no—
429C2×#131—64no—
430C22×M16—22no—
431C22×M16—22no—
432C22×M16—28no—
433C22×M16—32no—
434C22×M16—32no—
435C22×M16—32no—
436C22×M16—64no—
437C22×M16C2×Dic312yes—
438C22×M16C22×D312yes—
439C23×C8C2×Dic312yes—
440C2×#117—32no—
441#421—68no—
442#421—124no—
443C2×#104—64no—
444C2×#104—64no—
445#418—68no—
446#418—124no—
447C2×#102—68no—
448C2×#100—68no—
449C2×#100—68no—
450C2×#100—124no—
451#408—64no—
452#408—616no—
453#408—64no—
454#407—32no—
455#407—32no—
456#407—64no—
457#407—68no—
458#407—61no—
459#407—61no—
460#407—62no—
461#407—62no—
462#407—61no—
463#407—61no—
464#407—62no—
465C2×C22⋊C8—34no—
466C2×C22⋊C8—68no—
467C2×C22⋊C8—62no—
468C2×C22⋊C8—62no—
469#381—61no—
470#380—62no—
471#379—61no—
472C4×C22⋊C4—62no—
473#344—68no—
474#338—68no—
475C24×C3—24no—
476C24×C3—21no—
477C24×C3—24no—
478C24×C3—24no—
479C24×C3—21no—
480C24×C3—28no—
481C24×C3—44no—
482C24×C3—48no—
483C24×C3—48no—
484C24×C3—44no—
485C24×C3—416no—
486C24×C3—416no—
487C24×C3—42no—
488C24×C3—42no—
489C24×C3—44no—
490C24×C3—44no—
491C24×C3—44no—
492C24×C3—84no—
493C24×C3—88no—
494C24×C3—88no—
495C24×C3—88no—
496C24×C3—88no—
497C24×C3—88no—
498C24×C3—88no—
499C24×C3—88no—
500C24×C3—864no—
501C24×C3C4×D411yescharacteristic
502C24×C3C4×D411yescharacteristic
503C24×C3#12112yes—
504C24×C3#12312yes—
505C24×C3C2×#4111yescharacteristic
506C3×#41—24no—
507C3×#41—24no—
508C3×#41—28no—
509C3×#41—28no—
510C3×#41—28no—
511C3×#41—28no—
512C3×#41—24no—
513C3×#41—24no—
514C3×#41—24no—
515C3×#41—24no—
516C3×#41—416no—
517C3×#41—416no—
518C3×#41—44no—
519C3×#41—44no—
520C3×#41—416no—
521C3×#41—416no—
522C3×#41—48no—
523C3×#41—48no—
524C3×#41—44no—
525C3×#41—44no—
526C3×#41#12018yes—
527C3×#41#12018yes—
528C2×C3×Q8—21no—
529C2×C3×Q8—21no—
530C2×C3×Q8—22no—
531C2×C3×Q8—24no—
532C2×C3×Q8—28no—
533C2×C3×Q8—22no—
534C2×C3×Q8—22no—
535C2×C3×Q8—44no—
536C2×C3×Q8—44no—
537C2×C3×Q8—48no—
538C2×C3×Q8C2×C22⋊C412yes—
539C2×C3×Q8C2×C22⋊C412yes—
540C2×C3×Q8C2×C22⋊C414yes—
541C2×C3×D4—22no—
542C2×C3×D4—22no—
543C2×C3×D4—28no—
544C2×C3×D4—216no—
545C2×C3×D4—216no—
546C2×C3×D4—28no—
547C2×C3×D4—22no—
548C2×C3×D4—22no—
549C2×C3×D4—24no—
550C2×C3×D4—24no—
551C2×C3×D4—22no—
552C2×C3×D4—24no—
553C2×C3×D4—24no—
554C2×C3×D4—21no—
555C2×C3×D4—24no—
556C2×C3×D4—21no—
557C2×C3×D4—22no—
558C2×C3×D4—24no—
559C2×C3×D4—22no—
560C2×C3×D4—24no—
561C2×C3×D4—28no—
562C2×C3×D4—28no—
563C2×C3×D4—28no—
564C2×C3×D4—28no—
565C2×C3×D4—28no—
566C2×C3×D4—24no—
567C2×C3×D4—44no—
568C2×C3×D4—416no—
569C2×C3×D4—416no—
570C2×C3×D4—48no—
571C2×C3×D4—48no—
572C2×C3×D4—48no—
573C2×C3×D4—44no—
574C2×C3×D4—44no—
575C2×C3×D4—416no—
576C2×C3×D4—416no—
577C2×C3×D4—48no—
578C2×C3×D4—48no—
579C2×C3×D4—416no—
580C2×C3×D4—416no—
581C2×C3×D4—416no—
582C2×C3×D4—416no—
583C2×C3×D4—416no—
584C2×C3×D4—416no—
585C2×C3×D4—44no—
586C2×C3×D4—44no—
587C2×C3×D4—42no—
588C2×C3×D4—42no—
589C2×C3×D4—44no—
590C2×C3×D4—44no—
591C2×C3×D4—44no—
592C2×C3×D4—44no—
593C2×C3×D4—44no—
594C2×C3×D4—44no—
595C2×C3×D4—44no—
596C2×C3×D4C2×C22⋊C412yes—
597C2×C3×D4C2×C22⋊C418yes—
598C2×C3×D4C2×C22⋊C412yes—
599C2×C3×D4C2×C22⋊C414yes—
600C22×C3×C4—21no—
601C22×C3×C4—24no—
602C22×C3×C4—22no—
603C22×C3×C4—22no—
604C22×C3×C4—22no—
605C22×C3×C4—22no—
606C22×C3×C4—22no—
607C22×C3×C4—24no—
608C22×C3×C4—24no—
609C22×C3×C4—22no—
610C22×C3×C4—24no—
611C22×C3×C4—24no—
612C22×C3×C4—28no—
613C22×C3×C4—24no—
614C22×C3×C4—24no—
615C22×C3×C4—28no—
616C22×C3×C4—28no—
617C22×C3×C4—21no—
618C22×C3×C4—24no—
619C22×C3×C4—22no—
620C22×C3×C4—22no—
621C22×C3×C4—24no—
622C22×C3×C4—24no—
623C22×C3×C4—44no—
624C22×C3×C4—416no—
625C22×C3×C4—416no—
626C22×C3×C4—44no—
627C22×C3×C4—44no—
628C22×C3×C4—44no—
629C22×C3×C4C2×C22⋊C412yes—
630C22×C3×C4C2×C22⋊C412yes—
631C22×C3×C4C4×D412yes—
632C22×C3×C4C4×D412yes—
633C22×C3×C4C4×D411yescharacteristic
634C22×C3×C4C4×D411yescharacteristic
635C22×C3×C4#12012yes—
636C22×C3×C4#12012yes—
637C22×C3×C4#12112yes—
638C22×C3×C4#12112yes—
639C22×C3×C4#12112yes—
640C22×C3×C4#12312yes—
641C22×C3×C4C23×C411yescharacteristic
642C22×C3×C4C22×D411yescharacteristic
643C22×C3×C4C22×D411yescharacteristic
644C22×C3×C4C22×D411yescharacteristic
645C22×C3×C4C22×D411yescharacteristic
646C22×C3×C4C22×D414yes—
647C22×C3×C4C2×#4111yescharacteristic
648C22×C3×C4H(5,𝔽2)14yes—
649C22×Dic3—42no—
650C3×SD16—232no—
651C3×SD16—232no—
652C3×D8—232no—
653C3×D8—232no—
654C3×M16—216no—
655C3×M16—28no—
656C3×M16—28no—
657C2×C3×C8—216no—
658C2×C3×C8—24no—
659C2×C3×C8—24no—
660C2×C3×C8C2×C22⋊C418yes—
661#217—44no—
662#217—84no—
663C4⋊Dic3—44no—
664C4×Dic3—42no—
665C4×Dic3—42no—
666#208—28no—
667#208—416no—
668#208—42no—
669#208—42no—
670#208—44no—
671#208—44no—
672#208—42no—
673#208—42no—
674#208—44no—
675C2×C3⋊C8—24no—
676C2×C3⋊C8—24no—
677C2×C3⋊C8—28no—
678C2×C3⋊C8—416no—
679C2×C3⋊C8—42no—
680C2×C3⋊C8—42no—
681C2×C3⋊C8—42no—
682C2×C3⋊C8—44no—
683C25—21no—
684C25—22no—
685C25—22no—
686C25—22no—
687C25—48no—
688C25—42no—
689C25—42no—
690C25—88no—
691C25#23711yescharacteristic
692C2×#41—22no—
693C2×#41—22no—
694C2×#41—24no—
695C2×#41—24no—
696C2×#41—24no—
697C2×#41—24no—
698C2×#41—21no—
699C2×#41—21no—
700C2×#41—21no—
701C2×#41—21no—
702C2×#41—24no—
703C2×#41—216no—
704C2×#41—216no—
705C2×#41—24no—
706C2×#41—24no—
707C2×#41—24no—
708C2×#41—24no—
709C2×#41—48no—
710C2×#41—42no—
711C2×#41—42no—
712C2×#41—48no—
713C2×#41—48no—
714C2×#41—48no—
715C2×#41—416no—
716C2×#41—416no—
717C2×#41#21714yes—
718C2×#41#21714yes—
719C2×#41C2×#6712yes—
720C2×#41C2×#6712yes—
721C2×#41C2×#6712yes—
722C2×#41C2×#6718yes—
723C2×#41C2×#6712yes—
724C22×Q8—21no—
725C22×Q8—22no—
726C22×Q8—24no—
727C22×Q8—42no—
728C22×Q8#21714yes—
729C22×Q8C22×Dic311yescharacteristic
730C22×Q8C22×Dic311yescharacteristic
731C22×D4—21no—
732C22×D4—216no—
733C22×D4—216no—
734C22×D4—24no—
735C22×D4—28no—
736C22×D4—28no—
737C22×D4—21no—
738C22×D4—21no—
739C22×D4—24no—
740C22×D4—24no—
741C22×D4—21no—
742C22×D4—21no—
743C22×D4—22no—
744C22×D4—24no—
745C22×D4—24no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—24no—
749C22×D4—24no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—24no—
754C22×D4—24no—
755C22×D4—22no—
756C22×D4—24no—
757C22×D4—22no—
758C22×D4—44no—
759C22×D4—44no—
760C22×D4—42no—
761C22×D4—48no—
762C22×D4—416no—
763C22×D4—48no—
764C22×D4—416no—
765C22×D4—48no—
766C22×D4—48no—
767C22×D4—48no—
768C22×D4—48no—
769C22×D4—42no—
770C22×D4—42no—
771C22×D4—42no—
772C22×D4—42no—
773C22×D4—42no—
774C22×D4—42no—
775C22×D4#21714yes—
776C22×D4C22×Dic311yescharacteristic
777C22×D4C22×Dic314yes—
778C22×D4C22×Dic311yescharacteristic
779C22×D4C2×#6718yes—
780C23×C4—21no—
781C23×C4—24no—
782C23×C4—24no—
783C23×C4—21no—
784C23×C4—21no—
785C23×C4—21no—
786C23×C4—24no—
787C23×C4—24no—
788C23×C4—21no—
789C23×C4—48no—
790C23×C4D3×D412yes—
791C23×C4D3×D411yescharacteristic
792C23×C4D3×D411yescharacteristic
793C23×C4#23711yescharacteristic
794C23×C4#23712yes—
795C23×C4C22×Dic311yescharacteristic
796C23×C4C22×Dic311yescharacteristic
797C23×C4C2×#6712yes—
798C23×C4C2×#6712yes—
799C23×C4C23×D311yescharacteristic
800AGL(1,ℤ/8)—264no—
801AGL(1,ℤ/8)—264no—
802AGL(1,ℤ/8)—232no—
803AGL(1,ℤ/8)—232no—
804AGL(1,ℤ/8)—232no—
805AGL(1,ℤ/8)—232no—
806C2×SD16—264no—
807C2×SD16—28no—
808C2×SD16—28no—
809C2×SD16—28no—
810C2×SD16—28no—
811C2×SD16—28no—
812C2×SD16#217116yescomplemented
813C2×D8—264no—
814C2×D8—28no—
815C2×D8—28no—
816C2×D8—28no—
817C2×D8—28no—
818C2×D8—28no—
819C2×D8#217116yescomplemented
820#131—1216no—
821#131—128no—
822#131—128no—
823C2×M16—216no—
824C2×M16—216no—
825C2×M16—24no—
826C2×M16—22no—
827C2×M16—24no—
828C2×M16—22no—
829C2×M16—28no—
830C2×M16—34no—
831C2×M16—68no—
832C2×M16—62no—
833C2×M16—62no—
834C2×M16—64no—
835C2×M16—62no—
836C2×M16—64no—
837C2×M16—64no—
838C2×M16—64no—
839C2×M16—62no—
840C2×M16—64no—
841C2×M16—64no—
842C2×M16—62no—
843C2×M16—1216no—
844C2×M16C2×#6718yes—
845C22×C8—24no—
846C22×C8—28no—
847C22×C8—34no—
848C22×C8—68no—
849C22×C8—62no—
850C22×C8—62no—
851C22×C8C22×Dic314yes—
852#117—64no—
853#117—64no—
854C2×C4⋊C4—62no—
855C2×C22⋊C4—62no—
856C2×C22⋊C4—122no—
857C2×C42—62no—
858#104—128no—
859#104—128no—
860#102—1216no—
861#100—1216no—
862C22⋊C8—616no—
863C22⋊C8—64no—
864C22⋊C8—64no—
865C22⋊C8—64no—
866C22⋊C8—64no—
867C22⋊C8—122no—
868C22⋊C8—122no—
869#95—122no—
870C23×C3—22no—
871C23×C3—24no—
872C23×C3—22no—
873C23×C3—24no—
874C23×C3—24no—
875C23×C3—24no—
876C23×C3—24no—
877C23×C3—22no—
878C23×C3—24no—
879C23×C3—22no—
880C23×C3—28no—
881C23×C3—42no—
882C23×C3—42no—
883C23×C3—42no—
884C23×C3—42no—
885C23×C3—48no—
886C23×C3—416no—
887C23×C3—416no—
888C23×C3—416no—
889C23×C3—42no—
890C23×C3—44no—
891C23×C3—48no—
892C23×C3—48no—
893C23×C3—48no—
894C23×C3—44no—
895C23×C3—82no—
896C23×C3—82no—
897C23×C3—84no—
898C23×C3—88no—
899C23×C3—816no—
900C23×C3—88no—
901C23×C3—88no—
902C23×C3—832no—
903C23×C3—88no—
904C23×C3—88no—
905C23×C3—88no—
906C23×C3—816no—
907C23×C3—816no—
908C23×C3—864no—
909C23×C3—864no—
910C23×C3—832no—
911C23×C3—88no—
912C23×C3#38612yes—
913C23×C3#38612yes—
914C23×C3C2×C4×D411yescharacteristic
915C23×C3C2×#12111yescharacteristic
916C23×C3C2×#12311yescharacteristic
917C23×C3#54614yes—
918C3×Q8—22no—
919C3×Q8—24no—
920C3×Q8—22no—
921C3×Q8—22no—
922C3×Q8—48no—
923C3×Q8—42no—
924C3×Q8#37914yes—
925C3×D4—28no—
926C3×D4—28no—
927C3×D4—22no—
928C3×D4—22no—
929C3×D4—24no—
930C3×D4—28no—
931C3×D4—22no—
932C3×D4—28no—
933C3×D4—48no—
934C3×D4—48no—
935C3×D4—416no—
936C3×D4—416no—
937C3×D4—48no—
938C3×D4—44no—
939C3×D4—44no—
940C3×D4—44no—
941C3×D4—44no—
942C3×D4—42no—
943C3×D4—48no—
944C3×D4—48no—
945C3×D4#37914yes—
946C2×C3×C4—22no—
947C2×C3×C4—22no—
948C2×C3×C4—24no—
949C2×C3×C4—24no—
950C2×C3×C4—24no—
951C2×C3×C4—22no—
952C2×C3×C4—22no—
953C2×C3×C4—22no—
954C2×C3×C4—24no—
955C2×C3×C4—24no—
956C2×C3×C4—28no—
957C2×C3×C4—24no—
958C2×C3×C4—24no—
959C2×C3×C4—24no—
960C2×C3×C4—24no—
961C2×C3×C4—28no—
962C2×C3×C4—22no—
963C2×C3×C4—22no—
964C2×C3×C4—22no—
965C2×C3×C4—48no—
966C2×C3×C4—48no—
967C2×C3×C4—48no—
968C2×C3×C4—42no—
969C2×C3×C4—44no—
970C2×C3×C4—44no—
971C2×C3×C4#38612yes—
972C2×C3×C4#38612yes—
973C2×C3×C4C22×C22⋊C411yescharacteristic
974C2×C3×C4C22×C22⋊C412yes—
975C2×C3×C4C2×C4×D411yescharacteristic
976C2×C3×C4#51812yes—
977C2×C3×C4C2×#12011yescharacteristic
978C2×C3×C4C2×#12012yes—
979C2×C3×C4C2×#12012yes—
980C2×C3×C4C2×#12111yescharacteristic
981C2×C3×C4#53412yes—
982C2×C3×C4#53412yes—
983C2×C3×C4D4214yes—
984C2×C3×C4D4214yes—
985C2×C3×C4#54614yes—
986C2×Dic3—84no—
987C2×Dic3—82no—
988C3×C8—28no—
989C3⋊C8—44no—
990C3⋊C8—44no—
991C3⋊C8—82no—
992C24—24no—
993C24—21no—
994C24—24no—
995C24—21no—
996C24—24no—
997C24—28no—
998C24—44no—
999C24—44no—
1000C24—48no—
1001C24—48no—
1002C24—416no—
1003C24—416no—
1004C24—44no—
1005C24—44no—
1006C24—42no—
1007C24—42no—
1008C24—44no—
1009C24—84no—
1010C24—88no—
1011C24—88no—
1012C24—88no—
1013C24—88no—
1014C24—88no—
1015C24—88no—
1016C24—88no—
1017C24—864no—
1018C24D4×Dic311yescharacteristic
1019C24D4×Dic311yescharacteristic
1020C24#93512yes—
1021C24#93912yes—
1022C24C2×#23711yescharacteristic
1023#41—28no—
1024#41—24no—
1025#41—24no—
1026#41—28no—
1027#41—28no—
1028#41—28no—
1029#41—24no—
1030#41—24no—
1031#41—24no—
1032#41—24no—
1033#41—416no—
1034#41—416no—
1035#41—44no—
1036#41—44no—
1037#41—416no—
1038#41—416no—
1039#41—48no—
1040#41—48no—
1041#41—44no—
1042#41—44no—
1043#41#95318yes—
1044#41#95318yes—
1045C2×Q8—24no—
1046C2×Q8—21no—
1047C2×Q8—21no—
1048C2×Q8—22no—
1049C2×Q8—28no—
1050C2×Q8—22no—
1051C2×Q8—22no—
1052C2×Q8—44no—
1053C2×Q8—44no—
1054C2×Q8—48no—
1055C2×Q8C2×#21712yes—
1056C2×Q8C2×#21712yes—
1057C2×Q8C2×#21714yes—
1058C2×D4—22no—
1059C2×D4—22no—
1060C2×D4—28no—
1061C2×D4—216no—
1062C2×D4—216no—
1063C2×D4—28no—
1064C2×D4—24no—
1065C2×D4—24no—
1066C2×D4—22no—
1067C2×D4—22no—
1068C2×D4—24no—
1069C2×D4—21no—
1070C2×D4—24no—
1071C2×D4—21no—
1072C2×D4—22no—
1073C2×D4—24no—
1074C2×D4—22no—
1075C2×D4—24no—
1076C2×D4—28no—
1077C2×D4—28no—
1078C2×D4—28no—
1079C2×D4—22no—
1080C2×D4—24no—
1081C2×D4—24no—
1082C2×D4—28no—
1083C2×D4—28no—
1084C2×D4—44no—
1085C2×D4—416no—
1086C2×D4—416no—
1087C2×D4—48no—
1088C2×D4—48no—
1089C2×D4—48no—
1090C2×D4—44no—
1091C2×D4—44no—
1092C2×D4—416no—
1093C2×D4—416no—
1094C2×D4—48no—
1095C2×D4—48no—
1096C2×D4—416no—
1097C2×D4—416no—
1098C2×D4—416no—
1099C2×D4—416no—
1100C2×D4—416no—
1101C2×D4—416no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—42no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—42no—
1110C2×D4—44no—
1111C2×D4—44no—
1112C2×D4—44no—
1113C2×D4C2×#21712yes—
1114C2×D4C2×#21718yes—
1115C2×D4C2×#21712yes—
1116C2×D4C2×#21714yes—
1117C22×C4—21no—
1118C22×C4—24no—
1119C22×C4—22no—
1120C22×C4—22no—
1121C22×C4—22no—
1122C22×C4—28no—
1123C22×C4—24no—
1124C22×C4—24no—
1125C22×C4—28no—
1126C22×C4—22no—
1127C22×C4—24no—
1128C22×C4—24no—
1129C22×C4—28no—
1130C22×C4—22no—
1131C22×C4—22no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—24no—
1135C22×C4—21no—
1136C22×C4—24no—
1137C22×C4—24no—
1138C22×C4—22no—
1139C22×C4—22no—
1140C22×C4—44no—
1141C22×C4—416no—
1142C22×C4—416no—
1143C22×C4—44no—
1144C22×C4—44no—
1145C22×C4—44no—
1146C22×C4—122no—
1147C22×C4D4×Dic311yescharacteristic
1148C22×C4D4×Dic311yescharacteristic
1149C22×C4D4×Dic312yes—
1150C22×C4D4×Dic312yes—
1151C22×C4#93512yes—
1152C22×C4#93712yes—
1153C22×C4#93712yes—
1154C22×C4#93912yes—
1155C22×C4#93912yes—
1156C22×C4#93912yes—
1157C22×C4C2×#21712yes—
1158C22×C4C2×#21712yes—
1159C22×C4C2×D3×D411yescharacteristic
1160C22×C4C2×D3×D411yescharacteristic
1161C22×C4C2×#23711yescharacteristic
1162C22×C4#100414yes—
1163C22×C4C23×Dic311yescharacteristic
1164C22×C4C22×#6711yescharacteristic
1165C22×C4C22×#6714yes—
1166C22×C4C22×#6711yescharacteristic
1167SD16—232no—
1168SD16—232no—
1169D8—232no—
1170D8—232no—
1171M16—216no—
1172M16—28no—
1173M16—28no—
1174M16—68no—
1175M16—1216no—
1176M16—124no—
1177M16—124no—
1178M16—122no—
1179M16—122no—
1180M16—124no—
1181M16—122no—
1182M16—122no—
1183C2×C8—216no—
1184C2×C8—24no—
1185C2×C8—24no—
1186C2×C8—64no—
1187C2×C8—64no—
1188C2×C8—68no—
1189C2×C8—1216no—
1190C2×C8—122no—
1191C2×C8—122no—
1192C2×C8—122no—
1193C2×C8—124no—
1194C2×C8C2×#21718yes—
1195C4⋊C4—124no—
1196C22⋊C4—124no—
1197C22⋊C4—244no—
1198C42—122no—
1199C42—122no—
1200C22×C3—28no—
1201C22×C3—22no—
1202C22×C3—22no—
1203C22×C3—22no—
1204C22×C3—22no—
1205C22×C3—22no—
1206C22×C3—22no—
1207C22×C3—22no—
1208C22×C3—22no—
1209C22×C3—24no—
1210C22×C3—44no—
1211C22×C3—48no—
1212C22×C3—48no—
1213C22×C3—44no—
1214C22×C3—44no—
1215C22×C3—44no—
1216C22×C3—42no—
1217C22×C3—48no—
1218C22×C3—84no—
1219C22×C3—816no—
1220C22×C3—88no—
1221C22×C3—84no—
1222C22×C3—816no—
1223C22×C3—816no—
1224C22×C3—88no—
1225C22×C3—832no—
1226C22×C3—832no—
1227C22×C3—88no—
1228C22×C3#190314yescomplemented
1229C22×C3C2×#38611yescharacteristic
1230C22×C3D4×C22⋊C412yes—
1231C22×C3#240512yes—
1232C22×C3#241012yes—
1233C3×C4—22no—
1234C3×C4—22no—
1235C3×C4—24no—
1236C3×C4—42no—
1237C3×C4C2×#37911yescharacteristic
1238C3×C4#230811yescharacteristic
1239C3×C4D4×C22⋊C412yes—
1240C3×C4#240312yes—
1241C3×C4#241012yes—
1242Dic3—162no—
1243C23—22no—
1244C23—24no—
1245C23—22no—
1246C23—22no—
1247C23—24no—
1248C23—24no—
1249C23—24no—
1250C23—24no—
1251C23—24no—
1252C23—22no—
1253C23—28no—
1254C23—42no—
1255C23—42no—
1256C23—42no—
1257C23—42no—
1258C23—48no—
1259C23—416no—
1260C23—416no—
1261C23—416no—
1262C23—44no—
1263C23—42no—
1264C23—44no—
1265C23—48no—
1266C23—48no—
1267C23—48no—
1268C23—84no—
1269C23—82no—
1270C23—82no—
1271C23—88no—
1272C23—832no—
1273C23—88no—
1274C23—88no—
1275C23—88no—
1276C23—88no—
1277C23—88no—
1278C23—816no—
1279C23—816no—
1280C23—816no—
1281C23—864no—
1282C23—864no—
1283C23—832no—
1284C23—88no—
1285C23#522012yes—
1286C23#522012yes—
1287C23C2×D4×Dic311yescharacteristic
1288C23C2×#93511yescharacteristic
1289C23C2×#93911yescharacteristic
1290C23#580614yes—
1291Q8—22no—
1292Q8—24no—
1293Q8—22no—
1294Q8—22no—
1295Q8—48no—
1296Q8—42no—
1297Q8#524714yes—
1298D4—28no—
1299D4—28no—
1300D4—22no—
1301D4—22no—
1302D4—24no—
1303D4—28no—
1304D4—22no—
1305D4—28no—
1306D4—48no—
1307D4—48no—
1308D4—416no—
1309D4—416no—
1310D4—48no—
1311D4—44no—
1312D4—44no—
1313D4—44no—
1314D4—44no—
1315D4—42no—
1316D4—48no—
1317D4—48no—
1318D4#524714yes—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—28no—
1332C2×C4—28no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—48no—
1339C2×C4—48no—
1340C2×C4—48no—
1341C2×C4—42no—
1342C2×C4—44no—
1343C2×C4—44no—
1344C2×C4—244no—
1345C2×C4—242no—
1346C2×C4#522012yes—
1347C2×C4#522012yes—
1348C2×C4C2×D4×Dic311yescharacteristic
1349C2×C4#579812yes—
1350C2×C4C2×#93711yescharacteristic
1351C2×C4D4×#6714yes—
1352C2×C4D4×#6714yes—
1353C2×C4C2×#93911yescharacteristic
1354C2×C4#580412yes—
1355C2×C4#580412yes—
1356C2×C4#580614yes—
1357C2×C4C22×#21711yescharacteristic
1358C2×C4C22×#21712yes—
1359C2×C4C2×#95312yes—
1360C2×C4C2×#95312yes—
1361C8—28no—
1362C8—124no—
1363C8—124no—
1364C8—242no—
1365C2×C3—22no—
1366C2×C3—22no—
1367C2×C3—24no—
1368C2×C3—22no—
1369C2×C3—42no—
1370C2×C3—44no—
1371C2×C3—82no—
1372C2×C3—88no—
1373C2×C3#1386711yescharacteristic
1374C2×C3C2×#190312yes—
1375C22—28no—
1376C22—22no—
1377C22—22no—
1378C22—22no—
1379C22—22no—
1380C22—22no—
1381C22—22no—
1382C22—24no—
1383C22—22no—
1384C22—22no—
1385C22—44no—
1386C22—48no—
1387C22—48no—
1388C22—44no—
1389C22—44no—
1390C22—42no—
1391C22—48no—
1392C22—44no—
1393C22—84no—
1394C22—816no—
1395C22—88no—
1396C22—816no—
1397C22—88no—
1398C22—832no—
1399C22—816no—
1400C22—84no—
1401C22—832no—
1402C22—88no—
1403C22#7209014yescomplemented
1404C22C2×#522011yescharacteristic
1405C22D4×#21712yes—
1406C22#8404712yes—
1407C22#8404812yes—
1408C4—22no—
1409C4—22no—
1410C4—24no—
1411C4—42no—
1412C4—482no—
1413C4#8404311yescharacteristic
1414C4D4×#21712yes—
1415C4#8404812yes—
1416C4#8405212yes—
1417C4C2×#524711yescharacteristic
1418C3#35947611yescharacteristic, complemented, Sylow
1419C2—22no—
1420C2—22no—
1421C2—24no—
1422C2—22no—
1423C2—42no—
1424C2—44no—
1425C2—82no—
1426C2—88no—
1427C2#1071705711yescharacteristic
1428C2C2×#7209012yes—
subgroupG/H
centerC22C2×#5220
commutatorC22×C3×C4C23×C4
FrattiniC23×C4C23×D3
Fitting, prime radicalC23×C3×AGL(1,ℤ/8)C2
socleC22×C3C2×#386
cosocleC23×C3×C4C24
hypercenterC23×AGL(1,ℤ/8)D3
hypocenterC3#359476
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24×C4 ◁ C23×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #11658639C2semidirect
2. C2×#72090C2semidirect
3. #10794436C2semidirect
4. #10794390C2semidirect
5. C2×#72129C2semidirect
6. #10701930C2semidirect
7. #10700461C2semidirect
8. #10700426C2semidirect
16. C22×C3×AGL(1,ℤ/8)C4semidirect
17. C22×C3×AGL(1,ℤ/8)C4semidirect
20. C23×C3×SD16C4semidirect
21. C23×C3×D8C4semidirect
23. C2×#5819C22semidirect
24. C2×#5236C22semidirect
25. C2×#5236C22semidirect
29. #84074C22semidirect
30. C22×#833C22semidirect
31. C2×#5215C22semidirect
42. C2×C3⋊#338C22semidirect
43. C2×#4556C22semidirect
159. C22×AGL(1,ℤ/8)Dic3semidirect
160. C22×AGL(1,ℤ/8)Dic3semidirect
163. C23×SD16Dic3semidirect
164. C23×D8Dic3semidirect
316. C2×C3×SD16C22⋊C4semidirect
323. C2×C3×D8C22⋊C4semidirect
812. C2×SD16#217semidirect
819. C2×D8#217semidirect
1228. C22×C3#1903semidirect
1403. C22#72090semidirect
1418. C3#359476semidirect

Maximal subgroups

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

subgroupindex
#116586392
C2×#720902
#107944362
#107943902
C2×#721292
#107019302
#107004612
#107004262
C23×C3×AGL(1,ℤ/8)2
#3594763