Finite Group Databasebeta

← #72270333

Subgroups — #72270333

Order 1536.

4688 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#5215C211yesmaximal, characteristic
2C2×#70322C212yesmaximal, complemented
3#10794810C211yesmaximal, characteristic, complemented
4C2×#72129C211yesmaximal, characteristic
5#10702943C212yesmaximal, complemented
6#10702814C212yesmaximal, complemented
7#10702661C212yesmaximal, complemented
8#10700496C211yesmaximal, characteristic, complemented
9#10700460C211yesmaximal, characteristic, complemented
10#10700418C211yesmaximal, characteristic, complemented
11C3×#20598C211yesmaximal, characteristic
12#401626—31nomaximal, Sylow
13C24×C3×D4C2211yescharacteristic
14C22×#926C2211yescharacteristic
15C23×#208C2211yescharacteristic
16C2×C3×#418C2212yes—
17C2×C3×#418C2212yes—
18C2×C3×#407C2211yescharacteristic
19C3×#2280C2211yescharacteristic
20C22×#833C2212yes—
21C22×#833C2212yes—
22C2×#5215—22no—
23C2×#5215—28no—
24C2×#5215C2212yes—
25C2×#5215C2212yes—
26C22×#832—22no—
27C2×#5207C2211yescharacteristic
28C2×#5207C2211yescharacteristic
29C2×#5124C2211yescharacteristic, complemented
30C2×#5124C2211yescharacteristic, complemented
31C3×#1786—24no—
32#72129—24no—
33C2×#4559C2212yescomplemented
34C2×#4559C2212yescomplemented
35#71994C2211yescharacteristic, complemented
36#71994C2211yescharacteristic, complemented
37C2×#4533C2212yescomplemented
38C2×#4533C2212yescomplemented
39C2×#4531C2212yescomplemented
40C2×#4531C2212yescomplemented
41#70322—28no—
42#69983—22no—
43#69982—22no—
44C22×#418—31no—
45C2×#2081—32no—
46#20667—31no—
47#20598D311yescharacteristic
48C2×#1783—31no—
49#11181—32no—
50#11157—32no—
51#11133—32no—
52#10738—31no—
53#10729—31no—
54#10716—31no—
55C26×C3—21no—
56C23×C3×D4—21no—
57C23×C3×D4—22no—
58C23×C3×D4—24no—
59C23×C3×D4—24no—
60C23×C3×D4—21no—
61C23×C3×D4—21no—
62C23×C3×D4—22no—
63C23×C3×D4—21no—
64C23×C3×D4—21no—
65C23×C3×D4—22no—
66C23×C3×D4—42no—
67C23×C3×D4—42no—
68C23×C3×D4D414yes—
69C23×C3×D4C2312yes—
70C24×C3×C4C2311yescharacteristic
71C22×C3×M16C2311yescharacteristic
72C22×C3×M16C2311yescharacteristic
73C2×C3×#117C2312yes—
74C22×#217—21no—
75C2×#926—21no—
76C2×#926—21no—
77C2×#926—24no—
78C2×#926—21no—
79C2×#926—42no—
80C2×#926C2312yes—
81C22×C4⋊Dic3—21no—
82C22×C4×Dic3—21no—
83C22×#208—22no—
84C22×#208—22no—
85C22×#208—24no—
86C22×#208—42no—
87C22×#208D412yes—
88C22×#208C2311yescharacteristic
89C22×#208C2311yescharacteristic
90C22×#208C2312yes—
91C22×#208C2311yescharacteristic
92C22×#208C2311yescharacteristic
93C23×C3⋊C8D412yes—
94C3×#418—24no—
95C3×#418—24no—
96C3×#418—42no—
97C3×#418—42no—
98C2×C3×#102—24no—
99C2×C3×#102—24no—
100C3×#407—21no—
101C3×#407—21no—
102C3×#407—22no—
103C2×C3×C22⋊C8—22no—
104C3×#381—21no—
105C3×#380—22no—
106C3×#379—21no—
107C3×C4×C22⋊C4—22no—
108C2×#833—24no—
109C2×#833—24no—
110C2×#833—24no—
111C2×#833—24no—
112C2×#833—42no—
113C2×#833—42no—
114#5215—216no—
115#5215—24no—
116#5215—24no—
117#5215—24no—
118#5215D418yes—
119C2×#832—216no—
120C2×#832—24no—
121C2×#832—24no—
122#5207—21no—
123#5207—21no—
124#5207—22no—
125#5207—22no—
126#5207—21no—
127#5207—21no—
128C2×#830—22no—
129C2×#830—22no—
130#5124—24no—
131#5124—42no—
132C2×#822—22no—
133C2×#822—22no—
134#4559—24no—
135#4559—42no—
136#4558—22no—
137#4558—22no—
138#4533—24no—
139#4533—42no—
140#4531—24no—
141#4531—42no—
142C24×D4C2×D311yescharacteristic
143C23×M16—31no—
144C22×#117—31no—
145C2×#430—31no—
146C2×#430—31no—
147C2×#418—32no—
148C2×#418—32no—
149C2×#418—62no—
150C2×#418—68no—
151C2×#418C2×D312yes—
152C2×#418C2×D312yes—
153C22×#102—62no—
154C22×#100—32no—
155C22×#100—32no—
156C2×#407—31no—
157C2×#407—31no—
158C2×#407C2×D311yescharacteristic
159#2280C2×D311yescharacteristic
160#2081—68no—
161#1811—62no—
162#1810—62no—
163#1786—24no—
164#1783—64no—
165C2×#344—32no—
166C2×#344—32no—
167C2×#344—32no—
168C2×#344—32no—
169#1738—31no—
170#1738—31no—
171C2×H(3,ℤ/4)—32no—
172C2×H(3,ℤ/4)—32no—
173C25×C3—22no—
174C25×C3—24no—
175C25×C3—44no—
176C25×C3—44no—
177C25×C3—41no—
178C25×C3—41no—
179C25×C3—42no—
180C25×C3—88no—
181C25×C3#4111yescharacteristic
182C22×C3×D4—24no—
183C22×C3×D4—24no—
184C22×C3×D4—216no—
185C22×C3×D4—24no—
186C22×C3×D4—24no—
187C22×C3×D4—216no—
188C22×C3×D4—24no—
189C22×C3×D4—24no—
190C22×C3×D4—24no—
191C22×C3×D4—24no—
192C22×C3×D4—24no—
193C22×C3×D4—22no—
194C22×C3×D4—22no—
195C22×C3×D4—22no—
196C22×C3×D4—22no—
197C22×C3×D4—22no—
198C22×C3×D4—22no—
199C22×C3×D4—22no—
200C22×C3×D4—22no—
201C22×C3×D4—22no—
202C22×C3×D4—22no—
203C22×C3×D4—22no—
204C22×C3×D4—48no—
205C22×C3×D4—48no—
206C22×C3×D4—48no—
207C22×C3×D4—44no—
208C22×C3×D4—44no—
209C22×C3×D4—44no—
210C22×C3×D4—44no—
211C22×C3×D4—48no—
212C22×C3×D4—48no—
213C22×C3×D4—44no—
214C22×C3×D4—44no—
215C22×C3×D4—42no—
216C22×C3×D4—42no—
217C22×C3×D4—42no—
218C22×C3×D4—42no—
219C22×C3×D4—48no—
220C22×C3×D4—42no—
221C22×C3×D4—42no—
222C22×C3×D4—41no—
223C22×C3×D4—41no—
224C22×C3×D4—42no—
225C22×C3×D4—42no—
226C22×C3×D4—42no—
227C22×C3×D4C2×D414yes—
228C22×C3×D4C2×D414yes—
229C22×C3×D4#4114yes—
230C23×C3×C4—22no—
231C23×C3×C4—22no—
232C23×C3×C4—22no—
233C23×C3×C4—22no—
234C23×C3×C4C2×D411yescharacteristic
235C23×C3×C4C2×D411yescharacteristic
236C23×C3×C4C2×D412yes—
237C23×C3×C4#4112yes—
238C23×C3×C4#4111yescharacteristic
239C23×C3×C4#4111yescharacteristic
240C23×C3×C4#4112yes—
241C23×C3×C4#4112yes—
242C23×C3×C4#4111yescharacteristic
243C23×C3×C4C2411yescharacteristic
244C23×Dic3—41no—
245C2×C3×M16—21no—
246C2×C3×M16—21no—
247C2×C3×M16—22no—
248C2×C3×M16—21no—
249C2×C3×M16—21no—
250C2×C3×M16—22no—
251C2×C3×M16—22no—
252C2×C3×M16—22no—
253C22×C3×C8—21no—
254C22×C3×C8—21no—
255C3×#117—22no—
256C3×#117—22no—
257C3×#117—22no—
258C3×#117—22no—
259C2×C3×C4⋊C4—22no—
260C2×C3×C22⋊C4—22no—
261C2×C3×C22⋊C4—42no—
262C2×C3×C42—22no—
263C2×#217—22no—
264C2×#217—44no—
265C2×#217—41no—
266#926—22no—
267#926—24no—
268#926—22no—
269#926—22no—
270#926—44no—
271#926—44no—
272#926—42no—
273#926C2×D414yes—
274C2×C4⋊Dic3—24no—
275C2×C4⋊Dic3—22no—
276C2×C4⋊Dic3—42no—
277C2×C4⋊Dic3—41no—
278C2×C4×Dic3—22no—
279C2×C4×Dic3—44no—
280C2×C4×Dic3—41no—
281C2×#208—21no—
282C2×#208—21no—
283C2×#208—22no—
284C2×#208—24no—
285C2×#208—22no—
286C2×#208—21no—
287C2×#208—21no—
288C2×#208—22no—
289C2×#208—24no—
290C2×#208—21no—
291C2×#208—21no—
292C2×#208—22no—
293C2×#208—21no—
294C2×#208—21no—
295C2×#208—22no—
296C2×#208—22no—
297C2×#208—22no—
298C2×#208—22no—
299C2×#208—22no—
300C2×#208—22no—
301C2×#208—22no—
302C2×#208—22no—
303C2×#208—22no—
304C2×#208—42no—
305C2×#208—48no—
306C2×#208—48no—
307C2×#208C2×D414yes—
308C22×C3⋊C8—24no—
309C22×C3⋊C8—24no—
310C22×C3⋊C8—22no—
311C22×C3⋊C8—21no—
312C22×C3⋊C8—21no—
313C22×C3⋊C8—42no—
314C22×C3⋊C8C2×D412yes—
315C22×C3⋊C8C2×D412yes—
316C3×#102—48no—
317C3×#102—48no—
318C3×C22⋊C8—42no—
319C3×C22⋊C8—42no—
320C3×#95—42no—
321#833—48no—
322#833—48no—
323#832—216no—
324#832—216no—
325#830—42no—
326#830—42no—
327#830—42no—
328#830—42no—
329#822—44no—
330#822—44no—
331C26—21no—
332C23×D4—24no—
333C23×D4—24no—
334C23×D4—21no—
335C23×D4—21no—
336C23×D4—22no—
337C23×D4—21no—
338C23×D4—21no—
339C23×D4—22no—
340C23×D4—22no—
341C23×D4—21no—
342C23×D4—42no—
343C23×D4—42no—
344C23×D4#6714yes—
345C23×D4C22×D312yes—
346C24×C4C22×D311yescharacteristic
347C22×M16—31no—
348C22×M16—31no—
349C22×M16—32no—
350C22×M16—31no—
351C22×M16—31no—
352C22×M16—32no—
353C22×M16—64no—
354C22×M16—62no—
355C22×M16—62no—
356C22×M16—122no—
357C22×M16C22×D311yescharacteristic
358C22×M16C22×D311yescharacteristic
359C23×C8—32no—
360C2×#117—32no—
361C2×#117—61no—
362C2×#117—61no—
363C2×#117—64no—
364C2×#117—61no—
365C2×#117—122no—
366C2×#117C22×D312yes—
367C22×C4⋊C4—61no—
368C22×C22⋊C4—61no—
369C22×C42—61no—
370#430—64no—
371#430—122no—
372C2×#108—62no—
373C2×#108—62no—
374#418—24no—
375#418—24no—
376#418—38no—
377#418—42no—
378#418—42no—
379#418—64no—
380#418—64no—
381#418—616no—
382#418—64no—
383C2×#102—24no—
384C2×#102—24no—
385C2×#102—64no—
386C2×#102—64no—
387C2×#102—616no—
388C2×#100—64no—
389C2×#100—64no—
390C2×#100—64no—
391C2×#100—64no—
392C2×#100—122no—
393C2×#100—122no—
394#407—21no—
395#407—21no—
396#407—22no—
397#407—61no—
398#407—61no—
399#407—61no—
400#407—61no—
401#407—62no—
402#407—62no—
403C2×C22⋊C8—22no—
404C2×C22⋊C8—62no—
405C2×C22⋊C8—62no—
406#381—21no—
407#380—22no—
408#379—21no—
409C4×C22⋊C4—22no—
410#344—64no—
411#344—64no—
412#344—122no—
413#344—122no—
414#341—62no—
415#341—62no—
416H(3,ℤ/4)—64no—
417H(3,ℤ/4)—122no—
418C24×C3—22no—
419C24×C3—22no—
420C24×C3—24no—
421C24×C3—24no—
422C24×C3—24no—
423C24×C3—44no—
424C24×C3—416no—
425C24×C3—44no—
426C24×C3—44no—
427C24×C3—44no—
428C24×C3—44no—
429C24×C3—416no—
430C24×C3—42no—
431C24×C3—42no—
432C24×C3—42no—
433C24×C3—42no—
434C24×C3—44no—
435C24×C3—44no—
436C24×C3—88no—
437C24×C3—88no—
438C24×C3—88no—
439C24×C3—88no—
440C24×C3—88no—
441C24×C3—88no—
442C24×C3—88no—
443C24×C3—832no—
444C24×C3—832no—
445C24×C3#12312yes—
446C24×C3#12411yescharacteristic
447C24×C3#12411yescharacteristic
448C24×C3#12612yes—
449C24×C3C2×#4111yescharacteristic
450C2×C3×D4—216no—
451C2×C3×D4—216no—
452C2×C3×D4—24no—
453C2×C3×D4—24no—
454C2×C3×D4—24no—
455C2×C3×D4—24no—
456C2×C3×D4—24no—
457C2×C3×D4—24no—
458C2×C3×D4—24no—
459C2×C3×D4—24no—
460C2×C3×D4—24no—
461C2×C3×D4—24no—
462C2×C3×D4—24no—
463C2×C3×D4—24no—
464C2×C3×D4—24no—
465C2×C3×D4—24no—
466C2×C3×D4—24no—
467C2×C3×D4—416no—
468C2×C3×D4—416no—
469C2×C3×D4—416no—
470C2×C3×D4—44no—
471C2×C3×D4—44no—
472C2×C3×D4—44no—
473C2×C3×D4—44no—
474C2×C3×D4—416no—
475C2×C3×D4—48no—
476C2×C3×D4—48no—
477C2×C3×D4—48no—
478C2×C3×D4—48no—
479C2×C3×D4—416no—
480C2×C3×D4—416no—
481C2×C3×D4—48no—
482C2×C3×D4—48no—
483C2×C3×D4—42no—
484C2×C3×D4—42no—
485C2×C3×D4—42no—
486C2×C3×D4—42no—
487C2×C3×D4—42no—
488C2×C3×D4—42no—
489C2×C3×D4—42no—
490C2×C3×D4—42no—
491C2×C3×D4—42no—
492C2×C3×D4—42no—
493C2×C3×D4—42no—
494C2×C3×D4—42no—
495C2×C3×D4—44no—
496C2×C3×D4—44no—
497C2×C3×D4#12118yes—
498C22×C3×C4—22no—
499C22×C3×C4—22no—
500C22×C3×C4—21no—
501C22×C3×C4—21no—
502C22×C3×C4—24no—
503C22×C3×C4—21no—
504C22×C3×C4—21no—
505C22×C3×C4—24no—
506C22×C3×C4—21no—
507C22×C3×C4—21no—
508C22×C3×C4—24no—
509C22×C3×C4—21no—
510C22×C3×C4—21no—
511C22×C3×C4—24no—
512C22×C3×C4—24no—
513C22×C3×C4—24no—
514C22×C3×C4—22no—
515C22×C3×C4—22no—
516C22×C3×C4—22no—
517C22×C3×C4—22no—
518C22×C3×C4—24no—
519C22×C3×C4—24no—
520C22×C3×C4—42no—
521C22×C3×C4#12112yes—
522C22×C3×C4#12112yes—
523C22×C3×C4#12312yes—
524C22×C3×C4#12312yes—
525C22×C3×C4#12312yes—
526C22×C3×C4#12312yes—
527C22×C3×C4#12312yes—
528C22×C3×C4#12411yescharacteristic
529C22×C3×C4#12411yescharacteristic
530C22×C3×C4#12612yes—
531C22×C3×C4#12612yes—
532C22×C3×C4#12612yes—
533C22×C3×C4C22×D411yescharacteristic
534C22×C3×C4C22×D412yes—
535C22×C3×C4C22×D411yescharacteristic
536C22×C3×C4C2×#4111yescharacteristic
537C22×C3×C4C2×#4111yescharacteristic
538C22×C3×C4C2×#4111yescharacteristic
539C22×C3×C4C2×#4112yes—
540C22×C3×C4C2×#4111yescharacteristic
541C22×C3×C4H(5,𝔽2)12yes—
542C22×C3×C4H(5,𝔽2)12yes—
543C22×Dic3—44no—
544C22×Dic3—42no—
545C22×Dic3—84no—
546C3×M16—41no—
547C3×M16—42no—
548C3×M16—41no—
549C3×M16—41no—
550C3×M16—41no—
551C3×M16—42no—
552C2×C3×C8—41no—
553C2×C3×C8—41no—
554C2×C3×C8—42no—
555C2×C3×C8—42no—
556C3×C4⋊C4—42no—
557C3×C4⋊C4—42no—
558C3×C22⋊C4—42no—
559C3×C22⋊C4—42no—
560C3×C22⋊C4—84no—
561C3×C42—42no—
562C3×C42—42no—
563#217—24no—
564#217—44no—
565#217—42no—
566C4⋊Dic3—24no—
567C4⋊Dic3—44no—
568C4⋊Dic3—42no—
569C4×Dic3—24no—
570C4×Dic3—44no—
571C4×Dic3—42no—
572#208—24no—
573#208—24no—
574#208—48no—
575#208—42no—
576#208—42no—
577#208—41no—
578#208—42no—
579#208—42no—
580#208—41no—
581#208—41no—
582#208—42no—
583#208—42no—
584#208—41no—
585#208—42no—
586#208—42no—
587C2×C3⋊C8—22no—
588C2×C3⋊C8—22no—
589C2×C3⋊C8—22no—
590C2×C3⋊C8—22no—
591C2×C3⋊C8—22no—
592C2×C3⋊C8—48no—
593C2×C3⋊C8—41no—
594C2×C3⋊C8—41no—
595C2×C3⋊C8—42no—
596C2×C3⋊C8—42no—
597C2×C3⋊C8—42no—
598C2×C3⋊C8—42no—
599C2×C3⋊C8—42no—
600C2×C3⋊C8#12014yes—
601C25—22no—
602C25—24no—
603C25—44no—
604C25—44no—
605C25—42no—
606C25—41no—
607C25—41no—
608C25—88no—
609C25#23711yescharacteristic
610C22×D4—24no—
611C22×D4—24no—
612C22×D4—24no—
613C22×D4—24no—
614C22×D4—216no—
615C22×D4—216no—
616C22×D4—24no—
617C22×D4—24no—
618C22×D4—24no—
619C22×D4—24no—
620C22×D4—24no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—22no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—22no—
632C22×D4—48no—
633C22×D4—44no—
634C22×D4—44no—
635C22×D4—48no—
636C22×D4—48no—
637C22×D4—44no—
638C22×D4—44no—
639C22×D4—48no—
640C22×D4—48no—
641C22×D4—44no—
642C22×D4—44no—
643C22×D4—42no—
644C22×D4—42no—
645C22×D4—42no—
646C22×D4—42no—
647C22×D4—48no—
648C22×D4—42no—
649C22×D4—42no—
650C22×D4—42no—
651C22×D4—42no—
652C22×D4—42no—
653C22×D4—41no—
654C22×D4—41no—
655C22×D4D3×D414yes—
656C22×D4#23714yes—
657C22×D4C2×#6714yes—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—121no—
663C23×C4#23511yescharacteristic
664C23×C4#23511yescharacteristic
665C23×C4#23512yes—
666C23×C4D3×D411yescharacteristic
667C23×C4D3×D411yescharacteristic
668C23×C4#23712yes—
669C23×C4#23712yes—
670C23×C4#23711yescharacteristic
671C23×C4C2×#6712yes—
672C23×C4C23×D311yescharacteristic
673C2×M16—21no—
674C2×M16—21no—
675C2×M16—22no—
676C2×M16—21no—
677C2×M16—21no—
678C2×M16—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16—34no—
682C2×M16—64no—
683C2×M16—61no—
684C2×M16—61no—
685C2×M16—62no—
686C2×M16—64no—
687C2×M16—61no—
688C2×M16—62no—
689C2×M16—61no—
690C2×M16—62no—
691C2×M16—62no—
692C2×M16—62no—
693C2×M16—61no—
694C2×M16—61no—
695C2×M16—62no—
696C2×M16—62no—
697C2×M16—62no—
698C2×M16—62no—
699C2×M16—62no—
700C2×M16—62no—
701C2×M16—62no—
702C2×M16—62no—
703C2×M16—61no—
704C2×M16—61no—
705C2×M16—122no—
706C2×M16—128no—
707C2×M16—128no—
708C22×C8—21no—
709C22×C8—21no—
710C22×C8—32no—
711C22×C8—32no—
712C22×C8—64no—
713C22×C8—64no—
714C22×C8—62no—
715C22×C8—61no—
716C22×C8—61no—
717C22×C8—122no—
718#117—22no—
719#117—22no—
720#117—22no—
721#117—22no—
722#117—34no—
723#117—62no—
724#117—62no—
725#117—64no—
726#117—62no—
727#117—124no—
728#117—124no—
729#117—122no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—64no—
732C2×C4⋊C4—62no—
733C2×C4⋊C4—122no—
734C2×C4⋊C4—121no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—42no—
737C2×C22⋊C4—62no—
738C2×C22⋊C4—124no—
739C2×C22⋊C4—121no—
740C2×C42—22no—
741C2×C42—62no—
742C2×C42—124no—
743C2×C42—121no—
744#108—124no—
745#108—124no—
746#102—48no—
747#102—48no—
748#102—616no—
749#102—616no—
750#100—128no—
751#100—128no—
752C22⋊C8—42no—
753C22⋊C8—42no—
754C22⋊C8—122no—
755C22⋊C8—122no—
756C22⋊C8—122no—
757C22⋊C8—122no—
758#95—42no—
759C23×C3—21no—
760C23×C3—24no—
761C23×C3—21no—
762C23×C3—21no—
763C23×C3—24no—
764C23×C3—24no—
765C23×C3—24no—
766C23×C3—21no—
767C23×C3—24no—
768C23×C3—28no—
769C23×C3—42no—
770C23×C3—42no—
771C23×C3—42no—
772C23×C3—42no—
773C23×C3—48no—
774C23×C3—48no—
775C23×C3—416no—
776C23×C3—416no—
777C23×C3—44no—
778C23×C3—44no—
779C23×C3—44no—
780C23×C3—44no—
781C23×C3—44no—
782C23×C3—44no—
783C23×C3—88no—
784C23×C3—88no—
785C23×C3—88no—
786C23×C3—816no—
787C23×C3—816no—
788C23×C3—88no—
789C23×C3—88no—
790C23×C3—88no—
791C23×C3—88no—
792C23×C3—88no—
793C23×C3—88no—
794C23×C3—88no—
795C23×C3—864no—
796C23×C3—864no—
797C23×C3—816no—
798C23×C3—816no—
799C23×C3—88no—
800C23×C3#39712yes—
801C23×C3#39712yes—
802C23×C3C2×#12311yescharacteristic
803C23×C3C2×#12411yescharacteristic
804C23×C3C2×#12611yescharacteristic
805C23×C3#54612yes—
806C23×C3#55112yes—
807C3×D4—28no—
808C3×D4—28no—
809C3×D4—416no—
810C3×D4—416no—
811C3×D4—44no—
812C3×D4—44no—
813C3×D4—44no—
814C3×D4—44no—
815C3×D4—44no—
816C3×D4—44no—
817C2×C3×C4—21no—
818C2×C3×C4—21no—
819C2×C3×C4—24no—
820C2×C3×C4—21no—
821C2×C3×C4—21no—
822C2×C3×C4—24no—
823C2×C3×C4—22no—
824C2×C3×C4—22no—
825C2×C3×C4—22no—
826C2×C3×C4—22no—
827C2×C3×C4—22no—
828C2×C3×C4—22no—
829C2×C3×C4—24no—
830C2×C3×C4—24no—
831C2×C3×C4—24no—
832C2×C3×C4—24no—
833C2×C3×C4—22no—
834C2×C3×C4—22no—
835C2×C3×C4—84no—
836C2×C3×C4—82no—
837C2×C3×C4#39712yes—
838C2×C3×C4#39712yes—
839C2×C3×C4C2×#12011yescharacteristic
840C2×C3×C4C2×#12111yescharacteristic
841C2×C3×C4C2×#12112yes—
842C2×C3×C4C2×#12311yescharacteristic
843C2×C3×C4C2×#12311yescharacteristic
844C2×C3×C4#52512yes—
845C2×C3×C4#52511yescharacteristic
846C2×C3×C4C2×#12611yescharacteristic
847C2×C3×C4#53412yes—
848C2×C3×C4#53411yescharacteristic
849C2×C3×C4#53511yescharacteristic
850C2×C3×C4#53812yes—
851C2×C3×C4#54612yes—
852C2×C3×C4#54612yes—
853C2×C3×C4#54612yes—
854C2×C3×C4#55112yes—
855C2×C3×C4#55112yes—
856C2×C3×C4#55112yes—
857C2×Dic3—44no—
858C2×Dic3—88no—
859C2×Dic3—84no—
860C3×C8—81no—
861C3×C8—81no—
862C3⋊C8—24no—
863C3⋊C8—42no—
864C3⋊C8—81no—
865C3⋊C8—81no—
866C3⋊C8—82no—
867C24—22no—
868C24—22no—
869C24—24no—
870C24—24no—
871C24—24no—
872C24—44no—
873C24—416no—
874C24—44no—
875C24—44no—
876C24—44no—
877C24—416no—
878C24—44no—
879C24—44no—
880C24—44no—
881C24—42no—
882C24—42no—
883C24—42no—
884C24—42no—
885C24—88no—
886C24—88no—
887C24—88no—
888C24—88no—
889C24—88no—
890C24—88no—
891C24—88no—
892C24—832no—
893C24—832no—
894C24#87912yes—
895C24#88511yescharacteristic
896C24#88511yescharacteristic
897C24#93512yes—
898C24C2×#23711yescharacteristic
899C2×D4—216no—
900C2×D4—216no—
901C2×D4—24no—
902C2×D4—24no—
903C2×D4—24no—
904C2×D4—24no—
905C2×D4—24no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—24no—
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—24no—
913C2×D4—24no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—416no—
917C2×D4—416no—
918C2×D4—416no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—416no—
922C2×D4—44no—
923C2×D4—44no—
924C2×D4—416no—
925C2×D4—416no—
926C2×D4—48no—
927C2×D4—48no—
928C2×D4—48no—
929C2×D4—48no—
930C2×D4—48no—
931C2×D4—48no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—42no—
943C2×D4—42no—
944C2×D4—42no—
945C2×D4—42no—
946C2×D4#93918yes—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—22no—
954C22×C4—22no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—24no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—24no—
969C22×C4—42no—
970C22×C4—124no—
971C22×C4—122no—
972C22×C4—244no—
973C22×C4#87912yes—
974C22×C4#87912yes—
975C22×C4#87912yes—
976C22×C4#88312yes—
977C22×C4#88312yes—
978C22×C4#88511yescharacteristic
979C22×C4#88511yescharacteristic
980C22×C4#92912yes—
981C22×C4#92912yes—
982C22×C4#93512yes—
983C22×C4#93912yes—
984C22×C4#93912yes—
985C22×C4C2×#23511yescharacteristic
986C22×C4C2×#23511yescharacteristic
987C22×C4C2×D3×D411yescharacteristic
988C22×C4C2×D3×D412yes—
989C22×C4C2×#23711yescharacteristic
990C22×C4C2×#23711yescharacteristic
991C22×C4C2×#23712yes—
992C22×C4#100412yes—
993C22×C4#100412yes—
994C22×C4C22×#6711yescharacteristic
995M16—42no—
996M16—41no—
997M16—41no—
998M16—41no—
999M16—41no—
1000M16—42no—
1001M16—64no—
1002M16—64no—
1003M16—128no—
1004M16—122no—
1005M16—122no—
1006M16—122no—
1007M16—122no—
1008M16—122no—
1009M16—122no—
1010M16—122no—
1011M16—122no—
1012M16—121no—
1013M16—121no—
1014M16—121no—
1015M16—121no—
1016C2×C8—34no—
1017C2×C8—41no—
1018C2×C8—41no—
1019C2×C8—42no—
1020C2×C8—42no—
1021C2×C8—62no—
1022C2×C8—62no—
1023C2×C8—62no—
1024C2×C8—62no—
1025C2×C8—62no—
1026C2×C8—128no—
1027C2×C8—122no—
1028C2×C8—122no—
1029C2×C8—122no—
1030C2×C8—121no—
1031C2×C8—121no—
1032C2×C8—122no—
1033C2×C8—122no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—64no—
1037C4⋊C4—124no—
1038C4⋊C4—122no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—64no—
1042C22⋊C4—84no—
1043C22⋊C4—124no—
1044C22⋊C4—122no—
1045C42—42no—
1046C42—42no—
1047C42—64no—
1048C42—124no—
1049C42—122no—
1050C22×C3—24no—
1051C22×C3—24no—
1052C22×C3—22no—
1053C22×C3—22no—
1054C22×C3—22no—
1055C22×C3—22no—
1056C22×C3—22no—
1057C22×C3—22no—
1058C22×C3—22no—
1059C22×C3—22no—
1060C22×C3—42no—
1061C22×C3—42no—
1062C22×C3—48no—
1063C22×C3—48no—
1064C22×C3—42no—
1065C22×C3—42no—
1066C22×C3—48no—
1067C22×C3—88no—
1068C22×C3—88no—
1069C22×C3—88no—
1070C22×C3—88no—
1071C22×C3—88no—
1072C22×C3—88no—
1073C22×C3—832no—
1074C22×C3—832no—
1075C22×C3—88no—
1076C22×C3#208114yescomplemented
1077C22×C3C2×#39711yescharacteristic
1078C22×C3#241212yes—
1079C22×C3#243511yescharacteristic
1080C22×C3#248012yes—
1081C22×C3#256111yescharacteristic
1082C3×C4—22no—
1083C3×C4—22no—
1084C3×C4—162no—
1085C3×C4#240511yescharacteristic
1086C3×C4#241212yes—
1087C3×C4#248012yes—
1088C3×C4#248211yescharacteristic
1089C3×C4#261711yescharacteristic
1090C3×C4#284711yescharacteristic
1091Dic3—84no—
1092C23—21no—
1093C23—21no—
1094C23—24no—
1095C23—21no—
1096C23—24no—
1097C23—21no—
1098C23—24no—
1099C23—24no—
1100C23—24no—
1101C23—28no—
1102C23—42no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—48no—
1107C23—48no—
1108C23—416no—
1109C23—416no—
1110C23—44no—
1111C23—44no—
1112C23—44no—
1113C23—44no—
1114C23—44no—
1115C23—44no—
1116C23—88no—
1117C23—816no—
1118C23—816no—
1119C23—88no—
1120C23—88no—
1121C23—88no—
1122C23—88no—
1123C23—88no—
1124C23—88no—
1125C23—88no—
1126C23—88no—
1127C23—88no—
1128C23—864no—
1129C23—864no—
1130C23—816no—
1131C23—816no—
1132C23—88no—
1133C23#495212yes—
1134C23#495212yes—
1135C23C2×#87911yescharacteristic
1136C23C2×#88511yescharacteristic
1137C23#558712yes—
1138C23#559112yes—
1139C23C2×#93511yescharacteristic
1140D4—28no—
1141D4—28no—
1142D4—416no—
1143D4—416no—
1144D4—44no—
1145D4—44no—
1146D4—44no—
1147D4—44no—
1148D4—44no—
1149D4—44no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—24no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—84no—
1169C2×C4—82no—
1170C2×C4—124no—
1171C2×C4—248no—
1172C2×C4—244no—
1173C2×C4#495212yes—
1174C2×C4#495212yes—
1175C2×C4C2×#87911yescharacteristic
1176C2×C4C2×#88311yescharacteristic
1177C2×C4#549012yes—
1178C2×C4#549012yes—
1179C2×C4#549512yes—
1180C2×C4#549512yes—
1181C2×C4#558612yes—
1182C2×C4#558611yescharacteristic
1183C2×C4#558712yes—
1184C2×C4D3×#12011yescharacteristic
1185C2×C4#558911yescharacteristic
1186C2×C4#559112yes—
1187C2×C4#559211yescharacteristic
1188C2×C4#559312yes—
1189C2×C4C2×#92911yescharacteristic
1190C2×C4C2×#93911yescharacteristic
1191C2×C4C2×#93912yes—
1192C2×C4#580412yes—
1193C8—64no—
1194C8—81no—
1195C8—81no—
1196C8—122no—
1197C8—241no—
1198C8—241no—
1199C8—242no—
1200C2×C3—21no—
1201C2×C3—22no—
1202C2×C3—21no—
1203C2×C3—24no—
1204C2×C3—22no—
1205C2×C3—42no—
1206C2×C3—88no—
1207C2×C3#1482011yescharacteristic
1208C2×C3C2×#208112yes—
1209C22—24no—
1210C22—24no—
1211C22—22no—
1212C22—22no—
1213C22—22no—
1214C22—22no—
1215C22—22no—
1216C22—22no—
1217C22—22no—
1218C22—22no—
1219C22—42no—
1220C22—42no—
1221C22—48no—
1222C22—48no—
1223C22—42no—
1224C22—42no—
1225C22—48no—
1226C22—88no—
1227C22—88no—
1228C22—88no—
1229C22—88no—
1230C22—832no—
1231C22—88no—
1232C22—88no—
1233C22—832no—
1234C22—88no—
1235C22#7032214yescomplemented
1236C22#7382711yescharacteristic
1237C22#7383012yes—
1238C22#7383511yescharacteristic
1239C22C2×#495211yescharacteristic
1240C22#8258412yes—
1241C4—22no—
1242C4—22no—
1243C4—162no—
1244C4—244no—
1245C4#7383112yes—
1246C4#7383211yescharacteristic
1247C4#7385311yescharacteristic
1248C4#8210712yes—
1249C4#8259211yescharacteristic
1250C4#8260111yescharacteristic
1251C3#40162611yescharacteristic, complemented, Sylow
1252C2—22no—
1253C2—21no—
1254C2—21no—
1255C2—24no—
1256C2—22no—
1257C2—42no—
1258C2—88no—
1259C2#1072793411yescharacteristic
1260C2C2×#7032212yes—
subgroupG/H
centerC22C2×#4952
commutator, cosocleC23×C3×C4C24
FrattiniC23×C4C23×D3
FittingC3×#20598C2
socleC22×C3C2×#397
prime radicalC24×C3×D4C22
hypercenter#20598D3
hypocenterC3#401626
LCSG ▷ C23×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24×C4 ◁ #20598

Complements

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

NH ≅ G/Ntype
2. C2×#70322C2semidirect
3. #10794810C2semidirect
5. #10702943C2semidirect
6. #10702814C2semidirect
7. #10702661C2semidirect
8. #10700496C2semidirect
9. #10700460C2semidirect
10. #10700418C2semidirect
29. C2×#5124C22semidirect
30. C2×#5124C22semidirect
33. C2×#4559C22semidirect
34. C2×#4559C22semidirect
35. #71994C22semidirect
36. #71994C22semidirect
37. C2×#4533C22semidirect
38. C2×#4533C22semidirect
39. C2×#4531C22semidirect
40. C2×#4531C22semidirect
1076. C22×C3#2081semidirect
1235. C22#70322semidirect
1251. C3#401626semidirect

Maximal subgroups

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

subgroupindex
C22×#52152
C2×#703222
#107948102
C2×#721292
#107029432
#107028142
#107026612
#107004962
#107004602
#107004182
C3×#205982
#4016263