Finite Group Databasebeta

← C2×C3×#32898 #72253424

Subgroups — C2×C3×#32898 #72253424

Order 1536.

39956 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C22×C3×B(4,𝔽2)C214yesmaximal, complemented
3C2×C3×#2403C213yesmaximal, complemented
4C3×#32898C2116yesmaximal, direct product factor
5C2×C3×#1790C214yesmaximal, complemented
6C2×C3×#1781C213yesmaximal, complemented
7C2×#32898C311yesmaximal, characteristic, direct product factor, Sylow
8C22×C3×H(5,𝔽2)—232no—
9C22×C3×H(5,𝔽2)—26no—
10C22×C3×H(5,𝔽2)—212no—
11C22×C3×H(5,𝔽2)C2214yes—
12C22×C3×H(5,𝔽2)C2218yescomplemented
13C23×C3×#41—23no—
14C24×C3×D4—23no—
15C24×C3×D4C2213yes—
16C24×C3×D4C2211yescharacteristic, complemented
17C22×C3×#120—23no—
18C22×C3×#120C2216yescomplemented
19C2×C3×B(4,𝔽2)—232no—
20C2×C3×B(4,𝔽2)C22132yescomplemented
21C22×C3×#99C22112yescomplemented
22C3×#2403—212no—
23C3×#2403C22124yescomplemented
24C2×C3×#392—26no—
25C2×C3×#386—23no—
26C2×C3×#386C2216yescomplemented
27C2×C3×#379C2213yescomplemented
28C3×#1790C22132yescomplemented
29C3×#1781C22124yescomplemented
30C23×H(5,𝔽2)C2×C311yescharacteristic, complemented
31C22×B(4,𝔽2)C2×C314yescomplemented
32C2×#2403C2×C313yescomplemented
33#32898C2×C3116yesdirect product factor
34C2×#1790C2×C314yescomplemented
35C2×#1781C2×C313yescomplemented
36C26×C3—21no—
37C26×C3D413yescomplemented
38C26×C3C2311yescharacteristic
39C26×C3C2311yescharacteristic, complemented
40C2×C3×H(5,𝔽2)—2384no—
41C2×C3×H(5,𝔽2)—296no—
42C2×C3×H(5,𝔽2)—248no—
43C2×C3×H(5,𝔽2)—296no—
44C2×C3×H(5,𝔽2)—2128no—
45C2×C3×H(5,𝔽2)—248no—
46C2×C3×H(5,𝔽2)—224no—
47C2×C3×H(5,𝔽2)—248no—
48C2×C3×H(5,𝔽2)D4132yescomplemented
49C2×C3×H(5,𝔽2)C23116yes—
50C22×C3×#41—224no—
51C22×C3×#41—212no—
52C22×C3×#41—296no—
53C22×C3×#41—212no—
54C22×C3×#41—224no—
55C23×C3×Q8—21no—
56C23×C3×D4—23no—
57C23×C3×D4—224no—
58C23×C3×D4—212no—
59C23×C3×D4—296no—
60C23×C3×D4—248no—
61C23×C3×D4—26no—
62C23×C3×D4—212no—
63C23×C3×D4—26no—
64C23×C3×D4—212no—
65C23×C3×D4—23no—
66C23×C3×D4—23no—
67C23×C3×D4—26no—
68C23×C3×D4—26no—
69C23×C3×D4—224no—
70C23×C3×D4—48no—
71C23×C3×D4D416yescomplemented
72C23×C3×D4D4112yescomplemented
73C23×C3×D4C2316yes—
74C23×C3×D4C23112yes—
75C23×C3×D4C2314yescomplemented
76C24×C3×C4—23no—
77C24×C3×C4D413yescomplemented
78C24×C3×C4C2311yescharacteristic, complemented
79C2×C3×#120—212no—
80C2×C3×#120—248no—
81C2×C3×#120—224no—
82C2×C3×#120—424no—
83C2×C3×#120C23124yescomplemented
84C22×C3×C22⋊C4—26no—
85C22×C3×C22⋊C4—26no—
86C22×C3×C22⋊C4—23no—
87C22×C3×C22⋊C4—23no—
88C22×C3×C22⋊C4C2316yescomplemented
89C3×B(4,𝔽2)—2128no—
90C2×C3×#99—248no—
91C2×C3×#99C23148yescomplemented
92C3×#392—248no—
93C3×#386—212no—
94C3×#386—224no—
95C3×#386C23124yescomplemented
96C3×#379—26no—
97C3×#379C23112yescomplemented
98C2×C3×#95—26no—
99C22×H(5,𝔽2)—232no—
100C22×H(5,𝔽2)—26no—
101C22×H(5,𝔽2)—212no—
102C22×H(5,𝔽2)C22×C314yes—
103C22×H(5,𝔽2)C22×C318yescomplemented
104C23×#41—23no—
105C24×D4—23no—
106C24×D4C22×C313yes—
107C24×D4C22×C311yescharacteristic, complemented
108C22×#120—23no—
109C22×#120C22×C316yescomplemented
110C2×B(4,𝔽2)—232no—
111C2×B(4,𝔽2)C22×C3132yescomplemented
112C22×#99C22×C3112yescomplemented
113#2403—212no—
114#2403C22×C3124yescomplemented
115C2×#392—26no—
116C2×#386—23no—
117C2×#386C22×C316yescomplemented
118C2×#379C22×C313yescomplemented
119#1790C22×C3132yescomplemented
120#1781C22×C3124yescomplemented
121C25×C3—216no—
122C25×C3—28no—
123C25×C3—24no—
124C25×C3—23no—
125C25×C3—26no—
126C25×C3—23no—
127C25×C3—224no—
128C25×C3—28no—
129C25×C3—23no—
130C25×C3—23no—
131C25×C3—28no—
132C25×C3—44no—
133C25×C3—44no—
134C25×C3—412no—
135C25×C3—82no—
136C25×C3—82no—
137C25×C3—86no—
138C25×C3—84no—
139C25×C3—84no—
140C25×C3C2×D413yes—
141C25×C3C2×D413yes—
142C25×C3C2×D416yes—
143C25×C3C2×D416yes—
144C25×C3C2×D4112yescomplemented
145C25×C3C2412yes—
146C25×C3C2411yescharacteristic
147C25×C3C2412yescomplemented
148C3×H(5,𝔽2)—2768no—
149C3×H(5,𝔽2)—2384no—
150C3×H(5,𝔽2)—2192no—
151C3×H(5,𝔽2)—2384no—
152C3×H(5,𝔽2)—2192no—
153C3×H(5,𝔽2)—296no—
154C3×H(5,𝔽2)C2×D4164yescomplemented
155C2×C3×#41—2384no—
156C2×C3×#41—2192no—
157C2×C3×#41—296no—
158C2×C3×#41—248no—
159C2×C3×#41—296no—
160C2×C3×#41—2384no—
161C2×C3×#41—296no—
162C2×C3×#41—248no—
163C22×C3×Q8—216no—
164C22×C3×Q8—28no—
165C22×C3×Q8—24no—
166C22×C3×D4—248no—
167C22×C3×D4—296no—
168C22×C3×D4—224no—
169C22×C3×D4—212no—
170C22×C3×D4—2384no—
171C22×C3×D4—2192no—
172C22×C3×D4—2192no—
173C22×C3×D4—2384no—
174C22×C3×D4—296no—
175C22×C3×D4—248no—
176C22×C3×D4—296no—
177C22×C3×D4—296no—
178C22×C3×D4—224no—
179C22×C3×D4—212no—
180C22×C3×D4—212no—
181C22×C3×D4—224no—
182C22×C3×D4—296no—
183C22×C3×D4—224no—
184C22×C3×D4—224no—
185C22×C3×D4—212no—
186C22×C3×D4—248no—
187C22×C3×D4—224no—
188C22×C3×D4—212no—
189C22×C3×D4—224no—
190C22×C3×D4—296no—
191C22×C3×D4—296no—
192C22×C3×D4—224no—
193C22×C3×D4—212no—
194C22×C3×D4—212no—
195C22×C3×D4—224no—
196C22×C3×D4—224no—
197C22×C3×D4—412no—
198C22×C3×D4—416no—
199C22×C3×D4—448no—
200C22×C3×D4—412no—
201C22×C3×D4—412no—
202C22×C3×D4—46no—
203C22×C3×D4—46no—
204C22×C3×D4—43no—
205C22×C3×D4—41no—
206C22×C3×D4—424no—
207C22×C3×D4—424no—
208C22×C3×D4—812no—
209C22×C3×D4C2×D4148yes—
210C22×C3×D4C2×D4112yes—
211C22×C3×D4C2×D4124yescomplemented
212C22×C3×D4C24112yes—
213C23×C3×C4—248no—
214C23×C3×C4—224no—
215C23×C3×C4—212no—
216C23×C3×C4—23no—
217C23×C3×C4—26no—
218C23×C3×C4—23no—
219C23×C3×C4—224no—
220C23×C3×C4—23no—
221C23×C3×C4—23no—
222C23×C3×C4—26no—
223C23×C3×C4—44no—
224C23×C3×C4C2×D416yes—
225C23×C3×C4C2×D4112yescomplemented
226C23×C3×C4C2412yescomplemented
227C3×#120—296no—
228C3×#120—496no—
229C3×#120—448no—
230C2×C3×C22⋊C4—224no—
231C2×C3×C22⋊C4—26no—
232C2×C3×C22⋊C4—212no—
233C2×C3×C22⋊C4—224no—
234C2×C3×C22⋊C4—224no—
235C2×C3×C22⋊C4—212no—
236C2×C3×C22⋊C4—424no—
237C2×C3×C22⋊C4—412no—
238C2×C3×C22⋊C4—424no—
239C2×C3×C22⋊C4—86no—
240C2×C3×C22⋊C4C24112yescomplemented
241C3×#99—296no—
242C3×#95—224no—
243C26—21no—
244C26C3×D413yescomplemented
245C26C23×C311yescharacteristic
246C26C23×C311yescharacteristic, complemented
247C2×H(5,𝔽2)—2384no—
248C2×H(5,𝔽2)—296no—
249C2×H(5,𝔽2)—248no—
250C2×H(5,𝔽2)—296no—
251C2×H(5,𝔽2)—2128no—
252C2×H(5,𝔽2)—248no—
253C2×H(5,𝔽2)—224no—
254C2×H(5,𝔽2)—248no—
255C2×H(5,𝔽2)C3×D4132yescomplemented
256C2×H(5,𝔽2)C23×C3116yes—
257C22×#41—212no—
258C22×#41—224no—
259C22×#41—296no—
260C22×#41—212no—
261C22×#41—224no—
262C23×Q8—21no—
263C23×D4—23no—
264C23×D4—296no—
265C23×D4—212no—
266C23×D4—224no—
267C23×D4—26no—
268C23×D4—212no—
269C23×D4—26no—
270C23×D4—212no—
271C23×D4—224no—
272C23×D4—248no—
273C23×D4—23no—
274C23×D4—23no—
275C23×D4—26no—
276C23×D4—26no—
277C23×D4—48no—
278C23×D4C3×D416yescomplemented
279C23×D4C3×D4112yescomplemented
280C23×D4C23×C316yes—
281C23×D4C23×C3112yes—
282C23×D4C23×C314yescomplemented
283C24×C4—23no—
284C24×C4C3×D413yescomplemented
285C24×C4C23×C311yescharacteristic, complemented
286C2×#120—224no—
287C2×#120—212no—
288C2×#120—248no—
289C2×#120—424no—
290C2×#120C23×C3124yescomplemented
291C22×C22⋊C4—26no—
292C22×C22⋊C4—23no—
293C22×C22⋊C4—26no—
294C22×C22⋊C4—23no—
295C22×C22⋊C4C23×C316yescomplemented
296B(4,𝔽2)—2128no—
297C2×#99—248no—
298C2×#99C23×C3148yescomplemented
299#392—248no—
300#386—212no—
301#386—224no—
302#386C23×C3124yescomplemented
303#379—26no—
304#379C23×C3112yescomplemented
305C2×#95—26no—
306C24×C3—224no—
307C24×C3—264no—
308C24×C3—248no—
309C24×C3—224no—
310C24×C3—232no—
311C24×C3—216no—
312C24×C3—212no—
313C24×C3—212no—
314C24×C3—26no—
315C24×C3—212no—
316C24×C3—224no—
317C24×C3—212no—
318C24×C3—212no—
319C24×C3—26no—
320C24×C3—212no—
321C24×C3—248no—
322C24×C3—28no—
323C24×C3—212no—
324C24×C3—26no—
325C24×C3—28no—
326C24×C3—42no—
327C24×C3—46no—
328C24×C3—42no—
329C24×C3—46no—
330C24×C3—412no—
331C24×C3—44no—
332C24×C3—44no—
333C24×C3—46no—
334C24×C3—412no—
335C24×C3—412no—
336C24×C3—412no—
337C24×C3—46no—
338C24×C3—412no—
339C24×C3—412no—
340C24×C3—424no—
341C24×C3—412no—
342C24×C3—412no—
343C24×C3—43no—
344C24×C3—41no—
345C24×C3—412no—
346C24×C3—86no—
347C24×C3—812no—
348C24×C3—86no—
349C24×C3—86no—
350C24×C3—82no—
351C24×C3—82no—
352C24×C3—812no—
353C24×C3—832no—
354C24×C3—832no—
355C24×C3—896no—
356C24×C3—812no—
357C24×C3—86no—
358C24×C3—864no—
359C24×C3—816no—
360C24×C3—88no—
361C24×C3—816no—
362C24×C3—88no—
363C24×C3#12013yes—
364C24×C3#12016yes—
365C24×C3#12011yescharacteristic
366C24×C3#12016yes—
367C24×C3#120124yescomplemented
368C24×C3C22×D416yes—
369C24×C3C22×D413yes—
370C24×C3C22×D416yes—
371C24×C3C22×D4112yes—
372C24×C3C22×D418yes—
373C24×C3C22×D413yes—
374C24×C3C2511yescharacteristic
375C3×#41—2768no—
376C3×#41—2384no—
377C3×#41—2192no—
378C3×#41—2192no—
379C2×C3×Q8—264no—
380C2×C3×Q8—232no—
381C2×C3×Q8—216no—
382C2×C3×D4—2192no—
383C2×C3×D4—2192no—
384C2×C3×D4—2192no—
385C2×C3×D4—296no—
386C2×C3×D4—296no—
387C2×C3×D4—248no—
388C2×C3×D4—2768no—
389C2×C3×D4—2192no—
390C2×C3×D4—2384no—
391C2×C3×D4—2192no—
392C2×C3×D4—2192no—
393C2×C3×D4—296no—
394C2×C3×D4—296no—
395C2×C3×D4—224no—
396C2×C3×D4—248no—
397C2×C3×D4—296no—
398C2×C3×D4—224no—
399C2×C3×D4—2192no—
400C2×C3×D4—248no—
401C2×C3×D4—224no—
402C2×C3×D4—224no—
403C2×C3×D4—248no—
404C2×C3×D4—248no—
405C2×C3×D4—424no—
406C2×C3×D4—424no—
407C2×C3×D4—424no—
408C2×C3×D4—448no—
409C2×C3×D4—424no—
410C2×C3×D4—448no—
411C2×C3×D4—412no—
412C2×C3×D4—44no—
413C2×C3×D4—48no—
414C2×C3×D4—448no—
415C2×C3×D4—448no—
416C2×C3×D4—824no—
417C2×C3×D4—896no—
418C2×C3×D4#120148yescomplemented
419C2×C3×D4C22×D4148yes—
420C22×C3×C4—224no—
421C22×C3×C4—2192no—
422C22×C3×C4—248no—
423C22×C3×C4—224no—
424C22×C3×C4—296no—
425C22×C3×C4—248no—
426C22×C3×C4—212no—
427C22×C3×C4—212no—
428C22×C3×C4—26no—
429C22×C3×C4—212no—
430C22×C3×C4—26no—
431C22×C3×C4—248no—
432C22×C3×C4—212no—
433C22×C3×C4—26no—
434C22×C3×C4—212no—
435C22×C3×C4—44no—
436C22×C3×C4—412no—
437C22×C3×C4—46no—
438C22×C3×C4—43no—
439C22×C3×C4—41no—
440C22×C3×C4—412no—
441C22×C3×C4—412no—
442C22×C3×C4—412no—
443C22×C3×C4#120124yescomplemented
444C22×C3×C4C22×D4112yes—
445C3×C22⋊C4—224no—
446C3×C22⋊C4—448no—
447C3×C22⋊C4—424no—
448C3×C22⋊C4—412no—
449C3×C22⋊C4—448no—
450C3×C22⋊C4—812no—
451C25—216no—
452C25—24no—
453C25—28no—
454C25—23no—
455C25—23no—
456C25—26no—
457C25—224no—
458C25—28no—
459C25—23no—
460C25—23no—
461C25—28no—
462C25—44no—
463C25—44no—
464C25—412no—
465C25—82no—
466C25—82no—
467C25—86no—
468C25—84no—
469C25—84no—
470C25C2×C3×D413yes—
471C25C2×C3×D413yes—
472C25C2×C3×D416yes—
473C25C2×C3×D416yes—
474C25C2×C3×D4112yescomplemented
475C25C24×C312yes—
476C25C24×C311yescharacteristic
477C25C24×C312yescomplemented
478H(5,𝔽2)—2768no—
479H(5,𝔽2)—2384no—
480H(5,𝔽2)—2192no—
481H(5,𝔽2)—2384no—
482H(5,𝔽2)—2192no—
483H(5,𝔽2)—296no—
484H(5,𝔽2)C2×C3×D4164yescomplemented
485C2×#41—2384no—
486C2×#41—2192no—
487C2×#41—248no—
488C2×#41—296no—
489C2×#41—296no—
490C2×#41—2384no—
491C2×#41—296no—
492C2×#41—248no—
493C22×Q8—216no—
494C22×Q8—24no—
495C22×Q8—28no—
496C22×D4—248no—
497C22×D4—296no—
498C22×D4—212no—
499C22×D4—224no—
500C22×D4—2384no—
501C22×D4—2192no—
502C22×D4—2192no—
503C22×D4—2384no—
504C22×D4—248no—
505C22×D4—296no—
506C22×D4—296no—
507C22×D4—296no—
508C22×D4—212no—
509C22×D4—224no—
510C22×D4—212no—
511C22×D4—224no—
512C22×D4—296no—
513C22×D4—224no—
514C22×D4—212no—
515C22×D4—224no—
516C22×D4—248no—
517C22×D4—212no—
518C22×D4—224no—
519C22×D4—224no—
520C22×D4—296no—
521C22×D4—296no—
522C22×D4—224no—
523C22×D4—212no—
524C22×D4—212no—
525C22×D4—224no—
526C22×D4—224no—
527C22×D4—412no—
528C22×D4—416no—
529C22×D4—448no—
530C22×D4—412no—
531C22×D4—412no—
532C22×D4—43no—
533C22×D4—46no—
534C22×D4—46no—
535C22×D4—41no—
536C22×D4—424no—
537C22×D4—424no—
538C22×D4—812no—
539C22×D4C2×C3×D4148yes—
540C22×D4C2×C3×D4112yes—
541C22×D4C2×C3×D4124yescomplemented
542C22×D4C24×C3112yes—
543C23×C4—248no—
544C23×C4—212no—
545C23×C4—224no—
546C23×C4—23no—
547C23×C4—23no—
548C23×C4—26no—
549C23×C4—224no—
550C23×C4—23no—
551C23×C4—26no—
552C23×C4—23no—
553C23×C4—44no—
554C23×C4C2×C3×D416yes—
555C23×C4C2×C3×D4112yescomplemented
556C23×C4C24×C312yescomplemented
557#120—296no—
558#120—496no—
559#120—448no—
560C2×C22⋊C4—224no—
561C2×C22⋊C4—212no—
562C2×C22⋊C4—224no—
563C2×C22⋊C4—26no—
564C2×C22⋊C4—224no—
565C2×C22⋊C4—212no—
566C2×C22⋊C4—424no—
567C2×C22⋊C4—412no—
568C2×C22⋊C4—424no—
569C2×C22⋊C4—86no—
570C2×C22⋊C4C24×C3112yescomplemented
571#99—296no—
572#95—224no—
573C23×C3—22no—
574C23×C3—26no—
575C23×C3—26no—
576C23×C3—22no—
577C23×C3—248no—
578C23×C3—248no—
579C23×C3—264no—
580C23×C3—212no—
581C23×C3—26no—
582C23×C3—224no—
583C23×C3—212no—
584C23×C3—212no—
585C23×C3—26no—
586C23×C3—212no—
587C23×C3—212no—
588C23×C3—26no—
589C23×C3—212no—
590C23×C3—224no—
591C23×C3—212no—
592C23×C3—212no—
593C23×C3—212no—
594C23×C3—43no—
595C23×C3—41no—
596C23×C3—46no—
597C23×C3—416no—
598C23×C3—46no—
599C23×C3—43no—
600C23×C3—41no—
601C23×C3—46no—
602C23×C3—46no—
603C23×C3—46no—
604C23×C3—46no—
605C23×C3—448no—
606C23×C3—496no—
607C23×C3—424no—
608C23×C3—412no—
609C23×C3—448no—
610C23×C3—412no—
611C23×C3—46no—
612C23×C3—412no—
613C23×C3—448no—
614C23×C3—412no—
615C23×C3—412no—
616C23×C3—424no—
617C23×C3—412no—
618C23×C3—412no—
619C23×C3—42no—
620C23×C3—44no—
621C23×C3—824no—
622C23×C3—824no—
623C23×C3—86no—
624C23×C3—86no—
625C23×C3—812no—
626C23×C3—812no—
627C23×C3—824no—
628C23×C3—86no—
629C23×C3—848no—
630C23×C3—816no—
631C23×C3—816no—
632C23×C3—896no—
633C23×C3—896no—
634C23×C3—8128no—
635C23×C3—848no—
636C23×C3—864no—
637C23×C3—816no—
638C23×C3—816no—
639C23×C3—848no—
640C23×C3—86no—
641C23×C3—82no—
642C23×C3—82no—
643C23×C3B(4,𝔽2)14yescomplemented
644C23×C3C2×#12016yes—
645C23×C3C2×#12013yes—
646C23×C3C2×#120112yes—
647C23×C3C2×#12012yes—
648C23×C3C2×#120112yes—
649C23×C3C2×#12011yescharacteristic
650C23×C3C2×#120124yescomplemented
651C23×C3C23×D413yes—
652C23×C3C23×D414yes—
653C3×Q8—264no—
654C3×D4—2192no—
655C3×D4—2192no—
656C3×D4—296no—
657C3×D4—296no—
658C3×D4—448no—
659C3×D4—416no—
660C3×D4—896no—
661C2×C3×C4—248no—
662C2×C3×C4—248no—
663C2×C3×C4—2192no—
664C2×C3×C4—224no—
665C2×C3×C4—224no—
666C2×C3×C4—212no—
667C2×C3×C4—212no—
668C2×C3×C4—212no—
669C2×C3×C4—46no—
670C2×C3×C4—412no—
671C2×C3×C4—42no—
672C2×C3×C4—44no—
673C2×C3×C4—412no—
674C2×C3×C4—412no—
675C2×C3×C4—412no—
676C2×C3×C4—824no—
677C2×C3×C4C2×#120124yescomplemented
678C24—224no—
679C24—264no—
680C24—248no—
681C24—216no—
682C24—224no—
683C24—232no—
684C24—212no—
685C24—212no—
686C24—26no—
687C24—212no—
688C24—28no—
689C24—26no—
690C24—224no—
691C24—212no—
692C24—212no—
693C24—212no—
694C24—248no—
695C24—212no—
696C24—26no—
697C24—28no—
698C24—42no—
699C24—46no—
700C24—42no—
701C24—46no—
702C24—46no—
703C24—412no—
704C24—44no—
705C24—44no—
706C24—412no—
707C24—412no—
708C24—412no—
709C24—46no—
710C24—412no—
711C24—412no—
712C24—424no—
713C24—412no—
714C24—412no—
715C24—43no—
716C24—41no—
717C24—412no—
718C24—86no—
719C24—812no—
720C24—86no—
721C24—86no—
722C24—82no—
723C24—82no—
724C24—812no—
725C24—832no—
726C24—832no—
727C24—896no—
728C24—812no—
729C24—86no—
730C24—864no—
731C24—816no—
732C24—88no—
733C24—816no—
734C24—88no—
735C24C3×#12013yes—
736C24C3×#12016yes—
737C24C3×#12011yescharacteristic
738C24C3×#12016yes—
739C24C3×#120124yescomplemented
740C24C22×C3×D416yes—
741C24C22×C3×D413yes—
742C24C22×C3×D416yes—
743C24C22×C3×D4112yes—
744C24C22×C3×D418yes—
745C24C22×C3×D413yes—
746C24C25×C311yescharacteristic
747#41—2768no—
748#41—2192no—
749#41—2384no—
750#41—2192no—
751C2×Q8—264no—
752C2×Q8—216no—
753C2×Q8—232no—
754C2×D4—2192no—
755C2×D4—2192no—
756C2×D4—2192no—
757C2×D4—248no—
758C2×D4—296no—
759C2×D4—296no—
760C2×D4—2768no—
761C2×D4—2192no—
762C2×D4—2192no—
763C2×D4—2192no—
764C2×D4—2384no—
765C2×D4—296no—
766C2×D4—224no—
767C2×D4—224no—
768C2×D4—224no—
769C2×D4—296no—
770C2×D4—248no—
771C2×D4—224no—
772C2×D4—296no—
773C2×D4—2192no—
774C2×D4—248no—
775C2×D4—248no—
776C2×D4—248no—
777C2×D4—424no—
778C2×D4—424no—
779C2×D4—424no—
780C2×D4—448no—
781C2×D4—424no—
782C2×D4—448no—
783C2×D4—48no—
784C2×D4—412no—
785C2×D4—44no—
786C2×D4—448no—
787C2×D4—448no—
788C2×D4—824no—
789C2×D4—896no—
790C2×D4C3×#120148yescomplemented
791C2×D4C22×C3×D4148yes—
792C22×C4—224no—
793C22×C4—2192no—
794C22×C4—248no—
795C22×C4—248no—
796C22×C4—224no—
797C22×C4—296no—
798C22×C4—26no—
799C22×C4—212no—
800C22×C4—26no—
801C22×C4—212no—
802C22×C4—212no—
803C22×C4—248no—
804C22×C4—212no—
805C22×C4—26no—
806C22×C4—212no—
807C22×C4—44no—
808C22×C4—412no—
809C22×C4—46no—
810C22×C4—43no—
811C22×C4—41no—
812C22×C4—412no—
813C22×C4—412no—
814C22×C4—412no—
815C22×C4C3×#120124yescomplemented
816C22×C4C22×C3×D4112yes—
817C22⋊C4—224no—
818C22⋊C4—448no—
819C22⋊C4—424no—
820C22⋊C4—412no—
821C22⋊C4—448no—
822C22⋊C4—812no—
823C22×C3—22no—
824C22×C3—224no—
825C22×C3—28no—
826C22×C3—23no—
827C22×C3—23no—
828C22×C3—23no—
829C22×C3—22no—
830C22×C3—23no—
831C22×C3—26no—
832C22×C3—224no—
833C22×C3—26no—
834C22×C3—26no—
835C22×C3—412no—
836C22×C3—44no—
837C22×C3—424no—
838C22×C3—424no—
839C22×C3—424no—
840C22×C3—496no—
841C22×C3—424no—
842C22×C3—412no—
843C22×C3—448no—
844C22×C3—412no—
845C22×C3—412no—
846C22×C3—44no—
847C22×C3—812no—
848C22×C3—812no—
849C22×C3—812no—
850C22×C3—824no—
851C22×C3—812no—
852C22×C3—824no—
853C22×C3—848no—
854C22×C3—864no—
855C22×C3—82no—
856C22×C3—88no—
857C22×C3—82no—
858C22×C3#284616yes—
859C22×C3#284612yes—
860C22×C3C2×B(4,𝔽2)12yes—
861C22×C3C2×B(4,𝔽2)14yescomplemented
862C22×C3#302612yes—
863C22×C3C22×#12016yes—
864C22×C3C22×#12011yescharacteristic
865C3×C4—224no—
866C3×C4—44no—
867C3×C4—812no—
868C23—26no—
869C23—26no—
870C23—22no—
871C23—22no—
872C23—248no—
873C23—248no—
874C23—264no—
875C23—212no—
876C23—212no—
877C23—26no—
878C23—212no—
879C23—212no—
880C23—26no—
881C23—212no—
882C23—26no—
883C23—224no—
884C23—212no—
885C23—212no—
886C23—212no—
887C23—224no—
888C23—212no—
889C23—41no—
890C23—43no—
891C23—41no—
892C23—46no—
893C23—416no—
894C23—46no—
895C23—43no—
896C23—46no—
897C23—46no—
898C23—46no—
899C23—46no—
900C23—448no—
901C23—496no—
902C23—424no—
903C23—412no—
904C23—448no—
905C23—412no—
906C23—46no—
907C23—412no—
908C23—448no—
909C23—412no—
910C23—412no—
911C23—424no—
912C23—412no—
913C23—412no—
914C23—42no—
915C23—44no—
916C23—824no—
917C23—824no—
918C23—86no—
919C23—86no—
920C23—812no—
921C23—812no—
922C23—824no—
923C23—86no—
924C23—816no—
925C23—816no—
926C23—848no—
927C23—896no—
928C23—896no—
929C23—8128no—
930C23—848no—
931C23—864no—
932C23—816no—
933C23—816no—
934C23—848no—
935C23—82no—
936C23—86no—
937C23—82no—
938C23C3×B(4,𝔽2)14yescomplemented
939C23C2×C3×#12016yes—
940C23C2×C3×#12012yes—
941C23C2×C3×#12013yes—
942C23C2×C3×#120112yes—
943C23C2×C3×#120112yes—
944C23C2×C3×#12011yescharacteristic
945C23C2×C3×#120124yescomplemented
946C23C23×C3×D413yes—
947C23C23×C3×D414yes—
948Q8—264no—
949D4—2192no—
950D4—2192no—
951D4—296no—
952D4—296no—
953D4—448no—
954D4—416no—
955D4—896no—
956C2×C4—248no—
957C2×C4—248no—
958C2×C4—2192no—
959C2×C4—212no—
960C2×C4—212no—
961C2×C4—224no—
962C2×C4—224no—
963C2×C4—212no—
964C2×C4—46no—
965C2×C4—412no—
966C2×C4—42no—
967C2×C4—44no—
968C2×C4—412no—
969C2×C4—412no—
970C2×C4—412no—
971C2×C4—824no—
972C2×C4C2×C3×#120124yescomplemented
973C2×C3—26no—
974C2×C3—24no—
975C2×C3—26no—
976C2×C3—46no—
977C2×C3—424no—
978C2×C3—84no—
979C2×C3#3289814yesdirect product factor
980C2×C3C2×#284611yescharacteristic
981C2×C3C22×B(4,𝔽2)11yescharacteristic
982C2×C3C2×#302611yescharacteristic
983C22—224no—
984C22—28no—
985C22—23no—
986C22—23no—
987C22—23no—
988C22—22no—
989C22—23no—
990C22—22no—
991C22—26no—
992C22—26no—
993C22—26no—
994C22—224no—
995C22—44no—
996C22—412no—
997C22—424no—
998C22—424no—
999C22—424no—
1000C22—496no—
1001C22—424no—
1002C22—412no—
1003C22—448no—
1004C22—412no—
1005C22—412no—
1006C22—44no—
1007C22—812no—
1008C22—812no—
1009C22—812no—
1010C22—824no—
1011C22—812no—
1012C22—824no—
1013C22—848no—
1014C22—864no—
1015C22—88no—
1016C22—82no—
1017C22—82no—
1018C22C3×#284616yes—
1019C22C3×#284612yes—
1020C22C2×C3×B(4,𝔽2)12yes—
1021C22C2×C3×B(4,𝔽2)14yescomplemented
1022C22C3×#302612yes—
1023C22C22×C3×#12016yes—
1024C22C22×C3×#12011yescharacteristic
1025C4—224no—
1026C4—44no—
1027C4—812no—
1028C3C2×#3289811yescharacteristic, direct product factor, Sylow
1029C2—26no—
1030C2—24no—
1031C2—26no—
1032C2—46no—
1033C2—424no—
1034C2—84no—
1035C2C3×#3289814yesdirect product factor
1036C2C2×C3×#284611yescharacteristic
1037C2C22×C3×B(4,𝔽2)11yescharacteristic
1038C2C2×C3×#302611yescharacteristic
subgroupG/H
center, socleC23×C3C2×#120
commutator, Frattini, cosocleC24C25×C3
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C26×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C3×H(5,𝔽2)C2semidirect
2. C22×C3×B(4,𝔽2)C2semidirect
3. C2×C3×#2403C2semidirect
4. C3×#32898C2direct (N × H)
5. C2×C3×#1790C2semidirect
6. C2×C3×#1781C2semidirect
7. C2×#32898C3direct (N × H)
12. C22×C3×H(5,𝔽2)C22semidirect
16. C24×C3×D4C22semidirect
18. C22×C3×#120C22semidirect
20. C2×C3×B(4,𝔽2)C22semidirect
21. C22×C3×#99C22semidirect
23. C3×#2403C22semidirect
26. C2×C3×#386C22semidirect
27. C2×C3×#379C22semidirect
28. C3×#1790C22semidirect
29. C3×#1781C22semidirect
30. C23×H(5,𝔽2)C2×C3semidirect
31. C22×B(4,𝔽2)C2×C3semidirect
32. C2×#2403C2×C3semidirect
33. #32898C2×C3direct (N × H)
34. C2×#1790C2×C3semidirect
35. C2×#1781C2×C3semidirect
37. C26×C3D4semidirect
39. C26×C3C23semidirect
48. C2×C3×H(5,𝔽2)D4semidirect
71. C23×C3×D4D4semidirect
72. C23×C3×D4D4semidirect
75. C23×C3×D4C23semidirect
77. C24×C3×C4D4semidirect
78. C24×C3×C4C23semidirect
83. C2×C3×#120C23semidirect
88. C22×C3×C22⋊C4C23semidirect
91. C2×C3×#99C23semidirect
95. C3×#386C23semidirect
97. C3×#379C23semidirect
103. C22×H(5,𝔽2)C22×C3semidirect
107. C24×D4C22×C3semidirect
109. C22×#120C22×C3semidirect
111. C2×B(4,𝔽2)C22×C3semidirect
112. C22×#99C22×C3semidirect
114. #2403C22×C3semidirect
117. C2×#386C22×C3semidirect
118. C2×#379C22×C3semidirect
119. #1790C22×C3semidirect
120. #1781C22×C3semidirect
144. C25×C3C2×D4semidirect
147. C25×C3C24semidirect
154. C3×H(5,𝔽2)C2×D4semidirect
211. C22×C3×D4C2×D4semidirect
225. C23×C3×C4C2×D4semidirect
226. C23×C3×C4C24semidirect
240. C2×C3×C22⋊C4C24semidirect
244. C26C3×D4semidirect
246. C26C23×C3semidirect
255. C2×H(5,𝔽2)C3×D4semidirect
278. C23×D4C3×D4semidirect
279. C23×D4C3×D4semidirect
282. C23×D4C23×C3semidirect
284. C24×C4C3×D4semidirect
285. C24×C4C23×C3semidirect
290. C2×#120C23×C3semidirect
295. C22×C22⋊C4C23×C3semidirect
298. C2×#99C23×C3semidirect
302. #386C23×C3semidirect
304. #379C23×C3semidirect
367. C24×C3#120semidirect
418. C2×C3×D4#120semidirect
443. C22×C3×C4#120semidirect
474. C25C2×C3×D4semidirect
477. C25C24×C3semidirect
484. H(5,𝔽2)C2×C3×D4semidirect
541. C22×D4C2×C3×D4semidirect
555. C23×C4C2×C3×D4semidirect
556. C23×C4C24×C3semidirect
570. C2×C22⋊C4C24×C3semidirect
643. C23×C3B(4,𝔽2)semidirect
650. C23×C3C2×#120semidirect
677. C2×C3×C4C2×#120semidirect
739. C24C3×#120semidirect
790. C2×D4C3×#120semidirect
815. C22×C4C3×#120semidirect
861. C22×C3C2×B(4,𝔽2)semidirect
938. C23C3×B(4,𝔽2)semidirect
945. C23C2×C3×#120semidirect
972. C2×C4C2×C3×#120semidirect
979. C2×C3#32898direct (N × H)
1021. C22C2×C3×B(4,𝔽2)semidirect
1028. C3C2×#32898direct (N × H)
1035. C2C3×#32898direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×H(5,𝔽2)2
C22×C3×B(4,𝔽2)2
C2×C3×#24032
C3×#328982
C2×C3×#17902
C2×C3×#17812
C2×#328983