Finite Group Databasebeta

← C3×#111458 #72253548

Subgroups — C3×#111458 #72253548

Order 1536.

7768 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#2403C211yesmaximal, characteristic
2C2×C3×#1781C212yesmaximal, complemented
3C3×#13867C212yesmaximal, complemented
4C3×#10725C211yesmaximal, characteristic, complemented
5C2×C3×#1304C211yesmaximal, characteristic, complemented
6#111458C311yesmaximal, characteristic, direct product factor, Sylow
7C24×C3×D4C2212yes—
8C22×C3×#120—22no—
9C23×C3×C22⋊C4C2211yescharacteristic
10C22×C3×#99—24no—
11C3×#2403—22no—
12C3×#2403—24no—
13C3×#2403C414yescomplemented
14C2×C3×#392—22no—
15C2×C3×#386—22no—
16C2×C3×#386—24no—
17C2×C3×#379—22no—
18C2×C3×#379C2212yes—
19C2×C3×#379C2211yescharacteristic
20C2×C3×#379C2211yescharacteristic
21C3×#1781—24no—
22C3×#1781—24no—
23C2×C3×#342—22no—
24C3×#1438—24no—
25C3×C22⋊#95—22no—
26C3×#1304—22no—
27C2×#2403C2×C311yescharacteristic
28C2×#1781C2×C312yescomplemented
29#13867C2×C312yescomplemented
30#10725C2×C311yescharacteristic, complemented
31C2×#1304C2×C311yescharacteristic, complemented
32C26×C3D412yes—
33C26×C3C2311yescharacteristic
34C23×C3×D4—22no—
35C23×C3×D4—22no—
36C23×C3×D4—22no—
37C23×C3×D4—22no—
38C23×C3×D4—22no—
39C23×C3×D4—22no—
40C23×C3×D4—22no—
41C23×C3×D4—22no—
42C23×C3×D4—22no—
43C23×C3×D4—22no—
44C23×C3×D4—22no—
45C23×C3×D4—22no—
46C23×C3×D4—22no—
47C23×C3×D4—416no—
48C23×C3×D4C2×C414yes—
49C23×C3×D4D414yes—
50C24×C3×C4D412yes—
51C24×C3×C4D412yescomplemented
52C2×C3×#120—28no—
53C2×C3×#120—28no—
54C2×C3×#120—416no—
55C22×C3×C22⋊C4—24no—
56C22×C3×C22⋊C4—28no—
57C22×C3×C22⋊C4—21no—
58C22×C3×C22⋊C4—22no—
59C22×C3×C22⋊C4—22no—
60C22×C3×C22⋊C4—21no—
61C22×C3×C22⋊C4—22no—
62C22×C3×C22⋊C4—22no—
63C22×C3×C22⋊C4—22no—
64C22×C3×C22⋊C4—22no—
65C22×C3×C22⋊C4—21no—
66C22×C3×C22⋊C4—44no—
67C22×C3×C22⋊C4D412yes—
68C22×C3×C22⋊C4D414yescomplemented
69C2×C3×#99—216no—
70C2×C3×#99—416no—
71C3×#392—28no—
72C3×#392—28no—
73C3×#386—28no—
74C3×#386—28no—
75C3×#386—416no—
76C3×#379—22no—
77C3×#379—22no—
78C3×#379—22no—
79C3×#379—22no—
80C3×#379—22no—
81C3×#379—21no—
82C3×#379—22no—
83C3×#379—48no—
84C3×#379C2×C412yes—
85C3×#379D412yes—
86C3×#379D412yescomplemented
87C2×C3×#95—22no—
88C2×C3×#95—28no—
89C3×#342—44no—
90C24×D4C22×C312yes—
91C22×#120—22no—
92C23×C22⋊C4C22×C311yescharacteristic
93C22×#99—24no—
94#2403—22no—
95#2403—24no—
96#2403C3×C414yescomplemented
97C2×#392—22no—
98C2×#386—22no—
99C2×#386—24no—
100C2×#379—22no—
101C2×#379C22×C311yescharacteristic
102C2×#379C22×C311yescharacteristic
103C2×#379C22×C312yes—
104#1781—24no—
105#1781—24no—
106C2×#342—22no—
107#1438—24no—
108C22⋊#95—22no—
109#1304—22no—
110C25×C3—22no—
111C25×C3—22no—
112C25×C3—22no—
113C25×C3—22no—
114C25×C3—22no—
115C25×C3—22no—
116C25×C3—48no—
117C25×C3—48no—
118C25×C3—42no—
119C25×C3—42no—
120C25×C3—44no—
121C25×C3—44no—
122C25×C3—48no—
123C25×C3C22⋊C414yescomplemented
124C25×C3C22×C411yescharacteristic
125C25×C3C2×D412yes—
126C25×C3C2×D411yescharacteristic
127C25×C3C2×D411yescharacteristic
128C25×C3C2×D412yes—
129C25×C3C2×D412yes—
130C25×C3C2×D411yescharacteristic
131C25×C3C2×D411yescharacteristic
132C25×C3#4111yescharacteristic
133C25×C3#4112yes—
134C25×C3#4111yescharacteristic
135C22×C3×D4—216no—
136C22×C3×D4—216no—
137C22×C3×D4—216no—
138C22×C3×D4—24no—
139C22×C3×D4—24no—
140C22×C3×D4—24no—
141C22×C3×D4—24no—
142C22×C3×D4—24no—
143C22×C3×D4—24no—
144C22×C3×D4—24no—
145C22×C3×D4—24no—
146C22×C3×D4—24no—
147C22×C3×D4—24no—
148C22×C3×D4—24no—
149C22×C3×D4—24no—
150C22×C3×D4—28no—
151C22×C3×D4—48no—
152C22×C3×D4—48no—
153C22×C3×D4—48no—
154C22×C3×D4—416no—
155C22×C3×D4—416no—
156C22×C3×D4—416no—
157C22×C3×D4—416no—
158C22×C3×D4—416no—
159C22×C3×D4—416no—
160C22×C3×D4—416no—
161C22×C3×D4—416no—
162C22×C3×D4—48no—
163C22×C3×D4—48no—
164C22×C3×D4—48no—
165C22×C3×D4—48no—
166C22×C3×D4—48no—
167C22×C3×D4—48no—
168C22×C3×D4—42no—
169C22×C3×D4—42no—
170C22×C3×D4—42no—
171C22×C3×D4—42no—
172C22×C3×D4—42no—
173C22×C3×D4—42no—
174C22×C3×D4—42no—
175C22×C3×D4—42no—
176C22×C3×D4—42no—
177C22×C3×D4—42no—
178C22×C3×D4—42no—
179C22×C3×D4—42no—
180C22×C3×D4—42no—
181C22×C3×D4—42no—
182C22×C3×D4—42no—
183C22×C3×D4—42no—
184C22×C3×D4—416no—
185C22×C3×D4—82no—
186C22×C3×D4—82no—
187C23×C3×C4—22no—
188C23×C3×C4—22no—
189C23×C3×C4—22no—
190C23×C3×C4—22no—
191C23×C3×C4—24no—
192C23×C3×C4—22no—
193C23×C3×C4—22no—
194C23×C3×C4—22no—
195C23×C3×C4—22no—
196C23×C3×C4—24no—
197C23×C3×C4—48no—
198C23×C3×C4—44no—
199C23×C3×C4—48no—
200C23×C3×C4—41no—
201C23×C3×C4C22⋊C414yescomplemented
202C3×#120—432no—
203C3×#120—432no—
204C2×C3×C22⋊C4—28no—
205C2×C3×C22⋊C4—216no—
206C2×C3×C22⋊C4—24no—
207C2×C3×C22⋊C4—24no—
208C2×C3×C22⋊C4—24no—
209C2×C3×C22⋊C4—24no—
210C2×C3×C22⋊C4—24no—
211C2×C3×C22⋊C4—22no—
212C2×C3×C22⋊C4—22no—
213C2×C3×C22⋊C4—24no—
214C2×C3×C22⋊C4—48no—
215C2×C3×C22⋊C4—44no—
216C2×C3×C22⋊C4—416no—
217C2×C3×C22⋊C4—44no—
218C2×C3×C22⋊C4—42no—
219C2×C3×C22⋊C4—48no—
220C2×C3×C22⋊C4—41no—
221C2×C3×C22⋊C4—42no—
222C2×C3×C22⋊C4—41no—
223C2×C3×C22⋊C4—48no—
224C2×C3×C22⋊C4—42no—
225C2×C3×C22⋊C4—42no—
226C2×C3×C22⋊C4—48no—
227C2×C3×C22⋊C4—42no—
228C2×C3×C22⋊C4—42no—
229C2×C3×C22⋊C4—416no—
230C2×C3×C22⋊C4—44no—
231C2×C3×C22⋊C4—416no—
232C2×C3×C22⋊C4—48no—
233C2×C3×C22⋊C4—44no—
234C2×C3×C22⋊C4—41no—
235C2×C3×C22⋊C4—42no—
236C2×C3×C22⋊C4—42no—
237C2×C3×C22⋊C4—42no—
238C2×C3×C22⋊C4—42no—
239C2×C3×C22⋊C4—42no—
240C2×C3×C22⋊C4—88no—
241C2×C3×C22⋊C4C22⋊C414yescomplemented
242C3×#99—432no—
243C3×#95—28no—
244C3×#95—416no—
245C26C3×D412yes—
246C26C23×C311yescharacteristic
247C23×D4—22no—
248C23×D4—22no—
249C23×D4—22no—
250C23×D4—22no—
251C23×D4—22no—
252C23×D4—22no—
253C23×D4—22no—
254C23×D4—22no—
255C23×D4—22no—
256C23×D4—22no—
257C23×D4—22no—
258C23×D4—22no—
259C23×D4—22no—
260C23×D4—416no—
261C23×D4C2×C3×C414yes—
262C23×D4C3×D414yes—
263C24×C4C3×D412yes—
264C24×C4C3×D412yescomplemented
265C2×#120—28no—
266C2×#120—28no—
267C2×#120—416no—
268C22×C22⋊C4—24no—
269C22×C22⋊C4—22no—
270C22×C22⋊C4—21no—
271C22×C22⋊C4—22no—
272C22×C22⋊C4—22no—
273C22×C22⋊C4—21no—
274C22×C22⋊C4—22no—
275C22×C22⋊C4—22no—
276C22×C22⋊C4—22no—
277C22×C22⋊C4—21no—
278C22×C22⋊C4—28no—
279C22×C22⋊C4—44no—
280C22×C22⋊C4C3×D412yes—
281C22×C22⋊C4C3×D414yescomplemented
282C2×#99—216no—
283C2×#99—416no—
284#392—28no—
285#392—28no—
286#386—28no—
287#386—28no—
288#386—416no—
289#379—22no—
290#379—22no—
291#379—22no—
292#379—22no—
293#379—22no—
294#379—21no—
295#379—22no—
296#379—48no—
297#379C2×C3×C412yes—
298#379C3×D412yes—
299#379C3×D412yescomplemented
300C2×#95—22no—
301C2×#95—28no—
302#342—44no—
303C24×C3—24no—
304C24×C3—28no—
305C24×C3—28no—
306C24×C3—24no—
307C24×C3—22no—
308C24×C3—28no—
309C24×C3—22no—
310C24×C3—28no—
311C24×C3—28no—
312C24×C3—28no—
313C24×C3—24no—
314C24×C3—24no—
315C24×C3—24no—
316C24×C3—44no—
317C24×C3—41no—
318C24×C3—41no—
319C24×C3—48no—
320C24×C3—42no—
321C24×C3—44no—
322C24×C3—42no—
323C24×C3—42no—
324C24×C3—42no—
325C24×C3—44no—
326C24×C3—42no—
327C24×C3—44no—
328C24×C3—44no—
329C24×C3—44no—
330C24×C3—44no—
331C24×C3—44no—
332C24×C3—44no—
333C24×C3—41no—
334C24×C3—44no—
335C24×C3—42no—
336C24×C3—41no—
337C24×C3—44no—
338C24×C3—44no—
339C24×C3—44no—
340C24×C3—44no—
341C24×C3—44no—
342C24×C3—44no—
343C24×C3—48no—
344C24×C3—44no—
345C24×C3—44no—
346C24×C3—44no—
347C24×C3—48no—
348C24×C3—48no—
349C24×C3—48no—
350C24×C3—48no—
351C24×C3—48no—
352C24×C3—48no—
353C24×C3—48no—
354C24×C3—42no—
355C24×C3—42no—
356C24×C3—42no—
357C24×C3—42no—
358C24×C3—48no—
359C24×C3—44no—
360C24×C3—44no—
361C24×C3—84no—
362C24×C3—84no—
363C24×C3—82no—
364C24×C3—84no—
365C24×C3—84no—
366C24×C3—82no—
367C24×C3—84no—
368C24×C3—816no—
369C24×C3—816no—
370C24×C3—832no—
371C24×C3—832no—
372C24×C3C2×C22⋊C412yes—
373C24×C3C2×C22⋊C411yescharacteristic
374C24×C3C4×D411yescharacteristic
375C24×C3C4×D412yes—
376C24×C3C4×D411yescharacteristic
377C24×C3#12012yes—
378C24×C3#12011yescharacteristic
379C24×C3#12012yes—
380C24×C3#12011yescharacteristic
381C24×C3#12012yes—
382C24×C3#12112yes—
383C24×C3#12111yescharacteristic
384C24×C3#12112yes—
385C24×C3#12112yes—
386C24×C3#12112yes—
387C24×C3#12112yes—
388C24×C3#12111yescharacteristic
389C24×C3#12312yes—
390C24×C3#12312yes—
391C24×C3#12411yescharacteristic
392C24×C3#12411yescharacteristic
393C24×C3#12711yescharacteristic
394C24×C3#12711yescharacteristic
395C2×C3×D4—216no—
396C2×C3×D4—216no—
397C2×C3×D4—216no—
398C2×C3×D4—216no—
399C2×C3×D4—216no—
400C2×C3×D4—216no—
401C2×C3×D4—48no—
402C2×C3×D4—48no—
403C2×C3×D4—48no—
404C2×C3×D4—48no—
405C2×C3×D4—48no—
406C2×C3×D4—48no—
407C2×C3×D4—48no—
408C2×C3×D4—48no—
409C2×C3×D4—48no—
410C2×C3×D4—48no—
411C2×C3×D4—48no—
412C2×C3×D4—48no—
413C2×C3×D4—48no—
414C2×C3×D4—416no—
415C2×C3×D4—48no—
416C2×C3×D4—416no—
417C2×C3×D4—416no—
418C2×C3×D4—48no—
419C2×C3×D4—48no—
420C2×C3×D4—416no—
421C2×C3×D4—48no—
422C2×C3×D4—416no—
423C2×C3×D4—48no—
424C2×C3×D4—416no—
425C2×C3×D4—416no—
426C2×C3×D4—416no—
427C2×C3×D4—416no—
428C2×C3×D4—416no—
429C2×C3×D4—416no—
430C2×C3×D4—416no—
431C2×C3×D4—416no—
432C2×C3×D4—416no—
433C2×C3×D4—416no—
434C2×C3×D4—44no—
435C2×C3×D4—44no—
436C2×C3×D4—44no—
437C2×C3×D4—44no—
438C2×C3×D4—44no—
439C2×C3×D4—44no—
440C2×C3×D4—44no—
441C2×C3×D4—44no—
442C2×C3×D4—416no—
443C2×C3×D4—432no—
444C2×C3×D4—88no—
445C2×C3×D4—816no—
446C2×C3×D4—816no—
447C22×C3×C4—28no—
448C22×C3×C4—28no—
449C22×C3×C4—28no—
450C22×C3×C4—24no—
451C22×C3×C4—24no—
452C22×C3×C4—24no—
453C22×C3×C4—28no—
454C22×C3×C4—24no—
455C22×C3×C4—24no—
456C22×C3×C4—48no—
457C22×C3×C4—48no—
458C22×C3×C4—48no—
459C22×C3×C4—48no—
460C22×C3×C4—44no—
461C22×C3×C4—44no—
462C22×C3×C4—44no—
463C22×C3×C4—42no—
464C22×C3×C4—42no—
465C22×C3×C4—42no—
466C22×C3×C4—42no—
467C22×C3×C4—48no—
468C22×C3×C4—44no—
469C22×C3×C4—42no—
470C22×C3×C4—48no—
471C22×C3×C4—42no—
472C22×C3×C4—42no—
473C22×C3×C4—48no—
474C22×C3×C4—42no—
475C22×C3×C4—48no—
476C22×C3×C4—44no—
477C22×C3×C4—44no—
478C22×C3×C4—42no—
479C22×C3×C4—44no—
480C22×C3×C4—48no—
481C22×C3×C4—816no—
482C22×C3×C4—84no—
483C22×C3×C4—81no—
484C22×C3×C4—84no—
485C22×C3×C4—81no—
486C3×C22⋊C4—432no—
487C3×C22⋊C4—44no—
488C3×C22⋊C4—48no—
489C3×C22⋊C4—48no—
490C3×C22⋊C4—48no—
491C3×C22⋊C4—44no—
492C3×C22⋊C4—44no—
493C3×C22⋊C4—48no—
494C3×C22⋊C4—48no—
495C3×C22⋊C4—44no—
496C3×C22⋊C4—82no—
497C3×C22⋊C4—832no—
498C3×C22⋊C4—84no—
499C3×C22⋊C4—82no—
500C3×C22⋊C4—84no—
501C3×C22⋊C4—84no—
502C3×C22⋊C4—84no—
503C3×C22⋊C4—84no—
504C3×C22⋊C4—84no—
505C25—22no—
506C25—22no—
507C25—22no—
508C25—22no—
509C25—22no—
510C25—22no—
511C25—42no—
512C25—48no—
513C25—48no—
514C25—42no—
515C25—48no—
516C25—44no—
517C25—44no—
518C25C3×C22⋊C414yescomplemented
519C25C22×C3×C411yescharacteristic
520C25C2×C3×D412yes—
521C25C2×C3×D411yescharacteristic
522C25C2×C3×D411yescharacteristic
523C25C2×C3×D412yes—
524C25C2×C3×D412yes—
525C25C2×C3×D411yescharacteristic
526C25C2×C3×D411yescharacteristic
527C25C3×#4111yescharacteristic
528C25C3×#4111yescharacteristic
529C25C3×#4112yes—
530C22×D4—216no—
531C22×D4—216no—
532C22×D4—216no—
533C22×D4—24no—
534C22×D4—24no—
535C22×D4—24no—
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—24no—
539C22×D4—24no—
540C22×D4—24no—
541C22×D4—24no—
542C22×D4—24no—
543C22×D4—24no—
544C22×D4—24no—
545C22×D4—28no—
546C22×D4—48no—
547C22×D4—48no—
548C22×D4—48no—
549C22×D4—416no—
550C22×D4—416no—
551C22×D4—416no—
552C22×D4—416no—
553C22×D4—416no—
554C22×D4—416no—
555C22×D4—416no—
556C22×D4—416no—
557C22×D4—48no—
558C22×D4—48no—
559C22×D4—48no—
560C22×D4—48no—
561C22×D4—48no—
562C22×D4—48no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4—42no—
566C22×D4—42no—
567C22×D4—42no—
568C22×D4—42no—
569C22×D4—42no—
570C22×D4—42no—
571C22×D4—42no—
572C22×D4—42no—
573C22×D4—42no—
574C22×D4—42no—
575C22×D4—42no—
576C22×D4—42no—
577C22×D4—42no—
578C22×D4—42no—
579C22×D4—416no—
580C22×D4—82no—
581C22×D4—82no—
582C23×C4—22no—
583C23×C4—22no—
584C23×C4—22no—
585C23×C4—22no—
586C23×C4—24no—
587C23×C4—22no—
588C23×C4—22no—
589C23×C4—22no—
590C23×C4—22no—
591C23×C4—24no—
592C23×C4—48no—
593C23×C4—44no—
594C23×C4—48no—
595C23×C4—41no—
596C23×C4C3×C22⋊C414yescomplemented
597#120—432no—
598#120—432no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—28no—
601C2×C22⋊C4—216no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—48no—
610C2×C22⋊C4—44no—
611C2×C22⋊C4—416no—
612C2×C22⋊C4—44no—
613C2×C22⋊C4—42no—
614C2×C22⋊C4—48no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—42no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—42no—
619C2×C22⋊C4—42no—
620C2×C22⋊C4—48no—
621C2×C22⋊C4—42no—
622C2×C22⋊C4—48no—
623C2×C22⋊C4—42no—
624C2×C22⋊C4—416no—
625C2×C22⋊C4—44no—
626C2×C22⋊C4—416no—
627C2×C22⋊C4—48no—
628C2×C22⋊C4—44no—
629C2×C22⋊C4—41no—
630C2×C22⋊C4—42no—
631C2×C22⋊C4—42no—
632C2×C22⋊C4—42no—
633C2×C22⋊C4—42no—
634C2×C22⋊C4—42no—
635C2×C22⋊C4—88no—
636C2×C22⋊C4C3×C22⋊C414yescomplemented
637#99—432no—
638#95—28no—
639#95—416no—
640C23×C3—22no—
641C23×C3—24no—
642C23×C3—24no—
643C23×C3—22no—
644C23×C3—24no—
645C23×C3—24no—
646C23×C3—24no—
647C23×C3—24no—
648C23×C3—21no—
649C23×C3—22no—
650C23×C3—24no—
651C23×C3—24no—
652C23×C3—21no—
653C23×C3—24no—
654C23×C3—24no—
655C23×C3—24no—
656C23×C3—24no—
657C23×C3—24no—
658C23×C3—24no—
659C23×C3—21no—
660C23×C3—22no—
661C23×C3—21no—
662C23×C3—24no—
663C23×C3—24no—
664C23×C3—24no—
665C23×C3—24no—
666C23×C3—24no—
667C23×C3—24no—
668C23×C3—24no—
669C23×C3—24no—
670C23×C3—22no—
671C23×C3—22no—
672C23×C3—22no—
673C23×C3—22no—
674C23×C3—28no—
675C23×C3—28no—
676C23×C3—28no—
677C23×C3—42no—
678C23×C3—42no—
679C23×C3—42no—
680C23×C3—42no—
681C23×C3—41no—
682C23×C3—42no—
683C23×C3—41no—
684C23×C3—42no—
685C23×C3—42no—
686C23×C3—42no—
687C23×C3—42no—
688C23×C3—42no—
689C23×C3—42no—
690C23×C3—42no—
691C23×C3—42no—
692C23×C3—42no—
693C23×C3—42no—
694C23×C3—42no—
695C23×C3—42no—
696C23×C3—42no—
697C23×C3—41no—
698C23×C3—42no—
699C23×C3—42no—
700C23×C3—42no—
701C23×C3—42no—
702C23×C3—41no—
703C23×C3—48no—
704C23×C3—48no—
705C23×C3—416no—
706C23×C3—416no—
707C23×C3—48no—
708C23×C3—416no—
709C23×C3—44no—
710C23×C3—44no—
711C23×C3—48no—
712C23×C3—48no—
713C23×C3—44no—
714C23×C3—48no—
715C23×C3—416no—
716C23×C3—416no—
717C23×C3—48no—
718C23×C3—416no—
719C23×C3—48no—
720C23×C3—44no—
721C23×C3—48no—
722C23×C3—48no—
723C23×C3—88no—
724C23×C3—84no—
725C23×C3—84no—
726C23×C3—88no—
727C23×C3—84no—
728C23×C3—84no—
729C23×C3—88no—
730C23×C3—88no—
731C23×C3—88no—
732C23×C3—88no—
733C23×C3—84no—
734C23×C3—84no—
735C23×C3—84no—
736C23×C3—84no—
737C23×C3—88no—
738C23×C3—88no—
739C23×C3—88no—
740C23×C3—816no—
741C23×C3—816no—
742C23×C3—88no—
743C23×C3—832no—
744C23×C3—84no—
745C23×C3—84no—
746C23×C3—832no—
747C23×C3—832no—
748C23×C3—88no—
749C23×C3—88no—
750C23×C3—832no—
751C23×C3—88no—
752C23×C3—88no—
753C23×C3—84no—
754C23×C3—82no—
755C23×C3—84no—
756C23×C3—82no—
757C23×C3—84no—
758C23×C3#37911yescharacteristic
759C23×C3#38612yes—
760C23×C3#38612yes—
761C23×C3#39011yescharacteristic
762C23×C3#39011yescharacteristic
763C23×C3#39211yescharacteristic
764C23×C3#39212yes—
765C23×C3#39211yescharacteristic
766C23×C3#39412yes—
767C23×C3#39411yescharacteristic
768C23×C3#39411yescharacteristic
769C23×C3B(4,𝔽2)18yes—
770C23×C3B(4,𝔽2)12yes—
771C23×C3#45812yes—
772C3×D4—416no—
773C3×D4—416no—
774C3×D4—416no—
775C3×D4—416no—
776C3×D4—416no—
777C3×D4—416no—
778C3×D4—416no—
779C3×D4—416no—
780C3×D4—832no—
781C2×C3×C4—28no—
782C2×C3×C4—28no—
783C2×C3×C4—28no—
784C2×C3×C4—44no—
785C2×C3×C4—44no—
786C2×C3×C4—48no—
787C2×C3×C4—48no—
788C2×C3×C4—44no—
789C2×C3×C4—48no—
790C2×C3×C4—44no—
791C2×C3×C4—48no—
792C2×C3×C4—48no—
793C2×C3×C4—416no—
794C2×C3×C4—44no—
795C2×C3×C4—44no—
796C2×C3×C4—88no—
797C2×C3×C4—84no—
798C2×C3×C4—84no—
799C2×C3×C4—84no—
800C2×C3×C4—84no—
801C2×C3×C4—84no—
802C2×C3×C4—84no—
803C2×C3×C4—82no—
804C2×C3×C4—88no—
805C2×C3×C4—84no—
806C2×C3×C4—84no—
807C2×C3×C4—88no—
808C2×C3×C4—84no—
809C2×C3×C4—162no—
810C2×C3×C4—162no—
811C24—24no—
812C24—28no—
813C24—28no—
814C24—24no—
815C24—22no—
816C24—28no—
817C24—22no—
818C24—28no—
819C24—28no—
820C24—28no—
821C24—24no—
822C24—24no—
823C24—24no—
824C24—41no—
825C24—44no—
826C24—41no—
827C24—42no—
828C24—41no—
829C24—48no—
830C24—44no—
831C24—44no—
832C24—44no—
833C24—44no—
834C24—44no—
835C24—44no—
836C24—44no—
837C24—44no—
838C24—44no—
839C24—44no—
840C24—44no—
841C24—42no—
842C24—42no—
843C24—42no—
844C24—42no—
845C24—44no—
846C24—41no—
847C24—44no—
848C24—42no—
849C24—44no—
850C24—48no—
851C24—44no—
852C24—44no—
853C24—44no—
854C24—48no—
855C24—48no—
856C24—48no—
857C24—44no—
858C24—48no—
859C24—48no—
860C24—48no—
861C24—48no—
862C24—42no—
863C24—42no—
864C24—42no—
865C24—42no—
866C24—48no—
867C24—44no—
868C24—44no—
869C24—84no—
870C24—84no—
871C24—82no—
872C24—84no—
873C24—84no—
874C24—82no—
875C24—84no—
876C24—816no—
877C24—816no—
878C24—832no—
879C24—832no—
880C24C2×C3×C22⋊C412yes—
881C24C2×C3×C22⋊C411yescharacteristic
882C24C3×C4×D411yescharacteristic
883C24C3×C4×D412yes—
884C24C3×C4×D411yescharacteristic
885C24C3×#12012yes—
886C24C3×#12011yescharacteristic
887C24C3×#12012yes—
888C24C3×#12011yescharacteristic
889C24C3×#12012yes—
890C24C3×#12112yes—
891C24C3×#12111yescharacteristic
892C24C3×#12112yes—
893C24C3×#12112yes—
894C24C3×#12112yes—
895C24C3×#12112yes—
896C24C3×#12111yescharacteristic
897C24C3×#12312yes—
898C24C3×#12312yes—
899C24C3×#12411yescharacteristic
900C24C3×#12411yescharacteristic
901C24C3×#12711yescharacteristic
902C24C3×#12711yescharacteristic
903C2×D4—216no—
904C2×D4—216no—
905C2×D4—216no—
906C2×D4—216no—
907C2×D4—216no—
908C2×D4—216no—
909C2×D4—48no—
910C2×D4—48no—
911C2×D4—48no—
912C2×D4—48no—
913C2×D4—48no—
914C2×D4—48no—
915C2×D4—48no—
916C2×D4—48no—
917C2×D4—48no—
918C2×D4—48no—
919C2×D4—48no—
920C2×D4—48no—
921C2×D4—48no—
922C2×D4—416no—
923C2×D4—48no—
924C2×D4—416no—
925C2×D4—48no—
926C2×D4—416no—
927C2×D4—48no—
928C2×D4—416no—
929C2×D4—48no—
930C2×D4—416no—
931C2×D4—416no—
932C2×D4—48no—
933C2×D4—416no—
934C2×D4—416no—
935C2×D4—416no—
936C2×D4—416no—
937C2×D4—416no—
938C2×D4—416no—
939C2×D4—416no—
940C2×D4—416no—
941C2×D4—416no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—416no—
951C2×D4—432no—
952C2×D4—88no—
953C2×D4—816no—
954C2×D4—816no—
955C22×C4—28no—
956C22×C4—28no—
957C22×C4—28no—
958C22×C4—24no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—28no—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—48no—
965C22×C4—48no—
966C22×C4—48no—
967C22×C4—48no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—48no—
976C22×C4—44no—
977C22×C4—42no—
978C22×C4—48no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—48no—
982C22×C4—42no—
983C22×C4—48no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—42no—
987C22×C4—44no—
988C22×C4—48no—
989C22×C4—816no—
990C22×C4—84no—
991C22×C4—81no—
992C22×C4—84no—
993C22×C4—81no—
994C22⋊C4—432no—
995C22⋊C4—44no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—48no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—48no—
1002C22⋊C4—48no—
1003C22⋊C4—44no—
1004C22⋊C4—82no—
1005C22⋊C4—832no—
1006C22⋊C4—82no—
1007C22⋊C4—84no—
1008C22⋊C4—84no—
1009C22⋊C4—84no—
1010C22⋊C4—84no—
1011C22⋊C4—84no—
1012C22⋊C4—84no—
1013C22×C3—28no—
1014C22×C3—24no—
1015C22×C3—24no—
1016C22×C3—28no—
1017C22×C3—22no—
1018C22×C3—22no—
1019C22×C3—22no—
1020C22×C3—22no—
1021C22×C3—22no—
1022C22×C3—22no—
1023C22×C3—22no—
1024C22×C3—22no—
1025C22×C3—22no—
1026C22×C3—22no—
1027C22×C3—22no—
1028C22×C3—22no—
1029C22×C3—22no—
1030C22×C3—22no—
1031C22×C3—21no—
1032C22×C3—22no—
1033C22×C3—22no—
1034C22×C3—21no—
1035C22×C3—21no—
1036C22×C3—21no—
1037C22×C3—44no—
1038C22×C3—48no—
1039C22×C3—44no—
1040C22×C3—48no—
1041C22×C3—48no—
1042C22×C3—48no—
1043C22×C3—48no—
1044C22×C3—416no—
1045C22×C3—416no—
1046C22×C3—42no—
1047C22×C3—42no—
1048C22×C3—44no—
1049C22×C3—42no—
1050C22×C3—42no—
1051C22×C3—44no—
1052C22×C3—48no—
1053C22×C3—82no—
1054C22×C3—82no—
1055C22×C3—84no—
1056C22×C3—84no—
1057C22×C3—84no—
1058C22×C3—84no—
1059C22×C3—82no—
1060C22×C3—82no—
1061C22×C3—88no—
1062C22×C3—816no—
1063C22×C3—88no—
1064C22×C3—816no—
1065C22×C3—82no—
1066C22×C3—84no—
1067C22×C3—82no—
1068C22×C3—88no—
1069C22×C3—88no—
1070C22×C3—816no—
1071C22×C3—88no—
1072C22×C3—88no—
1073C22×C3—84no—
1074C22×C3—84no—
1075C22×C3#143811yescharacteristic
1076C22×C3#179012yes—
1077C22×C3#188914yes—
1078C22×C3#202114yes—
1079C22×C3#202111yescharacteristic
1080C22×C3#202114yes—
1081C22×C3#202211yescharacteristic
1082C22×C3#204412yes—
1083C3×C4—48no—
1084C3×C4—84no—
1085C3×C4—84no—
1086C3×C4—164no—
1087C3×C4—162no—
1088C23—22no—
1089C23—24no—
1090C23—24no—
1091C23—22no—
1092C23—21no—
1093C23—22no—
1094C23—24no—
1095C23—24no—
1096C23—21no—
1097C23—24no—
1098C23—24no—
1099C23—24no—
1100C23—24no—
1101C23—24no—
1102C23—24no—
1103C23—21no—
1104C23—22no—
1105C23—21no—
1106C23—24no—
1107C23—24no—
1108C23—24no—
1109C23—24no—
1110C23—24no—
1111C23—24no—
1112C23—24no—
1113C23—24no—
1114C23—24no—
1115C23—24no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—24no—
1121C23—24no—
1122C23—28no—
1123C23—28no—
1124C23—28no—
1125C23—42no—
1126C23—42no—
1127C23—42no—
1128C23—42no—
1129C23—41no—
1130C23—42no—
1131C23—41no—
1132C23—42no—
1133C23—42no—
1134C23—42no—
1135C23—42no—
1136C23—42no—
1137C23—42no—
1138C23—42no—
1139C23—42no—
1140C23—42no—
1141C23—42no—
1142C23—42no—
1143C23—42no—
1144C23—42no—
1145C23—41no—
1146C23—42no—
1147C23—42no—
1148C23—42no—
1149C23—42no—
1150C23—41no—
1151C23—48no—
1152C23—416no—
1153C23—416no—
1154C23—48no—
1155C23—48no—
1156C23—416no—
1157C23—44no—
1158C23—44no—
1159C23—48no—
1160C23—48no—
1161C23—44no—
1162C23—48no—
1163C23—416no—
1164C23—416no—
1165C23—48no—
1166C23—416no—
1167C23—48no—
1168C23—48no—
1169C23—48no—
1170C23—44no—
1171C23—88no—
1172C23—84no—
1173C23—84no—
1174C23—88no—
1175C23—84no—
1176C23—84no—
1177C23—88no—
1178C23—88no—
1179C23—88no—
1180C23—88no—
1181C23—84no—
1182C23—84no—
1183C23—84no—
1184C23—84no—
1185C23—88no—
1186C23—88no—
1187C23—816no—
1188C23—88no—
1189C23—816no—
1190C23—88no—
1191C23—832no—
1192C23—84no—
1193C23—84no—
1194C23—832no—
1195C23—832no—
1196C23—88no—
1197C23—88no—
1198C23—832no—
1199C23—88no—
1200C23—88no—
1201C23—84no—
1202C23—82no—
1203C23—84no—
1204C23—82no—
1205C23—84no—
1206C23C3×#37911yescharacteristic
1207C23C3×#38612yes—
1208C23C3×#38612yes—
1209C23C3×#39011yescharacteristic
1210C23C3×#39011yescharacteristic
1211C23C3×#39211yescharacteristic
1212C23C3×#39212yes—
1213C23C3×#39211yescharacteristic
1214C23C3×#39412yes—
1215C23C3×#39411yescharacteristic
1216C23C3×#39411yescharacteristic
1217C23C3×B(4,𝔽2)18yes—
1218C23C3×B(4,𝔽2)12yes—
1219C23C3×#45812yes—
1220D4—416no—
1221D4—416no—
1222D4—416no—
1223D4—416no—
1224D4—416no—
1225D4—416no—
1226D4—416no—
1227D4—416no—
1228D4—832no—
1229C2×C4—28no—
1230C2×C4—28no—
1231C2×C4—28no—
1232C2×C4—44no—
1233C2×C4—44no—
1234C2×C4—48no—
1235C2×C4—48no—
1236C2×C4—44no—
1237C2×C4—48no—
1238C2×C4—48no—
1239C2×C4—44no—
1240C2×C4—48no—
1241C2×C4—416no—
1242C2×C4—44no—
1243C2×C4—44no—
1244C2×C4—88no—
1245C2×C4—84no—
1246C2×C4—84no—
1247C2×C4—84no—
1248C2×C4—84no—
1249C2×C4—84no—
1250C2×C4—84no—
1251C2×C4—82no—
1252C2×C4—88no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4—88no—
1256C2×C4—84no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C3—22no—
1260C2×C3—24no—
1261C2×C3—24no—
1262C2×C3—22no—
1263C2×C3—41no—
1264C2×C3—41no—
1265C2×C3—41no—
1266C2×C3—42no—
1267C2×C3—42no—
1268C2×C3—41no—
1269C2×C3—88no—
1270C2×C3#1033612yes—
1271C2×C3#1033712yes—
1272C2×C3#1099112yes—
1273C2×C3#1099511yescharacteristic
1274C22—28no—
1275C22—24no—
1276C22—24no—
1277C22—28no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—21no—
1293C22—22no—
1294C22—22no—
1295C22—21no—
1296C22—21no—
1297C22—21no—
1298C22—48no—
1299C22—48no—
1300C22—48no—
1301C22—48no—
1302C22—44no—
1303C22—48no—
1304C22—44no—
1305C22—416no—
1306C22—416no—
1307C22—42no—
1308C22—42no—
1309C22—44no—
1310C22—42no—
1311C22—44no—
1312C22—42no—
1313C22—48no—
1314C22—82no—
1315C22—82no—
1316C22—84no—
1317C22—84no—
1318C22—84no—
1319C22—84no—
1320C22—82no—
1321C22—82no—
1322C22—88no—
1323C22—816no—
1324C22—88no—
1325C22—816no—
1326C22—82no—
1327C22—84no—
1328C22—82no—
1329C22—88no—
1330C22—88no—
1331C22—816no—
1332C22—88no—
1333C22—88no—
1334C22—84no—
1335C22—84no—
1336C22C3×#143811yescharacteristic
1337C22C3×#179012yes—
1338C22C3×#188914yes—
1339C22C3×#202114yes—
1340C22C3×#202111yescharacteristic
1341C22C3×#202114yes—
1342C22C3×#202211yescharacteristic
1343C22C3×#204412yes—
1344C4—48no—
1345C4—84no—
1346C4—84no—
1347C4—164no—
1348C4—162no—
1349C3#11145811yescharacteristic, direct product factor, Sylow
1350C2—22no—
1351C2—24no—
1352C2—24no—
1353C2—22no—
1354C2—41no—
1355C2—42no—
1356C2—42no—
1357C2—41no—
1358C2—41no—
1359C2—41no—
1360C2—88no—
1361C2C3×#1033612yes—
1362C2C3×#1033712yes—
1363C2C3×#1099112yes—
1364C2C3×#1099511yescharacteristic
subgroupG/H
center, socleC23×C3#392
commutatorC25C22×C3×C4
Frattini, cosocleC26C23×C3
prime radicalC2×C3×#2403C2
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C23×C3 ◁ C26×C3 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#1781C2semidirect
3. C3×#13867C2semidirect
4. C3×#10725C2semidirect
5. C2×C3×#1304C2semidirect
6. #111458C3direct (N × H)
13. C3×#2403C4semidirect
28. C2×#1781C2×C3semidirect
29. #13867C2×C3semidirect
30. #10725C2×C3semidirect
31. C2×#1304C2×C3semidirect
51. C24×C3×C4D4semidirect
68. C22×C3×C22⋊C4D4semidirect
86. C3×#379D4semidirect
96. #2403C3×C4semidirect
123. C25×C3C22⋊C4semidirect
201. C23×C3×C4C22⋊C4semidirect
241. C2×C3×C22⋊C4C22⋊C4semidirect
264. C24×C4C3×D4semidirect
281. C22×C22⋊C4C3×D4semidirect
299. #379C3×D4semidirect
518. C25C3×C22⋊C4semidirect
596. C23×C4C3×C22⋊C4semidirect
636. C2×C22⋊C4C3×C22⋊C4semidirect
1349. C3#111458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#24032
C2×C3×#17812
C3×#138672
C3×#107252
C2×C3×#13042
#1114583