Finite Group Databasebeta

← C3×#146479 #72271312

Subgroups — C3×#146479 #72271312

Order 1536.

4952 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#34171C211yesmaximal, characteristic
2C2×C3×#1781C212yesmaximal
3C3×#12582C214yesmaximal, complemented
4#146479C311yesmaximal, characteristic, direct product factor, Sylow
5C24×C3×D4C2211yescharacteristic
6C2×C3×#518C411yescharacteristic, complemented
7C2×C3×#518C411yescharacteristic, complemented
8C22×C3×#99—22no—
9C22×C3×#99C2214yes—
10C3×D4×C22⋊C4—28no—
11C3×#2309C2212yes—
12C3×#2308—22no—
13C3×#2280C412yescomplemented
14C2×C3×#379—22no—
15C2×C3×#379—22no—
16C3×#1781—24no—
17C3×#1781C418yescomplemented
18C3×#1393—28no—
19#34171C2×C311yescharacteristic
20C2×#1781C2×C312yes—
21#12582C2×C314yescomplemented
22C26×C3D412yes—
23C23×C3×D4—24no—
24C23×C3×D4—24no—
25C23×C3×D4—44no—
26C23×C3×D4—44no—
27C23×C3×D4C2×C411yescharacteristic
28C23×C3×D4C2×C414yes—
29C23×C3×D4D412yes—
30C23×C3×D4D412yes—
31C23×C3×D4Q812yes—
32C23×C3×D4C2311yescharacteristic
33C24×C3×C4C2×C411yescharacteristic
34C3×#518—44no—
35C3×#518—44no—
36C2×C3×C4×D4—24no—
37C2×C3×C4×D4—24no—
38C2×C3×#117C2×C412yes—
39C2×C3×#117C2×C412yes—
40C22×C3×C22⋊C4—28no—
41C22×C3×C22⋊C4—22no—
42C22×C3×C22⋊C4—22no—
43C22×C3×C22⋊C4—24no—
44C22×C3×C22⋊C4—44no—
45C2×C3×#99—28no—
46C2×C3×#99—28no—
47C2×C3×#99—28no—
48C2×C3×#99—24no—
49C2×C3×#99—44no—
50C2×C3×#99—44no—
51C2×C3×#99C2×C418yescomplemented
52C3×#390—24no—
53C3×#390D418yes—
54C3×#386—28no—
55C3×#386—28no—
56C3×#381—22no—
57C3×#380—24no—
58C3×#379—28no—
59C3×#379—22no—
60C3×#379—28no—
61C3×#379—24no—
62C3×#379—44no—
63C3×C4×C22⋊C4—24no—
64C24×D4C22×C311yescharacteristic
65C2×#518C3×C411yescharacteristic, complemented
66C2×#518C3×C411yescharacteristic, complemented
67C22×#99—22no—
68C22×#99C22×C314yes—
69D4×C22⋊C4—28no—
70#2309C22×C312yes—
71#2308—22no—
72#2280C3×C412yescomplemented
73C2×#379—22no—
74C2×#379—22no—
75#1781—24no—
76#1781C3×C418yescomplemented
77#1393—28no—
78C25×C3—24no—
79C25×C3—24no—
80C25×C3—24no—
81C25×C3—24no—
82C25×C3—42no—
83C25×C3—42no—
84C25×C3—88no—
85C25×C3C22⋊C411yescharacteristic
86C25×C3C22⋊C414yes—
87C25×C3C22⋊C412yes—
88C25×C3C4⋊C414yes—
89C25×C3C2×D412yes—
90C22×C3×D4—24no—
91C22×C3×D4—24no—
92C22×C3×D4—24no—
93C22×C3×D4—24no—
94C22×C3×D4—24no—
95C22×C3×D4—24no—
96C22×C3×D4—216no—
97C22×C3×D4—28no—
98C22×C3×D4—28no—
99C22×C3×D4—22no—
100C22×C3×D4—22no—
101C22×C3×D4—42no—
102C22×C3×D4—42no—
103C22×C3×D4—42no—
104C22×C3×D4—42no—
105C22×C3×D4—48no—
106C22×C3×D4—48no—
107C22×C3×D4—48no—
108C22×C3×D4—48no—
109C22×C3×D4—416no—
110C22×C3×D4—416no—
111C22×C3×D4—432no—
112C22×C3×D4C4212yes—
113C22×C3×D4C22⋊C414yes—
114C22×C3×D4C4⋊C414yes—
115C22×C3×D4C4⋊C412yes—
116C22×C3×D4C22×C412yes—
117C22×C3×D4C2×D414yes—
118C22×C3×D4C2×D411yescharacteristic
119C22×C3×D4C2×Q811yescharacteristic
120C22×C3×D4#4114yes—
121C23×C3×C4—22no—
122C23×C3×C4—22no—
123C23×C3×C4—24no—
124C23×C3×C4—24no—
125C23×C3×C4—42no—
126C23×C3×C4—42no—
127C23×C3×C4—44no—
128C23×C3×C4C4212yes—
129C23×C3×C4C22⋊C411yescharacteristic
130C23×C3×C4C4⋊C412yes—
131C23×C3×C4C22×C411yescharacteristic
132C3×C4×D4—416no—
133C3×C4×D4—416no—
134C3×#117—44no—
135C3×#117—44no—
136C2×C3×C4⋊C4—22no—
137C2×C3×C4⋊C4C22⋊C414yescomplemented
138C2×C3×C22⋊C4—28no—
139C2×C3×C22⋊C4—24no—
140C2×C3×C22⋊C4—24no—
141C2×C3×C22⋊C4—22no—
142C2×C3×C22⋊C4—22no—
143C2×C3×C22⋊C4—28no—
144C2×C3×C22⋊C4—216no—
145C2×C3×C22⋊C4—44no—
146C2×C3×C22⋊C4—44no—
147C2×C3×C22⋊C4—44no—
148C2×C3×C22⋊C4—44no—
149C2×C3×C22⋊C4—44no—
150C2×C3×C22⋊C4—44no—
151C2×C3×C22⋊C4—44no—
152C2×C3×C22⋊C4—44no—
153C2×C3×C22⋊C4—416no—
154C2×C3×C22⋊C4—44no—
155C2×C3×C22⋊C4—816no—
156C2×C3×C22⋊C4—816no—
157C2×C3×C42—22no—
158C2×C3×C42C22⋊C414yescomplemented
159C3×#99—216no—
160C3×#99—416no—
161C3×#99—48no—
162C3×#95—28no—
163C26C3×D412yes—
164C23×D4—24no—
165C23×D4—24no—
166C23×D4—44no—
167C23×D4—44no—
168C23×D4C2×C3×C414yes—
169C23×D4C2×C3×C411yescharacteristic
170C23×D4C3×D412yes—
171C23×D4C3×D412yes—
172C23×D4C3×Q812yes—
173C23×D4C23×C311yescharacteristic
174C24×C4C2×C3×C411yescharacteristic
175#518—44no—
176#518—44no—
177C2×C4×D4—24no—
178C2×C4×D4—24no—
179C2×#117C2×C3×C412yes—
180C2×#117C2×C3×C412yes—
181C22×C22⋊C4—22no—
182C22×C22⋊C4—22no—
183C22×C22⋊C4—28no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—44no—
186C2×#99—28no—
187C2×#99—28no—
188C2×#99—28no—
189C2×#99—24no—
190C2×#99—44no—
191C2×#99—44no—
192C2×#99C2×C3×C418yescomplemented
193#390—24no—
194#390C3×D418yes—
195#386—28no—
196#386—28no—
197#381—22no—
198#380—24no—
199#379—28no—
200#379—22no—
201#379—24no—
202#379—28no—
203#379—44no—
204C4×C22⋊C4—24no—
205C24×C3—21no—
206C24×C3—22no—
207C24×C3—22no—
208C24×C3—22no—
209C24×C3—22no—
210C24×C3—22no—
211C24×C3—22no—
212C24×C3—22no—
213C24×C3—22no—
214C24×C3—22no—
215C24×C3—21no—
216C24×C3—22no—
217C24×C3—28no—
218C24×C3—28no—
219C24×C3—28no—
220C24×C3—28no—
221C24×C3—44no—
222C24×C3—44no—
223C24×C3—44no—
224C24×C3—48no—
225C24×C3—48no—
226C24×C3—48no—
227C24×C3—48no—
228C24×C3—416no—
229C24×C3—416no—
230C24×C3—88no—
231C24×C3—88no—
232C24×C3—84no—
233C24×C3—88no—
234C24×C3—84no—
235C24×C3—88no—
236C24×C3—88no—
237C24×C3—816no—
238C24×C3—816no—
239C24×C3—88no—
240C24×C3—816no—
241C24×C3#9512yes—
242C24×C3#9514yes—
243C24×C3#9914yes—
244C24×C3#9914yes—
245C24×C3C2×C22⋊C412yes—
246C24×C3C2×C22⋊C411yescharacteristic
247C24×C3C2×C4⋊C412yes—
248C24×C3#12014yes—
249C24×C3#12314yes—
250C2×C3×D4—28no—
251C2×C3×D4—28no—
252C2×C3×D4—216no—
253C2×C3×D4—28no—
254C2×C3×D4—28no—
255C2×C3×D4—28no—
256C2×C3×D4—28no—
257C2×C3×D4—28no—
258C2×C3×D4—28no—
259C2×C3×D4—24no—
260C2×C3×D4—24no—
261C2×C3×D4—44no—
262C2×C3×D4—44no—
263C2×C3×D4—42no—
264C2×C3×D4—42no—
265C2×C3×D4—42no—
266C2×C3×D4—44no—
267C2×C3×D4—44no—
268C2×C3×D4—42no—
269C2×C3×D4—48no—
270C2×C3×D4—464no—
271C2×C3×D4—432no—
272C2×C3×D4—432no—
273C2×C3×D4—48no—
274C2×C3×D4—48no—
275C2×C3×D4—48no—
276C2×C3×D4—48no—
277C2×C3×D4C4×D418yes—
278C2×C3×D4#12114yes—
279C2×C3×D4C22⋊Q814yes—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—24no—
287C22×C3×C4—24no—
288C22×C3×C4—24no—
289C22×C3×C4—24no—
290C22×C3×C4—44no—
291C22×C3×C4—44no—
292C22×C3×C4—48no—
293C22×C3×C4—44no—
294C22×C3×C4—44no—
295C22×C3×C4—48no—
296C22×C3×C4—48no—
297C22×C3×C4—48no—
298C22×C3×C4—88no—
299C22×C3×C4—88no—
300C22×C3×C4—84no—
301C22×C3×C4—84no—
302C22×C3×C4—816no—
303C22×C3×C4#9512yes—
304C22×C3×C4C2×C4211yescharacteristic
305C22×C3×C4C2×C22⋊C412yes—
306C22×C3×C4C2×C4⋊C411yescharacteristic
307C22×C3×C4#11712yes—
308C3×C4⋊C4—44no—
309C3×C4⋊C4—44no—
310C3×C22⋊C4—48no—
311C3×C22⋊C4—48no—
312C3×C22⋊C4—416no—
313C3×C22⋊C4—44no—
314C3×C22⋊C4—44no—
315C3×C22⋊C4—48no—
316C3×C22⋊C4—48no—
317C3×C22⋊C4—816no—
318C3×C22⋊C4—84no—
319C3×C22⋊C4—84no—
320C3×C22⋊C4—832no—
321C3×C42—44no—
322C3×C42—44no—
323C25—24no—
324C25—24no—
325C25—24no—
326C25—24no—
327C25—42no—
328C25—42no—
329C25—88no—
330C25C3×C22⋊C411yescharacteristic
331C25C3×C22⋊C414yes—
332C25C3×C22⋊C412yes—
333C25C3×C4⋊C414yes—
334C25C2×C3×D412yes—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—216no—
342C22×D4—28no—
343C22×D4—28no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—42no—
347C22×D4—42no—
348C22×D4—42no—
349C22×D4—42no—
350C22×D4—48no—
351C22×D4—48no—
352C22×D4—48no—
353C22×D4—48no—
354C22×D4—416no—
355C22×D4—416no—
356C22×D4—432no—
357C22×D4C3×C4212yes—
358C22×D4C3×C22⋊C414yes—
359C22×D4C3×C4⋊C414yes—
360C22×D4C3×C4⋊C412yes—
361C22×D4C22×C3×C412yes—
362C22×D4C2×C3×D414yes—
363C22×D4C2×C3×D411yescharacteristic
364C22×D4C2×C3×Q811yescharacteristic
365C22×D4C3×#4114yes—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—44no—
373C23×C4C3×C4212yes—
374C23×C4C3×C22⋊C411yescharacteristic
375C23×C4C3×C4⋊C412yes—
376C23×C4C22×C3×C411yescharacteristic
377C4×D4—416no—
378C4×D4—416no—
379#117—44no—
380#117—44no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4C3×C22⋊C414yescomplemented
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—216no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—416no—
400C2×C22⋊C4—816no—
401C2×C22⋊C4—816no—
402C2×C42—22no—
403C2×C42C3×C22⋊C414yescomplemented
404#99—216no—
405#99—416no—
406#99—48no—
407#95—28no—
408C23×C3—24no—
409C23×C3—28no—
410C23×C3—24no—
411C23×C3—22no—
412C23×C3—24no—
413C23×C3—22no—
414C23×C3—24no—
415C23×C3—22no—
416C23×C3—24no—
417C23×C3—24no—
418C23×C3—24no—
419C23×C3—24no—
420C23×C3—24no—
421C23×C3—24no—
422C23×C3—22no—
423C23×C3—24no—
424C23×C3—22no—
425C23×C3—24no—
426C23×C3—44no—
427C23×C3—42no—
428C23×C3—416no—
429C23×C3—416no—
430C23×C3—48no—
431C23×C3—48no—
432C23×C3—42no—
433C23×C3—44no—
434C23×C3—44no—
435C23×C3—48no—
436C23×C3—48no—
437C23×C3—48no—
438C23×C3—416no—
439C23×C3—416no—
440C23×C3—416no—
441C23×C3—416no—
442C23×C3—42no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—84no—
446C23×C3—84no—
447C23×C3—88no—
448C23×C3—88no—
449C23×C3—84no—
450C23×C3—84no—
451C23×C3—82no—
452C23×C3—82no—
453C23×C3—84no—
454C23×C3—84no—
455C23×C3—84no—
456C23×C3—84no—
457C23×C3—84no—
458C23×C3—88no—
459C23×C3—88no—
460C23×C3—88no—
461C23×C3—88no—
462C23×C3—832no—
463C23×C3—832no—
464C23×C3—832no—
465C23×C3—88no—
466C23×C3—88no—
467C23×C3—832no—
468C23×C3#34218yes—
469C23×C3C2×#9511yescharacteristic
470C23×C3#37911yescharacteristic
471C23×C3#38111yescharacteristic
472C23×C3#38514yes—
473C23×C3#38614yes—
474C23×C3C2×#9912yes—
475C23×C3C2×#9912yes—
476C3×D4—216no—
477C3×D4—216no—
478C3×D4—48no—
479C3×D4—44no—
480C3×D4—44no—
481C3×D4—416no—
482C3×D4—416no—
483C2×C3×C4—24no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—24no—
490C2×C3×C4—48no—
491C2×C3×C4—48no—
492C2×C3×C4—42no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—48no—
496C2×C3×C4—48no—
497C2×C3×C4—44no—
498C2×C3×C4—44no—
499C2×C3×C4—88no—
500C2×C3×C4—816no—
501C2×C3×C4—168no—
502C2×C3×C4—168no—
503C2×C3×C4—168no—
504C2×C3×C4—168no—
505C2×C3×C4C4×C22⋊C412yes—
506C2×C3×C4#38012yes—
507C24—21no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—21no—
518C24—22no—
519C24—28no—
520C24—28no—
521C24—28no—
522C24—28no—
523C24—44no—
524C24—44no—
525C24—44no—
526C24—48no—
527C24—48no—
528C24—48no—
529C24—48no—
530C24—416no—
531C24—416no—
532C24—88no—
533C24—88no—
534C24—84no—
535C24—88no—
536C24—84no—
537C24—88no—
538C24—88no—
539C24—816no—
540C24—816no—
541C24—88no—
542C24—816no—
543C24C3×#9512yes—
544C24C3×#9514yes—
545C24C3×#9914yes—
546C24C3×#9914yes—
547C24C2×C3×C22⋊C412yes—
548C24C2×C3×C22⋊C411yescharacteristic
549C24C2×C3×C4⋊C412yes—
550C24C3×#12014yes—
551C24C3×#12314yes—
552C2×D4—28no—
553C2×D4—28no—
554C2×D4—216no—
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—44no—
564C2×D4—44no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—48no—
572C2×D4—464no—
573C2×D4—432no—
574C2×D4—432no—
575C2×D4—48no—
576C2×D4—48no—
577C2×D4—48no—
578C2×D4—48no—
579C2×D4C3×C4×D418yes—
580C2×D4C3×#12114yes—
581C2×D4C3×C22⋊Q814yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—88no—
601C22×C4—88no—
602C22×C4—84no—
603C22×C4—84no—
604C22×C4—816no—
605C22×C4C3×#9512yes—
606C22×C4C2×C3×C4211yescharacteristic
607C22×C4C2×C3×C22⋊C412yes—
608C22×C4C2×C3×C4⋊C411yescharacteristic
609C22×C4C3×#11712yes—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—416no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—816no—
620C22⋊C4—84no—
621C22⋊C4—84no—
622C22⋊C4—832no—
623C42—44no—
624C42—44no—
625C22×C3—22no—
626C22×C3—24no—
627C22×C3—24no—
628C22×C3—28no—
629C22×C3—24no—
630C22×C3—28no—
631C22×C3—24no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—42no—
635C22×C3—48no—
636C22×C3—44no—
637C22×C3—44no—
638C22×C3—44no—
639C22×C3—48no—
640C22×C3—48no—
641C22×C3—48no—
642C22×C3—44no—
643C22×C3—44no—
644C22×C3—42no—
645C22×C3—44no—
646C22×C3—48no—
647C22×C3—48no—
648C22×C3—48no—
649C22×C3—44no—
650C22×C3—42no—
651C22×C3—84no—
652C22×C3—84no—
653C22×C3—82no—
654C22×C3—84no—
655C22×C3—82no—
656C22×C3—84no—
657C22×C3—84no—
658C22×C3—832no—
659C22×C3—832no—
660C22×C3C22⋊#9511yescharacteristic
661C22×C3C2×#34212yes—
662C22×C3#178111yescharacteristic
663C22×C3#178111yescharacteristic
664C22×C3#181912yes—
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—42no—
668C3×C4—84no—
669C3×C4—84no—
670C3×C4—168no—
671C23—24no—
672C23—28no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—24no—
682C23—22no—
683C23—24no—
684C23—22no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—44no—
690C23—42no—
691C23—416no—
692C23—416no—
693C23—48no—
694C23—48no—
695C23—42no—
696C23—44no—
697C23—44no—
698C23—48no—
699C23—48no—
700C23—48no—
701C23—416no—
702C23—416no—
703C23—416no—
704C23—416no—
705C23—41no—
706C23—41no—
707C23—42no—
708C23—84no—
709C23—84no—
710C23—88no—
711C23—88no—
712C23—84no—
713C23—84no—
714C23—82no—
715C23—82no—
716C23—84no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23—88no—
722C23—88no—
723C23—88no—
724C23—88no—
725C23—832no—
726C23—832no—
727C23—832no—
728C23—88no—
729C23—88no—
730C23—832no—
731C23C3×#34218yes—
732C23C2×C3×#9511yescharacteristic
733C23C3×#37911yescharacteristic
734C23C3×#38111yescharacteristic
735C23C3×#38514yes—
736C23C3×#38614yes—
737C23C2×C3×#9912yes—
738C23C2×C3×#9912yes—
739D4—216no—
740D4—216no—
741D4—48no—
742D4—44no—
743D4—44no—
744D4—416no—
745D4—416no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—48no—
754C2×C4—48no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—88no—
763C2×C4—816no—
764C2×C4—168no—
765C2×C4—168no—
766C2×C4—168no—
767C2×C4—168no—
768C2×C4C3×C4×C22⋊C412yes—
769C2×C4C3×#38012yes—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—22no—
773C2×C3—22no—
774C2×C3—44no—
775C2×C3—44no—
776C2×C3—48no—
777C2×C3—44no—
778C2×C3#1072511yescharacteristic
779C2×C3#1270712yes—
780C22—22no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—24no—
785C22—28no—
786C22—24no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—44no—
791C22—44no—
792C22—48no—
793C22—44no—
794C22—48no—
795C22—48no—
796C22—44no—
797C22—42no—
798C22—44no—
799C22—48no—
800C22—48no—
801C22—44no—
802C22—48no—
803C22—48no—
804C22—44no—
805C22—42no—
806C22—84no—
807C22—84no—
808C22—82no—
809C22—84no—
810C22—82no—
811C22—84no—
812C22—84no—
813C22—832no—
814C22—832no—
815C22C3×C22⋊#9511yescharacteristic
816C22C2×C3×#34212yes—
817C22C3×#178111yescharacteristic
818C22C3×#178111yescharacteristic
819C22C3×#181912yes—
820C4—22no—
821C4—22no—
822C4—42no—
823C4—84no—
824C4—84no—
825C4—168no—
826C3#14647911yescharacteristic, direct product factor, Sylow
827C2—21no—
828C2—21no—
829C2—22no—
830C2—22no—
831C2—44no—
832C2—44no—
833C2—48no—
834C2—44no—
835C2C3×#1072511yescharacteristic
836C2C3×#1270712yes—
subgroupG/H
center, socleC22×C3#1781
commutatorC22×C4C2×C3×C42
Frattini, cosocleC23×D4C23×C3
prime radicalC24×C3×D4C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C24×C3×D4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C3×#12582C2semidirect
4. #146479C3direct (N × H)
6. C2×C3×#518C4semidirect
7. C2×C3×#518C4semidirect
13. C3×#2280C4semidirect
17. C3×#1781C4semidirect
21. #12582C2×C3semidirect
51. C2×C3×#99C2×C4semidirect
65. C2×#518C3×C4semidirect
66. C2×#518C3×C4semidirect
72. #2280C3×C4semidirect
76. #1781C3×C4semidirect
137. C2×C3×C4⋊C4C22⋊C4semidirect
158. C2×C3×C42C22⋊C4semidirect
192. C2×#99C2×C3×C4semidirect
382. C2×C4⋊C4C3×C22⋊C4semidirect
403. C2×C42C3×C22⋊C4semidirect
826. C3#146479direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#341712
C2×C3×#17812
C3×#125822
#1464793