Finite Group Databasebeta

← C3×#128059 #72271645

Subgroups — C3×#128059 #72271645

Order 1536.

3052 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#20591C212yesmaximal
2C3×#13956C211yesmaximal, characteristic
3C3×#7308C214yesmaximal, complemented
4#128059C311yesmaximal, characteristic, direct product factor, Sylow
5C23×C3×#41C2211yescharacteristic
6C2×C3×#413—22no—
7C2×C3×#413C414yescomplemented
8C2×C3×#407—22no—
9C2×C3×#386—22no—
10C2×C3×#381C411yescharacteristic
11C22×C3×#95C411yescharacteristic
12C3×#1785—22no—
13C3×#1785C414yescomplemented
14C3×#1784C2214yes—
15C3×#1783—22no—
16C3×#1446C2212yes—
17C3×#1438C412yes—
18C3×C22⋊#95—22no—
19#20591C2×C312yes—
20#13956C2×C311yescharacteristic
21#7308C2×C314yescomplemented
22C22×C3×#41—42no—
23C22×C3×#41—41no—
24C22×C3×#41—41no—
25C22×C3×#41—48no—
26C22×C3×#41C2×C412yes—
27C22×C3×#41C2×C412yes—
28C22×C3×#41D412yes—
29C22×C3×#41Q812yes—
30C23×C3×Q8C2311yescharacteristic
31C23×C3×D4C2×C411yescharacteristic
32C23×C3×D4D412yes—
33C24×C3×C4—21no—
34C24×C3×C4C2×C411yescharacteristic
35C24×C3×C4D412yes—
36C22×C3×M16—24no—
37C22×C3×C22⋊C4—21no—
38C22×C3×C22⋊C4—24no—
39C3×#413—48no—
40C3×#413—48no—
41C2×C3×#101—24no—
42C2×C3×#101C2×C418yescomplemented
43C2×C3×#100—24no—
44C2×C3×#100—24no—
45C3×#407—24no—
46C3×#407—24no—
47C3×#407—42no—
48C3×#407—42no—
49C2×C3×C22⋊C8—42no—
50C2×C3×C22⋊C8—42no—
51C3×#386—48no—
52C3×#381—41no—
53C3×#381—41no—
54C2×C3×#95—21no—
55C2×C3×#95—21no—
56C2×C3×#95—24no—
57C2×C3×#95—42no—
58C2×C3×#95C2×C412yes—
59C2×C3×#95C2×C412yes—
60C23×#41C22×C311yescharacteristic
61C2×#413—22no—
62C2×#413C3×C414yescomplemented
63C2×#407—22no—
64C2×#386—22no—
65C2×#381C3×C411yescharacteristic
66C22×#95C3×C411yescharacteristic
67#1785—22no—
68#1785C3×C414yescomplemented
69#1784C22×C314yes—
70#1783—22no—
71#1446C22×C312yes—
72#1438C3×C412yes—
73C22⋊#95—22no—
74C25×C3C22⋊C411yescharacteristic
75C25×C3C22⋊C412yes—
76C2×C3×#41—28no—
77C2×C3×#41—28no—
78C2×C3×#41—42no—
79C2×C3×#41—42no—
80C2×C3×#41—42no—
81C2×C3×#41—42no—
82C2×C3×#41—42no—
83C2×C3×#41—42no—
84C2×C3×#41—42no—
85C2×C3×#41—42no—
86C2×C3×#41—44no—
87C2×C3×#41—44no—
88C2×C3×#41—44no—
89C2×C3×#41—44no—
90C2×C3×#41—44no—
91C2×C3×#41—44no—
92C2×C3×#41—416no—
93C2×C3×#41—432no—
94C2×C3×#41—416no—
95C22×C3×Q8—41no—
96C22×C3×Q8—41no—
97C22×C3×Q8—44no—
98C22×C3×Q8C22×C412yes—
99C22×C3×Q8C2×D411yescharacteristic
100C22×C3×Q8C2×Q811yescharacteristic
101C22×C3×D4—28no—
102C22×C3×D4—41no—
103C22×C3×D4—41no—
104C22×C3×D4—42no—
105C22×C3×D4—42no—
106C22×C3×D4—44no—
107C22×C3×D4—44no—
108C22×C3×D4C4211yescharacteristic
109C22×C3×D4C4211yescharacteristic
110C22×C3×D4C22⋊C412yes—
111C22×C3×D4C22⋊C412yes—
112C22×C3×D4C4⋊C412yes—
113C22×C3×D4C4⋊C412yes—
114C22×C3×D4C4⋊C412yes—
115C23×C3×C4—22no—
116C23×C3×C4—21no—
117C23×C3×C4—21no—
118C23×C3×C4—22no—
119C23×C3×C4—22no—
120C23×C3×C4—22no—
121C23×C3×C4—22no—
122C23×C3×C4—22no—
123C23×C3×C4—22no—
124C23×C3×C4—44no—
125C23×C3×C4—44no—
126C23×C3×C4—44no—
127C23×C3×C4—44no—
128C23×C3×C4—42no—
129C23×C3×C4—44no—
130C23×C3×C4—82no—
131C23×C3×C4C4212yes—
132C23×C3×C4C22⋊C412yes—
133C23×C3×C4C22⋊C412yes—
134C23×C3×C4C22⋊C411yescharacteristic
135C23×C3×C4C4⋊C412yes—
136C23×C3×C4C4⋊C412yes—
137C23×C3×C4C4⋊C412yes—
138C23×C3×C4C22×C411yescharacteristic
139C23×C3×C4C2×D412yes—
140C2×C3×M16—28no—
141C2×C3×M16—44no—
142C2×C3×M16—48no—
143C2×C3×M16—48no—
144C22×C3×C8—44no—
145C2×C3×C22⋊C4—48no—
146C2×C3×C22⋊C4—42no—
147C2×C3×C22⋊C4—48no—
148C2×C3×C22⋊C4—44no—
149C2×C3×C22⋊C4—84no—
150C3×#101—48no—
151C3×#101—48no—
152C3×#100—48no—
153C3×#100—48no—
154C3×C22⋊C8—44no—
155C3×C22⋊C8—44no—
156C3×C22⋊C8—44no—
157C3×C22⋊C8—44no—
158C3×#95—42no—
159C3×#95—42no—
160C3×#95—48no—
161C3×#95—42no—
162C3×#95—41no—
163C3×#95—41no—
164C22×#41—42no—
165C22×#41—41no—
166C22×#41—41no—
167C22×#41—48no—
168C22×#41C2×C3×C412yes—
169C22×#41C2×C3×C412yes—
170C22×#41C3×D412yes—
171C22×#41C3×Q812yes—
172C23×Q8C23×C311yescharacteristic
173C23×D4C2×C3×C411yescharacteristic
174C23×D4C3×D412yes—
175C24×C4—21no—
176C24×C4C2×C3×C411yescharacteristic
177C24×C4C3×D412yes—
178C22×M16—24no—
179C22×C22⋊C4—21no—
180C22×C22⋊C4—24no—
181#413—48no—
182#413—48no—
183C2×#101—24no—
184C2×#101C2×C3×C418yescomplemented
185C2×#100—24no—
186C2×#100—24no—
187#407—24no—
188#407—24no—
189#407—42no—
190#407—42no—
191C2×C22⋊C8—42no—
192C2×C22⋊C8—42no—
193#386—48no—
194#381—41no—
195#381—41no—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—24no—
199C2×#95—42no—
200C2×#95C2×C3×C412yes—
201C2×#95C2×C3×C412yes—
202C24×C3—24no—
203C24×C3—21no—
204C24×C3—21no—
205C24×C3—24no—
206C24×C3—22no—
207C24×C3—22no—
208C24×C3—42no—
209C24×C3—41no—
210C24×C3—42no—
211C24×C3—41no—
212C24×C3—42no—
213C24×C3—44no—
214C24×C3—42no—
215C24×C3#9512yes—
216C24×C3#9512yes—
217C24×C3#9512yes—
218C24×C3C2×C22⋊C411yescharacteristic
219C3×#41—416no—
220C3×#41—416no—
221C3×#41—416no—
222C3×#41—416no—
223C3×#41—416no—
224C3×#41—416no—
225C3×#41—416no—
226C3×#41—416no—
227C2×C3×Q8—24no—
228C2×C3×Q8—24no—
229C2×C3×Q8—42no—
230C2×C3×Q8—42no—
231C2×C3×Q8—41no—
232C2×C3×Q8—42no—
233C2×C3×Q8—41no—
234C2×C3×Q8—48no—
235C2×C3×Q8—48no—
236C2×C3×D4—24no—
237C2×C3×D4—24no—
238C2×C3×D4—24no—
239C2×C3×D4—24no—
240C2×C3×D4—24no—
241C2×C3×D4—24no—
242C2×C3×D4—24no—
243C2×C3×D4—42no—
244C2×C3×D4—41no—
245C2×C3×D4—41no—
246C2×C3×D4—42no—
247C2×C3×D4—42no—
248C2×C3×D4—42no—
249C2×C3×D4—42no—
250C2×C3×D4—42no—
251C2×C3×D4—42no—
252C2×C3×D4—42no—
253C2×C3×D4—42no—
254C2×C3×D4—416no—
255C2×C3×D4—416no—
256C2×C3×D4—48no—
257C2×C3×D4—48no—
258C2×C3×D4#9918yes—
259C22×C3×C4—24no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—24no—
263C22×C3×C4—24no—
264C22×C3×C4—24no—
265C22×C3×C4—24no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—24no—
281C22×C3×C4—24no—
282C22×C3×C4—24no—
283C22×C3×C4—42no—
284C22×C3×C4—42no—
285C22×C3×C4—42no—
286C22×C3×C4—42no—
287C22×C3×C4—42no—
288C22×C3×C4—42no—
289C22×C3×C4—42no—
290C22×C3×C4—42no—
291C22×C3×C4—42no—
292C22×C3×C4—48no—
293C22×C3×C4—48no—
294C22×C3×C4—48no—
295C22×C3×C4—48no—
296C22×C3×C4—44no—
297C22×C3×C4—44no—
298C22×C3×C4—48no—
299C22×C3×C4—44no—
300C22×C3×C4—44no—
301C22×C3×C4—42no—
302C22×C3×C4—48no—
303C22×C3×C4—42no—
304C22×C3×C4—44no—
305C22×C3×C4—44no—
306C22×C3×C4—42no—
307C22×C3×C4—42no—
308C22×C3×C4—42no—
309C22×C3×C4—816no—
310C22×C3×C4—84no—
311C22×C3×C4—84no—
312C22×C3×C4#9512yes—
313C22×C3×C4#9911yescharacteristic
314C22×C3×C4#9911yescharacteristic
315C22×C3×C4#9912yes—
316C22×C3×C4C2×C4211yescharacteristic
317C22×C3×C4C2×C22⋊C412yes—
318C22×C3×C4C2×C4⋊C411yescharacteristic
319C22×C3×C4C2×C4⋊C412yes—
320C3×M16—48no—
321C3×M16—48no—
322C3×M16—88no—
323C2×C3×C8—48no—
324C2×C3×C8—88no—
325C3×C22⋊C4—816no—
326C3×C22⋊C4—84no—
327C25C3×C22⋊C411yescharacteristic
328C25C3×C22⋊C412yes—
329C2×#41—28no—
330C2×#41—28no—
331C2×#41—42no—
332C2×#41—42no—
333C2×#41—42no—
334C2×#41—42no—
335C2×#41—42no—
336C2×#41—42no—
337C2×#41—42no—
338C2×#41—42no—
339C2×#41—44no—
340C2×#41—44no—
341C2×#41—44no—
342C2×#41—44no—
343C2×#41—44no—
344C2×#41—44no—
345C2×#41—416no—
346C2×#41—432no—
347C2×#41—416no—
348C22×Q8—41no—
349C22×Q8—41no—
350C22×Q8—44no—
351C22×Q8C22×C3×C412yes—
352C22×Q8C2×C3×D411yescharacteristic
353C22×Q8C2×C3×Q811yescharacteristic
354C22×D4—28no—
355C22×D4—41no—
356C22×D4—41no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—44no—
360C22×D4—44no—
361C22×D4C3×C4211yescharacteristic
362C22×D4C3×C4211yescharacteristic
363C22×D4C3×C22⋊C412yes—
364C22×D4C3×C22⋊C412yes—
365C22×D4C3×C4⋊C412yes—
366C22×D4C3×C4⋊C412yes—
367C22×D4C3×C4⋊C412yes—
368C23×C4—22no—
369C23×C4—21no—
370C23×C4—21no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—44no—
378C23×C4—44no—
379C23×C4—44no—
380C23×C4—44no—
381C23×C4—42no—
382C23×C4—44no—
383C23×C4—82no—
384C23×C4C3×C4212yes—
385C23×C4C3×C22⋊C412yes—
386C23×C4C3×C22⋊C412yes—
387C23×C4C3×C22⋊C411yescharacteristic
388C23×C4C3×C4⋊C412yes—
389C23×C4C3×C4⋊C412yes—
390C23×C4C3×C4⋊C412yes—
391C23×C4C22×C3×C411yescharacteristic
392C23×C4C2×C3×D412yes—
393C2×M16—28no—
394C2×M16—44no—
395C2×M16—48no—
396C2×M16—48no—
397C22×C8—44no—
398C2×C22⋊C4—48no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—48no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—84no—
403#101—48no—
404#101—48no—
405#100—48no—
406#100—48no—
407C22⋊C8—44no—
408C22⋊C8—44no—
409C22⋊C8—44no—
410C22⋊C8—44no—
411#95—42no—
412#95—42no—
413#95—48no—
414#95—42no—
415#95—41no—
416#95—41no—
417C23×C3—22no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—22no—
421C23×C3—24no—
422C23×C3—24no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—42no—
435C23×C3—48no—
436C23×C3—48no—
437C23×C3—42no—
438C23×C3—42no—
439C23×C3—42no—
440C23×C3—42no—
441C23×C3—42no—
442C23×C3—48no—
443C23×C3—48no—
444C23×C3—42no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—44no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3—82no—
451C23×C3—82no—
452C23×C3—84no—
453C23×C3—84no—
454C23×C3#34214yes—
455C23×C3#34214yes—
456C23×C3C2×#9511yescharacteristic
457C23×C3C2×#9911yescharacteristic
458C23×C3C2×#9911yescharacteristic
459C3×Q8—44no—
460C3×Q8—48no—
461C3×Q8—44no—
462C3×D4—48no—
463C3×D4—48no—
464C3×D4—44no—
465C3×D4—48no—
466C3×D4—48no—
467C3×D4—48no—
468C3×D4—44no—
469C2×C3×C4—28no—
470C2×C3×C4—28no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—41no—
483C2×C3×C4—42no—
484C2×C3×C4—41no—
485C2×C3×C4—44no—
486C2×C3×C4—44no—
487C2×C3×C4—44no—
488C2×C3×C4—44no—
489C2×C3×C4—44no—
490C2×C3×C4—44no—
491C2×C3×C4—44no—
492C2×C3×C4—44no—
493C2×C3×C4—44no—
494C2×C3×C4—44no—
495C2×C3×C4—44no—
496C2×C3×C4—44no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—48no—
500C2×C3×C4—44no—
501C2×C3×C4—84no—
502C2×C3×C4—82no—
503C2×C3×C4—816no—
504C2×C3×C4—82no—
505C2×C3×C4—84no—
506C2×C3×C4—82no—
507C2×C3×C4—84no—
508C2×C3×C4—82no—
509C2×C3×C4—82no—
510C2×C3×C4#34212yes—
511C2×C3×C4#34212yes—
512C2×C3×C4C2×#9914yes—
513C3×C8—88no—
514C24—21no—
515C24—21no—
516C24—24no—
517C24—24no—
518C24—22no—
519C24—22no—
520C24—42no—
521C24—42no—
522C24—41no—
523C24—41no—
524C24—44no—
525C24—42no—
526C24—42no—
527C24C3×#9512yes—
528C24C3×#9512yes—
529C24C3×#9512yes—
530C24C2×C3×C22⋊C411yescharacteristic
531#41—416no—
532#41—416no—
533#41—416no—
534#41—416no—
535#41—416no—
536#41—416no—
537#41—416no—
538#41—416no—
539C2×Q8—24no—
540C2×Q8—24no—
541C2×Q8—42no—
542C2×Q8—42no—
543C2×Q8—41no—
544C2×Q8—41no—
545C2×Q8—42no—
546C2×Q8—48no—
547C2×Q8—48no—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—24no—
553C2×D4—24no—
554C2×D4—24no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—416no—
567C2×D4—416no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4C3×#9918yes—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—48no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—42no—
614C22×C4—48no—
615C22×C4—42no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—816no—
622C22×C4—84no—
623C22×C4—84no—
624C22×C4C3×#9512yes—
625C22×C4C3×#9911yescharacteristic
626C22×C4C3×#9911yescharacteristic
627C22×C4C3×#9912yes—
628C22×C4C2×C3×C4211yescharacteristic
629C22×C4C2×C3×C22⋊C412yes—
630C22×C4C2×C3×C4⋊C411yescharacteristic
631C22×C4C2×C3×C4⋊C412yes—
632M16—48no—
633M16—48no—
634M16—88no—
635C2×C8—48no—
636C2×C8—88no—
637C22⋊C4—816no—
638C22⋊C4—84no—
639C22×C3—24no—
640C22×C3—24no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—24no—
648C22×C3—24no—
649C22×C3—44no—
650C22×C3—44no—
651C22×C3—44no—
652C22×C3—48no—
653C22×C3—44no—
654C22×C3—44no—
655C22×C3—44no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—82no—
664C22×C3—84no—
665C22×C3—88no—
666C22×C3—84no—
667C22×C3—82no—
668C22×C3C2×#34212yes—
669C22×C3C2×#34211yescharacteristic
670C22×C3#213212yes—
671C22×C3#213411yescharacteristic
672C22×C3#213511yescharacteristic
673C3×C4—24no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—41no—
677C3×C4—42no—
678C3×C4—41no—
679C3×C4—84no—
680C3×C4—162no—
681C23—22no—
682C23—22no—
683C23—21no—
684C23—21no—
685C23—24no—
686C23—24no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—44no—
695C23—44no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—48no—
700C23—48no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—48no—
707C23—48no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—44no—
712C23—42no—
713C23—42no—
714C23—82no—
715C23—82no—
716C23—84no—
717C23—84no—
718C23C3×#34214yes—
719C23C3×#34214yes—
720C23C2×C3×#9511yescharacteristic
721C23C2×C3×#9911yescharacteristic
722C23C2×C3×#9911yescharacteristic
723Q8—44no—
724Q8—48no—
725Q8—44no—
726D4—48no—
727D4—48no—
728D4—44no—
729D4—48no—
730D4—48no—
731D4—48no—
732D4—44no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—48no—
764C2×C4—44no—
765C2×C4—84no—
766C2×C4—82no—
767C2×C4—816no—
768C2×C4—82no—
769C2×C4—84no—
770C2×C4—82no—
771C2×C4—84no—
772C2×C4—82no—
773C2×C4—82no—
774C2×C4C3×#34212yes—
775C2×C4C3×#34212yes—
776C2×C4C2×C3×#9914yes—
777C8—88no—
778C2×C3—21no—
779C2×C3—22no—
780C2×C3—22no—
781C2×C3—21no—
782C2×C3—44no—
783C2×C3—44no—
784C2×C3—82no—
785C2×C3#810111yescharacteristic
786C2×C3#1258511yescharacteristic
787C2×C3#1258711yescharacteristic
788C22—24no—
789C22—24no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—24no—
797C22—24no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—48no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—82no—
813C22—84no—
814C22—88no—
815C22—84no—
816C22—82no—
817C22C2×C3×#34212yes—
818C22C2×C3×#34211yescharacteristic
819C22C3×#213212yes—
820C22C3×#213411yescharacteristic
821C22C3×#213511yescharacteristic
822C4—24no—
823C4—22no—
824C4—22no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—84no—
829C4—162no—
830C3#12805911yescharacteristic, direct product factor, Sylow
831C2—21no—
832C2—22no—
833C2—22no—
834C2—21no—
835C2—44no—
836C2—44no—
837C2—82no—
838C2C3×#810111yescharacteristic
839C2C3×#1258511yescharacteristic
840C2C3×#1258711yescharacteristic
subgroupG/H
center, socleC22×C3C2×#342
commutatorC22×C4C2×C3×C42
Frattini, cosocleC23×Q8C23×C3
prime radicalC23×C3×#41C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ C23×C3×#41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C3×#7308C2semidirect
4. #128059C3direct (N × H)
7. C2×C3×#413C4semidirect
13. C3×#1785C4semidirect
21. #7308C2×C3semidirect
42. C2×C3×#101C2×C4semidirect
62. C2×#413C3×C4semidirect
68. #1785C3×C4semidirect
184. C2×#101C2×C3×C4semidirect
830. C3#128059direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#205912
C3×#139562
C3×#73082
#1280593