Finite Group Databasebeta

← C3×#23403 #10642010

Subgroups — C3×#23403 #10642010

Order 768.

1942 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#575C211yesmaximal, characteristic
2C2×C3×#536C211yesmaximal, characteristic, complemented
3C2×C3×#536C211yesmaximal, characteristic, complemented
4C2×C3×#421C211yesmaximal, characteristic, complemented
5C3×#2896C211yesmaximal, characteristic, complemented
6C22×C3×#101C211yesmaximal, characteristic, complemented
7C3×#2005C214yesmaximal, complemented
8C3×#2003C214yesmaximal, complemented
9C3×#1733C211yesmaximal, characteristic, complemented
10#23403C311yesmaximal, characteristic, direct product factor, Sylow
11C22×C3×#41C2211yescharacteristic
12C22×C3×#41C2211yescharacteristic
13C23×C3×Q8C2211yescharacteristic
14C3×#575—24no—
15C3×#575—24no—
16C2×C3×#137—21no—
17C2×C3×#137C2212yes—
18C2×C3×AGL(1,ℤ/8)—21no—
19C2×C3×AGL(1,ℤ/8)C2212yes—
20C2×C3×#135—22no—
21C22×C3×M16C2211yescharacteristic
22C22×C3×M16C2211yescharacteristic
23C3×#536—22no—
24C3×#536—24no—
25C3×#536—22no—
26C3×#536—22no—
27C3×#536—24no—
28C3×#536C2214yes—
29C2×C3×C4⋊Q8—21no—
30C2×C3×C4⋊Q8C2212yescomplemented
31C2×C3×#124—21no—
32C2×C3×#124C2212yescomplemented
33C2×C3×#123—22no—
34C2×C3×#123—22no—
35C2×C3×C22⋊Q8—22no—
36C2×C3×C22⋊Q8—22no—
37C2×C3×#117C2211yescharacteristic
38C2×C3×#117C2211yescharacteristic
39C3×#421—24no—
40C2×C3×#104C2214yes—
41C3×#419C2212yescomplemented
42C3×#418C2212yescomplemented
43C3×#417—22no—
44C3×#416—22no—
45C2×C3×#101—24no—
46C2×C3×#101C2214yescomplemented
47C3×#339C2214yescomplemented
48C2×#575C2×C311yescharacteristic
49C2×#536C2×C311yescharacteristic, complemented
50C2×#536C2×C311yescharacteristic, complemented
51C2×#421C2×C311yescharacteristic, complemented
52#2896C2×C311yescharacteristic, complemented
53C22×#101C2×C311yescharacteristic, complemented
54#2005C2×C314yescomplemented
55#2003C2×C314yescomplemented
56#1733C2×C311yescharacteristic, complemented
57C2×C3×#41—21no—
58C2×C3×#41—22no—
59C2×C3×#41—21no—
60C2×C3×#41—21no—
61C2×C3×#41—21no—
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—22no—
65C2×C3×#41—21no—
66C2×C3×#41—21no—
67C2×C3×#41—22no—
68C2×C3×#41—22no—
69C2×C3×#41—22no—
70C2×C3×#41D412yes—
71C2×C3×#41D414yes—
72C2×C3×#41C2312yes—
73C22×C3×Q8—22no—
74C22×C3×Q8—21no—
75C22×C3×Q8—21no—
76C22×C3×Q8—21no—
77C22×C3×Q8—22no—
78C22×C3×Q8—21no—
79C22×C3×Q8—22no—
80C22×C3×Q8—22no—
81C22×C3×Q8D411yescharacteristic
82C22×C3×Q8D412yes—
83C22×C3×Q8C2311yescharacteristic
84C22×C3×Q8C2312yes—
85C22×C3×D4—21no—
86C22×C3×D4—21no—
87C22×C3×D4D411yescharacteristic
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4—21no—
91C23×C3×C4D412yes—
92C23×C3×C4C2311yescharacteristic
93C3×#137—28no—
94C3×#137—24no—
95C3×#137—24no—
96C3×AGL(1,ℤ/8)—28no—
97C3×AGL(1,ℤ/8)—24no—
98C3×AGL(1,ℤ/8)—24no—
99C3×#135—216no—
100C2×C3×Q16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×D8—22no—
104C2×C3×M16—21no—
105C2×C3×M16—22no—
106C2×C3×M16—21no—
107C2×C3×M16—22no—
108C2×C3×M16—22no—
109C2×C3×M16D414yes—
110C2×C3×M16C2312yes—
111C2×C3×M16C2312yes—
112C22×C3×C8—21no—
113C22×C3×C8—21no—
114C3×C4⋊Q8—24no—
115C3×C4⋊Q8—24no—
116C3×C4⋊Q8—24no—
117C3×C4⋊Q8—24no—
118C3×#124—24no—
119C3×#124—24no—
120C3×#124—24no—
121C3×#124—24no—
122C3×#123—216no—
123C3×#123—28no—
124C3×#123—28no—
125C3×C22⋊Q8—216no—
126C3×C22⋊Q8—28no—
127C3×C22⋊Q8—28no—
128C3×#117—21no—
129C3×#117—21no—
130C3×#117—22no—
131C3×#117D412yes—
132C3×#117D414yes—
133C3×#117C2312yes—
134C2×C3×C4⋊C4—24no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—24no—
137C2×C3×C4⋊C4D412yes—
138C2×C3×C22⋊C4—24no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—24no—
142C2×C3×C42—21no—
143C2×C3×C42C2312yes—
144C3×#104—28no—
145C3×#103—24no—
146C3×#102—24no—
147C3×#101—28no—
148C22×#41C22×C311yescharacteristic
149C22×#41C22×C311yescharacteristic
150C23×Q8C22×C311yescharacteristic
151#575—24no—
152#575—24no—
153C2×#137—21no—
154C2×#137C22×C312yes—
155C2×AGL(1,ℤ/8)—21no—
156C2×AGL(1,ℤ/8)C22×C312yes—
157C2×#135—22no—
158C22×M16C22×C311yescharacteristic
159C22×M16C22×C311yescharacteristic
160#536—22no—
161#536—24no—
162#536—22no—
163#536—22no—
164#536—24no—
165#536C22×C314yes—
166C2×C4⋊Q8—21no—
167C2×C4⋊Q8C22×C312yescomplemented
168C2×#124—21no—
169C2×#124C22×C312yescomplemented
170C2×#123—22no—
171C2×#123—22no—
172C2×C22⋊Q8—22no—
173C2×C22⋊Q8—22no—
174C2×#117C22×C311yescharacteristic
175C2×#117C22×C311yescharacteristic
176#421—24no—
177C2×#104C22×C314yes—
178#419C22×C312yescomplemented
179#418C22×C312yescomplemented
180#417—22no—
181#416—22no—
182C2×#101—24no—
183C2×#101C22×C314yescomplemented
184#339C22×C314yescomplemented
185C24×C3—21no—
186C24×C3—21no—
187C24×C3C2×D411yescharacteristic
188C3×#41—24no—
189C3×#41—24no—
190C3×#41—24no—
191C3×#41—24no—
192C3×#41—24no—
193C3×#41—24no—
194C3×#41—22no—
195C3×#41—22no—
196C3×#41—22no—
197C3×#41—22no—
198C3×#41—42no—
199C3×#41—42no—
200C3×#41—42no—
201C3×#41—42no—
202C3×#41—42no—
203C3×#41—42no—
204C3×#41—42no—
205C3×#41—42no—
206C2×C3×Q8—24no—
207C2×C3×Q8—22no—
208C2×C3×Q8—22no—
209C2×C3×Q8—21no—
210C2×C3×Q8—24no—
211C2×C3×Q8—22no—
212C2×C3×Q8—22no—
213C2×C3×Q8—22no—
214C2×C3×Q8—22no—
215C2×C3×Q8—22no—
216C2×C3×Q8—21no—
217C2×C3×Q8—22no—
218C2×C3×Q8—22no—
219C2×C3×Q8—22no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—42no—
225C2×C3×Q8—42no—
226C2×C3×Q8—42no—
227C2×C3×Q8—42no—
228C2×C3×Q8—42no—
229C2×C3×Q8—42no—
230C2×C3×Q8—42no—
231C2×C3×Q8—42no—
232C2×C3×Q8C2×D412yes—
233C2×C3×Q8C2×D412yes—
234C2×C3×D4—24no—
235C2×C3×D4—22no—
236C2×C3×D4—22no—
237C2×C3×D4—22no—
238C2×C3×D4—21no—
239C2×C3×D4—22no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—41no—
246C2×C3×D4—41no—
247C2×C3×D4—42no—
248C2×C3×D4—42no—
249C2×C3×D4—42no—
250C2×C3×D4C2×D412yes—
251C2×C3×D4C2×D412yes—
252C22×C3×C4—22no—
253C22×C3×C4—22no—
254C22×C3×C4—21no—
255C22×C3×C4—24no—
256C22×C3×C4—22no—
257C22×C3×C4—24no—
258C22×C3×C4—22no—
259C22×C3×C4—21no—
260C22×C3×C4—24no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—41no—
264C22×C3×C4—41no—
265C22×C3×C4—42no—
266C22×C3×C4—42no—
267C22×C3×C4—42no—
268C22×C3×C4C2×D414yes—
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D412yes—
273C22×C3×C4C2×D412yes—
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2×D412yes—
277C22×C3×C4#4112yes—
278C22×C3×C4C2411yescharacteristic
279C3×Q16—28no—
280C3×SD16—28no—
281C3×SD16—28no—
282C3×D8—28no—
283C3×M16—24no—
284C3×M16—22no—
285C3×M16—22no—
286C3×M16—22no—
287C3×M16—42no—
288C3×M16C2×D414yes—
289C2×C3×C8—24no—
290C2×C3×C8—22no—
291C2×C3×C8—22no—
292C2×C3×C8—42no—
293C3×C4⋊C4—216no—
294C3×C4⋊C4—216no—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—22no—
297C3×C4⋊C4C2×D414yes—
298C3×C22⋊C4—216no—
299C3×C22⋊C4—216no—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—22no—
303C3×C42—22no—
304C3×C42—22no—
305C3×C42—22no—
306C3×C42C2×D414yes—
307C2×#41—21no—
308C2×#41—22no—
309C2×#41—21no—
310C2×#41—21no—
311C2×#41—21no—
312C2×#41—22no—
313C2×#41—22no—
314C2×#41—22no—
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—22no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41C3×D412yes—
321C2×#41C3×D414yes—
322C2×#41C23×C312yes—
323C22×Q8—21no—
324C22×Q8—21no—
325C22×Q8—21no—
326C22×Q8—22no—
327C22×Q8—21no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8C3×D411yescharacteristic
332C22×Q8C3×D412yes—
333C22×Q8C23×C311yescharacteristic
334C22×Q8C23×C312yes—
335C22×D4—21no—
336C22×D4—21no—
337C22×D4C3×D411yescharacteristic
338C22×D4C23×C311yescharacteristic
339C23×C4—21no—
340C23×C4—21no—
341C23×C4C3×D412yes—
342C23×C4C23×C311yescharacteristic
343#137—28no—
344#137—24no—
345#137—24no—
346AGL(1,ℤ/8)—28no—
347AGL(1,ℤ/8)—24no—
348AGL(1,ℤ/8)—24no—
349#135—216no—
350C2×Q16—22no—
351C2×SD16—22no—
352C2×SD16—22no—
353C2×D8—22no—
354C2×M16—21no—
355C2×M16—22no—
356C2×M16—21no—
357C2×M16—22no—
358C2×M16—22no—
359C2×M16C3×D414yes—
360C2×M16C23×C312yes—
361C2×M16C23×C312yes—
362C22×C8—21no—
363C22×C8—21no—
364C4⋊Q8—24no—
365C4⋊Q8—24no—
366C4⋊Q8—24no—
367C4⋊Q8—24no—
368#124—24no—
369#124—24no—
370#124—24no—
371#124—24no—
372#123—28no—
373#123—216no—
374#123—28no—
375C22⋊Q8—216no—
376C22⋊Q8—28no—
377C22⋊Q8—28no—
378#117—21no—
379#117—21no—
380#117—22no—
381#117C3×D412yes—
382#117C3×D414yes—
383#117C23×C312yes—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4C3×D412yes—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—24no—
392C2×C42—21no—
393C2×C42C23×C312yes—
394#104—28no—
395#103—24no—
396#102—24no—
397#101—28no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—42no—
401C23×C3—44no—
402C23×C3—44no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—42no—
406C23×C3#12011yescharacteristic
407C23×C3#12011yescharacteristic
408C23×C3#12012yes—
409C23×C3#12112yes—
410C23×C3C22×D411yescharacteristic
411C3×Q8—22no—
412C3×Q8—22no—
413C3×Q8—22no—
414C3×Q8—22no—
415C3×Q8—42no—
416C3×Q8—42no—
417C3×Q8—42no—
418C3×Q8—41no—
419C3×Q8—42no—
420C3×Q8—41no—
421C3×Q8—44no—
422C3×Q8—44no—
423C3×Q8—42no—
424C3×D4—22no—
425C3×D4—22no—
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—42no—
429C3×D4—42no—
430C3×D4—44no—
431C3×D4—44no—
432C3×D4—44no—
433C3×D4—41no—
434C3×D4—41no—
435C3×D4—42no—
436C2×C3×C4—24no—
437C2×C3×C4—24no—
438C2×C3×C4—22no—
439C2×C3×C4—24no—
440C2×C3×C4—24no—
441C2×C3×C4—22no—
442C2×C3×C4—24no—
443C2×C3×C4—44no—
444C2×C3×C4—44no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—44no—
448C2×C3×C4—44no—
449C2×C3×C4—42no—
450C2×C3×C4—42no—
451C2×C3×C4—42no—
452C2×C3×C4—44no—
453C2×C3×C4—44no—
454C2×C3×C4—44no—
455C2×C3×C4#12012yes—
456C2×C3×C4#12012yes—
457C2×C3×C4#12012yes—
458C2×C3×C4#12011yescharacteristic
459C2×C3×C4#12011yescharacteristic
460C2×C3×C4#12112yes—
461C2×C3×C4#12112yes—
462C2×C3×C4#12112yes—
463C2×C3×C4#12112yes—
464C2×C3×C4#12112yes—
465C2×C3×C4#12712yes—
466C2×C3×C4#12712yes—
467C2×C3×C4C22×D411yescharacteristic
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D411yescharacteristic
470C2×C3×C4C22×D411yescharacteristic
471C2×C3×C4C22×D411yescharacteristic
472C2×C3×C4C2×#4111yescharacteristic
473C3×C8—24no—
474C3×C8—42no—
475C24—21no—
476C24—21no—
477C24C2×C3×D411yescharacteristic
478#41—24no—
479#41—24no—
480#41—24no—
481#41—24no—
482#41—24no—
483#41—24no—
484#41—22no—
485#41—22no—
486#41—22no—
487#41—22no—
488#41—42no—
489#41—42no—
490#41—42no—
491#41—42no—
492#41—42no—
493#41—42no—
494#41—42no—
495#41—42no—
496C2×Q8—22no—
497C2×Q8—24no—
498C2×Q8—22no—
499C2×Q8—21no—
500C2×Q8—24no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—21no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8C2×C3×D412yes—
523C2×Q8C2×C3×D412yes—
524C2×D4—22no—
525C2×D4—24no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—21no—
529C2×D4—22no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—42no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4C2×C3×D412yes—
541C2×D4C2×C3×D412yes—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4C2×C3×D414yes—
559C22×C4C2×C3×D411yescharacteristic
560C22×C4C2×C3×D411yescharacteristic
561C22×C4C2×C3×D411yescharacteristic
562C22×C4C2×C3×D412yes—
563C22×C4C2×C3×D412yes—
564C22×C4C2×C3×D411yescharacteristic
565C22×C4C2×C3×D411yescharacteristic
566C22×C4C2×C3×D412yes—
567C22×C4C3×#4112yes—
568C22×C4C24×C311yescharacteristic
569Q16—28no—
570SD16—28no—
571SD16—28no—
572D8—28no—
573M16—24no—
574M16—22no—
575M16—22no—
576M16—22no—
577M16—42no—
578M16C2×C3×D414yes—
579C2×C8—24no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—42no—
583C4⋊C4—216no—
584C4⋊C4—216no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4C2×C3×D414yes—
588C22⋊C4—216no—
589C22⋊C4—216no—
590C22⋊C4—22no—
591C22⋊C4—24no—
592C22⋊C4—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42C2×C3×D414yes—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—44no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—44no—
606C22×C3—82no—
607C22×C3—84no—
608C22×C3—82no—
609C22×C3#39212yes—
610C22×C3#39212yes—
611C22×C3C2×#12011yescharacteristic
612C22×C3C2×#12011yescharacteristic
613C22×C3C2×#12111yescharacteristic
614C3×C4—44no—
615C3×C4—44no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—44no—
619C3×C4#39212yes—
620C3×C4#39212yes—
621C3×C4C2×#12011yescharacteristic
622C3×C4C2×#12111yescharacteristic
623C3×C4C2×#12111yescharacteristic
624C3×C4C2×#12711yescharacteristic
625C23—22no—
626C23—22no—
627C23—42no—
628C23—44no—
629C23—44no—
630C23—42no—
631C23—41no—
632C23—41no—
633C23C3×#12011yescharacteristic
634C23C3×#12011yescharacteristic
635C23C3×#12012yes—
636C23C3×#12112yes—
637C23C22×C3×D411yescharacteristic
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—22no—
642Q8—44no—
643Q8—44no—
644Q8—42no—
645Q8—42no—
646Q8—42no—
647Q8—42no—
648Q8—41no—
649Q8—42no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—44no—
656D4—44no—
657D4—44no—
658D4—42no—
659D4—42no—
660D4—42no—
661D4—41no—
662D4—41no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4C3×#12011yescharacteristic
683C2×C4C3×#12011yescharacteristic
684C2×C4C3×#12012yes—
685C2×C4C3×#12012yes—
686C2×C4C3×#12012yes—
687C2×C4C3×#12112yes—
688C2×C4C3×#12112yes—
689C2×C4C3×#12112yes—
690C2×C4C3×#12112yes—
691C2×C4C3×#12112yes—
692C2×C4C3×#12712yes—
693C2×C4C3×#12712yes—
694C2×C4C22×C3×D411yescharacteristic
695C2×C4C22×C3×D411yescharacteristic
696C2×C4C22×C3×D411yescharacteristic
697C2×C4C22×C3×D411yescharacteristic
698C2×C4C22×C3×D411yescharacteristic
699C2×C4C2×C3×#4111yescharacteristic
700C8—24no—
701C8—42no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—22no—
705C2×C3—22no—
706C2×C3—82no—
707C2×C3—82no—
708C2×C3C2×#39211yescharacteristic
709C2×C3#302012yes—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—42no—
714C22—42no—
715C22—44no—
716C22—42no—
717C22—42no—
718C22—44no—
719C22—84no—
720C22—82no—
721C22—82no—
722C22C3×#39212yes—
723C22C3×#39212yes—
724C22C2×C3×#12011yescharacteristic
725C22C2×C3×#12011yescharacteristic
726C22C2×C3×#12111yescharacteristic
727C4—44no—
728C4—44no—
729C4—42no—
730C4—42no—
731C4—44no—
732C4C3×#39212yes—
733C4C3×#39212yes—
734C4C2×C3×#12011yescharacteristic
735C4C2×C3×#12111yescharacteristic
736C4C2×C3×#12111yescharacteristic
737C4C2×C3×#12711yescharacteristic
738C3#2340311yescharacteristic, direct product factor, Sylow
739C2—21no—
740C2—22no—
741C2—21no—
742C2—22no—
743C2—82no—
744C2—82no—
745C2C2×C3×#39211yescharacteristic
746C2C3×#302012yes—
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#536C2semidirect
3. C2×C3×#536C2semidirect
4. C2×C3×#421C2semidirect
5. C3×#2896C2semidirect
6. C22×C3×#101C2semidirect
7. C3×#2005C2semidirect
8. C3×#2003C2semidirect
9. C3×#1733C2semidirect
10. #23403C3direct (N × H)
30. C2×C3×C4⋊Q8C22semidirect
32. C2×C3×#124C22semidirect
41. C3×#419C22semidirect
42. C3×#418C22semidirect
46. C2×C3×#101C22semidirect
47. C3×#339C22semidirect
49. C2×#536C2×C3semidirect
50. C2×#536C2×C3semidirect
51. C2×#421C2×C3semidirect
52. #2896C2×C3semidirect
53. C22×#101C2×C3semidirect
54. #2005C2×C3semidirect
55. #2003C2×C3semidirect
56. #1733C2×C3semidirect
167. C2×C4⋊Q8C22×C3semidirect
169. C2×#124C22×C3semidirect
178. #419C22×C3semidirect
179. #418C22×C3semidirect
183. C2×#101C22×C3semidirect
184. #339C22×C3semidirect
738. C3#23403direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5752
C2×C3×#5362
C2×C3×#4212
C3×#28962
C22×C3×#1012
C3×#20052
C3×#20032
C3×#17332
#234033