Finite Group Databasebeta

← #10826951

Subgroups — #10826951

Order 768.

1908 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#946C211yesmaximal, characteristic
2C2×D3×C22⋊Q8C211yesmaximal, characteristic
3C2×C3×#451C211yesmaximal, characteristic, complemented
4C2×#5228C211yesmaximal, characteristic, complemented
5C2×#5186C212yesmaximal, complemented
6#72071C212yesmaximal, complemented
7#71692C211yesmaximal, characteristic, complemented
8#70273C212yesmaximal, complemented
9#70268C212yesmaximal, complemented
10#69955C211yesmaximal, characteristic
11#69930C211yesmaximal, characteristic, complemented
12#23921—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C22×D3×Q8C2211yescharacteristic
15C23×C4×D3C2211yescharacteristic
16C22×C3×Q16C2212yescomplemented
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×#946—21no—
19C2×#946—21no—
20C2×#946—28no—
21C2×#946C2212yes—
22C2×#946C2211yescharacteristic
23C2×#946C2212yes—
24C22×#216C2212yescomplemented
25C22×(C2×D3)⋊C4—21no—
26C22×C4⋊Dic3C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C22×Dic3⋊C4—21no—
29D3×C22⋊Q8—24no—
30D3×C22⋊Q8—24no—
31C2×#897C2211yescharacteristic
32C2×#896—21no—
33C2×D3×C4⋊C4—21no—
34C2×D3×C4⋊C4C2211yescharacteristic
35C2×D3×C22⋊C4—21no—
36C2×#878—21no—
37C3×#451—24no—
38C2×C3×#103C2212yescomplemented
39C2×C3×C22⋊C8C2211yescharacteristic
40#5228—24no—
41C2×#835C2212yescomplemented
42C2×#835C2212yescomplemented
43C2×#830C2211yescharacteristic
44#5186—28no—
45C2×(C2×D3)⋊C8C2212yes—
46C2×(C2×D3)⋊C8C2212yes—
47C2×#816C2212yescomplemented
48#4551C2212yescomplemented
49#4529C2212yescomplemented
50C22×C22⋊Q8—31no—
51C22×C22⋊Q8—31no—
52C2×#451—31no—
53C2×#451—32no—
54C2×#451D311yescharacteristic, complemented
55#2001—32no—
56#2001—32no—
57#1872—32no—
58#1872—31no—
59#1872—31no—
60#1779—31no—
61C24×D3D411yescharacteristic
62C22×C3×Q8—24no—
63C22×C3×Q8—21no—
64C22×C3×Q8—22no—
65C22×C3×Q8—22no—
66C22×C3×Q8—42no—
67C22×C3×Q8C2311yescharacteristic
68C22×C3×Q8C2312yes—
69C23×C3×C4—21no—
70C23×C3×C4C2311yescharacteristic
71C23×Dic3—21no—
72C23×Dic3D411yescharacteristic
73C2×D3×Q8—22no—
74C2×D3×Q8—22no—
75C2×D3×Q8—24no—
76C2×D3×Q8—42no—
77C22×C4×D3—21no—
78C22×C4×D3—21no—
79C22×C4×D3—22no—
80C22×C4×D3—22no—
81C22×C4×D3—24no—
82C22×C4×D3—42no—
83C22×C4×D3D411yescharacteristic
84C22×C4×D3D411yescharacteristic
85C22×C4×D3C2311yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C22×Dic6—21no—
88C22×Dic6C2311yescharacteristic
89C2×C3×Q16—24no—
90C2×C3×Q16—24no—
91C2×C3×Q16—42no—
92C22×C3×C8C2312yes—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8D414yes—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C22⋊C4—21no—
98C2×#217—21no—
99#946—28no—
100#946—28no—
101#946—24no—
102#946—22no—
103#946—24no—
104#946—24no—
105#946—22no—
106#946D418yes—
107C2×#216—24no—
108C2×#216—24no—
109C2×#216—42no—
110C2×(C2×D3)⋊C4—28no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—22no—
115C2×C4⋊Dic3—21no—
116C2×C4⋊Dic3—21no—
117C2×C4⋊Dic3—24no—
118C2×C4⋊Dic3C2311yescharacteristic
119C2×C4⋊Dic3C2312yes—
120#924—22no—
121#924D414yes—
122C2×Dic3⋊C4—28no—
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—22no—
127C2×Dic3⋊C4—22no—
128C22×C3⋊C8C2312yes—
129#897—22no—
130#897—22no—
131#896—28no—
132D3×C4⋊C4—28no—
133D3×C4⋊C4—22no—
134D3×C4⋊C4—22no—
135D3×C22⋊C4—28no—
136#878—28no—
137C3×#103—24no—
138C3×C22⋊C8—22no—
139#835—24no—
140#835—24no—
141#830—22no—
142(C2×D3)⋊C8—24no—
143(C2×D3)⋊C8—42no—
144#816—24no—
145C23×Q8—31no—
146C23×Q8C2×D311yescharacteristic
147C24×C4—31no—
148C22×Q16—32no—
149C22×Q16C2×D312yescomplemented
150C2×C22⋊Q8—32no—
151C2×C22⋊Q8—31no—
152C2×C22⋊Q8—32no—
153C2×C22⋊Q8—31no—
154C2×C22⋊Q8—31no—
155C2×C22⋊Q8—61no—
156C2×C22⋊Q8—61no—
157C2×C22⋊Q8—64no—
158C2×C22⋊Q8—68no—
159C2×C22⋊Q8—61no—
160C2×C22⋊Q8—61no—
161C2×C22⋊Q8—64no—
162C2×C22⋊Q8C2×D311yescharacteristic
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—61no—
166C22×C4⋊C4—61no—
167C22×C22⋊C4—61no—
168C22×C22⋊C4—61no—
169#451—24no—
170#451—68no—
171#451—64no—
172C2×#103—32no—
173C2×#103—32no—
174C2×#103—32no—
175C2×#103C2×D312yescomplemented
176C2×C22⋊C8—31no—
177C2×C22⋊C8—32no—
178C2×C22⋊C8—32no—
179C2×C22⋊C8C2×D311yescharacteristic
180#340—32no—
181#340—32no—
182C24×C3C2×D411yescharacteristic
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3—41no—
188C23×D3—41no—
189C23×D3Q1614yescomplemented
190C23×D3C2×D411yescharacteristic
191C23×D3C2×D411yescharacteristic
192C2×C3×Q8—24no—
193C2×C3×Q8—22no—
194C2×C3×Q8—21no—
195C2×C3×Q8—22no—
196C2×C3×Q8—22no—
197C2×C3×Q8—22no—
198C2×C3×Q8—22no—
199C2×C3×Q8—22no—
200C2×C3×Q8—22no—
201C2×C3×Q8—48no—
202C2×C3×Q8—48no—
203C2×C3×Q8—42no—
204C2×C3×Q8—42no—
205C2×C3×Q8C2×D414yes—
206C2×C3×Q8C2×D412yes—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—24no—
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—42no—
214C22×C3×C4—42no—
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×D412yes—
218C22×C3×C4C2411yescharacteristic
219C22×Dic3—24no—
220C22×Dic3—22no—
221C22×Dic3—21no—
222C22×Dic3—22no—
223C22×Dic3—21no—
224C22×Dic3—22no—
225C22×Dic3—41no—
226C22×Dic3—42no—
227C22×Dic3—42no—
228C22×Dic3C2×D411yescharacteristic
229C22×Dic3C2×D411yescharacteristic
230D3×Q8—48no—
231D3×Q8—48no—
232C2×C4×D3—21no—
233C2×C4×D3—21no—
234C2×C4×D3—22no—
235C2×C4×D3—24no—
236C2×C4×D3—24no—
237C2×C4×D3—22no—
238C2×C4×D3—22no—
239C2×C4×D3—22no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—22no—
243C2×C4×D3—22no—
244C2×C4×D3—22no—
245C2×C4×D3—48no—
246C2×C4×D3—48no—
247C2×C4×D3—41no—
248C2×C4×D3—41no—
249C2×C4×D3—42no—
250C2×C4×D3—42no—
251C2×C4×D3—42no—
252C2×C4×D3—42no—
253C2×C4×D3C2×D414yes—
254C2×Dic6—22no—
255C2×Dic6—22no—
256C2×Dic6—24no—
257C2×Dic6—21no—
258C2×Dic6—42no—
259C2×Dic6—42no—
260C2×Dic6C2×D412yes—
261C3×Q16—48no—
262C2×C3×C8—22no—
263C2×C3×C8—22no—
264C2×C3×C8—22no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4C2×D412yes—
268C3×C22⋊C4—24no—
269#217—24no—
270#216—48no—
271(C2×D3)⋊C4—24no—
272(C2×D3)⋊C4—24no—
273(C2×D3)⋊C4—28no—
274(C2×D3)⋊C4—28no—
275C4⋊Dic3—24no—
276C4⋊Dic3—24no—
277C4⋊Dic3—21no—
278C4⋊Dic3—22no—
279C4⋊Dic3C2×D414yes—
280C4⋊Dic3C2×D412yes—
281Dic3⋊C4—24no—
282Dic3⋊C4—24no—
283Dic3⋊C4—28no—
284Dic3⋊C4—24no—
285Dic3⋊C4—28no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8—22no—
288C2×C3⋊C8—22no—
289C25—31no—
290C22×Q8—24no—
291C22×Q8—21no—
292C22×Q8—22no—
293C22×Q8—22no—
294C22×Q8—31no—
295C22×Q8—42no—
296C22×Q8—61no—
297C22×Q8—64no—
298C22×Q8—62no—
299C22×Q8—62no—
300C22×Q8—122no—
301C22×Q8C22×D312yes—
302C22×Q8C22×D311yescharacteristic
303C23×C4—21no—
304C23×C4—31no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—64no—
310C23×C4—61no—
311C23×C4—61no—
312C23×C4—61no—
313C23×C4—62no—
314C23×C4—62no—
315C23×C4—122no—
316C23×C4C22×D311yescharacteristic
317C2×Q16—24no—
318C2×Q16—24no—
319C2×Q16—42no—
320C2×Q16—64no—
321C2×Q16—64no—
322C2×Q16—122no—
323C22×C8—32no—
324C22×C8C22×D312yes—
325C22⋊Q8—22no—
326C22⋊Q8—38no—
327C22⋊Q8—34no—
328C22⋊Q8—68no—
329C22⋊Q8—62no—
330C22⋊Q8—68no—
331C22⋊Q8—62no—
332C22⋊Q8—64no—
333C22⋊Q8—64no—
334C22⋊Q8—68no—
335C22⋊Q8—68no—
336C22⋊Q8—64no—
337C22⋊Q8—62no—
338C22⋊Q8—62no—
339C22⋊Q8—62no—
340C22⋊Q8#6714yes—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—32no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—62no—
345C2×C4⋊C4—68no—
346C2×C4⋊C4—64no—
347C2×C4⋊C4—61no—
348C2×C4⋊C4—62no—
349C2×C4⋊C4—61no—
350C2×C4⋊C4—62no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4—68no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—62no—
356C2×C4⋊C4C22×D311yescharacteristic
357C2×C22⋊C4—21no—
358C2×C22⋊C4—68no—
359C2×C22⋊C4—62no—
360C2×C22⋊C4—61no—
361C2×C22⋊C4—61no—
362C2×C22⋊C4—62no—
363C2×C22⋊C4—68no—
364C2×C22⋊C4—61no—
365#103—24no—
366#103—64no—
367#103—64no—
368#103—64no—
369C22⋊C8—22no—
370C22⋊C8—64no—
371C22⋊C8—62no—
372C22⋊C8—122no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3#12012yes—
378C23×C3C2×Q1612yes—
379C23×C3#13712yes—
380C23×C3C22×D411yescharacteristic
381C22×D3—21no—
382C22×D3—21no—
383C22×D3—21no—
384C22×D3—21no—
385C22×D3—21no—
386C22×D3—21no—
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—28no—
392C22×D3—28no—
393C22×D3—44no—
394C22×D3—44no—
395C22×D3—44no—
396C22×D3—44no—
397C22×D3—44no—
398C22×D3#12012yes—
399C22×D3C2×Q1612yes—
400C22×D3C2×Q1612yes—
401C22×D3#13712yes—
402C3×Q8—24no—
403C3×Q8—24no—
404C3×Q8—24no—
405C3×Q8—48no—
406C3×Q8—42no—
407C3×Q8—42no—
408C3×Q8—42no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—24no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—48no—
417C2×C3×C4—41no—
418C2×C3×C4—42no—
419C2×C3×C4—41no—
420C2×C3×C4—42no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4#12012yes—
424C2×C3×C4C22×D411yescharacteristic
425C2×C3×C4C22×D412yes—
426C2×C3×C4C22×D411yescharacteristic
427C2×C3×C4H(5,𝔽2)12yes—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—22no—
432C2×Dic3—21no—
433C2×Dic3—24no—
434C2×Dic3—22no—
435C2×Dic3—21no—
436C2×Dic3—44no—
437C2×Dic3—48no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—42no—
442C2×Dic3—41no—
443C2×Dic3—42no—
444C2×Dic3#12012yes—
445C4×D3—24no—
446C4×D3—24no—
447C4×D3—44no—
448C4×D3—44no—
449C4×D3—48no—
450C4×D3—48no—
451C4×D3—42no—
452C4×D3—42no—
453Dic6—24no—
454Dic6—48no—
455Dic6—42no—
456C3×C8—42no—
457C3⋊C8—42no—
458C24—31no—
459C24—31no—
460C24—34no—
461C24—62no—
462C24—62no—
463C24—62no—
464C24—62no—
465C24—121no—
466C24—121no—
467C24D3×D411yescharacteristic
468C2×Q8—24no—
469C2×Q8—21no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—22no—
477C2×Q8—32no—
478C2×Q8—48no—
479C2×Q8—48no—
480C2×Q8—42no—
481C2×Q8—42no—
482C2×Q8—64no—
483C2×Q8—61no—
484C2×Q8—62no—
485C2×Q8—62no—
486C2×Q8—122no—
487C2×Q8—122no—
488C2×Q8—128no—
489C2×Q8—128no—
490C2×Q8D3×D414yes—
491C2×Q8C2×#6712yes—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—31no—
499C22×C4—34no—
500C22×C4—31no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—64no—
506C22×C4—64no—
507C22×C4—62no—
508C22×C4—61no—
509C22×C4—62no—
510C22×C4—61no—
511C22×C4—64no—
512C22×C4—62no—
513C22×C4—61no—
514C22×C4—62no—
515C22×C4—61no—
516C22×C4—62no—
517C22×C4—62no—
518C22×C4—61no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—61no—
522C22×C4—121no—
523C22×C4—121no—
524C22×C4—128no—
525C22×C4—128no—
526C22×C4—122no—
527C22×C4—122no—
528C22×C4—122no—
529C22×C4—122no—
530C22×C4—121no—
531C22×C4—122no—
532C22×C4—122no—
533C22×C4D3×D411yescharacteristic
534C22×C4D3×D412yes—
535C22×C4C2×#6712yes—
536C22×C4C23×D311yescharacteristic
537Q16—48no—
538Q16—128no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—62no—
543C2×C8—62no—
544C2×C8—62no—
545C4⋊C4—24no—
546C4⋊C4—21no—
547C4⋊C4—32no—
548C4⋊C4—34no—
549C4⋊C4—68no—
550C4⋊C4—64no—
551C4⋊C4—64no—
552C4⋊C4—68no—
553C4⋊C4—64no—
554C4⋊C4—64no—
555C4⋊C4—64no—
556C4⋊C4—62no—
557C4⋊C4—61no—
558C4⋊C4C2×#6712yes—
559C22⋊C4—24no—
560C22⋊C4—68no—
561C22⋊C4—64no—
562C22⋊C4—64no—
563C22⋊C4—68no—
564C22⋊C4—64no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3#45114yescomplemented
572C22×C3C2×#12011yescharacteristic
573C22×C3C2×#12011yescharacteristic
574C22×C3#53411yescharacteristic
575C22×C3C22×Q1611yescharacteristic
576C22×C3C2×#13711yescharacteristic
577C22×C3C2×#13711yescharacteristic
578C22×C3#57511yescharacteristic
579C2×D3—22no—
580C2×D3—22no—
581C2×D3—22no—
582C2×D3—22no—
583C2×D3—22no—
584C2×D3—22no—
585C2×D3—22no—
586C2×D3—22no—
587C2×D3—22no—
588C2×D3—416no—
589C2×D3—41no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3#45114yescomplemented
594C3×C4—22no—
595C3×C4—42no—
596C3×C4—44no—
597C3×C4—42no—
598C3×C4D4212yes—
599C3×C4D4212yes—
600Dic3—22no—
601Dic3—42no—
602Dic3—41no—
603Dic3—42no—
604Dic3—44no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—32no—
610C23—32no—
611C23—32no—
612C23—32no—
613C23—68no—
614C23—61no—
615C23—61no—
616C23—61no—
617C23—61no—
618C23—68no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23—61no—
624C23—61no—
625C23—124no—
626C23—124no—
627C23—124no—
628C23—124no—
629C23—124no—
630C23D3×Q1612yes—
631C23#91812yes—
632C23#93712yes—
633C23C2×D3×D411yescharacteristic
634Q8—24no—
635Q8—24no—
636Q8—24no—
637Q8—48no—
638Q8—42no—
639Q8—42no—
640Q8—42no—
641Q8—64no—
642Q8—128no—
643Q8—122no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—32no—
652C2×C4—48no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—64no—
662C2×C4—64no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—61no—
666C2×C4—64no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—124no—
670C2×C4—124no—
671C2×C4—128no—
672C2×C4—128no—
673C2×C4—124no—
674C2×C4—128no—
675C2×C4—122no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—122no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4—122no—
682C2×C4—122no—
683C2×C4#93712yes—
684C2×C4C2×D3×D412yes—
685C2×C4C2×D3×D411yescharacteristic
686C2×C4#100412yes—
687C2×C4C22×#6711yescharacteristic
688C8—42no—
689C8—122no—
690C2×C3—24no—
691C2×C3#240311yescharacteristic
692C2×C3C2×#45111yescharacteristic
693C2×C3C2×#45111yescharacteristic
694C2×C3#300711yescharacteristic
695C2×C3#300711yescharacteristic
696C2×C3#318911yescharacteristic
697C2×C3#319511yescharacteristic
698D3—24no—
699D3—42no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—34no—
707C22—62no—
708C22—62no—
709C22—62no—
710C22—62no—
711C22—62no—
712C22—62no—
713C22—62no—
714C22—62no—
715C22—62no—
716C22—1216no—
717C22—121no—
718C22—121no—
719C22—121no—
720C22—121no—
721C22#518614yescomplemented
722C22D3×#12011yescharacteristic
723C22#558911yescharacteristic
724C22C2×D3×Q1611yescharacteristic
725C22C2×#91811yescharacteristic
726C22D3×#13711yescharacteristic
727C22#577711yescharacteristic
728C22C2×#93711yescharacteristic
729C4—22no—
730C4—42no—
731C4—44no—
732C4—42no—
733C4—62no—
734C4—122no—
735C4—124no—
736C4—121no—
737C4—122no—
738C4#559012yes—
739C4D4×#6712yes—
740C3#2392111yescharacteristic, complemented, Sylow
741C2—24no—
742C2—64no—
743C2—122no—
744C2D3×#45111yescharacteristic
745C2#8018411yescharacteristic
746C2#8018711yescharacteristic
747C2#8018911yescharacteristic
748C2#8260411yescharacteristic
749C2C2×#518611yescharacteristic
750C2#8398111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#451C2
socleC23×C3C22×D4
prime radicalC24×D3D4
hypercenterC2×#451D3
hypocenterC3#23921
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. C2×C3×#451C2semidirect
4. C2×#5228C2semidirect
5. C2×#5186C2semidirect
6. #72071C2semidirect
7. #71692C2semidirect
8. #70273C2semidirect
9. #70268C2semidirect
11. #69930C2semidirect
16. C22×C3×Q16C22semidirect
24. C22×#216C22semidirect
38. C2×C3×#103C22semidirect
41. C2×#835C22semidirect
42. C2×#835C22semidirect
47. C2×#816C22semidirect
48. #4551C22semidirect
49. #4529C22semidirect
54. C2×#451D3semidirect
149. C22×Q16C2×D3semidirect
175. C2×#103C2×D3semidirect
189. C23×D3Q16semidirect
571. C22×C3#451semidirect
593. C2×D3#451semidirect
721. C22#5186semidirect
740. C3#23921semidirect

Maximal subgroups

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

subgroupindex
C22×#9462
C2×D3×C22⋊Q82
C2×C3×#4512
C2×#52282
C2×#51862
#720712
#716922
#702732
#702682
#699552
#699302
#239213