Finite Group Databasebeta

← #10794583

Subgroups — #10794583

Order 768.

1522 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#237C211yesmaximal, characteristic
2C2×#4740C212yesmaximal
3#73864C212yesmaximal, complemented
4C3×#1799C211yesmaximal, characteristic, complemented
5#71619C211yesmaximal, characteristic, complemented
6#70028C212yesmaximal, complemented
7#69530C212yesmaximal, complemented
8#68959C212yesmaximal, complemented
9#68951C212yesmaximal, complemented
10#20632—31nomaximal, Sylow
11C22×#237C2211yescharacteristic
12C2×C3×C4×D4C2211yescharacteristic
13C2×D4×Dic3C2211yescharacteristic
14C2×C4×#67C411yescharacteristic, complemented
15C2×C4×#67C2211yescharacteristic
16C22×C4×Dic3C411yescharacteristic, complemented
17C22×C4×Dic3C2211yescharacteristic
18C4×#237—22no—
19C4×#237—22no—
20C4×#237—22no—
21C4×#237—22no—
22C2×#892C411yescharacteristic, complemented
23C2×#887C411yescharacteristic, complemented
24C2×#67⋊C4C411yescharacteristic, complemented
25C2×#67⋊C4C2211yescharacteristic
26C2×#877C411yescharacteristic, complemented
27C2×#877C2214yes—
28C2×#877C2211yescharacteristic
29C2×C42×D3C411yescharacteristic, complemented
30C2×C4×Dic6C411yescharacteristic, complemented
31C2×C3×#99C2212yes—
32C3×#380C2212yes—
33C2×#834C2212yes—
34#5212C2212yes—
35#4975—22no—
36Dic3×C4⋊C4—22no—
37C2×#806C2214yes—
38#4942C2214yes—
39#4740—28no—
40#4650—22no—
41#4649—22no—
42C3×#342C2212yes—
43#4527C2214yes—
44#4526C2212yes—
45C2×C4×#41—31no—
46C2×#410—32no—
47#2285—32no—
48#1799—32no—
49#1799—32no—
50#1799—32no—
51#1799—31no—
52#1799D311yescharacteristic, complemented
53#1740—32no—
54C22×C3×D4C2311yescharacteristic
55C23×C3×C4C2×C411yescharacteristic
56C23×C3×C4C2311yescharacteristic
57C22×#67C2×C411yescharacteristic
58C22×#67C2311yescharacteristic
59C23×Dic3C2×C411yescharacteristic
60C23×Dic3C2×C411yescharacteristic
61C23×Dic3C2311yescharacteristic
62C23×Dic3C2311yescharacteristic
63C2×#237—22no—
64C2×#237—22no—
65C2×#237—24no—
66C2×#237D414yes—
67C2×#237Q814yes—
68C22×C4×D3C2×C411yescharacteristic
69C22×C4×D3C2×C411yescharacteristic
70C22×C4×D3C2×C411yescharacteristic
71C22×Dic6C2×C411yescharacteristic
72C3×C4×D4—22no—
73C3×C4×D4—22no—
74C2×C3×C4⋊C4—22no—
75C2×C3×C4⋊C4C2×C411yescharacteristic
76C2×C3×C22⋊C4C2×C411yescharacteristic
77C2×C3×C22⋊C4C2314yes—
78C2×C3×C22⋊C4C2311yescharacteristic
79C2×C3×C42C2×C411yescharacteristic
80C2×#217C2×C411yescharacteristic
81C2×#217C2314yes—
82C2×#217C2311yescharacteristic
83D4×Dic3—22no—
84D4×Dic3—22no—
85C4×#67—22no—
86C4×#67—22no—
87C4×#67—22no—
88C4×#67—22no—
89C2×(C2×D3)⋊C4C2×C411yescharacteristic
90C2×(C2×D3)⋊C4C2×C411yescharacteristic
91C2×C4⋊Dic3—22no—
92C2×C4⋊Dic3C2×C411yescharacteristic
93C2×Dic3⋊C4—24no—
94C2×Dic3⋊C4—24no—
95C2×Dic3⋊C4C2×C411yescharacteristic
96C2×Dic3⋊C4C2×C411yescharacteristic
97C2×Dic3⋊C4C2×C411yescharacteristic
98C2×Dic3⋊C4C2×C411yescharacteristic
99C2×C4×Dic3—21no—
100C2×C4×Dic3—21no—
101C2×C4×Dic3—21no—
102C2×C4×Dic3—21no—
103C2×C4×Dic3—24no—
104C2×C4×Dic3C2×C411yescharacteristic
105C2×C4×Dic3C2×C411yescharacteristic
106C2×C4×Dic3C2×C411yescharacteristic
107C2×C4×Dic3C2×C411yescharacteristic
108C2×C4×Dic3C2×C411yescharacteristic
109C2×C4×Dic3C2×C411yescharacteristic
110C2×C4×Dic3C2×C411yescharacteristic
111C2×C4×Dic3C2×C411yescharacteristic
112C2×C4×Dic3C2×C411yescharacteristic
113C2×C4×Dic3D412yes—
114C2×C4×Dic3D412yes—
115C2×C4×Dic3D412yes—
116C2×C4×Dic3D412yes—
117#892—22no—
118#892—22no—
119#887—22no—
120#887—22no—
121#67⋊C4—22no—
122#67⋊C4—22no—
123#67⋊C4—22no—
124#67⋊C4—22no—
125#877—22no—
126#877—22no—
127#877—22no—
128#877—22no—
129#877—28no—
130#877—28no—
131C42×D3—21no—
132C42×D3—21no—
133C42×D3—21no—
134C42×D3—21no—
135C4×Dic6—22no—
136C4×Dic6—22no—
137C3×#99—24no—
138C3×#95—22no—
139#834—24no—
140C3⋊#95—22no—
141C3⋊#95—24no—
142#806—28no—
143C22×#41—31no—
144C4×#41—62no—
145C4×#41—62no—
146C4×#41—62no—
147C4×#41—62no—
148C2×C4×Q8—31no—
149C2×C4×Q8—31no—
150C2×C4×D4—31no—
151C2×C4×D4—31no—
152C2×C4×D4—31no—
153C2×C4×D4—31no—
154C2×C4×D4—31no—
155C2×C4×D4C2×D311yescharacteristic
156C2×#117—31no—
157C2×#117—31no—
158C2×#117—31no—
159C2×#117—34no—
160C22×C42—31no—
161C22×C42—31no—
162C22×C42—31no—
163#410—68no—
164C2×#99—32no—
165C2×#99—34no—
166C2×#99C2×D312yes—
167#384—62no—
168#382—62no—
169#380—32no—
170#380—34no—
171#380C2×D312yes—
172C4×C4⋊C4—62no—
173C4×C4⋊C4—62no—
174#342—32no—
175#342—34no—
176#342C2×D312yes—
177C24×C3C22×C411yescharacteristic
178C24×C3C2411yescharacteristic
179C23×D3C22×C411yescharacteristic
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4C2×D412yes—
183C2×C3×D4C2×Q812yes—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—24no—
187C22×C3×C4—42no—
188C22×C3×C4—42no—
189C22×C3×C4C22×C411yescharacteristic
190C22×C3×C4C22×C411yescharacteristic
191C22×C3×C4C22×C411yescharacteristic
192C22×C3×C4C22×C411yescharacteristic
193C22×C3×C4C22×C411yescharacteristic
194C22×C3×C4C2×D412yes—
195C22×C3×C4C2×D412yes—
196C2×#67—22no—
197C2×#67—22no—
198C2×#67—22no—
199C2×#67—22no—
200C2×#67C4⋊C414yescomplemented
201C2×#67C2×D412yes—
202C2×#67C2×Q812yes—
203C22×Dic3—21no—
204C22×Dic3—21no—
205C22×Dic3—22no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—24no—
209C22×Dic3—42no—
210C22×Dic3—42no—
211C22×Dic3C4⋊C414yescomplemented
212C22×Dic3C22×C411yescharacteristic
213C22×Dic3C22×C411yescharacteristic
214C22×Dic3C22×C411yescharacteristic
215C22×Dic3C22×C411yescharacteristic
216C22×Dic3C22×C411yescharacteristic
217C22×Dic3C22×C411yescharacteristic
218C22×Dic3C22×C411yescharacteristic
219C22×Dic3C2×D412yes—
220C22×Dic3C2×D412yes—
221C22×Dic3C2×D412yes—
222C22×Dic3C2×D412yes—
223C22×Dic3C2×D412yes—
224C22×Dic3C2×Q812yes—
225C22×Dic3#4114yes—
226#237—28no—
227#237—28no—
228#237—28no—
229#237—28no—
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3—22no—
233C2×C4×D3—21no—
234C2×C4×D3—21no—
235C2×C4×D3—21no—
236C2×C4×D3—21no—
237C2×C4×D3—42no—
238C2×C4×D3—42no—
239C2×C4×D3C4⋊C414yescomplemented
240C2×Dic6—22no—
241C2×Dic6—22no—
242C2×Dic6C4⋊C414yescomplemented
243C3×C4⋊C4—22no—
244C3×C4⋊C4—44no—
245C3×C22⋊C4—22no—
246C3×C22⋊C4—22no—
247C3×C22⋊C4—24no—
248C3×C22⋊C4—24no—
249C3×C42—21no—
250C3×C42—21no—
251#217—22no—
252#217—22no—
253#217—24no—
254#217—24no—
255(C2×D3)⋊C4—22no—
256(C2×D3)⋊C4—22no—
257C4⋊Dic3—22no—
258C4⋊Dic3—44no—
259Dic3⋊C4—22no—
260Dic3⋊C4—22no—
261Dic3⋊C4—22no—
262Dic3⋊C4—22no—
263Dic3⋊C4—48no—
264Dic3⋊C4—48no—
265C4×Dic3—21no—
266C4×Dic3—21no—
267C4×Dic3—21no—
268C4×Dic3—21no—
269C4×Dic3—21no—
270C4×Dic3—21no—
271C4×Dic3—21no—
272C4×Dic3—21no—
273C4×Dic3—21no—
274C4×Dic3—21no—
275C4×Dic3—48no—
276C4×Dic3C22⋊C412yes—
277C4×Dic3C22⋊C412yes—
278C4×Dic3C22⋊C411yescharacteristic
279C4×Dic3C22⋊C411yescharacteristic
280C4×Dic3C22⋊C411yescharacteristic
281C4×Dic3C22⋊C411yescharacteristic
282C4×Dic3C22⋊C412yes—
283C4×Dic3C22⋊C412yes—
284C4×Dic3C22⋊C412yes—
285C4×Dic3C22⋊C412yes—
286C2×#41—34no—
287C2×#41—34no—
288C2×#41—62no—
289C2×#41—62no—
290C2×#41—64no—
291C22×Q8—31no—
292C22×D4—31no—
293C22×D4—31no—
294C22×D4C22×D311yescharacteristic
295C23×C4—31no—
296C23×C4—31no—
297C23×C4—31no—
298C23×C4—31no—
299C23×C4—31no—
300C23×C4—31no—
301C23×C4—31no—
302C23×C4C4×D311yescharacteristic
303C23×C4C22×D311yescharacteristic
304C4×Q8—62no—
305C4×Q8—62no—
306C4×Q8—62no—
307C4×Q8—62no—
308C4×D4—22no—
309C4×D4—22no—
310C4×D4—62no—
311C4×D4—62no—
312C4×D4—62no—
313C4×D4—62no—
314C4×D4—62no—
315C4×D4—62no—
316C4×D4—62no—
317C4×D4—62no—
318C4×D4—62no—
319C4×D4—62no—
320#117—62no—
321#117—62no—
322#117—62no—
323#117—62no—
324#117—62no—
325#117—62no—
326#117—68no—
327#117—68no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—31no—
330C2×C4⋊C4—31no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—31no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—64no—
335C2×C4⋊C4—64no—
336C2×C4⋊C4—62no—
337C2×C4⋊C4C4×D311yescharacteristic
338C2×C22⋊C4—31no—
339C2×C22⋊C4—31no—
340C2×C22⋊C4—31no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—34no—
343C2×C22⋊C4C4×D311yescharacteristic
344C2×C22⋊C4C22×D314yes—
345C2×C22⋊C4C22×D311yescharacteristic
346C2×C42—31no—
347C2×C42—31no—
348C2×C42—31no—
349C2×C42—31no—
350C2×C42—32no—
351C2×C42—32no—
352C2×C42—32no—
353C2×C42—32no—
354C2×C42—31no—
355C2×C42—31no—
356C2×C42—31no—
357C2×C42—31no—
358C2×C42—31no—
359C2×C42—61no—
360C2×C42—61no—
361C2×C42—61no—
362C2×C42—61no—
363C2×C42—61no—
364C2×C42—61no—
365C2×C42—61no—
366C2×C42—61no—
367C2×C42—64no—
368C2×C42C4×D311yescharacteristic
369#99—24no—
370#99—68no—
371#99—64no—
372#95—22no—
373#95—64no—
374#95—62no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3C2×C4⋊C412yes—
382C23×C3C23×C411yescharacteristic
383C23×C3C22×D412yes—
384C23×C3C22×D411yescharacteristic
385C23×C3C22×Q811yescharacteristic
386C23×C3C2×#4112yes—
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—41no—
390C22×D3—41no—
391C22×D3C2×C4⋊C412yes—
392C3×D4—24no—
393C3×D4—24no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—24no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—41no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—44no—
407C2×C3×C4—44no—
408C2×C3×C4—44no—
409C2×C3×C4C2×C22⋊C411yescharacteristic
410C2×C3×C4C2×C22⋊C412yes—
411C2×C3×C4C2×C22⋊C411yescharacteristic
412C2×C3×C4C2×C4⋊C412yes—
413#67—24no—
414#67—24no—
415#67—28no—
416C2×Dic3—21no—
417C2×Dic3—21no—
418C2×Dic3—24no—
419C2×Dic3—24no—
420C2×Dic3—24no—
421C2×Dic3—22no—
422C2×Dic3—21no—
423C2×Dic3—21no—
424C2×Dic3—41no—
425C2×Dic3—42no—
426C2×Dic3—42no—
427C2×Dic3—42no—
428C2×Dic3—41no—
429C2×Dic3—41no—
430C2×Dic3—44no—
431C2×Dic3—44no—
432C2×Dic3—44no—
433C2×Dic3C2×C22⋊C411yescharacteristic
434C2×Dic3C2×C22⋊C412yes—
435C2×Dic3C2×C22⋊C411yescharacteristic
436C2×Dic3C2×C22⋊C411yescharacteristic
437C2×Dic3C2×C22⋊C412yes—
438C2×Dic3C2×C22⋊C411yescharacteristic
439C2×Dic3C2×C4⋊C412yes—
440C2×Dic3C2×C4⋊C412yes—
441C2×Dic3C2×C4⋊C412yes—
442C2×Dic3#11712yes—
443C2×Dic3#11712yes—
444C2×Dic3#12114yes—
445C2×Dic3#12114yes—
446C2×Dic3C22⋊Q814yes—
447C2×Dic3C22⋊Q814yes—
448C4×D3—24no—
449C4×D3—24no—
450C4×D3—42no—
451C4×D3—42no—
452C4×D3—42no—
453C4×D3—42no—
454Dic6—28no—
455C24—31no—
456C24C2×C4×D311yescharacteristic
457C24C23×D311yescharacteristic
458#41—68no—
459#41—68no—
460#41—68no—
461#41—68no—
462C2×Q8—34no—
463C2×Q8—62no—
464C2×Q8—62no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—34no—
468C2×D4—32no—
469C2×D4—32no—
470C2×D4—62no—
471C2×D4—62no—
472C2×D4—62no—
473C2×D4—62no—
474C2×D4D3×D412yes—
475C2×D4D3×Q812yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—24no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—32no—
482C22×C4—32no—
483C22×C4—32no—
484C22×C4—32no—
485C22×C4—34no—
486C22×C4—34no—
487C22×C4—31no—
488C22×C4—31no—
489C22×C4—32no—
490C22×C4—31no—
491C22×C4—32no—
492C22×C4—34no—
493C22×C4—31no—
494C22×C4—31no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—62no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—62no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—64no—
510C22×C4—122no—
511C22×C4—122no—
512C22×C4—122no—
513C22×C4—122no—
514C22×C4C2×C4×D311yescharacteristic
515C22×C4C2×C4×D311yescharacteristic
516C22×C4C2×C4×D311yescharacteristic
517C22×C4C2×C4×D311yescharacteristic
518C22×C4C2×C4×D311yescharacteristic
519C22×C4D3×D412yes—
520C22×C4D3×D412yes—
521C4⋊C4—22no—
522C4⋊C4—44no—
523C4⋊C4—62no—
524C4⋊C4—62no—
525C4⋊C4—62no—
526C4⋊C4—62no—
527C4⋊C4—62no—
528C4⋊C4—124no—
529C4⋊C4—128no—
530C4⋊C4—128no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—62no—
536C22⋊C4—62no—
537C22⋊C4—62no—
538C22⋊C4—62no—
539C22⋊C4—64no—
540C22⋊C4—64no—
541C42—21no—
542C42—21no—
543C42—31no—
544C42—31no—
545C42—31no—
546C42—31no—
547C42—32no—
548C42—32no—
549C42—32no—
550C42—32no—
551C42—32no—
552C42—32no—
553C42—61no—
554C42—61no—
555C42—61no—
556C42—61no—
557C42—61no—
558C42—61no—
559C42—61no—
560C42—61no—
561C42—61no—
562C42—61no—
563C42—128no—
564C22×C3—22no—
565C22×C3—21no—
566C22×C3—22no—
567C22×C3—21no—
568C22×C3—22no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3C22×C22⋊C411yescharacteristic
577C22×C3C22×C4⋊C411yescharacteristic
578C22×C3C2×#11711yescharacteristic
579C22×C3C2×#12112yes—
580C22×C3C2×C22⋊Q812yes—
581C2×D3—22no—
582C2×D3—42no—
583C2×D3—41no—
584C2×D3—41no—
585C2×D3—42no—
586C3×C4—21no—
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—41no—
590C3×C4—41no—
591C3×C4—84no—
592C3×C4#41012yescomplemented
593Dic3—21no—
594Dic3—22no—
595Dic3—22no—
596Dic3—41no—
597Dic3—41no—
598Dic3—84no—
599Dic3#38014yes—
600Dic3#38012yes—
601Dic3#38012yes—
602Dic3#41012yescomplemented
603C23—21no—
604C23—21no—
605C23—32no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—61no—
611C23—61no—
612C23—121no—
613C23—121no—
614C23D3×C4⋊C412yes—
615C23C22×C4×D311yescharacteristic
616C23C2×D3×D412yes—
617C23C2×D3×D411yescharacteristic
618C23C2×D3×Q811yescharacteristic
619C23D3×#4112yes—
620Q8—68no—
621D4—24no—
622D4—24no—
623D4—68no—
624D4—64no—
625D4—64no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—31no—
633C2×C4—31no—
634C2×C4—31no—
635C2×C4—32no—
636C2×C4—32no—
637C2×C4—32no—
638C2×C4—32no—
639C2×C4—32no—
640C2×C4—34no—
641C2×C4—34no—
642C2×C4—34no—
643C2×C4—34no—
644C2×C4—31no—
645C2×C4—32no—
646C2×C4—32no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—44no—
654C2×C4—44no—
655C2×C4—44no—
656C2×C4—64no—
657C2×C4—64no—
658C2×C4—64no—
659C2×C4—64no—
660C2×C4—64no—
661C2×C4—62no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—122no—
667C2×C4—122no—
668C2×C4—122no—
669C2×C4—122no—
670C2×C4—122no—
671C2×C4—121no—
672C2×C4—122no—
673C2×C4—122no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—124no—
677C2×C4—124no—
678C2×C4—124no—
679C2×C4D3×C22⋊C411yescharacteristic
680C2×C4D3×C22⋊C412yes—
681C2×C4D3×C22⋊C411yescharacteristic
682C2×C4D3×C4⋊C412yes—
683C2×C3—22no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—22no—
687C2×C3—42no—
688C2×C3C2×#38011yescharacteristic
689C2×C3C2×#41011yescharacteristic
690C2×C3C2×#41011yescharacteristic
691D3—42no—
692C22—22no—
693C22—21no—
694C22—22no—
695C22—21no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—41no—
703C22—41no—
704C22—62no—
705C22—122no—
706C22—122no—
707C22—121no—
708C22—121no—
709C22C2×D3×C22⋊C411yescharacteristic
710C22C2×D3×C4⋊C411yescharacteristic
711C22D3×#11711yescharacteristic
712C22D3×#12112yes—
713C22D3×C22⋊Q812yes—
714C4—22no—
715C4—21no—
716C4—22no—
717C4—32no—
718C4—32no—
719C4—34no—
720C4—32no—
721C4—41no—
722C4—41no—
723C4—62no—
724C4—61no—
725C4—62no—
726C4—84no—
727C4—121no—
728C4—121no—
729C4—244no—
730C4#474012yescomplemented
731C3#2063211yescharacteristic, complemented, Sylow
732C2—22no—
733C2—21no—
734C2—21no—
735C2—22no—
736C2—42no—
737C2—122no—
738C2D3×#38011yescharacteristic
739C2C2×#474011yescharacteristic
740C2D3×#41011yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC3×#1799C2
socleC22×C3C22×C22⋊C4
prime radicalC22×#237C22
cosocleC24×C3C24
hypercenter#1799D3
hypocenterC3#20632
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #73864C2semidirect
4. C3×#1799C2semidirect
5. #71619C2semidirect
6. #70028C2semidirect
7. #69530C2semidirect
8. #68959C2semidirect
9. #68951C2semidirect
14. C2×C4×#67C4semidirect
16. C22×C4×Dic3C4semidirect
22. C2×#892C4semidirect
23. C2×#887C4semidirect
24. C2×#67⋊C4C4semidirect
26. C2×#877C4semidirect
29. C2×C42×D3C4semidirect
30. C2×C4×Dic6C4semidirect
52. #1799D3semidirect
200. C2×#67C4⋊C4semidirect
211. C22×Dic3C4⋊C4semidirect
239. C2×C4×D3C4⋊C4semidirect
242. C2×Dic6C4⋊C4semidirect
592. C3×C4#410semidirect
602. Dic3#410semidirect
730. C4#4740semidirect
731. C3#20632semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#2372
C2×#47402
#738642
C3×#17992
#716192
#700282
#695302
#689592
#689512
#206323