Finite Group Databasebeta

← #10686641

Subgroups — #10686641

Order 768.

1296 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5627C211yesmaximal, characteristic
2C2×C3×#328C211yesmaximal, characteristic, complemented
3C2×#4538C211yesmaximal, characteristic, complemented
4#69955C211yesmaximal, characteristic, complemented
5C2×#4470C211yesmaximal, characteristic, complemented
6(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
7C2×#4451C211yesmaximal, characteristic, complemented
8#8331—31nomaximal, Sylow
9C22×#239C411yescharacteristic, complemented
10C23×C4×D3C2211yescharacteristic
11C2×C3×C22⋊Q8C2211yescharacteristic
12C2×#946C411yescharacteristic, complemented
13C2×#930C2211yescharacteristic
14C22×(C2×D3)⋊C4—21no—
15#5627—22no—
16#5627—22no—
17#5627—22no—
18#5627—22no—
19C2×#895C411yescharacteristic, complemented
20C2×#894—21no—
21C2×#893—21no—
22C2×#892C411yescharacteristic, complemented
23C2×#882—21no—
24C2×#67⋊C4—21no—
25C2×C3×C22⋊C8C2211yescharacteristic
26C2×C3×#95C2211yescharacteristic
27C2×C3⋊#95—21no—
28C2×C3⋊#95C2211yescharacteristic
29C2×#830C2211yescharacteristic
30C2×(C2×D3)⋊C8—21no—
31C2×(C2×D3)⋊C8—21no—
32C3×#328—22no—
33#4538—22no—
34#4470—22no—
35#4451—22no—
36C2×#525—31no—
37#1779—31no—
38C2×#328—31no—
39C2×#328D311yescharacteristic, complemented
40C2×#327—31no—
41C2×#327—31no—
42C22⋊#95—31no—
43C24×D3D411yescharacteristic
44C22×C3×Q8C2×C411yescharacteristic
45C23×C3×C4—21no—
46C23×C3×C4C2311yescharacteristic
47C22×#67—21no—
48C23×Dic3—21no—
49C23×Dic3D411yescharacteristic
50C2×#239—22no—
51C2×#239—22no—
52C2×#239—42no—
53C2×#239—42no—
54C22×D12—21no—
55C22×D12—21no—
56C22×D12C2×C411yescharacteristic
57C22×C4×D3—21no—
58C22×C4×D3—21no—
59C22×C4×D3—21no—
60C22×C4×D3—21no—
61C22×C4×D3—21no—
62C22×C4×D3—42no—
63C22×C4×D3—42no—
64C22×C4×D3C2×C411yescharacteristic
65C22×C4×D3C2×C411yescharacteristic
66C22×C4×D3D411yescharacteristic
67C22×C4×D3D411yescharacteristic
68C22×C3×C8—21no—
69C3×C22⋊Q8—21no—
70C3×C22⋊Q8—21no—
71C3×C22⋊Q8D412yes—
72C3×C22⋊Q8D412yes—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4C2×C411yescharacteristic
75C2×C3×C22⋊C4—21no—
76#946—22no—
77#946—22no—
78#930—21no—
79#930—21no—
80#930D412yes—
81#930D412yes—
82C2×(C2×D3)⋊C4—21no—
83C2×(C2×D3)⋊C4—21no—
84C2×(C2×D3)⋊C4—21no—
85C2×(C2×D3)⋊C4—21no—
86C2×(C2×D3)⋊C4—24no—
87C2×(C2×D3)⋊C4—42no—
88C2×(C2×D3)⋊C4—42no—
89C2×C4⋊Dic3C2×C411yescharacteristic
90C2×Dic3⋊C4—21no—
91C2×C4×Dic3—21no—
92C22×C3⋊C8—21no—
93#895—22no—
94#895—22no—
95#894—24no—
96#894—24no—
97#893—24no—
98#893—24no—
99#892—22no—
100#892—22no—
101#882—24no—
102#882—24no—
103#67⋊C4—24no—
104#67⋊C4—24no—
105C3×C22⋊C8—21no—
106C3×C22⋊C8—21no—
107C3×#95—21no—
108C3×#95—21no—
109C3⋊#95—21no—
110C3⋊#95—21no—
111C3⋊#95—42no—
112#830—21no—
113#830—21no—
114(C2×D3)⋊C8—42no—
115(C2×D3)⋊C8—42no—
116C22×#41—31no—
117C24×C4—31no—
118#525—62no—
119#525—62no—
120#525—62no—
121#525—62no—
122C2×#123—61no—
123C2×C22⋊Q8—31no—
124C2×C22⋊Q8C2×D311yescharacteristic
125C2×#121—31no—
126C2×#121—31no—
127C2×#120—61no—
128C2×C4×D4—61no—
129C2×C4×D4—61no—
130C2×#117—31no—
131C22×C22⋊C4—61no—
132C2×C22⋊C8—31no—
133C2×C22⋊C8—61no—
134C2×C22⋊C8—61no—
135C2×C22⋊C8C2×D311yescharacteristic
136C2×#95—31no—
137C2×#95—61no—
138C2×#95C2×D311yescharacteristic
139#328—22no—
140#328—62no—
141#327—62no—
142#327—62no—
143C24×C3C2×D411yescharacteristic
144C23×D3—21no—
145C23×D3—21no—
146C23×D3—22no—
147C23×D3—22no—
148C23×D3—21no—
149C23×D3—21no—
150C23×D3—21no—
151C23×D3—21no—
152C23×D3—21no—
153C23×D3—41no—
154C23×D3—41no—
155C23×D3C22⋊C411yescharacteristic
156C23×D3C22⋊C411yescharacteristic
157C2×C3×Q8—21no—
158C2×C3×Q8—41no—
159C2×C3×Q8—41no—
160C2×C3×Q8C22⋊C412yescomplemented
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—22no—
164C22×C3×C4—41no—
165C22×C3×C4—41no—
166C22×C3×C4—41no—
167C22×C3×C4—41no—
168C22×C3×C4—41no—
169C22×C3×C4—41no—
170C22×C3×C4—41no—
171C22×C3×C4—41no—
172C22×C3×C4C22×C411yescharacteristic
173C22×C3×C4C2×D411yescharacteristic
174C22×C3×C4C2×D411yescharacteristic
175C22×C3×C4C2×D411yescharacteristic
176C22×C3×C4C2×D411yescharacteristic
177C22×C3×C4C2×D411yescharacteristic
178C2×#67—22no—
179C2×#67—22no—
180C2×#67—41no—
181C2×#67—41no—
182C2×#67—41no—
183C2×#67—41no—
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—22no—
188C22×Dic3—22no—
189C22×Dic3—41no—
190C22×Dic3—41no—
191C22×Dic3—41no—
192C22×Dic3—41no—
193C22×Dic3—41no—
194C22×Dic3—41no—
195C22×Dic3—41no—
196C22×Dic3C22⋊C411yescharacteristic
197C22×Dic3C22⋊C411yescharacteristic
198#239—48no—
199#239—48no—
200C2×D12—24no—
201C2×D12—24no—
202C2×D12—21no—
203C2×D12—41no—
204C2×D12—41no—
205C2×D12—42no—
206C2×D12—42no—
207C2×D12—42no—
208C2×D12—42no—
209C2×D12C22⋊C412yescomplemented
210C2×C4×D3—22no—
211C2×C4×D3—21no—
212C2×C4×D3—21no—
213C2×C4×D3—22no—
214C2×C4×D3—24no—
215C2×C4×D3—22no—
216C2×C4×D3—21no—
217C2×C4×D3—21no—
218C2×C4×D3—21no—
219C2×C4×D3—21no—
220C2×C4×D3—21no—
221C2×C4×D3—21no—
222C2×C4×D3—22no—
223C2×C4×D3—44no—
224C2×C4×D3—44no—
225C2×C4×D3—44no—
226C2×C4×D3—44no—
227C2×C4×D3—41no—
228C2×C4×D3—41no—
229C2×C4×D3—41no—
230C2×C4×D3—41no—
231C2×C4×D3—42no—
232C2×C4×D3—42no—
233C2×C3×C8—41no—
234C2×C3×C8—41no—
235C2×C3×C8—41no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4C22⋊C412yescomplemented
240C3×C22⋊C4—22no—
241C3×C22⋊C4—22no—
242(C2×D3)⋊C4—24no—
243(C2×D3)⋊C4—24no—
244(C2×D3)⋊C4—24no—
245(C2×D3)⋊C4—22no—
246(C2×D3)⋊C4—22no—
247(C2×D3)⋊C4—48no—
248C4⋊Dic3—21no—
249C4⋊Dic3C22⋊C412yescomplemented
250Dic3⋊C4—24no—
251C4×Dic3—24no—
252C2×C3⋊C8—41no—
253C2×C3⋊C8—41no—
254C2×C3⋊C8—41no—
255C25—31no—
256C2×#41—62no—
257C2×#41—62no—
258C2×#41—122no—
259C2×#41—122no—
260C22×Q8C4×D311yescharacteristic
261C22×D4—31no—
262C22×D4—61no—
263C22×D4—61no—
264C22×D4—61no—
265C23×C4—21no—
266C23×C4—31no—
267C23×C4—31no—
268C23×C4—31no—
269C23×C4—31no—
270C23×C4—31no—
271C23×C4—61no—
272C23×C4—61no—
273C23×C4—61no—
274C23×C4—61no—
275C23×C4—61no—
276C23×C4—61no—
277C23×C4—122no—
278C23×C4—122no—
279C23×C4C22×D311yescharacteristic
280C22×C8—21no—
281C22×C8—61no—
282#123—64no—
283#123—64no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—62no—
287C22⋊Q8—62no—
288C22⋊Q8D1212yes—
289C22⋊Q8#6712yes—
290#121—32no—
291#121—32no—
292#121—62no—
293#121—61no—
294#121—61no—
295#121—62no—
296#120—64no—
297#120—64no—
298C4×D4—64no—
299C4×D4—64no—
300C4×D4—64no—
301C4×D4—64no—
302#117—62no—
303#117—62no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—61no—
307C2×C4⋊C4C4×D311yescharacteristic
308C2×C22⋊C4—21no—
309C2×C22⋊C4—61no—
310C2×C22⋊C4—61no—
311C2×C22⋊C4—61no—
312C2×C22⋊C4—61no—
313C2×C22⋊C4—64no—
314C2×C22⋊C4—122no—
315C2×C22⋊C4—122no—
316C2×C42—61no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—61no—
320C22⋊C8—61no—
321C22⋊C8—122no—
322C22⋊C8—122no—
323#95—21no—
324#95—21no—
325#95—61no—
326#95—61no—
327#95—122no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3C2×C22⋊C411yescharacteristic
333C23×C3#12011yescharacteristic
334C23×C3#12011yescharacteristic
335C23×C3#13511yescharacteristic
336C23×C3#13511yescharacteristic
337C23×C3AGL(1,ℤ/8)11yescharacteristic
338C23×C3#13711yescharacteristic
339C22×D3—24no—
340C22×D3—24no—
341C22×D3—21no—
342C22×D3—21no—
343C22×D3—21no—
344C22×D3—21no—
345C22×D3—21no—
346C22×D3—21no—
347C22×D3—21no—
348C22×D3—21no—
349C22×D3—21no—
350C22×D3—21no—
351C22×D3—21no—
352C22×D3—21no—
353C22×D3—22no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—42no—
357C22×D3—42no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—42no—
364C22×D3—41no—
365C22×D3—41no—
366C22×D3—41no—
367C22×D3—41no—
368C22×D3—41no—
369C22×D3—41no—
370C22×D3—41no—
371C22×D3—41no—
372C22×D3—41no—
373C22×D3—41no—
374C22×D3#9912yes—
375C22×D3#10412yes—
376C3×Q8—42no—
377C3×Q8—42no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—81no—
396C2×C3×C4—81no—
397C2×C3×C4—81no—
398C2×C3×C4—81no—
399C2×C3×C4C2×C22⋊C411yescharacteristic
400C2×C3×C4C2×C22⋊C411yescharacteristic
401C2×C3×C4#12011yescharacteristic
402C2×C3×C4#12011yescharacteristic
403#67—42no—
404#67—42no—
405#67—42no—
406#67—42no—
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410C2×Dic3—21no—
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—42no—
414C2×Dic3—42no—
415C2×Dic3—41no—
416C2×Dic3—41no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—81no—
421C2×Dic3—81no—
422C2×Dic3—81no—
423C2×Dic3—81no—
424C2×Dic3#9912yes—
425D12—42no—
426D12—42no—
427D12—48no—
428D12—48no—
429C4×D3—24no—
430C4×D3—24no—
431C4×D3—42no—
432C4×D3—42no—
433C4×D3—48no—
434C4×D3—42no—
435C4×D3—42no—
436C4×D3—42no—
437C4×D3—42no—
438C3×C8—81no—
439C3⋊C8—81no—
440C24—31no—
441C24—31no—
442C24—62no—
443C24—62no—
444C24—61no—
445C24—61no—
446C24—61no—
447C24—61no—
448C24—61no—
449C24—61no—
450C24—61no—
451C24—121no—
452C24—121no—
453C24D3×D411yescharacteristic
454#41—128no—
455#41—128no—
456C2×Q8—21no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8(C2×D3)⋊C412yescomplemented
460C2×D4—32no—
461C2×D4—64no—
462C2×D4—64no—
463C2×D4—62no—
464C2×D4—62no—
465C2×D4—61no—
466C2×D4—121no—
467C2×D4—121no—
468C2×D4—122no—
469C2×D4—122no—
470C2×D4—122no—
471C2×D4—122no—
472C2×D4—121no—
473C2×D4—121no—
474C2×D4—121no—
475C2×D4—121no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—64no—
494C22×C4—62no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—61no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—62no—
507C22×C4—121no—
508C22×C4—121no—
509C22×C4—121no—
510C22×C4—121no—
511C22×C4—122no—
512C22×C4—124no—
513C22×C4—124no—
514C22×C4—124no—
515C22×C4—124no—
516C22×C4—122no—
517C22×C4—121no—
518C22×C4—121no—
519C22×C4—121no—
520C22×C4—121no—
521C22×C4—121no—
522C22×C4—121no—
523C22×C4—121no—
524C22×C4C2×C4×D311yescharacteristic
525C22×C4C2×D1211yescharacteristic
526C22×C4D3×D411yescharacteristic
527C22×C4D3×D411yescharacteristic
528C22×C4D3×D411yescharacteristic
529C22×C4C2×#6711yescharacteristic
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—121no—
534C2×C8—121no—
535C2×C8—121no—
536C4⋊C4—21no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—32no—
540C4⋊C4—64no—
541C4⋊C4—61no—
542C4⋊C4(C2×D3)⋊C412yescomplemented
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—64no—
546C22⋊C4—64no—
547C22⋊C4—64no—
548C22⋊C4—62no—
549C22⋊C4—62no—
550C22⋊C4—128no—
551C42—64no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3#37911yescharacteristic
565C22×C3C2×#9911yescharacteristic
566C22×C3C2×#9911yescharacteristic
567C22×C3#41611yescharacteristic
568C22×C3#41711yescharacteristic
569C22×C3C2×#10411yescharacteristic
570C22×C3#42111yescharacteristic
571C22×C3#44911yescharacteristic
572C22×C3#44911yescharacteristic
573C22×C3#45211yescharacteristic
574C22×C3#45211yescharacteristic
575C2×D3—22no—
576C2×D3—22no—
577C2×D3—22no—
578C2×D3—22no—
579C2×D3—22no—
580C2×D3—22no—
581C2×D3—44no—
582C2×D3—44no—
583C2×D3—44no—
584C2×D3—44no—
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—42no—
594C2×D3—42no—
595C2×D3—42no—
596C2×D3—81no—
597C2×D3—81no—
598C2×D3—81no—
599C2×D3—81no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—21no—
604C3×C4—42no—
605C3×C4—42no—
606C3×C4—82no—
607Dic3—22no—
608Dic3—41no—
609Dic3—42no—
610Dic3—82no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—32no—
616C23—32no—
617C23—64no—
618C23—64no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23—61no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—62no—
632C23—122no—
633C23—122no—
634C23—122no—
635C23—122no—
636C23—122no—
637C23—122no—
638C23—122no—
639C23—122no—
640C23—122no—
641C23—122no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23—121no—
651C23—121no—
652C23D3×C22⋊C411yescharacteristic
653C23#88211yescharacteristic
654C23#91411yescharacteristic
655C23#91611yescharacteristic
656C23#91811yescharacteristic
657C23#91911yescharacteristic
658C23#93711yescharacteristic
659Q8—42no—
660Q8—42no—
661D4—122no—
662D4—122no—
663D4—128no—
664D4—128no—
665D4—122no—
666D4—122no—
667D4—122no—
668D4—122no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—32no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—64no—
688C2×C4—64no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—62no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4—122no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4—128no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—241no—
714C2×C4—241no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4D3×C22⋊C411yescharacteristic
718C2×C4#88211yescharacteristic
719C2×C4C2×(C2×D3)⋊C411yescharacteristic
720C2×C4#93711yescharacteristic
721C8—81no—
722C8—241no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3#150111yescharacteristic
728C2×C3#150411yescharacteristic
729C2×C3#151311yescharacteristic
730C2×C3#151611yescharacteristic
731C2×C3#178111yescharacteristic
732C2×C3#178811yescharacteristic
733C2×C3#178911yescharacteristic
734D3—42no—
735D3—42no—
736D3—82no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—62no—
750C22—62no—
751C22—62no—
752C22—62no—
753C22—62no—
754C22—62no—
755C22—124no—
756C22—124no—
757C22—124no—
758C22—124no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—122no—
768C22—122no—
769C22—122no—
770C22—241no—
771C22—241no—
772C22—241no—
773C22—241no—
774C22D3×#9911yescharacteristic
775C22D3×#9911yescharacteristic
776C22#480311yescharacteristic
777C22#480411yescharacteristic
778C22#480811yescharacteristic
779C22#481011yescharacteristic
780C22D3×#10411yescharacteristic
781C22#482111yescharacteristic
782C22#495511yescharacteristic
783C22#517211yescharacteristic
784C22#518711yescharacteristic
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—42no—
790C4—42no—
791C4—62no—
792C4—82no—
793C4—122no—
794C4—121no—
795C4—242no—
796C3#833111yescharacteristic, complemented, Sylow
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—122no—
802C2—122no—
803C2—242no—
804C2#6833311yescharacteristic
805C2#6833411yescharacteristic
806C2#6833711yescharacteristic
807C2#6833811yescharacteristic
808C2#7003511yescharacteristic
809C2#7026711yescharacteristic
810C2#7038011yescharacteristic
subgroupG/H
centerC23D3×C22⋊C4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#328C2
socleC23×C3C2×C22⋊C4
prime radicalC2×#5627C2
cosocleC23×C3×C4C23
hypercenterC2×#328D3
hypocenterC3#8331
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. C2×C3×#328C2semidirect
3. C2×#4538C2semidirect
4. #69955C2semidirect
5. C2×#4470C2semidirect
6. (C2×D3)⋊#95C2semidirect
7. C2×#4451C2semidirect
9. C22×#239C4semidirect
12. C2×#946C4semidirect
19. C2×#895C4semidirect
22. C2×#892C4semidirect
39. C2×#328D3semidirect
160. C2×C3×Q8C22⋊C4semidirect
209. C2×D12C22⋊C4semidirect
239. C3×C4⋊C4C22⋊C4semidirect
249. C4⋊Dic3C22⋊C4semidirect
459. C2×Q8(C2×D3)⋊C4semidirect
542. C4⋊C4(C2×D3)⋊C4semidirect
796. C3#8331semidirect

Maximal subgroups

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

subgroupindex
C2×#56272
C2×C3×#3282
C2×#45382
#699552
C2×#44702
(C2×D3)⋊#952
C2×#44512
#83313