Finite Group Databasebeta

← #10690741

Subgroups — #10690741

Order 768.

984 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C22⋊C8C211yesmaximal, characteristic
2#74049C211yesmaximal, characteristic
3C2×#4467C211yesmaximal, characteristic, complemented
4(C2×D3)⋊#95C211yesmaximal, characteristic
5C2×#4452C211yesmaximal, characteristic, complemented
6C3×#1294C211yesmaximal, characteristic, complemented
7#67624C211yesmaximal, characteristic, complemented
8#9111—31nomaximal, Sylow
9C23×C4×D3C2211yescharacteristic
10C22×(C2×D3)⋊C4—21no—
11C2×#924C2211yescharacteristic
12C22×D3×C8—21no—
13C2×#897C411yescharacteristic, complemented
14C2×#897C411yescharacteristic, complemented
15C2×C3×C22⋊C8C2211yescharacteristic
16C3×#380C2211yescharacteristic
17C2×C3×#95C2211yescharacteristic
18C2×C3⋊#95—21no—
19C2×C3⋊#95C2211yescharacteristic
20C2×#830C2211yescharacteristic
21C2×(C2×D3)⋊C8—21no—
22#4987C411yescharacteristic, complemented
23#4987C411yescharacteristic, complemented
24#4955—21no—
25#4950—21no—
26D3×C22⋊C8—22no—
27D3×C22⋊C8—22no—
28#4668—21no—
29#4668—21no—
30#4467—22no—
31#4452—22no—
32C22×C22⋊C8—31no—
33#2848—31no—
34C2×#328—31no—
35C2×#328—31no—
36C22⋊#95—31no—
37#1294—31no—
38#1294D311yescharacteristic, complemented
39C24×D3D411yescharacteristic
40C23×C3×C4—21no—
41C23×C3×C4C2311yescharacteristic
42C23×Dic3—21no—
43C23×Dic3D411yescharacteristic
44C22×C4×D3—21no—
45C22×C4×D3—21no—
46C22×C4×D3—21no—
47C22×C4×D3—21no—
48C22×C4×D3—42no—
49C22×C4×D3—42no—
50C22×C4×D3C2×C411yescharacteristic
51C22×C4×D3C2×C411yescharacteristic
52C22×C4×D3D411yescharacteristic
53C22×C4×D3D411yescharacteristic
54C22×Dic6C2×C411yescharacteristic
55C22×C3×C8—21no—
56C2×C3×C4⋊C4C2×C411yescharacteristic
57C2×C3×C4⋊C4C2×C411yescharacteristic
58C2×C3×C22⋊C4—21no—
59C2×#217—21no—
60C2×(C2×D3)⋊C4—24no—
61C2×(C2×D3)⋊C4—21no—
62C2×(C2×D3)⋊C4—21no—
63C2×(C2×D3)⋊C4—21no—
64C2×(C2×D3)⋊C4—21no—
65C2×(C2×D3)⋊C4—42no—
66C2×(C2×D3)⋊C4—42no—
67C2×C4⋊Dic3—21no—
68C2×C4⋊Dic3—21no—
69C2×C4⋊Dic3C2×C411yescharacteristic
70#924—21no—
71#924—21no—
72#924—21no—
73#924—21no—
74C2×Dic3⋊C4—21no—
75C22×C3⋊C8—21no—
76C2×D3×C8—24no—
77C2×D3×C8—42no—
78C2×D3×C8—42no—
79#897—42no—
80#897—42no—
81C3×C22⋊C8—21no—
82C3×C22⋊C8D412yes—
83C3×#95—21no—
84C3×#95—21no—
85C3×#95—21no—
86C3⋊#95—21no—
87C3⋊#95—21no—
88C3⋊#95—21no—
89C3⋊#95—21no—
90C3⋊#95—42no—
91#830—21no—
92#830D412yes—
93(C2×D3)⋊C8—24no—
94C24×C4—31no—
95C23×C8—61no—
96C2×C22⋊Q8—31no—
97C2×C22⋊Q8—31no—
98C2×C22⋊Q8—31no—
99C22×C22⋊C4—61no—
100C2×C22⋊C8—31no—
101C2×C22⋊C8—62no—
102C2×C22⋊C8—61no—
103C2×C22⋊C8—62no—
104C2×C22⋊C8C2×D311yescharacteristic
105#385—61no—
106#385—61no—
107#385—61no—
108#380—31no—
109#380—31no—
110#380C2×D311yescharacteristic
111#379—61no—
112C2×#95—31no—
113C2×#95—61no—
114C2×#95C2×D311yescharacteristic
115#328—62no—
116#328—62no—
117C24×C3C2×D411yescharacteristic
118C23×D3—21no—
119C23×D3—21no—
120C23×D3—21no—
121C23×D3—21no—
122C23×D3—22no—
123C23×D3—22no—
124C23×D3—41no—
125C23×D3—41no—
126C23×D3C22⋊C411yescharacteristic
127C23×D3C22⋊C411yescharacteristic
128C23×D3SD1612yes—
129C23×D3Q1612yes—
130C22×C3×C4—22no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—41no—
134C22×C3×C4—41no—
135C22×C3×C4—41no—
136C22×C3×C4—41no—
137C22×C3×C4—41no—
138C22×C3×C4—41no—
139C22×C3×C4—41no—
140C22×C3×C4—41no—
141C22×C3×C4C22×C411yescharacteristic
142C22×C3×C4C2×D411yescharacteristic
143C22×C3×C4C2×D411yescharacteristic
144C22×C3×C4C2×D411yescharacteristic
145C22×C3×C4#4111yescharacteristic
146C22×C3×C4#4111yescharacteristic
147C22×Dic3—21no—
148C22×Dic3—21no—
149C22×Dic3—22no—
150C22×Dic3—22no—
151C22×Dic3—21no—
152C22×Dic3—21no—
153C22×Dic3—41no—
154C22×Dic3—41no—
155C22×Dic3—41no—
156C22×Dic3—41no—
157C22×Dic3—41no—
158C22×Dic3—41no—
159C22×Dic3—41no—
160C22×Dic3C22⋊C411yescharacteristic
161C22×Dic3C22⋊C411yescharacteristic
162C2×C4×D3—22no—
163C2×C4×D3—21no—
164C2×C4×D3—21no—
165C2×C4×D3—22no—
166C2×C4×D3—22no—
167C2×C4×D3—21no—
168C2×C4×D3—21no—
169C2×C4×D3—21no—
170C2×C4×D3—21no—
171C2×C4×D3—21no—
172C2×C4×D3—21no—
173C2×C4×D3—22no—
174C2×C4×D3—44no—
175C2×C4×D3—44no—
176C2×C4×D3—44no—
177C2×C4×D3—44no—
178C2×C4×D3—41no—
179C2×C4×D3—41no—
180C2×C4×D3—41no—
181C2×C4×D3—41no—
182C2×Dic6—21no—
183C2×Dic6—21no—
184C2×Dic6—41no—
185C2×Dic6—41no—
186C2×C3×C8—22no—
187C2×C3×C8—41no—
188C2×C3×C8—41no—
189C3×C4⋊C4—41no—
190C3×C4⋊C4—41no—
191C3×C22⋊C4—41no—
192C3×C22⋊C4—41no—
193#217—41no—
194#217—41no—
195(C2×D3)⋊C4—42no—
196(C2×D3)⋊C4—42no—
197(C2×D3)⋊C4—48no—
198(C2×D3)⋊C4—42no—
199(C2×D3)⋊C4—42no—
200C4⋊Dic3—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3—42no—
203C4⋊Dic3—42no—
204Dic3⋊C4—41no—
205Dic3⋊C4—41no—
206C2×C3⋊C8—22no—
207C2×C3⋊C8—41no—
208C2×C3⋊C8—41no—
209D3×C8—48no—
210C25—31no—
211C22×Q8—31no—
212C23×C4—21no—
213C23×C4—31no—
214C23×C4—31no—
215C23×C4—31no—
216C23×C4—31no—
217C23×C4—31no—
218C23×C4—61no—
219C23×C4—61no—
220C23×C4—61no—
221C23×C4—61no—
222C23×C4—61no—
223C23×C4—122no—
224C23×C4—122no—
225C23×C4C22×D311yescharacteristic
226C22×C8—21no—
227C22×C8—64no—
228C22×C8—61no—
229C22×C8—122no—
230C22×C8—122no—
231C22⋊Q8—61no—
232C22⋊Q8—61no—
233C22⋊Q8—61no—
234C22⋊Q8—61no—
235C22⋊Q8—122no—
236C22⋊Q8—122no—
237C2×C4⋊C4—31no—
238C2×C4⋊C4—61no—
239C2×C4⋊C4—61no—
240C2×C4⋊C4—61no—
241C2×C4⋊C4C4×D311yescharacteristic
242C2×C4⋊C4C4×D311yescharacteristic
243C2×C22⋊C4—21no—
244C2×C22⋊C4—61no—
245C2×C22⋊C4—61no—
246C2×C22⋊C4—61no—
247C2×C22⋊C4—61no—
248C2×C22⋊C4—64no—
249C2×C22⋊C4—61no—
250C2×C22⋊C4—122no—
251C2×C22⋊C4—122no—
252C22⋊C8—21no—
253C22⋊C8—32no—
254C22⋊C8—64no—
255C22⋊C8—61no—
256C22⋊C8D1212yes—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—61no—
261#95—61no—
262#95—61no—
263#95—61no—
264#95—122no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—21no—
269C23×C3C2×C22⋊C411yescharacteristic
270C23×C3#12111yescharacteristic
271C23×C3#12111yescharacteristic
272C23×C3C2×SD1611yescharacteristic
273C23×C3C2×Q1611yescharacteristic
274C23×C3#13511yescharacteristic
275C23×C3#13511yescharacteristic
276C22×D3—21no—
277C22×D3—21no—
278C22×D3—21no—
279C22×D3—21no—
280C22×D3—21no—
281C22×D3—21no—
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—21no—
285C22×D3—21no—
286C22×D3—22no—
287C22×D3—22no—
288C22×D3—22no—
289C22×D3—22no—
290C22×D3—24no—
291C22×D3—24no—
292C22×D3—42no—
293C22×D3—42no—
294C22×D3—42no—
295C22×D3—42no—
296C22×D3—42no—
297C22×D3—42no—
298C22×D3—42no—
299C22×D3—42no—
300C22×D3—42no—
301C22×D3—42no—
302C22×D3#9912yes—
303C22×D3#10312yes—
304C22×D3#10312yes—
305C22×D3#10412yes—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—81no—
324C2×C3×C4—81no—
325C2×C3×C4—81no—
326C2×C3×C4—81no—
327C2×C3×C4C4×D411yescharacteristic
328C2×C3×C4C4×D411yescharacteristic
329C2×C3×C4#12011yescharacteristic
330C2×C3×C4#12311yescharacteristic
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—42no—
337C2×Dic3—42no—
338C2×Dic3—42no—
339C2×Dic3—42no—
340C2×Dic3—42no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—81no—
348C2×Dic3—81no—
349C2×Dic3—81no—
350C2×Dic3—81no—
351C2×Dic3#9912yes—
352C4×D3—24no—
353C4×D3—24no—
354C4×D3—42no—
355C4×D3—42no—
356C4×D3—42no—
357C4×D3—42no—
358C4×D3—42no—
359C4×D3—42no—
360Dic6—81no—
361Dic6—81no—
362C3×C8—42no—
363C3⋊C8—42no—
364C24—31no—
365C24—31no—
366C24—32no—
367C24—32no—
368C24—62no—
369C24—62no—
370C24—61no—
371C24—61no—
372C24—61no—
373C24—61no—
374C24—121no—
375C24—121no—
376C24D3×D411yescharacteristic
377C2×Q8—61no—
378C2×Q8—61no—
379C2×Q8—121no—
380C2×Q8—121no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—62no—
395C22×C4—62no—
396C22×C4—62no—
397C22×C4—62no—
398C22×C4—62no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4—61no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—62no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—121no—
413C22×C4—121no—
414C22×C4—121no—
415C22×C4—121no—
416C22×C4—124no—
417C22×C4—124no—
418C22×C4—124no—
419C22×C4—124no—
420C22×C4—121no—
421C22×C4—121no—
422C22×C4—121no—
423C22×C4—121no—
424C22×C4—121no—
425C22×C4—121no—
426C22×C4—121no—
427C22×C4C2×C4×D311yescharacteristic
428C22×C4C2×D1211yescharacteristic
429C22×C4#23511yescharacteristic
430C22×C4D3×D411yescharacteristic
431C22×C4D3×D411yescharacteristic
432C22×C4#23911yescharacteristic
433C2×C8—22no—
434C2×C8—41no—
435C2×C8—41no—
436C2×C8—62no—
437C2×C8—128no—
438C2×C8—121no—
439C2×C8—121no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4—61no—
443C4⋊C4—61no—
444C4⋊C4—122no—
445C4⋊C4—122no—
446C4⋊C4—121no—
447C4⋊C4—121no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—122no—
451C22⋊C4—122no—
452C22⋊C4—128no—
453C22⋊C4—122no—
454C22⋊C4—122no—
455C22⋊C4—121no—
456C22⋊C4—121no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3#38611yescharacteristic
470C22×C3C2×#9911yescharacteristic
471C22×C3C2×#9911yescharacteristic
472C22×C3C2×#10311yescharacteristic
473C22×C3#41611yescharacteristic
474C22×C3C2×#10411yescharacteristic
475C22×C3#42111yescharacteristic
476C22×C3#46511yescharacteristic
477C22×C3#46511yescharacteristic
478C22×C3#46711yescharacteristic
479C22×C3#46711yescharacteristic
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—22no—
487C2×D3—22no—
488C2×D3—22no—
489C2×D3—44no—
490C2×D3—44no—
491C2×D3—44no—
492C2×D3—44no—
493C2×D3—41no—
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—41no—
497C2×D3#32814yescomplemented
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—82no—
503C3×C4—81no—
504C3×C4—81no—
505Dic3—22no—
506Dic3—41no—
507Dic3—82no—
508Dic3—81no—
509Dic3—81no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—32no—
515C23—32no—
516C23—32no—
517C23—32no—
518C23—64no—
519C23—64no—
520C23—61no—
521C23—61no—
522C23—61no—
523C23—61no—
524C23—62no—
525C23—62no—
526C23—61no—
527C23—61no—
528C23—61no—
529C23—61no—
530C23—62no—
531C23—62no—
532C23—61no—
533C23—61no—
534C23—122no—
535C23—122no—
536C23—122no—
537C23—122no—
538C23—122no—
539C23—122no—
540C23—122no—
541C23—122no—
542C23—122no—
543C23—122no—
544C23D3×C22⋊C411yescharacteristic
545C23#88411yescharacteristic
546C23#89511yescharacteristic
547C23#91211yescharacteristic
548C23D3×SD1611yescharacteristic
549C23#91611yescharacteristic
550C23D3×Q1611yescharacteristic
551Q8—241no—
552Q8—241no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—32no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—64no—
572C2×C4—64no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—61no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—122no—
583C2×C4—122no—
584C2×C4—122no—
585C2×C4—122no—
586C2×C4—122no—
587C2×C4—122no—
588C2×C4—122no—
589C2×C4—122no—
590C2×C4—122no—
591C2×C4—122no—
592C2×C4—122no—
593C2×C4—121no—
594C2×C4—121no—
595C2×C4—121no—
596C2×C4—121no—
597C2×C4—121no—
598C2×C4—121no—
599C2×C4—241no—
600C2×C4—241no—
601C2×C4—241no—
602C2×C4—241no—
603C2×C4C4×D1211yescharacteristic
604C2×C4#88211yescharacteristic
605C2×C4#89311yescharacteristic
606C2×C4#89411yescharacteristic
607C8—42no—
608C8—122no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3C2×#32811yescharacteristic
614C2×C3#150111yescharacteristic
615C2×C3#151611yescharacteristic
616C2×C3#152011yescharacteristic
617C2×C3#187111yescharacteristic
618C2×C3#189211yescharacteristic
619C2×C3#189811yescharacteristic
620D3—24no—
621D3—42no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—34no—
635C22—62no—
636C22—62no—
637C22—62no—
638C22—62no—
639C22—62no—
640C22—62no—
641C22—62no—
642C22—62no—
643C22—62no—
644C22—124no—
645C22—124no—
646C22—124no—
647C22—124no—
648C22—121no—
649C22—121no—
650C22—121no—
651C22—121no—
652C22#466511yescharacteristic
653C22D3×#9911yescharacteristic
654C22D3×#9911yescharacteristic
655C22#477211yescharacteristic
656C22#477811yescharacteristic
657C22D3×#10311yescharacteristic
658C22#481311yescharacteristic
659C22D3×#10411yescharacteristic
660C22#482111yescharacteristic
661C22#486411yescharacteristic
662C22#488711yescharacteristic
663C4—21no—
664C4—21no—
665C4—21no—
666C4—21no—
667C4—62no—
668C4—82no—
669C4—81no—
670C4—81no—
671C4—121no—
672C4—242no—
673C4—241no—
674C4—241no—
675C3#911111yescharacteristic, complemented, Sylow
676C2—21no—
677C2—21no—
678C2—21no—
679C2—21no—
680C2—64no—
681C2—122no—
682C2#6830111yescharacteristic
683C2#6830611yescharacteristic
684C2D3×#32811yescharacteristic
685C2#6833911yescharacteristic
686C2#6875511yescharacteristic
687C2#6888211yescharacteristic
688C2#6897011yescharacteristic
subgroupG/H
centerC23D3×C22⋊C4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC3×#1294C2
socleC23×C3C2×C22⋊C4
prime radicalC24×D3D4
cosocleC23×C3×C4C23
hypercenter#1294D3
hypocenterC3#9111
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
3. C2×#4467C2semidirect
5. C2×#4452C2semidirect
6. C3×#1294C2semidirect
7. #67624C2semidirect
13. C2×#897C4semidirect
14. C2×#897C4semidirect
22. #4987C4semidirect
23. #4987C4semidirect
38. #1294D3semidirect
497. C2×D3#328semidirect
675. C3#9111semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C22⋊C82
#740492
C2×#44672
(C2×D3)⋊#952
C2×#44522
C3×#12942
#676242
#91113