Finite Group Databasebeta

← #10731984

Subgroups — #10731984

Order 768.

1106 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊#401C212yesmaximal
2C3×C4⋊#95C211yesmaximal, characteristic
3#71563C211yesmaximal, characteristic
4#71563C211yesmaximal, characteristic
5#71563C211yesmaximal, characteristic
6#71563C211yesmaximal, characteristic
7#71535C211yesmaximal, characteristic
8C4×C3⋊#95C211yesmaximal, characteristic
9#69418C212yesmaximal
10#69417C212yesmaximal
11#69416C212yesmaximal
12C4⋊#401—31nomaximal, Sylow
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C42C2211yescharacteristic
16C22×C4⋊Dic3C2211yescharacteristic
17C22×C4⋊Dic3C2211yescharacteristic
18C22×C4×Dic3C2211yescharacteristic
19C22×C4×Dic3C2211yescharacteristic
20C2×C3×#95C2212yes—
21C2×C3×#95C2212yes—
22C2×C3⋊#95C2211yescharacteristic
23C2×C3⋊#95C2212yes—
24C2×C3⋊#95C2212yes—
25C2×C3⋊#95C2212yes—
26C2×C3⋊#95C2211yescharacteristic
27C2×C3⋊#95C2212yes—
28C2×C3⋊#95C2212yes—
29C2×C3⋊#95C2212yes—
30C2×C3⋊#95C2211yescharacteristic
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C3⋊#401—28no—
37C2×#401—32no—
38#1443—32no—
39#1443—32no—
40#1443—32no—
41C4⋊#95—31no—
42C4⋊#95—31no—
43C4⋊#95—31no—
44C4⋊#95—31no—
45C4⋊#95—31no—
46C4⋊#95D311yescharacteristic
47C4×#95—31no—
48C23×C3×C4C2312yes—
49C23×C3×C4C2312yes—
50C23×C3×C4C2311yescharacteristic
51C23×C3×C4C2311yescharacteristic
52C23×C3×C4C2311yescharacteristic
53C23×Dic3C2312yes—
54C23×Dic3C2312yes—
55C23×Dic3C2311yescharacteristic
56C23×Dic3C2311yescharacteristic
57C23×Dic3C2311yescharacteristic
58C23×Dic3C2311yescharacteristic
59C2×C3×C4⋊C4—22no—
60C2×C3×C4⋊C4—22no—
61C2×C3×C4⋊C4—22no—
62C2×C3×C4⋊C4—22no—
63C2×C3×C4⋊C4—22no—
64C2×C3×C4⋊C4—22no—
65C2×C3×C42—22no—
66C2×C3×C42—22no—
67C2×C3×C42—22no—
68C2×C4⋊Dic3—22no—
69C2×C4⋊Dic3—22no—
70C2×C4⋊Dic3—22no—
71C2×C4⋊Dic3—22no—
72C2×C4⋊Dic3—22no—
73C2×C4⋊Dic3—22no—
74C2×C4×Dic3—22no—
75C2×C4×Dic3—22no—
76C2×C4×Dic3—22no—
77C2×C4×Dic3—22no—
78C2×C4×Dic3—22no—
79C2×C4×Dic3—22no—
80C3×#95—24no—
81C3×#95—24no—
82C3⋊#95—24no—
83C3⋊#95—22no—
84C3⋊#95—24no—
85C3⋊#95—24no—
86C3⋊#95—24no—
87C3⋊#95—24no—
88C3⋊#95—22no—
89C3⋊#95—22no—
90C3⋊#95—24no—
91C3⋊#95—24no—
92C3⋊#95—42no—
93C3⋊#95—42no—
94C3⋊#95—42no—
95C3⋊#95D414yes—
96C22×C4⋊C4—31no—
97C22×C4⋊C4—31no—
98C22×C4⋊C4C2×D311yescharacteristic
99C22×C4⋊C4C2×D311yescharacteristic
100C22×C42—31no—
101C22×C42—31no—
102C22×C42C2×D311yescharacteristic
103#401—68no—
104C2×#95—31no—
105C2×#95—32no—
106C2×#95—32no—
107C2×#95—32no—
108C2×#95—32no—
109C2×#95—32no—
110C2×#95—31no—
111C2×#95—31no—
112C2×#95—31no—
113C2×#95—32no—
114C2×#95—32no—
115C2×#95—32no—
116C2×#95—32no—
117C2×#95—32no—
118C2×#95C2×D312yes—
119C2×#95C2×D312yes—
120C24×C3C2411yescharacteristic
121C22×C3×C4—21no—
122C22×C3×C4—21no—
123C22×C3×C4—21no—
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4C2×D412yes—
148C22×C3×C4#4112yes—
149C22×C3×C4#4112yes—
150C22×C3×C4#4112yes—
151C22×C3×C4#4112yes—
152C22×C3×C4#4112yes—
153C22×C3×C4#4112yes—
154C22×C3×C4#4112yes—
155C22×C3×C4#4112yes—
156C22×Dic3—21no—
157C22×Dic3—21no—
158C22×Dic3—21no—
159C22×Dic3—21no—
160C22×Dic3—21no—
161C22×Dic3—21no—
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—21no—
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—21no—
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—21no—
180C22×Dic3—22no—
181C22×Dic3—22no—
182C22×Dic3—22no—
183C22×Dic3—22no—
184C22×Dic3—22no—
185C22×Dic3—22no—
186C22×Dic3—22no—
187C22×Dic3—22no—
188C22×Dic3—22no—
189C22×Dic3—22no—
190C22×Dic3—22no—
191C22×Dic3—22no—
192C22×Dic3—22no—
193C22×Dic3—22no—
194C22×Dic3C2×D412yes—
195C22×Dic3C2×D412yes—
196C22×Dic3#4112yes—
197C22×Dic3#4112yes—
198C3×C4⋊C4—44no—
199C3×C4⋊C4—44no—
200C3×C42—44no—
201C4⋊Dic3—44no—
202C4⋊Dic3—44no—
203C4×Dic3—44no—
204C4×Dic3—44no—
205C23×C4—31no—
206C23×C4—31no—
207C23×C4—31no—
208C23×C4—31no—
209C23×C4—32no—
210C23×C4—32no—
211C23×C4C22×D312yes—
212C23×C4C22×D312yes—
213C23×C4C22×D311yescharacteristic
214C23×C4C22×D311yescharacteristic
215C23×C4C22×D311yescharacteristic
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—62no—
223C2×C4⋊C4—62no—
224C2×C4⋊C4—62no—
225C2×C4⋊C4—62no—
226C2×C4⋊C4—62no—
227C2×C4⋊C4—62no—
228C2×C42—22no—
229C2×C42—22no—
230C2×C42—22no—
231C2×C42—62no—
232C2×C42—62no—
233C2×C42—62no—
234C2×C42—62no—
235C2×C42—62no—
236C2×C42—62no—
237#95—24no—
238#95—24no—
239#95—34no—
240#95—62no—
241#95—62no—
242#95—64no—
243#95—64no—
244#95—64no—
245#95—64no—
246#95—64no—
247#95—64no—
248#95—64no—
249#95—62no—
250#95—122no—
251#95—122no—
252#95—122no—
253C23×C3C22×D411yescharacteristic
254C23×C3C2×#4111yescharacteristic
255C23×C3C2×#4111yescharacteristic
256C23×C3C2×#4111yescharacteristic
257C23×C3C2×#4111yescharacteristic
258C23×C3C2×#4111yescharacteristic
259C23×C3C2×#4111yescharacteristic
260C23×C3C2×#4111yescharacteristic
261C23×C3C2×#4111yescharacteristic
262C23×C3C2×#4111yescharacteristic
263C23×C3C2×#4111yescharacteristic
264C23×C3H(5,𝔽2)11yescharacteristic
265C23×C32−1+411yescharacteristic
266C23×C32−1+411yescharacteristic
267C23×C32−1+411yescharacteristic
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4#12614yes—
297C2×C3×C4#12614yes—
298C2×C3×C4#12614yes—
299C2×C3×C4#12614yes—
300C2×C3×C4#12614yes—
301C2×C3×C4#12614yes—
302C2×C3×C4#12614yes—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—41no—
316C2×Dic3—41no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—42no—
332C2×Dic3—42no—
333C2×Dic3—42no—
334C2×Dic3—42no—
335C2×Dic3—42no—
336C2×Dic3—42no—
337C2×Dic3—42no—
338C2×Dic3—42no—
339C2×Dic3—42no—
340C2×Dic3—42no—
341C2×Dic3—42no—
342C2×Dic3—42no—
343C2×Dic3—42no—
344C2×Dic3—42no—
345C24C23×D311yescharacteristic
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—32no—
373C22×C4—32no—
374C22×C4—32no—
375C22×C4—32no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—61no—
379C22×C4—61no—
380C22×C4—61no—
381C22×C4—61no—
382C22×C4—61no—
383C22×C4—61no—
384C22×C4—61no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4—61no—
388C22×C4—61no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—62no—
401C22×C4—62no—
402C22×C4—62no—
403C22×C4—62no—
404C22×C4—62no—
405C22×C4—62no—
406C22×C4—62no—
407C22×C4—62no—
408C22×C4—62no—
409C22×C4—62no—
410C22×C4—62no—
411C22×C4—62no—
412C22×C4—62no—
413C22×C4—62no—
414C22×C4#23512yes—
415C22×C4#23512yes—
416C22×C4#23512yes—
417C22×C4D3×D412yes—
418C22×C4#23712yes—
419C22×C4#23712yes—
420C22×C4#23712yes—
421C22×C4#23712yes—
422C22×C4#23912yes—
423C4⋊C4—44no—
424C4⋊C4—44no—
425C4⋊C4—124no—
426C4⋊C4—124no—
427C42—44no—
428C42—124no—
429C42—124no—
430C22×C3C2×#12611yescharacteristic
431C22×C3C2×#12611yescharacteristic
432C22×C3C2×#12611yescharacteristic
433C22×C3C2×#12611yescharacteristic
434C22×C3C2×#12611yescharacteristic
435C22×C3C2×#12611yescharacteristic
436C22×C3C2×#12611yescharacteristic
437C22×C3#52911yescharacteristic
438C22×C3#52911yescharacteristic
439C22×C3#52911yescharacteristic
440C22×C3#53211yescharacteristic
441C22×C3#53211yescharacteristic
442C22×C3#53211yescharacteristic
443C22×C3#54111yescharacteristic
444C22×C3#54111yescharacteristic
445C22×C3#54111yescharacteristic
446C22×C3#54211yescharacteristic
447C22×C3#54211yescharacteristic
448C22×C3#54211yescharacteristic
449C22×C3#54711yescharacteristic
450C22×C3#54711yescharacteristic
451C22×C3#54711yescharacteristic
452C22×C3#55011yescharacteristic
453C22×C3#55211yescharacteristic
454C22×C3#55211yescharacteristic
455C22×C3#55211yescharacteristic
456C22×C3#55311yescharacteristic
457C22×C3#55311yescharacteristic
458C22×C3#55311yescharacteristic
459C22×C3#55611yescharacteristic
460C22×C3#55611yescharacteristic
461C22×C3#55611yescharacteristic
462C22×C3#55611yescharacteristic
463C22×C3#55611yescharacteristic
464C22×C3#55611yescharacteristic
465C3×C4—42no—
466C3×C4—42no—
467C3×C4—82no—
468C3×C4—82no—
469C3×C4#40118yescomplemented
470Dic3—42no—
471Dic3—42no—
472Dic3—42no—
473Dic3—42no—
474Dic3—82no—
475Dic3—82no—
476C23C2×#23511yescharacteristic
477C23C2×#23511yescharacteristic
478C23C2×#23511yescharacteristic
479C23C2×D3×D411yescharacteristic
480C23C2×#23711yescharacteristic
481C23C2×#23711yescharacteristic
482C23C2×#23711yescharacteristic
483C23C2×#23711yescharacteristic
484C23C2×#23911yescharacteristic
485C23#100711yescharacteristic
486C23#100711yescharacteristic
487C23D3×#4111yescharacteristic
488C23D3×#4111yescharacteristic
489C23#100911yescharacteristic
490C23#101011yescharacteristic
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4—121no—
534C2×C4—121no—
535C2×C4—121no—
536C2×C4—121no—
537C2×C4—121no—
538C2×C4—121no—
539C2×C4—121no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—121no—
543C2×C4—121no—
544C2×C4—121no—
545C2×C4—121no—
546C2×C4—121no—
547C2×C4—122no—
548C2×C4—122no—
549C2×C4—122no—
550C2×C4—122no—
551C2×C4—122no—
552C2×C4—122no—
553C2×C4—122no—
554C2×C4—122no—
555C2×C4—122no—
556C2×C4—122no—
557C2×C4—122no—
558C2×C4—122no—
559C2×C4—122no—
560C2×C4—122no—
561C2×C4#87614yes—
562C2×C4#87914yes—
563C2×C4#87914yes—
564C2×C4#87914yes—
565C2×C4#89814yes—
566C2×C4#89814yes—
567C2×C4#89814yes—
568C2×C3C2×#40111yescharacteristic
569C2×C3#249411yescharacteristic
570C2×C3#249411yescharacteristic
571C2×C3#249411yescharacteristic
572C2×C3#249611yescharacteristic
573C2×C3#249611yescharacteristic
574C2×C3#249611yescharacteristic
575C2×C3#251211yescharacteristic
576C2×C3#251211yescharacteristic
577C2×C3#251211yescharacteristic
578C2×C3#251411yescharacteristic
579C2×C3#251411yescharacteristic
580C2×C3#251411yescharacteristic
581C2×C3#264511yescharacteristic
582C2×C3#286011yescharacteristic
583C22C2×#87611yescharacteristic
584C22C2×#87911yescharacteristic
585C22C2×#87911yescharacteristic
586C22C2×#87911yescharacteristic
587C22#550711yescharacteristic
588C22C2×#89811yescharacteristic
589C22C2×#89811yescharacteristic
590C22C2×#89811yescharacteristic
591C22#551311yescharacteristic
592C22#553011yescharacteristic
593C22#553311yescharacteristic
594C22#554211yescharacteristic
595C22#554811yescharacteristic
596C22#555311yescharacteristic
597C22#555711yescharacteristic
598C22#556811yescharacteristic
599C22#556811yescharacteristic
600C22#558211yescharacteristic
601C22#558311yescharacteristic
602C22#559611yescharacteristic
603C22#560011yescharacteristic
604C22#561111yescharacteristic
605C22#561811yescharacteristic
606C22#562511yescharacteristic
607C22#563911yescharacteristic
608C22#564111yescharacteristic
609C22#564311yescharacteristic
610C22#568011yescharacteristic
611C22#568211yescharacteristic
612C22#569411yescharacteristic
613C22#569511yescharacteristic
614C22#571611yescharacteristic
615C22#572611yescharacteristic
616C22#573111yescharacteristic
617C22#573211yescharacteristic
618C4—42no—
619C4—42no—
620C4—82no—
621C4—82no—
622C4—122no—
623C4—122no—
624C4—122no—
625C4—122no—
626C4—242no—
627C4—242no—
628C4C3⋊#40118yescomplemented
629C3C4⋊#40111yescharacteristic, complemented, Sylow
630C2C2×C3⋊#40111yescharacteristic
631C2#7369311yescharacteristic
632C2#7369711yescharacteristic
633C2#7391811yescharacteristic
634C2#7392211yescharacteristic
635C2#7423411yescharacteristic
636C2#7436411yescharacteristic
637C2#7604711yescharacteristic
638C2#7604911yescharacteristic
639C2#7623311yescharacteristic
640C2#7623711yescharacteristic
641C2#7633711yescharacteristic
642C2#7642511yescharacteristic
643C2#7652411yescharacteristic
644C2#7656011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC3×C4⋊#95C2
hypercenterC4⋊#95D3
hypocenterC3C4⋊#401
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
469. C3×C4#401semidirect
628. C4C3⋊#401semidirect
629. C3C4⋊#401semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#4012
C3×C4⋊#952
#715632
#715352
C4×C3⋊#952
#694182
#694172
#694162
C4⋊#4013