Finite Group Databasebeta

← #10731993

Subgroups — #10731993

Order 768.

1266 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4972C211yesmaximal, characteristic
2C2×C4×Dic3⋊C4C211yesmaximal, characteristic
3C2×#4658C212yesmaximal
4C3×C4⋊#95C211yesmaximal, characteristic
5#71563C211yesmaximal, characteristic
6#71563C211yesmaximal, characteristic
7#71563C211yesmaximal, characteristic
8#71535C211yesmaximal, characteristic
9#69418C212yesmaximal
10#69416C212yesmaximal
11#69409C212yesmaximal
12#15156—31nomaximal, Sylow
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C42C2211yescharacteristic
16C22×C4⋊Dic3C2211yescharacteristic
17C22×C4⋊Dic3C2211yescharacteristic
18C22×Dic3⋊C4C2211yescharacteristic
19C22×Dic3⋊C4C2212yes—
20C22×Dic3⋊C4C2211yescharacteristic
21C22×C4×Dic3C2211yescharacteristic
22C22×C4×Dic3C2211yescharacteristic
23C2×C3×#95C2212yes—
24C2×C3×#95C2212yes—
25C2×C3⋊#95C2212yes—
26C2×C3⋊#95C2212yes—
27C2×C3⋊#95C2211yescharacteristic
28C2×C3⋊#95C2212yes—
29C2×C3⋊#95C2212yes—
30C2×C3⋊#95C2212yes—
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36#4972—24no—
37C4×Dic3⋊C4—24no—
38#4658—28no—
39C2×#400—32no—
40C2×#389—31no—
41C2×C4×C4⋊C4—31no—
42#1443—32no—
43#1443—32no—
44#1441—32no—
45C4⋊#95—31no—
46C4⋊#95—31no—
47C4⋊#95—31no—
48C4⋊#95—31no—
49C4⋊#95D311yescharacteristic
50C23×C3×C4C2312yes—
51C23×C3×C4C2312yes—
52C23×C3×C4C2311yescharacteristic
53C23×C3×C4C2311yescharacteristic
54C23×C3×C4C2311yescharacteristic
55C23×Dic3C2312yes—
56C23×Dic3C2311yescharacteristic
57C23×Dic3C2311yescharacteristic
58C23×Dic3C2312yes—
59C23×Dic3C2311yescharacteristic
60C23×Dic3C2311yescharacteristic
61C2×C3×C4⋊C4—22no—
62C2×C3×C4⋊C4—22no—
63C2×C3×C4⋊C4—22no—
64C2×C3×C4⋊C4—22no—
65C2×C3×C4⋊C4—22no—
66C2×C3×C4⋊C4—22no—
67C2×C3×C42—22no—
68C2×C3×C42—22no—
69C2×C3×C42—22no—
70C2×C4⋊Dic3—22no—
71C2×C4⋊Dic3—22no—
72C2×C4⋊Dic3—22no—
73C2×C4⋊Dic3—22no—
74C2×C4⋊Dic3—22no—
75C2×C4⋊Dic3Q814yes—
76C2×Dic3⋊C4—22no—
77C2×Dic3⋊C4—22no—
78C2×Dic3⋊C4—22no—
79C2×Dic3⋊C4—22no—
80C2×Dic3⋊C4—22no—
81C2×Dic3⋊C4—24no—
82C2×Dic3⋊C4—24no—
83C2×Dic3⋊C4—24no—
84C2×Dic3⋊C4D414yes—
85C2×C4×Dic3—22no—
86C2×C4×Dic3—22no—
87C2×C4×Dic3—22no—
88C2×C4×Dic3—22no—
89C2×C4×Dic3—22no—
90C2×C4×Dic3D414yes—
91C3×#95—24no—
92C3×#95—24no—
93C3⋊#95—24no—
94C3⋊#95—24no—
95C3⋊#95—24no—
96C3⋊#95—24no—
97C3⋊#95—22no—
98C3⋊#95—22no—
99C3⋊#95—24no—
100C3⋊#95—24no—
101C3⋊#95—42no—
102C3⋊#95—42no—
103C3⋊#95—42no—
104C22×C4⋊C4—31no—
105C22×C4⋊C4—31no—
106C22×C4⋊C4—32no—
107C22×C4⋊C4—31no—
108C22×C4⋊C4—31no—
109C22×C4⋊C4C2×D311yescharacteristic
110C22×C4⋊C4C2×D311yescharacteristic
111C22×C42—31no—
112C22×C42—31no—
113C22×C42C2×D311yescharacteristic
114#400—68no—
115#389—64no—
116C4×C4⋊C4—64no—
117C2×#95—32no—
118C2×#95—32no—
119C2×#95—32no—
120C2×#95—32no—
121C2×#95—32no—
122C2×#95—31no—
123C2×#95—31no—
124C2×#95—32no—
125C2×#95—32no—
126C2×#95—32no—
127C2×#95—32no—
128C2×#95C2×D312yes—
129C2×#95C2×D312yes—
130C24×C3C2411yescharacteristic
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—22no—
144C22×C3×C4—22no—
145C22×C3×C4—22no—
146C22×C3×C4—22no—
147C22×C3×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4C2×D412yes—
158C22×C3×C4C2×D412yes—
159C22×C3×C4C2×Q812yes—
160C22×C3×C4#4112yes—
161C22×C3×C4#4112yes—
162C22×C3×C4#4112yes—
163C22×C3×C4#4112yes—
164C22×C3×C4#4112yes—
165C22×C3×C4#4112yes—
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—21no—
170C22×Dic3—22no—
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—22no—
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—21no—
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—22no—
183C22×Dic3—22no—
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—22no—
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—22no—
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—21no—
194C22×Dic3—22no—
195C22×Dic3—22no—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3—22no—
201C22×Dic3C2×D412yes—
202C22×Dic3C2×D412yes—
203C22×Dic3C2×D412yes—
204C22×Dic3C2×D412yes—
205C22×Dic3C2×Q814yes—
206C22×Dic3#4112yes—
207C22×Dic3#4112yes—
208C3×C4⋊C4—44no—
209C3×C4⋊C4—44no—
210C3×C42—44no—
211C4⋊Dic3—28no—
212C4⋊Dic3—44no—
213Dic3⋊C4—28no—
214Dic3⋊C4—28no—
215Dic3⋊C4—48no—
216C4×Dic3—28no—
217C4×Dic3—44no—
218C23×C4—31no—
219C23×C4—32no—
220C23×C4—31no—
221C23×C4—31no—
222C23×C4—31no—
223C23×C4—32no—
224C23×C4C22×D312yes—
225C23×C4C22×D312yes—
226C23×C4C22×D311yescharacteristic
227C23×C4C22×D311yescharacteristic
228C23×C4C22×D311yescharacteristic
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—34no—
236C2×C4⋊C4—34no—
237C2×C4⋊C4—62no—
238C2×C4⋊C4—62no—
239C2×C4⋊C4—62no—
240C2×C4⋊C4—62no—
241C2×C4⋊C4—62no—
242C2×C4⋊C4—62no—
243C2×C4⋊C4—62no—
244C2×C4⋊C4—64no—
245C2×C4⋊C4—64no—
246C2×C4⋊C4—64no—
247C2×C4⋊C4—62no—
248C2×C4⋊C4—62no—
249C2×C4⋊C4—62no—
250C2×C42—22no—
251C2×C42—22no—
252C2×C42—22no—
253C2×C42—34no—
254C2×C42—62no—
255C2×C42—62no—
256C2×C42—62no—
257C2×C42—62no—
258C2×C42—62no—
259#95—24no—
260#95—24no—
261#95—64no—
262#95—62no—
263#95—62no—
264#95—64no—
265#95—64no—
266#95—64no—
267#95—64no—
268#95—64no—
269#95—122no—
270#95—122no—
271#95—122no—
272C23×C3C22×D411yescharacteristic
273C23×C3C22×D411yescharacteristic
274C23×C3C22×Q811yescharacteristic
275C23×C3C2×#4111yescharacteristic
276C23×C3C2×#4111yescharacteristic
277C23×C3C2×#4111yescharacteristic
278C23×C3C2×#4111yescharacteristic
279C23×C3C2×#4111yescharacteristic
280C23×C3C2×#4111yescharacteristic
281C23×C3C2×#4111yescharacteristic
282C23×C3C2×#4111yescharacteristic
283C23×C3H(5,𝔽2)11yescharacteristic
284C23×C32−1+411yescharacteristic
285C23×C32−1+411yescharacteristic
286C23×C32−1+411yescharacteristic
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—42no—
305C2×C3×C4—42no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—42no—
315C2×C3×C4C22⋊Q814yes—
316C2×C3×C4#12314yes—
317C2×C3×C4#12414yes—
318C2×C3×C4#12514yes—
319C2×C3×C4#12514yes—
320C2×C3×C4#12614yes—
321C2×C3×C4#12614yes—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—24no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—24no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—24no—
340C2×Dic3—42no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—42no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—42no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—41no—
354C2×Dic3—41no—
355C2×Dic3—42no—
356C2×Dic3—42no—
357C2×Dic3—42no—
358C2×Dic3—42no—
359C2×Dic3—42no—
360C2×Dic3—42no—
361C2×Dic3—42no—
362C2×Dic3—42no—
363C2×Dic3#12114yes—
364C24C23×D311yescharacteristic
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—32no—
392C22×C4—32no—
393C22×C4—32no—
394C22×C4—32no—
395C22×C4—32no—
396C22×C4—34no—
397C22×C4—32no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4—61no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4—62no—
406C22×C4—62no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—62no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4—62no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4—62no—
420C22×C4—61no—
421C22×C4—62no—
422C22×C4—61no—
423C22×C4—61no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—62no—
427C22×C4—62no—
428C22×C4—62no—
429C22×C4—62no—
430C22×C4—62no—
431C22×C4—62no—
432C22×C4—62no—
433C22×C4#23512yes—
434C22×C4#23512yes—
435C22×C4#23512yes—
436C22×C4D3×D412yes—
437C22×C4D3×D412yes—
438C22×C4#23712yes—
439C22×C4#23712yes—
440C22×C4#23712yes—
441C22×C4D3×Q812yes—
442C4⋊C4—44no—
443C4⋊C4—44no—
444C4⋊C4—68no—
445C4⋊C4—68no—
446C4⋊C4—68no—
447C4⋊C4—128no—
448C4⋊C4—124no—
449C42—44no—
450C42—68no—
451C42—124no—
452C22×C3C2×#12111yescharacteristic
453C22×C3C2×C22⋊Q811yescharacteristic
454C22×C3C2×#12311yescharacteristic
455C22×C3#52511yescharacteristic
456C22×C3C2×#12411yescharacteristic
457C22×C3C2×#12511yescharacteristic
458C22×C3C2×#12511yescharacteristic
459C22×C3C2×#12611yescharacteristic
460C22×C3C2×#12611yescharacteristic
461C22×C3#52911yescharacteristic
462C22×C3#52911yescharacteristic
463C22×C3#53211yescharacteristic
464C22×C3#53211yescharacteristic
465C22×C3#53611yescharacteristic
466C22×C3#53711yescharacteristic
467C22×C3#54111yescharacteristic
468C22×C3#54111yescharacteristic
469C22×C3#54211yescharacteristic
470C22×C3#54211yescharacteristic
471C22×C3#54711yescharacteristic
472C22×C3#54711yescharacteristic
473C22×C3D4×Q811yescharacteristic
474C22×C3#55011yescharacteristic
475C22×C3#55211yescharacteristic
476C22×C3#55211yescharacteristic
477C22×C3#55311yescharacteristic
478C22×C3#55311yescharacteristic
479C22×C3#55411yescharacteristic
480C22×C3#55611yescharacteristic
481C22×C3#55611yescharacteristic
482C22×C3#55611yescharacteristic
483C22×C3#55611yescharacteristic
484C22×C3#55611yescharacteristic
485C22×C3#55711yescharacteristic
486C22×C3#55711yescharacteristic
487C3×C4—42no—
488C3×C4—42no—
489C3×C4—82no—
490C3×C4—82no—
491C3×C4#40018yescomplemented
492Dic3—24no—
493Dic3—42no—
494Dic3—42no—
495Dic3—44no—
496Dic3—42no—
497Dic3—82no—
498C23C2×#23511yescharacteristic
499C23C2×#23511yescharacteristic
500C23C2×#23511yescharacteristic
501C23C2×D3×D411yescharacteristic
502C23C2×D3×D411yescharacteristic
503C23C2×#23711yescharacteristic
504C23C2×#23711yescharacteristic
505C23C2×#23711yescharacteristic
506C23C2×D3×Q811yescharacteristic
507C23#100711yescharacteristic
508C23#100711yescharacteristic
509C23D3×#4111yescharacteristic
510C23D3×#4111yescharacteristic
511C23#100911yescharacteristic
512C23#101011yescharacteristic
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—34no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—64no—
550C2×C4—64no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—64no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—121no—
561C2×C4—121no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—121no—
566C2×C4—121no—
567C2×C4—122no—
568C2×C4—122no—
569C2×C4—121no—
570C2×C4—121no—
571C2×C4—122no—
572C2×C4—121no—
573C2×C4—121no—
574C2×C4—122no—
575C2×C4—121no—
576C2×C4—122no—
577C2×C4—122no—
578C2×C4—122no—
579C2×C4—122no—
580C2×C4—122no—
581C2×C4—122no—
582C2×C4—122no—
583C2×C4#87614yes—
584C2×C4#87914yes—
585C2×C4#88314yes—
586C2×C4#88514yes—
587C2×C4#88914yes—
588C2×C4#88914yes—
589C2×C4#89614yes—
590C2×C3C2×#40011yescharacteristic
591C2×C3#250611yescharacteristic
592C2×C3#250611yescharacteristic
593C2×C3#250911yescharacteristic
594C2×C3#250911yescharacteristic
595C2×C3#251211yescharacteristic
596C2×C3#251211yescharacteristic
597C2×C3#251411yescharacteristic
598C2×C3#251411yescharacteristic
599C2×C3#253811yescharacteristic
600C2×C3#254711yescharacteristic
601C2×C3#256211yescharacteristic
602C2×C3#258111yescharacteristic
603C2×C3#262511yescharacteristic
604C2×C3#285411yescharacteristic
605C22C2×#87611yescharacteristic
606C22C2×#87911yescharacteristic
607C22C2×#88311yescharacteristic
608C22C2×#88511yescharacteristic
609C22C2×#88911yescharacteristic
610C22C2×#88911yescharacteristic
611C22#550711yescharacteristic
612C22C2×#89611yescharacteristic
613C22#551311yescharacteristic
614C22#553011yescharacteristic
615C22#553311yescharacteristic
616C22#554211yescharacteristic
617C22#554811yescharacteristic
618C22#555311yescharacteristic
619C22#555711yescharacteristic
620C22#556811yescharacteristic
621C22#556811yescharacteristic
622C22#558211yescharacteristic
623C22#558311yescharacteristic
624C22D3×#12111yescharacteristic
625C22#560611yescharacteristic
626C22#561111yescharacteristic
627C22#561811yescharacteristic
628C22#562811yescharacteristic
629C22#562911yescharacteristic
630C22#563911yescharacteristic
631C22#564111yescharacteristic
632C22#568011yescharacteristic
633C22#568211yescharacteristic
634C22#568511yescharacteristic
635C22#569011yescharacteristic
636C22#571611yescharacteristic
637C22#572111yescharacteristic
638C22#572711yescharacteristic
639C22#573111yescharacteristic
640C4—42no—
641C4—42no—
642C4—64no—
643C4—82no—
644C4—82no—
645C4—124no—
646C4—122no—
647C4—122no—
648C4—122no—
649C4—242no—
650C4#465818yescomplemented
651C3#1515611yescharacteristic, complemented, Sylow
652C2C2×#465811yescharacteristic
653C2#7369311yescharacteristic
654C2#7369711yescharacteristic
655C2#7393711yescharacteristic
656C2#7394011yescharacteristic
657C2#7417111yescharacteristic
658C2#7433011yescharacteristic
659C2#7602911yescharacteristic
660C2#7604211yescharacteristic
661C2#7605911yescharacteristic
662C2#7607611yescharacteristic
663C2#7633711yescharacteristic
664C2#7647511yescharacteristic
665C2#7652411yescharacteristic
666C2#7664211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC3×C4⋊#95C2
hypercenterC4⋊#95D3
hypocenterC3#15156
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
491. C3×C4#400semidirect
650. C4#4658semidirect
651. C3#15156semidirect

Maximal subgroups

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

subgroupindex
C2×#49722
C2×C4×Dic3⋊C42
C2×#46582
C3×C4⋊#952
#715632
#715352
#694182
#694162
#694092
#151563