Finite Group Databasebeta

← #10731970

Subgroups — #10731970

Order 768.

1310 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4975C211yesmaximal, characteristic
2C2×C4×C4⋊Dic3C211yesmaximal, characteristic
3C2×#4660C212yesmaximal
4C3×C4⋊#95C211yesmaximal, characteristic
5#71563C211yesmaximal, characteristic
6#71563C211yesmaximal, characteristic
7#71563C211yesmaximal, characteristic
8#71535C211yesmaximal, characteristic
9#69421C212yesmaximal
10#69414C212yesmaximal
11#69411C212yesmaximal
12#15152—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
20C22×Dic3⋊C4C2212yes—
21C22×Dic3⋊C4C2212yes—
22C22×C4×Dic3C2211yescharacteristic
23C22×C4×Dic3C2211yescharacteristic
24C2×C3×#95C2212yes—
25C2×C3×#95C2212yes—
26C2×C3⋊#95C2212yes—
27C2×C3⋊#95C2212yes—
28C2×C3⋊#95C2211yescharacteristic
29C2×C3⋊#95C2212yes—
30C2×C3⋊#95C2212yes—
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36#4975—24no—
37C4×C4⋊Dic3—24no—
38#4660—28no—
39C2×#400—32no—
40C2×#384—31no—
41C2×C4×C4⋊C4—31no—
42#1445—32no—
43#1442—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×Dic3C2312yes—
57C23×Dic3C2311yescharacteristic
58C23×Dic3C2311yescharacteristic
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×C42Q814yes—
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—
80C2×C4⋊Dic3D414yes—
81C2×C4⋊Dic3Q814yes—
82C2×Dic3⋊C4—24no—
83C2×Dic3⋊C4—24no—
84C2×Dic3⋊C4—24no—
85C2×Dic3⋊C4—24no—
86C2×Dic3⋊C4—42no—
87C2×Dic3⋊C4—42no—
88C2×C4×Dic3—22no—
89C2×C4×Dic3—22no—
90C2×C4×Dic3—22no—
91C2×C4×Dic3—22no—
92C2×C4×Dic3—22no—
93C2×C4×Dic3D414yes—
94C3×#95—24no—
95C3×#95—42no—
96C3⋊#95—24no—
97C3⋊#95—24no—
98C3⋊#95—24no—
99C3⋊#95—24no—
100C3⋊#95—22no—
101C3⋊#95—22no—
102C3⋊#95—24no—
103C3⋊#95—42no—
104C3⋊#95—42no—
105C3⋊#95—42no—
106C22×C4⋊C4—31no—
107C22×C4⋊C4—31no—
108C22×C4⋊C4—32no—
109C22×C4⋊C4—31no—
110C22×C4⋊C4—31no—
111C22×C4⋊C4—32no—
112C22×C4⋊C4C2×D311yescharacteristic
113C22×C4⋊C4C2×D311yescharacteristic
114C22×C42—31no—
115C22×C42—31no—
116C22×C42C2×D311yescharacteristic
117#400—68no—
118#384—64no—
119C4×C4⋊C4—64no—
120C2×#95—32no—
121C2×#95—32no—
122C2×#95—32no—
123C2×#95—32no—
124C2×#95—32no—
125C2×#95—31no—
126C2×#95—31no—
127C2×#95—32no—
128C2×#95—32no—
129C2×#95—32no—
130C2×#95C2×D312yes—
131C2×#95C2×D312yes—
132C24×C3C2411yescharacteristic
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×C4C2×Q812yes—
161C22×C3×C4C2×Q812yes—
162C22×C3×C4C2×Q812yes—
163C22×C3×C4#4112yes—
164C22×C3×C4#4112yes—
165C22×C3×C4#4112yes—
166C22×C3×C4#4112yes—
167C22×C3×C4#4112yes—
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—21no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—21no—
188C22×Dic3—22no—
189C22×Dic3—22no—
190C22×Dic3—22no—
191C22×Dic3—22no—
192C22×Dic3—22no—
193C22×Dic3—22no—
194C22×Dic3—22no—
195C22×Dic3—22no—
196C22×Dic3—22no—
197C22×Dic3—22no—
198C22×Dic3—22no—
199C22×Dic3—22no—
200C22×Dic3—22no—
201C22×Dic3—22no—
202C22×Dic3C2×D412yes—
203C22×Dic3C2×D412yes—
204C22×Dic3C2×D412yes—
205C22×Dic3C2×D412yes—
206C22×Dic3C2×Q812yes—
207C22×Dic3C2×Q812yes—
208C22×Dic3#4112yes—
209C22×Dic3#4112yes—
210C3×C4⋊C4—44no—
211C3×C4⋊C4—44no—
212C3×C42—28no—
213C4⋊Dic3—28no—
214C4⋊Dic3—28no—
215C4⋊Dic3—44no—
216C4⋊Dic3—44no—
217Dic3⋊C4—48no—
218Dic3⋊C4—48no—
219C4×Dic3—28no—
220C4×Dic3—44no—
221C23×C4—31no—
222C23×C4—31no—
223C23×C4—31no—
224C23×C4—31no—
225C23×C4—32no—
226C23×C4—32no—
227C23×C4C22×D312yes—
228C23×C4C22×D312yes—
229C23×C4C22×D311yescharacteristic
230C23×C4C22×D311yescharacteristic
231C23×C4C22×D311yescharacteristic
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—34no—
239C2×C4⋊C4—34no—
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—64no—
248C2×C4⋊C4—62no—
249C2×C4⋊C4—62no—
250C2×C4⋊C4—62no—
251C2×C4⋊C4—62no—
252C2×C4⋊C4—62no—
253C2×C4⋊C4—62no—
254C2×C4⋊C4—122no—
255C2×C4⋊C4—122no—
256C2×C42—22no—
257C2×C42—22no—
258C2×C42—34no—
259C2×C42—62no—
260C2×C42—62no—
261C2×C42—62no—
262C2×C42—62no—
263C2×C42—62no—
264C2×C42Dic614yes—
265#95—24no—
266#95—42no—
267#95—64no—
268#95—62no—
269#95—62no—
270#95—64no—
271#95—64no—
272#95—64no—
273#95—64no—
274#95—122no—
275#95—122no—
276#95—122no—
277C23×C3C22×D411yescharacteristic
278C23×C3C22×D411yescharacteristic
279C23×C3C22×Q811yescharacteristic
280C23×C3C22×Q811yescharacteristic
281C23×C3C2×#4111yescharacteristic
282C23×C3C2×#4111yescharacteristic
283C23×C3C2×#4111yescharacteristic
284C23×C3C2×#4111yescharacteristic
285C23×C3C2×#4111yescharacteristic
286C23×C3C2×#4111yescharacteristic
287C23×C3C2×#4111yescharacteristic
288C23×C3H(5,𝔽2)11yescharacteristic
289C23×C3H(5,𝔽2)11yescharacteristic
290C23×C32−1+411yescharacteristic
291C23×C32−1+411yescharacteristic
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
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×C4—42no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4C22⋊Q814yes—
320C2×C3×C4#12314yes—
321C2×C3×C4#12414yes—
322C2×C3×C4#12514yes—
323C2×C3×C4#12514yes—
324C2×C3×C4#12614yes—
325C2×C3×C4#12614yes—
326C2×C3×C4C4⋊Q814yes—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—42no—
354C2×Dic3—42no—
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—42no—
364C2×Dic3—42no—
365C2×Dic3—42no—
366C2×Dic3—42no—
367C2×Dic3#12114yes—
368C2×Dic3C22⋊Q814yes—
369C24C23×D311yescharacteristic
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
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—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—32no—
395C22×C4—32no—
396C22×C4—32no—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—32no—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—61no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—61no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4—61no—
420C22×C4—61no—
421C22×C4—61no—
422C22×C4—62no—
423C22×C4—62no—
424C22×C4—62no—
425C22×C4—62no—
426C22×C4—62no—
427C22×C4—62no—
428C22×C4—62no—
429C22×C4—62no—
430C22×C4—62no—
431C22×C4—62no—
432C22×C4—62no—
433C22×C4—62no—
434C22×C4—62no—
435C22×C4—62no—
436C22×C4C2×Dic612yes—
437C22×C4C2×Dic612yes—
438C22×C4C2×Dic612yes—
439C22×C4#23512yes—
440C22×C4#23512yes—
441C22×C4D3×D412yes—
442C22×C4D3×D412yes—
443C22×C4#23712yes—
444C22×C4#23712yes—
445C22×C4D3×Q812yes—
446C22×C4#23912yes—
447C4⋊C4—44no—
448C4⋊C4—44no—
449C4⋊C4—68no—
450C4⋊C4—68no—
451C4⋊C4—128no—
452C4⋊C4—128no—
453C4⋊C4—124no—
454C4⋊C4—124no—
455C42—28no—
456C42—68no—
457C42—124no—
458C22×C3C2×#12111yescharacteristic
459C22×C3C2×C22⋊Q811yescharacteristic
460C22×C3C2×C22⋊Q811yescharacteristic
461C22×C3C2×#12311yescharacteristic
462C22×C3C2×#12411yescharacteristic
463C22×C3C2×#12511yescharacteristic
464C22×C3C2×#12511yescharacteristic
465C22×C3C2×#12611yescharacteristic
466C22×C3C2×#12611yescharacteristic
467C22×C3C2×C4⋊Q811yescharacteristic
468C22×C3#53211yescharacteristic
469C22×C3#53311yescharacteristic
470C22×C3#53311yescharacteristic
471C22×C3#53511yescharacteristic
472C22×C3#53611yescharacteristic
473C22×C3#54211yescharacteristic
474C22×C3#54211yescharacteristic
475C22×C3#54411yescharacteristic
476C22×C3#54411yescharacteristic
477C22×C3#54711yescharacteristic
478C22×C3#54711yescharacteristic
479C22×C3#55011yescharacteristic
480C22×C3#55011yescharacteristic
481C22×C3#55211yescharacteristic
482C22×C3#55211yescharacteristic
483C22×C3#55311yescharacteristic
484C22×C3#55311yescharacteristic
485C22×C3#55411yescharacteristic
486C22×C3#55411yescharacteristic
487C22×C3#55611yescharacteristic
488C22×C3#55611yescharacteristic
489C22×C3#55711yescharacteristic
490C22×C3#55711yescharacteristic
491C22×C3#55911yescharacteristic
492C22×C3#55911yescharacteristic
493C3×C4—24no—
494C3×C4—42no—
495C3×C4—82no—
496C3×C4—82no—
497C3×C4#40018yescomplemented
498Dic3—24no—
499Dic3—24no—
500Dic3—42no—
501Dic3—42no—
502Dic3—82no—
503Dic3—82no—
504C23C22×Dic611yescharacteristic
505C23C2×#23511yescharacteristic
506C23C2×#23511yescharacteristic
507C23C2×D3×D411yescharacteristic
508C23C2×D3×D411yescharacteristic
509C23C2×#23711yescharacteristic
510C23C2×#23711yescharacteristic
511C23#100411yescharacteristic
512C23C2×D3×Q811yescharacteristic
513C23C2×#23911yescharacteristic
514C23#100711yescharacteristic
515C23D3×#4111yescharacteristic
516C23D3×#4111yescharacteristic
517C23#100911yescharacteristic
518C23#101011yescharacteristic
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—34no—
529C2×C4—34no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
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—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—121no—
567C2×C4—121no—
568C2×C4—121no—
569C2×C4—121no—
570C2×C4—121no—
571C2×C4—121no—
572C2×C4—121no—
573C2×C4—121no—
574C2×C4—122no—
575C2×C4—122no—
576C2×C4—122no—
577C2×C4—122no—
578C2×C4—122no—
579C2×C4—122no—
580C2×C4—122no—
581C2×C4—122no—
582C2×C4—122no—
583C2×C4—122no—
584C2×C4—122no—
585C2×C4—122no—
586C2×C4—122no—
587C2×C4—122no—
588C2×C4#87014yes—
589C2×C4#87814yes—
590C2×C4#87914yes—
591C2×C4#88514yes—
592C2×C4#88814yes—
593C2×C4#89014yes—
594C2×C4#89414yes—
595C2×C4#89814yes—
596C2×C3C2×#40011yescharacteristic
597C2×C3#248611yescharacteristic
598C2×C3#248711yescharacteristic
599C2×C3#251111yescharacteristic
600C2×C3#251111yescharacteristic
601C2×C3#251211yescharacteristic
602C2×C3#251211yescharacteristic
603C2×C3#254811yescharacteristic
604C2×C3#255211yescharacteristic
605C2×C3#255211yescharacteristic
606C2×C3#256811yescharacteristic
607C2×C3#257011yescharacteristic
608C2×C3#257011yescharacteristic
609C2×C3#262811yescharacteristic
610C2×C3#285711yescharacteristic
611C22C2×#87011yescharacteristic
612C22C2×#87811yescharacteristic
613C22C2×#87911yescharacteristic
614C22C2×#88511yescharacteristic
615C22C2×#88811yescharacteristic
616C22C2×#89011yescharacteristic
617C22#550011yescharacteristic
618C22C2×#89411yescharacteristic
619C22C2×#89811yescharacteristic
620C22#551711yescharacteristic
621C22#551911yescharacteristic
622C22#555111yescharacteristic
623C22#555311yescharacteristic
624C22#555811yescharacteristic
625C22#555911yescharacteristic
626C22#556711yescharacteristic
627C22#556811yescharacteristic
628C22#557911yescharacteristic
629C22#558111yescharacteristic
630C22#559611yescharacteristic
631C22#560311yescharacteristic
632C22D3×#12111yescharacteristic
633C22#560711yescharacteristic
634C22#562211yescharacteristic
635C22D3×C22⋊Q811yescharacteristic
636C22#562811yescharacteristic
637C22#564311yescharacteristic
638C22#567111yescharacteristic
639C22#568111yescharacteristic
640C22#569411yescharacteristic
641C22#569511yescharacteristic
642C22#571811yescharacteristic
643C22#572111yescharacteristic
644C22#572611yescharacteristic
645C22#573011yescharacteristic
646C4—24no—
647C4—42no—
648C4—64no—
649C4—64no—
650C4—82no—
651C4—82no—
652C4—122no—
653C4—122no—
654C4—242no—
655C4—242no—
656C4#466018yescomplemented
657C3#1515211yescharacteristic, complemented, Sylow
658C2C2×#466011yescharacteristic
659C2#7371611yescharacteristic
660C2#7372411yescharacteristic
661C2#7395411yescharacteristic
662C2#7400111yescharacteristic
663C2#7418611yescharacteristic
664C2#7433611yescharacteristic
665C2#7604611yescharacteristic
666C2#7604711yescharacteristic
667C2#7623111yescharacteristic
668C2#7623211yescharacteristic
669C2#7633911yescharacteristic
670C2#7635311yescharacteristic
671C2#7652311yescharacteristic
672C2#7654511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC3×C4⋊#95C2
hypercenterC4⋊#95D3
hypocenterC3#15152
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
497. C3×C4#400semidirect
656. C4#4660semidirect
657. C3#15152semidirect

Maximal subgroups

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

subgroupindex
C2×#49752
C2×C4×C4⋊Dic32
C2×#46602
C3×C4⋊#952
#715632
#715352
#694212
#694142
#694112
#151523