Finite Group Databasebeta

← #10731995

Subgroups — #10731995

Order 768.

1266 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4986C211yesmaximal, characteristic
2C2×#4976C211yesmaximal, characteristic
3C2×Dic3×C4⋊C4C211yesmaximal, characteristic
4C2×#4659C211yesmaximal, characteristic
5C3×#1441C211yesmaximal, characteristic
6#71566C211yesmaximal, characteristic
7#69417C212yesmaximal
8#69416C212yesmaximal
9Dic3⋊#95C212yesmaximal
10Dic3⋊#95C212yesmaximal
11Dic3⋊#95C211yesmaximal, characteristic
12#15156—31nomaximal, Sylow
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic3C2211yescharacteristic
16C22×Dic3⋊C4C2212yes—
17C22×Dic3⋊C4C2211yescharacteristic
18C22×Dic3⋊C4C2211yescharacteristic
19C22×Dic3⋊C4C2211yescharacteristic
20C22×C4×Dic3C2212yes—
21C22×C4×Dic3C2211yescharacteristic
22C2×C3×#95C2212yes—
23C2×C3×#95C2211yescharacteristic
24C2×C3×#95C2212yes—
25C2×C3⋊#95C2212yes—
26C2×C3⋊#95C2212yes—
27C2×C3⋊#95C2212yes—
28C2×C3⋊#95C2212yes—
29C2×C3⋊#95C2212yes—
30C2×C3⋊#95C2211yescharacteristic
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2212yes—
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36#4986—24no—
37#4976—24no—
38Dic3×C4⋊C4—24no—
39#4659—24no—
40C2×#400—31no—
41C2×#400—31no—
42C2×#389—31no—
43C2×C4×C4⋊C4—31no—
44#1443—32no—
45#1443—32no—
46#1441—31no—
47#1441D311yescharacteristic
48C4⋊#95—32no—
49C4⋊#95—31no—
50C4⋊#95—32no—
51C23×C3×C4C2312yes—
52C23×C3×C4C2311yescharacteristic
53C23×C3×C4C2311yescharacteristic
54C23×C3×C4C2312yes—
55C23×C3×C4C2311yescharacteristic
56C23×Dic3C2312yes—
57C23×Dic3C2311yescharacteristic
58C23×Dic3C2311yescharacteristic
59C23×Dic3C2312yes—
60C23×Dic3C2311yescharacteristic
61C23×Dic3C2311yescharacteristic
62C2×C3×C4⋊C4—22no—
63C2×C3×C4⋊C4—24no—
64C2×C3×C4⋊C4—22no—
65C2×C3×C4⋊C4—22no—
66C2×C3×C4⋊C4—22no—
67C2×C4⋊Dic3—22no—
68C2×C4⋊Dic3—22no—
69C2×C4⋊Dic3D414yes—
70C2×Dic3⋊C4—22no—
71C2×Dic3⋊C4—22no—
72C2×Dic3⋊C4—22no—
73C2×Dic3⋊C4—22no—
74C2×Dic3⋊C4—22no—
75C2×Dic3⋊C4—22no—
76C2×Dic3⋊C4—24no—
77C2×Dic3⋊C4—24no—
78C2×Dic3⋊C4—24no—
79C2×Dic3⋊C4—24no—
80C2×Dic3⋊C4Q814yes—
81C2×C4×Dic3—24no—
82C2×C4×Dic3—24no—
83C2×C4×Dic3—24no—
84C2×C4×Dic3—24no—
85C2×C4×Dic3D414yes—
86C3×#95—22no—
87C3×#95—24no—
88C3×#95—42no—
89C3⋊#95—22no—
90C3⋊#95—24no—
91C3⋊#95—24no—
92C3⋊#95—24no—
93C3⋊#95—24no—
94C3⋊#95—22no—
95C3⋊#95—22no—
96C3⋊#95—24no—
97C3⋊#95—24no—
98C3⋊#95—42no—
99C3⋊#95—42no—
100C22×C4⋊C4—31no—
101C22×C4⋊C4—31no—
102C22×C4⋊C4—31no—
103C22×C4⋊C4—32no—
104C22×C4⋊C4—31no—
105C22×C4⋊C4C2×D311yescharacteristic
106C22×C4⋊C4C2×D311yescharacteristic
107C22×C42—31no—
108C22×C42—32no—
109#400—64no—
110#400—64no—
111#389—64no—
112C4×C4⋊C4—64no—
113C2×#95—31no—
114C2×#95—32no—
115C2×#95—32no—
116C2×#95—32no—
117C2×#95—32no—
118C2×#95—32no—
119C2×#95—32no—
120C2×#95—31no—
121C2×#95—31no—
122C2×#95—32no—
123C2×#95—32no—
124C2×#95C2×D311yescharacteristic
125C2×#95C2×D312yes—
126C2×#95C2×D312yes—
127C24×C3C2411yescharacteristic
128C22×C3×C4—22no—
129C22×C3×C4—22no—
130C22×C3×C4—21no—
131C22×C3×C4—22no—
132C22×C3×C4—21no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
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—21no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4C2×D412yes—
155C22×C3×C4C2×D412yes—
156C22×C3×C4C2×Q812yes—
157C22×C3×C4#4112yes—
158C22×C3×C4#4114yes—
159C22×Dic3—21no—
160C22×Dic3—22no—
161C22×Dic3—21no—
162C22×Dic3—22no—
163C22×Dic3—22no—
164C22×Dic3—22no—
165C22×Dic3—21no—
166C22×Dic3—21no—
167C22×Dic3—22no—
168C22×Dic3—21no—
169C22×Dic3—21no—
170C22×Dic3—22no—
171C22×Dic3—22no—
172C22×Dic3—22no—
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—22no—
176C22×Dic3—21no—
177C22×Dic3—21no—
178C22×Dic3—22no—
179C22×Dic3—22no—
180C22×Dic3—21no—
181C22×Dic3—22no—
182C22×Dic3—22no—
183C22×Dic3—22no—
184C22×Dic3—22no—
185C22×Dic3—22no—
186C22×Dic3—22no—
187C22×Dic3C2×D412yes—
188C22×Dic3C2×D414yes—
189C22×Dic3C2×D412yes—
190C22×Dic3C2×Q812yes—
191C22×Dic3C2×Q812yes—
192C22×Dic3#4112yes—
193C22×Dic3#4114yes—
194C22×Dic3#4114yes—
195C3×C4⋊C4—28no—
196C3×C4⋊C4—44no—
197C4⋊Dic3—28no—
198Dic3⋊C4—28no—
199Dic3⋊C4—44no—
200Dic3⋊C4—44no—
201Dic3⋊C4—48no—
202C4×Dic3—28no—
203C4×Dic3—48no—
204C23×C4—31no—
205C23×C4—31no—
206C23×C4—32no—
207C23×C4—31no—
208C23×C4—31no—
209C23×C4—32no—
210C23×C4C22×D311yescharacteristic
211C23×C4C22×D312yes—
212C23×C4C22×D312yes—
213C23×C4C22×D311yescharacteristic
214C23×C4C22×D311yescharacteristic
215C2×C4⋊C4—22no—
216C2×C4⋊C4—24no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—34no—
221C2×C4⋊C4—34no—
222C2×C4⋊C4—62no—
223C2×C4⋊C4—62no—
224C2×C4⋊C4—62no—
225C2×C4⋊C4—62no—
226C2×C4⋊C4—62no—
227C2×C4⋊C4—64no—
228C2×C4⋊C4—64no—
229C2×C4⋊C4—64no—
230C2×C4⋊C4—64no—
231C2×C4⋊C4—62no—
232C2×C4⋊C4—62no—
233C2×C4⋊C4—62no—
234C2×C42—34no—
235C2×C42—64no—
236C2×C42—64no—
237C2×C42—64no—
238C2×C42—64no—
239#95—22no—
240#95—24no—
241#95—42no—
242#95—64no—
243#95—62no—
244#95—62no—
245#95—64no—
246#95—64no—
247#95—64no—
248#95—64no—
249#95—62no—
250#95—64no—
251#95—122no—
252#95—122no—
253C23×C3C22×D411yescharacteristic
254C23×C3C22×D411yescharacteristic
255C23×C3C22×Q811yescharacteristic
256C23×C3C2×#4111yescharacteristic
257C23×C3C2×#4112yes—
258C23×C3C2×#4111yescharacteristic
259C23×C3C2×#4112yes—
260C23×C3C2×#4112yes—
261C23×C3H(5,𝔽2)11yescharacteristic
262C23×C32−1+412yes—
263C23×C32−1+411yescharacteristic
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—24no—
267C2×C3×C4—24no—
268C2×C3×C4—22no—
269C2×C3×C4—24no—
270C2×C3×C4—22no—
271C2×C3×C4—24no—
272C2×C3×C4—24no—
273C2×C3×C4—22no—
274C2×C3×C4—41no—
275C2×C3×C4—42no—
276C2×C3×C4—42no—
277C2×C3×C4—41no—
278C2×C3×C4—41no—
279C2×C3×C4—42no—
280C2×C3×C4—42no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
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#12114yes—
295C2×Dic3—24no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—24no—
301C2×Dic3—24no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—41no—
305C2×Dic3—42no—
306C2×Dic3—42no—
307C2×Dic3—41no—
308C2×Dic3—42no—
309C2×Dic3—42no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—42no—
313C2×Dic3—42no—
314C2×Dic3—41no—
315C2×Dic3—41no—
316C2×Dic3—41no—
317C2×Dic3—42no—
318C2×Dic3—42no—
319C2×Dic3—42no—
320C2×Dic3—42no—
321C2×Dic3—42no—
322C2×Dic3—42no—
323C2×Dic3—42no—
324C2×Dic3—42no—
325C2×Dic3—42no—
326C2×Dic3C22⋊Q814yes—
327C2×Dic3#12314yes—
328C2×Dic3#12414yes—
329C2×Dic3#12518yes—
330C2×Dic3#12618yes—
331C24C23×D311yescharacteristic
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—32no—
359C22×C4—32no—
360C22×C4—34no—
361C22×C4—34no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—34no—
365C22×C4—32no—
366C22×C4—62no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—62no—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—61no—
373C22×C4—62no—
374C22×C4—62no—
375C22×C4—62no—
376C22×C4—62no—
377C22×C4—62no—
378C22×C4—62no—
379C22×C4—61no—
380C22×C4—61no—
381C22×C4—61no—
382C22×C4—61no—
383C22×C4—62no—
384C22×C4—61no—
385C22×C4—61no—
386C22×C4—62no—
387C22×C4—62no—
388C22×C4—62no—
389C22×C4—62no—
390C22×C4—62no—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—62no—
394C22×C4#23512yes—
395C22×C4D3×D412yes—
396C22×C4D3×D412yes—
397C22×C4#23714yes—
398C22×C4D3×Q812yes—
399C4⋊C4—28no—
400C4⋊C4—44no—
401C4⋊C4—68no—
402C4⋊C4—68no—
403C4⋊C4—124no—
404C4⋊C4—128no—
405C4⋊C4—124no—
406C42—68no—
407C42—128no—
408C22×C3C2×#12111yescharacteristic
409C22×C3C2×C22⋊Q811yescharacteristic
410C22×C3C2×#12311yescharacteristic
411C22×C3#52511yescharacteristic
412C22×C3C2×#12411yescharacteristic
413C22×C3C2×#12512yes—
414C22×C3C2×#12612yes—
415C22×C3#52912yes—
416C22×C3#53212yes—
417C22×C3#53611yescharacteristic
418C22×C3#53711yescharacteristic
419C22×C3#54112yes—
420C22×C3#54212yes—
421C22×C3#54712yes—
422C22×C3D4×Q811yescharacteristic
423C22×C3#55011yescharacteristic
424C22×C3#55212yes—
425C22×C3#55312yes—
426C22×C3#55411yescharacteristic
427C22×C3#55612yes—
428C22×C3#55611yescharacteristic
429C22×C3#55612yes—
430C22×C3#55712yes—
431C3×C4—24no—
432C3×C4—44no—
433C3×C4—42no—
434C3×C4—81no—
435C3×C4—82no—
436Dic3—42no—
437Dic3—42no—
438Dic3—44no—
439Dic3—81no—
440Dic3—82no—
441Dic3#40018yescomplemented
442C23C2×#23511yescharacteristic
443C23C2×D3×D411yescharacteristic
444C23C2×D3×D411yescharacteristic
445C23C2×#23712yes—
446C23#100411yescharacteristic
447C23C2×D3×Q811yescharacteristic
448C23#100712yes—
449C23D3×#4112yes—
450C23D3×#4111yescharacteristic
451C23D3×#4112yes—
452C23#101011yescharacteristic
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—24no—
457C2×C4—22no—
458C2×C4—24no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—34no—
464C2×C4—34no—
465C2×C4—38no—
466C2×C4—38no—
467C2×C4—34no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—64no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—64no—
496C2×C4—64no—
497C2×C4—122no—
498C2×C4—122no—
499C2×C4—122no—
500C2×C4—122no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—122no—
504C2×C4—122no—
505C2×C4—121no—
506C2×C4—121no—
507C2×C4—122no—
508C2×C4—122no—
509C2×C4—121no—
510C2×C4—122no—
511C2×C4—121no—
512C2×C4—122no—
513C2×C4—121no—
514C2×C4—122no—
515C2×C4—122no—
516C2×C4—122no—
517C2×C4—122no—
518C2×C4—122no—
519C2×C4#88414yes—
520C2×C3C2×#40011yescharacteristic
521C2×C3#250612yes—
522C2×C3#250912yes—
523C2×C3#251212yes—
524C2×C3#251412yes—
525C2×C3#253811yescharacteristic
526C2×C3#254711yescharacteristic
527C2×C3#256211yescharacteristic
528C2×C3#258111yescharacteristic
529C2×C3#262511yescharacteristic
530C2×C3#285411yescharacteristic
531C22C2×#88411yescharacteristic
532C22#551111yescharacteristic
533C22#553311yescharacteristic
534C22#553812yes—
535C22#556812yes—
536C22#558611yescharacteristic
537C22#559612yes—
538C22#559911yescharacteristic
539C22#560112yes—
540C22#560811yescharacteristic
541C22D3×C22⋊Q811yescharacteristic
542C22#563112yes—
543C22#563211yescharacteristic
544C22#564012yes—
545C22#564112yes—
546C22#565012yes—
547C22D3×#12311yescharacteristic
548C22D3×#12411yescharacteristic
549C22D3×#12512yes—
550C22#569612yes—
551C22D3×#12612yes—
552C22#572112yes—
553C22#572411yescharacteristic
554C4—24no—
555C4—38no—
556C4—44no—
557C4—42no—
558C4—81no—
559C4—82no—
560C4—122no—
561C4—124no—
562C4—122no—
563C4—241no—
564C4—242no—
565C3#1515611yescharacteristic, complemented, Sylow
566C2#7393611yescharacteristic
567C2#7487211yescharacteristic
568C2#7503212yes—
569C2#7604512yes—
570C2#7653611yescharacteristic
571C2#7695511yescharacteristic
572C2#7719111yescharacteristic
573C2#7730612yes—
574C2#7776612yes—
575C2#7781911yescharacteristic
576C2D3×#40011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC3×#1441C2
hypercenter#1441D3
hypocenterC3#15156
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
441. Dic3#400semidirect
565. C3#15156semidirect

Maximal subgroups

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

subgroupindex
C2×#49862
C2×#49762
C2×Dic3×C4⋊C42
C2×#46592
C3×#14412
#715662
#694172
#694162
Dic3⋊#952
#151563