Finite Group Databasebeta

← #10731969

Subgroups — #10731969

Order 768.

1310 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4975C211yesmaximal, characteristic
2C2×#4658C212yesmaximal
3C2×#4649C211yesmaximal, characteristic
4C3×#1442C211yesmaximal, characteristic
5#71566C211yesmaximal, characteristic
6#69421C212yesmaximal
7#69415C211yesmaximal, characteristic
8#69410C211yesmaximal, characteristic
9Dic3⋊#95C212yesmaximal
10Dic3⋊#95C212yesmaximal
11Dic3⋊#95C211yesmaximal, characteristic
12#15152—31nomaximal, Sylow
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic3C2211yescharacteristic
15C22×Dic3⋊C4C2212yes—
16C22×Dic3⋊C4C2212yes—
17C22×Dic3⋊C4C2212yes—
18C22×Dic3⋊C4C2211yescharacteristic
19C22×Dic3⋊C4C2211yescharacteristic
20C22×C4×Dic3C2211yescharacteristic
21C22×C4×Dic3C2211yescharacteristic
22C22×C4×Dic3C2211yescharacteristic
23C2×C3×#95C2211yescharacteristic
24C2×C3×#95C2212yes—
25C2×C3×#95C2211yescharacteristic
26C2×C3×#95C2212yes—
27C2×C3⋊#95C2212yes—
28C2×C3⋊#95C2212yes—
29C2×C3⋊#95C2211yescharacteristic
30C2×C3⋊#95C2212yes—
31C2×C3⋊#95C2212yes—
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2212yes—
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2212yes—
36#4975—24no—
37#4658—28no—
38#4649—24no—
39C2×#400—32no—
40C2×#384—31no—
41C2×C4×C4⋊C4—31no—
42#1445—32no—
43#1442—31no—
44#1442D311yescharacteristic
45#1441—31no—
46#1441—31no—
47C4⋊#95—31no—
48C4⋊#95—32no—
49C4⋊#95—32no—
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—42no—
63C2×C4⋊Dic3—22no—
64C2×C4⋊Dic3—42no—
65C2×Dic3⋊C4—22no—
66C2×Dic3⋊C4—22no—
67C2×Dic3⋊C4—22no—
68C2×Dic3⋊C4—22no—
69C2×Dic3⋊C4—24no—
70C2×Dic3⋊C4—24no—
71C2×Dic3⋊C4—24no—
72C2×Dic3⋊C4—24no—
73C2×Dic3⋊C4—24no—
74C2×Dic3⋊C4—24no—
75C2×Dic3⋊C4—24no—
76C2×Dic3⋊C4—24no—
77C2×Dic3⋊C4—24no—
78C2×Dic3⋊C4D414yes—
79C2×Dic3⋊C4Q814yes—
80C2×C4×Dic3—22no—
81C2×C4×Dic3—22no—
82C2×C4×Dic3—24no—
83C2×C4×Dic3—22no—
84C2×C4×Dic3—24no—
85C2×C4×Dic3D414yes—
86C2×C4×Dic3Q814yes—
87C3×#95—22no—
88C3×#95—24no—
89C3×#95—22no—
90C3×#95—42no—
91C3⋊#95—24no—
92C3⋊#95—22no—
93C3⋊#95—22no—
94C3⋊#95—24no—
95C3⋊#95—24no—
96C3⋊#95—24no—
97C3⋊#95—42no—
98C3⋊#95—42no—
99C3⋊#95—42no—
100C22×C4⋊C4—31no—
101C22×C4⋊C4—31no—
102C22×C4⋊C4—32no—
103C22×C4⋊C4—32no—
104C22×C4⋊C4—32no—
105C22×C4⋊C4—31no—
106C22×C4⋊C4C2×D311yescharacteristic
107C22×C42—31no—
108C22×C42—31no—
109C22×C42—31no—
110#400—68no—
111#384—64no—
112C4×C4⋊C4—64no—
113C2×#95—32no—
114C2×#95—32no—
115C2×#95—32no—
116C2×#95—32no—
117C2×#95—31no—
118C2×#95—31no—
119C2×#95—32no—
120C2×#95—32no—
121C2×#95—32no—
122C2×#95C2×D312yes—
123C2×#95C2×D311yescharacteristic
124C2×#95C2×D311yescharacteristic
125C2×#95C2×D312yes—
126C24×C3C2411yescharacteristic
127C22×C3×C4—22no—
128C22×C3×C4—22no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—22no—
133C22×C3×C4—21no—
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×C4—22no—
148C22×C3×C4—22no—
149C22×C3×C4—22no—
150C22×C3×C4—22no—
151C22×C3×C4C2×D412yes—
152C22×C3×C4C2×D412yes—
153C22×C3×C4C2×Q812yes—
154C22×C3×C4C2×Q812yes—
155C22×C3×C4#4112yes—
156C22×Dic3—21no—
157C22×Dic3—21no—
158C22×Dic3—22no—
159C22×Dic3—21no—
160C22×Dic3—21no—
161C22×Dic3—22no—
162C22×Dic3—21no—
163C22×Dic3—22no—
164C22×Dic3—21no—
165C22×Dic3—22no—
166C22×Dic3—22no—
167C22×Dic3—22no—
168C22×Dic3—22no—
169C22×Dic3—22no—
170C22×Dic3—22no—
171C22×Dic3—22no—
172C22×Dic3—22no—
173C22×Dic3—22no—
174C22×Dic3—22no—
175C22×Dic3—22no—
176C22×Dic3—22no—
177C22×Dic3—22no—
178C22×Dic3—22no—
179C22×Dic3—22no—
180C22×Dic3C2×D412yes—
181C22×Dic3C2×D412yes—
182C22×Dic3C2×D412yes—
183C22×Dic3C2×D412yes—
184C22×Dic3C2×Q812yes—
185C22×Dic3C2×Q812yes—
186C22×Dic3C2×Q812yes—
187C22×Dic3C2×Q812yes—
188C22×Dic3#4112yes—
189C22×Dic3#4112yes—
190C22×Dic3#4114yes—
191C22×Dic3#4114yes—
192C3×C4⋊C4—44no—
193C4⋊Dic3—44no—
194Dic3⋊C4—28no—
195Dic3⋊C4—28no—
196Dic3⋊C4—48no—
197Dic3⋊C4—48no—
198Dic3⋊C4—48no—
199C4×Dic3—28no—
200C4×Dic3—28no—
201C4×Dic3—44no—
202C23×C4—31no—
203C23×C4—31no—
204C23×C4—31no—
205C23×C4—31no—
206C23×C4—32no—
207C23×C4—32no—
208C23×C4C22×D312yes—
209C23×C4C22×D312yes—
210C23×C4C22×D311yescharacteristic
211C23×C4C22×D311yescharacteristic
212C23×C4C22×D311yescharacteristic
213C2×C4⋊C4—22no—
214C2×C4⋊C4—34no—
215C2×C4⋊C4—34no—
216C2×C4⋊C4—42no—
217C2×C4⋊C4—62no—
218C2×C4⋊C4—62no—
219C2×C4⋊C4—62no—
220C2×C4⋊C4—62no—
221C2×C4⋊C4—64no—
222C2×C4⋊C4—64no—
223C2×C4⋊C4—64no—
224C2×C4⋊C4—64no—
225C2×C4⋊C4—64no—
226C2×C4⋊C4—64no—
227C2×C4⋊C4—64no—
228C2×C4⋊C4—64no—
229C2×C4⋊C4—64no—
230C2×C4⋊C4—62no—
231C2×C4⋊C4—122no—
232C2×C42—34no—
233C2×C42—34no—
234C2×C42—62no—
235C2×C42—64no—
236C2×C42—62no—
237C2×C42—62no—
238C2×C42—64no—
239#95—22no—
240#95—22no—
241#95—24no—
242#95—42no—
243#95—62no—
244#95—64no—
245#95—64no—
246#95—64no—
247#95—62no—
248#95—64no—
249#95—122no—
250#95—122no—
251#95—122no—
252C23×C3C22×D411yescharacteristic
253C23×C3C22×D411yescharacteristic
254C23×C3C22×Q811yescharacteristic
255C23×C3C22×Q811yescharacteristic
256C23×C3C2×#4111yescharacteristic
257C23×C3C2×#4111yescharacteristic
258C23×C3C2×#4111yescharacteristic
259C23×C3C2×#4112yes—
260C23×C3C2×#4112yes—
261C23×C3H(5,𝔽2)12yes—
262C23×C32−1+412yes—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—42no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—42no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
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×C4C22⋊Q814yes—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—24no—
301C2×Dic3—24no—
302C2×Dic3—22no—
303C2×Dic3—24no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—42no—
307C2×Dic3—42no—
308C2×Dic3—42no—
309C2×Dic3—42no—
310C2×Dic3—42no—
311C2×Dic3—42no—
312C2×Dic3—42no—
313C2×Dic3—42no—
314C2×Dic3—42no—
315C2×Dic3—42no—
316C2×Dic3—42no—
317C2×Dic3—42no—
318C2×Dic3—42no—
319C2×Dic3—42no—
320C2×Dic3—42no—
321C2×Dic3#12114yes—
322C2×Dic3C22⋊Q814yes—
323C2×Dic3#12314yes—
324C2×Dic3#12414yes—
325C2×Dic3#12518yes—
326C2×Dic3#12618yes—
327C2×Dic3C4⋊Q814yes—
328C24C23×D311yescharacteristic
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—32no—
354C22×C4—32no—
355C22×C4—34no—
356C22×C4—32no—
357C22×C4—34no—
358C22×C4—32no—
359C22×C4—32no—
360C22×C4—32no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—32no—
365C22×C4—61no—
366C22×C4—61no—
367C22×C4—62no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—62no—
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—62no—
380C22×C4—62no—
381C22×C4—62no—
382C22×C4—62no—
383C22×C4—62no—
384C22×C4—62no—
385C22×C4—62no—
386C22×C4—62no—
387C22×C4—62no—
388C22×C4—62no—
389C22×C4#23512yes—
390C22×C4D3×D412yes—
391C22×C4D3×D412yes—
392C22×C4D3×Q812yes—
393C22×C4D3×Q812yes—
394C4⋊C4—44no—
395C4⋊C4—68no—
396C4⋊C4—68no—
397C4⋊C4—124no—
398C4⋊C4—128no—
399C4⋊C4—128no—
400C4⋊C4—128no—
401C42—68no—
402C42—68no—
403C42—124no—
404C22×C3C2×#12111yescharacteristic
405C22×C3C2×C22⋊Q811yescharacteristic
406C22×C3C2×C22⋊Q811yescharacteristic
407C22×C3C2×#12311yescharacteristic
408C22×C3C2×#12411yescharacteristic
409C22×C3C2×#12512yes—
410C22×C3C2×#12612yes—
411C22×C3C2×C4⋊Q811yescharacteristic
412C22×C3#53211yescharacteristic
413C22×C3#53311yescharacteristic
414C22×C3#53311yescharacteristic
415C22×C3#53511yescharacteristic
416C22×C3#53611yescharacteristic
417C22×C3#54212yes—
418C22×C3#54412yes—
419C22×C3#54712yes—
420C22×C3#55012yes—
421C22×C3#55212yes—
422C22×C3#55312yes—
423C22×C3#55412yes—
424C22×C3#55612yes—
425C22×C3#55712yes—
426C22×C3#55912yes—
427C3×C4—24no—
428C3×C4—42no—
429C3×C4—42no—
430C3×C4—82no—
431C3×C4—82no—
432Dic3—24no—
433Dic3—24no—
434Dic3—42no—
435Dic3—82no—
436Dic3—82no—
437Dic3#40018yescomplemented
438C23C2×#23511yescharacteristic
439C23C2×D3×D411yescharacteristic
440C23C2×D3×D411yescharacteristic
441C23#100412yes—
442C23C2×D3×Q811yescharacteristic
443C23C2×D3×Q811yescharacteristic
444C23D3×#4112yes—
445C23D3×#4111yescharacteristic
446C23D3×#4112yes—
447C23D3×#4111yescharacteristic
448C23#101012yes—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—34no—
458C2×C4—34no—
459C2×C4—38no—
460C2×C4—38no—
461C2×C4—34no—
462C2×C4—34no—
463C2×C4—34no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—62no—
485C2×C4—64no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—64no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—64no—
495C2×C4—62no—
496C2×C4—121no—
497C2×C4—122no—
498C2×C4—121no—
499C2×C4—122no—
500C2×C4—122no—
501C2×C4—122no—
502C2×C4—122no—
503C2×C4—122no—
504C2×C4—122no—
505C2×C4—122no—
506C2×C4—122no—
507C2×C4—122no—
508C2×C4—122no—
509C2×C4—122no—
510C2×C4—122no—
511C2×C4—122no—
512C2×C4—122no—
513C2×C4#89614yes—
514C2×C3C2×#40011yescharacteristic
515C2×C3#248611yescharacteristic
516C2×C3#248711yescharacteristic
517C2×C3#251112yes—
518C2×C3#251212yes—
519C2×C3#254811yescharacteristic
520C2×C3#255212yes—
521C2×C3#256811yescharacteristic
522C2×C3#257012yes—
523C2×C3#262811yescharacteristic
524C2×C3#285711yescharacteristic
525C22C2×#89611yescharacteristic
526C22#553312yes—
527C22#554012yes—
528C22#554811yescharacteristic
529C22#557811yescharacteristic
530C22#559211yescharacteristic
531C22#559912yes—
532C22D3×#12111yescharacteristic
533C22#562312yes—
534C22D3×C22⋊Q811yescharacteristic
535C22#563612yes—
536C22D3×#12311yescharacteristic
537C22#565512yes—
538C22#566412yes—
539C22#566912yes—
540C22D3×#12411yescharacteristic
541C22#567511yescharacteristic
542C22#568512yes—
543C22D3×#12512yes—
544C22#568811yescharacteristic
545C22D3×#12612yes—
546C22#570812yes—
547C22D3×C4⋊Q811yescharacteristic
548C4—24no—
549C4—38no—
550C4—42no—
551C4—42no—
552C4—64no—
553C4—64no—
554C4—82no—
555C4—82no—
556C4—122no—
557C4—242no—
558C4—242no—
559C3#1515211yescharacteristic, complemented, Sylow
560C2#7418511yescharacteristic
561C2#7445711yescharacteristic
562C2#7507812yes—
563C2#7555212yes—
564C2#7628811yescharacteristic
565C2#7681011yescharacteristic
566C2#7694611yescharacteristic
567C2#7748511yescharacteristic
568C2#7778712yes—
569C2#7815812yes—
570C2D3×#40011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, prime radical, cosocleC24×C3C24
FittingC3×#1442C2
hypercenter#1442D3
hypocenterC3#15152
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
437. Dic3#400semidirect
559. 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×#46582
C2×#46492
C3×#14422
#715662
#694212
#694152
#694102
Dic3⋊#952
#151523