Finite Group Databasebeta

← #11805092

Subgroups — #11805092

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2#10592636C211yesmaximal, characteristic, complemented
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#10591377C212yesmaximal
5Dic3×(C2×D3)⋊C4C212yesmaximal
6D3×C3⋊#95C211yesmaximal, characteristic
7#10591294C211yesmaximal, characteristic
8#10591262C212yesmaximal, complemented
9#10591239C211yesmaximal, characteristic, complemented
10#10591206C211yesmaximal, characteristic, complemented
11#10591201C212yesmaximal, complemented
12#82237—31nomaximal
13#73766—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×D3×Dic3C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4C2211yescharacteristic
19C2×C3×C4⋊Dic3C2212yes—
20C2×C3×Dic3⋊C4C2211yescharacteristic
21C2×C3×Dic3⋊C4C2211yescharacteristic
22C2×C3×C4×Dic3C2212yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#872C418yescomplemented
25C2×Dic3⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×Dic32C2212yes—
28#63658C2211yescharacteristic
29#63658C2212yes—
30#63658C2211yescharacteristic
31#63658C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×#117—31no—
39C2×#872D311yescharacteristic
40C3×C4×C4⋊C4—31no—
41#5211—31no—
42C2×C3⋊#95—31no—
43#4989—32no—
44#4980—32no—
45#4980—32no—
46#4978—32no—
47#4950—32no—
48Dic3×C22⋊C4—32no—
49C4×(C2×D3)⋊C4—32no—
50#4937—31no—
51#4937—31no—
52#4937—61no—
53#4936—31no—
54C4×C4⋊Dic3D311yescharacteristic, complemented
55#4933—32no—
56#4932—31no—
57#4664—31no—
58D3×#95—31no—
59#4650—31no—
60#4648—31no—
61C23×C3×D3C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3C2×C414yes—
74C2×D3×Dic3—24no—
75C2×D3×Dic3—24no—
76C2×D3×Dic3—42no—
77C32×C42C2×C414yescomplemented
78C3×(C2×D3)⋊C4C2×C414yes—
79C3×(C2×D3)⋊C4C2×C414yes—
80C3×C4⋊Dic3—24no—
81C3×Dic3⋊C4C2×C414yescomplemented
82C3×Dic3⋊C4C2×C414yescomplemented
83C3×C4×Dic3—42no—
84C3×C4×Dic3C2×C414yescomplemented
85Dic3⋊Dic3—42no—
86(C2×D3)⋊Dic3—24no—
87Dic32—24no—
88#2343—91noSylow
89C23×C3×C4—31no—
90C23×Dic3—32no—
91C22×C4×D3—32no—
92C22×C4×D3C2×D311yescharacteristic
93C3×#117—38no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—32no—
97C2×C3×C22⋊C4—31no—
98C2×C3×C22⋊C4—31no—
99C2×C3×C42—21no—
100C2×C3×C42—31no—
101C2×C3×C42—32no—
102C2×C3×C42C2×D311yescharacteristic
103C2×C3×C42C2×D311yescharacteristic
104C2×#217—32no—
105C2×(C2×D3)⋊C4—32no—
106C2×(C2×D3)⋊C4C2×D311yescharacteristic
107C2×(C2×D3)⋊C4C2×D311yescharacteristic
108C2×C4⋊Dic3—32no—
109C2×C4⋊Dic3C2×D312yes—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4C2×D311yescharacteristic
112C2×Dic3⋊C4C2×D311yescharacteristic
113C2×C4×Dic3—32no—
114C2×C4×Dic3—32no—
115C2×C4×Dic3C2×D312yes—
116C2×C4×Dic3C2×D311yescharacteristic
117#872Dic318yescomplemented
118C3×#95—31no—
119C3×#95—31no—
120C3⋊#95—31no—
121C3⋊#95—31no—
122C3⋊#95—31no—
123C3⋊#95—32no—
124C3⋊#95—31no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—61no—
137C3⋊#95—61no—
138C3⋊#95—62no—
139C3⋊#95—62no—
140C3⋊#95C2×D311yescharacteristic
141C3⋊#95C2×D311yescharacteristic
142C23×C32C2411yescharacteristic
143C22×C3×D3—22no—
144C22×C3×D3—21no—
145C22×C3×D3—21no—
146C22×C3×D3C22×C412yes—
147C22×C3×D3#4114yes—
148C2×C32×C4—22no—
149C2×C32×C4—22no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C22×C412yes—
154C2×C32×C4C22×C412yes—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3C22×C412yes—
171C2×C3×Dic3C22×C412yes—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3#4114yes—
174C3×C4×D3—28no—
175D3×Dic3—48no—
176C2×#117—31no—
177#387—92no—
178#387—92no—
179#385—92no—
180#383—91no—
181#382—91no—
182#381—91no—
183C4×C4⋊C4—31no—
184C4×C22⋊C4—92no—
185#376—91no—
186C2×#95—91no—
187C24×C3—31no—
188C23×D3C22×D311yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—31no—
193C22×C3×C4—32no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—34no—
197C22×C3×C4—32no—
198C22×C3×C4—64no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—32no—
209C22×Dic3—62no—
210C22×Dic3—62no—
211C22×Dic3—64no—
212C22×Dic3—64no—
213C22×Dic3—122no—
214C22×Dic3C22×D312yes—
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D311yescharacteristic
217C22×Dic3C22×D311yescharacteristic
218C22×Dic3C22×D311yescharacteristic
219C2×C4×D3—24no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—122no—
223C2×C4×D3C2×Dic314yes—
224C3×C4⋊C4—34no—
225C3×C4⋊C4—34no—
226C3×C4⋊C4—64no—
227C3×C22⋊C4—34no—
228C3×C22⋊C4—34no—
229C3×C42—24no—
230C3×C42—34no—
231C3×C42—122no—
232C3×C42C4×D314yescomplemented
233C3×C42C2×Dic314yescomplemented
234#217—64no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4C2×Dic314yes—
237(C2×D3)⋊C4C2×Dic314yes—
238C4⋊Dic3—24no—
239C4⋊Dic3—122no—
240Dic3⋊C4—122no—
241Dic3⋊C4C2×Dic314yescomplemented
242Dic3⋊C4C2×Dic314yescomplemented
243C4×Dic3—42no—
244C4×Dic3—64no—
245C4×Dic3—64no—
246C4×Dic3C2×Dic314yescomplemented
247C22×C32C23×C411yescharacteristic
248C22×C32C2×#4112yes—
249C22×C32C2×#4112yes—
250C22×C32H(5,𝔽2)11yescharacteristic
251C22×C322−1+411yescharacteristic
252C2×C3×D3—22no—
253C2×C3×D3—22no—
254C2×C3×D3—24no—
255C2×C3×D3—24no—
256C2×C3×D3#11714yes—
257C32×C4—22no—
258C32×C4—22no—
259C32×C4—22no—
260C3⋊Dic3—42no—
261C3⋊Dic3—42no—
262C3×Dic3—22no—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—24no—
266C3×Dic3—42no—
267C23×C4—31no—
268C23×C4—92no—
269#117—38no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—32no—
273C2×C4⋊C4—92no—
274C2×C22⋊C4—31no—
275C2×C22⋊C4—31no—
276C2×C22⋊C4—92no—
277C2×C42—31no—
278C2×C42—32no—
279C2×C42—92no—
280C2×C42D3211yescharacteristic
281#95—31no—
282#95—31no—
283#95—92no—
284#95—92no—
285#95—92no—
286#95—92no—
287#95—91no—
288#95—91no—
289#95—92no—
290#95—92no—
291C23×C3—21no—
292C23×C3—32no—
293C23×C3—34no—
294C23×C3—62no—
295C23×C3—61no—
296C23×C3—61no—
297C23×C3C23×D311yescharacteristic
298C23×C3C23×D311yescharacteristic
299C22×D3—22no—
300C22×D3—21no—
301C22×D3—21no—
302C22×D3#23514yes—
303C22×D3C22×Dic312yes—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—32no—
316C2×C3×C4—32no—
317C2×C3×C4—32no—
318C2×C3×C4—34no—
319C2×C3×C4—41no—
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—41no—
323C2×C3×C4—68no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4C2×C4×D312yes—
334C2×C3×C4C2×C4×D312yes—
335C2×C3×C4C2×C4×D312yes—
336C2×C3×C4C22×Dic312yes—
337C2×C3×C4C22×Dic312yes—
338C2×C3×C4C22×Dic312yes—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—122no—
361C2×Dic3—122no—
362C2×Dic3—122no—
363C2×Dic3—122no—
364C2×Dic3—122no—
365C2×Dic3—122no—
366C2×Dic3—128no—
367C2×Dic3#23514yes—
368C2×Dic3C22×Dic312yes—
369C2×Dic3C22×Dic312yes—
370C2×Dic3C22×Dic312yes—
371C4×D3—28no—
372C4×D3—128no—
373C2×C32C2×#11711yescharacteristic
374C2×C32C4×#4111yescharacteristic
375C2×C32#52011yescharacteristic
376C2×C32#55112yes—
377C2×C32#55212yes—
378C3×D3—24no—
379C24—31no—
380C22×C4—32no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—34no—
385C22×C4—32no—
386C22×C4—64no—
387C22×C4—92no—
388C22×C4—92no—
389C22×C4—184no—
390C22×C4—184no—
391C22×C4—362no—
392C22×C4C2×D3211yescharacteristic
393C22×C4C2×D3211yescharacteristic
394C22×C4C2×D3211yescharacteristic
395C4⋊C4—34no—
396C4⋊C4—34no—
397C4⋊C4—64no—
398C4⋊C4—362no—
399C22⋊C4—34no—
400C22⋊C4—34no—
401C22⋊C4—184no—
402C42—34no—
403C42—122no—
404C42—184no—
405C42D3×Dic314yescomplemented
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—34no—
412C22×C3—62no—
413C22×C3—62no—
414C22×C3—64no—
415C22×C3—64no—
416C22×C3C22×C4×D311yescharacteristic
417C22×C3C2×#23512yes—
418C22×C3C2×#23512yes—
419C22×C3#100411yescharacteristic
420C22×C3#100711yescharacteristic
421C22×C3D3×#4112yes—
422C22×C3D3×#4112yes—
423C22×C3#100911yescharacteristic
424C22×C3#101011yescharacteristic
425C22×C3C23×Dic311yescharacteristic
426C2×D3—24no—
427C2×D3—24no—
428C2×D3—22no—
429C2×D3—22no—
430C2×D3#92614yes—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—22no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—42no—
440C3×C4—62no—
441C3×C4—62no—
442C3×C4—62no—
443C3×C4—64no—
444C3×C4—122no—
445Dic3—22no—
446Dic3—24no—
447Dic3—22no—
448Dic3—22no—
449Dic3—42no—
450Dic3—122no—
451Dic3—122no—
452Dic3—122no—
453Dic3—122no—
454Dic3—242no—
455Dic3—242no—
456C32#234311yescharacteristic, complemented, Sylow
457C23—34no—
458C23—32no—
459C23—61no—
460C23—62no—
461C23—61no—
462C23C22×D3211yescharacteristic
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—34no—
468C2×C4—32no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—68no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—61no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4—182no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—182no—
487C2×C4—368no—
488C2×C4C2×D3×Dic312yes—
489C2×C4C2×D3×Dic312yes—
490C2×C4C2×D3×Dic312yes—
491C2×C3—21no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—22no—
496C2×C3—64no—
497C2×C3C4×#23511yescharacteristic
498C2×C3#550411yescharacteristic
499C2×C3D3×#11711yescharacteristic
500C2×C3#552712yes—
501C2×C3#553112yes—
502C2×C3#555612yes—
503C2×C3#558112yes—
504C2×C3C2×#92611yescharacteristic
505C2×C3Dic3×#4111yescharacteristic
506C2×C3#582711yescharacteristic
507D3—24no—
508C22—34no—
509C22—64no—
510C22—62no—
511C22—62no—
512C22—64no—
513C22#6429711yescharacteristic
514C22D3×#23512yes—
515C22D3×#23512yes—
516C22#6430711yescharacteristic
517C22C22×D3×Dic311yescharacteristic
518C4—22no—
519C4—22no—
520C4—22no—
521C4—62no—
522C4—62no—
523C4—62no—
524C4—64no—
525C4—122no—
526C4—362no—
527C4—362no—
528C3—21no—
529C3#7376611yescharacteristic, complemented
530C3#8223711yescharacteristic, complemented
531C2—64no—
532C2#1059391612yes—
533C2#1059401512yes—
534C2D3×#92611yescharacteristic
535C2Dic3×#23511yescharacteristic
536C2#1059498611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2343
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592636C2semidirect
3. C3×C4×C4⋊Dic3C2semidirect
8. #10591262C2semidirect
9. #10591239C2semidirect
10. #10591206C2semidirect
11. #10591201C2semidirect
24. C3×#872C4semidirect
54. C4×C4⋊Dic3D3semidirect
77. C32×C42C2×C4semidirect
81. C3×Dic3⋊C4C2×C4semidirect
82. C3×Dic3⋊C4C2×C4semidirect
84. C3×C4×Dic3C2×C4semidirect
117. #872Dic3semidirect
232. C3×C42C4×D3semidirect
233. C3×C42C2×Dic3semidirect
241. Dic3⋊C4C2×Dic3semidirect
242. Dic3⋊C4C2×Dic3semidirect
246. C4×Dic3C2×Dic3semidirect
405. C42D3×Dic3semidirect
456. C32#2343semidirect
529. C3#73766semidirect
530. C3#82237semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8722
#105926362
C3×C4×C4⋊Dic32
#105913772
Dic3×(C2×D3)⋊C42
D3×C3⋊#952
#105912942
#105912622
#105912392
#105912062
#105912012
#822373
#737663