Finite Group Databasebeta

← #11805372

Subgroups — #11805372

Order 1152.

1077 conjugacy classes of subgroups.

The subgroup lattice has 534 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#10591307C212yesmaximal
5#10591305C212yesmaximal
6#10591295C211yesmaximal, characteristic
7#10591265C212yesmaximal, complemented
8#10591242C211yesmaximal, characteristic, complemented
9Dic3×Dic3⋊C4C212yesmaximal, complemented
10#10591237C211yesmaximal, characteristic
11#10591223C211yesmaximal, characteristic, complemented
12#82240—31nomaximal
13#73635—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4C2211yescharacteristic
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×Dic3⋊C4C2211yescharacteristic
20C2×C3×Dic3⋊C4C2211yescharacteristic
21C2×C3×C4×Dic3C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C3×#872C418yescomplemented
24C2×Dic3⋊Dic3C2212yes—
25C2×Dic3⋊Dic3C2212yes—
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30#63658C2211yescharacteristic
31#63658C2212yes—
32#63658C2211yescharacteristic
33#63658C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×#117—31no—
39C2×#872D311yescharacteristic
40C3×C4×C4⋊C4—31no—
41#5212—31no—
42C4×#217—31no—
43#4990—32no—
44#4984—32no—
45#4976—32no—
46Dic3×C4⋊C4—32no—
47#4951—32no—
48#4951—32no—
49#4940—32no—
50#4937—31no—
51#4937—31no—
52#4937—31no—
53#4937—61no—
54C4×C4⋊Dic3—31no—
55C4×C4⋊Dic3D311yescharacteristic, complemented
56C4×Dic3⋊C4—32no—
57#4667—31no—
58#4666—31no—
59#4651—31no—
60#4649—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×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C2×C3×C4×D3—24no—
73C2×C3×C4×D3C2×C414yes—
74C32×C42C2×C414yes—
75C3×(C2×D3)⋊C4C2×C414yes—
76C3×(C2×D3)⋊C4C2×C414yes—
77C3×C4⋊Dic3—24no—
78C3×Dic3⋊C4C2×C414yes—
79C3×Dic3⋊C4C2×C414yes—
80C3×C4×Dic3—42no—
81C3×C4×Dic3C2×C414yes—
82Dic3⋊Dic3—24no—
83Dic3⋊Dic3—24no—
84(C2×D3)⋊Dic3—24no—
85(C2×D3)⋊Dic3—42no—
86Dic32—24no—
87Dic32—42no—
88#2347—91noSylow
89C23×C3×C4—31no—
90C22×C4×D3C2×D311yescharacteristic
91C3×#117—38no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—32no—
95C2×C3×C22⋊C4—31no—
96C2×C3×C22⋊C4—31no—
97C2×C3×C42—21no—
98C2×C3×C42—31no—
99C2×C3×C42—32no—
100C2×C3×C42C2×D311yescharacteristic
101C2×C3×C42C2×D311yescharacteristic
102C2×#217—32no—
103C2×#217—32no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—32no—
106C2×(C2×D3)⋊C4C2×D311yescharacteristic
107C2×(C2×D3)⋊C4C2×D311yescharacteristic
108C2×C4⋊Dic3—32no—
109C2×C4⋊Dic3—32no—
110C2×C4⋊Dic3C2×D312yes—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4C2×D311yescharacteristic
114C2×Dic3⋊C4C2×D311yescharacteristic
115C2×C4×Dic3—32no—
116C2×C4×Dic3—32no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—32no—
119C2×C4×Dic3C2×D312yes—
120C2×C4×Dic3C2×D311yescharacteristic
121#872Dic318yescomplemented
122C3×#95—31no—
123C3×#95—31no—
124C3⋊#95—31no—
125C3⋊#95—31no—
126C3⋊#95—32no—
127C3⋊#95—31no—
128C3⋊#95—31no—
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—22no—
145C22×C3×D3—21no—
146C22×C3×D3—21no—
147C22×C3×D3C22×C412yes—
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—21no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3C22×C412yes—
170C2×C3×Dic3C22×C412yes—
171C2×C3×Dic3C22×C412yes—
172C2×C3×Dic3#4114yes—
173C2×C3×Dic3#4114yes—
174C3×C4×D3—28no—
175C2×#117—31no—
176#389—92no—
177#388—92no—
178#388—92no—
179#383—91no—
180#383—91no—
181#380—91no—
182C4×C4⋊C4—31no—
183C4×C4⋊C4—91no—
184C4×C4⋊C4—92no—
185C4×C22⋊C4—91no—
186C24×C3—31no—
187C23×D3C22×D311yescharacteristic
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—32no—
195C22×C3×C4—34no—
196C22×C3×C4—32no—
197C22×C3×C4—64no—
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—62no—
209C22×Dic3—62no—
210C22×Dic3C22×D312yes—
211C22×Dic3C22×D312yes—
212C22×Dic3C22×D311yescharacteristic
213C22×Dic3C22×D311yescharacteristic
214C22×Dic3C22×D311yescharacteristic
215C2×C4×D3—24no—
216C2×C4×D3C2×Dic314yes—
217C3×C4⋊C4—34no—
218C3×C4⋊C4—34no—
219C3×C4⋊C4—64no—
220C3×C22⋊C4—34no—
221C3×C22⋊C4—34no—
222C3×C42—24no—
223C3×C42—34no—
224C3×C42—122no—
225C3×C42C4×D314yes—
226C3×C42C2×Dic314yes—
227#217—64no—
228#217—122no—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—122no—
231(C2×D3)⋊C4C2×Dic314yes—
232(C2×D3)⋊C4C2×Dic314yes—
233C4⋊Dic3—24no—
234C4⋊Dic3—64no—
235C4⋊Dic3—64no—
236Dic3⋊C4—64no—
237Dic3⋊C4—64no—
238Dic3⋊C4C2×Dic314yes—
239Dic3⋊C4C2×Dic314yes—
240C4×Dic3—42no—
241C4×Dic3—64no—
242C4×Dic3—64no—
243C4×Dic3—122no—
244C4×Dic3—122no—
245C4×Dic3C2×Dic314yes—
246C22×C32C23×C411yescharacteristic
247C22×C32C2×#4112yes—
248C22×C32C2×#4112yes—
249C22×C32H(5,𝔽2)11yescharacteristic
250C22×C322−1+411yescharacteristic
251C2×C3×D3—22no—
252C2×C3×D3—22no—
253C2×C3×D3—22no—
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C32×C4—22no—
257C32×C4—22no—
258C32×C4—22no—
259C3⋊Dic3—42no—
260C3⋊Dic3—42no—
261C3×Dic3—22no—
262C3×Dic3—22no—
263C3×Dic3—24no—
264C3×Dic3—42no—
265C3×Dic3#11714yes—
266C23×C4—31no—
267#117—38no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—32no—
271C2×C4⋊C4—92no—
272C2×C4⋊C4—92no—
273C2×C22⋊C4—31no—
274C2×C22⋊C4—31no—
275C2×C22⋊C4—92no—
276C2×C22⋊C4—92no—
277C2×C42—31no—
278C2×C42—32no—
279C2×C42—92no—
280C2×C42—92no—
281C2×C42D3211yescharacteristic
282#95—31no—
283#95—31no—
284#95—92no—
285#95—92no—
286#95—91no—
287#95—91no—
288#95—92no—
289#95—92no—
290C23×C3—21no—
291C23×C3—32no—
292C23×C3—62no—
293C23×C3—61no—
294C23×C3—61no—
295C23×C3—62no—
296C23×C3C23×D311yescharacteristic
297C23×C3C23×D311yescharacteristic
298C22×D3—22no—
299C22×D3—22no—
300C22×D3—21no—
301C22×D3—21no—
302C22×D3C22×Dic312yes—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—32no—
315C2×C3×C4—34no—
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×C4C2×C4×D312yes—
333C2×C3×C4C2×C4×D312yes—
334C2×C3×C4C2×C4×D312yes—
335C2×C3×C4C22×Dic312yes—
336C2×C3×C4C22×Dic312yes—
337C2×C3×C4C22×Dic312yes—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—62no—
347C2×Dic3—62no—
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—122no—
359C2×Dic3—122no—
360C2×Dic3—122no—
361C2×Dic3—122no—
362C2×Dic3—122no—
363C2×Dic3—122no—
364C2×Dic3#23514yes—
365C2×Dic3#23514yes—
366C2×Dic3C22×Dic312yes—
367C2×Dic3C22×Dic312yes—
368C2×Dic3C22×Dic312yes—
369C4×D3—28no—
370C2×C32C2×#11711yescharacteristic
371C2×C32C4×#4111yescharacteristic
372C2×C32#52011yescharacteristic
373C2×C32#55312yes—
374C2×C32#55612yes—
375C3×D3—42no—
376C24—31no—
377C22×C4—31no—
378C22×C4—32no—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—34no—
382C22×C4—32no—
383C22×C4—64no—
384C22×C4—92no—
385C22×C4—92no—
386C22×C4C2×D3211yescharacteristic
387C22×C4C2×D3211yescharacteristic
388C22×C4C2×D3211yescharacteristic
389C4⋊C4—34no—
390C4⋊C4—34no—
391C4⋊C4—64no—
392C4⋊C4—184no—
393C4⋊C4—184no—
394C22⋊C4—34no—
395C22⋊C4—34no—
396C22⋊C4—184no—
397C22⋊C4—362no—
398C42—34no—
399C42—122no—
400C42—184no—
401C42—362no—
402C42D3×Dic314yes—
403C22×C3—21no—
404C22×C3—22no—
405C22×C3—22no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—62no—
409C22×C3—62no—
410C22×C3—62no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3C22×C4×D311yescharacteristic
414C22×C3C2×#23512yes—
415C22×C3C2×#23512yes—
416C22×C3#100411yescharacteristic
417C22×C3#100711yescharacteristic
418C22×C3D3×#4112yes—
419C22×C3D3×#4112yes—
420C22×C3#100911yescharacteristic
421C22×C3#101011yescharacteristic
422C22×C3C23×Dic311yescharacteristic
423C2×D3—22no—
424C2×D3—22no—
425C2×D3—22no—
426C2×D3—42no—
427C2×D3—42no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—22no—
434C3×C4—34no—
435C3×C4—42no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—62no—
439C3×C4—62no—
440C3×C4—64no—
441C3×C4—122no—
442Dic3—24no—
443Dic3—22no—
444Dic3—22no—
445Dic3—42no—
446Dic3—122no—
447Dic3—122no—
448Dic3—122no—
449Dic3—122no—
450Dic3—242no—
451Dic3—242no—
452Dic3#92614yes—
453C32#234711yescharacteristic, complemented, Sylow
454C23—32no—
455C23—61no—
456C23—62no—
457C23—62no—
458C23—61no—
459C23C22×D3211yescharacteristic
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—21no—
464C2×C4—34no—
465C2×C4—32no—
466C2×C4—34no—
467C2×C4—32no—
468C2×C4—32no—
469C2×C4—68no—
470C2×C4—61no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—182no—
479C2×C4—182no—
480C2×C4—182no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4—182no—
484C2×C4C2×D3×Dic312yes—
485C2×C4C2×D3×Dic312yes—
486C2×C4C2×D3×Dic312yes—
487C2×C3—22no—
488C2×C3—21no—
489C2×C3—22no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—122no—
493C2×C3C4×#23511yescharacteristic
494C2×C3#550411yescharacteristic
495C2×C3D3×#11711yescharacteristic
496C2×C3#553012yes—
497C2×C3#553312yes—
498C2×C3#554012yes—
499C2×C3#556812yes—
500C2×C3C2×#92611yescharacteristic
501C2×C3Dic3×#4111yescharacteristic
502C2×C3#582711yescharacteristic
503D3—42no—
504C22—62no—
505C22—62no—
506C22—62no—
507C22—122no—
508C22—122no—
509C22#6429711yescharacteristic
510C22D3×#23512yes—
511C22D3×#23512yes—
512C22#6430711yescharacteristic
513C22C22×D3×Dic311yescharacteristic
514C4—22no—
515C4—22no—
516C4—22no—
517C4—34no—
518C4—64no—
519C4—62no—
520C4—62no—
521C4—122no—
522C4—362no—
523C4—362no—
524C3—21no—
525C3#7363511yescharacteristic, complemented
526C3#8224011yescharacteristic, complemented
527C2—122no—
528C2#1059387112yes—
529C2#1059392212yes—
530C2D3×#92611yescharacteristic
531C2Dic3×#23511yescharacteristic
532C2#1059498611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2347
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
7. #10591265C2semidirect
8. #10591242C2semidirect
9. Dic3×Dic3⋊C4C2semidirect
11. #10591223C2semidirect
23. C3×#872C4semidirect
55. C4×C4⋊Dic3D3semidirect
121. #872Dic3semidirect
453. C32#2347semidirect
525. C3#73635semidirect
526. C3#82240semidirect

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
#105913072
#105913052
#105912952
#105912652
#105912422
Dic3×Dic3⋊C42
#105912372
#105912232
#822403
#736353