Finite Group Databasebeta

← #11806079

Subgroups — #11806079

Order 1152.

1217 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63902C211yesmaximal, characteristic
2C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#4990C212yesmaximal, complemented
4#10591385C211yesmaximal, characteristic
5#10591385C211yesmaximal, characteristic
6Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
7#10591362C212yesmaximal, complemented
8#10591360C211yesmaximal, characteristic, complemented
9C4×#3724C211yesmaximal, characteristic, complemented
10#10591316C212yesmaximal, complemented
11#10591257C211yesmaximal, characteristic, complemented
12#75476—32nomaximal
13C22×#625C2211yescharacteristic
14C22×D3×Dic3C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C2×#3724C2211yescharacteristic
25C2×#3724C2211yescharacteristic
26C2×#3724C2211yescharacteristic
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30#63902C418yescomplemented
31#63658C2211yescharacteristic
32#63658C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37C2×#67⋊C4—32no—
38C3×#388—32no—
39#4990D312yescomplemented
40Dic3×C4⋊C4—32no—
41Dic3×C4⋊C4—61no—
42#4957—32no—
43#4957—32no—
44#4951—32no—
45#4943—32no—
46Dic3×C22⋊C4—32no—
47C4×(C2×D3)⋊C4—32no—
48C4×Dic3⋊C4—32no—
49#4670—32no—
50#4664—32no—
51#4650—32no—
52#4649—32no—
53C23×C3×D3C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C2×#625—22no—
65C2×#625—22no—
66C2×#625C2×C414yes—
67C2×D3×Dic3—42no—
68C2×D3×Dic3—42no—
69C2×D3×Dic3C2×C418yes—
70C32×C4⋊C4—22no—
71C4⋊(C3⋊Dic3)—22no—
72C4×C3⋊Dic3—22no—
73C4×C3⋊Dic3—22no—
74C4×C3⋊Dic3C2×C414yes—
75C3×(C2×D3)⋊C4—24no—
76C3×(C2×D3)⋊C4—42no—
77C3×(C2×D3)⋊C4C2×C418yes—
78C3×C4×Dic3—42no—
79#3724—22no—
80#3724—22no—
81#3724C2×C414yes—
82(C2×D3)⋊Dic3—24no—
83(C2×D3)⋊Dic3—42no—
84Dic32—42no—
85#2357—91noSylow
86C22×#67—32no—
87C23×Dic3—32no—
88C22×C4×D3—32no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4C2×D312yes—
91C2×C3×C22⋊C4—32no—
92C2×C3×C22⋊C4—32no—
93C2×C3×C22⋊C4—32no—
94C2×C3×C42—32no—
95C2×#217—32no—
96C2×#217—32no—
97C2×(C2×D3)⋊C4—32no—
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4C2×D312yes—
100C2×(C2×D3)⋊C4C2×D312yes—
101C2×(C2×D3)⋊C4C2×D312yes—
102C2×C4⋊Dic3—32no—
103C2×C4⋊Dic3—61no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—32no—
107C2×C4×Dic3—32no—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—32no—
110C2×C4×Dic3—32no—
111C2×C4×Dic3—32no—
112C2×C4×Dic3—61no—
113C2×C4×Dic3—61no—
114C2×C4×Dic3—61no—
115C2×C4×Dic3C2×D312yes—
116#67⋊C4—316no—
117C3×#95—32no—
118C3×#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—61no—
126C3⋊#95—61no—
127C3⋊#95C2×D312yes—
128C3⋊#95C2×D312yes—
129C23×C32C2411yescharacteristic
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3C22×C414yes—
137C2×C32×C4—21no—
138C2×C32×C4—21no—
139C2×C32×C4—21no—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4C22×C412yes—
145C2×C32×C4#4112yes—
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3C22×C412yes—
154C2×C3⋊Dic3C22×C412yes—
155C2×C3⋊Dic3#4112yes—
156C2×C3⋊Dic3#4112yes—
157C2×C3⋊Dic3#4112yes—
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—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C22×C414yes—
167#625—28no—
168D3×Dic3—48no—
169C2×C4×D4—91no—
170#390—91no—
171#390—91no—
172#388—32no—
173#388—92no—
174#382—91no—
175#381—92no—
176C4×C4⋊C4—91no—
177C4×C4⋊C4—91no—
178C4×C4⋊C4—91no—
179C4×C22⋊C4—92no—
180C24×C3—32no—
181C23×D3C22×D312yes—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4—32no—
188C22×C3×C4C22×D312yes—
189C22×C3×C4C22×D312yes—
190C22×C3×C4C22×D312yes—
191C2×#67—38no—
192C2×#67—64no—
193C2×#67—64no—
194C22×Dic3—32no—
195C22×Dic3—32no—
196C22×Dic3—32no—
197C22×Dic3—38no—
198C22×Dic3—32no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C22×Dic3—122no—
204C22×Dic3—122no—
205C22×Dic3C22×D312yes—
206C22×Dic3C22×D312yes—
207C22×Dic3C22×D312yes—
208C2×C4×D3—38no—
209C2×C4×D3—122no—
210C2×C4×D3—122no—
211C3×C4⋊C4—24no—
212C3×C4⋊C4—24no—
213C3×C22⋊C4—38no—
214C3×C22⋊C4—64no—
215C3×C22⋊C4—122no—
216C3×C42—122no—
217#217—64no—
218#217—122no—
219(C2×D3)⋊C4—24no—
220(C2×D3)⋊C4—42no—
221(C2×D3)⋊C4—64no—
222(C2×D3)⋊C4—122no—
223(C2×D3)⋊C4C4×D318yes—
224C4⋊Dic3—64no—
225C4⋊Dic3—64no—
226Dic3⋊C4—38no—
227Dic3⋊C4—64no—
228Dic3⋊C4—64no—
229C4×Dic3—38no—
230C4×Dic3—42no—
231C4×Dic3—64no—
232C4×Dic3—64no—
233C4×Dic3—64no—
234C4×Dic3—122no—
235C4×Dic3—122no—
236C4×Dic3—122no—
237C4×Dic3—122no—
238C22×C32C23×C411yescharacteristic
239C22×C32C2×#4111yescharacteristic
240C22×C32C2×#4111yescharacteristic
241C22×C32C2×#4111yescharacteristic
242C22×C32C2×#4111yescharacteristic
243C22×C32H(5,𝔽2)11yescharacteristic
244C22×C32H(5,𝔽2)11yescharacteristic
245C2×C3×D3—24no—
246C2×C3×D3—24no—
247C2×C3×D3—24no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C32×C4—22no—
253C32×C4—22no—
254C32×C4—41no—
255C3⋊Dic3—22no—
256C3⋊Dic3—22no—
257C3⋊Dic3—41no—
258C3⋊Dic3#11714yes—
259C3×Dic3—24no—
260C3×Dic3—42no—
261C3×Dic3—42no—
262C22×D4—91no—
263C23×C4—92no—
264C4×D4—98no—
265C2×C4⋊C4—91no—
266C2×C4⋊C4—91no—
267C2×C4⋊C4—91no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4D3211yescharacteristic
270C2×C22⋊C4—32no—
271C2×C22⋊C4—32no—
272C2×C22⋊C4—32no—
273C2×C22⋊C4—92no—
274C2×C22⋊C4—92no—
275C2×C42—32no—
276C2×C42—91no—
277C2×C42—91no—
278C2×C42—91no—
279C2×C42—92no—
280#95—32no—
281#95—32no—
282#95—92no—
283#95—92no—
284#95—91no—
285#95—91no—
286C23×C3—21no—
287C23×C3—34no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3—62no—
291C23×C3—62no—
292C23×C3—62no—
293C23×C3—62no—
294C23×C3C23×D312yes—
295C22×D3—22no—
296C22×D3—22no—
297C22×D3—22no—
298C22×D3—22no—
299C22×D3—22no—
300C22×D3—22no—
301C22×D3C2×C4×D314yes—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—34no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4C2×C4×D314yes—
328C2×C3×C4#23714yes—
329#67—616no—
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—34no—
339C2×Dic3—34no—
340C2×Dic3—34no—
341C2×Dic3—34no—
342C2×Dic3—34no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345C2×Dic3—62no—
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—121no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3—121no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—128no—
363C2×Dic3C2×C4×D314yes—
364C4×D3—128no—
365C2×C32C2×#11711yescharacteristic
366C2×C32C4×#4111yescharacteristic
367C2×C32#51811yescharacteristic
368C2×C32#55311yescharacteristic
369C2×C32#55311yescharacteristic
370C2×C32#55911yescharacteristic
371C2×C32#55911yescharacteristic
372C3×D3—44no—
373C24—32no—
374C2×D4—94no—
375C2×D4—182no—
376C2×D4—182no—
377C22×C4—32no—
378C22×C4—32no—
379C22×C4—32no—
380C22×C4—98no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—362no—
386C22×C4—362no—
387C22×C4C2×D3211yescharacteristic
388C22×C4C2×D3211yescharacteristic
389C22×C4C2×D3211yescharacteristic
390C4⋊C4—22no—
391C4⋊C4—94no—
392C4⋊C4—182no—
393C4⋊C4—182no—
394C4⋊C4—182no—
395C22⋊C4—38no—
396C22⋊C4—64no—
397C22⋊C4—122no—
398C22⋊C4—184no—
399C22⋊C4—362no—
400C42—94no—
401C42—122no—
402C42—182no—
403C42—182no—
404C42—362no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—64no—
413C22×C3—64no—
414C22×C3—64no—
415C22×C3—122no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3C22×C4×D312yes—
420C22×C3C2×#23712yes—
421C22×C3#100412yes—
422C22×C3D3×#4112yes—
423C22×C3D3×#4112yes—
424C22×C3D3×#4112yes—
425C22×C3#100912yes—
426C2×D3—24no—
427C2×D3—24no—
428C2×D3—24no—
429C2×D3—42no—
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—42no—
433C3×C4—24no—
434C3×C4—24no—
435C3×C4—24no—
436C3×C4—42no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—64no—
440C3×C4—122no—
441C3×C4—122no—
442Dic3—24no—
443Dic3—38no—
444Dic3—42no—
445Dic3—42no—
446Dic3—64no—
447Dic3—64no—
448Dic3—64no—
449Dic3—122no—
450Dic3—122no—
451Dic3—122no—
452Dic3—122no—
453C32#235711yescharacteristic, complemented, Sylow
454C23—34no—
455C23—62no—
456C23—62no—
457C23—62no—
458C23—62no—
459C23—62no—
460C23—62no—
461C23C22×D3211yescharacteristic
462D4—188no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—34no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—92no—
480C2×C4—92no—
481C2×C4—92no—
482C2×C4—92no—
483C2×C4—92no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—368no—
492C2×C4C4×D3212yes—
493C2×C4#380512yes—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—124no—
502C2×C3D3×#11712yes—
503C2×C3C4×#23712yes—
504C2×C3#554512yes—
505C2×C3#560112yes—
506C2×C3#566412yes—
507C2×C3#568112yes—
508C2×C3#570912yes—
509D3—44no—
510C22—64no—
511C22—64no—
512C22—64no—
513C22—122no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22C2×C4×D3211yescharacteristic
518C22#6430611yescharacteristic
519C22#6431211yescharacteristic
520C22#6431311yescharacteristic
521C22#6431911yescharacteristic
522C22#6432011yescharacteristic
523C22C2×#380511yescharacteristic
524C4—22no—
525C4—22no—
526C4—41no—
527C4—64no—
528C4—94no—
529C4—122no—
530C4—122no—
531C4—182no—
532C4—182no—
533C4—361no—
534C3—21no—
535C3#7547612yescomplemented
536C2—124no—
537C2#1059447511yescharacteristic
538C2#1059457011yescharacteristic
539C2#1059460211yescharacteristic
540C2#1059460611yescharacteristic
541C2C4×#380511yescharacteristic
542C2#1059520611yescharacteristic
543C2#1059539211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#625C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2357
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×C3⋊Dic3C2semidirect
3. C3×#4990C2semidirect
6. Dic3×(C2×D3)⋊C4C2semidirect
7. #10591362C2semidirect
8. #10591360C2semidirect
9. C4×#3724C2semidirect
10. #10591316C2semidirect
11. #10591257C2semidirect
30. #63902C4semidirect
39. #4990D3semidirect
453. C32#2357semidirect
535. C3#75476semidirect

Maximal subgroups

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

subgroupindex
C2×#639022
C4⋊C4×C3⋊Dic32
C3×#49902
#105913852
Dic3×(C2×D3)⋊C42
#105913622
#105913602
C4×#37242
#105913162
#105912572
#754763