Finite Group Databasebeta

← #11789819

Subgroups — #11789819

Order 1152.

641 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#4988C211yesmaximal, characteristic
2#10591352C211yesmaximal, characteristic, complemented
3C2×#63563C211yesmaximal, characteristic
4C2×#63562C211yesmaximal, characteristic
5C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8#69644—31nomaximal
9#68853—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20#63579—21no—
21#63563—22no—
22#63562C414yescomplemented
23Dic3×C3⋊C8—22no—
24C3×#390—31no—
25C2×#832—31no—
26C2×#832—31no—
27C2×#821—31no—
28C2×C8×Dic3—31no—
29#4988D311yescharacteristic
30#4984—31no—
31C2×#809—31no—
32#4928—31no—
33C2×C4×C3⋊C8—31no—
34C3×#340—31no—
35#4529—31no—
36#4529—31no—
37#4529—61no—
38#4529D311yescharacteristic, complemented
39C23×C3×D3—21no—
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—21no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3D411yescharacteristic
45C22×C3×Dic3D411yescharacteristic
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)C2×C412yes—
59C3×(C2×D3)⋊C4—42no—
60C3×(C2×D3)⋊C4—42no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3C2×C412yes—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8D412yes—
68Dic3⋊Dic3—42no—
69#1934—91noSylow
70C22×C3×D4—31no—
71C22×D12C2×D311yescharacteristic
72C22×C3×C8—31no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4C2×D311yescharacteristic
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C22⋊C4—61no—
78C2×C3×C22⋊C4—61no—
79C2×C3×C42—31no—
80C2×(C2×D3)⋊C4—21no—
81C2×(C2×D3)⋊C4—21no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—61no—
85C2×C4⋊Dic3—61no—
86C2×C4⋊Dic3C2×D311yescharacteristic
87C2×Dic3⋊C4—61no—
88C2×C4×Dic3C2×D311yescharacteristic
89C22×C3⋊C8—31no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—61no—
92C22×C3⋊C8C2×D311yescharacteristic
93#832—34no—
94#832—62no—
95C3⋊#95—61no—
96C3⋊#95—61no—
97#821—62no—
98C8×Dic3—62no—
99#809—34no—
100C4×C3⋊C8—62no—
101C23×C32C2×D411yescharacteristic
102C22×C3×D3—22no—
103C22×C3×D3—41no—
104C22×C3×D3—41no—
105C22×C3×D3—41no—
106C22×C3×D3—41no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3—41no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3D812yes—
129C2×C3×Dic3SD1612yes—
130C3×D12—22no—
131C3×D12—22no—
132C3×D12—41no—
133C3×D12—41no—
134C3⋊(C3⋊C8)—22no—
135C3×C3⋊C8—22no—
136C2×#102—91no—
137C2×#102—91no—
138C2×C4×C8—91no—
139#390—31no—
140#389—91no—
141#340—31no—
142#340—91no—
143C24×C3—61no—
144C23×D3—21no—
145C2×C3×D4—32no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—41no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×Dic3—21no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—121no—
164C22×Dic3#6711yescharacteristic
165C22×Dic3#6711yescharacteristic
166C2×D12—21no—
167C2×D12—21no—
168C2×D12—21no—
169C2×D12—21no—
170C2×D12—21no—
171C2×D12C4×D312yes—
172C2×C3×C8—32no—
173C2×C3×C8—61no—
174C2×C3×C8—61no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—32no—
181C3×C4⋊C4—41no—
182C3×C4⋊C4—61no—
183C3×C22⋊C4—122no—
184C3×C22⋊C4—122no—
185C3×C42—61no—
186C3×C42—61no—
187(C2×D3)⋊C4—42no—
188(C2×D3)⋊C4—42no—
189C4⋊Dic3—21no—
190C4⋊Dic3—62no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—121no—
196C4⋊Dic3—122no—
197C4⋊Dic3C4×D312yes—
198Dic3⋊C4—122no—
199C4×Dic3—21no—
200C4×Dic3—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—32no—
204C2×C3⋊C8—32no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—121no—
211C2×C3⋊C8—121no—
212C2×C3⋊C8D1212yes—
213C22×C32C4×D411yescharacteristic
214C22×C32#12111yescharacteristic
215C22×C32#12411yescharacteristic
216C22×C32C2×D811yescharacteristic
217C22×C32C2×SD1611yescharacteristic
218C22×C32#13511yescharacteristic
219C22×C32#13511yescharacteristic
220C2×C3×D3—42no—
221C2×C3×D3—42no—
222C2×C3×D3—42no—
223C2×C3×D3—81no—
224C2×C3×D3—81no—
225C2×C3×D3—81no—
226C2×C3×D3—81no—
227C32×C4—81no—
228C32×C4#11711yescharacteristic
229C32×C4C4×D411yescharacteristic
230C32×C4#12311yescharacteristic
231C32×C4#12611yescharacteristic
232C3⋊Dic3—81no—
233C3×Dic3—22no—
234C3×Dic3—22no—
235C3×Dic3—42no—
236C22×D4—31no—
237C22×C8—31no—
238C22×C8—91no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—91no—
241C2×C4⋊C4—181no—
242C2×C4⋊C4D3211yescharacteristic
243C2×C22⋊C4—61no—
244C2×C22⋊C4—61no—
245C2×C42—31no—
246#102—94no—
247#102—182no—
248C4×C8—182no—
249#95—181no—
250C23×C3—21no—
251C23×C3—62no—
252C23×C3—121no—
253C23×C3—121no—
254C23×C3—121no—
255C23×C3—121no—
256C23×C3—121no—
257C23×C3—121no—
258C23×C3D3×D411yescharacteristic
259C23×C3C2×#6711yescharacteristic
260C22×D3—22no—
261C22×D3—41no—
262C22×D3—41no—
263C22×D3—41no—
264C22×D3—41no—
265C22×D3—41no—
266C22×D3—41no—
267C3×D4—62no—
268C3×D4—62no—
269C3×D4—121no—
270C3×D4—121no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—32no—
278C2×C3×C4—32no—
279C2×C3×C4—42no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—62no—
291C2×C3×C4—81no—
292C2×C3×C4—81no—
293C2×C3×C4—121no—
294C2×C3×C4—121no—
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×D1211yescharacteristic
298C2×C3×C4#23511yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4#23711yescharacteristic
303C2×C3×C4#23711yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4#23911yescharacteristic
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—22no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—122no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—241no—
322C2×Dic3—241no—
323C2×Dic3#21312yes—
324C2×Dic3#21412yes—
325D12—22no—
326D12—22no—
327D12—41no—
328D12—41no—
329C3×C8—62no—
330C3⋊C8—22no—
331C3⋊C8—62no—
332C3⋊C8—62no—
333C3⋊C8—122no—
334C2×C32#38811yescharacteristic
335C2×C32C4×D811yescharacteristic
336C2×C32C4×SD1611yescharacteristic
337C2×C32#46511yescharacteristic
338C2×C32#46611yescharacteristic
339C2×C32#48611yescharacteristic
340C2×C32#48811yescharacteristic
341C3×D3—82no—
342C24—61no—
343C2×D4—32no—
344C2×D4—61no—
345C2×D4—61no—
346C2×D4—61no—
347C2×D4—61no—
348C2×D4—61no—
349C22×C4—21no—
350C22×C4—31no—
351C22×C4—31no—
352C22×C4—61no—
353C22×C4—181no—
354C22×C4C2×D3211yescharacteristic
355C2×C8—32no—
356C2×C8—61no—
357C2×C8—61no—
358C2×C8—92no—
359C2×C8—181no—
360C2×C8—181no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—32no—
364C4⋊C4—61no—
365C4⋊C4—181no—
366C4⋊C4—181no—
367C4⋊C4—362no—
368C22⋊C4—122no—
369C22⋊C4—122no—
370C42—61no—
371C42—61no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—122no—
380C22×C3—122no—
381C22×C3—122no—
382C22×C3—241no—
383C22×C3—241no—
384C22×C3—241no—
385C22×C3—241no—
386C22×C3#67⋊C411yescharacteristic
387C22×C3#88511yescharacteristic
388C22×C3#89511yescharacteristic
389C22×C3D3×D811yescharacteristic
390C22×C3D3×SD1611yescharacteristic
391C22×C3#91611yescharacteristic
392C22×C3#91911yescharacteristic
393C22×C3C4×#6711yescharacteristic
394C22×C3C2×#21311yescharacteristic
395C22×C3C2×#21411yescharacteristic
396C22×C3#93611yescharacteristic
397C22×C3#93911yescharacteristic
398C22×C3#95011yescharacteristic
399C22×C3#95011yescharacteristic
400C2×D3—42no—
401C2×D3—42no—
402C2×D3—42no—
403C2×D3—81no—
404C2×D3—81no—
405C2×D3—81no—
406C2×D3—81no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—62no—
412C3×C4—62no—
413C3×C4—82no—
414C3×C4—81no—
415C3×C4—81no—
416C3×C4—122no—
417C3×C4C4×D1211yescharacteristic
418C3×C4#87711yescharacteristic
419C3×C4#87911yescharacteristic
420C3×C4#67⋊C411yescharacteristic
421C3×C4#88311yescharacteristic
422C3×C4#88611yescharacteristic
423C3×C4#89211yescharacteristic
424C3×C4#89811yescharacteristic
425Dic3—22no—
426Dic3—22no—
427Dic3—42no—
428Dic3—242no—
429Dic3—241no—
430Dic3—241no—
431C32#193411yescharacteristic, complemented, Sylow
432C23—62no—
433C23—121no—
434C23—121no—
435C23—121no—
436C23—121no—
437C23—121no—
438C23—121no—
439C23D3×#6711yescharacteristic
440D4—62no—
441D4—62no—
442D4—121no—
443D4—121no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—62no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—361no—
457C2×C4—361no—
458C2×C4—361no—
459C2×C4#379511yescharacteristic
460C2×C4#379611yescharacteristic
461C2×C4C4×D3211yescharacteristic
462C2×C4D3×D1211yescharacteristic
463C2×C4#380411yescharacteristic
464C2×C4#380511yescharacteristic
465C8—62no—
466C8—182no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—242no—
475C2×C3#467011yescharacteristic
476C2×C3#475611yescharacteristic
477C2×C3#476011yescharacteristic
478C2×C3#478811yescharacteristic
479C2×C3#480011yescharacteristic
480C2×C3#486411yescharacteristic
481C2×C3#488311yescharacteristic
482C2×C3#494511yescharacteristic
483C2×C3C4×#21311yescharacteristic
484C2×C3C4×#21411yescharacteristic
485C2×C3#503811yescharacteristic
486C2×C3#504111yescharacteristic
487C2×C3#505611yescharacteristic
488C2×C3#507011yescharacteristic
489D3—82no—
490C22—122no—
491C22—122no—
492C22—122no—
493C22—241no—
494C22—241no—
495C22—241no—
496C22—241no—
497C22#6387911yescharacteristic
498C22#6388611yescharacteristic
499C22D3×#21311yescharacteristic
500C22D3×#21411yescharacteristic
501C22#6394711yescharacteristic
502C22#6394911yescharacteristic
503C22#6395911yescharacteristic
504C4—62no—
505C4—62no—
506C4—81no—
507C4—122no—
508C4—721no—
509C4#6385811yescharacteristic
510C4#6387811yescharacteristic
511C4#6388011yescharacteristic
512C4#6389111yescharacteristic
513C3—21no—
514C3#6885311yescharacteristic, complemented
515C3#6964411yescharacteristic, complemented
516C2—242no—
517C2#1059045211yescharacteristic
518C2#1059047511yescharacteristic
519C2#1059057611yescharacteristic
520C2#1059057811yescharacteristic
521C2#1059128411yescharacteristic
522C2#1059148711yescharacteristic
523C2#1059161411yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1934
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10591352C2semidirect
5. C2×Dic3×C3⋊C8C2semidirect
6. #10589395C2semidirect
7. C3×#4529C2semidirect
22. #63562C4semidirect
38. #4529D3semidirect
431. C32#1934semidirect
514. C3#68853semidirect
515. C3#69644semidirect

Maximal subgroups

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

subgroupindex
C3×#49882
#105913522
C2×#635632
C2×#635622
C2×Dic3×C3⋊C82
#105893952
C3×#45292
#696443
#688533