Finite Group Databasebeta

← #11785725

Subgroups — #11785725

Order 1152.

681 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic3C211yesmaximal, characteristic
2C3×#5126C211yesmaximal, characteristic
3#10591069C211yesmaximal, characteristic
4#10589420C211yesmaximal, characteristic, complemented
5C3×#4554C211yesmaximal, characteristic, complemented
6#10589168C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#69973—31nomaximal
9#68990—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×D3×Dic3C412yes—
12C2×C32×M16C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×Dic3⋊Dic3C412yes—
19D3×C4⋊Dic3—21no—
20D3×C4⋊Dic3—21no—
21D3×C4⋊Dic3—21no—
22D3×C4⋊Dic3—21no—
23C3×(C2×D3)⋊C8—21no—
24C3×(C2×D3)⋊C8—21no—
25(C2×D3)⋊(C3⋊C8)—21no—
26(C2×D3)⋊(C3⋊C8)—21no—
27C22×C4⋊Dic3—31no—
28C2×D3×C4⋊C4—31no—
29C3×#407—31no—
30#5207—31no—
31#5126—31no—
32#5126D311yescharacteristic
33C3×#343—31no—
34#4554—31no—
35#4554—31no—
36#4554—31no—
37#4554—31no—
38#4554—31no—
39#4554—61no—
40#4554D311yescharacteristic, complemented
41#4530—31no—
42C23×C3×D3C2×C411yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3C2×C412yes—
45C22×C3×Dic3C2×C411yescharacteristic
46C22×C3×Dic3C2×C412yes—
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3D411yescharacteristic
52C2×C3×C4×D3D411yescharacteristic
53C2×C3×C4×D3D411yescharacteristic
54C2×C3×C4×D3D411yescharacteristic
55C2×D3×Dic3—22no—
56C2×D3×Dic3—22no—
57C2×D3×Dic3—44no—
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63#3748—21no—
64#3748—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74Dic3⋊Dic3—22no—
75Dic3⋊Dic3—22no—
76#1821—91noSylow
77C23×C3×C4—31no—
78C23×Dic3—32no—
79C22×C4×D3—32no—
80C22×C4×D3C2×D311yescharacteristic
81C2×C3×M16—21no—
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C2×C3×M16C2×D311yescharacteristic
85C2×C3×M16C2×D311yescharacteristic
86C2×C3×C4⋊C4—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—32no—
90C2×C4⋊Dic3—61no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3—61no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3—61no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×Dic3⋊C4—32no—
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—61no—
100C2×#208C2×D311yescharacteristic
101C2×#208C2×D311yescharacteristic
102D3×C4⋊C4—61no—
103D3×C4⋊C4—61no—
104D3×C4⋊C4—61no—
105D3×C4⋊C4—61no—
106C3×C22⋊C8—61no—
107C3×C22⋊C8—61no—
108#830—61no—
109#830—61no—
110(C2×D3)⋊C8—21no—
111(C2×D3)⋊C8—21no—
112(C2×D3)⋊C8—61no—
113(C2×D3)⋊C8—61no—
114C23×C32C22×C411yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3—21no—
117C22×C3×D3—22no—
118C22×C3×D3—22no—
119C22×C3×D3C22⋊C411yescharacteristic
120C22×C3×D3C22⋊C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—42no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3C22⋊C411yescharacteristic
134C2×C3×Dic3C22⋊C411yescharacteristic
135C3×C4×D3—21no—
136C3×C4×D3—21no—
137C3×C4×D3—21no—
138C3×C4×D3—21no—
139C3×C4×D3—21no—
140C3×C4×D3—21no—
141C3×C4×D3—21no—
142C3×C4×D3—21no—
143D3×Dic3—44no—
144D3×Dic3—44no—
145C32×C8—41no—
146C3⋊(C3⋊C8)—41no—
147C3×C3⋊C8—41no—
148C3×C3⋊C8—41no—
149C22×C4⋊C4—91no—
150#407—31no—
151#407—91no—
152#343—31no—
153#343—91no—
154#343—91no—
155#343—91no—
156C24×C3—31no—
157C23×D3C4×D311yescharacteristic
158C22×C3×C4—21no—
159C22×C3×C4—31no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—32no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—32no—
172C22×Dic3—32no—
173C22×Dic3—62no—
174C22×Dic3—62no—
175C22×Dic3—62no—
176C22×Dic3—124no—
177C22×Dic3C4×D311yescharacteristic
178C22×Dic3C4×D312yes—
179C2×C4×D3—21no—
180C2×C4×D3—21no—
181C2×C4×D3—21no—
182C2×C4×D3—21no—
183C2×C4×D3—62no—
184C2×C4×D3—62no—
185C2×C4×D3—124no—
186C2×C4×D3D1211yescharacteristic
187C2×C4×D3D1211yescharacteristic
188C2×C4×D3#6711yescharacteristic
189C2×C4×D3#6711yescharacteristic
190C3×M16—22no—
191C3×M16—21no—
192C3×M16—21no—
193C3×M16—21no—
194C3×M16—21no—
195C3×M16—41no—
196C3×M16—61no—
197C3×M16—61no—
198C3×M16—61no—
199C3×M16—61no—
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C2×C3×C8—41no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C4⋊Dic3—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—62no—
210C4⋊Dic3—62no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—121no—
216C4⋊Dic3—121no—
217Dic3⋊C4—62no—
218Dic3⋊C4—62no—
219#208—21no—
220#208—21no—
221#208—21no—
222#208—21no—
223#208—62no—
224#208—61no—
225#208—61no—
226#208—61no—
227#208—61no—
228#208—121no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—121no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32C2×C22⋊C411yescharacteristic
237C22×C32#11711yescharacteristic
238C22×C32#11711yescharacteristic
239C2×C3×D3—24no—
240C2×C3×D3—24no—
241C2×C3×D3—21no—
242C2×C3×D3—21no—
243C2×C3×D3—21no—
244C2×C3×D3—21no—
245C2×C3×D3#10012yes—
246C2×C3×D3#10112yes—
247C32×C4#12311yescharacteristic
248C32×C4#12311yescharacteristic
249C32×C4#12311yescharacteristic
250C32×C4#12311yescharacteristic
251C3⋊Dic3—42no—
252C3×Dic3—21no—
253C3×Dic3—21no—
254C3×Dic3—42no—
255C23×C4—31no—
256C23×C4—92no—
257C2×M16—31no—
258C2×M16—31no—
259C2×M16—91no—
260C2×M16D3211yescharacteristic
261C2×C4⋊C4—31no—
262C2×C4⋊C4—92no—
263C2×C4⋊C4—91no—
264C2×C4⋊C4—181no—
265C2×C4⋊C4—181no—
266C2×C4⋊C4—181no—
267C2×C4⋊C4—181no—
268C22⋊C8—61no—
269C22⋊C8—61no—
270C22⋊C8—181no—
271C22⋊C8—181no—
272C23×C3—21no—
273C23×C3—31no—
274C23×C3—31no—
275C23×C3—62no—
276C23×C3—62no—
277C23×C3—61no—
278C23×C3—61no—
279C23×C3C2×C4×D311yescharacteristic
280C23×C3C2×C4×D311yescharacteristic
281C22×D3—21no—
282C22×D3—21no—
283C22×D3—22no—
284C22×D3—22no—
285C22×D3(C2×D3)⋊C411yescharacteristic
286C22×D3(C2×D3)⋊C411yescharacteristic
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—31no—
294C2×C3×C4—31no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—62no—
306C2×C3×C4—122no—
307C2×C3×C4C2×D1211yescharacteristic
308C2×C3×C4#23511yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4#23711yescharacteristic
313C2×C3×C4#23711yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4#23711yescharacteristic
316C2×C3×C4#23711yescharacteristic
317C2×C3×C4#23911yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319C2×Dic3—21no—
320C2×Dic3—21no—
321C2×Dic3—22no—
322C2×Dic3—42no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—122no—
326C2×Dic3—124no—
327C2×Dic3—124no—
328C2×Dic3—122no—
329C2×Dic3—122no—
330C2×Dic3—242no—
331C2×Dic3(C2×D3)⋊C411yescharacteristic
332C2×Dic3(C2×D3)⋊C411yescharacteristic
333C4×D3—21no—
334C4×D3—21no—
335C4×D3—21no—
336C4×D3—21no—
337C4×D3—21no—
338C4×D3—21no—
339C4×D3—21no—
340C4×D3—21no—
341C4×D3—124no—
342C4×D3—124no—
343C3×C8—42no—
344C3×C8—41no—
345C3×C8—41no—
346C3×C8—121no—
347C3×C8—121no—
348C3⋊C8—41no—
349C3⋊C8—41no—
350C3⋊C8—122no—
351C3⋊C8—121no—
352C3⋊C8—121no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32#38111yescharacteristic
356C2×C32C2×#10011yescharacteristic
357C2×C32C2×#10111yescharacteristic
358C3×D3—22no—
359C3×D3—22no—
360C24—31no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—32no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—92no—
372C22×C4—182no—
373C22×C4—182no—
374C22×C4—364no—
375C22×C4C2×D3211yescharacteristic
376M16—21no—
377M16—21no—
378M16—61no—
379M16—61no—
380M16—61no—
381M16—61no—
382M16—181no—
383M16—181no—
384C2×C8—21no—
385C2×C8—61no—
386C2×C8—61no—
387C2×C8—181no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—182no—
391C4⋊C4—182no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—32no—
402C22×C3—32no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—64no—
406C22×C3—64no—
407C22×C3—61no—
408C22×C3—61no—
409C22×C3—61no—
410C22×C3—61no—
411C22×C3#87211yescharacteristic
412C22×C3#87711yescharacteristic
413C22×C3#87711yescharacteristic
414C22×C3D3×C22⋊C411yescharacteristic
415C22×C3#89211yescharacteristic
416C22×C3C2×(C2×D3)⋊C411yescharacteristic
417C2×D3—24no—
418C2×D3—24no—
419C2×D3—21no—
420C2×D3—21no—
421C2×D3—21no—
422C2×D3—21no—
423C2×D3#82312yes—
424C2×D3#82412yes—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—61no—
430C3×C4—61no—
431C3×C4—122no—
432C3×C4#88311yescharacteristic
433C3×C4#88311yescharacteristic
434C3×C4#88611yescharacteristic
435C3×C4#88611yescharacteristic
436C3×C4#89411yescharacteristic
437C3×C4#89411yescharacteristic
438C3×C4#93511yescharacteristic
439C3×C4#93511yescharacteristic
440Dic3—21no—
441Dic3—21no—
442Dic3—42no—
443Dic3—122no—
444Dic3—122no—
445Dic3—242no—
446C32#182111yescharacteristic, complemented, Sylow
447C23—31no—
448C23—31no—
449C23—62no—
450C23—62no—
451C23—61no—
452C23—61no—
453C23C4×D3211yescharacteristic
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—62no—
467C2×C4—122no—
468C2×C4—182no—
469C2×C4—364no—
470C2×C4—364no—
471C2×C4—362no—
472C2×C4#379511yescharacteristic
473C2×C4#379611yescharacteristic
474C2×C4D3×D1211yescharacteristic
475C2×C4#380411yescharacteristic
476C2×C4#380511yescharacteristic
477C2×C4D3×#6711yescharacteristic
478C8—41no—
479C8—121no—
480C8—121no—
481C8—361no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—41no—
490C2×C3—41no—
491C2×C3—62no—
492C2×C3—62no—
493C2×C3#466411yescharacteristic
494C2×C3D3×#10011yescharacteristic
495C2×C3D3×#10111yescharacteristic
496C2×C3#494311yescharacteristic
497C2×C3C2×#82311yescharacteristic
498C2×C3C2×#82411yescharacteristic
499D3—22no—
500D3—22no—
501C22—21no—
502C22—21no—
503C22—32no—
504C22—32no—
505C22—64no—
506C22—64no—
507C22—61no—
508C22—61no—
509C22—61no—
510C22—61no—
511C22#6387711yescharacteristic
512C22#6387811yescharacteristic
513C22D3×(C2×D3)⋊C411yescharacteristic
514C4—61no—
515C4—61no—
516C4—122no—
517C4—362no—
518C4#6388411yescharacteristic
519C4#6389011yescharacteristic
520C4#6389111yescharacteristic
521C4#6396911yescharacteristic
522C3—21no—
523C3#6899011yescharacteristic, complemented
524C3#6997311yescharacteristic, complemented
525C2—21no—
526C2—21no—
527C2—62no—
528C2—62no—
529C2D3×#82311yescharacteristic
530C2D3×#82411yescharacteristic
531C2#1059136211yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1821
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10589420C2semidirect
5. C3×#4554C2semidirect
6. #10589168C2semidirect
7. #10589167C2semidirect
40. #4554D3semidirect
446. C32#1821semidirect
523. C3#68990semidirect
524. C3#69973semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic32
C3×#51262
#105910692
#105894202
C3×#45542
#105891682
#105891672
#699733
#689903