Finite Group Databasebeta

← #11790765

Subgroups — #11790765

Order 1152.

925 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C2×#63659C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4#10591224C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#71765—31nomaximal
9#70160—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67—22no—
12C22×C3×D12C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×#940—22no—
16C3×#940C414yescomplemented
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20#63659—22no—
21C3×#832—22no—
22#63579—22no—
23#63563—22no—
24#63562—22no—
25#63554—22no—
26C2×C3×#127—31no—
27C2×#940D311yescharacteristic
28C2×C3×#102—31no—
29C2×#832—31no—
30C2×#832—31no—
31C2×#832—31no—
32C2×#832—31no—
33C2×#832—61no—
34C2×#832D311yescharacteristic, complemented
35C2×#821—31no—
36C2×#815—31no—
37#4977—31no—
38C2×#809—31no—
39#4936—31no—
40C2×#803—31no—
41C24×C32—21no—
42C23×C3×D3—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4C2×C412yes—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C2×C3×#67—28no—
52C2×C3×#67—44no—
53C2×C3×#67—44no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D412yes—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)D412yescomplemented
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3C2×C412yes—
70C3×C4×Dic3D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8D412yescomplemented
74#1961—91noSylow
75C22×C3×D4—21no—
76C22×C3×D4—31no—
77C22×C3×D4—62no—
78C22×C3×D4C2×D311yescharacteristic
79C22×C3×D4C2×D311yescharacteristic
80C22×#67—22no—
81C22×D12C2×D311yescharacteristic
82C22×C3×C8—31no—
83C3×#127—34no—
84C3×#127—62no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C42—31no—
87#940—22no—
88#940Dic314yescomplemented
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×C4×Dic3C2×D311yescharacteristic
94C22×C3⋊C8—31no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—61no—
97C22×C3⋊C8C2×D311yescharacteristic
98C3×#102—62no—
99#832—22no—
100#832—62no—
101#832—62no—
102#832—62no—
103#832—64no—
104#832—62no—
105C3⋊#95—62no—
106C3⋊#95—62no—
107#821—62no—
108#815—62no—
109#809—62no—
110#803—62no—
111C23×C32—22no—
112C23×C32—41no—
113C23×C32—41no—
114C23×C32—42no—
115C23×C32—42no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—42no—
121C22×C3×D3—42no—
122C32×D4—22no—
123C32×D4—22no—
124C32×D4—41no—
125C32×D4—41no—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—42no—
134C3×#67—416no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—42no—
139C2×C3×Dic3C22⋊C414yes—
140C3×D12—22no—
141C3×D12—22no—
142C3×D12—41no—
143C3×D12—41no—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—22no—
146C2×#127—31no—
147C2×#102—31no—
148C2×#102—91no—
149C2×#102—91no—
150C2×#102—91no—
151C2×#97—91no—
152#382—91no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—41no—
156C24×C3—61no—
157C23×D3—21no—
158C2×C3×D4—22no—
159C2×C3×D4—22no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—22no—
171C2×C3×D4—32no—
172C2×C3×D4—41no—
173C2×C3×D4—41no—
174C2×C3×D4—41no—
175C2×C3×D4—68no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—124no—
182C2×C3×D4—124no—
183C2×C3×D4C4×D312yes—
184C2×C3×D4C2×Dic312yes—
185C22×C3×C4—21no—
186C22×C3×C4—32no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—28no—
191C2×#67—44no—
192C2×#67—44no—
193C22×Dic3—21no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—121no—
197C22×Dic3#6712yes—
198C2×D12—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12C2×Dic312yes—
204C2×C3×C8—32no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C3×C4⋊C4—61no—
208C3×C4⋊C4—61no—
209C3×C42—32no—
210C3×C42—32no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4⋊Dic3—62no—
214C4⋊Dic3—61no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—121no—
219C4×Dic3C2×Dic312yes—
220C4×Dic3#6712yes—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—32no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—121no—
231C2×C3⋊C8—121no—
232C2×C3⋊C8#6712yescomplemented
233C22×C32—42no—
234C22×C32—44no—
235C22×C32—82no—
236C22×C32—81no—
237C22×C32—81no—
238C22×C32C2×C22⋊C411yescharacteristic
239C22×C32#12411yescharacteristic
240C22×C32#12711yescharacteristic
241C22×C32AGL(1,ℤ/8)12yes—
242C22×C32AGL(1,ℤ/8)12yes—
243C2×C3×D3—42no—
244C2×C3×D3—44no—
245C2×C3×D3—82no—
246C2×C3×D3—81no—
247C2×C3×D3—81no—
248C32×C4C4×D411yescharacteristic
249C32×C4C4×D411yescharacteristic
250C32×C4#12111yescharacteristic
251C32×C4#12111yescharacteristic
252C3⋊Dic3—81no—
253C3×Dic3—24no—
254C3×Dic3—81no—
255C22×D4—31no—
256C22×D4—62no—
257C22×D4D3211yescharacteristic
258C22×C8—31no—
259C22×C8—91no—
260#127—34no—
261#127—62no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4—91no—
264C2×C42—31no—
265#102—62no—
266#102—182no—
267#102—182no—
268#102—182no—
269#97—182no—
270#95—182no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—21no—
274C23×C3—42no—
275C23×C3—42no—
276C23×C3—42no—
277C23×C3—41no—
278C23×C3—42no—
279C23×C3—42no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—62no—
286C23×C3—82no—
287C23×C3—82no—
288C23×C3—121no—
289C23×C3—122no—
290C23×C3—122no—
291C23×C3—121no—
292C23×C3D3×D411yescharacteristic
293C23×C3C2×#6711yescharacteristic
294C22×D3—22no—
295C22×D3—42no—
296C22×D3—42no—
297C22×D3—41no—
298C22×D3—41no—
299C3×D4—24no—
300C3×D4—22no—
301C3×D4—22no—
302C3×D4—22no—
303C3×D4—22no—
304C3×D4—42no—
305C3×D4—42no—
306C3×D4—42no—
307C3×D4—41no—
308C3×D4—41no—
309C3×D4—41no—
310C3×D4—41no—
311C3×D4—62no—
312C3×D4—62no—
313C3×D4—1216no—
314C3×D4—121no—
315C3×D4—121no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—34no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—122no—
326C2×C3×C4—121no—
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4#23511yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4#23711yescharacteristic
334C2×C3×C4#23711yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4C22×Dic311yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339#67—416no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—42no—
343C2×Dic3—41no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—122no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—242no—
350C2×Dic3#21714yes—
351D12—22no—
352D12—22no—
353D12—41no—
354D12—41no—
355C3×C8—62no—
356C3⋊C8—22no—
357C3⋊C8—62no—
358C3⋊C8—62no—
359C3⋊C8—122no—
360C2×C32—82no—
361C2×C32#39011yescharacteristic
362C2×C32#41812yes—
363C2×C32#49012yes—
364C2×C32#49611yescharacteristic
365C2×C32#49611yescharacteristic
366C3×D3—82no—
367C24—21no—
368C24—61no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—32no—
375C2×D4—68no—
376C2×D4—61no—
377C2×D4—61no—
378C2×D4—61no—
379C2×D4—61no—
380C2×D4—61no—
381C2×D4—124no—
382C2×D4—124no—
383C2×D4D3×Dic312yes—
384C22×C4—32no—
385C22×C4—61no—
386C22×C4—181no—
387C22×C4C2×D3211yescharacteristic
388C2×C8—32no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—92no—
392C2×C8—181no—
393C2×C8—181no—
394C4⋊C4—61no—
395C4⋊C4—61no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C42—32no—
399C42—32no—
400C22×C3—22no—
401C22×C3—22no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—44no—
406C22×C3—42no—
407C22×C3—44no—
408C22×C3—42no—
409C22×C3—44no—
410C22×C3—84no—
411C22×C3—82no—
412C22×C3—82no—
413C22×C3—84no—
414C22×C3—81no—
415C22×C3—81no—
416C22×C3—82no—
417C22×C3—82no—
418C22×C3—81no—
419C22×C3—81no—
420C22×C3—122no—
421C22×C3—124no—
422C22×C3—241no—
423C22×C3—241no—
424C22×C3—242no—
425C22×C3D3×C22⋊C411yescharacteristic
426C22×C3#88511yescharacteristic
427C22×C3#91112yes—
428C22×C3#91412yes—
429C22×C3#93212yes—
430C22×C3#93212yes—
431C22×C3#93611yescharacteristic
432C22×C3#94011yescharacteristic
433C22×C3#94011yescharacteristic
434C22×C3C2×#21711yescharacteristic
435C2×D3—44no—
436C2×D3—42no—
437C2×D3—82no—
438C2×D3—81no—
439C2×D3—81no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—64no—
445C3×C4—241no—
446C3×C4#67⋊C411yescharacteristic
447C3×C4#88411yescharacteristic
448C3×C4C4×#6711yescharacteristic
449C3×C4D4×Dic311yescharacteristic
450C3×C4D4×Dic311yescharacteristic
451C3×C4#93811yescharacteristic
452C3×C4#93811yescharacteristic
453C3×C4#93911yescharacteristic
454Dic3—24no—
455Dic3—81no—
456Dic3—242no—
457Dic3—241no—
458Dic3—241no—
459C32#196111yescharacteristic, complemented, Sylow
460C23—22no—
461C23—42no—
462C23—42no—
463C23—41no—
464C23—41no—
465C23—62no—
466C23—122no—
467C23—122no—
468C23—121no—
469C23—121no—
470C23D3×#6711yescharacteristic
471D4—22no—
472D4—22no—
473D4—41no—
474D4—41no—
475D4—62no—
476D4—62no—
477D4—1216no—
478D4—121no—
479D4—121no—
480C2×C4—34no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—122no—
484C2×C4—121no—
485C2×C4—362no—
486C2×C4—361no—
487C2×C4C2×D3×Dic311yescharacteristic
488C2×C4#380411yescharacteristic
489C2×C4#380511yescharacteristic
490C2×C4D3×#6711yescharacteristic
491C2×C4D3×#6711yescharacteristic
492C2×C4#381111yescharacteristic
493C8—62no—
494C8—182no—
495C2×C3—22no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—22no—
500C2×C3—84no—
501C2×C3—82no—
502C2×C3—82no—
503C2×C3—242no—
504C2×C3#476412yes—
505C2×C3#477012yes—
506C2×C3#495711yescharacteristic
507C2×C3#507112yes—
508C2×C3#507411yescharacteristic
509C2×C3#507411yescharacteristic
510C2×C3#515411yescharacteristic
511C2×C3#517611yescharacteristic
512C2×C3#521512yes—
513C2×C3#522111yescharacteristic
514D3—82no—
515C22—44no—
516C22—42no—
517C22—81no—
518C22—81no—
519C22—82no—
520C22—124no—
521C22—122no—
522C22—241no—
523C22—241no—
524C22—242no—
525C22#6393212yes—
526C22#6393412yes—
527C22#6395911yescharacteristic
528C22D3×#21711yescharacteristic
529C22#6397911yescharacteristic
530C4—64no—
531C4—241no—
532C4—721no—
533C4#6395811yescharacteristic
534C4#6397011yescharacteristic
535C4Dic3×#6711yescharacteristic
536C4#67⋊Dic311yescharacteristic
537C3—21no—
538C3#7016011yescharacteristic, complemented
539C3#7176511yescharacteristic, complemented
540C2—82no—
541C2—242no—
542C2#1059142112yes—
543C2#1059146911yescharacteristic
544C2#1059147211yescharacteristic
545C2#1059147712yes—
546C2#1059170711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#940C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1961
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63659C2semidirect
3. C2×C3×#832C2semidirect
4. #10591224C2semidirect
5. C2×#63563C2semidirect
6. C2×#63562C2semidirect
7. C2×#63554C2semidirect
16. C3×#940C4semidirect
34. C2×#832D3semidirect
66. C2×C3⋊(C3⋊C8)D4semidirect
73. C2×C3×C3⋊C8D4semidirect
88. #940Dic3semidirect
232. C2×C3⋊C8#67semidirect
459. C32#1961semidirect
538. C3#70160semidirect
539. C3#71765semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×#636592
C2×C3×#8322
#105912242
C2×#635632
C2×#635622
C2×#635542
#717653
#701603