Finite Group Databasebeta

← #11794067

Subgroups — #11794067

Order 1152.

705 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
3#10591318C211yesmaximal, characteristic
4#10591220C211yesmaximal, characteristic, complemented
5C2×#63566C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7#10589417C211yesmaximal, characteristic, complemented
8#72051—31nomaximal
9#70482—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×C3×#204—22no—
18C2×C3×#204—22no—
19C2×C3×#204—22no—
20C2×(C2×D3)⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22C3×Dic3⋊C8—22no—
23#63579—21no—
24#63579—21no—
25#63566—22no—
26#63563—22no—
27C22×C3×SD16—31no—
28C22×#204D311yescharacteristic
29C2×C3×C4⋊C8—31no—
30#5229—31no—
31C2×#835—31no—
32#5221—31no—
33C2×#832—31no—
34C2×#821—31no—
35C2×#816—31no—
36C2×Dic3⋊C8D311yescharacteristic, complemented
37#4939—31no—
38#4929—31no—
39#4551—31no—
40#4551—31no—
41#4551—61no—
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D411yescharacteristic
48C22×C3×Dic3D411yescharacteristic
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12D412yes—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6D412yes—
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8D412yes—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C3×#204—28no—
74(C2×D3)⋊Dic3—42no—
75(C2×D3)⋊Dic3—42no—
76#2055—91noSylow
77C22×C3×Q8—31no—
78C22×C3×D4—31no—
79C22×D12C2×D311yescharacteristic
80C22×Dic6C2×D311yescharacteristic
81C2×C3×SD16—62no—
82C2×C3×SD16—62no—
83C2×C3×SD16—62no—
84C22×C3×C8—21no—
85C22×C3×C8—31no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C2×D311yescharacteristic
88C2×C3×C42—31no—
89C2×#217—61no—
90C2×#217—61no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3—61no—
99C2×C4×Dic3C2×D311yescharacteristic
100C22×C3⋊C8C2×D311yescharacteristic
101C2×#204—22no—
102C2×#204—22no—
103C2×#204—22no—
104C3×C4⋊C8—62no—
105#835—62no—
106#832—62no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111#821—62no—
112#816—62no—
113Dic3⋊C8—22no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—22no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3SD1612yescomplemented
143C3×D12—22no—
144C3×D12—22no—
145C3×D12—41no—
146C3×D12—41no—
147C3×Dic6—22no—
148C3×Dic6—22no—
149C3×Dic6—41no—
150C3×Dic6—41no—
151C32×C8—22no—
152C3×C3⋊C8—41no—
153C22×SD16—31no—
154C2×C4⋊C8—31no—
155C2×#103—91no—
156C2×#102—91no—
157#391—91no—
158#390—91no—
159#340—91no—
160C24×C3—61no—
161C23×D3—21no—
162C2×C3×Q8—32no—
163C2×C3×Q8—61no—
164C2×C3×Q8—61no—
165C2×C3×Q8—61no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×D4—32no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3—121no—
186C22×Dic3—121no—
187C22×Dic3D1211yescharacteristic
188C22×Dic3D1211yescharacteristic
189C2×D12—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12#6712yes—
195C2×Dic6—21no—
196C2×Dic6—21no—
197C2×Dic6—21no—
198C2×Dic6—21no—
199C2×Dic6—21no—
200C2×Dic6#6712yes—
201C3×SD16—68no—
202C2×C3×C8—21no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—22no—
207C2×C3×C8—41no—
208C2×C3×C8—41no—
209C2×C3×C8—61no—
210C2×C3×C8—61no—
211C2×C3×C8—61no—
212C2×C3×C8#6712yes—
213C2×C3×C8#6712yes—
214C3×C42—61no—
215C3×C42—61no—
216#217—122no—
217#217—122no—
218(C2×D3)⋊C4—122no—
219(C2×D3)⋊C4—122no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3—61no—
230C4⋊Dic3—121no—
231C4⋊Dic3—121no—
232C4×Dic3—21no—
233C4×Dic3—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237#204—28no—
238C22×C32#12111yescharacteristic
239C22×C32#12111yescharacteristic
240C22×C32#12111yescharacteristic
241C22×C32C2×SD1611yescharacteristic
242C22×C32#13511yescharacteristic
243C22×C32AGL(1,ℤ/8)11yescharacteristic
244C22×C32#13711yescharacteristic
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C2×C3×D3—81no—
249C2×C3×D3—81no—
250C2×C3×D3—81no—
251C2×C3×D3—81no—
252C32×C4#12011yescharacteristic
253C32×C4#12311yescharacteristic
254C32×C4#12311yescharacteristic
255C32×C4#12411yescharacteristic
256C3⋊Dic3—81no—
257C3⋊Dic3—81no—
258C3×Dic3—22no—
259C3×Dic3—42no—
260C3×Dic3—41no—
261C22×Q8—31no—
262C22×D4—31no—
263C2×SD16—62no—
264C2×SD16—62no—
265C2×SD16—62no—
266C22×C8—31no—
267C22×C8D3211yescharacteristic
268C2×C4⋊C4—91no—
269C2×C4⋊C4—91no—
270C2×C22⋊C4—181no—
271C2×C22⋊C4—181no—
272C2×C42—31no—
273C4⋊C8—62no—
274#103—182no—
275#102—182no—
276#95—181no—
277#95—181no—
278C23×C3—21no—
279C23×C3—62no—
280C23×C3—121no—
281C23×C3—121no—
282C23×C3—121no—
283C23×C3—121no—
284C23×C3—121no—
285C23×C3—121no—
286C23×C3C2×D1211yescharacteristic
287C23×C3D3×D411yescharacteristic
288C22×D3—22no—
289C22×D3—41no—
290C22×D3—41no—
291C22×D3—41no—
292C22×D3—41no—
293C22×D3—41no—
294C22×D3—41no—
295C3×Q8—62no—
296C3×Q8—62no—
297C3×Q8—121no—
298C3×Q8—121no—
299C3×D4—62no—
300C3×D4—62no—
301C3×D4—121no—
302C3×D4—121no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—32no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—62no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—121no—
317C2×C3×C4—121no—
318C2×C3×C4#23511yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4#23711yescharacteristic
322C2×C3×C4#23711yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4#23911yescharacteristic
325C2×C3×C4#23911yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327C2×C3×C4C2×#6711yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330C2×Dic3—21no—
331C2×Dic3—21no—
332C2×Dic3—21no—
333C2×Dic3—21no—
334C2×Dic3—21no—
335C2×Dic3—22no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—122no—
339C2×Dic3—122no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—121no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—241no—
353C2×Dic3—241no—
354C2×Dic3—241no—
355C2×Dic3—241no—
356C2×Dic3#20412yescomplemented
357D12—22no—
358D12—22no—
359D12—41no—
360D12—41no—
361Dic6—22no—
362Dic6—22no—
363Dic6—41no—
364Dic6—41no—
365C3×C8—22no—
366C3×C8—22no—
367C3×C8—42no—
368C3×C8—121no—
369C3⋊C8—41no—
370C2×C32#39411yescharacteristic
371C2×C32#46011yescharacteristic
372C2×C32#46111yescharacteristic
373C2×C32#46311yescharacteristic
374C2×C32#46411yescharacteristic
375C2×C32#46511yescharacteristic
376C2×C32#46811yescharacteristic
377C3×D3—82no—
378C24—61no—
379C2×Q8—32no—
380C2×Q8—61no—
381C2×Q8—61no—
382C2×Q8—61no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×D4—32no—
386C2×D4—61no—
387C2×D4—61no—
388C2×D4—61no—
389C2×D4—61no—
390C2×D4—61no—
391C22×C4—31no—
392C22×C4—31no—
393C22×C4—61no—
394C22×C4—181no—
395C22×C4—181no—
396C22×C4C2×D3211yescharacteristic
397SD16—68no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—61no—
401C2×C8—61no—
402C2×C8—61no—
403C2×C8#62512yes—
404C4⋊C4—181no—
405C4⋊C4—181no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C22⋊C4—362no—
409C22⋊C4—362no—
410C42—61no—
411C42—61no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3—241no—
423C22×C3—241no—
424C22×C3—241no—
425C22×C3—241no—
426C22×C3#89511yescharacteristic
427C22×C3#89511yescharacteristic
428C22×C3C2×#20411yescharacteristic
429C22×C3#90411yescharacteristic
430C22×C3#90811yescharacteristic
431C22×C3#90911yescharacteristic
432C22×C3D3×SD1611yescharacteristic
433C22×C3#91411yescharacteristic
434C22×C3#91511yescharacteristic
435C22×C3#91611yescharacteristic
436C22×C3#93011yescharacteristic
437C22×C3#93811yescharacteristic
438C22×C3#93911yescharacteristic
439C22×C3#93911yescharacteristic
440C2×D3—42no—
441C2×D3—42no—
442C2×D3—42no—
443C2×D3—81no—
444C2×D3—81no—
445C2×D3—81no—
446C2×D3—81no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—62no—
452C3×C4—121no—
453C3×C4—122no—
454C3×C4#89411yescharacteristic
455C3×C4#89411yescharacteristic
456C3×C4#93511yescharacteristic
457C3×C4#93511yescharacteristic
458C3×C4#93611yescharacteristic
459C3×C4#93711yescharacteristic
460C3×C4#94711yescharacteristic
461C3×C4#95311yescharacteristic
462Dic3—22no—
463Dic3—41no—
464Dic3—42no—
465Dic3—242no—
466Dic3—242no—
467Dic3—241no—
468Dic3—241no—
469Dic3—241no—
470Dic3—241no—
471C32#205511yescharacteristic, complemented, Sylow
472C23—62no—
473C23—121no—
474C23—121no—
475C23—121no—
476C23—121no—
477C23—121no—
478C23—121no—
479C23D3×D1211yescharacteristic
480Q8—62no—
481Q8—62no—
482Q8—121no—
483Q8—121no—
484D4—62no—
485D4—62no—
486D4—121no—
487D4—121no—
488C2×C4—32no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—62no—
494C2×C4—61no—
495C2×C4—121no—
496C2×C4—121no—
497C2×C4—361no—
498C2×C4—361no—
499C2×C4—361no—
500C2×C4—361no—
501C2×C4—361no—
502C2×C4—361no—
503C2×C4#379511yescharacteristic
504C2×C4#379611yescharacteristic
505C2×C4#379611yescharacteristic
506C2×C4C2×#62511yescharacteristic
507C2×C4D3×#6711yescharacteristic
508C2×C4D3×#6711yescharacteristic
509C8—22no—
510C8—121no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—242no—
519C2×C3#484111yescharacteristic
520C2×C3#484411yescharacteristic
521C2×C3#484511yescharacteristic
522C2×C3#484811yescharacteristic
523C2×C3#499111yescharacteristic
524C2×C3#511411yescharacteristic
525C2×C3#513411yescharacteristic
526C2×C3#516211yescharacteristic
527C2×C3#516311yescharacteristic
528C2×C3#516511yescharacteristic
529C2×C3#516611yescharacteristic
530C2×C3#517111yescharacteristic
531C2×C3#517411yescharacteristic
532C2×C3#522211yescharacteristic
533D3—82no—
534C22—122no—
535C22—122no—
536C22—122no—
537C22—241no—
538C22—241no—
539C22—241no—
540C22—241no—
541C22D3×#20411yescharacteristic
542C22#6379411yescharacteristic
543C22#6380011yescharacteristic
544C22#6380611yescharacteristic
545C22#6388611yescharacteristic
546C22#6388611yescharacteristic
547C22#6390811yescharacteristic
548C4—62no—
549C4—122no—
550C4—121no—
551C4—721no—
552C4—721no—
553C4#6386311yescharacteristic
554C4#6388411yescharacteristic
555C4#6388411yescharacteristic
556C4#6397611yescharacteristic
557C3—21no—
558C3#7048211yescharacteristic, complemented
559C3#7205111yescharacteristic, complemented
560C2—242no—
561C2#1059075211yescharacteristic
562C2#1059075411yescharacteristic
563C2#1059079911yescharacteristic
564C2#1059082911yescharacteristic
565C2#1059083311yescharacteristic
566C2#1059085911yescharacteristic
567C2#1059130011yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×Dic3⋊C8C2semidirect
4. #10591220C2semidirect
5. C2×#63566C2semidirect
7. #10589417C2semidirect
36. C2×Dic3⋊C8D3semidirect
142. C2×C3×Dic3SD16semidirect
356. C2×Dic3#204semidirect
471. C32#2055semidirect
558. C3#70482semidirect
559. C3#72051semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×C3×Dic3⋊C82
#105913182
#105912202
C2×#635662
C2×#635632
#105894172
#720513
#704823