Finite Group Databasebeta

← #11794069

Subgroups — #11794069

Order 1152.

729 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3716C211yesmaximal, characteristic
2C2×#63637C211yesmaximal, characteristic, complemented
3C3×#4988C211yesmaximal, characteristic
4#10591213C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7C3×#4529C211yesmaximal, characteristic, complemented
8#69651—31nomaximal
9#68863—31nomaximal
10C22×#634C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
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×#3716—22no—
20C2×#3716—22no—
21C2×#3716—22no—
22#63637—22no—
23#63579—21no—
24#63579—21no—
25Dic3⋊(C3⋊C8)—22no—
26#63562—22no—
27C22×#214—31no—
28C22×#204—31no—
29C3×#390—31no—
30C2×#832—31no—
31C2×Dic3⋊C8—31no—
32#4988D311yescharacteristic
33#4973—31no—
34C2×#810—31no—
35C2×#810—31no—
36C2×#810—61no—
37C2×#809—31no—
38#4929—31no—
39C2×C4⋊(C3⋊C8)—31no—
40C3×#340—31no—
41#4529D311yescharacteristic, complemented
42C23×C3×D3—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634D412yes—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×(C2×D3)⋊C4—42no—
67C3×(C2×D3)⋊C4—42no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8D412yes—
75#3716—28no—
76#2055—91noSylow
77C22×C3×D4—31no—
78C22×D12C2×D311yescharacteristic
79C22×Dic6—31no—
80C22×Dic6—31no—
81C22×Dic6—61no—
82C22×C3×C8—31no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C22⋊C4—61no—
88C2×C3×C22⋊C4—61no—
89C2×C3×C42—31no—
90C2×#214—62no—
91C2×#214—62no—
92C2×#214—62no—
93C2×(C2×D3)⋊C4—21no—
94C2×(C2×D3)⋊C4—21no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4×Dic3C2×D311yescharacteristic
97C22×C3⋊C8—31no—
98C22×C3⋊C8—31no—
99C22×C3⋊C8—61no—
100C22×C3⋊C8C2×D311yescharacteristic
101C2×#204—62no—
102C2×#204—62no—
103C2×#204—62no—
104#832—62no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109Dic3⋊C8—62no—
110#810—62no—
111#810—62no—
112#810—64no—
113#809—62no—
114C4⋊(C3⋊C8)—62no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—41no—
134C2×C3⋊Dic3—41no—
135#634—22no—
136#634—22no—
137#634—41no—
138#634—41no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3SD1612yescomplemented
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—41no—
151C3×D12—41no—
152C3⋊(C3⋊C8)—41no—
153C3×C3⋊C8—22no—
154C22×SD16—91no—
155C2×C4⋊C8—91no—
156C2×#103—91no—
157C2×#102—91no—
158#391—91no—
159#390—31no—
160#340—31no—
161C24×C3—61no—
162C23×D3—21no—
163C2×C3×D4—32no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C2×C3×D4—61no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—41no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×Dic3—21no—
179C22×Dic3—61no—
180C22×Dic3—61no—
181C22×Dic3—121no—
182C22×Dic3#6711yescharacteristic
183C22×Dic3#6711yescharacteristic
184C2×D12—21no—
185C2×D12—21no—
186C2×D12—21no—
187C2×D12—21no—
188C2×D12—21no—
189C2×D12D1212yes—
190C2×Dic6—32no—
191C2×Dic6—32no—
192C2×Dic6—62no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×Dic6—61no—
196C2×Dic6—61no—
197C2×Dic6—61no—
198C2×Dic6—61no—
199C2×Dic6—61no—
200C2×Dic6—61no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×Dic6—121no—
206C2×Dic6—121no—
207C2×Dic6—121no—
208C2×C3×C8—32no—
209C2×C3×C8—61no—
210C2×C3×C8—61no—
211C3×C4⋊C4—22no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—41no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219C3×C22⋊C4—122no—
220C3×C22⋊C4—122no—
221C3×C42—61no—
222C3×C42—61no—
223#214—68no—
224(C2×D3)⋊C4—42no—
225(C2×D3)⋊C4—42no—
226C4⋊Dic3—21no—
227C4⋊Dic3—21no—
228C4×Dic3—21no—
229C4×Dic3—21no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—61no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—121no—
240C2×C3⋊C8—121no—
241C2×C3⋊C8D1212yes—
242#204—68no—
243C22×C32#12111yescharacteristic
244C22×C32#12111yescharacteristic
245C22×C32#12111yescharacteristic
246C22×C32C2×SD1611yescharacteristic
247C22×C32#13511yescharacteristic
248C22×C32AGL(1,ℤ/8)11yescharacteristic
249C22×C32#13711yescharacteristic
250C2×C3×D3—42no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—81no—
254C2×C3×D3—81no—
255C2×C3×D3—81no—
256C2×C3×D3—81no—
257C32×C4—81no—
258C32×C4#12011yescharacteristic
259C32×C4#12311yescharacteristic
260C32×C4#12311yescharacteristic
261C32×C4#12411yescharacteristic
262C3⋊Dic3—42no—
263C3×Dic3—22no—
264C3×Dic3—41no—
265C3×Dic3—81no—
266C22×Q8—91no—
267C22×D4—31no—
268C2×SD16—182no—
269C2×SD16—182no—
270C2×SD16—182no—
271C22×C8—31no—
272C22×C8—91no—
273C2×C4⋊C4—31no—
274C2×C4⋊C4D3211yescharacteristic
275C2×C22⋊C4—61no—
276C2×C22⋊C4—61no—
277C2×C42—31no—
278C4⋊C8—182no—
279#103—182no—
280#102—182no—
281#95—181no—
282#95—181no—
283C23×C3—21no—
284C23×C3—62no—
285C23×C3—121no—
286C23×C3—121no—
287C23×C3—121no—
288C23×C3—121no—
289C23×C3—121no—
290C23×C3—121no—
291C23×C3D3×D411yescharacteristic
292C23×C3C2×#6711yescharacteristic
293C22×D3—22no—
294C22×D3—41no—
295C22×D3—41no—
296C22×D3—41no—
297C22×D3—41no—
298C22×D3—41no—
299C22×D3—41no—
300C3×D4—62no—
301C3×D4—62no—
302C3×D4—121no—
303C3×D4—121no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—32no—
311C2×C3×C4—42no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—61no—
319C2×C3×C4—61no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—61no—
323C2×C3×C4—81no—
324C2×C3×C4—81no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4C2×D1211yescharacteristic
330C2×C3×C4#23511yescharacteristic
331C2×C3×C4#23511yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23711yescharacteristic
338C2×C3×C4#23711yescharacteristic
339C2×C3×C4#23911yescharacteristic
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—122no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3#21412yescomplemented
358D12—22no—
359D12—22no—
360D12—41no—
361D12—41no—
362Dic6—64no—
363Dic6—62no—
364Dic6—62no—
365Dic6—62no—
366Dic6—62no—
367Dic6—122no—
368Dic6—122no—
369Dic6—122no—
370Dic6—121no—
371Dic6—121no—
372Dic6—121no—
373Dic6—121no—
374C3×C8—62no—
375C3⋊C8—22no—
376C3⋊C8—122no—
377C3⋊C8—121no—
378C3⋊C8—121no—
379C2×C32#39411yescharacteristic
380C2×C32#46011yescharacteristic
381C2×C32#46111yescharacteristic
382C2×C32#46311yescharacteristic
383C2×C32#46411yescharacteristic
384C2×C32#46511yescharacteristic
385C2×C32#46811yescharacteristic
386C3×D3—82no—
387C24—61no—
388C2×Q8—92no—
389C2×Q8—181no—
390C2×Q8—181no—
391C2×Q8—181no—
392C2×Q8—181no—
393C2×Q8—181no—
394C2×D4—32no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C22×C4—21no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—61no—
404C22×C4—181no—
405C22×C4C2×D3211yescharacteristic
406SD16—188no—
407C2×C8—32no—
408C2×C8—61no—
409C2×C8—61no—
410C2×C8—181no—
411C2×C8—181no—
412C2×C8—181no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—61no—
416C4⋊C4—61no—
417C22⋊C4—122no—
418C22⋊C4—122no—
419C42—61no—
420C42—61no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—122no—
429C22×C3—122no—
430C22×C3—122no—
431C22×C3—241no—
432C22×C3—241no—
433C22×C3—241no—
434C22×C3—241no—
435C22×C3#88411yescharacteristic
436C22×C3#88411yescharacteristic
437C22×C3#89511yescharacteristic
438C22×C3#91111yescharacteristic
439C22×C3D3×SD1611yescharacteristic
440C22×C3#91611yescharacteristic
441C22×C3#91811yescharacteristic
442C22×C3#93011yescharacteristic
443C22×C3#93211yescharacteristic
444C22×C3C2×#21411yescharacteristic
445C22×C3#93811yescharacteristic
446C22×C3#93911yescharacteristic
447C22×C3#95011yescharacteristic
448C22×C3#95111yescharacteristic
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—42no—
452C2×D3—81no—
453C2×D3—81no—
454C2×D3—81no—
455C2×D3—81no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—62no—
461C3×C4—82no—
462C3×C4—81no—
463C3×C4—81no—
464C3×C4—121no—
465C3×C4—241no—
466C3×C4#87511yescharacteristic
467C3×C4#88211yescharacteristic
468C3×C4#88211yescharacteristic
469C3×C4#88311yescharacteristic
470C3×C4#88511yescharacteristic
471C3×C4#88611yescharacteristic
472C3×C4#89411yescharacteristic
473C3×C4#89411yescharacteristic
474Dic3—22no—
475Dic3—41no—
476Dic3—81no—
477Dic3—124no—
478Dic3—122no—
479Dic3—122no—
480C32#205511yescharacteristic, complemented, Sylow
481C23—62no—
482C23—121no—
483C23—121no—
484C23—121no—
485C23—121no—
486C23—121no—
487C23—121no—
488C23D3×#6711yescharacteristic
489Q8—182no—
490Q8—182no—
491Q8—361no—
492Q8—361no—
493D4—62no—
494D4—62no—
495D4—121no—
496D4—121no—
497C2×C4—32no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—121no—
507C2×C4—121no—
508C2×C4—121no—
509C2×C4—182no—
510C2×C4—361no—
511C2×C4—361no—
512C2×C4#379611yescharacteristic
513C2×C4#379811yescharacteristic
514C2×C4D3×D1211yescharacteristic
515C2×C4D3×D1211yescharacteristic
516C2×C4#380411yescharacteristic
517C2×C4#381111yescharacteristic
518C8—62no—
519C8—361no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—242no—
528C2×C3#467211yescharacteristic
529C2×C3#476211yescharacteristic
530C2×C3#478711yescharacteristic
531C2×C3#479811yescharacteristic
532C2×C3#481811yescharacteristic
533C2×C3#486411yescharacteristic
534C2×C3#488611yescharacteristic
535C2×C3#496111yescharacteristic
536C2×C3#501611yescharacteristic
537C2×C3#501911yescharacteristic
538C2×C3#504111yescharacteristic
539C2×C3#504211yescharacteristic
540C2×C3#505411yescharacteristic
541C2×C3#507511yescharacteristic
542D3—82no—
543C22—122no—
544C22—122no—
545C22—122no—
546C22—241no—
547C22—241no—
548C22—241no—
549C22—241no—
550C22#6388611yescharacteristic
551C22#6390611yescharacteristic
552C22D3×#21411yescharacteristic
553C22#6393211yescharacteristic
554C22#6394311yescharacteristic
555C22#6394711yescharacteristic
556C22#6395811yescharacteristic
557C4—62no—
558C4—81no—
559C4—121no—
560C4—241no—
561C4—362no—
562C4#6385211yescharacteristic
563C4#6385311yescharacteristic
564C4#6389011yescharacteristic
565C4#6392311yescharacteristic
566C3—21no—
567C3#6886311yescharacteristic, complemented
568C3#6965111yescharacteristic, complemented
569C2—242no—
570C2#1059053011yescharacteristic
571C2#1059055911yescharacteristic
572C2#1059057811yescharacteristic
573C2#1059058811yescharacteristic
574C2#1059131211yescharacteristic
575C2#1059143911yescharacteristic
576C2#1059157711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2055
LCSG ▷ C22×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. C2×#63637C2semidirect
4. #10591213C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
7. C3×#4529C2semidirect
41. #4529D3semidirect
147. C2×C3×Dic3SD16semidirect
357. C2×Dic3#214semidirect
480. C32#2055semidirect
567. C3#68863semidirect
568. C3#69651semidirect

Maximal subgroups

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

subgroupindex
C22×#37162
C2×#636372
C3×#49882
#105912132
C2×Dic3⋊(C3⋊C8)2
C2×#635622
C3×#45292
#696513
#688633