Finite Group Databasebeta

← #11895355

Subgroups — #11895355

Order 1152.

785 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5543C211yesmaximal, characteristic, complemented
2#10593951C211yesmaximal, characteristic, complemented
3C4×#3754C211yesmaximal, characteristic, complemented
4C3×#5015C211yesmaximal, characteristic
5#10591468C212yesmaximal, complemented
6Dic3×#213C212yesmaximal, complemented
7#10590533C212yesmaximal, complemented
8#10590469C212yesmaximal, complemented
9#10590284C211yesmaximal, characteristic, complemented
10#10590277C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83643—31nomaximal
13#80319—31nomaximal
14C32×C4×D4C2211yescharacteristic
15C2×#3754C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×D4×Dic3C2212yes—
18C2×C3×#213C2212yes—
19C2×C3×C4⋊Dic3—21no—
20C3×#924—21no—
21C3×#890C2212yes—
22C3×#878—22no—
23C3×#874C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63898—21no—
27Dic3×D12C2212yes—
28#63884—22no—
29#63863—21no—
30#63860C2212yes—
31#63659C2211yescharacteristic
32#63637C2211yescharacteristic
33#63635C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#809C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63575C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63567C2212yes—
40#63562C2212yes—
41#63562C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#554—31no—
44#5713—31no—
45#5585—31no—
46#5543D311yescharacteristic, complemented
47C3×#459—31no—
48#5153—32no—
49Dic3×D8—32no—
50#5091—31no—
51#5088—31no—
52#5070—31no—
53#5068—32no—
54#5066—32no—
55Q8×C3⋊C8—31no—
56C4×#214—31no—
57C4×#214—31no—
58C4×#214—61no—
59#5016—32no—
60#5015D311yescharacteristic
61C4×#213—32no—
62#4850—31no—
63#4830—31no—
64#4768—32no—
65#4766—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×#634C2311yescharacteristic
69C22×C3×Dic3—22no—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12C2312yes—
73C2×C3×Dic6—21no—
74C2×C3×Dic6D411yescharacteristic
75C2×D3×Dic3—22no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C22⋊C4—21no—
78C32×C42C2311yescharacteristic
79#3754—22no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—21no—
82C4×C3⋊Dic3—21no—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C3×#217—22no—
86C3×#213—24no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4D412yes—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8C2312yes—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97(C2×D3)⋊Dic3—22no—
98#3361—91noSylow
99C2×C3×D8—32no—
100C3×C4⋊Q8—31no—
101C3×#127—31no—
102C3×#125—32no—
103C3×C22⋊Q8—62no—
104C3×C22⋊Q8—61no—
105C3×C4×Q8—31no—
106C3×C4×D4—21no—
107C3×C4×D4—32no—
108C3×C4×D4C2×D311yescharacteristic
109C3×C4×D4C2×D311yescharacteristic
110C2×C3×C4⋊C4—61no—
111#947—61no—
112#936—32no—
113#936—61no—
114#935—62no—
115D4×Dic3—32no—
116D4×Dic3—61no—
117D4×Dic3C2×D312yes—
118C2×#214—31no—
119C2×#214—31no—
120C2×#214—61no—
121C2×#213C2×D312yes—
122C2×C4⋊Dic3—21no—
123#924—21no—
124#894—62no—
125#893—61no—
126#890C2×D312yes—
127#878—22no—
128#875—32no—
129#874C2×D311yescharacteristic
130C4×D12—32no—
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—31no—
137C3×#102—32no—
138#832—31no—
139#832—31no—
140#832—32no—
141#832—32no—
142#832—61no—
143#818—32no—
144#816—32no—
145Dic3⋊C8—32no—
146C8×Dic3—32no—
147#810—31no—
148#810—31no—
149#810—32no—
150#810—61no—
151#809—32no—
152#809—32no—
153#809C2×D312yes—
154#808—31no—
155#808—31no—
156#808—61no—
157#807—32no—
158C4⋊(C3⋊C8)—32no—
159C4⋊(C3⋊C8)C2×D311yescharacteristic
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—32no—
163C4×C3⋊C8—61no—
164C23×C32—21no—
165C22×C3×D3—22no—
166C32×D4—21no—
167C32×D4#4112yes—
168C2×C32×C4—21no—
169C2×C32×C4—42no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175#634—21no—
176#634—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—82no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—22no—
182C3×D12—22no—
183C3×D12—42no—
184C3×D12—81no—
185C3×Dic6—22no—
186C3×Dic6—81no—
187D3×Dic3—82no—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—21no—
190C3×C3⋊C8—22no—
191#559—91no—
192#554—31no—
193#488—92no—
194#486—91no—
195#478—92no—
196#477—91no—
197#463—92no—
198#459—31no—
199C8×Q8—91no—
200C4×SD16—91no—
201C4×D8—92no—
202C2×C3×Q8—31no—
203C2×C3×Q8—61no—
204C2×C3×D4—21no—
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C2×C3×D4C22×D311yescharacteristic
209C2×C3×D4C22×D311yescharacteristic
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—41no—
213C22×C3×C4—62no—
214C22×Dic3—22no—
215C22×Dic3—62no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12C22×D312yes—
219C2×C4×D3—62no—
220C2×Dic6—21no—
221C2×Dic6—31no—
222C2×Dic6—31no—
223C2×Dic6—61no—
224C2×Dic6#6711yescharacteristic
225C3×D8—64no—
226C2×C3×C8—32no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—32no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—62no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—41no—
239C3×C22⋊C4—62no—
240C3×C42—21no—
241C3×C42—32no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—22no—
245#217—62no—
246#217—62no—
247#217—62no—
248#214—64no—
249#214—62no—
250#214—62no—
251#213—24no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255C4⋊Dic3—21no—
256C4⋊Dic3—22no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—61no—
260C4⋊Dic3#6711yescharacteristic
261C4⋊Dic3C22×D312yes—
262Dic3⋊C4—22no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—121no—
266Dic3⋊C4#6712yes—
267C4×Dic3—61no—
268C4×Dic3—61no—
269C4×Dic3—121no—
270C4×Dic3C22×D312yes—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8C22×D312yes—
278C22×C32—22no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32C22×D411yescharacteristic
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—21no—
286C32×C4—41no—
287C32×C4#13512yes—
288C32×C4C2×#4111yescharacteristic
289C32×C42−1+411yescharacteristic
290C3⋊Dic3—41no—
291C3⋊Dic3—41no—
292C3×Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—42no—
295C2×SD16—91no—
296C2×D8—32no—
297C4⋊Q8—31no—
298#127—31no—
299#125—32no—
300#124—92no—
301#124—181no—
302#123—182no—
303C22⋊Q8—62no—
304C22⋊Q8—61no—
305C4×Q8—31no—
306C4×Q8—91no—
307C4×D4—32no—
308C4×D4—92no—
309C4×D4—181no—
310C4×D4D3211yescharacteristic
311C2×C4⋊C4—61no—
312#107—92no—
313#106—91no—
314C4⋊C8—31no—
315C4⋊C8—92no—
316#103—92no—
317#103—91no—
318#102—32no—
319#102—92no—
320#102—92no—
321#102—91no—
322C4×C8—92no—
323C4×C8—91no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—41no—
327C23×C3—62no—
328C22×D3—22no—
329C3×Q8—62no—
330C3×Q8—241no—
331C3×D4—21no—
332C3×D4—21no—
333C3×D4—22no—
334C3×D4—41no—
335C3×D4—62no—
336C3×D4—62no—
337C3×D4—122no—
338C3×D4—241no—
339C3×D4#23712yes—
340C3×D4#23912yes—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—32no—
347C2×C3×C4—32no—
348C2×C3×C4—41no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—62no—
352C2×C3×C4—82no—
353C2×C3×C4—242no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×Dic3—22no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—82no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368C2×Dic3—242no—
369C2×Dic3C2×#6712yes—
370C2×Dic3C2×#6712yes—
371D12—22no—
372D12—22no—
373D12—42no—
374D12—81no—
375C4×D3—242no—
376Dic6—22no—
377Dic6—62no—
378Dic6—61no—
379Dic6—61no—
380Dic6—61no—
381Dic6—61no—
382Dic6—81no—
383Dic6—121no—
384C3×C8—62no—
385C3⋊C8—22no—
386C3⋊C8—62no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C3⋊C8—61no—
390C3⋊C8—61no—
391C3⋊C8—121no—
392C2×C32—42no—
393C2×C32#54811yescharacteristic
394C2×C32C2×#13511yescharacteristic
395C2×C32#57611yescharacteristic
396C3×D3—82no—
397C2×Q8—31no—
398C2×Q8—61no—
399C2×Q8—91no—
400C2×D4—32no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4C2×D3211yescharacteristic
404C22×C4—21no—
405C22×C4—62no—
406C22×C4—182no—
407SD16—182no—
408D8—64no—
409C2×C8—32no—
410C2×C8—91no—
411C2×C8—91no—
412C4⋊C4—31no—
413C4⋊C4—32no—
414C4⋊C4—32no—
415C4⋊C4—62no—
416C4⋊C4—62no—
417C4⋊C4—61no—
418C4⋊C4—91no—
419C4⋊C4—181no—
420C4⋊C4C2×D3211yescharacteristic
421C22⋊C4—21no—
422C22⋊C4—62no—
423C22⋊C4—182no—
424C22⋊C4—182no—
425C22⋊C4—182no—
426C42—32no—
427C42—181no—
428C42C2×D3211yescharacteristic
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—42no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—81no—
438C22×C3—81no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3C2×D3×D411yescharacteristic
443C22×C3C22×#6711yescharacteristic
444C2×D3—42no—
445C2×D3—42no—
446C2×D3—42no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—22no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4—81no—
458C3×C4—122no—
459C3×C4#91212yes—
460C3×C4#95012yes—
461C3×C4C2×#23711yescharacteristic
462C3×C4C2×#23911yescharacteristic
463C3×C4#100711yescharacteristic
464C3×C4#101011yescharacteristic
465Dic3—22no—
466Dic3—22no—
467Dic3—42no—
468Dic3—122no—
469Dic3—121no—
470Dic3—121no—
471Dic3—121no—
472Dic3—121no—
473Dic3—241no—
474C32#336111yescharacteristic, complemented, Sylow
475C23—21no—
476C23—62no—
477Q8—62no—
478Q8—181no—
479Q8—181no—
480Q8—241no—
481D4—21no—
482D4—62no—
483D4—62no—
484D4—122no—
485D4—241no—
486D4#379612yes—
487C2×C4—21no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—42no—
491C2×C4—62no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—242no—
495C2×C4—722no—
496C2×C4D3×#6711yescharacteristic
497C2×C4D3×#6711yescharacteristic
498C2×C4C22×D3211yescharacteristic
499C8—62no—
500C8—181no—
501C8—181no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—42no—
506C2×C3—42no—
507C2×C3—82no—
508C2×C3—242no—
509C2×C3#559811yescharacteristic
510C2×C3C2×#91211yescharacteristic
511C2×C3#577411yescharacteristic
512C2×C3#581711yescharacteristic
513C2×C3C2×#95011yescharacteristic
514C2×C3#583511yescharacteristic
515D3—82no—
516C22—22no—
517C22—41no—
518C22—41no—
519C22—122no—
520C22—122no—
521C22—122no—
522C22C2×D3×#6711yescharacteristic
523C4—21no—
524C4—41no—
525C4—62no—
526C4—62no—
527C4—122no—
528C4—361no—
529C4—361no—
530C4#6393312yes—
531C4C2×#379611yescharacteristic
532C4#6429711yescharacteristic
533C3—21no—
534C3#8031911yescharacteristic, complemented
535C3#8364311yescharacteristic, complemented
536C2—42no—
537C2—242no—
538C2#1059490011yescharacteristic
539C2C2×#6393311yescharacteristic
540C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5015C2
hypercenterC4×D4D32
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5543C2semidirect
2. #10593951C2semidirect
3. C4×#3754C2semidirect
5. #10591468C2semidirect
6. Dic3×#213C2semidirect
7. #10590533C2semidirect
8. #10590469C2semidirect
9. #10590284C2semidirect
10. #10590277C2semidirect
11. #10590250C2semidirect
46. #5543D3semidirect
474. C32#3361semidirect
534. C3#80319semidirect
535. C3#83643semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
#105939512
C4×#37542
C3×#50152
#105914682
Dic3×#2132
#105905332
#105904692
#105902842
#105902772
#105902502
#836433
#803193