Finite Group Databasebeta

← #11895254

Subgroups — #11895254

Order 1152.

767 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5543C211yesmaximal, characteristic, complemented
2#10593865C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic
4C3×#5019C211yesmaximal, characteristic, complemented
5#10591471C212yesmaximal
6Dic3×#214C212yesmaximal, complemented
7#10590537C212yesmaximal, complemented
8#10590493C212yesmaximal, complemented
9#10590300C211yesmaximal, characteristic, complemented
10#10590290C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12#83637—31nomaximal
13#80415—31nomaximal
14C32×C4×D4C2211yescharacteristic
15C2×#3753C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×D4×Dic3C2212yes—
18C2×C3×#214C2212yes—
19C2×C3×C4⋊Dic3—21no—
20C3×#924—21no—
21C3×#890C2212yes—
22C3×#878—22no—
23C3×#869C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26#63871—21no—
27#63864C2212yes—
28#63849—21no—
29#63848—22no—
30Dic3×Dic6C2212yes—
31#63659C2211yescharacteristic
32#63636C2211yescharacteristic
33#63634C2211yescharacteristic
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#810C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37#63573C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63565C2212yes—
40#63565C2212yes—
41#63564C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×#554—31no—
44#5732—31no—
45#5584—31no—
46#5543D311yescharacteristic, complemented
47C3×#461—31no—
48#5165—32no—
49Dic3×SD16—32no—
50#5093—31no—
51#5084—31no—
52#5079—31no—
53#5068—32no—
54#5063—32no—
55Q8×C3⋊C8—31no—
56#5019D311yescharacteristic, complemented
57C4×#214—32no—
58#5016—32no—
59C4×#213—31no—
60C4×#213—31no—
61C4×#213—61no—
62#4842—31no—
63#4830—31no—
64#4800—32no—
65#4799—32no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C22×C3×Dic3—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2312yes—
74C32×C4⋊C4C2311yescharacteristic
75C32×C22⋊C4—21no—
76C32×C42C2311yescharacteristic
77#3753—22no—
78#3752—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×#217—22no—
83C3×#214—24no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4D412yes—
92C3×C4×Dic3C2312yes—
93C2×C3×C3⋊C8C2312yes—
94Dic3⋊Dic3—22no—
95#3722—22no—
96#3722—22no—
97Dic32—22no—
98#3360—91noSylow
99C2×C3×SD16—32no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8—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—32no—
112#946—61no—
113Q8×Dic3—32no—
114D4×Dic3C2×D312yes—
115C2×#214C2×D312yes—
116C2×#213—31no—
117C2×#213—31no—
118C2×#213—61no—
119C2×C4⋊Dic3—21no—
120#924—21no—
121#898—62no—
122#898—62no—
123#897—61no—
124#892—61no—
125#892—61no—
126#890C2×D312yes—
127#878—22no—
128#875—32no—
129C4×D12—31no—
130C4×D12—31no—
131C4×D12—61no—
132#869C2×D311yescharacteristic
133#869C2×D311yescharacteristic
134C4×Dic6—32no—
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—31no—
137C3×#103—32no—
138#835—32no—
139#835—32no—
140#832—31no—
141#832—31no—
142#832—61no—
143#821—32no—
144#817—32no—
145Dic3⋊C8—32no—
146C8×Dic3—32no—
147#810—32no—
148#810—32no—
149#810C2×D312yes—
150#809—31no—
151#809—31no—
152#809—32no—
153#809—61no—
154#808—32no—
155#807—31no—
156#807—31no—
157#807—61no—
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—21no—
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—
174C4⋊(C3⋊D3)—21no—
175C4⋊(C3⋊D3)—21no—
176C4×C3⋊D3—42no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—82no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—22no—
185C3×Dic6—81no—
186C3⋊(C3⋊C8)—21no—
187C3⋊(C3⋊C8)—21no—
188C3×C3⋊C8—22no—
189#556—91no—
190#554—31no—
191#488—92no—
192#487—91no—
193#479—92no—
194#476—91no—
195#463—92no—
196#461—31no—
197C8×Q8—91no—
198C4×SD16—92no—
199C4×D8—91no—
200C2×C3×Q8—31no—
201C2×C3×Q8—32no—
202C2×C3×Q8—61no—
203C2×C3×D4—21no—
204C2×C3×D4C22×D311yescharacteristic
205C2×C3×D4C22×D311yescharacteristic
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—41no—
209C22×C3×C4—62no—
210C22×Dic3—22no—
211C2×D12—31no—
212C2×D12—31no—
213C2×D12—61no—
214C2×C4×D3—61no—
215C2×C4×D3—61no—
216C2×C4×D3—121no—
217C2×Dic6—21no—
218C2×Dic6#6711yescharacteristic
219C2×Dic6C22×D312yes—
220C3×SD16—64no—
221C2×C3×C8—32no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—62no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—61no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4C22×D311yescharacteristic
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C22⋊C4—21no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—41no—
236C3×C22⋊C4—62no—
237C3×C42—21no—
238C3×C42—32no—
239C3×C42C22×D311yescharacteristic
240C3×C42C22×D311yescharacteristic
241#217—22no—
242#214—24no—
243#213—64no—
244#213—62no—
245#213—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—121no—
253C4⋊Dic3—21no—
254C4⋊Dic3—21no—
255C4⋊Dic3—21no—
256C4⋊Dic3—22no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—61no—
260C4⋊Dic3—62no—
261C4⋊Dic3#6711yescharacteristic
262C4⋊Dic3C22×D312yes—
263Dic3⋊C4—22no—
264Dic3⋊C4—62no—
265Dic3⋊C4#6712yes—
266C4×Dic3—62no—
267C4×Dic3—62no—
268C4×Dic3C22×D312yes—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8C22×D312yes—
276C22×C32—22no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32C22×D411yescharacteristic
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C32×C4—21no—
284C32×C4—41no—
285C32×C4#13512yes—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3⋊Dic3—41no—
289C3×Dic3—22no—
290C3×Dic3—22no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C2×SD16—32no—
294C2×D8—91no—
295C4⋊Q8—31no—
296C4⋊Q8—31no—
297#126—182no—
298#125—32no—
299#124—92no—
300C22⋊Q8—62no—
301C22⋊Q8—61no—
302C22⋊Q8—181no—
303C4×Q8—31no—
304C4×Q8—92no—
305C4×D4—32no—
306C4×D4—91no—
307C4×D4D3211yescharacteristic
308#117—181no—
309C2×C4⋊C4—61no—
310#107—91no—
311#106—92no—
312C4⋊C8—31no—
313C4⋊C8—92no—
314#103—32no—
315#103—92no—
316#103—92no—
317#102—92no—
318#102—91no—
319#102—91no—
320C4×C8—92no—
321C4×C8—91no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—41no—
325C22×D3—61no—
326C22×D3—61no—
327C22×D3—121no—
328C3×Q8—62no—
329C3×Q8—62no—
330C3×Q8—62no—
331C3×Q8—241no—
332C3×D4—21no—
333C3×D4—21no—
334C3×D4—22no—
335C3×D4—41no—
336C3×D4#23712yes—
337C3×D4#23912yes—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—41no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—82no—
351C2×C3×C4—242no—
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—82no—
363C2×Dic3—121no—
364C2×Dic3C2×#6712yes—
365C2×Dic3C2×#6712yes—
366D12—62no—
367D12—61no—
368D12—61no—
369D12—61no—
370D12—61no—
371D12—121no—
372C4×D3—122no—
373C4×D3—122no—
374C4×D3—242no—
375Dic6—22no—
376Dic6—22no—
377Dic6—22no—
378Dic6—81no—
379C3×C8—62no—
380C3⋊C8—22no—
381C3⋊C8—62no—
382C3⋊C8—61no—
383C3⋊C8—61no—
384C3⋊C8—61no—
385C3⋊C8—61no—
386C3⋊C8—121no—
387C2×C32—42no—
388C2×C32#54811yescharacteristic
389C2×C32C2×#13511yescharacteristic
390C2×C32#57711yescharacteristic
391C3⋊D3—81no—
392C2×Q8—31no—
393C2×Q8—32no—
394C2×Q8—61no—
395C2×D4—91no—
396C2×D4C2×D3211yescharacteristic
397C22×C4—21no—
398C22×C4—62no—
399C22×C4—181no—
400SD16—64no—
401D8—182no—
402C2×C8—32no—
403C2×C8—91no—
404C2×C8—91no—
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—32no—
408C4⋊C4—62no—
409C4⋊C4—62no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—61no—
413C4⋊C4—91no—
414C4⋊C4—182no—
415C4⋊C4C2×D3211yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—62no—
418C22⋊C4—182no—
419C22⋊C4—182no—
420C22⋊C4—181no—
421C42—32no—
422C42—182no—
423C42C2×D3211yescharacteristic
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—42no—
428C22×C3—41no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C22×#6711yescharacteristic
436C2×D3—122no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—241no—
444C2×D3—241no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—41no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—62no—
454C3×C4—62no—
455C3×C4—81no—
456C3×C4—122no—
457C3×C4—122no—
458C3×C4#91612yes—
459C3×C4#95012yes—
460C3×C4C2×#23711yescharacteristic
461C3×C4C2×#23911yescharacteristic
462C3×C4#100711yescharacteristic
463C3×C4#101011yescharacteristic
464Dic3—22no—
465Dic3—22no—
466Dic3—42no—
467Dic3—42no—
468Dic3—121no—
469Dic3—121no—
470Dic3—241no—
471C32#336011yescharacteristic, complemented, Sylow
472C23—21no—
473C23—181no—
474Q8—62no—
475Q8—62no—
476Q8—62no—
477Q8—241no—
478D4—21no—
479D4—181no—
480D4—181no—
481D4#379612yes—
482C2×C4—21no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—42no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—181no—
489C2×C4—242no—
490C2×C4—362no—
491C2×C4D3×#6711yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C2×C4C22×D3211yescharacteristic
494C8—62no—
495C8—181no—
496C8—181no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—42no—
501C2×C3—42no—
502C2×C3—82no—
503C2×C3#559811yescharacteristic
504C2×C3C2×#91611yescharacteristic
505C2×C3#577811yescharacteristic
506C2×C3#581711yescharacteristic
507C2×C3C2×#95011yescharacteristic
508C2×C3#583611yescharacteristic
509D3—242no—
510D3—241no—
511D3—241no—
512C22—22no—
513C22—41no—
514C22—41no—
515C22—361no—
516C22—361no—
517C22—361no—
518C22C2×D3×#6711yescharacteristic
519C4—21no—
520C4—41no—
521C4—62no—
522C4—62no—
523C4—122no—
524C4—122no—
525C4—361no—
526C4#6393512yes—
527C4C2×#379611yescharacteristic
528C4#6429711yescharacteristic
529C3—21no—
530C3#8041511yescharacteristic, complemented
531C3#8363711yescharacteristic, complemented
532C2—42no—
533C2—721no—
534C2#1059490011yescharacteristic
535C2C2×#6393511yescharacteristic
536C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenterC4×D4D32
hypocenterC32#3360
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. #10593865C2semidirect
4. C3×#5019C2semidirect
6. Dic3×#214C2semidirect
7. #10590537C2semidirect
8. #10590493C2semidirect
9. #10590300C2semidirect
10. #10590290C2semidirect
11. #10590250C2semidirect
46. #5543D3semidirect
56. #5019D3semidirect
471. C32#3360semidirect
530. C3#80415semidirect
531. C3#83637semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
#105938652
C4×#37532
C3×#50192
#105914712
Dic3×#2142
#105905372
#105904932
#105903002
#105902902
#105902502
#836373
#804153