Finite Group Databasebeta

← #11802405

Subgroups — #11802405

Order 1152.

1548 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64107C211yesmaximal, characteristic
2C32×#387C211yesmaximal, characteristic, complemented
3#10592689C211yesmaximal, characteristic
4C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10592639C211yesmaximal, characteristic
7C42×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#10592369C211yesmaximal, characteristic
9#10592365C211yesmaximal, characteristic
10#10592365C211yesmaximal, characteristic
11#10592365C211yesmaximal, characteristic
12#10592354C211yesmaximal, characteristic, complemented
13#10592352C211yesmaximal, characteristic, complemented
14#10592350C211yesmaximal, characteristic, complemented
15#10592348C211yesmaximal, characteristic, complemented
16#74942—34nomaximal
17C22×C4×C3⋊D3C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C42C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×C4×C3⋊Dic3C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35C2×C4×C3⋊Dic3C2211yescharacteristic
36C2×C4×C3⋊Dic3C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38C2×C4×C3⋊Dic3C2211yescharacteristic
39C2×C4×C3⋊Dic3C2211yescharacteristic
40#64107C418yescomplemented
41C32×#95C2211yescharacteristic
42C32×#95C2211yescharacteristic
43C32×#95C2211yescharacteristic
44C32×#95C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53C2×#898—34no—
54C3×#387D314yescomplemented
55#4990—34no—
56Dic3×C4⋊C4—34no—
57Dic3×C4⋊C4—34no—
58#4940—34no—
59C42×Dic3—34no—
60#4670—34no—
61#4666—34no—
62#4666—34no—
63#4666—34no—
64#4655—34no—
65#4653—34no—
66#4651—34no—
67#4649—34no—
68C23×C3⋊D3C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C2×C4×C3⋊D3—22no—
84C2×C4×C3⋊D3—22no—
85C2×C4×C3⋊D3—22no—
86C32×C4⋊C4—22no—
87C32×C4⋊C4C2×C414yescomplemented
88C32×C42—22no—
89#3752—22no—
90#3752—22no—
91#3752—22no—
92#3752C2×C414yes—
93#3752C2×C414yes—
94#3752C2×C414yes—
95C4⋊(C3⋊Dic3)—22no—
96C4⋊(C3⋊Dic3)C2×C414yescomplemented
97#3750—22no—
98#3750C2×C414yescomplemented
99C4×C3⋊Dic3—22no—
100C4×C3⋊Dic3—22no—
101C4×C3⋊Dic3—22no—
102C4×C3⋊Dic3—22no—
103C4×C3⋊Dic3—22no—
104C4×C3⋊Dic3—22no—
105C4×C3⋊Dic3—22no—
106C4×C3⋊Dic3—22no—
107C4×C3⋊Dic3C2×C414yescomplemented
108C4×#126—91noSylow
109C22×C4×D3—34no—
110C2×C3×C4⋊C4C2×D314yes—
111C2×C3×C4⋊C4C2×D314yes—
112C2×C3×C42C2×D314yes—
113C2×(C2×D3)⋊C4—34no—
114C2×(C2×D3)⋊C4—34no—
115C2×(C2×D3)⋊C4—34no—
116C2×(C2×D3)⋊C4—34no—
117C2×(C2×D3)⋊C4—34no—
118C2×(C2×D3)⋊C4—34no—
119C2×C4⋊Dic3—34no—
120C2×C4⋊Dic3—34no—
121C2×Dic3⋊C4—34no—
122C2×Dic3⋊C4—34no—
123C2×C4×Dic3—34no—
124C2×C4×Dic3—34no—
125C2×C4×Dic3—34no—
126C2×C4×Dic3—34no—
127C2×C4×Dic3—34no—
128C2×C4×Dic3—34no—
129C2×C4×Dic3—34no—
130C2×C4×Dic3—34no—
131C2×C4×Dic3—34no—
132#898—332no—
133C3×#95C2×D314yes—
134C3×#95C2×D314yes—
135C3×#95C2×D314yes—
136C3×#95C2×D314yes—
137C3⋊#95—34no—
138C3⋊#95—34no—
139C3⋊#95—34no—
140C3⋊#95—34no—
141C3⋊#95—34no—
142C3⋊#95—34no—
143C3⋊#95—34no—
144C3⋊#95—34no—
145C23×C32C2411yescharacteristic
146C22×C3⋊D3—21no—
147C22×C3⋊D3—21no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3—21no—
150C22×C3⋊D3—21no—
151C22×C3⋊D3—21no—
152C22×C3⋊D3C22×C412yes—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4C22×C412yes—
170C2×C32×C4C22×C412yes—
171C2×C32×C4C22×C412yes—
172C2×C32×C4#4112yes—
173C2×C32×C4#4112yes—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3C22×C412yes—
189C2×C3⋊Dic3C22×C412yes—
190C2×C3⋊Dic3C22×C412yes—
191C2×C3⋊Dic3#4112yes—
192C2×C3⋊Dic3#4112yes—
193C2×C3⋊Dic3#4112yes—
194C2×C3⋊Dic3#4112yes—
195C4×C3⋊D3—44no—
196C2×#126—91no—
197#388—91no—
198#388—91no—
199#388—91no—
200#387—91no—
201#387—91no—
202#387C3⋊D311yescharacteristic, complemented
203#383—91no—
204C4×C4⋊C4—91no—
205C4×C4⋊C4—91no—
206C4×C4⋊C4—91no—
207C4×C22⋊C4—91no—
208C4×C22⋊C4—91no—
209C4×C22⋊C4—91no—
210C43—91no—
211C23×D3—34no—
212C22×C3×C4C22×D314yes—
213C22×C3×C4C22×D314yes—
214C22×C3×C4C22×D314yes—
215C22×C3×C4C22×D314yes—
216C22×C3×C4C22×D314yes—
217C22×C3×C4C22×D314yes—
218C22×C3×C4C22×D314yes—
219C22×Dic3—34no—
220C22×Dic3—34no—
221C22×Dic3—34no—
222C22×Dic3—34no—
223C22×Dic3—34no—
224C22×Dic3—34no—
225C22×Dic3—34no—
226C2×C4×D3—68no—
227C2×C4×D3—68no—
228C2×C4×D3—68no—
229C3×C4⋊C4—28no—
230C3×C4⋊C4C4×D3116yescomplemented
231C3×C42—28no—
232(C2×D3)⋊C4—316no—
233(C2×D3)⋊C4—316no—
234(C2×D3)⋊C4—316no—
235(C2×D3)⋊C4—68no—
236(C2×D3)⋊C4—68no—
237(C2×D3)⋊C4—68no—
238C4⋊Dic3—316no—
239C4⋊Dic3—68no—
240Dic3⋊C4—316no—
241Dic3⋊C4—68no—
242C4×Dic3—316no—
243C4×Dic3—68no—
244C4×Dic3—68no—
245C4×Dic3—68no—
246C4×Dic3—68no—
247C4×Dic3—68no—
248C4×Dic3—68no—
249C4×Dic3—68no—
250C4×Dic3—68no—
251C22×C32C23×C411yescharacteristic
252C22×C32C2×#4111yescharacteristic
253C22×C32C2×#4111yescharacteristic
254C22×C32C2×#4111yescharacteristic
255C22×C32C2×#4111yescharacteristic
256C22×C32C2×#4111yescharacteristic
257C22×C32C2×#4111yescharacteristic
258C2×C3⋊D3—22no—
259C2×C3⋊D3—22no—
260C2×C3⋊D3—22no—
261C2×C3⋊D3—41no—
262C2×C3⋊D3—41no—
263C2×C3⋊D3—41no—
264C2×C3⋊D3—41no—
265C32×C4—22no—
266C32×C4—22no—
267C32×C4—22no—
268C32×C4—22no—
269C32×C4—22no—
270C32×C4—41no—
271C32×C4—41no—
272C3⋊Dic3—22no—
273C3⋊Dic3—22no—
274C3⋊Dic3—22no—
275C3⋊Dic3—22no—
276C3⋊Dic3—41no—
277C3⋊Dic3—41no—
278C3⋊Dic3#12614yescomplemented
279C23×C4—91no—
280#126—98no—
281C2×C4⋊C4—91no—
282C2×C4⋊C4—91no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4C2×C3⋊D311yescharacteristic
286C2×C4⋊C4C2×C3⋊D311yescharacteristic
287C2×C22⋊C4—91no—
288C2×C22⋊C4—91no—
289C2×C22⋊C4—91no—
290C2×C22⋊C4—91no—
291C2×C22⋊C4—91no—
292C2×C22⋊C4—91no—
293C2×C42—91no—
294C2×C42—91no—
295C2×C42—91no—
296C2×C42—91no—
297C2×C42—91no—
298C2×C42—91no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42—91no—
302C2×C42C2×C3⋊D311yescharacteristic
303#95—91no—
304#95—91no—
305#95—91no—
306#95—91no—
307#95—91no—
308#95—91no—
309#95—91no—
310#95—91no—
311#95C2×C3⋊D311yescharacteristic
312#95C2×C3⋊D311yescharacteristic
313#95C2×C3⋊D311yescharacteristic
314#95C2×C3⋊D311yescharacteristic
315C23×C3C23×D314yes—
316C22×D3—38no—
317C22×D3—64no—
318C22×D3—64no—
319C22×D3—64no—
320C22×D3—64no—
321C22×D3—64no—
322C22×D3—64no—
323C2×C3×C4—24no—
324C2×C3×C4—24no—
325C2×C3×C4—24no—
326C2×C3×C4—24no—
327C2×C3×C4—24no—
328C2×C3×C4—24no—
329C2×C3×C4—24no—
330C2×C3×C4—24no—
331C2×C3×C4—24no—
332C2×C3×C4—24no—
333C2×C3×C4—24no—
334C2×C3×C4—24no—
335C2×C3×C4—24no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—24no—
339C2×C3×C4C2×C4×D318yes—
340C2×C3×C4C2×C4×D318yes—
341C2×C3×C4C2×C4×D318yes—
342C2×C3×C4#23718yes—
343C2×C3×C4#23918yes—
344C2×Dic3—38no—
345C2×Dic3—38no—
346C2×Dic3—38no—
347C2×Dic3—38no—
348C2×Dic3—38no—
349C2×Dic3—38no—
350C2×Dic3—38no—
351C2×Dic3—64no—
352C2×Dic3—64no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—64no—
357C2×Dic3—64no—
358C2×Dic3—64no—
359C2×Dic3—64no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—64no—
363C2×Dic3—64no—
364C2×Dic3—64no—
365C4×D3—1216no—
366C2×C32C4×#4111yescharacteristic
367C2×C32C4×#4111yescharacteristic
368C2×C32C4×#4111yescharacteristic
369C2×C32C2×#12611yescharacteristic
370C2×C32#52911yescharacteristic
371C2×C32#52911yescharacteristic
372C2×C32#52911yescharacteristic
373C3⋊D3—42no—
374C24—91no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—91no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—91no—
382C22×C4—182no—
383C22×C4—182no—
384C22×C4—182no—
385C22×C4C22×C3⋊D311yescharacteristic
386C22×C4C22×C3⋊D311yescharacteristic
387C22×C4C22×C3⋊D311yescharacteristic
388C22×C4C22×C3⋊D311yescharacteristic
389C22×C4C22×C3⋊D311yescharacteristic
390C22×C4C22×C3⋊D311yescharacteristic
391C22×C4C22×C3⋊D311yescharacteristic
392C4⋊C4—22no—
393C4⋊C4—94no—
394C4⋊C4—94no—
395C4⋊C4—182no—
396C4⋊C4—182no—
397C4⋊C4C4×C3⋊D314yescomplemented
398C22⋊C4—94no—
399C22⋊C4—94no—
400C22⋊C4—94no—
401C22⋊C4—182no—
402C22⋊C4—182no—
403C22⋊C4—182no—
404C42—22no—
405C42—94no—
406C42—182no—
407C42—182no—
408C42—182no—
409C42—182no—
410C42—182no—
411C42—182no—
412C42—182no—
413C42—182no—
414C22×C3C22×C4×D314yes—
415C22×C3C2×#23714yes—
416C22×C3C2×#23914yes—
417C22×C3D3×#4114yes—
418C22×C3D3×#4114yes—
419C22×C3D3×#4114yes—
420C22×C3D3×#4114yes—
421C2×D3—68no—
422C2×D3—68no—
423C2×D3—68no—
424C2×D3—124no—
425C2×D3—124no—
426C2×D3—124no—
427C2×D3—124no—
428C3×C4—28no—
429C3×C4—28no—
430C3×C4—28no—
431C3×C4—28no—
432C3×C4—28no—
433C3×C4—44no—
434C3×C4—44no—
435Dic3—316no—
436Dic3—68no—
437Dic3—68no—
438Dic3—68no—
439Dic3—68no—
440Dic3—124no—
441Dic3—124no—
442C32C4×#12611yescharacteristic, complemented, Sylow
443C23—92no—
444C23—181no—
445C23—181no—
446C23—181no—
447C23—181no—
448C23—181no—
449C23—181no—
450C23C23×C3⋊D311yescharacteristic
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—92no—
468C2×C4—92no—
469C2×C4—92no—
470C2×C4—92no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—92no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—364no—
489C2×C4C2×C4×C3⋊D312yes—
490C2×C4C2×C4×C3⋊D312yes—
491C2×C4C2×C4×C3⋊D312yes—
492C2×C4#383012yes—
493C2×C4#383212yes—
494C2×C3#552214yes—
495C2×C3C4×#23714yes—
496C2×C3C4×#23914yes—
497C2×C3#562414yes—
498C2×C3#564914yes—
499C2×C3#569114yes—
500C2×C3D3×#12614yes—
501D3—128no—
502C22—182no—
503C22—182no—
504C22—182no—
505C22—361no—
506C22—361no—
507C22—361no—
508C22—361no—
509C22C22×C4×C3⋊D311yescharacteristic
510C22C2×#383011yescharacteristic
511C22C2×#383211yescharacteristic
512C22#41×C3⋊D311yescharacteristic
513C22#41×C3⋊D311yescharacteristic
514C22#41×C3⋊D311yescharacteristic
515C22#41×C3⋊D311yescharacteristic
516C4—22no—
517C4—22no—
518C4—22no—
519C4—22no—
520C4—22no—
521C4—41no—
522C4—41no—
523C4—94no—
524C4—182no—
525C4—182no—
526C4—182no—
527C4—182no—
528C4—361no—
529C4—361no—
530C3#7494214yescomplemented
531C2—362no—
532C2#1059599311yescharacteristic
533C2C4×#383011yescharacteristic
534C2C4×#383211yescharacteristic
535C2#1059609511yescharacteristic
536C2#1059612011yescharacteristic
537C2#1059616211yescharacteristic
538C2C3⋊D3×#12611yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#387C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#387C3⋊D3
hypocenterC32C4×#126
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C32×#387C2semidirect
4. C4⋊C4×C3⋊Dic3C2semidirect
5. C4⋊C4×C3⋊Dic3C2semidirect
7. C42×C3⋊Dic3C2semidirect
12. #10592354C2semidirect
13. #10592352C2semidirect
14. #10592350C2semidirect
15. #10592348C2semidirect
40. #64107C4semidirect
54. C3×#387D3semidirect
87. C32×C4⋊C4C2×C4semidirect
96. C4⋊(C3⋊Dic3)C2×C4semidirect
98. #3750C2×C4semidirect
107. C4×C3⋊Dic3C2×C4semidirect
202. #387C3⋊D3semidirect
230. C3×C4⋊C4C4×D3semidirect
278. C3⋊Dic3#126semidirect
397. C4⋊C4C4×C3⋊D3semidirect
442. C32C4×#126semidirect
530. C3#74942semidirect

Maximal subgroups

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

subgroupindex
C2×#641072
C32×#3872
#105926892
C4⋊C4×C3⋊Dic32
#105926392
C42×C3⋊Dic32
#105923692
#105923652
#105923542
#105923522
#105923502
#105923482
#749423