Finite Group Databasebeta

← #11807672

Subgroups — #11807672

Order 1152.

1167 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#935C211yesmaximal, characteristic
2#10592919C211yesmaximal, characteristic
3C3×#5221C211yesmaximal, characteristic
4#10591719C212yesmaximal, complemented
5#10591716C212yesmaximal, complemented
6#10591702C212yesmaximal, complemented
7#10591701C212yesmaximal, complemented
8#10591265C212yesmaximal, complemented
9#10591201C212yesmaximal, complemented
10#82840—31nomaximal
11#76309—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C2×#3757C2211yescharacteristic
16C2×#3757C2212yes—
17C2×C3×#217C2212yes—
18C2×C3×#217C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×#217C2211yescharacteristic
21C3×#935C418yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic32C2212yes—
29#63658C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33#63579C2212yes—
34C2×C3×#123—31no—
35C2×#935D311yescharacteristic
36C3×#390—31no—
37#5221D311yescharacteristic
38#5220—31no—
39#5220—31no—
40#5220—61no—
41#5212—32no—
42#4984—32no—
43#4980—32no—
44#4976—32no—
45#4951—32no—
46#4951—32no—
47#4950—32no—
48#4946—32no—
49#4945—32no—
50#4944—32no—
51#4942—32no—
52#4933—32no—
53C24×C32C2311yescharacteristic
54C24×C32C2311yescharacteristic
55C2×C32×D4—41no—
56C2×C32×D4—41no—
57C2×C32×D4C2×C414yes—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—42no—
60C22×C3⋊Dic3—41no—
61C22×C3⋊Dic3C2312yes—
62C22×C3⋊Dic3C2312yes—
63C22×C3×Dic3—41no—
64C22×C3×Dic3—41no—
65C22×C3×Dic3C2×C414yescomplemented
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70#3757—42no—
71#3757—41no—
72C3×#217—42no—
73C3×#217—42no—
74C3×#217C2×C418yes—
75C3×#217C2×C414yescomplemented
76C3×C4⋊Dic3—41no—
77C3×Dic3⋊C4C2×C418yescomplemented
78C3×C4×Dic3—41no—
79Dic3⋊Dic3—42no—
80Dic3⋊Dic3—42no—
81Dic3⋊Dic3—42no—
82Dic32—42no—
83#2376—91noSylow
84C22×C3×D4—21no—
85C22×C3×D4C2×D311yescharacteristic
86C22×C3×D4C2×D311yescharacteristic
87C23×C3×C4—31no—
88C23×Dic3—31no—
89C23×Dic3—31no—
90C23×Dic3—61no—
91C23×Dic3C2×D311yescharacteristic
92C3×#123—38no—
93C2×C3×C4⋊C4—32no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C22⋊C4—32no—
96C2×C3×C22⋊C4—31no—
97C2×C3×C22⋊C4—32no—
98C2×C3×C22⋊C4—32no—
99C2×C3×C42—31no—
100C2×#217—32no—
101C2×#217—31no—
102C2×#217—31no—
103C2×#217—32no—
104C2×#217—62no—
105C2×#217—61no—
106C2×#217C2×D312yes—
107C2×#217C2×D312yes—
108C2×#217C2×D312yes—
109C2×#217C2×D311yescharacteristic
110#935Dic318yescomplemented
111C2×C4⋊Dic3—32no—
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3C2×D311yescharacteristic
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4C2×D312yes—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3C2×D311yescharacteristic
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—62no—
133C23×C32—21no—
134C23×C32—21no—
135C23×C32—22no—
136C23×C32—22no—
137C23×C32—21no—
138C23×C32—21no—
139C23×C32—22no—
140C23×C32—22no—
141C23×C32C22×C412yes—
142C23×C32C22×C412yes—
143C23×C32C2411yescharacteristic
144C32×D4—44no—
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4C22×C412yes—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—44no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—44no—
166C2×C3×Dic3C22×C414yes—
167C2×C3×Dic3C22×C414yes—
168C2×#123—31no—
169#390—31no—
170#389—92no—
171#388—92no—
172#388—92no—
173#387—92no—
174#386—91no—
175#385—92no—
176#380—92no—
177C24×C3—21no—
178C24×C3—21no—
179C24×C3C22×D311yescharacteristic
180C24×C3C22×D311yescharacteristic
181C24×C3C22×D311yescharacteristic
182C24×C3C22×D311yescharacteristic
183C2×C3×D4—24no—
184C2×C3×D4—41no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—42no—
189C2×C3×D4—42no—
190C2×C3×D4C4×D314yes—
191C2×C3×D4C2×Dic314yes—
192C22×C3×C4—21no—
193C22×C3×C4—32no—
194C22×C3×C4—32no—
195C22×C3×C4—34no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—121no—
199C22×C3×C4—121no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—32no—
203C22×Dic3—32no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—41no—
207C22×Dic3—41no—
208C22×Dic3—62no—
209C22×Dic3—62no—
210C22×Dic3—121no—
211C22×Dic3—121no—
212C22×Dic3—122no—
213C22×Dic3—122no—
214C22×Dic3—124no—
215C22×Dic3—122no—
216C22×Dic3C2×Dic314yescomplemented
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C3×C4⋊C4—38no—
222C3×C4⋊C4—121no—
223C3×C22⋊C4—38no—
224C3×C22⋊C4—34no—
225C3×C22⋊C4—122no—
226C3×C22⋊C4—122no—
227C3×C42—121no—
228#217—42no—
229#217—42no—
230#217—122no—
231#217—121no—
232#217—121no—
233#217—122no—
234#217—124no—
235#217—122no—
236#217C2×Dic318yes—
237#217C2×Dic314yescomplemented
238C4⋊Dic3—41no—
239C4⋊Dic3—122no—
240C4⋊Dic3—122no—
241C4⋊Dic3—122no—
242Dic3⋊C4—122no—
243Dic3⋊C4—122no—
244Dic3⋊C4—122no—
245Dic3⋊C4C2×Dic318yescomplemented
246C4×Dic3—41no—
247C4×Dic3—122no—
248C4×Dic3—122no—
249C22×C32—22no—
250C22×C32—22no—
251C22×C32—24no—
252C22×C32—24no—
253C22×C32—41no—
254C22×C32—42no—
255C22×C32—41no—
256C22×C32—41no—
257C22×C32—42no—
258C22×C32—41no—
259C22×C32C23×C411yescharacteristic
260C22×C32H(5,𝔽2)11yescharacteristic
261C22×C32H(5,𝔽2)11yescharacteristic
262C22×C32H(5,𝔽2)12yes—
263C22×C322−1+412yes—
264C32×C4—22no—
265C3⋊Dic3—42no—
266C3⋊Dic3—42no—
267C3×Dic3—24no—
268C3×Dic3—24no—
269C3×Dic3—42no—
270C3×Dic3—42no—
271C22×D4D3211yescharacteristic
272C23×C4—31no—
273C23×C4—91no—
274#123—38no—
275C2×C4⋊C4—32no—
276C2×C4⋊C4—31no—
277C2×C4⋊C4—92no—
278C2×C4⋊C4—92no—
279C2×C4⋊C4—92no—
280C2×C22⋊C4—32no—
281C2×C22⋊C4—31no—
282C2×C22⋊C4—32no—
283C2×C22⋊C4—32no—
284C2×C22⋊C4—92no—
285C2×C22⋊C4—91no—
286C2×C42—31no—
287C2×C42—92no—
288#95—92no—
289#95—92no—
290#95—92no—
291#95—92no—
292#95—92no—
293C23×C3—22no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—22no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—21no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—42no—
320C23×C3C2×C4×D312yes—
321C23×C3C2×C4×D312yes—
322C23×C3C22×Dic312yes—
323C23×C3C22×Dic312yes—
324C23×C3C23×D311yescharacteristic
325C23×C3C23×D311yescharacteristic
326C3×D4—44no—
327C3×D4—44no—
328C3×D4—48no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—34no—
335C2×C3×C4—34no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—124no—
349C2×C3×C4C2×C4×D312yes—
350C2×C3×C4C22×Dic312yes—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—44no—
362C2×Dic3—64no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—122no—
380C2×Dic3—128no—
381C2×Dic3—124no—
382C2×Dic3—124no—
383C2×Dic3C22×Dic314yes—
384C2×Dic3C22×Dic314yes—
385C2×C32—42no—
386C2×C32—42no—
387C2×C32#51811yescharacteristic
388C2×C32#52012yes—
389C2×C32#56011yescharacteristic
390C2×C32#56212yes—
391C2×C32#56311yescharacteristic
392C24C2×D3211yescharacteristic
393C24C2×D3211yescharacteristic
394C2×D4—41no—
395C2×D4—41no—
396C2×D4D3×Dic314yes—
397C22×C4—32no—
398C22×C4—32no—
399C22×C4—34no—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—92no—
403C22×C4—92no—
404C22×C4—121no—
405C22×C4—121no—
406C22×C4—362no—
407C22×C4—361no—
408C22×C4C2×D3211yescharacteristic
409C4⋊C4—38no—
410C4⋊C4—121no—
411C4⋊C4—362no—
412C4⋊C4—362no—
413C4⋊C4—362no—
414C22⋊C4—38no—
415C22⋊C4—34no—
416C22⋊C4—122no—
417C22⋊C4—122no—
418C22⋊C4—362no—
419C22⋊C4—361no—
420C42—121no—
421C42—362no—
422C22×C3—24no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—24no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—24no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—44no—
437C22×C3—42no—
438C22×C3—44no—
439C22×C3—42no—
440C22×C3—44no—
441C22×C3—42no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3—41no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—82no—
455C22×C3—81no—
456C22×C3—81no—
457C22×C3C22×C4×D311yescharacteristic
458C22×C3#100412yes—
459C22×C3#100411yescharacteristic
460C22×C3#100411yescharacteristic
461C22×C3#100411yescharacteristic
462C22×C3#100411yescharacteristic
463C22×C3#100912yes—
464C22×C3#101012yes—
465C22×C3#101012yes—
466C22×C3C23×Dic311yescharacteristic
467C3×C4—22no—
468C3×C4—22no—
469C3×C4—42no—
470C3×C4—64no—
471C3×C4—64no—
472C3×C4—122no—
473C3×C4—122no—
474Dic3—24no—
475Dic3—24no—
476Dic3—42no—
477Dic3—42no—
478Dic3—124no—
479Dic3—122no—
480Dic3—122no—
481Dic3—122no—
482Dic3—122no—
483Dic3—242no—
484C32#237611yescharacteristic, complemented, Sylow
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23C2×D3×Dic312yes—
494C23C2×D3×Dic312yes—
495C23C22×D3211yescharacteristic
496D4—44no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—34no—
500C2×C4—34no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—124no—
512C2×C4—182no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—364no—
519C2×C4C2×D3×Dic312yes—
520C2×C3—22no—
521C2×C3—21no—
522C2×C3—22no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—44no—
526C2×C3—42no—
527C2×C3—42no—
528C2×C3—42no—
529C2×C3—42no—
530C2×C3—82no—
531C2×C3#548611yescharacteristic
532C2×C3#554612yes—
533C2×C3#562112yes—
534C2×C3#565111yescharacteristic
535C2×C3#566611yescharacteristic
536C2×C3#566712yes—
537C2×C3#567211yescharacteristic
538C2×C3#572011yescharacteristic
539C2×C3#579811yescharacteristic
540C2×C3#582712yes—
541C22—24no—
542C22—24no—
543C22—22no—
544C22—22no—
545C22—42no—
546C22—42no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22#6430912yes—
552C22#6431412yes—
553C22C22×D3×Dic311yescharacteristic
554C22#6433011yescharacteristic
555C22#6433011yescharacteristic
556C4—22no—
557C4—64no—
558C4—64no—
559C4—122no—
560C4—122no—
561C4—362no—
562C4—362no—
563C3—21no—
564C3#7630911yescharacteristic, complemented
565C3#8284011yescharacteristic, complemented
566C2—42no—
567C2—42no—
568C2#1059522212yes—
569C2#1059526312yes—
570C2#1059526611yescharacteristic
571C2#1059527611yescharacteristic
572C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
Fitting, prime radicalC22×C32×D4C22
socle, cosocleC23×C32C24
hypercenterC22×D4D32
hypocenterC32#2376
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591719C2semidirect
5. #10591716C2semidirect
6. #10591702C2semidirect
7. #10591701C2semidirect
8. #10591265C2semidirect
9. #10591201C2semidirect
21. C3×#935C4semidirect
65. C22×C3×Dic3C2×C4semidirect
75. C3×#217C2×C4semidirect
77. C3×Dic3⋊C4C2×C4semidirect
110. #935Dic3semidirect
216. C22×Dic3C2×Dic3semidirect
237. #217C2×Dic3semidirect
245. Dic3⋊C4C2×Dic3semidirect
484. C32#2376semidirect
564. C3#76309semidirect
565. C3#82840semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9352
#105929192
C3×#52212
#105917192
#105917162
#105917022
#105917012
#105912652
#105912012
#828403
#763093