Finite Group Databasebeta

← #11807573

Subgroups — #11807573

Order 1152.

1275 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C3×#5220C211yesmaximal, characteristic
4#10591705C212yesmaximal, complemented
5#10591703C212yesmaximal, complemented
6#10591703C212yesmaximal, complemented
7Dic3×#217C212yesmaximal, complemented
8#10591263C212yesmaximal, complemented
9#10591243C212yesmaximal, complemented
10#76308—31nomaximal
11#74681—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C2×#3757C2212yes—
16C2×#3757C2211yescharacteristic
17#64144C418yescomplemented
18C2×#3750C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×#217C2212yes—
21C2×C3×#217C2212yes—
22C2×C3×#217C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×#3724C2212yes—
26C2×Dic32C2212yes—
27C2×Dic32C2212yes—
28C2×Dic32C2212yes—
29C3×C3⋊#95C2212yes—
30#63579C2212yes—
31#63579C2212yes—
32#63579C2212yes—
33#63579C2212yes—
34C2×#935—31no—
35C2×#935—31no—
36C2×#935—61no—
37C3×#390—31no—
38C3×#386—31no—
39#5221D311yescharacteristic
40#5220D311yescharacteristic
41C4×#217—32no—
42#4978—32no—
43#4945—32no—
44#4945—32no—
45#4944—32no—
46#4944—32no—
47Dic3×C22⋊C4—32no—
48Dic3×C22⋊C4—32no—
49Dic3×C22⋊C4—32no—
50C4×Dic3⋊C4—32no—
51#4655—32no—
52#4649—32no—
53C24×C32C2311yescharacteristic
54C24×C32C2311yescharacteristic
55C2×C32×D4—41no—
56C2×C32×D4—41no—
57C2×C32×D4C2×C414yes—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—41no—
60C22×C3⋊Dic3—41no—
61C22×C3⋊Dic3C2×C414yescomplemented
62C22×C3⋊Dic3C2312yes—
63C22×C3⋊Dic3C2312yes—
64C22×C3×Dic3—24no—
65C22×C3×Dic3—41no—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70#3757C2×C418yes—
71#3757C2×C414yescomplemented
72#3750C2×C418yescomplemented
73C3×#217—24no—
74C3×#217—24no—
75C3×#217—24no—
76C3×#217—41no—
77C3×C4⋊Dic3—41no—
78C3×C4×Dic3—41no—
79#3724—24no—
80Dic32—24no—
81Dic32—42no—
82Dic32—42no—
83#2374—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
92C2×C3×C4⋊C4—31no—
93C2×C3×C22⋊C4—32no—
94C2×C3×C22⋊C4—32no—
95C2×C3×C22⋊C4—32no—
96C2×C3×C22⋊C4—31no—
97C2×C3×C42—31no—
98C2×#217—32no—
99C2×#217—31no—
100C2×#217—32no—
101C2×#217—31no—
102C2×#217—62no—
103C2×#217—61no—
104C2×#217C2×D312yes—
105C2×#217C2×D312yes—
106C2×#217C2×D312yes—
107C2×#217C2×D311yescharacteristic
108#935—38no—
109#935—38no—
110#935—68no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—62no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—32no—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3C2×D311yescharacteristic
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—32no—
133C3⋊#95C2×D312yes—
134C23×C32—21no—
135C23×C32—21no—
136C23×C32—22no—
137C23×C32—22no—
138C23×C32—22no—
139C23×C32—22no—
140C23×C32—21no—
141C23×C32—21no—
142C23×C32C22×C412yes—
143C23×C32C22×C412yes—
144C23×C32C2411yescharacteristic
145C32×D4—44no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4C22×C412yes—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—44no—
154C2×C3⋊Dic3C22×C414yes—
155C2×C3⋊Dic3C22×C414yes—
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—22no—
166C2×C3×Dic3—44no—
167C2×C3×Dic3#4114yes—
168C2×C3×Dic3#4114yes—
169C2×#123—91no—
170#390—31no—
171#388—92no—
172#388—92no—
173#387—92no—
174#386—31no—
175C4×C4⋊C4—92no—
176C4×C22⋊C4—92no—
177C4×C22⋊C4—92no—
178C24×C3—21no—
179C24×C3—21no—
180C24×C3C22×D311yescharacteristic
181C24×C3C22×D311yescharacteristic
182C24×C3C22×D311yescharacteristic
183C24×C3C22×D311yescharacteristic
184C2×C3×D4—24no—
185C2×C3×D4—41no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4—42no—
190C2×C3×D4—42no—
191C2×C3×D4C4×D314yes—
192C2×C3×D4C4×D314yes—
193C22×C3×C4—21no—
194C22×C3×C4—32no—
195C22×C3×C4—32no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—64no—
199C22×C3×C4—121no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—24no—
203C22×Dic3—32no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—34no—
208C22×Dic3—34no—
209C22×Dic3—41no—
210C22×Dic3—62no—
211C22×Dic3—62no—
212C22×Dic3—64no—
213C22×Dic3—121no—
214C22×Dic3—121no—
215C22×Dic3—121no—
216C22×Dic3—121no—
217C22×Dic3—122no—
218C22×Dic3—122no—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D312yes—
223C3×C4⋊C4—121no—
224C3×C22⋊C4—64no—
225C3×C22⋊C4—64no—
226C3×C22⋊C4—64no—
227C3×C22⋊C4—121no—
228C3×C42—121no—
229#217—24no—
230#217—24no—
231#217—24no—
232#217—38no—
233#217—38no—
234#217—34no—
235#217—34no—
236#217—41no—
237#217—68no—
238#217—64no—
239C4⋊Dic3—41no—
240Dic3⋊C4—38no—
241Dic3⋊C4—38no—
242Dic3⋊C4—68no—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245C4×Dic3—41no—
246C4×Dic3—64no—
247C4×Dic3—64no—
248C4×Dic3—122no—
249C4×Dic3—122no—
250C4×Dic3—122no—
251C4×Dic3—122no—
252C22×C32—22no—
253C22×C32—24no—
254C22×C32—24no—
255C22×C32—22no—
256C22×C32—41no—
257C22×C32—42no—
258C22×C32—41no—
259C22×C32—41no—
260C22×C32—42no—
261C22×C32—41no—
262C22×C32C23×C411yescharacteristic
263C22×C32C2×#4112yes—
264C22×C32C2×#4112yes—
265C22×C32H(5,𝔽2)11yescharacteristic
266C22×C32H(5,𝔽2)11yescharacteristic
267C32×C4—22no—
268C3⋊Dic3—24no—
269C3⋊Dic3—24no—
270C3×Dic3—24no—
271C3×Dic3—24no—
272C3×Dic3—42no—
273C3×Dic3—42no—
274C22×D4D3211yescharacteristic
275C23×C4—31no—
276C23×C4—91no—
277#123—98no—
278C2×C4⋊C4—31no—
279C2×C4⋊C4—92no—
280C2×C4⋊C4—92no—
281C2×C22⋊C4—32no—
282C2×C22⋊C4—32no—
283C2×C22⋊C4—32no—
284C2×C22⋊C4—31no—
285C2×C22⋊C4—92no—
286C2×C22⋊C4—91no—
287C2×C42—31no—
288C2×C42—92no—
289C2×C42—92no—
290C2×C42—92no—
291#95—32no—
292#95—92no—
293#95—92no—
294#95—92no—
295#95—92no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—21no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—42no—
318C23×C3—42no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—42no—
322C23×C3—42no—
323C23×C3C2×C4×D312yes—
324C23×C3C2×C4×D312yes—
325C23×C3C2×C4×D312yes—
326C23×C3C2×C4×D312yes—
327C23×C3C23×D311yescharacteristic
328C23×C3C23×D311yescharacteristic
329C3×D4—44no—
330C3×D4—44no—
331C3×D4—48no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—34no—
338C2×C3×C4—34no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
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—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—124no—
352C2×C3×C4C2×C4×D312yes—
353C2×C3×C4C2×C4×D312yes—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—34no—
365C2×Dic3—34no—
366C2×Dic3—34no—
367C2×Dic3—34no—
368C2×Dic3—44no—
369C2×Dic3—64no—
370C2×Dic3—64no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—122no—
380C2×Dic3—122no—
381C2×Dic3—122no—
382C2×Dic3—122no—
383C2×Dic3—124no—
384C2×Dic3—124no—
385C2×Dic3—128no—
386C2×Dic3#23714yes—
387C2×Dic3#23714yes—
388C2×C32—42no—
389C2×C32—42no—
390C2×C32C4×#4112yes—
391C2×C32#51811yescharacteristic
392C2×C32#55111yescharacteristic
393C2×C32#55312yes—
394C2×C32#55911yescharacteristic
395C24C2×D3211yescharacteristic
396C24C2×D3211yescharacteristic
397C2×D4—41no—
398C2×D4—41no—
399C2×D4#62414yes—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—32no—
403C22×C4—32no—
404C22×C4—64no—
405C22×C4—92no—
406C22×C4—92no—
407C22×C4—94no—
408C22×C4—121no—
409C22×C4—361no—
410C22×C4—361no—
411C22×C4C2×D3211yescharacteristic
412C4⋊C4—98no—
413C4⋊C4—121no—
414C4⋊C4—184no—
415C22⋊C4—64no—
416C22⋊C4—64no—
417C22⋊C4—64no—
418C22⋊C4—94no—
419C22⋊C4—98no—
420C22⋊C4—121no—
421C42—121no—
422C42—184no—
423C42—362no—
424C42—362no—
425C22×C3—24no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—24no—
431C22×C3—24no—
432C22×C3—24no—
433C22×C3—24no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—44no—
440C22×C3—42no—
441C22×C3—44no—
442C22×C3—42no—
443C22×C3—44no—
444C22×C3—42no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—41no—
450C22×C3—41no—
451C22×C3—41no—
452C22×C3—41no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3—81no—
458C22×C3—82no—
459C22×C3—81no—
460C22×C3C22×C4×D311yescharacteristic
461C22×C3C22×C4×D311yescharacteristic
462C22×C3C2×#23712yes—
463C22×C3C2×#23712yes—
464C22×C3#100411yescharacteristic
465C22×C3#100411yescharacteristic
466C22×C3#100411yescharacteristic
467C22×C3#100411yescharacteristic
468C22×C3D3×#4112yes—
469C22×C3D3×#4112yes—
470C3×C4—22no—
471C3×C4—22no—
472C3×C4—42no—
473C3×C4—64no—
474C3×C4—64no—
475C3×C4—122no—
476C3×C4—122no—
477Dic3—24no—
478Dic3—24no—
479Dic3—42no—
480Dic3—42no—
481Dic3—64no—
482Dic3—64no—
483Dic3—64no—
484Dic3—64no—
485Dic3—124no—
486Dic3—124no—
487C32#237411yescharacteristic, complemented, Sylow
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23C2×#62412yes—
497C23C2×#62412yes—
498C23C22×D3211yescharacteristic
499D4—44no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—34no—
503C2×C4—34no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—94no—
515C2×C4—94no—
516C2×C4—124no—
517C2×C4—182no—
518C2×C4—182no—
519C2×C4—182no—
520C2×C4—182no—
521C2×C4—364no—
522C2×C4C2×#62412yes—
523C2×C3—21no—
524C2×C3—22no—
525C2×C3—22no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—44no—
529C2×C3—42no—
530C2×C3—42no—
531C2×C3—42no—
532C2×C3—42no—
533C2×C3—82no—
534C2×C3#548611yescharacteristic
535C2×C3#548611yescharacteristic
536C2×C3C4×#23712yes—
537C2×C3C4×#23712yes—
538C2×C3#558711yescharacteristic
539C2×C3#560112yes—
540C2×C3#561412yes—
541C2×C3#566411yescharacteristic
542C2×C3#567911yescharacteristic
543C2×C3#571311yescharacteristic
544C22—24no—
545C22—24no—
546C22—22no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—42no—
552C22—41no—
553C22—41no—
554C22D3×#23712yes—
555C22D3×#23712yes—
556C22C22×#62411yescharacteristic
557C22#6433011yescharacteristic
558C22#6433011yescharacteristic
559C4—22no—
560C4—64no—
561C4—64no—
562C4—122no—
563C4—122no—
564C4—184no—
565C4—184no—
566C3—21no—
567C3#7468111yescharacteristic, complemented
568C3#7630811yescharacteristic, complemented
569C2—42no—
570C2—42no—
571C2#1059517611yescharacteristic
572C2#1059517912yes—
573C2#1059519012yes—
574C2#1059520011yescharacteristic
575C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
Fitting, prime radicalC22×C32×D4C22
socle, cosocleC23×C32C24
hypercenterC22×D4D32
hypocenterC32#2374
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591705C2semidirect
5. #10591703C2semidirect
6. #10591703C2semidirect
7. Dic3×#217C2semidirect
8. #10591263C2semidirect
9. #10591243C2semidirect
17. #64144C4semidirect
61. C22×C3⋊Dic3C2×C4semidirect
71. #3757C2×C4semidirect
72. #3750C2×C4semidirect
487. C32#2374semidirect
567. C3#74681semidirect
568. C3#76308semidirect

Maximal subgroups

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

subgroupindex
C2×#641442
C3×#52212
C3×#52202
#105917052
#105917032
Dic3×#2172
#105912632
#105912432
#763083
#746813