Finite Group Databasebeta

← #11787980

Subgroups — #11787980

Order 1152.

843 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#886C211yesmaximal, characteristic
2#10595506C211yesmaximal, characteristic
3C2×#63580C211yesmaximal, characteristic
4#10591696C211yesmaximal, characteristic, complemented
5#10591696C211yesmaximal, characteristic, complemented
6#10589393C211yesmaximal, characteristic, complemented
7C3×#4527C211yesmaximal, characteristic, complemented
8#71704—31nomaximal
9#68963—31nomaximal
10C22×C3×#67C2211yescharacteristic
11C23×C3×Dic3C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C2×#3757C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3—21no—
19C3×#886—22no—
20C3×#886C414yescomplemented
21#67⋊Dic3—22no—
22Dic3×#67—22no—
23D3×#217—21no—
24#63955—21no—
25#63580—22no—
26#63579—22no—
27#63579—22no—
28C2×C3×#123—31no—
29#5798—31no—
30C2×#886D311yescharacteristic
31#5486—31no—
32C2×#834—31no—
33#5211—31no—
34#5211—31no—
35C2×#806—31no—
36#4943—31no—
37#4943—31no—
38C3×#342—31no—
39#4527—31no—
40#4527—31no—
41#4527—61no—
42#4527D311yescharacteristic, complemented
43C24×C32C2311yescharacteristic
44C23×C3×D3D411yescharacteristic
45C22×C32×C4—21no—
46C22×C3⋊Dic3—21no—
47C22×C3⋊Dic3D412yes—
48C2×C3×#67—21no—
49C2×C3×#67—21no—
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C2×C3×#67C2×C412yes—
53C2×C3×#67D412yes—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3C2×C412yescomplemented
62C22×C3×Dic3D411yescharacteristic
63C22×C3×Dic3D412yes—
64C2×D3×Dic3—22no—
65C32×C22⋊C4—21no—
66C32×C22⋊C4C2×C412yescomplemented
67#3757—21no—
68#3757—21no—
69#3757—21no—
70#3757—21no—
71C3×#217—21no—
72C3×#217—21no—
73C3×#217—21no—
74C3×#217—21no—
75C3×(C2×D3)⋊C4—24no—
76C3×C4⋊Dic3—24no—
77Dic3⋊Dic3—22no—
78(C2×D3)⋊Dic3—22no—
79Dic32—22no—
80#1890—91noSylow
81C22×C3×D4—31no—
82C23×C3×C4—31no—
83C22×#67C2×D311yescharacteristic
84C23×Dic3C2×D311yescharacteristic
85C3×#123—34no—
86C3×#123—62no—
87C2×C3×C4⋊C4—61no—
88C2×C3×C22⋊C4—21no—
89C2×C3×C22⋊C4—31no—
90C2×C3×C22⋊C4—31no—
91C2×C3×C22⋊C4—61no—
92C2×C3×C22⋊C4C2×D311yescharacteristic
93C2×C3×C22⋊C4C2×D311yescharacteristic
94C2×#217—31no—
95C2×#217—31no—
96C2×#217—31no—
97C2×#217—31no—
98C2×#217—61no—
99C2×#217—61no—
100C2×#217—61no—
101C2×#217C2×D311yescharacteristic
102C2×#217C2×D311yescharacteristic
103D4×Dic3—62no—
104D4×Dic3—62no—
105C4×#67—62no—
106C2×(C2×D3)⋊C4—21no—
107#926—61no—
108C2×C4⋊Dic3—21no—
109#886—22no—
110#886Dic314yescomplemented
111#67⋊C4—62no—
112D3×C22⋊C4—61no—
113#877—61no—
114#834—62no—
115C3⋊#95—62no—
116C3⋊#95—62no—
117C3⋊#95—62no—
118C3⋊#95—62no—
119#806—62no—
120C23×C32—42no—
121C23×C32C22×C411yescharacteristic
122C23×C32C2×D411yescharacteristic
123C23×C32C2×D411yescharacteristic
124C23×C32C2×D411yescharacteristic
125C23×C32C2×D411yescharacteristic
126C23×C32#4111yescharacteristic
127C23×C32#4111yescharacteristic
128C22×C3×D3—21no—
129C22×C3×D3—21no—
130C22×C3×D3—42no—
131C22×C3×D3C22⋊C412yes—
132C2×C32×C4—22no—
133C2×C32×C4—42no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3—42no—
137C2×C3⋊Dic3—42no—
138C3×#67—22no—
139C3×#67—22no—
140C3×#67—22no—
141C3×#67—22no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3—42no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3C22⋊C412yes—
156D3×Dic3—82no—
157C2×#123—31no—
158#518—91no—
159C2×#99—91no—
160#381—91no—
161#381—91no—
162#342—31no—
163#342—91no—
164C24×C3—21no—
165C24×C3—31no—
166C24×C3C22×D311yescharacteristic
167C24×C3C22×D311yescharacteristic
168C23×D3#6711yescharacteristic
169C2×C3×D4—32no—
170C2×C3×D4—32no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—31no—
178C22×C3×C4—32no—
179C22×C3×C4—32no—
180C22×C3×C4—41no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C2×#67—21no—
189C2×#67—21no—
190C2×#67—21no—
191C2×#67—21no—
192C2×#67C2×Dic312yes—
193C2×#67#6712yes—
194C22×Dic3—21no—
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3—21no—
201C22×Dic3—32no—
202C22×Dic3—32no—
203C22×Dic3—62no—
204C22×Dic3—62no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3—121no—
208C22×Dic3D1212yes—
209C22×Dic3C2×Dic312yescomplemented
210C22×Dic3#6711yescharacteristic
211C2×C4×D3—62no—
212C3×C4⋊C4—64no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—21no—
215C3×C22⋊C4—22no—
216C3×C22⋊C4—41no—
217C3×C22⋊C4—64no—
218C3×C22⋊C4—61no—
219C3×C22⋊C4—61no—
220C3×C22⋊C4—61no—
221C3×C22⋊C4—61no—
222C3×C22⋊C4C4×D312yescomplemented
223C3×C22⋊C4C2×Dic312yescomplemented
224#217—21no—
225#217—21no—
226#217—21no—
227#217—21no—
228#217—62no—
229#217—61no—
230#217—61no—
231#217—61no—
232#217—61no—
233#217—62no—
234#217—61no—
235#217—61no—
236#217—61no—
237#217—61no—
238#217—121no—
239#217—121no—
240#217—121no—
241(C2×D3)⋊C4—24no—
242(C2×D3)⋊C4—62no—
243C4⋊Dic3—24no—
244C4⋊Dic3—62no—
245Dic3⋊C4—62no—
246C4×Dic3—62no—
247C4×Dic3—62no—
248C22×C32—22no—
249C22×C32—22no—
250C22×C32—22no—
251C22×C32—41no—
252C22×C32—41no—
253C22×C32—41no—
254C22×C32—41no—
255C22×C32C2×C22⋊C411yescharacteristic
256C22×C32C4×D411yescharacteristic
257C22×C32C4×D411yescharacteristic
258C22×C32#12011yescharacteristic
259C22×C32#12111yescharacteristic
260C22×C32#12111yescharacteristic
261C22×C32#12311yescharacteristic
262C2×C3×D3—22no—
263C2×C3×D3—42no—
264C2×C3×D3—42no—
265C2×C3×D3—81no—
266C32×C4—42no—
267C3⋊Dic3—42no—
268C3⋊Dic3—81no—
269C3×Dic3—22no—
270C3×Dic3—42no—
271C3×Dic3—42no—
272C3×Dic3—81no—
273C22×D4—31no—
274C23×C4—31no—
275#123—34no—
276#123—62no—
277C4×D4—182no—
278C4×D4—182no—
279#117—181no—
280C2×C4⋊C4—61no—
281C2×C22⋊C4—31no—
282C2×C22⋊C4—31no—
283C2×C22⋊C4—61no—
284C2×C22⋊C4—91no—
285C2×C22⋊C4—91no—
286C2×C22⋊C4—181no—
287C2×C22⋊C4D3211yescharacteristic
288#99—182no—
289#95—182no—
290#95—182no—
291C23×C3—21no—
292C23×C3—21no—
293C23×C3—21no—
294C23×C3—21no—
295C23×C3—21no—
296C23×C3—21no—
297C23×C3—21no—
298C23×C3—32no—
299C23×C3—42no—
300C23×C3—42no—
301C23×C3—61no—
302C23×C3—61no—
303C23×C3—82no—
304C23×C3—122no—
305C23×C3C2×C4×D311yescharacteristic
306C23×C3C2×D1211yescharacteristic
307C23×C3#23511yescharacteristic
308C23×C3D3×D411yescharacteristic
309C23×C3D3×D411yescharacteristic
310C23×C3D3×D411yescharacteristic
311C23×C3D3×D411yescharacteristic
312C23×C3D3×D411yescharacteristic
313C23×C3#23711yescharacteristic
314C23×C3#23711yescharacteristic
315C23×C3#23911yescharacteristic
316C23×C3C22×Dic311yescharacteristic
317C23×C3C2×#6711yescharacteristic
318C23×C3C2×#6711yescharacteristic
319C22×D3—21no—
320C22×D3—21no—
321C22×D3—42no—
322C22×D3#21712yes—
323C3×D4—62no—
324C3×D4—62no—
325C3×D4—62no—
326C3×D4—62no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—32no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—82no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4—122no—
345C2×C3×C4—122no—
346C2×C3×C4—121no—
347#67—22no—
348#67—22no—
349#67—22no—
350#67—22no—
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—41no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3—41no—
361C2×Dic3—42no—
362C2×Dic3—42no—
363C2×Dic3—41no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—122no—
367C2×Dic3—122no—
368C2×Dic3—122no—
369C2×Dic3—122no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—242no—
375C2×Dic3—242no—
376C2×Dic3—242no—
377C2×Dic3#21712yes—
378C4×D3—242no—
379C2×C32—21no—
380C2×C32—21no—
381C2×C32—21no—
382C2×C32—21no—
383C2×C32—21no—
384C2×C32—21no—
385C2×C32#38611yescharacteristic
386C2×C32#45812yes—
387C3×D3—42no—
388C24—31no—
389C24C2×D3211yescharacteristic
390C2×D4—32no—
391C2×D4—32no—
392C2×D4—61no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—61no—
396C22×C4—21no—
397C22×C4—31no—
398C22×C4—32no—
399C22×C4—32no—
400C22×C4—61no—
401C22×C4—61no—
402C22×C4—61no—
403C22×C4—61no—
404C22×C4—61no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—92no—
408C22×C4—182no—
409C22×C4—181no—
410C4⋊C4—64no—
411C4⋊C4—182no—
412C22⋊C4—21no—
413C22⋊C4—64no—
414C22⋊C4—61no—
415C22⋊C4—61no—
416C22⋊C4—61no—
417C22⋊C4—61no—
418C22⋊C4—182no—
419C22⋊C4—181no—
420C22⋊C4—181no—
421C22⋊C4—181no—
422C22⋊C4—181no—
423C22⋊C4D3×Dic312yescomplemented
424C42—182no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—62no—
450C22×C3—81no—
451C22×C3—81no—
452C22×C3—81no—
453C22×C3—81no—
454C22×C3—122no—
455C22×C3—122no—
456C22×C3—241no—
457C22×C3C4×D1211yescharacteristic
458C22×C3D3×C22⋊C411yescharacteristic
459C22×C3#88211yescharacteristic
460C22×C3#88411yescharacteristic
461C22×C3#89311yescharacteristic
462C22×C3#89411yescharacteristic
463C22×C3#89511yescharacteristic
464C22×C3D4×Dic311yescharacteristic
465C22×C3D4×Dic311yescharacteristic
466C22×C3#93511yescharacteristic
467C22×C3#93711yescharacteristic
468C22×C3#93911yescharacteristic
469C22×C3#93911yescharacteristic
470C22×C3C2×#21711yescharacteristic
471C2×D3—22no—
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—81no—
475C3×C4—42no—
476C3×C4—42no—
477C3×C4—62no—
478C3×C4—82no—
479C3×C4—122no—
480C3×C4—122no—
481C3×C4—241no—
482Dic3—22no—
483Dic3—42no—
484Dic3—42no—
485Dic3—81no—
486Dic3—122no—
487Dic3—122no—
488Dic3—242no—
489Dic3—241no—
490Dic3—241no—
491Dic3—242no—
492C32#189011yescharacteristic, complemented, Sylow
493C23—32no—
494C23—42no—
495C23—61no—
496C23—61no—
497C23—122no—
498C23#379511yescharacteristic
499C23#379611yescharacteristic
500C23D3×D1211yescharacteristic
501C23#380211yescharacteristic
502C23C2×D3×Dic311yescharacteristic
503C23D3×#6711yescharacteristic
504C23D3×#6711yescharacteristic
505D4—62no—
506D4—62no—
507D4—62no—
508D4—62no—
509C2×C4—22no—
510C2×C4—32no—
511C2×C4—42no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4—121no—
521C2×C4—121no—
522C2×C4—122no—
523C2×C4—122no—
524C2×C4—121no—
525C2×C4—182no—
526C2×C4—362no—
527C2×C4—362no—
528C2×C4—361no—
529C2×C4—722no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—21no—
543C2×C3—22no—
544C2×C3—41no—
545C2×C3—41no—
546C2×C3—41no—
547C2×C3—41no—
548C2×C3—41no—
549C2×C3—41no—
550C2×C3—122no—
551C2×C3#466511yescharacteristic
552C2×C3#474212yes—
553C2×C3#505312yes—
554C2×C3#522011yescharacteristic
555D3—42no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—62no—
564C22—122no—
565C22—122no—
566C22—241no—
567C22#6388411yescharacteristic
568C22#6388511yescharacteristic
569C22#6388611yescharacteristic
570C22Dic3×D1211yescharacteristic
571C22#6389811yescharacteristic
572C22#6392211yescharacteristic
573C22D3×#21711yescharacteristic
574C4—42no—
575C4—62no—
576C4—122no—
577C4—122no—
578C4—241no—
579C4—362no—
580C4—721no—
581C3—21no—
582C3#6896311yescharacteristic, complemented
583C3#7170411yescharacteristic, complemented
584C2—21no—
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—122no—
591C2#1059040812yes—
592C2#1059137611yescharacteristic
subgroupG/H
centerC22#63922
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC22×C3×#67C22
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1890
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #10591696C2semidirect
5. #10591696C2semidirect
6. #10589393C2semidirect
7. C3×#4527C2semidirect
20. C3×#886C4semidirect
42. #4527D3semidirect
61. C22×C3×Dic3C2×C4semidirect
66. C32×C22⋊C4C2×C4semidirect
110. #886Dic3semidirect
209. C22×Dic3C2×Dic3semidirect
222. C3×C22⋊C4C4×D3semidirect
223. C3×C22⋊C4C2×Dic3semidirect
423. C22⋊C4D3×Dic3semidirect
492. C32#1890semidirect
582. C3#68963semidirect
583. C3#71704semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8862
#105955062
C2×#635802
#105916962
#105893932
C3×#45272
#717043
#689633