Finite Group Databasebeta

← #11801059

Subgroups — #11801059

Order 1152.

2293 conjugacy classes of subgroups.

The subgroup lattice has 611 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic
2C2×#63841C212yesmaximal, complemented
3#10592911C211yesmaximal, characteristic, complemented
4C3×#5212C211yesmaximal, characteristic, complemented
5#10591706C212yesmaximal
6Dic3×#217C212yesmaximal, complemented
7#10591313C212yesmaximal, complemented
8#10591294C212yesmaximal, complemented
9#10591237C212yesmaximal, complemented
10#84027—31nomaximal
11#73862—31nomaximal
12C24×C3×D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3×Dic3C2211yescharacteristic
15C22×C3×C4×D3—28no—
16C22×C3×C4×D3C418yescomplemented
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×#3757C2212yes—
22C2×C4⋊(C3⋊Dic3)C2212yescomplemented
23C2×C3×#217C2212yes—
24C2×C3×C4⋊Dic3C2212yescomplemented
25C2×(C2×D3)⋊Dic3C2214yes—
26C2×(C2×D3)⋊Dic3C2214yes—
27C2×Dic32C2214yescomplemented
28#63841—28no—
29#63658C2212yescomplemented
30C3×C3⋊#95C2212yescomplemented
31#63579C2214yescomplemented
32C24×C3×C4—31no—
33C23×C4×D3D311yescharacteristic
34C2×#926—32no—
35C2×#892—32no—
36C3×#380—31no—
37#5247—32no—
38#5212—31no—
39#5212—31no—
40#5212—32no—
41#5212—61no—
42#5212D311yescharacteristic, complemented
43#5211—32no—
44C4×#217—32no—
45C4×#217—32no—
46#4987—32no—
47#4955—32no—
48Dic3×C22⋊C4—32no—
49#4666—32no—
50#4664—32no—
51C24×C32C2311yescharacteristic
52C23×C3×D3—22no—
53C23×C3×D3—22no—
54C23×C3×D3—24no—
55C23×C3×D3—24no—
56C23×C3×D3C2×C414yes—
57C23×C3×D3C2311yescharacteristic
58C23×C3×D3C2311yescharacteristic
59C22×C32×C4—24no—
60C22×C32×C4C2×C414yes—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C3⋊Dic3C2314yes—
64C22×C3×Dic3—24no—
65C22×C3×Dic3C2×C414yes—
66C22×C3×Dic3C2314yes—
67C22×C3×Dic3C2311yescharacteristic
68C22×C3×Dic3C2311yescharacteristic
69C2×C3×C4×D3—24no—
70C2×C3×C4×D3—24no—
71C2×C3×C4×D3—24no—
72C2×C3×C4×D3—232no—
73C2×C3×C4×D3C2×C414yes—
74C2×C3×C4×D3C2×C414yes—
75C2×C3×C4×D3C2×C414yes—
76C2×C3×C4×D3C2×C414yes—
77C2×C3×C4×D3D418yes—
78#3757—24no—
79C4⋊(C3⋊Dic3)—24no—
80C3×#217—24no—
81C3×C4⋊Dic3—24no—
82(C2×D3)⋊Dic3—28no—
83(C2×D3)⋊Dic3—28no—
84Dic32—28no—
85#2280—91noSylow
86C25×C3—31no—
87C24×D3C2×D311yescharacteristic
88C23×C3×C4—21no—
89C23×C3×C4—31no—
90C23×C3×C4—31no—
91C23×C3×C4—38no—
92C23×C3×C4—31no—
93C23×C3×C4—31no—
94C23×C3×C4—31no—
95C23×C3×C4—68no—
96C23×C3×C4C2×D311yescharacteristic
97C23×C3×C4C2×D311yescharacteristic
98C23×Dic3C2×D311yescharacteristic
99C22×C4×D3—28no—
100C22×C4×D3Dic318yescomplemented
101C22×C4×D3C2×D311yescharacteristic
102C22×C4×D3C2×D311yescharacteristic
103C22×C4×D3C2×D311yescharacteristic
104C22×C4×D3C2×D311yescharacteristic
105C2×C3×C4⋊C4—32no—
106C2×C3×C22⋊C4—32no—
107C2×#217—32no—
108C2×#217—32no—
109C2×#217—34no—
110C2×#217—34no—
111C2×#217—62no—
112C2×#217C2×D312yes—
113C2×(C2×D3)⋊C4—34no—
114C2×(C2×D3)⋊C4—34no—
115#926—68no—
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—62no—
119C2×C4⋊Dic3C2×D312yescomplemented
120C2×C4×Dic3—34no—
121C2×C4×Dic3—34no—
122#892—68no—
123C3×#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—34no—
127C3⋊#95—34no—
128C3⋊#95—62no—
129C3⋊#95C2×D312yescomplemented
130C23×C32—22no—
131C23×C32—22no—
132C23×C32C22×C412yes—
133C23×C32#4112yes—
134C23×C32#4112yes—
135C23×C32C2411yescharacteristic
136C22×C3×D3—216no—
137C22×C3×D3—216no—
138C22×C3×D3—28no—
139C22×C3×D3—22no—
140C22×C3×D3—21no—
141C22×C3×D3—21no—
142C22×C3×D3—21no—
143C22×C3×D3—21no—
144C22×C3×D3—22no—
145C22×C3×D3—28no—
146C22×C3×D3—28no—
147C22×C3×D3C22×C412yes—
148C22×C3×D3C22×C412yes—
149C22×C3×D3C2×D414yes—
150C22×C3×D3#4114yes—
151C2×C32×C4—22no—
152C2×C32×C4—28no—
153C2×C32×C4C22×C412yes—
154C2×C32×C4C22×C412yes—
155C2×C32×C4C2×D414yes—
156C2×C3⋊Dic3—24no—
157C2×C3⋊Dic3—24no—
158C2×C3⋊Dic3—24no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—28no—
161C2×C3×Dic3—24no—
162C2×C3×Dic3—24no—
163C2×C3×Dic3—24no—
164C2×C3×Dic3C22×C412yes—
165C2×C3×Dic3C22×C412yes—
166C2×C3×Dic3C2×D414yes—
167C3×C4×D3—28no—
168C3×C4×D3—28no—
169C3×C4×D3—28no—
170C3×C4×D3C22⋊C4116yescomplemented
171C24×C4—31no—
172C2×#117—92no—
173#381—92no—
174#380—31no—
175#380—92no—
176#380—91no—
177#379—92no—
178C4×C22⋊C4—92no—
179C4×C22⋊C4—92no—
180C24×C3—21no—
181C24×C3—31no—
182C24×C3—31no—
183C24×C3—34no—
184C24×C3—64no—
185C24×C3—64no—
186C24×C3—62no—
187C24×C3—62no—
188C24×C3C22×D311yescharacteristic
189C24×C3C22×D311yescharacteristic
190C23×D3—22no—
191C23×D3—22no—
192C23×D3—24no—
193C23×D3—24no—
194C23×D3C2×Dic314yes—
195C23×D3C22×D311yescharacteristic
196C23×D3C22×D311yescharacteristic
197C22×C3×C4—24no—
198C22×C3×C4—24no—
199C22×C3×C4—24no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—31no—
203C22×C3×C4—34no—
204C22×C3×C4—38no—
205C22×C3×C4—34no—
206C22×C3×C4—31no—
207C22×C3×C4—34no—
208C22×C3×C4—34no—
209C22×C3×C4—34no—
210C22×C3×C4—34no—
211C22×C3×C4—44no—
212C22×C3×C4—64no—
213C22×C3×C4—632no—
214C22×C3×C4—64no—
215C22×C3×C4—64no—
216C22×C3×C4—64no—
217C22×C3×C4C4×D314yes—
218C22×C3×C4C2×Dic314yes—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×Dic3—24no—
224C22×Dic3—34no—
225C22×Dic3—34no—
226C22×Dic3—64no—
227C22×Dic3C2×Dic314yes—
228C22×Dic3C22×D314yes—
229C22×Dic3C22×D311yescharacteristic
230C22×Dic3C22×D311yescharacteristic
231C2×C4×D3—24no—
232C2×C4×D3—24no—
233C2×C4×D3—24no—
234C2×C4×D3—232no—
235C2×C4×D3C2×Dic314yes—
236C2×C4×D3C2×Dic314yes—
237C2×C4×D3C2×Dic314yes—
238C2×C4×D3C2×Dic314yes—
239C2×C4×D3#6718yes—
240C3×C4⋊C4—64no—
241C3×C22⋊C4—64no—
242#217—24no—
243#217—68no—
244#217—68no—
245#217—64no—
246#217—64no—
247#217—124no—
248(C2×D3)⋊C4—68no—
249(C2×D3)⋊C4—68no—
250C4⋊Dic3—24no—
251C4⋊Dic3—64no—
252C4⋊Dic3—64no—
253C4⋊Dic3—124no—
254C4×Dic3—68no—
255C4×Dic3—68no—
256C22×C32—22no—
257C22×C32—22no—
258C22×C32—24no—
259C22×C32—24no—
260C22×C32#11714yescomplemented
261C22×C32C23×C411yescharacteristic
262C22×C32C22×D412yes—
263C22×C32C2×#4111yescharacteristic
264C22×C32C2×#4111yescharacteristic
265C22×C32C2×#4112yes—
266C2×C3×D3—232no—
267C2×C3×D3—22no—
268C2×C3×D3—22no—
269C2×C3×D3—22no—
270C2×C3×D3—22no—
271C2×C3×D3—24no—
272C2×C3×D3—24no—
273C2×C3×D3—24no—
274C2×C3×D3—24no—
275C2×C3×D3C2×C22⋊C414yes—
276C2×C3×D3#11714yescomplemented
277C32×C4—22no—
278C32×C4C2×C22⋊C414yes—
279C3⋊Dic3—44no—
280C3×Dic3—22no—
281C3×Dic3—44no—
282C3×Dic3C2×C22⋊C414yes—
283C25—31no—
284C23×C4—31no—
285C23×C4—31no—
286C23×C4—38no—
287C23×C4—31no—
288C23×C4—31no—
289C23×C4—31no—
290C23×C4—68no—
291C23×C4D3211yescharacteristic
292#117—188no—
293C2×C4⋊C4—32no—
294C2×C4⋊C4—92no—
295C2×C22⋊C4—32no—
296C2×C22⋊C4—94no—
297C2×C22⋊C4—94no—
298C2×C22⋊C4—92no—
299C2×C42—94no—
300#95—32no—
301#95—94no—
302#95—92no—
303C23×C3—22no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—21no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—32no—
312C23×C3—32no—
313C23×C3—34no—
314C23×C3—34no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3—68no—
318C23×C3—68no—
319C23×C3—616no—
320C23×C3—616no—
321C23×C3—68no—
322C23×C3—62no—
323C23×C3—61no—
324C23×C3—61no—
325C23×C3—61no—
326C23×C3—61no—
327C23×C3—62no—
328C23×C3C2×C4×D312yes—
329C23×C3#23512yes—
330C23×C3#23512yes—
331C23×C3#23712yes—
332C23×C3#23912yes—
333C23×C3C22×Dic312yes—
334C23×C3C23×D311yescharacteristic
335C23×C3C23×D311yescharacteristic
336C22×D3—216no—
337C22×D3—216no—
338C22×D3—28no—
339C22×D3—21no—
340C22×D3—21no—
341C22×D3—21no—
342C22×D3—21no—
343C22×D3—22no—
344C22×D3—22no—
345C22×D3—28no—
346C22×D3—28no—
347C22×D3#23514yes—
348C22×D3C22×Dic312yes—
349C22×D3C22×Dic312yes—
350C22×D3C2×#6714yes—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—28no—
354C2×C3×C4—28no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—24no—
358C2×C3×C4—32no—
359C2×C3×C4—34no—
360C2×C3×C4—316no—
361C2×C3×C4—32no—
362C2×C3×C4—48no—
363C2×C3×C4—42no—
364C2×C3×C4—68no—
365C2×C3×C4—68no—
366C2×C3×C4—68no—
367C2×C3×C4—62no—
368C2×C3×C4—68no—
369C2×C3×C4—64no—
370C2×C3×C4—64no—
371C2×C3×C4—64no—
372C2×C3×C4C2×C4×D312yes—
373C2×C3×C4C2×C4×D312yes—
374C2×C3×C4D3×D414yes—
375C2×C3×C4C22×Dic312yes—
376C2×C3×C4C22×Dic312yes—
377C2×C3×C4C2×#6714yes—
378C2×Dic3—22no—
379C2×Dic3—28no—
380C2×Dic3—24no—
381C2×Dic3—24no—
382C2×Dic3—24no—
383C2×Dic3—64no—
384C2×Dic3—64no—
385C2×Dic3—64no—
386C2×Dic3—64no—
387C2×Dic3—64no—
388C2×Dic3—64no—
389C2×Dic3—124no—
390C2×Dic3—124no—
391C2×Dic3—124no—
392C2×Dic3C22×Dic312yes—
393C2×Dic3C22×Dic312yes—
394C2×Dic3C2×#6714yes—
395C4×D3—28no—
396C4×D3—28no—
397C4×D3—28no—
398C4×D3#217116yescomplemented
399C2×C32—24no—
400C2×C32C22×C22⋊C411yescharacteristic
401C2×C32C2×#11711yescharacteristic
402C2×C32C2×#11711yescharacteristic
403C2×C32#52512yes—
404C2×C32#52512yes—
405C3×D3—24no—
406C3×D3—24no—
407C24—31no—
408C24—31no—
409C24—34no—
410C24—64no—
411C24—64no—
412C24—62no—
413C24—62no—
414C24C2×D3211yescharacteristic
415C22×C4—24no—
416C22×C4—31no—
417C22×C4—34no—
418C22×C4—38no—
419C22×C4—31no—
420C22×C4—34no—
421C22×C4—34no—
422C22×C4—34no—
423C22×C4—34no—
424C22×C4—34no—
425C22×C4—64no—
426C22×C4—632no—
427C22×C4—64no—
428C22×C4—64no—
429C22×C4—64no—
430C22×C4—94no—
431C22×C4D3×Dic314yes—
432C22×C4C2×D3211yescharacteristic
433C22×C4C2×D3211yescharacteristic
434C4⋊C4—64no—
435C4⋊C4—184no—
436C22⋊C4—64no—
437C22⋊C4—188no—
438C22⋊C4—188no—
439C22⋊C4—184no—
440C42—188no—
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—24no—
445C22×C3—24no—
446C22×C3—22no—
447C22×C3—24no—
448C22×C3—24no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—22no—
452C22×C3—21no—
453C22×C3—22no—
454C22×C3—24no—
455C22×C3—34no—
456C22×C3—34no—
457C22×C3—42no—
458C22×C3—44no—
459C22×C3—42no—
460C22×C3—44no—
461C22×C3—632no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—62no—
466C22×C3—64no—
467C22×C3—64no—
468C22×C3—64no—
469C22×C3—64no—
470C22×C3#89214yescomplemented
471C22×C3#92614yescomplemented
472C22×C3C22×C4×D311yescharacteristic
473C22×C3C2×#23511yescharacteristic
474C22×C3C2×#23511yescharacteristic
475C22×C3C2×#23512yes—
476C22×C3C2×D3×D412yes—
477C22×C3C2×#23711yescharacteristic
478C22×C3C2×#23911yescharacteristic
479C22×C3D3×#4112yes—
480C22×C3C23×Dic311yescharacteristic
481C22×C3C22×#6712yes—
482C2×D3—232no—
483C2×D3—22no—
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—24no—
487C2×D3—24no—
488C2×D3—24no—
489C2×D3—24no—
490C2×D3—22no—
491C2×D3#92614yescomplemented
492C2×D3C2×#21714yes—
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—24no—
496C3×C4—34no—
497C3×C4—42no—
498C3×C4—62no—
499C3×C4—124no—
500C3×C4D3×C22⋊C414yes—
501C3×C4C2×#21714yes—
502Dic3—22no—
503Dic3—44no—
504Dic3—124no—
505Dic3—124no—
506Dic3—244no—
507Dic3C2×#21714yes—
508C32#228011yescharacteristic, complemented, Sylow
509C23—22no—
510C23—22no—
511C23—34no—
512C23—32no—
513C23—32no—
514C23—34no—
515C23—68no—
516C23—68no—
517C23—616no—
518C23—616no—
519C23—61no—
520C23—61no—
521C23—61no—
522C23—61no—
523C23—62no—
524C23—62no—
525C23—68no—
526C23#379512yes—
527C23#379912yes—
528C23C2×D3×Dic312yes—
529C23C22×D3211yescharacteristic
530C2×C4—22no—
531C2×C4—28no—
532C2×C4—32no—
533C2×C4—34no—
534C2×C4—316no—
535C2×C4—32no—
536C2×C4—68no—
537C2×C4—68no—
538C2×C4—68no—
539C2×C4—62no—
540C2×C4—68no—
541C2×C4—64no—
542C2×C4—64no—
543C2×C4—64no—
544C2×C4—184no—
545C2×C4—184no—
546C2×C4—184no—
547C2×C4C2×D3×Dic312yes—
548C2×C4C2×D3×Dic312yes—
549C2×C4D3×#6714yes—
550C2×C3—24no—
551C2×C3—24no—
552C2×C3—22no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—22no—
556C2×C3—21no—
557C2×C3—44no—
558C2×C3—64no—
559C2×C3—64no—
560C2×C3C2×D3×C22⋊C411yescharacteristic
561C2×C3C2×#89211yescharacteristic
562C2×C3D3×#11711yescharacteristic
563C2×C3#560612yes—
564C2×C3#562712yes—
565C2×C3C2×#92611yescharacteristic
566C2×C3C2×#92611yescharacteristic
567C2×C3#579112yes—
568C2×C3#579112yes—
569C2×C3C22×#21711yescharacteristic
570D3—24no—
571D3—24no—
572C22—24no—
573C22—22no—
574C22—22no—
575C22—24no—
576C22—34no—
577C22—34no—
578C22—632no—
579C22—64no—
580C22—64no—
581C22—62no—
582C22—62no—
583C22—64no—
584C22—64no—
585C22—62no—
586C22—62no—
587C22#6384114yescomplemented
588C22C2×#379511yescharacteristic
589C22C2×#379911yescharacteristic
590C22D3×#23512yes—
591C22C22×D3×Dic311yescharacteristic
592C22C2×D3×#6712yes—
593C4—22no—
594C4—34no—
595C4—62no—
596C4—124no—
597C4—364no—
598C4D3×#21714yes—
599C3—21no—
600C3#7386211yescharacteristic, complemented
601C3#8402711yescharacteristic, complemented
602C2—24no—
603C2—64no—
604C2—64no—
605C2C2×#6384111yescharacteristic
606C2#1059489212yes—
607C2D3×#92611yescharacteristic
608C2#1059500512yes—
609C2C2×D3×#21711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC23×C4D32
hypocenterC32#2280
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63841C2semidirect
3. #10592911C2semidirect
4. C3×#5212C2semidirect
6. Dic3×#217C2semidirect
7. #10591313C2semidirect
8. #10591294C2semidirect
9. #10591237C2semidirect
16. C22×C3×C4×D3C4semidirect
22. C2×C4⋊(C3⋊Dic3)C22semidirect
24. C2×C3×C4⋊Dic3C22semidirect
27. C2×Dic32C22semidirect
29. #63658C22semidirect
30. C3×C3⋊#95C22semidirect
31. #63579C22semidirect
42. #5212D3semidirect
100. C22×C4×D3Dic3semidirect
119. C2×C4⋊Dic3C2×D3semidirect
129. C3⋊#95C2×D3semidirect
170. C3×C4×D3C22⋊C4semidirect
260. C22×C32#117semidirect
276. C2×C3×D3#117semidirect
398. C4×D3#217semidirect
470. C22×C3#892semidirect
471. C22×C3#926semidirect
491. C2×D3#926semidirect
508. C32#2280semidirect
587. C22#63841semidirect
600. C3#73862semidirect
601. C3#84027semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C2×#638412
#105929112
C3×#52122
#105917062
Dic3×#2172
#105913132
#105912942
#105912372
#840273
#738623