Finite Group Databasebeta

← #11805181

Subgroups — #11805181

Order 1152.

1337 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63900C211yesmaximal, characteristic
2C2×#63836C212yesmaximal
3C4×#3752C211yesmaximal, characteristic
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#4928C211yesmaximal, characteristic, complemented
6#10591371C212yesmaximal
7#10591357C211yesmaximal, characteristic, complemented
8#10591325C211yesmaximal, characteristic
9#10591274C211yesmaximal, characteristic, complemented
10#10591249C212yesmaximal, complemented
11#10591193C212yesmaximal, complemented
12#76200—31nomaximal
13#73767—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#624C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×#3752C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×#3724C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×#3722C2212yes—
29C2×Dic32C2212yes—
30#63900C418yescomplemented
31#63836—28no—
32#63658C2211yescharacteristic
33#63658C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×#892—32no—
40C2×D3×C4⋊C4—31no—
41C2×D3×C4⋊C4—31no—
42C2×#872—32no—
43C3×#389—31no—
44C3×C4×C4⋊C4—31no—
45#4987—31no—
46#4987—31no—
47#4984—31no—
48#4978—32no—
49Dic3×C4⋊C4—31no—
50Dic3×C4⋊C4—31no—
51#4972—31no—
52C4×(C2×D3)⋊C4—31no—
53C4×(C2×D3)⋊C4—31no—
54C4×(C2×D3)⋊C4—61no—
55C4×C4⋊Dic3D311yescharacteristic, complemented
56#4933—32no—
57#4928D311yescharacteristic, complemented
58#4664—32no—
59#4664—32no—
60#4655—32no—
61#4652—32no—
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3C2×C414yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×#624—24no—
77C2×#624—24no—
78C2×#624C2×C418yes—
79C32×C42—22no—
80#3752—22no—
81#3752D414yes—
82C4×C3⋊Dic3—22no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3C2×C414yes—
86C3×C4⋊Dic3C2×C414yes—
87C3×Dic3⋊C4—24no—
88C3×C4×Dic3—24no—
89#3724C2×C418yes—
90Dic3⋊Dic3—24no—
91#3722—24no—
92Dic32—24no—
93#2344—91noSylow
94C22×C4×D3—31no—
95C22×C4×D3—31no—
96C22×C4×D3—32no—
97C22×C4×D3—32no—
98C22×C4×D3—61no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C42—21no—
105C2×C3×C42—32no—
106C2×C3×C42C2×D311yescharacteristic
107C2×C3×C42C2×D311yescharacteristic
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4—31no—
111C2×(C2×D3)⋊C4—31no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—61no—
115C2×(C2×D3)⋊C4—61no—
116C2×C4⋊Dic3—32no—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×C4⋊Dic3C2×D311yescharacteristic
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4C2×D312yes—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—61no—
130C2×C4×Dic3C2×D312yes—
131#892—68no—
132D3×C4⋊C4—38no—
133D3×C4⋊C4—38no—
134#872—68no—
135C3×#95—32no—
136C3×#95—32no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C3⋊#95—31no—
140C3⋊#95—31no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—61no—
148C3⋊#95—61no—
149C3⋊#95C2×D312yes—
150C3⋊#95C2×D312yes—
151C23×C32C2411yescharacteristic
152C22×C3⋊D3—21no—
153C22×C3⋊D3—21no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3C22×C412yes—
157C22×C3⋊D3C2×D412yes—
158C22×C3⋊D3#4112yes—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4C22×C412yes—
165C2×C32×C4C2×D412yes—
166C2×C32×C4#4112yes—
167C2×C32×C4#4112yes—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C22×C412yes—
176C2×C3⋊Dic3C2×D412yes—
177C4×C3⋊D3—28no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C22×C414yes—
189C2×C3×Dic3C22×C414yes—
190#624—216no—
191C2×#117—92no—
192C22×C4⋊C4—91no—
193#389—31no—
194#389—91no—
195#387—92no—
196#387—92no—
197#381—92no—
198#380—91no—
199C4×C4⋊C4—31no—
200C4×C4⋊C4—91no—
201C4×C22⋊C4—91no—
202C23×D3—31no—
203C23×D3—31no—
204C23×D3—61no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—61no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3C22×D312yes—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D312yes—
231C2×C4×D3—34no—
232C2×C4×D3—34no—
233C2×C4×D3—38no—
234C2×C4×D3—38no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—62no—
241C2×C4×D3—62no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×C4×D3—122no—
245C2×C4×D3—122no—
246C3×C4⋊C4—34no—
247C3×C4⋊C4—34no—
248C3×C4⋊C4—62no—
249C3×C4⋊C4—64no—
250C3×C4⋊C4—62no—
251C3×C42—22no—
252C3×C42—22no—
253C3×C42—42no—
254C3×C42—64no—
255(C2×D3)⋊C4—34no—
256(C2×D3)⋊C4—34no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—64no—
263C4⋊Dic3—22no—
264C4⋊Dic3—22no—
265C4⋊Dic3—64no—
266C4⋊Dic3C4×D314yes—
267C4⋊Dic3C4×D314yes—
268Dic3⋊C4—24no—
269Dic3⋊C4—38no—
270Dic3⋊C4—38no—
271Dic3⋊C4—64no—
272C4×Dic3—24no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—122no—
278C22×C32C23×C411yescharacteristic
279C22×C32C22×D411yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C22×C32C2×#4111yescharacteristic
282C22×C32C2×#4111yescharacteristic
283C22×C322−1+411yescharacteristic
284C22×C322−1+411yescharacteristic
285C2×C3⋊D3—22no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—22no—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—22no—
291C2×C3⋊D3C4×D414yes—
292C32×C4—22no—
293C32×C4—41no—
294C32×C4#11714yescomplemented
295C3⋊Dic3—22no—
296C3⋊Dic3—22no—
297C3⋊Dic3—41no—
298C3×Dic3—24no—
299C3×Dic3—24no—
300C3×Dic3—42no—
301C3×Dic3—42no—
302C23×C4—92no—
303C23×C4—91no—
304#117—188no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—32no—
308C2×C4⋊C4—31no—
309C2×C4⋊C4—31no—
310C2×C4⋊C4—98no—
311C2×C4⋊C4—92no—
312C2×C4⋊C4—92no—
313C2×C22⋊C4—91no—
314C2×C22⋊C4—92no—
315C2×C22⋊C4—91no—
316C2×C42—32no—
317C2×C42—92no—
318C2×C42—91no—
319C2×C42D3211yescharacteristic
320#95—32no—
321#95—32no—
322#95—92no—
323#95—92no—
324#95—92no—
325#95—91no—
326#95—91no—
327C23×C3—21no—
328C23×C3C23×D311yescharacteristic
329C23×C3C23×D311yescharacteristic
330C22×D3—32no—
331C22×D3—32no—
332C22×D3—32no—
333C22×D3—32no—
334C22×D3—32no—
335C22×D3—32no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—121no—
348C22×D3—121no—
349C22×D3—121no—
350C22×D3—121no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—34no—
367C2×C3×C4—34no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4C2×C4×D312yes—
383C2×C3×C4C2×C4×D312yes—
384C2×C3×C4#23512yes—
385C2×C3×C4#23512yes—
386C2×C3×C4D3×D412yes—
387C2×C3×C4D3×D412yes—
388C2×C3×C4#23712yes—
389C2×C3×C4#23912yes—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—32no—
401C2×Dic3—32no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—62no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—121no—
422C2×Dic3—121no—
423C2×Dic3—121no—
424C2×Dic3—121no—
425C2×Dic3—121no—
426C2×Dic3—121no—
427C2×Dic3C2×C4×D314yes—
428C2×Dic3C2×C4×D314yes—
429C4×D3—616no—
430C4×D3—616no—
431C4×D3—68no—
432C4×D3—68no—
433C4×D3—128no—
434C2×C32C2×#11711yescharacteristic
435C2×C32C2×C4×D411yescharacteristic
436C2×C32#51911yescharacteristic
437C2×C32#54711yescharacteristic
438C2×C32#54711yescharacteristic
439C2×C32#55211yescharacteristic
440C2×C32#55211yescharacteristic
441C3⋊D3—24no—
442C24—91no—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—32no—
447C22×C4—98no—
448C22×C4—91no—
449C22×C4—91no—
450C22×C4—94no—
451C22×C4—91no—
452C22×C4—184no—
453C22×C4—184no—
454C22×C4—182no—
455C22×C4—182no—
456C22×C4C2×D3211yescharacteristic
457C22×C4C2×D3211yescharacteristic
458C22×C4C2×D3211yescharacteristic
459C4⋊C4—34no—
460C4⋊C4—34no—
461C4⋊C4—62no—
462C4⋊C4—64no—
463C4⋊C4—62no—
464C4⋊C4—98no—
465C4⋊C4—184no—
466C22⋊C4—94no—
467C22⋊C4—182no—
468C22⋊C4—184no—
469C42—22no—
470C42—64no—
471C42—184no—
472C42—182no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3C22×C4×D311yescharacteristic
481C22×C3C22×C4×D311yescharacteristic
482C22×C3C2×#23511yescharacteristic
483C22×C3C2×#23511yescharacteristic
484C22×C3C2×D3×D411yescharacteristic
485C22×C3C2×D3×D411yescharacteristic
486C22×C3C2×#23711yescharacteristic
487C22×C3C2×#23911yescharacteristic
488C22×C3#100711yescharacteristic
489C22×C3#100711yescharacteristic
490C22×C3D3×#4111yescharacteristic
491C22×C3D3×#4111yescharacteristic
492C22×C3#101011yescharacteristic
493C22×C3#101011yescharacteristic
494C2×D3—34no—
495C2×D3—34no—
496C2×D3—64no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—62no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—122no—
515C3×C4—22no—
516C3×C4—22no—
517C3×C4—24no—
518C3×C4—42no—
519C3×C4—42no—
520C3×C4—41no—
521C3×C4—41no—
522C3×C4—64no—
523C3×C4—64no—
524C3×C4—122no—
525C3×C4—122no—
526C3×C4#87214yescomplemented
527C3×C4#89214yescomplemented
528Dic3—24no—
529Dic3—24no—
530Dic3—42no—
531Dic3—42no—
532Dic3—62no—
533Dic3—62no—
534Dic3—62no—
535Dic3—62no—
536Dic3—122no—
537Dic3—122no—
538Dic3—122no—
539Dic3—121no—
540Dic3—121no—
541C32#234411yescharacteristic, complemented, Sylow
542C23—92no—
543C23—92no—
544C23—92no—
545C23—181no—
546C23—181no—
547C23—181no—
548C23—181no—
549C23C22×D3211yescharacteristic
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—34no—
556C2×C4—34no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—92no—
568C2×C4—92no—
569C2×C4—1816no—
570C2×C4—181no—
571C2×C4—181no—
572C2×C4—181no—
573C2×C4—181no—
574C2×C4—188no—
575C2×C4—181no—
576C2×C4—181no—
577C2×C4—181no—
578C2×C4#379912yes—
579C2×C4C4×D3212yes—
580C2×C4#380212yes—
581C2×C4#380412yes—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3C2×#87211yescharacteristic
590C2×C3C2×#89211yescharacteristic
591C2×C3#550711yescharacteristic
592C2×C3#552911yescharacteristic
593C2×C3C4×D3×D411yescharacteristic
594C2×C3C4×D3×D411yescharacteristic
595C2×C3#555111yescharacteristic
596C2×C3#557211yescharacteristic
597C2×C3#557211yescharacteristic
598C2×C3#558111yescharacteristic
599C2×C3#561111yescharacteristic
600C2×C3#563911yescharacteristic
601C2×C3#569411yescharacteristic
602C2×C3#572611yescharacteristic
603D3—64no—
604D3—64no—
605D3—124no—
606C22—94no—
607C22—182no—
608C22—182no—
609C22—182no—
610C22—182no—
611C22—182no—
612C22—182no—
613C22#6429711yescharacteristic
614C22#6429711yescharacteristic
615C22C2×#379911yescharacteristic
616C22C2×C4×D3211yescharacteristic
617C22C2×#380211yescharacteristic
618C22#6430611yescharacteristic
619C22C2×#380411yescharacteristic
620C4—22no—
621C4—41no—
622C4—64no—
623C4—64no—
624C4—122no—
625C4—122no—
626C4—182no—
627C4—182no—
628C4—361no—
629C4#6383614yescomplemented
630C3—21no—
631C3#7376711yescharacteristic, complemented
632C3#7620011yescharacteristic, complemented
633C2—184no—
634C2#1059384811yescharacteristic
635C2#1059386911yescharacteristic
636C2#1059394711yescharacteristic
637C2C4×#380211yescharacteristic
638C2C2×#6383611yescharacteristic
639C2#1059492811yescharacteristic
640C2#1059497011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2344
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C3×C4×C4⋊Dic3C2semidirect
5. C3×#4928C2semidirect
7. #10591357C2semidirect
9. #10591274C2semidirect
10. #10591249C2semidirect
11. #10591193C2semidirect
30. #63900C4semidirect
55. C4×C4⋊Dic3D3semidirect
57. #4928D3semidirect
294. C32×C4#117semidirect
526. C3×C4#872semidirect
527. C3×C4#892semidirect
541. C32#2344semidirect
629. C4#63836semidirect
631. C3#73767semidirect
632. C3#76200semidirect

Maximal subgroups

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

subgroupindex
C2×#639002
C2×#638362
C4×#37522
C3×C4×C4⋊Dic32
C3×#49282
#105913712
#105913572
#105913252
#105912742
#105912492
#105911932
#762003
#737673