Finite Group Databasebeta

← #11805508

Subgroups — #11805508

Order 1152.

1525 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C2×Dic3×#67C212yesmaximal
3#10592911C211yesmaximal, characteristic, complemented
4C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
5#10591718C212yesmaximal, complemented
6#10591379C212yesmaximal, complemented
7D3×C3⋊#95C211yesmaximal, characteristic, complemented
8#10591295C211yesmaximal, characteristic, complemented
9#10591268C212yesmaximal, complemented
10#10591242C211yesmaximal, characteristic, complemented
11#10591206C211yesmaximal, characteristic, complemented
12#82333—31nomaximal
13#73369—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×#3757C2212yes—
20C2×C4⋊(C3⋊Dic3)C2212yes—
21C2×C3×#217C2211yescharacteristic
22C3×C4×#67C418yescomplemented
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26Dic3×#67—28no—
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×Dic32C2212yes—
32#63658C2211yescharacteristic
33#63658C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×D4—31no—
40C2×D4×Dic3—32no—
41C2×C4×#67—32no—
42C2×C4×#67D311yescharacteristic
43C2×C3×#95—31no—
44#5212—31no—
45#5212—31no—
46#5212—31no—
47#5212—61no—
48#5210—32no—
49C2×C3⋊#95—31no—
50C2×C3⋊#95D311yescharacteristic, complemented
51#4984—32no—
52#4950—32no—
53#4950—32no—
54#4936—31no—
55C4×C4⋊Dic3—31no—
56#4668—32no—
57#4667—31no—
58D3×#95—31no—
59#4650—31no—
60#4649—31no—
61#4647—32no—
62C24×C32C2311yescharacteristic
63C23×C3×D3C2311yescharacteristic
64C22×C32×C4—42no—
65C22×C32×C4C2×C414yescomplemented
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C2×C3×#67C2×C414yes—
71C2×C3×#67D414yes—
72C2×C3×#67Q814yes—
73C22×C3×Dic3—24no—
74C22×C3×Dic3—24no—
75C22×C3×Dic3—42no—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C2×C3×C4×D3—42no—
82C2×C3×C4×D3C2×C414yescomplemented
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85C2×D3×Dic3—42no—
86#3757—24no—
87C4⋊(C3⋊Dic3)—42no—
88C3×#217C2×C414yescomplemented
89C3×(C2×D3)⋊C4C2×C414yescomplemented
90C3×Dic3⋊C4C2×C414yescomplemented
91C3×C4×Dic3C2×C414yescomplemented
92Dic3⋊Dic3—24no—
93Dic3⋊Dic3—24no—
94Dic3⋊Dic3—42no—
95(C2×D3)⋊Dic3—24no—
96Dic32—24no—
97#2349—91noSylow
98C22×C3×D4—31no—
99C23×C3×C4—21no—
100C23×C3×C4—31no—
101C23×C3×C4—32no—
102C23×C3×C4C2×D311yescharacteristic
103C23×C3×C4C2×D311yescharacteristic
104C22×#67C2×D311yescharacteristic
105C23×Dic3—32no—
106C23×Dic3C2×D312yes—
107C22×C4×D3—32no—
108C22×C4×D3C2×D311yescharacteristic
109C3×C4×D4—38no—
110C2×C3×C4⋊C4—31no—
111C2×C3×C22⋊C4—31no—
112C2×C3×C22⋊C4—31no—
113C2×C3×C42—31no—
114C2×#217—32no—
115C2×#217—32no—
116C2×#217—32no—
117C2×#217—62no—
118C2×#217C2×D311yescharacteristic
119D4×Dic3—68no—
120C4×#67—68no—
121C4×#67Dic318yescomplemented
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4C2×D311yescharacteristic
124C2×C4⋊Dic3—32no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3—32no—
127C2×C4⋊Dic3—32no—
128C2×C4⋊Dic3—32no—
129C2×C4⋊Dic3—62no—
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4C2×D311yescharacteristic
134C2×C4×Dic3—32no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3C2×D311yescharacteristic
137C3×#95—32no—
138C3×#95—31no—
139C3×#95—31no—
140C3⋊#95—31no—
141C3⋊#95—31no—
142C3⋊#95—31no—
143C3⋊#95—31no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—61no—
149C3⋊#95—61no—
150C3⋊#95C2×D311yescharacteristic
151C3⋊#95C2×D311yescharacteristic
152C3⋊#95C2×D312yes—
153C23×C32—22no—
154C23×C32—22no—
155C23×C32C22×C412yes—
156C23×C32C2×D412yes—
157C23×C32C2×Q812yes—
158C23×C32C2411yescharacteristic
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3C22×C412yes—
162C22×C3×D3C2×D412yes—
163C22×C3×D3C2×Q812yes—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4—44no—
167C2×C32×C4C22×C412yes—
168C2×C32×C4C22×C412yes—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—22no—
175C3×#67C4⋊C4116yescomplemented
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—48no—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C22×C412yes—
186C2×C3×Dic3C22×C412yes—
187C2×C3×Dic3C2×D412yes—
188C2×C3×Dic3C2×Q812yes—
189C2×C3×Dic3#4114yes—
190C3×C4×D3—44no—
191D3×Dic3—48no—
192C2×C4×D4—31no—
193C2×C4×D4—92no—
194#389—92no—
195#385—92no—
196#385—92no—
197#382—91no—
198#380—91no—
199#380—91no—
200C4×C4⋊C4—91no—
201C2×#95—31no—
202C2×#95—91no—
203C24×C3—21no—
204C24×C3—31no—
205C24×C3C22×D311yescharacteristic
206C24×C3C22×D311yescharacteristic
207C23×D3C22×D311yescharacteristic
208C2×C3×D4—34no—
209C2×C3×D4—34no—
210C2×C3×D4—34no—
211C22×C3×C4—24no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—31no—
217C22×C3×C4—32no—
218C22×C3×C4—34no—
219C22×C3×C4—32no—
220C22×C3×C4—42no—
221C22×C3×C4—42no—
222C22×C3×C4—44no—
223C22×C3×C4—64no—
224C22×C3×C4—64no—
225C22×C3×C4—122no—
226C22×C3×C4—122no—
227C22×C3×C4C4×D314yescomplemented
228C22×C3×C4C2×Dic314yescomplemented
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67Dic614yes—
234C2×#67D1214yes—
235C2×#67C2×Dic314yes—
236C22×Dic3—24no—
237C22×Dic3—24no—
238C22×Dic3—32no—
239C22×Dic3—32no—
240C22×Dic3—32no—
241C22×Dic3—32no—
242C22×Dic3—42no—
243C22×Dic3—62no—
244C22×Dic3—62no—
245C22×Dic3—64no—
246C22×Dic3—64no—
247C22×Dic3—122no—
248C22×Dic3C22×D312yes—
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D311yescharacteristic
251C22×Dic3C22×D311yescharacteristic
252C22×Dic3C22×D311yescharacteristic
253C2×C4×D3—42no—
254C2×C4×D3—64no—
255C2×C4×D3—64no—
256C2×C4×D3—122no—
257C2×C4×D3C2×Dic314yescomplemented
258C3×C4⋊C4—34no—
259C3×C22⋊C4—34no—
260C3×C22⋊C4—34no—
261C3×C42—34no—
262#217—64no—
263#217—64no—
264#217—64no—
265#217—124no—
266#217C2×Dic314yescomplemented
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4C2×Dic314yescomplemented
269C4⋊Dic3—64no—
270C4⋊Dic3—64no—
271C4⋊Dic3—122no—
272C4⋊Dic3—122no—
273C4⋊Dic3—122no—
274C4⋊Dic3—124no—
275Dic3⋊C4—64no—
276Dic3⋊C4—64no—
277Dic3⋊C4—122no—
278Dic3⋊C4C2×Dic314yescomplemented
279C4×Dic3—64no—
280C4×Dic3—64no—
281C4×Dic3C2×Dic314yescomplemented
282C22×C32—22no—
283C22×C32—22no—
284C22×C32—24no—
285C22×C32—24no—
286C22×C32C2×C4⋊C414yes—
287C22×C32C23×C411yescharacteristic
288C22×C32C22×D411yescharacteristic
289C22×C32C22×Q811yescharacteristic
290C22×C32C2×#4112yes—
291C22×C32H(5,𝔽2)12yes—
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C2×C3×D3—24no—
295C2×C3×D3—24no—
296C2×C3×D3C2×C4⋊C414yes—
297C32×C4—22no—
298C32×C4—22no—
299C3⋊Dic3—42no—
300C3⋊Dic3—42no—
301C3×Dic3—22no—
302C3×Dic3—22no—
303C3×Dic3—24no—
304C3×Dic3—42no—
305C3×Dic3C2×C4⋊C414yes—
306C22×D4—31no—
307C23×C4—31no—
308C23×C4—32no—
309C23×C4—92no—
310C23×C4D3211yescharacteristic
311C4×D4—38no—
312C4×D4—188no—
313C2×C4⋊C4—31no—
314C2×C4⋊C4—92no—
315C2×C4⋊C4—92no—
316C2×C4⋊C4—92no—
317C2×C4⋊C4—92no—
318C2×C22⋊C4—31no—
319C2×C22⋊C4—31no—
320C2×C22⋊C4—92no—
321C2×C22⋊C4—92no—
322C2×C42—31no—
323C2×C42—92no—
324#95—31no—
325#95—31no—
326#95—32no—
327#95—92no—
328#95—92no—
329#95—91no—
330#95—91no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—21no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—32no—
340C23×C3—32no—
341C23×C3—32no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—62no—
345C23×C3—62no—
346C23×C3C2×Dic612yes—
347C23×C3C2×C4×D312yes—
348C23×C3C2×D1212yes—
349C23×C3D3×D412yes—
350C23×C3D3×Q812yes—
351C23×C3C22×Dic312yes—
352C23×C3C23×D311yescharacteristic
353C23×C3C23×D311yescharacteristic
354C22×D3—22no—
355C22×D3—22no—
356C22×D3C2×Dic612yes—
357C22×D3C2×D1212yes—
358C22×D3C22×Dic312yes—
359C3×D4—316no—
360C2×C3×C4—24no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—32no—
368C2×C3×C4—32no—
369C2×C3×C4—32no—
370C2×C3×C4—32no—
371C2×C3×C4—32no—
372C2×C3×C4—34no—
373C2×C3×C4—42no—
374C2×C3×C4—44no—
375C2×C3×C4—44no—
376C2×C3×C4—48no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—124no—
385C2×C3×C4—128no—
386C2×C3×C4C2×C4×D312yes—
387C2×C3×C4C2×C4×D312yes—
388C2×C3×C4C22×Dic312yes—
389C2×C3×C4C22×Dic312yes—
390#67C4⋊Dic3116yescomplemented
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—48no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3—122no—
415C2×Dic3—122no—
416C2×Dic3—122no—
417C2×Dic3—128no—
418C2×Dic3C2×Dic612yes—
419C2×Dic3C2×D1212yes—
420C2×Dic3#23514yes—
421C2×Dic3C22×Dic312yes—
422C2×Dic3C22×Dic312yes—
423C2×Dic3C22×Dic312yes—
424C4×D3—44no—
425C4×D3—128no—
426C2×C32—24no—
427C2×C32C22×C4⋊C411yescharacteristic
428C2×C32C4×#4111yescharacteristic
429C2×C32#51811yescharacteristic
430C2×C32#54612yes—
431C2×C32#55412yes—
432C3×D3—24no—
433C24—31no—
434C24C2×D3211yescharacteristic
435C2×D4—34no—
436C2×D4—34no—
437C2×D4—34no—
438C22×C4—31no—
439C22×C4—32no—
440C22×C4—31no—
441C22×C4—31no—
442C22×C4—34no—
443C22×C4—32no—
444C22×C4—42no—
445C22×C4—64no—
446C22×C4—64no—
447C22×C4—92no—
448C22×C4—92no—
449C22×C4—122no—
450C22×C4—122no—
451C22×C4—184no—
452C22×C4—184no—
453C22×C4—362no—
454C22×C4D3×Dic314yescomplemented
455C22×C4C2×D3211yescharacteristic
456C22×C4C2×D3211yescharacteristic
457C4⋊C4—34no—
458C4⋊C4—184no—
459C4⋊C4—184no—
460C4⋊C4—362no—
461C4⋊C4—362no—
462C22⋊C4—34no—
463C22⋊C4—34no—
464C22⋊C4—184no—
465C22⋊C4—184no—
466C42—34no—
467C42—184no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—24no—
471C22×C3—24no—
472C22×C3—24no—
473C22×C3—22no—
474C22×C3—24no—
475C22×C3—22no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—22no—
479C22×C3—21no—
480C22×C3—22no—
481C22×C3—24no—
482C22×C3—34no—
483C22×C3—42no—
484C22×C3—44no—
485C22×C3—42no—
486C22×C3—44no—
487C22×C3—62no—
488C22×C3—62no—
489C22×C3—64no—
490C22×C3—64no—
491C22×C3D3×C4⋊C414yes—
492C22×C3C2×C4⋊Dic314yes—
493C22×C3C22×Dic611yescharacteristic
494C22×C3C22×C4×D311yescharacteristic
495C22×C3C22×D1211yescharacteristic
496C22×C3C2×#23512yes—
497C22×C3C2×D3×D411yescharacteristic
498C22×C3#100412yes—
499C22×C3#100412yes—
500C22×C3C2×D3×Q811yescharacteristic
501C22×C3D3×#4112yes—
502C22×C3C23×Dic311yescharacteristic
503C2×D3—24no—
504C2×D3—22no—
505C2×D3—24no—
506C2×D3—22no—
507C2×D3C2×C4⋊Dic314yes—
508C3×C4—24no—
509C3×C4—22no—
510C3×C4—22no—
511C3×C4—22no—
512C3×C4—22no—
513C3×C4—34no—
514C3×C4—42no—
515C3×C4—62no—
516C3×C4—62no—
517C3×C4—64no—
518C3×C4—122no—
519Dic3—24no—
520Dic3—22no—
521Dic3—22no—
522Dic3—42no—
523Dic3—122no—
524Dic3—122no—
525Dic3—122no—
526Dic3—122no—
527Dic3—242no—
528Dic3—242no—
529Dic3C2×C4⋊Dic314yes—
530C32#234911yescharacteristic, complemented, Sylow
531C23—22no—
532C23—22no—
533C23—32no—
534C23—32no—
535C23—32no—
536C23—62no—
537C23—62no—
538C23D3×Dic612yes—
539C23D3×D1212yes—
540C23C2×D3×Dic312yes—
541C23C22×D3211yescharacteristic
542D4—316no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—32no—
546C2×C4—32no—
547C2×C4—32no—
548C2×C4—34no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—44no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—124no—
560C2×C4—128no—
561C2×C4—182no—
562C2×C4—182no—
563C2×C4—182no—
564C2×C4—182no—
565C2×C4—182no—
566C2×C4—182no—
567C2×C4—368no—
568C2×C4C2×D3×Dic312yes—
569C2×C4C2×D3×Dic312yes—
570C2×C3—24no—
571C2×C3—24no—
572C2×C3—22no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—22no—
576C2×C3—21no—
577C2×C3—44no—
578C2×C3—64no—
579C2×C3C4×#23511yescharacteristic
580C2×C3#548611yescharacteristic
581C2×C3#549012yes—
582C2×C3C2×D3×C4⋊C411yescharacteristic
583C2×C3#551112yes—
584C2×C3#553912yes—
585C2×C3#555412yes—
586C2×C3C22×C4⋊Dic311yescharacteristic
587C2×C3#579811yescharacteristic
588C2×C3Dic3×#4111yescharacteristic
589D3—24no—
590C22—24no—
591C22—22no—
592C22—24no—
593C22—22no—
594C22—34no—
595C22—64no—
596C22—62no—
597C22—64no—
598C22—62no—
599C22D3×C4⋊Dic314yes—
600C22C2×D3×Dic611yescharacteristic
601C22C2×D3×D1211yescharacteristic
602C22D3×#23512yes—
603C22C22×D3×Dic311yescharacteristic
604C22#6433012yes—
605C4—22no—
606C4—22no—
607C4—34no—
608C4—64no—
609C4—62no—
610C4—62no—
611C4—122no—
612C4—362no—
613C4—362no—
614C3—21no—
615C3#7336911yescharacteristic, complemented
616C3#8233311yescharacteristic, complemented
617C2—24no—
618C2—64no—
619C2C2×D3×C4⋊Dic311yescharacteristic
620C2Dic3×#23511yescharacteristic
621C2#1059495112yes—
622C2#1059507312yes—
623C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10592911C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. #10591718C2semidirect
6. #10591379C2semidirect
7. D3×C3⋊#95C2semidirect
8. #10591295C2semidirect
9. #10591268C2semidirect
10. #10591242C2semidirect
11. #10591206C2semidirect
22. C3×C4×#67C4semidirect
50. C2×C3⋊#95D3semidirect
65. C22×C32×C4C2×C4semidirect
82. C2×C3×C4×D3C2×C4semidirect
88. C3×#217C2×C4semidirect
89. C3×(C2×D3)⋊C4C2×C4semidirect
90. C3×Dic3⋊C4C2×C4semidirect
91. C3×C4×Dic3C2×C4semidirect
121. C4×#67Dic3semidirect
175. C3×#67C4⋊C4semidirect
227. C22×C3×C4C4×D3semidirect
228. C22×C3×C4C2×Dic3semidirect
257. C2×C4×D3C2×Dic3semidirect
266. #217C2×Dic3semidirect
268. (C2×D3)⋊C4C2×Dic3semidirect
278. Dic3⋊C4C2×Dic3semidirect
281. C4×Dic3C2×Dic3semidirect
390. #67C4⋊Dic3semidirect
454. C22×C4D3×Dic3semidirect
530. C32#2349semidirect
615. C3#73369semidirect
616. C3#82333semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×Dic3×#672
#105929112
C2×C3×C3⋊#952
#105917182
#105913792
D3×C3⋊#952
#105912952
#105912682
#105912422
#105912062
#823333
#733693