Finite Group Databasebeta

← #11800917

Subgroups — #11800917

Order 1152.

1689 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C2×Dic3×#67C212yesmaximal
3C4×#3757C211yesmaximal, characteristic, complemented
4C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
5Dic3×#217C212yesmaximal, complemented
6#10591368C212yesmaximal, complemented
7D3×C3⋊#95C211yesmaximal, characteristic, complemented
8#10591242C211yesmaximal, characteristic, complemented
9#10591241C212yesmaximal, complemented
10#10591239C211yesmaximal, characteristic, complemented
11#10591237C211yesmaximal, characteristic, complemented
12#82317—31nomaximal
13#73322—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×#3757C2212yes—
20C2×C4×C3⋊Dic3C2212yes—
21C2×C3×#217C2211yescharacteristic
22C3×C4×#67C418yescomplemented
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26Dic3×#67C4116yescomplemented
27C2×Dic3⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32#63658C2211yescharacteristic
33#63658C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×D4—31no—
40C2×D4×Dic3—32no—
41C2×C4×#67—32no—
42C2×C4×#67D311yescharacteristic
43C2×C3×#95—31no—
44C4×#217—31no—
45C4×#217—31no—
46C4×#217—32no—
47C4×#217—31no—
48C4×#217—61no—
49C2×C3⋊#95—31no—
50C2×C3⋊#95D311yescharacteristic, complemented
51Dic3×C4⋊C4—32no—
52Dic3×C22⋊C4—32no—
53Dic3×C22⋊C4—32no—
54C4×C4⋊Dic3—31no—
55#4932—31no—
56#4666—31no—
57#4666—32no—
58D3×#95—31no—
59#4649—32no—
60#4649—31no—
61#4648—31no—
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×C418yes—
71C2×C3×#67C2×C414yes—
72C22×C3×Dic3—42no—
73C22×C3×Dic3—42no—
74C22×C3×Dic3C2×C418yescomplemented
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2311yescharacteristic
80C2×C3×C4×D3—42no—
81C2×C3×C4×D3C2×C414yescomplemented
82C2×D3×Dic3—42no—
83C2×D3×Dic3—42no—
84C2×D3×Dic3C2×C418yescomplemented
85#3757C2×C418yescomplemented
86C4×C3⋊Dic3—42no—
87C3×#217C2×C414yescomplemented
88C3×(C2×D3)⋊C4C2×C414yescomplemented
89C3×Dic3⋊C4C2×C414yescomplemented
90C3×C4×Dic3C2×C414yescomplemented
91Dic3⋊Dic3C2×C418yescomplemented
92(C2×D3)⋊Dic3C2×C418yescomplemented
93Dic32—42no—
94Dic32—42no—
95Dic32C2×C418yescomplemented
96#2275—91noSylow
97C22×C3×D4—31no—
98C23×C3×C4—21no—
99C23×C3×C4—32no—
100C23×C3×C4—31no—
101C23×C3×C4C2×D311yescharacteristic
102C23×C3×C4C2×D311yescharacteristic
103C22×#67C2×D311yescharacteristic
104C23×Dic3—32no—
105C23×Dic3C2×D312yes—
106C22×C4×D3—32no—
107C22×C4×D3C2×D311yescharacteristic
108C3×C4×D4—38no—
109C2×C3×C4⋊C4—31no—
110C2×C3×C22⋊C4—31no—
111C2×C3×C22⋊C4—31no—
112C2×C3×C42—31no—
113C2×#217—32no—
114C2×#217—32no—
115C2×#217—32no—
116C2×#217—62no—
117C2×#217C2×D311yescharacteristic
118D4×Dic3—316no—
119C4×#67—316no—
120C4×#67Dic318yescomplemented
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4C2×D311yescharacteristic
123C2×C4⋊Dic3—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4C2×D311yescharacteristic
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—62no—
135C2×C4×Dic3C2×D311yescharacteristic
136C3×#95—31no—
137C3×#95—32no—
138C3×#95—31no—
139C3⋊#95—31no—
140C3⋊#95—31no—
141C3⋊#95—31no—
142C3⋊#95—31no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—61no—
148C3⋊#95—61no—
149C3⋊#95C2×D311yescharacteristic
150C3⋊#95C2×D311yescharacteristic
151C3⋊#95C2×D312yes—
152C23×C32—21no—
153C23×C32—22no—
154C23×C32—21no—
155C23×C32C22×C414yes—
156C23×C32C22×C412yes—
157C23×C32C2411yescharacteristic
158C22×C3×D3—21no—
159C22×C3×D3—22no—
160C22×C3×D3—21no—
161C22×C3×D3C22×C414yes—
162C22×C3×D3C22×C412yes—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4—44no—
166C2×C32×C4C22×C412yes—
167C2×C32×C4C22×C412yes—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3C22×C414yes—
173C2×C3⋊Dic3C22×C414yes—
174C3×#67C42116yescomplemented
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—48no—
183C2×C3×Dic3C22×C414yes—
184C2×C3×Dic3C22×C414yes—
185C2×C3×Dic3C22×C414yes—
186C2×C3×Dic3C22×C412yes—
187C2×C3×Dic3C22×C412yes—
188C2×C3×Dic3C22×C412yes—
189C3×C4×D3—44no—
190D3×Dic3—48no—
191C2×C4×D4—31no—
192C2×C4×D4—92no—
193C4×C4⋊C4—91no—
194C4×C4⋊C4—92no—
195C4×C22⋊C4—92no—
196C4×C22⋊C4—91no—
197C4×C22⋊C4—92no—
198C4×C22⋊C4—91no—
199#376—91no—
200C2×#95—31no—
201C2×#95—91no—
202C24×C3—21no—
203C24×C3—31no—
204C24×C3C22×D311yescharacteristic
205C24×C3C22×D311yescharacteristic
206C23×D3C22×D311yescharacteristic
207C2×C3×D4—38no—
208C2×C3×D4—34no—
209C22×C3×C4—24no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—31no—
213C22×C3×C4—32no—
214C22×C3×C4—31no—
215C22×C3×C4—31no—
216C22×C3×C4—32no—
217C22×C3×C4—38no—
218C22×C3×C4—34no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4—44no—
222C22×C3×C4—122no—
223C22×C3×C4—122no—
224C22×C3×C4—122no—
225C22×C3×C4C4×D314yescomplemented
226C22×C3×C4C2×Dic314yescomplemented
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67C4×D318yes—
232C2×#67C2×Dic314yes—
233C22×Dic3—32no—
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—32no—
237C22×Dic3—38no—
238C22×Dic3—42no—
239C22×Dic3—42no—
240C22×Dic3—62no—
241C22×Dic3—62no—
242C22×Dic3—122no—
243C22×Dic3—122no—
244C22×Dic3C4×D318yescomplemented
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D311yescharacteristic
248C22×Dic3C22×D311yescharacteristic
249C22×Dic3C22×D311yescharacteristic
250C2×C4×D3—38no—
251C2×C4×D3—42no—
252C2×C4×D3—122no—
253C2×C4×D3—122no—
254C2×C4×D3C2×Dic314yescomplemented
255C3×C4⋊C4—34no—
256C3×C22⋊C4—34no—
257C3×C22⋊C4—34no—
258C3×C42—34no—
259#217—38no—
260#217—38no—
261#217—38no—
262#217—68no—
263#217C2×Dic314yescomplemented
264(C2×D3)⋊C4—38no—
265(C2×D3)⋊C4C2×Dic314yescomplemented
266C4⋊Dic3—38no—
267Dic3⋊C4—38no—
268Dic3⋊C4C2×Dic314yescomplemented
269C4×Dic3—38no—
270C4×Dic3—38no—
271C4×Dic3—122no—
272C4×Dic3—122no—
273C4×Dic3—122no—
274C4×Dic3—122no—
275C4×Dic3—122no—
276C4×Dic3—122no—
277C4×Dic3—124no—
278C4×Dic3C2×Dic314yescomplemented
279C22×C32—24no—
280C22×C32—22no—
281C22×C32—24no—
282C22×C32—22no—
283C22×C32C2×C4214yes—
284C22×C32C23×C412yes—
285C22×C32C23×C411yescharacteristic
286C22×C32H(5,𝔽2)12yes—
287C22×C32H(5,𝔽2)11yescharacteristic
288C22×C322−1+411yescharacteristic
289C2×C3×D3—24no—
290C2×C3×D3—22no—
291C2×C3×D3—24no—
292C2×C3×D3—22no—
293C2×C3×D3C2×C4214yes—
294C32×C4—22no—
295C32×C4—22no—
296C3⋊Dic3—24no—
297C3⋊Dic3—24no—
298C3×Dic3—24no—
299C3×Dic3—22no—
300C3×Dic3—24no—
301C3×Dic3—22no—
302C3×Dic3C2×C4214yes—
303C22×D4—31no—
304C23×C4—32no—
305C23×C4—31no—
306C23×C4—92no—
307C23×C4D3211yescharacteristic
308C4×D4—38no—
309C4×D4—916no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—92no—
312C2×C22⋊C4—31no—
313C2×C22⋊C4—31no—
314C2×C22⋊C4—92no—
315C2×C22⋊C4—92no—
316C2×C42—31no—
317C2×C42—92no—
318C2×C42—92no—
319C2×C42—92no—
320C2×C42—92no—
321#95—31no—
322#95—32no—
323#95—31no—
324#95—92no—
325#95—92no—
326#95—91no—
327#95—91no—
328C23×C3—21no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—24no—
336C23×C3—22no—
337C23×C3—34no—
338C23×C3—32no—
339C23×C3—42no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—61no—
343C23×C3—62no—
344C23×C3—61no—
345C23×C3C2×C4×D314yes—
346C23×C3C2×C4×D314yes—
347C23×C3C2×C4×D312yes—
348C23×C3C22×Dic312yes—
349C23×C3C23×D311yescharacteristic
350C23×C3C23×D311yescharacteristic
351C22×D3—22no—
352C22×D3—21no—
353C22×D3—21no—
354C22×D3C2×C4×D314yes—
355C22×D3C22×Dic312yes—
356C3×D4—316no—
357C2×C3×C4—24no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—34no—
365C2×C3×C4—32no—
366C2×C3×C4—34no—
367C2×C3×C4—34no—
368C2×C3×C4—32no—
369C2×C3×C4—32no—
370C2×C3×C4—42no—
371C2×C3×C4—44no—
372C2×C3×C4—44no—
373C2×C3×C4—48no—
374C2×C3×C4—61no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—124no—
382C2×C3×C4—128no—
383C2×C3×C4C2×C4×D312yes—
384C2×C3×C4C2×C4×D312yes—
385C2×C3×C4C22×Dic312yes—
386C2×C3×C4C22×Dic312yes—
387#67C4×Dic3116yescomplemented
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—34no—
396C2×Dic3—34no—
397C2×Dic3—34no—
398C2×Dic3—34no—
399C2×Dic3—48no—
400C2×Dic3—64no—
401C2×Dic3—64no—
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—122no—
411C2×Dic3—122no—
412C2×Dic3—122no—
413C2×Dic3—122no—
414C2×Dic3—128no—
415C2×Dic3C2×C4×D314yes—
416C2×Dic3C2×C4×D314yes—
417C2×Dic3C2×C4×D314yes—
418C2×Dic3C22×Dic312yes—
419C2×Dic3C22×Dic312yes—
420C2×Dic3C22×Dic312yes—
421C4×D3—44no—
422C4×D3—128no—
423C2×C32—24no—
424C2×C32C22×C4211yescharacteristic
425C2×C32#51811yescharacteristic
426C2×C32#51812yes—
427C2×C32#52012yes—
428C2×C32#52011yescharacteristic
429C3×D3—24no—
430C24—31no—
431C24C2×D3211yescharacteristic
432C2×D4—38no—
433C2×D4—34no—
434C22×C4—31no—
435C22×C4—32no—
436C22×C4—32no—
437C22×C4—31no—
438C22×C4—31no—
439C22×C4—38no—
440C22×C4—34no—
441C22×C4—42no—
442C22×C4—98no—
443C22×C4—92no—
444C22×C4—92no—
445C22×C4—122no—
446C22×C4—122no—
447C22×C4—122no—
448C22×C4—362no—
449C22×C4—362no—
450C22×C4D3×Dic314yescomplemented
451C22×C4C2×D3211yescharacteristic
452C22×C4C2×D3211yescharacteristic
453C4⋊C4—34no—
454C4⋊C4—98no—
455C22⋊C4—34no—
456C22⋊C4—34no—
457C22⋊C4—98no—
458C22⋊C4—98no—
459C42—34no—
460C42—98no—
461C42—362no—
462C42—362no—
463C42—362no—
464C22×C3—24no—
465C22×C3—22no—
466C22×C3—24no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—22no—
472C22×C3—21no—
473C22×C3—22no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—22no—
477C22×C3—24no—
478C22×C3—34no—
479C22×C3—42no—
480C22×C3—44no—
481C22×C3—42no—
482C22×C3—44no—
483C22×C3—64no—
484C22×C3—62no—
485C22×C3—64no—
486C22×C3—62no—
487C22×C3C42×D314yes—
488C22×C3C2×C4×Dic314yes—
489C22×C3C22×C4×D312yes—
490C22×C3C22×C4×D312yes—
491C22×C3C22×C4×D311yescharacteristic
492C22×C3#100411yescharacteristic
493C22×C3#100412yes—
494C22×C3#100412yes—
495C22×C3#100711yescharacteristic
496C22×C3#100911yescharacteristic
497C22×C3#101011yescharacteristic
498C22×C3C23×Dic311yescharacteristic
499C2×D3—22no—
500C2×D3—24no—
501C2×D3—24no—
502C2×D3—22no—
503C2×D3C2×C4×Dic314yes—
504C3×C4—24no—
505C3×C4—22no—
506C3×C4—22no—
507C3×C4—22no—
508C3×C4—22no—
509C3×C4—34no—
510C3×C4—42no—
511C3×C4—62no—
512C3×C4—62no—
513C3×C4—64no—
514C3×C4—64no—
515Dic3—24no—
516Dic3—24no—
517Dic3—22no—
518Dic3—22no—
519Dic3—64no—
520Dic3—64no—
521Dic3—64no—
522Dic3—64no—
523Dic3—124no—
524Dic3—124no—
525Dic3C2×C4×Dic314yes—
526C32#227511yescharacteristic, complemented, Sylow
527C23—21no—
528C23—21no—
529C23—22no—
530C23—34no—
531C23—32no—
532C23—61no—
533C23—61no—
534C23—62no—
535C23C4×D3214yes—
536C23C2×D3×Dic312yes—
537C23C22×D3211yescharacteristic
538D4—316no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—34no—
542C2×C4—32no—
543C2×C4—34no—
544C2×C4—34no—
545C2×C4—32no—
546C2×C4—32no—
547C2×C4—44no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—94no—
556C2×C4—94no—
557C2×C4—124no—
558C2×C4—128no—
559C2×C4—182no—
560C2×C4—182no—
561C2×C4—182no—
562C2×C4—182no—
563C2×C4—368no—
564C2×C4C2×D3×Dic312yes—
565C2×C4C2×D3×Dic312yes—
566C2×C3—24no—
567C2×C3—24no—
568C2×C3—21no—
569C2×C3—22no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—22no—
573C2×C3—44no—
574C2×C3—64no—
575C2×C3C2×C42×D311yescharacteristic
576C2×C3#548611yescharacteristic
577C2×C3#548612yes—
578C2×C3#550412yes—
579C2×C3#550411yescharacteristic
580C2×C3#554512yes—
581C2×C3#554612yes—
582C2×C3C22×C4×Dic311yescharacteristic
583C2×C3#579811yescharacteristic
584C2×C3#582711yescharacteristic
585D3—24no—
586C22—24no—
587C22—22no—
588C22—22no—
589C22—24no—
590C22—34no—
591C22—64no—
592C22—62no—
593C22—62no—
594C22—64no—
595C22C4×D3×Dic314yes—
596C22#6429711yescharacteristic
597C22C2×C4×D3212yes—
598C22#6430711yescharacteristic
599C22C22×D3×Dic311yescharacteristic
600C22#6433012yes—
601C4—22no—
602C4—22no—
603C4—34no—
604C4—62no—
605C4—62no—
606C4—64no—
607C4—64no—
608C4—184no—
609C4—184no—
610C3—21no—
611C3#7332211yescharacteristic, complemented
612C3#8231711yescharacteristic, complemented
613C2—24no—
614C2—64no—
615C2C2×C4×D3×Dic311yescharacteristic
616C2#1059487412yes—
617C2#1059498611yescharacteristic
618C2#1059505612yes—
619C2#1059550611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32#2275
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C4×#3757C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. Dic3×#217C2semidirect
6. #10591368C2semidirect
7. D3×C3⋊#95C2semidirect
8. #10591242C2semidirect
9. #10591241C2semidirect
10. #10591239C2semidirect
11. #10591237C2semidirect
22. C3×C4×#67C4semidirect
26. Dic3×#67C4semidirect
50. C2×C3⋊#95D3semidirect
65. C22×C32×C4C2×C4semidirect
74. C22×C3×Dic3C2×C4semidirect
81. C2×C3×C4×D3C2×C4semidirect
84. C2×D3×Dic3C2×C4semidirect
85. #3757C2×C4semidirect
87. C3×#217C2×C4semidirect
88. C3×(C2×D3)⋊C4C2×C4semidirect
89. C3×Dic3⋊C4C2×C4semidirect
90. C3×C4×Dic3C2×C4semidirect
91. Dic3⋊Dic3C2×C4semidirect
92. (C2×D3)⋊Dic3C2×C4semidirect
95. Dic32C2×C4semidirect
120. C4×#67Dic3semidirect
174. C3×#67C42semidirect
225. C22×C3×C4C4×D3semidirect
226. C22×C3×C4C2×Dic3semidirect
244. C22×Dic3C4×D3semidirect
254. C2×C4×D3C2×Dic3semidirect
263. #217C2×Dic3semidirect
265. (C2×D3)⋊C4C2×Dic3semidirect
268. Dic3⋊C4C2×Dic3semidirect
278. C4×Dic3C2×Dic3semidirect
387. #67C4×Dic3semidirect
450. C22×C4D3×Dic3semidirect
526. C32#2275semidirect
611. C3#73322semidirect
612. C3#82317semidirect

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
C4×#37572
C2×C3×C3⋊#952
Dic3×#2172
#105913682
D3×C3⋊#952
#105912422
#105912412
#105912392
#105912372
#823173
#733223