Finite Group Databasebeta

← #11805528

Subgroups — #11805528

Order 1152.

1485 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic
2C2×#63898C211yesmaximal, characteristic
3C2×Dic3×D12C211yesmaximal, characteristic
4#10592676C211yesmaximal, characteristic, complemented
5C3×#4972C211yesmaximal, characteristic, complemented
6#10591373C212yesmaximal, complemented
7#10591366C212yesmaximal, complemented
8D3×C3⋊#95C212yesmaximal, complemented
9#10591352C211yesmaximal, characteristic, complemented
10C4×#3724C211yesmaximal, characteristic, complemented
11#10591277C212yesmaximal, complemented
12#82334—31nomaximal
13#76203—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×D3×Dic3C2212yes—
17C22×D3×Dic3C2212yes—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×#893—24no—
27C2×#3724C2211yescharacteristic
28C2×#3724C2211yescharacteristic
29C2×Dic3⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32#63898C418yescomplemented
33Dic3×D12—24no—
34#63658C2212yes—
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2211yescharacteristic
39#63579C2211yescharacteristic
40C2×C3×C4×D4—31no—
41C2×D4×Dic3—31no—
42C2×D4×Dic3—31no—
43C2×#893—31no—
44C2×#893D311yescharacteristic
45C2×C4×D12—31no—
46C3×#389—31no—
47#5210—32no—
48C2×C3⋊#95—32no—
49#4989—32no—
50#4987—32no—
51#4984—31no—
52#4977—31no—
53#4977—31no—
54#4977—61no—
55#4972D311yescharacteristic, complemented
56#4946—32no—
57#4942—32no—
58C4×Dic3⋊C4—31no—
59C4×Dic3⋊C4—31no—
60#4928—31no—
61#4668—32no—
62D3×#95—32no—
63C23×C3×D3C2312yes—
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×D12C2×C414yes—
75C2×C3×D12D414yes—
76C2×C3×D12Q814yes—
77C2×C3×C4×D3—24no—
78C2×C3×C4×D3—24no—
79C2×C3×C4×D3—42no—
80C2×D3×Dic3—24no—
81C2×D3×Dic3—24no—
82C2×D3×Dic3—42no—
83C2×D3×Dic3—42no—
84C2×D3×Dic3—42no—
85C2×D3×Dic3C2×C418yescomplemented
86C32×C4⋊C4—22no—
87C4⋊(C3⋊Dic3)—22no—
88C4×C3⋊Dic3C2×C414yescomplemented
89C3×(C2×D3)⋊C4—24no—
90C3×C4⋊Dic3C2×C414yescomplemented
91C3×Dic3⋊C4—42no—
92C3×C4×Dic3—22no—
93C3×C4×Dic3—22no—
94#3724—22no—
95#3724—22no—
96Dic3⋊Dic3—42no—
97(C2×D3)⋊Dic3—24no—
98(C2×D3)⋊Dic3C2×C418yescomplemented
99#2349—91noSylow
100C22×C3×D4—31no—
101C23×C3×C4—32no—
102C23×Dic3—32no—
103C23×Dic3—32no—
104C22×D12C2×D311yescharacteristic
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3C2×D312yes—
108C3×C4×D4—64no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—31no—
111C2×C3×C4⋊C4—32no—
112C2×C3×C4⋊C4C2×D311yescharacteristic
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×C3×C22⋊C4—32no—
115C2×C3×C42—31no—
116C2×C3×C42—31no—
117C2×#217—32no—
118C2×#217—32no—
119D4×Dic3—38no—
120D4×Dic3—64no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4C2×D312yes—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—31no—
126C2×C4⋊Dic3—32no—
127C2×C4⋊Dic3—61no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129C2×Dic3⋊C4—31no—
130C2×Dic3⋊C4—31no—
131C2×Dic3⋊C4—31no—
132C2×Dic3⋊C4—31no—
133C2×Dic3⋊C4—32no—
134C2×Dic3⋊C4C2×D312yes—
135C2×C4×Dic3—31no—
136C2×C4×Dic3—31no—
137C2×C4×Dic3—61no—
138C2×C4×Dic3C2×D311yescharacteristic
139C2×C4×Dic3C2×D311yescharacteristic
140#893—24no—
141#893—38no—
142C4×D12—64no—
143C3×#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—31no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—31no—
152C3⋊#95—31no—
153C3⋊#95—31no—
154C3⋊#95—62no—
155C3⋊#95—62no—
156C3⋊#95C2×D312yes—
157C23×C32C2411yescharacteristic
158C22×C3×D3—22no—
159C22×C3×D3—22no—
160C22×C3×D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3C22×C414yes—
163C22×C3×D3C2×D414yes—
164C22×C3×D3C2×Q814yes—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4—22no—
168C2×C32×C4C22×C412yes—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×Q812yes—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3C22×C412yes—
179C2×C3⋊Dic3C22×C412yes—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3C22×C414yes—
193C2×C3×Dic3#4112yes—
194C2×C3×Dic3#4112yes—
195C3×D12C4⋊C4116yescomplemented
196C3×C4×D3—48no—
197D3×Dic3—48no—
198D3×Dic3—48no—
199C2×C4×D4—31no—
200C2×C4×D4—91no—
201C2×C4×D4—91no—
202#389—31no—
203#389—91no—
204#385—92no—
205#385—92no—
206#382—91no—
207#380—92no—
208C4×C4⋊C4—91no—
209C2×#95—92no—
210C24×C3—32no—
211C23×D3C22×D312yes—
212C2×C3×D4—34no—
213C2×C3×D4—34no—
214C2×C3×D4—34no—
215C22×C3×C4—21no—
216C22×C3×C4—22no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—64no—
223C22×C3×C4—64no—
224C22×C3×C4—122no—
225C22×C3×C4C22×D312yes—
226C22×C3×C4C22×D312yes—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—38no—
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238C22×Dic3—62no—
239C22×Dic3—64no—
240C22×Dic3—64no—
241C22×Dic3—122no—
242C22×Dic3—122no—
243C22×Dic3—122no—
244C22×Dic3C22×D311yescharacteristic
245C22×Dic3C22×D311yescharacteristic
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D311yescharacteristic
248C22×Dic3C22×D311yescharacteristic
249C2×D12Dic614yes—
250C2×D12C4×D314yes—
251C2×D12#6714yes—
252C2×C4×D3—24no—
253C2×C4×D3—24no—
254C2×C4×D3—38no—
255C2×C4×D3—42no—
256C2×C4×D3—64no—
257C2×C4×D3—64no—
258C2×C4×D3—122no—
259C2×C4×D3—122no—
260C2×C4×D3—122no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—34no—
264C3×C4⋊C4—42no—
265C3×C4⋊C4—122no—
266C3×C22⋊C4—64no—
267C3×C42—62no—
268C3×C42—62no—
269#217—38no—
270#217—64no—
271(C2×D3)⋊C4—24no—
272(C2×D3)⋊C4—38no—
273(C2×D3)⋊C4—64no—
274C4⋊Dic3—62no—
275C4⋊Dic3—62no—
276C4⋊Dic3—122no—
277C4⋊Dic3—122no—
278C4⋊Dic3C4×D314yescomplemented
279Dic3⋊C4—42no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—122no—
285C4×Dic3—22no—
286C4×Dic3—22no—
287C4×Dic3—34no—
288C4×Dic3—34no—
289C4×Dic3—64no—
290C22×C32C23×C411yescharacteristic
291C22×C32C22×D411yescharacteristic
292C22×C32C22×Q811yescharacteristic
293C22×C32C2×#4111yescharacteristic
294C22×C32C2×#4111yescharacteristic
295C22×C32H(5,𝔽2)11yescharacteristic
296C22×C32H(5,𝔽2)11yescharacteristic
297C2×C3×D3—24no—
298C2×C3×D3—24no—
299C2×C3×D3—24no—
300C2×C3×D3—24no—
301C2×C3×D3—24no—
302C2×C3×D3—24no—
303C2×C3×D3C2×C4⋊C418yes—
304C32×C4—42no—
305C32×C4C2×C4⋊C414yes—
306C3⋊Dic3—22no—
307C3⋊Dic3—22no—
308C3⋊Dic3—42no—
309C3×Dic3—24no—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—41no—
313C3×Dic3—41no—
314C22×D4—31no—
315C23×C4—32no—
316C23×C4—92no—
317C23×C4—92no—
318C4×D4—64no—
319C4×D4—98no—
320C4×D4—184no—
321C2×C4⋊C4—31no—
322C2×C4⋊C4—32no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—92no—
327C2×C4⋊C4D3211yescharacteristic
328C2×C22⋊C4—32no—
329C2×C22⋊C4—92no—
330C2×C22⋊C4—92no—
331C2×C42—31no—
332C2×C42—31no—
333C2×C42—91no—
334#95—32no—
335#95—91no—
336#95—92no—
337#95—91no—
338#95—92no—
339#95—92no—
340C23×C3—21no—
341C23×C3—34no—
342C23×C3—34no—
343C23×C3—34no—
344C23×C3—62no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—62no—
348C23×C3C23×D311yescharacteristic
349C23×C3C23×D311yescharacteristic
350C22×D3—22no—
351C22×D3—22no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3C2×Dic614yes—
355C22×D3C2×C4×D314yes—
356C22×D3C2×#6714yes—
357C3×D4—316no—
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—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—34no—
368C2×C3×C4—32no—
369C2×C3×C4—32no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—42no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4—62no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—128no—
386C2×C3×C4C2×Dic612yes—
387C2×C3×C4C2×C4×D312yes—
388C2×C3×C4C2×C4×D312yes—
389C2×C3×C4D3×D412yes—
390C2×C3×C4D3×Q812yes—
391C2×C3×C4C2×#6712yes—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—32no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—121no—
425C2×Dic3—121no—
426C2×Dic3—121no—
427C2×Dic3—121no—
428C2×Dic3—122no—
429C2×Dic3—122no—
430C2×Dic3—122no—
431C2×Dic3—128no—
432C2×Dic3—128no—
433C2×Dic3C2×C4×D314yes—
434C2×Dic3#23712yes—
435C2×Dic3#23912yes—
436D12Dic3⋊C4116yescomplemented
437C4×D3—48no—
438C4×D3—128no—
439C4×D3—128no—
440C2×C32C22×C4⋊C411yescharacteristic
441C2×C32C4×#4111yescharacteristic
442C2×C32#51811yescharacteristic
443C2×C32#54611yescharacteristic
444C2×C32#54611yescharacteristic
445C2×C32#55411yescharacteristic
446C2×C32#55411yescharacteristic
447C3×D3—28no—
448C24—32no—
449C2×D4—34no—
450C2×D4—34no—
451C2×D4—34no—
452C22×C4—31no—
453C22×C4—32no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—64no—
458C22×C4—64no—
459C22×C4—98no—
460C22×C4—91no—
461C22×C4—91no—
462C22×C4—92no—
463C22×C4—122no—
464C22×C4—184no—
465C22×C4—184no—
466C22×C4—362no—
467C22×C4—362no—
468C22×C4—362no—
469C22×C4C2×D3212yes—
470C22×C4C2×D3211yescharacteristic
471C4⋊C4—22no—
472C4⋊C4—34no—
473C4⋊C4—122no—
474C4⋊C4—182no—
475C4⋊C4—182no—
476C4⋊C4—182no—
477C4⋊C4—362no—
478C22⋊C4—64no—
479C22⋊C4—98no—
480C22⋊C4—184no—
481C42—62no—
482C42—62no—
483C42—94no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—38no—
492C22×C3—64no—
493C22×C3—64no—
494C22×C3—64no—
495C22×C3—64no—
496C22×C3—64no—
497C22×C3—64no—
498C22×C3C22×Dic611yescharacteristic
499C22×C3C22×C4×D311yescharacteristic
500C22×C3C22×C4×D311yescharacteristic
501C22×C3C2×D3×D411yescharacteristic
502C22×C3C2×#23711yescharacteristic
503C22×C3#100411yescharacteristic
504C22×C3#100411yescharacteristic
505C22×C3C2×D3×Q811yescharacteristic
506C22×C3C2×#23911yescharacteristic
507C22×C3D3×#4111yescharacteristic
508C22×C3D3×#4111yescharacteristic
509C22×C3#100911yescharacteristic
510C22×C3#100911yescharacteristic
511C22×C3C22×#6711yescharacteristic
512C2×D3—24no—
513C2×D3—24no—
514C2×D3—24no—
515C2×D3—24no—
516C2×D3—24no—
517C2×D3—24no—
518C2×D3C2×Dic3⋊C418yes—
519C3×C4—24no—
520C3×C4—42no—
521C3×C4—42no—
522C3×C4—64no—
523C3×C4—62no—
524C3×C4—62no—
525C3×C4—82no—
526C3×C4—121no—
527C3×C4—121no—
528C3×C4D3×C4⋊C414yes—
529C3×C4C2×Dic3⋊C414yes—
530Dic3—24no—
531Dic3—22no—
532Dic3—22no—
533Dic3—41no—
534Dic3—41no—
535Dic3—62no—
536Dic3—62no—
537Dic3—62no—
538Dic3—62no—
539Dic3—122no—
540Dic3—122no—
541Dic3—122no—
542Dic3—122no—
543Dic3—242no—
544C32#234911yescharacteristic, complemented, Sylow
545C23—34no—
546C23—34no—
547C23—34no—
548C23—62no—
549C23—62no—
550C23—62no—
551C23—62no—
552C23C22×D3211yescharacteristic
553D4—316no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—34no—
558C2×C4—32no—
559C2×C4—32no—
560C2×C4—62no—
561C2×C4—61no—
562C2×C4—62no—
563C2×C4—61no—
564C2×C4—61no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—61no—
572C2×C4—92no—
573C2×C4—92no—
574C2×C4—128no—
575C2×C4—181no—
576C2×C4—181no—
577C2×C4—181no—
578C2×C4—181no—
579C2×C4—182no—
580C2×C4—182no—
581C2×C4—182no—
582C2×C4—368no—
583C2×C4—368no—
584C2×C4D3×Dic612yes—
585C2×C4C4×D3212yes—
586C2×C4D3×#6712yes—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—68no—
595C2×C3C2×D3×C4⋊C411yescharacteristic
596C2×C3C4×#23711yescharacteristic
597C2×C3#553911yescharacteristic
598C2×C3#554311yescharacteristic
599C2×C3#554511yescharacteristic
600C2×C3#554511yescharacteristic
601C2×C3C4×#23911yescharacteristic
602C2×C3#561211yescharacteristic
603C2×C3#563011yescharacteristic
604C2×C3#569011yescharacteristic
605C2×C3#573011yescharacteristic
606C2×C3C22×Dic3⋊C411yescharacteristic
607C2×C3#580611yescharacteristic
608C2×C3#582911yescharacteristic
609D3—28no—
610C22—38no—
611C22—64no—
612C22—64no—
613C22—64no—
614C22—64no—
615C22—64no—
616C22—64no—
617C22C2×D3×Dic611yescharacteristic
618C22C2×C4×D3211yescharacteristic
619C22D3×#23711yescharacteristic
620C22#6431311yescharacteristic
621C22D3×#23911yescharacteristic
622C22#6432011yescharacteristic
623C22C2×D3×#6711yescharacteristic
624C4—42no—
625C4—64no—
626C4—62no—
627C4—62no—
628C4—121no—
629C4—121no—
630C4—182no—
631C4—182no—
632C4—362no—
633C4D3×Dic3⋊C414yes—
634C3—21no—
635C3#7620311yescharacteristic, complemented
636C3#8233411yescharacteristic, complemented
637C2—68no—
638C2#1059436011yescharacteristic
639C2#1059445211yescharacteristic
640C2#1059446011yescharacteristic
641C2#1059460611yescharacteristic
642C2C2×D3×Dic3⋊C411yescharacteristic
643C2#1059522811yescharacteristic
644C2#1059542711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10592676C2semidirect
5. C3×#4972C2semidirect
6. #10591373C2semidirect
7. #10591366C2semidirect
8. D3×C3⋊#95C2semidirect
9. #10591352C2semidirect
10. C4×#3724C2semidirect
11. #10591277C2semidirect
32. #63898C4semidirect
55. #4972D3semidirect
85. C2×D3×Dic3C2×C4semidirect
88. C4×C3⋊Dic3C2×C4semidirect
90. C3×C4⋊Dic3C2×C4semidirect
98. (C2×D3)⋊Dic3C2×C4semidirect
195. C3×D12C4⋊C4semidirect
278. C4⋊Dic3C4×D3semidirect
436. D12Dic3⋊C4semidirect
544. C32#2349semidirect
635. C3#76203semidirect
636. C3#82334semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×#638982
C2×Dic3×D122
#105926762
C3×#49722
#105913732
#105913662
D3×C3⋊#952
#105913522
C4×#37242
#105912772
#823343
#762033