Finite Group Databasebeta

← #11824489

Subgroups — #11824489

Order 1152.

1445 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#888C211yesmaximal, characteristic, complemented
2C2×#63888C212yesmaximal, complemented
3C2×#63887C212yesmaximal, complemented
4C2×#63880C211yesmaximal, characteristic
5#10592692C211yesmaximal, characteristic, complemented
6C3×#4993C211yesmaximal, characteristic, complemented
7#10591384C212yesmaximal
8#10591350C211yesmaximal, characteristic, complemented
9#10591324C211yesmaximal, characteristic, complemented
10#10591244C212yesmaximal, complemented
11#10591242C211yesmaximal, characteristic, complemented
12#83259—31nomaximal
13#78037—31nomaximal
14C22×C3×Dic6C2212yes—
15C22×#626C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C22×D3×Dic3C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3752C2212yes—
21C2×#3750C2212yes—
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C3×#888—24no—
29C2×#3724C2212yes—
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2212yes—
32C2×Dic3⋊Dic3C2212yes—
33C2×#3722C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×Dic32C2212yes—
36#63888—28no—
37#63887—28no—
38#63880—24no—
39#63658C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C2×C3×C4⋊Q8—31no—
42C2×#946—32no—
43C2×#946—32no—
44C2×#896—32no—
45C2×#888D311yescharacteristic, complemented
46C2×#67⋊C4—31no—
47C2×#878—32no—
48C2×C4×D12—31no—
49C3×#399—31no—
50#4993—31no—
51#4993—31no—
52#4993—31no—
53#4993—31no—
54#4993—61no—
55#4993D311yescharacteristic, complemented
56#4988—32no—
57#4975—32no—
58#4975—32no—
59#4957—32no—
60#4949—31no—
61C4×C4⋊Dic3—31no—
62#4677—31no—
63#4649—31no—
64C23×C3⋊D3C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×C3×Dic6—24no—
76C2×C3×Dic6—24no—
77C2×C3×Dic6—24no—
78C2×#626—22no—
79C2×#626—22no—
80C2×#626Q814yescomplemented
81C2×#624—22no—
82C2×#624—24no—
83C2×D3×Dic3—22no—
84C2×D3×Dic3—24no—
85C32×C4⋊C4—22no—
86#3752—22no—
87#3752—24no—
88#3750—24no—
89C3×(C2×D3)⋊C4—22no—
90C3×(C2×D3)⋊C4—24no—
91C3×C4⋊Dic3—22no—
92C3×Dic3⋊C4—24no—
93C3×Dic3⋊C4—24no—
94C3×C4×Dic3D414yes—
95#3724—24no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—24no—
98Dic3⋊Dic3D418yescomplemented
99#3722—24no—
100(C2×D3)⋊Dic3—24no—
101Dic32—24no—
102#2542—91noSylow
103C22×C3×Q8—32no—
104C22×#67—31no—
105C23×Dic3—31no—
106C22×D12—31no—
107C22×C4×D3—31no—
108C22×C4×D3—31no—
109C22×C4×D3—31no—
110C22×Dic6C2×D312yes—
111C3×C4⋊Q8—64no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4C2×D311yescharacteristic
117C2×C3×C4⋊C4C2×D311yescharacteristic
118C2×C3×C22⋊C4—31no—
119C2×C3×C22⋊C4—32no—
120C2×C3×C42—31no—
121C2×#217—32no—
122#946—68no—
123#946—68no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—61no—
132C2×(C2×D3)⋊C4—62no—
133C2×(C2×D3)⋊C4C2×D311yescharacteristic
134C2×(C2×D3)⋊C4C2×D312yes—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—32no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3C2×D311yescharacteristic
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—32no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—32no—
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4—62no—
147C2×Dic3⋊C4C2×D312yes—
148C2×Dic3⋊C4C2×D312yes—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—32no—
151C2×C4×Dic3C2×D311yescharacteristic
152#896—68no—
153#888—24no—
154#67⋊C4—64no—
155#878—68no—
156C4×D12—64no—
157C3×#95—31no—
158C3⋊#95—31no—
159C3⋊#95—31no—
160C3⋊#95—61no—
161C3⋊#95C2×D311yescharacteristic
162C23×C32C2411yescharacteristic
163C22×C3⋊D3—22no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3C2×Q812yes—
168C22×C3×D3—22no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3—22no—
172C22×C3×D3C2×Q812yes—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C2×D412yes—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3C2×D414yes—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D414yes—
191C2×C3×Dic3C2×D414yes—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3C2×Q812yes—
195C2×C3×Dic3#4112yes—
196C3×Dic6—48no—
197#626—28no—
198#624—44no—
199D3×Dic3—44no—
200C2×C4⋊Q8—31no—
201C2×C22⋊Q8—92no—
202C2×C22⋊Q8—92no—
203C2×C4×D4—91no—
204#399—31no—
205#399—91no—
206#399—91no—
207#399—91no—
208#390—92no—
209#384—92no—
210C4×C4⋊C4—91no—
211C24×C3—31no—
212C23×D3—31no—
213C23×D3—31no—
214C23×D3—61no—
215C23×D3C22×D311yescharacteristic
216C2×C3×Q8—64no—
217C2×C3×Q8—64no—
218C2×C3×Q8—64no—
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—32no—
224C22×C3×C4—31no—
225C22×C3×C4—32no—
226C22×C3×C4C22×D312yes—
227C22×C3×C4C22×D312yes—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—34no—
231C2×#67—62no—
232C2×#67—62no—
233C22×Dic3—32no—
234C22×Dic3—32no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—62no—
238C22×Dic3—61no—
239C22×Dic3—64no—
240C22×Dic3—62no—
241C22×Dic3C22×D311yescharacteristic
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D311yescharacteristic
245C22×Dic3C22×D311yescharacteristic
246C2×D12—34no—
247C2×D12—62no—
248C2×D12—62no—
249C2×C4×D3—62no—
250C2×C4×D3—64no—
251C2×C4×D3—62no—
252C2×C4×D3—64no—
253C2×C4×D3—64no—
254C2×C4×D3—62no—
255C2×Dic6—24no—
256C2×Dic6—24no—
257C2×Dic6—24no—
258C3×C4⋊C4—22no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—42no—
261C3×C4⋊C4—64no—
262C3×C4⋊C4—64no—
263C3×C4⋊C4—62no—
264C3×C22⋊C4—64no—
265C3×C22⋊C4—62no—
266C3×C42—34no—
267#217—64no—
268(C2×D3)⋊C4—22no—
269(C2×D3)⋊C4—24no—
270(C2×D3)⋊C4—64no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—64no—
273(C2×D3)⋊C4—64no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—64no—
277(C2×D3)⋊C4—124no—
278(C2×D3)⋊C4—122no—
279C4⋊Dic3—22no—
280C4⋊Dic3—38no—
281C4⋊Dic3—62no—
282C4⋊Dic3—64no—
283Dic3⋊C4—24no—
284Dic3⋊C4—24no—
285Dic3⋊C4—38no—
286Dic3⋊C4—64no—
287Dic3⋊C4—64no—
288Dic3⋊C4—64no—
289Dic3⋊C4—64no—
290Dic3⋊C4—64no—
291Dic3⋊C4—62no—
292Dic3⋊C4—124no—
293C4×Dic3—64no—
294C4×Dic3—64no—
295C4×Dic3#6714yes—
296C22×C32C22×D412yes—
297C22×C32C22×D411yescharacteristic
298C22×C32C22×Q811yescharacteristic
299C22×C32C2×#4111yescharacteristic
300C22×C322−1+412yes—
301C2×C3⋊D3—22no—
302C2×C3⋊D3—24no—
303C2×C3⋊D3—41no—
304C2×C3⋊D3—41no—
305C2×C3⋊D3—42no—
306C2×C3×D3—22no—
307C2×C3×D3—24no—
308C2×C3×D3—41no—
309C2×C3×D3—41no—
310C2×C3×D3—42no—
311C32×C4—22no—
312C32×C4—42no—
313C3⋊Dic3—24no—
314C3⋊Dic3—41no—
315C3×Dic3—24no—
316C3×Dic3—41no—
317C3×Dic3—42no—
318C3×Dic3C22⋊Q814yescomplemented
319C3×Dic3#12714yes—
320C22×Q8—32no—
321C22×D4—91no—
322C23×C4—91no—
323C23×C4—91no—
324C4⋊Q8—64no—
325C22⋊Q8—188no—
326C22⋊Q8—188no—
327C4×D4—184no—
328C2×C4⋊C4—32no—
329C2×C4⋊C4—32no—
330C2×C4⋊C4—31no—
331C2×C4⋊C4—92no—
332C2×C4⋊C4—91no—
333C2×C4⋊C4—92no—
334C2×C4⋊C4—92no—
335C2×C4⋊C4—92no—
336C2×C4⋊C4D3211yescharacteristic
337C2×C22⋊C4—31no—
338C2×C22⋊C4—32no—
339C2×C22⋊C4—92no—
340C2×C22⋊C4—92no—
341C2×C22⋊C4—91no—
342C2×C22⋊C4—92no—
343C2×C42—31no—
344C2×C42—92no—
345#95—31no—
346#95—91no—
347C23×C3—21no—
348C23×C3—32no—
349C23×C3—62no—
350C23×C3—61no—
351C23×C3—62no—
352C23×C3—61no—
353C23×C3C23×D311yescharacteristic
354C23×C3C23×D311yescharacteristic
355C22×D3—22no—
356C22×D3—21no—
357C22×D3—21no—
358C22×D3—22no—
359C22×D3—32no—
360C22×D3—32no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3—61no—
365C22×D3—61no—
366C22×D3—62no—
367C22×D3—61no—
368C22×D3—62no—
369C22×D3—61no—
370C22×D3—122no—
371C22×D3—121no—
372C22×D3—122no—
373C22×D3—121no—
374C22×D3D3×Q812yes—
375C3×Q8—128no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—34no—
386C2×C3×C4—32no—
387C2×C3×C4—32no—
388C2×C3×C4—32no—
389C2×C3×C4—32no—
390C2×C3×C4—34no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—61no—
402C2×C3×C4D3×D412yes—
403C2×C3×C4C2×#6712yes—
404#67—68no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—21no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—34no—
413C2×Dic3—34no—
414C2×Dic3—64no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—122no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426C2×Dic3—121no—
427C2×Dic3—124no—
428C2×Dic3D3×D414yes—
429C2×Dic3D3×D414yes—
430C2×Dic3D3×Q812yes—
431C2×Dic3#23912yes—
432C2×Dic3C2×#6712yes—
433C2×Dic3C2×#6712yes—
434D12—68no—
435C4×D3—124no—
436C4×D3—124no—
437C4×D3—124no—
438Dic6—48no—
439C2×C32C2×C22⋊Q811yescharacteristic
440C2×C32C2×#12711yescharacteristic
441C2×C32#53611yescharacteristic
442C2×C32#54712yes—
443C2×C32D4×Q812yes—
444C3⋊D3—42no—
445C3×D3—42no—
446C24—31no—
447C24—91no—
448C2×Q8—64no—
449C2×Q8—64no—
450C2×Q8—64no—
451C2×D4—94no—
452C2×D4—182no—
453C2×D4—182no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—32no—
457C22×C4—31no—
458C22×C4—32no—
459C22×C4—92no—
460C22×C4—91no—
461C22×C4—182no—
462C22×C4—184no—
463C22×C4—182no—
464C22×C4—184no—
465C22×C4C2×D3212yes—
466C22×C4C2×D3211yescharacteristic
467C4⋊C4—22no—
468C4⋊C4—64no—
469C4⋊C4—64no—
470C4⋊C4—62no—
471C4⋊C4—98no—
472C4⋊C4—184no—
473C4⋊C4—182no—
474C4⋊C4—184no—
475C4⋊C4—184no—
476C22⋊C4—64no—
477C22⋊C4—62no—
478C22⋊C4—184no—
479C22⋊C4—184no—
480C22⋊C4—184no—
481C22⋊C4—182no—
482C42—34no—
483C42—184no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—64no—
490C22×C3—62no—
491C22×C3—122no—
492C22×C3—121no—
493C22×C3—121no—
494C22×C3C2×D3×D412yes—
495C22×C3C2×D3×D412yes—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C2×D3×Q811yescharacteristic
498C22×C3C2×D3×Q811yescharacteristic
499C22×C3C2×#23911yescharacteristic
500C22×C3#100712yes—
501C22×C3D3×#4111yescharacteristic
502C22×C3#101012yes—
503C22×C3C22×#6711yescharacteristic
504C2×D3—24no—
505C2×D3—22no—
506C2×D3—41no—
507C2×D3—42no—
508C2×D3—41no—
509C2×D3—64no—
510C2×D3—64no—
511C2×D3—62no—
512C2×D3—62no—
513C2×D3—124no—
514C2×D3—122no—
515C2×D3—121no—
516C2×D3—122no—
517C2×D3—121no—
518C2×D3—122no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—242no—
522C2×D3—241no—
523C2×D3—241no—
524C3×C4—22no—
525C3×C4—22no—
526C3×C4—34no—
527C3×C4—34no—
528C3×C4—42no—
529C3×C4—42no—
530C3×C4—42no—
531C3×C4—64no—
532C3×C4—82no—
533C3×C4—122no—
534C3×C4—121no—
535Dic3—24no—
536Dic3—41no—
537Dic3—42no—
538Dic3—64no—
539Dic3—64no—
540Dic3—124no—
541Dic3—121no—
542Dic3—121no—
543Dic3—241no—
544Dic3#94014yes—
545Dic3#94614yescomplemented
546C32#254211yescharacteristic, complemented, Sylow
547C23—32no—
548C23—62no—
549C23—62no—
550C23—61no—
551C23—61no—
552C23—92no—
553C23—182no—
554C23—182no—
555C23—181no—
556C23—181no—
557C23C22×D3211yescharacteristic
558Q8—128no—
559D4—188no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—34no—
565C2×C4—32no—
566C2×C4—32no—
567C2×C4—32no—
568C2×C4—32no—
569C2×C4—34no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—61no—
576C2×C4—62no—
577C2×C4—94no—
578C2×C4—182no—
579C2×C4—182no—
580C2×C4—182no—
581C2×C4—181no—
582C2×C4—364no—
583C2×C4—364no—
584C2×C4D3×#6712yes—
585C2×C3—22no—
586C2×C3—22no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—122no—
591C2×C3D3×C22⋊Q811yescharacteristic
592C2×C3#563212yes—
593C2×C3#564811yescharacteristic
594C2×C3#565512yes—
595C2×C3D3×#12711yescharacteristic
596C2×C3#572612yes—
597C2×C3#572712yes—
598C2×C3C2×#94011yescharacteristic
599C2×C3C2×#94611yescharacteristic
600C2×C3#581611yescharacteristic
601D3—42no—
602D3—122no—
603D3—122no—
604D3—242no—
605C22—64no—
606C22—62no—
607C22—122no—
608C22—121no—
609C22—121no—
610C22—184no—
611C22—182no—
612C22—362no—
613C22—361no—
614C22—361no—
615C22#6429712yes—
616C22D32×D412yes—
617C22D32×Q811yescharacteristic
618C22D3×#23911yescharacteristic
619C22C2×D3×#6711yescharacteristic
620C4—22no—
621C4—34no—
622C4—34no—
623C4—42no—
624C4—64no—
625C4—121no—
626C4—122no—
627C4—184no—
628C4—361no—
629C3—21no—
630C3#7803711yescharacteristic, complemented
631C3#8325911yescharacteristic, complemented
632C2—122no—
633C2—362no—
634C2#1059437212yes—
635C2#1059437812yes—
636C2#1059489711yescharacteristic
637C2D3×#94011yescharacteristic
638C2D3×#94611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2542
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#888C2semidirect
2. C2×#63888C2semidirect
3. C2×#63887C2semidirect
5. #10592692C2semidirect
6. C3×#4993C2semidirect
8. #10591350C2semidirect
9. #10591324C2semidirect
10. #10591244C2semidirect
11. #10591242C2semidirect
45. C2×#888D3semidirect
55. #4993D3semidirect
80. C2×#626Q8semidirect
98. Dic3⋊Dic3D4semidirect
318. C3×Dic3C22⋊Q8semidirect
545. Dic3#946semidirect
546. C32#2542semidirect
630. C3#78037semidirect
631. C3#83259semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8882
C2×#638882
C2×#638872
C2×#638802
#105926922
C3×#49932
#105913842
#105913502
#105913242
#105912442
#105912422
#832593
#780373