Finite Group Databasebeta

← #11808402

Subgroups — #11808402

Order 1152.

1477 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#877C211yesmaximal, characteristic, complemented
2C2×Dic3×#67C212yesmaximal, complemented
3C2×Dic3×D12C211yesmaximal, characteristic, complemented
4#10592652C211yesmaximal, characteristic, complemented
5C3×#4960C211yesmaximal, characteristic
6#10591709C212yesmaximal, complemented
7Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
8#10591353C211yesmaximal, characteristic, complemented
9#10591306C212yesmaximal, complemented
10#10591300C211yesmaximal, characteristic, complemented
11#10591242C211yesmaximal, characteristic, complemented
12#82273—31nomaximal
13#76666—31nomaximal
14C22×C3×#67C2212yes—
15C23×C3×Dic3C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3757C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×#877—24no—
28Dic3×#67—28no—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×Dic32C2212yes—
35Dic3×D12—24no—
36#63658C2211yescharacteristic
37#63658C2212yes—
38C3×C3⋊#95C2211yescharacteristic
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×D4×Dic3—32no—
42C2×D4×Dic3—31no—
43C2×C4×#67—32no—
44C2×#877D311yescharacteristic, complemented
45C2×C4×D12—31no—
46C3×#392—31no—
47#5222—32no—
48#5222—31no—
49#4994—32no—
50#4991—31no—
51#4981—31no—
52#4961—32no—
53#4960D311yescharacteristic
54#4953—31no—
55#4953—31no—
56#4953—61no—
57#4948—32no—
58Dic3×C22⋊C4—32no—
59C4×(C2×D3)⋊C4—32no—
60C4×C4⋊Dic3—31no—
61#4661—31no—
62#4649—31no—
63C24×C32C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2312yes—
69C2×C3×#67—24no—
70C2×C3×#67—24no—
71C2×C3×#67—24no—
72C22×C3×Dic3—22no—
73C22×C3×Dic3—22no—
74C22×C3×Dic3D414yescomplemented
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2311yescharacteristic
80C2×C3×D12—24no—
81C2×C3×D12—22no—
82C2×D3×Dic3—24no—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85C32×C22⋊C4—22no—
86#3757—24no—
87C4⋊(C3⋊Dic3)—22no—
88C3×#217—22no—
89C3×(C2×D3)⋊C4—24no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—22no—
93C3×C4×Dic3D414yescomplemented
94Dic3⋊Dic3—24no—
95Dic3⋊Dic3—24no—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3—24no—
98(C2×D3)⋊Dic3—24no—
99Dic32—24no—
100#2392—91noSylow
101C22×C3×D4—32no—
102C22×C3×D4—31no—
103C23×C3×C4—31no—
104C22×#67C2×D312yes—
105C23×Dic3—32no—
106C23×Dic3C2×D311yescharacteristic
107C22×D12C2×D311yescharacteristic
108C22×C4×D3—32no—
109C3×#117—64no—
110C2×C3×C4⋊C4—31no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C22⋊C4C2×D311yescharacteristic
116C2×C3×C22⋊C4C2×D311yescharacteristic
117C2×C3×C42—31no—
118C2×C3×C42—31no—
119C2×#217—32no—
120C2×#217—32no—
121C2×#217—32no—
122C2×#217—32no—
123C2×#217—32no—
124C2×#217—62no—
125C2×#217C2×D311yescharacteristic
126D4×Dic3—68no—
127D4×Dic3—64no—
128C4×#67—68no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4C2×D312yes—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—32no—
137C2×C4⋊Dic3—61no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4C2×D311yescharacteristic
141C2×Dic3⋊C4C2×D311yescharacteristic
142C2×C4×Dic3—32no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3C2×D311yescharacteristic
145C2×C4×Dic3C2×D311yescharacteristic
146#877—24no—
147C4×D12—64no—
148C3×#95—31no—
149C3⋊#95—31no—
150C3⋊#95—31no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—62no—
156C3⋊#95—61no—
157C3⋊#95C2×D311yescharacteristic
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32C2×D412yes—
163C23×C32C2411yescharacteristic
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3—22no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3#4114yes—
171C2×C32×C4—22no—
172C2×C32×C4—21no—
173C2×C32×C4—22no—
174C2×C32×C4C2×D412yes—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C3×#67—216no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—28no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D412yes—
191C2×C3×Dic3C2×D412yes—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3#4112yes—
195C2×C3×Dic3#4114yes—
196C3×D12—28no—
197D3×Dic3—48no—
198C2×C4×D4—91no—
199C2×C4×D4—92no—
200C2×#117—31no—
201#398—91no—
202#397—91no—
203#396—92no—
204#394—92no—
205#394—91no—
206#392—31no—
207C4×C4⋊C4—91no—
208C4×C22⋊C4—92no—
209C24×C3—21no—
210C24×C3—32no—
211C24×C3C22×D311yescharacteristic
212C24×C3C22×D311yescharacteristic
213C23×D3C22×D312yes—
214C2×C3×D4—64no—
215C2×C3×D4—64no—
216C2×C3×D4—64no—
217C2×C3×D4—64no—
218C2×C3×D4—62no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—31no—
222C22×C3×C4—34no—
223C22×C3×C4—32no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—31no—
227C22×C3×C4—62no—
228C22×C3×C4—62no—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—24no—
234C2×#67—24no—
235C2×#67—24no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—32no—
239C22×Dic3—32no—
240C22×Dic3—32no—
241C22×Dic3—32no—
242C22×Dic3—62no—
243C22×Dic3—62no—
244C22×Dic3—64no—
245C22×Dic3—64no—
246C22×Dic3—64no—
247C22×Dic3D1214yescomplemented
248C22×Dic3C22×D311yescharacteristic
249C22×Dic3C22×D311yescharacteristic
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D311yescharacteristic
252C22×Dic3C22×D311yescharacteristic
253C2×D12—24no—
254C2×D12—22no—
255C2×C4×D3—64no—
256C2×C4×D3—64no—
257C2×C4×D3—64no—
258C3×C4⋊C4—62no—
259C3×C4⋊C4—62no—
260C3×C22⋊C4—22no—
261C3×C22⋊C4—22no—
262C3×C22⋊C4—42no—
263C3×C22⋊C4—64no—
264C3×C22⋊C4—62no—
265C3×C42—34no—
266C3×C42—62no—
267#217—22no—
268#217—64no—
269#217—64no—
270#217—64no—
271#217—64no—
272#217—64no—
273#217—124no—
274(C2×D3)⋊C4—24no—
275(C2×D3)⋊C4—64no—
276(C2×D3)⋊C4—64no—
277(C2×D3)⋊C4—64no—
278C4⋊Dic3—62no—
279C4⋊Dic3—62no—
280C4⋊Dic3—64no—
281C4⋊Dic3—64no—
282C4⋊Dic3—122no—
283Dic3⋊C4—22no—
284Dic3⋊C4—22no—
285Dic3⋊C4—64no—
286Dic3⋊C4—64no—
287C4×Dic3—22no—
288C4×Dic3—64no—
289C4×Dic3—64no—
290C4×Dic3#6714yescomplemented
291C22×C32—22no—
292C22×C32—24no—
293C22×C32—41no—
294C22×C32—42no—
295C22×C32—41no—
296C22×C32C22×D411yescharacteristic
297C22×C32C22×D411yescharacteristic
298C22×C32C2×#4111yescharacteristic
299C22×C32C2×#4112yes—
300C22×C32C2×#4112yes—
301C2×C3×D3—24no—
302C2×C3×D3—24no—
303C2×C3×D3—24no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C2×C3×D3—42no—
307C2×C3×D3—42no—
308C32×C4—22no—
309C32×C4—41no—
310C3⋊Dic3—42no—
311C3⋊Dic3—42no—
312C3×Dic3—22no—
313C3×Dic3—24no—
314C3×Dic3—22no—
315C3×Dic3—41no—
316C3×Dic3#12114yes—
317C22×D4—32no—
318C22×D4—31no—
319C23×C4—31no—
320C23×C4—92no—
321C4×D4—184no—
322C4×D4—188no—
323#117—64no—
324C2×C4⋊C4—31no—
325C2×C4⋊C4—31no—
326C2×C4⋊C4—92no—
327C2×C4⋊C4—92no—
328C2×C4⋊C4—91no—
329C2×C22⋊C4—31no—
330C2×C22⋊C4—32no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4D3211yescharacteristic
336C2×C42—31no—
337C2×C42—31no—
338C2×C42—92no—
339#95—31no—
340#95—92no—
341#95—92no—
342#95—91no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—21no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—22no—
353C23×C3—34no—
354C23×C3—41no—
355C23×C3—41no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—62no—
359C23×C3—62no—
360C23×C3—62no—
361C23×C3—62no—
362C23×C3—62no—
363C23×C3—62no—
364C23×C3C2×D1212yes—
365C23×C3D3×D412yes—
366C23×C3C23×D311yescharacteristic
367C23×C3C23×D311yescharacteristic
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—22no—
373C22×D3—22no—
374C22×D3#23714yes—
375C3×D4—68no—
376C3×D4—616no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—32no—
385C2×C3×C4—32no—
386C2×C3×C4—32no—
387C2×C3×C4—32no—
388C2×C3×C4—32no—
389C2×C3×C4—34no—
390C2×C3×C4—42no—
391C2×C3×C4—41no—
392C2×C3×C4—42no—
393C2×C3×C4—68no—
394C2×C3×C4—62no—
395C2×C3×C4—61no—
396C2×C3×C4—62no—
397C2×C3×C4—61no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4—62no—
401C2×C3×C4D3×D412yes—
402C2×C3×C4C2×#6712yes—
403#67—216no—
404C2×Dic3—21no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—21no—
409C2×Dic3—28no—
410C2×Dic3—22no—
411C2×Dic3—21no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427C2×Dic3—122no—
428C2×Dic3—122no—
429C2×Dic3—122no—
430C2×Dic3—128no—
431C2×Dic3C2×D1212yes—
432C2×Dic3C2×D1212yes—
433C2×Dic3#23512yes—
434C2×Dic3#23714yes—
435C2×Dic3C2×#6712yes—
436C2×Dic3C2×#6712yes—
437D12—28no—
438C4×D3—128no—
439C2×C32—42no—
440C2×C32C2×#12111yescharacteristic
441C2×C32#52512yes—
442C2×C32#52511yescharacteristic
443C2×C32#52912yes—
444C2×C32#53211yescharacteristic
445C3×D3—44no—
446C24—32no—
447C24C2×D3211yescharacteristic
448C2×D4—64no—
449C2×D4—64no—
450C2×D4—64no—
451C2×D4—64no—
452C2×D4—62no—
453C22×C4—31no—
454C22×C4—32no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—34no—
458C22×C4—31no—
459C22×C4—62no—
460C22×C4—62no—
461C22×C4—92no—
462C22×C4—92no—
463C22×C4—184no—
464C22×C4—184no—
465C22×C4—184no—
466C22×C4C2×D3211yescharacteristic
467C22×C4C2×D3211yescharacteristic
468C4⋊C4—62no—
469C4⋊C4—62no—
470C4⋊C4—184no—
471C4⋊C4—184no—
472C4⋊C4—182no—
473C22⋊C4—22no—
474C22⋊C4—64no—
475C22⋊C4—62no—
476C22⋊C4—184no—
477C22⋊C4—184no—
478C22⋊C4—184no—
479C22⋊C4—184no—
480C42—34no—
481C42—62no—
482C42—184no—
483C22×C3—24no—
484C22×C3—22no—
485C22×C3—24no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—21no—
492C22×C3—44no—
493C22×C3—42no—
494C22×C3—41no—
495C22×C3—42no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—42no—
500C22×C3—64no—
501C22×C3—64no—
502C22×C3—64no—
503C22×C3—82no—
504C22×C3—81no—
505C22×C3—81no—
506C22×C3—122no—
507C22×C3—122no—
508C22×C3—122no—
509C22×C3—122no—
510C22×C3C22×D1211yescharacteristic
511C22×C3C2×#23511yescharacteristic
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C2×D3×D411yescharacteristic
514C22×C3C2×#23712yes—
515C22×C3C2×#23712yes—
516C22×C3D3×#4111yescharacteristic
517C22×C3D3×#4112yes—
518C22×C3D3×#4112yes—
519C22×C3C22×#6711yescharacteristic
520C2×D3—24no—
521C2×D3—24no—
522C2×D3—24no—
523C2×D3—42no—
524C2×D3—42no—
525C2×D3—42no—
526C2×D3—42no—
527C3×C4—22no—
528C3×C4—22no—
529C3×C4—34no—
530C3×C4—42no—
531C3×C4—41no—
532C3×C4—41no—
533C3×C4—62no—
534C3×C4—64no—
535C3×C4—62no—
536C3×C4—81no—
537C3×C4—121no—
538Dic3—22no—
539Dic3—22no—
540Dic3—24no—
541Dic3—41no—
542Dic3—122no—
543Dic3—122no—
544Dic3—122no—
545Dic3—122no—
546Dic3—242no—
547Dic3—242no—
548Dic3#93014yes—
549C32#239211yescharacteristic, complemented, Sylow
550C23—21no—
551C23—22no—
552C23—22no—
553C23—21no—
554C23—34no—
555C23—62no—
556C23—62no—
557C23—62no—
558C23—62no—
559C23—62no—
560C23—62no—
561C23D3×D1212yes—
562C23C22×D3211yescharacteristic
563D4—68no—
564D4—616no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—32no—
569C2×C4—32no—
570C2×C4—32no—
571C2×C4—32no—
572C2×C4—34no—
573C2×C4—32no—
574C2×C4—68no—
575C2×C4—62no—
576C2×C4—61no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—61no—
580C2×C4—62no—
581C2×C4—61no—
582C2×C4—182no—
583C2×C4—182no—
584C2×C4—182no—
585C2×C4—182no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4—368no—
589C2×C4D3×#6712yes—
590C2×C3—22no—
591C2×C3—22no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—42no—
596C2×C3—42no—
597C2×C3—82no—
598C2×C3—124no—
599C2×C3#552412yes—
600C2×C3#552812yes—
601C2×C3#558612yes—
602C2×C3#558611yescharacteristic
603C2×C3#560012yes—
604C2×C3D3×#12111yescharacteristic
605C2×C3#571611yescharacteristic
606C2×C3C2×#93011yescharacteristic
607C2×C3#582811yescharacteristic
608C2×C3#583211yescharacteristic
609D3—44no—
610C22—24no—
611C22—22no—
612C22—42no—
613C22—41no—
614C22—41no—
615C22—64no—
616C22—64no—
617C22—64no—
618C22—122no—
619C22—122no—
620C22—122no—
621C22—122no—
622C22C2×D3×D1211yescharacteristic
623C22D3×#23511yescharacteristic
624C22D3×#23712yes—
625C22D3×#23712yes—
626C22C2×D3×#6711yescharacteristic
627C4—22no—
628C4—34no—
629C4—41no—
630C4—64no—
631C4—62no—
632C4—62no—
633C4—121no—
634C4—362no—
635C4—362no—
636C3—21no—
637C3#7666611yescharacteristic, complemented
638C3#8227311yescharacteristic, complemented
639C2—42no—
640C2—124no—
641C2#1059407812yes—
642C2#1059408612yes—
643C2D3×#93011yescharacteristic
644C2#1059515211yescharacteristic
645C2#1059515411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC3×#4960C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#877C2semidirect
2. C2×Dic3×#67C2semidirect
3. C2×Dic3×D12C2semidirect
4. #10592652C2semidirect
6. #10591709C2semidirect
7. Dic3×(C2×D3)⋊C4C2semidirect
8. #10591353C2semidirect
9. #10591306C2semidirect
10. #10591300C2semidirect
11. #10591242C2semidirect
44. C2×#877D3semidirect
74. C22×C3×Dic3D4semidirect
93. C3×C4×Dic3D4semidirect
247. C22×Dic3D12semidirect
290. C4×Dic3#67semidirect
549. C32#2392semidirect
637. C3#76666semidirect
638. C3#82273semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8772
C2×Dic3×#672
C2×Dic3×D122
#105926522
C3×#49602
#105917092
Dic3×(C2×D3)⋊C42
#105913532
#105913062
#105913002
#105912422
#822733
#766663