Finite Group Databasebeta

← #11808412

Subgroups — #11808412

Order 1152.

1605 conjugacy classes of subgroups.

The subgroup lattice has 659 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×#67⋊Dic3C212yesmaximal, complemented
3C2×#63878C211yesmaximal, characteristic, complemented
4C3×#5223C211yesmaximal, characteristic
5C3×#5222C211yesmaximal, characteristic, complemented
6#10591708C212yesmaximal, complemented
7#10591705C212yesmaximal, complemented
8#10591691C212yesmaximal, complemented
9#10591353C211yesmaximal, characteristic, complemented
10#10591315C211yesmaximal, characteristic, complemented
11#10591257C211yesmaximal, characteristic, complemented
12#76891—31nomaximal
13#76666—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C23×C3⋊Dic3C2212yes—
16C22×C3×#67C2212yes—
17C22×D3×Dic3C2211yescharacteristic
18C2×#3757C2212yes—
19D4×C3⋊Dic3—24no—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27#67⋊Dic3—28no—
28C2×#3724C2212yes—
29C2×Dic3⋊Dic3C2211yescharacteristic
30C2×Dic3⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×Dic32C2212yes—
34C2×Dic32C2211yescharacteristic
35#63878—24no—
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2211yescharacteristic
38#63579C2212yes—
39#63579C2212yes—
40C2×D4×Dic3—31no—
41C2×D4×Dic3—31no—
42C2×D4×Dic3—32no—
43C2×D4×Dic3—61no—
44C2×#892—31no—
45C2×#67⋊C4—32no—
46C2×#877—31no—
47C3×#394—31no—
48C3×#392—31no—
49#5223D311yescharacteristic
50#5222—32no—
51#5222D311yescharacteristic, complemented
52#4981—31no—
53#4959—32no—
54#4953—31no—
55#4948—32no—
56#4948—32no—
57Dic3×C22⋊C4—32no—
58Dic3×C22⋊C4—32no—
59#4674—31no—
60#4661—31no—
61#4649—31no—
62#4649—31no—
63C24×C32C2312yes—
64C23×C3×D3C2311yescharacteristic
65C2×C32×D4—24no—
66C2×C32×D4—22no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—24no—
69C22×C3⋊Dic3—24no—
70C22×C3⋊Dic3—24no—
71C22×C3⋊Dic3C2312yes—
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C2×C3×#67—24no—
75C2×C3×#67—24no—
76C2×C3×#67—24no—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2312yes—
82C2×D3×Dic3—22no—
83C2×D3×Dic3—22no—
84C2×D3×Dic3D414yescomplemented
85#3757—24no—
86C4⋊(C3⋊Dic3)—22no—
87C4×C3⋊Dic3D414yescomplemented
88C3×#217—24no—
89C3×#217—24no—
90C3×#217—24no—
91C3×(C2×D3)⋊C4—22no—
92C3×Dic3⋊C4—22no—
93#3724—24no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—24no—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3—22no—
98Dic32—22no—
99Dic32—24no—
100#2392—91noSylow
101C22×C3×D4—21no—
102C22×C3×D4—32no—
103C22×C3×D4C2×D311yescharacteristic
104C22×C3×D4C2×D311yescharacteristic
105C22×#67C2×D312yes—
106C23×Dic3—31no—
107C23×Dic3—32no—
108C23×Dic3—32no—
109C23×Dic3—62no—
110C22×C4×D3—31no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—32no—
115C2×C3×C22⋊C4—31no—
116C2×#217—32no—
117C2×#217—32no—
118C2×#217—32no—
119C2×#217—31no—
120C2×#217—62no—
121C2×#217C2×D312yes—
122C2×#217C2×D312yes—
123C2×#217C2×D312yes—
124D4×Dic3—64no—
125D4×Dic3—64no—
126D4×Dic3—68no—
127D4×Dic3—68no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4C2×D311yescharacteristic
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—32no—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—61no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4C2×D311yescharacteristic
141C2×C4×Dic3—31no—
142C2×C4×Dic3—31no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—31no—
146C2×C4×Dic3—31no—
147C2×C4×Dic3—61no—
148#892—64no—
149#67⋊C4—68no—
150#877—64no—
151C3×#95—31no—
152C3×#95—31no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95C2×D311yescharacteristic
158C3⋊#95C2×D311yescharacteristic
159C23×C32—22no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32#4114yes—
166C23×C32C2411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3C2×D412yes—
172C32×D4—28no—
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—48no—
180C2×C3⋊Dic3C2×D412yes—
181C2×C3⋊Dic3C2×D412yes—
182C2×C3⋊Dic3C2×D412yes—
183C2×C3⋊Dic3#4112yes—
184C3×#67—216no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3C2×D412yes—
197C2×C3×Dic3#4114yes—
198D3×Dic3—28no—
199C2×C4×D4—92no—
200C2×C4×D4—91no—
201C2×#117—91no—
202#398—91no—
203#397—91no—
204#396—92no—
205#394—31no—
206#394—92no—
207#392—31no—
208C4×C4⋊C4—91no—
209C4×C22⋊C4—92no—
210C24×C3—22no—
211C24×C3—31no—
212C24×C3C22×D312yes—
213C24×C3C22×D312yes—
214C23×D3C22×D311yescharacteristic
215C2×C3×D4—24no—
216C2×C3×D4—28no—
217C2×C3×D4—24no—
218C2×C3×D4—24no—
219C2×C3×D4—22no—
220C2×C3×D4—22no—
221C2×C3×D4—64no—
222C2×C3×D4—64no—
223C2×C3×D4—64no—
224C22×C3×C4—21no—
225C22×C3×C4—32no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—32no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—24no—
233C2×#67—24no—
234C2×#67—24no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—34no—
240C22×Dic3—32no—
241C22×Dic3—32no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—62no—
245C22×Dic3—62no—
246C22×Dic3—62no—
247C22×Dic3—64no—
248C22×Dic3—64no—
249C22×Dic3—64no—
250C22×Dic3—64no—
251C22×Dic3—64no—
252C22×Dic3—64no—
253C22×Dic3—68no—
254C22×Dic3—124no—
255C22×Dic3—124no—
256C22×Dic3C22×D311yescharacteristic
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D311yescharacteristic
260C22×Dic3C22×D312yes—
261C2×C4×D3—34no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C3×C4⋊C4—62no—
265C3×C22⋊C4—64no—
266C3×C22⋊C4—64no—
267C3×C22⋊C4—64no—
268C3×C22⋊C4—62no—
269#217—24no—
270#217—24no—
271#217—24no—
272#217—62no—
273#217—64no—
274#217—64no—
275#217—64no—
276#217—68no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—64no—
280C4⋊Dic3—62no—
281C4⋊Dic3—64no—
282C4⋊Dic3—62no—
283C4⋊Dic3—62no—
284C4⋊Dic3—64no—
285Dic3⋊C4—22no—
286Dic3⋊C4—62no—
287Dic3⋊C4—64no—
288Dic3⋊C4—64no—
289Dic3⋊C4—64no—
290C4×Dic3—34no—
291C4×Dic3—34no—
292C4×Dic3—64no—
293C4×Dic3—62no—
294C4×Dic3—64no—
295C4×Dic3—62no—
296C4×Dic3—64no—
297C22×C32—24no—
298C22×C32—24no—
299C22×C32—24no—
300C22×C32—42no—
301C22×C32—42no—
302C22×C32—42no—
303C22×C32—42no—
304C22×C32C22×D411yescharacteristic
305C22×C32C22×D411yescharacteristic
306C22×C32C2×#4112yes—
307C22×C32C2×#4112yes—
308C22×C32C2×#4111yescharacteristic
309C2×C3×D3—22no—
310C2×C3×D3—24no—
311C2×C3×D3—41no—
312C2×C3×D3—42no—
313C2×C3×D3—41no—
314C32×C4—22no—
315C3⋊Dic3—22no—
316C3⋊Dic3—42no—
317C3⋊Dic3#12114yes—
318C3×Dic3—22no—
319C3×Dic3—24no—
320C3×Dic3—41no—
321C3×Dic3—42no—
322C3×Dic3—41no—
323C22×D4—32no—
324C22×D4D3211yescharacteristic
325C23×C4—91no—
326C23×C4—92no—
327C4×D4—184no—
328C4×D4—188no—
329#117—184no—
330C2×C4⋊C4—31no—
331C2×C4⋊C4—91no—
332C2×C4⋊C4—92no—
333C2×C4⋊C4—92no—
334C2×C4⋊C4—91no—
335C2×C22⋊C4—32no—
336C2×C22⋊C4—32no—
337C2×C22⋊C4—32no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—91no—
340C2×C22⋊C4—92no—
341C2×C22⋊C4—92no—
342C2×C42—91no—
343C2×C42—91no—
344C2×C42—92no—
345#95—31no—
346#95—31no—
347#95—92no—
348#95—92no—
349C23×C3—24no—
350C23×C3—24no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—21no—
364C23×C3—24no—
365C23×C3—32no—
366C23×C3—42no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—61no—
371C23×C3—62no—
372C23×C3—61no—
373C23×C3—62no—
374C23×C3#23714yes—
375C23×C3#23714yes—
376C23×C3C23×D311yescharacteristic
377C23×C3C23×D311yescharacteristic
378C22×D3—21no—
379C22×D3—22no—
380C22×D3—22no—
381C22×D3—21no—
382C22×D3D3×D412yes—
383C3×D4—216no—
384C3×D4—28no—
385C3×D4—28no—
386C3×D4—616no—
387C2×C3×C4—24no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—32no—
392C2×C3×C4—34no—
393C2×C3×C4—62no—
394C2×C3×C4—61no—
395C2×C3×C4—62no—
396C2×C3×C4—61no—
397C2×C3×C4—61no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4D3×D412yes—
405C2×C3×C4D3×D412yes—
406#67—216no—
407C2×Dic3—22no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410C2×Dic3—21no—
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—32no—
419C2×Dic3—32no—
420C2×Dic3—32no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—68no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—64no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—62no—
440C2×Dic3—122no—
441C2×Dic3—122no—
442C2×Dic3—122no—
443C2×Dic3—128no—
444C2×Dic3—128no—
445C2×Dic3—1216no—
446C2×Dic3D3×D412yes—
447C2×Dic3#23714yes—
448C4×D3—68no—
449C2×C32—44no—
450C2×C32C2×#12111yescharacteristic
451C2×C32#52511yescharacteristic
452C2×C32#52512yes—
453C2×C32#52912yes—
454C2×C32#53211yescharacteristic
455C3×D3—42no—
456C24—31no—
457C24C2×D3212yes—
458C2×D4—24no—
459C2×D4—22no—
460C2×D4—64no—
461C2×D4—64no—
462C2×D4—64no—
463C22×C4—32no—
464C22×C4—31no—
465C22×C4—32no—
466C22×C4—31no—
467C22×C4—31no—
468C22×C4—94no—
469C22×C4—91no—
470C22×C4—91no—
471C22×C4—92no—
472C22×C4—182no—
473C22×C4—182no—
474C22×C4—184no—
475C22×C4—184no—
476C22×C4—184no—
477C22×C4C2×D3211yescharacteristic
478C4⋊C4—62no—
479C4⋊C4—184no—
480C4⋊C4—184no—
481C4⋊C4—182no—
482C4⋊C4—182no—
483C22⋊C4—64no—
484C22⋊C4—64no—
485C22⋊C4—64no—
486C22⋊C4—62no—
487C22⋊C4—182no—
488C22⋊C4—184no—
489C22⋊C4—184no—
490C42—94no—
491C42—182no—
492C42—184no—
493C22×C3—28no—
494C22×C3—24no—
495C22×C3—24no—
496C22×C3—24no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—21no—
501C22×C3—22no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—21no—
505C22×C3—44no—
506C22×C3—44no—
507C22×C3—44no—
508C22×C3—44no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—62no—
520C22×C3—64no—
521C22×C3—122no—
522C22×C3—121no—
523C22×C3—121no—
524C22×C3C2×D3×D411yescharacteristic
525C22×C3C2×D3×D411yescharacteristic
526C22×C3C2×D3×D411yescharacteristic
527C22×C3C2×D3×D411yescharacteristic
528C22×C3C2×#23712yes—
529C22×C3C2×#23712yes—
530C22×C3C2×#23712yes—
531C22×C3D3×#4112yes—
532C22×C3D3×#4111yescharacteristic
533C22×C3D3×#4111yescharacteristic
534C2×D3—24no—
535C2×D3—22no—
536C2×D3—41no—
537C2×D3—41no—
538C2×D3—42no—
539C3×C4—24no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—62no—
543C3×C4—64no—
544C3×C4—121no—
545C3×C4—122no—
546C3×C4—121no—
547Dic3—24no—
548Dic3—22no—
549Dic3—34no—
550Dic3—34no—
551Dic3—41no—
552Dic3—41no—
553Dic3—42no—
554Dic3—64no—
555Dic3—62no—
556Dic3—62no—
557Dic3—122no—
558Dic3—124no—
559Dic3—122no—
560Dic3—122no—
561C32#239211yescharacteristic, complemented, Sylow
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—32no—
569C23—62no—
570C23—61no—
571C23—62no—
572C23—61no—
573C23#380514yes—
574C23C22×D3211yescharacteristic
575D4—28no—
576D4—616no—
577C2×C4—22no—
578C2×C4—32no—
579C2×C4—34no—
580C2×C4—62no—
581C2×C4—61no—
582C2×C4—62no—
583C2×C4—61no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—61no—
590C2×C4—61no—
591C2×C4—92no—
592C2×C4—92no—
593C2×C4—92no—
594C2×C4—92no—
595C2×C4—188no—
596C2×C4—182no—
597C2×C4—182no—
598C2×C4—182no—
599C2×C4—182no—
600C2×C4—368no—
601C2×C4#381112yes—
602C2×C3—22no—
603C2×C3—21no—
604C2×C3—22no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—48no—
608C2×C3—44no—
609C2×C3—44no—
610C2×C3—122no—
611C2×C3#558612yes—
612C2×C3#558611yescharacteristic
613C2×C3#558611yescharacteristic
614C2×C3#560012yes—
615C2×C3D3×#12111yescharacteristic
616C2×C3D3×#12111yescharacteristic
617C2×C3#560612yes—
618C2×C3#564912yes—
619C2×C3#566811yescharacteristic
620C2×C3#571611yescharacteristic
621D3—42no—
622C22—24no—
623C22—24no—
624C22—24no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—64no—
630C22—62no—
631C22—121no—
632C22—122no—
633C22—121no—
634C22D32×D411yescharacteristic
635C22D3×#23712yes—
636C22#6431211yescharacteristic
637C22C2×#380512yes—
638C22C2×#381111yescharacteristic
639C4—22no—
640C4—64no—
641C4—62no—
642C4—94no—
643C4—122no—
644C4—121no—
645C4—121no—
646C4—182no—
647C4—362no—
648C3—21no—
649C3#7666611yescharacteristic, complemented
650C3#7689111yescharacteristic, complemented
651C2—44no—
652C2—122no—
653C2#1059513012yes—
654C2#1059516711yescharacteristic
655C2#1059520212yes—
656C2#1059528211yescharacteristic
657C2#1059550111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC3×#5223C2
hypercenterC22×D4D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. C2×#67⋊Dic3C2semidirect
3. C2×#63878C2semidirect
5. C3×#5222C2semidirect
6. #10591708C2semidirect
7. #10591705C2semidirect
8. #10591691C2semidirect
9. #10591353C2semidirect
10. #10591315C2semidirect
11. #10591257C2semidirect
51. #5222D3semidirect
84. C2×D3×Dic3D4semidirect
87. C4×C3⋊Dic3D4semidirect
561. C32#2392semidirect
649. C3#76666semidirect
650. C3#76891semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×#67⋊Dic32
C2×#638782
C3×#52232
C3×#52222
#105917082
#105917052
#105916912
#105913532
#105913152
#105912572
#768913
#766663