Finite Group Databasebeta

← #11801688

Subgroups — #11801688

Order 1152.

1517 conjugacy classes of subgroups.

The subgroup lattice has 663 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×#63874C211yesmaximal, characteristic, complemented
4C3×C4×#217C211yesmaximal, characteristic, complemented
5#10591704C212yesmaximal
6#10591703C212yesmaximal, complemented
7C4×#3724C211yesmaximal, characteristic, complemented
8C4×#3722C211yesmaximal, characteristic, complemented
9#10591266C212yesmaximal, complemented
10#10591264C212yesmaximal, complemented
11C4×Dic32C211yesmaximal, characteristic, complemented
12#82225—31nomaximal
13#73439—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C4×#638C418yescomplemented
19C2×#3752C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C3×#926—24no—
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×#3724C2212yes—
31C2×#3724C2212yes—
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×Dic32C2212yes—
35C2×Dic32C2212yes—
36#63874—24no—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×C4×#67—31no—
42C2×C4×#67—31no—
43C2×C4×#67—61no—
44C2×#926D311yescharacteristic, complemented
45C2×#872—31no—
46C2×#872—31no—
47C3×C4×C22⋊C4—31no—
48C4×#217D311yescharacteristic, complemented
49#4990—32no—
50#4976—32no—
51#4957—32no—
52#4957—32no—
53#4945—32no—
54#4944—32no—
55C4×(C2×D3)⋊C4—31no—
56C4×(C2×D3)⋊C4—31no—
57C4×Dic3⋊C4—31no—
58C4×Dic3⋊C4—31no—
59C42×Dic3—31no—
60C42×Dic3—31no—
61#4670—32no—
62#4647—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2311yescharacteristic
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yes—
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C2×#638—24no—
71C2×#638C2×C414yes—
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3—22no—
77C2×C4×C3⋊D3C2×C414yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82#3757C2×C414yes—
83#3752C2×C414yes—
84#3750C2×C414yes—
85C4×C3⋊Dic3C2×C414yes—
86C3×#217—24no—
87C3×#217—24no—
88C3×C4⋊Dic3—24no—
89C3×C4×Dic3—22no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3—22no—
92C3×C4×Dic3D414yescomplemented
93#3724—24no—
94#3724—24no—
95#3722—24no—
96#3722—24no—
97Dic32—24no—
98Dic32—24no—
99#2293—91noSylow
100C23×C3×C4—21no—
101C23×C3×C4C2×D311yescharacteristic
102C23×C3×C4C2×D311yescharacteristic
103C22×#67—31no—
104C22×#67—31no—
105C22×#67—61no—
106C22×C4×D3—31no—
107C22×C4×D3—31no—
108C22×C4×D3—61no—
109C3×#117—64no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C22⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C42—31no—
114C2×C3×C42—31no—
115C2×C3×C42—31no—
116C2×C3×C42—31no—
117C2×#217—31no—
118C2×#217—31no—
119C2×#217—61no—
120C2×#217C2×D312yes—
121C2×#217C2×D312yes—
122C4×#67—38no—
123C4×#67—38no—
124C4×#67—68no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—61no—
132#926—24no—
133C2×C4⋊Dic3C2×D312yes—
134C2×Dic3⋊C4—31no—
135C2×Dic3⋊C4—31no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—61no—
141C2×C4×Dic3—31no—
142C2×C4×Dic3—31no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—32no—
145C2×C4×Dic3—32no—
146C2×C4×Dic3—32no—
147C2×C4×Dic3—61no—
148C2×C4×Dic3C2×D311yescharacteristic
149C2×C4×Dic3C2×D311yescharacteristic
150C2×C4×Dic3C2×D311yescharacteristic
151C2×C4×Dic3C2×D311yescharacteristic
152#872—64no—
153#872—64no—
154C3×#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95C2×D312yes—
160C23×C32—22no—
161C23×C32—21no—
162C23×C32—22no—
163C23×C32—21no—
164C23×C32C22×C412yes—
165C23×C32C2411yescharacteristic
166C22×C3⋊D3—22no—
167C22×C3⋊D3—21no—
168C22×C3⋊D3—22no—
169C22×C3⋊D3—21no—
170C22×C3⋊D3C22×C412yes—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—28no—
174C2×C32×C4C22×C412yes—
175C2×C32×C4C22×C412yes—
176C2×C32×C4C2×D412yes—
177C2×C32×C4#4112yes—
178#638—28no—
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3C22×C412yes—
183C2×C3⋊Dic3C22×C412yes—
184C2×C3⋊Dic3C22×C412yes—
185C2×C3⋊Dic3#4114yes—
186C4×C3⋊D3—28no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3C2×D414yes—
198C2×C3×Dic3#4114yes—
199C2×C4×D4—91no—
200C2×#117—31no—
201C2×#117—91no—
202#390—92no—
203#389—92no—
204#388—92no—
205#388—92no—
206C4×C4⋊C4—91no—
207C4×C22⋊C4—31no—
208C4×C22⋊C4—91no—
209C43—91no—
210C24×C3—21no—
211C24×C3C22×D311yescharacteristic
212C24×C3C22×D311yescharacteristic
213C23×D3—31no—
214C23×D3—31no—
215C23×D3—61no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—24no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4—42no—
228C22×C3×C4—42no—
229C22×C3×C4C4×D314yes—
230C22×C3×C4C4×D314yes—
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—34no—
236C2×#67—34no—
237C2×#67—64no—
238C2×#67—64no—
239C2×#67—64no—
240C2×#67—68no—
241C22×Dic3—31no—
242C22×Dic3—31no—
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—61no—
248C22×Dic3—61no—
249C22×Dic3—61no—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D312yes—
252C22×Dic3C22×D312yes—
253C22×Dic3C22×D312yes—
254C2×C4×D3—34no—
255C2×C4×D3—34no—
256C2×C4×D3—64no—
257C2×C4×D3—62no—
258C2×C4×D3—62no—
259C2×C4×D3—62no—
260C2×C4×D3—62no—
261C2×C4×D3—122no—
262C2×C4×D3—122no—
263C3×C4⋊C4—64no—
264C3×C22⋊C4—64no—
265C3×C22⋊C4—64no—
266C3×C42—34no—
267C3×C42—62no—
268C3×C42—62no—
269C3×C42—62no—
270#217—24no—
271#217—24no—
272#217—34no—
273#217—34no—
274#217—64no—
275(C2×D3)⋊C4—34no—
276(C2×D3)⋊C4—34no—
277(C2×D3)⋊C4—64no—
278(C2×D3)⋊C4—64no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281(C2×D3)⋊C4—64no—
282C4⋊Dic3—24no—
283Dic3⋊C4—34no—
284Dic3⋊C4—34no—
285Dic3⋊C4—64no—
286Dic3⋊C4—64no—
287Dic3⋊C4—64no—
288Dic3⋊C4—64no—
289Dic3⋊C4—64no—
290C4×Dic3—22no—
291C4×Dic3—22no—
292C4×Dic3—22no—
293C4×Dic3—34no—
294C4×Dic3—34no—
295C4×Dic3—64no—
296C4×Dic3—64no—
297C4×Dic3—64no—
298C4×Dic3—64no—
299C4×Dic3—64no—
300C4×Dic3#6714yescomplemented
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—22no—
304C22×C32—42no—
305C22×C32—42no—
306C22×C32C23×C411yescharacteristic
307C22×C32C22×D411yescharacteristic
308C22×C32C2×#4111yescharacteristic
309C22×C32C2×#4112yes—
310C22×C32C2×#4112yes—
311C2×C3⋊D3—22no—
312C2×C3⋊D3—22no—
313C2×C3⋊D3—22no—
314C2×C3⋊D3—42no—
315C2×C3⋊D3—42no—
316C32×C4—22no—
317C32×C4C4×D414yes—
318C3⋊Dic3—22no—
319C3⋊Dic3—22no—
320C3⋊Dic3#11714yescomplemented
321C3×Dic3—24no—
322C3×Dic3—24no—
323C3×Dic3—42no—
324C3×Dic3—42no—
325C22×D4—91no—
326C23×C4—91no—
327C23×C4D3211yescharacteristic
328C4×D4—98no—
329#117—64no—
330#117—184no—
331C2×C4⋊C4—32no—
332C2×C4⋊C4—91no—
333C2×C4⋊C4—92no—
334C2×C4⋊C4—92no—
335C2×C22⋊C4—32no—
336C2×C22⋊C4—32no—
337C2×C22⋊C4—91no—
338C2×C22⋊C4—91no—
339C2×C22⋊C4—92no—
340C2×C22⋊C4—92no—
341C2×C42—31no—
342C2×C42—31no—
343C2×C42—31no—
344C2×C42—31no—
345C2×C42—91no—
346C2×C42—92no—
347C2×C42—92no—
348#95—32no—
349#95—92no—
350#95—92no—
351C23×C3—24no—
352C23×C3—22no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—22no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—22no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—42no—
365C23×C3C2×C4×D312yes—
366C23×C3C2×C4×D312yes—
367C23×C3C23×D311yescharacteristic
368C23×C3C23×D311yescharacteristic
369C22×D3—32no—
370C22×D3—32no—
371C22×D3—62no—
372C22×D3—64no—
373C22×D3—62no—
374C22×D3—61no—
375C22×D3—61no—
376C22×D3—61no—
377C22×D3—62no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—61no—
381C22×D3—121no—
382C22×D3—121no—
383C22×D3—122no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—28no—
389C2×C3×C4—28no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—34no—
395C2×C3×C4—34no—
396C2×C3×C4—48no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4C2×C4×D312yes—
410C2×C3×C4C2×C4×D312yes—
411C2×C3×C4C2×C4×D312yes—
412C2×C3×C4C2×C4×D312yes—
413C2×C3×C4#23512yes—
414C2×C3×C4D3×D412yes—
415C2×C3×C4#23712yes—
416C2×C3×C4C2×#6712yes—
417#67—68no—
418#67—68no—
419#67—616no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—32no—
431C2×Dic3—32no—
432C2×Dic3—34no—
433C2×Dic3—34no—
434C2×Dic3—32no—
435C2×Dic3—32no—
436C2×Dic3—32no—
437C2×Dic3—32no—
438C2×Dic3—62no—
439C2×Dic3—64no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—62no—
447C2×Dic3—61no—
448C2×Dic3—121no—
449C2×Dic3—121no—
450C2×Dic3—122no—
451C2×Dic3#23514yes—
452C2×Dic3C2×#6714yes—
453C4×D3—68no—
454C4×D3—68no—
455C4×D3—128no—
456C2×C32—42no—
457C2×C32C2×#11711yescharacteristic
458C2×C32C2×C4×D411yescharacteristic
459C2×C32C4×#4111yescharacteristic
460C2×C32#52912yes—
461C2×C32#53212yes—
462C3⋊D3—42no—
463C24—91no—
464C24C2×D3211yescharacteristic
465C2×D4—94no—
466C2×D4—184no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—32no—
470C22×C4—32no—
471C22×C4—32no—
472C22×C4—32no—
473C22×C4—91no—
474C22×C4—91no—
475C22×C4—91no—
476C22×C4—94no—
477C22×C4—182no—
478C22×C4—182no—
479C22×C4#62414yes—
480C22×C4C2×D3211yescharacteristic
481C22×C4C2×D3211yescharacteristic
482C4⋊C4—64no—
483C4⋊C4—94no—
484C4⋊C4—184no—
485C4⋊C4—184no—
486C22⋊C4—64no—
487C22⋊C4—64no—
488C22⋊C4—94no—
489C22⋊C4—94no—
490C22⋊C4—184no—
491C22⋊C4—184no—
492C42—34no—
493C42—62no—
494C42—62no—
495C42—62no—
496C42—94no—
497C42—184no—
498C42—184no—
499C22×C3—24no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—44no—
514C22×C3—44no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3C22×C4×D311yescharacteristic
520C22×C3C22×C4×D311yescharacteristic
521C22×C3C2×#23512yes—
522C22×C3C2×#23511yescharacteristic
523C22×C3C2×D3×D411yescharacteristic
524C22×C3C2×#23711yescharacteristic
525C22×C3D3×#4112yes—
526C22×C3D3×#4112yes—
527C22×C3D3×#4112yes—
528C22×C3C22×#6711yescharacteristic
529C2×D3—64no—
530C2×D3—62no—
531C2×D3—62no—
532C2×D3—62no—
533C2×D3—62no—
534C2×D3—62no—
535C2×D3—62no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—124no—
539C2×D3—124no—
540C2×D3—122no—
541C2×D3—122no—
542C2×D3—122no—
543C2×D3—122no—
544C3×C4—22no—
545C3×C4—22no—
546C3×C4—24no—
547C3×C4—42no—
548C3×C4—64no—
549C3×C4—64no—
550C3×C4—122no—
551C3×C4—122no—
552C3×C4#67⋊C414yes—
553C3×C4C4×#6714yes—
554Dic3—24no—
555Dic3—24no—
556Dic3—34no—
557Dic3—34no—
558Dic3—42no—
559Dic3—42no—
560Dic3—64no—
561Dic3—62no—
562Dic3—62no—
563Dic3—62no—
564Dic3—62no—
565Dic3—122no—
566Dic3—122no—
567C32#229311yescharacteristic, complemented, Sylow
568C23—22no—
569C23—22no—
570C23—21no—
571C23—21no—
572C23—92no—
573C23—182no—
574C23—182no—
575C23—181no—
576C23—181no—
577C23C2×#62412yes—
578C23C22×D3211yescharacteristic
579D4—188no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—28no—
583C2×C4—34no—
584C2×C4—34no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—94no—
596C2×C4—92no—
597C2×C4—92no—
598C2×C4—92no—
599C2×C4—182no—
600C2×C4—181no—
601C2×C4—181no—
602C2×C4—188no—
603C2×C4#380412yes—
604C2×C4C2×#62412yes—
605C2×C4C2×#62412yes—
606C2×C4D3×#6712yes—
607C2×C3—22no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—22no—
612C2×C3—44no—
613C2×C3—42no—
614C2×C3—42no—
615C2×C3C4×#23511yescharacteristic
616C2×C3C2×#67⋊C411yescharacteristic
617C2×C3D3×#11711yescharacteristic
618C2×C3D3×#11711yescharacteristic
619C2×C3#552211yescharacteristic
620C2×C3#552812yes—
621C2×C3#553812yes—
622C2×C3#554812yes—
623C2×C3C2×C4×#6711yescharacteristic
624C2×C3#583212yes—
625D3—124no—
626D3—122no—
627D3—122no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—42no—
632C22—42no—
633C22—182no—
634C22—182no—
635C22—182no—
636C22—362no—
637C22—362no—
638C22D3×#23512yes—
639C22#6430612yes—
640C22C2×#380411yescharacteristic
641C22C22×#62411yescharacteristic
642C22C2×D3×#6711yescharacteristic
643C4—22no—
644C4—64no—
645C4—64no—
646C4—94no—
647C4—122no—
648C4—122no—
649C4—182no—
650C4—182no—
651C4#6395214yes—
652C3—21no—
653C3#7343911yescharacteristic, complemented
654C3#8222511yescharacteristic, complemented
655C2—42no—
656C2—362no—
657C2#1059493312yes—
658C2#1059495411yescharacteristic
659C2#1059496911yescharacteristic
660C2#1059500312yes—
661C2C2×#6395211yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2293
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×#63874C2semidirect
4. C3×C4×#217C2semidirect
6. #10591703C2semidirect
7. C4×#3724C2semidirect
8. C4×#3722C2semidirect
9. #10591266C2semidirect
10. #10591264C2semidirect
11. C4×Dic32C2semidirect
18. C4×#638C4semidirect
44. C2×#926D3semidirect
48. C4×#217D3semidirect
92. C3×C4×Dic3D4semidirect
300. C4×Dic3#67semidirect
320. C3⋊Dic3#117semidirect
567. C32#2293semidirect
653. C3#73439semidirect
654. C3#82225semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C3×#9262
C2×#638742
C3×C4×#2172
#105917042
#105917032
C4×#37242
C4×#37222
#105912662
#105912642
C4×Dic322
#822253
#734393