Finite Group Databasebeta

← #11808427

Subgroups — #11808427

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×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×#872C211yesmaximal, characteristic, complemented
3C2×C4×#626C212yesmaximal, complemented
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#10591395C211yesmaximal, characteristic
6#10591392C212yesmaximal, complemented
7#10591353C211yesmaximal, characteristic, complemented
8#10591321C211yesmaximal, characteristic, complemented
9#10591315C211yesmaximal, characteristic, complemented
10#10591311C212yesmaximal, complemented
11C4×#3722C212yesmaximal, complemented
12#82273—31nomaximal
13#73776—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2212yes—
16C22×C3×C4×D3C2211yescharacteristic
17C22×#626C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C4×C4⋊(C3⋊D3)—24no—
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2212yes—
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×#872—24no—
30C2×Dic3⋊Dic3C2212yes—
31C2×#3722C2212yes—
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C4×#626—28no—
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2211yescharacteristic
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×C4×#67—32no—
42C2×C4×D12—32no—
43C2×C4×D12—31no—
44C2×C4×D12—31no—
45C2×C4×D12—61no—
46C2×#872D311yescharacteristic, complemented
47C3×C4×C4⋊C4—31no—
48#4994—32no—
49#4994—32no—
50#4991—32no—
51#4991—31no—
52#4981—31no—
53#4961—32no—
54#4960—31no—
55#4953—31no—
56C4×(C2×D3)⋊C4—32no—
57C4×(C2×D3)⋊C4—32no—
58C4×C4⋊Dic3D311yescharacteristic, complemented
59#4674—31no—
60#4672—31no—
61#4671—31no—
62#4661—31no—
63C23×C3⋊D3C2312yes—
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C2×C4⋊(C3⋊D3)—24no—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4×C3⋊D3—24no—
72C2×C4×C3⋊D3—24no—
73C2×C4×C3⋊D3—24no—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2312yes—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3D414yescomplemented
82C2×#626—24no—
83C2×#626—24no—
84C2×#626—24no—
85C32×C42D414yescomplemented
86#3752—24no—
87C4⋊(C3⋊Dic3)—22no—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—24no—
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×C4×Dic3—24no—
94C3×C4×Dic3—22no—
95Dic3⋊Dic3—24no—
96#3722—24no—
97#3722—24no—
98#3722—24no—
99(C2×D3)⋊Dic3—24no—
100#2392—91noSylow
101C23×C3×C4—31no—
102C22×#67—32no—
103C22×D12—32no—
104C22×D12—31no—
105C22×D12—31no—
106C22×D12—61no—
107C22×C4×D3—32no—
108C22×C4×D3—32no—
109C22×C4×D3—62no—
110C22×C4×D3C2×D311yescharacteristic
111C3×#117—64no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C22⋊C4—31no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C42—21no—
118C2×C3×C42—31no—
119C2×C3×C42—32no—
120C2×C3×C42C2×D311yescharacteristic
121C2×C3×C42C2×D311yescharacteristic
122C2×#217—32no—
123C4×#67—68no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—62no—
134C2×(C2×D3)⋊C4C2×D311yescharacteristic
135C2×(C2×D3)⋊C4C2×D311yescharacteristic
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—32no—
139C2×C4⋊Dic3—61no—
140C2×C4⋊Dic3C2×D312yes—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4C2×D311yescharacteristic
143C2×Dic3⋊C4C2×D311yescharacteristic
144C2×C4×Dic3C2×D312yes—
145C2×C4×Dic3C2×D311yescharacteristic
146C4×D12—68no—
147C4×D12—68no—
148C4×D12—64no—
149C4×D12—64no—
150#872—24no—
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×C32C2411yescharacteristic
160C22×C3⋊D3—22no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3—22no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3#4114yes—
167C22×C3×D3—21no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—21no—
171C22×C3×D3C2×D412yes—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4#4112yes—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—22no—
182C4⋊(C3⋊D3)—28no—
183C4×C3⋊D3—48no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3C2×D412yes—
196C2×C3×Dic3#4114yes—
197C3×C4×D3—28no—
198#626—216no—
199C2×C4×D4—92no—
200C2×C4×D4—91no—
201C2×#117—31no—
202#398—91no—
203#397—91no—
204#396—92no—
205#394—91no—
206#394—92no—
207#392—91no—
208C4×C4⋊C4—31no—
209C4×C22⋊C4—92no—
210C24×C3—31no—
211C23×D3—32no—
212C23×D3—32no—
213C23×D3—62no—
214C23×D3C22×D311yescharacteristic
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—32no—
219C22×C3×C4—31no—
220C22×C3×C4—34no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—32no—
224C22×C3×C4—62no—
225C22×C3×C4—62no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—64no—
233C2×#67—64no—
234C2×#67—64no—
235C22×Dic3—32no—
236C22×Dic3—32no—
237C22×Dic3—62no—
238C22×Dic3C22×D311yescharacteristic
239C22×Dic3C22×D311yescharacteristic
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D311yescharacteristic
242C22×Dic3C22×D312yes—
243C2×D12—64no—
244C2×D12—64no—
245C2×D12—64no—
246C2×D12—68no—
247C2×D12—64no—
248C2×D12—64no—
249C2×D12—64no—
250C2×D12—62no—
251C2×D12—62no—
252C2×C4×D3—22no—
253C2×C4×D3—22no—
254C2×C4×D3—68no—
255C2×C4×D3—64no—
256C2×C4×D3—64no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—124no—
262C2×C4×D3—124no—
263C2×C4×D3D1214yescomplemented
264C3×C4⋊C4—64no—
265C3×C4⋊C4—62no—
266C3×C4⋊C4—62no—
267C3×C22⋊C4—62no—
268C3×C22⋊C4—62no—
269C3×C42—24no—
270C3×C42—64no—
271C3×C42—62no—
272C3×C42D1214yescomplemented
273C3×C42#6714yescomplemented
274#217—64no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—22no—
277(C2×D3)⋊C4—64no—
278(C2×D3)⋊C4—64no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281(C2×D3)⋊C4—68no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—64no—
285(C2×D3)⋊C4—64no—
286(C2×D3)⋊C4—64no—
287C4⋊Dic3—24no—
288C4⋊Dic3—64no—
289C4⋊Dic3—62no—
290C4⋊Dic3—62no—
291C4⋊Dic3—64no—
292Dic3⋊C4—22no—
293Dic3⋊C4—22no—
294Dic3⋊C4—64no—
295C4×Dic3—24no—
296C4×Dic3—22no—
297C22×C32C22×D411yescharacteristic
298C22×C32C22×D411yescharacteristic
299C22×C32C2×#4111yescharacteristic
300C22×C32C2×#4112yes—
301C22×C32C2×#4112yes—
302C2×C3⋊D3—24no—
303C2×C3⋊D3—24no—
304C2×C3⋊D3—24no—
305C2×C3⋊D3—42no—
306C2×C3⋊D3—42no—
307C2×C3⋊D3—42no—
308C2×C3⋊D3—42no—
309C2×C3×D3—22no—
310C2×C3×D3—24no—
311C2×C3×D3—41no—
312C2×C3×D3—42no—
313C2×C3×D3—41no—
314C32×C4—22no—
315C32×C4—22no—
316C32×C4#12114yes—
317C3⋊Dic3—42no—
318C3×Dic3—22no—
319C3×Dic3—24no—
320C3×Dic3—42no—
321C3×Dic3—41no—
322C3×Dic3—41no—
323C22×D4—92no—
324C22×D4—91no—
325C23×C4—31no—
326C23×C4—92no—
327C4×D4—188no—
328C4×D4—184no—
329#117—64no—
330C2×C4⋊C4—31no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—32no—
333C2×C4⋊C4—92no—
334C2×C4⋊C4—91no—
335C2×C22⋊C4—31no—
336C2×C22⋊C4—31no—
337C2×C22⋊C4—92no—
338C2×C22⋊C4—92no—
339C2×C22⋊C4—92no—
340C2×C22⋊C4—92no—
341C2×C22⋊C4—92no—
342C2×C42—31no—
343C2×C42—32no—
344C2×C42D3211yescharacteristic
345#95—31no—
346#95—31no—
347#95—92no—
348#95—92no—
349C23×C3—21no—
350C23×C3—32no—
351C23×C3—61no—
352C23×C3—62no—
353C23×C3—61no—
354C23×C3—62no—
355C23×C3C23×D311yescharacteristic
356C23×C3C23×D311yescharacteristic
357C22×D3—21no—
358C22×D3—22no—
359C22×D3—22no—
360C22×D3—21no—
361C22×D3—34no—
362C22×D3—34no—
363C22×D3—64no—
364C22×D3—64no—
365C22×D3—64no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—122no—
379C22×D3—122no—
380C22×D3—122no—
381C22×D3—122no—
382C22×D3C2×D1212yes—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—32no—
394C2×C3×C4—34no—
395C2×C3×C4—42no—
396C2×C3×C4—62no—
397C2×C3×C4—61no—
398C2×C3×C4—61no—
399C2×C3×C4—62no—
400C2×C3×C4—68no—
401C2×C3×C4—62no—
402C2×C3×C4—61no—
403C2×C3×C4—61no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4C2×D1212yes—
409C2×C3×C4C2×D1212yes—
410C2×C3×C4C2×D1212yes—
411C2×C3×C4C2×D1212yes—
412C2×C3×C4#23512yes—
413C2×C3×C4D3×D412yes—
414C2×C3×C4#23912yes—
415C2×C3×C4C2×#6712yes—
416C2×C3×C4C2×#6712yes—
417C2×C3×C4C2×#6712yes—
418#67—616no—
419C2×Dic3—21no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—21no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—64no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—122no—
438C2×Dic3—122no—
439C2×Dic3C2×D1212yes—
440C2×Dic3#23514yes—
441D12—616no—
442D12—68no—
443D12—68no—
444D12—616no—
445C4×D3—28no—
446C4×D3—1216no—
447C4×D3—128no—
448C4×D3—128no—
449C2×C32C2×#12111yescharacteristic
450C2×C32#52512yes—
451C2×C32#52511yescharacteristic
452C2×C32#52912yes—
453C2×C32#53211yescharacteristic
454C3⋊D3—44no—
455C3×D3—42no—
456C24—31no—
457C24—92no—
458C2×D4—184no—
459C2×D4—184no—
460C2×D4—184no—
461C2×D4—184no—
462C2×D4—182no—
463C22×C4—32no—
464C22×C4—31no—
465C22×C4—34no—
466C22×C4—32no—
467C22×C4—31no—
468C22×C4—31no—
469C22×C4—62no—
470C22×C4—62no—
471C22×C4—92no—
472C22×C4—184no—
473C22×C4—184no—
474C22×C4—184no—
475C22×C4C2×D3211yescharacteristic
476C22×C4C2×D3211yescharacteristic
477C22×C4C2×D3211yescharacteristic
478C4⋊C4—64no—
479C4⋊C4—62no—
480C4⋊C4—62no—
481C4⋊C4—184no—
482C4⋊C4—182no—
483C22⋊C4—62no—
484C22⋊C4—62no—
485C22⋊C4—184no—
486C22⋊C4—184no—
487C22⋊C4—184no—
488C22⋊C4—184no—
489C22⋊C4—184no—
490C42—64no—
491C42—62no—
492C42#62614yescomplemented
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—21no—
498C22×C3—62no—
499C22×C3—64no—
500C22×C3—121no—
501C22×C3—121no—
502C22×C3—122no—
503C22×C3C22×D1211yescharacteristic
504C22×C3C22×D1211yescharacteristic
505C22×C3C2×#23511yescharacteristic
506C22×C3C2×#23512yes—
507C22×C3C2×D3×D411yescharacteristic
508C22×C3C2×#23911yescharacteristic
509C22×C3D3×#4112yes—
510C22×C3D3×#4112yes—
511C22×C3D3×#4112yes—
512C22×C3C22×#6711yescharacteristic
513C2×D3—24no—
514C2×D3—22no—
515C2×D3—42no—
516C2×D3—41no—
517C2×D3—41no—
518C2×D3—68no—
519C2×D3—64no—
520C2×D3—64no—
521C2×D3—64no—
522C2×D3—64no—
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—124no—
526C2×D3—124no—
527C2×D3—124no—
528C2×D3—124no—
529C2×D3—124no—
530C2×D3—124no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—122no—
538C2×D3—122no—
539C3×C4—24no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—22no—
543C3×C4—22no—
544C3×C4—24no—
545C3×C4—42no—
546C3×C4—62no—
547C3×C4—64no—
548C3×C4—121no—
549C3×C4—122no—
550C3×C4—121no—
551C3×C4#89514yes—
552C3×C4#93014yes—
553Dic3—22no—
554Dic3—24no—
555Dic3—42no—
556Dic3—41no—
557Dic3—41no—
558Dic3—124no—
559Dic3—122no—
560Dic3—122no—
561C32#239211yescharacteristic, complemented, Sylow
562C23—32no—
563C23—61no—
564C23—62no—
565C23—62no—
566C23—61no—
567C23—94no—
568C23—182no—
569C23—182no—
570C23—182no—
571C23—182no—
572C23—182no—
573C23—182no—
574C23C22×D3211yescharacteristic
575D4—188no—
576D4—1816no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—32no—
580C2×C4—34no—
581C2×C4—61no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—61no—
585C2×C4—68no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—182no—
594C2×C4—182no—
595C2×C4—182no—
596C2×C4—368no—
597C2×C4#379912yes—
598C2×C4D3×D1212yes—
599C2×C4C2×#62612yes—
600C2×C4C2×#62612yes—
601C2×C4C2×#62612yes—
602C2×C3—22no—
603C2×C3—21no—
604C2×C3—22no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—122no—
608C2×C3#547711yescharacteristic
609C2×C3C2×#89511yescharacteristic
610C2×C3#552412yes—
611C2×C3#552411yescharacteristic
612C2×C3#552812yes—
613C2×C3#554712yes—
614C2×C3#558012yes—
615C2×C3C2×#93011yescharacteristic
616C2×C3#582811yescharacteristic
617C2×C3#583211yescharacteristic
618D3—42no—
619D3—128no—
620D3—124no—
621D3—124no—
622C22—62no—
623C22—64no—
624C22—122no—
625C22—121no—
626C22—121no—
627C22—184no—
628C22—184no—
629C22—184no—
630C22—362no—
631C22—362no—
632C22—362no—
633C22—362no—
634C22C2×#379911yescharacteristic
635C22C2×D3×D1211yescharacteristic
636C22D3×#23512yes—
637C22#6430612yes—
638C22C22×#62611yescharacteristic
639C4—22no—
640C4—22no—
641C4—62no—
642C4—64no—
643C4—122no—
644C4—121no—
645C4—121no—
646C4—362no—
647C4#6390914yes—
648C3—21no—
649C3#7377611yescharacteristic, complemented
650C3#8227311yescharacteristic, complemented
651C2—122no—
652C2—364no—
653C2#1059393412yes—
654C2#1059399712yes—
655C2C2×#6390911yescharacteristic
656C2#1059502911yescharacteristic
657C2#1059503411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
prime radical#10591395C2
hypercenterC2×C42D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C4⋊(C3⋊D3)C2semidirect
2. C2×C3×#872C2semidirect
3. C2×C4×#626C2semidirect
4. C3×C4×C4⋊Dic3C2semidirect
6. #10591392C2semidirect
7. #10591353C2semidirect
8. #10591321C2semidirect
9. #10591315C2semidirect
10. #10591311C2semidirect
11. C4×#3722C2semidirect
46. C2×#872D3semidirect
58. C4×C4⋊Dic3D3semidirect
81. C2×C3×C4×D3D4semidirect
85. C32×C42D4semidirect
263. C2×C4×D3D12semidirect
272. C3×C42D12semidirect
273. C3×C42#67semidirect
492. C42#626semidirect
561. C32#2392semidirect
649. C3#73776semidirect
650. C3#82273semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×C3×#8722
C2×C4×#6262
C3×C4×C4⋊Dic32
#105913952
#105913922
#105913532
#105913212
#105913152
#105913112
C4×#37222
#822733
#737763