Finite Group Databasebeta

← #11808426

Subgroups — #11808426

Order 1152.

1557 conjugacy classes of subgroups.

The subgroup lattice has 665 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×C4×#626C212yesmaximal, complemented
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#10591392C212yesmaximal, complemented
6#10591391C211yesmaximal, characteristic
7#10591358C211yesmaximal, characteristic, complemented
8#10591326C211yesmaximal, characteristic, complemented
9#10591308C212yesmaximal, complemented
10#10591302C211yesmaximal, characteristic, complemented
11C4×(C2×D3)⋊Dic3C212yesmaximal, complemented
12#82401—31nomaximal
13#73776—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×#626C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24#64081—24no—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2212yes—
29C3×C4×D12—24no—
30C2×Dic3⋊Dic3C2212yes—
31C2×#3722C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C4×#626—28no—
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2211yescharacteristic
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C4×D4—31no—
41C2×C4×#67—32no—
42C2×C4×D12—32no—
43C2×C4×D12D311yescharacteristic, complemented
44C2×#872—31no—
45C2×#872—31no—
46C2×#872—61no—
47C3×C4×C4⋊C4—31no—
48#5223—31no—
49#5222—31no—
50C4×#217—32no—
51#4994—32no—
52#4992—31no—
53#4991—32no—
54#4983—31no—
55#4961—32no—
56#4948—32no—
57C4×(C2×D3)⋊C4—32no—
58C4×C4⋊Dic3D311yescharacteristic, complemented
59#4674—31no—
60#4672—31no—
61#4671—31no—
62#4661—31no—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C2×C4×C3⋊D3—22no—
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3D414yescomplemented
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C2×C3×D12—24no—
78C2×C3×D12—22no—
79C2×C3×C4×D3—24no—
80C2×C3×C4×D3—24no—
81C2×C3×C4×D3—24no—
82C2×#626—24no—
83C2×#626—24no—
84C2×#626—24no—
85C32×C42D414yescomplemented
86#3752—22no—
87#3752—22no—
88#3750—22no—
89#3750—22no—
90C4×C3⋊Dic3—22no—
91C3×(C2×D3)⋊C4—24no—
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3—24no—
94C3×C4×Dic3—24no—
95Dic3⋊Dic3—24no—
96#3722—24no—
97(C2×D3)⋊Dic3—24no—
98(C2×D3)⋊Dic3—24no—
99(C2×D3)⋊Dic3—24no—
100#2392—91noSylow
101C22×C3×D4—31no—
102C23×C3×C4—32no—
103C22×#67—32no—
104C22×D12—32no—
105C22×D12C2×D311yescharacteristic
106C22×C4×D3—31no—
107C22×C4×D3—31no—
108C22×C4×D3—61no—
109C22×C4×D3C2×D312yes—
110C3×C4×D4—64no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C42—21no—
115C2×C3×C42—32no—
116C2×C3×C42C2×D311yescharacteristic
117C2×C3×C42C2×D311yescharacteristic
118C2×#217—32no—
119C2×#217—32no—
120C2×#217—32no—
121C4×#67—68no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—61no—
132C2×(C2×D3)⋊C4—61no—
133C2×(C2×D3)⋊C4C2×D312yes—
134C2×C4⋊Dic3—32no—
135C2×C4⋊Dic3C2×D311yescharacteristic
136C2×C4⋊Dic3C2×D312yes—
137C2×Dic3⋊C4—31no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—31no—
140C2×Dic3⋊C4—31no—
141C2×Dic3⋊C4—32no—
142C2×Dic3⋊C4—61no—
143C2×Dic3⋊C4—61no—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—31no—
146C2×C4×Dic3—61no—
147C2×C4×Dic3C2×D312yes—
148C4×D12—24no—
149C4×D12—68no—
150#872—68no—
151#872—64no—
152#872—64no—
153C3×#95—31no—
154C3×#95—31no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95C2×D311yescharacteristic
160C3⋊#95C2×D311yescharacteristic
161C23×C32C2411yescharacteristic
162C22×C3⋊D3—21no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3C2×D412yes—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3#4114yes—
174C2×C32×C4—22no—
175C2×C32×C4—22no—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D412yes—
180C2×C32×C4#4112yes—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3C2×D412yes—
188C4×C3⋊D3—28no—
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×Dic3#4114yes—
198C3×D12—28no—
199C3×C4×D3—48no—
200#626—216no—
201C2×C4×D4—31no—
202C2×C4×D4—92no—
203C2×#117—91no—
204#398—91no—
205#397—91no—
206#396—92no—
207#394—91no—
208#394—92no—
209#392—91no—
210C4×C4⋊C4—31no—
211C4×C22⋊C4—92no—
212C24×C3—32no—
213C23×D3—31no—
214C23×D3—31no—
215C23×D3—61no—
216C23×D3C22×D312yes—
217C2×C3×D4—64no—
218C2×C3×D4—62no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—64no—
226C22×C3×C4—64no—
227C22×C3×C4—64no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—64no—
235C2×#67—64no—
236C2×#67—64no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—31no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D312yes—
249C2×D12—24no—
250C2×D12—22no—
251C2×D12—64no—
252C2×D12—64no—
253C2×D12—64no—
254C2×C4×D3—24no—
255C2×C4×D3—24no—
256C2×C4×D3—24no—
257C2×C4×D3—34no—
258C2×C4×D3—34no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C3×C4⋊C4—64no—
267C3×C4⋊C4—62no—
268C3×C22⋊C4—64no—
269C3×C42—24no—
270C3×C42—64no—
271C3×C42D1214yescomplemented
272C3×C42#6714yescomplemented
273#217—64no—
274#217—64no—
275#217—64no—
276(C2×D3)⋊C4—24no—
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—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—62no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—62no—
288C4⋊Dic3—22no—
289C4⋊Dic3—24no—
290C4⋊Dic3—64no—
291Dic3⋊C4—64no—
292Dic3⋊C4—64no—
293Dic3⋊C4—64no—
294Dic3⋊C4—62no—
295Dic3⋊C4—62no—
296Dic3⋊C4—62no—
297Dic3⋊C4—62no—
298C4×Dic3—24no—
299C4×Dic3—64no—
300C4×Dic3—62no—
301C4×Dic3—62no—
302C22×C32C22×D411yescharacteristic
303C22×C32C22×D411yescharacteristic
304C22×C32C2×#4112yes—
305C22×C32C2×#4112yes—
306C22×C32C2×#4111yescharacteristic
307C2×C3⋊D3—22no—
308C2×C3⋊D3—24no—
309C2×C3⋊D3—41no—
310C2×C3⋊D3—42no—
311C2×C3⋊D3—41no—
312C2×C3×D3—24no—
313C2×C3×D3—24no—
314C2×C3×D3—24no—
315C2×C3×D3—42no—
316C2×C3×D3—42no—
317C2×C3×D3—42no—
318C2×C3×D3—42no—
319C32×C4—22no—
320C32×C4—22no—
321C32×C4#12114yes—
322C3⋊Dic3—22no—
323C3⋊Dic3—41no—
324C3⋊Dic3—41no—
325C3×Dic3—24no—
326C3×Dic3—42no—
327C3×Dic3—42no—
328C22×D4—31no—
329C22×D4—92no—
330C23×C4—32no—
331C23×C4—91no—
332C4×D4—64no—
333C4×D4—188no—
334#117—184no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—32no—
337C2×C4⋊C4—92no—
338C2×C4⋊C4—91no—
339C2×C4⋊C4—91no—
340C2×C22⋊C4—32no—
341C2×C22⋊C4—92no—
342C2×C22⋊C4—92no—
343C2×C22⋊C4—92no—
344C2×C22⋊C4—92no—
345C2×C22⋊C4—91no—
346C2×C22⋊C4—91no—
347C2×C42—32no—
348C2×C42—91no—
349C2×C42D3211yescharacteristic
350#95—31no—
351#95—31no—
352#95—92no—
353#95—92no—
354C23×C3—21no—
355C23×C3—34no—
356C23×C3—62no—
357C23×C3—62no—
358C23×C3—62no—
359C23×C3—62no—
360C23×C3—62no—
361C23×C3—62no—
362C23×C3C23×D311yescharacteristic
363C23×C3C23×D311yescharacteristic
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—22no—
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—32no—
371C22×D3—32no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—61no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—61no—
379C22×D3—61no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—61no—
383C22×D3—122no—
384C22×D3—122no—
385C22×D3#23514yes—
386C3×D4—68no—
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—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—34no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
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—128no—
408C2×C3×C4C2×D1212yes—
409C2×C3×C4C2×D1212yes—
410C2×C3×C4C2×D1212yes—
411C2×C3×C4D3×D412yes—
412C2×C3×C4D3×D412yes—
413C2×C3×C4#23712yes—
414C2×C3×C4#23912yes—
415C2×C3×C4C2×#6712yes—
416C2×C3×C4C2×#6712yes—
417C2×C3×C4C2×#6712yes—
418#67—616no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—32no—
428C2×Dic3—32no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—61no—
439C2×Dic3—61no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—61no—
445C2×Dic3—61no—
446C2×Dic3—122no—
447C2×Dic3—122no—
448C2×Dic3#23514yes—
449D12—28no—
450D12—616no—
451C4×D3—48no—
452C4×D3—616no—
453C4×D3—68no—
454C4×D3—68no—
455C2×C32C2×#12111yescharacteristic
456C2×C32#52511yescharacteristic
457C2×C32#52512yes—
458C2×C32#52912yes—
459C2×C32#53211yescharacteristic
460C3⋊D3—42no—
461C3×D3—44no—
462C24—32no—
463C24—91no—
464C2×D4—64no—
465C2×D4—62no—
466C2×D4—184no—
467C2×D4—184no—
468C2×D4—184no—
469C22×C4—32no—
470C22×C4—32no—
471C22×C4—32no—
472C22×C4—64no—
473C22×C4—64no—
474C22×C4—64no—
475C22×C4—91no—
476C22×C4—94no—
477C22×C4—91no—
478C22×C4—91no—
479C22×C4—182no—
480C22×C4—182no—
481C22×C4C2×D3211yescharacteristic
482C22×C4C2×D3211yescharacteristic
483C22×C4C2×D3211yescharacteristic
484C4⋊C4—64no—
485C4⋊C4—62no—
486C4⋊C4—184no—
487C4⋊C4—182no—
488C4⋊C4—182no—
489C22⋊C4—64no—
490C22⋊C4—184no—
491C22⋊C4—184no—
492C22⋊C4—184no—
493C22⋊C4—184no—
494C22⋊C4—182no—
495C22⋊C4—182no—
496C42—64no—
497C42—182no—
498C42#62614yescomplemented
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—21no—
504C22×C3—64no—
505C22×C3—64no—
506C22×C3—64no—
507C22×C3—122no—
508C22×C3—122no—
509C22×C3—122no—
510C22×C3—122no—
511C22×C3C22×D1211yescharacteristic
512C22×C3C2×#23512yes—
513C22×C3C2×#23512yes—
514C22×C3C2×D3×D411yescharacteristic
515C22×C3C2×D3×D411yescharacteristic
516C22×C3C2×#23711yescharacteristic
517C22×C3C2×#23911yescharacteristic
518C22×C3D3×#4112yes—
519C22×C3D3×#4112yes—
520C22×C3C22×#6711yescharacteristic
521C2×D3—24no—
522C2×D3—24no—
523C2×D3—24no—
524C2×D3—42no—
525C2×D3—42no—
526C2×D3—42no—
527C2×D3—42no—
528C2×D3—64no—
529C2×D3—62no—
530C2×D3—62no—
531C2×D3—64no—
532C2×D3—64no—
533C2×D3—124no—
534C2×D3—124no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—121no—
538C2×D3—121no—
539C2×D3—121no—
540C2×D3—122no—
541C2×D3—121no—
542C2×D3—122no—
543C3×C4—22no—
544C3×C4—22no—
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—24no—
548C3×C4—42no—
549C3×C4—42no—
550C3×C4—64no—
551C3×C4—122no—
552C3×C4—122no—
553C3×C4#89514yes—
554C3×C4#93814yes—
555Dic3—24no—
556Dic3—42no—
557Dic3—42no—
558Dic3—64no—
559Dic3—62no—
560Dic3—62no—
561Dic3—122no—
562Dic3—122no—
563Dic3—121no—
564Dic3—121no—
565Dic3—121no—
566Dic3—121no—
567C32#239211yescharacteristic, complemented, Sylow
568C23—34no—
569C23—62no—
570C23—62no—
571C23—62no—
572C23—62no—
573C23—62no—
574C23—62no—
575C23—92no—
576C23—181no—
577C23—182no—
578C23—182no—
579C23—181no—
580C23C22×D3211yescharacteristic
581D4—68no—
582D4—1816no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—34no—
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—92no—
595C2×C4—128no—
596C2×C4—181no—
597C2×C4—181no—
598C2×C4—188no—
599C2×C4—182no—
600C2×C4—182no—
601C2×C4—181no—
602C2×C4—181no—
603C2×C4#379612yes—
604C2×C4#380212yes—
605C2×C4C2×#62612yes—
606C2×C4C2×#62612yes—
607C2×C4C2×#62612yes—
608C2×C3—22no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—22no—
613C2×C3—124no—
614C2×C3#547711yescharacteristic
615C2×C3C2×#89511yescharacteristic
616C2×C3#552411yescharacteristic
617C2×C3#553812yes—
618C2×C3#554712yes—
619C2×C3#554712yes—
620C2×C3#558012yes—
621C2×C3#579111yescharacteristic
622C2×C3C2×#93811yescharacteristic
623C2×C3#583211yescharacteristic
624D3—44no—
625D3—124no—
626D3—122no—
627D3—122no—
628C22—64no—
629C22—64no—
630C22—64no—
631C22—122no—
632C22—122no—
633C22—122no—
634C22—122no—
635C22—182no—
636C22—184no—
637C22—362no—
638C22—361no—
639C22—361no—
640C22C2×#379611yescharacteristic
641C22C2×#380211yescharacteristic
642C22D3×#23512yes—
643C22D3×#23512yes—
644C22C22×#62611yescharacteristic
645C4—22no—
646C4—22no—
647C4—64no—
648C4—122no—
649C4—122no—
650C4—182no—
651C4—361no—
652C4—361no—
653C4#6391614yes—
654C3—21no—
655C3#7377611yescharacteristic, complemented
656C3#8240111yescharacteristic, complemented
657C2—124no—
658C2—362no—
659C2#1059391112yes—
660C2#1059400612yes—
661C2C2×#6391611yescharacteristic
662C2#1059502311yescharacteristic
663C2#1059502911yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
prime radical#10591391C2
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×#64081C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C2×C4×#626C2semidirect
4. C3×C4×C4⋊Dic3C2semidirect
5. #10591392C2semidirect
7. #10591358C2semidirect
8. #10591326C2semidirect
9. #10591308C2semidirect
10. #10591302C2semidirect
11. C4×(C2×D3)⋊Dic3C2semidirect
43. C2×C4×D12D3semidirect
58. C4×C4⋊Dic3D3semidirect
73. C2×C4×C3⋊D3D4semidirect
85. C32×C42D4semidirect
271. C3×C42D12semidirect
272. C3×C42#67semidirect
498. C42#626semidirect
567. C32#2392semidirect
655. C3#73776semidirect
656. C3#82401semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C3×C4×D122
C2×C4×#6262
C3×C4×C4⋊Dic32
#105913922
#105913912
#105913582
#105913262
#105913082
#105913022
C4×(C2×D3)⋊Dic32
#824013
#737763