Finite Group Databasebeta

← #11787549

Subgroups — #11787549

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic, complemented
2C22×#3714C211yesmaximal, characteristic
3#10592687C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#70172—31nomaximal
9#68897—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×#3752—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×(C2×D3)⋊Dic3—21no—
21#63898—22no—
22#63898—22no—
23C2×#3714—22no—
24C2×#3714—22no—
25C2×#3714C414yescomplemented
26C3×#809—22no—
27#63564—22no—
28C2×D4×Dic3—31no—
29C22×#213—31no—
30C22×D24—31no—
31C2×#893—31no—
32C2×C3×#102—31no—
33C2×#821—31no—
34#4988—31no—
35#4988—31no—
36#4988—61no—
37C2×#809—31no—
38C2×#809D311yescharacteristic, complemented
39C3×#340—31no—
40#4550—31no—
41#4550—31no—
42#4529D311yescharacteristic, complemented
43C23×C3⋊D3—21no—
44C23×C3×D3—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2×C412yescomplemented
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12C2×C412yes—
60C2×C3×D12D412yes—
61C2×C3×D12D412yes—
62C2×D3×Dic3—24no—
63C2×D3×Dic3—42no—
64C2×D3×Dic3—42no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67#3752—42no—
68#3752—42no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3D412yes—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8C2×C412yescomplemented
79(C2×D3)⋊Dic3—24no—
80#3714—28no—
81#1879—91noSylow
82C22×C3×D4—31no—
83C23×Dic3—61no—
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C22×D12C2×D311yescharacteristic
88C22×C4×D3—61no—
89C22×C3×C8—31no—
90C22×C3×C8—31no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×#217—61no—
96D4×Dic3—62no—
97D4×Dic3—62no—
98C2×#213—34no—
99C2×#213—62no—
100C2×#213—62no—
101C2×(C2×D3)⋊C4—61no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
106C2×(C2×D3)⋊C4—62no—
107C2×(C2×D3)⋊C4—62no—
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×C4×Dic3—31no—
110C2×C4×Dic3—31no—
111C2×C4×Dic3—61no—
112C22×C3⋊C8C2×D311yescharacteristic
113C22×C3⋊C8C2×D311yescharacteristic
114C2×D24—34no—
115C2×D24—62no—
116C2×D24—62no—
117#893—62no—
118#893—62no—
119C3×#102—62no—
120#821—62no—
121#809—22no—
122#809—62no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3—22no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C22×C3×D3—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4—41no—
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C32×C4#4111yescharacteristic
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3D812yescomplemented
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—41no—
156C4⋊(C3⋊D3)—41no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—41no—
159C2×C3×Dic3—41no—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12C22⋊C414yescomplemented
164D3×Dic3—48no—
165C3×C3⋊C8—22no—
166C3×C3⋊C8—41no—
167C22×D8—91no—
168C2×C4×D4—91no—
169C2×#102—31no—
170C2×#102—91no—
171#390—91no—
172#340—31no—
173#336—91no—
174C24×C3—61no—
175C23×D3—21no—
176C23×D3—62no—
177C23×D3—61no—
178C23×D3—61no—
179C2×C3×D4—32no—
180C2×C3×D4—32no—
181C2×C3×D4—32no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C22×C3×C4—22no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—61no—
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×Dic3—21no—
193C22×Dic3—31no—
194C22×Dic3—31no—
195C22×Dic3—31no—
196C22×Dic3—31no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—64no—
200C22×Dic3—122no—
201C22×Dic3—122no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—32no—
206C2×D12—32no—
207C2×D12—62no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—121no—
220C2×D12—121no—
221C2×D12—121no—
222C2×D12—121no—
223C2×D12C4×D312yes—
224C2×D12D1212yes—
225C2×D12#6712yes—
226C2×C4×D3—64no—
227C2×C4×D3—122no—
228C2×C4×D3—122no—
229C2×C3×C8—32no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—41no—
241C3×C4⋊C4—41no—
242C3×C4⋊C4—61no—
243#217—64no—
244#213—68no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—122no—
247(C2×D3)⋊C4—122no—
248(C2×D3)⋊C4—124no—
249(C2×D3)⋊C4—124no—
250(C2×D3)⋊C4—122no—
251(C2×D3)⋊C4—122no—
252C4⋊Dic3—21no—
253C4⋊Dic3D1212yes—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3—121no—
259C4×Dic3—121no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8C4×D312yescomplemented
266D24—68no—
267C22×C32C4×D411yescharacteristic
268C22×C32#12011yescharacteristic
269C22×C32#12111yescharacteristic
270C22×C32C2×D811yescharacteristic
271C22×C32#13511yescharacteristic
272C22×C32AGL(1,ℤ/8)11yescharacteristic
273C22×C32AGL(1,ℤ/8)11yescharacteristic
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C2×C3⋊D3—42no—
277C2×C3⋊D3—81no—
278C2×C3⋊D3—81no—
279C2×C3⋊D3—81no—
280C2×C3⋊D3—81no—
281C2×C3×D3—24no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C2×C3×D3—42no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C32×C4—81no—
289C32×C4C2×C22⋊C411yescharacteristic
290C32×C4C4×D411yescharacteristic
291C32×C4#12111yescharacteristic
292C32×C4#12311yescharacteristic
293C3⋊Dic3—22no—
294C3⋊Dic3—41no—
295C3×Dic3—42no—
296C22×D4—31no—
297C22×D4—91no—
298C23×C4—181no—
299C2×D8—94no—
300C2×D8—182no—
301C2×D8—182no—
302C22×C8—31no—
303C22×C8—31no—
304C4×D4—182no—
305C4×D4—182no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4D3211yescharacteristic
308C2×C22⋊C4—181no—
309C2×C22⋊C4—181no—
310C2×C22⋊C4—181no—
311C2×C42—91no—
312#102—62no—
313#102—182no—
314C23×C3—21no—
315C23×C3—62no—
316C23×C3—62no—
317C23×C3—62no—
318C23×C3—121no—
319C23×C3—121no—
320C23×C3—121no—
321C23×C3—121no—
322C23×C3D3×D411yescharacteristic
323C23×C3D3×D411yescharacteristic
324C22×D3—22no—
325C22×D3—22no—
326C22×D3—22no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—41no—
330C22×D3—41no—
331C22×D3—64no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—122no—
335C22×D3—122no—
336C22×D3—122no—
337C22×D3—122no—
338C22×D3—122no—
339C22×D3—122no—
340C22×D3—121no—
341C22×D3—121no—
342C22×D3—121no—
343C22×D3—121no—
344C22×D3—121no—
345C22×D3—121no—
346C22×D3—121no—
347C22×D3—121no—
348C22×D3—121no—
349C22×D3—121no—
350C22×D3—121no—
351C22×D3—121no—
352C3×D4—34no—
353C3×D4—62no—
354C3×D4—62no—
355C3×D4—62no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—62no—
372C2×C3×C4—121no—
373C2×C3×C4—121no—
374C2×C3×C4C2×C4×D311yescharacteristic
375C2×C3×C4C2×C4×D311yescharacteristic
376C2×C3×C4C2×D1211yescharacteristic
377C2×C3×C4C2×D1211yescharacteristic
378C2×C3×C4#23511yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4#23711yescharacteristic
383C2×C3×C4#23711yescharacteristic
384C2×C3×C4#23911yescharacteristic
385C2×C3×C4C2×#6711yescharacteristic
386C2×Dic3—22no—
387C2×Dic3—32no—
388C2×Dic3—32no—
389C2×Dic3—41no—
390C2×Dic3—41no—
391C2×Dic3—62no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—62no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407C2×Dic3—128no—
408D12—22no—
409D12—22no—
410D12—22no—
411D12—62no—
412D12—62no—
413D12—62no—
414D12—62no—
415D12—122no—
416D12—122no—
417D12—122no—
418D12—122no—
419D12—121no—
420D12—121no—
421D12—121no—
422D12—121no—
423D12(C2×D3)⋊C414yescomplemented
424C4×D3—128no—
425C3×C8—62no—
426C3×C8—121no—
427C3⋊C8—22no—
428C3⋊C8—41no—
429C2×C32#38611yescharacteristic
430C2×C32C4×D811yescharacteristic
431C2×C32#44211yescharacteristic
432C2×C32#44711yescharacteristic
433C2×C32#44911yescharacteristic
434C2×C32#45911yescharacteristic
435C2×C32#46311yescharacteristic
436C3⋊D3—82no—
437C3×D3—44no—
438C24—61no—
439C24—181no—
440C2×D4—32no—
441C2×D4—32no—
442C2×D4—32no—
443C2×D4—61no—
444C2×D4—61no—
445C2×D4—61no—
446C2×D4—92no—
447C2×D4—181no—
448C2×D4—181no—
449C2×D4—181no—
450C2×D4—181no—
451C2×D4—181no—
452C22×C4—21no—
453C22×C4—61no—
454C22×C4—91no—
455C22×C4—91no—
456C22×C4—184no—
457C22×C4—362no—
458C22×C4—362no—
459C22×C4C2×D3211yescharacteristic
460D8—188no—
461C2×C8—32no—
462C2×C8—61no—
463C2×C8—61no—
464C2×C8—61no—
465C2×C8—61no—
466C2×C8—61no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—32no—
470C4⋊C4—61no—
471C22⋊C4—184no—
472C22⋊C4—362no—
473C22⋊C4—362no—
474C42—181no—
475C42—181no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—64no—
484C22×C3—122no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—122no—
488C22×C3—122no—
489C22×C3—122no—
490C22×C3#67⋊C411yescharacteristic
491C22×C3#88211yescharacteristic
492C22×C3#88211yescharacteristic
493C22×C3#88411yescharacteristic
494C22×C3#89311yescharacteristic
495C22×C3D3×D811yescharacteristic
496C22×C3D3×D811yescharacteristic
497C22×C3#91111yescharacteristic
498C22×C3#91411yescharacteristic
499C22×C3#91411yescharacteristic
500C22×C3#91411yescharacteristic
501C22×C3#91611yescharacteristic
502C22×C3#91911yescharacteristic
503C22×C3#93911yescharacteristic
504C2×D3—24no—
505C2×D3—42no—
506C2×D3—42no—
507C2×D3—42no—
508C2×D3—42no—
509C2×D3—42no—
510C2×D3—42no—
511C2×D3—124no—
512C2×D3—124no—
513C2×D3—124no—
514C2×D3—122no—
515C2×D3—122no—
516C2×D3—122no—
517C2×D3—122no—
518C2×D3—122no—
519C2×D3—122no—
520C2×D3—242no—
521C2×D3—242no—
522C2×D3—242no—
523C2×D3—242no—
524C2×D3—241no—
525C2×D3—241no—
526C2×D3—241no—
527C2×D3—241no—
528C2×D3—241no—
529C2×D3—241no—
530C2×D3—241no—
531C2×D3—241no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—82no—
537C3×C4—81no—
538C3×C4—81no—
539C3×C4—122no—
540C3×C4C4×D1211yescharacteristic
541C3×C4D3×C22⋊C411yescharacteristic
542C3×C4#67⋊C411yescharacteristic
543C3×C4#88611yescharacteristic
544C3×C4#89411yescharacteristic
545C3×C4#89511yescharacteristic
546C3×C4C2×(C2×D3)⋊C411yescharacteristic
547C3×C4#93911yescharacteristic
548Dic3—42no—
549Dic3—62no—
550Dic3—62no—
551Dic3—122no—
552Dic3—122no—
553Dic3—121no—
554Dic3—121no—
555C32#187911yescharacteristic, complemented, Sylow
556C23—62no—
557C23—62no—
558C23—62no—
559C23—121no—
560C23—121no—
561C23—121no—
562C23—121no—
563C23—182no—
564C23—361no—
565C23—361no—
566C23—361no—
567C23—361no—
568C23—361no—
569C23—361no—
570C23#381111yescharacteristic
571D4—34no—
572D4—62no—
573D4—62no—
574D4—62no—
575D4—182no—
576D4—182no—
577D4—361no—
578D4—361no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—62no—
583C2×C4—92no—
584C2×C4—121no—
585C2×C4—121no—
586C2×C4—181no—
587C2×C4—181no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—368no—
592C2×C4#379611yescharacteristic
593C2×C4C4×D3211yescharacteristic
594C2×C4D3×D1211yescharacteristic
595C2×C4D3×D1211yescharacteristic
596C2×C4#380411yescharacteristic
597C2×C4D3×#6711yescharacteristic
598C8—62no—
599C8—121no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—124no—
608C2×C3#466511yescharacteristic
609C2×C3#475611yescharacteristic
610C2×C3#477311yescharacteristic
611C2×C3#477311yescharacteristic
612C2×C3#478111yescharacteristic
613C2×C3#478511yescharacteristic
614C2×C3#478611yescharacteristic
615C2×C3#481011yescharacteristic
616C2×C3#481911yescharacteristic
617C2×C3#486911yescharacteristic
618C2×C3#487211yescharacteristic
619C2×C3#495811yescharacteristic
620C2×C3#515011yescharacteristic
621C2×C3#516511yescharacteristic
622D3—44no—
623D3—244no—
624D3—242no—
625D3—242no—
626C22—64no—
627C22—122no—
628C22—122no—
629C22—122no—
630C22—122no—
631C22—122no—
632C22—122no—
633C22—362no—
634C22—362no—
635C22—362no—
636C22—721no—
637C22—721no—
638C22—721no—
639C22—721no—
640C22#6388111yescharacteristic
641C22#6392311yescharacteristic
642C22#6392611yescharacteristic
643C22#6393711yescharacteristic
644C22#6394111yescharacteristic
645C22#6395011yescharacteristic
646C22#6397111yescharacteristic
647C4—81no—
648C4—122no—
649C4—182no—
650C4—361no—
651C4#6388011yescharacteristic
652C4#6388611yescharacteristic
653C4#6389011yescharacteristic
654C4D3×(C2×D3)⋊C411yescharacteristic
655C3—21no—
656C3#6889711yescharacteristic, complemented
657C3#7017211yescharacteristic, complemented
658C2—124no—
659C2—722no—
660C2#1059045911yescharacteristic
661C2#1059046211yescharacteristic
662C2#1059059811yescharacteristic
663C2#1059061711yescharacteristic
664C2#1059136411yescharacteristic
665C2#1059143311yescharacteristic
666C2#1059157011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1879
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#63898C2semidirect
3. #10592687C2semidirect
4. C2×C3×#809C2semidirect
5. C2×#63564C2semidirect
6. C3×#4529C2semidirect
7. #10589156C2semidirect
25. C2×#3714C4semidirect
38. C2×#809D3semidirect
42. #4529D3semidirect
54. C2×C4⋊(C3⋊D3)C2×C4semidirect
78. C2×C3×C3⋊C8C2×C4semidirect
152. C2×C3⋊Dic3D8semidirect
163. C3×D12C22⋊C4semidirect
265. C2×C3⋊C8C4×D3semidirect
423. D12(C2×D3)⋊C4semidirect
555. C32#1879semidirect
656. C3#68897semidirect
657. C3#70172semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
C22×#37142
#105926872
C2×C3×#8092
C2×#635642
C3×#45292
#105891562
#701723
#688973