Finite Group Databasebeta

← #11787554

Subgroups — #11787554

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 679 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3745C211yesmaximal, characteristic
2C2×#63894C211yesmaximal, characteristic, complemented
3#10591320C211yesmaximal, characteristic, complemented
4C2×#63564C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C3×#4551C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#68897—31nomaximal
9#68673—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#624—21no—
13C22×C32×C8C2211yescharacteristic
14C2×#3745—22no—
15C2×#3745—22no—
16C2×#3745C414yescomplemented
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3722—21no—
22C2×#3722—21no—
23C2×#3722—21no—
24#63894—22no—
25#63894—22no—
26#63564—22no—
27#63564—22no—
28C22×D24—31no—
29C22×D24—31no—
30C22×D24—61no—
31C2×#893—31no—
32C2×C4×D12—31no—
33C2×#821—31no—
34C2×#821—31no—
35#4988—31no—
36C2×#809—31no—
37C2×#809—31no—
38#4939—31no—
39C3×#340—31no—
40C3×#336—31no—
41#4551D311yescharacteristic, complemented
42#4550D311yescharacteristic, complemented
43C23×C3⋊D3—21no—
44C23×C3⋊D3—21no—
45C22×C32×C4C2311yescharacteristic
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
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×C412yes—
55C2×C4⋊(C3⋊D3)C2×C412yescomplemented
56C2×C4⋊(C3⋊D3)D412yes—
57C2×C4⋊(C3⋊D3)D412yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C22×C3×Dic3D411yescharacteristic
62C2×#624—24no—
63C2×#624—42no—
64C2×#624—42no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8C2×C412yescomplemented
68#3745—28no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3D412yes—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78#3722—24no—
79#3722—42no—
80#3722—42no—
81#1879—91noSylow
82C22×D12—31no—
83C22×D12—31no—
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C22×D12—61no—
88C22×C4×D3—61no—
89C22×C4×D3—61no—
90C22×C3×C8—21no—
91C22×C3×C8—31no—
92C22×C3×C8C2×D311yescharacteristic
93C22×C3×C8C2×D311yescharacteristic
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C42—31no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101C2×(C2×D3)⋊C4—61no—
102C2×(C2×D3)⋊C4—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8C2×D311yescharacteristic
107C2×D24—34no—
108C2×D24—34no—
109C2×D24—64no—
110C2×D24—62no—
111C2×D24—62no—
112C2×D24—62no—
113C2×D24—62no—
114C2×D24—64no—
115C2×D24—64no—
116#893—62no—
117#893—62no—
118C4×D12—62no—
119C4×D12—62no—
120#821—62no—
121#821—62no—
122#809—62no—
123#809—62no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—22no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C22×C3⋊D3—41no—
132C22×C3⋊D3—41no—
133C22×C3⋊D3—41no—
134C22×C3⋊D3—41no—
135C22×C3⋊D3—41no—
136C22×C3⋊D3—41no—
137C22×C3⋊D3—41no—
138C22×C3⋊D3—41no—
139C2×C32×C4C22×C411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—41no—
151C4⋊(C3⋊D3)—41no—
152C4⋊(C3⋊D3)C22⋊C414yescomplemented
153C2×C3×Dic3—21no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C2×C3×Dic3—41no—
162C2×C3×Dic3—41no—
163C2×C3×Dic3—41no—
164C2×C3×Dic3D812yescomplemented
165#624—48no—
166C32×C8—22no—
167C3×C3⋊C8—41no—
168C22×D8—91no—
169C2×C4×D4—91no—
170C2×#102—91no—
171C2×#102—91no—
172#390—91no—
173#340—31no—
174#336—31no—
175C23×D3—61no—
176C23×D3—61no—
177C23×D3—61no—
178C23×D3—61no—
179C23×D3—121no—
180C23×D3—121no—
181C22×C3×C4—21no—
182C22×C3×C4—31no—
183C22×C3×C4—31no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3D1211yescharacteristic
191C22×Dic3D1211yescharacteristic
192C2×D12—32no—
193C2×D12—32no—
194C2×D12—32no—
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—32no—
198C2×D12—32no—
199C2×D12—32no—
200C2×D12—62no—
201C2×D12—62no—
202C2×D12—62no—
203C2×D12—62no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—61no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—61no—
221C2×D12—61no—
222C2×D12—121no—
223C2×D12—121no—
224C2×D12—121no—
225C2×D12—121no—
226C2×D12—121no—
227C2×D12—121no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—122no—
231C2×C4×D3—122no—
232C2×C4×D3—122no—
233C2×C4×D3—122no—
234C2×C3×C8—22no—
235C2×C3×C8—22no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—22no—
241C2×C3×C8—61no—
242C2×C3×C8—61no—
243C2×C3×C8—61no—
244C2×C3×C8C4×D312yescomplemented
245C2×C3×C8C4×D312yescomplemented
246C3×C4⋊C4—32no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4—61no—
250C3×C42—61no—
251C3×C42—61no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—122no—
255(C2×D3)⋊C4—122no—
256(C2×D3)⋊C4—122no—
257(C2×D3)⋊C4—122no—
258C4⋊Dic3—21no—
259C4⋊Dic3—21no—
260C4⋊Dic3—21no—
261C4⋊Dic3D1212yes—
262C4×Dic3—21no—
263C4×Dic3—21no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267D24—68no—
268D24—68no—
269D24—616no—
270C22×C32C4×D411yescharacteristic
271C22×C32#12011yescharacteristic
272C22×C32#12111yescharacteristic
273C22×C32C2×D811yescharacteristic
274C22×C32#13511yescharacteristic
275C22×C32AGL(1,ℤ/8)11yescharacteristic
276C22×C32AGL(1,ℤ/8)11yescharacteristic
277C2×C3⋊D3—24no—
278C2×C3⋊D3—42no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—42no—
281C2×C3⋊D3—42no—
282C2×C3⋊D3—42no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—42no—
285C2×C3⋊D3—42no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—81no—
288C2×C3⋊D3—81no—
289C2×C3⋊D3—81no—
290C2×C3⋊D3—81no—
291C32×C4C2×C22⋊C411yescharacteristic
292C32×C4C4×D411yescharacteristic
293C32×C4#12111yescharacteristic
294C32×C4#12311yescharacteristic
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C3×Dic3—81no—
299C22×D4—91no—
300C22×D4—91no—
301C23×C4—181no—
302C2×D8—94no—
303C2×D8—182no—
304C2×D8—182no—
305C22×C8—31no—
306C22×C8D3211yescharacteristic
307C4×D4—182no—
308C4×D4—182no—
309C2×C4⋊C4—31no—
310C2×C4⋊C4—31no—
311C2×C22⋊C4—181no—
312C2×C22⋊C4—181no—
313C2×C22⋊C4—181no—
314C2×C42—31no—
315#102—182no—
316#102—182no—
317C23×C3—21no—
318C23×C3C2×D1211yescharacteristic
319C23×C3D3×D411yescharacteristic
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—122no—
329C22×D3—122no—
330C22×D3—122no—
331C22×D3—122no—
332C22×D3—121no—
333C22×D3—121no—
334C22×D3—121no—
335C22×D3—121no—
336C22×D3—121no—
337C22×D3—121no—
338C22×D3—121no—
339C22×D3—121no—
340C22×D3—122no—
341C22×D3—122no—
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—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—241no—
355C22×D3—241no—
356C22×D3—241no—
357C22×D3—241no—
358C22×D3—241no—
359C22×D3—241no—
360C22×D3—241no—
361C22×D3—241no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—32no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—62no—
373C2×C3×C4—61no—
374C2×C3×C4—61no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4—121no—
379C2×C3×C4—121no—
380C2×C3×C4C2×C4×D311yescharacteristic
381C2×C3×C4C2×C4×D311yescharacteristic
382C2×C3×C4C2×D1211yescharacteristic
383C2×C3×C4#23511yescharacteristic
384C2×C3×C4#23511yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4D3×D411yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4#23911yescharacteristic
391C2×C3×C4#23911yescharacteristic
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—41no—
399C2×Dic3—41no—
400C2×Dic3—41no—
401C2×Dic3—41no—
402C2×Dic3—41no—
403C2×Dic3D2412yescomplemented
404D12—34no—
405D12—34no—
406D12—64no—
407D12—64no—
408D12—62no—
409D12—62no—
410D12—62no—
411D12—62no—
412D12—62no—
413D12—62no—
414D12—62no—
415D12—62no—
416D12—62no—
417D12—62no—
418D12—122no—
419D12—122no—
420D12—122no—
421D12—122no—
422D12—122no—
423D12—122no—
424D12—121no—
425D12—121no—
426D12—121no—
427D12—121no—
428C4×D3—128no—
429C4×D3—128no—
430C3×C8—24no—
431C3×C8—22no—
432C3×C8—22no—
433C3×C8—121no—
434C3⋊C8—41no—
435C2×C32#38611yescharacteristic
436C2×C32C4×D811yescharacteristic
437C2×C32#44211yescharacteristic
438C2×C32#44711yescharacteristic
439C2×C32#44911yescharacteristic
440C2×C32#45911yescharacteristic
441C2×C32#46311yescharacteristic
442C3⋊D3—44no—
443C3⋊D3—82no—
444C24—181no—
445C24—181no—
446C2×D4—92no—
447C2×D4—92no—
448C2×D4—92no—
449C2×D4—92no—
450C2×D4—181no—
451C2×D4—181no—
452C2×D4—181no—
453C2×D4—181no—
454C2×D4—181no—
455C2×D4—181no—
456C2×D4—181no—
457C2×D4—181no—
458C22×C4—31no—
459C22×C4—31no—
460C22×C4—61no—
461C22×C4—61no—
462C22×C4—184no—
463C22×C4—362no—
464C22×C4—362no—
465C22×C4C2×D3211yescharacteristic
466D8—188no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—61no—
470C2×C8—61no—
471C2×C8—61no—
472C2×C8#62412yescomplemented
473C4⋊C4—32no—
474C4⋊C4—61no—
475C4⋊C4—61no—
476C4⋊C4—61no—
477C22⋊C4—184no—
478C22⋊C4—362no—
479C22⋊C4—362no—
480C42—61no—
481C42—61no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3C4×D1211yescharacteristic
490C22×C3#88211yescharacteristic
491C22×C3#88211yescharacteristic
492C22×C3#88411yescharacteristic
493C22×C3#89311yescharacteristic
494C22×C3#89511yescharacteristic
495C22×C3C2×D2411yescharacteristic
496C22×C3#90411yescharacteristic
497C22×C3#90811yescharacteristic
498C22×C3#90811yescharacteristic
499C22×C3D3×D811yescharacteristic
500C22×C3#91411yescharacteristic
501C22×C3#91411yescharacteristic
502C22×C3#91911yescharacteristic
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—124no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—122no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—122no—
515C2×D3—122no—
516C2×D3—122no—
517C2×D3—122no—
518C2×D3—124no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—122no—
523C2×D3—122no—
524C2×D3—122no—
525C2×D3—242no—
526C2×D3—242no—
527C2×D3—242no—
528C2×D3—242no—
529C2×D3—242no—
530C2×D3—242no—
531C2×D3—242no—
532C2×D3—242no—
533C2×D3—242no—
534C2×D3—242no—
535C2×D3—242no—
536C2×D3—242no—
537C2×D3—241no—
538C2×D3—241no—
539C2×D3—241no—
540C2×D3—241no—
541C2×D3—241no—
542C2×D3—241no—
543C2×D3—241no—
544C2×D3—241no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—62no—
550C3×C4—122no—
551C3×C4—121no—
552C3×C4—241no—
553C3×C4C4×D1211yescharacteristic
554C3×C4D3×C22⋊C411yescharacteristic
555C3×C4D3×C22⋊C411yescharacteristic
556C3×C4#88411yescharacteristic
557C3×C4#89311yescharacteristic
558C3×C4#89411yescharacteristic
559C3×C4#89411yescharacteristic
560C3×C4#89511yescharacteristic
561Dic3—22no—
562Dic3—41no—
563Dic3—42no—
564Dic3—81no—
565C32#187911yescharacteristic, complemented, Sylow
566C23—182no—
567C23—182no—
568C23—182no—
569C23—182no—
570C23—361no—
571C23—361no—
572C23—361no—
573C23—361no—
574C23—361no—
575C23—361no—
576C23—361no—
577C23—361no—
578C23—361no—
579C23—361no—
580C23D3×D1211yescharacteristic
581D4—94no—
582D4—182no—
583D4—182no—
584D4—182no—
585D4—182no—
586D4—182no—
587D4—361no—
588D4—361no—
589C2×C4—32no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4—61no—
593C2×C4—61no—
594C2×C4—61no—
595C2×C4—62no—
596C2×C4—121no—
597C2×C4—121no—
598C2×C4—121no—
599C2×C4—121no—
600C2×C4—121no—
601C2×C4—368no—
602C2×C4#379911yescharacteristic
603C2×C4#379911yescharacteristic
604C2×C4D3×D1211yescharacteristic
605C2×C4C2×#62411yescharacteristic
606C2×C4#381111yescharacteristic
607C2×C4#381111yescharacteristic
608C8—22no—
609C8—121no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3#466511yescharacteristic
618C2×C3#466511yescharacteristic
619C2×C3C4×D2411yescharacteristic
620C2×C3#471111yescharacteristic
621C2×C3#473211yescharacteristic
622C2×C3#473411yescharacteristic
623C2×C3#477311yescharacteristic
624C2×C3#478611yescharacteristic
625C2×C3#481011yescharacteristic
626C2×C3#481911yescharacteristic
627C2×C3#484311yescharacteristic
628C2×C3#484411yescharacteristic
629C2×C3#486911yescharacteristic
630C2×C3#487211yescharacteristic
631D3—124no—
632D3—124no—
633D3—244no—
634D3—244no—
635D3—242no—
636D3—242no—
637C22—184no—
638C22—362no—
639C22—362no—
640C22—362no—
641C22—362no—
642C22—362no—
643C22—362no—
644C22—362no—
645C22—362no—
646C22—362no—
647C22—721no—
648C22—721no—
649C22—721no—
650C22—721no—
651C22D3×D2411yescharacteristic
652C22#6379411yescharacteristic
653C22#6379411yescharacteristic
654C22#6380811yescharacteristic
655C22#6389411yescharacteristic
656C22#6391011yescharacteristic
657C22#6392311yescharacteristic
658C4—62no—
659C4—122no—
660C4—121no—
661C4—241no—
662C4#6389411yescharacteristic
663C4#6389711yescharacteristic
664C4#6391011yescharacteristic
665C4#6397411yescharacteristic
666C3—21no—
667C3#6867311yescharacteristic, complemented
668C3#6889711yescharacteristic, complemented
669C2—364no—
670C2—722no—
671C2#1059076311yescharacteristic
672C2#1059076511yescharacteristic
673C2#1059076811yescharacteristic
674C2#1059077011yescharacteristic
675C2#1059094711yescharacteristic
676C2#1059096711yescharacteristic
677C2#1059138011yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3745C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1879
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63894C2semidirect
3. #10591320C2semidirect
4. C2×#63564C2semidirect
5. C2×#63564C2semidirect
6. C3×#4551C2semidirect
7. C3×#4550C2semidirect
16. C2×#3745C4semidirect
41. #4551D3semidirect
42. #4550D3semidirect
55. C2×C4⋊(C3⋊D3)C2×C4semidirect
67. C2×C32×C8C2×C4semidirect
152. C4⋊(C3⋊D3)C22⋊C4semidirect
164. C2×C3×Dic3D8semidirect
244. C2×C3×C8C4×D3semidirect
245. C2×C3×C8C4×D3semidirect
403. C2×Dic3D24semidirect
472. C2×C8#624semidirect
565. C32#1879semidirect
667. C3#68673semidirect
668. C3#68897semidirect

Maximal subgroups

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

subgroupindex
C22×#37452
C2×#638942
#105913202
C2×#635642
C3×#45512
C3×#45502
#688973
#686733