Finite Group Databasebeta

← #11787535

Subgroups — #11787535

Order 1152.

977 conjugacy classes of subgroups.

The subgroup lattice has 657 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×D12C211yesmaximal, characteristic, complemented
2C22×#3714C211yesmaximal, characteristic
3C2×#63648C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5#10591320C211yesmaximal, characteristic, complemented
6C3×#4550C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70172—31nomaximal
9#68673—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3722—21no—
19C2×#3722—21no—
20C2×(C2×D3)⋊Dic3—21no—
21Dic3×D12—22no—
22Dic3×D12—22no—
23C2×#3714—22no—
24C2×#3714—22no—
25C2×#3714C414yescomplemented
26#63648—22no—
27C3×#821—22no—
28C2×D4×Dic3—31no—
29C22×#213—31no—
30C22×D24—31no—
31C2×C4×D12—31no—
32C2×C3×#102—31no—
33C2×#821—31no—
34C2×#821—31no—
35C2×#821—61no—
36C2×#821D311yescharacteristic, complemented
37#4988—31no—
38#4939—31no—
39C3×#336—31no—
40#4551—31no—
41#4550D311yescharacteristic, complemented
42#4529—31no—
43C23×C3⋊D3—21no—
44C23×C3×D3—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—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)C2×C412yescomplemented
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
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—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)D412yes—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8C2×C412yescomplemented
77#3722—42no—
78#3722—42no—
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—21no—
90C22×C3×C8—31no—
91C22×C3×C8C2×D311yescharacteristic
92C22×C3×C8C2×D311yescharacteristic
93C2×C3×C4⋊C4—31no—
94C2×C3×C42—31no—
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×C4⋊Dic3—31no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×C4×Dic3C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112C2×D24—34no—
113C2×D24—62no—
114C2×D24—62no—
115C4×D12—62no—
116C4×D12—62no—
117C3×#102—62no—
118#821—22no—
119#821—62no—
120#821—62no—
121#821—64no—
122C23×C32C2×D411yescharacteristic
123C22×C3⋊D3—22no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—41no—
145C2×C3⋊Dic3—41no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—41no—
149C4⋊(C3⋊D3)—41no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3D812yescomplemented
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12C22⋊C414yescomplemented
163D3×Dic3—48no—
164C32×C8—41no—
165C3×C3⋊C8—22no—
166C22×D8—91no—
167C2×C4×D4—91no—
168C2×#102—31no—
169C2×#102—91no—
170#390—91no—
171#340—91no—
172#336—31no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—61no—
176C23×D3—61no—
177C23×D3—121no—
178C2×C3×D4—32no—
179C2×C3×D4—32no—
180C2×C3×D4—32no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C22×C3×C4—21no—
185C22×C3×C4—31no—
186C22×C3×C4—31no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×Dic3—21no—
191C22×Dic3—64no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3—121no—
195C22×Dic3—122no—
196C22×Dic3—122no—
197C22×Dic3D1211yescharacteristic
198C22×Dic3D1211yescharacteristic
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—21no—
202C2×D12—32no—
203C2×D12—32no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—61no—
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—61no—
217C2×D12—121no—
218C2×D12—121no—
219C2×D12—121no—
220C2×D12C4×D312yes—
221C2×D12D1212yes—
222C2×D12#6712yes—
223C2×C4×D3—64no—
224C2×C4×D3—122no—
225C2×C4×D3—122no—
226C2×C3×C8—22no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—32no—
234C2×C3×C8—41no—
235C2×C3×C8—41no—
236C2×C3×C8—61no—
237C2×C3×C8—61no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C42—61no—
241C3×C42—61no—
242#217—64no—
243#213—68no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—122no—
246(C2×D3)⋊C4—122no—
247(C2×D3)⋊C4—122no—
248(C2×D3)⋊C4—122no—
249C4⋊Dic3—21no—
250C4⋊Dic3—21no—
251C4⋊Dic3—32no—
252C4⋊Dic3—32no—
253C4⋊Dic3—62no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—121no—
257C4×Dic3—21no—
258C4×Dic3—21no—
259C2×C3⋊C8—21no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8C4×D312yescomplemented
262D24—68no—
263C22×C32C4×D411yescharacteristic
264C22×C32#12011yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32C2×D811yescharacteristic
267C22×C32#13511yescharacteristic
268C22×C32AGL(1,ℤ/8)11yescharacteristic
269C22×C32AGL(1,ℤ/8)11yescharacteristic
270C2×C3⋊D3—42no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—81no—
274C2×C3⋊D3—81no—
275C2×C3⋊D3—81no—
276C2×C3⋊D3—81no—
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—
284C32×C4C2×C22⋊C411yescharacteristic
285C32×C4C4×D411yescharacteristic
286C32×C4#12111yescharacteristic
287C32×C4#12311yescharacteristic
288C3⋊Dic3—42no—
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—81no—
292C22×D4—31no—
293C22×D4—91no—
294C23×C4—181no—
295C2×D8—94no—
296C2×D8—182no—
297C2×D8—182no—
298C22×C8—31no—
299C22×C8D3211yescharacteristic
300C4×D4—182no—
301C4×D4—182no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—91no—
304C2×C22⋊C4—181no—
305C2×C22⋊C4—181no—
306C2×C22⋊C4—181no—
307C2×C42—31no—
308#102—62no—
309#102—182no—
310C23×C3—21no—
311C23×C3—62no—
312C23×C3—62no—
313C23×C3—62no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—121no—
318C23×C3C2×D1211yescharacteristic
319C23×C3D3×D411yescharacteristic
320C22×D3—22no—
321C22×D3—22no—
322C22×D3—22no—
323C22×D3—41no—
324C22×D3—41no—
325C22×D3—41no—
326C22×D3—41no—
327C22×D3—62no—
328C22×D3—62no—
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—121no—
341C22×D3—121no—
342C22×D3—121no—
343C22×D3—121no—
344C22×D3—241no—
345C22×D3—241no—
346C22×D3—241no—
347C22×D3—241no—
348C3×D4—34no—
349C3×D4—62no—
350C3×D4—62no—
351C3×D4—62no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—32no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—61no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—121no—
365C2×C3×C4—121no—
366C2×C3×C4—121no—
367C2×C3×C4C2×C4×D311yescharacteristic
368C2×C3×C4C2×C4×D311yescharacteristic
369C2×C3×C4C2×D1211yescharacteristic
370C2×C3×C4#23511yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D411yescharacteristic
375C2×C3×C4#23711yescharacteristic
376C2×C3×C4#23711yescharacteristic
377C2×C3×C4#23911yescharacteristic
378C2×C3×C4C2×#6711yescharacteristic
379C2×Dic3—21no—
380C2×Dic3—21no—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—41no—
385C2×Dic3—41no—
386C2×Dic3—41no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—122no—
390C2×Dic3—128no—
391C2×Dic3—121no—
392C2×Dic3—121no—
393C2×Dic3—121no—
394C2×Dic3—121no—
395C2×Dic3—241no—
396C2×Dic3—241no—
397C2×Dic3D2412yescomplemented
398D12—22no—
399D12—22no—
400D12—22no—
401D12—64no—
402D12—62no—
403D12—62no—
404D12—62no—
405D12—62no—
406D12—122no—
407D12—122no—
408D12—122no—
409D12—121no—
410D12—121no—
411D12—121no—
412D12—121no—
413D12(C2×D3)⋊C414yescomplemented
414C4×D3—128no—
415C3×C8—42no—
416C3×C8—41no—
417C3×C8—41no—
418C3×C8—62no—
419C3⋊C8—22no—
420C2×C32#38611yescharacteristic
421C2×C32C4×D811yescharacteristic
422C2×C32#44211yescharacteristic
423C2×C32#44711yescharacteristic
424C2×C32#44911yescharacteristic
425C2×C32#45911yescharacteristic
426C2×C32#46311yescharacteristic
427C3⋊D3—82no—
428C3×D3—44no—
429C24—61no—
430C24—181no—
431C2×D4—32no—
432C2×D4—32no—
433C2×D4—32no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—92no—
438C2×D4—181no—
439C2×D4—181no—
440C2×D4—181no—
441C2×D4—181no—
442C2×D4—181no—
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—61no—
446C22×C4—184no—
447C22×C4—181no—
448C22×C4—362no—
449C22×C4—362no—
450C22×C4C2×D3211yescharacteristic
451D8—188no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—32no—
456C2×C8—61no—
457C2×C8—61no—
458C4⋊C4—61no—
459C4⋊C4—61no—
460C4⋊C4—92no—
461C4⋊C4—181no—
462C22⋊C4—184no—
463C22⋊C4—362no—
464C22⋊C4—362no—
465C42—61no—
466C42—61no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—64no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3—122no—
480C22×C3—122no—
481C22×C3C4×D1211yescharacteristic
482C22×C3#67⋊C411yescharacteristic
483C22×C3#88211yescharacteristic
484C22×C3#88211yescharacteristic
485C22×C3#89511yescharacteristic
486C22×C3C2×D2411yescharacteristic
487C22×C3#90411yescharacteristic
488C22×C3#90811yescharacteristic
489C22×C3#90811yescharacteristic
490C22×C3D3×D811yescharacteristic
491C22×C3#91111yescharacteristic
492C22×C3#91411yescharacteristic
493C22×C3#91611yescharacteristic
494C22×C3#93911yescharacteristic
495C2×D3—24no—
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—42no—
499C2×D3—42no—
500C2×D3—42no—
501C2×D3—42no—
502C2×D3—124no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—242no—
510C2×D3—242no—
511C2×D3—242no—
512C2×D3—242no—
513C2×D3—242no—
514C2×D3—242no—
515C2×D3—241no—
516C2×D3—241no—
517C2×D3—241no—
518C2×D3—241no—
519C2×D3—241no—
520C2×D3—241no—
521C2×D3—241no—
522C2×D3—241no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—62no—
528C3×C4—121no—
529C3×C4—241no—
530C3×C4D3×C22⋊C411yescharacteristic
531C3×C4#67⋊C411yescharacteristic
532C3×C4#88411yescharacteristic
533C3×C4#88611yescharacteristic
534C3×C4#89311yescharacteristic
535C3×C4#89411yescharacteristic
536C3×C4C2×(C2×D3)⋊C411yescharacteristic
537C3×C4#93911yescharacteristic
538Dic3—22no—
539Dic3—41no—
540Dic3—81no—
541Dic3—122no—
542Dic3—122no—
543Dic3—242no—
544C32#187911yescharacteristic, complemented, Sylow
545C23—62no—
546C23—62no—
547C23—62no—
548C23—121no—
549C23—121no—
550C23—121no—
551C23—121no—
552C23—182no—
553C23—361no—
554C23—361no—
555C23—361no—
556C23—361no—
557C23—361no—
558C23—361no—
559C23D3×D1211yescharacteristic
560D4—34no—
561D4—62no—
562D4—62no—
563D4—62no—
564D4—182no—
565D4—182no—
566D4—361no—
567D4—361no—
568C2×C4—32no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—61no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—121no—
575C2×C4—121no—
576C2×C4—121no—
577C2×C4—182no—
578C2×C4—368no—
579C2×C4—361no—
580C2×C4—361no—
581C2×C4#379611yescharacteristic
582C2×C4C4×D3211yescharacteristic
583C2×C4D3×D1211yescharacteristic
584C2×C4#380411yescharacteristic
585C2×C4D3×#6711yescharacteristic
586C2×C4#381111yescharacteristic
587C8—41no—
588C8—62no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—124no—
597C2×C3#466511yescharacteristic
598C2×C3C4×D2411yescharacteristic
599C2×C3#471111yescharacteristic
600C2×C3#473211yescharacteristic
601C2×C3#473411yescharacteristic
602C2×C3#475611yescharacteristic
603C2×C3#477311yescharacteristic
604C2×C3#478111yescharacteristic
605C2×C3#478511yescharacteristic
606C2×C3#484311yescharacteristic
607C2×C3#484411yescharacteristic
608C2×C3#495811yescharacteristic
609C2×C3#515011yescharacteristic
610C2×C3#516511yescharacteristic
611D3—44no—
612D3—244no—
613D3—242no—
614D3—242no—
615C22—64no—
616C22—122no—
617C22—122no—
618C22—122no—
619C22—122no—
620C22—122no—
621C22—122no—
622C22—362no—
623C22—362no—
624C22—362no—
625C22—721no—
626C22—721no—
627C22—721no—
628C22—721no—
629C22D3×D2411yescharacteristic
630C22#6379411yescharacteristic
631C22#6379511yescharacteristic
632C22#6380611yescharacteristic
633C22#6388011yescharacteristic
634C22#6388611yescharacteristic
635C22#6392311yescharacteristic
636C4—62no—
637C4—121no—
638C4—241no—
639C4—362no—
640C4#6388111yescharacteristic
641C4#6389011yescharacteristic
642C4D3×(C2×D3)⋊C411yescharacteristic
643C4#6397111yescharacteristic
644C3—21no—
645C3#6867311yescharacteristic, complemented
646C3#7017211yescharacteristic, complemented
647C2—124no—
648C2—722no—
649C2#1059074511yescharacteristic
650C2#1059074611yescharacteristic
651C2#1059075311yescharacteristic
652C2#1059075411yescharacteristic
653C2#1059094711yescharacteristic
654C2#1059096811yescharacteristic
655C2#1059136411yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
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
1. C2×Dic3×D12C2semidirect
3. C2×#63648C2semidirect
4. C2×C3×#821C2semidirect
5. #10591320C2semidirect
6. C3×#4550C2semidirect
7. #10589164C2semidirect
25. C2×#3714C4semidirect
36. C2×#821D3semidirect
41. #4550D3semidirect
52. C2×C4⋊(C3⋊D3)C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
158. C2×C3×Dic3D8semidirect
162. C3×D12C22⋊C4semidirect
261. C2×C3⋊C8C4×D3semidirect
397. C2×Dic3D24semidirect
413. D12(C2×D3)⋊C4semidirect
544. C32#1879semidirect
645. C3#68673semidirect
646. C3#70172semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D122
C22×#37142
C2×#636482
C2×C3×#8212
#105913202
C3×#45502
#105891642
#701723
#686733