Finite Group Databasebeta

← #11787548

Subgroups — #11787548

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×#63894C211yesmaximal, characteristic, complemented
2C22×#3714C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic, complemented
4C3×#4988C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic, complemented
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#69657—31nomaximal
9#68897—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×#624—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3722—21no—
21#63894—22no—
22#63894—22no—
23C2×#3714—22no—
24C2×#3714—22no—
25C2×#3714C414yescomplemented
26#63636—22no—
27#63562—22no—
28C22×#213—31no—
29C22×D24—31no—
30C2×#893—31no—
31C2×C4×D12—31no—
32C3×#390—31no—
33C2×#832—31no—
34#4988D311yescharacteristic, complemented
35C2×#809—31no—
36C2×#809—31no—
37C2×#809—31no—
38C2×#809—61no—
39C3×#340—31no—
40#4550—31no—
41#4529D311yescharacteristic, complemented
42#4524—31no—
43C23×C3⋊D3—21no—
44C23×C3×D3—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)C2×C412yes—
51C2×C4⋊(C3⋊D3)D412yes—
52C2×C4⋊(C3⋊D3)D412yes—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yescomplemented
62C2×#624—24no—
63C2×#624—42no—
64C2×#624—42no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×(C2×D3)⋊C4—42no—
71C3×(C2×D3)⋊C4—42no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3D412yes—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8C2×C412yescomplemented
79#3722—24no—
80#3714—28no—
81#1879—91noSylow
82C22×C3×D4—31no—
83C22×D12—31no—
84C22×D12—31no—
85C22×D12—61no—
86C22×D12C2×D311yescharacteristic
87C22×C4×D3—61no—
88C22×C4×D3—61no—
89C22×C3×C8—31no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C22⋊C4—61no—
95C2×C3×C22⋊C4—61no—
96C2×C3×C42—31no—
97C2×#213—34no—
98C2×#213—62no—
99C2×#213—62no—
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4—21no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110C2×D24—34no—
111C2×D24—62no—
112C2×D24—62no—
113#893—62no—
114#893—62no—
115C4×D12—62no—
116C4×D12—62no—
117#832—62no—
118#809—62no—
119#809—62no—
120#809—64no—
121#809—62no—
122C23×C32C2×D411yescharacteristic
123C22×C3⋊D3—22no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3×D3—22no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)C22⋊C414yescomplemented
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—21no—
155C2×C3×Dic3—21no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3D812yescomplemented
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—41no—
162C3×D12—41no—
163#624—48no—
164C3⋊(C3⋊C8)—41no—
165C3×C3⋊C8—22no—
166C22×D8—91no—
167C2×C4×D4—91no—
168C2×#102—91no—
169C2×#102—91no—
170#390—31no—
171#340—31no—
172#336—91no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—61no—
176C23×D3—61no—
177C23×D3—121no—
178C2×C3×D4—32no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—31no—
188C22×C3×C4—31no—
189C22×C3×C4—41no—
190C22×C3×C4—61no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×Dic3—21no—
194C22×Dic3#6711yescharacteristic
195C22×Dic3#6711yescharacteristic
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—32no—
202C2×D12—32no—
203C2×D12—32no—
204C2×D12—32no—
205C2×D12—32no—
206C2×D12—32no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—121no—
217C2×D12—121no—
218C2×D12—121no—
219C2×D12C4×D312yescomplemented
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—122no—
223C2×C4×D3—122no—
224C2×C4×D3—122no—
225C2×C4×D3—122no—
226C2×C3×C8—32no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C3×C4⋊C4—22no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—41no—
236C3×C4⋊C4—61no—
237C3×C22⋊C4—122no—
238C3×C22⋊C4—122no—
239C3×C42—61no—
240C3×C42—61no—
241#213—68no—
242(C2×D3)⋊C4—42no—
243(C2×D3)⋊C4—42no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246C4⋊Dic3—21no—
247C4⋊Dic3D1212yes—
248C4×Dic3—21no—
249C4×Dic3—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C2×C3⋊C8—121no—
260C2×C3⋊C8—121no—
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—24no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—42no—
275C2×C3⋊D3—42no—
276C2×C3⋊D3—42no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—81no—
281C2×C3×D3—81no—
282C2×C3×D3—81no—
283C2×C3×D3—81no—
284C32×C4—81no—
285C32×C4C2×C22⋊C411yescharacteristic
286C32×C4C4×D411yescharacteristic
287C32×C4#12111yescharacteristic
288C32×C4#12311yescharacteristic
289C3×Dic3—22no—
290C3×Dic3—42no—
291C3×Dic3—41no—
292C22×D4—31no—
293C22×D4—91no—
294C23×C4—181no—
295C2×D8—94no—
296C2×D8—182no—
297C2×D8—182no—
298C22×C8—31no—
299C22×C8—91no—
300C4×D4—182no—
301C4×D4—182no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4D3211yescharacteristic
304C2×C22⋊C4—61no—
305C2×C22⋊C4—61no—
306C2×C22⋊C4—181no—
307C2×C42—31no—
308#102—182no—
309#102—182no—
310C23×C3—21no—
311C23×C3—62no—
312C23×C3—121no—
313C23×C3—121no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—121no—
318C23×C3D3×D411yescharacteristic
319C23×C3C2×#6711yescharacteristic
320C22×D3—22no—
321C22×D3—41no—
322C22×D3—41no—
323C22×D3—41no—
324C22×D3—41no—
325C22×D3—41no—
326C22×D3—41no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—122no—
334C22×D3—122no—
335C22×D3—122no—
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—62no—
349C3×D4—62no—
350C3×D4—121no—
351C3×D4—121no—
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—42no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—62no—
372C2×C3×C4—81no—
373C2×C3×C4—81no—
374C2×C3×C4—121no—
375C2×C3×C4—121no—
376C2×C3×C4C2×C4×D311yescharacteristic
377C2×C3×C4C2×C4×D311yescharacteristic
378C2×C3×C4C2×D1211yescharacteristic
379C2×C3×C4#23511yescharacteristic
380C2×C3×C4#23511yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4#23711yescharacteristic
387C2×C3×C4#23911yescharacteristic
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—22no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—41no—
395C2×Dic3—41no—
396C2×Dic3#21312yescomplemented
397D12—22no—
398D12—22no—
399D12—34no—
400D12—34no—
401D12—41no—
402D12—41no—
403D12—64no—
404D12—62no—
405D12—62no—
406D12—62no—
407D12—62no—
408D12—62no—
409D12—62no—
410D12—122no—
411D12—122no—
412D12—122no—
413C4×D3—128no—
414C4×D3—128no—
415C3×C8—62no—
416C3⋊C8—22no—
417C3⋊C8—122no—
418C3⋊C8—121no—
419C3⋊C8—121no—
420C2×C32#38611yescharacteristic
421C2×C32C4×D811yescharacteristic
422C2×C32#44211yescharacteristic
423C2×C32#44711yescharacteristic
424C2×C32#44911yescharacteristic
425C2×C32#45911yescharacteristic
426C2×C32#46311yescharacteristic
427C3⋊D3—44no—
428C3×D3—82no—
429C24—61no—
430C24—181no—
431C2×D4—32no—
432C2×D4—61no—
433C2×D4—61no—
434C2×D4—61no—
435C2×D4—61no—
436C2×D4—61no—
437C2×D4—92no—
438C2×D4—92no—
439C2×D4—92no—
440C2×D4—181no—
441C2×D4—181no—
442C2×D4—181no—
443C22×C4—21no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—61no—
447C22×C4—184no—
448C22×C4—362no—
449C22×C4—362no—
450C22×C4C2×D3211yescharacteristic
451D8—188no—
452C2×C8—32no—
453C2×C8—61no—
454C2×C8—61no—
455C2×C8—181no—
456C2×C8—181no—
457C2×C8—181no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—32no—
461C4⋊C4—61no—
462C22⋊C4—122no—
463C22⋊C4—122no—
464C22⋊C4—184no—
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—122no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3—241no—
478C22×C3—241no—
479C22×C3—241no—
480C22×C3—241no—
481C22×C3#88211yescharacteristic
482C22×C3#88411yescharacteristic
483C22×C3#89311yescharacteristic
484C22×C3D3×D811yescharacteristic
485C22×C3#91411yescharacteristic
486C22×C3#91411yescharacteristic
487C22×C3#91911yescharacteristic
488C22×C3C4×#6711yescharacteristic
489C22×C3C2×#21311yescharacteristic
490C22×C3#93211yescharacteristic
491C22×C3#93711yescharacteristic
492C22×C3#93811yescharacteristic
493C22×C3#94911yescharacteristic
494C22×C3#95011yescharacteristic
495C2×D3—42no—
496C2×D3—42no—
497C2×D3—42no—
498C2×D3—64no—
499C2×D3—64no—
500C2×D3—81no—
501C2×D3—81no—
502C2×D3—81no—
503C2×D3—81no—
504C2×D3—124no—
505C2×D3—122no—
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—242no—
518C2×D3—242no—
519C2×D3—242no—
520C2×D3—242no—
521C2×D3—242no—
522C2×D3—242no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—62no—
528C3×C4—82no—
529C3×C4—81no—
530C3×C4—81no—
531C3×C4—122no—
532C3×C4—121no—
533C3×C4C4×D1211yescharacteristic
534C3×C4D3×C22⋊C411yescharacteristic
535C3×C4D3×C22⋊C411yescharacteristic
536C3×C4#67⋊C411yescharacteristic
537C3×C4#88311yescharacteristic
538C3×C4#88411yescharacteristic
539C3×C4#89411yescharacteristic
540C3×C4#89511yescharacteristic
541Dic3—22no—
542Dic3—42no—
543Dic3—41no—
544C32#187911yescharacteristic, complemented, Sylow
545C23—62no—
546C23—121no—
547C23—121no—
548C23—121no—
549C23—121no—
550C23—121no—
551C23—121no—
552C23—182no—
553C23—182no—
554C23—182no—
555C23—361no—
556C23—361no—
557C23—361no—
558C23—361no—
559C23D3×#6711yescharacteristic
560D4—62no—
561D4—62no—
562D4—94no—
563D4—121no—
564D4—121no—
565D4—182no—
566D4—182no—
567D4—182no—
568C2×C4—32no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—62no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—121no—
579C2×C4—121no—
580C2×C4—368no—
581C2×C4#379911yescharacteristic
582C2×C4C4×D3211yescharacteristic
583C2×C4D3×D1211yescharacteristic
584C2×C4#380211yescharacteristic
585C2×C4#380411yescharacteristic
586C2×C4#381111yescharacteristic
587C8—62no—
588C8—361no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—242no—
597C2×C3#466511yescharacteristic
598C2×C3#477311yescharacteristic
599C2×C3#478611yescharacteristic
600C2×C3#481011yescharacteristic
601C2×C3#481911yescharacteristic
602C2×C3#486911yescharacteristic
603C2×C3#487211yescharacteristic
604C2×C3#495611yescharacteristic
605C2×C3C4×#21311yescharacteristic
606C2×C3#501411yescharacteristic
607C2×C3#503611yescharacteristic
608C2×C3#503711yescharacteristic
609C2×C3#505711yescharacteristic
610C2×C3#507211yescharacteristic
611D3—82no—
612D3—124no—
613D3—124no—
614D3—244no—
615C22—122no—
616C22—122no—
617C22—122no—
618C22—184no—
619C22—241no—
620C22—241no—
621C22—241no—
622C22—241no—
623C22—362no—
624C22—362no—
625C22—362no—
626C22—362no—
627C22—362no—
628C22—362no—
629C22#6390411yescharacteristic
630C22#6392211yescharacteristic
631C22D3×#21311yescharacteristic
632C22#6393411yescharacteristic
633C22#6393911yescharacteristic
634C22#6394911yescharacteristic
635C22#6395811yescharacteristic
636C4—62no—
637C4—81no—
638C4—122no—
639C4—121no—
640C4#6385411yescharacteristic
641C4#6388011yescharacteristic
642C4#6391011yescharacteristic
643C4#6392111yescharacteristic
644C3—21no—
645C3#6889711yescharacteristic, complemented
646C3#6965711yescharacteristic, complemented
647C2—242no—
648C2—364no—
649C2#1059045611yescharacteristic
650C2#1059058911yescharacteristic
651C2#1059059511yescharacteristic
652C2#1059061511yescharacteristic
653C2#1059127511yescharacteristic
654C2#1059142911yescharacteristic
655C2#1059156811yescharacteristic
subgroupG/H
centerC23D3×#67
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×#63894C2semidirect
3. C2×#63636C2semidirect
4. C3×#4988C2semidirect
5. C2×#63562C2semidirect
6. C3×#4529C2semidirect
7. #10589155C2semidirect
25. C2×#3714C4semidirect
34. #4988D3semidirect
41. #4529D3semidirect
61. C2×C3×D12C2×C4semidirect
78. C2×C3×C3⋊C8C2×C4semidirect
149. C4⋊(C3⋊D3)C22⋊C4semidirect
158. C2×C3×Dic3D8semidirect
219. C2×D12C4×D3semidirect
261. C2×C3⋊C8C4×D3semidirect
396. C2×Dic3#213semidirect
544. C32#1879semidirect
645. C3#68897semidirect
646. C3#69657semidirect

Maximal subgroups

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

subgroupindex
C2×#638942
C22×#37142
C2×#636362
C3×#49882
C2×#635622
C3×#45292
#105891552
#696573
#688973