Finite Group Databasebeta

← #11787597

Subgroups — #11787597

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63843C211yesmaximal, characteristic, complemented
2C22×#3717C211yesmaximal, characteristic
3#10592687C211yesmaximal, characteristic
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#70240—31nomaximal
9#68909—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752—21no—
14C2×#3752—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20C2×Dic32—21no—
21#63843—22no—
22#63843—22no—
23C2×#3717—22no—
24C2×#3717—22no—
25C2×#3717C414yescomplemented
26C3×#810—22no—
27#63564—22no—
28C2×Q8×Dic3—31no—
29C22×#215—31no—
30C22×#204—31no—
31C2×#887—31no—
32C2×C3×#103—31no—
33C2×#821—31no—
34#4988—31no—
35#4988—31no—
36#4988—61no—
37C2×#810D311yescharacteristic, complemented
38C2×#809—31no—
39C3×#340—31no—
40#4550—31no—
41#4550—31no—
42#4529D311yescharacteristic, complemented
43C23×C3⋊D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
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)C2×C412yes—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6C2×C412yes—
60C2×C3×Dic6D412yes—
61C2×C3×Dic6D412yes—
62C32×C4⋊C4—21no—
63C32×C4⋊C4—21no—
64#3752—42no—
65#3752—42no—
66C4×C3⋊Dic3—21no—
67C4×C3⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3D412yes—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8C2×C412yes—
76Dic3⋊Dic3—24no—
77Dic32—24no—
78#3717—28no—
79#1880—91noSylow
80C22×C3×Q8—31no—
81C22×D12—31no—
82C22×D12—31no—
83C22×D12—61no—
84C22×Dic6C2×D311yescharacteristic
85C22×C3×C8—31no—
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C2×D311yescharacteristic
91Q8×Dic3—62no—
92Q8×Dic3—62no—
93C2×#215—34no—
94C2×#215—62no—
95C2×#215—62no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—62no—
101C2×(C2×D3)⋊C4—62no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×Dic3⋊C4—61no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112C2×#204—34no—
113C2×#204—62no—
114C2×#204—62no—
115#887—62no—
116#887—62no—
117C3×#103—62no—
118#821—62no—
119#810—22no—
120#809—62no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—22no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3SD1612yescomplemented
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—41no—
147C4⋊(C3⋊D3)—41no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6C22⋊C414yescomplemented
158C3×C3⋊C8—22no—
159C3×C3⋊C8—41no—
160C22×SD16—91no—
161C2×C4×Q8—91no—
162C2×#103—31no—
163C2×#102—91no—
164#390—91no—
165#340—31no—
166#336—91no—
167C23×D3—62no—
168C23×D3—61no—
169C23×D3—61no—
170C2×C3×Q8—32no—
171C2×C3×Q8—32no—
172C2×C3×Q8—32no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C22×C3×C4—22no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—31no—
187C22×Dic3—31no—
188C22×Dic3—31no—
189C22×Dic3—31no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C2×D12—32no—
193C2×D12—32no—
194C2×D12—62no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—61no—
203C2×D12—62no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—121no—
207C2×D12—121no—
208C2×D12—121no—
209C2×D12—121no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6C4×D312yes—
214C2×Dic6D1212yes—
215C2×Dic6#6712yes—
216C2×C3×C8—32no—
217C2×C3×C8—61no—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—61no—
230#215—68no—
231(C2×D3)⋊C4—122no—
232(C2×D3)⋊C4—122no—
233(C2×D3)⋊C4—124no—
234(C2×D3)⋊C4—124no—
235(C2×D3)⋊C4—122no—
236(C2×D3)⋊C4—122no—
237C4⋊Dic3—21no—
238C4⋊Dic3—64no—
239C4⋊Dic3D1212yes—
240Dic3⋊C4—64no—
241C4×Dic3—64no—
242C4×Dic3—64no—
243C4×Dic3—61no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—121no—
248C4×Dic3—121no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8C4×D312yes—
255#204—68no—
256C22×C32C4×D411yescharacteristic
257C22×C32#12011yescharacteristic
258C22×C32#12111yescharacteristic
259C22×C32C2×SD1611yescharacteristic
260C22×C32#13511yescharacteristic
261C22×C32AGL(1,ℤ/8)11yescharacteristic
262C22×C32#13711yescharacteristic
263C2×C3⋊D3—42no—
264C2×C3⋊D3—42no—
265C2×C3⋊D3—42no—
266C2×C3⋊D3—81no—
267C2×C3⋊D3—81no—
268C2×C3⋊D3—81no—
269C2×C3⋊D3—81no—
270C32×C4—81no—
271C32×C4C2×C22⋊C411yescharacteristic
272C32×C4C4×D411yescharacteristic
273C32×C4#12111yescharacteristic
274C32×C4#12311yescharacteristic
275C3⋊Dic3—22no—
276C3⋊Dic3—41no—
277C3×Dic3—24no—
278C3×Dic3—42no—
279C22×Q8—31no—
280C22×D4—91no—
281C2×SD16—94no—
282C2×SD16—182no—
283C2×SD16—182no—
284C22×C8—31no—
285C22×C8—31no—
286C4×Q8—182no—
287C4×Q8—182no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—181no—
290C2×C4⋊C4D3211yescharacteristic
291C2×C22⋊C4—181no—
292C2×C22⋊C4—181no—
293C2×C42—91no—
294C2×C42—181no—
295#103—62no—
296#102—182no—
297C23×C3—21no—
298C23×C3D3×D411yescharacteristic
299C23×C3D3×D411yescharacteristic
300C22×D3—64no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—122no—
304C22×D3—122no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—122no—
308C22×D3—122no—
309C22×D3—121no—
310C22×D3—121no—
311C22×D3—121no—
312C22×D3—121no—
313C22×D3—121no—
314C22×D3—121no—
315C22×D3—121no—
316C22×D3—121no—
317C22×D3—121no—
318C22×D3—121no—
319C22×D3—121no—
320C22×D3—121no—
321C3×Q8—34no—
322C3×Q8—62no—
323C3×Q8—62no—
324C3×Q8—62no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—121no—
345C2×C3×C4—121no—
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4#23711yescharacteristic
356C2×C3×C4#23911yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—41no—
365C2×Dic3—41no—
366C2×Dic3—62no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—62no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382D12—62no—
383D12—62no—
384D12—62no—
385D12—62no—
386D12—122no—
387D12—122no—
388D12—122no—
389D12—122no—
390D12—121no—
391D12—121no—
392D12—121no—
393D12—121no—
394Dic6—22no—
395Dic6—22no—
396Dic6—22no—
397Dic6(C2×D3)⋊C414yescomplemented
398C3×C8—62no—
399C3×C8—121no—
400C3⋊C8—22no—
401C3⋊C8—41no—
402C2×C32#38611yescharacteristic
403C2×C32C4×SD1611yescharacteristic
404C2×C32#44011yescharacteristic
405C2×C32#44811yescharacteristic
406C2×C32#44911yescharacteristic
407C2×C32#46011yescharacteristic
408C2×C32#46411yescharacteristic
409C3⋊D3—82no—
410C24—181no—
411C2×Q8—32no—
412C2×Q8—32no—
413C2×Q8—32no—
414C2×Q8—61no—
415C2×Q8—61no—
416C2×Q8—61no—
417C2×D4—92no—
418C2×D4—181no—
419C2×D4—181no—
420C2×D4—181no—
421C2×D4—181no—
422C2×D4—181no—
423C22×C4—21no—
424C22×C4—61no—
425C22×C4—61no—
426C22×C4—91no—
427C22×C4—91no—
428C22×C4C2×D3211yescharacteristic
429SD16—188no—
430C2×C8—32no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C2×C8—61no—
435C2×C8—61no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—32no—
439C4⋊C4—61no—
440C4⋊C4—184no—
441C22⋊C4—362no—
442C22⋊C4—362no—
443C42—184no—
444C42—181no—
445C42—181no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3#67⋊C411yescharacteristic
454C22×C3#88211yescharacteristic
455C22×C3#88211yescharacteristic
456C22×C3#88411yescharacteristic
457C22×C3#89311yescharacteristic
458C22×C3#91111yescharacteristic
459C22×C3D3×SD1611yescharacteristic
460C22×C3D3×SD1611yescharacteristic
461C22×C3#91411yescharacteristic
462C22×C3#91611yescharacteristic
463C22×C3#91811yescharacteristic
464C22×C3#91811yescharacteristic
465C22×C3#91911yescharacteristic
466C22×C3#93911yescharacteristic
467C2×D3—124no—
468C2×D3—124no—
469C2×D3—124no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—122no—
476C2×D3—242no—
477C2×D3—242no—
478C2×D3—242no—
479C2×D3—242no—
480C2×D3—241no—
481C2×D3—241no—
482C2×D3—241no—
483C2×D3—241no—
484C2×D3—241no—
485C2×D3—241no—
486C2×D3—241no—
487C2×D3—241no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—64no—
493C3×C4—82no—
494C3×C4—81no—
495C3×C4—81no—
496C3×C4—122no—
497C3×C4C4×D1211yescharacteristic
498C3×C4D3×C22⋊C411yescharacteristic
499C3×C4#67⋊C411yescharacteristic
500C3×C4#88611yescharacteristic
501C3×C4#89411yescharacteristic
502C3×C4#89511yescharacteristic
503C3×C4C2×(C2×D3)⋊C411yescharacteristic
504C3×C4#93911yescharacteristic
505Dic3—24no—
506Dic3—42no—
507Dic3—62no—
508Dic3—62no—
509Dic3—122no—
510Dic3—122no—
511Dic3—121no—
512Dic3—121no—
513C32#188011yescharacteristic, complemented, Sylow
514C23—182no—
515C23—361no—
516C23—361no—
517C23—361no—
518C23—361no—
519C23—361no—
520C23—361no—
521C23#381111yescharacteristic
522Q8—34no—
523Q8—62no—
524Q8—62no—
525Q8—62no—
526D4—182no—
527D4—182no—
528D4—361no—
529D4—361no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—92no—
538C2×C4—121no—
539C2×C4—121no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4—181no—
544C2×C4—181no—
545C2×C4#379611yescharacteristic
546C2×C4C4×D3211yescharacteristic
547C2×C4D3×D1211yescharacteristic
548C2×C4D3×D1211yescharacteristic
549C2×C4#380411yescharacteristic
550C2×C4D3×#6711yescharacteristic
551C8—62no—
552C8—121no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3#466511yescharacteristic
561C2×C3#476211yescharacteristic
562C2×C3#478111yescharacteristic
563C2×C3#478811yescharacteristic
564C2×C3#479811yescharacteristic
565C2×C3#480611yescharacteristic
566C2×C3#480611yescharacteristic
567C2×C3#481011yescharacteristic
568C2×C3#481711yescharacteristic
569C2×C3#485211yescharacteristic
570C2×C3#488911yescharacteristic
571C2×C3#495811yescharacteristic
572C2×C3#516311yescharacteristic
573C2×C3#518511yescharacteristic
574D3—244no—
575D3—242no—
576D3—242no—
577C22—362no—
578C22—362no—
579C22—362no—
580C22—721no—
581C22—721no—
582C22—721no—
583C22—721no—
584C22#6388111yescharacteristic
585C22#6392311yescharacteristic
586C22#6393011yescharacteristic
587C22#6393711yescharacteristic
588C22#6394511yescharacteristic
589C22#6395011yescharacteristic
590C22#6397111yescharacteristic
591C4—64no—
592C4—81no—
593C4—122no—
594C4—182no—
595C4—361no—
596C4#6388011yescharacteristic
597C4#6388611yescharacteristic
598C4#6389011yescharacteristic
599C4D3×(C2×D3)⋊C411yescharacteristic
600C3—21no—
601C3#6890911yescharacteristic, complemented
602C3#7024011yescharacteristic, complemented
603C2—722no—
604C2#1059048311yescharacteristic
605C2#1059048411yescharacteristic
606C2#1059060611yescharacteristic
607C2#1059061711yescharacteristic
608C2#1059136411yescharacteristic
609C2#1059144411yescharacteristic
610C2#1059157911yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1880
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×#63843C2semidirect
4. C2×C3×#810C2semidirect
6. C3×#4529C2semidirect
7. #10589156C2semidirect
25. C2×#3717C4semidirect
37. C2×#810D3semidirect
42. #4529D3semidirect
143. C2×C3⋊Dic3SD16semidirect
157. C3×Dic6C22⋊C4semidirect
397. Dic6(C2×D3)⋊C4semidirect
513. C32#1880semidirect
601. C3#68909semidirect
602. C3#70240semidirect

Maximal subgroups

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

subgroupindex
C2×#638432
C22×#37172
#105926872
C2×C3×#8102
C2×#635642
C3×#45292
#105891562
#702403
#689093