Finite Group Databasebeta

← #11787586

Subgroups — #11787586

Order 1152.

849 conjugacy classes of subgroups.

The subgroup lattice has 601 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic, complemented
2C22×#3717C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic
4#10591320C211yesmaximal, characteristic
5C2×#63565C211yesmaximal, characteristic, complemented
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#71633—31nomaximal
9#68909—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×Dic3⋊C4—21no—
16C2×C3×C4×Dic3—21no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C3×#887—22no—
20C3×#887—22no—
21C2×#3722—21no—
22C2×#3722—21no—
23C2×#3717—22no—
24C2×#3717—22no—
25C2×#3717C414yescomplemented
26#63636—22no—
27#63565—22no—
28C2×C3×C4×Q8—31no—
29C22×#215—31no—
30C22×#204—31no—
31C2×#887D311yescharacteristic, complemented
32C2×#835—31no—
33#4988—31no—
34C2×#810—31no—
35C2×#809—31no—
36C2×#809—31no—
37C2×#809—61no—
38#4939—31no—
39C3×#340—31no—
40#4550—31no—
41#4529D311yescharacteristic, complemented
42#4524—31no—
43C23×C3⋊D3—21no—
44C22×C32×C4—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)C2×C412yes—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
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⋊C4D412yes—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×Dic3⋊C4—24no—
70C3×C4×Dic3—24no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8C2×C412yes—
76#3722—42no—
77#3722—42no—
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—
86C3×C4×Q8—62no—
87C3×C4×Q8—62no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—61no—
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C42—31no—
94C2×C3×C42—61no—
95C2×#215—34no—
96C2×#215—62no—
97C2×#215—62no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101C2×(C2×D3)⋊C4—61no—
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×Dic3⋊C4—21no—
104C2×C4×Dic3—21no—
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110C2×#204—34no—
111C2×#204—62no—
112C2×#204—62no—
113#887—22no—
114#887—22no—
115#835—62no—
116#810—62no—
117#809—64no—
118#809—62no—
119#809—62no—
120C23×C32C2×D411yescharacteristic
121C22×C3⋊D3—22no—
122C22×C3⋊D3—41no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C2×C32×C4—22no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C4⋊(C3⋊D3)—22no—
138C4⋊(C3⋊D3)—22no—
139C4⋊(C3⋊D3)—41no—
140C4⋊(C3⋊D3)—41no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3SD1612yescomplemented
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6C22⋊C414yescomplemented
157C3⋊(C3⋊C8)—41no—
158C3×C3⋊C8—22no—
159C22×SD16—91no—
160C2×C4×Q8—31no—
161C2×#103—91no—
162C2×#102—91no—
163#390—91no—
164#340—31no—
165#336—91no—
166C23×D3—61no—
167C23×D3—61no—
168C23×D3—121no—
169C2×C3×Q8—32no—
170C2×C3×Q8—32no—
171C2×C3×Q8—32no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×Q8—61no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—41no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3#6711yescharacteristic
188C22×Dic3#6711yescharacteristic
189C2×D12—32no—
190C2×D12—32no—
191C2×D12—62no—
192C2×D12—62no—
193C2×D12—62no—
194C2×D12—61no—
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—61no—
204C2×D12—121no—
205C2×D12—121no—
206C2×D12—121no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6C4×D312yes—
211C2×Dic6D1212yes—
212C2×Dic6#6712yes—
213C2×C3×C8—32no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—41no—
220C3×C4⋊C4—64no—
221C3×C4⋊C4—61no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4D1212yes—
224C3×C4⋊C4#6712yes—
225C3×C42—64no—
226C3×C42—61no—
227C3×C42—61no—
228#215—68no—
229(C2×D3)⋊C4—122no—
230(C2×D3)⋊C4—122no—
231(C2×D3)⋊C4—122no—
232(C2×D3)⋊C4—122no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235Dic3⋊C4—24no—
236C4×Dic3—24no—
237C4×Dic3—21no—
238C4×Dic3—21no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—121no—
249C2×C3⋊C8—121no—
250C2×C3⋊C8C4×D312yes—
251#204—68no—
252C22×C32C4×D411yescharacteristic
253C22×C32#12011yescharacteristic
254C22×C32#12111yescharacteristic
255C22×C32C2×SD1611yescharacteristic
256C22×C32#13511yescharacteristic
257C22×C32AGL(1,ℤ/8)11yescharacteristic
258C22×C32#13711yescharacteristic
259C2×C3⋊D3—42no—
260C2×C3⋊D3—42no—
261C2×C3⋊D3—42no—
262C2×C3⋊D3—81no—
263C2×C3⋊D3—81no—
264C2×C3⋊D3—81no—
265C2×C3⋊D3—81no—
266C32×C4—42no—
267C32×C4C2×C22⋊C411yescharacteristic
268C32×C4C4×D411yescharacteristic
269C32×C4#12111yescharacteristic
270C32×C4#12311yescharacteristic
271C3×Dic3—24no—
272C3×Dic3—22no—
273C3×Dic3—41no—
274C3×Dic3—81no—
275C22×Q8—31no—
276C22×D4—91no—
277C2×SD16—94no—
278C2×SD16—182no—
279C2×SD16—182no—
280C22×C8—31no—
281C22×C8—91no—
282C4×Q8—62no—
283C4×Q8—62no—
284C2×C4⋊C4—31no—
285C2×C4⋊C4—61no—
286C2×C4⋊C4D3211yescharacteristic
287C2×C22⋊C4—181no—
288C2×C22⋊C4—181no—
289C2×C42—31no—
290C2×C42—61no—
291#103—182no—
292#102—182no—
293C23×C3—21no—
294C23×C3D3×D411yescharacteristic
295C23×C3C2×#6711yescharacteristic
296C22×D3—62no—
297C22×D3—62no—
298C22×D3—122no—
299C22×D3—122no—
300C22×D3—122no—
301C22×D3—121no—
302C22×D3—121no—
303C22×D3—121no—
304C22×D3—121no—
305C22×D3—121no—
306C22×D3—121no—
307C22×D3—121no—
308C22×D3—121no—
309C22×D3—121no—
310C22×D3—121no—
311C22×D3—121no—
312C22×D3—121no—
313C22×D3—241no—
314C22×D3—241no—
315C22×D3—241no—
316C22×D3—241no—
317C3×Q8—34no—
318C3×Q8—62no—
319C3×Q8—62no—
320C3×Q8—62no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—32no—
330C2×C3×C4—42no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—61no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—81no—
344C2×C3×C4—81no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4—121no—
348C2×C3×C4C2×C4×D311yescharacteristic
349C2×C3×C4C2×C4×D311yescharacteristic
350C2×C3×C4C2×D1211yescharacteristic
351C2×C3×C4C2×D1211yescharacteristic
352C2×C3×C4#23511yescharacteristic
353C2×C3×C4#23511yescharacteristic
354C2×C3×C4#23511yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4#23911yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—22no—
365C2×Dic3—21no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—41no—
369C2×Dic3—41no—
370C2×Dic3—41no—
371C2×Dic3#21512yescomplemented
372D12—64no—
373D12—62no—
374D12—62no—
375D12—62no—
376D12—62no—
377D12—122no—
378D12—122no—
379D12—122no—
380D12—121no—
381D12—121no—
382D12—121no—
383D12—121no—
384Dic6—22no—
385Dic6—22no—
386Dic6—22no—
387Dic6(C2×D3)⋊C414yescomplemented
388C3×C8—62no—
389C3⋊C8—22no—
390C3⋊C8—122no—
391C3⋊C8—121no—
392C3⋊C8—121no—
393C2×C32#38611yescharacteristic
394C2×C32C4×SD1611yescharacteristic
395C2×C32#44011yescharacteristic
396C2×C32#44811yescharacteristic
397C2×C32#44911yescharacteristic
398C2×C32#46011yescharacteristic
399C2×C32#46411yescharacteristic
400C3⋊D3—82no—
401C24—181no—
402C2×Q8—32no—
403C2×Q8—32no—
404C2×Q8—32no—
405C2×Q8—61no—
406C2×Q8—61no—
407C2×Q8—61no—
408C2×D4—92no—
409C2×D4—181no—
410C2×D4—181no—
411C2×D4—181no—
412C2×D4—181no—
413C2×D4—181no—
414C22×C4—21no—
415C22×C4—31no—
416C22×C4—31no—
417C22×C4—61no—
418C22×C4—61no—
419C22×C4C2×D3211yescharacteristic
420SD16—188no—
421C2×C8—32no—
422C2×C8—61no—
423C2×C8—61no—
424C2×C8—181no—
425C2×C8—181no—
426C2×C8—181no—
427C4⋊C4—21no—
428C4⋊C4—64no—
429C4⋊C4—61no—
430C4⋊C4—61no—
431C4⋊C4#62612yes—
432C22⋊C4—362no—
433C22⋊C4—362no—
434C42—64no—
435C42—61no—
436C42—61no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3#88211yescharacteristic
445C22×C3#88411yescharacteristic
446C22×C3#89311yescharacteristic
447C22×C3#91111yescharacteristic
448C22×C3D3×SD1611yescharacteristic
449C22×C3#91611yescharacteristic
450C22×C3#91811yescharacteristic
451C22×C3C4×#6711yescharacteristic
452C22×C3#93011yescharacteristic
453C22×C3C2×#21511yescharacteristic
454C22×C3#94211yescharacteristic
455C22×C3#94911yescharacteristic
456C22×C3#95011yescharacteristic
457C22×C3#95311yescharacteristic
458C2×D3—124no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—122no—
465C2×D3—242no—
466C2×D3—242no—
467C2×D3—242no—
468C2×D3—242no—
469C2×D3—242no—
470C2×D3—242no—
471C2×D3—241no—
472C2×D3—241no—
473C2×D3—241no—
474C2×D3—241no—
475C2×D3—241no—
476C2×D3—241no—
477C2×D3—241no—
478C2×D3—241no—
479C3×C4—21no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—21no—
483C3×C4—42no—
484C3×C4—42no—
485C3×C4—64no—
486C3×C4—62no—
487C3×C4—82no—
488C3×C4—121no—
489C3×C4—241no—
490C3×C4C4×D1211yescharacteristic
491C3×C4D3×C22⋊C411yescharacteristic
492C3×C4#89411yescharacteristic
493C3×C4#89511yescharacteristic
494C3×C4C2×(C2×D3)⋊C411yescharacteristic
495C3×C4C4×#6711yescharacteristic
496C3×C4#92911yescharacteristic
497C3×C4#93011yescharacteristic
498Dic3—24no—
499Dic3—22no—
500Dic3—41no—
501Dic3—81no—
502C32#188011yescharacteristic, complemented, Sylow
503C23—182no—
504C23—361no—
505C23—361no—
506C23—361no—
507C23—361no—
508C23—361no—
509C23—361no—
510C23D3×#6711yescharacteristic
511Q8—34no—
512Q8—62no—
513Q8—62no—
514Q8—62no—
515D4—182no—
516D4—182no—
517D4—361no—
518D4—361no—
519C2×C4—22no—
520C2×C4—32no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—61no—
526C2×C4—61no—
527C2×C4—62no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—121no—
532C2×C4—121no—
533C2×C4—121no—
534C2×C4#379811yescharacteristic
535C2×C4#379911yescharacteristic
536C2×C4C4×D3211yescharacteristic
537C2×C4D3×D1211yescharacteristic
538C2×C4C2×#62611yescharacteristic
539C2×C4D3×#6711yescharacteristic
540C8—62no—
541C8—361no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3#466511yescharacteristic
550C2×C3#476211yescharacteristic
551C2×C3#478111yescharacteristic
552C2×C3#479811yescharacteristic
553C2×C3#480611yescharacteristic
554C2×C3#485211yescharacteristic
555C2×C3#488911yescharacteristic
556C2×C3C4×#21511yescharacteristic
557C2×C3#502611yescharacteristic
558C2×C3#502711yescharacteristic
559C2×C3#502811yescharacteristic
560C2×C3#521311yescharacteristic
561C2×C3#522711yescharacteristic
562C2×C3#523811yescharacteristic
563D3—244no—
564D3—242no—
565D3—242no—
566C22—362no—
567C22—362no—
568C22—362no—
569C22—721no—
570C22—721no—
571C22—721no—
572C22—721no—
573C22#6390411yescharacteristic
574C22#6390611yescharacteristic
575C22#6392511yescharacteristic
576C22#6393511yescharacteristic
577C22D3×#21511yescharacteristic
578C22#6394811yescharacteristic
579C22#6397711yescharacteristic
580C4—42no—
581C4—62no—
582C4—64no—
583C4—121no—
584C4—241no—
585C4#6385011yescharacteristic
586C4C4×#62611yescharacteristic
587C4#6390911yescharacteristic
588C4D3×(C2×D3)⋊C411yescharacteristic
589C3—21no—
590C3#6890911yescharacteristic, complemented
591C3#7163311yescharacteristic, complemented
592C2—722no—
593C2#1059045711yescharacteristic
594C2#1059045811yescharacteristic
595C2#1059053611yescharacteristic
596C2#1059054911yescharacteristic
597C2#1059138211yescharacteristic
598C2#1059145211yescharacteristic
599C2#1059158411yescharacteristic
subgroupG/H
centerC23D3×#67
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×C3×#887C2semidirect
5. C2×#63565C2semidirect
6. C3×#4529C2semidirect
7. #10589155C2semidirect
25. C2×#3717C4semidirect
31. C2×#887D3semidirect
41. #4529D3semidirect
152. C2×C3×Dic3SD16semidirect
156. C3×Dic6C22⋊C4semidirect
371. C2×Dic3#215semidirect
387. Dic6(C2×D3)⋊C4semidirect
502. C32#1880semidirect
590. C3#68909semidirect
591. C3#71633semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C22×#37172
C2×#636362
#105913202
C2×#635652
C3×#45292
#105891552
#716333
#689093