Finite Group Databasebeta

← #11787591

Subgroups — #11787591

Order 1152.

897 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
1C22×#3755C211yesmaximal, characteristic
2C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#835C211yesmaximal, characteristic, complemented
4#10591320C211yesmaximal, characteristic
5C2×#63564C211yesmaximal, characteristic
6#10589163C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#71633—31nomaximal
9#70240—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×#3755—22no—
13C2×#3755—22no—
14C2×#3755C414yescomplemented
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×Q8×Dic3—22no—
17C3×Q8×Dic3—22no—
18C2×C3×C4⋊Dic3—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3—21no—
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×#3722—21no—
25C2×#3722—21no—
26C3×#835—22no—
27#63564—22no—
28C2×C3×C4×Q8—31no—
29C2×Q8×Dic3D311yescharacteristic, complemented
30C22×#215—31no—
31C22×#215—31no—
32C22×#215—61no—
33C2×C3×#103—31no—
34C2×#835D311yescharacteristic, complemented
35C2×#821—31no—
36#4988—31no—
37C2×#809—31no—
38#4939—31no—
39#4550—31no—
40#4529—31no—
41#4529—31no—
42#4524—31no—
43C23×C3⋊D3—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8—21no—
47C2×C32×Q8C2×C412yes—
48C2×C32×Q8D412yes—
49C2×C32×Q8D412yes—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)C2×C412yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C22×C3×Dic3D411yescharacteristic
62#3755—28no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)C2×C412yes—
66C3×C4⋊Dic3—24no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3D412yes—
71C3×C4×Dic3—24no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77#3722—42no—
78#3722—42no—
79#1880—91noSylow
80C22×C3×Q8—21no—
81C22×C3×Q8C2×D311yescharacteristic
82C22×C3×Q8C2×D311yescharacteristic
83C22×D12—31no—
84C22×D12—31no—
85C22×D12—61no—
86C22×C3×C8—31no—
87C3×C4×Q8—62no—
88C3×C4×Q8—62no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—61no—
92C2×C3×C42—31no—
93C2×C3×C42—61no—
94Q8×Dic3—22no—
95Q8×Dic3—22no—
96C2×#215—34no—
97C2×#215—34no—
98C2×#215—64no—
99C2×#215—64no—
100C2×#215—64no—
101C2×#215—62no—
102C2×#215—62no—
103C2×#215—62no—
104C2×#215—62no—
105C2×(C2×D3)⋊C4—61no—
106C2×(C2×D3)⋊C4—61no—
107C2×(C2×D3)⋊C4—61no—
108C2×(C2×D3)⋊C4—61no—
109C2×C4⋊Dic3—21no—
110C2×C4⋊Dic3C2×D311yescharacteristic
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×C4×Dic3—21no—
113C2×C4×Dic3C2×D311yescharacteristic
114C22×C3⋊C8—31no—
115C22×C3⋊C8—31no—
116C22×C3⋊C8—61no—
117C22×C3⋊C8C2×D311yescharacteristic
118C3×#103—62no—
119#835—22no—
120#821—62no—
121#809—62no—
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—
130C32×Q8—22no—
131C32×Q8—22no—
132C32×Q8—22no—
133C32×Q8C22⋊C414yescomplemented
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—41no—
146C4⋊(C3⋊D3)—41no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3SD1612yescomplemented
159C3⋊(C3⋊C8)—22no—
160C3×C3⋊C8—41no—
161C22×SD16—91no—
162C2×C4×Q8—31no—
163C2×#103—31no—
164C2×#102—91no—
165#390—91no—
166#340—91no—
167#336—91no—
168C23×D3—61no—
169C23×D3—61no—
170C23×D3—121no—
171C2×C3×Q8—21no—
172C2×C3×Q8—21no—
173C2×C3×Q8—21no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—22no—
178C2×C3×Q8—22no—
179C2×C3×Q8—22no—
180C2×C3×Q8—41no—
181C2×C3×Q8—41no—
182C2×C3×Q8—41no—
183C2×C3×Q8C4×D312yes—
184C2×C3×Q8C4×D312yes—
185C2×C3×Q8D1212yes—
186C2×C3×Q8D1212yes—
187C2×C3×Q8#6712yes—
188C2×C3×Q8#6712yes—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—31no—
193C22×C3×C4—31no—
194C22×C3×C4—41no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C22×Dic3—21no—
200C22×Dic3—21no—
201C22×Dic3#6711yescharacteristic
202C22×Dic3#6711yescharacteristic
203C2×D12—32no—
204C2×D12—32no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—62no—
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—61no—
218C2×D12—121no—
219C2×D12—121no—
220C2×D12—121no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—64no—
226C3×C4⋊C4—61no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C42—64no—
230C3×C42—61no—
231C3×C42—61no—
232#215—616no—
233#215—68no—
234#215—68no—
235(C2×D3)⋊C4—122no—
236(C2×D3)⋊C4—122no—
237(C2×D3)⋊C4—122no—
238(C2×D3)⋊C4—122no—
239C4⋊Dic3—24no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3#6712yes—
244C4×Dic3—24no—
245C4×Dic3—21no—
246C4×Dic3—21no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C22×C32C4×D411yescharacteristic
260C22×C32#12011yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32C2×SD1611yescharacteristic
263C22×C32#13511yescharacteristic
264C22×C32AGL(1,ℤ/8)11yescharacteristic
265C22×C32#13711yescharacteristic
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—81no—
270C2×C3⋊D3—81no—
271C2×C3⋊D3—81no—
272C2×C3⋊D3—81no—
273C32×C4—24no—
274C32×C4C2×C22⋊C411yescharacteristic
275C32×C4C4×D411yescharacteristic
276C32×C4#12111yescharacteristic
277C32×C4#12311yescharacteristic
278C3×Dic3—22no—
279C3×Dic3—41no—
280C3×Dic3—42no—
281C3×Dic3—81no—
282C22×Q8D3211yescharacteristic
283C22×D4—91no—
284C2×SD16—94no—
285C2×SD16—182no—
286C2×SD16—182no—
287C22×C8—31no—
288C22×C8—91no—
289C4×Q8—62no—
290C4×Q8—62no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—61no—
294C2×C22⋊C4—181no—
295C2×C22⋊C4—181no—
296C2×C42—31no—
297C2×C42—61no—
298#103—62no—
299#102—182no—
300C23×C3—21no—
301C23×C3D3×D411yescharacteristic
302C23×C3C2×#6711yescharacteristic
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—122no—
308C22×D3—121no—
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—241no—
321C22×D3—241no—
322C22×D3—241no—
323C22×D3—241no—
324C3×Q8—22no—
325C3×Q8—22no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—24no—
331C3×Q8—42no—
332C3×Q8—42no—
333C3×Q8—42no—
334C3×Q8(C2×D3)⋊C414yescomplemented
335C3×Q8(C2×D3)⋊C414yescomplemented
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—121no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4C2×C4×D311yescharacteristic
364C2×C3×C4C2×C4×D311yescharacteristic
365C2×C3×C4C2×D1211yescharacteristic
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4#23511yescharacteristic
368C2×C3×C4#23511yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4#23711yescharacteristic
371C2×C3×C4#23711yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—22no—
381C2×Dic3—41no—
382C2×Dic3—41no—
383C2×Dic3—41no—
384C2×Dic3—41no—
385C2×Dic3—41no—
386C2×Dic3#21512yescomplemented
387D12—64no—
388D12—62no—
389D12—62no—
390D12—62no—
391D12—62no—
392D12—122no—
393D12—122no—
394D12—122no—
395D12—121no—
396D12—121no—
397D12—121no—
398D12—121no—
399C3×C8—121no—
400C3⋊C8—41no—
401C3⋊C8—64no—
402C3⋊C8—62no—
403C3⋊C8—62no—
404C2×C32#38611yescharacteristic
405C2×C32C4×SD1611yescharacteristic
406C2×C32#44011yescharacteristic
407C2×C32#44811yescharacteristic
408C2×C32#44911yescharacteristic
409C2×C32#46011yescharacteristic
410C2×C32#46411yescharacteristic
411C3⋊D3—82no—
412C24—181no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8#62412yes—
417C2×Q8#62612yes—
418C2×Q8#62612yes—
419C2×D4—92no—
420C2×D4—181no—
421C2×D4—181no—
422C2×D4—181no—
423C2×D4—181no—
424C2×D4—181no—
425C22×C4—21no—
426C22×C4—31no—
427C22×C4—31no—
428C22×C4—61no—
429C22×C4—61no—
430C22×C4C2×D3211yescharacteristic
431SD16—188no—
432C2×C8—61no—
433C2×C8—61no—
434C2×C8—61no—
435C2×C8—92no—
436C2×C8—181no—
437C2×C8—181no—
438C4⋊C4—32no—
439C4⋊C4—64no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C22⋊C4—362no—
444C22⋊C4—362no—
445C42—64no—
446C42—61no—
447C42—61no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3#67⋊C411yescharacteristic
456C22×C3#88211yescharacteristic
457C22×C3D3×SD1611yescharacteristic
458C22×C3#91411yescharacteristic
459C22×C3#91811yescharacteristic
460C22×C3#91911yescharacteristic
461C22×C3C4×#6711yescharacteristic
462C22×C3#93011yescharacteristic
463C22×C3#93911yescharacteristic
464C22×C3C2×#21511yescharacteristic
465C22×C3#94211yescharacteristic
466C22×C3#94911yescharacteristic
467C22×C3#95011yescharacteristic
468C22×C3#95311yescharacteristic
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—242no—
481C2×D3—242no—
482C2×D3—241no—
483C2×D3—241no—
484C2×D3—241no—
485C2×D3—241no—
486C2×D3—241no—
487C2×D3—241no—
488C2×D3—241no—
489C2×D3—241no—
490C3×C4—24no—
491C3×C4—24no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—44no—
497C3×C4—62no—
498C3×C4—121no—
499C3×C4—122no—
500C3×C4—241no—
501C3×C4#67⋊C411yescharacteristic
502C3×C4#88611yescharacteristic
503C3×C4C2×(C2×D3)⋊C411yescharacteristic
504C3×C4C2×(C2×D3)⋊C411yescharacteristic
505C3×C4C4×#6711yescharacteristic
506C3×C4#92911yescharacteristic
507C3×C4#93011yescharacteristic
508C3×C4#93911yescharacteristic
509Dic3—22no—
510Dic3—41no—
511Dic3—42no—
512Dic3—81no—
513C32#188011yescharacteristic, complemented, Sylow
514C23—182no—
515C23—361no—
516C23—361no—
517C23—361no—
518C23—361no—
519C23—361no—
520C23—361no—
521C23D3×#6711yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—22no—
525Q8#372214yescomplemented
526D4—182no—
527D4—182no—
528D4—361no—
529D4—361no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—32no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—62no—
539C2×C4—61no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—121no—
543C2×C4—121no—
544C2×C4—121no—
545C2×C4#380411yescharacteristic
546C2×C4#380411yescharacteristic
547C2×C4C2×#62411yescharacteristic
548C2×C4C2×#62611yescharacteristic
549C2×C4C2×#62611yescharacteristic
550C2×C4D3×#6711yescharacteristic
551C8—121no—
552C8—182no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3#478811yescharacteristic
561C2×C3#480611yescharacteristic
562C2×C3#481011yescharacteristic
563C2×C3#481711yescharacteristic
564C2×C3#495811yescharacteristic
565C2×C3C4×#21511yescharacteristic
566C2×C3#502611yescharacteristic
567C2×C3#502711yescharacteristic
568C2×C3#502811yescharacteristic
569C2×C3#516311yescharacteristic
570C2×C3#518511yescharacteristic
571C2×C3#521311yescharacteristic
572C2×C3#522711yescharacteristic
573C2×C3#523811yescharacteristic
574D3—244no—
575D3—242no—
576D3—242no—
577C22—362no—
578C22—362no—
579C22—362no—
580C22—721no—
581C22—721no—
582C22—721no—
583C22—721no—
584C22D3×#21511yescharacteristic
585C22#6393911yescharacteristic
586C22#6394811yescharacteristic
587C22#6394911yescharacteristic
588C22#6395211yescharacteristic
589C22#6397711yescharacteristic
590C22#6397811yescharacteristic
591C4—24no—
592C4—62no—
593C4—121no—
594C4—122no—
595C4—241no—
596C4#6395211yescharacteristic
597C4C2×#372211yescharacteristic
598C4#6396611yescharacteristic
599C4#6397811yescharacteristic
600C3—21no—
601C3#7024011yescharacteristic, complemented
602C3#7163311yescharacteristic, complemented
603C2—722no—
604C2#1059153611yescharacteristic
605C2#1059154011yescharacteristic
606C2#1059158411yescharacteristic
607C2#1059158811yescharacteristic
608C2#1059160711yescharacteristic
609C2#1059161711yescharacteristic
610C2#1059171111yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1880
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×Q8×Dic3C2semidirect
3. C2×C3×#835C2semidirect
6. #10589163C2semidirect
7. #10589155C2semidirect
14. C2×#3755C4semidirect
29. C2×Q8×Dic3D3semidirect
34. C2×#835D3semidirect
133. C32×Q8C22⋊C4semidirect
158. C2×C3×Dic3SD16semidirect
334. C3×Q8(C2×D3)⋊C4semidirect
335. C3×Q8(C2×D3)⋊C4semidirect
386. C2×Dic3#215semidirect
513. C32#1880semidirect
525. Q8#3722semidirect
601. C3#70240semidirect
602. C3#71633semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C2×C3×Q8×Dic32
C2×C3×#8352
#105913202
C2×#635642
#105891632
#105891552
#716333
#702403