Finite Group Databasebeta

← #11787595

Subgroups — #11787595

Order 1152.

805 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
2C22×#3715C211yesmaximal, characteristic
3C3×#4988C211yesmaximal, characteristic
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic
6#10589395C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#70240—31nomaximal
9#69660—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20C2×Dic32—21no—
21Dic3×Dic6—22no—
22Dic3×Dic6—22no—
23C2×#3715—22no—
24C2×#3715—22no—
25C2×#3715C414yescomplemented
26C3×#810—22no—
27#63563—22no—
28C2×Q8×Dic3—31no—
29C22×#215—31no—
30C22×#214—31no—
31C2×C4×Dic6—31no—
32C2×C3×#103—31no—
33C3×#390—31no—
34C2×#832—31no—
35C2×#821—31no—
36#4988D311yescharacteristic
37C2×#810D311yescharacteristic, complemented
38#4550—31no—
39#4529—31no—
40#4529—31no—
41#4529—61no—
42#4524—31no—
43C23×C3×D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3D411yescharacteristic
49C22×C3×Dic3D411yescharacteristic
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12C2×C412yes—
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—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)D412yes—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)C2×C412yes—
69C3×(C2×D3)⋊C4—42no—
70C3×(C2×D3)⋊C4—42no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76Dic3⋊Dic3—24no—
77Dic32—24no—
78#3715—28no—
79#1880—91noSylow
80C22×C3×Q8—31no—
81C22×C3×D4—31no—
82C22×D12C2×D311yescharacteristic
83C22×Dic6C2×D311yescharacteristic
84C22×C3×C8—31no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C22⋊C4—61no—
89C2×C3×C22⋊C4—61no—
90C2×C3×C42—31no—
91Q8×Dic3—62no—
92Q8×Dic3—62no—
93C2×#215—34no—
94C2×#215—62no—
95C2×#215—62no—
96C2×#214—34no—
97C2×#214—62no—
98C2×#214—62no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3—61no—
105C2×Dic3⋊C4—61no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3C2×D311yescharacteristic
109C22×C3⋊C8—31no—
110C22×C3⋊C8—31no—
111C22×C3⋊C8—61no—
112C22×C3⋊C8C2×D311yescharacteristic
113C4×Dic6—62no—
114C4×Dic6—62no—
115C3×#103—62no—
116#832—62no—
117#821—62no—
118#810—22no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—22no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—41no—
138C2×C3⋊Dic3—41no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—21no—
144C2×C3×Dic3—21no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3SD1612yescomplemented
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—41no—
151C3×D12—41no—
152C3×Dic6—22no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6C22⋊C414yescomplemented
156C3⋊(C3⋊C8)—22no—
157C3×C3⋊C8—41no—
158C22×SD16—91no—
159C2×C4×Q8—91no—
160C2×#103—31no—
161C2×#102—91no—
162#390—31no—
163#340—91no—
164#336—91no—
165C24×C3—61no—
166C23×D3—21no—
167C2×C3×Q8—32no—
168C2×C3×Q8—32no—
169C2×C3×Q8—32no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—31no—
183C22×C3×C4—31no—
184C22×C3×C4—41no—
185C22×C3×C4—61no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×Dic3—21no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—121no—
192C22×Dic3#6711yescharacteristic
193C22×Dic3#6711yescharacteristic
194C2×D12—21no—
195C2×D12—21no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12C4×D312yes—
200C2×Dic6—21no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6C4×D312yes—
204C2×Dic6D1212yes—
205C2×Dic6#6712yes—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C2×C3×C8—61no—
209C3×C4⋊C4—22no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—41no—
215C3×C22⋊C4—122no—
216C3×C22⋊C4—122no—
217C3×C42—61no—
218C3×C42—61no—
219#215—68no—
220#214—68no—
221(C2×D3)⋊C4—42no—
222(C2×D3)⋊C4—42no—
223C4⋊Dic3—32no—
224C4⋊Dic3—32no—
225C4⋊Dic3—62no—
226C4⋊Dic3—64no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3—121no—
230Dic3⋊C4—64no—
231C4×Dic3—21no—
232C4×Dic3—21no—
233C4×Dic3—64no—
234C4×Dic3—64no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—121no—
246C2×C3⋊C8—121no—
247C22×C32C4×D411yescharacteristic
248C22×C32#12011yescharacteristic
249C22×C32#12111yescharacteristic
250C22×C32C2×SD1611yescharacteristic
251C22×C32#13511yescharacteristic
252C22×C32AGL(1,ℤ/8)11yescharacteristic
253C22×C32#13711yescharacteristic
254C2×C3×D3—42no—
255C2×C3×D3—42no—
256C2×C3×D3—42no—
257C2×C3×D3—81no—
258C2×C3×D3—81no—
259C2×C3×D3—81no—
260C2×C3×D3—81no—
261C32×C4—81no—
262C32×C4C2×C22⋊C411yescharacteristic
263C32×C4C4×D411yescharacteristic
264C32×C4#12111yescharacteristic
265C32×C4#12311yescharacteristic
266C3⋊Dic3—42no—
267C3×Dic3—24no—
268C3×Dic3—22no—
269C3×Dic3—41no—
270C22×Q8—31no—
271C22×D4—31no—
272C2×SD16—94no—
273C2×SD16—182no—
274C2×SD16—182no—
275C22×C8—31no—
276C22×C8—91no—
277C4×Q8—182no—
278C4×Q8—182no—
279C2×C4⋊C4—91no—
280C2×C4⋊C4—181no—
281C2×C4⋊C4D3211yescharacteristic
282C2×C22⋊C4—61no—
283C2×C22⋊C4—61no—
284C2×C42—31no—
285C2×C42—181no—
286#103—62no—
287#102—182no—
288C23×C3—21no—
289C23×C3—62no—
290C23×C3—121no—
291C23×C3—121no—
292C23×C3—121no—
293C23×C3—121no—
294C23×C3—121no—
295C23×C3—121no—
296C23×C3D3×D411yescharacteristic
297C23×C3C2×#6711yescharacteristic
298C22×D3—22no—
299C22×D3—41no—
300C22×D3—41no—
301C22×D3—41no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—41no—
305C3×Q8—34no—
306C3×Q8—62no—
307C3×Q8—62no—
308C3×Q8—62no—
309C3×D4—62no—
310C3×D4—62no—
311C3×D4—121no—
312C3×D4—121no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—32no—
320C2×C3×C4—42no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—61no—
335C2×C3×C4—81no—
336C2×C3×C4—81no—
337C2×C3×C4C2×C4×D311yescharacteristic
338C2×C3×C4C2×C4×D311yescharacteristic
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4#23511yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4#23711yescharacteristic
346C2×C3×C4#23711yescharacteristic
347C2×C3×C4#23711yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—21no—
352C2×Dic3—22no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—122no—
360C2×Dic3—121no—
361C2×Dic3—121no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—241no—
365C2×Dic3—241no—
366C2×Dic3#21412yescomplemented
367D12—22no—
368D12—22no—
369D12—41no—
370D12—41no—
371Dic6—22no—
372Dic6—22no—
373Dic6—22no—
374Dic6(C2×D3)⋊C414yescomplemented
375C3×C8—121no—
376C3⋊C8—41no—
377C3⋊C8—62no—
378C3⋊C8—62no—
379C3⋊C8—122no—
380C2×C32#38611yescharacteristic
381C2×C32C4×SD1611yescharacteristic
382C2×C32#44011yescharacteristic
383C2×C32#44811yescharacteristic
384C2×C32#44911yescharacteristic
385C2×C32#46011yescharacteristic
386C2×C32#46411yescharacteristic
387C3×D3—82no—
388C24—61no—
389C2×Q8—32no—
390C2×Q8—32no—
391C2×Q8—32no—
392C2×Q8—61no—
393C2×Q8—61no—
394C2×Q8—61no—
395C2×D4—32no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—61no—
401C22×C4—21no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—61no—
405C22×C4—181no—
406C22×C4C2×D3211yescharacteristic
407SD16—188no—
408C2×C8—61no—
409C2×C8—61no—
410C2×C8—61no—
411C2×C8—92no—
412C2×C8—181no—
413C2×C8—181no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—92no—
417C4⋊C4—184no—
418C4⋊C4—181no—
419C22⋊C4—122no—
420C22⋊C4—122no—
421C42—61no—
422C42—61no—
423C42—184no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—122no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—241no—
435C22×C3—241no—
436C22×C3—241no—
437C22×C3—241no—
438C22×C3#67⋊C411yescharacteristic
439C22×C3#88211yescharacteristic
440C22×C3D3×SD1611yescharacteristic
441C22×C3#91411yescharacteristic
442C22×C3#91811yescharacteristic
443C22×C3#91911yescharacteristic
444C22×C3C4×#6711yescharacteristic
445C22×C3#93211yescharacteristic
446C22×C3C2×#21411yescharacteristic
447C22×C3#93711yescharacteristic
448C22×C3#93811yescharacteristic
449C22×C3#93911yescharacteristic
450C22×C3#95011yescharacteristic
451C22×C3#95111yescharacteristic
452C2×D3—42no—
453C2×D3—42no—
454C2×D3—42no—
455C2×D3—81no—
456C2×D3—81no—
457C2×D3—81no—
458C2×D3—81no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—64no—
464C3×C4—62no—
465C3×C4—82no—
466C3×C4—81no—
467C3×C4—81no—
468C3×C4—121no—
469C3×C4D3×C22⋊C411yescharacteristic
470C3×C4#67⋊C411yescharacteristic
471C3×C4#67⋊C411yescharacteristic
472C3×C4#88311yescharacteristic
473C3×C4#88411yescharacteristic
474C3×C4#88611yescharacteristic
475C3×C4C2×(C2×D3)⋊C411yescharacteristic
476C3×C4#93911yescharacteristic
477Dic3—24no—
478Dic3—22no—
479Dic3—41no—
480Dic3—122no—
481Dic3—122no—
482Dic3—242no—
483C32#188011yescharacteristic, complemented, Sylow
484C23—62no—
485C23—121no—
486C23—121no—
487C23—121no—
488C23—121no—
489C23—121no—
490C23—121no—
491C23D3×#6711yescharacteristic
492Q8—34no—
493Q8—62no—
494Q8—62no—
495Q8—62no—
496D4—62no—
497D4—62no—
498D4—121no—
499D4—121no—
500C2×C4—32no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—62no—
505C2×C4—61no—
506C2×C4—62no—
507C2×C4—61no—
508C2×C4—62no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—182no—
513C2×C4—361no—
514C2×C4—361no—
515C2×C4#379511yescharacteristic
516C2×C4C4×D3211yescharacteristic
517C2×C4D3×D1211yescharacteristic
518C2×C4#380211yescharacteristic
519C2×C4#380511yescharacteristic
520C2×C4D3×#6711yescharacteristic
521C8—121no—
522C8—182no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—242no—
531C2×C3#478811yescharacteristic
532C2×C3#480611yescharacteristic
533C2×C3#481011yescharacteristic
534C2×C3#481711yescharacteristic
535C2×C3#495611yescharacteristic
536C2×C3#495811yescharacteristic
537C2×C3C4×#21411yescharacteristic
538C2×C3#501811yescharacteristic
539C2×C3#503711yescharacteristic
540C2×C3#504011yescharacteristic
541C2×C3#505411yescharacteristic
542C2×C3#507511yescharacteristic
543C2×C3#516311yescharacteristic
544C2×C3#518511yescharacteristic
545D3—82no—
546C22—122no—
547C22—122no—
548C22—122no—
549C22—241no—
550C22—241no—
551C22—241no—
552C22—241no—
553C22#6387911yescharacteristic
554C22#6392211yescharacteristic
555C22D3×#21411yescharacteristic
556C22#6393411yescharacteristic
557C22#6394311yescharacteristic
558C22#6394911yescharacteristic
559C22#6397011yescharacteristic
560C4—64no—
561C4—62no—
562C4—81no—
563C4—121no—
564C4—362no—
565C4#6388511yescharacteristic
566C4#6389111yescharacteristic
567C4#6390211yescharacteristic
568C4D3×(C2×D3)⋊C411yescharacteristic
569C3—21no—
570C3#6966011yescharacteristic, complemented
571C3#7024011yescharacteristic, complemented
572C2—242no—
573C2#1059047511yescharacteristic
574C2#1059047811yescharacteristic
575C2#1059060311yescharacteristic
576C2#1059061511yescharacteristic
577C2#1059136311yescharacteristic
578C2#1059143811yescharacteristic
579C2#1059157811yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
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×Dic3×Dic6C2semidirect
4. C2×C3×#810C2semidirect
6. #10589395C2semidirect
7. #10589155C2semidirect
25. C2×#3715C4semidirect
37. C2×#810D3semidirect
147. C2×C3×Dic3SD16semidirect
155. C3×Dic6C22⋊C4semidirect
366. C2×Dic3#214semidirect
374. Dic6(C2×D3)⋊C4semidirect
483. C32#1880semidirect
570. C3#69660semidirect
571. C3#70240semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×Dic62
C22×#37152
C3×#49882
C2×C3×#8102
C2×#635632
#105893952
#105891552
#702403
#696603