Finite Group Databasebeta

← #11787440

Subgroups — #11787440

Order 1152.

863 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2C22×#3715C211yesmaximal, characteristic
3C2×C3×#821C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5#10591221C211yesmaximal, characteristic, complemented
6#10589416C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70276—31nomaximal
9#70171—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×D3×Dic3—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—21no—
19#63898—22no—
20#63898—22no—
21C2×#3715—22no—
22C2×#3715—22no—
23C2×#3715C414yescomplemented
24C3×#821—22no—
25C3×#816—22no—
26#63579—21no—
27#63579—21no—
28C22×#215—31no—
29C2×D4×Dic3—31no—
30C22×#214—31no—
31C2×#893—31no—
32C2×C3×#103—31no—
33C2×C3×#102—31no—
34#5229—31no—
35C2×#821D311yescharacteristic
36C2×#816D311yescharacteristic, complemented
37#4973—31no—
38#4550—31no—
39#4550—31no—
40#4550—61no—
41#4529—31no—
42#4529—31no—
43C23×C3×D3—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12C2×C412yes—
54C2×C3×D12D412yes—
55C2×C3×D12D412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yescomplemented
62C2×D3×Dic3—24no—
63C2×D3×Dic3—42no—
64C2×D3×Dic3—42no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)C2×C412yescomplemented
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3D412yes—
77(C2×D3)⋊Dic3—24no—
78#3715—28no—
79#1877—91noSylow
80C22×C3×Q8—31no—
81C22×C3×D4—31no—
82C23×Dic3—61no—
83C22×D12C2×D311yescharacteristic
84C22×C4×D3—61no—
85C22×Dic6C2×D311yescharacteristic
86C22×C3×C8—21no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C2×D311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—31no—
91C2×#217—61no—
92C2×#215—34no—
93C2×#215—62no—
94C2×#215—62no—
95D4×Dic3—62no—
96D4×Dic3—62no—
97C2×#214—34no—
98C2×#214—62no—
99C2×#214—62no—
100C2×(C2×D3)⋊C4—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×C4×Dic3—31no—
104C2×C4×Dic3—31no—
105C2×C4×Dic3—61no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109#893—62no—
110#893—62no—
111C3×#103—62no—
112C3×#102—62no—
113C3⋊#95—61no—
114C3⋊#95—61no—
115C3⋊#95—61no—
116C3⋊#95—61no—
117#821—22no—
118#816—22no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—22no—
121C22×C3×D3—22no—
122C22×C3×D3—22no—
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3SD1612yescomplemented
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—41no—
148C3×D12—22no—
149C3×D12—22no—
150C3×D12—22no—
151C3×D12C22⋊C414yes—
152C3×Dic6—22no—
153C3×Dic6—22no—
154C3×Dic6—41no—
155C3×Dic6—41no—
156D3×Dic3—48no—
157C32×C8—41no—
158C3⋊(C3⋊C8)—22no—
159C22×SD16—91no—
160C2×C4×D4—91no—
161C2×#103—31no—
162C2×#102—31no—
163#391—91no—
164#340—91no—
165#336—91no—
166C24×C3—61no—
167C23×D3—21no—
168C2×C3×Q8—32no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C2×C3×Q8—61no—
173C2×C3×Q8—61no—
174C2×C3×D4—32no—
175C2×C3×D4—32no—
176C2×C3×D4—32no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C22×C3×C4—21no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—31no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—64no—
196C22×Dic3—122no—
197C22×Dic3—122no—
198C2×D12—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12C4×D312yes—
202C2×D12D1212yes—
203C2×D12#6712yes—
204C2×C4×D3—64no—
205C2×C4×D3—122no—
206C2×C4×D3—122no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6—21no—
212C2×Dic6C4×D312yescomplemented
213C2×C3×C8—22no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—41no—
221C2×C3×C8—41no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—61no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226#217—64no—
227#215—68no—
228#214—68no—
229(C2×D3)⋊C4—64no—
230C4⋊Dic3—21no—
231C4⋊Dic3—21no—
232C4⋊Dic3—21no—
233C4⋊Dic3#6712yes—
234C4×Dic3—61no—
235C4×Dic3—61no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238C4×Dic3—121no—
239C4×Dic3—121no—
240C2×C3⋊C8—32no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—62no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—121no—
248C2×C3⋊C8—121no—
249C22×C32C4×D411yescharacteristic
250C22×C32#12011yescharacteristic
251C22×C32#12111yescharacteristic
252C22×C32C2×SD1611yescharacteristic
253C22×C32#13511yescharacteristic
254C22×C32AGL(1,ℤ/8)11yescharacteristic
255C22×C32#13711yescharacteristic
256C2×C3×D3—24no—
257C2×C3×D3—42no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C32×C4C2×C22⋊C411yescharacteristic
264C32×C4C4×D411yescharacteristic
265C32×C4#12111yescharacteristic
266C32×C4#12311yescharacteristic
267C3⋊Dic3—22no—
268C3⋊Dic3—41no—
269C3×Dic3—42no—
270C3×Dic3—42no—
271C3×Dic3—81no—
272C22×Q8—31no—
273C22×D4—31no—
274C23×C4—181no—
275C2×SD16—94no—
276C2×SD16—182no—
277C2×SD16—182no—
278C22×C8—91no—
279C22×C8D3211yescharacteristic
280C4×D4—182no—
281C4×D4—182no—
282C2×C4⋊C4—31no—
283C2×C4⋊C4—31no—
284C2×C22⋊C4—181no—
285C2×C42—91no—
286#103—62no—
287#102—62no—
288#95—181no—
289#95—181no—
290C23×C3—21no—
291C23×C3—62no—
292C23×C3—62no—
293C23×C3—62no—
294C23×C3—121no—
295C23×C3—121no—
296C23×C3—121no—
297C23×C3—121no—
298C23×C3D3×D411yescharacteristic
299C23×C3D3×D411yescharacteristic
300C22×D3—22no—
301C22×D3—22no—
302C22×D3—22no—
303C22×D3—41no—
304C22×D3—41no—
305C22×D3—41no—
306C22×D3—41no—
307C3×Q8—62no—
308C3×Q8—62no—
309C3×Q8—121no—
310C3×Q8—121no—
311C3×D4—34no—
312C3×D4—62no—
313C3×D4—62no—
314C3×D4—62no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4C2×C4×D311yescharacteristic
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C2×D1211yescharacteristic
333C2×C3×C4#23511yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23711yescharacteristic
338C2×C3×C4#23711yescharacteristic
339C2×C3×C4#23711yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—32no—
345C2×Dic3—32no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—41no—
351C2×Dic3—41no—
352C2×Dic3—41no—
353C2×Dic3—62no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—62no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368C2×Dic3—121no—
369C2×Dic3—128no—
370D12—22no—
371D12—22no—
372D12—22no—
373D12(C2×D3)⋊C414yes—
374C4×D3—128no—
375Dic6—22no—
376Dic6—22no—
377Dic6—41no—
378Dic6—41no—
379C3×C8—42no—
380C3×C8—41no—
381C3×C8—41no—
382C3⋊C8—62no—
383C3⋊C8—62no—
384C3⋊C8—122no—
385C2×C32#38611yescharacteristic
386C2×C32C4×SD1611yescharacteristic
387C2×C32#44011yescharacteristic
388C2×C32#45011yescharacteristic
389C2×C32#45211yescharacteristic
390C2×C32#46111yescharacteristic
391C2×C32#46311yescharacteristic
392C3×D3—44no—
393C24—61no—
394C2×Q8—32no—
395C2×Q8—61no—
396C2×Q8—61no—
397C2×Q8—61no—
398C2×Q8—61no—
399C2×Q8—61no—
400C2×D4—32no—
401C2×D4—32no—
402C2×D4—32no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4—91no—
410C22×C4—91no—
411C22×C4—184no—
412C22×C4—362no—
413C22×C4—362no—
414C22×C4C2×D3211yescharacteristic
415SD16—188no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—92no—
420C2×C8—181no—
421C2×C8—181no—
422C4⋊C4—32no—
423C4⋊C4—61no—
424C4⋊C4—61no—
425C4⋊C4—61no—
426C22⋊C4—184no—
427C42—181no—
428C42—181no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—64no—
437C22×C3—122no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3#67⋊C411yescharacteristic
444C22×C3#67⋊C411yescharacteristic
445C22×C3#88211yescharacteristic
446C22×C3#88411yescharacteristic
447C22×C3#91111yescharacteristic
448C22×C3#91211yescharacteristic
449C22×C3D3×SD1611yescharacteristic
450C22×C3D3×SD1611yescharacteristic
451C22×C3#91411yescharacteristic
452C22×C3#91511yescharacteristic
453C22×C3#91811yescharacteristic
454C22×C3#91911yescharacteristic
455C22×C3#93711yescharacteristic
456C22×C3#93911yescharacteristic
457C2×D3—24no—
458C2×D3—42no—
459C2×D3—42no—
460C2×D3—42no—
461C2×D3—42no—
462C2×D3—42no—
463C2×D3—42no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—122no—
469C3×C4—122no—
470C3×C4—241no—
471C3×C4D3×C22⋊C411yescharacteristic
472C3×C4#67⋊C411yescharacteristic
473C3×C4#88311yescharacteristic
474C3×C4#88611yescharacteristic
475C3×C4C2×(C2×D3)⋊C411yescharacteristic
476C3×C4C4×#6711yescharacteristic
477C3×C4#93811yescharacteristic
478C3×C4#93911yescharacteristic
479Dic3—42no—
480Dic3—42no—
481Dic3—62no—
482Dic3—62no—
483Dic3—81no—
484Dic3—122no—
485Dic3—122no—
486Dic3—121no—
487Dic3—121no—
488C32#187711yescharacteristic, complemented, Sylow
489C23—62no—
490C23—62no—
491C23—62no—
492C23—121no—
493C23—121no—
494C23—121no—
495C23—121no—
496C23#380211yescharacteristic
497Q8—62no—
498Q8—62no—
499Q8—121no—
500Q8—121no—
501D4—34no—
502D4—62no—
503D4—62no—
504D4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—92no—
508C2×C4—121no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4—121no—
513C2×C4—121no—
514C2×C4—121no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—368no—
521C2×C4#379511yescharacteristic
522C2×C4C4×D3211yescharacteristic
523C2×C4D3×D1211yescharacteristic
524C2×C4#380511yescharacteristic
525C2×C4D3×#6711yescharacteristic
526C2×C4D3×#6711yescharacteristic
527C8—41no—
528C8—182no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—124no—
537C2×C3#475711yescharacteristic
538C2×C3#475811yescharacteristic
539C2×C3#477611yescharacteristic
540C2×C3#478311yescharacteristic
541C2×C3#478811yescharacteristic
542C2×C3#481711yescharacteristic
543C2×C3#481811yescharacteristic
544C2×C3#481911yescharacteristic
545C2×C3#495611yescharacteristic
546C2×C3#495811yescharacteristic
547C2×C3#515311yescharacteristic
548C2×C3#516211yescharacteristic
549C2×C3#516911yescharacteristic
550C2×C3#518711yescharacteristic
551D3—44no—
552C22—64no—
553C22—122no—
554C22—122no—
555C22—122no—
556C22—122no—
557C22—122no—
558C22—122no—
559C22#6379611yescharacteristic
560C22#6379811yescharacteristic
561C22#6381011yescharacteristic
562C22#6381111yescharacteristic
563C22#6388511yescharacteristic
564C22#6390211yescharacteristic
565C22#6392211yescharacteristic
566C4—122no—
567C4—122no—
568C4—182no—
569C4—241no—
570C4—361no—
571C4#6387911yescharacteristic
572C4#6389111yescharacteristic
573C4D3×(C2×D3)⋊C411yescharacteristic
574C4#6397011yescharacteristic
575C3—21no—
576C3#7017111yescharacteristic, complemented
577C3#7027611yescharacteristic, complemented
578C2—124no—
579C2#1059074211yescharacteristic
580C2#1059074311yescharacteristic
581C2#1059074811yescharacteristic
582C2#1059075111yescharacteristic
583C2#1059094311yescharacteristic
584C2#1059096511yescharacteristic
585C2#1059136311yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1877
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×C3×#816C2semidirect
5. #10591221C2semidirect
6. #10589416C2semidirect
7. #10589163C2semidirect
23. C2×#3715C4semidirect
36. C2×#816D3semidirect
61. C2×C3×Dic6C2×C4semidirect
72. C2×C3⋊(C3⋊C8)C2×C4semidirect
138. C2×C3⋊Dic3SD16semidirect
212. C2×Dic6C4×D3semidirect
488. C32#1877semidirect
576. C3#70171semidirect
577. C3#70276semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
C22×#37152
C2×C3×#8212
C2×C3×#8162
#105912212
#105894162
#105891632
#702763
#701713