Finite Group Databasebeta

← #11785252

Subgroups — #11785252

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C2×#63659C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591224C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#71605—31nomaximal
9#70154—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3×Dic3—21no—
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#217—21no—
15C3×D4×Dic3—22no—
16C3×D4×Dic3C414yescomplemented
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#63659—22no—
22C3×#832—22no—
23#63579—21no—
24#63579—21no—
25Dic3⋊(C3⋊C8)—22no—
26C2×C3×C4×D4—31no—
27C2×D4×Dic3D311yescharacteristic
28C2×C3×#102—31no—
29C2×#832—31no—
30C2×#832—31no—
31C2×#832—61no—
32C2×#832D311yescharacteristic
33C2×Dic3⋊C8—31no—
34#4977—31no—
35#4936—31no—
36C2×C4⋊(C3⋊C8)—31no—
37#4551—31no—
38#4529—31no—
39#4529—31no—
40#4529—31no—
41C24×C32—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4C2×C412yes—
46C2×C32×D4D412yes—
47C2×C32×D4Q812yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—42no—
54C22×C3×Dic3—42no—
55C22×C3×Dic3D411yescharacteristic
56C22×C3×Dic3D411yescharacteristic
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×#217—24no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3C2×C412yes—
67C3×C4×Dic3C2×C412yes—
68C3×C4×Dic3D412yes—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72#1804—91noSylow
73C22×C3×D4—21no—
74C22×C3×D4C2×D311yescharacteristic
75C22×C3×D4C2×D311yescharacteristic
76C23×C3×C4—61no—
77C23×Dic3—21no—
78C22×C3×C8—31no—
79C3×C4×D4—34no—
80C3×C4×D4—62no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C22⋊C4—61no—
84C2×C3×C42—31no—
85C2×#217—21no—
86D4×Dic3—22no—
87D4×Dic3Dic314yescomplemented
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—61no—
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×C4×Dic3C2×D311yescharacteristic
94C22×C3⋊C8—31no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—61no—
97C22×C3⋊C8C2×D311yescharacteristic
98C3×#102—62no—
99#832—22no—
100#832—64no—
101#832—62no—
102#832—62no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106C3⋊#95—61no—
107Dic3⋊C8—62no—
108C4⋊(C3⋊C8)—62no—
109C23×C32—22no—
110C23×C32—22no—
111C23×C32—22no—
112C23×C32—41no—
113C23×C32—41no—
114C23×C32—41no—
115C23×C32—41no—
116C23×C32C2×D411yescharacteristic
117C32×D4—22no—
118C32×D4—22no—
119C32×D4—22no—
120C32×D4C4⋊C414yes—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×Q811yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—48no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3C22⋊C412yes—
142C2×C3×Dic3C22⋊C412yes—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—41no—
145C2×C4×D4—31no—
146C2×C4⋊C8—91no—
147C2×#102—31no—
148C2×#102—91no—
149#382—91no—
150#340—91no—
151#340—91no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—41no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—22no—
162C2×C3×D4—22no—
163C2×C3×D4—22no—
164C2×C3×D4—41no—
165C2×C3×D4—41no—
166C2×C3×D4—41no—
167C2×C3×D4Dic612yes—
168C2×C3×D4Dic612yes—
169C2×C3×D4C4×D312yes—
170C2×C3×D4D1212yes—
171C2×C3×D4C2×Dic312yes—
172C2×C3×D4#6712yes—
173C22×C3×C4—21no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—64no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4—122no—
180C22×C3×C4—122no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×Dic3—21no—
184C22×Dic3—24no—
185C22×Dic3—21no—
186C22×Dic3—42no—
187C22×Dic3—42no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—121no—
191C22×Dic3#6711yescharacteristic
192C22×Dic3#6711yescharacteristic
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C2×C3×C8—61no—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C22⋊C4—64no—
201C3×C42—32no—
202C3×C42—32no—
203#217—24no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—62no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—121no—
213C4⋊Dic3C2×Dic312yes—
214C4×Dic3C2×Dic312yes—
215C4×Dic3#6712yes—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—121no—
227C2×C3⋊C8—121no—
228C22×C32—24no—
229C22×C32—42no—
230C22×C32—42no—
231C22×C32—42no—
232C22×C32—42no—
233C22×C32—42no—
234C22×C32—42no—
235C22×C32C2×C22⋊C411yescharacteristic
236C22×C32#12111yescharacteristic
237C22×C32C22⋊Q811yescharacteristic
238C22×C32#13511yescharacteristic
239C22×C32#13511yescharacteristic
240C22×C32AGL(1,ℤ/8)11yescharacteristic
241C22×C32AGL(1,ℤ/8)11yescharacteristic
242C32×C4C2×C4⋊C411yescharacteristic
243C32×C4#11711yescharacteristic
244C32×C4#12111yescharacteristic
245C32×C4C22⋊Q811yescharacteristic
246C3⋊Dic3—81no—
247C3×Dic3—22no—
248C3×Dic3—22no—
249C3×Dic3—42no—
250C3×Dic3—81no—
251C22×D4D3211yescharacteristic
252C23×C4—61no—
253C22×C8—31no—
254C22×C8—91no—
255C4×D4—34no—
256C4×D4—62no—
257C2×C4⋊C4—31no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—91no—
260C2×C22⋊C4—61no—
261C2×C42—31no—
262C4⋊C8—182no—
263#102—62no—
264#102—182no—
265#95—181no—
266#95—181no—
267C23×C3—22no—
268C23×C3—22no—
269C23×C3—22no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—21no—
274C23×C3—42no—
275C23×C3—42no—
276C23×C3—42no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—41no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—81no—
286C23×C3—81no—
287C23×C3—81no—
288C23×C3—81no—
289C23×C3D3×D411yescharacteristic
290C23×C3C2×#6711yescharacteristic
291C3×D4—22no—
292C3×D4—22no—
293C3×D4—22no—
294C3×D4—22no—
295C3×D4—22no—
296C3×D4—22no—
297C3×D4—24no—
298C3×D4—42no—
299C3×D4—42no—
300C3×D4—42no—
301C3×D4Dic3⋊C414yes—
302C3×D4C4⋊Dic314yes—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—32no—
310C2×C3×C4—32no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—62no—
316C2×C3×C4—128no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4C2×Dic611yescharacteristic
323C2×C3×C4C2×Dic611yescharacteristic
324C2×C3×C4C2×C4×D311yescharacteristic
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4#23511yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4#23711yescharacteristic
330C2×C3×C4#23711yescharacteristic
331C2×C3×C4C22×Dic311yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×Dic3—21no—
335C2×Dic3—21no—
336C2×Dic3—21no—
337C2×Dic3—21no—
338C2×Dic3—22no—
339C2×Dic3—48no—
340C2×Dic3—41no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—122no—
346C2×Dic3—121no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—241no—
353C2×Dic3—241no—
354C2×Dic3#21712yes—
355C2×Dic3#21712yes—
356C3×C8—121no—
357C3⋊C8—41no—
358C3⋊C8—122no—
359C3⋊C8—121no—
360C3⋊C8—121no—
361C2×C32—44no—
362C2×C32#38011yescharacteristic
363C2×C32#41611yescharacteristic
364C2×C32#41811yescharacteristic
365C2×C32#46311yescharacteristic
366C2×C32#46311yescharacteristic
367C2×C32#47811yescharacteristic
368C2×C32#47811yescharacteristic
369C24—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4D3×Dic312yes—
374C2×D4#62612yes—
375C2×D4#62712yes—
376C22×C4—31no—
377C22×C4—31no—
378C22×C4—64no—
379C22×C4—61no—
380C22×C4—61no—
381C22×C4—122no—
382C22×C4—122no—
383C22×C4—181no—
384C22×C4C2×D3211yescharacteristic
385C2×C8—61no—
386C2×C8—61no—
387C2×C8—61no—
388C2×C8—181no—
389C2×C8—181no—
390C2×C8—181no—
391C4⋊C4—32no—
392C4⋊C4—61no—
393C4⋊C4—61no—
394C4⋊C4—61no—
395C4⋊C4—181no—
396C4⋊C4—181no—
397C22⋊C4—64no—
398C42—32no—
399C42—32no—
400C22×C3—24no—
401C22×C3—24no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—44no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—82no—
423C22×C3—82no—
424C22×C3—82no—
425C22×C3—82no—
426C22×C3—82no—
427C22×C3—82no—
428C22×C3#87811yescharacteristic
429C22×C3D3×C22⋊C411yescharacteristic
430C22×C3#91111yescharacteristic
431C22×C3#91211yescharacteristic
432C22×C3#91411yescharacteristic
433C22×C3#91611yescharacteristic
434C22×C3#92411yescharacteristic
435C22×C3#93011yescharacteristic
436C22×C3#93211yescharacteristic
437C22×C3#93211yescharacteristic
438C22×C3#93911yescharacteristic
439C22×C3#95011yescharacteristic
440C22×C3#95011yescharacteristic
441C22×C3C2×#21711yescharacteristic
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—122no—
449C3×C4—241no—
450C3×C4#87711yescharacteristic
451C3×C4#87811yescharacteristic
452C3×C4C2×Dic3⋊C411yescharacteristic
453C3×C4#92411yescharacteristic
454C3×C4C2×C4⋊Dic311yescharacteristic
455C3×C4#92611yescharacteristic
456C3×C4#93011yescharacteristic
457C3×C4#93911yescharacteristic
458Dic3—22no—
459Dic3—22no—
460Dic3—42no—
461Dic3—81no—
462Dic3—242no—
463Dic3—241no—
464Dic3—241no—
465C32#180411yescharacteristic, complemented, Sylow
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23D3×#6711yescharacteristic
474D4—22no—
475D4—22no—
476D4—22no—
477D4Dic3⋊Dic314yes—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—62no—
485C2×C4—128no—
486C2×C4—121no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—361no—
492C2×C4—361no—
493C2×C4—361no—
494C2×C4C2×D3×Dic311yescharacteristic
495C2×C4#380411yescharacteristic
496C2×C4#380411yescharacteristic
497C2×C4C2×#62611yescharacteristic
498C2×C4C2×#62711yescharacteristic
499C2×C4D3×#6711yescharacteristic
500C8—121no—
501C8—361no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—44no—
510C2×C3—44no—
511C2×C3—84no—
512C2×C3#476311yescharacteristic
513C2×C3#476611yescharacteristic
514C2×C3#477011yescharacteristic
515C2×C3#477211yescharacteristic
516C2×C3#494211yescharacteristic
517C2×C3#500911yescharacteristic
518C2×C3#500911yescharacteristic
519C2×C3#501611yescharacteristic
520C2×C3#501611yescharacteristic
521C2×C3#515311yescharacteristic
522C2×C3#516511yescharacteristic
523C2×C3#521211yescharacteristic
524C2×C3#521511yescharacteristic
525C2×C3#523311yescharacteristic
526C22—24no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22#6393211yescharacteristic
534C22#6393311yescharacteristic
535C22#6393411yescharacteristic
536C22#6393511yescharacteristic
537C22#6396411yescharacteristic
538C22D3×#21711yescharacteristic
539C22#6397811yescharacteristic
540C4—62no—
541C4—62no—
542C4—122no—
543C4—241no—
544C4—721no—
545C4#6395511yescharacteristic
546C4#6396411yescharacteristic
547C4C2×Dic3⋊Dic311yescharacteristic
548C4#6397811yescharacteristic
549C3—21no—
550C3#7015411yescharacteristic, complemented
551C3#7160511yescharacteristic, complemented
552C2—44no—
553C2#1059140911yescharacteristic
554C2#1059141111yescharacteristic
555C2#1059142011yescharacteristic
556C2#1059142111yescharacteristic
557C2#1059146811yescharacteristic
558C2#1059147111yescharacteristic
559C2#1059171611yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1804
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591224C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. #10589164C2semidirect
7. #10589163C2semidirect
16. C3×D4×Dic3C4semidirect
87. D4×Dic3Dic3semidirect
465. C32#1804semidirect
550. C3#70154semidirect
551. C3#71605semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×#636592
C2×C3×#8322
#105912242
C2×Dic3⋊(C3⋊C8)2
#105891642
#105891632
#716053
#701543