Finite Group Databasebeta

← #11865874

Subgroups — #11865874

Order 1152.

1309 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C2×#63825C212yesmaximal, complemented
4C3×#4924C211yesmaximal, characteristic, complemented
5#10591088C212yesmaximal, complemented
6#10590379C212yesmaximal, complemented
7#10590356C214yesmaximal, complemented
8#10590355C212yesmaximal, complemented
9#83297—31nomaximal
10#79055—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C2×C3×#235C2212yes—
14C2×C32×C42C2211yescharacteristic
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C4×C4⋊(C3⋊D3)—21no—
18C4×C4⋊(C3⋊D3)—21no—
19C4×C4⋊(C3⋊D3)C2212yes—
20C4×C4⋊(C3⋊D3)C2212yes—
21C3×#930—21no—
22C3×#930—21no—
23C2×C3×#208C2212yes—
24C3×#875C2212yescomplemented
25C3×#874C2211yescharacteristic, complemented
26C3×C4×D12—21no—
27C3×C4×D12—21no—
28C3×#869C2211yescharacteristic, complemented
29C2×#3717C2214yes—
30#63825—28no—
31C2×#3714C2214yes—
32C3×C4⋊(C3⋊C8)C2212yescomplemented
33C3×C4⋊(C3⋊C8)C2212yescomplemented
34#63566C2214yescomplemented
35#63563C2214yescomplemented
36C3×#532—31no—
37C2×#949—32no—
38C2×#908—32no—
39#5477D311yescharacteristic, complemented
40C2×C4×D12—31no—
41C2×C4×D12—31no—
42C2×C4×D12—61no—
43C3×#423—31no—
44#5232—32no—
45#5133—32no—
46#5083—32no—
47#5072—32no—
48#5057—34no—
49#4924D311yescharacteristic, complemented
50#4844—34no—
51#4843—32no—
52#4841—32no—
53C23×C3⋊D3—21no—
54C22×C32×C4D411yescharacteristic
55C22×C32×C4D411yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)D414yescomplemented
61C2×C4⋊(C3⋊D3)C2312yes—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—44no—
65C2×C3×#67—22no—
66C3×#235—24no—
67C3×#235—24no—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6C2312yes—
73C32×C42D411yescharacteristic
74C32×C42D411yescharacteristic
75C32×C42C2311yescharacteristic
76C32×C42C2311yescharacteristic
77#3752—22no—
78#3752—22no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2312yes—
81C3×(C2×D3)⋊C4—22no—
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3—21no—
85C3×#208—24no—
86C2×C3×C3⋊C8C2314yes—
87#3717—28no—
88#3714—28no—
89#3036—91noSylow
90C2×C3×#41—32no—
91C2×#235C2×D312yes—
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×C4×D3—62no—
96C22×C4×D3—61no—
97C22×C4×D3—61no—
98C2×C3×M16—32no—
99C3×C4⋊Q8—31no—
100C3×#127—31no—
101C3×#124—32no—
102C3×#121—61no—
103C3×#121—61no—
104C3×C4×D4—61no—
105C3×C4×D4—61no—
106C2×C3×C42—21no—
107C2×C3×C42C2×D311yescharacteristic
108C2×C3×C42C2×D311yescharacteristic
109#949—68no—
110C2×#215—34no—
111C2×#213—34no—
112#930—21no—
113#930—21no—
114C2×(C2×D3)⋊C4—62no—
115C2×(C2×D3)⋊C4—61no—
116C2×(C2×D3)⋊C4—61no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—61no—
120C2×#208C2×D312yes—
121#908—68no—
122C2×D24—34no—
123C2×#204—34no—
124#875C2×D312yescomplemented
125#874C2×D311yescharacteristic, complemented
126C4×D12—21no—
127C4×D12—21no—
128C4×D12—32no—
129C4×D12—32no—
130C4×D12—32no—
131C4×D12—32no—
132C4×D12—62no—
133C4×D12—62no—
134C4×D12—62no—
135C4×D12—62no—
136C4×D12—61no—
137C4×D12—61no—
138C4×D12—61no—
139C4×D12—61no—
140#869C2×D311yescharacteristic, complemented
141C3×C4⋊C8—32no—
142C3×C4⋊C8—32no—
143#835—34no—
144#832—34no—
145#821—34no—
146#816—34no—
147C4⋊(C3⋊C8)C2×D312yescomplemented
148C4⋊(C3⋊C8)C2×D312yescomplemented
149C23×C32C2×D411yescharacteristic
150C22×C3⋊D3—24no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—42no—
153C22×C3⋊D3—42no—
154C22×C3×D3—22no—
155C2×C32×C4—22no—
156C2×C32×C4—41no—
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D412yes—
163C2×C32×C4#4112yes—
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—42no—
167C4⋊(C3⋊D3)—24no—
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)C2×D414yes—
170C4×C3⋊D3—44no—
171C4×C3⋊D3—44no—
172C3×#67—44no—
173C2×C3×Dic3—22no—
174C3×D12—22no—
175C3×D12—22no—
176C3×D12—42no—
177C3×D12—42no—
178C3×C4×D3—44no—
179C3×Dic6—22no—
180C3×Dic6—22no—
181C3×C3⋊C8—24no—
182C2×AGL(1,ℤ/8)—92no—
183#532—31no—
184C2×C4×D4—91no—
185#463—94no—
186#461—92no—
187#459—92no—
188#423—31no—
189#417—92no—
190C23×D3—62no—
191C23×D3—61no—
192C23×D3—61no—
193C3×#41—64no—
194C3×#41—64no—
195C2×C3×Q8—32no—
196C2×C3×D4—32no—
197C2×C3×D4—62no—
198C2×C3×D4—61no—
199C2×C3×D4—61no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—62no—
204C22×C3×C4D1211yescharacteristic
205C22×C3×C4D1211yescharacteristic
206C22×C3×C4#6711yescharacteristic
207C22×C3×C4#6711yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C2×#67—22no—
211C22×Dic3—62no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214#235—24no—
215#235—24no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12—34no—
219C2×D12—34no—
220C2×D12—32no—
221C2×D12—32no—
222C2×D12—62no—
223C2×D12—64no—
224C2×D12—62no—
225C2×D12—64no—
226C2×D12—61no—
227C2×D12—62no—
228C2×D12—62no—
229C2×D12—61no—
230C2×D12C22×D312yes—
231C2×C4×D3—22no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—62no—
238C2×C4×D3—128no—
239C2×C4×D3—124no—
240C2×C4×D3—124no—
241C2×Dic6C22×D312yes—
242C3×M16—64no—
243C2×C3×C8—34no—
244C3×C4⋊C4—61no—
245C3×C4⋊C4—61no—
246C3×C22⋊C4—62no—
247C3×C22⋊C4—62no—
248C3×C42—21no—
249C3×C42—21no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42D1211yescharacteristic
253C3×C42D1211yescharacteristic
254C3×C42#6711yescharacteristic
255C3×C42#6711yescharacteristic
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D311yescharacteristic
258C3×C42C22×D311yescharacteristic
259C3×C42C22×D311yescharacteristic
260#215—68no—
261#213—68no—
262(C2×D3)⋊C4—22no—
263(C2×D3)⋊C4—22no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—62no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—62no—
270C4⋊Dic3—21no—
271C4⋊Dic3—21no—
272C4⋊Dic3—32no—
273C4⋊Dic3—32no—
274C4⋊Dic3—62no—
275C4⋊Dic3—62no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278#208—24no—
279C2×C3⋊C8C22×D314yes—
280D24—68no—
281#204—68no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32#12112yes—
285C22×C32C22×D411yescharacteristic
286C2×C3⋊D3—24no—
287C2×C3⋊D3—48no—
288C2×C3⋊D3—42no—
289C2×C3⋊D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293C32×C4—21no—
294C32×C4—21no—
295C32×C4—21no—
296C32×C4#12112yes—
297C32×C4AGL(1,ℤ/8)12yescomplemented
298C32×C4C22×D411yescharacteristic
299C32×C4C2×#4111yescharacteristic
300C3⋊Dic3—42no—
301C3×Dic3—42no—
302C2×#41—32no—
303C22×D4—91no—
304C23×C4—181no—
305AGL(1,ℤ/8)—188no—
306C2×SD16—94no—
307C2×D8—94no—
308C2×M16—32no—
309C4⋊Q8—31no—
310#127—31no—
311#124—32no—
312#121—61no—
313#121—61no—
314C4×D4—61no—
315C4×D4—61no—
316C4×D4—92no—
317C4×D4—92no—
318C4×D4—181no—
319C4×D4—181no—
320C2×C4⋊C4—91no—
321C2×C22⋊C4—181no—
322C2×C42D3211yescharacteristic
323C4⋊C8—32no—
324C4⋊C8—32no—
325#103—94no—
326#102—94no—
327C23×C3—21no—
328C23×C3—62no—
329C23×C3C2×D1211yescharacteristic
330C23×C3C2×#6711yescharacteristic
331C22×D3—22no—
332C22×D3—64no—
333C22×D3—68no—
334C22×D3—64no—
335C22×D3—64no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—124no—
339C22×D3—122no—
340C22×D3—122no—
341C22×D3—124no—
342C22×D3—122no—
343C22×D3—122no—
344C3×Q8—62no—
345C3×Q8—62no—
346C3×D4—62no—
347C3×D4—62no—
348C3×D4—122no—
349C3×D4—124no—
350C3×D4—122no—
351C2×C3×C4—24no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—42no—
365C2×C3×C4—62no—
366C2×C3×C4—124no—
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4C2×D1211yescharacteristic
369C2×C3×C4C2×D1211yescharacteristic
370C2×C3×C4C2×D1211yescharacteristic
371C2×C3×C4C2×D1211yescharacteristic
372C2×C3×C4D3×D412yes—
373C2×C3×C4D3×D412yes—
374C2×C3×C4#23712yes—
375C2×C3×C4#23912yes—
376C2×C3×C4C2×#6711yescharacteristic
377C2×C3×C4C2×#6711yescharacteristic
378C2×C3×C4C2×#6711yescharacteristic
379C2×C3×C4C2×#6711yescharacteristic
380C2×C3×C4C2×#6711yescharacteristic
381C2×C3×C4C23×D311yescharacteristic
382C2×C3×C4C23×D311yescharacteristic
383#67—44no—
384C2×Dic3—22no—
385C2×Dic3—64no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—124no—
389C2×Dic3—122no—
390C2×Dic3—122no—
391D12—22no—
392D12—22no—
393D12—34no—
394D12—34no—
395D12—42no—
396D12—42no—
397D12—64no—
398D12—64no—
399D12—68no—
400D12—64no—
401D12—64no—
402D12—62no—
403D12—62no—
404C4×D3—44no—
405C4×D3—128no—
406C4×D3—124no—
407C4×D3—124no—
408C4×D3—128no—
409C4×D3—124no—
410C4×D3—124no—
411Dic6—22no—
412Dic6—22no—
413C3×C8—64no—
414C3⋊C8—24no—
415C2×C32—22no—
416C2×C32C2×#12111yescharacteristic
417C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
418C2×C32#57511yescharacteristic
419C3⋊D3—44no—
420C3×D3—82no—
421C24—181no—
422#41—64no—
423#41—64no—
424C2×Q8—32no—
425C2×D4—32no—
426C2×D4—62no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—92no—
430C2×D4—94no—
431C2×D4—182no—
432C2×D4—181no—
433C22×C4—62no—
434C22×C4—181no—
435C22×C4—182no—
436C22×C4—182no—
437C22×C4—364no—
438C22×C4#62611yescharacteristic
439C22×C4#62611yescharacteristic
440C22×C4C2×D3211yescharacteristic
441SD16—188no—
442D8—188no—
443M16—64no—
444C2×C8—34no—
445C4⋊C4—61no—
446C4⋊C4—61no—
447C4⋊C4—92no—
448C4⋊C4—181no—
449C22⋊C4—62no—
450C22⋊C4—62no—
451C22⋊C4—182no—
452C22⋊C4—182no—
453C42#62611yescharacteristic
454C42#62611yescharacteristic
455C42C2×D3211yescharacteristic
456C42C2×D3211yescharacteristic
457C22×C3—22no—
458C22×C3—22no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—22no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—122no—
468C22×C3#89512yes—
469C22×C3#93812yes—
470C22×C3C22×D1211yescharacteristic
471C22×C3C22×#6711yescharacteristic
472C2×D3—42no—
473C2×D3—42no—
474C2×D3—42no—
475C2×D3—68no—
476C2×D3—64no—
477C2×D3—64no—
478C2×D3—124no—
479C2×D3—1216no—
480C2×D3—128no—
481C2×D3—128no—
482C2×D3—124no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—122no—
486C2×D3—122no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—22no—
497C3×C4—22no—
498C3×C4—41no—
499C3×C4—41no—
500C3×C4—122no—
501C3×C4#89512yes—
502C3×C4#90812yescomplemented
503C3×C4#93812yes—
504C3×C4#94912yescomplemented
505C3×C4C2×D3×D411yescharacteristic
506C3×C4C2×D3×D411yescharacteristic
507C3×C4C2×#23711yescharacteristic
508C3×C4C2×#23911yescharacteristic
509Dic3—42no—
510Dic3—124no—
511Dic3—122no—
512Dic3—122no—
513C32#303611yescharacteristic, complemented, Sylow
514C23—62no—
515C23—182no—
516C23—184no—
517C23—362no—
518C23—362no—
519C23C2×#62611yescharacteristic
520Q8—62no—
521Q8—62no—
522D4—62no—
523D4—62no—
524D4—94no—
525D4—122no—
526D4—124no—
527D4—122no—
528D4—182no—
529D4—184no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—62no—
533C2×C4—124no—
534C2×C4—182no—
535C2×C4—364no—
536C2×C4—362no—
537C2×C4—364no—
538C2×C4#379612yes—
539C2×C4#380212yes—
540C2×C4C2×#62611yescharacteristic
541C2×C4C2×#62611yescharacteristic
542C2×C4C2×#62611yescharacteristic
543C2×C4C2×#62611yescharacteristic
544C2×C4C2×#62611yescharacteristic
545C2×C4C22×D3211yescharacteristic
546C8—64no—
547C2×C3—24no—
548C2×C3—22no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—242no—
554C2×C3C2×#89511yescharacteristic
555C2×C3C2×#90811yescharacteristic
556C2×C3#574811yescharacteristic
557C2×C3C2×#93811yescharacteristic
558C2×C3C2×#94911yescharacteristic
559C2×C3#582211yescharacteristic
560D3—82no—
561D3—128no—
562D3—124no—
563D3—124no—
564C22—21no—
565C22—21no—
566C22—122no—
567C22—122no—
568C22—122no—
569C22—184no—
570C22—368no—
571C22—362no—
572C22—362no—
573C22#6391612yes—
574C22C22×#62611yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—122no—
579C4—362no—
580C4#6382512yescomplemented
581C4#6391612yes—
582C4C2×#379611yescharacteristic
583C4C2×#380211yescharacteristic
584C3—21no—
585C3#7905511yescharacteristic, complemented
586C3#8329711yescharacteristic, complemented
587C2—22no—
588C2—242no—
589C2—364no—
590C2C2×#6382511yescharacteristic
591C2#1059479511yescharacteristic
592C2C2×#6391611yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3036
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C4⋊(C3⋊D3)C2semidirect
2. C3×#5477C2semidirect
3. C2×#63825C2semidirect
4. C3×#4924C2semidirect
5. #10591088C2semidirect
6. #10590379C2semidirect
7. #10590356C2semidirect
8. #10590355C2semidirect
24. C3×#875C22semidirect
25. C3×#874C22semidirect
28. C3×#869C22semidirect
32. C3×C4⋊(C3⋊C8)C22semidirect
33. C3×C4⋊(C3⋊C8)C22semidirect
34. #63566C22semidirect
35. #63563C22semidirect
39. #5477D3semidirect
49. #4924D3semidirect
60. C2×C4⋊(C3⋊D3)D4semidirect
124. #875C2×D3semidirect
125. #874C2×D3semidirect
140. #869C2×D3semidirect
147. C4⋊(C3⋊C8)C2×D3semidirect
148. C4⋊(C3⋊C8)C2×D3semidirect
297. C32×C4AGL(1,ℤ/8)semidirect
502. C3×C4#908semidirect
504. C3×C4#949semidirect
513. C32#3036semidirect
580. C4#63825semidirect
585. C3#79055semidirect
586. C3#83297semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C3×#54772
C2×#638252
C3×#49242
#105910882
#105903792
#105903562
#105903552
#832973
#790553