Finite Group Databasebeta

← #11865785

Subgroups — #11865785

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 687 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C2×#63829C212yesmaximal, complemented
4C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5#10591084C212yesmaximal, complemented
6#10590388C211yesmaximal, characteristic, complemented
7#10590379C211yesmaximal, characteristic, complemented
8#10590378C212yesmaximal, complemented
9#10590377C211yesmaximal, characteristic, complemented
10#10590356C212yesmaximal, complemented
11#10590355C211yesmaximal, characteristic, complemented
12#83296—31nomaximal
13#79021—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2212yes—
16C2×C32×C42C2211yescharacteristic
17C4×#638—21no—
18C4×#638—21no—
19#64135C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22#64081—21no—
23C42×C3⋊D3—21no—
24C4×#634C2211yescharacteristic
25C4×#634C2211yescharacteristic
26C3×#930—21no—
27C3×#930—21no—
28C22×C3×C3⋊C8C2212yes—
29C3×#875C2212yes—
30C3×#874C2211yescharacteristic
31C3×C4×D12—21no—
32C3×C4×D12—21no—
33C3×#869C2211yescharacteristic
34C2×#3719C2212yes—
35C2×#3717C2212yes—
36#63829—28no—
37C2×#3716C2212yes—
38C2×#3714C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40C3×C4⋊(C3⋊C8)C2212yes—
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42#63566C2212yes—
43#63566C2212yes—
44#63563C2212yes—
45#63563C2212yes—
46C3×#532—31no—
47C2×#950—32no—
48C2×#904—32no—
49#5477D311yescharacteristic, complemented
50C4×#235—31no—
51C4×#235—31no—
52C4×#235—61no—
53C2×C3×C4⋊C8—31no—
54#5233—32no—
55#5113—32no—
56#5090—31no—
57#5083—31no—
58#5075—31no—
59#5072—31no—
60#5057—32no—
61#5054—32no—
62C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
63#4849—31no—
64#4848—31no—
65#4845—32no—
66#4844—32no—
67#4843—31no—
68#4841—31no—
69C22×C32×C4D411yescharacteristic
70C22×C32×C4D411yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×#638—21no—
73#3828—22no—
74#3828D414yescomplemented
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×C4×C3⋊D3—21no—
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3—21no—
79C2×#634C2311yescharacteristic
80C2×C3×#67—22no—
81C3×#235—24no—
82C3×#235—24no—
83C2×C3×D12—21no—
84C2×C3×D12—21no—
85C2×C3×D12C2312yes—
86C2×C3×C4×D3—22no—
87C2×C3×Dic6C2312yes—
88C32×C42D411yescharacteristic
89C32×C42D411yescharacteristic
90C32×C42C2311yescharacteristic
91C32×C42C2311yescharacteristic
92#3757—21no—
93#3752—21no—
94#3752—21no—
95C4⋊(C3⋊Dic3)C2311yescharacteristic
96C4⋊(C3⋊Dic3)C2311yescharacteristic
97#3750—21no—
98#3750—21no—
99C4×C3⋊Dic3—21no—
100C4×C3⋊Dic3—21no—
101C4×C3⋊Dic3—21no—
102C3×(C2×D3)⋊C4—22no—
103C3×(C2×D3)⋊C4—22no—
104C3×C4⋊Dic3—21no—
105C3×C4⋊Dic3—21no—
106C2×C3×C3⋊C8—24no—
107C2×C3×C3⋊C8C2312yes—
108C2×C3×C3⋊C8C2312yes—
109#3719—24no—
110#3717—24no—
111#3716—24no—
112#3714—24no—
113#3035—91noSylow
114C2×C3×#41—32no—
115C2×#235—31no—
116C2×#235—31no—
117C2×#235—61no—
118C2×#235C2×D312yes—
119C22×C3×C8—32no—
120C3×C4⋊Q8—31no—
121C3×#127—31no—
122C3×#124—32no—
123C3×#121—61no—
124C3×#121—61no—
125C3×C4×D4—61no—
126C3×C4×D4—61no—
127C2×C3×C42—21no—
128C2×C3×C42C2×D311yescharacteristic
129C2×C3×C42C2×D311yescharacteristic
130#950—68no—
131C2×#216—32no—
132C2×#215—32no—
133C2×#214—32no—
134C2×#213—32no—
135#930—21no—
136#930—21no—
137C4×#67—62no—
138C4×#67—62no—
139C4×#67—61no—
140C4×#67—61no—
141C4×#67—61no—
142C4×#67—61no—
143#926—31no—
144#926—31no—
145#926—61no—
146C22×C3⋊C8C2×D312yes—
147C2×Dic12—32no—
148#904—68no—
149C2×D24—32no—
150C2×#204—32no—
151C2×#204—32no—
152#875C2×D312yes—
153#874C2×D311yescharacteristic
154C4×D12—21no—
155C4×D12—21no—
156C4×D12—31no—
157C4×D12—31no—
158C4×D12—31no—
159C4×D12—31no—
160C4×D12—61no—
161C4×D12—61no—
162#872—62no—
163#872—61no—
164#872—61no—
165C42×D3—62no—
166C42×D3—61no—
167C42×D3—61no—
168#869C2×D311yescharacteristic
169C4×Dic6—31no—
170C4×Dic6—31no—
171C4×Dic6—31no—
172C4×Dic6—31no—
173C4×Dic6—61no—
174C4×Dic6—61no—
175C3×C4⋊C8—31no—
176C3×C4⋊C8—31no—
177C3×C4⋊C8—32no—
178#835—32no—
179#835—32no—
180#832—32no—
181#832—32no—
182#821—32no—
183#821—32no—
184#816—32no—
185#816—32no—
186C4⋊(C3⋊C8)C2×D312yes—
187C4⋊(C3⋊C8)C2×D311yescharacteristic
188C4⋊(C3⋊C8)C2×D311yescharacteristic
189C23×C32C2×D411yescharacteristic
190C22×C3⋊D3—21no—
191C22×C3×D3—22no—
192C2×C32×C4—22no—
193C2×C32×C4—41no—
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2×D411yescharacteristic
197C2×C32×C4C2×D411yescharacteristic
198C2×C32×C4C2×D411yescharacteristic
199C2×C32×C4C2×D412yes—
200C2×C32×C4#4112yes—
201C2×C32×C4C2411yescharacteristic
202#638—24no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C4⋊(C3⋊D3)—21no—
207C4⋊(C3⋊D3)C2×D412yes—
208C4×C3⋊D3—24no—
209C4×C3⋊D3—42no—
210C4×C3⋊D3—42no—
211#634—21no—
212#634C2×D412yes—
213C3×#67—44no—
214C2×C3×Dic3—22no—
215C3×D12—22no—
216C3×D12—22no—
217C3×D12—42no—
218C3×D12—42no—
219C3×C4×D3—44no—
220C3×Dic6—22no—
221C3×Dic6—22no—
222C3×C3⋊C8—22no—
223C3×C3⋊C8—22no—
224C2×#135—92no—
225#532—31no—
226C4×#41—91no—
227#464—92no—
228#463—92no—
229#462—91no—
230#461—91no—
231#460—91no—
232#459—91no—
233C2×C4⋊C8—31no—
234#416—92no—
235C3×#41—64no—
236C3×#41—64no—
237C2×C3×Q8—32no—
238C2×C3×D4—32no—
239C2×C3×D4—62no—
240C2×C3×D4—61no—
241C2×C3×D4—61no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—62no—
246C22×C3×C4D1211yescharacteristic
247C22×C3×C4D1211yescharacteristic
248C22×C3×C4#6711yescharacteristic
249C22×C3×C4#6711yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—22no—
253C2×#67—62no—
254C2×#67—61no—
255C2×#67—61no—
256#235—24no—
257#235—24no—
258#235—34no—
259#235—34no—
260#235—64no—
261#235—64no—
262#235—62no—
263#235—62no—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—31no—
267C2×D12—31no—
268C2×D12—61no—
269C2×D12C22×D312yes—
270C2×C4×D3—22no—
271C2×C4×D3—62no—
272C2×C4×D3—61no—
273C2×C4×D3—61no—
274C2×C4×D3—62no—
275C2×C4×D3—62no—
276C2×C4×D3—61no—
277C2×C4×D3—61no—
278C2×C4×D3—61no—
279C2×C4×D3—61no—
280C2×Dic6—31no—
281C2×Dic6—31no—
282C2×Dic6—61no—
283C2×Dic6C22×D312yes—
284C2×C3×C8—32no—
285C2×C3×C8—32no—
286C2×C3×C8—64no—
287C3×C4⋊C4—61no—
288C3×C4⋊C4—61no—
289C3×C22⋊C4—62no—
290C3×C22⋊C4—62no—
291C3×C42—21no—
292C3×C42—21no—
293C3×C42—21no—
294C3×C42—21no—
295C3×C42D1211yescharacteristic
296C3×C42D1211yescharacteristic
297C3×C42#6711yescharacteristic
298C3×C42#6711yescharacteristic
299C3×C42C22×D311yescharacteristic
300C3×C42C22×D311yescharacteristic
301C3×C42C22×D311yescharacteristic
302C3×C42C22×D311yescharacteristic
303#217—62no—
304#217—61no—
305#217—61no—
306#216—64no—
307#215—64no—
308#214—64no—
309#213—64no—
310(C2×D3)⋊C4—22no—
311(C2×D3)⋊C4—22no—
312(C2×D3)⋊C4—62no—
313(C2×D3)⋊C4—62no—
314(C2×D3)⋊C4—61no—
315(C2×D3)⋊C4—61no—
316(C2×D3)⋊C4—61no—
317(C2×D3)⋊C4—61no—
318C4⋊Dic3—21no—
319C4⋊Dic3—21no—
320C4⋊Dic3—31no—
321C4⋊Dic3—31no—
322C4⋊Dic3—31no—
323C4⋊Dic3—31no—
324C4⋊Dic3—61no—
325C4⋊Dic3—61no—
326Dic3⋊C4—62no—
327Dic3⋊C4—62no—
328Dic3⋊C4—61no—
329Dic3⋊C4—61no—
330Dic3⋊C4—61no—
331Dic3⋊C4—61no—
332C4×Dic3—62no—
333C4×Dic3—62no—
334C4×Dic3—62no—
335C4×Dic3—61no—
336C4×Dic3—61no—
337C4×Dic3—61no—
338C4×Dic3—61no—
339C4×Dic3—61no—
340C4×Dic3—61no—
341C2×C3⋊C8—24no—
342C2×C3⋊C8C22×D312yes—
343C2×C3⋊C8C22×D312yes—
344Dic12—64no—
345D24—64no—
346#204—64no—
347#204—64no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32#12112yes—
351C22×C32C22×D411yescharacteristic
352C2×C3⋊D3—22no—
353C2×C3⋊D3—41no—
354C2×C3⋊D3—41no—
355C2×C3×D3—42no—
356C2×C3×D3—42no—
357C2×C3×D3—42no—
358C32×C4—21no—
359C32×C4—21no—
360C32×C4—21no—
361C32×C4#12112yes—
362C32×C4#13512yescomplemented
363C32×C4C22×D411yescharacteristic
364C32×C4C2×#4111yescharacteristic
365C3⋊Dic3—22no—
366C3⋊Dic3—41no—
367C3⋊Dic3—41no—
368C3×Dic3—42no—
369C2×#41—32no—
370C2×#41—91no—
371#135—188no—
372C2×Q16—92no—
373C2×SD16—92no—
374C2×SD16—92no—
375C2×D8—92no—
376C22×C8—32no—
377C4⋊Q8—31no—
378#127—31no—
379#124—32no—
380#121—61no—
381#121—61no—
382C4×Q8—91no—
383C4×Q8—91no—
384C4×D4—61no—
385C4×D4—61no—
386C4×D4—91no—
387C4×D4—91no—
388C4×D4—181no—
389C4×D4—181no—
390#117—91no—
391#117—181no—
392C2×C42—181no—
393C2×C42D3211yescharacteristic
394C4⋊C8—31no—
395C4⋊C8—31no—
396C4⋊C8—32no—
397#103—92no—
398#103—92no—
399#102—92no—
400#102—92no—
401C23×C3—21no—
402C23×C3—62no—
403C23×C3C2×D1211yescharacteristic
404C23×C3C2×#6711yescharacteristic
405C22×D3—22no—
406C22×D3—62no—
407C22×D3—61no—
408C22×D3—61no—
409C3×Q8—62no—
410C3×Q8—62no—
411C3×D4—62no—
412C3×D4—62no—
413C3×D4—122no—
414C3×D4—124no—
415C3×D4—122no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—21no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—42no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—42no—
430C2×C3×C4—62no—
431C2×C3×C4—124no—
432C2×C3×C4C2×D1211yescharacteristic
433C2×C3×C4C2×D1211yescharacteristic
434C2×C3×C4C2×D1211yescharacteristic
435C2×C3×C4C2×D1211yescharacteristic
436C2×C3×C4C2×D1211yescharacteristic
437C2×C3×C4D3×D412yes—
438C2×C3×C4D3×D412yes—
439C2×C3×C4#23712yes—
440C2×C3×C4#23912yes—
441C2×C3×C4C2×#6711yescharacteristic
442C2×C3×C4C2×#6711yescharacteristic
443C2×C3×C4C2×#6711yescharacteristic
444C2×C3×C4C2×#6711yescharacteristic
445C2×C3×C4C2×#6711yescharacteristic
446C2×C3×C4C23×D311yescharacteristic
447C2×C3×C4C23×D311yescharacteristic
448#67—44no—
449#67—68no—
450#67—64no—
451#67—64no—
452C2×Dic3—22no—
453C2×Dic3—62no—
454C2×Dic3—61no—
455C2×Dic3—61no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—61no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—61no—
462D12—22no—
463D12—22no—
464D12—32no—
465D12—32no—
466D12—42no—
467D12—42no—
468D12—62no—
469D12—62no—
470D12—61no—
471D12—61no—
472C4×D3—44no—
473C4×D3—68no—
474C4×D3—64no—
475C4×D3—64no—
476C4×D3—124no—
477C4×D3—122no—
478C4×D3—122no—
479C4×D3—124no—
480C4×D3—122no—
481C4×D3—122no—
482Dic6—22no—
483Dic6—22no—
484Dic6—32no—
485Dic6—32no—
486Dic6—62no—
487Dic6—62no—
488Dic6—61no—
489Dic6—61no—
490C3×C8—62no—
491C3×C8—62no—
492C3⋊C8—22no—
493C3⋊C8—22no—
494C2×C32—22no—
495C2×C32C2×#12111yescharacteristic
496C2×C32C2×#13511yescharacteristic
497C2×C32#57511yescharacteristic
498C3⋊D3—42no—
499C3×D3—82no—
500#41—64no—
501#41—64no—
502#41—94no—
503#41—182no—
504C2×Q8—32no—
505C2×Q8—91no—
506C2×D4—32no—
507C2×D4—62no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—91no—
511C2×D4—181no—
512C22×C4—62no—
513C22×C4—181no—
514C22×C4—181no—
515C22×C4—181no—
516C22×C4#62611yescharacteristic
517C22×C4#62611yescharacteristic
518C22×C4C2×D3211yescharacteristic
519Q16—184no—
520SD16—184no—
521SD16—184no—
522D8—184no—
523C2×C8—32no—
524C2×C8—32no—
525C2×C8—64no—
526C4⋊C4—61no—
527C4⋊C4—61no—
528C4⋊C4—91no—
529C4⋊C4—91no—
530C4⋊C4—181no—
531C4⋊C4—181no—
532C22⋊C4—62no—
533C22⋊C4—62no—
534C22⋊C4—181no—
535C22⋊C4—181no—
536C22⋊C4—181no—
537C42—181no—
538C42—181no—
539C42—181no—
540C42#62611yescharacteristic
541C42#62611yescharacteristic
542C42C2×D3211yescharacteristic
543C42C2×D3211yescharacteristic
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—22no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—122no—
553C22×C3—122no—
554C22×C3—122no—
555C22×C3#89512yes—
556C22×C3#93812yes—
557C22×C3C22×D1211yescharacteristic
558C22×C3C22×#6711yescharacteristic
559C2×D3—42no—
560C2×D3—42no—
561C2×D3—42no—
562C2×D3—64no—
563C2×D3—62no—
564C2×D3—62no—
565C2×D3—122no—
566C2×D3—122no—
567C2×D3—121no—
568C2×D3—121no—
569C2×D3—121no—
570C2×D3—121no—
571C3×C4—22no—
572C3×C4—21no—
573C3×C4—21no—
574C3×C4—21no—
575C3×C4—21no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—122no—
585C3×C4#89512yes—
586C3×C4#90412yescomplemented
587C3×C4#93812yes—
588C3×C4#95012yescomplemented
589C3×C4C2×D3×D411yescharacteristic
590C3×C4C2×D3×D411yescharacteristic
591C3×C4C2×#23711yescharacteristic
592C3×C4C2×#23911yescharacteristic
593Dic3—42no—
594Dic3—64no—
595Dic3—62no—
596Dic3—62no—
597Dic3—122no—
598Dic3—122no—
599Dic3—121no—
600Dic3—121no—
601Dic3—121no—
602Dic3—121no—
603C32#303511yescharacteristic, complemented, Sylow
604C23—62no—
605C23—181no—
606C23C2×#62611yescharacteristic
607Q8—62no—
608Q8—62no—
609Q8—92no—
610Q8—181no—
611D4—62no—
612D4—62no—
613D4—92no—
614D4—122no—
615D4—124no—
616D4—122no—
617D4—184no—
618D4—181no—
619C2×C4—22no—
620C2×C4—41no—
621C2×C4—62no—
622C2×C4—124no—
623C2×C4—181no—
624C2×C4—184no—
625C2×C4—181no—
626C2×C4—181no—
627C2×C4—362no—
628C2×C4—362no—
629C2×C4#379612yes—
630C2×C4#380212yes—
631C2×C4C2×#62611yescharacteristic
632C2×C4C2×#62611yescharacteristic
633C2×C4C2×#62611yescharacteristic
634C2×C4C2×#62611yescharacteristic
635C2×C4C2×#62611yescharacteristic
636C2×C4C22×D3211yescharacteristic
637C8—62no—
638C8—62no—
639C2×C3—22no—
640C2×C3—22no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—42no—
645C2×C3—242no—
646C2×C3C2×#89511yescharacteristic
647C2×C3C2×#90411yescharacteristic
648C2×C3#574811yescharacteristic
649C2×C3C2×#93811yescharacteristic
650C2×C3C2×#95011yescharacteristic
651C2×C3#582211yescharacteristic
652D3—82no—
653D3—124no—
654D3—122no—
655D3—122no—
656C22—21no—
657C22—21no—
658C22—122no—
659C22—122no—
660C22—122no—
661C22—182no—
662C22—361no—
663C22—361no—
664C22#6391612yes—
665C22C22×#62611yescharacteristic
666C4—21no—
667C4—21no—
668C4—21no—
669C4—122no—
670C4—182no—
671C4—361no—
672C4—361no—
673C4#6382912yescomplemented
674C4#6391612yes—
675C4C2×#379611yescharacteristic
676C4C2×#380211yescharacteristic
677C3—21no—
678C3#7902111yescharacteristic, complemented
679C3#8329611yescharacteristic, complemented
680C2—22no—
681C2—242no—
682C2—362no—
683C2C2×#6382911yescharacteristic
684C2#1059479511yescharacteristic
685C2C2×#6391611yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C4×#3828C2semidirect
2. C3×#5477C2semidirect
3. C2×#63829C2semidirect
4. C2×C3×C4⋊(C3⋊C8)C2semidirect
5. #10591084C2semidirect
6. #10590388C2semidirect
7. #10590379C2semidirect
8. #10590378C2semidirect
9. #10590377C2semidirect
10. #10590356C2semidirect
11. #10590355C2semidirect
49. #5477D3semidirect
62. C2×C4⋊(C3⋊C8)D3semidirect
74. #3828D4semidirect
362. C32×C4#135semidirect
586. C3×C4#904semidirect
588. C3×C4#950semidirect
603. C32#3035semidirect
673. C4#63829semidirect
678. C3#79021semidirect
679. C3#83296semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C3×#54772
C2×#638292
C2×C3×C4⋊(C3⋊C8)2
#105910842
#105903882
#105903792
#105903782
#105903772
#105903562
#105903552
#832963
#790213