Finite Group Databasebeta

← #11865775

Subgroups — #11865775

Order 1152.

1052 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#237C211yesmaximal, characteristic, complemented
2C2×#63933C212yesmaximal, complemented
3#10593897C211yesmaximal, characteristic, complemented
4#10592718C211yesmaximal, characteristic, complemented
5C3×#5015C211yesmaximal, characteristic, complemented
6#10591468C212yesmaximal, complemented
7#10590608C212yesmaximal, complemented
8#10590532C212yesmaximal, complemented
9#10590385C211yesmaximal, characteristic, complemented
10#10590364C211yesmaximal, characteristic, complemented
11D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#82525—31nomaximal
13#80331—31nomaximal
14C2×C3×#237C2211yescharacteristic
15C2×#3795C2212yes—
16C32×C4×D4C2211yescharacteristic
17C2×#3754C2212yes—
18#64078C2211yescharacteristic
19C3×D4×Dic3C2211yescharacteristic
20C2×C3×#213C2212yes—
21C3×C4×#67—21no—
22C2×C3×C4×Dic3—21no—
23C3×#892C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C3×#67⋊C4—21no—
26C3×#877—21no—
27C3×#874C2211yescharacteristic
28C3×C42×D3C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30#63933—28no—
31#63908—21no—
32#63908—21no—
33Dic3×D12—21no—
34Dic3×D12—21no—
35#63860C2212yes—
36C2×#3719C2212yes—
37C2×#3715C2212yes—
38C2×D3×C3⋊C8C2212yes—
39#63637C2212yes—
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
41C3×#809C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43Dic3⋊(C3⋊C8)C2212yes—
44#63567C2212yes—
45#63562C2212yes—
46C3×C4×#41—31no—
47C2×#950—32no—
48C2×#912—32no—
49#5716—31no—
50C4×#237D311yescharacteristic, complemented
51#5477—31no—
52C3×#459—31no—
53#5153—32no—
54#5075—31no—
55#5031—31no—
56#5028—32no—
57#5027—31no—
58#5019—31no—
59#5019—31no—
60#5019—61no—
61#5016—32no—
62#5015D311yescharacteristic, complemented
63#5002—32no—
64C2×C4⋊(C3⋊C8)—31no—
65#4849—31no—
66D3×C4⋊C8—31no—
67#4772—32no—
68#4767—32no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×#634C2312yes—
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—21no—
75C3×#237—22no—
76C3×#237D414yescomplemented
77C2×C3×D12—21no—
78C2×C3×D12—21no—
79C2×C3×D12C2312yes—
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×C4×D3D411yescharacteristic
82C2×C3×C4×D3C2311yescharacteristic
83C2×C3×Dic6C2311yescharacteristic
84C2×#625—22no—
85C2×D3×Dic3—22no—
86#3795—24no—
87#3795—24no—
88C32×C4⋊C4C2311yescharacteristic
89C32×C22⋊C4—21no—
90C32×C42C2311yescharacteristic
91#3754—24no—
92C4⋊(C3⋊Dic3)—21no—
93C4⋊(C3⋊Dic3)—21no—
94C2×C3⋊(C3⋊C8)C2312yes—
95C3×#217—21no—
96C3×#213—24no—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3—21no—
103C3×C4×Dic3—21no—
104C3×C4×Dic3D411yescharacteristic
105C3×C4×Dic3D411yescharacteristic
106C3×C4×Dic3C2311yescharacteristic
107C2×C3×C3⋊C8C2312yes—
108(C2×D3)⋊Dic3—22no—
109(C2×D3)⋊Dic3—22no—
110#3719—24no—
111#3715—24no—
112D3×C3⋊C8—24no—
113#3035—91noSylow
114C2×C3×#41—31no—
115C2×#237—32no—
116C2×#237C2×D311yescharacteristic
117C2×#235—32no—
118C2×C3×D8—32no—
119C3×#127—31no—
120C3×C4×Q8—31no—
121C3×C4×Q8—31no—
122C3×C4×D4—21no—
123C3×C4×D4—31no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C3×C4×D4C2×D311yescharacteristic
127C3×C4×D4C2×D311yescharacteristic
128C3×#117—31no—
129C3×#117—61no—
130C2×C3×C42—31no—
131C2×C3×C42—61no—
132#950—68no—
133C2×#216—32no—
134C2×#215—32no—
135#938—61no—
136#938—61no—
137#936—32no—
138D4×Dic3—61no—
139D4×Dic3—61no—
140D4×Dic3C2×D311yescharacteristic
141C2×#214—32no—
142C2×#214—32no—
143C2×#214—32no—
144C2×#214—62no—
145C2×#213C2×D312yes—
146#930—61no—
147#930—61no—
148C4×#67—21no—
149C2×C4×Dic3—21no—
150C22×C3⋊C8—32no—
151#912—68no—
152C2×Dic12—32no—
153C2×D3×C8—32no—
154#892C2×D311yescharacteristic
155#887C2×D311yescharacteristic
156#67⋊C4—21no—
157#877—21no—
158#875—32no—
159#874C2×D311yescharacteristic
160C4×D12—61no—
161C4×D12—61no—
162C42×D3C2×D311yescharacteristic
163#869—31no—
164#869—31no—
165#869—61no—
166C4×Dic6C2×D311yescharacteristic
167C3×C4⋊C8—31no—
168C3×#102—32no—
169#832—32no—
170#816—32no—
171Dic3⋊C8—32no—
172#810—32no—
173#810—32no—
174#810—32no—
175#810—62no—
176#809—32no—
177#809C2×D312yes—
178C4⋊(C3⋊C8)—31no—
179C4⋊(C3⋊C8)—31no—
180C4⋊(C3⋊C8)—32no—
181C4⋊(C3⋊C8)—61no—
182C4⋊(C3⋊C8)C2×D311yescharacteristic
183C23×C32—21no—
184C22×C3×D3—22no—
185C22×C3×D3C2×D411yescharacteristic
186C32×D4—21no—
187C32×D4C2×D412yes—
188C2×C32×C4—21no—
189C2×C32×C4—42no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193C2×C3⋊Dic3—22no—
194#634—22no—
195#634—22no—
196C3×#67—24no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—24no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—42no—
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C3×D12—22no—
205C3×D12—22no—
206C3×D12—42no—
207C3×D12—42no—
208C3×C4×D3—22no—
209C3×C4×D3—41no—
210C3×C4×D3C2×D412yes—
211C3×C4×D3#4112yes—
212C3×Dic6—21no—
213C3×Dic6C2×D412yes—
214#625—44no—
215D3×Dic3—44no—
216C3⋊(C3⋊C8)—22no—
217C3×C3⋊C8—22no—
218C2×#135—92no—
219#532—91no—
220C4×#41—31no—
221#464—92no—
222#463—92no—
223#462—91no—
224#461—91no—
225#460—91no—
226#459—31no—
227C2×C4⋊C8—91no—
228#416—92no—
229C3×#41—34no—
230C3×#41—62no—
231C2×C3×Q8—31no—
232C2×C3×D4—21no—
233C2×C3×D4—32no—
234C2×C3×D4—61no—
235C2×C3×D4—61no—
236C2×C3×D4—61no—
237C2×C3×D4C22×D311yescharacteristic
238C2×C3×D4C22×D311yescharacteristic
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—31no—
244C22×C3×C4—41no—
245C22×C3×C4—61no—
246C22×C3×C4—61no—
247C2×#67—21no—
248C2×#67—62no—
249C2×#67—62no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—62no—
253#237—22no—
254#237—64no—
255#237—64no—
256#237D1214yescomplemented
257#235—64no—
258#235—64no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12C22×D312yes—
262C2×C4×D3—62no—
263C2×C4×D3#6711yescharacteristic
264C2×C4×D3#6711yescharacteristic
265C2×C4×D3C22×D311yescharacteristic
266C2×Dic6—32no—
267C2×Dic6—32no—
268C2×Dic6—62no—
269C2×Dic6C22×D311yescharacteristic
270C3×D8—64no—
271C2×C3×C8—32no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—31no—
274C3×C4⋊C4—61no—
275C3×C4⋊C4—61no—
276C3×C4⋊C4C22×D311yescharacteristic
277C3×C4⋊C4C22×D311yescharacteristic
278C3×C22⋊C4—21no—
279C3×C22⋊C4—21no—
280C3×C22⋊C4—41no—
281C3×C22⋊C4—61no—
282C3×C22⋊C4—61no—
283C3×C42—21no—
284C3×C42—31no—
285C3×C42—31no—
286C3×C42—31no—
287C3×C42—61no—
288C3×C42—61no—
289C3×C42—61no—
290C3×C42C22×D311yescharacteristic
291C3×C42C22×D311yescharacteristic
292#217—21no—
293#217—62no—
294#217—62no—
295#216—64no—
296#215—64no—
297#214—64no—
298#214—64no—
299#214—64no—
300#214—124no—
301#213—24no—
302(C2×D3)⋊C4—21no—
303(C2×D3)⋊C4—62no—
304(C2×D3)⋊C4—62no—
305C4⋊Dic3—61no—
306C4⋊Dic3—61no—
307C4⋊Dic3—61no—
308C4⋊Dic3—61no—
309C4⋊Dic3—121no—
310C4⋊Dic3—121no—
311C4⋊Dic3C22×D311yescharacteristic
312Dic3⋊C4—21no—
313Dic3⋊C4—21no—
314C4×Dic3—21no—
315C4×Dic3—21no—
316C4×Dic3—21no—
317C4×Dic3#6711yescharacteristic
318C4×Dic3#6711yescharacteristic
319C4×Dic3C22×D311yescharacteristic
320C2×C3⋊C8—32no—
321C2×C3⋊C8—32no—
322C2×C3⋊C8—62no—
323C2×C3⋊C8—64no—
324C2×C3⋊C8C22×D312yes—
325Dic12—64no—
326D3×C8—64no—
327C22×C32—22no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32C22×D411yescharacteristic
331C2×C3×D3—21no—
332C2×C3×D3—21no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—42no—
336C2×C3×D3#12112yes—
337C32×C4—21no—
338C32×C4—41no—
339C32×C4#13512yescomplemented
340C32×C4C22×D411yescharacteristic
341C32×C4C2×#4111yescharacteristic
342C3⋊Dic3—42no—
343C3×Dic3—22no—
344C3×Dic3—21no—
345C3×Dic3—21no—
346C3×Dic3—41no—
347C3×Dic3#12112yes—
348C2×#41—31no—
349C2×#41—92no—
350#135—188no—
351C2×Q16—92no—
352C2×SD16—92no—
353C2×SD16—92no—
354C2×D8—32no—
355C22×C8—92no—
356C4⋊Q8—91no—
357#127—31no—
358#124—92no—
359#121—181no—
360#121—181no—
361C4×Q8—31no—
362C4×Q8—31no—
363C4×D4—31no—
364C4×D4—61no—
365C4×D4—61no—
366C4×D4—181no—
367C4×D4—181no—
368C4×D4D3211yescharacteristic
369#117—31no—
370#117—61no—
371C2×C42—31no—
372C2×C42—61no—
373C4⋊C8—31no—
374C4⋊C8—92no—
375C4⋊C8—91no—
376#103—92no—
377#103—92no—
378#102—32no—
379#102—92no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—31no—
383C23×C3—41no—
384C23×C3—62no—
385C22×D3—22no—
386C22×D3C2×#6711yescharacteristic
387C3×Q8—32no—
388C3×Q8—61no—
389C3×D4—21no—
390C3×D4—21no—
391C3×D4—22no—
392C3×D4—41no—
393C3×D4—64no—
394C3×D4—62no—
395C3×D4—62no—
396C3×D4—122no—
397C3×D4—122no—
398C3×D4C2×D1212yes—
399C3×D4D3×D412yes—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—31no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—31no—
409C2×C3×C4—31no—
410C2×C3×C4—41no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—64no—
414C2×C3×C4—61no—
415C2×C3×C4—62no—
416C2×C3×C4—61no—
417C2×C3×C4—82no—
418C2×C3×C4—121no—
419C2×C3×C4—122no—
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—24no—
427#67—124no—
428#67—124no—
429C2×Dic3—21no—
430C2×Dic3—24no—
431C2×Dic3—21no—
432C2×Dic3—42no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—122no—
436C2×Dic3—124no—
437C2×Dic3C2×#6711yescharacteristic
438C2×Dic3C2×#6711yescharacteristic
439C2×Dic3C2×#6711yescharacteristic
440D12—22no—
441D12—22no—
442D12—42no—
443D12—42no—
444C4×D3—22no—
445C4×D3—41no—
446C4×D3—124no—
447C4×D3C2×D1212yes—
448C4×D3#23512yes—
449Dic6—21no—
450Dic6—62no—
451Dic6—62no—
452Dic6—62no—
453Dic6—62no—
454Dic6—122no—
455Dic6—122no—
456Dic6C2×D1212yes—
457C3×C8—62no—
458C3⋊C8—22no—
459C3⋊C8—62no—
460C3⋊C8—62no—
461C3⋊C8—122no—
462C2×C32—42no—
463C2×C32C2×#12111yescharacteristic
464C2×C32C2×#13511yescharacteristic
465C2×C32#57511yescharacteristic
466C3×D3—22no—
467C3×D3—82no—
468#41—34no—
469#41—62no—
470#41—184no—
471#41—184no—
472C2×Q8—31no—
473C2×Q8—92no—
474C2×D4—32no—
475C2×D4—61no—
476C2×D4—61no—
477C2×D4—61no—
478C2×D4—182no—
479C2×D4C2×D3211yescharacteristic
480C22×C4—21no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—182no—
487Q16—184no—
488SD16—184no—
489SD16—184no—
490D8—64no—
491C2×C8—32no—
492C2×C8—92no—
493C2×C8—184no—
494C4⋊C4—31no—
495C4⋊C4—61no—
496C4⋊C4—61no—
497C4⋊C4—181no—
498C4⋊C4—181no—
499C4⋊C4C2×D3211yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—61no—
502C22⋊C4—61no—
503C22⋊C4—182no—
504C22⋊C4—182no—
505C42—31no—
506C42—31no—
507C42—31no—
508C42—61no—
509C42—61no—
510C42—61no—
511C42C2×D3211yescharacteristic
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—32no—
516C22×C3—42no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—61no—
522C22×C3—61no—
523C22×C3—81no—
524C22×C3—81no—
525C22×C3—122no—
526C22×C3—122no—
527C22×C3—122no—
528C22×C3C2×D3×D411yescharacteristic
529C22×C3C22×#6711yescharacteristic
530C2×D3—21no—
531C2×D3—21no—
532C2×D3—42no—
533C2×D3—42no—
534C2×D3—42no—
535C2×D3#93012yes—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—22no—
541C3×C4—32no—
542C3×C4—41no—
543C3×C4—41no—
544C3×C4—41no—
545C3×C4—61no—
546C3×C4—61no—
547C3×C4—62no—
548C3×C4—81no—
549C3×C4—121no—
550C3×C4#91212yescomplemented
551C3×C4#95012yescomplemented
552C3×C4C22×D1211yescharacteristic
553C3×C4C2×#23511yescharacteristic
554C3×C4C2×D3×D411yescharacteristic
555C3×C4D3×#4111yescharacteristic
556Dic3—22no—
557Dic3—21no—
558Dic3—21no—
559Dic3—41no—
560Dic3—122no—
561Dic3—122no—
562Dic3—242no—
563Dic3#93012yes—
564C32#303511yescharacteristic, complemented, Sylow
565C23—21no—
566C23—31no—
567C23—62no—
568Q8—32no—
569Q8—61no—
570Q8—182no—
571Q8—182no—
572D4—21no—
573D4—64no—
574D4—62no—
575D4—62no—
576D4—122no—
577D4—122no—
578D4—364no—
579D4D3×D1212yes—
580C2×C4—21no—
581C2×C4—31no—
582C2×C4—32no—
583C2×C4—32no—
584C2×C4—31no—
585C2×C4—31no—
586C2×C4—42no—
587C2×C4—64no—
588C2×C4—61no—
589C2×C4—62no—
590C2×C4—61no—
591C2×C4—121no—
592C2×C4—122no—
593C2×C4—182no—
594C2×C4—364no—
595C2×C4D3×#6711yescharacteristic
596C2×C4D3×#6711yescharacteristic
597C2×C4C22×D3211yescharacteristic
598C8—62no—
599C8—182no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—42no—
604C2×C3—42no—
605C2×C3—62no—
606C2×C3—82no—
607C2×C3—242no—
608C2×C3D3×#12111yescharacteristic
609C2×C3C2×#91211yescharacteristic
610C2×C3#577311yescharacteristic
611C2×C3C2×#93011yescharacteristic
612C2×C3C2×#95011yescharacteristic
613C2×C3#582211yescharacteristic
614D3—22no—
615D3—82no—
616C22—22no—
617C22—32no—
618C22—41no—
619C22—41no—
620C22—61no—
621C22—61no—
622C22—122no—
623C22—122no—
624C22—122no—
625C22C2×D3×#6711yescharacteristic
626C4—21no—
627C4—32no—
628C4—41no—
629C4—61no—
630C4—61no—
631C4—62no—
632C4—121no—
633C4—362no—
634C4#6393312yescomplemented
635C4C2×D3×D1211yescharacteristic
636C4D3×#23511yescharacteristic
637C3—21no—
638C3#8033111yescharacteristic, complemented
639C3#8252511yescharacteristic, complemented
640C2—42no—
641C2—62no—
642C2—242no—
643C2D3×#93011yescharacteristic
644C2C2×#6393311yescharacteristic
645C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×C4×#237C2semidirect
2. C2×#63933C2semidirect
3. #10593897C2semidirect
4. #10592718C2semidirect
5. C3×#5015C2semidirect
6. #10591468C2semidirect
7. #10590608C2semidirect
8. #10590532C2semidirect
9. #10590385C2semidirect
10. #10590364C2semidirect
11. D3×C4⋊(C3⋊C8)C2semidirect
50. C4×#237D3semidirect
62. #5015D3semidirect
76. C3×#237D4semidirect
256. #237D12semidirect
339. C32×C4#135semidirect
550. C3×C4#912semidirect
551. C3×C4#950semidirect
564. C32#3035semidirect
634. C4#63933semidirect
638. C3#80331semidirect
639. C3#82525semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2372
C2×#639332
#105938972
#105927182
C3×#50152
#105914682
#105906082
#105905322
#105903852
#105903642
D3×C4⋊(C3⋊C8)2
#825253
#803313