Finite Group Databasebeta

← #11865811

Subgroups — #11865811

Order 1152.

1046 conjugacy classes of subgroups.

The subgroup lattice has 643 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#239C211yesmaximal, characteristic, complemented
2C2×#63947C212yesmaximal, complemented
3#10593897C211yesmaximal, characteristic, complemented
4#10592730C211yesmaximal, characteristic, complemented
5C3×#5027C211yesmaximal, characteristic, complemented
6#10591604C212yesmaximal, complemented
7#10590608C212yesmaximal, complemented
8#10590530C212yesmaximal, complemented
9#10590365C211yesmaximal, characteristic, complemented
10#10590347C211yesmaximal, characteristic, complemented
11D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#82525—31nomaximal
13#80382—31nomaximal
14C2×C3×#239C2211yescharacteristic
15C2×#3795C2212yes—
16C32×C4×Q8C2211yescharacteristic
17C2×#3756C2212yes—
18#64078C2211yescharacteristic
19C3×Q8×Dic3C2211yescharacteristic
20C2×C3×#215C2212yes—
21C3×#893—21no—
22C3×#893C2211yescharacteristic
23C3×#892—21no—
24C3×#892C2211yescharacteristic
25C3×#874C2211yescharacteristic
26C3×C4×D12—21no—
27C3×C4×D12C2211yescharacteristic
28C3×C42×D3—21no—
29C3×C42×D3C2211yescharacteristic
30#63947—28no—
31#63908—21no—
32#63908—21no—
33Dic3×D12—21no—
34Dic3×D12—21no—
35#63860C2212yes—
36C2×#3716C2212yes—
37C2×#3713C2212yes—
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×#916—32no—
49#5716—31no—
50C4×#239D311yescharacteristic, complemented
51#5477—31no—
52C3×#460—31no—
53#5166—32no—
54#5072—31no—
55#5031—31no—
56#5031—31no—
57#5031—61no—
58#5028—32no—
59#5027D311yescharacteristic, complemented
60#5019—31no—
61#5016—32no—
62#5015—31no—
63#5002—32no—
64C2×C4⋊(C3⋊C8)—31no—
65#4841—31no—
66D3×C4⋊C8—31no—
67#4787—32no—
68#4772—32no—
69C2×C32×Q8C2311yescharacteristic
70C2×#634C2312yes—
71C3×#239—22no—
72C3×#239D414yescomplemented
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3D411yescharacteristic
82C2×C3×C4×D3D411yescharacteristic
83C2×C3×C4×D3C2311yescharacteristic
84C2×#625—22no—
85C2×D3×Dic3—22no—
86#3795—24no—
87#3795—24no—
88C32×C4⋊C4—21no—
89C32×C4⋊C4C2311yescharacteristic
90C32×C42—21no—
91C32×C42C2311yescharacteristic
92#3756—24no—
93C4⋊(C3⋊Dic3)—21no—
94C4⋊(C3⋊Dic3)—21no—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#215—24no—
97C3×(C2×D3)⋊C4—21no—
98C3×(C2×D3)⋊C4—21no—
99C3×(C2×D3)⋊C4—21no—
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3C2311yescharacteristic
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#3716—24no—
111#3713—24no—
112D3×C3⋊C8—24no—
113#3035—91noSylow
114C2×C3×#41—31no—
115C2×#239C2×D311yescharacteristic
116C2×#237—32no—
117C2×#235—32no—
118C2×C3×SD16—32no—
119C3×#127—31no—
120C3×C4×Q8—21no—
121C3×C4×Q8—31no—
122C3×C4×Q8C2×D311yescharacteristic
123C3×C4×Q8C2×D311yescharacteristic
124C3×C4×D4—31no—
125C3×C4×D4—31no—
126C3×C4×D4—61no—
127C3×C4×D4—61no—
128C3×#117—31no—
129C3×#117—61no—
130C2×C3×C42—31no—
131C2×C3×C42—61no—
132#950—68no—
133Q8×Dic3C2×D311yescharacteristic
134C2×#216—32no—
135C2×#216—32no—
136C2×#216—62no—
137C2×#215C2×D312yes—
138#938—61no—
139#938—61no—
140#936—32no—
141D4×Dic3—61no—
142D4×Dic3—61no—
143C2×#214—32no—
144C2×#213—32no—
145C2×#213—32no—
146#930—61no—
147#930—61no—
148C22×C3⋊C8—32no—
149#916—68no—
150C2×#204—32no—
151C2×D3×C8—32no—
152#893—21no—
153#893C2×D311yescharacteristic
154#892—21no—
155#892C2×D311yescharacteristic
156#875—32no—
157#874C2×D311yescharacteristic
158C4×D12—21no—
159C4×D12—61no—
160C4×D12—61no—
161C4×D12C2×D311yescharacteristic
162C42×D3—21no—
163C42×D3C2×D311yescharacteristic
164#869—31no—
165#869—31no—
166#869—61no—
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
183C22×C3×D3—21no—
184C22×C3×D3—22no—
185C22×C3×D3C2×D411yescharacteristic
186C32×Q8—21no—
187C32×Q8C2×D412yes—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193C2×C3⋊Dic3—22no—
194#634—22no—
195#634—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C3×D12—24no—
201C3×D12—22no—
202C3×D12—21no—
203C3×D12—22no—
204C3×D12—42no—
205C3×D12—42no—
206C3×D12C2×D412yes—
207C3×C4×D3—22no—
208C3×C4×D3—24no—
209C3×C4×D3—41no—
210C3×C4×D3—42no—
211C3×C4×D3—42no—
212C3×C4×D3C2×D412yes—
213C3×C4×D3#4112yes—
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—31no—
226#459—91no—
227C2×C4⋊C8—91no—
228#416—92no—
229C3×#41—34no—
230C3×#41—62no—
231C2×C3×Q8—21no—
232C2×C3×Q8C22×D311yescharacteristic
233C2×C3×Q8C22×D311yescharacteristic
234C2×C3×D4—31no—
235C2×C3×D4—32no—
236C2×C3×D4—61no—
237C2×C3×D4—61no—
238C2×C3×D4—61no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—61no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C2×#67—62no—
246C2×#67—62no—
247C22×Dic3—62no—
248#239—22no—
249#239D1214yescomplemented
250#237—64no—
251#237—64no—
252#235—64no—
253#235—64no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—21no—
257C2×D12C22×D312yes—
258C2×D12C22×D311yescharacteristic
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
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—
269C3×SD16—64no—
270C2×C3×C8—32no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—31no—
275C3×C4⋊C4—41no—
276C3×C4⋊C4—61no—
277C3×C4⋊C4C22×D311yescharacteristic
278C3×C4⋊C4C22×D311yescharacteristic
279C3×C22⋊C4—61no—
280C3×C22⋊C4—61no—
281C3×C22⋊C4—61no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—31no—
286C3×C42—31no—
287C3×C42—31no—
288C3×C42—41no—
289C3×C42—61no—
290C3×C42—61no—
291C3×C42C22×D311yescharacteristic
292C3×C42C22×D311yescharacteristic
293#217—62no—
294#217—62no—
295#216—64no—
296#216—64no—
297#216—124no—
298#215—24no—
299#214—64no—
300#213—64no—
301#213—64no—
302(C2×D3)⋊C4—21no—
303(C2×D3)⋊C4—21no—
304(C2×D3)⋊C4—21no—
305(C2×D3)⋊C4—62no—
306(C2×D3)⋊C4—62no—
307C4⋊Dic3—21no—
308C4⋊Dic3—61no—
309C4⋊Dic3—61no—
310C4⋊Dic3—61no—
311C4⋊Dic3—61no—
312C4⋊Dic3—121no—
313C4⋊Dic3—121no—
314C4⋊Dic3C22×D311yescharacteristic
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—
325#204—64no—
326D3×C8—64no—
327C22×C32C22×D411yescharacteristic
328C2×C3×D3—21no—
329C2×C3×D3—21no—
330C2×C3×D3—22no—
331C2×C3×D3—41no—
332C2×C3×D3—41no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—42no—
336C2×C3×D3#12112yes—
337C32×C4—22no—
338C32×C4—21no—
339C32×C4—41no—
340C32×C4#13512yescomplemented
341C32×C4C22×D411yescharacteristic
342C32×C4C2×#4111yescharacteristic
343C3⋊Dic3—42no—
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—32no—
353C2×SD16—92no—
354C2×D8—92no—
355C22×C8—92no—
356C4⋊Q8—91no—
357#127—31no—
358#124—92no—
359#121—181no—
360#121—181no—
361C4×Q8—31no—
362C4×Q8D3211yescharacteristic
363C4×D4—31no—
364C4×D4—31no—
365C4×D4—61no—
366C4×D4—61no—
367C4×D4—181no—
368C4×D4—181no—
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—31no—
381C23×C3—61no—
382C23×C3—62no—
383C22×D3—21no—
384C22×D3—22no—
385C22×D3C2×#6711yescharacteristic
386C3×Q8—21no—
387C3×Q8—21no—
388C3×Q8—22no—
389C3×Q8—41no—
390C3×Q8C2×D1212yes—
391C3×Q8D3×D412yes—
392C3×D4—32no—
393C3×D4—64no—
394C3×D4—62no—
395C3×D4—62no—
396C3×D4—61no—
397C3×D4—122no—
398C3×D4—122no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—31no—
407C2×C3×C4—32no—
408C2×C3×C4—32no—
409C2×C3×C4—31no—
410C2×C3×C4—31no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—64no—
414C2×C3×C4—62no—
415C2×C3×C4—61no—
416C2×C3×C4—121no—
417C2×C3×C4—122no—
418C2×C3×C4—122no—
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4C2×#6711yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C23×D311yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425#67—124no—
426#67—124no—
427C2×Dic3—21no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—122no—
431C2×Dic3—124no—
432C2×Dic3C2×#6711yescharacteristic
433C2×Dic3C2×#6711yescharacteristic
434C2×Dic3C2×#6711yescharacteristic
435D12—24no—
436D12—21no—
437D12—22no—
438D12—22no—
439D12—42no—
440D12—42no—
441D12C2×D1212yes—
442C4×D3—22no—
443C4×D3—24no—
444C4×D3—41no—
445C4×D3—42no—
446C4×D3—42no—
447C4×D3—124no—
448C4×D3C2×D1212yes—
449C4×D3#23512yes—
450Dic6—62no—
451Dic6—62no—
452Dic6—62no—
453Dic6—62no—
454Dic6—122no—
455Dic6—122no—
456C3×C8—62no—
457C3⋊C8—22no—
458C3⋊C8—62no—
459C3⋊C8—62no—
460C3⋊C8—122no—
461C2×C32C2×#12111yescharacteristic
462C2×C32C2×#13511yescharacteristic
463C2×C32#57511yescharacteristic
464C3×D3—22no—
465C3×D3—42no—
466C3×D3—82no—
467#41—34no—
468#41—62no—
469#41—184no—
470#41—184no—
471C2×Q8—92no—
472C2×Q8C2×D3211yescharacteristic
473C2×D4—31no—
474C2×D4—32no—
475C2×D4—61no—
476C2×D4—61no—
477C2×D4—61no—
478C2×D4—182no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—182no—
486Q16—184no—
487SD16—64no—
488SD16—184no—
489D8—184no—
490C2×C8—32no—
491C2×C8—92no—
492C2×C8—184no—
493C4⋊C4—21no—
494C4⋊C4—31no—
495C4⋊C4—61no—
496C4⋊C4—181no—
497C4⋊C4—181no—
498C4⋊C4C2×D3211yescharacteristic
499C22⋊C4—61no—
500C22⋊C4—61no—
501C22⋊C4—61no—
502C22⋊C4—182no—
503C22⋊C4—182no—
504C42—21no—
505C42—31no—
506C42—31no—
507C42—31no—
508C42—61no—
509C42—61no—
510C42C2×D3211yescharacteristic
511C22×C3—21no—
512C22×C3—32no—
513C22×C3—61no—
514C22×C3—61no—
515C22×C3—62no—
516C22×C3—121no—
517C22×C3—121no—
518C22×C3—122no—
519C22×C3—122no—
520C22×C3—122no—
521C22×C3C2×D3×D411yescharacteristic
522C22×C3C22×#6711yescharacteristic
523C2×D3—21no—
524C2×D3—21no—
525C2×D3—22no—
526C2×D3—41no—
527C2×D3—41no—
528C2×D3—42no—
529C2×D3—42no—
530C2×D3—42no—
531C2×D3#93012yes—
532C3×C4—21no—
533C3×C4—22no—
534C3×C4—21no—
535C3×C4—22no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—22no—
539C3×C4—32no—
540C3×C4—41no—
541C3×C4—42no—
542C3×C4—41no—
543C3×C4—41no—
544C3×C4—61no—
545C3×C4—61no—
546C3×C4—81no—
547C3×C4—121no—
548C3×C4#91612yescomplemented
549C3×C4#95012yescomplemented
550C3×C4C22×D1211yescharacteristic
551C3×C4C2×#23511yescharacteristic
552C3×C4C2×D3×D411yescharacteristic
553C3×C4D3×#4111yescharacteristic
554Dic3—21no—
555Dic3—21no—
556Dic3—41no—
557Dic3—122no—
558Dic3—122no—
559Dic3—242no—
560Dic3#93012yes—
561C32#303511yescharacteristic, complemented, Sylow
562C23—31no—
563C23—61no—
564C23—62no—
565Q8—21no—
566Q8—182no—
567Q8—182no—
568Q8D3×D1212yes—
569D4—32no—
570D4—64no—
571D4—62no—
572D4—61no—
573D4—62no—
574D4—122no—
575D4—122no—
576D4—364no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—31no—
580C2×C4—32no—
581C2×C4—32no—
582C2×C4—31no—
583C2×C4—31no—
584C2×C4—64no—
585C2×C4—62no—
586C2×C4—61no—
587C2×C4—121no—
588C2×C4—122no—
589C2×C4—122no—
590C2×C4—182no—
591C2×C4—364no—
592C2×C4D3×#6711yescharacteristic
593C2×C4D3×#6711yescharacteristic
594C2×C4C22×D3211yescharacteristic
595C8—62no—
596C8—182no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—62no—
601C2×C3—122no—
602C2×C3—242no—
603C2×C3D3×#12111yescharacteristic
604C2×C3C2×#91611yescharacteristic
605C2×C3#577311yescharacteristic
606C2×C3C2×#93011yescharacteristic
607C2×C3C2×#95011yescharacteristic
608C2×C3#582211yescharacteristic
609D3—22no—
610D3—42no—
611D3—82no—
612C22—32no—
613C22—61no—
614C22—61no—
615C22—62no—
616C22—121no—
617C22—121no—
618C22—122no—
619C22—122no—
620C22—122no—
621C22C2×D3×#6711yescharacteristic
622C4—21no—
623C4—22no—
624C4—32no—
625C4—41no—
626C4—61no—
627C4—61no—
628C4—121no—
629C4—362no—
630C4#6394712yescomplemented
631C4C2×D3×D1211yescharacteristic
632C4D3×#23511yescharacteristic
633C3—21no—
634C3#8038211yescharacteristic, complemented
635C3#8252511yescharacteristic, complemented
636C2—62no—
637C2—122no—
638C2—242no—
639C2D3×#93011yescharacteristic
640C2C2×#6394711yescharacteristic
641C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×C4×#239C2semidirect
2. C2×#63947C2semidirect
3. #10593897C2semidirect
4. #10592730C2semidirect
5. C3×#5027C2semidirect
6. #10591604C2semidirect
7. #10590608C2semidirect
8. #10590530C2semidirect
9. #10590365C2semidirect
10. #10590347C2semidirect
11. D3×C4⋊(C3⋊C8)C2semidirect
50. C4×#239D3semidirect
59. #5027D3semidirect
72. C3×#239D4semidirect
249. #239D12semidirect
340. C32×C4#135semidirect
548. C3×C4#916semidirect
549. C3×C4#950semidirect
561. C32#3035semidirect
630. C4#63947semidirect
634. C3#80382semidirect
635. C3#82525semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2392
C2×#639472
#105938972
#105927302
C3×#50272
#105916042
#105906082
#105905302
#105903652
#105903472
D3×C4⋊(C3⋊C8)2
#825253
#803823