Finite Group Databasebeta

← #11864148

Subgroups — #11864148

Order 1152.

1761 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2C2×#64117C211yesmaximal, characteristic, complemented
3C2×#63909C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5133C211yesmaximal, characteristic, complemented
6C3×#5126C211yesmaximal, characteristic, complemented
7#10591106C211yesmaximal, characteristic, complemented
8#10590968C212yesmaximal, complemented
9#10590967C212yesmaximal, complemented
10#10590951C212yesmaximal, complemented
11#10590947C212yesmaximal, complemented
12#78884—31nomaximal
13#78639—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
16C2×C3×#235C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×D3×#67—21no—
19C22×#626—21no—
20C2×#3804—21no—
21D3×#235—24no—
22D3×#235—24no—
23C2×D3×D12C2211yescharacteristic, complemented
24C2×C4×D32—21no—
25C2×#3799C2211yescharacteristic, complemented
26C2×#3798—21no—
27C2×#3795C2211yescharacteristic, complemented
28C2×D3×Dic6C2211yescharacteristic, complemented
29C2×C32×M16C2211yescharacteristic, complemented
30#64117—24no—
31C2×#3745C2212yescomplemented
32C2×#3744C2212yescomplemented
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C2×C3×#208C2211yescharacteristic, complemented
35C2×#3722—21no—
36#63909—21no—
37#63909—21no—
38#63909C2212yes—
39#63909C2212yescomplemented
40C2×#3717C2212yescomplemented
41#63825—24no—
42C2×#3714C2212yescomplemented
43C3×#821C2212yescomplemented
44C3×(C2×D3)⋊C8C2212yescomplemented
45C3×(C2×D3)⋊C8C2212yescomplemented
46C3×#816C2212yescomplemented
47#63567C2212yescomplemented
48#63564C2212yescomplemented
49C2×D3×#41—31no—
50C22×#235—31no—
51C2×#949—31no—
52C2×#930—31no—
53C2×#908—31no—
54C2×#908—31no—
55C2×#908—31no—
56C2×#908—61no—
57C2×#895—31no—
58C3×#417—31no—
59C3×#407—31no—
60#5133—31no—
61#5133D311yescharacteristic, complemented
62#5126D311yescharacteristic, complemented
63#4966—31no—
64#4810—32no—
65#4806—32no—
66#4781—32no—
67#4773—32no—
68#4738—32no—
69#4734—32no—
70#4734—32no—
71#4732—32no—
72C23×C3⋊D3—21no—
73C23×C3×D3D411yescharacteristic
74C22×D32—21no—
75C22×C32×C4C2311yescharacteristic
76C2×#638—21no—
77#3828—22no—
78#3828D414yescomplemented
79C2×C4⋊(C3⋊D3)—22no—
80C2×C4⋊(C3⋊D3)—22no—
81C2×C4⋊(C3⋊D3)—21no—
82C2×C4⋊(C3⋊D3)C2312yes—
83C2×C4⋊(C3⋊D3)C2311yescharacteristic
84C2×C4×C3⋊D3—21no—
85C2×#634C2311yescharacteristic
86C2×C3×#67—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3D411yescharacteristic
89C3×#235—22no—
90C3×#235D414yescomplemented
91C2×C3×D12C2311yescharacteristic
92C2×C3×C4×D3—21no—
93C2×C3×C4×D3—22no—
94C2×C3×C4×D3—22no—
95C2×C3×C4×D3D411yescharacteristic
96C2×C3×C4×D3D411yescharacteristic
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100D3×#67—28no—
101C2×#627—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#626—22no—
105C2×#626—22no—
106C2×#626—44no—
107C2×#625—21no—
108C2×#624—21no—
109#3804—28no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112D3×D12—22no—
113D3×D12—22no—
114C4×D32—28no—
115#3799—22no—
116#3799—22no—
117#3798—28no—
118#3795—22no—
119#3795—22no—
120D3×Dic6—22no—
121D3×Dic6—22no—
122C32×M16—22no—
123C2×C32×C8C2312yes—
124#3745—24no—
125#3744—24no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2312yes—
128C3×#208—22no—
129C2×C3×C3⋊C8C2312yes—
130#3722—22no—
131#3722—22no—
132#3717—24no—
133#3714—24no—
134#3006—91noSylow
135C2×C3×#41—31no—
136C23×C3×C4—31no—
137C22×#67—61no—
138C22×#67—61no—
139D3×#41—64no—
140D3×#41—64no—
141C2×#239—31no—
142C2×D3×Q8—31no—
143C2×#237—31no—
144C2×#237—61no—
145C2×D3×D4—31no—
146C2×D3×D4—61no—
147C2×#235—31no—
148C2×#235—31no—
149C2×#235—31no—
150C2×#235—31no—
151C2×#235—61no—
152C2×#235—61no—
153C2×#235—64no—
154C2×#235—61no—
155C2×#235—64no—
156C2×#235—61no—
157C2×#235C2×D311yescharacteristic
158C22×D12—31no—
159C22×D12—31no—
160C22×D12—31no—
161C22×D12—61no—
162C22×D12—61no—
163C22×C4×D3—61no—
164C22×C4×D3—61no—
165C22×C4×D3C2×D311yescharacteristic
166C22×Dic6—31no—
167C2×C3×M16—21no—
168C2×C3×M16—31no—
169C2×C3×M16C2×D311yescharacteristic, complemented
170C2×C3×M16C2×D311yescharacteristic, complemented
171C2×C3×C4⋊C4—31no—
172#949—64no—
173C2×#215—32no—
174C2×#213—32no—
175#930—32no—
176#930—32no—
177#930—61no—
178#930—61no—
179C2×(C2×D3)⋊C4—61no—
180C2×(C2×D3)⋊C4—61no—
181C2×C4⋊Dic3C2×D311yescharacteristic, complemented
182C2×#208C2×D311yescharacteristic, complemented
183#908—64no—
184#908—64no—
185#908—68no—
186#908—64no—
187C2×D24—32no—
188C2×D24—32no—
189C2×D24—32no—
190C2×D24—62no—
191C2×#204—32no—
192C2×#204—32no—
193C2×#204—32no—
194C2×#204—62no—
195#895—32no—
196#895—32no—
197#895—61no—
198#895—61no—
199C3×#103—32no—
200C3×#102—32no—
201C3×C22⋊C8—32no—
202C3×C22⋊C8—32no—
203#821—32no—
204#821C2×D312yescomplemented
205(C2×D3)⋊C8C2×D312yescomplemented
206(C2×D3)⋊C8C2×D312yescomplemented
207#816—32no—
208#816C2×D312yescomplemented
209#810—32no—
210#809—32no—
211C23×C32C2×D411yescharacteristic
212C22×C3⋊D3—21no—
213C22×C3⋊D3—22no—
214C22×C3⋊D3—42no—
215C22×C3⋊D3—42no—
216C22×C3⋊D3—42no—
217C22×C3×D3—22no—
218C22×C3×D3—21no—
219C22×C3×D3—22no—
220C22×C3×D3—41no—
221C22×C3×D3C2×D411yescharacteristic
222C22×C3×D3C2×D411yescharacteristic
223C2×D32—24no—
224C2×D32—42no—
225C2×D32—42no—
226C2×C32×C4C2×D411yescharacteristic
227C2×C32×C4C2×D412yes—
228C2×C32×C4C2×D412yes—
229C2×C32×C4C2411yescharacteristic
230#638—24no—
231C2×C3⋊Dic3—21no—
232C4⋊(C3⋊D3)—22no—
233C4⋊(C3⋊D3)—21no—
234C4⋊(C3⋊D3)—22no—
235C4⋊(C3⋊D3)—42no—
236C4⋊(C3⋊D3)C2×D412yescomplemented
237C4×C3⋊D3—24no—
238#634—21no—
239#634C2×D412yescomplemented
240C3×#67—24no—
241C2×C3×Dic3—22no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—22no—
244C2×C3×Dic3—42no—
245C2×C3×Dic3C2×D411yescharacteristic
246C2×C3×Dic3C2×D411yescharacteristic
247C3×D12—21no—
248C3×D12C2×D412yescomplemented
249C3×C4×D3—22no—
250C3×C4×D3—24no—
251C3×C4×D3—22no—
252C3×C4×D3—21no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×C4×D3—21no—
256C3×Dic6—21no—
257C3×Dic6C2×D412yescomplemented
258#627—24no—
259#626—24no—
260#626—24no—
261#626—44no—
262#626—44no—
263#625—24no—
264#624—24no—
265D3×Dic3—24no—
266D3×Dic3—24no—
267C32×C8—22no—
268C3×C3⋊C8—22no—
269C22×#41—91no—
270C2×AGL(1,ℤ/8)—91no—
271C2×AGL(1,ℤ/8)—91no—
272C2×#121—91no—
273#449—92no—
274#449—92no—
275#448—92no—
276#447—92no—
277#417—31no—
278#417—91no—
279#407—31no—
280C24×C3—31no—
281C23×D3—61no—
282C23×D3—61no—
283C23×D3—61no—
284C23×D3—61no—
285C23×D3—121no—
286C23×D3D1211yescharacteristic
287C3×#41—34no—
288C3×#41—62no—
289C2×C3×Q8—31no—
290C2×C3×D4—31no—
291C2×C3×D4—61no—
292C22×C3×C4—21no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—61no—
299C22×C3×C4—62no—
300C22×C3×C4—62no—
301C22×C3×C4—61no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—21no—
305C2×#67—61no—
306C2×#67—62no—
307C2×#67—62no—
308C2×#67—68no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—121no—
315C2×#67—124no—
316C22×Dic3—21no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3D1211yescharacteristic
320#239—62no—
321#239—62no—
322D3×Q8—62no—
323D3×Q8—62no—
324#237—62no—
325#237—62no—
326#237—68no—
327D3×D4—62no—
328D3×D4—62no—
329D3×D4—68no—
330#235—22no—
331#235—34no—
332#235—34no—
333#235—64no—
334#235—62no—
335#235—62no—
336#235—68no—
337#235—68no—
338#235—68no—
339#235—62no—
340#235—62no—
341#235—62no—
342#235—62no—
343#235—122no—
344#235D1214yescomplemented
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—32no—
348C2×D12—32no—
349C2×D12—62no—
350C2×D12—61no—
351C2×D12—62no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—62no—
355C2×D12—64no—
356C2×D12—62no—
357C2×D12—62no—
358C2×D12—62no—
359C2×D12—62no—
360C2×D12—62no—
361C2×D12—62no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—122no—
365C2×D12—121no—
366C2×D12—124no—
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—21no—
369C2×C4×D3—22no—
370C2×C4×D3—22no—
371C2×C4×D3—68no—
372C2×C4×D3—68no—
373C2×C4×D3—61no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—121no—
380C2×C4×D3D1211yescharacteristic
381C2×C4×D3D1211yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×C4×D3C22×D311yescharacteristic
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6—62no—
388C2×Dic6—61no—
389C2×Dic6—61no—
390C2×Dic6—62no—
391C2×Dic6C22×D311yescharacteristic
392C3×M16—24no—
393C3×M16—22no—
394C3×M16—22no—
395C3×M16—62no—
396C2×C3×C8—22no—
397C2×C3×C8—32no—
398C2×C3×C8C22×D312yes—
399C2×C3×C8C22×D312yes—
400C3×C4⋊C4—32no—
401C3×C4⋊C4—61no—
402#215—64no—
403#213—64no—
404(C2×D3)⋊C4—62no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408C4⋊Dic3—21no—
409C4⋊Dic3C22×D312yes—
410#208—22no—
411C2×C3⋊C8C22×D312yes—
412D24—64no—
413D24—64no—
414D24—68no—
415D24—64no—
416#204—64no—
417#204—64no—
418#204—68no—
419#204—64no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32#12012yes—
423C22×C32C22×D411yescharacteristic
424C2×C3⋊D3—22no—
425C2×C3⋊D3—42no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—42no—
429C2×C3⋊D3—42no—
430C2×C3⋊D3—84no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C2×C3×D3—22no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—44no—
438C2×C3×D3—41no—
439C2×C3×D3—41no—
440C2×C3×D3AGL(1,ℤ/8)12yescomplemented
441D32—48no—
442C32×C4#12012yes—
443C32×C4C22×D411yescharacteristic
444C32×C4C22×D411yescharacteristic
445C3⋊Dic3—22no—
446C3×Dic3—21no—
447C3×Dic3—22no—
448C3×Dic3—21no—
449C3×Dic3—42no—
450C2×#41—31no—
451C2×#41—91no—
452C2×#41—91no—
453C2×#41—91no—
454C2×#41—181no—
455C2×#41—181no—
456C2×#41—184no—
457C2×#41—184no—
458C22×Q8—91no—
459C22×D4—91no—
460C22×D4—91no—
461C22×D4—181no—
462C22×D4—181no—
463C23×C4—31no—
464C23×C4—181no—
465AGL(1,ℤ/8)—184no—
466AGL(1,ℤ/8)—184no—
467C2×SD16—92no—
468C2×SD16—92no—
469C2×D8—92no—
470C2×D8—92no—
471C2×M16—31no—
472C2×M16D3211yescharacteristic, complemented
473#121—92no—
474#121—92no—
475#121—181no—
476#121—181no—
477C2×C4⋊C4—31no—
478C2×C22⋊C4—181no—
479#103—32no—
480#103—92no—
481#102—32no—
482#102—92no—
483C22⋊C8—32no—
484C22⋊C8—32no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—31no—
488C23×C3—62no—
489C23×C3—62no—
490C23×C3—61no—
491C23×C3—121no—
492C23×C3C2×D1211yescharacteristic
493C23×C3D3×D411yescharacteristic
494C22×D3—22no—
495C22×D3—21no—
496C22×D3—22no—
497C22×D3—41no—
498C22×D3—64no—
499C22×D3—64no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—62no—
503C22×D3—62no—
504C22×D3—121no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—124no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—122no—
517C22×D3—242no—
518C22×D3—242no—
519C22×D3C2×D1211yescharacteristic
520C22×D3C2×D1211yescharacteristic
521C3×Q8—32no—
522C3×Q8—61no—
523C3×D4—32no—
524C3×D4—64no—
525C3×D4—61no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—62no—
533C2×C3×C4—61no—
534C2×C3×C4—62no—
535C2×C3×C4—64no—
536C2×C3×C4—62no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—62no—
542C2×C3×C4—122no—
543C2×C3×C4C2×D1211yescharacteristic
544C2×C3×C4C2×D1212yes—
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4D3×D412yes—
547C2×C3×C4D3×D412yes—
548C2×C3×C4D3×D412yes—
549C2×C3×C4C23×D311yescharacteristic
550C2×C3×C4C23×D311yescharacteristic
551#67—24no—
552#67—64no—
553#67—64no—
554#67—64no—
555#67—64no—
556#67—64no—
557#67—64no—
558#67—124no—
559#67—124no—
560#67—124no—
561C2×Dic3—22no—
562C2×Dic3—21no—
563C2×Dic3—22no—
564C2×Dic3—42no—
565C2×Dic3—64no—
566C2×Dic3—64no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—121no—
570C2×Dic3C2×D1211yescharacteristic
571C2×Dic3C2×D1211yescharacteristic
572D12—21no—
573D12—32no—
574D12—32no—
575D12—62no—
576D12—64no—
577D12—64no—
578D12—64no—
579D12—61no—
580D12—62no—
581D12—61no—
582D12—62no—
583D12—62no—
584D12—62no—
585D12—122no—
586D12—121no—
587D12—124no—
588D12—124no—
589D12—124no—
590D12—122no—
591D12—122no—
592D12C2×D1212yescomplemented
593C4×D3—22no—
594C4×D3—22no—
595C4×D3—24no—
596C4×D3—21no—
597C4×D3—21no—
598C4×D3—21no—
599C4×D3—21no—
600C4×D3—64no—
601C4×D3—64no—
602C4×D3—64no—
603C4×D3—64no—
604C4×D3—64no—
605C4×D3—64no—
606C4×D3—124no—
607Dic6—21no—
608Dic6—32no—
609Dic6—32no—
610Dic6—62no—
611Dic6—64no—
612Dic6—64no—
613Dic6—61no—
614Dic6—61no—
615Dic6—121no—
616Dic6C2×D1212yescomplemented
617C3×C8—24no—
618C3×C8—22no—
619C3×C8—22no—
620C3×C8—62no—
621C3⋊C8—22no—
622C2×C32—22no—
623C2×C32C2×#12011yescharacteristic
624C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
625C2×C32#57511yescharacteristic
626C3⋊D3—42no—
627C3⋊D3—82no—
628C3×D3—22no—
629C3×D3—42no—
630C3×D3—41no—
631C24—31no—
632C24—181no—
633C24—181no—
634#41—34no—
635#41—62no—
636#41—94no—
637#41—188no—
638#41—182no—
639#41—182no—
640#41—188no—
641#41—182no—
642#41—182no—
643#41—182no—
644C2×Q8—31no—
645C2×Q8—91no—
646C2×Q8—181no—
647C2×Q8—182no—
648C2×Q8—182no—
649C2×D4—31no—
650C2×D4—61no—
651C2×D4—91no—
652C2×D4—92no—
653C2×D4—181no—
654C2×D4—182no—
655C2×D4—182no—
656C2×D4—181no—
657C2×D4—182no—
658C2×D4—182no—
659C2×D4—188no—
660C2×D4—181no—
661C2×D4—181no—
662C2×D4—182no—
663C2×D4—181no—
664C2×D4—182no—
665C2×D4—364no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—62no—
672C22×C4—61no—
673C22×C4—62no—
674C22×C4—61no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—188no—
678C22×C4—181no—
679C22×C4—181no—
680C22×C4C2×D3211yescharacteristic
681SD16—184no—
682SD16—184no—
683D8—184no—
684D8—184no—
685M16—22no—
686M16—62no—
687C2×C8—32no—
688C2×C8C2×D3212yes—
689C4⋊C4—32no—
690C4⋊C4—61no—
691C22⋊C4—182no—
692C22⋊C4—182no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—22no—
699C22×C3—32no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—62no—
705C22×C3—61no—
706C22×C3—61no—
707C22×C3—61no—
708C22×C3—124no—
709C22×C3—121no—
710C22×C3—121no—
711C22×C3#88212yes—
712C22×C3#88212yes—
713C22×C3C22×D1211yescharacteristic
714C22×C3C2×D3×D411yescharacteristic
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—21no—
718C2×D3—22no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—44no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3—62no—
725C2×D3—62no—
726C2×D3—122no—
727C2×D3—128no—
728C2×D3—128no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—121no—
732C2×D3—121no—
733C2×D3—124no—
734C2×D3—122no—
735C2×D3—122no—
736C2×D3—122no—
737C2×D3—122no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3—242no—
741C2×D3—242no—
742C2×D3—241no—
743C2×D3—241no—
744C2×D3—244no—
745C2×D3—244no—
746C2×D3—248no—
747C2×D3#90812yescomplemented
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—22no—
751C3×C4—61no—
752C3×C4—62no—
753C3×C4—61no—
754C3×C4—122no—
755C3×C4#88212yes—
756C3×C4#88212yes—
757C3×C4C22×D1211yescharacteristic
758C3×C4C2×D3×D411yescharacteristic
759C3×C4C2×D3×D411yescharacteristic
760C3×C4C2×D3×D411yescharacteristic
761Dic3—22no—
762Dic3—21no—
763Dic3—21no—
764Dic3—42no—
765Dic3—62no—
766Dic3—62no—
767Dic3—122no—
768C32#300611yescharacteristic, complemented, Sylow
769C23—31no—
770C23—31no—
771C23—62no—
772C23—61no—
773C23—62no—
774C23—121no—
775C23—184no—
776C23—181no—
777C23—182no—
778C23—362no—
779C23—362no—
780C23—362no—
781C23—362no—
782C23—362no—
783C23D3×D1211yescharacteristic
784Q8—32no—
785Q8—61no—
786Q8—92no—
787Q8—184no—
788Q8—181no—
789D4—32no—
790D4—64no—
791D4—61no—
792D4—92no—
793D4—184no—
794D4—184no—
795D4—184no—
796D4—184no—
797D4—181no—
798D4—182no—
799D4—182no—
800D4—364no—
801D4—364no—
802D4—362no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—61no—
806C2×C4—62no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—64no—
814C2×C4—62no—
815C2×C4—122no—
816C2×C4—184no—
817C2×C4—184no—
818C2×C4—184no—
819C2×C4—181no—
820C2×C4—184no—
821C2×C4D3×D1212yes—
822C2×C4D3×D1211yescharacteristic
823C2×C4#381112yes—
824C2×C4C22×D3211yescharacteristic
825C8—22no—
826C8—62no—
827C2×C3—22no—
828C2×C3—22no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—42no—
833C2×C3—62no—
834C2×C3—121no—
835C2×C3—122no—
836C2×C3C2×#88211yescharacteristic
837C2×C3C2×#88211yescharacteristic
838C2×C3C2×#90811yescharacteristic
839C2×C3#574811yescharacteristic
840C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
841C2×C3#577711yescharacteristic
842D3—22no—
843D3—42no—
844D3—41no—
845D3—122no—
846D3—122no—
847D3—242no—
848D3—244no—
849D3—242no—
850D3—242no—
851C22—21no—
852C22—21no—
853C22—32no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—62no—
860C22—124no—
861C22—121no—
862C22—121no—
863C22—182no—
864C22—368no—
865C22—361no—
866C22—361no—
867C22—362no—
868C22—362no—
869C22—362no—
870C22—724no—
871C22#6392312yes—
872C22C2×D3×D1211yescharacteristic
873C4—61no—
874C4—61no—
875C4—62no—
876C4—122no—
877C4—182no—
878C4#6392312yes—
879C4C2×D3×D1211yescharacteristic
880C4C2×#381111yescharacteristic
881C3—21no—
882C3#7863911yescharacteristic, complemented
883C3#7888411yescharacteristic, complemented
884C2—22no—
885C2—62no—
886C2—121no—
887C2—122no—
888C2—362no—
889C2—722no—
890C2D3×#90811yescharacteristic
891C2#1059471111yescharacteristic
892C2C2×#6392311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×D3×#235C2semidirect
2. C2×#64117C2semidirect
3. C2×#63909C2semidirect
4. C2×#63825C2semidirect
5. C3×#5133C2semidirect
6. C3×#5126C2semidirect
7. #10591106C2semidirect
8. #10590968C2semidirect
9. #10590967C2semidirect
10. #10590951C2semidirect
11. #10590947C2semidirect
15. C22×C4⋊(C3⋊D3)C22semidirect
23. C2×D3×D12C22semidirect
25. C2×#3799C22semidirect
27. C2×#3795C22semidirect
28. C2×D3×Dic6C22semidirect
29. C2×C32×M16C22semidirect
31. C2×#3745C22semidirect
32. C2×#3744C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C2×C3×#208C22semidirect
39. #63909C22semidirect
40. C2×#3717C22semidirect
42. C2×#3714C22semidirect
43. C3×#821C22semidirect
44. C3×(C2×D3)⋊C8C22semidirect
45. C3×(C2×D3)⋊C8C22semidirect
46. C3×#816C22semidirect
47. #63567C22semidirect
48. #63564C22semidirect
61. #5133D3semidirect
62. #5126D3semidirect
78. #3828D4semidirect
90. C3×#235D4semidirect
169. C2×C3×M16C2×D3semidirect
170. C2×C3×M16C2×D3semidirect
181. C2×C4⋊Dic3C2×D3semidirect
182. C2×#208C2×D3semidirect
204. #821C2×D3semidirect
205. (C2×D3)⋊C8C2×D3semidirect
206. (C2×D3)⋊C8C2×D3semidirect
208. #816C2×D3semidirect
236. C4⋊(C3⋊D3)C2×D4semidirect
239. #634C2×D4semidirect
248. C3×D12C2×D4semidirect
257. C3×Dic6C2×D4semidirect
344. #235D12semidirect
440. C2×C3×D3AGL(1,ℤ/8)semidirect
472. C2×M16D32semidirect
592. D12C2×D12semidirect
616. Dic6C2×D12semidirect
747. C2×D3#908semidirect
768. C32#3006semidirect
882. C3#78639semidirect
883. C3#78884semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×#641172
C2×#639092
C2×#638252
C3×#51332
C3×#51262
#105911062
#105909682
#105909672
#105909512
#105909472
#788843
#786393