Finite Group Databasebeta

← #11864150

Subgroups — #11864150

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2C2×C3×#908C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic, complemented
4C2×#63830C211yesmaximal, characteristic, complemented
5#10592832C211yesmaximal, characteristic, complemented
6C3×#5126C211yesmaximal, characteristic, complemented
7#10591088C211yesmaximal, characteristic, complemented
8#10590962C212yesmaximal, complemented
9#10590944C212yesmaximal, complemented
10#10590823C212yesmaximal, complemented
11#10590822C212yesmaximal, complemented
12#83946—31nomaximal
13#78639—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic, complemented
17C22×C3×C4×D3C2211yescharacteristic
18C2×D3×#67—21no—
19C22×#625—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
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C2×C3×#208C2211yescharacteristic, complemented
32C3×#908—24no—
33C2×C3×D24C2212yescomplemented
34C2×C3×#204C2212yescomplemented
35C2×(C2×D3)⋊Dic3—21no—
36#63908—21no—
37#63908—21no—
38#63908C2212yes—
39#63908C2212yescomplemented
40#63830—24no—
41C2×#3716C2212yescomplemented
42C2×#3714C2212yescomplemented
43#63648C2212yescomplemented
44#63643C2212yescomplemented
45C3×(C2×D3)⋊C8C2212yescomplemented
46C3×(C2×D3)⋊C8C2212yescomplemented
47#63566C2212yescomplemented
48#63563C2212yescomplemented
49C2×D3×#41—31no—
50C22×#235—31no—
51C2×C3×AGL(1,ℤ/8)—31no—
52C2×#938—31no—
53C2×#932—31no—
54C2×#930—31no—
55C2×#908—31no—
56C2×#908D311yescharacteristic, complemented
57C3×#407—31no—
58#5232—31no—
59#5172—32no—
60#5170—32no—
61#5158—32no—
62#5156—32no—
63#5133—31no—
64#5133—31no—
65#5133—31no—
66#5133—61no—
67#5126D311yescharacteristic, complemented
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—
77C22×C3⋊Dic3—21no—
78#3828—22no—
79#3828D414yescomplemented
80C2×C4⋊(C3⋊D3)C2311yescharacteristic
81C2×C4×C3⋊D3—21no—
82C2×#634C2311yescharacteristic
83C2×C3×#67—21no—
84C22×C3×Dic3D411yescharacteristic
85C3×#235—22no—
86C3×#235D414yescomplemented
87C2×C3×D12—22no—
88C2×C3×D12—22no—
89C2×C3×D12—21no—
90C2×C3×D12C2312yes—
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×#625—21no—
105C2×#625—22no—
106C2×#625—22no—
107C2×#625—44no—
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—
124C4⋊(C3⋊Dic3)—21no—
125C4⋊(C3⋊Dic3)C2312yes—
126C3×#208—22no—
127C2×C3×C3⋊C8C2312yes—
128C3×D24—24no—
129C3×#204—24no—
130(C2×D3)⋊Dic3—22no—
131(C2×D3)⋊Dic3—22no—
132#3716—24no—
133#3714—24no—
134#3006—91noSylow
135C2×C3×#41—31no—
136C22×C3×D4—31no—
137C23×C3×C4—31no—
138C22×#67—61no—
139C22×#67—61no—
140C22×#67—61no—
141D3×#41—64no—
142D3×#41—64no—
143C2×#239—31no—
144C2×D3×Q8—31no—
145C2×#237—31no—
146C2×#237—61no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×#235—31no—
150C2×#235—31no—
151C2×#235—31no—
152C2×#235—31no—
153C2×#235—61no—
154C2×#235—61no—
155C2×#235—64no—
156C2×#235—61no—
157C2×#235—64no—
158C2×#235—61no—
159C2×#235C2×D311yescharacteristic
160C22×D12—31no—
161C22×D12C2×D311yescharacteristic, complemented
162C22×C4×D3—61no—
163C22×C4×D3—61no—
164C22×C4×D3C2×D311yescharacteristic
165C22×Dic6—31no—
166C3×AGL(1,ℤ/8)—64no—
167C2×C3×SD16—32no—
168C2×C3×D8—32no—
169C2×C3×M16—21no—
170C2×C3×M16—31no—
171C2×C3×M16C2×D311yescharacteristic, complemented
172C2×C3×M16C2×D311yescharacteristic, complemented
173C2×#217—61no—
174#938—32no—
175#938—32no—
176#938—61no—
177#938—61no—
178C2×#214—32no—
179#932—64no—
180C2×#213—32no—
181#930—32no—
182#930—32no—
183#930—61no—
184#930—61no—
185C2×(C2×D3)⋊C4—61no—
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3—31no—
188C2×C4⋊Dic3—61no—
189C2×#208C2×D311yescharacteristic, complemented
190#908—24no—
191#908—64no—
192C2×D24—32no—
193C2×D24C2×D312yescomplemented
194C2×#204—32no—
195C2×#204C2×D312yescomplemented
196C3×C22⋊C8—32no—
197C3×C22⋊C8—32no—
198#835—32no—
199#832—32no—
200#821—32no—
201#821—32no—
202#821—32no—
203#821—62no—
204(C2×D3)⋊C8C2×D312yescomplemented
205(C2×D3)⋊C8C2×D312yescomplemented
206#816—32no—
207#816—32no—
208#816—32no—
209#816—62no—
210C23×C32C2×D411yescharacteristic
211C22×C3⋊D3—21no—
212C22×C3×D3—22no—
213C22×C3×D3—21no—
214C22×C3×D3—22no—
215C22×C3×D3—22no—
216C22×C3×D3—41no—
217C22×C3×D3—42no—
218C22×C3×D3—42no—
219C22×C3×D3—42no—
220C22×C3×D3C2×D411yescharacteristic
221C22×C3×D3C2×D411yescharacteristic
222C2×D32—24no—
223C2×D32—42no—
224C2×D32—42no—
225C2×C32×C4C2×D411yescharacteristic
226C2×C32×C4C2×D412yes—
227C2×C32×C4C2×D412yes—
228C2×C32×C4C2411yescharacteristic
229#638—24no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—22no—
232C2×C3⋊Dic3—42no—
233C4⋊(C3⋊D3)—21no—
234C4⋊(C3⋊D3)C2×D412yescomplemented
235C4×C3⋊D3—24no—
236#634—21no—
237#634C2×D412yescomplemented
238C3×#67—24no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3C2×D411yescharacteristic
242C2×C3×Dic3C2×D411yescharacteristic
243C3×D12—21no—
244C3×D12—22no—
245C3×D12—22no—
246C3×D12—42no—
247C3×D12C2×D412yescomplemented
248C3×C4×D3—22no—
249C3×C4×D3—24no—
250C3×C4×D3—22no—
251C3×C4×D3—21no—
252C3×C4×D3—21no—
253C3×C4×D3—21no—
254C3×C4×D3—21no—
255C3×Dic6—21no—
256C3×Dic6C2×D412yescomplemented
257#627—24no—
258#626—24no—
259#626—24no—
260#625—24no—
261#625—44no—
262#625—44no—
263#624—24no—
264D3×Dic3—24no—
265D3×Dic3—24no—
266C32×C8—22no—
267C3×C3⋊C8—22no—
268C22×#41—91no—
269C2×AGL(1,ℤ/8)—31no—
270C2×AGL(1,ℤ/8)—91no—
271C2×#121—91no—
272#449—92no—
273#449—92no—
274#448—92no—
275#447—92no—
276#417—91no—
277#417—91no—
278#407—31no—
279C24×C3—31no—
280C24×C3—61no—
281C23×D3—21no—
282C23×D3—61no—
283C23×D3—61no—
284C23×D3D1211yescharacteristic
285C3×#41—34no—
286C3×#41—62no—
287C2×C3×Q8—31no—
288C2×C3×D4—31no—
289C2×C3×D4—32no—
290C2×C3×D4—61no—
291C2×C3×D4—61no—
292C2×C3×D4—62no—
293C2×C3×D4—62no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—62no—
302C22×C3×C4—62no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C2×#67—21no—
306C2×#67—61no—
307C2×#67—68no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—62no—
313C2×#67—62no—
314C2×#67—62no—
315C2×#67—62no—
316C2×#67—61no—
317C2×#67—121no—
318C2×#67—124no—
319C2×#67—124no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—121no—
325C22×Dic3D1211yescharacteristic
326#239—62no—
327#239—62no—
328D3×Q8—62no—
329D3×Q8—62no—
330#237—62no—
331#237—62no—
332#237—68no—
333D3×D4—62no—
334D3×D4—62no—
335D3×D4—68no—
336#235—22no—
337#235—34no—
338#235—34no—
339#235—64no—
340#235—62no—
341#235—62no—
342#235—68no—
343#235—68no—
344#235—68no—
345#235—62no—
346#235—62no—
347#235—62no—
348#235—62no—
349#235—122no—
350#235#6714yescomplemented
351C2×D12—22no—
352C2×D12—22no—
353C2×D12—21no—
354C2×D12—31no—
355C2×D12—31no—
356C2×D12—61no—
357C2×D12—62no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—62no—
361C2×D12C22×D312yes—
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—21no—
364C2×C4×D3—22no—
365C2×C4×D3—22no—
366C2×C4×D3—68no—
367C2×C4×D3—68no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—121no—
375C2×C4×D3D1211yescharacteristic
376C2×C4×D3D1211yescharacteristic
377C2×C4×D3C22×D311yescharacteristic
378C2×C4×D3C22×D311yescharacteristic
379C2×Dic6—31no—
380C2×Dic6—31no—
381C2×Dic6—61no—
382C2×Dic6—62no—
383C2×Dic6—61no—
384C2×Dic6—61no—
385C2×Dic6—62no—
386C2×Dic6C22×D311yescharacteristic
387C3×SD16—64no—
388C3×D8—64no—
389C3×M16—22no—
390C3×M16—22no—
391C3×M16—42no—
392C3×M16—62no—
393C2×C3×C8—22no—
394C2×C3×C8—32no—
395C2×C3×C8C22×D312yes—
396C2×C3×C8C22×D312yes—
397#217—62no—
398#217—62no—
399#214—64no—
400#213—64no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—62no—
403C4⋊Dic3—32no—
404C4⋊Dic3—32no—
405C4⋊Dic3—62no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3—121no—
409#208—22no—
410C2×C3⋊C8C22×D312yes—
411D24—24no—
412D24—64no—
413#204—24no—
414#204—64no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32#12012yes—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—22no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—44no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—42no—
432C2×C3×D3—42no—
433C2×C3×D3—42no—
434C2×C3×D3—84no—
435C2×C3×D3AGL(1,ℤ/8)12yescomplemented
436D32—48no—
437C32×C4#12012yes—
438C32×C4C22×D411yescharacteristic
439C32×C4C22×D411yescharacteristic
440C3⋊Dic3—22no—
441C3⋊Dic3—42no—
442C3×Dic3—21no—
443C3×Dic3—22no—
444C3×Dic3—21no—
445C2×#41—31no—
446C2×#41—91no—
447C2×#41—91no—
448C2×#41—91no—
449C2×#41—181no—
450C2×#41—181no—
451C2×#41—184no—
452C2×#41—184no—
453C22×Q8—91no—
454C22×D4—31no—
455C22×D4—91no—
456C22×D4—181no—
457C22×D4—181no—
458C23×C4—31no—
459C23×C4—181no—
460AGL(1,ℤ/8)—64no—
461AGL(1,ℤ/8)—184no—
462C2×SD16—32no—
463C2×SD16—92no—
464C2×D8—32no—
465C2×D8—92no—
466C2×M16—31no—
467C2×M16D3211yescharacteristic, complemented
468#121—92no—
469#121—92no—
470#121—181no—
471#121—181no—
472C2×C4⋊C4—91no—
473C2×C22⋊C4—181no—
474#103—92no—
475#103—92no—
476#102—92no—
477#102—92no—
478C22⋊C8—32no—
479C22⋊C8—32no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—31no—
483C23×C3—62no—
484C23×C3—62no—
485C23×C3—61no—
486C23×C3—62no—
487C23×C3—121no—
488C23×C3—122no—
489C23×C3—122no—
490C23×C3—122no—
491C23×C3C2×D1211yescharacteristic
492C23×C3D3×D411yescharacteristic
493C22×D3—22no—
494C22×D3—21no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—41no—
498C22×D3—42no—
499C22×D3—42no—
500C22×D3—42no—
501C22×D3—64no—
502C22×D3—64no—
503C22×D3—61no—
504C22×D3—61no—
505C22×D3—121no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3C2×D1211yescharacteristic
511C22×D3C2×D1211yescharacteristic
512C3×Q8—32no—
513C3×Q8—61no—
514C3×D4—32no—
515C3×D4—64no—
516C3×D4—61no—
517C3×D4—62no—
518C3×D4—62no—
519C3×D4—122no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—62no—
527C2×C3×C4—61no—
528C2×C3×C4—64no—
529C2×C3×C4—62no—
530C2×C3×C4—62no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4C2×D1211yescharacteristic
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4D3×D412yes—
538C2×C3×C4D3×D412yes—
539C2×C3×C4D3×D412yes—
540C2×C3×C4C2×#6712yes—
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543#67—24no—
544#67—64no—
545#67—64no—
546#67—64no—
547#67—64no—
548#67—64no—
549#67—64no—
550#67—124no—
551#67—124no—
552#67—124no—
553#67—124no—
554#67—124no—
555C2×Dic3—22no—
556C2×Dic3—21no—
557C2×Dic3—64no—
558C2×Dic3—64no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—62no—
562C2×Dic3—62no—
563C2×Dic3—121no—
564C2×Dic3—122no—
565C2×Dic3—122no—
566C2×Dic3—122no—
567C2×Dic3—242no—
568C2×Dic3C2×D1211yescharacteristic
569C2×Dic3C2×D1211yescharacteristic
570D12—21no—
571D12—22no—
572D12—22no—
573D12—32no—
574D12—32no—
575D12—42no—
576D12—62no—
577D12—64no—
578D12—64no—
579D12—61no—
580D12—61no—
581D12—121no—
582D12C2×#6712yescomplemented
583C4×D3—22no—
584C4×D3—22no—
585C4×D3—24no—
586C4×D3—21no—
587C4×D3—21no—
588C4×D3—21no—
589C4×D3—21no—
590C4×D3—64no—
591C4×D3—64no—
592C4×D3—64no—
593C4×D3—64no—
594C4×D3—64no—
595C4×D3—64no—
596C4×D3—124no—
597Dic6—21no—
598Dic6—32no—
599Dic6—32no—
600Dic6—62no—
601Dic6—64no—
602Dic6—64no—
603Dic6—61no—
604Dic6—61no—
605Dic6—121no—
606Dic6C2×#6712yescomplemented
607C3×C8—22no—
608C3×C8—22no—
609C3×C8—42no—
610C3×C8—62no—
611C3⋊C8—22no—
612C2×C32—22no—
613C2×C32C2×#12011yescharacteristic
614C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
615C2×C32#57511yescharacteristic
616C3⋊D3—42no—
617C3×D3—22no—
618C3×D3—42no—
619C3×D3—41no—
620C3×D3—82no—
621C24—31no—
622C24—61no—
623C24—181no—
624#41—34no—
625#41—62no—
626#41—94no—
627#41—188no—
628#41—182no—
629#41—182no—
630#41—188no—
631#41—182no—
632#41—182no—
633#41—182no—
634C2×Q8—31no—
635C2×Q8—91no—
636C2×Q8—181no—
637C2×Q8—182no—
638C2×Q8—182no—
639C2×D4—31no—
640C2×D4—32no—
641C2×D4—61no—
642C2×D4—61no—
643C2×D4—62no—
644C2×D4—62no—
645C2×D4—91no—
646C2×D4—181no—
647C2×D4—182no—
648C2×D4—182no—
649C2×D4—181no—
650C2×D4—188no—
651C2×D4—181no—
652C2×D4—181no—
653C2×D4—182no—
654C2×D4—182no—
655C2×D4—364no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—61no—
662C22×C4—62no—
663C22×C4—62no—
664C22×C4—181no—
665C22×C4—181no—
666C22×C4—188no—
667C22×C4—181no—
668C22×C4—181no—
669C22×C4—181no—
670C22×C4C2×D3211yescharacteristic
671SD16—64no—
672SD16—184no—
673D8—64no—
674D8—184no—
675M16—22no—
676M16—62no—
677C2×C8—32no—
678C2×C8C2×D3212yes—
679C4⋊C4—92no—
680C4⋊C4—181no—
681C22⋊C4—182no—
682C22⋊C4—182no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—22no—
689C22×C3—32no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—62no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—124no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—122no—
702C22×C3—122no—
703C22×C3—122no—
704C22×C3—244no—
705C22×C3#88212yes—
706C22×C3#93712yes—
707C22×C3C22×D1211yescharacteristic
708C22×C3C2×D3×D411yescharacteristic
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—22no—
715C2×D3—44no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3—42no—
721C2×D3—62no—
722C2×D3—62no—
723C2×D3—84no—
724C2×D3—122no—
725C2×D3—128no—
726C2×D3—128no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—241no—
732C2×D3—241no—
733C2×D3#90812yescomplemented
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—22no—
737C3×C4—62no—
738C3×C4—61no—
739C3×C4—61no—
740C3×C4#88212yes—
741C3×C4#93712yes—
742C3×C4C2×D3×D411yescharacteristic
743C3×C4C2×D3×D411yescharacteristic
744C3×C4C2×D3×D411yescharacteristic
745C3×C4C22×#6711yescharacteristic
746Dic3—21no—
747Dic3—21no—
748Dic3—22no—
749Dic3—62no—
750Dic3—62no—
751Dic3—122no—
752Dic3—122no—
753Dic3—122no—
754Dic3—242no—
755C32#300611yescharacteristic, complemented, Sylow
756C23—31no—
757C23—31no—
758C23—62no—
759C23—61no—
760C23—62no—
761C23—62no—
762C23—121no—
763C23—122no—
764C23—122no—
765C23—122no—
766C23—184no—
767C23—181no—
768C23—362no—
769C23—362no—
770C23D3×D1211yescharacteristic
771Q8—32no—
772Q8—61no—
773Q8—92no—
774Q8—184no—
775Q8—181no—
776D4—32no—
777D4—64no—
778D4—61no—
779D4—62no—
780D4—62no—
781D4—92no—
782D4—122no—
783D4—184no—
784D4—184no—
785D4—184no—
786D4—184no—
787D4—181no—
788D4—364no—
789D4—364no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—61no—
793C2×C4—62no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—62no—
799C2×C4—62no—
800C2×C4—64no—
801C2×C4—184no—
802C2×C4—184no—
803C2×C4—184no—
804C2×C4—181no—
805C2×C4—184no—
806C2×C4—182no—
807C2×C4—362no—
808C2×C4D3×D1211yescharacteristic
809C2×C4#380212yes—
810C2×C4D3×#6712yes—
811C2×C4C22×D3211yescharacteristic
812C8—22no—
813C8—62no—
814C2×C3—22no—
815C2×C3—22no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—42no—
820C2×C3—62no—
821C2×C3—122no—
822C2×C3—121no—
823C2×C3—242no—
824C2×C3C2×#88211yescharacteristic
825C2×C3C2×#90811yescharacteristic
826C2×C3#574811yescharacteristic
827C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
828C2×C3#577311yescharacteristic
829C2×C3C2×#93711yescharacteristic
830D3—22no—
831D3—41no—
832D3—42no—
833D3—82no—
834D3—122no—
835D3—122no—
836D3—242no—
837C22—21no—
838C22—21no—
839C22—32no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—61no—
844C22—61no—
845C22—62no—
846C22—124no—
847C22—121no—
848C22—121no—
849C22—122no—
850C22—122no—
851C22—122no—
852C22—182no—
853C22—244no—
854C22—368no—
855C22—361no—
856C22—361no—
857C22#6392212yes—
858C22C2×D3×D1211yescharacteristic
859C4—61no—
860C4—61no—
861C4—62no—
862C4—182no—
863C4—362no—
864C4#6392212yes—
865C4C2×#380211yescharacteristic
866C4C2×D3×#6711yescharacteristic
867C3—21no—
868C3#7863911yescharacteristic, complemented
869C3#8394611yescharacteristic, complemented
870C2—22no—
871C2—62no—
872C2—121no—
873C2—122no—
874C2—242no—
875C2—362no—
876C2D3×#90811yescharacteristic
877C2#1059471211yescharacteristic
878C2C2×#6392211yescharacteristic
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×C3×#908C2semidirect
3. C2×#63908C2semidirect
4. C2×#63830C2semidirect
5. #10592832C2semidirect
6. C3×#5126C2semidirect
7. #10591088C2semidirect
8. #10590962C2semidirect
9. #10590944C2semidirect
10. #10590823C2semidirect
11. #10590822C2semidirect
16. C22×C3×D12C22semidirect
23. C2×D3×D12C22semidirect
25. C2×#3799C22semidirect
27. C2×#3795C22semidirect
28. C2×D3×Dic6C22semidirect
29. C2×C32×M16C22semidirect
30. C2×C4⋊(C3⋊Dic3)C22semidirect
31. C2×C3×#208C22semidirect
33. C2×C3×D24C22semidirect
34. C2×C3×#204C22semidirect
39. #63908C22semidirect
41. C2×#3716C22semidirect
42. C2×#3714C22semidirect
43. #63648C22semidirect
44. #63643C22semidirect
45. C3×(C2×D3)⋊C8C22semidirect
46. C3×(C2×D3)⋊C8C22semidirect
47. #63566C22semidirect
48. #63563C22semidirect
56. C2×#908D3semidirect
67. #5126D3semidirect
79. #3828D4semidirect
86. C3×#235D4semidirect
161. C22×D12C2×D3semidirect
171. C2×C3×M16C2×D3semidirect
172. C2×C3×M16C2×D3semidirect
189. C2×#208C2×D3semidirect
193. C2×D24C2×D3semidirect
195. C2×#204C2×D3semidirect
204. (C2×D3)⋊C8C2×D3semidirect
205. (C2×D3)⋊C8C2×D3semidirect
234. C4⋊(C3⋊D3)C2×D4semidirect
237. #634C2×D4semidirect
247. C3×D12C2×D4semidirect
256. C3×Dic6C2×D4semidirect
350. #235#67semidirect
435. C2×C3×D3AGL(1,ℤ/8)semidirect
467. C2×M16D32semidirect
582. D12C2×#67semidirect
606. Dic6C2×#67semidirect
733. C2×D3#908semidirect
755. C32#3006semidirect
868. C3#78639semidirect
869. C3#83946semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×C3×#9082
C2×#639082
C2×#638302
#105928322
C3×#51262
#105910882
#105909622
#105909442
#105908232
#105908222
#839463
#786393