Finite Group Databasebeta

← D3×#4734 #11863714

Subgroups — D3×#4734 #11863714

Order 1152.

1705 conjugacy classes of subgroups.

The subgroup lattice has 1057 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2D3×#930C211yesmaximal, characteristic, complemented
3C2×D3×D24C211yesmaximal, characteristic, complemented
4C2×D3×#204C211yesmaximal, characteristic, complemented
5#10592433C211yesmaximal, characteristic, complemented
6C3×#4734C211yesmaximal, characteristic, complemented
7C3×D3×C22⋊C8C211yesmaximal, characteristic, complemented
8#10591182C211yesmaximal, characteristic, complemented
9#10591163C211yesmaximal, characteristic, complemented
10#10590968C211yesmaximal, characteristic, complemented
11#10590967C211yesmaximal, characteristic, complemented
12#10590962C211yesmaximal, characteristic, complemented
13D3×#821C211yesmaximal, characteristic, complemented
14#10590823C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16D3×#449—31nomaximal
17C2×#4734—31nomaximal
18C2×#3828C2211yescharacteristic, complemented
19C2×C3×#235C2211yescharacteristic, complemented
20C22×C3×C4×D3C2211yescharacteristic
21C2×D3×#67—21no—
22C2×D3×#67—21no—
23C2×#3804—21no—
24D3×#235—24no—
25D3×#235—24no—
26C2×D3×D12C2211yescharacteristic
27C2×D3×D12C2211yescharacteristic
28C2×C4×D32—21no—
29C2×#3799C2211yescharacteristic, complemented
30C2×#3798—21no—
31C2×#3795C2211yescharacteristic, complemented
32C2×D3×Dic6C2211yescharacteristic
33#64139C2211yescharacteristic, complemented
34C2×#3745C2211yescharacteristic, complemented
35C2×#3744C2211yescharacteristic, complemented
36C3×#930C2211yescharacteristic, complemented
37C2×C3×D24C2211yescharacteristic, complemented
38C2×C3×#204C2211yescharacteristic, complemented
39C2×C3×D3×C8C2211yescharacteristic
40C2×C3×D3×C8C2211yescharacteristic
41#63978—21no—
42D3×(C2×D3)⋊C4—21no—
43#63909C2211yescharacteristic, complemented
44#63908C2211yescharacteristic, complemented
45#63906—21no—
46D3×C4⋊Dic3C2211yescharacteristic
47C2×#3717C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51D3×D24—24no—
52D3×#204—24no—
53C32×C22⋊C8C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63643C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63566C2211yescharacteristic, complemented
63#63564C2211yescharacteristic, complemented
64#63563C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#235—31no—
67C2×#930—31no—
68C2×D3×SD16—31no—
69C2×D3×D8—31no—
70C22×D24—31no—
71C22×#204—31no—
72D3×#121—31no—
73C3×#449—31no—
74C2×C3×C22⋊C8—31no—
75#5238—31no—
76#5172—31no—
77#5158—31no—
78C2×#821—31no—
79C2×#816—31no—
80#5037—31no—
81#4810—31no—
82D3×#103—31no—
83#4781—31no—
84D3×#102—31no—
85#4734—31no—
86#4734—31no—
87#4734—31no—
88#4734—31no—
89#4734—31no—
90#4734—31no—
91#4734—31no—
92#4734—31no—
93#4734—61no—
94#4734D311yescharacteristic, direct product factor
95D3×C22⋊C8D311yescharacteristic, complemented
96C23×C3×D3D411yescharacteristic
97C22×D32—21no—
98C22×D32—21no—
99C22×C32×C4C2311yescharacteristic
100C2×#638—21no—
101C2×#638—21no—
102#3828—22no—
103#3828—22no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C22×C3×Dic3D411yescharacteristic
111C3×#235—22no—
112C3×#235—22no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3D411yescharacteristic
119C2×C3×C4×D3D411yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
123D3×#67—28no—
124D3×#67—44no—
125C2×#627—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#625—21no—
131C2×#625—21no—
132C2×#624—21no—
133#3804—28no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3—21no—
136C2×D3×Dic3—21no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12—22no—
140D3×D12D414yescomplemented
141C4×D32—28no—
142#3799—22no—
143#3799—22no—
144#3798—28no—
145#3795—22no—
146#3795—22no—
147D3×Dic6—22no—
148D3×Dic6D414yescomplemented
149C2×C32×C8C2311yescharacteristic
150C2×C32×C8C2311yescharacteristic
151#3752—21no—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153#3745—22no—
154#3744—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159C3×D24—22no—
160C3×#204—22no—
161C3×D3×C8—22no—
162C3×D3×C8—22no—
163Dic3⋊Dic3—21no—
164#3722—21no—
165(C2×D3)⋊Dic3—21no—
166#3717—22no—
167#3716—22no—
168#3714—22no—
169#3714—22no—
170C2×#449—91noSylow
171C2×C3×#41—31no—
172C23×C3×C4—31no—
173C22×#67—61no—
174C22×#67—61no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239—31no—
178C2×D3×Q8—31no—
179C2×#237—31no—
180C2×#237—61no—
181C2×D3×D4—31no—
182C2×D3×D4—31no—
183C2×D3×D4—61no—
184C2×D3×D4—61no—
185C2×#235—31no—
186C2×#235—31no—
187C2×#235—31no—
188C2×#235—31no—
189C2×#235—61no—
190C2×#235—64no—
191C2×#235—61no—
192C2×#235—64no—
193C2×#235—61no—
194C2×#235—61no—
195C2×#235C2×D311yescharacteristic, complemented
196C22×D12—31no—
197C22×D12—31no—
198C22×C4×D3—61no—
199C22×C4×D3—61no—
200C22×C4×D3C2×D311yescharacteristic
201C22×Dic6—31no—
202C2×C3×SD16—31no—
203C2×C3×D8—31no—
204C22×C3×C8—31no—
205C22×C3×C8—31no—
206C3×#121—31no—
207C2×#215—31no—
208#939—61no—
209#938—31no—
210C2×#214—31no—
211C2×#213—31no—
212C2×#213—31no—
213#930—31no—
214#930—31no—
215#930—31no—
216#930—31no—
217#930—61no—
218#930—61no—
219#930—61no—
220#930C2×D311yescharacteristic, complemented
221C2×(C2×D3)⋊C4—61no—
222C2×C4⋊Dic3—31no—
223D3×SD16—64no—
224D3×D8—64no—
225C2×D24—31no—
226C2×D24—31no—
227C2×D24—31no—
228C2×D24—31no—
229C2×D24—61no—
230C2×D24—64no—
231C2×D24C2×D311yescharacteristic, complemented
232C2×#204—31no—
233C2×#204—31no—
234C2×#204—31no—
235C2×#204—31no—
236C2×#204—61no—
237C2×#204—64no—
238C2×#204C2×D311yescharacteristic, complemented
239C2×D3×C8C2×D311yescharacteristic
240C2×D3×C8C2×D311yescharacteristic
241#895—31no—
242D3×C4⋊C4—31no—
243#884—61no—
244D3×C22⋊C4—61no—
245C3×#103—31no—
246C3×#102—31no—
247C3×C22⋊C8—21no—
248C3×C22⋊C8—31no—
249C3×C22⋊C8—31no—
250C3×C22⋊C8—31no—
251C3×C22⋊C8C2×D311yescharacteristic, complemented
252C3×C22⋊C8C2×D311yescharacteristic, complemented
253#835—31no—
254#832—31no—
255#830C2×D311yescharacteristic, complemented
256#821—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—61no—
261#821C2×D311yescharacteristic, complemented
262(C2×D3)⋊C8C2×D311yescharacteristic, complemented
263(C2×D3)⋊C8C2×D311yescharacteristic, complemented
264#816—31no—
265#816—31no—
266#816—31no—
267#816—31no—
268#816—61no—
269#816C2×D311yescharacteristic, complemented
270#810—31no—
271#809—31no—
272C23×C32C2×D411yescharacteristic
273C22×C3⋊D3—21no—
274C22×C3⋊D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—22no—
279C22×C3×D3—21no—
280C22×C3×D3C2×D411yescharacteristic
281C22×C3×D3C2×D411yescharacteristic
282C2×D32—24no—
283C2×D32—42no—
284C2×D32—42no—
285C2×D32—42no—
286C2×D32—42no—
287C2×D32—42no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4C2×D411yescharacteristic
291C2×C32×C4C2411yescharacteristic
292#638—24no—
293#638—42no—
294C2×C3⋊Dic3—21no—
295C2×C3⋊Dic3—21no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)—21no—
299C4⋊(C3⋊D3)C2×D412yescomplemented
300C4×C3⋊D3—24no—
301#634—21no—
302#634C2×D412yescomplemented
303C3×#67—24no—
304C3×#67—42no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3C2×D411yescharacteristic
309C2×C3×Dic3C2×D411yescharacteristic
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12C2×D412yescomplemented
314C3×C4×D3—24no—
315C3×C4×D3—22no—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—22no—
319C3×C4×D3C2×D412yes—
320C3×C4×D3C2×D412yes—
321C3×Dic6—21no—
322C3×Dic6C2×D412yescomplemented
323#627—24no—
324#626—24no—
325#626—24no—
326#626—42no—
327#626—42no—
328#625—24no—
329#625—42no—
330#624—24no—
331D3×Dic3—24no—
332D3×Dic3—24no—
333D3×Dic3—42no—
334C32×C8—21no—
335C32×C8—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—91no—
339C22×SD16—91no—
340C22×D8—91no—
341C2×#121—91no—
342#449—31no—
343#449—91no—
344#449—91no—
345#449—91no—
346#449—91no—
347#449—91no—
348#449—91no—
349#449—91no—
350C2×#103—91no—
351C2×#102—91no—
352C2×C22⋊C8—31no—
353C24×C3—31no—
354C23×D3—61no—
355C23×D3—61no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3D1211yescharacteristic
359C3×#41—62no—
360C3×#41—62no—
361C2×C3×Q8—31no—
362C2×C3×D4—31no—
363C2×C3×D4—31no—
364C2×C3×D4—61no—
365C2×C3×D4—61no—
366C22×C3×C4—21no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—62no—
373C22×C3×C4—62no—
374C22×C3×C4—61no—
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C2×#67—21no—
378C2×#67—21no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—68no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—61no—
392C2×#67—121no—
393C2×#67—121no—
394C2×#67—124no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397C22×Dic3—61no—
398C22×Dic3D1211yescharacteristic
399#239—62no—
400#239—62no—
401D3×Q8—34no—
402D3×Q8—62no—
403#237—62no—
404#237—62no—
405#237—68no—
406D3×D4—34no—
407D3×D4—68no—
408D3×D4—62no—
409D3×D4—62no—
410D3×D4—62no—
411D3×D4—124no—
412#235—22no—
413#235—22no—
414#235—62no—
415#235—62no—
416#235—62no—
417#235—62no—
418#235—68no—
419#235—68no—
420#235—62no—
421#235—62no—
422#235—68no—
423#235—62no—
424#235—62no—
425#235—122no—
426#235—122no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—34no—
430C2×D12—31no—
431C2×D12—31no—
432C2×D12—61no—
433C2×D12—61no—
434C2×D12—62no—
435C2×D12—62no—
436C2×D12—62no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12—61no—
441C2×D12C22×D311yescharacteristic
442C2×D12C22×D311yescharacteristic
443C2×C4×D3—21no—
444C2×C4×D3—22no—
445C2×C4×D3—22no—
446C2×C4×D3—68no—
447C2×C4×D3—68no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3—61no—
455C2×C4×D3—121no—
456C2×C4×D3D1211yescharacteristic
457C2×C4×D3D1211yescharacteristic
458C2×C4×D3C22×D311yescharacteristic
459C2×C4×D3C22×D311yescharacteristic
460C2×Dic6—31no—
461C2×Dic6—31no—
462C2×Dic6—34no—
463C2×Dic6—61no—
464C2×Dic6—62no—
465C2×Dic6—61no—
466C2×Dic6—61no—
467C2×Dic6C22×D311yescharacteristic
468C3×SD16—62no—
469C3×D8—62no—
470C2×C3×C8—21no—
471C2×C3×C8—21no—
472C2×C3×C8—31no—
473C2×C3×C8—31no—
474C2×C3×C8—62no—
475C2×C3×C8—62no—
476C2×C3×C8C22×D311yescharacteristic
477C2×C3×C8C22×D311yescharacteristic
478C2×C3×C8C22×D311yescharacteristic
479C2×C3×C8C22×D311yescharacteristic
480C3×C4⋊C4—31no—
481C3×C22⋊C4—61no—
482#217—61no—
483#215—62no—
484#214—62no—
485#213—62no—
486#213—62no—
487(C2×D3)⋊C4—21no—
488(C2×D3)⋊C4—61no—
489(C2×D3)⋊C4—61no—
490(C2×D3)⋊C4—61no—
491(C2×D3)⋊C4—61no—
492(C2×D3)⋊C4—61no—
493(C2×D3)⋊C4—121no—
494C4⋊Dic3—31no—
495C4⋊Dic3—31no—
496C4⋊Dic3—61no—
497C4⋊Dic3—61no—
498C4⋊Dic3C22×D311yescharacteristic
499Dic3⋊C4—61no—
500C2×C3⋊C8C22×D311yescharacteristic
501C2×C3⋊C8C22×D311yescharacteristic
502D24—22no—
503D24—62no—
504D24—62no—
505D24—62no—
506D24—62no—
507D24—122no—
508#204—22no—
509#204—62no—
510#204—62no—
511#204—62no—
512#204—62no—
513#204—122no—
514D3×C8—22no—
515D3×C8—22no—
516C22×C32—21no—
517C22×C32—21no—
518C22×C32—21no—
519C22×C32C22×D411yescharacteristic
520C2×C3⋊D3—22no—
521C2×C3⋊D3—41no—
522C2×C3⋊D3—41no—
523C2×C3⋊D3—41no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3×D3—22no—
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—44no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3#12012yes—
537C2×C3×D3#13512yes—
538C2×C3×D3AGL(1,ℤ/8)12yes—
539D32—48no—
540D32—84no—
541C32×C4—21no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3⋊Dic3—22no—
545C3⋊Dic3—41no—
546C3×Dic3—21no—
547C3×Dic3—22no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—91no—
552C2×#41—91no—
553C2×#41—91no—
554C2×#41—181no—
555C2×#41—181no—
556C2×#41—184no—
557C2×#41—184no—
558C22×Q8—91no—
559C22×D4—91no—
560C22×D4—91no—
561C22×D4—181no—
562C22×D4—181no—
563C23×C4—31no—
564C23×C4—181no—
565C2×SD16—31no—
566C2×SD16—91no—
567C2×SD16—91no—
568C2×SD16—91no—
569C2×SD16—184no—
570C2×D8—31no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8—184no—
575C22×C8—31no—
576C22×C8—31no—
577#121—31no—
578#121—91no—
579#121—91no—
580#121—91no—
581#121—181no—
582#121—181no—
583C2×C4⋊C4—91no—
584C2×C22⋊C4—181no—
585#103—31no—
586#103—91no—
587#103—91no—
588#103—91no—
589#102—31no—
590#102—91no—
591#102—91no—
592#102—91no—
593C22⋊C8—31no—
594C22⋊C8—31no—
595C22⋊C8—31no—
596C22⋊C8D3211yescharacteristic, complemented
597C23×C3—21no—
598C23×C3—31no—
599C23×C3—31no—
600C23×C3—62no—
601C23×C3—62no—
602C23×C3—62no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3C2×D1211yescharacteristic
606C23×C3D3×D411yescharacteristic
607C22×D3—21no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—21no—
612C22×D3—64no—
613C22×D3—61no—
614C22×D3—61no—
615C22×D3—64no—
616C22×D3—61no—
617C22×D3—61no—
618C22×D3—121no—
619C22×D3—121no—
620C22×D3—122no—
621C22×D3—122no—
622C22×D3—122no—
623C22×D3—122no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3C2×D1211yescharacteristic
631C22×D3C2×D1211yescharacteristic
632C3×Q8—32no—
633C3×Q8—61no—
634C3×D4—32no—
635C3×D4—64no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—122no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—31no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—31no—
650C2×C3×C4—41no—
651C2×C3×C4—41no—
652C2×C3×C4—62no—
653C2×C3×C4—62no—
654C2×C3×C4—64no—
655C2×C3×C4—62no—
656C2×C3×C4—61no—
657C2×C3×C4—61no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4C2×D1211yescharacteristic
661C2×C3×C4D3×D411yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664#67—24no—
665#67—42no—
666#67—64no—
667#67—64no—
668#67—64no—
669#67—64no—
670#67—64no—
671#67—64no—
672#67—124no—
673#67—122no—
674#67—122no—
675#67—122no—
676#67—122no—
677#67—122no—
678#67—122no—
679#67—242no—
680C2×Dic3—21no—
681C2×Dic3—22no—
682C2×Dic3—21no—
683C2×Dic3—64no—
684C2×Dic3—64no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—121no—
690C2×Dic3—121no—
691C2×Dic3—122no—
692C2×Dic3C2×D1211yescharacteristic
693C2×Dic3C2×D1211yescharacteristic
694D12—21no—
695D12—21no—
696D12—21no—
697D12—32no—
698D12—32no—
699D12—62no—
700D12—64no—
701D12—64no—
702D12—61no—
703D12—61no—
704D12—61no—
705D12—61no—
706D12—61no—
707D12—61no—
708D12—121no—
709D12—121no—
710D12—121no—
711D12—122no—
712D12—122no—
713D12D3×D412yescomplemented
714C4×D3—24no—
715C4×D3—22no—
716C4×D3—21no—
717C4×D3—21no—
718C4×D3—22no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—64no—
723C4×D3—64no—
724C4×D3—64no—
725C4×D3—124no—
726C4×D3—122no—
727C4×D3D3×D412yes—
728C4×D3D3×D412yes—
729Dic6—21no—
730Dic6—32no—
731Dic6—32no—
732Dic6—62no—
733Dic6—64no—
734Dic6—61no—
735Dic6—61no—
736Dic6—64no—
737Dic6—121no—
738Dic6D3×D412yescomplemented
739C3×C8—21no—
740C3×C8—21no—
741C3×C8—21no—
742C3×C8—21no—
743C3×C8—41no—
744C3×C8—41no—
745C3×C8—61no—
746C3×C8—61no—
747C3⋊C8—21no—
748C3⋊C8—21no—
749C2×C32—41no—
750C2×C32C2×#12011yescharacteristic
751C2×C32C2×#13511yescharacteristic
752C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
753C3⋊D3—42no—
754C3⋊D3—81no—
755C3×D3—42no—
756C3×D3—41no—
757C3×D3—81no—
758C3×D3#44914yescomplemented
759C24—31no—
760C24—181no—
761C24—181no—
762#41—62no—
763#41—62no—
764#41—182no—
765#41—182no—
766#41—188no—
767#41—182no—
768#41—182no—
769#41—188no—
770#41—182no—
771#41—182no—
772C2×Q8—31no—
773C2×Q8—94no—
774C2×Q8—91no—
775C2×Q8—181no—
776C2×Q8—182no—
777C2×D4—31no—
778C2×D4—31no—
779C2×D4—61no—
780C2×D4—61no—
781C2×D4—94no—
782C2×D4—91no—
783C2×D4—91no—
784C2×D4—182no—
785C2×D4—182no—
786C2×D4—182no—
787C2×D4—181no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—188no—
792C2×D4—181no—
793C2×D4—181no—
794C2×D4—181no—
795C2×D4—181no—
796C2×D4—364no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—62no—
803C22×C4—62no—
804C22×C4—61no—
805C22×C4—181no—
806C22×C4—181no—
807C22×C4—188no—
808C22×C4—181no—
809C22×C4—181no—
810C22×C4—181no—
811C22×C4C2×D3211yescharacteristic
812SD16—62no—
813SD16—182no—
814SD16—182no—
815SD16—182no—
816D8—62no—
817D8—182no—
818D8—182no—
819D8—182no—
820C2×C8—31no—
821C2×C8—31no—
822C2×C8—62no—
823C2×C8—62no—
824C2×C8C2×D3211yescharacteristic
825C2×C8C2×D3211yescharacteristic
826C4⋊C4—31no—
827C4⋊C4—91no—
828C4⋊C4—181no—
829C22⋊C4—61no—
830C22⋊C4—181no—
831C22⋊C4—181no—
832C22⋊C4—181no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—32no—
841C22×C3—32no—
842C22×C3—32no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—62no—
847C22×C3—61no—
848C22×C3—61no—
849C22×C3—61no—
850C22×C3—124no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—121no—
856C22×C3C22×D1211yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C2×D3—21no—
859C2×D3—21no—
860C2×D3—21no—
861C2×D3—22no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—44no—
865C2×D3—41no—
866C2×D3—41no—
867C2×D3—41no—
868C2×D3—62no—
869C2×D3—62no—
870C2×D3—122no—
871C2×D3—128no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—128no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—121no—
881C2×D3—121no—
882C2×D3—121no—
883C2×D3—241no—
884C2×D3—241no—
885C2×D3—241no—
886C2×D3—241no—
887C2×D3—241no—
888C2×D3—244no—
889C2×D3—244no—
890C2×D3#88212yes—
891C2×D3#90412yes—
892C2×D3#90812yes—
893C3×C4—21no—
894C3×C4—21no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—32no—
898C3×C4—41no—
899C3×C4—62no—
900C3×C4—61no—
901C3×C4—121no—
902C3×C4C2×D3×D411yescharacteristic
903C3×C4C2×D3×D411yescharacteristic
904C3×C4C2×D3×D411yescharacteristic
905C3×C4C2×D3×D411yescharacteristic
906Dic3—21no—
907Dic3—22no—
908Dic3—41no—
909Dic3—62no—
910Dic3—62no—
911Dic3—122no—
912Dic3—121no—
913Dic3—121no—
914Dic3—241no—
915Dic3#88212yes—
916C32C2×#44911yescharacteristic, complemented, Sylow
917C23—31no—
918C23—31no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—61no—
923C23—61no—
924C23—184no—
925C23—181no—
926C23—181no—
927C23—362no—
928C23—362no—
929C23—362no—
930C23—362no—
931C23—362no—
932C23D3×D1211yescharacteristic
933Q8—32no—
934Q8—61no—
935Q8—92no—
936Q8—184no—
937Q8—181no—
938D4—32no—
939D4—64no—
940D4—61no—
941D4—61no—
942D4—61no—
943D4—92no—
944D4—122no—
945D4—184no—
946D4—184no—
947D4—184no—
948D4—184no—
949D4—181no—
950D4—181no—
951D4—181no—
952D4—362no—
953D4—362no—
954D4—362no—
955D4—362no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—31no—
959C2×C4—32no—
960C2×C4—32no—
961C2×C4—31no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—64no—
965C2×C4—62no—
966C2×C4—61no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—184no—
971C2×C4—184no—
972C2×C4—184no—
973C2×C4—184no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—362no—
977C2×C4D3×D1211yescharacteristic
978C2×C4C22×D3211yescharacteristic
979C8—21no—
980C8—21no—
981C8—61no—
982C8—61no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—34no—
987C2×C3—41no—
988C2×C3—41no—
989C2×C3—81no—
990C2×C3—122no—
991C2×C3—121no—
992C2×C3—241no—
993C2×C3C2×#88211yescharacteristic
994C2×C3D3×#12011yescharacteristic
995C2×C3C2×#90411yescharacteristic
996C2×C3C2×#90811yescharacteristic
997C2×C3D3×#13511yescharacteristic
998C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
999D3—41no—
1000D3—42no—
1001D3—81no—
1002D3—122no—
1003D3—122no—
1004D3—242no—
1005D3—241no—
1006D3—241no—
1007D3—481no—
1008D3#473414yesdirect product factor
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—32no—
1013C22—32no—
1014C22—32no—
1015C22—61no—
1016C22—61no—
1017C22—61no—
1018C22—62no—
1019C22—124no—
1020C22—121no—
1021C22—121no—
1022C22—121no—
1023C22—121no—
1024C22—121no—
1025C22—182no—
1026C22—368no—
1027C22—361no—
1028C22—361no—
1029C22—361no—
1030C22—361no—
1031C22—361no—
1032C22—724no—
1033C22C2×D3×D1211yescharacteristic
1034C4—21no—
1035C4—32no—
1036C4—61no—
1037C4—62no—
1038C4—121no—
1039C4—182no—
1040C4—361no—
1041C4D32×D411yescharacteristic
1042C4D32×D411yescharacteristic
1043C3—21no—
1044C3C2×#473411yescharacteristic, complemented
1045C3D3×#44911yescharacteristic, complemented
1046C2—34no—
1047C2—41no—
1048C2—121no—
1049C2—122no—
1050C2—241no—
1051C2—362no—
1052C2—721no—
1053C2D3×#88211yescharacteristic
1054C2D3×#90411yescharacteristic
1055C2D3×#90811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#235C2semidirect
2. D3×#930C2semidirect
3. C2×D3×D24C2semidirect
4. C2×D3×#204C2semidirect
5. #10592433C2semidirect
6. C3×#4734C2semidirect
7. C3×D3×C22⋊C8C2semidirect
8. #10591182C2semidirect
9. #10591163C2semidirect
10. #10590968C2semidirect
11. #10590967C2semidirect
12. #10590962C2semidirect
13. D3×#821C2semidirect
14. #10590823C2semidirect
15. D3×#816C2semidirect
18. C2×#3828C22semidirect
19. C2×C3×#235C22semidirect
29. C2×#3799C22semidirect
31. C2×#3795C22semidirect
33. #64139C22semidirect
34. C2×#3745C22semidirect
35. C2×#3744C22semidirect
36. C3×#930C22semidirect
37. C2×C3×D24C22semidirect
38. C2×C3×#204C22semidirect
43. #63909C22semidirect
44. #63908C22semidirect
47. C2×#3717C22semidirect
48. C2×#3716C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
53. C32×C22⋊C8C22semidirect
54. #63648C22semidirect
55. #63643C22semidirect
56. C3×#830C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. C3×(C2×D3)⋊C8C22semidirect
60. C3×#816C22semidirect
61. #63567C22semidirect
62. #63566C22semidirect
63. #63564C22semidirect
64. #63563C22semidirect
94. #4734D3direct (N × H)
95. D3×C22⋊C8D3semidirect
140. D3×D12D4semidirect
148. D3×Dic6D4semidirect
195. C2×#235C2×D3semidirect
220. #930C2×D3semidirect
231. C2×D24C2×D3semidirect
238. C2×#204C2×D3semidirect
251. C3×C22⋊C8C2×D3semidirect
252. C3×C22⋊C8C2×D3semidirect
255. #830C2×D3semidirect
261. #821C2×D3semidirect
262. (C2×D3)⋊C8C2×D3semidirect
263. (C2×D3)⋊C8C2×D3semidirect
269. #816C2×D3semidirect
299. C4⋊(C3⋊D3)C2×D4semidirect
302. #634C2×D4semidirect
313. C3×D12C2×D4semidirect
322. C3×Dic6C2×D4semidirect
596. C22⋊C8D32semidirect
713. D12D3×D4semidirect
738. Dic6D3×D4semidirect
758. C3×D3#449semidirect
916. C32C2×#449semidirect
1008. D3#4734direct (N × H)
1044. C3C2×#4734semidirect
1045. C3D3×#449semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
D3×#9302
C2×D3×D242
C2×D3×#2042
#105924332
C3×#47342
C3×D3×C22⋊C82
#105911822
#105911632
#105909682
#105909672
#105909622
D3×#8212
#105908232
D3×#8162
D3×#4493
C2×#47343