Finite Group Databasebeta

← D3×#5172 #11863737

Subgroups — D3×#5172 #11863737

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×#239C211yesmaximal, characteristic, complemented
2C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
3D3×#938C211yesmaximal, characteristic, complemented
4C2×D3×#213C211yesmaximal, characteristic, complemented
5#10592871C211yesmaximal, characteristic, complemented
6C3×#5172C211yesmaximal, characteristic, complemented
7#10591593C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10591521C211yesmaximal, characteristic, complemented
11#10591520C211yesmaximal, characteristic, complemented
12#10590964C211yesmaximal, characteristic, complemented
13D3×#821C211yesmaximal, characteristic, complemented
14D3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
15#10590823C211yesmaximal, characteristic, complemented
16C2×#5172—31nomaximal
17D3×#449—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×D3×#67—21no—
23D3×#239—24no—
24D3×#239—24no—
25C2×D3×D12—21no—
26C2×D3×D12C2211yescharacteristic
27C2×C4×D32—21no—
28C2×C4×D32C2211yescharacteristic
29C2×#3799—21no—
30C2×#3799C2211yescharacteristic, complemented
31C2×#3796—21no—
32C2×#3796C2211yescharacteristic, complemented
33C2×C32×SD16C2211yescharacteristic, complemented
34#64147C2211yescharacteristic, complemented
35C2×#3753C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C3×#938C2211yescharacteristic, complemented
38C2×C3×#214C2211yescharacteristic, complemented
39C2×C3×#213C2211yescharacteristic, complemented
40C3×D3×SD16—24no—
41C2×C3×#204C2211yescharacteristic, complemented
42C2×C3×D3×C8C2211yescharacteristic
43#63970—21no—
44D3×#217—21no—
45#63958—21no—
46D3×#213—24no—
47#63916C2211yescharacteristic, complemented
48#63908C2211yescharacteristic, complemented
49D3×C4⋊Dic3C2211yescharacteristic
50C2×#3714C2211yescharacteristic, complemented
51C2×#3713C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic
53#63662C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#821C2211yescharacteristic, complemented
58C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C22×#239—31no—
67C22×C3×SD16—31no—
68C2×#938—31no—
69C22×#213—31no—
70C2×D3×SD16D311yescharacteristic, complemented
71C2×D3×D8—31no—
72D3×#121—31no—
73C3×#449—31no—
74#5238—31no—
75C2×#835—31no—
76#5172—31no—
77#5172—31no—
78#5172—31no—
79#5172—31no—
80#5172—31no—
81#5172—31no—
82#5172—31no—
83#5172—31no—
84#5172—61no—
85#5172D311yescharacteristic, direct product factor
86#5158—31no—
87C2×#821—31no—
88C2×(C2×D3)⋊C8—31no—
89#5037—31no—
90#4810—31no—
91D3×#103—31no—
92#4781—31no—
93D3×#102—31no—
94#4734—31no—
95D3×C22⋊C8—31no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C22×D32D411yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C2×#638—21no—
102#3832—22no—
103#3832—22no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C3×#239—22no—
111C3×#239—22no—
112C3×D3×Q8—22no—
113C3×D3×Q8D414yescomplemented
114C3×D3×D4—22no—
115C3×D3×D4—22no—
116C2×C3×D12—21no—
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123C2×C3×Dic6—21no—
124C2×C3×Dic6C2311yescharacteristic
125D3×#67—44no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#625—21no—
131C2×#624—21no—
132C2×#624D411yescharacteristic
133C2×D3×Dic3—21no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3D411yescharacteristic
136C2×D3×Dic3D411yescharacteristic
137D3×D12—28no—
138D3×D12—22no—
139D3×D12D414yescomplemented
140C4×D32—28no—
141C4×D32—22no—
142C4×D32—22no—
143#3799—28no—
144#3799—22no—
145#3799—22no—
146#3796—28no—
147#3796—22no—
148#3796—22no—
149C32×SD16—22no—
150C2×C32×C8C2311yescharacteristic
151#3757—21no—
152#3753—22no—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C2×C3⋊(C3⋊C8)C2311yescharacteristic
155C3×#217—21no—
156C3×#215—22no—
157C3×#214—22no—
158C3×#213—22no—
159C3×C4⋊Dic3C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C2×C3×C3⋊C8C2311yescharacteristic
162C3×#204—22no—
163C3×D3×C8—22no—
164Dic3⋊Dic3—21no—
165(C2×D3)⋊Dic3—21no—
166(C2×D3)⋊Dic3—21no—
167#3714—22no—
168#3713—22no—
169D3×C3⋊C8—22no—
170C2×#449—91noSylow
171C2×C3×#41—31no—
172C22×C3×Q8—31no—
173C22×C3×D4—31no—
174C22×#67—61no—
175D3×#41—64no—
176D3×#41—64no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—31no—
180C2×#239—31no—
181C2×#239—61no—
182C2×#239—61no—
183C2×#239—61no—
184C2×#239—64no—
185C2×#239—64no—
186C2×#239C2×D311yescharacteristic, complemented
187C2×D3×Q8C2×D311yescharacteristic
188C2×#237—31no—
189C2×#237—61no—
190C2×D3×D4—31no—
191C2×D3×D4—61no—
192C2×D3×D4—61no—
193C2×D3×D4C2×D311yescharacteristic
194C2×#235—31no—
195C2×#235—61no—
196C22×D12—31no—
197C22×D12—61no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×C4×D3—61no—
201C22×C4×D3—61no—
202C2×C3×SD16—21no—
203C2×C3×SD16—31no—
204C2×C3×SD16—31no—
205C2×C3×SD16—31no—
206C2×C3×SD16—64no—
207C2×C3×SD16C2×D311yescharacteristic, complemented
208C2×C3×SD16C2×D311yescharacteristic, complemented
209C2×C3×D8—31no—
210C22×C3×C8—31no—
211C3×#121—31no—
212C2×#217—61no—
213C2×#215C2×D311yescharacteristic, complemented
214#939—61no—
215#938—31no—
216#938—31no—
217#938—31no—
218#938—31no—
219#938—61no—
220#938—61no—
221#938—61no—
222#938C2×D311yescharacteristic, complemented
223C2×#214C2×D311yescharacteristic, complemented
224C2×#213—31no—
225C2×#213—31no—
226C2×#213—31no—
227C2×#213—31no—
228C2×#213—31no—
229C2×#213—61no—
230C2×#213—64no—
231C2×#213C2×D311yescharacteristic, complemented
232#930—31no—
233C2×C4⋊Dic3—31no—
234C22×C3⋊C8—31no—
235D3×SD16—24no—
236D3×D8—64no—
237C2×D24—31no—
238C2×#204C2×D311yescharacteristic, complemented
239C2×D3×C8—31no—
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—31no—
248#835—31no—
249#835—31no—
250#835—31no—
251#835—31no—
252#835—61no—
253#835C2×D311yescharacteristic, complemented
254#832—31no—
255#830—31no—
256#821—31no—
257#821—31no—
258#821—31no—
259#821—31no—
260#821—61no—
261#821C2×D311yescharacteristic, complemented
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—61no—
268(C2×D3)⋊C8C2×D311yescharacteristic, complemented
269#816—31no—
270#810—31no—
271#809—31no—
272C23×C32—21no—
273C22×C3⋊D3—21no—
274C22×C3⋊D3C2×D411yescharacteristic
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3—42no—
278C22×C3×D3—42no—
279C22×C3×D3—42no—
280C22×C3×D3C2×D411yescharacteristic
281C22×C3×D3C2×D411yescharacteristic
282C2×D32—24no—
283C2×D32—22no—
284C2×D32—22no—
285C2×D32—22no—
286C2×D32—42no—
287C2×D32—42no—
288C32×Q8—21no—
289C32×Q8C2×D412yescomplemented
290C32×D4—21no—
291C32×D4—21no—
292C2×C32×C4—21no—
293C2×C32×C4C2411yescharacteristic
294#638—42no—
295C2×C3⋊Dic3—21no—
296C2×C3⋊Dic3C2×D411yescharacteristic
297C4⋊(C3⋊D3)—24no—
298C4⋊(C3⋊D3)—21no—
299C4⋊(C3⋊D3)C2×D412yescomplemented
300C4×C3⋊D3—24no—
301C4×C3⋊D3—21no—
302C4×C3⋊D3—21no—
303C3×#67—42no—
304C3×#67—42no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3C2×D411yescharacteristic
308C2×C3×Dic3C2×D411yescharacteristic
309C3×D12—24no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12C2×D412yescomplemented
314C3×C4×D3—24no—
315C3×C4×D3—24no—
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3C2×D412yes—
319C3×C4×D3C2×D412yes—
320C3×Dic6—21no—
321C3×Dic6—24no—
322C3×Dic6C2×D412yescomplemented
323#626—24no—
324#626—24no—
325#626—24no—
326#626—42no—
327#625—42no—
328#624—24no—
329#624—22no—
330D3×Dic3—24no—
331D3×Dic3—22no—
332D3×Dic3—22no—
333D3×Dic3—42no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—91no—
339C22×SD16—31no—
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—91no—
353C24×C3—61no—
354C23×D3—21no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—61no—
358C23×D3—61no—
359C3×#41—62no—
360C3×#41—62no—
361C2×C3×Q8—21no—
362C2×C3×Q8—34no—
363C2×C3×Q8—31no—
364C2×C3×Q8—61no—
365C2×C3×Q8—62no—
366C2×C3×Q8C22×D311yescharacteristic
367C2×C3×Q8C22×D311yescharacteristic
368C2×C3×D4—21no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—61no—
372C2×C3×D4—62no—
373C2×C3×D4—62no—
374C2×C3×D4—61no—
375C2×C3×D4—61no—
376C2×C3×D4C22×D311yescharacteristic
377C2×C3×D4C22×D311yescharacteristic
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—61no—
381C22×C3×C4—61no—
382C2×#67—21no—
383C2×#67—21no—
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—124no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—61no—
397C22×Dic3—61no—
398#239—22no—
399#239—22no—
400#239—62no—
401#239—62no—
402#239—68no—
403#239—62no—
404#239—68no—
405#239—62no—
406#239—62no—
407#239—62no—
408#239—62no—
409#239—62no—
410#239—122no—
411#239—122no—
412D3×Q8—22no—
413D3×Q8#6714yescomplemented
414#237—62no—
415#237—68no—
416#237—62no—
417D3×D4—22no—
418D3×D4—22no—
419D3×D4—34no—
420D3×D4—68no—
421D3×D4—62no—
422D3×D4—124no—
423#235—62no—
424#235—68no—
425#235—62no—
426C2×D12—21no—
427C2×D12—31no—
428C2×D12—31no—
429C2×D12—34no—
430C2×D12—61no—
431C2×D12—62no—
432C2×D12—68no—
433C2×D12—61no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12—61no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—121no—
440C2×D12C22×D311yescharacteristic
441C2×D12C22×D311yescharacteristic
442C2×C4×D3—21no—
443C2×C4×D3—21no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—61no—
451C2×C4×D3—62no—
452C2×C4×D3—62no—
453C2×C4×D3—68no—
454C2×C4×D3—68no—
455C2×C4×D3—61no—
456C2×C4×D3—61no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—61no—
460C2×C4×D3—62no—
461C2×C4×D3—62no—
462C2×C4×D3—61no—
463C2×C4×D3—121no—
464C2×C4×D3C22×D311yescharacteristic
465C2×C4×D3C22×D311yescharacteristic
466C2×Dic6—21no—
467C2×Dic6C22×D311yescharacteristic
468C3×SD16—22no—
469C3×SD16—22no—
470C3×SD16—42no—
471C3×SD16—62no—
472C3×SD16—62no—
473C3×SD16—62no—
474C3×D8—62no—
475C2×C3×C8—21no—
476C2×C3×C8—31no—
477C2×C3×C8—31no—
478C2×C3×C8—62no—
479C2×C3×C8C22×D311yescharacteristic
480C2×C3×C8C22×D311yescharacteristic
481C3×C4⋊C4—31no—
482C3×C22⋊C4—61no—
483#217—21no—
484#217—61no—
485#217—61no—
486#217—61no—
487#217—61no—
488#217—121no—
489#215—22no—
490#214—22no—
491#213—22no—
492#213—62no—
493#213—62no—
494#213—62no—
495#213—62no—
496#213—62no—
497#213—122no—
498(C2×D3)⋊C4—61no—
499(C2×D3)⋊C4—61no—
500C4⋊Dic3—31no—
501C4⋊Dic3—31no—
502C4⋊Dic3—61no—
503C4⋊Dic3—61no—
504C4⋊Dic3C22×D311yescharacteristic
505Dic3⋊C4—61no—
506C2×C3⋊C8—31no—
507C2×C3⋊C8—31no—
508C2×C3⋊C8—61no—
509C2×C3⋊C8—62no—
510C2×C3⋊C8C22×D311yescharacteristic
511C2×C3⋊C8C22×D311yescharacteristic
512D24—62no—
513#204—22no—
514D3×C8—22no—
515D3×C8—62no—
516C22×C32—41no—
517C22×C32—41no—
518C22×C32—41no—
519C22×C32C22×D411yescharacteristic
520C2×C3⋊D3—21no—
521C2×C3⋊D3—22no—
522C2×C3⋊D3—21no—
523C2×C3⋊D3—21no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
526C2×C3×D3—21no—
527C2×C3×D3—22no—
528C2×C3×D3—21no—
529C2×C3×D3—21no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—84no—
536C2×C3×D3#12012yes—
537C2×C3×D3#13512yes—
538C2×C3×D3AGL(1,ℤ/8)12yes—
539D32—44no—
540D32—48no—
541C32×C4—22no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3⋊Dic3—21no—
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—31no—
559C22×D4—31no—
560C22×D4—91no—
561C22×D4—181no—
562C22×D4—181no—
563C23×C4—91no—
564C23×C4—181no—
565C2×SD16—31no—
566C2×SD16—31no—
567C2×SD16—31no—
568C2×SD16—64no—
569C2×SD16D3211yescharacteristic, complemented
570C2×D8—31no—
571C2×D8—91no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8—184no—
575C22×C8—31no—
576C22×C8—91no—
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—91no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—41no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—122no—
605C23×C3—122no—
606C23×C3—122no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—31no—
610C22×D3—31no—
611C22×D3—42no—
612C22×D3—42no—
613C22×D3—42no—
614C22×D3—61no—
615C22×D3—64no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—61no—
620C22×D3—61no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—64no—
624C22×D3—62no—
625C22×D3—121no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3D3×D411yescharacteristic
631C22×D3D3×D411yescharacteristic
632C3×Q8—21no—
633C3×Q8—21no—
634C3×Q8—22no—
635C3×Q8—32no—
636C3×Q8—41no—
637C3×Q8—64no—
638C3×Q8—61no—
639C3×Q8D3×D412yescomplemented
640C3×Q8C2×#6712yescomplemented
641C3×D4—21no—
642C3×D4—21no—
643C3×D4—21no—
644C3×D4—21no—
645C3×D4—32no—
646C3×D4—41no—
647C3×D4—41no—
648C3×D4—64no—
649C3×D4—61no—
650C3×D4—61no—
651C3×D4—61no—
652C3×D4—122no—
653C3×D4—122no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—31no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—31no—
661C2×C3×C4—41no—
662C2×C3×C4—64no—
663C2×C3×C4—64no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670#67—42no—
671#67—42no—
672#67—64no—
673#67—64no—
674#67—64no—
675#67—122no—
676#67—122no—
677#67—122no—
678#67—122no—
679#67—122no—
680#67—242no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—31no—
684C2×Dic3—31no—
685C2×Dic3—61no—
686C2×Dic3—62no—
687C2×Dic3—64no—
688C2×Dic3—62no—
689C2×Dic3—61no—
690C2×Dic3—61no—
691C2×Dic3—121no—
692C2×Dic3—122no—
693C2×Dic3D3×D411yescharacteristic
694C2×Dic3D3×D411yescharacteristic
695D12—24no—
696D12—21no—
697D12—21no—
698D12—21no—
699D12—32no—
700D12—32no—
701D12—62no—
702D12—64no—
703D12—64no—
704D12—64no—
705D12—64no—
706D12—64no—
707D12—61no—
708D12—61no—
709D12—121no—
710D12—124no—
711D12—122no—
712D12D3×D412yescomplemented
713C4×D3—24no—
714C4×D3—24no—
715C4×D3—21no—
716C4×D3—21no—
717C4×D3—62no—
718C4×D3—64no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—62no—
723C4×D3—64no—
724C4×D3—62no—
725C4×D3—61no—
726C4×D3—61no—
727C4×D3—61no—
728C4×D3—61no—
729C4×D3—62no—
730C4×D3—121no—
731C4×D3—121no—
732C4×D3—124no—
733C4×D3—122no—
734C4×D3D3×D412yes—
735C4×D3C2×#6712yes—
736Dic6—21no—
737Dic6—24no—
738Dic6C2×#6712yescomplemented
739C3×C8—21no—
740C3×C8—21no—
741C3×C8—41no—
742C3×C8—61no—
743C3×C8—61no—
744C3⋊C8—21no—
745C3⋊C8—21no—
746C3⋊C8—61no—
747C3⋊C8—61no—
748C3⋊C8—121no—
749C2×C32—81no—
750C2×C32C2×#12011yescharacteristic
751C2×C32C2×#13511yescharacteristic
752C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
753C3⋊D3—41no—
754C3⋊D3—42no—
755C3×D3—41no—
756C3×D3—42no—
757C3×D3—81no—
758C3×D3#44914yescomplemented
759C24—61no—
760C24—91no—
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—34no—
773C2×Q8—31no—
774C2×Q8—61no—
775C2×Q8—62no—
776C2×Q8C2×D3211yescharacteristic
777C2×D4—31no—
778C2×D4—31no—
779C2×D4—61no—
780C2×D4—62no—
781C2×D4—62no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—94no—
785C2×D4—91no—
786C2×D4—181no—
787C2×D4—182no—
788C2×D4—181no—
789C2×D4—188no—
790C2×D4—181no—
791C2×D4—181no—
792C2×D4—181no—
793C2×D4—181no—
794C2×D4—181no—
795C2×D4—364no—
796C2×D4C2×D3211yescharacteristic
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—91no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—91no—
805C22×C4—181no—
806C22×C4—182no—
807C22×C4—182no—
808C22×C4—181no—
809C22×C4—188no—
810C22×C4—181no—
811C22×C4—181no—
812SD16—22no—
813SD16—62no—
814SD16—62no—
815SD16—62no—
816D8—62no—
817D8—182no—
818D8—182no—
819D8—182no—
820C2×C8—31no—
821C2×C8—31no—
822C2×C8—62no—
823C2×C8—91no—
824C2×C8—182no—
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—32no—
835C22×C3—32no—
836C22×C3—32no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—41no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—61no—
844C22×C3—61no—
845C22×C3—62no—
846C22×C3—61no—
847C22×C3—81no—
848C22×C3—81no—
849C22×C3—81no—
850C22×C3—121no—
851C22×C3—121no—
852C22×C3—121no—
853C22×C3—121no—
854C22×C3—121no—
855C22×C3—244no—
856C22×C3C2×D3×D411yescharacteristic
857C22×C3C2×D3×D411yescharacteristic
858C2×D3—21no—
859C2×D3—21no—
860C2×D3—21no—
861C2×D3—22no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—41no—
865C2×D3—41no—
866C2×D3—41no—
867C2×D3—61no—
868C2×D3—61no—
869C2×D3—61no—
870C2×D3—61no—
871C2×D3—62no—
872C2×D3—61no—
873C2×D3—62no—
874C2×D3—61no—
875C2×D3—84no—
876C2×D3—122no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—124no—
881C2×D3—128no—
882C2×D3—121no—
883C2×D3—121no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—124no—
887C2×D3—128no—
888C2×D3—241no—
889C2×D3—241no—
890C2×D3#91412yes—
891C2×D3#91612yes—
892C2×D3#93712yes—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—32no—
898C3×C4—42no—
899C3×C4—61no—
900C3×C4—62no—
901C3×C4—121no—
902C3×C4C2×D3×D411yescharacteristic
903C3×C4C2×D3×D411yescharacteristic
904C3×C4C2×D3×D411yescharacteristic
905C3×C4C22×#6711yescharacteristic
906Dic3—22no—
907Dic3—21no—
908Dic3—41no—
909Dic3—61no—
910Dic3—61no—
911Dic3—121no—
912Dic3—121no—
913Dic3—121no—
914Dic3—241no—
915Dic3#93712yes—
916C32C2×#44911yescharacteristic, complemented, Sylow
917C23—21no—
918C23—31no—
919C23—31no—
920C23—61no—
921C23—61no—
922C23—91no—
923C23—122no—
924C23—122no—
925C23—122no—
926C23—184no—
927C23—182no—
928C23—182no—
929C23—182no—
930C23—181no—
931C23—362no—
932C23—362no—
933Q8—21no—
934Q8—32no—
935Q8—64no—
936Q8—61no—
937Q8D3×#6712yescomplemented
938D4—21no—
939D4—21no—
940D4—32no—
941D4—64no—
942D4—61no—
943D4—61no—
944D4—61no—
945D4—92no—
946D4—122no—
947D4—122no—
948D4—184no—
949D4—184no—
950D4—184no—
951D4—184no—
952D4—181no—
953D4—362no—
954D4—362no—
955D4—362no—
956C2×C4—21no—
957C2×C4—31no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—31no—
961C2×C4—64no—
962C2×C4—64no—
963C2×C4—61no—
964C2×C4—61no—
965C2×C4—61no—
966C2×C4—61no—
967C2×C4—91no—
968C2×C4—184no—
969C2×C4—182no—
970C2×C4—182no—
971C2×C4—184no—
972C2×C4—182no—
973C2×C4—184no—
974C2×C4—181no—
975C2×C4—181no—
976C2×C4—181no—
977C2×C4—362no—
978C2×C4C22×D3211yescharacteristic
979C8—21no—
980C8—61no—
981C8—61no—
982C8—181no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—34no—
987C2×C3—81no—
988C2×C3—81no—
989C2×C3—121no—
990C2×C3—122no—
991C2×C3—161no—
992C2×C3—241no—
993C2×C3D3×#12011yescharacteristic
994C2×C3C2×#91411yescharacteristic
995C2×C3C2×#91611yescharacteristic
996C2×C3D3×#13511yescharacteristic
997C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
998C2×C3C2×#93711yescharacteristic
999D3—41no—
1000D3—42no—
1001D3—81no—
1002D3—121no—
1003D3—122no—
1004D3—121no—
1005D3—122no—
1006D3—241no—
1007D3—242no—
1008D3#517214yesdirect product factor
1009C22—32no—
1010C22—32no—
1011C22—32no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—61no—
1016C22—61no—
1017C22—62no—
1018C22—61no—
1019C22—121no—
1020C22—121no—
1021C22—121no—
1022C22—121no—
1023C22—121no—
1024C22—181no—
1025C22—181no—
1026C22—182no—
1027C22—181no—
1028C22—244no—
1029C22—364no—
1030C22—368no—
1031C22—361no—
1032C22—361no—
1033C22D32×D411yescharacteristic
1034C4—22no—
1035C4—32no—
1036C4—61no—
1037C4—62no—
1038C4—121no—
1039C4—181no—
1040C4—361no—
1041C4D32×D411yescharacteristic
1042C4C2×D3×#6711yescharacteristic
1043C3—21no—
1044C3D3×#44911yescharacteristic, complemented
1045C3C2×#517211yescharacteristic, complemented
1046C2—34no—
1047C2—81no—
1048C2—121no—
1049C2—122no—
1050C2—241no—
1051C2—361no—
1052C2—362no—
1053C2D3×#91411yescharacteristic
1054C2D3×#91611yescharacteristic
1055C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C2×C3×D3×SD16C2semidirect
3. D3×#938C2semidirect
4. C2×D3×#213C2semidirect
5. #10592871C2semidirect
6. C3×#5172C2semidirect
7. #10591593C2semidirect
8. #10591586C2semidirect
9. D3×#835C2semidirect
10. #10591521C2semidirect
11. #10591520C2semidirect
12. #10590964C2semidirect
13. D3×#821C2semidirect
14. D3×(C2×D3)⋊C8C2semidirect
15. #10590823C2semidirect
18. C2×#3832C22semidirect
19. C2×C3×#239C22semidirect
30. C2×#3799C22semidirect
32. C2×#3796C22semidirect
33. C2×C32×SD16C22semidirect
34. #64147C22semidirect
35. C2×#3753C22semidirect
36. C2×C3×#215C22semidirect
37. C3×#938C22semidirect
38. C2×C3×#214C22semidirect
39. C2×C3×#213C22semidirect
41. C2×C3×#204C22semidirect
47. #63916C22semidirect
48. #63908C22semidirect
50. C2×#3714C22semidirect
51. C2×#3713C22semidirect
53. #63662C22semidirect
54. #63648C22semidirect
55. #63647C22semidirect
56. C3×#835C22semidirect
57. C3×#821C22semidirect
58. C3×(C2×D3)⋊C8C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
70. C2×D3×SD16D3semidirect
85. #5172D3direct (N × H)
113. C3×D3×Q8D4semidirect
139. D3×D12D4semidirect
186. C2×#239C2×D3semidirect
207. C2×C3×SD16C2×D3semidirect
208. C2×C3×SD16C2×D3semidirect
213. C2×#215C2×D3semidirect
222. #938C2×D3semidirect
223. C2×#214C2×D3semidirect
231. C2×#213C2×D3semidirect
238. C2×#204C2×D3semidirect
253. #835C2×D3semidirect
261. #821C2×D3semidirect
268. (C2×D3)⋊C8C2×D3semidirect
289. C32×Q8C2×D4semidirect
299. C4⋊(C3⋊D3)C2×D4semidirect
313. C3×D12C2×D4semidirect
322. C3×Dic6C2×D4semidirect
413. D3×Q8#67semidirect
569. C2×SD16D32semidirect
639. C3×Q8D3×D4semidirect
640. C3×Q8C2×#67semidirect
712. D12D3×D4semidirect
738. Dic6C2×#67semidirect
758. C3×D3#449semidirect
916. C32C2×#449semidirect
937. Q8D3×#67semidirect
1008. D3#5172direct (N × H)
1044. C3D3×#449semidirect
1045. C3C2×#5172semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×C3×D3×SD162
D3×#9382
C2×D3×#2132
#105928712
C3×#51722
#105915932
#105915862
D3×#8352
#105915212
#105915202
#105909642
D3×#8212
D3×(C2×D3)⋊C82
#105908232
C2×#51723
D3×#4493