Finite Group Databasebeta

← D3×#5171 #11866682

Subgroups — D3×#5171 #11866682

Order 1152.

1190 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2D3×#946C211yesmaximal, characteristic, complemented
3D3×#938C211yesmaximal, characteristic
4C2×D32×C8C211yesmaximal, characteristic, complemented
5#10592870C211yesmaximal, characteristic, complemented
6C3×#5171C211yesmaximal, characteristic, complemented
7#10591634C211yesmaximal, characteristic, complemented
8#10591591C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10591499C211yesmaximal, characteristic, complemented
11#10591465C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic, complemented
13#10590843C211yesmaximal, characteristic, complemented
14#10590829C211yesmaximal, characteristic, complemented
15D3×#817C211yesmaximal, characteristic, complemented
16C2×#5171—31nomaximal
17D3×#465—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×#67—21no—
21C2×C4×D32C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64155C2211yescharacteristic, complemented
24#64147C2211yescharacteristic
25C2×C8×C3⋊D3C2211yescharacteristic, complemented
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#938C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic, complemented
30C3×D3×SD16—24no—
31C2×C3×#204C2211yescharacteristic, complemented
32C2×C3×D3×C8C2211yescharacteristic
33C2×C3×D3×C8C2211yescharacteristic, complemented
34#63970—21no—
35D3×#217—21no—
36#63958—21no—
37D3×(C2×D3)⋊C4—21no—
38#63916C2211yescharacteristic
39#63908C2211yescharacteristic
40D3×C4⋊Dic3C2211yescharacteristic
41D3×C4⋊Dic3C2211yescharacteristic
42#63888—21no—
43#63887—21no—
44D3×Dic3⋊C4—21no—
45#63871C2211yescharacteristic, complemented
46#63856C2211yescharacteristic, complemented
47C2×#3710C2211yescharacteristic, complemented
48C2×D3×C3⋊C8C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic, complemented
50D32×C8—24no—
51#63662C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63644C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#817C2211yescharacteristic, complemented
57#63573C2211yescharacteristic, complemented
58#63573C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C22×C3×SD16—31no—
64C2×#946—31no—
65C2×#938—31no—
66C2×D3×SD16D311yescharacteristic, complemented
67C22×D3×C8—31no—
68C22×D3×C8—31no—
69D3×C22⋊Q8—31no—
70D3×#121—31no—
71C3×#465—31no—
72C2×#835—31no—
73C2×#832—31no—
74#5171—31no—
75#5171—31no—
76#5171—31no—
77#5171—31no—
78#5171—31no—
79#5171—31no—
80#5171—31no—
81#5171—31no—
82#5171—61no—
83#5171D311yescharacteristic, direct product factor
84#5114—31no—
85C2×#817—31no—
86#5048—31no—
87#5041—31no—
88#4864—31no—
89D3×#106—31no—
90#4807—31no—
91D3×#103—31no—
92#4778—31no—
93D3×#102—31no—
94C23×C3×D3—21no—
95C22×D32D411yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#638—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×D3×Q8—22no—
103C3×D3×Q8—22no—
104C3×D3×D4—22no—
105C3×D3×D4—22no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112D3×#67—44no—
113C2×#626—21no—
114C2×#625—21no—
115C2×#624D411yescharacteristic
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3D411yescharacteristic
119C2×D3×Dic3D411yescharacteristic
120C4×D32—22no—
121C4×D32—22no—
122C32×SD16—22no—
123C2×C32×C8C2311yescharacteristic
124#3757—21no—
125#3752—21no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3750—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C8×C3⋊D3—22no—
131C3×#217—21no—
132C3×#215—22no—
133C3×#214—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—22no—
141C3×D3×C8—22no—
142C3×D3×C8D414yescomplemented
143#3724—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3710—22no—
152D3×C3⋊C8—22no—
153D3×C3⋊C8—22no—
154C2×#465—91noSylow
155C22×C3×Q8—31no—
156C22×C3×D4—31no—
157C22×#67—61no—
158C2×D3×Q8C2×D311yescharacteristic
159C2×D3×D4—61no—
160C2×D3×D4C2×D311yescharacteristic
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C2×C3×SD16—21no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C2×C3×SD16—64no—
168C2×C3×SD16C2×D311yescharacteristic, complemented
169C2×C3×SD16C2×D311yescharacteristic, complemented
170C22×C3×C8—31no—
171C22×C3×C8—31no—
172C3×C22⋊Q8—31no—
173C3×#121—31no—
174C2×#217—61no—
175#946—31no—
176#946—31no—
177#946—31no—
178#946—31no—
179#946—61no—
180#946—61no—
181#946—61no—
182#946C2×D311yescharacteristic, complemented
183C2×#215C2×D311yescharacteristic, complemented
184#939—61no—
185#938—31no—
186#938—31no—
187#938—31no—
188#938—31no—
189#938—61no—
190#938—61no—
191#938—61no—
192#938C2×D311yescharacteristic
193C2×#214C2×D311yescharacteristic, complemented
194#930—31no—
195C2×(C2×D3)⋊C4—61no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198#924—31no—
199C2×Dic3⋊C4—61no—
200C22×C3⋊C8—31no—
201C22×C3⋊C8—31no—
202D3×SD16—24no—
203C2×#204C2×D311yescharacteristic, complemented
204C2×D3×C8—31no—
205C2×D3×C8—31no—
206C2×D3×C8—31no—
207C2×D3×C8—31no—
208C2×D3×C8—31no—
209C2×D3×C8—31no—
210C2×D3×C8—61no—
211C2×D3×C8—64no—
212C2×D3×C8—64no—
213C2×D3×C8C2×D311yescharacteristic
214C2×D3×C8C2×D311yescharacteristic, complemented
215#897—31no—
216#896—61no—
217#895—31no—
218D3×C4⋊C4—31no—
219D3×C4⋊C4—31no—
220D3×C4⋊C4—61no—
221#884—61no—
222D3×C22⋊C4—61no—
223D3×C22⋊C4—61no—
224#878—61no—
225C3×#106—31no—
226C3×#103—31no—
227C3×#102—31no—
228#835—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—61no—
233#835C2×D311yescharacteristic, complemented
234#832—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#832—61no—
239#832C2×D311yescharacteristic, complemented
240#821—31no—
241#817—31no—
242#817—31no—
243#817—31no—
244#817—31no—
245#817—61no—
246#817C2×D311yescharacteristic, complemented
247#816—31no—
248#810—31no—
249#809—31no—
250#808—31no—
251#808—31no—
252C23×C32—21no—
253C22×C3⋊D3C2×D411yescharacteristic
254C22×C3×D3—21no—
255C22×C3×D3—42no—
256C22×C3×D3—42no—
257C22×C3×D3—42no—
258C22×C3×D3C2×D411yescharacteristic
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—22no—
261C2×D32—22no—
262C2×D32SD1614yescomplemented
263C32×Q8—21no—
264C32×Q8—21no—
265C32×D4—21no—
266C32×D4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2411yescharacteristic
269#638—42no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275C3×#67—42no—
276C3×#67—42no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287C3×C4×D3C2×D412yes—
288C3×C4×D3#4112yes—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—42no—
292#626—42no—
293#625—42no—
294#624—22no—
295D3×Dic3—22no—
296D3×Dic3—22no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8C2×D412yescomplemented
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yescomplemented
303C22×SD16—31no—
304C23×C8—91no—
305C2×C22⋊Q8—91no—
306C2×#121—91no—
307#465—31no—
308#465—91no—
309#465—91no—
310#465—91no—
311#465—91no—
312#465—91no—
313#465—91no—
314#465—91no—
315C2×#106—91no—
316C2×#103—91no—
317C2×#102—91no—
318C24×C3—61no—
319C23×D3—21no—
320C23×D3—31no—
321C23×D3—31no—
322C2×C3×Q8—21no—
323C2×C3×Q8—31no—
324C2×C3×Q8—61no—
325C2×C3×Q8—62no—
326C2×C3×Q8—62no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—62no—
332C2×C3×D4—62no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—61no—
340C2×#67—21no—
341C2×#67—21no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—121no—
348C2×#67—124no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353D3×Q8—22no—
354D3×Q8—22no—
355D3×D4—22no—
356D3×D4—22no—
357D3×D4—124no—
358C2×D12—61no—
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—21no—
361C2×C4×D3—31no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—61no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3C22×D311yescharacteristic
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6—21no—
377C2×Dic6C22×D311yescharacteristic
378C3×SD16—22no—
379C3×SD16—22no—
380C3×SD16—42no—
381C3×SD16—62no—
382C3×SD16—62no—
383C3×SD16—62no—
384C2×C3×C8—21no—
385C2×C3×C8—31no—
386C2×C3×C8—34no—
387C2×C3×C8—31no—
388C2×C3×C8—62no—
389C2×C3×C8C22×D311yescharacteristic
390C2×C3×C8C22×D311yescharacteristic
391C3×C4⋊C4—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396#217—21no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—121no—
403#215—22no—
404#214—22no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—61no—
407(C2×D3)⋊C4—61no—
408(C2×D3)⋊C4—61no—
409(C2×D3)⋊C4—61no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—121no—
414C4⋊Dic3—31no—
415C4⋊Dic3—31no—
416C4⋊Dic3—31no—
417C4⋊Dic3—31no—
418C4⋊Dic3—61no—
419C4⋊Dic3—61no—
420C4⋊Dic3—61no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3C22×D311yescharacteristic
424C4⋊Dic3C22×D311yescharacteristic
425Dic3⋊C4—21no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—121no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—61no—
437C2×C3⋊C8—62no—
438C2×C3⋊C8—62no—
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441#204—22no—
442D3×C8—22no—
443D3×C8—62no—
444D3×C8—62no—
445D3×C8—62no—
446D3×C8—62no—
447D3×C8—62no—
448D3×C8—62no—
449D3×C8—122no—
450D3×C8#6714yescomplemented
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—21no—
456C2×C3⋊D3—21no—
457C2×C3⋊D3C2×SD1612yescomplemented
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—84no—
464C2×C3×D3#12112yes—
465C2×C3×D3C2×SD1612yes—
466C2×C3×D3C2×SD1612yescomplemented
467C2×C3×D3#13512yes—
468D32—28no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4C2×#4111yescharacteristic
472C3⋊Dic3—21no—
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3#12112yes—
480C22×Q8—31no—
481C22×D4—31no—
482C22×D4—181no—
483C23×C4—91no—
484C2×SD16—31no—
485C2×SD16—31no—
486C2×SD16—31no—
487C2×SD16—64no—
488C2×SD16D3211yescharacteristic, complemented
489C22×C8—31no—
490C22×C8—31no—
491C22×C8—91no—
492C22×C8—91no—
493C22×C8—91no—
494C22×C8—91no—
495C22×C8—184no—
496C22⋊Q8—31no—
497C22⋊Q8—91no—
498C22⋊Q8—91no—
499C22⋊Q8—91no—
500C22⋊Q8—181no—
501C22⋊Q8—181no—
502#121—31no—
503#121—91no—
504#121—91no—
505#121—91no—
506#121—181no—
507#121—181no—
508C2×C4⋊C4—91no—
509C2×C4⋊C4—91no—
510C2×C4⋊C4—181no—
511C2×C22⋊C4—181no—
512C2×C22⋊C4—181no—
513#106—31no—
514#106—91no—
515#106—91no—
516#106—91no—
517#103—31no—
518#103—91no—
519#103—91no—
520#103—91no—
521#102—31no—
522#102—91no—
523#102—91no—
524#102—91no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—31no—
528C23×C3—31no—
529C23×C3—41no—
530C23×C3—61no—
531C23×C3—122no—
532C23×C3—122no—
533C23×C3—122no—
534C22×D3—21no—
535C22×D3—31no—
536C22×D3—31no—
537C22×D3—34no—
538C22×D3—34no—
539C22×D3—42no—
540C22×D3—42no—
541C22×D3—42no—
542C22×D3—61no—
543C22×D3—62no—
544C22×D3—62no—
545C22×D3—62no—
546C22×D3—62no—
547C22×D3D3×D411yescharacteristic
548C22×D3D3×D411yescharacteristic
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—41no—
554C3×Q8—41no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—122no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—122no—
567C3×D4—122no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—31no—
575C2×C3×C4—41no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—122no—
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584#67—42no—
585#67—42no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—242no—
592C2×Dic3—21no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—61no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—121no—
605C2×Dic3—121no—
606C2×Dic3—122no—
607C2×Dic3—122no—
608C2×Dic3D3×D411yescharacteristic
609C2×Dic3D3×D411yescharacteristic
610D12—21no—
611D12—21no—
612D12—122no—
613C4×D3—21no—
614C4×D3—21no—
615C4×D3—42no—
616C4×D3—62no—
617C4×D3—62no—
618C4×D3—62no—
619C4×D3—61no—
620C4×D3—61no—
621C4×D3—61no—
622C4×D3—61no—
623C4×D3—62no—
624C4×D3—121no—
625C4×D3—121no—
626C4×D3—122no—
627C4×D3—122no—
628C4×D3#23712yes—
629C4×D3C2×#6712yes—
630Dic6—21no—
631Dic6—21no—
632Dic6—42no—
633C3×C8—22no—
634C3×C8—32no—
635C3×C8—61no—
636C3×C8D3×D412yescomplemented
637C3×C8C2×#6712yescomplemented
638C3⋊C8—21no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C3⋊C8C2×#6712yescomplemented
643C2×C32—81no—
644C2×C32C2×#12111yescharacteristic
645C2×C32C22×SD1611yescharacteristic
646C2×C32C2×#13511yescharacteristic
647C3⋊D3—22no—
648C3×D3—22no—
649C3×D3—81no—
650C3×D3#46514yescomplemented
651C24—61no—
652C24—91no—
653C2×Q8—31no—
654C2×Q8—61no—
655C2×Q8—62no—
656C2×Q8—62no—
657C2×Q8C2×D3211yescharacteristic
658C2×D4—31no—
659C2×D4—62no—
660C2×D4—62no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4—181no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—364no—
667C2×D4C2×D3211yescharacteristic
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—61no—
671C22×C4—91no—
672C22×C4—91no—
673C22×C4—91no—
674C22×C4—91no—
675C22×C4—182no—
676C22×C4—182no—
677C22×C4—181no—
678C22×C4—181no—
679SD16—22no—
680SD16—62no—
681SD16—62no—
682SD16—62no—
683C2×C8—31no—
684C2×C8—34no—
685C2×C8—31no—
686C2×C8—62no—
687C2×C8—91no—
688C2×C8—182no—
689C2×C8—182no—
690C2×C8—182no—
691C2×C8—182no—
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—91no—
697C4⋊C4—91no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C4⋊C4—181no—
702C4⋊C4—181no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C22×C3—21no—
712C22×C3—32no—
713C22×C3—32no—
714C22×C3—32no—
715C22×C3—32no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—81no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—244no—
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C2×D3×D411yescharacteristic
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—32no—
736C2×D3—32no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—62no—
741C2×D3—68no—
742C2×D3—61no—
743C2×D3—61no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—68no—
747C2×D3—84no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3D3×SD1612yes—
751C2×D3D3×SD1612yescomplemented
752C2×D3#91612yes—
753C2×D3#93812yes—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—32no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—61no—
760C3×C4—81no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4C2×D3×D411yescharacteristic
765C3×C4C2×#23711yescharacteristic
766C3×C4D3×#4111yescharacteristic
767C3×C4C22×#6711yescharacteristic
768Dic3—21no—
769Dic3—41no—
770Dic3—41no—
771Dic3—41no—
772Dic3—61no—
773Dic3—61no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—121no—
778Dic3—121no—
779Dic3—241no—
780Dic3—241no—
781Dic3#93812yes—
782C32C2×#46511yescharacteristic, complemented, Sylow
783C23—21no—
784C23—31no—
785C23—31no—
786C23—61no—
787C23—94no—
788C23—91no—
789C23—122no—
790C23—122no—
791C23—122no—
792C23—182no—
793C23—182no—
794Q8—21no—
795Q8—21no—
796Q8—61no—
797Q8—61no—
798Q8—122no—
799D4—21no—
800D4—21no—
801D4—61no—
802D4—61no—
803D4—122no—
804D4—122no—
805D4—362no—
806D4—362no—
807D4—362no—
808C2×C4—21no—
809C2×C4—31no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—31no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—91no—
819C2×C4—122no—
820C2×C4—182no—
821C2×C4—182no—
822C2×C4—182no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—181no—
827C2×C4—362no—
828C2×C4—362no—
829C2×C4C22×D3211yescharacteristic
830C8—32no—
831C8—61no—
832C8—181no—
833C8D3×#6712yescomplemented
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—34no—
838C2×C3—62no—
839C2×C3—81no—
840C2×C3—81no—
841C2×C3—161no—
842C2×C3—241no—
843C2×C3D3×#12111yescharacteristic
844C2×C3C2×D3×SD1611yescharacteristic
845C2×C3C2×D3×SD1611yescharacteristic
846C2×C3C2×#91611yescharacteristic
847C2×C3D3×#13511yescharacteristic
848C2×C3C2×#93811yescharacteristic
849D3—22no—
850D3—62no—
851D3—62no—
852D3—81no—
853D3—122no—
854D3#517114yesdirect product factor
855C22—32no—
856C22—32no—
857C22—32no—
858C22—32no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—61no—
863C22—61no—
864C22—92no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—188no—
869C22—181no—
870C22—181no—
871C22—244no—
872C22D32×D411yescharacteristic
873C4—32no—
874C4—41no—
875C4—61no—
876C4—121no—
877C4—121no—
878C4—121no—
879C4—181no—
880C4—361no—
881C4—361no—
882C4D3×#23711yescharacteristic
883C4C2×D3×#6711yescharacteristic
884C3—21no—
885C3D3×#46511yescharacteristic, complemented
886C3C2×#517111yescharacteristic, complemented
887C2—34no—
888C2—62no—
889C2—81no—
890C2—182no—
891C2—241no—
892C2D32×SD1611yescharacteristic
893C2D3×#91611yescharacteristic
894C2D3×#93811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalD3×#938C2
hypercenterC2×SD16D32
hypocenterC32C2×#465
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×C3×D3×SD16C2semidirect
2. D3×#946C2semidirect
4. C2×D32×C8C2semidirect
5. #10592870C2semidirect
6. C3×#5171C2semidirect
7. #10591634C2semidirect
8. #10591591C2semidirect
9. D3×#835C2semidirect
10. #10591499C2semidirect
11. #10591465C2semidirect
12. D3×#832C2semidirect
13. #10590843C2semidirect
14. #10590829C2semidirect
15. D3×#817C2semidirect
22. C2×C32×SD16C22semidirect
23. #64155C22semidirect
25. C2×C8×C3⋊D3C22semidirect
26. C3×#946C22semidirect
27. C2×C3×#215C22semidirect
29. C2×C3×#214C22semidirect
31. C2×C3×#204C22semidirect
33. C2×C3×D3×C8C22semidirect
45. #63871C22semidirect
46. #63856C22semidirect
47. C2×#3710C22semidirect
49. C2×D3×C3⋊C8C22semidirect
51. #63662C22semidirect
52. #63659C22semidirect
53. #63644C22semidirect
54. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×#817C22semidirect
57. #63573C22semidirect
58. #63573C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
66. C2×D3×SD16D3semidirect
83. #5171D3direct (N × H)
142. C3×D3×C8D4semidirect
168. C2×C3×SD16C2×D3semidirect
169. C2×C3×SD16C2×D3semidirect
182. #946C2×D3semidirect
183. C2×#215C2×D3semidirect
193. C2×#214C2×D3semidirect
203. C2×#204C2×D3semidirect
214. C2×D3×C8C2×D3semidirect
233. #835C2×D3semidirect
239. #832C2×D3semidirect
246. #817C2×D3semidirect
262. C2×D32SD16semidirect
299. C32×C8C2×D4semidirect
302. C3×C3⋊C8C2×D4semidirect
450. D3×C8#67semidirect
457. C2×C3⋊D3C2×SD16semidirect
466. C2×C3×D3C2×SD16semidirect
488. C2×SD16D32semidirect
636. C3×C8D3×D4semidirect
637. C3×C8C2×#67semidirect
642. C3⋊C8C2×#67semidirect
650. C3×D3#465semidirect
751. C2×D3D3×SD16semidirect
782. C32C2×#465semidirect
833. C8D3×#67semidirect
854. D3#5171direct (N × H)
885. C3D3×#465semidirect
886. C3C2×#5171semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×SD162
D3×#9462
D3×#9382
C2×D32×C82
#105928702
C3×#51712
#105916342
#105915912
D3×#8352
#105914992
#105914652
D3×#8322
#105908432
#105908292
D3×#8172
C2×#51713
D3×#4653