Finite Group Databasebeta

← D3×#5168 #11874244

Subgroups — D3×#5168 #11874244

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
2D3×#947C211yesmaximal, characteristic, complemented
3C2×D3×#216C211yesmaximal, characteristic, complemented
4D3×#936C211yesmaximal, characteristic, complemented
5C2×D3×#213C211yesmaximal, characteristic
6C2×D3×#204C211yesmaximal, characteristic, complemented
7#10592867C211yesmaximal, characteristic, complemented
8C3×#5168C211yesmaximal, characteristic, complemented
9#10591610C211yesmaximal, characteristic, complemented
10#10591606C211yesmaximal, characteristic, complemented
11#10591474C211yesmaximal, characteristic, complemented
12#10591473C211yesmaximal, characteristic, complemented
13#10590867C211yesmaximal, characteristic, complemented
14#10590862C211yesmaximal, characteristic, complemented
15D3×C8×Dic3C211yesmaximal, characteristic, complemented
16C2×#5168—31nomaximal
17D3×#495—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic, complemented
23#64156C2211yescharacteristic, complemented
24C2×#3756C2211yescharacteristic, complemented
25#64145C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic
27C2×#3744C2211yescharacteristic, complemented
28C3×#947C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic, complemented
31C3×#936C2211yescharacteristic, complemented
32C2×C3×#214C2211yescharacteristic, complemented
33C2×C3×#213C2211yescharacteristic
34C3×D3×SD16—24no—
35C2×C3×#204C2211yescharacteristic, complemented
36C2×C3×#204C2211yescharacteristic, complemented
37C2×C3×D3×C8C2211yescharacteristic
38D3×#217—22no—
39#63959—22no—
40D3×#216—24no—
41D3×#213—24no—
42D3×(C2×D3)⋊C4—22no—
43#63907—22no—
44C4×D3×Dic3C2211yescharacteristic
45#63864C2211yescharacteristic, complemented
46#63863C2211yescharacteristic, complemented
47#63863C2211yescharacteristic, complemented
48#63860C2211yescharacteristic, complemented
49C2×#3719C2211yescharacteristic, complemented
50C2×#3718C2211yescharacteristic, complemented
51C2×#3717C2211yescharacteristic, complemented
52C2×#3716C2211yescharacteristic, complemented
53C2×#3714C2211yescharacteristic
54C2×#3713C2211yescharacteristic
55C2×D3×C3⋊C8C2211yescharacteristic
56D3×#204—24no—
57C8×C3⋊Dic3C2211yescharacteristic, complemented
58C3×C8×Dic3C2211yescharacteristic, complemented
59#63553C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C22×C3×SD16—31no—
62C2×#947—31no—
63C22×#216—31no—
64C2×#936—31no—
65C22×#213—31no—
66C2×D3×Q16—31no—
67C2×D3×SD16—31no—
68C2×D3×SD16D311yescharacteristic, complemented
69C2×D3×D8—31no—
70C22×#204—31no—
71D3×#124—31no—
72D3×#124—31no—
73C3×#495—31no—
74#5191—31no—
75#5168—31no—
76#5168—31no—
77#5168—31no—
78#5168—31no—
79#5168—31no—
80#5168—31no—
81#5168—31no—
82#5168—31no—
83#5168—31no—
84#5168—61no—
85#5168D311yescharacteristic, direct product factor
86#5155—31no—
87C2×C8×Dic3—31no—
88#5059—31no—
89#5059—31no—
90#4696—31no—
91C4×D3×C8—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C3×D3×Q8—22no—
100C3×D3×Q8—22no—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×#627—21no—
111C2×#626—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3D412yes—
114D3×D12—22no—
115D3×D12—22no—
116D3×Dic6—22no—
117D3×Dic6—22no—
118C32×SD16—22no—
119C2×C32×C8C2311yescharacteristic
120#3757—22no—
121#3756—22no—
122#3753—22no—
123#3752—22no—
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744—22no—
127C3×#217—22no—
128C3×#216—22no—
129C3×#215—22no—
130C3×#214—22no—
131C3×#213—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×#204—22no—
137C3×#204—22no—
138C3×D3×C8D414yes—
139#3722—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143Dic32D412yes—
144#3719—22no—
145#3718—22no—
146#3717—22no—
147#3716—22no—
148#3714—22no—
149#3713—22no—
150D3×C3⋊C8D414yes—
151C2×#495—91noSylow
152C22×C3×Q8—31no—
153C22×C3×D4—31no—
154C2×D3×Q8—31no—
155C2×D3×Q8C2×D311yescharacteristic
156C2×D3×D4—31no—
157C2×D3×D4C2×D311yescharacteristic
158C22×D12—31no—
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—21no—
162C2×C3×SD16—31no—
163C2×C3×SD16—31no—
164C2×C3×SD16—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—64no—
167C2×C3×SD16C2×D311yescharacteristic, complemented
168C2×C3×SD16C2×D311yescharacteristic, complemented
169C2×C3×D8—31no—
170C22×C3×C8—31no—
171C3×#124—31no—
172C3×#124—31no—
173C2×#217—62no—
174#947—31no—
175#947—31no—
176#947—31no—
177#947—31no—
178#947—31no—
179#947—61no—
180#947—62no—
181#947C2×D311yescharacteristic, complemented
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—61no—
188C2×#216—64no—
189C2×#216C2×D311yescharacteristic, complemented
190C2×#215—31no—
191C2×#215C2×D311yescharacteristic, complemented
192#936—31no—
193#936—31no—
194#936—31no—
195#936—31no—
196#936—31no—
197#936—61no—
198#936—62no—
199#936C2×D311yescharacteristic, complemented
200C2×#214—31no—
201C2×#214C2×D311yescharacteristic, complemented
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—61no—
208C2×#213—64no—
209C2×#213C2×D311yescharacteristic
210C2×(C2×D3)⋊C4—62no—
211C2×C4×Dic3—31no—
212C22×C3⋊C8—31no—
213D3×Q16—64no—
214D3×SD16—24no—
215D3×SD16—64no—
216D3×D8—64no—
217C2×Dic12—31no—
218C2×D24—31no—
219C2×#204—31no—
220C2×#204—31no—
221C2×#204—31no—
222C2×#204—31no—
223C2×#204—61no—
224C2×#204—64no—
225C2×#204C2×D311yescharacteristic, complemented
226C2×#204C2×D311yescharacteristic, complemented
227C2×D3×C8—31no—
228C2×D3×C8C2×D311yescharacteristic
229#885—62no—
230#885—62no—
231D3×C22⋊C4—62no—
232D3×C22⋊C4—62no—
233#875—31no—
234#875—31no—
235C42×D3—31no—
236C3×C4×C8—31no—
237C8×Dic3—31no—
238C8×Dic3—31no—
239C8×Dic3—31no—
240C8×Dic3—31no—
241C8×Dic3—31no—
242C8×Dic3—61no—
243C8×Dic3C2×D311yescharacteristic, complemented
244C4×C3⋊C8—31no—
245C23×C32—21no—
246C22×C3⋊D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—42no—
250C22×C3×D3—44no—
251C22×C3×D3C2×D411yescharacteristic
252C2×D32—42no—
253C2×D32—44no—
254C32×Q8—21no—
255C32×Q8—21no—
256C32×D4—21no—
257C32×D4—21no—
258C2×C32×C4—21no—
259C2×C32×C4C2411yescharacteristic
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3C2×D412yes—
262C4⋊(C3⋊D3)—21no—
263C4⋊(C3⋊D3)—21no—
264#634—21no—
265#634—21no—
266C3×#67—42no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D412yes—
270C2×C3×Dic3C2×D411yescharacteristic
271C3×D12—21no—
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—21no—
275C3×C4×D3—42no—
276C3×C4×D3C2×D412yes—
277C3×C4×D3C2×D412yes—
278C3×Dic6—21no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281C3×Dic6—21no—
282C3×Dic6—42no—
283#627—42no—
284#626—42no—
285D3×Dic3—24no—
286D3×Dic3—42no—
287C32×C8C2×D412yes—
288C3⋊(C3⋊C8)C2×D412yes—
289C3×C3⋊C8C2×D412yes—
290C3×C3⋊C8C2×D412yes—
291C22×Q16—91no—
292C22×SD16—31no—
293C22×SD16—91no—
294C22×D8—91no—
295C2×#124—91no—
296C2×#124—91no—
297#495—31no—
298#495—91no—
299#495—91no—
300#495—91no—
301#495—91no—
302#495—91no—
303#495—91no—
304#495—91no—
305C2×C4×C8—91no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×Q8—21no—
311C2×C3×Q8—31no—
312C2×C3×Q8—31no—
313C2×C3×Q8—61no—
314C2×C3×Q8—62no—
315C2×C3×Q8—62no—
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×D4—21no—
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—62no—
322C2×C3×D4—62no—
323C2×C3×D4—61no—
324C2×C3×D4C22×D311yescharacteristic
325C2×C3×D4C22×D311yescharacteristic
326C22×C3×C4—31no—
327C22×C3×C4—61no—
328C2×#67—21no—
329C2×#67—61no—
330C22×Dic3—32no—
331C22×Dic3—61no—
332D3×Q8—22no—
333D3×Q8—22no—
334D3×Q8—62no—
335D3×Q8—62no—
336D3×D4—22no—
337D3×D4—22no—
338D3×D4—62no—
339D3×D4—62no—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—61no—
343C2×D12—62no—
344C2×D12—62no—
345C2×D12—61no—
346C2×D12C22×D311yescharacteristic
347C2×D12C22×D311yescharacteristic
348C2×C4×D3—21no—
349C2×C4×D3—32no—
350C2×C4×D3—61no—
351C2×C4×D3C22×D311yescharacteristic
352C2×Dic6—21no—
353C2×Dic6—31no—
354C2×Dic6—31no—
355C2×Dic6—61no—
356C2×Dic6—62no—
357C2×Dic6—62no—
358C2×Dic6—61no—
359C2×Dic6—61no—
360C2×Dic6C22×D311yescharacteristic
361C2×Dic6C22×D311yescharacteristic
362C3×Q16—62no—
363C3×SD16—22no—
364C3×SD16—22no—
365C3×SD16—42no—
366C3×SD16—62no—
367C3×SD16—62no—
368C3×SD16—62no—
369C3×SD16—62no—
370C3×D8—62no—
371C2×C3×C8—21no—
372C2×C3×C8—31no—
373C2×C3×C8—31no—
374C2×C3×C8—34no—
375C2×C3×C8C22×D311yescharacteristic
376C2×C3×C8C22×D311yescharacteristic
377C3×C22⋊C4—62no—
378C3×C22⋊C4—62no—
379C3×C42—31no—
380#217—22no—
381#217—62no—
382#217—62no—
383#217—62no—
384#217—62no—
385#217—62no—
386#217—122no—
387#216—22no—
388#216—62no—
389#216—62no—
390#216—62no—
391#216—62no—
392#216—62no—
393#216—122no—
394#215—22no—
395#215—62no—
396#214—22no—
397#214—62no—
398#213—22no—
399#213—62no—
400#213—62no—
401#213—62no—
402#213—62no—
403#213—62no—
404#213—122no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—122no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—32no—
417C4×Dic3—32no—
418C4×Dic3—61no—
419C4×Dic3C22×D311yescharacteristic
420C2×C3⋊C8—31no—
421C2×C3⋊C8—31no—
422C2×C3⋊C8—34no—
423C2×C3⋊C8—61no—
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426Dic12—62no—
427D24—62no—
428#204—22no—
429#204—22no—
430#204—62no—
431#204—62no—
432#204—62no—
433#204—62no—
434#204—122no—
435D3×C8—34no—
436D3×C8#6714yes—
437C22×C32—41no—
438C22×C32—42no—
439C22×C32C22×D411yescharacteristic
440C2×C3⋊D3—41no—
441C2×C3⋊D3—42no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—42no—
445C2×C3×D3—42no—
446C2×C3×D3—84no—
447C2×C3×D3#12712yes—
448C2×C3×D3#13514yes—
449D32—84no—
450C32×C4—41no—
451C32×C4C22×D411yescharacteristic
452C32×C4C22×D411yescharacteristic
453C3⋊Dic3—22no—
454C3⋊Dic3—41no—
455C3×Dic3—22no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3#12712yes—
459C22×Q8—31no—
460C22×Q8—91no—
461C22×D4—31no—
462C22×D4—91no—
463C2×Q16—31no—
464C2×Q16—91no—
465C2×Q16—91no—
466C2×Q16—91no—
467C2×Q16—184no—
468C2×SD16—31no—
469C2×SD16—31no—
470C2×SD16—31no—
471C2×SD16—31no—
472C2×SD16—64no—
473C2×SD16—91no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—184no—
477C2×SD16D3211yescharacteristic, complemented
478C2×D8—31no—
479C2×D8—91no—
480C2×D8—91no—
481C2×D8—91no—
482C2×D8—184no—
483C22×C8—31no—
484C22×C8—91no—
485#124—31no—
486#124—31no—
487#124—91no—
488#124—91no—
489#124—91no—
490#124—91no—
491#124—91no—
492#124—91no—
493#124—182no—
494#124—182no—
495C2×C22⋊C4—182no—
496C2×C22⋊C4—182no—
497C2×C42—91no—
498C4×C8—31no—
499C4×C8—91no—
500C4×C8—91no—
501C4×C8—91no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—31no—
505C23×C3—41no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3—122no—
509C23×C3—124no—
510C22×D3—21no—
511C22×D3—21no—
512C22×D3—44no—
513C22×D3—42no—
514C22×D3—61no—
515C22×D3—61no—
516C22×D3—121no—
517C22×D3—122no—
518C22×D3—124no—
519C22×D3—124no—
520C22×D3—122no—
521C22×D3D3×D411yescharacteristic
522C3×Q8—21no—
523C3×Q8—21no—
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—41no—
527C3×Q8—41no—
528C3×Q8—61no—
529C3×Q8—61no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—122no—
533C3×D4—21no—
534C3×D4—21no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—41no—
538C3×D4—41no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—61no—
542C3×D4—61no—
543C3×D4—122no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—31no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—32no—
551C2×C3×C4—41no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—122no—
555C2×C3×C4C23×D311yescharacteristic
556C2×C3×C4C23×D311yescharacteristic
557#67—42no—
558#67—122no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—32no—
562C2×Dic3—32no—
563C2×Dic3—62no—
564C2×Dic3—64no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—121no—
568C2×Dic3—122no—
569C2×Dic3D3×D412yes—
570C2×Dic3D3×D411yescharacteristic
571D12—21no—
572D12—21no—
573D12—21no—
574D12—21no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—121no—
580D12—121no—
581D12—122no—
582C4×D3—42no—
583C4×D3—64no—
584C4×D3—122no—
585C4×D3D3×D412yes—
586C4×D3C2×#6712yes—
587Dic6—21no—
588Dic6—21no—
589Dic6—21no—
590Dic6—21no—
591Dic6—42no—
592Dic6—61no—
593Dic6—61no—
594Dic6—61no—
595Dic6—61no—
596Dic6—121no—
597Dic6—121no—
598Dic6—122no—
599Dic6—122no—
600C3×C8—22no—
601C3×C8—32no—
602C3×C8—32no—
603C3×C8D3×D412yes—
604C3×C8C2×#6712yes—
605C3⋊C8—32no—
606C3⋊C8—32no—
607C3⋊C8—62no—
608C3⋊C8D3×D412yes—
609C3⋊C8C2×#6712yes—
610C2×C32—81no—
611C2×C32C2×#12711yescharacteristic
612C2×C32C2×#13512yes—
613C3⋊D3—81no—
614C3×D3—81no—
615C3×D3—81no—
616C3×D3#49514yescomplemented
617C24—61no—
618C24—181no—
619C2×Q8—31no—
620C2×Q8—31no—
621C2×Q8—61no—
622C2×Q8—62no—
623C2×Q8—62no—
624C2×Q8—91no—
625C2×Q8—181no—
626C2×Q8—182no—
627C2×Q8—182no—
628C2×Q8C2×D3211yescharacteristic
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—62no—
632C2×D4—62no—
633C2×D4—61no—
634C2×D4—91no—
635C2×D4—182no—
636C2×D4—182no—
637C2×D4—181no—
638C2×D4C2×D3211yescharacteristic
639C22×C4—31no—
640C22×C4—61no—
641C22×C4—92no—
642C22×C4—181no—
643Q16—62no—
644Q16—182no—
645Q16—182no—
646Q16—182no—
647SD16—22no—
648SD16—62no—
649SD16—62no—
650SD16—62no—
651SD16—62no—
652SD16—182no—
653SD16—182no—
654SD16—182no—
655D8—62no—
656D8—182no—
657D8—182no—
658D8—182no—
659C2×C8—31no—
660C2×C8—31no—
661C2×C8—34no—
662C2×C8—94no—
663C2×C8—91no—
664C2×C8C2×D3211yescharacteristic
665C22⋊C4—62no—
666C22⋊C4—62no—
667C22⋊C4—182no—
668C22⋊C4—182no—
669C22⋊C4—182no—
670C22⋊C4—182no—
671C22⋊C4—182no—
672C22⋊C4—182no—
673C42—31no—
674C42—92no—
675C42—91no—
676C22×C3—21no—
677C22×C3—32no—
678C22×C3—34no—
679C22×C3—41no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—41no—
683C22×C3—81no—
684C22×C3—82no—
685C22×C3—121no—
686C22×C3—122no—
687C22×C3—122no—
688C22×C3—121no—
689C22×C3—244no—
690C22×C3C2×D3×D411yescharacteristic
691C22×C3C2×D3×D411yescharacteristic
692C2×D3—41no—
693C2×D3—42no—
694C2×D3—42no—
695C2×D3—41no—
696C2×D3—84no—
697C2×D3—121no—
698C2×D3—122no—
699C2×D3—122no—
700C2×D3—121no—
701C2×D3—241no—
702C2×D3—242no—
703C2×D3—244no—
704C2×D3—244no—
705C2×D3#91614yes—
706C2×D3#94012yes—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—32no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—62no—
713C3×C4—81no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4C2×D3×D411yescharacteristic
717C3×C4C2×D3×D411yescharacteristic
718C3×C4C2×D3×D411yescharacteristic
719C3×C4C22×#6711yescharacteristic
720Dic3—22no—
721Dic3—41no—
722Dic3—41no—
723Dic3—62no—
724Dic3—62no—
725Dic3—122no—
726Dic3—121no—
727Dic3—121no—
728Dic3—241no—
729Dic3#94012yes—
730C32C2×#49511yescharacteristic, complemented, Sylow
731C23—21no—
732C23—31no—
733C23—61no—
734C23—61no—
735C23—122no—
736C23—124no—
737C23—181no—
738C23—362no—
739C23—364no—
740Q8—21no—
741Q8—21no—
742Q8—61no—
743Q8—61no—
744Q8—61no—
745Q8—61no—
746Q8—122no—
747Q8—181no—
748Q8—181no—
749Q8—362no—
750D4—21no—
751D4—21no—
752D4—61no—
753D4—61no—
754D4—61no—
755D4—61no—
756D4—122no—
757D4—181no—
758D4—181no—
759D4—362no—
760C2×C4—21no—
761C2×C4—31no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—92no—
768C2×C4—122no—
769C2×C4—184no—
770C2×C4—181no—
771C2×C4—362no—
772C2×C4C22×D3211yescharacteristic
773C8—32no—
774C8—32no—
775C8—92no—
776C8D3×#6712yes—
777C2×C3—22no—
778C2×C3—21no—
779C2×C3—34no—
780C2×C3—81no—
781C2×C3—81no—
782C2×C3—161no—
783C2×C3—241no—
784C2×C3—241no—
785C2×C3D3×#12711yescharacteristic
786C2×C3C2×#91612yes—
787C2×C3D3×#13512yes—
788C2×C3C2×#94011yescharacteristic
789D3—81no—
790D3—81no—
791D3—241no—
792D3—241no—
793D3—481no—
794D3#516814yesdirect product factor
795C22—34no—
796C22—32no—
797C22—42no—
798C22—41no—
799C22—122no—
800C22—122no—
801C22—121no—
802C22—121no—
803C22—244no—
804C22—362no—
805C22—361no—
806C22—724no—
807C22D32×D411yescharacteristic
808C4—32no—
809C4—41no—
810C4—62no—
811C4—121no—
812C4—121no—
813C4—182no—
814C4—361no—
815C4D32×D411yescharacteristic
816C4C2×D3×#6711yescharacteristic
817C3—21no—
818C3D3×#49511yescharacteristic, complemented
819C3C2×#516811yescharacteristic, complemented
820C2—34no—
821C2—81no—
822C2—241no—
823C2—241no—
824C2—721no—
825C2D3×#91612yes—
826C2D3×#94011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×D3×#213C2
hypercenterC2×SD16D32
hypocenterC32C2×#495
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×#947C2semidirect
3. C2×D3×#216C2semidirect
4. D3×#936C2semidirect
6. C2×D3×#204C2semidirect
7. #10592867C2semidirect
8. C3×#5168C2semidirect
9. #10591610C2semidirect
10. #10591606C2semidirect
11. #10591474C2semidirect
12. #10591473C2semidirect
13. #10590867C2semidirect
14. #10590862C2semidirect
15. D3×C8×Dic3C2semidirect
22. C2×C32×SD16C22semidirect
23. #64156C22semidirect
24. C2×#3756C22semidirect
25. #64145C22semidirect
27. C2×#3744C22semidirect
28. C3×#947C22semidirect
29. C2×C3×#216C22semidirect
30. C2×C3×#215C22semidirect
31. C3×#936C22semidirect
32. C2×C3×#214C22semidirect
35. C2×C3×#204C22semidirect
36. C2×C3×#204C22semidirect
45. #63864C22semidirect
46. #63863C22semidirect
47. #63863C22semidirect
48. #63860C22semidirect
49. C2×#3719C22semidirect
50. C2×#3718C22semidirect
51. C2×#3717C22semidirect
52. C2×#3716C22semidirect
57. C8×C3⋊Dic3C22semidirect
58. C3×C8×Dic3C22semidirect
59. #63553C22semidirect
60. Dic3×C3⋊C8C22semidirect
68. C2×D3×SD16D3semidirect
85. #5168D3direct (N × H)
167. C2×C3×SD16C2×D3semidirect
168. C2×C3×SD16C2×D3semidirect
181. #947C2×D3semidirect
189. C2×#216C2×D3semidirect
191. C2×#215C2×D3semidirect
199. #936C2×D3semidirect
201. C2×#214C2×D3semidirect
225. C2×#204C2×D3semidirect
226. C2×#204C2×D3semidirect
243. C8×Dic3C2×D3semidirect
477. C2×SD16D32semidirect
616. C3×D3#495semidirect
730. C32C2×#495semidirect
794. D3#5168direct (N × H)
818. C3D3×#495semidirect
819. C3C2×#5168semidirect

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×#9472
C2×D3×#2162
D3×#9362
C2×D3×#2132
C2×D3×#2042
#105928672
C3×#51682
#105916102
#105916062
#105914742
#105914732
#105908672
#105908622
D3×C8×Dic32
C2×#51683
D3×#4953