Finite Group Databasebeta

← D3×#4767 #11865717

Subgroups — D3×#4767 #11865717

Order 1152.

1056 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#936C211yesmaximal, characteristic
2C2×D3×#214C211yesmaximal, characteristic
3C2×D3×Dic12C211yesmaximal, characteristic, complemented
4D3×#887C211yesmaximal, characteristic, complemented
5#10592466C211yesmaximal, characteristic, complemented
6C3×D3×#102C211yesmaximal, characteristic
7C3×#4767C211yesmaximal, characteristic, complemented
8#10591443C211yesmaximal, characteristic, complemented
9#10591441C211yesmaximal, characteristic, complemented
10#10590861C211yesmaximal, characteristic, complemented
11#10590797C211yesmaximal, characteristic, complemented
12D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
13D3×#810C211yesmaximal, characteristic, complemented
14#10590538C211yesmaximal, characteristic, complemented
15#10590532C211yesmaximal, characteristic, complemented
16D3×#464—31nomaximal
17C2×#4767—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21#64145C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C2×#3746C2211yescharacteristic, complemented
24#64096C2211yescharacteristic, complemented
25C3×#936C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic, complemented
28C2×C3×D3×C8C2211yescharacteristic
29C3×D3×C4⋊C4C2211yescharacteristic
30C3×#887C2211yescharacteristic, complemented
31D3×#217—21no—
32D3×#217—21no—
33#63959—21no—
34#63959—21no—
35D3×#214—24no—
36D3×Dic3⋊C4—21no—
37C4×D3×Dic3—21no—
38C4×D3×Dic3C2211yescharacteristic
39#63863C2211yescharacteristic
40#63860C2211yescharacteristic
41#63844C2211yescharacteristic, complemented
42#63843C2211yescharacteristic, complemented
43#63838—21no—
44#63837—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic
50D3×Dic12—24no—
51C32×#102C2211yescharacteristic
52#63641C2211yescharacteristic, complemented
53#63637C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic
55C3×#821C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic
59#63572C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63C2×#936—31no—
64C22×#214—31no—
65C2×D3×Q16—31no—
66C2×D3×SD16—31no—
67C22×Dic12—31no—
68D3×#124—31no—
69C4×D3×Q8—31no—
70C2×#887—31no—
71C3×#464—31no—
72C2×C3×#102—31no—
73#5185—31no—
74#5166—31no—
75C2×Dic3⋊C8—31no—
76#5054—31no—
77#5028—31no—
78C2×#810—31no—
79#4845—31no—
80D3×C4⋊C8—31no—
81D3×#103—31no—
82#4798—31no—
83D3×#102D311yescharacteristic
84#4767—31no—
85#4767—31no—
86#4767—31no—
87#4767—31no—
88#4767—31no—
89#4767—31no—
90#4767—31no—
91#4767—31no—
92#4767—61no—
93#4767D311yescharacteristic, direct product factor
94C23×C3×D3—21no—
95C2×C32×D4C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×#627—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3D411yescharacteristic
111C2×D3×Dic3D411yescharacteristic
112D3×Dic6—22no—
113D3×Dic6—22no—
114D3×Dic6—22no—
115D3×Dic6D414yes—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3757—21no—
119#3757—21no—
120#3754—22no—
121#3750—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125#3746—22no—
126C3×#217—21no—
127C3×#217—21no—
128C3×#214—22no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×Dic12—22no—
137C3×D3×C8—22no—
138#3724—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32—21no—
145Dic32—21no—
146Dic32D411yescharacteristic
147Dic32D411yescharacteristic
148#3719—22no—
149#3719—22no—
150#3716—22no—
151#3715—22no—
152D3×C3⋊C8—22no—
153C2×#464—91noSylow
154C22×C3×D4—31no—
155C2×D3×Q8—31no—
156C2×D3×Q8—31no—
157C2×D3×D4C2×D311yescharacteristic
158C22×Dic6—31no—
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×SD16—31no—
162C22×C3×C8—31no—
163C3×#124—31no—
164C3×C4×Q8—31no—
165C2×C3×C4⋊C4—31no—
166C2×#217—61no—
167C2×#217—61no—
168#947—31no—
169Q8×Dic3—31no—
170C2×#216—31no—
171C2×#216—31no—
172C2×#215—31no—
173#936—31no—
174#936—31no—
175#936—31no—
176#936—31no—
177#936—61no—
178#936—61no—
179#936—61no—
180#936C2×D311yescharacteristic
181C2×#214—31no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—61no—
186C2×#214—64no—
187C2×#214C2×D311yescharacteristic
188C2×Dic3⋊C4—61no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—61no—
191C22×C3⋊C8—31no—
192D3×Q16—64no—
193D3×SD16—64no—
194C2×Dic12—31no—
195C2×Dic12—31no—
196C2×Dic12—31no—
197C2×Dic12—31no—
198C2×Dic12—61no—
199C2×Dic12—64no—
200C2×Dic12C2×D311yescharacteristic, complemented
201C2×#204—31no—
202C2×D3×C8—31no—
203C2×D3×C8C2×D311yescharacteristic
204D3×C4⋊C4—61no—
205D3×C4⋊C4C2×D311yescharacteristic
206#887—31no—
207#887—31no—
208#887—31no—
209#887—31no—
210#887—61no—
211#887—61no—
212#887—61no—
213#887—61no—
214#887C2×D311yescharacteristic, complemented
215#885—61no—
216#885—61no—
217D3×C22⋊C4—61no—
218D3×C22⋊C4—61no—
219#875—31no—
220C42×D3—31no—
221C42×D3—61no—
222C4×Dic6—31no—
223C4×Dic6—61no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#102—21no—
227C3×#102—31no—
228C3×#102—31no—
229C3×#102—31no—
230C3×#102C2×D311yescharacteristic
231C3×#102C2×D311yescharacteristic
232#835—31no—
233#832C2×D311yescharacteristic
234#821C2×D311yescharacteristic
235#816—31no—
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—31no—
239Dic3⋊C8—31no—
240Dic3⋊C8—31no—
241Dic3⋊C8—61no—
242Dic3⋊C8C2×D311yescharacteristic, complemented
243#810—31no—
244#810—31no—
245#810—31no—
246#810—31no—
247#810—61no—
248#810C2×D311yescharacteristic, complemented
249#809C2×D311yescharacteristic
250C4⋊(C3⋊C8)—31no—
251C23×C32—21no—
252C22×C3×D3—21no—
253C22×C3×D3—42no—
254C22×C3×D3—42no—
255C22×C3×D3—42no—
256C22×C3×D3C2×D411yescharacteristic
257C32×D4—21no—
258C32×D4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2411yescharacteristic
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
265#634—21no—
266#634—21no—
267#634—21no—
268#634C2×D412yes—
269C3×#67—42no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—21no—
277C3×D12—21no—
278C3×C4×D3—42no—
279C3×C4×D3C2×D412yes—
280C3×C4×D3#4112yes—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284C3×Dic6C2×D412yes—
285#627—24no—
286#627—42no—
287D3×Dic3—24no—
288D3×Dic3—22no—
289D3×Dic3—22no—
290D3×Dic3—42no—
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295C22×Q16—91no—
296C22×SD16—91no—
297C2×#124—91no—
298C2×C4×Q8—91no—
299#464—31no—
300#464—91no—
301#464—91no—
302#464—91no—
303#464—91no—
304#464—91no—
305#464—91no—
306#464—91no—
307C2×C4⋊C8—91no—
308C2×#103—91no—
309C2×#102—31no—
310C24×C3—61no—
311C23×D3—21no—
312C2×C3×Q8—31no—
313C2×C3×Q8—31no—
314C2×C3×D4—21no—
315C2×C3×D4—31no—
316C2×C3×D4—62no—
317C2×C3×D4—62no—
318C2×C3×D4—61no—
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C22×D311yescharacteristic
321C22×C3×C4—31no—
322C22×C3×C4—61no—
323C2×#67—21no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328D3×Q8—34no—
329D3×Q8—62no—
330D3×Q8—62no—
331D3×Q8—62no—
332D3×D4—22no—
333D3×D4—22no—
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—21no—
336C2×C4×D3—31no—
337C2×C4×D3—31no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3C22×D311yescharacteristic
341C2×Dic6—31no—
342C2×Dic6—31no—
343C2×Dic6—34no—
344C2×Dic6—31no—
345C2×Dic6—31no—
346C2×Dic6—61no—
347C2×Dic6—61no—
348C2×Dic6—62no—
349C2×Dic6—62no—
350C2×Dic6—62no—
351C2×Dic6—61no—
352C2×Dic6—61no—
353C2×Dic6—61no—
354C2×Dic6—61no—
355C2×Dic6C22×D311yescharacteristic
356C2×Dic6C22×D311yescharacteristic
357C3×Q16—62no—
358C3×SD16—62no—
359C2×C3×C8—21no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—62no—
363C2×C3×C8C22×D311yescharacteristic
364C2×C3×C8C22×D311yescharacteristic
365C3×C4⋊C4—21no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4C22×D311yescharacteristic
370C3×C4⋊C4C22×D311yescharacteristic
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C42—31no—
374C3×C42—61no—
375#217—21no—
376#217—21no—
377#217—61no—
378#217—61no—
379#217—61no—
380#217—61no—
381#217—61no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—121no—
386#217—121no—
387#216—62no—
388#216—62no—
389#215—62no—
390#214—22no—
391#214—62no—
392#214—62no—
393#214—62no—
394#214—62no—
395#214—122no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3C22×D311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—21no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—121no—
410C4×Dic3—21no—
411C4×Dic3—31no—
412C4×Dic3—31no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—31no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—121no—
425C4×Dic3C22×D311yescharacteristic
426C2×C3⋊C8—31no—
427C2×C3⋊C8—31no—
428C2×C3⋊C8—61no—
429C2×C3⋊C8—62no—
430C2×C3⋊C8C22×D311yescharacteristic
431C2×C3⋊C8C22×D311yescharacteristic
432Dic12—22no—
433Dic12—62no—
434Dic12—62no—
435Dic12—62no—
436Dic12—62no—
437Dic12—122no—
438#204—62no—
439D3×C8—22no—
440D3×C8—62no—
441C22×C32—41no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32C22×D411yescharacteristic
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—84no—
449C2×C3×D3#12112yes—
450C2×C3×D3#13512yes—
451C2×C3×D3#13712yes—
452C32×C4—41no—
453C32×C4C22×D411yescharacteristic
454C32×C4C2×#4111yescharacteristic
455C3⋊Dic3—22no—
456C3⋊Dic3—21no—
457C3⋊Dic3—21no—
458C3⋊Dic3—41no—
459C3×Dic3—22no—
460C3×Dic3—21no—
461C3×Dic3—21no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3#12112yes—
465C22×Q8—91no—
466C22×Q8—91no—
467C22×D4—31no—
468C2×Q16—31no—
469C2×Q16—91no—
470C2×Q16—91no—
471C2×Q16—91no—
472C2×Q16—184no—
473C2×SD16—31no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—184no—
478C22×C8—31no—
479C22×C8—91no—
480#124—31no—
481#124—91no—
482#124—91no—
483#124—91no—
484#124—181no—
485#124—181no—
486C4×Q8—31no—
487C4×Q8—91no—
488C4×Q8—91no—
489C4×Q8—91no—
490C4×Q8—181no—
491C4×Q8—181no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—181no—
494C2×C22⋊C4—181no—
495C2×C22⋊C4—181no—
496C2×C42—91no—
497C2×C42—181no—
498C4⋊C8—31no—
499C4⋊C8—91no—
500C4⋊C8—91no—
501C4⋊C8—91no—
502#103—31no—
503#103—91no—
504#103—91no—
505#103—91no—
506#102—31no—
507#102—31no—
508#102—31no—
509#102D3211yescharacteristic
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—31no—
513C23×C3—41no—
514C23×C3—61no—
515C23×C3—122no—
516C23×C3—122no—
517C23×C3—122no—
518C22×D3—21no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3—42no—
522C22×D3D3×D411yescharacteristic
523C3×Q8—32no—
524C3×Q8—61no—
525C3×Q8—61no—
526C3×Q8—61no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—21no—
531C3×D4—41no—
532C3×D4—41no—
533C3×D4—61no—
534C3×D4—61no—
535C3×D4—122no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—31no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—41no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—122no—
549C2×C3×C4C23×D311yescharacteristic
550C2×C3×C4C23×D311yescharacteristic
551#67—42no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—64no—
562C2×Dic3—62no—
563C2×Dic3—62no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—121no—
569C2×Dic3—121no—
570C2×Dic3—122no—
571C2×Dic3D3×D411yescharacteristic
572C2×Dic3D3×D411yescharacteristic
573C2×Dic3D3×D411yescharacteristic
574D12—21no—
575D12—21no—
576C4×D3—42no—
577C4×D3—64no—
578C4×D3—62no—
579C4×D3—62no—
580C4×D3—122no—
581C4×D3#23512yes—
582C4×D3D3×D412yes—
583Dic6—21no—
584Dic6—21no—
585Dic6—21no—
586Dic6—32no—
587Dic6—32no—
588Dic6—62no—
589Dic6—64no—
590Dic6—61no—
591Dic6—61no—
592Dic6—64no—
593Dic6—61no—
594Dic6—61no—
595Dic6—61no—
596Dic6—61no—
597Dic6—121no—
598Dic6—121no—
599Dic6—121no—
600Dic6—122no—
601Dic6—122no—
602Dic6D3×D412yes—
603C3×C8—21no—
604C3×C8—21no—
605C3×C8—41no—
606C3×C8—61no—
607C3×C8—61no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C3⋊C8—61no—
611C3⋊C8—61no—
612C3⋊C8—121no—
613C2×C32—81no—
614C2×C32C2×#12111yescharacteristic
615C2×C32C2×#13511yescharacteristic
616C2×C32C2×#13711yescharacteristic
617C3×D3—81no—
618C3×D3#46414yescomplemented
619C24—61no—
620C2×Q8—31no—
621C2×Q8—31no—
622C2×Q8—94no—
623C2×Q8—91no—
624C2×Q8—91no—
625C2×Q8—181no—
626C2×Q8—181no—
627C2×Q8—182no—
628C2×Q8—182no—
629C2×Q8—182no—
630C2×D4—31no—
631C2×D4—62no—
632C2×D4—62no—
633C2×D4—61no—
634C2×D4C2×D3211yescharacteristic
635C22×C4—31no—
636C22×C4—61no—
637C22×C4—91no—
638C22×C4—91no—
639C22×C4—181no—
640C22×C4—181no—
641Q16—62no—
642Q16—182no—
643Q16—182no—
644Q16—182no—
645SD16—62no—
646SD16—182no—
647SD16—182no—
648SD16—182no—
649C2×C8—31no—
650C2×C8—31no—
651C2×C8—62no—
652C2×C8—91no—
653C2×C8—182no—
654C2×C8C2×D3211yescharacteristic
655C4⋊C4—31no—
656C4⋊C4—61no—
657C4⋊C4—61no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4C2×D3211yescharacteristic
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C22⋊C4—181no—
670C42—31no—
671C42—61no—
672C42—91no—
673C42—91no—
674C42—91no—
675C42—181no—
676C42—181no—
677C42—181no—
678C22×C3—21no—
679C22×C3—32no—
680C22×C3—32no—
681C22×C3—32no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—244no—
695C22×C3C2×D3×D411yescharacteristic
696C22×C3C2×D3×D411yescharacteristic
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—84no—
701C2×D3#88412yes—
702C2×D3#91212yes—
703C2×D3#91512yes—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—32no—
707C3×C4—41no—
708C3×C4—41no—
709C3×C4—62no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—81no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4C2×#23511yescharacteristic
716C3×C4C2×D3×D411yescharacteristic
717C3×C4C2×D3×D411yescharacteristic
718C3×C4D3×#4111yescharacteristic
719Dic3—21no—
720Dic3—21no—
721Dic3—22no—
722Dic3—41no—
723Dic3—41no—
724Dic3—62no—
725Dic3—61no—
726Dic3—61no—
727Dic3—61no—
728Dic3—61no—
729Dic3—62no—
730Dic3—122no—
731Dic3—121no—
732Dic3—121no—
733Dic3—121no—
734Dic3—121no—
735Dic3—241no—
736Dic3#88412yes—
737C32C2×#46411yescharacteristic, complemented, Sylow
738C23—21no—
739C23—31no—
740C23—61no—
741C23—122no—
742C23—122no—
743C23—122no—
744Q8—32no—
745Q8—61no—
746Q8—61no—
747Q8—61no—
748Q8—92no—
749Q8—184no—
750Q8—181no—
751Q8—181no—
752Q8—181no—
753Q8—362no—
754D4—21no—
755D4—21no—
756D4—61no—
757D4—61no—
758D4—122no—
759C2×C4—21no—
760C2×C4—31no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—91no—
769C2×C4—91no—
770C2×C4—122no—
771C2×C4—182no—
772C2×C4—182no—
773C2×C4—184no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—362no—
777C2×C4C22×D3211yescharacteristic
778C8—21no—
779C8—61no—
780C8—61no—
781C8—181no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—34no—
786C2×C3—81no—
787C2×C3—81no—
788C2×C3—161no—
789C2×C3—241no—
790C2×C3C2×#88411yescharacteristic
791C2×C3D3×#12111yescharacteristic
792C2×C3C2×#91211yescharacteristic
793C2×C3C2×#91511yescharacteristic
794C2×C3D3×#13511yescharacteristic
795C2×C3D3×#13711yescharacteristic
796D3—81no—
797D3#476714yesdirect product factor
798C22—32no—
799C22—32no—
800C22—32no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—244no—
808C22D32×D411yescharacteristic
809C4—32no—
810C4—41no—
811C4—61no—
812C4—61no—
813C4—62no—
814C4—121no—
815C4—121no—
816C4—181no—
817C4—181no—
818C4—182no—
819C4—361no—
820C4D3×#23511yescharacteristic
821C4D32×D411yescharacteristic
822C3—21no—
823C3C2×#476711yescharacteristic, complemented
824C3D3×#46411yescharacteristic, complemented
825C2—34no—
826C2—81no—
827C2—241no—
828C2D3×#88411yescharacteristic
829C2D3×#91211yescharacteristic
830C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenter#102D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
3. C2×D3×Dic12C2semidirect
4. D3×#887C2semidirect
5. #10592466C2semidirect
7. C3×#4767C2semidirect
8. #10591443C2semidirect
9. #10591441C2semidirect
10. #10590861C2semidirect
11. #10590797C2semidirect
12. D3×Dic3⋊C8C2semidirect
13. D3×#810C2semidirect
14. #10590538C2semidirect
15. #10590532C2semidirect
23. C2×#3746C22semidirect
24. #64096C22semidirect
27. C2×C3×Dic12C22semidirect
30. C3×#887C22semidirect
41. #63844C22semidirect
42. #63843C22semidirect
45. C2×#3719C22semidirect
46. C2×#3719C22semidirect
52. #63641C22semidirect
53. #63637C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
59. #63572C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63567C22semidirect
62. #63565C22semidirect
93. #4767D3direct (N × H)
200. C2×Dic12C2×D3semidirect
214. #887C2×D3semidirect
242. Dic3⋊C8C2×D3semidirect
248. #810C2×D3semidirect
618. C3×D3#464semidirect
737. C32C2×#464semidirect
797. D3#4767direct (N × H)
823. C3C2×#4767semidirect
824. C3D3×#464semidirect

Maximal subgroups

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

subgroupindex
D3×#9362
C2×D3×#2142
C2×D3×Dic122
D3×#8872
#105924662
C3×D3×#1022
C3×#47672
#105914432
#105914412
#105908612
#105907972
D3×Dic3⋊C82
D3×#8102
#105905382
#105905322
D3×#4643
C2×#47673