Finite Group Databasebeta

← D3×#5042 #11866909

Subgroups — D3×#5042 #11866909

Order 1152.

1148 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
1C3×D3×#121C211yesmaximal, characteristic
2C2×D3×#214C211yesmaximal, characteristic, complemented
3D3×#924C211yesmaximal, characteristic, complemented
4C2×D3×#208C211yesmaximal, characteristic, complemented
5#10592741C211yesmaximal, characteristic, complemented
6C3×#5042C211yesmaximal, characteristic, complemented
7#10591502C211yesmaximal, characteristic, complemented
8#10591462C211yesmaximal, characteristic, complemented
9D3×#832C211yesmaximal, characteristic, complemented
10#10591180C211yesmaximal, characteristic, complemented
11#10591176C211yesmaximal, characteristic, complemented
12D3×#810C211yesmaximal, characteristic, complemented
13#10590588C211yesmaximal, characteristic, complemented
14D3×#807C211yesmaximal, characteristic, complemented
15#10590515C211yesmaximal, characteristic, complemented
16C2×#5042—31nomaximal
17D3×#468—31nomaximal
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C32×#121C2211yescharacteristic
23C2×#3754C2211yescharacteristic, complemented
24#64133C2211yescharacteristic, complemented
25C2×#3748C2211yescharacteristic, complemented
26C3×#939—21no—
27C3×#938C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic, complemented
29C3×#930C2211yescharacteristic
30C3×#924C2211yescharacteristic, complemented
31C2×C3×#208C2211yescharacteristic, complemented
32C3×#895C2211yescharacteristic
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×#884—21no—
35C3×D3×C22⋊C4—21no—
36D3×#217—21no—
37#63964—21no—
38D3×#214—24no—
39D3×C4⋊Dic3C2211yescharacteristic
40D3×Dic3⋊C4—21no—
41#63857C2211yescharacteristic, complemented
42#63856C2211yescharacteristic, complemented
43#63851—21no—
44C2×#3716C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic, complemented
46C2×#3711C2211yescharacteristic, complemented
47C2×#3711C2211yescharacteristic, complemented
48D3×#208—24no—
49C2×D3×C3⋊C8C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63659C2211yescharacteristic, complemented
52#63637C2211yescharacteristic, complemented
53#63634C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#807C2211yescharacteristic, complemented
57#63576C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×C3×#121—31no—
64C22×#214—31no—
65C2×#924—31no—
66C22×#208—31no—
67C2×D3×SD16—31no—
68C2×D3×M16—31no—
69D3×C22⋊Q8—31no—
70D3×#121D311yescharacteristic
71C3×#468—31no—
72C2×#832—31no—
73#5174—31no—
74#5134—31no—
75#5049—31no—
76#5042—31no—
77#5042—31no—
78#5042—31no—
79#5042—31no—
80#5042—31no—
81#5042—31no—
82#5042—31no—
83#5042—31no—
84#5042—61no—
85#5042D311yescharacteristic, direct product factor
86C2×#810—31no—
87C2×#807—31no—
88#4886—31no—
89D3×#107—31no—
90#4812—31no—
91D3×#103—31no—
92#4780—31no—
93D3×#102—31no—
94C23×C3×D3—21no—
95C23×C3×D3D411yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3D411yescharacteristic
104C3×D3×D4—22no—
105C3×D3×D4—22no—
106C3×D3×D4—44no—
107C2×C3×D12—21no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3D411yescharacteristic
113C2×C3×C4×D3D411yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3—21no—
120D3×Dic6—22no—
121D3×Dic6—22no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124#3757—21no—
125#3754—22no—
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128#3748—22no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#217—21no—
132C3×#217—21no—
133C3×#214—22no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×#208—22no—
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143#3724—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3716—22no—
149#3715—22no—
150#3711—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153D3×C3⋊C8D414yescomplemented
154C2×#468—91noSylow
155C22×C3×D4—31no—
156C22×C3×D4—61no—
157C23×C3×C4—31no—
158C2×D3×Q8—31no—
159C2×D3×D4—21no—
160C2×D3×D4C2×D311yescharacteristic
161C22×C4×D3C2×D311yescharacteristic
162C22×Dic6—31no—
163C2×C3×SD16—31no—
164C2×C3×M16—31no—
165C3×C22⋊Q8—31no—
166C3×#121—21no—
167C3×#121—31no—
168C3×#121—31no—
169C3×#121—31no—
170C3×#121—61no—
171C3×#121—61no—
172C3×#121C2×D311yescharacteristic
173C3×#121C2×D311yescharacteristic
174C2×C3×C4⋊C4—31no—
175C2×C3×C22⋊C4—61no—
176C2×#217—61no—
177#946—31no—
178C2×#215—31no—
179#939—21no—
180#938C2×D311yescharacteristic
181C2×#214—31no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—61no—
186C2×#214—64no—
187C2×#214C2×D311yescharacteristic, complemented
188#930C2×D311yescharacteristic
189C2×C4⋊Dic3—31no—
190#924—31no—
191#924—31no—
192#924—31no—
193#924—31no—
194#924—61no—
195#924—61no—
196#924—61no—
197#924C2×D311yescharacteristic, complemented
198C2×Dic3⋊C4—61no—
199C2×#208—31no—
200C2×#208—31no—
201C2×#208—31no—
202C2×#208—31no—
203C2×#208—61no—
204C2×#208—64no—
205C2×#208C2×D311yescharacteristic, complemented
206C22×C3⋊C8—31no—
207C22×C3⋊C8—31no—
208D3×SD16—64no—
209D3×M16—64no—
210C2×#204—31no—
211C2×ΓL(1,𝔽25)—31no—
212C2×ΓL(1,𝔽25)—31no—
213C2×D3×C8—31no—
214C2×D3×C8—31no—
215#897—31no—
216#896—61no—
217#895C2×D311yescharacteristic
218D3×C4⋊C4—31no—
219D3×C4⋊C4—61no—
220D3×C4⋊C4C2×D311yescharacteristic
221#884—21no—
222D3×C22⋊C4—21no—
223D3×C22⋊C4—61no—
224#878—61no—
225C3×#107—31no—
226C3×#103—31no—
227C3×#102—31no—
228#835—31no—
229#832—31no—
230#832—31no—
231#832—31no—
232#832—31no—
233#832—61no—
234#832C2×D311yescharacteristic, complemented
235#821—31no—
236#818—31no—
237#816—31no—
238#810—31no—
239#810—31no—
240#810—31no—
241#810—31no—
242#810—61no—
243#810C2×D311yescharacteristic, complemented
244#809—31no—
245#807—31no—
246#807—31no—
247#807—31no—
248#807—31no—
249#807—31no—
250#807—61no—
251#807C2×D311yescharacteristic, complemented
252C23×C32—21no—
253C23×C32C2×D411yescharacteristic
254C22×C3×D3—22no—
255C22×C3×D3—22no—
256C22×C3×D3—22no—
257C22×C3×D3—21no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—42no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273#634—21no—
274#634—21no—
275C3×#67—42no—
276C3×#67—42no—
277C3×#67—42no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×C4×D3—22no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—22no—
291C3×C4×D3—42no—
292C3×C4×D3C2×D412yes—
293C3×C4×D3#4112yes—
294C3×Dic6—21no—
295C3×Dic6—21no—
296#627—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)C2×D412yescomplemented
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yescomplemented
303C22×SD16—91no—
304C22×M16—91no—
305C2×C22⋊Q8—91no—
306C2×#121—31no—
307#468—31no—
308#468—91no—
309#468—91no—
310#468—91no—
311#468—91no—
312#468—91no—
313#468—91no—
314#468—91no—
315C2×#107—91no—
316C2×#103—91no—
317C2×#102—91no—
318C24×C3—31no—
319C24×C3—61no—
320C23×D3—21no—
321C23×D3#6711yescharacteristic
322C2×C3×Q8—31no—
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—31no—
327C2×C3×D4—41no—
328C2×C3×D4—61no—
329C2×C3×D4—62no—
330C2×C3×D4—62no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—61no—
334C2×C3×D4—124no—
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
337C22×C3×C4—21no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—62no—
344C22×C3×C4—62no—
345C22×C3×C4—61no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C2×#67—21no—
349C2×#67—21no—
350C2×#67—21no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3#6711yescharacteristic
354D3×Q8—62no—
355D3×Q8—62no—
356D3×D4—22no—
357D3×D4—22no—
358D3×D4—44no—
359C2×D12—21no—
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—22no—
362C2×C4×D3—22no—
363C2×C4×D3—21no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3#6711yescharacteristic
367C2×C4×D3#6711yescharacteristic
368C2×C4×D3C22×D311yescharacteristic
369C2×C4×D3C22×D311yescharacteristic
370C2×Dic6—31no—
371C2×Dic6—31no—
372C2×Dic6—61no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—61no—
376C2×Dic6—61no—
377C2×Dic6C22×D311yescharacteristic
378C3×SD16—62no—
379C3×M16—62no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—41no—
392C3×C22⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396#217—21no—
397#217—21no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—121no—
403#215—62no—
404#214—22no—
405#214—62no—
406#214—62no—
407#214—62no—
408#214—62no—
409#214—122no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414C4⋊Dic3—31no—
415C4⋊Dic3—31no—
416C4⋊Dic3—61no—
417C4⋊Dic3—61no—
418C4⋊Dic3—61no—
419C4⋊Dic3C22×D311yescharacteristic
420C4⋊Dic3C22×D311yescharacteristic
421Dic3⋊C4—21no—
422Dic3⋊C4—21no—
423Dic3⋊C4—61no—
424Dic3⋊C4—61no—
425Dic3⋊C4—61no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—121no—
430#208—22no—
431#208—62no—
432#208—62no—
433#208—62no—
434#208—62no—
435#208—122no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—31no—
438C2×C3⋊C8—34no—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—61no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8—62no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446#204—62no—
447ΓL(1,𝔽25)—62no—
448ΓL(1,𝔽25)—62no—
449D3×C8—34no—
450D3×C8—62no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32C22×D411yescharacteristic
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—44no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—84no—
466C2×C3×D3#12112yes—
467C2×C3×D3AGL(1,ℤ/8)12yes—
468C2×C3×D3#13712yes—
469C32×C4—21no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4C2×#4111yescharacteristic
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3#12112yes—
480C22×Q8—91no—
481C22×D4—31no—
482C22×D4—61no—
483C23×C4—31no—
484C2×SD16—31no—
485C2×SD16—91no—
486C2×SD16—91no—
487C2×SD16—91no—
488C2×SD16—184no—
489C2×M16—31no—
490C2×M16—91no—
491C2×M16—91no—
492C2×M16—91no—
493C2×M16—184no—
494C22×C8—91no—
495C22×C8—91no—
496C22⋊Q8—31no—
497C22⋊Q8—91no—
498C22⋊Q8—91no—
499C22⋊Q8—91no—
500C22⋊Q8—181no—
501C22⋊Q8—181no—
502#121—31no—
503#121—31no—
504#121—31no—
505#121—61no—
506#121—61no—
507#121D3211yescharacteristic
508C2×C4⋊C4—31no—
509C2×C4⋊C4—91no—
510C2×C4⋊C4—181no—
511C2×C22⋊C4—61no—
512C2×C22⋊C4—181no—
513#107—31no—
514#107—91no—
515#107—91no—
516#107—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—21no—
528C23×C3—31no—
529C23×C3—31no—
530C23×C3—41no—
531C23×C3—62no—
532C23×C3—62no—
533C23×C3—62no—
534C23×C3—61no—
535C23×C3—122no—
536C23×C3—122no—
537C23×C3—122no—
538C23×C3D3×D411yescharacteristic
539C23×C3C2×#6711yescharacteristic
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—21no—
544C22×D3—42no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3C2×#6711yescharacteristic
548C22×D3C2×#6711yescharacteristic
549C3×Q8—61no—
550C3×Q8—61no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—41no—
556C3×D4—41no—
557C3×D4—42no—
558C3×D4—42no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—82no—
562C3×D4—122no—
563C3×D4—122no—
564C3×D4—122no—
565C3×D4—122no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—31no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—31no—
578C2×C3×C4—41no—
579C2×C3×C4—41no—
580C2×C3×C4—41no—
581C2×C3×C4—62no—
582C2×C3×C4—62no—
583C2×C3×C4—62no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—122no—
590C2×C3×C4D3×D411yescharacteristic
591C2×C3×C4C2×#6711yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C23×D311yescharacteristic
594#67—42no—
595#67—42no—
596#67—42no—
597C2×Dic3—22no—
598C2×Dic3—21no—
599C2×Dic3—21no—
600C2×Dic3—21no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—121no—
606C2×Dic3—121no—
607C2×Dic3—122no—
608C2×Dic3—122no—
609C2×Dic3C2×#6711yescharacteristic
610C2×Dic3C2×#6711yescharacteristic
611D12—21no—
612D12—21no—
613D12—42no—
614C4×D3—22no—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—22no—
618C4×D3—42no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3D3×D412yes—
622C4×D3#23712yes—
623Dic6—21no—
624Dic6—21no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—121no—
630Dic6—121no—
631Dic6—122no—
632Dic6—122no—
633C3×C8—32no—
634C3×C8—61no—
635C3⋊C8—21no—
636C3⋊C8—32no—
637C3⋊C8—32no—
638C3⋊C8—62no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C3⋊C8D3×D412yescomplemented
643C2×C32—41no—
644C2×C32—81no—
645C2×C32C2×#12111yescharacteristic
646C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
647C2×C32C2×#13711yescharacteristic
648C3×D3—41no—
649C3×D3—81no—
650C3×D3#46814yescomplemented
651C24—31no—
652C24—61no—
653C2×Q8—31no—
654C2×Q8—91no—
655C2×Q8—181no—
656C2×Q8—182no—
657C2×Q8—182no—
658C2×D4—21no—
659C2×D4—31no—
660C2×D4—61no—
661C2×D4—62no—
662C2×D4—62no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—61no—
666C2×D4—124no—
667C2×D4C2×D3211yescharacteristic
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—61no—
676C22×C4—181no—
677C22×C4—181no—
678C22×C4C2×D3211yescharacteristic
679SD16—62no—
680SD16—182no—
681SD16—182no—
682SD16—182no—
683M16—62no—
684M16—182no—
685M16—182no—
686M16—182no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—94no—
690C2×C8—91no—
691C2×C8—91no—
692C2×C8—182no—
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—91no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C4⋊C4—181no—
702C4⋊C4C2×D3211yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—32no—
719C22×C3—32no—
720C22×C3—32no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—124no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—244no—
741C22×C3C2×D3×D411yescharacteristic
742C22×C3C22×#6711yescharacteristic
743C2×D3—21no—
744C2×D3—21no—
745C2×D3—21no—
746C2×D3—44no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—84no—
751C2×D3#93212yes—
752C2×D3#93912yes—
753C2×D3#95112yes—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—32no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—61no—
763C3×C4—81no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4—121no—
767C3×C4C2×D3×D411yescharacteristic
768C3×C4C2×D3×D411yescharacteristic
769C3×C4C2×#23711yescharacteristic
770C3×C4D3×#4111yescharacteristic
771Dic3—21no—
772Dic3—41no—
773Dic3—41no—
774Dic3—41no—
775Dic3—121no—
776Dic3—121no—
777Dic3—121no—
778Dic3—121no—
779Dic3—241no—
780Dic3—241no—
781Dic3#93912yes—
782C32C2×#46811yescharacteristic, complemented, Sylow
783C23—21no—
784C23—31no—
785C23—31no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—61no—
790C23—122no—
791C23—122no—
792C23—122no—
793C23D3×#6711yescharacteristic
794Q8—61no—
795Q8—61no—
796Q8—181no—
797Q8—181no—
798Q8—362no—
799D4—21no—
800D4—21no—
801D4—42no—
802D4—61no—
803D4—61no—
804D4—122no—
805D4—122no—
806D4—122no—
807D4—122no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—31no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—31no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—122no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—362no—
827C2×C4—362no—
828C2×C4D3×#6711yescharacteristic
829C2×C4C22×D3211yescharacteristic
830C8—32no—
831C8—61no—
832C8—92no—
833C8—181no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—34no—
838C2×C3—41no—
839C2×C3—41no—
840C2×C3—81no—
841C2×C3—81no—
842C2×C3—81no—
843C2×C3—121no—
844C2×C3—161no—
845C2×C3—241no—
846C2×C3D3×#12111yescharacteristic
847C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
848C2×C3D3×#13711yescharacteristic
849C2×C3C2×#93211yescharacteristic
850C2×C3C2×#93911yescharacteristic
851C2×C3C2×#95111yescharacteristic
852D3—41no—
853D3—81no—
854D3#504214yesdirect product factor
855C22—21no—
856C22—21no—
857C22—21no—
858C22—32no—
859C22—32no—
860C22—32no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—61no—
865C22—61no—
866C22—61no—
867C22—124no—
868C22—121no—
869C22—121no—
870C22—121no—
871C22—244no—
872C22C2×D3×#6711yescharacteristic
873C4—21no—
874C4—32no—
875C4—41no—
876C4—61no—
877C4—121no—
878C4—121no—
879C4—121no—
880C4—361no—
881C4—361no—
882C4D32×D411yescharacteristic
883C4D3×#23711yescharacteristic
884C3—21no—
885C3D3×#46811yescharacteristic, complemented
886C3C2×#504211yescharacteristic, complemented
887C2—34no—
888C2—41no—
889C2—81no—
890C2—121no—
891C2—241no—
892C2D3×#93211yescharacteristic
893C2D3×#93911yescharacteristic
894C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×D3×#121C2
hypercenter#121D32
hypocenterC32C2×#468
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C2×D3×#214C2semidirect
3. D3×#924C2semidirect
4. C2×D3×#208C2semidirect
5. #10592741C2semidirect
6. C3×#5042C2semidirect
7. #10591502C2semidirect
8. #10591462C2semidirect
9. D3×#832C2semidirect
10. #10591180C2semidirect
11. #10591176C2semidirect
12. D3×#810C2semidirect
13. #10590588C2semidirect
14. D3×#807C2semidirect
15. #10590515C2semidirect
23. C2×#3754C22semidirect
24. #64133C22semidirect
25. C2×#3748C22semidirect
28. C2×C3×#214C22semidirect
30. C3×#924C22semidirect
31. C2×C3×#208C22semidirect
41. #63857C22semidirect
42. #63856C22semidirect
44. C2×#3716C22semidirect
45. C2×#3715C22semidirect
46. C2×#3711C22semidirect
47. C2×#3711C22semidirect
51. #63659C22semidirect
52. #63637C22semidirect
53. #63634C22semidirect
54. C3×#832C22semidirect
55. C3×#810C22semidirect
56. C3×#807C22semidirect
57. #63576C22semidirect
58. #63575C22semidirect
59. #63567C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
85. #5042D3direct (N × H)
153. D3×C3⋊C8D4semidirect
187. C2×#214C2×D3semidirect
197. #924C2×D3semidirect
205. C2×#208C2×D3semidirect
234. #832C2×D3semidirect
243. #810C2×D3semidirect
251. #807C2×D3semidirect
300. C3⋊(C3⋊C8)C2×D4semidirect
302. C3×C3⋊C8C2×D4semidirect
642. C3⋊C8D3×D4semidirect
650. C3×D3#468semidirect
782. C32C2×#468semidirect
854. D3#5042direct (N × H)
885. C3D3×#468semidirect
886. C3C2×#5042semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1212
C2×D3×#2142
D3×#9242
C2×D3×#2082
#105927412
C3×#50422
#105915022
#105914622
D3×#8322
#105911802
#105911762
D3×#8102
#105905882
D3×#8072
#105905152
C2×#50423
D3×#4683