Finite Group Databasebeta

← D3×#5049 #11866913

Subgroups — D3×#5049 #11866913

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×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3D3×#930C211yesmaximal, characteristic
4C2×D3×#208C211yesmaximal, characteristic, complemented
5#10592748C211yesmaximal, characteristic, complemented
6C3×#5049C211yesmaximal, characteristic, complemented
7#10591589C211yesmaximal, characteristic, complemented
8#10591587C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10591180C211yesmaximal, characteristic, complemented
11#10591178C211yesmaximal, characteristic, complemented
12D3×#809C211yesmaximal, characteristic, complemented
13#10590585C211yesmaximal, characteristic, complemented
14D3×#807C211yesmaximal, characteristic, complemented
15#10590503C211yesmaximal, characteristic, complemented
16C2×#5049—31nomaximal
17D3×#468—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C32×C22⋊Q8C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic, complemented
24#64139C2211yescharacteristic
25C2×#3748C2211yescharacteristic, complemented
26C3×#946C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#930C2211yescharacteristic
29C3×#924C2211yescharacteristic, complemented
30C2×C3×#208C2211yescharacteristic, complemented
31C3×#897C2211yescharacteristic, complemented
32C3×#896—21no—
33C3×D3×C4⋊C4—21no—
34C3×D3×C4⋊C4C2211yescharacteristic
35C3×D3×C22⋊C4—21no—
36C3×#878—21no—
37#63978—21no—
38D3×#215—24no—
39D3×(C2×D3)⋊C4—21no—
40#63909C2211yescharacteristic
41#63908C2211yescharacteristic
42#63906—21no—
43D3×C4⋊Dic3C2211yescharacteristic
44C2×#3717C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic, complemented
46C2×#3711C2211yescharacteristic, complemented
47C2×#3711C2211yescharacteristic, complemented
48D3×#208—24no—
49C2×D3×C3⋊C8C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63636C2211yescharacteristic, complemented
53#63634C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×#807C2211yescharacteristic, complemented
57#63576C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×C3×C22⋊Q8—31no—
64C22×#215—31no—
65C2×#930—31no—
66C22×#208—31no—
67C2×D3×SD16—31no—
68C2×D3×M16—31no—
69D3×C22⋊Q8D311yescharacteristic, complemented
70D3×#121—31no—
71C3×#468—31no—
72C2×#835—31no—
73#5174—31no—
74#5134—31no—
75#5049—31no—
76#5049—31no—
77#5049—31no—
78#5049—31no—
79#5049—31no—
80#5049—31no—
81#5049—31no—
82#5049—31no—
83#5049—61no—
84#5049D311yescharacteristic, direct product factor
85#5042—31no—
86C2×#809—31no—
87C2×#807—31no—
88#4886—31no—
89D3×#107—31no—
90#4812—31no—
91D3×#103—31no—
92#4780—31no—
93D3×#102—31no—
94C23×C3×D3D411yescharacteristic
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C22×C3×Dic3D411yescharacteristic
102C3×D3×Q8—22no—
103C3×D3×Q8—22no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3D411yescharacteristic
110C2×C3×C4×D3D411yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6—21no—
114C2×C3×Dic6C2311yescharacteristic
115D3×#67—44no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#625—21no—
119C2×D3×Dic3—21no—
120D3×D12—22no—
121D3×D12—22no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125#3755—22no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128#3748—22no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#217—21no—
132C3×#215—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×#208—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145Dic3⋊Dic3—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148#3717—22no—
149#3715—22no—
150#3711—22no—
151#3711—22no—
152D3×C3⋊C8—22no—
153D3×C3⋊C8D414yescomplemented
154C2×#468—91noSylow
155C22×C3×Q8—31no—
156C23×C3×C4—31no—
157C22×#67—61no—
158C2×D3×Q8C2×D311yescharacteristic
159C2×D3×D4—31no—
160C2×D3×D4—61no—
161C22×D12—31no—
162C22×C4×D3C2×D311yescharacteristic
163C2×C3×SD16—31no—
164C2×C3×M16—31no—
165C3×C22⋊Q8—21no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—31no—
169C3×C22⋊Q8—61no—
170C3×C22⋊Q8—61no—
171C3×C22⋊Q8C2×D311yescharacteristic, complemented
172C3×C22⋊Q8C2×D311yescharacteristic, complemented
173C3×#121—31no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—61no—
176C2×C3×C22⋊C4—61no—
177#946C2×D311yescharacteristic, complemented
178C2×#215—31no—
179C2×#215—31no—
180C2×#215—31no—
181C2×#215—31no—
182C2×#215—61no—
183C2×#215—64no—
184C2×#215C2×D311yescharacteristic, complemented
185#939—61no—
186#938—31no—
187C2×#214—31no—
188#930—31no—
189#930—31no—
190#930—31no—
191#930—31no—
192#930—61no—
193#930—61no—
194#930—61no—
195#930C2×D311yescharacteristic
196C2×(C2×D3)⋊C4—61no—
197C2×C4⋊Dic3—31no—
198#924C2×D311yescharacteristic, complemented
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#897C2×D311yescharacteristic, complemented
216#896—21no—
217#895—31no—
218D3×C4⋊C4—21no—
219D3×C4⋊C4—31no—
220D3×C4⋊C4C2×D311yescharacteristic
221#884—61no—
222D3×C22⋊C4—21no—
223D3×C22⋊C4—61no—
224#878—21no—
225C3×#107—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#821—31no—
236#818—31no—
237#816—31no—
238#810—31no—
239#809—31no—
240#809—31no—
241#809—31no—
242#809—31no—
243#809—61no—
244#809C2×D311yescharacteristic, complemented
245#807—31no—
246#807—31no—
247#807—31no—
248#807—31no—
249#807—31no—
250#807—61no—
251#807C2×D311yescharacteristic, complemented
252C23×C32C2×D411yescharacteristic
253C22×C3⋊D3—21no—
254C22×C3×D3—22no—
255C22×C3×D3—22no—
256C22×C3×D3—22no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—42no—
263C32×Q8—21no—
264C32×Q8—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271#638—42no—
272C2×C3⋊Dic3—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C3×#67—42no—
276C2×C3×Dic3—22no—
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—22no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—22no—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×C4×D3C2×D412yes—
291C3×C4×D3#4112yes—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—42no—
295#626—42no—
296#626—42no—
297#625—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—31no—
306C2×#121—91no—
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—
319C23×D3—61no—
320C23×D3—61no—
321C23×D3#6711yescharacteristic
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—31no—
330C2×C3×D4—61no—
331C22×C3×C4—21no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—62no—
338C22×C3×C4—62no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C2×#67—21no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—121no—
351C2×#67—124no—
352C22×Dic3—61no—
353C22×Dic3#6711yescharacteristic
354D3×Q8—22no—
355D3×Q8—22no—
356D3×D4—62no—
357D3×D4—62no—
358D3×D4—124no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—61no—
362C2×D12—62no—
363C2×D12—62no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12C22×D311yescharacteristic
367C2×C4×D3—22no—
368C2×C4×D3—22no—
369C2×C4×D3—21no—
370C2×C4×D3—21no—
371C2×C4×D3—61no—
372C2×C4×D3#6711yescharacteristic
373C2×C4×D3#6711yescharacteristic
374C2×C4×D3C22×D311yescharacteristic
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6—21no—
377C2×Dic6C22×D311yescharacteristic
378C3×SD16—62no—
379C3×M16—62no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—31no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—41no—
388C3×C4⋊C4—61no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C22⋊C4—21no—
395C3×C22⋊C4—21no—
396C3×C22⋊C4—41no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401#217—21no—
402#217—61no—
403#215—22no—
404#215—62no—
405#215—62no—
406#215—62no—
407#215—62no—
408#215—122no—
409#214—62no—
410(C2×D3)⋊C4—21no—
411(C2×D3)⋊C4—21no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—121no—
419C4⋊Dic3—21no—
420C4⋊Dic3—31no—
421C4⋊Dic3—31no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3C22×D311yescharacteristic
425C4⋊Dic3C22×D311yescharacteristic
426Dic3⋊C4—21no—
427Dic3⋊C4—21no—
428Dic3⋊C4—21no—
429Dic3⋊C4—61no—
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×C32C22×D411yescharacteristic
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
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#12112yes—
466C2×C3×D3AGL(1,ℤ/8)12yes—
467C2×C3×D3#13712yes—
468D32—84no—
469C32×C4—21no—
470C32×C4—41no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4C2×#4111yescharacteristic
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3#12112yes—
480C22×Q8—31no—
481C22×D4—91no—
482C22×D4—181no—
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—31no—
498C22⋊Q8—31no—
499C22⋊Q8—61no—
500C22⋊Q8—61no—
501C22⋊Q8D3211yescharacteristic, complemented
502#121—31no—
503#121—91no—
504#121—91no—
505#121—91no—
506#121—181no—
507#121—181no—
508C2×C4⋊C4—31no—
509C2×C4⋊C4—61no—
510C2×C4⋊C4—91no—
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—31no—
527C23×C3—31no—
528C23×C3—62no—
529C23×C3—62no—
530C23×C3—62no—
531C23×C3—61no—
532C23×C3D3×D411yescharacteristic
533C23×C3C2×#6711yescharacteristic
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—21no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3C2×#6711yescharacteristic
548C22×D3C2×#6711yescharacteristic
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—61no—
559C3×D4—61no—
560C3×D4—122no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
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—41no—
577C2×C3×C4—41no—
578C2×C3×C4—41no—
579C2×C3×C4—62no—
580C2×C3×C4—62no—
581C2×C3×C4—62no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—122no—
588C2×C3×C4—122no—
589C2×C3×C4D3×D411yescharacteristic
590C2×C3×C4C2×#6711yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593#67—42no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67—242no—
601C2×Dic3—22no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—121no—
608C2×Dic3—122no—
609C2×Dic3C2×#6711yescharacteristic
610C2×Dic3C2×#6711yescharacteristic
611D12—21no—
612D12—21no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—61no—
617D12—121no—
618D12—121no—
619D12—122no—
620D12—122no—
621C4×D3—22no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—22no—
625C4×D3—42no—
626C4×D3—42no—
627C4×D3—122no—
628C4×D3D3×D412yes—
629C4×D3#23712yes—
630Dic6—21no—
631Dic6—21no—
632Dic6—42no—
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×C32C2×#12111yescharacteristic
645C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
646C2×C32C2×#13711yescharacteristic
647C3⋊D3—81no—
648C3×D3—41no—
649C3×D3—81no—
650C3×D3#46814yescomplemented
651C24—31no—
652C24—181no—
653C2×Q8—31no—
654C2×Q8—61no—
655C2×Q8—62no—
656C2×Q8—62no—
657C2×Q8C2×D3211yescharacteristic
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—91no—
661C2×D4—182no—
662C2×D4—182no—
663C2×D4—181no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—364no—
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—61no—
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—21no—
694C4⋊C4—31no—
695C4⋊C4—31no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—61no—
700C4⋊C4—91no—
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—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—124no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C22×#6711yescharacteristic
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—44no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—241no—
747C2×D3—241no—
748C2×D3—241no—
749C2×D3—244no—
750C2×D3—244no—
751C2×D3#93912yes—
752C2×D3#94212yes—
753C2×D3#94912yes—
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—41no—
763C3×C4—41no—
764C3×C4—61no—
765C3×C4—81no—
766C3×C4—81no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4—121no—
770C3×C4C2×D3×D411yescharacteristic
771C3×C4C2×D3×D411yescharacteristic
772C3×C4C2×#23711yescharacteristic
773C3×C4D3×#4111yescharacteristic
774Dic3—21no—
775Dic3—41no—
776Dic3—41no—
777Dic3—41no—
778Dic3—121no—
779Dic3—121no—
780Dic3—241no—
781Dic3#93912yes—
782C32C2×#46811yescharacteristic, complemented, Sylow
783C23—31no—
784C23—31no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—61no—
789C23—181no—
790C23—362no—
791C23—362no—
792C23—362no—
793C23D3×#6711yescharacteristic
794Q8—21no—
795Q8—21no—
796Q8—61no—
797Q8—61no—
798Q8—122no—
799D4—61no—
800D4—61no—
801D4—122no—
802D4—181no—
803D4—181no—
804D4—362no—
805D4—362no—
806D4—362no—
807D4—362no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—31no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—31no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—122no—
825C2×C4—122no—
826C2×C4—181no—
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—121no—
842C2×C3—241no—
843C2×C3D3×#12111yescharacteristic
844C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
845C2×C3D3×#13711yescharacteristic
846C2×C3C2×#93911yescharacteristic
847C2×C3C2×#94211yescharacteristic
848C2×C3C2×#94911yescharacteristic
849D3—41no—
850D3—81no—
851D3—241no—
852D3—241no—
853D3—481no—
854D3#504914yesdirect product factor
855C22—21no—
856C22—21no—
857C22—21no—
858C22—32no—
859C22—32no—
860C22—32no—
861C22—61no—
862C22—61no—
863C22—61no—
864C22—124no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—361no—
869C22—361no—
870C22—361no—
871C22—724no—
872C22C2×D3×#6711yescharacteristic
873C4—21no—
874C4—32no—
875C4—41no—
876C4—41no—
877C4—61no—
878C4—121no—
879C4—121no—
880C4—121no—
881C4—361no—
882C4D32×D411yescharacteristic
883C4D3×#23711yescharacteristic
884C3—21no—
885C3D3×#46811yescharacteristic, complemented
886C3C2×#504911yescharacteristic, complemented
887C2—34no—
888C2—41no—
889C2—121no—
890C2—241no—
891C2—721no—
892C2D3×#93911yescharacteristic
893C2D3×#94211yescharacteristic
894C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalD3×#930C2
hypercenterC22⋊Q8D32
hypocenterC32C2×#468
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×D3×C22⋊Q8C2semidirect
2. C2×D3×#215C2semidirect
4. C2×D3×#208C2semidirect
5. #10592748C2semidirect
6. C3×#5049C2semidirect
7. #10591589C2semidirect
8. #10591587C2semidirect
9. D3×#835C2semidirect
10. #10591180C2semidirect
11. #10591178C2semidirect
12. D3×#809C2semidirect
13. #10590585C2semidirect
14. D3×#807C2semidirect
15. #10590503C2semidirect
22. C32×C22⋊Q8C22semidirect
23. C2×#3755C22semidirect
25. C2×#3748C22semidirect
26. C3×#946C22semidirect
27. C2×C3×#215C22semidirect
29. C3×#924C22semidirect
30. C2×C3×#208C22semidirect
31. C3×#897C22semidirect
44. C2×#3717C22semidirect
45. C2×#3715C22semidirect
46. C2×#3711C22semidirect
47. C2×#3711C22semidirect
51. #63662C22semidirect
52. #63636C22semidirect
53. #63634C22semidirect
54. C3×#835C22semidirect
55. C3×#809C22semidirect
56. C3×#807C22semidirect
57. #63576C22semidirect
58. #63575C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63564C22semidirect
62. #63562C22semidirect
69. D3×C22⋊Q8D3semidirect
84. #5049D3direct (N × H)
153. D3×C3⋊C8D4semidirect
171. C3×C22⋊Q8C2×D3semidirect
172. C3×C22⋊Q8C2×D3semidirect
177. #946C2×D3semidirect
184. C2×#215C2×D3semidirect
198. #924C2×D3semidirect
205. C2×#208C2×D3semidirect
215. #897C2×D3semidirect
233. #835C2×D3semidirect
244. #809C2×D3semidirect
251. #807C2×D3semidirect
300. C3⋊(C3⋊C8)C2×D4semidirect
302. C3×C3⋊C8C2×D4semidirect
501. C22⋊Q8D32semidirect
642. C3⋊C8D3×D4semidirect
650. C3×D3#468semidirect
782. C32C2×#468semidirect
854. D3#5049direct (N × H)
885. C3D3×#468semidirect
886. C3C2×#5049semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C22⋊Q82
C2×D3×#2152
D3×#9302
C2×D3×#2082
#105927482
C3×#50492
#105915892
#105915872
D3×#8352
#105911802
#105911782
D3×#8092
#105905852
D3×#8072
#105905032
C2×#50493
D3×#4683