Finite Group Databasebeta

← D3×#4778 #11866713

Subgroups — D3×#4778 #11866713

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
1D3×#938C211yesmaximal, characteristic
2C2×D3×#214C211yesmaximal, characteristic, complemented
3C2×D32×C8C211yesmaximal, characteristic, complemented
4D3×#897C211yesmaximal, characteristic, complemented
5#10592477C211yesmaximal, characteristic, complemented
6C3×#4778C211yesmaximal, characteristic, complemented
7C3×D3×#102C211yesmaximal, characteristic, complemented
8#10591465C211yesmaximal, characteristic, complemented
9#10591460C211yesmaximal, characteristic, complemented
10#10590841C211yesmaximal, characteristic, complemented
11#10590825C211yesmaximal, characteristic, complemented
12D3×#816C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14#10590507C211yesmaximal, characteristic, complemented
15#10590501C211yesmaximal, characteristic, complemented
16D3×#465—31nomaximal
17C2×#4778—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×C4×D32C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22#64147C2211yescharacteristic
23C2×#3754C2211yescharacteristic, complemented
24C2×C8×C3⋊D3C2211yescharacteristic, complemented
25#64106C2211yescharacteristic, complemented
26C3×#938C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic, complemented
28C2×C3×D3×C8C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic, complemented
30C3×#897C2211yescharacteristic, complemented
31C3×D3×C4⋊C4C2211yescharacteristic
32#63970—21no—
33D3×#217—21no—
34#63958—21no—
35D3×#214—24no—
36D3×(C2×D3)⋊C4—21no—
37#63916C2211yescharacteristic
38#63908C2211yescharacteristic
39#63895—21no—
40#63893—21no—
41D3×C4⋊Dic3—21no—
42D3×C4⋊Dic3C2211yescharacteristic
43#63871C2211yescharacteristic, complemented
44#63857C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3710C2211yescharacteristic, complemented
48C2×D3×C3⋊C8C2211yescharacteristic
49C2×D3×C3⋊C8C2211yescharacteristic, complemented
50D32×C8—24no—
51C32×#102C2211yescharacteristic, complemented
52#63643C2211yescharacteristic, complemented
53#63635C2211yescharacteristic, complemented
54C3×#832C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#808C2211yescharacteristic, complemented
59#63574C2211yescharacteristic, complemented
60#63573C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63566C2211yescharacteristic, complemented
63C2×#938—31no—
64C22×#214—31no—
65C2×D3×SD16—31no—
66C22×D3×C8—31no—
67C22×D3×C8—31no—
68D3×C22⋊Q8—31no—
69D3×#121—31no—
70C2×#897—31no—
71C3×#465—31no—
72C2×C3×#102—31no—
73#5171—31no—
74#5114—31no—
75C2×#816—31no—
76#5048—31no—
77#5041—31no—
78C2×#808—31no—
79#4864—31no—
80D3×#106—31no—
81#4807—31no—
82D3×#103—31no—
83#4778—31no—
84#4778—31no—
85#4778—31no—
86#4778—31no—
87#4778—31no—
88#4778—31no—
89#4778—31no—
90#4778—31no—
91#4778—61no—
92#4778D311yescharacteristic, direct product factor
93D3×#102D311yescharacteristic, complemented
94C23×C3×D3—21no—
95C22×D32D411yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×D3×D4—22no—
103C3×D3×D4—22no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109D3×#67—44no—
110C2×#627—21no—
111C2×#626—21no—
112C2×#625—21no—
113C2×#624D411yescharacteristic
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3D411yescharacteristic
117C2×D3×Dic3D411yescharacteristic
118C4×D32—22no—
119C4×D32—22no—
120D3×Dic6—22no—
121D3×Dic6—22no—
122C2×C32×C8C2311yescharacteristic
123C32×C4⋊C4C2311yescharacteristic
124#3757—21no—
125#3754—22no—
126#3752—21no—
127C4⋊(C3⋊Dic3)—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C8×C3⋊D3—22no—
131C3×#217—21no—
132C3×#214—22no—
133C3×(C2×D3)⋊C4—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D3×C8—22no—
141C3×D3×C8—22no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3716—22no—
150#3715—22no—
151#3710—22no—
152D3×C3⋊C8—22no—
153D3×C3⋊C8D414yescomplemented
154C2×#465—91noSylow
155C22×C3×D4—31no—
156C22×#67—61no—
157C2×D3×Q8—31no—
158C2×D3×D4—61no—
159C2×D3×D4C2×D311yescharacteristic
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×Dic6—31no—
163C2×C3×SD16—31no—
164C22×C3×C8—31no—
165C22×C3×C8—31no—
166C3×C22⋊Q8—31no—
167C3×#121—31no—
168C2×C3×C4⋊C4—31no—
169C2×#217—61no—
170#946—31no—
171C2×#215—31no—
172#939—61no—
173#938—31no—
174#938—31no—
175#938—31no—
176#938—31no—
177#938—61no—
178#938—61no—
179#938—61no—
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#930—31no—
189C2×(C2×D3)⋊C4—61no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—61no—
192#924—31no—
193C22×C3⋊C8—31no—
194C22×C3⋊C8—31no—
195D3×SD16—64no—
196C2×#204—31no—
197C2×D3×C8—31no—
198C2×D3×C8—31no—
199C2×D3×C8—31no—
200C2×D3×C8—31no—
201C2×D3×C8—31no—
202C2×D3×C8—31no—
203C2×D3×C8—61no—
204C2×D3×C8—64no—
205C2×D3×C8—64no—
206C2×D3×C8C2×D311yescharacteristic
207C2×D3×C8C2×D311yescharacteristic, complemented
208#897—31no—
209#897—31no—
210#897—31no—
211#897—31no—
212#897—61no—
213#897—61no—
214#897—61no—
215#897C2×D311yescharacteristic, complemented
216#896—61no—
217#895—31no—
218D3×C4⋊C4—31no—
219D3×C4⋊C4—61no—
220D3×C4⋊C4C2×D311yescharacteristic
221#884—61no—
222D3×C22⋊C4—61no—
223D3×C22⋊C4—61no—
224#878—61no—
225C3×#106—31no—
226C3×#103—31no—
227C3×#102—21no—
228C3×#102—31no—
229C3×#102—31no—
230C3×#102—31no—
231C3×#102C2×D311yescharacteristic, complemented
232C3×#102C2×D311yescharacteristic, complemented
233#835—31no—
234#832C2×D311yescharacteristic, complemented
235#821C2×D311yescharacteristic, complemented
236#817—31no—
237#816—31no—
238#816—31no—
239#816—31no—
240#816—31no—
241#816—61no—
242#816C2×D311yescharacteristic, complemented
243#810—31no—
244#809C2×D311yescharacteristic, complemented
245#808—31no—
246#808—31no—
247#808—31no—
248#808—31no—
249#808—31no—
250#808—61no—
251#808C2×D311yescharacteristic, complemented
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×D4—21no—
264C32×D4—21no—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267#638—42no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4×C3⋊D3—21no—
272C4×C3⋊D3—21no—
273#634—21no—
274#634—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—
291#627—42no—
292#626—42no—
293#625—42no—
294#624—22no—
295D3×Dic3—22no—
296D3×Dic3—22no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8—21no—
300C3⋊(C3⋊C8)C2×D412yescomplemented
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yescomplemented
303C22×SD16—91no—
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—31no—
318C24×C3—61no—
319C23×D3—21no—
320C23×D3—31no—
321C23×D3—31no—
322C2×C3×Q8—31no—
323C2×C3×D4—21no—
324C2×C3×D4—31no—
325C2×C3×D4—62no—
326C2×C3×D4—62no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4C22×D311yescharacteristic
330C2×C3×D4C22×D311yescharacteristic
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C2×#67—21no—
335C2×#67—21no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—121no—
342C2×#67—124no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347D3×Q8—62no—
348D3×Q8—62no—
349D3×D4—22no—
350D3×D4—22no—
351D3×D4—124no—
352C2×D12—61no—
353C2×D12C22×D311yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—31no—
358C2×C4×D3—31no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—61no—
362C2×C4×D3—62no—
363C2×C4×D3—62no—
364C2×C4×D3—62no—
365C2×C4×D3—62no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
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—
379C2×C3×C8—21no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C2×C3×C8—62no—
383C2×C3×C8—62no—
384C2×C3×C8C22×D311yescharacteristic
385C2×C3×C8C22×D311yescharacteristic
386C3×C4⋊C4—21no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—61no—
391C3×C4⋊C4C22×D311yescharacteristic
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C22⋊C4—61no—
394C3×C22⋊C4—61no—
395#217—21no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—121no—
402#215—62no—
403#214—22no—
404#214—62no—
405#214—62no—
406#214—62no—
407#214—62no—
408#214—122no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—121no—
418C4⋊Dic3—21no—
419C4⋊Dic3—31no—
420C4⋊Dic3—31no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3—121no—
428C4⋊Dic3C22×D311yescharacteristic
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434C2×C3⋊C8—31no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—34no—
437C2×C3⋊C8—61no—
438C2×C3⋊C8—62no—
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441#204—62no—
442D3×C8—22no—
443D3×C8—22no—
444D3×C8—34no—
445D3×C8—62no—
446D3×C8—62no—
447D3×C8—62no—
448D3×C8—62no—
449D3×C8—62no—
450D3×C8—122no—
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—91no—
481C22×D4—31no—
482C22×D4—181no—
483C23×C4—91no—
484C2×SD16—31no—
485C2×SD16—91no—
486C2×SD16—91no—
487C2×SD16—91no—
488C2×SD16—184no—
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—31no—
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—31no—
523#102—31no—
524#102D3211yescharacteristic, complemented
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—61no—
550C3×Q8—61no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—41no—
556C3×D4—41no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—122no—
560C3×D4—122no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—31no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—31no—
568C2×C3×C4—41no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—122no—
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577#67—42no—
578#67—42no—
579#67—122no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—122no—
584#67—242no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—61no—
591C2×Dic3—62no—
592C2×Dic3—62no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—122no—
600C2×Dic3—122no—
601C2×Dic3D3×D411yescharacteristic
602C2×Dic3D3×D411yescharacteristic
603D12—21no—
604D12—21no—
605D12—122no—
606C4×D3—21no—
607C4×D3—21no—
608C4×D3—42no—
609C4×D3—62no—
610C4×D3—62no—
611C4×D3—62no—
612C4×D3—61no—
613C4×D3—61no—
614C4×D3—61no—
615C4×D3—61no—
616C4×D3—62no—
617C4×D3—121no—
618C4×D3—121no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3#23512yes—
622C4×D3D3×D412yes—
623Dic6—21no—
624Dic6—21no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—121no—
630Dic6—121no—
631Dic6—122no—
632Dic6—122no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—32no—
636C3×C8—41no—
637C3×C8—61no—
638C3⋊C8—21no—
639C3⋊C8—32no—
640C3⋊C8—32no—
641C3⋊C8—62no—
642C3⋊C8D3×D412yescomplemented
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—91no—
655C2×Q8—181no—
656C2×Q8—182no—
657C2×Q8—182no—
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—62no—
680SD16—182no—
681SD16—182no—
682SD16—182no—
683C2×C8—31no—
684C2×C8—31no—
685C2×C8—62no—
686C2×C8—62no—
687C2×C8—94no—
688C2×C8—91no—
689C2×C8—182no—
690C2×C8—182no—
691C2×C8—182no—
692C2×C8C2×D3211yescharacteristic
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—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×D3#88412yes—
751C2×D3#91212yes—
752C2×D3D3×SD1612yes—
753C2×D3D3×SD1612yescomplemented
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×#23511yescharacteristic
765C3×C4C2×D3×D411yescharacteristic
766C3×C4C2×D3×D411yescharacteristic
767C3×C4D3×#4111yescharacteristic
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#88412yes—
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—61no—
795Q8—61no—
796Q8—181no—
797Q8—181no—
798Q8—362no—
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—21no—
831C8—32no—
832C8—61no—
833C8—92no—
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×C3C2×#88411yescharacteristic
844C2×C3D3×#12111yescharacteristic
845C2×C3C2×#91211yescharacteristic
846C2×C3C2×D3×SD1611yescharacteristic
847C2×C3C2×D3×SD1611yescharacteristic
848C2×C3D3×#13511yescharacteristic
849D3—22no—
850D3—62no—
851D3—62no—
852D3—81no—
853D3—122no—
854D3#477814yesdirect 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×#23511yescharacteristic
883C4D32×D411yescharacteristic
884C3—21no—
885C3C2×#477811yescharacteristic, complemented
886C3D3×#46511yescharacteristic, complemented
887C2—34no—
888C2—62no—
889C2—81no—
890C2—182no—
891C2—241no—
892C2D3×#88411yescharacteristic
893C2D3×#91211yescharacteristic
894C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalD3×#938C2
hypercenter#102D32
hypocenterC32C2×#465
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
2. C2×D3×#214C2semidirect
3. C2×D32×C8C2semidirect
4. D3×#897C2semidirect
5. #10592477C2semidirect
6. C3×#4778C2semidirect
7. C3×D3×#102C2semidirect
8. #10591465C2semidirect
9. #10591460C2semidirect
10. #10590841C2semidirect
11. #10590825C2semidirect
12. D3×#816C2semidirect
13. D3×#808C2semidirect
14. #10590507C2semidirect
15. #10590501C2semidirect
23. C2×#3754C22semidirect
24. C2×C8×C3⋊D3C22semidirect
25. #64106C22semidirect
27. C2×C3×#214C22semidirect
29. C2×C3×D3×C8C22semidirect
30. C3×#897C22semidirect
43. #63871C22semidirect
44. #63857C22semidirect
45. C2×#3716C22semidirect
46. C2×#3715C22semidirect
47. C2×#3710C22semidirect
49. C2×D3×C3⋊C8C22semidirect
51. C32×#102C22semidirect
52. #63643C22semidirect
53. #63635C22semidirect
54. C3×#832C22semidirect
55. C3×#821C22semidirect
56. C3×#816C22semidirect
57. C3×#809C22semidirect
58. C3×#808C22semidirect
59. #63574C22semidirect
60. #63573C22semidirect
61. #63567C22semidirect
62. #63566C22semidirect
92. #4778D3direct (N × H)
93. D3×#102D3semidirect
153. D3×C3⋊C8D4semidirect
187. C2×#214C2×D3semidirect
207. C2×D3×C8C2×D3semidirect
215. #897C2×D3semidirect
231. C3×#102C2×D3semidirect
232. C3×#102C2×D3semidirect
234. #832C2×D3semidirect
235. #821C2×D3semidirect
242. #816C2×D3semidirect
244. #809C2×D3semidirect
251. #808C2×D3semidirect
262. C2×D32SD16semidirect
300. C3⋊(C3⋊C8)C2×D4semidirect
302. C3×C3⋊C8C2×D4semidirect
457. C2×C3⋊D3C2×SD16semidirect
466. C2×C3×D3C2×SD16semidirect
524. #102D32semidirect
642. C3⋊C8D3×D4semidirect
650. C3×D3#465semidirect
753. C2×D3D3×SD16semidirect
782. C32C2×#465semidirect
854. D3#4778direct (N × H)
885. C3C2×#4778semidirect
886. C3D3×#465semidirect

Maximal subgroups

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

subgroupindex
D3×#9382
C2×D3×#2142
C2×D32×C82
D3×#8972
#105924772
C3×#47782
C3×D3×#1022
#105914652
#105914602
#105908412
#105908252
D3×#8162
D3×#8082
#105905072
#105905012
D3×#4653
C2×#47783