Finite Group Databasebeta

← D3×#4862 #11869390

Subgroups — D3×#4862 #11869390

Order 1152.

972 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#897C211yesmaximal, characteristic
2D32×C4⋊C4C211yesmaximal, characteristic
3#10592561C211yesmaximal, characteristic, complemented
4C3×#4862C211yesmaximal, characteristic, complemented
5C3×D3×#106C211yesmaximal, characteristic, complemented
6D3×(C2×D3)⋊C8C211yesmaximal, characteristic
7#10590686C211yesmaximal, characteristic, complemented
8#10590674C211yesmaximal, characteristic, complemented
9D3×#816C211yesmaximal, characteristic, complemented
10D3×#810C211yesmaximal, characteristic, complemented
11D3×#808C211yesmaximal, characteristic, complemented
12#10590529C211yesmaximal, characteristic, complemented
13#10590443C211yesmaximal, characteristic, complemented
14#10590439C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16D3×#483—31nomaximal
17C2×#4862—31nomaximal
18C2×C4×D32—21no—
19C2×C4×D32C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21#64106C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C3×#897C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28D3×(C2×D3)⋊C4—21no—
29#63900C2211yescharacteristic
30#63895—21no—
31#63893—21no—
32D3×C4⋊Dic3—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63883—21no—
36D3×Dic3⋊C4—21no—
37D3×Dic3⋊C4—21no—
38#63871C2211yescharacteristic
39#63857C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#106C2211yescharacteristic, complemented
42#63647C2211yescharacteristic
43#63643C2211yescharacteristic, complemented
44#63637C2211yescharacteristic, complemented
45#63635C2211yescharacteristic, complemented
46C3×(C2×D3)⋊C8C2211yescharacteristic
47C3×#817C2211yescharacteristic, complemented
48C3×#816C2211yescharacteristic, complemented
49C3×#810C2211yescharacteristic, complemented
50C3×#808C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61D3×C22⋊Q8—31no—
62C2×#897—31no—
63C2×D3×C4⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65C3×#483—31no—
66C2×C3×#106—31no—
67C2×(C2×D3)⋊C8—31no—
68C2×#816—31no—
69#5043—31no—
70#4971—31no—
71C2×#810—31no—
72C2×#808—31no—
73#4862—31no—
74#4862—31no—
75#4862—31no—
76#4862—31no—
77#4862—31no—
78#4862—31no—
79#4862—31no—
80#4862—31no—
81#4862—31no—
82#4862—61no—
83#4862D311yescharacteristic, direct product factor
84D3×#106—31no—
85D3×#106D311yescharacteristic, complemented
86#4805—31no—
87#4805—31no—
88D3×#103—31no—
89D3×#103—31no—
90D3×C22⋊C8—31no—
91#4721—31no—
92C22×D32D411yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#624—21no—
104C2×#624D411yescharacteristic
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3D411yescharacteristic
109C2×D3×Dic3D411yescharacteristic
110C4×D32—22no—
111C4×D32—22no—
112C4×D32—44no—
113D3×Dic6—22no—
114D3×Dic6—22no—
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118#3752—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×D3×C8—22no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141D3×C3⋊C8—22no—
142C2×#483—91noSylow
143C2×D3×Q8—31no—
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—61no—
147C22×C4×D3—61no—
148C22×Dic6—31no—
149C22×C3×C8—31no—
150C3×C22⋊Q8—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153C2×C3×C4⋊C4—31no—
154#946—31no—
155C2×(C2×D3)⋊C4—61no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—61no—
159#924—31no—
160C2×Dic3⋊C4—61no—
161C2×Dic3⋊C4—61no—
162C22×C3⋊C8—31no—
163C2×D3×C8—31no—
164C2×D3×C8C2×D311yescharacteristic
165#897—31no—
166#897—31no—
167#897—31no—
168#897—31no—
169#897—61no—
170#897—61no—
171#897—61no—
172#897C2×D311yescharacteristic
173#896—61no—
174D3×C4⋊C4—31no—
175D3×C4⋊C4—31no—
176D3×C4⋊C4—31no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—31no—
180D3×C4⋊C4—61no—
181D3×C4⋊C4—61no—
182D3×C4⋊C4—61no—
183D3×C4⋊C4—61no—
184D3×C4⋊C4—61no—
185D3×C4⋊C4—61no—
186D3×C4⋊C4C2×D311yescharacteristic
187D3×C4⋊C4C2×D311yescharacteristic
188D3×C4⋊C4C2×D311yescharacteristic
189D3×C22⋊C4—61no—
190#878—61no—
191C3×#106—21no—
192C3×#106—31no—
193C3×#106—31no—
194C3×#106—31no—
195C3×#106—31no—
196C3×#106C2×D311yescharacteristic, complemented
197C3×#106C2×D311yescharacteristic, complemented
198C3×#103—31no—
199C3×#103—31no—
200C3×C22⋊C8—31no—
201#835—31no—
202#835—31no—
203#830—31no—
204(C2×D3)⋊C8—31no—
205(C2×D3)⋊C8—31no—
206(C2×D3)⋊C8—31no—
207(C2×D3)⋊C8—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—61no—
210(C2×D3)⋊C8C2×D311yescharacteristic
211#817—31no—
212#817C2×D311yescharacteristic, complemented
213#816—31no—
214#816—31no—
215#816—31no—
216#816—31no—
217#816—31no—
218#816—61no—
219#816C2×D311yescharacteristic, complemented
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—61no—
226#810C2×D311yescharacteristic, complemented
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808—31no—
232#808—61no—
233#808C2×D311yescharacteristic, complemented
234#808C2×D311yescharacteristic, complemented
235#808C2×D311yescharacteristic, complemented
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—22no—
240C2×D32—22no—
241C2×D32SD1614yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4×C3⋊D3—21no—
249C4×C3⋊D3—21no—
250C4×C3⋊D3—42no—
251#634—21no—
252#634—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—42no—
262C3×C4×D3—42no—
263C3×C4×D3—42no—
264C3×C4×D3#4112yes—
265C3×C4×D3#4112yes—
266C3×Dic6—21no—
267C3×Dic6—21no—
268#627—42no—
269#624—22no—
270#624—42no—
271D3×Dic3—22no—
272D3×Dic3—22no—
273D3×Dic3—42no—
274D3×Dic3—42no—
275D3×Dic3—42no—
276C32×C8—21no—
277C3⋊(C3⋊C8)—21no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280C2×C22⋊Q8—91no—
281C22×C4⋊C4—91no—
282#483—31no—
283#483—91no—
284#483—91no—
285#483—91no—
286#483—91no—
287#483—91no—
288#483—91no—
289#483—91no—
290C2×#106—31no—
291C2×#106—91no—
292C2×#103—91no—
293C2×#103—91no—
294C2×C22⋊C8—91no—
295C23×D3—31no—
296C23×D3—31no—
297C2×C3×Q8—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308D3×Q8—62no—
309D3×Q8—62no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—61no—
320C2×C4×D3—62no—
321C2×C4×D3—62no—
322C2×C4×D3—62no—
323C2×C4×D3—62no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3—124no—
333C2×C4×D3—124no—
334C2×C4×D3C22×D311yescharacteristic
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6—31no—
337C2×Dic6—31no—
338C2×Dic6—61no—
339C2×Dic6—62no—
340C2×Dic6—62no—
341C2×Dic6—61no—
342C2×Dic6—61no—
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—62no—
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—61no—
364#217—61no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—121no—
372C4⋊Dic3—21no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—121no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—62no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404D3×C8—22no—
405D3×C8—62no—
406C22×C32C22×D411yescharacteristic
407C2×C3⋊D3—21no—
408C2×C3⋊D3—21no—
409C2×C3⋊D3C2×SD1612yes—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3#12312yes—
413C2×C3×D3C2×SD1612yes—
414C2×C3×D3C2×SD1612yes—
415C2×C3×D3#13712yes—
416D32—28no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3⋊Dic3—21no—
422C3⋊Dic3—41no—
423C3⋊Dic3—41no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3#12312yes—
430C22×Q8—91no—
431C23×C4—91no—
432C23×C4—181no—
433C22×C8—31no—
434C22×C8—91no—
435C22⋊Q8—31no—
436C22⋊Q8—91no—
437C22⋊Q8—91no—
438C22⋊Q8—91no—
439C22⋊Q8—181no—
440C22⋊Q8—181no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—31no—
443C2×C4⋊C4—31no—
444C2×C4⋊C4—91no—
445C2×C4⋊C4—91no—
446C2×C4⋊C4—91no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—181no—
449C2×C4⋊C4—181no—
450C2×C4⋊C4—181no—
451C2×C4⋊C4—181no—
452C2×C22⋊C4—181no—
453#106—31no—
454#106—31no—
455#106—31no—
456#106—31no—
457#106—91no—
458#106—91no—
459#106—91no—
460#106D3211yescharacteristic, complemented
461#103—31no—
462#103—31no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469C22⋊C8—31no—
470C22⋊C8—91no—
471C22⋊C8—91no—
472C22⋊C8—91no—
473C23×C3—31no—
474C23×C3—31no—
475C22×D3—31no—
476C22×D3—31no—
477C22×D3—34no—
478C22×D3—34no—
479C22×D3—61no—
480C22×D3—62no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—62no—
484C22×D3D3×D411yescharacteristic
485C22×D3D3×D411yescharacteristic
486C3×Q8—61no—
487C3×Q8—61no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—31no—
494C2×C3×C4—32no—
495C2×C3×C4—32no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—122no—
506C2×C3×C4—122no—
507C2×C3×C4—122no—
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—61no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—122no—
526C2×Dic3—122no—
527C2×Dic3—122no—
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—42no—
533C4×D3—42no—
534C4×D3—42no—
535C4×D3—62no—
536C4×D3—62no—
537C4×D3—62no—
538C4×D3—61no—
539C4×D3—61no—
540C4×D3—61no—
541C4×D3—61no—
542C4×D3—62no—
543C4×D3—121no—
544C4×D3—121no—
545C4×D3—122no—
546C4×D3—122no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3—242no—
553C4×D3#23512yes—
554C4×D3#23912yes—
555Dic6—21no—
556Dic6—21no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562Dic6—121no—
563Dic6—122no—
564Dic6—122no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32C2×#12311yescharacteristic
576C2×C32C22×SD1611yescharacteristic
577C2×C32C2×#13711yescharacteristic
578C3⋊D3—22no—
579C3×D3—22no—
580C3×D3#48314yescomplemented
581C24—91no—
582C2×Q8—31no—
583C2×Q8—91no—
584C2×Q8—181no—
585C2×Q8—182no—
586C2×Q8—182no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—181no—
597C22×C4—182no—
598C22×C4—182no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—364no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—62no—
607C2×C8—91no—
608C2×C8—182no—
609C2×C8C2×D3211yescharacteristic
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—91no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4C2×D3211yescharacteristic
626C4⋊C4C2×D3211yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22×C3—21no—
632C22×C3—32no—
633C22×C3—32no—
634C22×C3—32no—
635C22×C3—32no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C2×D3×D411yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—32no—
643C2×D3—32no—
644C2×D3—62no—
645C2×D3—68no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—68no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3#89412yes—
654C2×D3D3×SD1612yes—
655C2×D3D3×SD1612yes—
656C2×D3#91512yes—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—32no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—61no—
665C3×C4—81no—
666C3×C4—81no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4C2×#23511yescharacteristic
672C3×C4C2×#23911yescharacteristic
673C3×C4D3×#4111yescharacteristic
674C3×C4D3×#4111yescharacteristic
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680Dic3—61no—
681Dic3—61no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—241no—
688Dic3—241no—
689Dic3#89412yes—
690C32C2×#48311yescharacteristic, complemented, Sylow
691C23—31no—
692C23—31no—
693C23—94no—
694C23—91no—
695C23—182no—
696C23—182no—
697Q8—61no—
698Q8—61no—
699Q8—181no—
700Q8—181no—
701Q8—362no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—31no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—91no—
715C2×C4—122no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—182no—
719C2×C4—182no—
720C2×C4—182no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—362no—
726C2×C4—362no—
727C2×C4—362no—
728C2×C4—362no—
729C2×C4—362no—
730C2×C4C22×D3211yescharacteristic
731C8—21no—
732C8—61no—
733C8—61no—
734C8—181no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—34no—
739C2×C3—62no—
740C2×C3C2×#89411yescharacteristic
741C2×C3D3×#12311yescharacteristic
742C2×C3C2×D3×SD1611yescharacteristic
743C2×C3C2×D3×SD1611yescharacteristic
744C2×C3C2×#91511yescharacteristic
745C2×C3D3×#13711yescharacteristic
746D3—22no—
747D3—62no—
748D3—62no—
749D3—122no—
750D3#486214yesdirect product factor
751C22—32no—
752C22—32no—
753C22—32no—
754C22—32no—
755C22—61no—
756C22—61no—
757C22—92no—
758C22—188no—
759C22—181no—
760C22—181no—
761C22D32×D411yescharacteristic
762C4—32no—
763C4—41no—
764C4—41no—
765C4—61no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—121no—
770C4—181no—
771C4—361no—
772C4—361no—
773C4D3×#23511yescharacteristic
774C4D3×#23911yescharacteristic
775C3—21no—
776C3C2×#486211yescharacteristic, complemented
777C3D3×#48311yescharacteristic, complemented
778C2—34no—
779C2—62no—
780C2—182no—
781C2D3×#89411yescharacteristic
782C2D32×SD1611yescharacteristic
783C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#106D32
hypocenterC32C2×#483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #10592561C2semidirect
4. C3×#4862C2semidirect
5. C3×D3×#106C2semidirect
7. #10590686C2semidirect
8. #10590674C2semidirect
9. D3×#816C2semidirect
10. D3×#810C2semidirect
11. D3×#808C2semidirect
12. #10590529C2semidirect
13. #10590443C2semidirect
14. #10590439C2semidirect
15. #10590426C2semidirect
41. C32×#106C22semidirect
43. #63643C22semidirect
44. #63637C22semidirect
45. #63635C22semidirect
47. C3×#817C22semidirect
48. C3×#816C22semidirect
49. C3×#810C22semidirect
50. C3×#808C22semidirect
51. C3×#808C22semidirect
52. C3×#808C22semidirect
53. #63574C22semidirect
54. #63573C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
83. #4862D3direct (N × H)
85. D3×#106D3semidirect
196. C3×#106C2×D3semidirect
197. C3×#106C2×D3semidirect
212. #817C2×D3semidirect
219. #816C2×D3semidirect
226. #810C2×D3semidirect
233. #808C2×D3semidirect
234. #808C2×D3semidirect
235. #808C2×D3semidirect
460. #106D32semidirect
580. C3×D3#483semidirect
690. C32C2×#483semidirect
750. D3#4862direct (N × H)
776. C3C2×#4862semidirect
777. C3D3×#483semidirect

Maximal subgroups

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

subgroupindex
D3×#8972
D32×C4⋊C42
#105925612
C3×#48622
C3×D3×#1062
D3×(C2×D3)⋊C82
#105906862
#105906742
D3×#8162
D3×#8102
D3×#8082
#105905292
#105904432
#105904392
#105904262
D3×#4833
C2×#48623