Finite Group Databasebeta

← D3×#4814 #11869526

Subgroups — D3×#4814 #11869526

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#946C211yesmaximal, characteristic
2D3×#892C211yesmaximal, characteristic
3#10592513C211yesmaximal, characteristic, complemented
4C3×#4814C211yesmaximal, characteristic, complemented
5C3×D3×#103C211yesmaximal, characteristic, complemented
6#10591561C211yesmaximal, characteristic, complemented
7#10591558C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9D3×(C2×D3)⋊C8C211yesmaximal, characteristic
10#10590715C211yesmaximal, characteristic, complemented
11#10590710C211yesmaximal, characteristic, complemented
12D3×#818C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14#10590527C211yesmaximal, characteristic, complemented
15#10590519C211yesmaximal, characteristic, complemented
16D3×#485—31nomaximal
17C2×#4814—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C4×D32C2211yescharacteristic
20#64155C2211yescharacteristic
21#64101C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26D3×(C2×D3)⋊C4—21no—
27D3×(C2×D3)⋊C4—21no—
28D3×C4⋊Dic3C2211yescharacteristic
29D3×C4⋊Dic3C2211yescharacteristic
30#63888—21no—
31#63887—21no—
32#63878—21no—
33D3×Dic3⋊C4—21no—
34C4×D3×Dic3—21no—
35#63871C2211yescharacteristic
36#63856C2211yescharacteristic
37#63849C2211yescharacteristic
38#63841C2211yescharacteristic
39#63836—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#103C2211yescharacteristic, complemented
42#63662C2211yescharacteristic, complemented
43#63647C2211yescharacteristic
44#63645C2211yescharacteristic, complemented
45#63635C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C2×#946—31no—
62D3×C22⋊Q8—31no—
63D3×#117—31no—
64C2×#892—31no—
65C3×#485—31no—
66C2×C3×#103—31no—
67C2×#835—31no—
68C2×(C2×D3)⋊C8—31no—
69C2×#818—31no—
70#5045—31no—
71#4996—31no—
72C2×#808—31no—
73#4888—31no—
74D3×#107—31no—
75#4868—31no—
76D3×#106—31no—
77#4815—31no—
78#4814—31no—
79#4814—31no—
80#4814—31no—
81#4814—31no—
82#4814—31no—
83#4814—31no—
84#4814—31no—
85#4814—31no—
86#4814—61no—
87#4814D311yescharacteristic, direct product factor
88D3×#103—31no—
89D3×#103D311yescharacteristic, complemented
90D3×C22⋊C8—31no—
91#4723—31no—
92C22×D32D411yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—22no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#624D411yescharacteristic
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3D411yescharacteristic
107C2×D3×Dic3D411yescharacteristic
108C4×D32—22no—
109C4×D32—22no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—22no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140D3×C3⋊C8—22no—
141C2×#485—91noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C2×D311yescharacteristic
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C3×C8—31no—
147C3×C22⋊Q8—31no—
148C3×#117—31no—
149C2×C3×C4⋊C4—31no—
150#946—31no—
151#946—31no—
152#946—31no—
153#946—31no—
154#946—61no—
155#946—61no—
156#946—61no—
157#946C2×D311yescharacteristic
158C2×(C2×D3)⋊C4—61no—
159C2×(C2×D3)⋊C4—61no—
160#926—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163#924—31no—
164C2×Dic3⋊C4—61no—
165C2×C4×Dic3—61no—
166C22×C3⋊C8—31no—
167C2×D3×C8—31no—
168C2×D3×C8C2×D311yescharacteristic
169#897—31no—
170#896—61no—
171#892—31no—
172#892—31no—
173#892—31no—
174#892—31no—
175#892—31no—
176#892—61no—
177#892—61no—
178#892—61no—
179#892C2×D311yescharacteristic
180D3×C4⋊C4—31no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—61no—
183D3×C4⋊C4C2×D311yescharacteristic
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186#878—61no—
187#877—61no—
188#872—61no—
189C42×D3—61no—
190C3×#107—31no—
191C3×#106—31no—
192C3×#103—21no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#103C2×D311yescharacteristic, complemented
198C3×#103C2×D311yescharacteristic, complemented
199C3×C22⋊C8—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#835—61no—
205#835C2×D311yescharacteristic, complemented
206#835C2×D311yescharacteristic, complemented
207#830—31no—
208(C2×D3)⋊C8—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—61no—
214(C2×D3)⋊C8C2×D311yescharacteristic
215#818—31no—
216#818—31no—
217#818—31no—
218#818—31no—
219#818—61no—
220#818C2×D311yescharacteristic, complemented
221#817—31no—
222#816—31no—
223#816C2×D311yescharacteristic, complemented
224#810—31no—
225#810C2×D311yescharacteristic, complemented
226#808—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808—61no—
232#808C2×D311yescharacteristic, complemented
233#807—31no—
234#807—31no—
235C22×C3⋊D3C2×D411yescharacteristic
236C22×C3×D3C2×D411yescharacteristic
237C22×C3×D3C2×D411yescharacteristic
238C2×D32—22no—
239C2×D32—22no—
240C2×D32—22no—
241C32×Q8—21no—
242C32×Q8—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C4×C3⋊D3—21no—
250C4×C3⋊D3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—42no—
260C3×C4×D3—42no—
261C3×C4×D3#4112yes—
262C3×C4×D3#4112yes—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—42no—
266#624—22no—
267D3×Dic3—22no—
268D3×Dic3—22no—
269D3×Dic3—42no—
270D3×Dic3—42no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C2×C22⋊Q8—91no—
276C2×#117—91no—
277#485—31no—
278#485—91no—
279#485—91no—
280#485—91no—
281#485—91no—
282#485—91no—
283#485—91no—
284#485—91no—
285C2×#107—91no—
286C2×#106—91no—
287C2×#103—31no—
288C2×#103—91no—
289C2×C22⋊C8—91no—
290C23×D3—31no—
291C23×D3—31no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—62no—
296C2×C3×Q8—62no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307D3×Q8—22no—
308D3×Q8—22no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—31no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—31no—
317C2×C4×D3—61no—
318C2×C4×D3—62no—
319C2×C4×D3—62no—
320C2×C4×D3—62no—
321C2×C4×D3—62no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3C22×D311yescharacteristic
325C2×C4×D3C22×D311yescharacteristic
326C2×Dic6—21no—
327C2×Dic6C22×D311yescharacteristic
328C2×C3×C8—21no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C2×C3×C8—62no—
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C42—61no—
345#217—61no—
346#217—61no—
347(C2×D3)⋊C4—21no—
348(C2×D3)⋊C4—21no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—121no—
360(C2×D3)⋊C4—121no—
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372C4⋊Dic3C22×D311yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—121no—
383C4×Dic3—21no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—121no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8—62no—
395C2×C3⋊C8C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397D3×C8—22no—
398D3×C8—62no—
399C22×C32C22×D411yescharacteristic
400C2×C3⋊D3—21no—
401C2×C3⋊D3—21no—
402C2×C3⋊D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3#12312yes—
407C2×C3×D3#13512yes—
408C2×C3×D3#13712yes—
409D32—44no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3⋊Dic3—21no—
415C3⋊Dic3—41no—
416C3⋊Dic3—41no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C3×Dic3#12312yes—
423C22×Q8—31no—
424C23×C4—91no—
425C22×C8—31no—
426C22×C8—91no—
427C22⋊Q8—31no—
428C22⋊Q8—91no—
429C22⋊Q8—91no—
430C22⋊Q8—91no—
431C22⋊Q8—181no—
432C22⋊Q8—181no—
433#117—31no—
434#117—91no—
435#117—91no—
436#117—91no—
437#117—181no—
438#117—181no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4—91no—
441C2×C4⋊C4—91no—
442C2×C4⋊C4—181no—
443C2×C22⋊C4—181no—
444C2×C22⋊C4—181no—
445C2×C42—181no—
446#107—31no—
447#107—91no—
448#107—91no—
449#107—91no—
450#106—31no—
451#106—91no—
452#106—91no—
453#106—91no—
454#103—31no—
455#103—31no—
456#103—31no—
457#103—31no—
458#103—91no—
459#103—91no—
460#103—91no—
461#103D3211yescharacteristic, complemented
462C22⋊C8—31no—
463C22⋊C8—91no—
464C22⋊C8—91no—
465C22⋊C8—91no—
466C23×C3—31no—
467C23×C3—31no—
468C22×D3—31no—
469C22×D3—31no—
470C22×D3—61no—
471C22×D3—62no—
472C22×D3—62no—
473C22×D3—62no—
474C22×D3—62no—
475C22×D3—62no—
476C22×D3—62no—
477C22×D3D3×D411yescharacteristic
478C22×D3D3×D411yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—122no—
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×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—61no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—122no—
525C2×Dic3—122no—
526C2×Dic3D3×D411yescharacteristic
527C2×Dic3D3×D411yescharacteristic
528C4×D3—21no—
529C4×D3—21no—
530C4×D3—42no—
531C4×D3—42no—
532C4×D3—62no—
533C4×D3—62no—
534C4×D3—62no—
535C4×D3—61no—
536C4×D3—61no—
537C4×D3—61no—
538C4×D3—61no—
539C4×D3—62no—
540C4×D3—121no—
541C4×D3—121no—
542C4×D3—122no—
543C4×D3—122no—
544C4×D3#23512yes—
545C4×D3#23712yes—
546Dic6—21no—
547Dic6—21no—
548Dic6—42no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—41no—
552C3×C8—61no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—121no—
559C2×C32C2×#12311yescharacteristic
560C2×C32C2×#13511yescharacteristic
561C2×C32C2×#13711yescharacteristic
562C3⋊D3—41no—
563C3×D3—41no—
564C3×D3#48514yescomplemented
565C24—91no—
566C2×Q8—31no—
567C2×Q8—61no—
568C2×Q8—62no—
569C2×Q8—62no—
570C2×Q8C2×D3211yescharacteristic
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—91no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—91no—
579C22×C4—182no—
580C22×C4—182no—
581C22×C4—181no—
582C22×C4—181no—
583C2×C8—31no—
584C2×C8—31no—
585C2×C8—62no—
586C2×C8—91no—
587C2×C8—182no—
588C2×C8C2×D3211yescharacteristic
589C4⋊C4—31no—
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—91no—
595C4⋊C4—91no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4C2×D3211yescharacteristic
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—181no—
605C22⋊C4—181no—
606C22⋊C4—181no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—61no—
611C42—181no—
612C42—181no—
613C42—181no—
614C22×C3—21no—
615C22×C3—32no—
616C22×C3—32no—
617C22×C3—32no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C2×D3×D411yescharacteristic
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—121no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—124no—
636C2×D3—124no—
637C2×D3#88312yes—
638C2×D3#91512yes—
639C2×D3#91912yes—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—32no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—61no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4C2×#23511yescharacteristic
655C3×C4C2×#23711yescharacteristic
656C3×C4D3×#4111yescharacteristic
657C3×C4D3×#4111yescharacteristic
658Dic3—21no—
659Dic3—41no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—61no—
664Dic3—61no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—241no—
671Dic3—241no—
672Dic3#88312yes—
673C32C2×#48511yescharacteristic, complemented, Sylow
674C23—31no—
675C23—31no—
676C23—91no—
677C23—182no—
678C23—182no—
679C23—182no—
680Q8—21no—
681Q8—21no—
682Q8—61no—
683Q8—61no—
684Q8—122no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—31no—
688C2×C4—32no—
689C2×C4—32no—
690C2×C4—31no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—91no—
698C2×C4—122no—
699C2×C4—122no—
700C2×C4—182no—
701C2×C4—182no—
702C2×C4—182no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—362no—
708C2×C4—362no—
709C2×C4C22×D3211yescharacteristic
710C8—21no—
711C8—61no—
712C8—61no—
713C8—181no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—34no—
718C2×C3—121no—
719C2×C3C2×#88311yescharacteristic
720C2×C3D3×#12311yescharacteristic
721C2×C3C2×#91511yescharacteristic
722C2×C3C2×#91911yescharacteristic
723C2×C3D3×#13511yescharacteristic
724C2×C3D3×#13711yescharacteristic
725D3—41no—
726D3—121no—
727D3—121no—
728D3—241no—
729D3#481414yesdirect product factor
730C22—32no—
731C22—32no—
732C22—32no—
733C22—61no—
734C22—61no—
735C22—61no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—364no—
740C22D32×D411yescharacteristic
741C4—32no—
742C4—41no—
743C4—41no—
744C4—61no—
745C4—121no—
746C4—121no—
747C4—121no—
748C4—121no—
749C4—181no—
750C4—361no—
751C4—361no—
752C4D3×#23511yescharacteristic
753C4D3×#23711yescharacteristic
754C3—21no—
755C3C2×#481411yescharacteristic, complemented
756C3D3×#48511yescharacteristic, complemented
757C2—34no—
758C2—121no—
759C2—361no—
760C2D3×#88311yescharacteristic
761C2D3×#91511yescharacteristic
762C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#103D32
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
3. #10592513C2semidirect
4. C3×#4814C2semidirect
5. C3×D3×#103C2semidirect
6. #10591561C2semidirect
7. #10591558C2semidirect
8. D3×#835C2semidirect
10. #10590715C2semidirect
11. #10590710C2semidirect
12. D3×#818C2semidirect
13. D3×#808C2semidirect
14. #10590527C2semidirect
15. #10590519C2semidirect
41. C32×#103C22semidirect
42. #63662C22semidirect
44. #63645C22semidirect
45. #63635C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
49. C3×#818C22semidirect
50. C3×#816C22semidirect
51. C3×#810C22semidirect
52. C3×#808C22semidirect
53. #63575C22semidirect
54. #63575C22semidirect
55. #63574C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
87. #4814D3direct (N × H)
89. D3×#103D3semidirect
197. C3×#103C2×D3semidirect
198. C3×#103C2×D3semidirect
205. #835C2×D3semidirect
206. #835C2×D3semidirect
220. #818C2×D3semidirect
223. #816C2×D3semidirect
225. #810C2×D3semidirect
232. #808C2×D3semidirect
461. #103D32semidirect
564. C3×D3#485semidirect
673. C32C2×#485semidirect
729. D3#4814direct (N × H)
755. C3C2×#4814semidirect
756. C3D3×#485semidirect

Maximal subgroups

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

subgroupindex
D3×#9462
D3×#8922
#105925132
C3×#48142
C3×D3×#1032
#105915612
#105915582
D3×#8352
D3×(C2×D3)⋊C82
#105907152
#105907102
D3×#8182
D3×#8082
#105905272
#105905192
D3×#4853
C2×#48143