Finite Group Databasebeta

← D3×#4891 #11868372

Subgroups — D3×#4891 #11868372

Order 1152.

947 conjugacy classes of subgroups.

The subgroup lattice has 751 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#893C211yesmaximal, characteristic
2D3×#890C211yesmaximal, characteristic, complemented
3#10592590C211yesmaximal, characteristic, complemented
4C3×#4891C211yesmaximal, characteristic, complemented
5C3×D3×#107C211yesmaximal, characteristic, complemented
6D3×#821C211yesmaximal, characteristic
7#10590780C211yesmaximal, characteristic, complemented
8#10590774C211yesmaximal, characteristic, complemented
9D3×Dic3⋊C8C211yesmaximal, characteristic, complemented
10D3×#809C211yesmaximal, characteristic
11D3×#808C211yesmaximal, characteristic, complemented
12#10590542C211yesmaximal, characteristic, complemented
13#10590473C211yesmaximal, characteristic, complemented
14#10590468C211yesmaximal, characteristic, complemented
15#10590435C211yesmaximal, characteristic, complemented
16D3×#478—31nomaximal
17C2×#4891—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×C4×D32—21no—
20#64102C2211yescharacteristic
21#64099C2211yescharacteristic, complemented
22C2×C3×D3×C8C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×D3×C4⋊C4C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#890C2211yescharacteristic, complemented
27D3×(C2×D3)⋊C4—21no—
28#63904—21no—
29#63898C2211yescharacteristic
30#63894C2211yescharacteristic
31D3×C4⋊Dic3—21no—
32D3×C4⋊Dic3C2211yescharacteristic
33#63881—21no—
34D3×Dic3⋊C4—21no—
35C4×D3×Dic3C2211yescharacteristic
36#63872C2211yescharacteristic, complemented
37#63869C2211yescharacteristic, complemented
38#63846—21no—
39#63845—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#107C2211yescharacteristic, complemented
42#63648C2211yescharacteristic
43#63641C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63635C2211yescharacteristic, complemented
46C3×#821C2211yescharacteristic
47C3×#818C2211yescharacteristic, complemented
48C3×Dic3⋊C8C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63574C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63572C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61D3×#125—31no—
62C4×D3×D4—31no—
63C2×#893—31no—
64C2×#890—31no—
65C3×#478—31no—
66C2×C3×#107—31no—
67C2×#821—31no—
68C2×Dic3⋊C8—31no—
69#5066—31no—
70#5009—31no—
71C2×#809—31no—
72C2×#808—31no—
73#4891—31no—
74#4891—31no—
75#4891—31no—
76#4891—31no—
77#4891—31no—
78#4891—31no—
79#4891—31no—
80#4891—31no—
81#4891—61no—
82#4891D311yescharacteristic, direct product factor
83D3×#107D311yescharacteristic, complemented
84#4871—31no—
85D3×#106—31no—
86#4847—31no—
87D3×C4⋊C8—31no—
88D3×#102—31no—
89D3×#102—31no—
90#4766—31no—
91#4763—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×D12C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×#626—21no—
101C2×#624—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3D411yescharacteristic
105C2×D3×Dic3D411yescharacteristic
106D3×D12—22no—
107D3×D12Q814yes—
108C4×D32—44no—
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3752—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—22no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32D411yescharacteristic
138Dic32D411yescharacteristic
139D3×C3⋊C8—22no—
140C2×#478—91noSylow
141C2×D3×D4—31no—
142C22×D12—31no—
143C22×C4×D3—61no—
144C22×C4×D3—61no—
145C22×C3×C8—31no—
146C3×#125—31no—
147C3×C4×D4—31no—
148C2×C3×C4⋊C4—31no—
149C2×C3×C4⋊C4—31no—
150D4×Dic3—31no—
151C4×#67—61no—
152C2×(C2×D3)⋊C4—61no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—61no—
155C2×Dic3⋊C4—61no—
156C2×C4×Dic3—31no—
157C22×C3⋊C8—31no—
158C2×D3×C8—31no—
159C2×D3×C8C2×D311yescharacteristic
160#893—31no—
161#893—31no—
162#893—31no—
163#893—31no—
164#893—61no—
165#893—61no—
166#893—61no—
167#893C2×D311yescharacteristic
168D3×C4⋊C4—31no—
169D3×C4⋊C4—61no—
170D3×C4⋊C4—61no—
171D3×C4⋊C4C2×D311yescharacteristic
172D3×C4⋊C4C2×D311yescharacteristic
173#890—31no—
174#890—31no—
175#890—31no—
176#890—31no—
177#890—31no—
178#890—61no—
179#890—61no—
180#890—61no—
181#890C2×D311yescharacteristic, complemented
182#889—61no—
183#889—61no—
184#67⋊C4—61no—
185D3×C22⋊C4—61no—
186C4×D12—31no—
187C42×D3—31no—
188#870—31no—
189C3×#107—21no—
190C3×#107—31no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#107C2×D311yescharacteristic, complemented
194C3×#107C2×D311yescharacteristic, complemented
195C3×#106—31no—
196C3×C4⋊C8—31no—
197C3×#102—31no—
198C3×#102—31no—
199#832—31no—
200#832—31no—
201#821—31no—
202#821—31no—
203#821—31no—
204#821—31no—
205#821—31no—
206#821—61no—
207#821C2×D311yescharacteristic
208#818C2×D311yescharacteristic, complemented
209#817—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—61no—
216Dic3⋊C8C2×D311yescharacteristic, complemented
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—61no—
223#809C2×D311yescharacteristic
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—61no—
230#808C2×D311yescharacteristic, complemented
231#807C2×D311yescharacteristic, complemented
232#807C2×D311yescharacteristic, complemented
233C4⋊(C3⋊C8)—31no—
234C22×C3⋊D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3C2×D411yescharacteristic
237C2×D32—24no—
238C2×D32—42no—
239C2×D32—42no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2411yescharacteristic
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3C2×D411yescharacteristic
245C2×C3⋊Dic3C2×D411yescharacteristic
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)C2×Q812yes—
248C4×C3⋊D3—42no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—21no—
256C3×D12C2×Q812yes—
257C3×C4×D3—42no—
258C3×C4×D3—42no—
259C3×C4×D3—42no—
260C3×C4×D3C2×Q812yes—
261C3×C4×D3#4112yes—
262#626—24no—
263#624—42no—
264D3×Dic3—22no—
265D3×Dic3—22no—
266D3×Dic3—42no—
267D3×Dic3—42no—
268C32×C8—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C2×#125—91no—
273C2×C4×D4—91no—
274#478—31no—
275#478—91no—
276#478—91no—
277#478—91no—
278#478—91no—
279#478—91no—
280#478—91no—
281#478—91no—
282C2×#107—31no—
283C2×#106—91no—
284C2×C4⋊C8—91no—
285C2×#102—91no—
286C2×#102—91no—
287C23×D3—61no—
288C23×D3—61no—
289C2×C3×D4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—61no—
292C22×C3×C4—61no—
293C22×C3×C4—61no—
294C2×#67—61no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299D3×D4—34no—
300D3×D4—62no—
301C2×D12—31no—
302C2×D12—31no—
303C2×D12—34no—
304C2×D12—61no—
305C2×D12—62no—
306C2×D12—61no—
307C2×D12C22×D311yescharacteristic
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—31no—
312C2×C4×D3—31no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—121no—
320C2×C4×D3—124no—
321C2×C4×D3—124no—
322C2×C4×D3C22×D311yescharacteristic
323C2×C3×C8—21no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C2×C3×C8—62no—
327C2×C3×C8C22×D311yescharacteristic
328C2×C3×C8C22×D311yescharacteristic
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C22⋊C4—61no—
343C3×C42—31no—
344#217—61no—
345(C2×D3)⋊C4—21no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—121no—
352C4⋊Dic3—21no—
353C4⋊Dic3—31no—
354C4⋊Dic3—31no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3—121no—
363C4⋊Dic3C22×D311yescharacteristic
364C4⋊Dic3C22×D311yescharacteristic
365C4⋊Dic3C22×D311yescharacteristic
366Dic3⋊C4—21no—
367Dic3⋊C4—21no—
368Dic3⋊C4—21no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—121no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—31no—
381C4×Dic3—31no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—61no—
385C4×Dic3C22×D311yescharacteristic
386C2×C3⋊C8—31no—
387C2×C3⋊C8—31no—
388C2×C3⋊C8—61no—
389C2×C3⋊C8—62no—
390C2×C3⋊C8C22×D311yescharacteristic
391C2×C3⋊C8C22×D311yescharacteristic
392D3×C8—22no—
393D3×C8—62no—
394C22×C32C22×D411yescharacteristic
395C2×C3⋊D3—22no—
396C2×C3⋊D3—41no—
397C2×C3⋊D3—41no—
398C2×C3×D3—22no—
399C2×C3×D3—41no—
400C2×C3×D3—41no—
401C2×C3×D3C22⋊Q812yes—
402C2×C3×D3#13512yes—
403C2×C3×D3AGL(1,ℤ/8)12yes—
404D32—48no—
405C32×C4—41no—
406C32×C4—41no—
407C32×C4C22×Q811yescharacteristic
408C32×C4C2×#4111yescharacteristic
409C3⋊Dic3—21no—
410C3⋊Dic3—21no—
411C3⋊Dic3—41no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C3×Dic3—41no—
417C3×Dic3C22⋊Q812yes—
418C22×D4—91no—
419C23×C4—181no—
420C22×C8—31no—
421C22×C8—91no—
422#125—31no—
423#125—91no—
424#125—91no—
425#125—91no—
426#125—181no—
427#125—181no—
428C4×D4—31no—
429C4×D4—91no—
430C4×D4—91no—
431C4×D4—91no—
432C4×D4—181no—
433C4×D4—181no—
434C2×C4⋊C4—31no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—91no—
437C2×C4⋊C4—181no—
438C2×C4⋊C4—181no—
439C2×C22⋊C4—181no—
440C2×C42—91no—
441#107—31no—
442#107—31no—
443#107—31no—
444#107D3211yescharacteristic, complemented
445#106—31no—
446#106—91no—
447#106—91no—
448#106—91no—
449C4⋊C8—31no—
450C4⋊C8—91no—
451C4⋊C8—91no—
452C4⋊C8—91no—
453#102—31no—
454#102—31no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459#102—91no—
460#102—91no—
461C23×C3—31no—
462C23×C3—61no—
463C22×D3—21no—
464C22×D3—64no—
465C22×D3—61no—
466C22×D3—61no—
467C22×D3—64no—
468C22×D3—121no—
469C22×D3—122no—
470C22×D3—122no—
471C22×D3—122no—
472C22×D3—122no—
473C22×D3D3×D411yescharacteristic
474C3×D4—32no—
475C3×D4—61no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—31no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—122no—
492C2×C3×C4—122no—
493C2×C3×C4—122no—
494C2×C3×C4C23×D311yescharacteristic
495C2×C3×C4C23×D311yescharacteristic
496#67—64no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—31no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—62no—
507C2×Dic3—62no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—121no—
511C2×Dic3—122no—
512C2×Dic3—122no—
513C2×Dic3D3×D411yescharacteristic
514C2×Dic3D3×D411yescharacteristic
515C2×Dic3D3×D411yescharacteristic
516D12—21no—
517D12—32no—
518D12—32no—
519D12—62no—
520D12—64no—
521D12—61no—
522D12—61no—
523D12—121no—
524D12D3×Q812yes—
525C4×D3—42no—
526C4×D3—42no—
527C4×D3—42no—
528C4×D3—62no—
529C4×D3—62no—
530C4×D3—122no—
531C4×D3—122no—
532C4×D3—122no—
533C4×D3—122no—
534C4×D3—122no—
535C4×D3—122no—
536C4×D3—242no—
537C4×D3#23512yes—
538C4×D3D3×Q812yes—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—41no—
542C3×C8—61no—
543C3×C8—61no—
544C3⋊C8—21no—
545C3⋊C8—21no—
546C3⋊C8—61no—
547C3⋊C8—61no—
548C3⋊C8—121no—
549C2×C32C2×C22⋊Q811yescharacteristic
550C2×C32C2×#13511yescharacteristic
551C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
552C3⋊D3—42no—
553C3×D3—42no—
554C3×D3#47814yescomplemented
555C24—181no—
556C2×D4—31no—
557C2×D4—94no—
558C2×D4—91no—
559C2×D4—182no—
560C2×D4—181no—
561C22×C4—31no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—91no—
566C22×C4—91no—
567C22×C4—181no—
568C22×C4—181no—
569C22×C4—181no—
570C22×C4—181no—
571C22×C4—364no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8—62no—
575C2×C8—91no—
576C2×C8—182no—
577C2×C8C2×D3211yescharacteristic
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—91no—
586C4⋊C4—181no—
587C4⋊C4—181no—
588C4⋊C4—181no—
589C4⋊C4—181no—
590C4⋊C4—181no—
591C4⋊C4—181no—
592C4⋊C4—181no—
593C4⋊C4C2×D3211yescharacteristic
594C4⋊C4C2×D3211yescharacteristic
595C22⋊C4—61no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C22⋊C4—181no—
599C42—31no—
600C42—91no—
601C42—91no—
602C42—91no—
603C22×C3—21no—
604C22×C3—32no—
605C22×C3—32no—
606C22×C3—32no—
607C22×C3—62no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3C2×D3×D411yescharacteristic
611C22×C3C2×D3×D411yescharacteristic
612C2×D3—22no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3—62no—
616C2×D3—62no—
617C2×D3—122no—
618C2×D3—128no—
619C2×D3—121no—
620C2×D3—121no—
621C2×D3—121no—
622C2×D3—121no—
623C2×D3—128no—
624C2×D3—241no—
625C2×D3—241no—
626C2×D3#89612yes—
627C2×D3#91112yes—
628C2×D3#91912yes—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—32no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—81no—
639C3×C4—81no—
640C3×C4—121no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4C2×#23511yescharacteristic
644C3×C4C2×D3×Q811yescharacteristic
645C3×C4C2×D3×Q811yescharacteristic
646C3×C4D3×#4111yescharacteristic
647Dic3—21no—
648Dic3—21no—
649Dic3—41no—
650Dic3—41no—
651Dic3—41no—
652Dic3—61no—
653Dic3—61no—
654Dic3—61no—
655Dic3—61no—
656Dic3—121no—
657Dic3—121no—
658Dic3—121no—
659Dic3—121no—
660Dic3—241no—
661Dic3#89612yes—
662C32C2×#47811yescharacteristic, complemented, Sylow
663C23—31no—
664C23—61no—
665C23—184no—
666C23—181no—
667C23—362no—
668C23—362no—
669D4—32no—
670D4—61no—
671D4—92no—
672D4—184no—
673D4—181no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—31no—
677C2×C4—32no—
678C2×C4—32no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—122no—
687C2×C4—122no—
688C2×C4—122no—
689C2×C4—182no—
690C2×C4—182no—
691C2×C4—181no—
692C2×C4—362no—
693C2×C4—362no—
694C2×C4—362no—
695C2×C4—362no—
696C2×C4C22×D3211yescharacteristic
697C8—21no—
698C8—61no—
699C8—61no—
700C8—181no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—34no—
705C2×C3—122no—
706C2×C3C2×#89611yescharacteristic
707C2×C3D3×C22⋊Q811yescharacteristic
708C2×C3C2×#91111yescharacteristic
709C2×C3C2×#91911yescharacteristic
710C2×C3D3×#13511yescharacteristic
711C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
712D3—42no—
713D3—122no—
714D3—122no—
715D3—242no—
716D3#489114yesdirect product factor
717C22—32no—
718C22—32no—
719C22—32no—
720C22—62no—
721C22—121no—
722C22—121no—
723C22—182no—
724C22—368no—
725C22—361no—
726C22—361no—
727C22D32×D411yescharacteristic
728C4—32no—
729C4—41no—
730C4—41no—
731C4—61no—
732C4—61no—
733C4—121no—
734C4—121no—
735C4—121no—
736C4—181no—
737C4—181no—
738C4—361no—
739C4D3×#23511yescharacteristic
740C4D32×Q811yescharacteristic
741C3—21no—
742C3C2×#489111yescharacteristic, complemented
743C3D3×#47811yescharacteristic, complemented
744C2—34no—
745C2—122no—
746C2—362no—
747C2D3×#89611yescharacteristic
748C2D3×#91111yescharacteristic
749C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenter#107D32
hypocenterC32C2×#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. D3×#890C2semidirect
3. #10592590C2semidirect
4. C3×#4891C2semidirect
5. C3×D3×#107C2semidirect
7. #10590780C2semidirect
8. #10590774C2semidirect
9. D3×Dic3⋊C8C2semidirect
11. D3×#808C2semidirect
12. #10590542C2semidirect
13. #10590473C2semidirect
14. #10590468C2semidirect
15. #10590435C2semidirect
21. #64099C22semidirect
26. C3×#890C22semidirect
36. #63872C22semidirect
37. #63869C22semidirect
41. C32×#107C22semidirect
43. #63641C22semidirect
45. #63635C22semidirect
47. C3×#818C22semidirect
48. C3×Dic3⋊C8C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×#807C22semidirect
53. #63574C22semidirect
54. #63573C22semidirect
55. #63572C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
82. #4891D3direct (N × H)
83. D3×#107D3semidirect
181. #890C2×D3semidirect
193. C3×#107C2×D3semidirect
194. C3×#107C2×D3semidirect
208. #818C2×D3semidirect
216. Dic3⋊C8C2×D3semidirect
230. #808C2×D3semidirect
231. #807C2×D3semidirect
232. #807C2×D3semidirect
444. #107D32semidirect
554. C3×D3#478semidirect
662. C32C2×#478semidirect
716. D3#4891direct (N × H)
742. C3C2×#4891semidirect
743. C3D3×#478semidirect

Maximal subgroups

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

subgroupindex
D3×#8932
D3×#8902
#105925902
C3×#48912
C3×D3×#1072
D3×#8212
#105907802
#105907742
D3×Dic3⋊C82
D3×#8092
D3×#8082
#105905422
#105904732
#105904682
#105904352
D3×#4783
C2×#48913