Finite Group Databasebeta

← D3×#4800 #11873439

Subgroups — D3×#4800 #11873439

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#947C211yesmaximal, characteristic
2D3×#890C211yesmaximal, characteristic, complemented
3#10592499C211yesmaximal, characteristic, complemented
4C3×D3×#103C211yesmaximal, characteristic, complemented
5C3×#4800C211yesmaximal, characteristic, complemented
6#10591614C211yesmaximal, characteristic, complemented
7D3×#835C211yesmaximal, characteristic, complemented
8#10591539C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic
10#10590872C211yesmaximal, characteristic, complemented
11#10590868C211yesmaximal, characteristic, complemented
12D3×C8×Dic3C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic
14#10590539C211yesmaximal, characteristic, complemented
15#10590537C211yesmaximal, characteristic, complemented
16D3×#488—31nomaximal
17C2×#4800—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20#64156C2211yescharacteristic
21#64099C2211yescharacteristic, complemented
22C3×#947C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C3×D3×C4⋊C4C2211yescharacteristic
25C3×#890C2211yescharacteristic, complemented
26D3×(C2×D3)⋊C4—21no—
27D3×(C2×D3)⋊C4—21no—
28#63907—21no—
29#63907—21no—
30D3×C4⋊Dic3—21no—
31D3×C4⋊Dic3C2211yescharacteristic
32D3×Dic3⋊C4—21no—
33C4×D3×Dic3C2211yescharacteristic
34#63872C2211yescharacteristic, complemented
35#63869C2211yescharacteristic, complemented
36#63864C2211yescharacteristic
37#63863C2211yescharacteristic
38#63846—21no—
39#63845—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#103C2211yescharacteristic, complemented
42#63662C2211yescharacteristic, complemented
43#63648C2211yescharacteristic
44C8×C3⋊Dic3C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53#63566C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63553C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C2×#947—31no—
62D3×#125—31no—
63D3×#124—31no—
64C2×#890—31no—
65C3×#488—31no—
66C2×C3×#103—31no—
67C2×#835—31no—
68C2×#821—31no—
69C2×C8×Dic3—31no—
70#5068—31no—
71#5056—31no—
72C2×#809—31no—
73D3×#103—31no—
74D3×#103D311yescharacteristic, complemented
75#4800—31no—
76#4800—31no—
77#4800—31no—
78#4800—31no—
79#4800—31no—
80#4800—31no—
81#4800—31no—
82#4800—31no—
83#4800—31no—
84#4800—61no—
85#4800D311yescharacteristic, direct product factor
86D3×#102—31no—
87D3×#102—31no—
88#4768—31no—
89#4768—31no—
90#4697—31no—
91C4×D3×C8—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—22no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3D411yescharacteristic
106C2×D3×Dic3D411yescharacteristic
107D3×D12—22no—
108D3×D12—22no—
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111#3752—21no—
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×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×D3×C8—22no—
129#3724—21no—
130Dic3⋊Dic3—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—
138Dic32D411yescharacteristic
139Dic32D411yescharacteristic
140D3×C3⋊C8—22no—
141C2×#488—91noSylow
142C22×C3×Q8—31no—
143C2×D3×Q8C2×D311yescharacteristic
144C2×D3×D4—31no—
145C22×D12—31no—
146C22×C3×C8—31no—
147C3×#125—31no—
148C3×#124—31no—
149C2×C3×C4⋊C4—31no—
150#947—31no—
151#947—31no—
152#947—31no—
153#947—31no—
154#947—61no—
155#947—61no—
156#947—61no—
157#947C2×D311yescharacteristic
158#936—31no—
159C2×(C2×D3)⋊C4—61no—
160C2×(C2×D3)⋊C4—61no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—61no—
163C2×Dic3⋊C4—61no—
164C2×C4×Dic3—31no—
165C22×C3⋊C8—31no—
166C2×D3×C8—31no—
167C2×D3×C8C2×D311yescharacteristic
168D3×C4⋊C4—31no—
169D3×C4⋊C4—61no—
170D3×C4⋊C4—61no—
171D3×C4⋊C4C2×D311yescharacteristic
172#890—31no—
173#890—31no—
174#890—31no—
175#890—31no—
176#890—31no—
177#890—61no—
178#890—61no—
179#890—61no—
180#890C2×D311yescharacteristic, complemented
181#889—61no—
182#889—61no—
183#885—61no—
184#885—61no—
185D3×C22⋊C4—61no—
186D3×C22⋊C4—61no—
187#875—31no—
188C42×D3—31no—
189#870—31no—
190C3×#103—21no—
191C3×#103—31no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103C2×D311yescharacteristic, complemented
196C3×#103C2×D311yescharacteristic, complemented
197C3×#102—31no—
198C3×#102—31no—
199C3×C4×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#832—31no—
208#832—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—61no—
215#821C2×D311yescharacteristic
216#816—31no—
217#816C2×D311yescharacteristic, complemented
218C8×Dic3—31no—
219C8×Dic3—31no—
220C8×Dic3—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—61no—
224C8×Dic3C2×D311yescharacteristic, complemented
225#810—31no—
226#810C2×D311yescharacteristic, complemented
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#809C2×D311yescharacteristic
234C4×C3⋊C8—31no—
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C2×D32—42no—
239C2×D32—42no—
240C2×D32—42no—
241C32×Q8—21no—
242C32×Q8—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
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×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—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#626—42no—
267D3×Dic3—22no—
268D3×Dic3—22no—
269D3×Dic3—42no—
270C32×C8—21no—
271C3⋊(C3⋊C8)—21no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C2×#125—91no—
275C2×#124—91no—
276#488—31no—
277#488—91no—
278#488—91no—
279#488—91no—
280#488—91no—
281#488—91no—
282#488—91no—
283#488—91no—
284C2×#103—31no—
285C2×#103—91no—
286C2×#102—91no—
287C2×#102—91no—
288C2×C4×C8—91no—
289C23×D3—61no—
290C23×D3—61no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×Q8—62no—
295C2×C3×Q8—62no—
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×D4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C2×#67—61no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—61no—
306D3×Q8—22no—
307D3×Q8—22no—
308D3×D4—62no—
309D3×D4—62no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—61no—
313C2×D12—62no—
314C2×D12—62no—
315C2×D12—61no—
316C2×D12C22×D311yescharacteristic
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—61no—
322C2×C4×D3C22×D311yescharacteristic
323C2×Dic6—21no—
324C2×Dic6C22×D311yescharacteristic
325C2×C3×C8—21no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C2×C3×C8—62no—
329C2×C3×C8C22×D311yescharacteristic
330C2×C3×C8C22×D311yescharacteristic
331C3×C4⋊C4—21no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C42—31no—
342#217—61no—
343#217—61no—
344(C2×D3)⋊C4—21no—
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—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—121no—
357(C2×D3)⋊C4—121no—
358C4⋊Dic3—21no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—121no—
369C4⋊Dic3C22×D311yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—121no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—61no—
389C4×Dic3C22×D311yescharacteristic
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—62no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396D3×C8—22no—
397D3×C8—62no—
398C22×C32C22×D411yescharacteristic
399C2×C3⋊D3—41no—
400C2×C3⋊D3—41no—
401C2×C3⋊D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3#12412yes—
406C2×C3×D3#13512yes—
407C2×C3×D3#13512yes—
408D32—84no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3⋊Dic3—21no—
414C3⋊Dic3—21no—
415C3⋊Dic3—41no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3#12412yes—
422C22×Q8—31no—
423C22×D4—91no—
424C22×C8—31no—
425C22×C8—91no—
426#125—31no—
427#125—91no—
428#125—91no—
429#125—91no—
430#125—181no—
431#125—181no—
432#124—31no—
433#124—91no—
434#124—91no—
435#124—91no—
436#124—181no—
437#124—181no—
438C2×C4⋊C4—31no—
439C2×C4⋊C4—91no—
440C2×C4⋊C4—181no—
441C2×C4⋊C4—181no—
442C2×C22⋊C4—181no—
443C2×C22⋊C4—181no—
444C2×C42—91no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103—91no—
450#103—91no—
451#103—91no—
452#103D3211yescharacteristic, complemented
453#102—31no—
454#102—31no—
455#102—91no—
456#102—91no—
457#102—91no—
458#102—91no—
459#102—91no—
460#102—91no—
461C4×C8—31no—
462C4×C8—91no—
463C4×C8—91no—
464C4×C8—91no—
465C23×C3—31no—
466C23×C3—61no—
467C22×D3—21no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—121no—
471C22×D3—122no—
472C22×D3—122no—
473C22×D3—122no—
474C22×D3—122no—
475C22×D3—122no—
476C22×D3—122no—
477C22×D3D3×D411yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—122no—
487C3×D4—61no—
488C3×D4—61no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—32no—
496C2×C3×C4—32no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—122no—
505C2×C3×C4—122no—
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508#67—122no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—122no—
524C2×Dic3D3×D411yescharacteristic
525C2×Dic3D3×D411yescharacteristic
526C2×Dic3D3×D411yescharacteristic
527D12—21no—
528D12—21no—
529D12—61no—
530D12—61no—
531D12—61no—
532D12—61no—
533D12—121no—
534D12—121no—
535D12—122no—
536C4×D3—42no—
537C4×D3—42no—
538C4×D3—62no—
539C4×D3—62no—
540C4×D3—122no—
541C4×D3#23512yes—
542C4×D3#23712yes—
543Dic6—21no—
544Dic6—21no—
545Dic6—42no—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—41no—
549C3×C8—61no—
550C3×C8—61no—
551C3⋊C8—21no—
552C3⋊C8—21no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—121no—
556C2×C32C2×#12411yescharacteristic
557C2×C32C2×#13511yescharacteristic
558C2×C32C2×#13511yescharacteristic
559C3⋊D3—81no—
560C3×D3—81no—
561C3×D3#48814yescomplemented
562C24—181no—
563C2×Q8—31no—
564C2×Q8—61no—
565C2×Q8—62no—
566C2×Q8—62no—
567C2×Q8C2×D3211yescharacteristic
568C2×D4—31no—
569C2×D4—91no—
570C2×D4—182no—
571C2×D4—182no—
572C2×D4—181no—
573C22×C4—31no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—181no—
579C2×C8—31no—
580C2×C8—31no—
581C2×C8—62no—
582C2×C8—91no—
583C2×C8—182no—
584C2×C8C2×D3211yescharacteristic
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—91no—
591C4⋊C4—181no—
592C4⋊C4—181no—
593C4⋊C4—181no—
594C4⋊C4—181no—
595C4⋊C4—181no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4C2×D3211yescharacteristic
599C22⋊C4—61no—
600C22⋊C4—61no—
601C22⋊C4—181no—
602C22⋊C4—181no—
603C22⋊C4—181no—
604C22⋊C4—181no—
605C22⋊C4—181no—
606C22⋊C4—181no—
607C42—31no—
608C42—91no—
609C42—91no—
610C42—91no—
611C22×C3—21no—
612C22×C3—32no—
613C22×C3—32no—
614C22×C3—32no—
615C22×C3—121no—
616C22×C3—121no—
617C22×C3—121no—
618C22×C3C2×D3×D411yescharacteristic
619C22×C3C2×D3×D411yescharacteristic
620C2×D3—41no—
621C2×D3—41no—
622C2×D3—41no—
623C2×D3—121no—
624C2×D3—121no—
625C2×D3—121no—
626C2×D3—121no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—241no—
630C2×D3—241no—
631C2×D3—241no—
632C2×D3—244no—
633C2×D3—244no—
634C2×D3#88512yes—
635C2×D3#91612yes—
636C2×D3#91912yes—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—32no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—81no—
647C3×C4—81no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4C2×#23511yescharacteristic
652C3×C4C2×#23711yescharacteristic
653C3×C4D3×#4111yescharacteristic
654C3×C4D3×#4111yescharacteristic
655Dic3—21no—
656Dic3—21no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—61no—
661Dic3—61no—
662Dic3—61no—
663Dic3—61no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—241no—
669Dic3#88512yes—
670C32C2×#48811yescharacteristic, complemented, Sylow
671C23—31no—
672C23—61no—
673C23—181no—
674C23—362no—
675C23—362no—
676C23—362no—
677Q8—21no—
678Q8—21no—
679Q8—61no—
680Q8—61no—
681Q8—122no—
682D4—61no—
683D4—61no—
684D4—181no—
685D4—181no—
686D4—362no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—31no—
690C2×C4—32no—
691C2×C4—32no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—91no—
698C2×C4—91no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—182no—
702C2×C4—182no—
703C2×C4—181no—
704C2×C4—362no—
705C2×C4C22×D3211yescharacteristic
706C8—21no—
707C8—61no—
708C8—61no—
709C8—181no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—34no—
714C2×C3—241no—
715C2×C3C2×#88511yescharacteristic
716C2×C3D3×#12411yescharacteristic
717C2×C3C2×#91611yescharacteristic
718C2×C3C2×#91911yescharacteristic
719C2×C3D3×#13511yescharacteristic
720C2×C3D3×#13511yescharacteristic
721D3—81no—
722D3—241no—
723D3—241no—
724D3—481no—
725D3#480014yesdirect product factor
726C22—32no—
727C22—32no—
728C22—32no—
729C22—121no—
730C22—121no—
731C22—121no—
732C22—361no—
733C22—361no—
734C22—361no—
735C22—724no—
736C22D32×D411yescharacteristic
737C4—32no—
738C4—41no—
739C4—41no—
740C4—61no—
741C4—61no—
742C4—121no—
743C4—121no—
744C4—121no—
745C4—181no—
746C4—181no—
747C4—361no—
748C4D3×#23511yescharacteristic
749C4D3×#23711yescharacteristic
750C3—21no—
751C3C2×#480011yescharacteristic, complemented
752C3D3×#48811yescharacteristic, complemented
753C2—34no—
754C2—241no—
755C2—721no—
756C2D3×#88511yescharacteristic
757C2D3×#91611yescharacteristic
758C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenter#103D32
hypocenterC32C2×#488
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
2. D3×#890C2semidirect
3. #10592499C2semidirect
4. C3×D3×#103C2semidirect
5. C3×#4800C2semidirect
6. #10591614C2semidirect
7. D3×#835C2semidirect
8. #10591539C2semidirect
10. #10590872C2semidirect
11. #10590868C2semidirect
12. D3×C8×Dic3C2semidirect
14. #10590539C2semidirect
15. #10590537C2semidirect
21. #64099C22semidirect
25. C3×#890C22semidirect
34. #63872C22semidirect
35. #63869C22semidirect
41. C32×#103C22semidirect
42. #63662C22semidirect
44. C8×C3⋊Dic3C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
49. C3×#816C22semidirect
50. C3×C8×Dic3C22semidirect
51. C3×#810C22semidirect
53. #63566C22semidirect
54. #63565C22semidirect
59. #63553C22semidirect
60. Dic3×C3⋊C8C22semidirect
74. D3×#103D3semidirect
85. #4800D3direct (N × H)
180. #890C2×D3semidirect
195. C3×#103C2×D3semidirect
196. C3×#103C2×D3semidirect
205. #835C2×D3semidirect
206. #835C2×D3semidirect
217. #816C2×D3semidirect
224. C8×Dic3C2×D3semidirect
226. #810C2×D3semidirect
452. #103D32semidirect
561. C3×D3#488semidirect
670. C32C2×#488semidirect
725. D3#4800direct (N × H)
751. C3C2×#4800semidirect
752. C3D3×#488semidirect

Maximal subgroups

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

subgroupindex
D3×#9472
D3×#8902
#105924992
C3×D3×#1032
C3×#48002
#105916142
D3×#8352
#105915392
D3×#8212
#105908722
#105908682
D3×C8×Dic32
D3×#8092
#105905392
#105905372
D3×#4883
C2×#48003