Finite Group Databasebeta

← D3×#71515 #72222737

Subgroups — D3×#71515 #72222737

Order 2304.

1497 conjugacy classes of subgroups.

The subgroup lattice has 1273 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#509C211yesmaximal, characteristic
2D3×#5197C211yesmaximal, characteristic, complemented
3D3×#5152C211yesmaximal, characteristic, complemented
4#11797986C211yesmaximal, characteristic, complemented
5#11797985C211yesmaximal, characteristic, complemented
6#11797980C211yesmaximal, characteristic, complemented
7#11797979C211yesmaximal, characteristic, complemented
8#11797970C211yesmaximal, characteristic, complemented
9#11797969C211yesmaximal, characteristic, complemented
10C3×#71515C211yesmaximal, characteristic, complemented
11#11797956C211yesmaximal, characteristic, complemented
12D3×#4513C211yesmaximal, characteristic, complemented
13D3×#4563C211yesmaximal, characteristic, complemented
14D3×#4566C211yesmaximal, characteristic, complemented
15D3×#4512C211yesmaximal, characteristic, complemented
16C2×#71515—31nomaximal
17D3×AGL(1,ℤ/16)—31nomaximal
18C3×D3×#135C2211yescharacteristic
19C2×C3×D3×D8C2211yescharacteristic
20D3×#948—21no—
21D3×D4×Dic3—21no—
22C32×#509C2211yescharacteristic
23#10592896C2211yescharacteristic, complemented
24#10592851C2211yescharacteristic, complemented
25C3×#5197C2211yescharacteristic, complemented
26C3×#5193C2211yescharacteristic
27C3×#5152C2211yescharacteristic, complemented
28C3×#5147C2211yescharacteristic
29C3×#4914C412yescomplemented
30C3×D3×SD32C412yescomplemented
31C3×#4911C412yescomplemented
32C3×D3×D16C412yescomplemented
33C3×#4908C2211yescharacteristic
34C3×D3×M32C2211yescharacteristic
35#10591676—21no—
36#10591674—21no—
37D3×#837—21no—
38#10591436—21no—
39#10591430—21no—
40D3×#832—21no—
41#10590920C2211yescharacteristic, complemented
42#10590916C2211yescharacteristic, complemented
43D3×#819C2211yescharacteristic
44#10590781C2211yescharacteristic, complemented
45#10590771C2211yescharacteristic, complemented
46D3×#817C2211yescharacteristic
47D3×#815C2211yescharacteristic
48D3×#812C2211yescharacteristic
49#10589432C2211yescharacteristic, complemented
50#10589429C2211yescharacteristic, complemented
51#10589379C2211yescharacteristic, complemented
52#10589378C2211yescharacteristic, complemented
53C3×#4566C2211yescharacteristic, complemented
54C3×#4563C2211yescharacteristic, complemented
55C3×#4513C2211yescharacteristic, complemented
56C3×#4512C2211yescharacteristic, complemented
57#10589137C2211yescharacteristic, complemented
58#10589136C2211yescharacteristic, complemented
59#10589127C2211yescharacteristic, complemented
60#10589126C2211yescharacteristic, complemented
61#10589124C2211yescharacteristic, complemented
62#10589123C2211yescharacteristic, complemented
63#10589106C2211yescharacteristic, complemented
64#10589105C2211yescharacteristic, complemented
65C2×C3×#509—31no—
66C2×#5197—31no—
67C2×#5152—31no—
68D3×#509D311yescharacteristic
69D3×#444—31no—
70D3×#442—31no—
71C3×AGL(1,ℤ/16)—31no—
72C2×#4566—31no—
73C2×#4563—31no—
74#71515—31no—
75#71515—31no—
76#71515—31no—
77#71515—31no—
78#71515—31no—
79#71515—31no—
80#71515—31no—
81#71515—31no—
82#71515—61no—
83#71515D311yescharacteristic, direct product factor
84C2×#4513—31no—
85C2×#4512—31no—
86#70929—31no—
87#70918—31no—
88D3×#365—31no—
89#69310—31no—
90D3×#361—31no—
91#69254—31no—
92D3×#360—31no—
93#69249—31no—
94#69091—31no—
95D3×#347—31no—
96C3×D3×#41—21no—
97C2×C3×D3×D4—21no—
98C22×D3×Dic3—41no—
99C32×#135C2311yescharacteristic
100C2×C32×D8C2311yescharacteristic
101#64157—21no—
102D4×C3⋊Dic3—21no—
103C3×#950—21no—
104C3×#948—21no—
105C3×D4×Dic3—21no—
106C2×C3×#213—21no—
107C3×#919C2×C411yescharacteristic, complemented
108C3×D3×Q16C2×C411yescharacteristic, complemented
109C3×#916—21no—
110C3×D3×SD16—21no—
111C3×#912C2×C411yescharacteristic, complemented
112C3×D3×D8—21no—
113C3×D3×D8—21no—
114C3×D3×D8C2×C412yes—
115C3×D3×D8C2×C412yes—
116C3×D3×D8C2×C411yescharacteristic, complemented
117C3×#904C2311yescharacteristic
118C2×C3×D24C2311yescharacteristic
119C2×C3×D3×C8C2311yescharacteristic
120#67⋊Dic3—41no—
121Dic3×#67—41no—
122D3×#217—41no—
123#63898—21no—
124Dic3×D12—21no—
125D3×C4⋊Dic3—21no—
126C4×D3×Dic3D411yescharacteristic
127#63815—21no—
128#63815—41no—
129#63814—21no—
130#63814—41no—
131D3×#208—21no—
132D3×#208—41no—
133C2×D3×C3⋊C8—41no—
134C2×D3×C3⋊C8D411yescharacteristic
135C32×SD32C2×C412yescomplemented
136C32×D16C2×C412yescomplemented
137C32×M32C2311yescharacteristic
138#63664—21no—
139#63659—21no—
140#63646C2311yescharacteristic
141#63644C2311yescharacteristic
142#63642C2311yescharacteristic
143#63639C2311yescharacteristic
144C3×#837—21no—
145C3×#832—21no—
146C3×#828C2×C412yescomplemented
147C3×#827C2×C412yescomplemented
148C3×#826C2×C412yescomplemented
149C3×#826C2×C412yescomplemented
150C3×#819C2311yescharacteristic
151C3×#817C2311yescharacteristic
152C3×#815C2311yescharacteristic
153C3×#812C2311yescharacteristic
154C3×#812C2311yescharacteristic
155C3×#800C2×C412yescomplemented
156C3×D48C2×C412yescomplemented
157C3×#798C2×C412yescomplemented
158C3×D3×C16C2×C412yescomplemented
159#63577—21no—
160#63573—21no—
161#63569—21no—
162#63568—21no—
163#63563—21no—
164#63562—21no—
165#63555D411yescharacteristic
166#63554D411yescharacteristic
167#63543—21no—
168D3×C3⋊C16—21no—
169C2×AGL(1,ℤ/16)—91noSylow
170C2×C3×#135—31no—
171C22×C3×D8—31no—
172C2×#948—61no—
173C2×D4×Dic3—61no—
174D3×#135C2×D311yescharacteristic
175C2×D3×D8C2×D311yescharacteristic
176D3×#131—61no—
177C4×D3×D4—61no—
178C3×#509—21no—
179C3×#509—31no—
180C3×#509—31no—
181C3×#509—32no—
182C3×#509—32no—
183C3×#509—31no—
184C3×#509C2×D311yescharacteristic
185C3×#509C2×D311yescharacteristic
186C2×C3×SD32—32no—
187C2×C3×D16—32no—
188C2×C3×M32—31no—
189C3×#444—31no—
190C3×#442—31no—
191C2×#837—61no—
192C2×#832—61no—
193#5197—31no—
194#5197—31no—
195#5197—31no—
196#5197—31no—
197#5197—61no—
198#5197—61no—
199#5197—61no—
200#5197C2×D311yescharacteristic, complemented
201#5193C2×D311yescharacteristic
202#5152—31no—
203#5152—31no—
204#5152—31no—
205#5152—31no—
206#5152—61no—
207#5152—61no—
208#5152—61no—
209#5152C2×D311yescharacteristic, complemented
210#5147C2×D311yescharacteristic
211#5145—61no—
212C2×#819—31no—
213C2×#817—31no—
214C2×#815—31no—
215C2×#812—31no—
216#5014—61no—
217#4914Dic312yescomplemented
218D3×SD32Dic312yescomplemented
219#4911Dic312yescomplemented
220D3×D16Dic312yescomplemented
221#4908C2×D311yescharacteristic
222D3×M32—31no—
223D3×M32C2×D311yescharacteristic
224#4894—31no—
225D3×#108—31no—
226#4869—31no—
227D3×#106—31no—
228#4823—61no—
229D3×#104—61no—
230#4785—61no—
231D3×#102—61no—
232#4717—31no—
233#4711—31no—
234D3×#97—31no—
235C3×#365—31no—
236C3×#361—31no—
237C3×#360—31no—
238C3×#347—31no—
239#4566—31no—
240#4566—31no—
241#4566—31no—
242#4566—31no—
243#4566—61no—
244#4566C2×D311yescharacteristic, complemented
245#4563—31no—
246#4563—31no—
247#4563—31no—
248#4563—31no—
249#4563—61no—
250#4563C2×D311yescharacteristic, complemented
251#4518—31no—
252#4516—31no—
253#4513—31no—
254#4513—31no—
255#4513—31no—
256#4513—31no—
257#4513—61no—
258#4513C2×D311yescharacteristic, complemented
259#4512—31no—
260#4512—31no—
261#4512—31no—
262#4512—31no—
263#4512—31no—
264#4512—61no—
265#4512C2×D311yescharacteristic, complemented
266#4495—31no—
267#4494—31no—
268#4488—31no—
269#4487—31no—
270#4466—31no—
271C23×C3×D3—41no—
272C32×#41—21no—
273C2×C32×D4—21no—
274C22×C3⋊Dic3—41no—
275C2×C3×#67—41no—
276C22×C3×Dic3—41no—
277C3×#239—21no—
278C3×D3×Q8—21no—
279C3×#237—21no—
280C3×#237—41no—
281C3×D3×D4—22no—
282C3×D3×D4—22no—
283C3×D3×D4—21no—
284C3×D3×D4—41no—
285C3×D3×D4—41no—
286C3×D3×D4—41no—
287C3×#235—21no—
288C3×#235—41no—
289C2×C3×D12—21no—
290C2×C3×C4×D3—41no—
291C2×C3×C4×D3C2×D411yescharacteristic
292C2×D3×Dic3—21no—
293C2×D3×Dic3—41no—
294C2×D3×Dic3—41no—
295C2×D3×Dic3—41no—
296C2×D3×Dic3—84no—
297C32×Q16C22×C411yescharacteristic, complemented
298C32×SD16—21no—
299C32×D8—21no—
300C32×D8C22×C412yes—
301C32×D8C22×C411yescharacteristic, complemented
302C2×C32×C8C2411yescharacteristic
303#3757—41no—
304C4⋊(C3⋊Dic3)—21no—
305C4×C3⋊Dic3C2×D411yescharacteristic
306#3748—21no—
307#3748—41no—
308C2×C3⋊(C3⋊C8)—41no—
309C2×C3⋊(C3⋊C8)C2×D411yescharacteristic
310C3×#217—41no—
311C3×#216—21no—
312C3×#215—21no—
313C3×#214—21no—
314C3×#213—22no—
315C3×#213—22no—
316C3×#213—21no—
317C3×C4⋊Dic3—21no—
318C3×C4×Dic3C2×D411yescharacteristic
319C3×#208—21no—
320C3×#208—41no—
321C2×C3×C3⋊C8—41no—
322C2×C3×C3⋊C8C2×D411yescharacteristic
323C2×C3×C3⋊C8C2×D411yescharacteristic
324C3×Dic12C22×C411yescharacteristic, complemented
325C3×D24—21no—
326C3×D24C22×C412yes—
327C3×D24C22×C411yescharacteristic, complemented
328C3×#204—21no—
329C3×D3×C8C22×C411yescharacteristic
330C3×D3×C8C22×C411yescharacteristic
331C3×D3×C8#4111yescharacteristic
332C3×D3×C8#4111yescharacteristic
333Dic3⋊Dic3—41no—
334(C2×D3)⋊Dic3—41no—
335(C2×D3)⋊Dic3—41no—
336Dic32—21no—
337#3711—41no—
338#3711—41no—
339#3711—41no—
340D3×C3⋊C8—21no—
341D3×C3⋊C8—21no—
342D3×C3⋊C8—41no—
343D3×C3⋊C8—41no—
344D3×C3⋊C8—41no—
345C32×C16C22×C412yescomplemented
346C3⋊(C3⋊C16)—21no—
347C3×C3⋊C16—21no—
348C3×C3⋊C16C22×C412yescomplemented
349C2×#509—31no—
350C2×#444—91no—
351C2×#442—91no—
352AGL(1,ℤ/16)—31no—
353AGL(1,ℤ/16)—91no—
354AGL(1,ℤ/16)—91no—
355AGL(1,ℤ/16)—91no—
356AGL(1,ℤ/16)—91no—
357AGL(1,ℤ/16)—91no—
358AGL(1,ℤ/16)—91no—
359AGL(1,ℤ/16)—91no—
360C2×#365—91no—
361C2×#361—91no—
362C2×#360—91no—
363C2×#347—91no—
364C2×C3×#41—61no—
365C22×C3×D4—61no—
366C23×Dic3—121no—
367D3×#41—21no—
368C2×D3×D4—21no—
369C22×C4×D3—121no—
370C3×#135—21no—
371C3×#135—31no—
372C3×#135—31no—
373C3×#135—31no—
374C3×#135—61no—
375C3×#135—61no—
376C3×#135C22×D311yescharacteristic
377C3×#135C22×D311yescharacteristic
378C2×C3×Q16—31no—
379C2×C3×SD16—61no—
380C2×C3×D8—21no—
381C2×C3×D8—32no—
382C2×C3×D8—32no—
383C2×C3×D8—31no—
384C2×C3×D8—31no—
385C2×C3×D8—61no—
386C2×C3×D8—61no—
387C2×C3×D8—61no—
388C2×C3×D8C22×D311yescharacteristic
389C2×C3×D8C22×D311yescharacteristic
390C3×#131—61no—
391C22×C3×C8—31no—
392C3×C4×D4—61no—
393C2×#217—121no—
394#950—21no—
395#948—21no—
396#948—61no—
397#948—61no—
398#948—61no—
399#948—61no—
400#948—121no—
401#948—121no—
402#948—121no—
403D4×Dic3—21no—
404D4×Dic3—61no—
405D4×Dic3—61no—
406D4×Dic3—61no—
407D4×Dic3—61no—
408D4×Dic3—121no—
409D4×Dic3—121no—
410D4×Dic3—121no—
411C2×#213—21no—
412C4×#67—121no—
413C2×C4⋊Dic3—61no—
414C2×C4×Dic3—31no—
415C2×#208—61no—
416C2×#208—121no—
417C22×C3⋊C8—31no—
418C22×C3⋊C8—121no—
419#919C2×Dic311yescharacteristic, complemented
420D3×Q16C2×Dic311yescharacteristic, complemented
421#916—21no—
422D3×SD16—21no—
423#912C2×Dic311yescharacteristic, complemented
424D3×D8—21no—
425D3×D8—21no—
426D3×D8C2×Dic312yes—
427D3×D8C2×Dic312yes—
428D3×D8C2×Dic311yescharacteristic, complemented
429#907—61no—
430#907—121no—
431D3×M16—61no—
432D3×M16—121no—
433#904C22×D311yescharacteristic
434C2×D24C22×D311yescharacteristic
435#901—61no—
436#901—121no—
437C2×D3×C8—31no—
438C2×D3×C8—121no—
439C2×D3×C8C22×D311yescharacteristic
440#893—61no—
441D3×C4⋊C4—61no—
442#67⋊C4—121no—
443D3×C22⋊C4—121no—
444C4×D12—61no—
445C42×D3—31no—
446C3×SD32—22no—
447C3×SD32—32no—
448C3×SD32—32no—
449C3×SD32—32no—
450C3×SD32C4×D312yescomplemented
451C3×SD32C2×Dic312yescomplemented
452C3×D16—22no—
453C3×D16—32no—
454C3×D16—32no—
455C3×D16—32no—
456C3×D16C4×D312yescomplemented
457C3×D16C2×Dic312yescomplemented
458C3×M32—21no—
459C3×M32—31no—
460C3×M32—32no—
461C3×M32—31no—
462C3×M32C22×D311yescharacteristic
463C3×M32C22×D311yescharacteristic
464C2×C3×C16—32no—
465C3×#108—31no—
466C3×#106—31no—
467C3×#104—61no—
468C3×#102—61no—
469C3×#97—31no—
470#837—21no—
471#837—61no—
472#837—61no—
473#837—61no—
474#837—61no—
475#837—121no—
476#832—21no—
477#832—61no—
478#832—61no—
479#832—61no—
480#832—61no—
481#832—121no—
482#828C2×Dic312yescomplemented
483#827C2×Dic312yescomplemented
484#826C2×Dic312yescomplemented
485#826C2×Dic312yescomplemented
486#825—61no—
487#822—61no—
488#821—61no—
489#819—31no—
490#819—31no—
491#819—61no—
492#819—61no—
493#819C22×D311yescharacteristic
494#817—31no—
495#817—31no—
496#817—61no—
497#817—61no—
498#817C22×D311yescharacteristic
499#815—31no—
500#815—31no—
501#815—31no—
502#815—31no—
503#815—31no—
504#815—61no—
505#815C22×D311yescharacteristic
506#812—31no—
507#812—31no—
508#812—61no—
509#812—61no—
510#812C22×D311yescharacteristic
511#812C22×D311yescharacteristic
512C2×C3⋊C16—61no—
513#809—61no—
514#808—61no—
515#805—61no—
516#803—31no—
517#800C2×Dic312yescomplemented
518D48C2×Dic312yescomplemented
519#798—61no—
520#798C2×Dic312yescomplemented
521D3×C16—61no—
522D3×C16C2×Dic312yescomplemented
523C23×C32—41no—
524C22×C3×D3—41no—
525C22×C3×D3—42no—
526C22×C3×D3—42no—
527C22×C3×D3—41no—
528C22×C3×D3—82no—
529C22×C3×D3—82no—
530C22×C3×D3AGL(1,ℤ/8)11yescharacteristic
531C32×Q8—21no—
532C32×D4—22no—
533C32×D4—21no—
534C32×D4—41no—
535C32×D4—41no—
536C2×C32×C4—41no—
537C2×C32×C4C22×D411yescharacteristic
538C2×C3⋊Dic3—21no—
539C2×C3⋊Dic3—41no—
540C2×C3⋊Dic3—82no—
541C3×#67—41no—
542C3×#67—41no—
543C3×#67—41no—
544C3×#67—42no—
545C3×#67—42no—
546C2×C3×Dic3—21no—
547C2×C3×Dic3—41no—
548C2×C3×Dic3—41no—
549C2×C3×Dic3—82no—
550C2×C3×Dic3AGL(1,ℤ/8)11yescharacteristic
551C3×D12—21no—
552C3×D12—22no—
553C3×D12—41no—
554C3×D12—41no—
555C3×C4×D3—41no—
556C3×C4×D3—41no—
557C3×C4×D3—41no—
558C3×C4×D3C4×D411yescharacteristic
559C3×C4×D3C4×D411yescharacteristic
560C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
561C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
562C3×Dic6—21no—
563C3×Dic6—41no—
564D3×Dic3—42no—
565D3×Dic3—82no—
566D3×Dic3—82no—
567D3×Dic3—82no—
568C32×C8C23×C411yescharacteristic
569C32×C8C2×#4111yescharacteristic
570C3⋊(C3⋊C8)—21no—
571C3⋊(C3⋊C8)—41no—
572C3×C3⋊C8—21no—
573C3×C3⋊C8—41no—
574C3×C3⋊C8C4×D411yescharacteristic
575C3×C3⋊C8C4×D411yescharacteristic
576C2×#135—31no—
577C22×D8—31no—
578C2×#131—181no—
579C2×C4×D4—181no—
580#509—31no—
581#509—31no—
582#509—32no—
583#509—32no—
584#509—31no—
585#509D3211yescharacteristic
586C2×SD32—32no—
587C2×D16—32no—
588C2×M32—31no—
589C2×M32—91no—
590#444—31no—
591#444—91no—
592#444—91no—
593#444—91no—
594#444—181no—
595#444—181no—
596#442—31no—
597#442—91no—
598#442—91no—
599#442—91no—
600#442—181no—
601#442—181no—
602C2×#108—91no—
603C2×#106—91no—
604C2×#104—181no—
605C2×#102—181no—
606C2×#97—91no—
607#365—31no—
608#365—91no—
609#365—91no—
610#365—91no—
611#361—31no—
612#361—91no—
613#361—91no—
614#361—91no—
615#360—31no—
616#360—91no—
617#360—91no—
618#360—91no—
619#347—31no—
620#347—91no—
621#347—91no—
622#347—91no—
623C24×C3—121no—
624C23×D3—41no—
625C3×#41—21no—
626C3×#41—21no—
627C3×#41—41no—
628C3×#41—61no—
629C3×#41—61no—
630C3×#41—61no—
631C3×#41—121no—
632C3×#41—121no—
633C2×C3×Q8—61no—
634C2×C3×D4—21no—
635C2×C3×D4—21no—
636C2×C3×D4—41no—
637C2×C3×D4—62no—
638C2×C3×D4—62no—
639C2×C3×D4—61no—
640C2×C3×D4—61no—
641C2×C3×D4—121no—
642C2×C3×D4—121no—
643C2×C3×D4—121no—
644C2×C3×D4—121no—
645C22×C3×C4—31no—
646C22×C3×C4—121no—
647C22×C3×C4—121no—
648C2×#67—41no—
649C22×Dic3—41no—
650C22×Dic3—61no—
651C22×Dic3—121no—
652C22×Dic3—121no—
653C22×Dic3—121no—
654C22×Dic3—121no—
655C22×Dic3—121no—
656C22×Dic3—241no—
657C22×Dic3—244no—
658#239—21no—
659D3×Q8—21no—
660#237—21no—
661#237—41no—
662D3×D4—22no—
663D3×D4—22no—
664D3×D4—21no—
665D3×D4—41no—
666D3×D4—41no—
667D3×D4—41no—
668#235—21no—
669#235—41no—
670C2×D12—21no—
671C2×C4×D3—41no—
672C2×C4×D3—61no—
673C2×C4×D3—121no—
674C2×C4×D3—121no—
675C2×C4×D3—121no—
676C2×C4×D3—244no—
677C2×C4×D3D3×D411yescharacteristic
678C3×Q16—21no—
679C3×Q16—31no—
680C3×Q16—61no—
681C3×Q16C2×C4×D311yescharacteristic, complemented
682C3×Q16C22×Dic311yescharacteristic, complemented
683C3×SD16—21no—
684C3×SD16—21no—
685C3×SD16—41no—
686C3×SD16—61no—
687C3×SD16—61no—
688C3×SD16—61no—
689C3×D8—21no—
690C3×D8—21no—
691C3×D8—22no—
692C3×D8—21no—
693C3×D8—31no—
694C3×D8—32no—
695C3×D8—41no—
696C3×D8—62no—
697C3×D8—62no—
698C3×D8—61no—
699C3×D8—61no—
700C3×D8C2×C4×D312yes—
701C3×D8C2×C4×D311yescharacteristic, complemented
702C3×D8C22×Dic312yes—
703C3×D8C22×Dic311yescharacteristic, complemented
704C3×M16—61no—
705C3×M16—121no—
706C2×C3×C8—21no—
707C2×C3×C8—31no—
708C2×C3×C8—31no—
709C2×C3×C8—31no—
710C2×C3×C8—31no—
711C2×C3×C8—31no—
712C2×C3×C8—31no—
713C2×C3×C8—121no—
714C2×C3×C8C23×D311yescharacteristic
715C2×C3×C8C23×D311yescharacteristic
716C3×C4⋊C4—61no—
717C3×C22⋊C4—121no—
718C3×C42—31no—
719#217—41no—
720#217—121no—
721#217—121no—
722#217—121no—
723#217—121no—
724#217—241no—
725#216—21no—
726#215—21no—
727#214—21no—
728#213—22no—
729#213—22no—
730#213—21no—
731(C2×D3)⋊C4—121no—
732(C2×D3)⋊C4—121no—
733C4⋊Dic3—21no—
734C4⋊Dic3—61no—
735C4⋊Dic3—61no—
736C4⋊Dic3—121no—
737C4⋊Dic3—121no—
738Dic3⋊C4—121no—
739C4×Dic3—31no—
740C4×Dic3—31no—
741C4×Dic3—61no—
742C4×Dic3—61no—
743C4×Dic3—61no—
744C4×Dic3D3×D411yescharacteristic
745#208—21no—
746#208—41no—
747#208—61no—
748#208—61no—
749#208—121no—
750#208—121no—
751#208—121no—
752#208—121no—
753#208—121no—
754#208—121no—
755#208—241no—
756C2×C3⋊C8—31no—
757C2×C3⋊C8—31no—
758C2×C3⋊C8—41no—
759C2×C3⋊C8—61no—
760C2×C3⋊C8—61no—
761C2×C3⋊C8—61no—
762C2×C3⋊C8—121no—
763C2×C3⋊C8—121no—
764C2×C3⋊C8—121no—
765C2×C3⋊C8—121no—
766C2×C3⋊C8—121no—
767C2×C3⋊C8—241no—
768C2×C3⋊C8D3×D411yescharacteristic
769C2×C3⋊C8D3×D411yescharacteristic
770Dic12C22×Dic311yescharacteristic, complemented
771D24—21no—
772D24C22×Dic312yes—
773D24C22×Dic311yescharacteristic, complemented
774#204—21no—
775ΓL(1,𝔽25)—121no—
776ΓL(1,𝔽25)—121no—
777ΓL(1,𝔽25)—121no—
778D3×C8—61no—
779D3×C8—61no—
780D3×C8—121no—
781D3×C8—121no—
782D3×C8—121no—
783D3×C8#23711yescharacteristic
784D3×C8#23711yescharacteristic
785D3×C8C22×Dic311yescharacteristic
786D3×C8C22×Dic311yescharacteristic
787C3×C16—22no—
788C3×C16—32no—
789C3×C16—61no—
790C3×C16C2×C4×D312yescomplemented
791C3×C16C22×Dic312yescomplemented
792C3⋊C16—21no—
793C3⋊C16—61no—
794C3⋊C16—61no—
795C3⋊C16—121no—
796C3⋊C16C22×Dic312yescomplemented
797C22×C32—41no—
798C22×C32—42no—
799C22×C32—81no—
800C22×C32—81no—
801C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
802C2×C3×D3—22no—
803C2×C3×D3—41no—
804C2×C3×D3—42no—
805C2×C3×D3—84no—
806C2×C3×D3—81no—
807C2×C3×D3—81no—
808C2×C3×D3—82no—
809C2×C3×D3—84no—
810C2×C3×D3#44211yescharacteristic
811C2×C3×D3#44211yescharacteristic
812C32×C4—41no—
813C32×C4C2×C4×D411yescharacteristic
814C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
815C3⋊Dic3—41no—
816C3⋊Dic3—81no—
817C3×Dic3—41no—
818C3×Dic3—41no—
819C3×Dic3—81no—
820C3×Dic3#44211yescharacteristic
821C3×Dic3#44211yescharacteristic
822C2×#41—61no—
823C22×D4—61no—
824C23×C4—361no—
825#135—31no—
826#135—31no—
827#135—31no—
828#135—61no—
829#135—61no—
830#135C2×D3211yescharacteristic
831C2×Q16—31no—
832C2×SD16—61no—
833C2×D8—32no—
834C2×D8—32no—
835C2×D8—31no—
836C2×D8—31no—
837C2×D8—61no—
838C2×D8—61no—
839C2×D8—61no—
840C2×D8C2×D3211yescharacteristic
841#131—61no—
842#131—181no—
843#131—181no—
844#131—181no—
845#131—361no—
846#131—361no—
847C2×M16—181no—
848C2×M16—361no—
849C22×C8—31no—
850C22×C8—91no—
851C22×C8—361no—
852C4×D4—61no—
853C4×D4—181no—
854C4×D4—181no—
855C4×D4—181no—
856C4×D4—361no—
857C4×D4—361no—
858C2×C4⋊C4—181no—
859C2×C22⋊C4—361no—
860C2×C42—91no—
861SD32—32no—
862SD32—32no—
863SD32—32no—
864SD32D3×Dic312yescomplemented
865D16—32no—
866D16—32no—
867D16—32no—
868D16D3×Dic312yescomplemented
869M32—31no—
870M32—32no—
871M32—31no—
872M32—91no—
873M32—181no—
874M32C2×D3211yescharacteristic
875C2×C16—32no—
876C2×C16—181no—
877#108—31no—
878#108—91no—
879#108—181no—
880#106—31no—
881#106—91no—
882#106—181no—
883#104—61no—
884#104—181no—
885#104—181no—
886#104—181no—
887#102—61no—
888#102—181no—
889#102—181no—
890#102—181no—
891#97—31no—
892#97—91no—
893#97—91no—
894#97—91no—
895C23×C3—31no—
896C23×C3—41no—
897C23×C3—41no—
898C23×C3—81no—
899C23×C3—121no—
900C23×C3—122no—
901C23×C3—122no—
902C23×C3—121no—
903C23×C3—242no—
904C23×C3—242no—
905C22×D3—41no—
906C22×D3—41no—
907C22×D3—42no—
908C22×D3—42no—
909C22×D3—82no—
910C22×D3—82no—
911C22×D3#91111yescharacteristic
912C3×Q8—21no—
913C3×Q8—21no—
914C3×Q8—41no—
915C3×Q8—61no—
916C3×Q8—121no—
917C3×D4—22no—
918C3×D4—21no—
919C3×D4—22no—
920C3×D4—21no—
921C3×D4—42no—
922C3×D4—41no—
923C3×D4—41no—
924C3×D4—41no—
925C3×D4—41no—
926C3×D4—41no—
927C3×D4—62no—
928C3×D4—61no—
929C3×D4—81no—
930C3×D4—81no—
931C3×D4—122no—
932C3×D4—122no—
933C3×D4—121no—
934C3×D4—121no—
935C3×D4—121no—
936C3×D4—121no—
937C3×D4—121no—
938C2×C3×C4—21no—
939C2×C3×C4—31no—
940C2×C3×C4—31no—
941C2×C3×C4—31no—
942C2×C3×C4—31no—
943C2×C3×C4—31no—
944C2×C3×C4—41no—
945C2×C3×C4—41no—
946C2×C3×C4—61no—
947C2×C3×C4—81no—
948C2×C3×C4—121no—
949C2×C3×C4—121no—
950C2×C3×C4—121no—
951C2×C3×C4—121no—
952C2×C3×C4—121no—
953C2×C3×C4—242no—
954C2×C3×C4C2×D3×D411yescharacteristic
955C2×C3×C4C2×D3×D411yescharacteristic
956#67—41no—
957#67—41no—
958#67—41no—
959#67—42no—
960#67—42no—
961C2×Dic3—21no—
962C2×Dic3—41no—
963C2×Dic3—41no—
964C2×Dic3—61no—
965C2×Dic3—61no—
966C2×Dic3—82no—
967C2×Dic3—121no—
968C2×Dic3—122no—
969C2×Dic3—121no—
970C2×Dic3—121no—
971C2×Dic3—241no—
972C2×Dic3—242no—
973C2×Dic3—242no—
974C2×Dic3—242no—
975C2×Dic3—242no—
976C2×Dic3—242no—
977C2×Dic3—482no—
978C2×Dic3#91111yescharacteristic
979D12—21no—
980D12—22no—
981D12—41no—
982D12—41no—
983C4×D3—41no—
984C4×D3—41no—
985C4×D3—41no—
986C4×D3—122no—
987C4×D3—242no—
988C4×D3—242no—
989C4×D3—242no—
990C4×D3#91111yescharacteristic
991C4×D3#91111yescharacteristic
992C4×D3D4×Dic311yescharacteristic
993C4×D3D4×Dic311yescharacteristic
994Dic6—21no—
995Dic6—41no—
996C3×C8—21no—
997C3×C8—21no—
998C3×C8—31no—
999C3×C8—31no—
1000C3×C8—61no—
1001C3×C8—121no—
1002C3×C8C22×C4×D311yescharacteristic
1003C3×C8C2×#23711yescharacteristic
1004C3×C8D3×#4111yescharacteristic
1005C3×C8C23×Dic311yescharacteristic
1006C3⋊C8—21no—
1007C3⋊C8—41no—
1008C3⋊C8—61no—
1009C3⋊C8—61no—
1010C3⋊C8—121no—
1011C3⋊C8—121no—
1012C3⋊C8—121no—
1013C3⋊C8—241no—
1014C3⋊C8D4×Dic311yescharacteristic
1015C3⋊C8D4×Dic311yescharacteristic
1016C2×C32—21no—
1017C2×C32—82no—
1018C2×C32—81no—
1019C2×C32C2×#44211yescharacteristic
1020C3×D3—21no—
1021C3×D3—81no—
1022C3×D3—82no—
1023C3×D3AGL(1,ℤ/16)12yescomplemented
1024C24—121no—
1025#41—21no—
1026#41—61no—
1027#41—61no—
1028#41—61no—
1029#41—121no—
1030#41—121no—
1031C2×Q8—61no—
1032C2×D4—21no—
1033C2×D4—62no—
1034C2×D4—62no—
1035C2×D4—61no—
1036C2×D4—61no—
1037C2×D4—121no—
1038C2×D4—121no—
1039C2×D4—121no—
1040C2×D4—121no—
1041C22×C4—31no—
1042C22×C4—121no—
1043C22×C4—121no—
1044C22×C4—181no—
1045C22×C4—361no—
1046C22×C4—361no—
1047C22×C4—361no—
1048C22×C4—361no—
1049C22×C4—724no—
1050Q16—31no—
1051Q16—61no—
1052Q16C2×D3×Dic311yescharacteristic, complemented
1053SD16—21no—
1054SD16—61no—
1055SD16—61no—
1056SD16—61no—
1057D8—21no—
1058D8—31no—
1059D8—32no—
1060D8—62no—
1061D8—62no—
1062D8—61no—
1063D8—61no—
1064D8C2×D3×Dic312yes—
1065D8C2×D3×Dic311yescharacteristic, complemented
1066M16—61no—
1067M16—121no—
1068M16—181no—
1069M16—361no—
1070M16—361no—
1071M16—361no—
1072M16—361no—
1073C2×C8—31no—
1074C2×C8—31no—
1075C2×C8—31no—
1076C2×C8—31no—
1077C2×C8—31no—
1078C2×C8—31no—
1079C2×C8—91no—
1080C2×C8—121no—
1081C2×C8—181no—
1082C2×C8—181no—
1083C2×C8—361no—
1084C2×C8—361no—
1085C2×C8—361no—
1086C2×C8—361no—
1087C2×C8C22×D3211yescharacteristic
1088C4⋊C4—61no—
1089C4⋊C4—181no—
1090C4⋊C4—361no—
1091C22⋊C4—121no—
1092C22⋊C4—361no—
1093C22⋊C4—361no—
1094C22⋊C4—361no—
1095C42—31no—
1096C42—91no—
1097C42—181no—
1098C16—32no—
1099C16—61no—
1100C16—181no—
1101C16C2×D3×Dic312yescomplemented
1102C22×C3—21no—
1103C22×C3—31no—
1104C22×C3—31no—
1105C22×C3—41no—
1106C22×C3—42no—
1107C22×C3—41no—
1108C22×C3—42no—
1109C22×C3—62no—
1110C22×C3—81no—
1111C22×C3—82no—
1112C22×C3—81no—
1113C22×C3—81no—
1114C22×C3—81no—
1115C22×C3—81no—
1116C22×C3—121no—
1117C22×C3—122no—
1118C22×C3—161no—
1119C22×C3—161no—
1120C22×C3—241no—
1121C22×C3—241no—
1122C22×C3—244no—
1123C22×C3—242no—
1124C22×C3—244no—
1125C22×C3C2×#91111yescharacteristic
1126C22×C3D3×AGL(1,ℤ/8)11yescharacteristic
1127C2×D3—22no—
1128C2×D3—41no—
1129C2×D3—42no—
1130C2×D3—84no—
1131C2×D3—81no—
1132C2×D3—81no—
1133C2×D3—84no—
1134C2×D3—82no—
1135C2×D3#515211yescharacteristic
1136C2×D3#515211yescharacteristic
1137C3×C4—21no—
1138C3×C4—21no—
1139C3×C4—31no—
1140C3×C4—31no—
1141C3×C4—41no—
1142C3×C4—41no—
1143C3×C4—81no—
1144C3×C4—121no—
1145C3×C4—121no—
1146C3×C4—241no—
1147C3×C4C4×D3×D411yescharacteristic
1148C3×C4C2×#91111yescharacteristic
1149C3×C4D3×AGL(1,ℤ/8)11yescharacteristic
1150C3×C4C2×D4×Dic311yescharacteristic
1151Dic3—41no—
1152Dic3—41no—
1153Dic3—81no—
1154Dic3—121no—
1155Dic3—121no—
1156Dic3—241no—
1157Dic3—241no—
1158Dic3—241no—
1159Dic3—481no—
1160Dic3#515211yescharacteristic
1161Dic3#515211yescharacteristic
1162C32C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
1163C23—31no—
1164C23—41no—
1165C23—121no—
1166C23—122no—
1167C23—122no—
1168C23—121no—
1169C23—242no—
1170C23—242no—
1171Q8—21no—
1172Q8—61no—
1173Q8—121no—
1174D4—22no—
1175D4—21no—
1176D4—41no—
1177D4—41no—
1178D4—62no—
1179D4—61no—
1180D4—122no—
1181D4—122no—
1182D4—121no—
1183D4—121no—
1184D4—121no—
1185D4—121no—
1186D4—121no—
1187C2×C4—31no—
1188C2×C4—31no—
1189C2×C4—31no—
1190C2×C4—31no—
1191C2×C4—31no—
1192C2×C4—41no—
1193C2×C4—61no—
1194C2×C4—121no—
1195C2×C4—121no—
1196C2×C4—121no—
1197C2×C4—121no—
1198C2×C4—121no—
1199C2×C4—181no—
1200C2×C4—242no—
1201C2×C4—362no—
1202C2×C4—361no—
1203C2×C4—722no—
1204C2×C4—722no—
1205C2×C4—722no—
1206C2×C4—722no—
1207C2×C4D32×D411yescharacteristic
1208C8—31no—
1209C8—31no—
1210C8—61no—
1211C8—121no—
1212C8—181no—
1213C8—361no—
1214C8D3×#23711yescharacteristic
1215C8C22×D3×Dic311yescharacteristic
1216C2×C3—21no—
1217C2×C3—21no—
1218C2×C3—21no—
1219C2×C3—32no—
1220C2×C3—41no—
1221C2×C3—61no—
1222C2×C3—82no—
1223C2×C3—81no—
1224C2×C3—82no—
1225C2×C3—81no—
1226C2×C3—162no—
1227C2×C3—161no—
1228C2×C3—242no—
1229C2×C3—241no—
1230C2×C3D3×#44211yescharacteristic
1231C2×C3C2×#515211yescharacteristic
1232D3—21no—
1233D3—82no—
1234D3—81no—
1235D3#7151512yesdirect product factor
1236C22—31no—
1237C22—31no—
1238C22—41no—
1239C22—42no—
1240C22—62no—
1241C22—81no—
1242C22—81no—
1243C22—121no—
1244C22—122no—
1245C22—241no—
1246C22—241no—
1247C22—244no—
1248C22—242no—
1249C22—244no—
1250C22D3×#91111yescharacteristic
1251C4—31no—
1252C4—31no—
1253C4—41no—
1254C4—121no—
1255C4—121no—
1256C4—241no—
1257C4—361no—
1258C4—721no—
1259C4D3×#91111yescharacteristic
1260C4D3×D4×Dic311yescharacteristic
1261C3—21no—
1262C3D3×AGL(1,ℤ/16)11yescharacteristic, complemented
1263C3C2×#7151511yescharacteristic, complemented
1264C2—21no—
1265C2—32no—
1266C2—61no—
1267C2—82no—
1268C2—81no—
1269C2—242no—
1270C2—241no—
1271C2D3×#515211yescharacteristic
subgroupG/H
centerC2D3×#5152
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC32×#509C22
socleC2×C32C2×#442
prime radicalC3×D3×#509C2
cosocleC2×C32×C8C24
hypercenter#509D32
hypocenterC32C2×AGL(1,ℤ/16)
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
2. D3×#5197C2semidirect
3. D3×#5152C2semidirect
4. #11797986C2semidirect
5. #11797985C2semidirect
6. #11797980C2semidirect
7. #11797979C2semidirect
8. #11797970C2semidirect
9. #11797969C2semidirect
10. C3×#71515C2semidirect
11. #11797956C2semidirect
12. D3×#4513C2semidirect
13. D3×#4563C2semidirect
14. D3×#4566C2semidirect
15. D3×#4512C2semidirect
23. #10592896C22semidirect
24. #10592851C22semidirect
25. C3×#5197C22semidirect
27. C3×#5152C22semidirect
29. C3×#4914C4semidirect
30. C3×D3×SD32C4semidirect
31. C3×#4911C4semidirect
32. C3×D3×D16C4semidirect
41. #10590920C22semidirect
42. #10590916C22semidirect
44. #10590781C22semidirect
45. #10590771C22semidirect
49. #10589432C22semidirect
50. #10589429C22semidirect
51. #10589379C22semidirect
52. #10589378C22semidirect
53. C3×#4566C22semidirect
54. C3×#4563C22semidirect
55. C3×#4513C22semidirect
56. C3×#4512C22semidirect
57. #10589137C22semidirect
58. #10589136C22semidirect
59. #10589127C22semidirect
60. #10589126C22semidirect
61. #10589124C22semidirect
62. #10589123C22semidirect
63. #10589106C22semidirect
64. #10589105C22semidirect
83. #71515D3direct (N × H)
107. C3×#919C2×C4semidirect
108. C3×D3×Q16C2×C4semidirect
111. C3×#912C2×C4semidirect
116. C3×D3×D8C2×C4semidirect
135. C32×SD32C2×C4semidirect
136. C32×D16C2×C4semidirect
146. C3×#828C2×C4semidirect
147. C3×#827C2×C4semidirect
148. C3×#826C2×C4semidirect
149. C3×#826C2×C4semidirect
155. C3×#800C2×C4semidirect
156. C3×D48C2×C4semidirect
157. C3×#798C2×C4semidirect
158. C3×D3×C16C2×C4semidirect
200. #5197C2×D3semidirect
209. #5152C2×D3semidirect
217. #4914Dic3semidirect
218. D3×SD32Dic3semidirect
219. #4911Dic3semidirect
220. D3×D16Dic3semidirect
244. #4566C2×D3semidirect
250. #4563C2×D3semidirect
258. #4513C2×D3semidirect
265. #4512C2×D3semidirect
297. C32×Q16C22×C4semidirect
301. C32×D8C22×C4semidirect
324. C3×Dic12C22×C4semidirect
327. C3×D24C22×C4semidirect
345. C32×C16C22×C4semidirect
348. C3×C3⋊C16C22×C4semidirect
419. #919C2×Dic3semidirect
420. D3×Q16C2×Dic3semidirect
423. #912C2×Dic3semidirect
428. D3×D8C2×Dic3semidirect
450. C3×SD32C4×D3semidirect
451. C3×SD32C2×Dic3semidirect
456. C3×D16C4×D3semidirect
457. C3×D16C2×Dic3semidirect
482. #828C2×Dic3semidirect
483. #827C2×Dic3semidirect
484. #826C2×Dic3semidirect
485. #826C2×Dic3semidirect
517. #800C2×Dic3semidirect
518. D48C2×Dic3semidirect
520. #798C2×Dic3semidirect
522. D3×C16C2×Dic3semidirect
681. C3×Q16C2×C4×D3semidirect
682. C3×Q16C22×Dic3semidirect
701. C3×D8C2×C4×D3semidirect
703. C3×D8C22×Dic3semidirect
770. Dic12C22×Dic3semidirect
773. D24C22×Dic3semidirect
790. C3×C16C2×C4×D3semidirect
791. C3×C16C22×Dic3semidirect
796. C3⋊C16C22×Dic3semidirect
864. SD32D3×Dic3semidirect
868. D16D3×Dic3semidirect
1023. C3×D3AGL(1,ℤ/16)semidirect
1052. Q16C2×D3×Dic3semidirect
1065. D8C2×D3×Dic3semidirect
1101. C16C2×D3×Dic3semidirect
1162. C32C2×AGL(1,ℤ/16)semidirect
1235. D3#71515direct (N × H)
1262. C3D3×AGL(1,ℤ/16)semidirect
1263. C3C2×#71515semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#5092
D3×#51972
D3×#51522
#117979862
#117979852
#117979802
#117979792
#117979702
#117979692
C3×#715152
#117979562
D3×#45132
D3×#45632
D3×#45662
D3×#45122
C2×#715153
D3×AGL(1,ℤ/16)3