Finite Group Databasebeta

← C3×#10948663 #72222786

Subgroups — C3×#10948663 #72222786

Order 2304.

1536 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#83910C211yesmaximal, characteristic, complemented
2C3×#83823C211yesmaximal, characteristic, complemented
3C3×#71515C218yesmaximal, complemented
4C3×#71427C211yesmaximal, characteristic, complemented
5C2×C3×#4563C211yesmaximal, characteristic, complemented
6C3×#72076C211yesmaximal, characteristic, complemented
7C3×#71425C211yesmaximal, characteristic, complemented
8C2×C32×#509C211yesmaximal, characteristic
9#10948663C311yesmaximal, characteristic, direct product factor
10C3×#33471—31nomaximal
11C2×C32×#135C2211yescharacteristic
12C22×C32×D8C2211yescharacteristic
13C3×#5819—21no—
14C3×#5798—21no—
15C32×#509C414yescomplemented
16C32×#509C2214yes—
17C2×C32×SD32C412yescomplemented
18C2×C32×D16C412yescomplemented
19C2×C32×M32C2211yescharacteristic
20C3×#5236—21no—
21C3×#5215—21no—
22C3×#5197C2214yescomplemented
23C3×#5196—22no—
24C3×#5152C2214yescomplemented
25C3×Dic3×D8—22no—
26C2×C3×#819C2211yescharacteristic
27C3×#5106C2211yescharacteristic
28C3×#5101C2211yescharacteristic
29C2×C3×#812C2211yescharacteristic
30C3×#4566C2214yescomplemented
31C3×#4563C2214yescomplemented
32C3×#4513C2214yescomplemented
33C3×#4512C2214yescomplemented
34C2×C3×#509—21no—
35C2×C3×#509D311yescharacteristic
36C2×C3×#509C2×C311yescharacteristic
37C3×#2957—31no—
38C3×#2948—31no—
39#83910C2×C311yescharacteristic, complemented
40#83823C2×C311yescharacteristic, complemented
41C3×AGL(1,ℤ/16)—38no—
42C3×#2155—31no—
43C2×C3×#361—31no—
44C3×#2145—31no—
45C3×#2110—31no—
46#72076C2×C311yescharacteristic, complemented
47C2×#4563C2×C311yescharacteristic, complemented
48#71515C2×C318yescomplemented
49#71427C2×C311yescharacteristic, complemented
50#71425C2×C311yescharacteristic, complemented
51C2×C32×#41—21no—
52C22×C32×D4—21no—
53C32×#135—21no—
54C32×#135—21no—
55C32×#135C2×C412yescomplemented
56C32×#135C2312yes—
57C2×C32×Q16C2×C411yescharacteristic, complemented
58C2×C32×SD16—21no—
59C2×C32×D8—21no—
60C2×C32×D8—21no—
61C2×C32×D8—21no—
62C2×C32×D8C2×C412yes—
63C2×C32×D8C2×C412yes—
64C2×C32×D8C2×C411yescharacteristic, complemented
65C2×C32×D8C2312yes—
66C22×C32×C8C2311yescharacteristic
67C2×C3×#217—42no—
68C3×#948—24no—
69C3×#948—42no—
70C3×D4×Dic3—24no—
71C3×D4×Dic3—42no—
72C3×#926—21no—
73C3×#926D411yescharacteristic
74C2×C3×#208—21no—
75C2×C3×#208—42no—
76C2×C3×#208D411yescharacteristic
77C32×SD32C2×C418yescomplemented
78C32×D16C2×C418yescomplemented
79C32×M32C2×C412yescomplemented
80C32×M32C2312yes—
81C2×C32×C16C2×C412yescomplemented
82C3×#837—24no—
83C3×#832—24no—
84C3×#819—21no—
85C3×#819C2312yes—
86C3×#818—21no—
87C3×#817C2312yes—
88C3×#815C2312yes—
89C3×C8×Dic3D412yes—
90C3×#812—21no—
91C3×#812C2312yes—
92C2×C3×C3⋊C16—21no—
93#33471—31noSylow
94C2×C3×#135—21no—
95C2×C3×#135C2×D311yescharacteristic
96C2×C3×#135C22×C311yescharacteristic
97C22×C3×D8—21no—
98C22×C3×D8C2×D311yescharacteristic
99C22×C3×D8C22×C311yescharacteristic
100C3×#568—61no—
101C3×#518—61no—
102#5819—21no—
103#5798—21no—
104C3×#509—24no—
105C3×#509—24no—
106C3×#509Dic314yescomplemented
107C3×#509C3×C414yescomplemented
108C3×#509C2×D314yes—
109C3×#509C22×C314yes—
110C2×C3×SD32—22no—
111C2×C3×SD32Dic312yescomplemented
112C2×C3×SD32C3×C412yescomplemented
113C2×C3×D16—22no—
114C2×C3×D16Dic312yescomplemented
115C2×C3×D16C3×C412yescomplemented
116C2×C3×M32—21no—
117C2×C3×M32—31no—
118C2×C3×M32C2×D311yescharacteristic
119C2×C3×M32C22×C311yescharacteristic
120C3×#444—34no—
121C3×#443—62no—
122C3×#442—34no—
123C3×C4×D8—62no—
124C2×C3×#108—31no—
125C3×#427—31no—
126C3×#421—61no—
127C3×#418—61no—
128C3×#405—31no—
129#5236—21no—
130#5215—21no—
131#5197C22×C314yescomplemented
132#5196—22no—
133#5152C22×C314yescomplemented
134Dic3×D8—22no—
135C2×#819C22×C311yescharacteristic
136#5106C22×C311yescharacteristic
137#5101C22×C311yescharacteristic
138C2×#812C22×C311yescharacteristic
139C3×#365—34no—
140C3×#361—34no—
141C3×#360—34no—
142C3×#347—34no—
143#4566C22×C314yescomplemented
144#4563C22×C314yescomplemented
145#4513C22×C314yescomplemented
146#4512C22×C314yescomplemented
147C24×C32—41no—
148C32×#41—22no—
149C32×#41—22no—
150C32×#41—41no—
151C32×#41—41no—
152C2×C32×Q8—21no—
153C2×C32×D4—22no—
154C2×C32×D4—22no—
155C2×C32×D4—21no—
156C2×C32×D4—22no—
157C2×C32×D4—41no—
158C2×C32×D4—41no—
159C2×C32×D4—41no—
160C2×C32×D4—41no—
161C22×C32×C4—41no—
162C22×C32×C4C2×D411yescharacteristic
163C22×C3×Dic3—44no—
164C32×Q16—21no—
165C32×Q16C22×C412yes—
166C32×SD16—22no—
167C32×SD16—22no—
168C32×D8—22no—
169C32×D8—22no—
170C32×D8—21no—
171C32×D8—22no—
172C32×D8C22×C414yes—
173C32×D8C22×C412yes—
174C2×C32×C8C22×C411yescharacteristic
175C2×C32×C8C22×C411yescharacteristic
176C2×C32×C8C2×D411yescharacteristic
177C2×C32×C8#4111yescharacteristic
178C2×C32×C8#4111yescharacteristic
179C2×C32×C8C2411yescharacteristic
180C3×#217—21no—
181C3×#217—44no—
182C3×#217—41no—
183C3×C4⋊Dic3—21no—
184C3×C4⋊Dic3—22no—
185C3×C4×Dic3—41no—
186C3×C4×Dic3C2×D412yes—
187C3×#208—21no—
188C3×#208—21no—
189C3×#208—22no—
190C3×#208—44no—
191C3×#208—41no—
192C2×C3×C3⋊C8—44no—
193C2×C3×C3⋊C8—41no—
194C2×C3×C3⋊C8C2×D412yes—
195C32×C16C22×C414yes—
196C3×C3⋊C16—22no—
197C2×#509C3×D311yescharacteristic
198#2957—31no—
199#2948—31no—
200AGL(1,ℤ/16)—38no—
201#2155—31no—
202C2×#361—31no—
203#2145—31no—
204#2110—31no—
205C2×C3×#41—21no—
206C2×C3×#41—21no—
207C2×C3×#41—41no—
208C22×C3×D4—21no—
209C22×C3×D4—21no—
210C22×C3×D4—41no—
211C3×#135—21no—
212C3×#135—21no—
213C3×#135—21no—
214C3×#135—21no—
215C3×#135—22no—
216C3×#135—22no—
217C3×#135—41no—
218C3×#135—41no—
219C3×#135C2×Dic312yescomplemented
220C3×#135C2×C3×C412yescomplemented
221C3×#135C22×D312yes—
222C3×#135C23×C312yes—
223C2×C3×Q16—21no—
224C2×C3×Q16C2×Dic311yescharacteristic, complemented
225C2×C3×Q16C2×C3×C411yescharacteristic, complemented
226C2×C3×SD16—21no—
227C2×C3×SD16—21no—
228C2×C3×SD16—41no—
229C2×C3×D8—21no—
230C2×C3×D8—21no—
231C2×C3×D8—21no—
232C2×C3×D8—21no—
233C2×C3×D8—21no—
234C2×C3×D8—21no—
235C2×C3×D8—22no—
236C2×C3×D8—22no—
237C2×C3×D8—21no—
238C2×C3×D8—22no—
239C2×C3×D8—41no—
240C2×C3×D8—41no—
241C2×C3×D8—41no—
242C2×C3×D8C2×Dic312yes—
243C2×C3×D8C2×Dic312yes—
244C2×C3×D8C2×Dic311yescharacteristic, complemented
245C2×C3×D8C2×C3×C412yes—
246C2×C3×D8C2×C3×C412yes—
247C2×C3×D8C2×C3×C411yescharacteristic, complemented
248C2×C3×D8C22×D312yes—
249C2×C3×D8C23×C312yes—
250C3×#131—64no—
251C3×#131—122no—
252C2×C3×M16—31no—
253C2×C3×M16—61no—
254C2×C3×M16—122no—
255C22×C3×C8—21no—
256C22×C3×C8C22×D311yescharacteristic
257C22×C3×C8C23×C311yescharacteristic
258C3×C4×D4—64no—
259C3×C4×D4—122no—
260C3×#117—31no—
261C3×#117—61no—
262C2×C3×C22⋊C4—122no—
263C2×#217—42no—
264#948—24no—
265#948—42no—
266D4×Dic3—24no—
267D4×Dic3—42no—
268#926—21no—
269#926C3×D411yescharacteristic
270C2×#208—21no—
271C2×#208—42no—
272C2×#208C3×D411yescharacteristic
273C3×SD32—28no—
274C3×SD32C2×Dic318yescomplemented
275C3×SD32C2×C3×C418yescomplemented
276C3×D16—28no—
277C3×D16C2×Dic318yescomplemented
278C3×D16C2×C3×C418yescomplemented
279C3×M32—22no—
280C3×M32—22no—
281C3×M32—32no—
282C3×M32—61no—
283C3×M32C2×Dic312yescomplemented
284C3×M32C2×C3×C412yescomplemented
285C3×M32C22×D312yes—
286C3×M32C23×C312yes—
287C2×C3×C16—22no—
288C2×C3×C16—61no—
289C2×C3×C16C2×Dic312yescomplemented
290C2×C3×C16C2×C3×C412yescomplemented
291C3×#108—32no—
292C3×#108—61no—
293C3×#107—61no—
294C3×#106—32no—
295C3×#104—64no—
296C3×#102—64no—
297C3×#97—32no—
298C3×C4×C8—32no—
299#837—24no—
300#832—24no—
301#819—21no—
302#819C23×C312yes—
303#818—21no—
304#817C23×C312yes—
305#815C23×C312yes—
306C8×Dic3C3×D412yes—
307#812—21no—
308#812C23×C312yes—
309C2×C3⋊C16—21no—
310C23×C32—42no—
311C23×C32—42no—
312C23×C32—42no—
313C23×C32—41no—
314C23×C32—162no—
315C23×C32AGL(1,ℤ/8)11yescharacteristic
316C32×Q8—22no—
317C32×Q8—41no—
318C32×D4—24no—
319C32×D4—22no—
320C32×D4—42no—
321C32×D4—42no—
322C32×D4—42no—
323C32×D4—42no—
324C32×D4—42no—
325C32×D4—41no—
326C2×C32×C4—41no—
327C2×C32×C4—42no—
328C2×C32×C4—42no—
329C2×C32×C4C4×D411yescharacteristic
330C2×C32×C4C4×D411yescharacteristic
331C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
332C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
333C2×C32×C4AGL(1,ℤ/8)11yescharacteristic
334C2×C32×C4C22×D411yescharacteristic
335C2×C3×Dic3—22no—
336C2×C3×Dic3—42no—
337C2×C3×Dic3—164no—
338C32×C8C4×D411yescharacteristic
339C32×C8C4×D411yescharacteristic
340C32×C8C23×C411yescharacteristic
341C32×C8C2×#4111yescharacteristic
342C3×C3⋊C8—22no—
343C3×C3⋊C8—42no—
344C2×#135C2×C3×D311yescharacteristic
345C22×D8C2×C3×D311yescharacteristic
346#568—61no—
347#518—61no—
348#509C3×Dic314yescomplemented
349#509C2×C3×D314yes—
350C2×SD32C3×Dic312yescomplemented
351C2×D16C3×Dic312yescomplemented
352C2×M32—31no—
353C2×M32C2×C3×D311yescharacteristic
354#444—34no—
355#443—62no—
356#442—34no—
357C4×D8—62no—
358C2×#108—31no—
359#427—31no—
360#421—61no—
361#418—61no—
362#405—31no—
363#365—34no—
364#361—34no—
365#360—34no—
366#347—34no—
367C24×C3—41no—
368C24×C3—41no—
369C24×C3—81no—
370C3×#41—22no—
371C3×#41—22no—
372C3×#41—22no—
373C3×#41—22no—
374C3×#41—42no—
375C3×#41—42no—
376C3×#41—41no—
377C3×#41—41no—
378C3×#41—41no—
379C3×#41—41no—
380C3×#41—81no—
381C3×#41—81no—
382C2×C3×Q8—21no—
383C2×C3×Q8—21no—
384C2×C3×Q8—41no—
385C2×C3×D4—22no—
386C2×C3×D4—22no—
387C2×C3×D4—21no—
388C2×C3×D4—22no—
389C2×C3×D4—22no—
390C2×C3×D4—21no—
391C2×C3×D4—22no—
392C2×C3×D4—22no—
393C2×C3×D4—42no—
394C2×C3×D4—42no—
395C2×C3×D4—42no—
396C2×C3×D4—41no—
397C2×C3×D4—41no—
398C2×C3×D4—41no—
399C2×C3×D4—41no—
400C2×C3×D4—41no—
401C2×C3×D4—41no—
402C2×C3×D4—41no—
403C2×C3×D4—41no—
404C2×C3×D4—41no—
405C2×C3×D4—81no—
406C2×C3×D4—81no—
407C2×C3×D4—81no—
408C2×C3×D4—81no—
409C22×C3×C4—21no—
410C22×C3×C4—41no—
411C22×C3×C4—41no—
412C22×C3×C4—81no—
413C22×C3×C4—124no—
414C22×C3×C4D3×D411yescharacteristic
415C22×C3×C4C2×C3×D411yescharacteristic
416C22×Dic3—44no—
417C3×Q16—21no—
418C3×Q16—21no—
419C3×Q16—22no—
420C3×Q16—41no—
421C3×Q16C22×Dic312yes—
422C3×Q16C22×C3×C412yes—
423C3×SD16—22no—
424C3×SD16—22no—
425C3×SD16—22no—
426C3×SD16—22no—
427C3×SD16—42no—
428C3×SD16—42no—
429C3×D8—22no—
430C3×D8—22no—
431C3×D8—21no—
432C3×D8—22no—
433C3×D8—22no—
434C3×D8—21no—
435C3×D8—22no—
436C3×D8—22no—
437C3×D8—22no—
438C3×D8—24no—
439C3×D8—42no—
440C3×D8—42no—
441C3×D8—42no—
442C3×D8—41no—
443C3×D8C22×Dic312yes—
444C3×D8C22×Dic314yes—
445C3×D8C22×C3×C412yes—
446C3×D8C22×C3×C414yes—
447C3×M16—61no—
448C3×M16—61no—
449C3×M16—62no—
450C3×M16—124no—
451C3×M16—121no—
452C2×C3×C8—21no—
453C2×C3×C8—21no—
454C2×C3×C8—21no—
455C2×C3×C8—21no—
456C2×C3×C8—21no—
457C2×C3×C8—21no—
458C2×C3×C8—32no—
459C2×C3×C8—124no—
460C2×C3×C8—121no—
461C2×C3×C8D3×D411yescharacteristic
462C2×C3×C8#23711yescharacteristic
463C2×C3×C8#23711yescharacteristic
464C2×C3×C8C22×Dic311yescharacteristic
465C2×C3×C8C22×Dic311yescharacteristic
466C2×C3×C8C22×C3×C411yescharacteristic
467C2×C3×C8C22×C3×C411yescharacteristic
468C2×C3×C8C2×C3×D411yescharacteristic
469C2×C3×C8C3×#4111yescharacteristic
470C2×C3×C8C3×#4111yescharacteristic
471C2×C3×C8C23×D311yescharacteristic
472C2×C3×C8C24×C311yescharacteristic
473C3×C4⋊C4—61no—
474C3×C4⋊C4—62no—
475C3×C22⋊C4—61no—
476C3×C22⋊C4—124no—
477C3×C22⋊C4—121no—
478C3×C42—32no—
479C3×C42—121no—
480#217—21no—
481#217—44no—
482#217—41no—
483C4⋊Dic3—21no—
484C4⋊Dic3—22no—
485C4×Dic3—41no—
486C4×Dic3C2×C3×D412yes—
487#208—21no—
488#208—21no—
489#208—22no—
490#208—44no—
491#208—41no—
492C2×C3⋊C8—44no—
493C2×C3⋊C8—41no—
494C2×C3⋊C8C2×C3×D412yes—
495C3×C16—24no—
496C3×C16—62no—
497C3×C16C22×Dic314yes—
498C3×C16C22×C3×C414yes—
499C3⋊C16—22no—
500C22×C32—41no—
501C22×C32—42no—
502C22×C32—44no—
503C22×C32—84no—
504C22×C32—161no—
505C22×C32—162no—
506C22×C32—162no—
507C22×C32#44211yescharacteristic
508C22×C32#44211yescharacteristic
509C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
510C32×C4—42no—
511C32×C4#44211yescharacteristic
512C32×C4#44211yescharacteristic
513C32×C4C2×C4×D411yescharacteristic
514C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
515C3×Dic3—42no—
516C3×Dic3—82no—
517C2×#41—21no—
518C22×D4—21no—
519#135—21no—
520#135—21no—
521#135C2×C3×Dic312yescomplemented
522#135C22×C3×D312yes—
523C2×Q16C2×C3×Dic311yescharacteristic, complemented
524C2×SD16—21no—
525C2×D8—21no—
526C2×D8—21no—
527C2×D8—21no—
528C2×D8C2×C3×Dic312yes—
529C2×D8C2×C3×Dic312yes—
530C2×D8C2×C3×Dic311yescharacteristic, complemented
531C2×D8C22×C3×D312yes—
532#131—64no—
533#131—122no—
534C2×M16—31no—
535C2×M16—61no—
536C2×M16—122no—
537C22×C8C22×C3×D311yescharacteristic
538C4×D4—64no—
539C4×D4—122no—
540#117—31no—
541#117—61no—
542C2×C22⋊C4—122no—
543SD32C2×C3×Dic318yescomplemented
544D16C2×C3×Dic318yescomplemented
545M32—32no—
546M32—61no—
547M32C2×C3×Dic312yescomplemented
548M32C22×C3×D312yes—
549C2×C16—61no—
550C2×C16C2×C3×Dic312yescomplemented
551#108—32no—
552#108—61no—
553#107—61no—
554#106—32no—
555#104—64no—
556#102—64no—
557#97—32no—
558C4×C8—32no—
559C23×C3—21no—
560C23×C3—42no—
561C23×C3—42no—
562C23×C3—41no—
563C23×C3—42no—
564C23×C3—42no—
565C23×C3—41no—
566C23×C3—42no—
567C23×C3—42no—
568C23×C3—81no—
569C23×C3—82no—
570C23×C3—82no—
571C23×C3—82no—
572C23×C3—162no—
573C23×C3—162no—
574C23×C3—164no—
575C23×C3#91111yescharacteristic
576C23×C3C3×AGL(1,ℤ/8)11yescharacteristic
577C3×Q8—22no—
578C3×Q8—22no—
579C3×Q8—42no—
580C3×Q8—41no—
581C3×Q8—41no—
582C3×Q8—81no—
583C3×D4—24no—
584C3×D4—22no—
585C3×D4—24no—
586C3×D4—22no—
587C3×D4—44no—
588C3×D4—42no—
589C3×D4—42no—
590C3×D4—42no—
591C3×D4—42no—
592C3×D4—42no—
593C3×D4—42no—
594C3×D4—42no—
595C3×D4—42no—
596C3×D4—41no—
597C3×D4—42no—
598C3×D4—42no—
599C3×D4—42no—
600C3×D4—41no—
601C3×D4—82no—
602C3×D4—82no—
603C3×D4—82no—
604C3×D4—81no—
605C3×D4—82no—
606C3×D4—82no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—42no—
616C2×C3×C4—42no—
617C2×C3×C4—42no—
618C2×C3×C4—42no—
619C2×C3×C4—62no—
620C2×C3×C4—82no—
621C2×C3×C4—82no—
622C2×C3×C4—81no—
623C2×C3×C4—122no—
624C2×C3×C4—484no—
625C2×C3×C4#91111yescharacteristic
626C2×C3×C4#91111yescharacteristic
627C2×C3×C4#91111yescharacteristic
628C2×C3×C4D4×Dic311yescharacteristic
629C2×C3×C4D4×Dic311yescharacteristic
630C2×C3×C4C3×C4×D411yescharacteristic
631C2×C3×C4C3×C4×D411yescharacteristic
632C2×C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
633C2×C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
634C2×C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
635C2×C3×C4C2×D3×D411yescharacteristic
636C2×C3×C4C22×C3×D411yescharacteristic
637C2×Dic3—22no—
638C2×Dic3—42no—
639C2×Dic3—164no—
640C3×C8—21no—
641C3×C8—21no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—62no—
645C3×C8—122no—
646C3×C8D4×Dic311yescharacteristic
647C3×C8D4×Dic311yescharacteristic
648C3×C8C3×C4×D411yescharacteristic
649C3×C8C3×C4×D411yescharacteristic
650C3×C8C2×#23711yescharacteristic
651C3×C8C23×Dic311yescharacteristic
652C3×C8C23×C3×C411yescharacteristic
653C3×C8C2×C3×#4111yescharacteristic
654C3⋊C8—22no—
655C3⋊C8—42no—
656C2×C32—21no—
657C2×C32—21no—
658C2×C32—21no—
659C2×C32—84no—
660C2×C32—82no—
661C2×C32C2×#44211yescharacteristic
662C24—41no—
663#41—22no—
664#41—22no—
665#41—41no—
666#41—41no—
667C2×Q8—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—21no—
671C2×D4—22no—
672C2×D4—41no—
673C2×D4—41no—
674C2×D4—41no—
675C2×D4—41no—
676C22×C4—41no—
677C22×C4—124no—
678C22×C4C3×D3×D411yescharacteristic
679Q16—21no—
680Q16C22×C3×Dic312yes—
681SD16—22no—
682SD16—22no—
683D8—22no—
684D8—22no—
685D8—21no—
686D8—22no—
687D8C22×C3×Dic312yes—
688D8C22×C3×Dic314yes—
689M16—61no—
690M16—61no—
691M16—62no—
692M16—124no—
693M16—121no—
694C2×C8—32no—
695C2×C8—124no—
696C2×C8—121no—
697C2×C8C3×D3×D411yescharacteristic
698C2×C8C3×#23711yescharacteristic
699C2×C8C3×#23711yescharacteristic
700C2×C8C22×C3×Dic311yescharacteristic
701C2×C8C22×C3×Dic311yescharacteristic
702C2×C8C23×C3×D311yescharacteristic
703C4⋊C4—61no—
704C4⋊C4—62no—
705C22⋊C4—61no—
706C22⋊C4—124no—
707C22⋊C4—121no—
708C42—32no—
709C42—121no—
710C16—62no—
711C16C22×C3×Dic314yes—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—44no—
720C22×C3—42no—
721C22×C3—44no—
722C22×C3—82no—
723C22×C3—84no—
724C22×C3—84no—
725C22×C3—84no—
726C22×C3—164no—
727C22×C3—162no—
728C22×C3—162no—
729C22×C3—162no—
730C22×C3—162no—
731C22×C3—161no—
732C22×C3—161no—
733C22×C3—164no—
734C22×C3—162no—
735C22×C3—164no—
736C22×C3#515211yescharacteristic
737C22×C3#515211yescharacteristic
738C22×C3C3×#44211yescharacteristic
739C22×C3C3×#44211yescharacteristic
740C22×C3C2×#91111yescharacteristic
741C22×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—42no—
747C3×C4—42no—
748C3×C4—82no—
749C3×C4—122no—
750C3×C4—242no—
751C3×C4#515211yescharacteristic
752C3×C4#515211yescharacteristic
753C3×C4C3×#44211yescharacteristic
754C3×C4C3×#44211yescharacteristic
755C3×C4C2×#91111yescharacteristic
756C3×C4C2×D4×Dic311yescharacteristic
757C3×C4C2×C3×C4×D411yescharacteristic
758C3×C4C2×C3×AGL(1,ℤ/8)11yescharacteristic
759Dic3—42no—
760Dic3—82no—
761C32#3347111yescharacteristic, complemented, Sylow
762C23—42no—
763C23—41no—
764C23—42no—
765C23—42no—
766C23—162no—
767C23C3×#91111yescharacteristic
768Q8—22no—
769Q8—41no—
770D4—24no—
771D4—22no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—42no—
777D4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—62no—
782C2×C4—122no—
783C2×C4—484no—
784C2×C4C3×#91111yescharacteristic
785C2×C4C3×#91111yescharacteristic
786C2×C4C3×#91111yescharacteristic
787C2×C4C3×D4×Dic311yescharacteristic
788C2×C4C3×D4×Dic311yescharacteristic
789C2×C4C2×C3×D3×D411yescharacteristic
790C8—62no—
791C8—122no—
792C8C3×D4×Dic311yescharacteristic
793C8C3×D4×Dic311yescharacteristic
794C8C2×C3×#23711yescharacteristic
795C8C23×C3×Dic311yescharacteristic
796C2×C3—22no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—41no—
805C2×C3—41no—
806C2×C3—84no—
807C2×C3—82no—
808C2×C3—84no—
809C2×C3—82no—
810C2×C3—164no—
811C2×C3—162no—
812C2×C3C2×#515211yescharacteristic
813C2×C3C2×C3×#44211yescharacteristic
814C22—41no—
815C22—42no—
816C22—44no—
817C22—84no—
818C22—162no—
819C22—162no—
820C22—161no—
821C22C3×#515211yescharacteristic
822C22C3×#515211yescharacteristic
823C22C2×C3×#91111yescharacteristic
824C4—42no—
825C4—122no—
826C4—242no—
827C4C3×#515211yescharacteristic
828C4C3×#515211yescharacteristic
829C4C2×C3×#91111yescharacteristic
830C4C2×C3×D4×Dic311yescharacteristic
831C3—21no—
832C3C3×#3347111yescharacteristic, complemented
833C3#1094866311yescharacteristic, direct product factor
834C2—21no—
835C2—21no—
836C2—21no—
837C2—84no—
838C2—82no—
839C2C2×C3×#515211yescharacteristic
subgroupG/H
centerC2×C3C2×#5152
commutatorC3×C8C23×C3×C4
FrattiniC2×C8C23×C3×D3
Fitting, prime radicalC2×C32×#509C2
socleC2×C32C2×#442
cosocleC2×C3×C8C24×C3
hypercenterC2×C3×#509D3
hypocenterC3C3×#33471
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×#509

Complements

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

NH ≅ G/Ntype
1. C3×#83910C2semidirect
2. C3×#83823C2semidirect
3. C3×#71515C2semidirect
4. C3×#71427C2semidirect
5. C2×C3×#4563C2semidirect
6. C3×#72076C2semidirect
7. C3×#71425C2semidirect
9. #10948663C3direct (N × H)
15. C32×#509C4semidirect
17. C2×C32×SD32C4semidirect
18. C2×C32×D16C4semidirect
22. C3×#5197C22semidirect
24. C3×#5152C22semidirect
30. C3×#4566C22semidirect
31. C3×#4563C22semidirect
32. C3×#4513C22semidirect
33. C3×#4512C22semidirect
39. #83910C2×C3semidirect
40. #83823C2×C3semidirect
46. #72076C2×C3semidirect
47. C2×#4563C2×C3semidirect
48. #71515C2×C3semidirect
49. #71427C2×C3semidirect
50. #71425C2×C3semidirect
55. C32×#135C2×C4semidirect
57. C2×C32×Q16C2×C4semidirect
64. C2×C32×D8C2×C4semidirect
77. C32×SD32C2×C4semidirect
78. C32×D16C2×C4semidirect
79. C32×M32C2×C4semidirect
81. C2×C32×C16C2×C4semidirect
106. C3×#509Dic3semidirect
107. C3×#509C3×C4semidirect
111. C2×C3×SD32Dic3semidirect
112. C2×C3×SD32C3×C4semidirect
114. C2×C3×D16Dic3semidirect
115. C2×C3×D16C3×C4semidirect
131. #5197C22×C3semidirect
133. #5152C22×C3semidirect
143. #4566C22×C3semidirect
144. #4563C22×C3semidirect
145. #4513C22×C3semidirect
146. #4512C22×C3semidirect
219. C3×#135C2×Dic3semidirect
220. C3×#135C2×C3×C4semidirect
224. C2×C3×Q16C2×Dic3semidirect
225. C2×C3×Q16C2×C3×C4semidirect
244. C2×C3×D8C2×Dic3semidirect
247. C2×C3×D8C2×C3×C4semidirect
274. C3×SD32C2×Dic3semidirect
275. C3×SD32C2×C3×C4semidirect
277. C3×D16C2×Dic3semidirect
278. C3×D16C2×C3×C4semidirect
283. C3×M32C2×Dic3semidirect
284. C3×M32C2×C3×C4semidirect
289. C2×C3×C16C2×Dic3semidirect
290. C2×C3×C16C2×C3×C4semidirect
348. #509C3×Dic3semidirect
350. C2×SD32C3×Dic3semidirect
351. C2×D16C3×Dic3semidirect
521. #135C2×C3×Dic3semidirect
523. C2×Q16C2×C3×Dic3semidirect
530. C2×D8C2×C3×Dic3semidirect
543. SD32C2×C3×Dic3semidirect
544. D16C2×C3×Dic3semidirect
547. M32C2×C3×Dic3semidirect
550. C2×C16C2×C3×Dic3semidirect
761. C32#33471semidirect
832. C3C3×#33471semidirect
833. C3#10948663direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#839102
C3×#838232
C3×#715152
C3×#714272
C2×C3×#45632
C3×#720762
C3×#714252
C2×C32×#5092
#109486633
C3×#334713