Finite Group Databasebeta

← C2×D3×#3717 #13170560

Subgroups — C2×D3×#3717 #13170560

Order 1728.

1618 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#88811C211yesmaximal, characteristic, complemented
4C2×#88797C211yesmaximal, characteristic, complemented
5C2×#88795C211yesmaximal, characteristic, complemented
6C2×C3×#3717C211yesmaximal, characteristic, complemented
7C2×C3×D3×C3⋊C8C211yesmaximal, characteristic, complemented
8D3×#3717C218yesmaximal, direct product factor
9C2×D3×#215—31nomaximal
10C22×#3717—31nomaximal
11C2×D3×#204—31nomaximal
12C22×D3×C3⋊D3—21no—
13C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
14C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C3×#634C2211yescharacteristic, complemented
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic, complemented
18C2×#6292—21no—
19D3×C4⋊(C3⋊D3)—22no—
20D3×C4⋊(C3⋊D3)C2214yes—
21C2×C3×#627—21no—
22C2×C3×D3×Dic3—21no—
23C3×D3×Dic6—22no—
24C3×D3×Dic6C2214yescomplemented
25C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C2×C32×C3⋊C8C2211yescharacteristic, complemented
27#88811C2214yescomplemented
28#88797C2214yescomplemented
29#88795C2214yescomplemented
30C3×#3717C2214yescomplemented
31C3×D3×C3⋊C8C2214yescomplemented
32C22×C4⋊(C3⋊D3)—31no—
33C2×C3×D3×Q8—31no—
34C22×C3×Dic6—31no—
35C2×D3×D12—31no—
36C2×D3×D12—31no—
37C2×D3×D12—61no—
38C2×D3×Dic6D311yescharacteristic, complemented
39C2×#3755—31no—
40C2×#3744—31no—
41C2×C3×#215—31no—
42C22×C3×C3⋊C8—31no—
43C2×C3×#204—31no—
44C2×C3×D3×C8—31no—
45D3×#215—38no—
46C2×#3717—31no—
47C2×#3717—31no—
48C2×#3717—31no—
49C2×#3717—31no—
50C2×#3717—31no—
51C2×#3717—38no—
52C2×#3717—61no—
53C2×#3717—61no—
54C2×#3717D311yescharacteristic, direct product factor
55C2×#3716—31no—
56C2×#3715—31no—
57C2×D3×C3⋊C8D311yescharacteristic, complemented
58D3×#204—38no—
59C22×C3⋊(C3⋊D3)—21no—
60C22×C3×C3⋊D3—21no—
61C22×C32×D3D411yescharacteristic
62C2×D3×C3⋊D3—24no—
63C2×D3×C3⋊D3—44no—
64C2×C33×C4C2311yescharacteristic
65C4⋊(C3⋊(C3⋊D3))—21no—
66C4⋊(C3⋊(C3⋊D3))C2312yes—
67C2×C3×C3⋊Dic3—21no—
68C3×C4⋊(C3⋊D3)—21no—
69C3×C4⋊(C3⋊D3)C2312yes—
70C3×#634—21no—
71C3×#634C2312yescomplemented
72C2×C32×Dic3—21no—
73C2×C32×Dic3D411yescharacteristic
74C32×C4×D3D412yes—
75C32×C4×D3C2312yes—
76C32×Dic6—21no—
77C32×Dic6C2312yescomplemented
78#6292—24no—
79C3×#627—24no—
80C3×D3×Dic3—24no—
81C3×C3⋊(C3⋊C8)C2312yescomplemented
82C32×C3⋊C8C2312yescomplemented
83C22×#215—91no—
84C2×D3×SD16—91no—
85C22×#204—91no—
86C23×C3⋊D3—61no—
87C22×D32—62no—
88C22×D32—61no—
89C22×D32—61no—
90C2×C32×Q8—31no—
91C22×C32×C4—31no—
92C2×C4⋊(C3⋊D3)—31no—
93C2×C4⋊(C3⋊D3)—31no—
94C2×C4⋊(C3⋊D3)—31no—
95C2×C4⋊(C3⋊D3)—34no—
96C2×C4⋊(C3⋊D3)—62no—
97C2×C4⋊(C3⋊D3)—61no—
98C2×C4⋊(C3⋊D3)—61no—
99C2×C4⋊(C3⋊D3)—61no—
100C2×C4⋊(C3⋊D3)—61no—
101C2×C4⋊(C3⋊D3)—121no—
102C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
103C2×#634C2×D311yescharacteristic, complemented
104C22×C3×Dic3—61no—
105C3×D3×Q8—34no—
106C3×D3×Q8—62no—
107C2×C3×D12—31no—
108C2×C3×D12—31no—
109C2×C3×D12—61no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—61no—
112C2×C3×C4×D3C2×D311yescharacteristic
113C2×C3×C4×D3C2×D311yescharacteristic
114C2×C3×Dic6—21no—
115C2×C3×Dic6—31no—
116C2×C3×Dic6—31no—
117C2×C3×Dic6—34no—
118C2×C3×Dic6—62no—
119C2×C3×Dic6—61no—
120C2×C3×Dic6—61no—
121C2×C3×Dic6—61no—
122C2×C3×Dic6C2×D311yescharacteristic, complemented
123C2×C3×Dic6C2×D311yescharacteristic, complemented
124C2×#627—21no—
125C2×#626—62no—
126C2×#626—61no—
127C2×#626—61no—
128C2×D3×Dic3—21no—
129D3×D12—34no—
130D3×D12—34no—
131D3×D12—64no—
132D3×D12—64no—
133D3×D12—62no—
134D3×D12—62no—
135D3×Dic6—22no—
136D3×Dic6C2×D314yescomplemented
137C2×C32×C8—31no—
138#3755—34no—
139C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
140#3744—34no—
141C3×#215—34no—
142C2×C3×C3⋊C8—21no—
143C2×C3×C3⋊C8—31no—
144C2×C3×C3⋊C8—31no—
145C2×C3×C3⋊C8—34no—
146C2×C3×C3⋊C8—61no—
147C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
148C2×C3×C3⋊C8C2×D311yescharacteristic, complemented
149C3×#204—34no—
150C3×D3×C8—34no—
151#3717—34no—
152#3717—34no—
153#3717—34no—
154#3717—34no—
155#3717—34no—
156#3717—64no—
157#3717—64no—
158#3717C2×D314yesdirect product factor
159#3716—34no—
160#3715—34no—
161D3×C3⋊C8C2×D314yescomplemented
162C22×C33C2×D411yescharacteristic
163C2×C3⋊(C3⋊D3)—22no—
164C2×C3⋊(C3⋊D3)—42no—
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3—42no—
167C2×C32×D3SD1614yescomplemented
168C2×C32×D3C2×D412yes—
169D3×C3⋊D3—48no—
170C33×C4C2×D411yescharacteristic
171C33×C4C2411yescharacteristic
172C3×C3⋊Dic3—22no—
173C32×Dic3—22no—
174C32×Dic3C2×D412yes—
175C22×C3×Q8—91no—
176C2×D3×Q8—31no—
177C2×D3×D4—91no—
178C22×D12—91no—
179C22×D12—91no—
180C22×D12—181no—
181C22×Dic6—31no—
182C2×C3×SD16—91no—
183C22×C3×C8—91no—
184C2×#215—31no—
185C2×#215—98no—
186C2×#215—91no—
187C2×#215—91no—
188C2×#215—91no—
189C2×#215—91no—
190C2×#215—181no—
191C2×#214—91no—
192C22×C3⋊C8—31no—
193D3×SD16—98no—
194C2×#204—31no—
195C2×#204—98no—
196C2×#204—91no—
197C2×#204—91no—
198C2×#204—91no—
199C2×#204—91no—
200C2×#204—181no—
201C2×D3×C8—31no—
202C23×C32—31no—
203C22×C3⋊D3—21no—
204C22×C3⋊D3—64no—
205C22×C3⋊D3—61no—
206C22×C3⋊D3—62no—
207C22×C3⋊D3—61no—
208C22×C3⋊D3—61no—
209C22×C3⋊D3—121no—
210C22×C3⋊D3—121no—
211C22×C3⋊D3—122no—
212C22×C3⋊D3—124no—
213C22×C3×D3—21no—
214C22×C3×D3—62no—
215C22×C3×D3—61no—
216C22×C3×D3—61no—
217C22×C3×D3D1211yescharacteristic
218C22×C3×D3#6711yescharacteristic
219C2×D32—68no—
220C2×D32—64no—
221C2×D32—64no—
222C2×D32—128no—
223C2×D32—124no—
224C2×D32—124no—
225C32×Q8—32no—
226C32×Q8—61no—
227C2×C32×C4—21no—
228C2×C32×C4—21no—
229C2×C32×C4—21no—
230C2×C32×C4—31no—
231C2×C32×C4—32no—
232C2×C32×C4—32no—
233C2×C32×C4—41no—
234C2×C32×C4—61no—
235C2×C32×C4C22×D311yescharacteristic
236C2×C32×C4C22×D311yescharacteristic
237C2×C32×C4C22×D311yescharacteristic
238C2×C3⋊Dic3—21no—
239C4⋊(C3⋊D3)—21no—
240C4⋊(C3⋊D3)—32no—
241C4⋊(C3⋊D3)—32no—
242C4⋊(C3⋊D3)—32no—
243C4⋊(C3⋊D3)—62no—
244C4⋊(C3⋊D3)—62no—
245C4⋊(C3⋊D3)—62no—
246C4⋊(C3⋊D3)—64no—
247C4⋊(C3⋊D3)—61no—
248C4⋊(C3⋊D3)—62no—
249C4⋊(C3⋊D3)—61no—
250C4⋊(C3⋊D3)—61no—
251C4⋊(C3⋊D3)—122no—
252C4⋊(C3⋊D3)—121no—
253C4⋊(C3⋊D3)—121no—
254C4⋊(C3⋊D3)—122no—
255C4⋊(C3⋊D3)C22×D312yes—
256#634—21no—
257#634C22×D312yescomplemented
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—41no—
262C2×C3×Dic3—64no—
263C2×C3×Dic3—61no—
264C2×C3×Dic3—61no—
265C2×C3×Dic3—121no—
266C2×C3×Dic3D1211yescharacteristic
267C2×C3×Dic3#6711yescharacteristic
268C3×D12—32no—
269C3×D12—32no—
270C3×D12—62no—
271C3×D12—62no—
272C3×D12—61no—
273C3×D12—61no—
274C3×C4×D3—22no—
275C3×C4×D3—22no—
276C3×C4×D3—64no—
277C3×C4×D3D1212yes—
278C3×C4×D3#6712yes—
279C3×C4×D3C22×D312yes—
280C3×C4×D3C22×D312yes—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—22no—
284C3×Dic6—32no—
285C3×Dic6—32no—
286C3×Dic6—41no—
287C3×Dic6—62no—
288C3×Dic6—64no—
289C3×Dic6—61no—
290C3×Dic6—61no—
291C3×Dic6—64no—
292C3×Dic6—121no—
293C3×Dic6C22×D312yescomplemented
294C3×Dic6C22×D312yescomplemented
295#627—24no—
296#626—68no—
297#626—64no—
298#626—64no—
299D3×Dic3—24no—
300C32×C8—32no—
301C3⋊(C3⋊C8)C22×D312yescomplemented
302C3×C3⋊C8—22no—
303C3×C3⋊C8—32no—
304C3×C3⋊C8—32no—
305C3×C3⋊C8—62no—
306C3×C3⋊C8C22×D312yescomplemented
307C3×C3⋊C8C22×D312yescomplemented
308C22×SD16—271noSylow
309C2×C33C2×SD1612yescomplemented
310C2×C33C22×D411yescharacteristic
311C3⋊(C3⋊D3)—42no—
312C3×C3⋊D3—42no—
313C32×D3C2×SD1614yescomplemented
314C23×D3—181no—
315C23×D3—181no—
316C23×D3—182no—
317C23×D3—181no—
318C2×C3×Q8—31no—
319C2×C3×Q8—31no—
320C2×C3×Q8—61no—
321C2×C3×Q8—94no—
322C2×C3×Q8—91no—
323C2×C3×Q8—181no—
324C2×C3×Q8—182no—
325C2×C3×D4—91no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—61no—
329C22×C3×C4—181no—
330C2×#67—181no—
331C22×Dic3—61no—
332D3×Q8—34no—
333D3×Q8—62no—
334D3×D4—94no—
335D3×D4—182no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—61no—
339C2×D12—94no—
340C2×D12—94no—
341C2×D12—91no—
342C2×D12—91no—
343C2×D12—91no—
344C2×D12—184no—
345C2×D12—181no—
346C2×D12—181no—
347C2×D12—181no—
348C2×D12—182no—
349C2×D12—182no—
350C2×D12—184no—
351C2×D12—181no—
352C2×D12—181no—
353C2×D12—182no—
354C2×D12—361no—
355C2×C4×D3—61no—
356C2×C4×D3D3211yescharacteristic
357C2×Dic6—31no—
358C2×Dic6—31no—
359C2×Dic6—34no—
360C2×Dic6—61no—
361C2×Dic6—62no—
362C2×Dic6—61no—
363C2×Dic6—61no—
364C2×Dic6D3211yescharacteristic, complemented
365C3×SD16—94no—
366C2×C3×C8—31no—
367C2×C3×C8—31no—
368C2×C3×C8—61no—
369C2×C3×C8—94no—
370C2×C3×C8—91no—
371#215—34no—
372#215—94no—
373#215—94no—
374#215—94no—
375#215—94no—
376#215—184no—
377#214—94no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—34no—
381C2×C3⋊C8—61no—
382C2×C3⋊C8D3211yescharacteristic, complemented
383#204—34no—
384#204—94no—
385#204—94no—
386#204—94no—
387#204—94no—
388#204—184no—
389D3×C8—34no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—34no—
394C22×C32—32no—
395C22×C32—41no—
396C22×C32C2×D1211yescharacteristic
397C22×C32D3×D411yescharacteristic
398C22×C32C2×#6711yescharacteristic
399C2×C3⋊D3—22no—
400C2×C3⋊D3—42no—
401C2×C3⋊D3—62no—
402C2×C3⋊D3—64no—
403C2×C3⋊D3—62no—
404C2×C3⋊D3—62no—
405C2×C3⋊D3—122no—
406C2×C3⋊D3—122no—
407C2×C3⋊D3—124no—
408C2×C3⋊D3—128no—
409C2×C3⋊D3—122no—
410C2×C3⋊D3—124no—
411C2×C3⋊D3—122no—
412C2×C3⋊D3—122no—
413C2×C3⋊D3—242no—
414C2×C3⋊D3—242no—
415C2×C3⋊D3—244no—
416C2×C3×D3—24no—
417C2×C3×D3—22no—
418C2×C3×D3—64no—
419C2×C3×D3—62no—
420C2×C3×D3—62no—
421C2×C3×D3—124no—
422C2×C3×D3—122no—
423C2×C3×D3—122no—
424C2×C3×D3#20414yescomplemented
425C2×C3×D3#21514yescomplemented
426C2×C3×D3C2×D1212yes—
427C2×C3×D3C2×#6712yes—
428D32—1216no—
429D32—128no—
430D32—128no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—21no—
437C32×C4—32no—
438C32×C4—41no—
439C32×C4—41no—
440C32×C4—62no—
441C32×C4C2×D1211yescharacteristic
442C32×C4D3×D411yescharacteristic
443C32×C4C2×#6711yescharacteristic
444C32×C4C23×D311yescharacteristic
445C32×C4C23×D311yescharacteristic
446C32×C4C23×D311yescharacteristic
447C3⋊Dic3—22no—
448C3×Dic3—22no—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—42no—
452C3×Dic3—62no—
453C3×Dic3—62no—
454C3×Dic3—122no—
455C3×Dic3C2×D1212yes—
456C3×Dic3C2×#6712yes—
457C22×Q8—91no—
458C22×D4—271no—
459C2×SD16—91no—
460C2×SD16—271no—
461C2×SD16—278no—
462C2×SD16—271no—
463C2×SD16—271no—
464C22×C8—91no—
465C33C22×SD1611yescharacteristic, complemented, Sylow
466C23×C3—31no—
467C23×C3—31no—
468C23×C3—61no—
469C23×C3—181no—
470C22×D3—62no—
471C22×D3—61no—
472C22×D3—61no—
473C22×D3—184no—
474C22×D3—184no—
475C22×D3—188no—
476C22×D3—182no—
477C22×D3—181no—
478C22×D3—181no—
479C22×D3—181no—
480C22×D3—184no—
481C22×D3—361no—
482C22×D3—361no—
483C22×D3—362no—
484C22×D3—364no—
485C22×D3—364no—
486C22×D3—368no—
487C22×D3—364no—
488C22×D3#62611yescharacteristic
489C3×Q8—32no—
490C3×Q8—32no—
491C3×Q8—62no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—92no—
495C3×Q8—121no—
496C3×Q8—184no—
497C3×Q8—181no—
498C3×D4—92no—
499C3×D4—181no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—32no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—32no—
509C2×C3×C4—41no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—121no—
516C2×C3×C4—184no—
517C2×C3×C4—181no—
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520C2×C3×C4C2×D3211yescharacteristic
521#67—184no—
522C2×Dic3—21no—
523C2×Dic3—64no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—121no—
527C2×Dic3#62611yescharacteristic
528D12—32no—
529D12—32no—
530D12—62no—
531D12—62no—
532D12—61no—
533D12—61no—
534D12—92no—
535D12—92no—
536D12—92no—
537D12—182no—
538D12—182no—
539D12—182no—
540D12—182no—
541D12—184no—
542D12—184no—
543D12—188no—
544D12—181no—
545D12—181no—
546D12—181no—
547D12—362no—
548D12—361no—
549D12—361no—
550D12—362no—
551C4×D3—64no—
552C4×D3#62612yes—
553C4×D3C2×D3212yes—
554Dic6—21no—
555Dic6—32no—
556Dic6—32no—
557Dic6—62no—
558Dic6—64no—
559Dic6—61no—
560Dic6—61no—
561Dic6—64no—
562Dic6—121no—
563Dic6C2×D3212yescomplemented
564C3×C8—32no—
565C3×C8—32no—
566C3×C8—62no—
567C3×C8—92no—
568C3⋊C8—32no—
569C3⋊C8—32no—
570C3⋊C8—62no—
571C3⋊C8C2×D3212yescomplemented
572C2×C32—21no—
573C2×C32—22no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—22no—
577C2×C32—22no—
578C2×C32—34no—
579C2×C32—42no—
580C2×C32—41no—
581C2×C32C2×#20412yescomplemented
582C2×C32D3×SD1612yescomplemented
583C2×C32C2×#21512yescomplemented
584C2×C32C22×D1211yescharacteristic
585C2×C32C2×D3×D411yescharacteristic
586C2×C32C22×#6711yescharacteristic
587C3⋊D3—42no—
588C3⋊D3—122no—
589C3⋊D3—124no—
590C3⋊D3—122no—
591C3⋊D3—122no—
592C3⋊D3—242no—
593C3⋊D3—242no—
594C3⋊D3—244no—
595C3×D3—24no—
596C3×D3—124no—
597C3×D3—122no—
598C3×D3—122no—
599C3×D3C2×#20414yescomplemented
600C3×D3C2×#21514yescomplemented
601C24—541no—
602C2×Q8—31no—
603C2×Q8—94no—
604C2×Q8—91no—
605C2×Q8—181no—
606C2×Q8—182no—
607C2×D4—91no—
608C2×D4—274no—
609C2×D4—271no—
610C2×D4—542no—
611C2×D4—541no—
612C22×C4—31no—
613C22×C4—181no—
614SD16—94no—
615SD16—274no—
616SD16—274no—
617SD16—274no—
618C2×C8—31no—
619C2×C8—94no—
620C2×C8—91no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—34no—
626C22×C3—32no—
627C22×C3—34no—
628C22×C3—41no—
629C22×C3—62no—
630C22×C3—64no—
631C22×C3—182no—
632C22×C3—362no—
633C22×C3D3×D1211yescharacteristic
634C22×C3C2×#62611yescharacteristic
635C22×C3D3×#6711yescharacteristic
636C2×D3—64no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—124no—
640C2×D3—122no—
641C2×D3—122no—
642C2×D3—184no—
643C2×D3—182no—
644C2×D3—182no—
645C2×D3—182no—
646C2×D3—362no—
647C2×D3—362no—
648C2×D3—364no—
649C2×D3—368no—
650C2×D3—368no—
651C2×D3—3616no—
652C2×D3—364no—
653C2×D3—362no—
654C2×D3—362no—
655C2×D3—362no—
656C2×D3—368no—
657C2×D3—722no—
658C2×D3—722no—
659C2×D3—724no—
660C2×D3#371714yesdirect product factor
661C2×D3C2×#62612yes—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—32no—
669C3×C4—32no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—62no—
673C3×C4—62no—
674C3×C4—62no—
675C3×C4—122no—
676C3×C4—182no—
677C3×C4D3×D1211yescharacteristic
678C3×C4C2×#62611yescharacteristic
679C3×C4D3×#6711yescharacteristic
680C3×C4C22×D3211yescharacteristic
681C3×C4C22×D3211yescharacteristic
682C3×C4C22×D3211yescharacteristic
683Dic3—22no—
684Dic3—62no—
685Dic3—62no—
686Dic3—122no—
687Dic3C2×#62612yes—
688C32—21no—
689C32—21no—
690C32—21no—
691C32—41no—
692C32C22×#20411yescharacteristic, complemented
693C32C2×D3×SD1611yescharacteristic, complemented
694C32C22×#21511yescharacteristic, complemented
695C23—31no—
696C23—181no—
697C23—544no—
698C23—541no—
699C23—1084no—
700Q8—32no—
701Q8—61no—
702Q8—92no—
703Q8—184no—
704Q8—181no—
705D4—92no—
706D4—181no—
707D4—272no—
708D4—544no—
709D4—541no—
710C2×C4—31no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—61no—
714C2×C4—184no—
715C2×C4—181no—
716C2×C4D3311yescharacteristic
717C8—32no—
718C8—92no—
719C2×C3—22no—
720C2×C3—22no—
721C2×C3—22no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—34no—
726C2×C3—34no—
727C2×C3—42no—
728C2×C3—41no—
729C2×C3—64no—
730C2×C3—362no—
731C2×C3D3×#20412yescomplemented
732C2×C3C2×#371712yescomplemented
733C2×C3D3×#21512yescomplemented
734C2×C3C2×D3×D1211yescharacteristic
735C2×C3C22×#62611yescharacteristic
736C2×C3C2×D3×#6711yescharacteristic
737D3—124no—
738D3—122no—
739D3—122no—
740D3—364no—
741D3—362no—
742D3—362no—
743D3—362no—
744D3—722no—
745D3—722no—
746D3—724no—
747D3C2×#371714yesdirect product factor
748C22—34no—
749C22—32no—
750C22—182no—
751C22—362no—
752C22—542no—
753C22—1088no—
754C22—1082no—
755C22D3×#62611yescharacteristic
756C4—32no—
757C4—62no—
758C4—182no—
759C4D3×#62611yescharacteristic
760C4C2×D3311yescharacteristic
761C3—21no—
762C3—21no—
763C3—21no—
764C3—41no—
765C3C2×D3×#20411yescharacteristic, complemented
766C3C22×#371711yescharacteristic, complemented
767C3C2×D3×#21511yescharacteristic, complemented
768C2—34no—
769C2—362no—
770C2—1082no—
771C2D3×#371712yesdirect product factor
772C2C2×D3×#62611yescharacteristic
subgroupG/H
centerC22D3×#626
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C2×D4
prime radicalC2×D3×C4⋊(C3⋊D3)C2
hypercenterC2×C4D33
hypocenterC33C22×SD16
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×Dic6C2semidirect
3. C2×#88811C2semidirect
4. C2×#88797C2semidirect
5. C2×#88795C2semidirect
6. C2×C3×#3717C2semidirect
7. C2×C3×D3×C3⋊C8C2semidirect
8. D3×#3717C2direct (N × H)
15. C2×C3×#634C22semidirect
17. C2×C32×Dic6C22semidirect
24. C3×D3×Dic6C22semidirect
25. C2×C3×C3⋊(C3⋊C8)C22semidirect
26. C2×C32×C3⋊C8C22semidirect
27. #88811C22semidirect
28. #88797C22semidirect
29. #88795C22semidirect
30. C3×#3717C22semidirect
31. C3×D3×C3⋊C8C22semidirect
38. C2×D3×Dic6D3semidirect
54. C2×#3717D3direct (N × H)
57. C2×D3×C3⋊C8D3semidirect
71. C3×#634C23semidirect
77. C32×Dic6C23semidirect
81. C3×C3⋊(C3⋊C8)C23semidirect
82. C32×C3⋊C8C23semidirect
103. C2×#634C2×D3semidirect
122. C2×C3×Dic6C2×D3semidirect
123. C2×C3×Dic6C2×D3semidirect
136. D3×Dic6C2×D3semidirect
139. C2×C3⋊(C3⋊C8)C2×D3semidirect
147. C2×C3×C3⋊C8C2×D3semidirect
148. C2×C3×C3⋊C8C2×D3semidirect
158. #3717C2×D3direct (N × H)
161. D3×C3⋊C8C2×D3semidirect
167. C2×C32×D3SD16semidirect
257. #634C22×D3semidirect
293. C3×Dic6C22×D3semidirect
294. C3×Dic6C22×D3semidirect
301. C3⋊(C3⋊C8)C22×D3semidirect
306. C3×C3⋊C8C22×D3semidirect
307. C3×C3⋊C8C22×D3semidirect
309. C2×C33C2×SD16semidirect
313. C32×D3C2×SD16semidirect
364. C2×Dic6D32semidirect
382. C2×C3⋊C8D32semidirect
424. C2×C3×D3#204semidirect
425. C2×C3×D3#215semidirect
465. C33C22×SD16semidirect
563. Dic6C2×D32semidirect
571. C3⋊C8C2×D32semidirect
581. C2×C32C2×#204semidirect
582. C2×C32D3×SD16semidirect
583. C2×C32C2×#215semidirect
599. C3×D3C2×#204semidirect
600. C3×D3C2×#215semidirect
660. C2×D3#3717direct (N × H)
692. C32C22×#204semidirect
693. C32C2×D3×SD16semidirect
694. C32C22×#215semidirect
731. C2×C3D3×#204semidirect
732. C2×C3C2×#3717semidirect
733. C2×C3D3×#215semidirect
747. D3C2×#3717direct (N × H)
765. C3C2×D3×#204semidirect
766. C3C22×#3717semidirect
767. C3C2×D3×#215semidirect
771. C2D3×#3717direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊(C3⋊D3)2
C2×C3×D3×Dic62
C2×#888112
C2×#887972
C2×#887952
C2×C3×#37172
C2×C3×D3×C3⋊C82
D3×#37172
C2×D3×#2153
C22×#37173
C2×D3×#2043