Finite Group Databasebeta

← C2×D3×#3715 #13170546

Subgroups — C2×D3×#3715 #13170546

Order 1728.

1426 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D12C211yesmaximal, characteristic
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#88811C211yesmaximal, characteristic, complemented
4C2×#88793C211yesmaximal, characteristic, complemented
5C2×#88792C211yesmaximal, characteristic, complemented
6C2×D3×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C2×C3×#3715C211yesmaximal, characteristic, complemented
8D3×#3715C218yesmaximal, direct product factor
9C2×D3×#215—31nomaximal
10C2×D3×#214—31nomaximal
11C22×#3715—31nomaximal
12C22×C3×D32—21no—
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×#634C2211yescharacteristic, complemented
15C2×C32×D12C2211yescharacteristic
16C2×C32×C4×D3C2211yescharacteristic
17C2×C32×Dic6C2211yescharacteristic, complemented
18C2×C3×#627—21no—
19C2×C3×#626—21no—
20C2×C3×D3×Dic3—21no—
21C3×D3×D12—22no—
22C3×D3×D12C2214yes—
23C3×D3×Dic6—22no—
24C3×D3×Dic6C2214yescomplemented
25C2×C3⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
26C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
27#88811C2214yescomplemented
28#88793C2214yescomplemented
29#88792C2214yescomplemented
30D3×C3⋊(C3⋊C8)C2214yescomplemented
31C3×#3715C2214yescomplemented
32C2×C3×D3×Q8—31no—
33C2×C3×D3×D4—31no—
34C22×C3×D12—31no—
35C22×C3×Dic6—31no—
36C2×D3×D12D311yescharacteristic
37C2×D3×Dic6D311yescharacteristic, complemented
38C2×#3755—31no—
39C2×#3754—31no—
40C22×C3⋊(C3⋊C8)—31no—
41C2×C3×#215—31no—
42C2×C3×#214—31no—
43D3×#215—38no—
44D3×#214—38no—
45C2×#3717—31no—
46C2×#3716—31no—
47C2×#3715—31no—
48C2×#3715—31no—
49C2×#3715—31no—
50C2×#3715—31no—
51C2×#3715—31no—
52C2×#3715—38no—
53C2×#3715—61no—
54C2×#3715—61no—
55C2×#3715D311yescharacteristic, direct product factor
56C2×D3×C3⋊C8—31no—
57C2×D3×C3⋊C8—31no—
58C2×D3×C3⋊C8—61no—
59C22×C3×C3⋊D3—21no—
60C22×C32×D3—21no—
61C22×C32×D3D411yescharacteristic
62C2×C3×D32—24no—
63C2×C3×D32—44no—
64C2×C33×C4C2311yescharacteristic
65C2×C3×C3⋊Dic3—21no—
66C3×C4⋊(C3⋊D3)—21no—
67C3×C4⋊(C3⋊D3)C2312yes—
68C3×#634—21no—
69C3×#634C2312yescomplemented
70C2×C32×Dic3—21no—
71C2×C32×Dic3D411yescharacteristic
72C32×D12—21no—
73C32×D12C2312yes—
74C32×C4×D3D412yes—
75C32×C4×D3C2312yes—
76C32×Dic6—21no—
77C32×Dic6C2312yescomplemented
78C3×#627—24no—
79C3×#626—24no—
80C3×D3×Dic3—24no—
81C3⋊(C3⋊(C3⋊C8))C2312yescomplemented
82C3×C3⋊(C3⋊C8)C2312yescomplemented
83C22×#215—91no—
84C22×#214—91no—
85C2×D3×SD16—91no—
86C23×C3×D3—61no—
87C23×C3×D3—61no—
88C22×D32—21no—
89C2×C32×Q8—31no—
90C2×C32×D4—31no—
91C22×C32×C4—31no—
92C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
93C2×#634C2×D311yescharacteristic, complemented
94C2×C3×#67—61no—
95C22×C3×Dic3—61no—
96C3×D3×Q8—34no—
97C3×D3×Q8—62no—
98C3×D3×D4—34no—
99C3×D3×D4—62no—
100C2×C3×D12—21no—
101C2×C3×D12—31no—
102C2×C3×D12—31no—
103C2×C3×D12—34no—
104C2×C3×D12—62no—
105C2×C3×D12—61no—
106C2×C3×D12—61no—
107C2×C3×D12C2×D311yescharacteristic
108C2×C3×D12C2×D311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—61no—
111C2×C3×C4×D3C2×D311yescharacteristic
112C2×C3×C4×D3C2×D311yescharacteristic
113C2×C3×Dic6—21no—
114C2×C3×Dic6—31no—
115C2×C3×Dic6—31no—
116C2×C3×Dic6—34no—
117C2×C3×Dic6—62no—
118C2×C3×Dic6—61no—
119C2×C3×Dic6—61no—
120C2×C3×Dic6—61no—
121C2×C3×Dic6C2×D311yescharacteristic, complemented
122C2×C3×Dic6C2×D311yescharacteristic, complemented
123C2×#627—21no—
124C2×#626—21no—
125C2×D3×Dic3—21no—
126D3×D12—22no—
127D3×D12C2×D314yes—
128D3×Dic6—22no—
129D3×Dic6C2×D314yescomplemented
130#3755—34no—
131#3754—34no—
132C2×C3⋊(C3⋊C8)—31no—
133C2×C3⋊(C3⋊C8)—31no—
134C2×C3⋊(C3⋊C8)—31no—
135C2×C3⋊(C3⋊C8)—34no—
136C2×C3⋊(C3⋊C8)—61no—
137C2×C3⋊(C3⋊C8)—61no—
138C2×C3⋊(C3⋊C8)—61no—
139C2×C3⋊(C3⋊C8)—121no—
140C2×C3⋊(C3⋊C8)C2×D311yescharacteristic, complemented
141C3×#215—34no—
142C3×#214—34no—
143C2×C3×C3⋊C8—31no—
144C2×C3×C3⋊C8—31no—
145C2×C3×C3⋊C8—61no—
146#3717—34no—
147#3716—34no—
148#3715—34no—
149#3715—34no—
150#3715—34no—
151#3715—34no—
152#3715—34no—
153#3715—64no—
154#3715—64no—
155#3715C2×D314yesdirect product factor
156D3×C3⋊C8—34no—
157D3×C3⋊C8—34no—
158D3×C3⋊C8—64no—
159C22×C33C2×D411yescharacteristic
160C2×C3×C3⋊D3—22no—
161C2×C3×C3⋊D3—42no—
162C2×C32×D3—22no—
163C2×C32×D3—42no—
164C2×C32×D3SD1614yescomplemented
165C2×C32×D3C2×D412yes—
166C3×D32—48no—
167C33×C4C2×D411yescharacteristic
168C33×C4C2411yescharacteristic
169C3×C3⋊Dic3—22no—
170C32×Dic3—22no—
171C32×Dic3C2×D412yes—
172C22×C3×Q8—91no—
173C22×C3×D4—91no—
174C2×D3×Q8—31no—
175C2×D3×D4—31no—
176C22×D12—31no—
177C22×Dic6—31no—
178C2×C3×SD16—91no—
179C2×#215—31no—
180C2×#215—91no—
181C2×#215—98no—
182C2×#215—91no—
183C2×#215—91no—
184C2×#215—91no—
185C2×#215—181no—
186C2×#214—31no—
187C2×#214—91no—
188C2×#214—98no—
189C2×#214—91no—
190C2×#214—91no—
191C2×#214—91no—
192C2×#214—181no—
193C22×C3⋊C8—91no—
194C22×C3⋊C8—91no—
195C22×C3⋊C8—181no—
196D3×SD16—98no—
197C2×#204—91no—
198C2×D3×C8—91no—
199C23×C32—31no—
200C23×C32—61no—
201C22×C3⋊D3—21no—
202C22×C3×D3—21no—
203C22×C3×D3—21no—
204C22×C3×D3—21no—
205C22×C3×D3—41no—
206C22×C3×D3—64no—
207C22×C3×D3—61no—
208C22×C3×D3—61no—
209C22×C3×D3—64no—
210C22×C3×D3—121no—
211C22×C3×D3—124no—
212C22×C3×D3—124no—
213C22×C3×D3#6711yescharacteristic
214C22×C3×D3#6711yescharacteristic
215C2×D32—24no—
216C2×D32—44no—
217C32×Q8—32no—
218C32×Q8—61no—
219C32×D4—32no—
220C32×D4—61no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—31no—
225C2×C32×C4—32no—
226C2×C32×C4—32no—
227C2×C32×C4—41no—
228C2×C32×C4—61no—
229C2×C32×C4C22×D311yescharacteristic
230C2×C32×C4C22×D311yescharacteristic
231C2×C32×C4C22×D311yescharacteristic
232C2×C3⋊Dic3—21no—
233C4⋊(C3⋊D3)—21no—
234C4⋊(C3⋊D3)C22×D312yes—
235#634—21no—
236#634C22×D312yescomplemented
237C3×#67—64no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—41no—
242C2×C3×Dic3—64no—
243C2×C3×Dic3—61no—
244C2×C3×Dic3—61no—
245C2×C3×Dic3—121no—
246C2×C3×Dic3#6711yescharacteristic
247C2×C3×Dic3#6711yescharacteristic
248C3×D12—21no—
249C3×D12—21no—
250C3×D12—22no—
251C3×D12—32no—
252C3×D12—32no—
253C3×D12—41no—
254C3×D12—62no—
255C3×D12—64no—
256C3×D12—61no—
257C3×D12—61no—
258C3×D12—121no—
259C3×D12C22×D312yes—
260C3×D12C22×D312yes—
261C3×C4×D3—22no—
262C3×C4×D3—22no—
263C3×C4×D3—64no—
264C3×C4×D3#6712yes—
265C3×C4×D3#6712yes—
266C3×C4×D3C22×D312yes—
267C3×C4×D3C22×D312yes—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—22no—
271C3×Dic6—32no—
272C3×Dic6—32no—
273C3×Dic6—41no—
274C3×Dic6—62no—
275C3×Dic6—64no—
276C3×Dic6—61no—
277C3×Dic6—61no—
278C3×Dic6—64no—
279C3×Dic6—121no—
280C3×Dic6C22×D312yescomplemented
281C3×Dic6C22×D312yescomplemented
282#627—24no—
283#626—24no—
284D3×Dic3—24no—
285C3⋊(C3⋊C8)—32no—
286C3⋊(C3⋊C8)—32no—
287C3⋊(C3⋊C8)—32no—
288C3⋊(C3⋊C8)—62no—
289C3⋊(C3⋊C8)—62no—
290C3⋊(C3⋊C8)—62no—
291C3⋊(C3⋊C8)—122no—
292C3⋊(C3⋊C8)C22×D312yescomplemented
293C3×C3⋊C8—32no—
294C3×C3⋊C8—32no—
295C3×C3⋊C8—62no—
296C22×SD16—271noSylow
297C2×C33C2×SD1612yescomplemented
298C2×C33C22×D411yescharacteristic
299C3×C3⋊D3—42no—
300C32×D3—42no—
301C32×D3C2×SD1614yescomplemented
302C24×C3—181no—
303C23×D3—61no—
304C23×D3—61no—
305C2×C3×Q8—31no—
306C2×C3×Q8—31no—
307C2×C3×Q8—61no—
308C2×C3×Q8—94no—
309C2×C3×Q8—91no—
310C2×C3×Q8—181no—
311C2×C3×Q8—182no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—61no—
315C2×C3×D4—94no—
316C2×C3×D4—91no—
317C2×C3×D4—182no—
318C2×C3×D4—181no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—61no—
322C22×C3×C4—181no—
323C2×#67—61no—
324C22×Dic3—61no—
325D3×Q8—34no—
326D3×Q8—62no—
327D3×D4—34no—
328D3×D4—62no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—34no—
332C2×D12—61no—
333C2×D12—62no—
334C2×D12—61no—
335C2×D12D3211yescharacteristic
336C2×C4×D3—61no—
337C2×C4×D3D3211yescharacteristic
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—34no—
341C2×Dic6—61no—
342C2×Dic6—62no—
343C2×Dic6—61no—
344C2×Dic6—61no—
345C2×Dic6D3211yescharacteristic, complemented
346C3×SD16—94no—
347C2×C3×C8—91no—
348#215—34no—
349#215—94no—
350#215—94no—
351#215—94no—
352#215—94no—
353#215—184no—
354#214—34no—
355#214—94no—
356#214—94no—
357#214—94no—
358#214—94no—
359#214—184no—
360C2×C3⋊C8—31no—
361C2×C3⋊C8—31no—
362C2×C3⋊C8—61no—
363C2×C3⋊C8—94no—
364C2×C3⋊C8—94no—
365C2×C3⋊C8—91no—
366C2×C3⋊C8—91no—
367C2×C3⋊C8—91no—
368C2×C3⋊C8—184no—
369C2×C3⋊C8—181no—
370C2×C3⋊C8—181no—
371C2×C3⋊C8—181no—
372C2×C3⋊C8—361no—
373#204—94no—
374D3×C8—94no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—34no—
379C22×C32—32no—
380C22×C32—41no—
381C22×C32—62no—
382C22×C32—122no—
383C22×C32D3×D411yescharacteristic
384C22×C32C2×#6711yescharacteristic
385C22×C32C2×#6711yescharacteristic
386C2×C3⋊D3—22no—
387C2×C3⋊D3—42no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—24no—
391C2×C3×D3—22no—
392C2×C3×D3—42no—
393C2×C3×D3—42no—
394C2×C3×D3—42no—
395C2×C3×D3—62no—
396C2×C3×D3—62no—
397C2×C3×D3—82no—
398C2×C3×D3—122no—
399C2×C3×D3—128no—
400C2×C3×D3—122no—
401C2×C3×D3—122no—
402C2×C3×D3—128no—
403C2×C3×D3—242no—
404C2×C3×D3#21414yescomplemented
405C2×C3×D3#21514yescomplemented
406C2×C3×D3C2×#6712yes—
407C2×C3×D3C2×#6712yes—
408D32—48no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—32no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4—62no—
419C32×C4D3×D411yescharacteristic
420C32×C4C2×#6711yescharacteristic
421C32×C4C2×#6711yescharacteristic
422C32×C4C23×D311yescharacteristic
423C32×C4C23×D311yescharacteristic
424C32×C4C23×D311yescharacteristic
425C3⋊Dic3—22no—
426C3×Dic3—22no—
427C3×Dic3—22no—
428C3×Dic3—22no—
429C3×Dic3—42no—
430C3×Dic3—62no—
431C3×Dic3—62no—
432C3×Dic3—122no—
433C3×Dic3C2×#6712yes—
434C3×Dic3C2×#6712yes—
435C22×Q8—91no—
436C22×D4—91no—
437C2×SD16—91no—
438C2×SD16—271no—
439C2×SD16—278no—
440C2×SD16—271no—
441C2×SD16—271no—
442C22×C8—271no—
443C33C22×SD1611yescharacteristic, complemented, Sylow
444C23×C3—31no—
445C23×C3—31no—
446C23×C3—61no—
447C23×C3—61no—
448C23×C3—61no—
449C23×C3—121no—
450C23×C3—184no—
451C23×C3—181no—
452C23×C3—364no—
453C22×D3—21no—
454C22×D3—64no—
455C22×D3—61no—
456C22×D3—61no—
457C22×D3—64no—
458C22×D3—121no—
459C22×D3—124no—
460C22×D3—124no—
461C22×D3#62511yescharacteristic
462C3×Q8—32no—
463C3×Q8—32no—
464C3×Q8—62no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—92no—
468C3×Q8—121no—
469C3×Q8—184no—
470C3×Q8—181no—
471C3×D4—32no—
472C3×D4—32no—
473C3×D4—62no—
474C3×D4—61no—
475C3×D4—61no—
476C3×D4—92no—
477C3×D4—121no—
478C3×D4—184no—
479C3×D4—181no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—41no—
490C2×C3×C4—62no—
491C2×C3×C4—62no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—121no—
496C2×C3×C4—184no—
497C2×C3×C4—181no—
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C2×D3211yescharacteristic
500C2×C3×C4C2×D3211yescharacteristic
501#67—64no—
502C2×Dic3—21no—
503C2×Dic3—64no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—121no—
507C2×Dic3#62511yescharacteristic
508D12—21no—
509D12—32no—
510D12—32no—
511D12—62no—
512D12—64no—
513D12—61no—
514D12—61no—
515D12—121no—
516D12C2×D3212yes—
517C4×D3—64no—
518C4×D3#62512yes—
519C4×D3C2×D3212yes—
520Dic6—21no—
521Dic6—32no—
522Dic6—32no—
523Dic6—62no—
524Dic6—64no—
525Dic6—61no—
526Dic6—61no—
527Dic6—64no—
528Dic6—121no—
529Dic6C2×D3212yescomplemented
530C3×C8—92no—
531C3⋊C8—32no—
532C3⋊C8—32no—
533C3⋊C8—62no—
534C3⋊C8—92no—
535C3⋊C8—92no—
536C3⋊C8—92no—
537C3⋊C8—182no—
538C3⋊C8—182no—
539C3⋊C8—182no—
540C3⋊C8—362no—
541C2×C32—21no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—22no—
545C2×C32—22no—
546C2×C32—22no—
547C2×C32—34no—
548C2×C32—42no—
549C2×C32—41no—
550C2×C32—122no—
551C2×C32D3×SD1612yescomplemented
552C2×C32C2×#21412yescomplemented
553C2×C32C2×#21512yescomplemented
554C2×C32C2×D3×D411yescharacteristic
555C2×C32C22×#6711yescharacteristic
556C2×C32C22×#6711yescharacteristic
557C3⋊D3—42no—
558C3×D3—24no—
559C3×D3—42no—
560C3×D3—42no—
561C3×D3—82no—
562C3×D3—122no—
563C3×D3—122no—
564C3×D3—242no—
565C3×D3C2×#21414yescomplemented
566C3×D3C2×#21514yescomplemented
567C24—181no—
568C2×Q8—31no—
569C2×Q8—94no—
570C2×Q8—91no—
571C2×Q8—181no—
572C2×Q8—182no—
573C2×D4—31no—
574C2×D4—94no—
575C2×D4—91no—
576C2×D4—182no—
577C2×D4—181no—
578C22×C4—31no—
579C22×C4—181no—
580SD16—94no—
581SD16—274no—
582SD16—274no—
583SD16—274no—
584C2×C8—91no—
585C2×C8—274no—
586C2×C8—271no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—32no—
591C22×C3—32no—
592C22×C3—34no—
593C22×C3—34no—
594C22×C3—41no—
595C22×C3—62no—
596C22×C3—64no—
597C22×C3—62no—
598C22×C3—62no—
599C22×C3—122no—
600C22×C3—122no—
601C22×C3—122no—
602C22×C3—182no—
603C22×C3—242no—
604C22×C3—368no—
605C22×C3—362no—
606C22×C3C2×#62511yescharacteristic
607C22×C3D3×#6711yescharacteristic
608C22×C3D3×#6711yescharacteristic
609C2×D3—22no—
610C2×D3—42no—
611C2×D3—62no—
612C2×D3—62no—
613C2×D3—122no—
614C2×D3—128no—
615C2×D3—122no—
616C2×D3—122no—
617C2×D3—128no—
618C2×D3—242no—
619C2×D3#371514yesdirect product factor
620C2×D3C2×#62512yes—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—32no—
628C3×C4—32no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—62no—
632C3×C4—62no—
633C3×C4—62no—
634C3×C4—122no—
635C3×C4—182no—
636C3×C4C2×#62511yescharacteristic
637C3×C4D3×#6711yescharacteristic
638C3×C4D3×#6711yescharacteristic
639C3×C4C22×D3211yescharacteristic
640C3×C4C22×D3211yescharacteristic
641C3×C4C22×D3211yescharacteristic
642Dic3—22no—
643Dic3—62no—
644Dic3—62no—
645Dic3—122no—
646Dic3C2×#62512yes—
647C32—21no—
648C32—21no—
649C32—21no—
650C32—41no—
651C32C2×D3×SD1611yescharacteristic, complemented
652C32C22×#21411yescharacteristic, complemented
653C32C22×#21511yescharacteristic, complemented
654C23—31no—
655C23—61no—
656C23—184no—
657C23—181no—
658C23—364no—
659Q8—32no—
660Q8—61no—
661Q8—92no—
662Q8—184no—
663Q8—181no—
664D4—32no—
665D4—61no—
666D4—92no—
667D4—184no—
668D4—181no—
669C2×C4—31no—
670C2×C4—32no—
671C2×C4—32no—
672C2×C4—61no—
673C2×C4—184no—
674C2×C4—181no—
675C2×C4D3311yescharacteristic
676C8—92no—
677C8—272no—
678C2×C3—22no—
679C2×C3—22no—
680C2×C3—22no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—34no—
685C2×C3—34no—
686C2×C3—42no—
687C2×C3—41no—
688C2×C3—64no—
689C2×C3—122no—
690C2×C3—122no—
691C2×C3—242no—
692C2×C3—362no—
693C2×C3C2×#371512yescomplemented
694C2×C3D3×#21412yescomplemented
695C2×C3D3×#21512yescomplemented
696C2×C3C22×#62511yescharacteristic
697C2×C3C2×D3×#6711yescharacteristic
698C2×C3C2×D3×#6711yescharacteristic
699D3—42no—
700D3—122no—
701D3—122no—
702D3—242no—
703D3C2×#371514yesdirect product factor
704C22—34no—
705C22—32no—
706C22—62no—
707C22—122no—
708C22—182no—
709C22—368no—
710C22—362no—
711C22D3×#62511yescharacteristic
712C4—32no—
713C4—62no—
714C4—182no—
715C4D3×#62511yescharacteristic
716C4C2×D3311yescharacteristic
717C3—21no—
718C3—21no—
719C3—21no—
720C3—41no—
721C3C22×#371511yescharacteristic, complemented
722C3C2×D3×#21411yescharacteristic, complemented
723C3C2×D3×#21511yescharacteristic, complemented
724C2—34no—
725C2—122no—
726C2—362no—
727C2D3×#371512yesdirect product factor
728C2C2×D3×#62511yescharacteristic
subgroupG/H
centerC22D3×#625
commutator, cosocleC33×C4C24
FrattiniC4C2×D33
FittingC2×C33×C4C23
socleC22×C33C2×D4
prime radicalC2×C3×D3×D12C2
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×#88793C2semidirect
5. C2×#88792C2semidirect
6. C2×D3×C3⋊(C3⋊C8)C2semidirect
7. C2×C3×#3715C2semidirect
8. D3×#3715C2direct (N × H)
14. C2×C3×#634C22semidirect
17. C2×C32×Dic6C22semidirect
24. C3×D3×Dic6C22semidirect
25. C2×C3⋊(C3⋊(C3⋊C8))C22semidirect
26. C2×C3×C3⋊(C3⋊C8)C22semidirect
27. #88811C22semidirect
28. #88793C22semidirect
29. #88792C22semidirect
30. D3×C3⋊(C3⋊C8)C22semidirect
31. C3×#3715C22semidirect
37. C2×D3×Dic6D3semidirect
55. C2×#3715D3direct (N × H)
69. C3×#634C23semidirect
77. C32×Dic6C23semidirect
81. C3⋊(C3⋊(C3⋊C8))C23semidirect
82. C3×C3⋊(C3⋊C8)C23semidirect
93. C2×#634C2×D3semidirect
121. C2×C3×Dic6C2×D3semidirect
122. C2×C3×Dic6C2×D3semidirect
129. D3×Dic6C2×D3semidirect
140. C2×C3⋊(C3⋊C8)C2×D3semidirect
155. #3715C2×D3direct (N × H)
164. C2×C32×D3SD16semidirect
236. #634C22×D3semidirect
280. C3×Dic6C22×D3semidirect
281. C3×Dic6C22×D3semidirect
292. C3⋊(C3⋊C8)C22×D3semidirect
297. C2×C33C2×SD16semidirect
301. C32×D3C2×SD16semidirect
345. C2×Dic6D32semidirect
404. C2×C3×D3#214semidirect
405. C2×C3×D3#215semidirect
443. C33C22×SD16semidirect
529. Dic6C2×D32semidirect
551. C2×C32D3×SD16semidirect
552. C2×C32C2×#214semidirect
553. C2×C32C2×#215semidirect
565. C3×D3C2×#214semidirect
566. C3×D3C2×#215semidirect
619. C2×D3#3715direct (N × H)
651. C32C2×D3×SD16semidirect
652. C32C22×#214semidirect
653. C32C22×#215semidirect
693. C2×C3C2×#3715semidirect
694. C2×C3D3×#214semidirect
695. C2×C3D3×#215semidirect
703. D3C2×#3715direct (N × H)
721. C3C22×#3715semidirect
722. C3C2×D3×#214semidirect
723. C3C2×D3×#215semidirect
727. C2D3×#3715direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D3×D122
C2×C3×D3×Dic62
C2×#888112
C2×#887932
C2×#887922
C2×D3×C3⋊(C3⋊C8)2
C2×C3×#37152
D3×#37152
C2×D3×#2153
C2×D3×#2143
C22×#37153