Finite Group Databasebeta

← C3×#10591163 #13158342

Subgroups — C3×#10591163 #13158342

Order 1728.

1010 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic, complemented
2C3×#64139C211yesmaximal, characteristic, complemented
3C2×C3×#3717C211yesmaximal, characteristic, complemented
4C2×C3×#3714C211yesmaximal, characteristic, complemented
5C32×#830C211yesmaximal, characteristic, complemented
6C3×#63566C211yesmaximal, characteristic, complemented
7C3×#63563C211yesmaximal, characteristic, complemented
8C3×#5238—31nomaximal
9C3×#4734—31nomaximal
10#10591163C311yesmaximal, characteristic, direct product factor
11C22×C33×C4C2211yescharacteristic
12C2×C3×#638—21no—
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C32×#67—21no—
15C32×#235—22no—
16C32×#235—22no—
17C2×C32×D12C2211yescharacteristic
18C2×C32×C4×D3—21no—
19C2×C32×Dic6C2211yescharacteristic
20C3×#3752—21no—
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C32×C3⋊C8C2211yescharacteristic
23C2×C32×C3⋊C8C2211yescharacteristic
24C3×#3717—22no—
25C3×#3714—22no—
26C2×C32×#41—31no—
27C2×C3×#235—21no—
28C2×C3×#235D311yescharacteristic, complemented
29C2×C3×#235C2×C311yescharacteristic, complemented
30#64139C2×C311yescharacteristic, complemented
31C2×C3×#215—31no—
32C2×C3×#213—31no—
33C3×#930—31no—
34C3×#930—31no—
35C3×#930—61no—
36C2×C3×D24—31no—
37C2×C3×#204—31no—
38C2×#3717C2×C311yescharacteristic, complemented
39C2×#3714C2×C311yescharacteristic, complemented
40C32×C22⋊C8—31no—
41C3×#835—31no—
42C3×#832—31no—
43C3×#830—21no—
44C3×#830D311yescharacteristic, complemented
45C3×#830C2×C311yescharacteristic, complemented
46C3×#821—31no—
47C3×#816—31no—
48#63566C2×C311yescharacteristic, complemented
49#63563C2×C311yescharacteristic, complemented
50C23×C33D411yescharacteristic
51C22×C3×C3⋊D3—21no—
52C22×C32×D3—21no—
53C2×C33×C4—21no—
54C2×C33×C4—21no—
55C2×C33×C4D411yescharacteristic
56C2×C33×C4C2311yescharacteristic
57C3×#638—42no—
58C2×C3×C3⋊Dic3—21no—
59C3×C4⋊(C3⋊D3)—21no—
60C3×C4⋊(C3⋊D3)—21no—
61C32×#67—24no—
62C2×C32×Dic3—21no—
63C32×D12—21no—
64C32×D12D412yescomplemented
65C32×C4×D3—24no—
66C32×Dic6—21no—
67C32×Dic6D412yescomplemented
68C32×C3⋊C8—21no—
69C32×C3⋊C8—21no—
70C3×#449—91no—
71#5238—31no—
72#4734—31no—
73C32×#41—62no—
74C32×#41—62no—
75C2×C32×Q8—31no—
76C2×C32×D4—31no—
77C2×C32×D4—61no—
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C22×C32×C4—21no—
81C22×C32×C4—41no—
82C22×C32×C4—61no—
83C22×C32×C4C2×D311yescharacteristic
84C22×C32×C4C2×D311yescharacteristic
85C22×C32×C4C22×C311yescharacteristic
86C2×#638—21no—
87C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
88C2×C3×#67—22no—
89C2×C3×#67—21no—
90C2×C3×#67—21no—
91C2×C3×#67—62no—
92C2×C3×#67—61no—
93C2×C3×#67—61no—
94C3×#235—24no—
95C3×#235—24no—
96C3×#235—22no—
97C3×#235—22no—
98C3×#235—22no—
99C3×#235—22no—
100C2×C3×D12—21no—
101C2×C3×D12—31no—
102C2×C3×D12—31no—
103C2×C3×D12—61no—
104C2×C3×D12C2×D311yescharacteristic
105C2×C3×D12C22×C311yescharacteristic
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2×D311yescharacteristic
111C2×C3×Dic6C22×C311yescharacteristic
112C2×C32×C8—31no—
113C2×C32×C8—31no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C22×C311yescharacteristic
116C3×#215—62no—
117C3×#213—62no—
118C3×(C2×D3)⋊C4—62no—
119C3×(C2×D3)⋊C4—61no—
120C3×(C2×D3)⋊C4—61no—
121C3×C4⋊Dic3—31no—
122C3×C4⋊Dic3—31no—
123C3×C4⋊Dic3—61no—
124C2×C3×C3⋊C8—21no—
125C2×C3×C3⋊C8—21no—
126C2×C3×C3⋊C8C2×D311yescharacteristic
127C2×C3×C3⋊C8C2×D311yescharacteristic
128C2×C3×C3⋊C8C22×C311yescharacteristic
129C2×C3×C3⋊C8C22×C311yescharacteristic
130C3×D24—62no—
131C3×#204—62no—
132#3717—22no—
133#3714—22no—
134C22×C33—21no—
135C22×C33—21no—
136C22×C33—21no—
137C22×C33C2×D411yescharacteristic
138C2×C3×C3⋊D3—41no—
139C2×C3×C3⋊D3—41no—
140C2×C3×C3⋊D3—41no—
141C2×C32×D3—22no—
142C2×C32×D3—41no—
143C2×C32×D3—41no—
144C33×C4—21no—
145C33×C4C2×D411yescharacteristic
146C33×C4C2×D411yescharacteristic
147C3×C3⋊Dic3—41no—
148C32×Dic3—22no—
149C2×C3×#41—31no—
150C2×C3×#41—31no—
151C2×C3×#41—61no—
152C2×#235C3×D311yescharacteristic, complemented
153C2×C3×SD16—91no—
154C2×C3×D8—91no—
155C3×#121—91no—
156C2×#215—31no—
157C2×#213—31no—
158#930—31no—
159#930—31no—
160#930—61no—
161C2×D24—31no—
162C2×#204—31no—
163C3×#103—91no—
164C3×#102—91no—
165C3×C22⋊C8—31no—
166C3×C22⋊C8—31no—
167C3×C22⋊C8—61no—
168#835—31no—
169#832—31no—
170#830C3×D311yescharacteristic, complemented
171#821—31no—
172#816—31no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—41no—
177C23×C32—61no—
178C23×C32D1211yescharacteristic
179C23×C32#6711yescharacteristic
180C23×C32C3×D411yescharacteristic
181C22×C3⋊D3—21no—
182C22×C3×D3—22no—
183C22×C3×D3—21no—
184C22×C3×D3—21no—
185C22×C3×D3—62no—
186C22×C3×D3—61no—
187C22×C3×D3—61no—
188C32×Q8—32no—
189C32×Q8—61no—
190C32×D4—32no—
191C32×D4—64no—
192C32×D4—61no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—22no—
196C2×C32×C4—22no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—21no—
207C2×C32×C4—41no—
208C2×C32×C4—41no—
209C2×C32×C4—41no—
210C2×C32×C4—41no—
211C2×C32×C4—41no—
212C2×C32×C4—41no—
213C2×C32×C4—42no—
214C2×C32×C4—42no—
215C2×C32×C4—64no—
216C2×C32×C4—61no—
217C2×C32×C4D1211yescharacteristic
218C2×C32×C4#6711yescharacteristic
219C2×C32×C4C3×D411yescharacteristic
220C2×C32×C4C22×D311yescharacteristic
221C2×C32×C4C22×D311yescharacteristic
222C2×C32×C4C23×C311yescharacteristic
223#638—42no—
224C2×C3⋊Dic3—21no—
225C4⋊(C3⋊D3)—21no—
226C4⋊(C3⋊D3)—21no—
227C3×#67—28no—
228C3×#67—24no—
229C3×#67—24no—
230C3×#67—124no—
231C3×#67—122no—
232C3×#67—122no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—62no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3—61no—
239C3×D12—22no—
240C3×D12—21no—
241C3×D12—21no—
242C3×D12—22no—
243C3×D12—61no—
244C3×D12—61no—
245C3×D12—61no—
246C3×D12—61no—
247C3×D12—121no—
248C3×D12—121no—
249C3×D12#6712yescomplemented
250C3×D12C3×D412yescomplemented
251C3×C4×D3—28no—
252C3×C4×D3—24no—
253C3×C4×D3—24no—
254C3×Dic6—22no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—22no—
258C3×Dic6#6712yescomplemented
259C3×Dic6C3×D412yescomplemented
260C32×C8—61no—
261C32×C8—61no—
262C3×C3⋊C8—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265C3×C3⋊C8—21no—
266C3×C3⋊C8—41no—
267C3×C3⋊C8—41no—
268#449—91noSylow
269C2×C33—41no—
270C2×C33#12011yescharacteristic
271C2×C33#13511yescharacteristic
272C2×C33AGL(1,ℤ/8)11yescharacteristic
273C3×C3⋊D3—81no—
274C32×D3—42no—
275C3×#41—62no—
276C3×#41—62no—
277C3×#41—62no—
278C3×#41—62no—
279C3×#41—64no—
280C3×#41—64no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×Q8—61no—
284C2×C3×D4—31no—
285C2×C3×D4—31no—
286C2×C3×D4—61no—
287C2×C3×D4—62no—
288C2×C3×D4—61no—
289C2×C3×D4—61no—
290C2×C3×D4—91no—
291C2×C3×D4—181no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—41no—
296C22×C3×C4—62no—
297C22×C3×C4—61no—
298C22×C3×C4—61no—
299C22×C3×C4D3211yescharacteristic
300C22×C3×C4C2×C3×D311yescharacteristic
301C22×C3×C4C2×C3×D311yescharacteristic
302C2×#67—21no—
303C2×#67—62no—
304C2×#67—61no—
305C2×#67—61no—
306#235—22no—
307#235—22no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—61no—
311C2×D12C2×C3×D311yescharacteristic
312C2×C4×D3—21no—
313C2×Dic6C2×C3×D311yescharacteristic
314C3×SD16—182no—
315C3×D8—182no—
316C2×C3×C8—31no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
319C2×C3×C8—31no—
320C2×C3×C8—61no—
321C2×C3×C8—61no—
322C3×C4⋊C4—91no—
323C3×C22⋊C4—181no—
324#215—62no—
325#213—62no—
326(C2×D3)⋊C4—62no—
327(C2×D3)⋊C4—61no—
328(C2×D3)⋊C4—61no—
329C4⋊Dic3—31no—
330C4⋊Dic3—31no—
331C4⋊Dic3—61no—
332C2×C3⋊C8C2×C3×D311yescharacteristic
333C2×C3⋊C8C2×C3×D311yescharacteristic
334D24—62no—
335#204—62no—
336C22×C32—21no—
337C22×C32—21no—
338C22×C32—21no—
339C22×C32—22no—
340C22×C32—22no—
341C22×C32—22no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—41no—
352C22×C32—41no—
353C22×C32—41no—
354C22×C32—41no—
355C22×C32—41no—
356C22×C32—41no—
357C22×C32—41no—
358C22×C32—42no—
359C22×C32—42no—
360C22×C32—42no—
361C22×C32—62no—
362C22×C32—121no—
363C22×C32—121no—
364C22×C32C2×D1211yescharacteristic
365C22×C32C2×#6711yescharacteristic
366C22×C32C2×C3×D411yescharacteristic
367C2×C3⋊D3—41no—
368C2×C3⋊D3—41no—
369C2×C3⋊D3—41no—
370C2×C3×D3—24no—
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—42no—
374C2×C3×D3—42no—
375C2×C3×D3—41no—
376C2×C3×D3—41no—
377C2×C3×D3—41no—
378C2×C3×D3—41no—
379C2×C3×D3—122no—
380C2×C3×D3—122no—
381C2×C3×D3—122no—
382C2×C3×D3—121no—
383C2×C3×D3—121no—
384C2×C3×D3—121no—
385C2×C3×D3—121no—
386C2×C3×D3—121no—
387C2×C3×D3—121no—
388C32×C4—21no—
389C32×C4—22no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—41no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4—42no—
403C32×C4—62no—
404C32×C4D3×D411yescharacteristic
405C32×C4D3×D411yescharacteristic
406C32×C4C2×#6711yescharacteristic
407C32×C4C2×#6711yescharacteristic
408C32×C4C2×C3×D411yescharacteristic
409C32×C4C2×C3×D411yescharacteristic
410C3⋊Dic3—41no—
411C3×Dic3—24no—
412C3×Dic3—22no—
413C3×Dic3—22no—
414C3×Dic3—122no—
415C3×Dic3—121no—
416C3×Dic3—121no—
417C2×#41—31no—
418C2×SD16—91no—
419C2×D8—91no—
420#121—91no—
421#103—91no—
422#102—91no—
423C22⋊C8—31no—
424C33#44911yescharacteristic, complemented, Sylow
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—41no—
429C23×C3—62no—
430C23×C3—61no—
431C23×C3—61no—
432C23×C3—181no—
433C23×C3#62611yescharacteristic
434C23×C3C3×D1211yescharacteristic
435C23×C3C3×#6711yescharacteristic
436C22×D3—21no—
437C22×D3—62no—
438C22×D3—61no—
439C22×D3—61no—
440C3×Q8—32no—
441C3×Q8—32no—
442C3×Q8—62no—
443C3×Q8—62no—
444C3×Q8—61no—
445C3×Q8—61no—
446C3×D4—32no—
447C3×D4—32no—
448C3×D4—62no—
449C3×D4—62no—
450C3×D4—68no—
451C3×D4—64no—
452C3×D4—64no—
453C3×D4—61no—
454C3×D4—61no—
455C3×D4—181no—
456C3×D4—181no—
457C3×D4—362no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—42no—
477C2×C3×C4—42no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—68no—
481C2×C3×C4—64no—
482C2×C3×C4—64no—
483C2×C3×C4—62no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—181no—
487C2×C3×C4#62611yescharacteristic
488C2×C3×C4C3×D1211yescharacteristic
489C2×C3×C4C3×#6711yescharacteristic
490C2×C3×C4C2×D3211yescharacteristic
491C2×C3×C4C22×C3×D311yescharacteristic
492C2×C3×C4C22×C3×D311yescharacteristic
493#67—24no—
494#67—124no—
495#67—122no—
496#67—122no—
497C2×Dic3—21no—
498C2×Dic3—62no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501D12—21no—
502D12—61no—
503D12—61no—
504D12—61no—
505D12—61no—
506D12—121no—
507D12—121no—
508D12C3×#6712yescomplemented
509C4×D3—24no—
510Dic6—21no—
511Dic6C3×#6712yescomplemented
512C3×C8—61no—
513C3×C8—61no—
514C3×C8—61no—
515C3×C8—61no—
516C3×C8—121no—
517C3×C8—121no—
518C3⋊C8—21no—
519C3⋊C8—21no—
520C2×C32—21no—
521C2×C32—21no—
522C2×C32—21no—
523C2×C32—21no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—41no—
530C2×C32—41no—
531C2×C32—41no—
532C2×C32—42no—
533C2×C32—42no—
534C2×C32—42no—
535C2×C32—44no—
536C2×C32—41no—
537C2×C32—41no—
538C2×C32—41no—
539C2×C32—122no—
540C2×C32#88211yescharacteristic
541C2×C32#90411yescharacteristic
542C2×C32#90811yescharacteristic
543C2×C32#94911yescharacteristic
544C2×C32#95011yescharacteristic
545C2×C32#95311yescharacteristic
546C2×C32C3×#12011yescharacteristic
547C2×C32C3×#13511yescharacteristic
548C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
549C3⋊D3—81no—
550C3×D3—44no—
551C3×D3—42no—
552C3×D3—42no—
553C3×D3—242no—
554C3×D3—241no—
555C3×D3—241no—
556#41—62no—
557#41—62no—
558C2×Q8—31no—
559C2×D4—31no—
560C2×D4—61no—
561C2×D4—91no—
562C2×D4—181no—
563C22×C4—61no—
564C22×C4C3×D3211yescharacteristic
565SD16—182no—
566D8—182no—
567C2×C8—31no—
568C2×C8—31no—
569C4⋊C4—91no—
570C22⋊C4—181no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—41no—
596C22×C3—64no—
597C22×C3—62no—
598C22×C3—62no—
599C22×C3—122no—
600C22×C3—122no—
601C22×C3—121no—
602C22×C3—121no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3—361no—
606C22×C3—361no—
607C22×C3—361no—
608C22×C3C2×#62611yescharacteristic
609C22×C3C2×C3×D1211yescharacteristic
610C22×C3C2×C3×#6711yescharacteristic
611C2×D3—22no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—122no—
615C2×D3—122no—
616C2×D3—122no—
617C2×D3—121no—
618C2×D3—121no—
619C2×D3—121no—
620C2×D3—121no—
621C2×D3—121no—
622C2×D3—121no—
623C3×C4—22no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—42no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—64no—
639C3×C4—62no—
640C3×C4—62no—
641C3×C4—361no—
642C3×C4D3×#6711yescharacteristic
643C3×C4D3×#6711yescharacteristic
644C3×C4C3×D3×D411yescharacteristic
645C3×C4C3×D3×D411yescharacteristic
646C3×C4C2×C3×#6711yescharacteristic
647C3×C4C2×C3×#6711yescharacteristic
648Dic3—22no—
649Dic3—122no—
650Dic3—121no—
651Dic3—121no—
652C32—21no—
653C32—21no—
654C32—21no—
655C32—41no—
656C32#473411yescharacteristic, complemented
657C32#523811yescharacteristic, complemented
658C32C3×#44911yescharacteristic, complemented
659C23—61no—
660C23—181no—
661C23C3×#62611yescharacteristic
662Q8—32no—
663Q8—61no—
664D4—32no—
665D4—64no—
666D4—61no—
667D4—181no—
668D4—181no—
669D4—362no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—64no—
673C2×C4—61no—
674C2×C4—181no—
675C2×C4C3×#62611yescharacteristic
676C2×C4C2×C3×D3211yescharacteristic
677C8—61no—
678C8—61no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—42no—
689C2×C3—42no—
690C2×C3—42no—
691C2×C3—44no—
692C2×C3—41no—
693C2×C3—41no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—41no—
697C2×C3—41no—
698C2×C3—124no—
699C2×C3—122no—
700C2×C3—122no—
701C2×C3—721no—
702C2×C3#6382511yescharacteristic
703C2×C3#6382911yescharacteristic
704C2×C3#6397711yescharacteristic
705C2×C3C3×#88211yescharacteristic
706C2×C3C3×#90411yescharacteristic
707C2×C3C3×#90811yescharacteristic
708C2×C3C3×#94911yescharacteristic
709C2×C3C3×#95011yescharacteristic
710C2×C3C3×#95311yescharacteristic
711D3—42no—
712D3—242no—
713D3—241no—
714D3—241no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—62no—
719C22—121no—
720C22—121no—
721C22—361no—
722C22—361no—
723C22—361no—
724C22C2×C3×#62611yescharacteristic
725C4—21no—
726C4—62no—
727C4—361no—
728C4C3×D3×#6711yescharacteristic
729C4C3×D3×#6711yescharacteristic
730C3—21no—
731C3—21no—
732C3—21no—
733C3—41no—
734C3#1059116311yescharacteristic, direct product factor
735C3C3×#473411yescharacteristic, complemented
736C3C3×#523811yescharacteristic, complemented
737C2—41no—
738C2—122no—
739C2—721no—
740C2C3×#6382511yescharacteristic
741C2C3×#6382911yescharacteristic
742C2C3×#6397711yescharacteristic
subgroupG/H
centerC22×C3C2×#626
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC22×C33×C4C22
socleC22×C33C2×D4
hypercenterC22×C3×C4D32
hypocenterC32C3×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#235C2semidirect
2. C3×#64139C2semidirect
3. C2×C3×#3717C2semidirect
4. C2×C3×#3714C2semidirect
5. C32×#830C2semidirect
6. C3×#63566C2semidirect
7. C3×#63563C2semidirect
10. #10591163C3direct (N × H)
28. C2×C3×#235D3semidirect
29. C2×C3×#235C2×C3semidirect
30. #64139C2×C3semidirect
38. C2×#3717C2×C3semidirect
39. C2×#3714C2×C3semidirect
44. C3×#830D3semidirect
45. C3×#830C2×C3semidirect
48. #63566C2×C3semidirect
49. #63563C2×C3semidirect
64. C32×D12D4semidirect
67. C32×Dic6D4semidirect
152. C2×#235C3×D3semidirect
170. #830C3×D3semidirect
249. C3×D12#67semidirect
250. C3×D12C3×D4semidirect
258. C3×Dic6#67semidirect
259. C3×Dic6C3×D4semidirect
424. C33#449semidirect
508. D12C3×#67semidirect
511. Dic6C3×#67semidirect
656. C32#4734semidirect
657. C32#5238semidirect
658. C32C3×#449semidirect
734. C3#10591163direct (N × H)
735. C3C3×#4734semidirect
736. C3C3×#5238semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C3×#641392
C2×C3×#37172
C2×C3×#37142
C32×#8302
C3×#635662
C3×#635632
C3×#52383
C3×#47343
#105911633