Finite Group Databasebeta

← C3×#10591161 #13158340

Subgroups — C3×#10591161 #13158340

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
2C32×#930C211yesmaximal, characteristic, complemented
3C2×C3×#3715C211yesmaximal, characteristic, complemented
4C2×C3×#3713C211yesmaximal, characteristic, complemented
5C3×#63657C211yesmaximal, characteristic, complemented
6C3×#63565C211yesmaximal, characteristic, complemented
7C3×#63562C211yesmaximal, characteristic, complemented
8C3×#5238—31nomaximal
9C3×#5037—31nomaximal
10#10591161C311yesmaximal, characteristic, direct product factor
11C22×C33×C4C2211yescharacteristic
12C2×C32×#67—21no—
13C2×C32×#67—21no—
14C32×#235—22no—
15C32×#235—22no—
16C2×C32×D12C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×C32×C4×D3—21no—
19C2×C32×Dic6C2211yescharacteristic
20C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
22C32×(C2×D3)⋊C4—21no—
23C32×C4⋊Dic3C2211yescharacteristic
24C3×#3715—22no—
25C3×#3713—22no—
26C2×C32×#41—31no—
27C2×C3×#235—21no—
28C2×C3×#235D311yescharacteristic, complemented
29C2×C3×#235C2×C311yescharacteristic, complemented
30C32×#121—31no—
31C2×C3×#215—31no—
32C2×C3×#214—31no—
33C2×C3×#213—31no—
34C2×C3×#213—31no—
35C3×#930—21no—
36C3×#930D311yescharacteristic, complemented
37C3×#930C2×C311yescharacteristic, complemented
38C2×#3715C2×C311yescharacteristic, complemented
39C2×#3713C2×C311yescharacteristic, complemented
40#63657C2×C311yescharacteristic, complemented
41C3×#835—31no—
42C3×#832—31no—
43C3×#830—31no—
44C3×#830—31no—
45C3×#830—61no—
46C3×#810—31no—
47C3×#809—31no—
48#63565C2×C311yescharacteristic, complemented
49#63562C2×C311yescharacteristic, complemented
50C23×C33D411yescharacteristic
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C2×C33×C4—21no—
54C2×C33×C4—21no—
55C2×C33×C4D411yescharacteristic
56C2×C33×C4C2311yescharacteristic
57C32×#67—24no—
58C32×#67—42no—
59C2×C32×Dic3—21no—
60C2×C32×Dic3—21no—
61C32×D12—21no—
62C32×D12—21no—
63C32×D12—21no—
64C32×D12D412yescomplemented
65C32×C4×D3—24no—
66C32×Dic6—21no—
67C32×Dic6D412yescomplemented
68C3×C3⋊(C3⋊C8)—21no—
69C3×C3⋊(C3⋊C8)—21no—
70C3×#449—91no—
71#5238—31no—
72#5037—31no—
73C32×#41—62no—
74C32×#41—62no—
75C2×C32×Q8—31no—
76C2×C32×D4—31no—
77C2×C32×D4—31no—
78C2×C32×D4—61no—
79C2×C32×D4—61no—
80C22×C32×C4—21no—
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4—41no—
84C22×C32×C4—61no—
85C22×C32×C4C2×D311yescharacteristic
86C22×C32×C4C2×D311yescharacteristic
87C22×C32×C4C22×C311yescharacteristic
88C2×C3×#67—22no—
89C2×C3×#67—21no—
90C2×C3×#67—21no—
91C2×C3×#67—22no—
92C2×C3×#67—21no—
93C2×C3×#67—21no—
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—21no—
102C2×C3×D12C2×D311yescharacteristic
103C2×C3×D12C2×D311yescharacteristic
104C2×C3×D12C22×C311yescharacteristic
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
112C32×C4⋊C4—31no—
113C32×C22⋊C4—61no—
114C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
115C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
116C3×#215—62no—
117C3×#214—62no—
118C3×#213—62no—
119C3×#213—62no—
120C3×(C2×D3)⋊C4—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2×D311yescharacteristic
125C3×C4⋊Dic3C22×C311yescharacteristic
126C2×C3×C3⋊C8—31no—
127C2×C3×C3⋊C8—31no—
128C2×C3×C3⋊C8—31no—
129C2×C3×C3⋊C8—31no—
130C2×C3×C3⋊C8—61no—
131C2×C3×C3⋊C8—61no—
132#3715—22no—
133#3713—22no—
134C22×C33—21no—
135C22×C33—21no—
136C22×C33—21no—
137C22×C33C2×D411yescharacteristic
138C2×C32×D3—22no—
139C2×C32×D3—41no—
140C2×C32×D3—41no—
141C2×C32×D3—41no—
142C2×C32×D3—41no—
143C2×C32×D3—41no—
144C33×C4—21no—
145C33×C4C2×D411yescharacteristic
146C33×C4C2×D411yescharacteristic
147C32×Dic3—22no—
148C32×Dic3—41no—
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—31no—
156C3×#121—31no—
157C3×#121—61no—
158C2×#215—31no—
159C2×#214—31no—
160C2×#213—31no—
161C2×#213—31no—
162#930C3×D311yescharacteristic, complemented
163C3×#103—91no—
164C3×#102—91no—
165C3×C22⋊C8—91no—
166#835—31no—
167#832—31no—
168#830—31no—
169#830—31no—
170#830—61no—
171#810—31no—
172#809—31no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32—41no—
177C23×C32—61no—
178C23×C32—61no—
179C23×C32#6711yescharacteristic
180C23×C32#6711yescharacteristic
181C23×C32C3×D411yescharacteristic
182C22×C3×D3—22no—
183C22×C3×D3—21no—
184C22×C3×D3—21no—
185C22×C3×D3—22no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C32×Q8—32no—
189C32×Q8—61no—
190C32×D4—32no—
191C32×D4—64no—
192C32×D4—61no—
193C32×D4—61no—
194C32×D4—61no—
195C32×D4—122no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—22no—
199C2×C32×C4—22no—
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—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—41no—
211C2×C32×C4—41no—
212C2×C32×C4—41no—
213C2×C32×C4—41no—
214C2×C32×C4—41no—
215C2×C32×C4—41no—
216C2×C32×C4—42no—
217C2×C32×C4—42no—
218C2×C32×C4—64no—
219C2×C32×C4—61no—
220C2×C32×C4—61no—
221C2×C32×C4#6711yescharacteristic
222C2×C32×C4#6711yescharacteristic
223C2×C32×C4C3×D411yescharacteristic
224C2×C32×C4C22×D311yescharacteristic
225C2×C32×C4C22×D311yescharacteristic
226C2×C32×C4C23×C311yescharacteristic
227C3×#67—28no—
228C3×#67—24no—
229C3×#67—24no—
230C3×#67—44no—
231C3×#67—42no—
232C3×#67—42no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C3×D12—22no—
240C3×D12—21no—
241C3×D12—21no—
242C3×D12—21no—
243C3×D12—21no—
244C3×D12—21no—
245C3×D12—21no—
246C3×D12—22no—
247C3×D12—41no—
248C3×D12—41no—
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
260C3⋊(C3⋊C8)—21no—
261C3⋊(C3⋊C8)—21no—
262C3×C3⋊C8—61no—
263C3×C3⋊C8—61no—
264C3×C3⋊C8—61no—
265C3×C3⋊C8—61no—
266C3×C3⋊C8—121no—
267C3×C3⋊C8—121no—
268#449—91noSylow
269C2×C33—41no—
270C2×C33#12011yescharacteristic
271C2×C33#13511yescharacteristic
272C2×C33AGL(1,ℤ/8)11yescharacteristic
273C32×D3—42no—
274C32×D3—81no—
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—31no—
287C2×C3×D4—31no—
288C2×C3×D4—61no—
289C2×C3×D4—61no—
290C2×C3×D4—62no—
291C2×C3×D4—61no—
292C2×C3×D4—61no—
293C2×C3×D4—62no—
294C2×C3×D4—61no—
295C2×C3×D4—61no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—41no—
300C22×C3×C4—62no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4D3211yescharacteristic
304C22×C3×C4C2×C3×D311yescharacteristic
305C22×C3×C4C2×C3×D311yescharacteristic
306C2×#67—21no—
307C2×#67—21no—
308#235—22no—
309#235—22no—
310C2×D12C2×C3×D311yescharacteristic
311C2×D12C2×C3×D311yescharacteristic
312C2×C4×D3—21no—
313C2×Dic6C2×C3×D311yescharacteristic
314C3×SD16—182no—
315C3×D8—182no—
316C2×C3×C8—91no—
317C2×C3×C8—91no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—61no—
321C3×C22⋊C4—62no—
322C3×C22⋊C4—61no—
323C3×C22⋊C4—61no—
324#215—62no—
325#214—62no—
326#213—62no—
327#213—62no—
328(C2×D3)⋊C4—21no—
329C4⋊Dic3C2×C3×D311yescharacteristic
330C2×C3⋊C8—31no—
331C2×C3⋊C8—31no—
332C2×C3⋊C8—31no—
333C2×C3⋊C8—31no—
334C2×C3⋊C8—61no—
335C2×C3⋊C8—61no—
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×C32—121no—
365C22×C32—121no—
366C22×C32—121no—
367C22×C32C2×#6711yescharacteristic
368C22×C32C2×#6711yescharacteristic
369C22×C32C2×C3×D411yescharacteristic
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—42no—
380C2×C3×D3—42no—
381C2×C3×D3—42no—
382C2×C3×D3—41no—
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C2×C3×D3—41no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
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×C4—121no—
405C32×C4D3×D411yescharacteristic
406C32×C4D3×D411yescharacteristic
407C32×C4C2×#6711yescharacteristic
408C32×C4C2×#6711yescharacteristic
409C32×C4C2×C3×D411yescharacteristic
410C32×C4C2×C3×D411yescharacteristic
411C3×Dic3—24no—
412C3×Dic3—22no—
413C3×Dic3—22no—
414C3×Dic3—42no—
415C3×Dic3—41no—
416C3×Dic3—41no—
417C2×#41—31no—
418C2×SD16—91no—
419C2×D8—91no—
420#121—31no—
421#103—91no—
422#102—91no—
423C22⋊C8—91no—
424C33#44911yescharacteristic, complemented, Sylow
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—41no—
429C23×C3—62no—
430C23×C3—62no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3—61no—
434C23×C3—61no—
435C23×C3#62511yescharacteristic
436C23×C3C3×#6711yescharacteristic
437C23×C3C3×#6711yescharacteristic
438C22×D3—21no—
439C22×D3—21no—
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—61no—
456C3×D4—61no—
457C3×D4—61no—
458C3×D4—61no—
459C3×D4—121no—
460C3×D4—121no—
461C3×D4—124no—
462C3×D4—122no—
463C3×D4—122no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
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—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—42no—
483C2×C3×C4—42no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—68no—
487C2×C3×C4—64no—
488C2×C3×C4—64no—
489C2×C3×C4—62no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—62no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4#62511yescharacteristic
496C2×C3×C4C3×#6711yescharacteristic
497C2×C3×C4C3×#6711yescharacteristic
498C2×C3×C4C2×D3211yescharacteristic
499C2×C3×C4C22×C3×D311yescharacteristic
500C2×C3×C4C22×C3×D311yescharacteristic
501#67—24no—
502#67—42no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505D12—21no—
506D12—21no—
507D12—21no—
508D12C3×#6712yescomplemented
509C4×D3—24no—
510Dic6—21no—
511Dic6C3×#6712yescomplemented
512C3×C8—181no—
513C3×C8—181no—
514C3⋊C8—61no—
515C3⋊C8—61no—
516C3⋊C8—61no—
517C3⋊C8—61no—
518C3⋊C8—121no—
519C3⋊C8—121no—
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—241no—
541C2×C32#93211yescharacteristic
542C2×C32#93711yescharacteristic
543C2×C32#94911yescharacteristic
544C2×C32#95011yescharacteristic
545C2×C32#95011yescharacteristic
546C2×C32#95311yescharacteristic
547C2×C32C3×#12011yescharacteristic
548C2×C32C3×#13511yescharacteristic
549C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
550C3×D3—44no—
551C3×D3—42no—
552C3×D3—42no—
553C3×D3—82no—
554C3×D3—81no—
555C3×D3—81no—
556#41—62no—
557#41—62no—
558C2×Q8—31no—
559C2×D4—31no—
560C2×D4—31no—
561C2×D4—61no—
562C2×D4—61no—
563C22×C4—61no—
564C22×C4C3×D3211yescharacteristic
565SD16—182no—
566D8—182no—
567C2×C8—91no—
568C2×C8—91no—
569C4⋊C4—31no—
570C22⋊C4—61no—
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—122no—
602C22×C3—122no—
603C22×C3—122no—
604C22×C3—121no—
605C22×C3—121no—
606C22×C3—121no—
607C22×C3—121no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3C2×#62511yescharacteristic
615C22×C3C2×C3×#6711yescharacteristic
616C22×C3C2×C3×#6711yescharacteristic
617C2×D3—22no—
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—41no—
622C2×D3—41no—
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—122no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4D3×#6711yescharacteristic
645C3×C4D3×#6711yescharacteristic
646C3×C4C3×D3×D411yescharacteristic
647C3×C4C3×D3×D411yescharacteristic
648C3×C4C2×C3×#6711yescharacteristic
649C3×C4C2×C3×#6711yescharacteristic
650Dic3—22no—
651Dic3—41no—
652C32—21no—
653C32—21no—
654C32—21no—
655C32—41no—
656C32#503711yescharacteristic, complemented
657C32#523811yescharacteristic, complemented
658C32C3×#44911yescharacteristic, complemented
659C23—61no—
660C23—61no—
661C23C3×#62511yescharacteristic
662Q8—32no—
663Q8—61no—
664D4—32no—
665D4—64no—
666D4—61no—
667D4—61no—
668D4—61no—
669D4—122no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—64no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4C3×#62511yescharacteristic
676C2×C4C2×C3×D3211yescharacteristic
677C8—181no—
678C8—181no—
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—242no—
702C2×C3—241no—
703C2×C3—241no—
704C2×C3#6382211yescharacteristic
705C2×C3#6382311yescharacteristic
706C2×C3#6397611yescharacteristic
707C2×C3C3×#93211yescharacteristic
708C2×C3C3×#93711yescharacteristic
709C2×C3C3×#94911yescharacteristic
710C2×C3C3×#95011yescharacteristic
711C2×C3C3×#95011yescharacteristic
712C2×C3C3×#95311yescharacteristic
713D3—42no—
714D3—81no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—62no—
719C22—121no—
720C22—121no—
721C22—121no—
722C22—121no—
723C22—121no—
724C22C2×C3×#62511yescharacteristic
725C4—21no—
726C4—62no—
727C4—121no—
728C4C3×D3×#6711yescharacteristic
729C4C3×D3×#6711yescharacteristic
730C3—21no—
731C3—21no—
732C3—21no—
733C3—41no—
734C3#1059116111yescharacteristic, direct product factor
735C3C3×#503711yescharacteristic, complemented
736C3C3×#523811yescharacteristic, complemented
737C2—41no—
738C2—122no—
739C2—241no—
740C2C3×#6382211yescharacteristic
741C2C3×#6382311yescharacteristic
742C2C3×#6397611yescharacteristic
subgroupG/H
centerC22×C3C2×#625
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. C32×#930C2semidirect
3. C2×C3×#3715C2semidirect
4. C2×C3×#3713C2semidirect
5. C3×#63657C2semidirect
6. C3×#63565C2semidirect
7. C3×#63562C2semidirect
10. #10591161C3direct (N × H)
28. C2×C3×#235D3semidirect
29. C2×C3×#235C2×C3semidirect
36. C3×#930D3semidirect
37. C3×#930C2×C3semidirect
38. C2×#3715C2×C3semidirect
39. C2×#3713C2×C3semidirect
40. #63657C2×C3semidirect
48. #63565C2×C3semidirect
49. #63562C2×C3semidirect
64. C32×D12D4semidirect
67. C32×Dic6D4semidirect
152. C2×#235C3×D3semidirect
162. #930C3×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#5037semidirect
657. C32#5238semidirect
658. C32C3×#449semidirect
734. C3#10591161direct (N × H)
735. C3C3×#5037semidirect
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
C32×#9302
C2×C3×#37152
C2×C3×#37132
C3×#636572
C3×#635652
C3×#635622
C3×#52383
C3×#50373
#105911613