Finite Group Databasebeta

← C3×#82671 #11824544

Subgroups — C3×#82671 #11824544

Order 1152.

1661 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic, complemented
2C2×C3×#939C212yesmaximal, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C3×#5223C211yesmaximal, characteristic, complemented
5C3×#5222C211yesmaximal, characteristic, complemented
6C3×#5220C212yesmaximal, complemented
7C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
8C3×#4992C211yesmaximal, characteristic, complemented
9C3×#4983C211yesmaximal, characteristic, complemented
10C3×#4956C212yesmaximal, complemented
11C3×#4944C212yesmaximal, complemented
12C3×#2543—31nomaximal
13#82671C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2212yes—
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2212yes—
20C22×C3×C4×D3C2211yescharacteristic
21C32×#121—24no—
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C32×C22⋊C4C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×#217C2212yes—
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2212yes—
28C3×#939—28no—
29C3×C4×#67—24no—
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×Dic3⋊C4C2212yes—
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2211yescharacteristic
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2212yes—
40C2×C3×#121—21no—
41C2×C3×#121—32no—
42C2×C3×#121D311yescharacteristic, complemented
43C2×C3×#121C2×C311yescharacteristic, complemented
44C2×C3×C4×D4—31no—
45C2×#939C2×C312yescomplemented
46C2×C4×#67C2×C311yescharacteristic, complemented
47C3×#398—31no—
48C3×#397—31no—
49C3×#394—31no—
50C3×#392—31no—
51C3×#388—32no—
52C3×#386—32no—
53C3×#386—32no—
54C2×C3×#95—31no—
55#5223C2×C311yescharacteristic, complemented
56#5222C2×C311yescharacteristic, complemented
57#5220C2×C312yescomplemented
58C2×C3⋊#95C2×C311yescharacteristic, complemented
59#4992C2×C311yescharacteristic, complemented
60#4983C2×C311yescharacteristic, complemented
61#4956C2×C312yescomplemented
62#4944C2×C312yescomplemented
63C24×C32C2312yes—
64C24×C32C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C2×C32×D4—24no—
67C2×C32×D4—24no—
68C2×C32×D4—24no—
69C2×C32×D4—22no—
70C2×C32×D4—42no—
71C22×C32×C4—42no—
72C22×C32×C4D414yescomplemented
73C22×C32×C4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C2×C3×#67—22no—
77C2×C3×#67—22no—
78C2×C3×#67—24no—
79C2×C3×#67—24no—
80C2×C3×#67—42no—
81C2×C3×#67D414yescomplemented
82C22×C3×Dic3—24no—
83C22×C3×Dic3—24no—
84C22×C3×Dic3—42no—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C2×C3×C4×D3—22no—
91C2×C3×C4×D3—42no—
92C32×C4⋊C4—22no—
93C32×C22⋊C4—24no—
94C3×#217—22no—
95C3×#217—24no—
96C3×#217—24no—
97C3×#217—42no—
98C3×(C2×D3)⋊C4—24no—
99C3×(C2×D3)⋊C4—22no—
100C3×Dic3⋊C4—22no—
101C3×Dic3⋊C4—24no—
102C3×C4×Dic3—22no—
103#2543—31noSylow
104C22×C3×D4—22no—
105C22×C3×D4—21no—
106C22×C3×D4—31no—
107C22×C3×D4—32no—
108C22×C3×D4C2×D312yes—
109C22×C3×D4C2×D311yescharacteristic
110C22×C3×D4C22×C312yes—
111C22×C3×D4C22×C311yescharacteristic
112C23×C3×C4—21no—
113C23×C3×C4—32no—
114C23×C3×C4—31no—
115C23×C3×C4C2×D311yescharacteristic
116C23×C3×C4C22×C311yescharacteristic
117C22×#67C22×C312yes—
118C22×#67C22×C311yescharacteristic
119C23×Dic3C22×C312yes—
120C22×C4×D3C22×C311yescharacteristic
121C3×#121—28no—
122C3×#121—24no—
123C3×#121—24no—
124C3×#121—68no—
125C3×C4×D4—64no—
126C2×C3×C4⋊C4—21no—
127C2×C3×C4⋊C4—32no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4C2×D311yescharacteristic
130C2×C3×C4⋊C4C22×C311yescharacteristic
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—31no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4C2×D312yes—
139C2×C3×C22⋊C4C22×C312yes—
140C2×C3×C42—31no—
141C2×#217C22×C312yes—
142C2×#217C22×C312yes—
143C2×#217C22×C311yescharacteristic
144C2×#217C22×C312yes—
145#939—28no—
146C4×#67—24no—
147C2×(C2×D3)⋊C4C22×C312yes—
148C2×(C2×D3)⋊C4C22×C311yescharacteristic
149C2×Dic3⋊C4C22×C312yes—
150C2×Dic3⋊C4C22×C311yescharacteristic
151C2×C4×Dic3C22×C311yescharacteristic
152C3×#95—32no—
153C3×#95—31no—
154C3×#95—31no—
155C3×#95—32no—
156C3×#95—32no—
157C3⋊#95C22×C312yes—
158C3⋊#95C22×C312yes—
159C3⋊#95C22×C311yescharacteristic
160C3⋊#95C22×C311yescharacteristic
161C3⋊#95C22×C312yes—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—22no—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32C2×D412yes—
172C23×C32C2×D412yes—
173C23×C32#4112yes—
174C23×C32C2411yescharacteristic
175C22×C3×D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3C2×D412yes—
180C32×D4—44no—
181C32×D4—48no—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4—44no—
188C2×C32×C4C2×D412yes—
189C2×C32×C4C2×D412yes—
190C3×#67—28no—
191C3×#67—48no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—48no—
204C2×C3×Dic3C2×D412yes—
205C2×C3×Dic3#4114yes—
206C3×C4×D3—44no—
207C2×#121—32no—
208C2×#121C3×D311yescharacteristic, complemented
209C2×C4×D4—31no—
210#398—31no—
211#397—31no—
212#394—31no—
213#392—31no—
214#388—32no—
215#386—32no—
216#386—32no—
217C2×#95—31no—
218C24×C3—21no—
219C24×C3—22no—
220C24×C3—31no—
221C24×C3C22×D312yes—
222C24×C3C22×D311yescharacteristic
223C24×C3C23×C312yes—
224C24×C3C23×C311yescharacteristic
225C23×D3C23×C311yescharacteristic
226C2×C3×D4—28no—
227C2×C3×D4—24no—
228C2×C3×D4—24no—
229C2×C3×D4—24no—
230C2×C3×D4—24no—
231C2×C3×D4—24no—
232C2×C3×D4—24no—
233C2×C3×D4—24no—
234C2×C3×D4—22no—
235C2×C3×D4—22no—
236C2×C3×D4—34no—
237C2×C3×D4—44no—
238C2×C3×D4—44no—
239C2×C3×D4—42no—
240C2×C3×D4—42no—
241C2×C3×D4—44no—
242C2×C3×D4—64no—
243C2×C3×D4—62no—
244C2×C3×D4—62no—
245C2×C3×D4—64no—
246C2×C3×D4—122no—
247C22×C3×C4—24no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—22no—
251C22×C3×C4—32no—
252C22×C3×C4—31no—
253C22×C3×C4—32no—
254C22×C3×C4—31no—
255C22×C3×C4—31no—
256C22×C3×C4—42no—
257C22×C3×C4—42no—
258C22×C3×C4—44no—
259C22×C3×C4—64no—
260C22×C3×C4—64no—
261C22×C3×C4—62no—
262C22×C3×C4—122no—
263C22×C3×C4—122no—
264C22×C3×C4#6714yescomplemented
265C22×C3×C4C3×D414yescomplemented
266C22×C3×C4C22×D312yes—
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C22×D311yescharacteristic
269C22×C3×C4C23×C312yes—
270C22×C3×C4C23×C311yescharacteristic
271C22×C3×C4C23×C311yescharacteristic
272C2×#67—22no—
273C2×#67—22no—
274C2×#67—24no—
275C2×#67—24no—
276C2×#67—42no—
277C2×#67C3×D414yescomplemented
278C22×Dic3—24no—
279C22×Dic3—24no—
280C22×Dic3—42no—
281C22×Dic3C23×C312yes—
282C22×Dic3C23×C311yescharacteristic
283C22×Dic3C23×C311yescharacteristic
284C22×Dic3C23×C311yescharacteristic
285C22×Dic3C23×C312yes—
286C2×C4×D3—22no—
287C2×C4×D3—42no—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—22no—
290C3×C4⋊C4—22no—
291C3×C4⋊C4—64no—
292C3×C4⋊C4—62no—
293C3×C22⋊C4—28no—
294C3×C22⋊C4—24no—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—64no—
297C3×C22⋊C4—64no—
298C3×C22⋊C4—64no—
299C3×C22⋊C4—62no—
300C3×C22⋊C4—62no—
301C3×C22⋊C4—122no—
302C3×C42—62no—
303#217—22no—
304#217—24no—
305#217—24no—
306#217—42no—
307(C2×D3)⋊C4—24no—
308(C2×D3)⋊C4—22no—
309Dic3⋊C4—22no—
310Dic3⋊C4—24no—
311C4×Dic3—22no—
312C22×C32—22no—
313C22×C32—22no—
314C22×C32—24no—
315C22×C32—24no—
316C22×C32—42no—
317C22×C32—42no—
318C22×C32—42no—
319C22×C32—42no—
320C22×C32—42no—
321C22×C32—42no—
322C22×C32—42no—
323C22×C32#12114yes—
324C22×C32C22×D411yescharacteristic
325C22×C32C22×D411yescharacteristic
326C22×C32C2×#4111yescharacteristic
327C22×C32C2×#4112yes—
328C22×C32H(5,𝔽2)12yes—
329C2×C3×D3—22no—
330C2×C3×D3—24no—
331C2×C3×D3—41no—
332C2×C3×D3—41no—
333C2×C3×D3—42no—
334C32×C4—22no—
335C32×C4—22no—
336C32×C4—42no—
337C3×Dic3—22no—
338C3×Dic3—24no—
339C3×Dic3—41no—
340C3×Dic3—41no—
341C3×Dic3—42no—
342C22×D4—31no—
343C22×D4—32no—
344C22×D4C2×C3×D312yes—
345C22×D4C2×C3×D311yescharacteristic
346C23×C4—32no—
347C23×C4—31no—
348C23×C4C2×C3×D311yescharacteristic
349#121—24no—
350#121—68no—
351C4×D4—64no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—32no—
354C2×C4⋊C4C2×C3×D311yescharacteristic
355C2×C22⋊C4—31no—
356C2×C22⋊C4—32no—
357C2×C22⋊C4—32no—
358C2×C22⋊C4—31no—
359C2×C22⋊C4—32no—
360C2×C22⋊C4—32no—
361C2×C22⋊C4C2×C3×D312yes—
362C2×C42—31no—
363#95—32no—
364#95—31no—
365#95—31no—
366#95—32no—
367#95—32no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—24no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—21no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—32no—
392C23×C3—42no—
393C23×C3—42no—
394C23×C3—42no—
395C23×C3—42no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—61no—
401C23×C3—62no—
402C23×C3—62no—
403C23×C3—61no—
404C23×C3D3×D412yes—
405C23×C3#23712yes—
406C23×C3C2×#6712yes—
407C23×C3C2×C3×D412yes—
408C23×C3C2×C3×D412yes—
409C23×C3C3×#4112yes—
410C23×C3C23×D311yescharacteristic
411C23×C3C24×C311yescharacteristic
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—22no—
415C22×D3—22no—
416C22×D3C2×C3×D412yes—
417C3×D4—48no—
418C3×D4—44no—
419C3×D4—44no—
420C3×D4—416no—
421C3×D4—48no—
422C3×D4—48no—
423C3×D4—68no—
424C3×D4—128no—
425C2×C3×C4—24no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—24no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—32no—
440C2×C3×C4—34no—
441C2×C3×C4—42no—
442C2×C3×C4—42no—
443C2×C3×C4—42no—
444C2×C3×C4—44no—
445C2×C3×C4—44no—
446C2×C3×C4—48no—
447C2×C3×C4—62no—
448C2×C3×C4—61no—
449C2×C3×C4—62no—
450C2×C3×C4—61no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—62no—
455C2×C3×C4—62no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—124no—
459C2×C3×C4—128no—
460C2×C3×C4C2×#6712yes—
461C2×C3×C4C2×#6712yes—
462C2×C3×C4C2×C3×D412yes—
463C2×C3×C4C2×C3×D412yes—
464#67—28no—
465#67—48no—
466C2×Dic3—21no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—22no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—48no—
478C2×Dic3C2×C3×D412yes—
479C2×Dic3C3×#4114yes—
480C4×D3—44no—
481C2×C32—24no—
482C2×C32—82no—
483C2×C32C2×#12111yescharacteristic
484C2×C32#53211yescharacteristic
485C2×C32#53411yescharacteristic
486C2×C32#54612yes—
487C2×C32#55312yes—
488C3×D3—42no—
489C24—31no—
490C24C22×C3×D312yes—
491C24C22×C3×D311yescharacteristic
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—22no—
496C2×D4—34no—
497C2×D4—42no—
498C2×D4—64no—
499C2×D4—62no—
500C2×D4—62no—
501C2×D4—64no—
502C2×D4—122no—
503C22×C4—32no—
504C22×C4—31no—
505C22×C4—32no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—42no—
509C22×C4—64no—
510C22×C4—64no—
511C22×C4—62no—
512C22×C4—122no—
513C22×C4—122no—
514C22×C4C3×#6714yescomplemented
515C22×C4C22×C3×D312yes—
516C22×C4C22×C3×D311yescharacteristic
517C22×C4C22×C3×D311yescharacteristic
518C4⋊C4—22no—
519C4⋊C4—64no—
520C4⋊C4—62no—
521C22⋊C4—24no—
522C22⋊C4—64no—
523C22⋊C4—64no—
524C22⋊C4—64no—
525C22⋊C4—62no—
526C22⋊C4—62no—
527C22⋊C4—122no—
528C42—62no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—24no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—24no—
535C22×C3—24no—
536C22×C3—24no—
537C22×C3—24no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—21no—
543C22×C3—42no—
544C22×C3—42no—
545C22×C3—44no—
546C22×C3—44no—
547C22×C3—44no—
548C22×C3—44no—
549C22×C3—44no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—62no—
565C22×C3—64no—
566C22×C3—82no—
567C22×C3—82no—
568C22×C3—82no—
569C22×C3—82no—
570C22×C3—121no—
571C22×C3—121no—
572C22×C3—122no—
573C22×C3#93814yes—
574C22×C3C3×#12114yes—
575C22×C3C2×D3×D411yescharacteristic
576C22×C3C2×#23711yescharacteristic
577C22×C3#100412yes—
578C22×C3D3×#4112yes—
579C22×C3C22×#6711yescharacteristic
580C22×C3C22×C3×D411yescharacteristic
581C22×C3C22×C3×D411yescharacteristic
582C22×C3C2×C3×#4111yescharacteristic
583C22×C3C2×C3×#4112yes—
584C22×C3C3×H(5,𝔽2)12yes—
585C2×D3—22no—
586C2×D3—24no—
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—42no—
590C3×C4—24no—
591C3×C4—22no—
592C3×C4—22no—
593C3×C4—22no—
594C3×C4—22no—
595C3×C4—42no—
596C3×C4—44no—
597C3×C4—42no—
598C3×C4—42no—
599C3×C4—62no—
600C3×C4—64no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4—122no—
604Dic3—22no—
605Dic3—24no—
606Dic3—41no—
607Dic3—41no—
608Dic3—42no—
609C32#254311yescharacteristic, complemented, Sylow
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—32no—
620C23—61no—
621C23—62no—
622C23—62no—
623C23—61no—
624C23C3×D3×D412yes—
625C23C3×#23712yes—
626C23C2×C3×#6712yes—
627C23C23×C3×D311yescharacteristic
628D4—44no—
629D4—48no—
630D4—68no—
631D4—128no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—32no—
638C2×C4—34no—
639C2×C4—44no—
640C2×C4—62no—
641C2×C4—61no—
642C2×C4—62no—
643C2×C4—61no—
644C2×C4—62no—
645C2×C4—62no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—124no—
652C2×C4—128no—
653C2×C4C2×C3×#6712yes—
654C2×C4C2×C3×#6712yes—
655C2×C3—24no—
656C2×C3—24no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—22no—
661C2×C3—22no—
662C2×C3—44no—
663C2×C3—84no—
664C2×C3—82no—
665C2×C3—82no—
666C2×C3—122no—
667C2×C3#560112yes—
668C2×C3#561012yes—
669C2×C3C2×#93811yescharacteristic
670C2×C3#580411yescharacteristic
671C2×C3#583211yescharacteristic
672C2×C3C2×C3×#12111yescharacteristic
673C2×C3C3×#53211yescharacteristic
674C2×C3C3×#53411yescharacteristic
675C2×C3C3×#54612yes—
676C2×C3C3×#55312yes—
677D3—42no—
678C22—22no—
679C22—22no—
680C22—24no—
681C22—24no—
682C22—42no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—42no—
689C22—62no—
690C22—64no—
691C22—121no—
692C22—121no—
693C22—122no—
694C22C3×#93814yes—
695C22C2×C3×D3×D411yescharacteristic
696C22C2×C3×#23711yescharacteristic
697C22C3×#100412yes—
698C22C3×D3×#4112yes—
699C22C22×C3×#6711yescharacteristic
700C4—22no—
701C4—22no—
702C4—42no—
703C4—62no—
704C4—64no—
705C4—121no—
706C4—121no—
707C4—122no—
708C3—21no—
709C3#8267111yescharacteristic, direct product factor
710C3C3×#254311yescharacteristic, complemented
711C2—24no—
712C2—82no—
713C2—122no—
714C2C3×#560112yes—
715C2C3×#561012yes—
716C2C2×C3×#93811yescharacteristic
717C2C3×#580411yescharacteristic
718C2C3×#583211yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C3×#2543
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
1. C2×C32×#121C2semidirect
2. C2×C3×#939C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C3×#5223C2semidirect
5. C3×#5222C2semidirect
6. C3×#5220C2semidirect
7. C2×C3×C3⋊#95C2semidirect
8. C3×#4992C2semidirect
9. C3×#4983C2semidirect
10. C3×#4956C2semidirect
11. C3×#4944C2semidirect
13. #82671C3direct (N × H)
42. C2×C3×#121D3semidirect
43. C2×C3×#121C2×C3semidirect
45. C2×#939C2×C3semidirect
46. C2×C4×#67C2×C3semidirect
55. #5223C2×C3semidirect
56. #5222C2×C3semidirect
57. #5220C2×C3semidirect
58. C2×C3⋊#95C2×C3semidirect
59. #4992C2×C3semidirect
60. #4983C2×C3semidirect
61. #4956C2×C3semidirect
62. #4944C2×C3semidirect
72. C22×C32×C4D4semidirect
81. C2×C3×#67D4semidirect
208. C2×#121C3×D3semidirect
264. C22×C3×C4#67semidirect
265. C22×C3×C4C3×D4semidirect
277. C2×#67C3×D4semidirect
514. C22×C4C3×#67semidirect
609. C32#2543semidirect
709. C3#82671direct (N × H)
710. C3C3×#2543semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C2×C3×#9392
C2×C3×C4×#672
C3×#52232
C3×#52222
C3×#52202
C2×C3×C3⋊#952
C3×#49922
C3×#49832
C3×#49562
C3×#49442
C3×#25433
#826713