Finite Group Databasebeta

← C3×#10595519 #13175113

Subgroups — C3×#10595519 #13175113

Order 1728.

2122 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#638C211yesmaximal, characteristic, complemented
2C22×C32×#67C211yesmaximal, characteristic, complemented
3C2×C32×#217C211yesmaximal, characteristic, complemented
4C3×#63981C212yesmaximal, complemented
5C3×#63978C214yesmaximal, complemented
6C3×#63977C212yesmaximal, complemented
7C3×#63966C212yesmaximal, complemented
8C3×#63962C212yesmaximal, complemented
9C3×#5804—31nomaximal
10C3×#5493—31nomaximal
11#10595519C311yesmaximal, characteristic, direct product factor
12C24×C33C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic, complemented
14C23×C32×D3C2211yescharacteristic, complemented
15C2×C3×#638—24no—
16C2×C3×#638C2212yes—
17C2×C3×#638C2212yescomplemented
18C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
19C2×C32×#67—24no—
20C2×C32×#67C2212yes—
21C2×C32×#67C2212yescomplemented
22C22×C32×Dic3C2211yescharacteristic, complemented
23C22×C32×Dic3C2212yescomplemented
24C2×C3×#626C2214yescomplemented
25C32×#217C2212yescomplemented
26C32×#217C2212yescomplemented
27C3×Dic3⋊Dic3C2214yescomplemented
28C3×#3722C2214yescomplemented
29C3×(C2×D3)⋊Dic3C2214yescomplemented
30C22×C32×D4—31no—
31C22×#638C2×C311yescharacteristic, complemented
32C22×C3×#67—21no—
33C22×C3×#67—31no—
34C22×C3×#67—31no—
35C22×C3×#67—61no—
36C22×C3×#67D311yescharacteristic, complemented
37C22×C3×#67C2×C311yescharacteristic, complemented
38C2×C32×C22⋊C4—31no—
39C3×#953—32no—
40C2×C3×#217—21no—
41C2×C3×#217D311yescharacteristic, complemented
42C2×C3×#217C2×C311yescharacteristic, complemented
43C3×#939—34no—
44C3×#937—32no—
45C3×#935—32no—
46C3×#930—34no—
47C3×#929—32no—
48C3×#886—32no—
49C3×#886—32no—
50C3×#882—32no—
51C3×#882—32no—
52#63981C2×C312yescomplemented
53#63978C2×C314yescomplemented
54#63977C2×C312yescomplemented
55#63966C2×C312yescomplemented
56#63962C2×C312yescomplemented
57C23×C33—42no—
58C23×C33D414yescomplemented
59C23×C33C2311yescharacteristic
60C23×C33C2311yescharacteristic
61C23×C33C2311yescharacteristic
62C22×C3×C3⋊D3—22no—
63C22×C3×C3⋊D3—42no—
64C22×C3×C3⋊D3C2312yes—
65C22×C32×D3—22no—
66C22×C32×D3—42no—
67C22×C32×D3C2312yes—
68C3×#638—24no—
69C3×#638—24no—
70C2×C3×C3⋊Dic3—22no—
71C2×C3×C3⋊Dic3C2312yes—
72C32×#67—24no—
73C32×#67—24no—
74C2×C32×Dic3—22no—
75C2×C32×Dic3—42no—
76C2×C32×Dic3C2314yes—
77C2×C32×Dic3C2312yes—
78C3×#626—44no—
79C3×#534—91no—
80#5804—31no—
81#5493—31no—
82C24×C32—21no—
83C24×C32—21no—
84C24×C32—21no—
85C24×C32—31no—
86C24×C32—41no—
87C24×C32C2×D311yescharacteristic
88C24×C32C2×D311yescharacteristic
89C24×C32C22×C311yescharacteristic
90C23×C3⋊D3C22×C311yescharacteristic, complemented
91C23×C3×D3—21no—
92C23×C3×D3—31no—
93C23×C3×D3—31no—
94C23×C3×D3—61no—
95C23×C3×D3C2×D311yescharacteristic, complemented
96C23×C3×D3C22×C311yescharacteristic, complemented
97C2×C32×D4—32no—
98C2×C32×D4—32no—
99C2×C32×D4—64no—
100C22×C32×C4—31no—
101C22×C32×C4—32no—
102C2×#638—24no—
103C2×#638C22×C312yes—
104C2×#638C22×C312yescomplemented
105C22×C3⋊Dic3C22×C311yescharacteristic, complemented
106C2×C3×#67—28no—
107C2×C3×#67—22no—
108C2×C3×#67—22no—
109C2×C3×#67—24no—
110C2×C3×#67—24no—
111C2×C3×#67—32no—
112C2×C3×#67—32no—
113C2×C3×#67—32no—
114C2×C3×#67—32no—
115C2×C3×#67—34no—
116C2×C3×#67—62no—
117C2×C3×#67—62no—
118C2×C3×#67—68no—
119C2×C3×#67—64no—
120C2×C3×#67—64no—
121C2×C3×#67C2×D312yes—
122C2×C3×#67C2×D312yescomplemented
123C2×C3×#67C22×C312yes—
124C2×C3×#67C22×C312yescomplemented
125C22×C3×Dic3—21no—
126C22×C3×Dic3—22no—
127C22×C3×Dic3—31no—
128C22×C3×Dic3—31no—
129C22×C3×Dic3—61no—
130C22×C3×Dic3C2×D311yescharacteristic, complemented
131C22×C3×Dic3C2×D312yescomplemented
132C22×C3×Dic3C22×C311yescharacteristic, complemented
133C22×C3×Dic3C22×C312yescomplemented
134C2×C3×D12—34no—
135C2×#626C22×C314yescomplemented
136C32×C22⋊C4—32no—
137C32×C22⋊C4—32no—
138C3×#217—22no—
139C3×#217—22no—
140C3×#217—34no—
141C3×#217C2×D312yescomplemented
142C3×#217C2×D312yescomplemented
143C3×#217C22×C312yescomplemented
144C3×#217C22×C312yescomplemented
145C3×(C2×D3)⋊C4—34no—
146C3×(C2×D3)⋊C4—34no—
147C3×(C2×D3)⋊C4—34no—
148C3×C4⋊Dic3—34no—
149C3×Dic3⋊C4—34no—
150Dic3⋊Dic3C22×C314yescomplemented
151#3722C22×C314yescomplemented
152(C2×D3)⋊Dic3C22×C314yescomplemented
153C22×C33—22no—
154C22×C33—22no—
155C22×C33—22no—
156C22×C33—44no—
157C22×C33C2×D412yes—
158C22×C33C2×D412yes—
159C22×C33C2×D412yes—
160C22×C33C2411yescharacteristic
161C2×C3×C3⋊D3—22no—
162C2×C3×C3⋊D3—24no—
163C2×C3×C3⋊D3—44no—
164C2×C32×D3—22no—
165C2×C32×D3—24no—
166C2×C32×D3—44no—
167C3×C3⋊Dic3—22no—
168C32×Dic3—22no—
169C32×Dic3—24no—
170C22×C3×D4—31no—
171C22×C3×D4—31no—
172C22×C3×D4—61no—
173C22×C3×D4—91no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—61no—
177C22×#67C3×D311yescharacteristic, complemented
178C3×#123—92no—
179C3×#123—92no—
180C3×#121—94no—
181C3×#120—92no—
182C3×#120—92no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—61no—
186#953—32no—
187C2×#217C3×D311yescharacteristic, complemented
188#939—34no—
189#937—32no—
190#935—32no—
191#930—34no—
192#929—32no—
193#886—32no—
194#886—32no—
195#882—32no—
196#882—32no—
197C23×C32—24no—
198C23×C32—24no—
199C23×C32—24no—
200C23×C32—21no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32—21no—
205C23×C32—21no—
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—32no—
210C23×C32—44no—
211C23×C32—41no—
212C23×C32—41no—
213C23×C32—41no—
214C23×C32—42no—
215C23×C32—42no—
216C23×C32—42no—
217C23×C32—44no—
218C23×C32—44no—
219C23×C32—44no—
220C23×C32—48no—
221C23×C32—62no—
222C23×C32—122no—
223C23×C32D1214yescomplemented
224C23×C32#6714yescomplemented
225C23×C32C3×D414yescomplemented
226C23×C32C22×D311yescharacteristic
227C23×C32C22×D311yescharacteristic
228C23×C32C22×D311yescharacteristic
229C23×C32C22×D311yescharacteristic
230C23×C32C22×D311yescharacteristic
231C23×C32C22×D311yescharacteristic
232C23×C32C23×C311yescharacteristic
233C23×C32C23×C311yescharacteristic
234C23×C32C23×C311yescharacteristic
235C22×C3⋊D3—22no—
236C22×C3⋊D3—42no—
237C22×C3⋊D3C23×C312yes—
238C22×C3×D3—24no—
239C22×C3×D3—22no—
240C22×C3×D3—22no—
241C22×C3×D3—22no—
242C22×C3×D3—32no—
243C22×C3×D3—32no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—44no—
247C22×C3×D3—62no—
248C22×C3×D3—64no—
249C22×C3×D3—62no—
250C22×C3×D3—62no—
251C22×C3×D3—122no—
252C22×C3×D3—122no—
253C22×C3×D3—124no—
254C22×C3×D3C22×D312yes—
255C22×C3×D3C23×C312yes—
256C32×D4—64no—
257C32×D4—64no—
258C2×C32×C4—32no—
259C2×C32×C4—34no—
260C2×C32×C4—62no—
261C2×C32×C4—122no—
262#638—24no—
263#638—24no—
264C2×C3⋊Dic3—22no—
265C2×C3⋊Dic3C23×C312yes—
266C3×#67—28no—
267C3×#67—28no—
268C3×#67—24no—
269C3×#67—24no—
270C3×#67—24no—
271C3×#67—24no—
272C3×#67—68no—
273C3×#67—68no—
274C3×#67—64no—
275C3×#67—64no—
276C3×#67—64no—
277C3×#67—64no—
278C3×#67—124no—
279C2×C3×Dic3—24no—
280C2×C3×Dic3—22no—
281C2×C3×Dic3—22no—
282C2×C3×Dic3—22no—
283C2×C3×Dic3—24no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—42no—
287C2×C3×Dic3—42no—
288C2×C3×Dic3—44no—
289C2×C3×Dic3—62no—
290C2×C3×Dic3—64no—
291C2×C3×Dic3—62no—
292C2×C3×Dic3—62no—
293C2×C3×Dic3C22×D314yes—
294C2×C3×Dic3C22×D312yes—
295C2×C3×Dic3C23×C314yes—
296C2×C3×Dic3C23×C312yes—
297C3×D12—124no—
298#626—44no—
299#534—91noSylow
300C2×C33—22no—
301C2×C33—22no—
302C2×C33—22no—
303C2×C33C22×D411yescharacteristic
304C2×C33H(5,𝔽2)12yes—
305C3×C3⋊D3—42no—
306C32×D3—42no—
307C24×C3—21no—
308C24×C3—21no—
309C24×C3—21no—
310C24×C3—31no—
311C24×C3—31no—
312C24×C3—41no—
313C24×C3—61no—
314C24×C3—91no—
315C24×C3D3211yescharacteristic
316C24×C3C2×C3×D311yescharacteristic
317C24×C3C2×C3×D311yescharacteristic
318C23×D3—31no—
319C23×D3—31no—
320C23×D3—61no—
321C23×D3C2×C3×D311yescharacteristic, complemented
322C2×C3×D4—32no—
323C2×C3×D4—32no—
324C2×C3×D4—32no—
325C2×C3×D4—32no—
326C2×C3×D4—62no—
327C2×C3×D4—62no—
328C2×C3×D4—68no—
329C2×C3×D4—64no—
330C2×C3×D4—64no—
331C2×C3×D4—94no—
332C2×C3×D4—92no—
333C2×C3×D4—92no—
334C2×C3×D4—184no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—32no—
338C22×C3×C4—32no—
339C22×C3×C4—61no—
340C22×C3×C4—62no—
341C22×C3×C4—91no—
342C2×#67—24no—
343C2×#67—32no—
344C2×#67—32no—
345C2×#67—32no—
346C2×#67—32no—
347C2×#67—34no—
348C2×#67—62no—
349C2×#67—62no—
350C2×#67—68no—
351C2×#67—64no—
352C2×#67—64no—
353C2×#67C2×C3×D312yes—
354C2×#67C2×C3×D312yescomplemented
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—61no—
358C22×Dic3C2×C3×D311yescharacteristic, complemented
359C22×Dic3C2×C3×D312yescomplemented
360C2×D12—34no—
361C3×C4⋊C4—94no—
362C3×C22⋊C4—32no—
363C3×C22⋊C4—32no—
364C3×C22⋊C4—32no—
365C3×C22⋊C4—32no—
366C3×C22⋊C4—62no—
367C3×C22⋊C4—62no—
368C3×C22⋊C4—94no—
369C3×C22⋊C4—94no—
370#217—34no—
371#217C2×C3×D312yescomplemented
372#217C2×C3×D312yescomplemented
373(C2×D3)⋊C4—34no—
374(C2×D3)⋊C4—34no—
375(C2×D3)⋊C4—34no—
376C4⋊Dic3—34no—
377Dic3⋊C4—34no—
378C22×C32—22no—
379C22×C32—22no—
380C22×C32—22no—
381C22×C32—24no—
382C22×C32—24no—
383C22×C32—24no—
384C22×C32—22no—
385C22×C32—22no—
386C22×C32—22no—
387C22×C32—22no—
388C22×C32—22no—
389C22×C32—22no—
390C22×C32—21no—
391C22×C32—21no—
392C22×C32—21no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—22no—
398C22×C32—22no—
399C22×C32—22no—
400C22×C32—22no—
401C22×C32—22no—
402C22×C32—42no—
403C22×C32—42no—
404C22×C32—42no—
405C22×C32—41no—
406C22×C32—42no—
407C22×C32—42no—
408C22×C32—42no—
409C22×C32—42no—
410C22×C32—42no—
411C22×C32—42no—
412C22×C32—44no—
413C22×C32—44no—
414C22×C32—44no—
415C22×C32—44no—
416C22×C32—44no—
417C22×C32—44no—
418C22×C32—48no—
419C22×C32—48no—
420C22×C32—48no—
421C22×C32—416no—
422C22×C32—62no—
423C22×C32—64no—
424C22×C32—124no—
425C22×C32C2×D1212yes—
426C22×C32C2×D1212yes—
427C22×C32C2×D1212yes—
428C22×C32C2×#6712yes—
429C22×C32C2×#6712yes—
430C22×C32C2×#6712yes—
431C22×C32C2×C3×D412yes—
432C22×C32C2×C3×D412yes—
433C22×C32C2×C3×D412yes—
434C22×C32C23×D311yescharacteristic
435C22×C32C23×D311yescharacteristic
436C22×C32C24×C311yescharacteristic
437C2×C3⋊D3—22no—
438C2×C3⋊D3—24no—
439C2×C3⋊D3—44no—
440C2×C3×D3—24no—
441C2×C3×D3—24no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—24no—
445C2×C3×D3—44no—
446C2×C3×D3—48no—
447C2×C3×D3—44no—
448C2×C3×D3—44no—
449C2×C3×D3—64no—
450C2×C3×D3—62no—
451C2×C3×D3—64no—
452C2×C3×D3—64no—
453C2×C3×D3—62no—
454C2×C3×D3—124no—
455C2×C3×D3—128no—
456C2×C3×D3—124no—
457C2×C3×D3—124no—
458C32×C4—62no—
459C32×C4—64no—
460C3⋊Dic3—22no—
461C3×Dic3—24no—
462C3×Dic3—24no—
463C3×Dic3—22no—
464C3×Dic3—22no—
465C3×Dic3—24no—
466C3×Dic3—44no—
467C3×Dic3—64no—
468C3×Dic3—62no—
469C3×Dic3—62no—
470C22×D4—31no—
471C22×D4—91no—
472#123—92no—
473#123—92no—
474#121—94no—
475#120—92no—
476#120—92no—
477C2×C22⋊C4—31no—
478C33#53411yescharacteristic, complemented, Sylow
479C23×C3—24no—
480C23×C3—24no—
481C23×C3—24no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—32no—
492C23×C3—32no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3—42no—
496C23×C3—44no—
497C23×C3—44no—
498C23×C3—44no—
499C23×C3—48no—
500C23×C3—44no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3—62no—
505C23×C3—64no—
506C23×C3—62no—
507C23×C3—62no—
508C23×C3—92no—
509C23×C3—122no—
510C23×C3—122no—
511C23×C3—124no—
512C23×C3—182no—
513C23×C3—362no—
514C23×C3#62614yescomplemented
515C23×C3C3×D1214yescomplemented
516C23×C3C3×#6714yescomplemented
517C23×C3C2×D3211yescharacteristic
518C23×C3C2×D3211yescharacteristic
519C23×C3C2×D3211yescharacteristic
520C23×C3C22×C3×D311yescharacteristic
521C23×C3C22×C3×D311yescharacteristic
522C23×C3C22×C3×D311yescharacteristic
523C23×C3C22×C3×D311yescharacteristic
524C23×C3C22×C3×D311yescharacteristic
525C23×C3C22×C3×D311yescharacteristic
526C22×D3—22no—
527C22×D3—32no—
528C22×D3—32no—
529C22×D3—42no—
530C22×D3—62no—
531C22×D3—64no—
532C22×D3—62no—
533C22×D3—62no—
534C22×D3—122no—
535C22×D3—122no—
536C22×D3—124no—
537C22×D3C22×C3×D312yes—
538C3×D4—68no—
539C3×D4—68no—
540C3×D4—64no—
541C3×D4—64no—
542C3×D4—64no—
543C3×D4—64no—
544C3×D4—184no—
545C3×D4—184no—
546C3×D4—364no—
547C2×C3×C4—34no—
548C2×C3×C4—32no—
549C2×C3×C4—32no—
550C2×C3×C4—34no—
551C2×C3×C4—62no—
552C2×C3×C4—64no—
553C2×C3×C4—64no—
554C2×C3×C4—62no—
555C2×C3×C4—62no—
556C2×C3×C4—92no—
557C2×C3×C4—122no—
558C2×C3×C4—122no—
559C2×C3×C4—124no—
560C2×C3×C4—182no—
561#67—24no—
562#67—24no—
563#67—68no—
564#67—68no—
565#67—64no—
566#67—64no—
567#67—64no—
568#67—64no—
569#67—124no—
570C2×Dic3—22no—
571C2×Dic3—32no—
572C2×Dic3—32no—
573C2×Dic3—42no—
574C2×Dic3—62no—
575C2×Dic3—64no—
576C2×Dic3—62no—
577C2×Dic3—62no—
578C2×Dic3C22×C3×D314yes—
579C2×Dic3C22×C3×D312yes—
580D12—124no—
581C2×C32—22no—
582C2×C32—22no—
583C2×C32—22no—
584C2×C32—24no—
585C2×C32—24no—
586C2×C32—24no—
587C2×C32—22no—
588C2×C32—22no—
589C2×C32—22no—
590C2×C32—22no—
591C2×C32—22no—
592C2×C32—22no—
593C2×C32—21no—
594C2×C32—22no—
595C2×C32—21no—
596C2×C32—22no—
597C2×C32—22no—
598C2×C32—21no—
599C2×C32—41no—
600C2×C32—42no—
601C2×C32—42no—
602C2×C32—42no—
603C2×C32—42no—
604C2×C32—42no—
605C2×C32—42no—
606C2×C32—42no—
607C2×C32—44no—
608C2×C32—44no—
609C2×C32—44no—
610C2×C32—122no—
611C2×C32C22×D1211yescharacteristic
612C2×C32#100412yes—
613C2×C32#100412yes—
614C2×C32C22×#6711yescharacteristic
615C2×C32C22×C3×D411yescharacteristic
616C2×C32C3×H(5,𝔽2)12yes—
617C3⋊D3—42no—
618C3×D3—44no—
619C3×D3—42no—
620C3×D3—42no—
621C3×D3—124no—
622C3×D3—122no—
623C3×D3—122no—
624C24—31no—
625C24—91no—
626C24C3×D3211yescharacteristic
627C2×D4—32no—
628C2×D4—32no—
629C2×D4—64no—
630C2×D4—94no—
631C2×D4—92no—
632C2×D4—92no—
633C2×D4—184no—
634C22×C4—31no—
635C22×C4—32no—
636C22×C4—91no—
637C4⋊C4—94no—
638C22⋊C4—32no—
639C22⋊C4—32no—
640C22⋊C4—94no—
641C22⋊C4—94no—
642C22×C3—24no—
643C22×C3—24no—
644C22×C3—24no—
645C22×C3—22no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—44no—
673C22×C3—44no—
674C22×C3—44no—
675C22×C3—44no—
676C22×C3—44no—
677C22×C3—44no—
678C22×C3—48no—
679C22×C3—48no—
680C22×C3—48no—
681C22×C3—416no—
682C22×C3—41no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—64no—
687C22×C3—62no—
688C22×C3—64no—
689C22×C3—62no—
690C22×C3—64no—
691C22×C3—124no—
692C22×C3—128no—
693C22×C3—124no—
694C22×C3—124no—
695C22×C3—182no—
696C22×C3—184no—
697C22×C3—364no—
698C22×C3C2×#62612yes—
699C22×C3C2×#62612yes—
700C22×C3C2×#62612yes—
701C22×C3C2×C3×D1212yes—
702C22×C3C2×C3×D1212yes—
703C22×C3C2×C3×D1212yes—
704C22×C3C2×C3×#6712yes—
705C22×C3C2×C3×#6712yes—
706C22×C3C2×C3×#6712yes—
707C22×C3C22×D3211yescharacteristic
708C22×C3C23×C3×D311yescharacteristic
709C22×C3C23×C3×D311yescharacteristic
710C2×D3—24no—
711C2×D3—22no—
712C2×D3—44no—
713C2×D3—64no—
714C2×D3—62no—
715C2×D3—64no—
716C2×D3—64no—
717C2×D3—62no—
718C2×D3—124no—
719C2×D3—128no—
720C2×D3—124no—
721C2×D3—124no—
722C3×C4—64no—
723C3×C4—62no—
724C3×C4—64no—
725C3×C4—62no—
726C3×C4—64no—
727C3×C4—124no—
728C3×C4—182no—
729Dic3—24no—
730Dic3—22no—
731Dic3—64no—
732Dic3—62no—
733Dic3—62no—
734C32—21no—
735C32—21no—
736C32—21no—
737C32—41no—
738C32#549311yescharacteristic, complemented
739C32#580411yescharacteristic, complemented
740C32C3×#53411yescharacteristic, complemented
741C23—32no—
742C23—42no—
743C23—62no—
744C23—92no—
745C23—122no—
746C23—182no—
747C23—362no—
748C23C3×#62614yescomplemented
749C23C2×C3×D3211yescharacteristic
750C23C2×C3×D3211yescharacteristic
751C23C2×C3×D3211yescharacteristic
752D4—64no—
753D4—64no—
754D4—184no—
755D4—184no—
756D4—364no—
757C2×C4—34no—
758C2×C4—32no—
759C2×C4—62no—
760C2×C4—92no—
761C2×C4—122no—
762C2×C4—182no—
763C2×C3—24no—
764C2×C3—24no—
765C2×C3—24no—
766C2×C3—22no—
767C2×C3—22no—
768C2×C3—22no—
769C2×C3—22no—
770C2×C3—22no—
771C2×C3—22no—
772C2×C3—22no—
773C2×C3—22no—
774C2×C3—22no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—22no—
779C2×C3—22no—
780C2×C3—22no—
781C2×C3—42no—
782C2×C3—42no—
783C2×C3—42no—
784C2×C3—42no—
785C2×C3—42no—
786C2×C3—42no—
787C2×C3—44no—
788C2×C3—44no—
789C2×C3—44no—
790C2×C3—41no—
791C2×C3—42no—
792C2×C3—124no—
793C2×C3—122no—
794C2×C3—122no—
795C2×C3—362no—
796C2×C3C22×#62611yescharacteristic
797C2×C3#6433012yes—
798C2×C3C22×C3×D1211yescharacteristic
799C2×C3C3×#100412yes—
800C2×C3C3×#100412yes—
801C2×C3C22×C3×#6711yescharacteristic
802D3—42no—
803D3—124no—
804D3—122no—
805D3—122no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—44no—
810C22—62no—
811C22—64no—
812C22—124no—
813C22—182no—
814C22—184no—
815C22—364no—
816C22C2×C3×#62612yes—
817C22C2×C3×#62612yes—
818C22C2×C3×#62612yes—
819C22C22×C3×D3211yescharacteristic
820C4—62no—
821C4—64no—
822C4—182no—
823C3—21no—
824C3—21no—
825C3—21no—
826C3—41no—
827C3#1059551911yescharacteristic, direct product factor
828C3C3×#549311yescharacteristic, complemented
829C3C3×#580411yescharacteristic, complemented
830C2—22no—
831C2—22no—
832C2—22no—
833C2—122no—
834C2—362no—
835C2C22×C3×#62611yescharacteristic
836C2C3×#6433012yes—
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC22×C33C24
hypercenterC24×C3D32
hypocenterC32C3×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×#638C2semidirect
2. C22×C32×#67C2semidirect
3. C2×C32×#217C2semidirect
4. C3×#63981C2semidirect
5. C3×#63978C2semidirect
6. C3×#63977C2semidirect
7. C3×#63966C2semidirect
8. C3×#63962C2semidirect
11. #10595519C3direct (N × H)
13. C23×C3×C3⋊D3C22semidirect
14. C23×C32×D3C22semidirect
17. C2×C3×#638C22semidirect
18. C22×C3×C3⋊Dic3C22semidirect
21. C2×C32×#67C22semidirect
22. C22×C32×Dic3C22semidirect
23. C22×C32×Dic3C22semidirect
24. C2×C3×#626C22semidirect
25. C32×#217C22semidirect
26. C32×#217C22semidirect
27. C3×Dic3⋊Dic3C22semidirect
28. C3×#3722C22semidirect
29. C3×(C2×D3)⋊Dic3C22semidirect
31. C22×#638C2×C3semidirect
36. C22×C3×#67D3semidirect
37. C22×C3×#67C2×C3semidirect
41. C2×C3×#217D3semidirect
42. C2×C3×#217C2×C3semidirect
52. #63981C2×C3semidirect
53. #63978C2×C3semidirect
54. #63977C2×C3semidirect
55. #63966C2×C3semidirect
56. #63962C2×C3semidirect
58. C23×C33D4semidirect
90. C23×C3⋊D3C22×C3semidirect
95. C23×C3×D3C2×D3semidirect
96. C23×C3×D3C22×C3semidirect
104. C2×#638C22×C3semidirect
105. C22×C3⋊Dic3C22×C3semidirect
122. C2×C3×#67C2×D3semidirect
124. C2×C3×#67C22×C3semidirect
130. C22×C3×Dic3C2×D3semidirect
131. C22×C3×Dic3C2×D3semidirect
132. C22×C3×Dic3C22×C3semidirect
133. C22×C3×Dic3C22×C3semidirect
135. C2×#626C22×C3semidirect
141. C3×#217C2×D3semidirect
142. C3×#217C2×D3semidirect
143. C3×#217C22×C3semidirect
144. C3×#217C22×C3semidirect
150. Dic3⋊Dic3C22×C3semidirect
151. #3722C22×C3semidirect
152. (C2×D3)⋊Dic3C22×C3semidirect
177. C22×#67C3×D3semidirect
187. C2×#217C3×D3semidirect
223. C23×C32D12semidirect
224. C23×C32#67semidirect
225. C23×C32C3×D4semidirect
321. C23×D3C2×C3×D3semidirect
354. C2×#67C2×C3×D3semidirect
358. C22×Dic3C2×C3×D3semidirect
359. C22×Dic3C2×C3×D3semidirect
371. #217C2×C3×D3semidirect
372. #217C2×C3×D3semidirect
478. C33#534semidirect
514. C23×C3#626semidirect
515. C23×C3C3×D12semidirect
516. C23×C3C3×#67semidirect
738. C32#5493semidirect
739. C32#5804semidirect
740. C32C3×#534semidirect
748. C23C3×#626semidirect
827. C3#10595519direct (N × H)
828. C3C3×#5493semidirect
829. C3C3×#5804semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6382
C22×C32×#672
C2×C32×#2172
C3×#639812
C3×#639782
C3×#639772
C3×#639662
C3×#639622
C3×#58043
C3×#54933
#105955193