Finite Group Databasebeta

← C3×#10591395 #13158405

Subgroups — C3×#10591395 #13158405

Order 1728.

1786 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C22×C3×#626C212yesmaximal, complemented
3C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#3722C212yesmaximal, complemented
5C32×C3⋊#95C211yesmaximal, characteristic, complemented
6C3×#4960—31nomaximal
7C3×#4671—31nomaximal
8#10591395C311yesmaximal, characteristic, direct product factor
9C23×C3×C3⋊D3C2212yes—
10C23×C32×D3C2211yescharacteristic
11C22×C33×C4C2211yescharacteristic
12C2×C3×C4⋊(C3⋊D3)—24no—
13C2×C3×C4⋊(C3⋊D3)—22no—
14C22×C32×Dic3C2211yescharacteristic
15C22×C32×Dic3C2212yes—
16C2×C3×#626—24no—
17C2×C3×#626—24no—
18C2×C3×#626—24no—
19C32×(C2×D3)⋊C4—22no—
20C3×#3722—24no—
21C22×C4⋊(C3⋊D3)C2×C311yescharacteristic, complemented
22C22×C3×#67—32no—
23C22×C3×D12—31no—
24C22×C3×D12—31no—
25C22×C3×D12—32no—
26C22×C3×D12—61no—
27C22×#626C2×C312yescomplemented
28C2×C32×C22⋊C4—31no—
29C2×C3×(C2×D3)⋊C4—21no—
30C2×C3×(C2×D3)⋊C4—32no—
31C2×C3×(C2×D3)⋊C4—32no—
32C2×C3×(C2×D3)⋊C4D311yescharacteristic, complemented
33C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
34C2×#3722C2×C312yescomplemented
35C32×#95—31no—
36C3×C3⋊#95—21no—
37C3×C3⋊#95D311yescharacteristic, complemented
38C3×C3⋊#95C2×C311yescharacteristic, complemented
39C23×C33C2311yescharacteristic
40C22×C3×C3⋊D3—22no—
41C22×C3×C3⋊D3—22no—
42C22×C3×C3⋊D3—22no—
43C22×C3×C3⋊D3—22no—
44C22×C3×C3⋊D3—22no—
45C22×C3×C3⋊D3—22no—
46C22×C3×C3⋊D3D414yescomplemented
47C22×C32×D3—21no—
48C22×C32×D3—22no—
49C22×C32×D3—22no—
50C22×C32×D3—21no—
51C22×C32×D3D412yescomplemented
52C2×C33×C4—22no—
53C2×C33×C4D412yescomplemented
54C3×C4⋊(C3⋊D3)—28no—
55C2×C32×Dic3—22no—
56C2×C32×Dic3—22no—
57C2×C32×Dic3—21no—
58C2×C32×Dic3—22no—
59C2×C32×Dic3D414yescomplemented
60C3×#626—216no—
61C3×#392—91no—
62#4960—31no—
63#4671—31no—
64C24×C32—31no—
65C23×C3⋊D3C22×C312yes—
66C23×C3×D3—21no—
67C23×C3×D3—32no—
68C23×C3×D3—32no—
69C23×C3×D3—62no—
70C23×C3×D3C2×D311yescharacteristic
71C23×C3×D3C22×C311yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4—21no—
74C22×C32×C4—21no—
75C22×C32×C4—32no—
76C22×C32×C4—31no—
77C22×C32×C4—41no—
78C22×C32×C4C2×D311yescharacteristic
79C22×C32×C4C2×D311yescharacteristic
80C22×C32×C4C22×C311yescharacteristic
81C2×C4⋊(C3⋊D3)—24no—
82C2×C4⋊(C3⋊D3)—22no—
83C2×C3×#67—64no—
84C2×C3×#67—64no—
85C2×C3×#67—64no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—22no—
88C22×C3×Dic3C2×D311yescharacteristic
89C22×C3×Dic3C2×D312yes—
90C22×C3×Dic3C22×C311yescharacteristic
91C22×C3×Dic3C22×C312yes—
92C2×C3×D12—64no—
93C2×C3×D12—64no—
94C2×C3×D12—68no—
95C2×C3×D12—64no—
96C2×C3×D12—64no—
97C2×C3×D12—64no—
98C2×C3×D12—64no—
99C2×C3×D12—62no—
100C2×C3×D12—62no—
101C2×#626—24no—
102C2×#626—24no—
103C2×#626—24no—
104C32×C22⋊C4—62no—
105C3×(C2×D3)⋊C4—24no—
106C3×(C2×D3)⋊C4—22no—
107C3×(C2×D3)⋊C4—22no—
108C3×(C2×D3)⋊C4—64no—
109C3×(C2×D3)⋊C4—64no—
110#3722—24no—
111C22×C33C2×D411yescharacteristic
112C22×C33C2×D412yes—
113C22×C33C2×D412yes—
114C22×C33C2×D411yescharacteristic
115C22×C33#4111yescharacteristic
116C2×C3×C3⋊D3—24no—
117C2×C3×C3⋊D3—24no—
118C2×C3×C3⋊D3—24no—
119C2×C3×C3⋊D3—42no—
120C2×C3×C3⋊D3—42no—
121C2×C3×C3⋊D3—42no—
122C2×C3×C3⋊D3—42no—
123C2×C32×D3—24no—
124C2×C32×D3—22no—
125C2×C32×D3—41no—
126C2×C32×D3—42no—
127C2×C32×D3—41no—
128C33×C4—22no—
129C32×Dic3—24no—
130C32×Dic3—41no—
131C22×C3×D4—92no—
132C22×C3×D4—91no—
133C22×#67—32no—
134C22×D12—32no—
135C22×D12—31no—
136C22×D12—31no—
137C22×D12—61no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—61no—
141C2×C3×C22⋊C4—92no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4C3×D311yescharacteristic, complemented
145C3×#95—31no—
146C3×#95—31no—
147C3×#95—61no—
148C3⋊#95C3×D311yescharacteristic, complemented
149C23×C32—21no—
150C23×C32—21no—
151C23×C32—21no—
152C23×C32—32no—
153C23×C32—41no—
154C23×C32—61no—
155C23×C32—61no—
156C23×C32—62no—
157C23×C32—62no—
158C23×C32C22×D311yescharacteristic
159C23×C32C22×D311yescharacteristic
160C23×C32C23×C311yescharacteristic
161C22×C3⋊D3—22no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3—22no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3C3×D414yescomplemented
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—21no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—21no—
174C22×C3×D3—21no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—21no—
178C22×C3×D3—22no—
179C22×C3×D3—34no—
180C22×C3×D3—34no—
181C22×C3×D3—42no—
182C22×C3×D3—42no—
183C22×C3×D3—64no—
184C22×C3×D3—64no—
185C22×C3×D3—64no—
186C22×C3×D3—62no—
187C22×C3×D3—62no—
188C22×C3×D3—62no—
189C22×C3×D3—62no—
190C22×C3×D3—62no—
191C22×C3×D3—62no—
192C22×C3×D3—62no—
193C22×C3×D3—62no—
194C22×C3×D3—62no—
195C22×C3×D3—62no—
196C22×C3×D3—62no—
197C22×C3×D3—62no—
198C22×C3×D3—122no—
199C22×C3×D3—122no—
200C22×C3×D3—122no—
201C22×C3×D3—122no—
202C22×C3×D3D1212yescomplemented
203C22×C3×D3C3×D412yescomplemented
204C2×C32×C4—22no—
205C2×C32×C4—24no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—22no—
209C2×C32×C4—22no—
210C2×C32×C4—22no—
211C2×C32×C4—34no—
212C2×C32×C4—42no—
213C2×C32×C4—42no—
214C2×C32×C4—42no—
215C2×C32×C4—44no—
216C2×C32×C4—61no—
217C2×C32×C4—62no—
218C2×C32×C4—62no—
219C2×C32×C4—62no—
220C2×C32×C4D1212yescomplemented
221C2×C32×C4#6712yescomplemented
222C2×C32×C4C3×D412yescomplemented
223C4⋊(C3⋊D3)—28no—
224C3×#67—616no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—24no—
235C2×C3×Dic3—42no—
236C2×C3×Dic3—42no—
237C2×C3×Dic3—42no—
238C2×C3×Dic3D1214yescomplemented
239C2×C3×Dic3C3×D414yescomplemented
240C3×D12—616no—
241C3×D12—68no—
242C3×D12—68no—
243C3×D12—616no—
244#626—216no—
245#392—91noSylow
246C2×C33#12012yes—
247C2×C33#12011yescharacteristic
248C2×C33#12112yes—
249C2×C33#12111yescharacteristic
250C2×C33#12711yescharacteristic
251C3×C3⋊D3—44no—
252C32×D3—42no—
253C24×C3—31no—
254C24×C3—31no—
255C24×C3—61no—
256C24×C3—92no—
257C23×D3—32no—
258C23×D3—32no—
259C23×D3—62no—
260C23×D3C2×C3×D311yescharacteristic
261C2×C3×D4—184no—
262C2×C3×D4—184no—
263C2×C3×D4—184no—
264C2×C3×D4—184no—
265C2×C3×D4—182no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—32no—
270C22×C3×C4—32no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—41no—
274C22×C3×C4—62no—
275C22×C3×C4—61no—
276C22×C3×C4D3211yescharacteristic
277C22×C3×C4C2×C3×D311yescharacteristic
278C22×C3×C4C2×C3×D311yescharacteristic
279C2×#67—64no—
280C2×#67—64no—
281C2×#67—64no—
282C22×Dic3C2×C3×D311yescharacteristic
283C22×Dic3C2×C3×D312yes—
284C2×D12—64no—
285C2×D12—64no—
286C2×D12—68no—
287C2×D12—64no—
288C2×D12—64no—
289C2×D12—64no—
290C2×D12—64no—
291C2×D12—62no—
292C2×D12—62no—
293C3×C22⋊C4—64no—
294C3×C22⋊C4—62no—
295C3×C22⋊C4—62no—
296C3×C22⋊C4—184no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—64no—
299(C2×D3)⋊C4—64no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32—22no—
303C22×C32—21no—
304C22×C32—22no—
305C22×C32—22no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—22no—
311C22×C32—22no—
312C22×C32—22no—
313C22×C32—21no—
314C22×C32—21no—
315C22×C32—41no—
316C22×C32—42no—
317C22×C32—42no—
318C22×C32—41no—
319C22×C32—41no—
320C22×C32—62no—
321C22×C32—64no—
322C22×C32—121no—
323C22×C32—121no—
324C22×C32—122no—
325C22×C32C2×D1212yes—
326C22×C32C2×D1211yescharacteristic
327C22×C32C2×D1211yescharacteristic
328C22×C32#23511yescharacteristic
329C22×C32D3×D411yescharacteristic
330C22×C32D3×D412yes—
331C22×C32D3×D412yes—
332C22×C32D3×D412yes—
333C22×C32#23911yescharacteristic
334C22×C32C2×#6711yescharacteristic
335C22×C32C2×C3×D411yescharacteristic
336C22×C32C2×C3×D412yes—
337C22×C32C2×C3×D411yescharacteristic
338C22×C32C2×C3×D412yes—
339C22×C32C3×#4111yescharacteristic
340C2×C3⋊D3—24no—
341C2×C3⋊D3—24no—
342C2×C3⋊D3—24no—
343C2×C3⋊D3—42no—
344C2×C3⋊D3—42no—
345C2×C3⋊D3—42no—
346C2×C3⋊D3—42no—
347C2×C3×D3—24no—
348C2×C3×D3—24no—
349C2×C3×D3—22no—
350C2×C3×D3—24no—
351C2×C3×D3—22no—
352C2×C3×D3—44no—
353C2×C3×D3—44no—
354C2×C3×D3—42no—
355C2×C3×D3—42no—
356C2×C3×D3—42no—
357C2×C3×D3—41no—
358C2×C3×D3—41no—
359C2×C3×D3—41no—
360C2×C3×D3—42no—
361C2×C3×D3—41no—
362C2×C3×D3—68no—
363C2×C3×D3—64no—
364C2×C3×D3—64no—
365C2×C3×D3—64no—
366C2×C3×D3—64no—
367C2×C3×D3—64no—
368C2×C3×D3—64no—
369C2×C3×D3—124no—
370C2×C3×D3—124no—
371C2×C3×D3—124no—
372C2×C3×D3—124no—
373C2×C3×D3—124no—
374C2×C3×D3—124no—
375C2×C3×D3—122no—
376C2×C3×D3—122no—
377C2×C3×D3—122no—
378C2×C3×D3—122no—
379C2×C3×D3—122no—
380C2×C3×D3—122no—
381C2×C3×D3—122no—
382C2×C3×D3—122no—
383C32×C4—22no—
384C32×C4—24no—
385C32×C4—22no—
386C32×C4—22no—
387C32×C4—42no—
388C32×C4—42no—
389C32×C4—44no—
390C32×C4—64no—
391C32×C4—121no—
392C3×Dic3—24no—
393C3×Dic3—24no—
394C3×Dic3—44no—
395C3×Dic3—42no—
396C3×Dic3—41no—
397C3×Dic3—41no—
398C22×D4—92no—
399C22×D4—91no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—92no—
402#95—31no—
403C33#39211yescharacteristic, complemented, Sylow
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—32no—
408C23×C3—32no—
409C23×C3—41no—
410C23×C3—62no—
411C23×C3—62no—
412C23×C3—62no—
413C23×C3—61no—
414C23×C3—62no—
415C23×C3—61no—
416C23×C3—62no—
417C23×C3—61no—
418C23×C3—62no—
419C23×C3—62no—
420C23×C3—61no—
421C23×C3—94no—
422C23×C3—122no—
423C23×C3—122no—
424C23×C3—182no—
425C23×C3—182no—
426C23×C3—182no—
427C23×C3—182no—
428C23×C3—182no—
429C23×C3—182no—
430C23×C3C2×D3211yescharacteristic
431C23×C3C22×C3×D311yescharacteristic
432C23×C3C22×C3×D311yescharacteristic
433C22×D3—21no—
434C22×D3—22no—
435C22×D3—22no—
436C22×D3—21no—
437C22×D3—34no—
438C22×D3—34no—
439C22×D3—64no—
440C22×D3—64no—
441C22×D3—64no—
442C22×D3—62no—
443C22×D3—62no—
444C22×D3—62no—
445C22×D3—62no—
446C22×D3—62no—
447C22×D3—62no—
448C22×D3—62no—
449C22×D3—62no—
450C22×D3—62no—
451C22×D3—62no—
452C22×D3—62no—
453C22×D3—62no—
454C22×D3—122no—
455C22×D3—122no—
456C22×D3—122no—
457C22×D3—122no—
458C22×D3C3×D1212yescomplemented
459C3×D4—188no—
460C3×D4—1816no—
461C2×C3×C4—24no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—34no—
469C2×C3×C4—34no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—44no—
473C2×C3×C4—42no—
474C2×C3×C4—64no—
475C2×C3×C4—62no—
476C2×C3×C4—62no—
477C2×C3×C4—62no—
478C2×C3×C4—62no—
479C2×C3×C4—62no—
480C2×C3×C4—62no—
481C2×C3×C4—61no—
482C2×C3×C4—62no—
483C2×C3×C4—61no—
484C2×C3×C4—122no—
485C2×C3×C4—122no—
486C2×C3×C4—122no—
487C2×C3×C4#62612yescomplemented
488C2×C3×C4C3×D1212yescomplemented
489C2×C3×C4C3×#6712yescomplemented
490#67—616no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—21no—
495C2×Dic3C3×D1214yescomplemented
496D12—616no—
497D12—68no—
498D12—68no—
499D12—616no—
500C2×C32—22no—
501C2×C32—21no—
502C2×C32—22no—
503C2×C32—22no—
504C2×C32—21no—
505C2×C32—22no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—21no—
510C2×C32—22no—
511C2×C32—21no—
512C2×C32—22no—
513C2×C32—21no—
514C2×C32—21no—
515C2×C32—41no—
516C2×C32—42no—
517C2×C32—41no—
518C2×C32—42no—
519C2×C32—41no—
520C2×C32—122no—
521C2×C32#87411yescharacteristic
522C2×C32#88212yes—
523C2×C32#88212yes—
524C2×C32#88211yescharacteristic
525C2×C32#88412yes—
526C2×C32#89511yescharacteristic
527C2×C32#89512yes—
528C2×C32#93011yescharacteristic
529C2×C32#93711yescharacteristic
530C2×C32#94011yescharacteristic
531C2×C32C3×#12012yes—
532C2×C32C3×#12011yescharacteristic
533C2×C32C3×#12112yes—
534C2×C32C3×#12111yescharacteristic
535C2×C32C3×#12711yescharacteristic
536C3⋊D3—44no—
537C3×D3—44no—
538C3×D3—42no—
539C3×D3—42no—
540C3×D3—128no—
541C3×D3—124no—
542C3×D3—124no—
543C24—31no—
544C24—92no—
545C2×D4—184no—
546C2×D4—184no—
547C2×D4—184no—
548C2×D4—184no—
549C2×D4—182no—
550C22×C4—32no—
551C22×C4—31no—
552C22×C4C3×D3211yescharacteristic
553C22⋊C4—62no—
554C22⋊C4—184no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—22no—
559C22×C3—21no—
560C22×C3—22no—
561C22×C3—21no—
562C22×C3—22no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—42no—
573C22×C3—41no—
574C22×C3—42no—
575C22×C3—64no—
576C22×C3—64no—
577C22×C3—62no—
578C22×C3—62no—
579C22×C3—64no—
580C22×C3—124no—
581C22×C3—122no—
582C22×C3—124no—
583C22×C3—122no—
584C22×C3—121no—
585C22×C3—122no—
586C22×C3—122no—
587C22×C3—121no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3—184no—
591C22×C3—184no—
592C22×C3—184no—
593C22×C3—362no—
594C22×C3—362no—
595C22×C3—362no—
596C22×C3—362no—
597C22×C3#379911yescharacteristic
598C22×C3D3×D1211yescharacteristic
599C22×C3D3×D1212yes—
600C22×C3C2×#62611yescharacteristic
601C22×C3#381112yes—
602C22×C3C2×C3×D1211yescharacteristic
603C22×C3C2×C3×D1212yes—
604C22×C3C2×C3×D1211yescharacteristic
605C22×C3C3×#23511yescharacteristic
606C22×C3C3×D3×D411yescharacteristic
607C22×C3C3×D3×D412yes—
608C22×C3C3×D3×D412yes—
609C22×C3C3×D3×D412yes—
610C22×C3C3×#23911yescharacteristic
611C22×C3C2×C3×#6711yescharacteristic
612C2×D3—24no—
613C2×D3—22no—
614C2×D3—42no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—68no—
618C2×D3—64no—
619C2×D3—64no—
620C2×D3—64no—
621C2×D3—64no—
622C2×D3—64no—
623C2×D3—64no—
624C2×D3—124no—
625C2×D3—124no—
626C2×D3—124no—
627C2×D3—124no—
628C2×D3—124no—
629C2×D3—124no—
630C2×D3—122no—
631C2×D3—122no—
632C2×D3—122no—
633C2×D3—122no—
634C2×D3—122no—
635C2×D3—122no—
636C2×D3—122no—
637C2×D3—122no—
638C3×C4—24no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—44no—
645C3×C4—64no—
646C3×C4—64no—
647C3×C4—124no—
648C3×C4—122no—
649C3×C4—121no—
650C3×C4—121no—
651Dic3—24no—
652Dic3—41no—
653C32—21no—
654C32—21no—
655C32—21no—
656C32—41no—
657C32#467111yescharacteristic, complemented
658C32#496011yescharacteristic, complemented
659C32C3×#39211yescharacteristic, complemented
660C23—32no—
661C23—61no—
662C23—62no—
663C23—61no—
664C23—62no—
665C23—94no—
666C23—182no—
667C23—182no—
668C23—182no—
669C23—182no—
670C23—182no—
671C23—182no—
672C23C2×C3×D3211yescharacteristic
673D4—188no—
674D4—1816no—
675C2×C4—22no—
676C2×C4—34no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—61no—
681C2×C4C3×#62612yescomplemented
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—22no—
689C2×C3—22no—
690C2×C3—22no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—22no—
695C2×C3—22no—
696C2×C3—22no—
697C2×C3—41no—
698C2×C3—41no—
699C2×C3—42no—
700C2×C3—41no—
701C2×C3—42no—
702C2×C3—124no—
703C2×C3—122no—
704C2×C3—122no—
705C2×C3—364no—
706C2×C3#6390911yescharacteristic
707C2×C3#6391012yes—
708C2×C3#6391111yescharacteristic
709C2×C3#6392312yes—
710C2×C3#6398111yescharacteristic
711C2×C3C3×#87411yescharacteristic
712C2×C3C3×#88211yescharacteristic
713C2×C3C3×#88212yes—
714C2×C3C3×#88212yes—
715C2×C3C3×#88412yes—
716C2×C3C3×#89511yescharacteristic
717C2×C3C3×#89512yes—
718C2×C3C3×#93011yescharacteristic
719C2×C3C3×#93711yescharacteristic
720C2×C3C3×#94011yescharacteristic
721D3—42no—
722D3—128no—
723D3—124no—
724D3—124no—
725C22—62no—
726C22—64no—
727C22—121no—
728C22—122no—
729C22—121no—
730C22—184no—
731C22—184no—
732C22—184no—
733C22—362no—
734C22—362no—
735C22—362no—
736C22—362no—
737C22C3×#379911yescharacteristic
738C22C3×D3×D1211yescharacteristic
739C22C3×D3×D1212yes—
740C22C2×C3×#62611yescharacteristic
741C22C3×#381112yes—
742C4—22no—
743C4—64no—
744C4—121no—
745C3—21no—
746C3—21no—
747C3—21no—
748C3—41no—
749C3#1059139511yescharacteristic, direct product factor
750C3C3×#467111yescharacteristic, complemented
751C3C3×#496011yescharacteristic, complemented
752C2—122no—
753C2—364no—
754C2C3×#6390911yescharacteristic
755C2C3×#6391012yes—
756C2C3×#6391111yescharacteristic
757C2C3×#6392312yes—
758C2C3×#6398111yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C3×#392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4⋊(C3⋊D3)C2semidirect
2. C22×C3×#626C2semidirect
3. C2×C32×(C2×D3)⋊C4C2semidirect
4. C2×C3×#3722C2semidirect
5. C32×C3⋊#95C2semidirect
8. #10591395C3direct (N × H)
21. C22×C4⋊(C3⋊D3)C2×C3semidirect
27. C22×#626C2×C3semidirect
32. C2×C3×(C2×D3)⋊C4D3semidirect
33. C2×C3×(C2×D3)⋊C4C2×C3semidirect
34. C2×#3722C2×C3semidirect
37. C3×C3⋊#95D3semidirect
38. C3×C3⋊#95C2×C3semidirect
46. C22×C3×C3⋊D3D4semidirect
51. C22×C32×D3D4semidirect
53. C2×C33×C4D4semidirect
59. C2×C32×Dic3D4semidirect
144. C2×(C2×D3)⋊C4C3×D3semidirect
148. C3⋊#95C3×D3semidirect
167. C22×C3⋊D3C3×D4semidirect
202. C22×C3×D3D12semidirect
203. C22×C3×D3C3×D4semidirect
220. C2×C32×C4D12semidirect
221. C2×C32×C4#67semidirect
222. C2×C32×C4C3×D4semidirect
238. C2×C3×Dic3D12semidirect
239. C2×C3×Dic3C3×D4semidirect
403. C33#392semidirect
458. C22×D3C3×D12semidirect
487. C2×C3×C4#626semidirect
488. C2×C3×C4C3×D12semidirect
489. C2×C3×C4C3×#67semidirect
495. C2×Dic3C3×D12semidirect
657. C32#4671semidirect
658. C32#4960semidirect
659. C32C3×#392semidirect
681. C2×C4C3×#626semidirect
749. C3#10591395direct (N × H)
750. C3C3×#4671semidirect
751. C3C3×#4960semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4⋊(C3⋊D3)2
C22×C3×#6262
C2×C32×(C2×D3)⋊C42
C2×C3×#37222
C32×C3⋊#952
C3×#49603
C3×#46713
#105913953