Finite Group Databasebeta

← C3×#74656 #11856264

Subgroups — C3×#74656 #11856264

Order 1152.

2321 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C2×C3×#894C212yesmaximal, complemented
3C2×C3×#882C211yesmaximal, characteristic
4C32×#385C211yesmaximal, characteristic, complemented
5C3×#5213C211yesmaximal, characteristic, complemented
6C3×#4989C212yesmaximal, complemented
7C3×#4958C211yesmaximal, characteristic, complemented
8C3×#4955C211yesmaximal, characteristic, complemented
9C3×#4946C211yesmaximal, characteristic, complemented
10C3×#4665C212yesmaximal, complemented
11C3×#4664C212yesmaximal, complemented
12C3×#2849—31nomaximal
13#74656C311yesmaximal, characteristic, direct product factor
14C24×C3×D3C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3—28no—
21C22×C3×C4×D3—24no—
22C22×C3×C4×D3C2212yes—
23C22×C3×C4×D3C2212yes—
24C2×C32×C4⋊C4C2212yescomplemented
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2212yes—
32C2×C3×(C2×D3)⋊C4C2212yescomplemented
33C2×C3×(C2×D3)⋊C4C2212yescomplemented
34C2×C3×Dic3⋊C4C2212yescomplemented
35C3×#894—28no—
36C3×#882—24no—
37C32×#95C2212yescomplemented
38C3×C3⋊#95C2212yescomplemented
39C3×C3⋊#95C2212yescomplemented
40C3×C3⋊#95C2212yescomplemented
41C24×C3×C4—31no—
42C23×C4×D3C2×C311yescharacteristic, complemented
43C2×C3×#123—32no—
44C2×C3×#120—31no—
45C2×#894C2×C312yescomplemented
46C2×#882C2×C311yescharacteristic
47C3×#386—31no—
48C3×#386—31no—
49C3×#386—32no—
50C3×#385—21no—
51C3×#385—32no—
52C3×#385—31no—
53C3×#385D311yescharacteristic, complemented
54C3×#385C2×C311yescharacteristic, complemented
55C3×#381—32no—
56C3×#379—31no—
57#5213C2×C311yescharacteristic, complemented
58#4989C2×C312yescomplemented
59#4958C2×C311yescharacteristic, complemented
60#4955C2×C311yescharacteristic, complemented
61#4946C2×C311yescharacteristic, complemented
62#4665C2×C312yescomplemented
63#4664C2×C312yescomplemented
64C24×C32C2311yescharacteristic
65C23×C3×D3—22no—
66C23×C3×D3—22no—
67C23×C3×D3—24no—
68C23×C3×D3—24no—
69C23×C3×D3D414yes—
70C23×C3×D3C2311yescharacteristic
71C23×C3×D3C2311yescharacteristic
72C23×C3×D3C2311yescharacteristic
73C22×C32×C4—22no—
74C22×C32×C4—24no—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2312yes—
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2312yes—
79C2×C3×#67—22no—
80C2×C3×#67—22no—
81C2×C3×#67—22no—
82C22×C3×Dic3—22no—
83C22×C3×Dic3—24no—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C2×C3×D12—22no—
88C2×C3×D12—22no—
89C2×C3×D12—24no—
90C2×C3×D12—24no—
91C2×C3×C4×D3—232no—
92C2×C3×C4×D3—24no—
93C2×C3×C4×D3—24no—
94C2×C3×C4×D3—24no—
95C2×C3×C4×D3—24no—
96C2×C3×C4×D3—24no—
97C2×C3×C4×D3D418yescomplemented
98C32×C4⋊C4—24no—
99C32×C22⋊C4—22no—
100C32×C22⋊C4—22no—
101C3×#217—22no—
102C3×(C2×D3)⋊C4—22no—
103C3×(C2×D3)⋊C4—22no—
104C3×(C2×D3)⋊C4—24no—
105C3×(C2×D3)⋊C4—24no—
106C3×(C2×D3)⋊C4—24no—
107C3×(C2×D3)⋊C4—24no—
108C3×Dic3⋊C4—24no—
109#2849—31noSylow
110C25×C3—31no—
111C24×D3C22×C311yescharacteristic
112C22×C3×D4—31no—
113C22×C3×D4—31no—
114C22×C3×D4—31no—
115C23×C3×C4—21no—
116C23×C3×C4—32no—
117C23×C3×C4—31no—
118C23×C3×C4—32no—
119C23×C3×C4—68no—
120C23×C3×C4—64no—
121C23×C3×C4C2×D311yescharacteristic
122C23×C3×C4C22×C311yescharacteristic
123C22×#67C22×C311yescharacteristic
124C23×Dic3C22×C311yescharacteristic
125C22×D12C22×C311yescharacteristic
126C22×D12C22×C311yescharacteristic
127C22×C4×D3—24no—
128C22×C4×D3—28no—
129C22×C4×D3C22×C312yes—
130C22×C4×D3C22×C312yes—
131C3×#123—68no—
132C3×#120—64no—
133C2×C3×C4⋊C4—22no—
134C2×C3×C4⋊C4—32no—
135C2×C3×C4⋊C4C2×D312yescomplemented
136C2×C3×C4⋊C4C22×C312yescomplemented
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—32no—
141C2×C3×C22⋊C4—32no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—32no—
145C2×C3×C22⋊C4—32no—
146C2×C3×C22⋊C4C2×D311yescharacteristic
147C2×C3×C22⋊C4C2×D311yescharacteristic
148C2×C3×C22⋊C4C22×C311yescharacteristic
149C2×C3×C22⋊C4C22×C311yescharacteristic
150C2×#217C22×C311yescharacteristic
151C2×(C2×D3)⋊C4C22×C311yescharacteristic
152C2×(C2×D3)⋊C4C22×C312yes—
153C2×(C2×D3)⋊C4C22×C312yes—
154C2×(C2×D3)⋊C4C22×C311yescharacteristic
155C2×(C2×D3)⋊C4C22×C312yescomplemented
156C2×(C2×D3)⋊C4C22×C312yescomplemented
157C2×Dic3⋊C4C22×C312yescomplemented
158#894—28no—
159#882—24no—
160C3×#95—22no—
161C3×#95—32no—
162C3×#95—32no—
163C3×#95—32no—
164C3×#95C2×D312yescomplemented
165C3×#95C22×C312yescomplemented
166C3⋊#95C22×C312yescomplemented
167C3⋊#95C22×C312yescomplemented
168C3⋊#95C22×C312yescomplemented
169C23×C32—22no—
170C23×C32—22no—
171C23×C32C2×D412yes—
172C23×C32#4112yes—
173C23×C32#4112yes—
174C23×C32C2411yescharacteristic
175C22×C3×D3—216no—
176C22×C3×D3—216no—
177C22×C3×D3—28no—
178C22×C3×D3—22no—
179C22×C3×D3—21no—
180C22×C3×D3—21no—
181C22×C3×D3—21no—
182C22×C3×D3—21no—
183C22×C3×D3—22no—
184C22×C3×D3—28no—
185C22×C3×D3—28no—
186C22×C3×D3—22no—
187C22×C3×D3—21no—
188C22×C3×D3—22no—
189C22×C3×D3—21no—
190C22×C3×D3—21no—
191C22×C3×D3C2×D414yes—
192C22×C3×D3C2×D412yes—
193C22×C3×D3C2×D412yes—
194C22×C3×D3#4114yes—
195C2×C32×C4—22no—
196C2×C32×C4—28no—
197C2×C32×C4—22no—
198C2×C32×C4—22no—
199C2×C32×C4—22no—
200C2×C32×C4—22no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—22no—
204C2×C32×C4—22no—
205C2×C32×C4C2×D414yes—
206C3×#67—44no—
207C2×C3×Dic3—28no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3C2×D414yes—
217C3×D12—44no—
218C3×D12—44no—
219C3×C4×D3—216no—
220C3×C4×D3—216no—
221C24×C4—31no—
222C2×#123—32no—
223C2×#120—31no—
224#386—31no—
225#386—31no—
226#386—32no—
227#385—32no—
228#385—31no—
229#385C3×D311yescharacteristic, complemented
230#381—32no—
231#379—31no—
232C24×C3—21no—
233C24×C3—31no—
234C24×C3—31no—
235C24×C3—34no—
236C24×C3—31no—
237C24×C3—64no—
238C24×C3—64no—
239C24×C3—62no—
240C24×C3—62no—
241C24×C3C22×D311yescharacteristic
242C24×C3C23×C311yescharacteristic
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—24no—
246C23×D3—24no—
247C23×D3C3×D414yes—
248C23×D3C23×C311yescharacteristic
249C23×D3C23×C311yescharacteristic
250C23×D3C23×C311yescharacteristic
251C2×C3×D4—62no—
252C2×C3×D4—62no—
253C2×C3×D4—64no—
254C2×C3×D4—64no—
255C2×C3×D4—62no—
256C2×C3×D4—62no—
257C2×C3×D4—62no—
258C22×C3×C4—22no—
259C22×C3×C4—22no—
260C22×C3×C4—24no—
261C22×C3×C4—24no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—32no—
267C22×C3×C4—38no—
268C22×C3×C4—31no—
269C22×C3×C4—32no—
270C22×C3×C4—44no—
271C22×C3×C4—42no—
272C22×C3×C4—64no—
273C22×C3×C4—64no—
274C22×C3×C4—64no—
275C22×C3×C4—64no—
276C22×C3×C4—632no—
277C22×C3×C4—64no—
278C22×C3×C4—62no—
279C22×C3×C4—64no—
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D312yes—
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D312yes—
284C22×C3×C4C23×C311yescharacteristic
285C22×C3×C4C23×C312yes—
286C22×C3×C4C23×C311yescharacteristic
287C22×C3×C4C23×C312yes—
288C2×#67—22no—
289C2×#67—22no—
290C2×#67—22no—
291C22×Dic3—22no—
292C22×Dic3—24no—
293C22×Dic3C23×C311yescharacteristic
294C22×Dic3C23×C312yes—
295C22×Dic3C23×C312yes—
296C2×D12—22no—
297C2×D12—22no—
298C2×D12—24no—
299C2×D12—24no—
300C2×C4×D3—232no—
301C2×C4×D3—24no—
302C2×C4×D3—24no—
303C2×C4×D3—24no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3C3×D418yescomplemented
307C3×C4⋊C4—24no—
308C3×C4⋊C4—24no—
309C3×C4⋊C4—44no—
310C3×C4⋊C4—64no—
311C3×C22⋊C4—24no—
312C3×C22⋊C4—22no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—22no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—42no—
317C3×C22⋊C4—64no—
318C3×C22⋊C4—64no—
319C3×C22⋊C4—62no—
320C3×C22⋊C4—62no—
321C3×C22⋊C4—64no—
322C3×C22⋊C4—62no—
323C3×C22⋊C4—64no—
324#217—22no—
325(C2×D3)⋊C4—22no—
326(C2×D3)⋊C4—22no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—24no—
330(C2×D3)⋊C4—24no—
331Dic3⋊C4—24no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—24no—
335C22×C32—24no—
336C22×C32#12314yescomplemented
337C22×C32C22×D411yescharacteristic
338C22×C32C22×D412yes—
339C22×C32C2×#4111yescharacteristic
340C22×C32C2×#4111yescharacteristic
341C22×C32C2×#4112yes—
342C2×C3×D3—232no—
343C2×C3×D3—22no—
344C2×C3×D3—22no—
345C2×C3×D3—22no—
346C2×C3×D3—22no—
347C2×C3×D3—24no—
348C2×C3×D3—24no—
349C2×C3×D3—24no—
350C2×C3×D3—24no—
351C2×C3×D3—41no—
352C2×C3×D3—41no—
353C2×C3×D3—41no—
354C2×C3×D3—42no—
355C2×C3×D3—42no—
356C2×C3×D3#12014yes—
357C2×C3×D3#12314yescomplemented
358C32×C4—24no—
359C32×C4—42no—
360C32×C4—41no—
361C32×C4—41no—
362C3×Dic3—24no—
363C3×Dic3—41no—
364C3×Dic3—42no—
365C25—31no—
366C22×D4—31no—
367C22×D4—31no—
368C22×D4—31no—
369C23×C4—32no—
370C23×C4—31no—
371C23×C4—32no—
372C23×C4—68no—
373C23×C4—64no—
374C23×C4C2×C3×D311yescharacteristic
375#123—68no—
376#120—64no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4C2×C3×D312yescomplemented
379C2×C22⋊C4—31no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—32no—
384C2×C22⋊C4—32no—
385C2×C22⋊C4—32no—
386C2×C22⋊C4C2×C3×D311yescharacteristic
387C2×C22⋊C4C2×C3×D311yescharacteristic
388#95—32no—
389#95—32no—
390#95—32no—
391#95C2×C3×D312yescomplemented
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—21no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—34no—
401C23×C3—32no—
402C23×C3—32no—
403C23×C3—34no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—68no—
407C23×C3—68no—
408C23×C3—616no—
409C23×C3—616no—
410C23×C3—68no—
411C23×C3—61no—
412C23×C3—61no—
413C23×C3—62no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3—62no—
417C23×C3—61no—
418C23×C3—62no—
419C23×C3—61no—
420C23×C3—61no—
421C23×C3—62no—
422C23×C3#23512yes—
423C23×C3D3×D412yes—
424C23×C3#23912yes—
425C23×C3C2×C3×D412yes—
426C23×C3C3×#4112yes—
427C23×C3C3×#4112yes—
428C23×C3C23×D311yescharacteristic
429C23×C3C24×C311yescharacteristic
430C22×D3—216no—
431C22×D3—216no—
432C22×D3—28no—
433C22×D3—22no—
434C22×D3—21no—
435C22×D3—21no—
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—22no—
439C22×D3—28no—
440C22×D3—28no—
441C22×D3—22no—
442C22×D3—21no—
443C22×D3—22no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3C2×C3×D412yes—
447C22×D3C2×C3×D414yes—
448C22×D3C2×C3×D412yes—
449C22×D3C3×#4114yes—
450C3×D4—124no—
451C3×D4—124no—
452C3×D4—124no—
453C2×C3×C4—28no—
454C2×C3×C4—28no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—22no—
459C2×C3×C4—24no—
460C2×C3×C4—22no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—24no—
475C2×C3×C4—34no—
476C2×C3×C4—42no—
477C2×C3×C4—42no—
478C2×C3×C4—42no—
479C2×C3×C4—42no—
480C2×C3×C4—48no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—42no—
484C2×C3×C4—42no—
485C2×C3×C4—616no—
486C2×C3×C4—616no—
487C2×C3×C4—68no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—61no—
491C2×C3×C4—62no—
492C2×C3×C4—61no—
493C2×C3×C4—62no—
494C2×C3×C4—61no—
495C2×C3×C4—62no—
496C2×C3×C4D3×D414yes—
497C2×C3×C4C2×C3×D414yes—
498#67—44no—
499C2×Dic3—28no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—21no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3C2×C3×D414yes—
509D12—44no—
510D12—44no—
511C4×D3—216no—
512C4×D3—216no—
513C2×C32—24no—
514C2×C32C2×#12011yescharacteristic
515C2×C32C2×#12311yescharacteristic
516C2×C32C2×#12311yescharacteristic
517C2×C32#52512yes—
518C2×C32#52512yes—
519C3×D3—24no—
520C3×D3—24no—
521C3×D3—81no—
522C24—31no—
523C24—31no—
524C24—34no—
525C24—31no—
526C24—64no—
527C24—64no—
528C24—62no—
529C24—62no—
530C24C22×C3×D311yescharacteristic
531C2×D4—62no—
532C2×D4—62no—
533C2×D4—64no—
534C2×D4—64no—
535C2×D4—62no—
536C2×D4—62no—
537C2×D4—62no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—32no—
541C22×C4—38no—
542C22×C4—31no—
543C22×C4—32no—
544C22×C4—64no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—64no—
548C22×C4—632no—
549C22×C4—64no—
550C22×C4—62no—
551C22×C4—64no—
552C22×C4C22×C3×D311yescharacteristic
553C22×C4C22×C3×D312yes—
554C22×C4C22×C3×D311yescharacteristic
555C22×C4C22×C3×D312yes—
556C4⋊C4—24no—
557C4⋊C4—64no—
558C22⋊C4—22no—
559C22⋊C4—22no—
560C22⋊C4—64no—
561C22⋊C4—62no—
562C22⋊C4—62no—
563C22⋊C4—64no—
564C22⋊C4—64no—
565C22⋊C4—62no—
566C22⋊C4—64no—
567C22×C3—22no—
568C22×C3—24no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—24no—
573C22×C3—24no—
574C22×C3—24no—
575C22×C3—24no—
576C22×C3—21no—
577C22×C3—22no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—22no—
581C22×C3—34no—
582C22×C3—34no—
583C22×C3—42no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—42no—
587C22×C3—632no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—62no—
591C22×C3—64no—
592C22×C3—64no—
593C22×C3—62no—
594C22×C3—64no—
595C22×C3—64no—
596C22×C3—121no—
597C22×C3—121no—
598C22×C3—122no—
599C22×C3—121no—
600C22×C3—122no—
601C22×C3#89414yescomplemented
602C22×C3C3×#12314yescomplemented
603C22×C3C2×#23511yescharacteristic
604C22×C3C2×D3×D411yescharacteristic
605C22×C3C2×D3×D412yes—
606C22×C3C2×#23911yescharacteristic
607C22×C3D3×#4112yes—
608C22×C3C22×C3×D411yescharacteristic
609C22×C3C22×C3×D412yes—
610C22×C3C2×C3×#4111yescharacteristic
611C22×C3C2×C3×#4111yescharacteristic
612C22×C3C2×C3×#4112yes—
613C2×D3—232no—
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—22no—
617C2×D3—22no—
618C2×D3—24no—
619C2×D3—24no—
620C2×D3—24no—
621C2×D3—24no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3C3×#12014yes—
628C2×D3C3×#12314yescomplemented
629C3×C4—24no—
630C3×C4—24no—
631C3×C4—44no—
632C3×C4—44no—
633C3×C4—41no—
634C3×C4—42no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—42no—
639C3×C4—64no—
640C3×C4—81no—
641C3×C4—81no—
642C3×C4—121no—
643C3×C4—122no—
644Dic3—24no—
645Dic3—41no—
646Dic3—42no—
647C32#284911yescharacteristic, complemented, Sylow
648C23—22no—
649C23—22no—
650C23—34no—
651C23—32no—
652C23—32no—
653C23—34no—
654C23—68no—
655C23—68no—
656C23—616no—
657C23—616no—
658C23—68no—
659C23—61no—
660C23—61no—
661C23—62no—
662C23—61no—
663C23—61no—
664C23—62no—
665C23—61no—
666C23—62no—
667C23—61no—
668C23—61no—
669C23—62no—
670C23C3×#23512yes—
671C23C3×D3×D412yes—
672C23C3×#23912yes—
673C23C23×C3×D311yescharacteristic
674D4—124no—
675D4—124no—
676D4—124no—
677C2×C4—28no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—34no—
688C2×C4—616no—
689C2×C4—616no—
690C2×C4—68no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—61no—
694C2×C4—62no—
695C2×C4—61no—
696C2×C4—62no—
697C2×C4—61no—
698C2×C4—62no—
699C2×C4C3×D3×D414yes—
700C2×C3—24no—
701C2×C3—24no—
702C2×C3—21no—
703C2×C3—22no—
704C2×C3—21no—
705C2×C3—22no—
706C2×C3—21no—
707C2×C3—44no—
708C2×C3—64no—
709C2×C3—64no—
710C2×C3—241no—
711C2×C3C2×#89411yescharacteristic
712C2×C3#554712yes—
713C2×C3D3×#12011yescharacteristic
714C2×C3#562712yes—
715C2×C3D3×#12311yescharacteristic
716C2×C3C2×C3×#12011yescharacteristic
717C2×C3C2×C3×#12311yescharacteristic
718C2×C3C2×C3×#12311yescharacteristic
719C2×C3C3×#52512yes—
720C2×C3C3×#52512yes—
721D3—24no—
722D3—24no—
723D3—81no—
724C22—24no—
725C22—22no—
726C22—24no—
727C22—22no—
728C22—34no—
729C22—34no—
730C22—632no—
731C22—62no—
732C22—62no—
733C22—64no—
734C22—64no—
735C22—62no—
736C22—64no—
737C22—64no—
738C22—62no—
739C22—121no—
740C22—122no—
741C22—121no—
742C22—122no—
743C22—121no—
744C22C3×#89414yescomplemented
745C22C2×C3×#23511yescharacteristic
746C22C2×C3×D3×D411yescharacteristic
747C22C2×C3×D3×D412yes—
748C22C2×C3×#23911yescharacteristic
749C22C3×D3×#4112yes—
750C4—24no—
751C4—42no—
752C4—41no—
753C4—41no—
754C4—64no—
755C4—121no—
756C4—122no—
757C3—21no—
758C3#7465611yescharacteristic, direct product factor
759C3C3×#284911yescharacteristic, complemented
760C2—24no—
761C2—64no—
762C2—64no—
763C2—241no—
764C2C2×C3×#89411yescharacteristic
765C2C3×#554712yes—
766C2C3×D3×#12011yescharacteristic
767C2C3×#562712yes—
768C2C3×D3×#12311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#385C2
socleC23×C32C24
prime radicalC2×C3×#882C2
hypercenterC3×#385D3
hypocenterC3C3×#2849
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
2. C2×C3×#894C2semidirect
4. C32×#385C2semidirect
5. C3×#5213C2semidirect
6. C3×#4989C2semidirect
7. C3×#4958C2semidirect
8. C3×#4955C2semidirect
9. C3×#4946C2semidirect
10. C3×#4665C2semidirect
11. C3×#4664C2semidirect
13. #74656C3direct (N × H)
24. C2×C32×C4⋊C4C22semidirect
32. C2×C3×(C2×D3)⋊C4C22semidirect
33. C2×C3×(C2×D3)⋊C4C22semidirect
34. C2×C3×Dic3⋊C4C22semidirect
37. C32×#95C22semidirect
38. C3×C3⋊#95C22semidirect
39. C3×C3⋊#95C22semidirect
40. C3×C3⋊#95C22semidirect
42. C23×C4×D3C2×C3semidirect
45. C2×#894C2×C3semidirect
53. C3×#385D3semidirect
54. C3×#385C2×C3semidirect
57. #5213C2×C3semidirect
58. #4989C2×C3semidirect
59. #4958C2×C3semidirect
60. #4955C2×C3semidirect
61. #4946C2×C3semidirect
62. #4665C2×C3semidirect
63. #4664C2×C3semidirect
97. C2×C3×C4×D3D4semidirect
135. C2×C3×C4⋊C4C2×D3semidirect
136. C2×C3×C4⋊C4C22×C3semidirect
155. C2×(C2×D3)⋊C4C22×C3semidirect
156. C2×(C2×D3)⋊C4C22×C3semidirect
157. C2×Dic3⋊C4C22×C3semidirect
164. C3×#95C2×D3semidirect
165. C3×#95C22×C3semidirect
166. C3⋊#95C22×C3semidirect
167. C3⋊#95C22×C3semidirect
168. C3⋊#95C22×C3semidirect
229. #385C3×D3semidirect
306. C2×C4×D3C3×D4semidirect
336. C22×C32#123semidirect
357. C2×C3×D3#123semidirect
378. C2×C4⋊C4C2×C3×D3semidirect
391. #95C2×C3×D3semidirect
601. C22×C3#894semidirect
602. C22×C3C3×#123semidirect
628. C2×D3C3×#123semidirect
647. C32#2849semidirect
744. C22C3×#894semidirect
758. C3#74656direct (N × H)
759. C3C3×#2849semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C4×D32
C2×C3×#8942
C2×C3×#8822
C32×#3852
C3×#52132
C3×#49892
C3×#49582
C3×#49552
C3×#49462
C3×#46652
C3×#46642
C3×#28493
#746563