Finite Group Databasebeta

← C3×#74936 #11856252

Subgroups — C3×#74936 #11856252

Order 1152.

2347 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D3C211yesmaximal, characteristic, complemented
2C2×C3×#937C211yesmaximal, characteristic
3C2×C3×#883C212yesmaximal, complemented
4C32×#386C211yesmaximal, characteristic, complemented
5C3×#5220C211yesmaximal, characteristic, complemented
6C3×#5210C211yesmaximal, characteristic, complemented
7C3×#4956C212yesmaximal, complemented
8C3×#4955C211yesmaximal, characteristic, complemented
9C3×#4950C211yesmaximal, characteristic, complemented
10C3×#4668C212yesmaximal, complemented
11C3×#4664C212yesmaximal, complemented
12C3×#2849—31nomaximal
13#74936C311yesmaximal, characteristic, direct product factor
14C24×C3×D3C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×C3×#67C2211yescharacteristic
18C22×C3×#67C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C22×C3×C4×D3—28no—
21C22×C3×C4×D3—24no—
22C22×C3×C4×D3C2212yes—
23C22×C3×C4×D3C2212yes—
24C2×C32×C22⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2212yescomplemented
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2212yescomplemented
29C3×#937—24no—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2212yes—
34C2×C3×C4⋊Dic3C2212yescomplemented
35C2×C3×Dic3⋊C4C2212yescomplemented
36C3×#883—28no—
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×#937C2×C311yescharacteristic
46C2×#883C2×C312yescomplemented
47C3×#386—21no—
48C3×#386—31no—
49C3×#386—32no—
50C3×#386D311yescharacteristic, complemented
51C3×#386C2×C311yescharacteristic, complemented
52C3×#385—31no—
53C3×#385—31no—
54C3×#385—32no—
55C3×#381—32no—
56C3×#379—31no—
57#5220C2×C311yescharacteristic, complemented
58#5210C2×C311yescharacteristic, complemented
59#4956C2×C312yescomplemented
60#4955C2×C311yescharacteristic, complemented
61#4950C2×C311yescharacteristic, complemented
62#4668C2×C312yescomplemented
63#4664C2×C312yescomplemented
64C24×C32C2311yescharacteristic
65C24×C32C2311yescharacteristic
66C23×C3×D3—22no—
67C23×C3×D3—22no—
68C23×C3×D3—24no—
69C23×C3×D3—24no—
70C23×C3×D3D414yes—
71C23×C3×D3C2311yescharacteristic
72C23×C3×D3C2311yescharacteristic
73C2×C32×D4—22no—
74C2×C32×D4—22no—
75C2×C32×D4—22no—
76C22×C32×C4—22no—
77C22×C32×C4—24no—
78C22×C32×C4C2312yes—
79C22×C32×C4C2311yescharacteristic
80C22×C32×C4C2312yes—
81C2×C3×#67—24no—
82C2×C3×#67—22no—
83C2×C3×#67—22no—
84C2×C3×#67—24no—
85C22×C3×Dic3—22no—
86C22×C3×Dic3—24no—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2312yes—
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×C22⋊C4—22no—
99C32×C22⋊C4—24no—
100C3×#217—22no—
101C3×#217—22no—
102C3×#217—24no—
103C3×(C2×D3)⋊C4—24no—
104C3×(C2×D3)⋊C4—22no—
105C3×(C2×D3)⋊C4—22no—
106C3×(C2×D3)⋊C4—24no—
107C3×C4⋊Dic3—24no—
108C3×Dic3⋊C4—24no—
109#2849—31noSylow
110C25×C3—31no—
111C24×D3C22×C311yescharacteristic
112C22×C3×D4—21no—
113C22×C3×D4—31no—
114C22×C3×D4—31no—
115C22×C3×D4C2×D311yescharacteristic
116C22×C3×D4C22×C311yescharacteristic
117C23×C3×C4—21no—
118C23×C3×C4—32no—
119C23×C3×C4—31no—
120C23×C3×C4—32no—
121C23×C3×C4—68no—
122C23×C3×C4—64no—
123C23×C3×C4C2×D311yescharacteristic
124C23×C3×C4C22×C311yescharacteristic
125C22×#67C22×C311yescharacteristic
126C22×#67C22×C311yescharacteristic
127C23×Dic3C22×C311yescharacteristic
128C22×C4×D3—24no—
129C22×C4×D3—28no—
130C22×C4×D3C22×C312yes—
131C22×C4×D3C22×C312yes—
132C3×#123—68no—
133C3×#120—64no—
134C2×C3×C4⋊C4—32no—
135C2×C3×C4⋊C4—32no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—22no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4—31no—
140C2×C3×C22⋊C4—32no—
141C2×C3×C22⋊C4—32no—
142C2×C3×C22⋊C4—32no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4C2×D311yescharacteristic
146C2×C3×C22⋊C4C2×D312yescomplemented
147C2×C3×C22⋊C4C22×C311yescharacteristic
148C2×C3×C22⋊C4C22×C312yescomplemented
149C2×#217C22×C311yescharacteristic
150C2×#217C22×C311yescharacteristic
151C2×#217C22×C312yescomplemented
152#937—24no—
153C2×(C2×D3)⋊C4C22×C311yescharacteristic
154C2×(C2×D3)⋊C4C22×C312yes—
155C2×(C2×D3)⋊C4C22×C311yescharacteristic
156C2×(C2×D3)⋊C4C22×C312yes—
157C2×C4⋊Dic3C22×C312yescomplemented
158C2×Dic3⋊C4C22×C312yescomplemented
159#883—28no—
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—21no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32—21no—
174C23×C32—22no—
175C23×C32—21no—
176C23×C32C2×D412yes—
177C23×C32#4112yes—
178C23×C32#4112yes—
179C23×C32C2411yescharacteristic
180C22×C3×D3—216no—
181C22×C3×D3—216no—
182C22×C3×D3—28no—
183C22×C3×D3—22no—
184C22×C3×D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C22×C3×D3—22no—
189C22×C3×D3—28no—
190C22×C3×D3—28no—
191C22×C3×D3C2×D414yes—
192C22×C3×D3C2×D412yes—
193C22×C3×D3C2×D412yes—
194C22×C3×D3#4114yes—
195C32×D4—44no—
196C2×C32×C4—21no—
197C2×C32×C4—28no—
198C2×C32×C4—22no—
199C2×C32×C4—22no—
200C2×C32×C4—22no—
201C2×C32×C4—21no—
202C2×C32×C4—22no—
203C2×C32×C4—22no—
204C2×C32×C4—21no—
205C2×C32×C4C2×D414yes—
206C3×#67—44no—
207C3×#67—44no—
208C2×C3×Dic3—28no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—22no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3C2×D414yes—
219C3×C4×D3—216no—
220C3×C4×D3—216no—
221C24×C4—31no—
222C2×#123—32no—
223C2×#120—31no—
224#386—31no—
225#386—32no—
226#386C3×D311yescharacteristic, complemented
227#385—31no—
228#385—31no—
229#385—32no—
230#381—32no—
231#379—31no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—31no—
235C24×C3—31no—
236C24×C3—34no—
237C24×C3—64no—
238C24×C3—64no—
239C24×C3—62no—
240C24×C3—62no—
241C24×C3C22×D311yescharacteristic
242C24×C3C22×D311yescharacteristic
243C24×C3C23×C311yescharacteristic
244C24×C3C23×C311yescharacteristic
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—24no—
248C23×D3—24no—
249C23×D3C3×D414yes—
250C23×D3C23×C311yescharacteristic
251C23×D3C23×C311yescharacteristic
252C2×C3×D4—24no—
253C2×C3×D4—22no—
254C2×C3×D4—22no—
255C2×C3×D4—22no—
256C2×C3×D4—22no—
257C2×C3×D4—22no—
258C2×C3×D4—22no—
259C2×C3×D4—42no—
260C2×C3×D4—42no—
261C2×C3×D4—62no—
262C2×C3×D4—62no—
263C2×C3×D4—64no—
264C2×C3×D4—64no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—21no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—32no—
273C22×C3×C4—38no—
274C22×C3×C4—31no—
275C22×C3×C4—32no—
276C22×C3×C4—31no—
277C22×C3×C4—44no—
278C22×C3×C4—42no—
279C22×C3×C4—64no—
280C22×C3×C4—64no—
281C22×C3×C4—64no—
282C22×C3×C4—64no—
283C22×C3×C4—632no—
284C22×C3×C4—64no—
285C22×C3×C4—62no—
286C22×C3×C4—64no—
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D312yes—
289C22×C3×C4C22×D312yes—
290C22×C3×C4C23×C311yescharacteristic
291C22×C3×C4C23×C312yes—
292C22×C3×C4C23×C312yes—
293C2×#67—24no—
294C2×#67—22no—
295C2×#67—22no—
296C2×#67—24no—
297C22×Dic3—22no—
298C22×Dic3—24no—
299C22×Dic3C23×C311yescharacteristic
300C22×Dic3C23×C312yes—
301C22×Dic3C23×C311yescharacteristic
302C22×Dic3C23×C312yes—
303C2×C4×D3—232no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3C3×D418yescomplemented
310C3×C4⋊C4—64no—
311C3×C4⋊C4—64no—
312C3×C22⋊C4—22no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—24no—
315C3×C22⋊C4—24no—
316C3×C22⋊C4—44no—
317C3×C22⋊C4—42no—
318C3×C22⋊C4—64no—
319C3×C22⋊C4—62no—
320C3×C22⋊C4—62no—
321C3×C22⋊C4—64no—
322C3×C22⋊C4—64no—
323C3×C22⋊C4—62no—
324C3×C22⋊C4—62no—
325#217—22no—
326#217—22no—
327#217—24no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—22no—
330(C2×D3)⋊C4—22no—
331(C2×D3)⋊C4—24no—
332C4⋊Dic3—24no—
333Dic3⋊C4—24no—
334C22×C32—22no—
335C22×C32—22no—
336C22×C32—24no—
337C22×C32—24no—
338C22×C32—41no—
339C22×C32—42no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32—42no—
343C22×C32#12314yescomplemented
344C22×C32C22×D411yescharacteristic
345C22×C32C22×D412yes—
346C22×C32C2×#4111yescharacteristic
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4112yes—
349C2×C3×D3—232no—
350C2×C3×D3—22no—
351C2×C3×D3—22no—
352C2×C3×D3—22no—
353C2×C3×D3—22no—
354C2×C3×D3—24no—
355C2×C3×D3—24no—
356C2×C3×D3—24no—
357C2×C3×D3—24no—
358C2×C3×D3#12014yes—
359C2×C3×D3#12314yescomplemented
360C32×C4—24no—
361C32×C4—41no—
362C32×C4—42no—
363C3×Dic3—24no—
364C3×Dic3—41no—
365C3×Dic3—41no—
366C3×Dic3—42no—
367C25—31no—
368C22×D4—31no—
369C22×D4—31no—
370C22×D4C2×C3×D311yescharacteristic
371C23×C4—32no—
372C23×C4—31no—
373C23×C4—32no—
374C23×C4—68no—
375C23×C4—64no—
376C23×C4C2×C3×D311yescharacteristic
377#123—68no—
378#120—64no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—32no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—31no—
384C2×C22⋊C4—31no—
385C2×C22⋊C4—31no—
386C2×C22⋊C4—32no—
387C2×C22⋊C4—32no—
388C2×C22⋊C4C2×C3×D311yescharacteristic
389C2×C22⋊C4C2×C3×D312yescomplemented
390#95—32no—
391#95—32no—
392#95—32no—
393#95C2×C3×D312yescomplemented
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—21no—
400C23×C3—22no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—34no—
414C23×C3—32no—
415C23×C3—32no—
416C23×C3—34no—
417C23×C3—42no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—42no—
423C23×C3—68no—
424C23×C3—68no—
425C23×C3—616no—
426C23×C3—616no—
427C23×C3—68no—
428C23×C3—61no—
429C23×C3—61no—
430C23×C3—62no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3—62no—
434C23×C3#23512yes—
435C23×C3D3×D412yes—
436C23×C3#23712yes—
437C23×C3C2×C3×D412yes—
438C23×C3C3×#4112yes—
439C23×C3C3×#4112yes—
440C23×C3C23×D311yescharacteristic
441C23×C3C24×C311yescharacteristic
442C22×D3—216no—
443C22×D3—216no—
444C22×D3—28no—
445C22×D3—22no—
446C22×D3—21no—
447C22×D3—21no—
448C22×D3—21no—
449C22×D3—21no—
450C22×D3—22no—
451C22×D3—28no—
452C22×D3—28no—
453C22×D3C2×C3×D412yes—
454C22×D3C2×C3×D414yes—
455C22×D3C2×C3×D412yes—
456C22×D3C3×#4114yes—
457C3×D4—48no—
458C3×D4—44no—
459C3×D4—44no—
460C3×D4—124no—
461C3×D4—124no—
462C2×C3×C4—28no—
463C2×C3×C4—28no—
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—22no—
471C2×C3×C4—21no—
472C2×C3×C4—22no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—21no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—24no—
482C2×C3×C4—34no—
483C2×C3×C4—42no—
484C2×C3×C4—42no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—48no—
488C2×C3×C4—42no—
489C2×C3×C4—42no—
490C2×C3×C4—42no—
491C2×C3×C4—616no—
492C2×C3×C4—616no—
493C2×C3×C4—68no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4D3×D414yes—
504C2×C3×C4C2×C3×D414yes—
505#67—44no—
506#67—44no—
507C2×Dic3—28no—
508C2×Dic3—22no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3—22no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3C2×C3×D414yes—
518C4×D3—216no—
519C4×D3—216no—
520C2×C32—24no—
521C2×C32—81no—
522C2×C32C2×#12011yescharacteristic
523C2×C32C2×#12311yescharacteristic
524C2×C32C2×#12311yescharacteristic
525C2×C32#52512yes—
526C2×C32#52512yes—
527C3×D3—24no—
528C3×D3—24no—
529C24—31no—
530C24—31no—
531C24—34no—
532C24—64no—
533C24—64no—
534C24—62no—
535C24—62no—
536C24C22×C3×D311yescharacteristic
537C24C22×C3×D311yescharacteristic
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—62no—
542C2×D4—62no—
543C2×D4—64no—
544C2×D4—64no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—32no—
548C22×C4—38no—
549C22×C4—31no—
550C22×C4—32no—
551C22×C4—31no—
552C22×C4—64no—
553C22×C4—64no—
554C22×C4—64no—
555C22×C4—64no—
556C22×C4—632no—
557C22×C4—64no—
558C22×C4—62no—
559C22×C4—64no—
560C22×C4C22×C3×D311yescharacteristic
561C22×C4C22×C3×D312yes—
562C22×C4C22×C3×D312yes—
563C4⋊C4—64no—
564C4⋊C4—64no—
565C22⋊C4—22no—
566C22⋊C4—24no—
567C22⋊C4—62no—
568C22⋊C4—62no—
569C22⋊C4—64no—
570C22⋊C4—64no—
571C22⋊C4—64no—
572C22⋊C4—62no—
573C22⋊C4—62no—
574C22×C3—22no—
575C22×C3—24no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—24no—
580C22×C3—24no—
581C22×C3—24no—
582C22×C3—24no—
583C22×C3—21no—
584C22×C3—22no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—22no—
588C22×C3—34no—
589C22×C3—34no—
590C22×C3—42no—
591C22×C3—44no—
592C22×C3—44no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—44no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—42no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—632no—
607C22×C3—62no—
608C22×C3—62no—
609C22×C3—62no—
610C22×C3—64no—
611C22×C3—64no—
612C22×C3—62no—
613C22×C3—64no—
614C22×C3—64no—
615C22×C3—81no—
616C22×C3—82no—
617C22×C3—81no—
618C22×C3#88314yescomplemented
619C22×C3C3×#12314yescomplemented
620C22×C3C2×#23511yescharacteristic
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C2×D3×D412yes—
623C22×C3C2×#23711yescharacteristic
624C22×C3D3×#4112yes—
625C22×C3C22×C3×D411yescharacteristic
626C22×C3C22×C3×D412yes—
627C22×C3C2×C3×#4111yescharacteristic
628C22×C3C2×C3×#4111yescharacteristic
629C22×C3C2×C3×#4112yes—
630C2×D3—232no—
631C2×D3—22no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—24no—
636C2×D3—24no—
637C2×D3—24no—
638C2×D3—24no—
639C2×D3C3×#12014yes—
640C2×D3C3×#12314yescomplemented
641C3×C4—24no—
642C3×C4—24no—
643C3×C4—44no—
644C3×C4—42no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4—64no—
650C3×C4—82no—
651C3×C4—121no—
652C3×C4—122no—
653C3×C4—121no—
654Dic3—24no—
655Dic3—41no—
656Dic3—41no—
657Dic3—42no—
658C32#284911yescharacteristic, complemented, Sylow
659C23—22no—
660C23—22no—
661C23—21no—
662C23—22no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—34no—
667C23—32no—
668C23—32no—
669C23—34no—
670C23—68no—
671C23—68no—
672C23—616no—
673C23—616no—
674C23—68no—
675C23—61no—
676C23—61no—
677C23—62no—
678C23—61no—
679C23—61no—
680C23—62no—
681C23C3×#23512yes—
682C23C3×D3×D412yes—
683C23C3×#23712yes—
684C23C23×C3×D311yescharacteristic
685D4—44no—
686D4—124no—
687D4—124no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—34no—
698C2×C4—616no—
699C2×C4—616no—
700C2×C4—68no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—62no—
708C2×C4—62no—
709C2×C4—62no—
710C2×C4C3×D3×D414yes—
711C2×C3—24no—
712C2×C3—24no—
713C2×C3—21no—
714C2×C3—22no—
715C2×C3—21no—
716C2×C3—22no—
717C2×C3—21no—
718C2×C3—44no—
719C2×C3—64no—
720C2×C3—64no—
721C2×C3—82no—
722C2×C3—81no—
723C2×C3—81no—
724C2×C3C2×#88311yescharacteristic
725C2×C3#554712yes—
726C2×C3D3×#12011yescharacteristic
727C2×C3#560612yes—
728C2×C3D3×#12311yescharacteristic
729C2×C3C2×C3×#12011yescharacteristic
730C2×C3C2×C3×#12311yescharacteristic
731C2×C3C2×C3×#12311yescharacteristic
732C2×C3C3×#52512yes—
733C2×C3C3×#52512yes—
734D3—24no—
735D3—24no—
736C22—24no—
737C22—22no—
738C22—24no—
739C22—22no—
740C22—34no—
741C22—34no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—632no—
748C22—62no—
749C22—62no—
750C22—64no—
751C22—64no—
752C22—62no—
753C22—64no—
754C22—64no—
755C22—62no—
756C22C3×#88314yescomplemented
757C22C2×C3×#23511yescharacteristic
758C22C2×C3×D3×D411yescharacteristic
759C22C2×C3×D3×D412yes—
760C22C2×C3×#23711yescharacteristic
761C22C3×D3×#4112yes—
762C4—24no—
763C4—41no—
764C4—42no—
765C4—64no—
766C4—122no—
767C4—121no—
768C4—121no—
769C3—21no—
770C3#7493611yescharacteristic, direct product factor
771C3C3×#284911yescharacteristic, complemented
772C2—24no—
773C2—64no—
774C2—64no—
775C2—81no—
776C2C2×C3×#88311yescharacteristic
777C2C3×#554712yes—
778C2C3×D3×#12011yescharacteristic
779C2C3×#560612yes—
780C2C3×D3×#12311yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#386C2
socleC23×C32C24
prime radicalC2×C3×#937C2
hypercenterC3×#386D3
hypocenterC3C3×#2849
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
1. C23×C3×C4×D3C2semidirect
3. C2×C3×#883C2semidirect
4. C32×#386C2semidirect
5. C3×#5220C2semidirect
6. C3×#5210C2semidirect
7. C3×#4956C2semidirect
8. C3×#4955C2semidirect
9. C3×#4950C2semidirect
10. C3×#4668C2semidirect
11. C3×#4664C2semidirect
13. #74936C3direct (N × H)
25. C2×C32×C22⋊C4C22semidirect
28. C2×C3×#217C22semidirect
34. C2×C3×C4⋊Dic3C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
37. C32×#95C22semidirect
38. C3×C3⋊#95C22semidirect
39. C3×C3⋊#95C22semidirect
40. C3×C3⋊#95C22semidirect
42. C23×C4×D3C2×C3semidirect
46. C2×#883C2×C3semidirect
50. C3×#386D3semidirect
51. C3×#386C2×C3semidirect
57. #5220C2×C3semidirect
58. #5210C2×C3semidirect
59. #4956C2×C3semidirect
60. #4955C2×C3semidirect
61. #4950C2×C3semidirect
62. #4668C2×C3semidirect
63. #4664C2×C3semidirect
97. C2×C3×C4×D3D4semidirect
146. C2×C3×C22⋊C4C2×D3semidirect
148. C2×C3×C22⋊C4C22×C3semidirect
151. C2×#217C22×C3semidirect
157. C2×C4⋊Dic3C22×C3semidirect
158. C2×Dic3⋊C4C22×C3semidirect
164. C3×#95C2×D3semidirect
165. C3×#95C22×C3semidirect
166. C3⋊#95C22×C3semidirect
167. C3⋊#95C22×C3semidirect
168. C3⋊#95C22×C3semidirect
226. #386C3×D3semidirect
309. C2×C4×D3C3×D4semidirect
343. C22×C32#123semidirect
359. C2×C3×D3#123semidirect
389. C2×C22⋊C4C2×C3×D3semidirect
393. #95C2×C3×D3semidirect
618. C22×C3#883semidirect
619. C22×C3C3×#123semidirect
640. C2×D3C3×#123semidirect
658. C32#2849semidirect
756. C22C3×#883semidirect
770. C3#74936direct (N × H)
771. 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×#9372
C2×C3×#8832
C32×#3862
C3×#52202
C3×#52102
C3×#49562
C3×#49552
C3×#49502
C3×#46682
C3×#46642
C3×#28493
#749363