Finite Group Databasebeta

← C3×#80504 #11870554

Subgroups — C3×#80504 #11870554

Order 1152.

854 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5680C211yesmaximal, characteristic, complemented
2C3×C4×#237C211yesmaximal, characteristic, complemented
3C32×#463C211yesmaximal, characteristic, complemented
4C3×#5173C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6C3×#5158C211yesmaximal, characteristic
7C3×Dic3×D8C211yesmaximal, characteristic, complemented
8C3×#5054C211yesmaximal, characteristic, complemented
9C3×#5009C211yesmaximal, characteristic, complemented
10C3×#4833C211yesmaximal, characteristic, complemented
11C3×#4829C211yesmaximal, characteristic, complemented
12C3×#4814C211yesmaximal, characteristic, complemented
13C3×#4790C211yesmaximal, characteristic, complemented
14C3×#4779C211yesmaximal, characteristic, complemented
15C3×#4758C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#80504C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21C32×#124C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C3×C4×#67—21no—
31C2×C3×C4×Dic3—21no—
32C3×#892C2211yescharacteristic
33C3×#887C2211yescharacteristic
34C3×#883—21no—
35C3×#67⋊C4—21no—
36C3×#67⋊C4—21no—
37C3×#879—21no—
38C3×#877—21no—
39C3×#877—21no—
40C3×C42×D3C2211yescharacteristic
41C3×#870C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45C32×#102C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×C8×Dic3C2211yescharacteristic
57C3×C8×Dic3C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63#5680C2×C311yescharacteristic, complemented
64C4×#237C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#479—31no—
68C3×#478—31no—
69C3×#464—31no—
70C3×#463—21no—
71C3×#463D311yescharacteristic, complemented
72C3×#463C2×C311yescharacteristic, complemented
73C3×#452—31no—
74C3×#449—31no—
75C3×C4×Q16—31no—
76C3×C4×SD16—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#431—31no—
80#5173C2×C311yescharacteristic, complemented
81Dic3×SD16C2×C311yescharacteristic, complemented
82#5158C2×C311yescharacteristic
83Dic3×D8C2×C311yescharacteristic, complemented
84#5054C2×C311yescharacteristic, complemented
85#5009C2×C311yescharacteristic, complemented
86#4833C2×C311yescharacteristic, complemented
87#4829C2×C311yescharacteristic, complemented
88#4814C2×C311yescharacteristic, complemented
89#4790C2×C311yescharacteristic, complemented
90#4779C2×C311yescharacteristic, complemented
91#4758C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×#237—22no—
102C3×#237—22no—
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C32×SD16—22no—
108C32×D8—22no—
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#216—22no—
120C3×#214—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3102—31noSylow
142C2×C3×#41—31no—
143C2×#237C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×SD16—21no—
146C2×C3×SD16—31no—
147C2×C3×SD16C2×D311yescharacteristic
148C2×C3×SD16C22×C311yescharacteristic
149C2×C3×D8—21no—
150C2×C3×D8C2×D311yescharacteristic
151C2×C3×D8C22×C311yescharacteristic
152C3×#126—61no—
153C3×#125—31no—
154C3×#124—21no—
155C3×#124C2×D311yescharacteristic
156C3×#124C22×C311yescharacteristic
157C3×#123—61no—
158C3×C22⋊Q8—31no—
159C3×#121—31no—
160C3×C4×Q8—31no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×D4—21no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—61no—
167C3×C4×D4—61no—
168C3×C4×D4—61no—
169C3×C4×D4C2×D311yescharacteristic
170C3×C4×D4C22×C311yescharacteristic
171C3×#117—31no—
172C3×#117—61no—
173C3×#117—61no—
174C2×C3×C42—31no—
175C2×C3×C42—61no—
176#946C22×C311yescharacteristic
177Q8×Dic3C22×C311yescharacteristic
178C2×#216C22×C311yescharacteristic
179#938C22×C311yescharacteristic
180D4×Dic3C22×C311yescharacteristic
181D4×Dic3C22×C311yescharacteristic
182C2×#214C22×C311yescharacteristic
183C4×#67—21no—
184C2×C4×Dic3—21no—
185#892C22×C311yescharacteristic
186#887C22×C311yescharacteristic
187#883—21no—
188#67⋊C4—21no—
189#67⋊C4—21no—
190#879—21no—
191#877—21no—
192#877—21no—
193C42×D3C22×C311yescharacteristic
194#870C22×C311yescharacteristic
195C4×Dic6C22×C311yescharacteristic
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—21no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8C2×D311yescharacteristic
203C3×C4⋊C8C22×C311yescharacteristic
204C3×#103—21no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103C2×D311yescharacteristic
209C3×#103C22×C311yescharacteristic
210C3×#102—21no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102C2×D311yescharacteristic
215C3×#102C22×C311yescharacteristic
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×C4×C8—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic
221#832C22×C311yescharacteristic
222#832C22×C311yescharacteristic
223#832C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226#818C22×C311yescharacteristic
227#817C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230C8×Dic3C22×C311yescharacteristic
231C8×Dic3C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234C4⋊(C3⋊C8)C22×C311yescharacteristic
235C23×C32—21no—
236C23×C32—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×Q8—21no—
239C32×Q8—21no—
240C32×D4—21no—
241C32×D4—21no—
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—42no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C3×#67—24no—
251C3×#67—42no—
252C2×C3×Dic3—24no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—22no—
265C3×C4×D3—41no—
266C3×Dic6—21no—
267C3×Dic6#4112yes—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#529—31no—
273C4×#41—31no—
274#485—31no—
275#482—31no—
276#479—31no—
277#478—31no—
278#464—31no—
279#463C3×D311yescharacteristic, complemented
280#452—31no—
281#449—31no—
282C4×Q16—31no—
283C4×SD16—31no—
284C4×SD16—31no—
285C4×D8—31no—
286#431—31no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C23×C311yescharacteristic
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C23×C311yescharacteristic
300C2×C3×D4C23×C311yescharacteristic
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—41no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—21no—
311C2×#67—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315#237—22no—
316#237—22no—
317C2×C4×D3C3×D411yescharacteristic
318C2×C4×D3C3×D411yescharacteristic
319C2×C4×D3C23×C311yescharacteristic
320C2×Dic6C23×C311yescharacteristic
321C3×Q16—62no—
322C3×SD16—22no—
323C3×SD16—22no—
324C3×SD16—42no—
325C3×SD16—62no—
326C3×D8—22no—
327C3×D8—22no—
328C3×D8—42no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C22×D311yescharacteristic
335C2×C3×C8C23×C311yescharacteristic
336C2×C3×C8C23×C311yescharacteristic
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C23×C311yescharacteristic
349C3×C22⋊C4—21no—
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—41no—
356C3×C22⋊C4—41no—
357C3×C22⋊C4—41no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—21no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—31no—
367C3×C42—61no—
368C3×C42—61no—
369C3×C42—61no—
370C3×C42—61no—
371C3×C42C22×D311yescharacteristic
372C3×C42C23×C311yescharacteristic
373#217—21no—
374#217—21no—
375#217—21no—
376#216—22no—
377#214—22no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3C23×C311yescharacteristic
382C4⋊Dic3C23×C311yescharacteristic
383C4⋊Dic3C23×C311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3C3×D411yescharacteristic
394C4×Dic3C3×D411yescharacteristic
395C4×Dic3C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397C2×C3⋊C8C23×C311yescharacteristic
398C22×C32—22no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32C22×D411yescharacteristic
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
414C3×Dic3—22no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C3×Dic3#13512yes—
421C2×#41—31no—
422C2×Q16—31no—
423C2×SD16—31no—
424C2×SD16C2×C3×D311yescharacteristic
425C2×D8C2×C3×D311yescharacteristic
426#126—61no—
427#125—31no—
428#124C2×C3×D311yescharacteristic
429#123—61no—
430C22⋊Q8—31no—
431#121—31no—
432C4×Q8—31no—
433C4×Q8—31no—
434C4×Q8—31no—
435C4×D4—31no—
436C4×D4—31no—
437C4×D4—61no—
438C4×D4—61no—
439C4×D4—61no—
440C4×D4C2×C3×D311yescharacteristic
441#117—31no—
442#117—61no—
443#117—61no—
444C2×C42—31no—
445C2×C42—61no—
446#107—31no—
447#107—31no—
448#106—31no—
449#106—31no—
450C4⋊C8—31no—
451C4⋊C8C2×C3×D311yescharacteristic
452#103—31no—
453#103—31no—
454#103—31no—
455#103C2×C3×D311yescharacteristic
456#102—31no—
457#102—31no—
458#102—31no—
459#102C2×C3×D311yescharacteristic
460C22⋊C8—31no—
461C22⋊C8—31no—
462C4×C8—31no—
463C4×C8—31no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—31no—
469C23×C3—41no—
470C23×C3—41no—
471C22×D3C2×C3×D411yescharacteristic
472C3×Q8—21no—
473C3×Q8—21no—
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—32no—
477C3×Q8—41no—
478C3×Q8—41no—
479C3×Q8—61no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—22no—
487C3×D4—41no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—64no—
491C3×D4—122no—
492C3×D4#23712yes—
493C3×D4C3×#4112yes—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—42no—
507C2×C3×C4—42no—
508C2×C3×C4—62no—
509C2×C3×C4—64no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—82no—
517C2×C3×C4—121no—
518C2×C3×C4—122no—
519C2×C3×C4—122no—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C2×C3×D411yescharacteristic
523C2×C3×C4C2×C3×D411yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C24×C311yescharacteristic
526#67—24no—
527#67—42no—
528C2×Dic3—24no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—42no—
534C2×Dic3—42no—
535C2×Dic3C2×C3×D411yescharacteristic
536C2×Dic3C2×C3×D411yescharacteristic
537C2×Dic3C2×C3×D411yescharacteristic
538C4×D3—21no—
539C4×D3—21no—
540C4×D3—22no—
541C4×D3—41no—
542Dic6—21no—
543Dic6C3×#4112yes—
544C3×C8—21no—
545C3×C8—21no—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—41no—
549C3×C8—41no—
550C3×C8—61no—
551C3×C8—61no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C2×C32—42no—
555C2×C32—81no—
556C2×C32#52511yescharacteristic
557C2×C32C2×#13511yescharacteristic
558C2×C32#57511yescharacteristic
559C3×D3—41no—
560#41—62no—
561#41—62no—
562C2×Q8—31no—
563C2×Q8C22×C3×D311yescharacteristic
564C2×D4—61no—
565C2×D4—61no—
566C2×D4C22×C3×D311yescharacteristic
567C2×D4C22×C3×D311yescharacteristic
568C22×C4—21no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575Q16—62no—
576SD16—22no—
577SD16—62no—
578D8—22no—
579C2×C8—31no—
580C2×C8—31no—
581C2×C8C22×C3×D311yescharacteristic
582C2×C8C22×C3×D311yescharacteristic
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—31no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4C22×C3×D311yescharacteristic
593C22⋊C4—21no—
594C22⋊C4—21no—
595C22⋊C4—21no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—61no—
599C22⋊C4—61no—
600C22⋊C4—61no—
601C42—31no—
602C42—31no—
603C42—31no—
604C42—61no—
605C42—61no—
606C42—61no—
607C42—61no—
608C42C22×C3×D311yescharacteristic
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—21no—
612C22×C3—42no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3C2×D3×D411yescharacteristic
632C22×C3C22×C3×D411yescharacteristic
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—32no—
643C3×C4—41no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—62no—
652C3×C4—81no—
653C3×C4—81no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4C2×#23711yescharacteristic
658C3×C4D3×#4111yescharacteristic
659C3×C4C2×C3×#4111yescharacteristic
660C3×C4C2×C3×#4111yescharacteristic
661Dic3—21no—
662Dic3—22no—
663Dic3—21no—
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667Dic3C3×#13512yes—
668C32#310211yescharacteristic, complemented, Sylow
669C23—21no—
670C23—21no—
671C23—31no—
672Q8—21no—
673Q8—21no—
674Q8—32no—
675Q8—61no—
676D4—21no—
677D4—21no—
678D4—21no—
679D4—64no—
680D4—122no—
681D4C3×#23712yes—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—42no—
688C2×C4—62no—
689C2×C4—64no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—121no—
697C2×C4—122no—
698C2×C4—122no—
699C2×C4C3×D3×D411yescharacteristic
700C2×C4C3×D3×D411yescharacteristic
701C2×C4C23×C3×D311yescharacteristic
702C8—21no—
703C8—21no—
704C8—61no—
705C8—61no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—42no—
710C2×C3—42no—
711C2×C3—82no—
712C2×C3—81no—
713C2×C3—81no—
714C2×C3—121no—
715C2×C3—161no—
716C2×C3#560611yescharacteristic
717C2×C3D3×#13511yescharacteristic
718C2×C3#577311yescharacteristic
719C2×C3C3×#52511yescharacteristic
720C2×C3C2×C3×#13511yescharacteristic
721C2×C3C3×#57511yescharacteristic
722D3—41no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—61no—
730C22—61no—
731C22—61no—
732C22C2×C3×D3×D411yescharacteristic
733C4—21no—
734C4—21no—
735C4—32no—
736C4—41no—
737C4—41no—
738C4—61no—
739C4—61no—
740C4—62no—
741C4—121no—
742C4—121no—
743C4—121no—
744C4C2×C3×#23711yescharacteristic
745C4C3×D3×#4111yescharacteristic
746C3—21no—
747C3#8050411yescharacteristic, direct product factor
748C3C3×#310211yescharacteristic, complemented
749C2—42no—
750C2—81no—
751C2—121no—
752C2C3×#560611yescharacteristic
753C2C3×D3×#13511yescharacteristic
754C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#463C2
socleC22×C32C22×D4
prime radicalC3×#5158C2
hypercenterC3×#463D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C3×#5680C2semidirect
2. C3×C4×#237C2semidirect
3. C32×#463C2semidirect
4. C3×#5173C2semidirect
5. C3×Dic3×SD16C2semidirect
7. C3×Dic3×D8C2semidirect
8. C3×#5054C2semidirect
9. C3×#5009C2semidirect
10. C3×#4833C2semidirect
11. C3×#4829C2semidirect
12. C3×#4814C2semidirect
13. C3×#4790C2semidirect
14. C3×#4779C2semidirect
15. C3×#4758C2semidirect
17. #80504C3direct (N × H)
63. #5680C2×C3semidirect
64. C4×#237C2×C3semidirect
71. C3×#463D3semidirect
72. C3×#463C2×C3semidirect
80. #5173C2×C3semidirect
81. Dic3×SD16C2×C3semidirect
83. Dic3×D8C2×C3semidirect
84. #5054C2×C3semidirect
85. #5009C2×C3semidirect
86. #4833C2×C3semidirect
87. #4829C2×C3semidirect
88. #4814C2×C3semidirect
89. #4790C2×C3semidirect
90. #4779C2×C3semidirect
91. #4758C2×C3semidirect
279. #463C3×D3semidirect
668. C32#3102semidirect
747. C3#80504direct (N × H)
748. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C3×#56802
C3×C4×#2372
C32×#4632
C3×#51732
C3×Dic3×SD162
C3×#51582
C3×Dic3×D82
C3×#50542
C3×#50092
C3×#48332
C3×#48292
C3×#48142
C3×#47902
C3×#47792
C3×#47582
C3×#31023
#805043