Finite Group Databasebeta

← C3×#80509 #11872099

Subgroups — C3×#80509 #11872099

Order 1152.

874 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5682C211yesmaximal, characteristic, complemented
2C3×#5545C211yesmaximal, characteristic, complemented
3C32×#463C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6C3×#5156C211yesmaximal, characteristic
7C3×#5152C211yesmaximal, characteristic, complemented
8C3×#5057C211yesmaximal, characteristic, complemented
9C3×#5007C211yesmaximal, characteristic, complemented
10C3×#4842C211yesmaximal, characteristic, complemented
11C3×#4840C211yesmaximal, characteristic, complemented
12C3×#4817C211yesmaximal, characteristic, complemented
13C3×#4815C211yesmaximal, characteristic, complemented
14C3×#4779C211yesmaximal, characteristic, complemented
15C3×#4756C211yesmaximal, characteristic, complemented
16C3×#3118—31nomaximal
17#80509C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C2×C32×D8C2211yescharacteristic
21C32×#124C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic
30C3×C4×#67—21no—
31C2×C3×(C2×D3)⋊C4—21no—
32C3×#893C2211yescharacteristic
33C3×#892C2211yescharacteristic
34C3×#886—21no—
35C3×#885—21no—
36C3×#67⋊C4—21no—
37C3×D3×C22⋊C4—21no—
38C3×#879—21no—
39C3×#878—21no—
40C3×C4×D12C2211yescharacteristic
41C3×#872C2211yescharacteristic
42C3×#869C2211yescharacteristic, complemented
43C32×C4⋊C8C2211yescharacteristic, complemented
44C32×#103C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic, complemented
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×(C2×D3)⋊C8C2211yescharacteristic
54C3×#817C2211yescharacteristic, complemented
55C3×#817C2211yescharacteristic, complemented
56C3×#815C2211yescharacteristic, complemented
57C3×C8×Dic3C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×#542—31no—
62C3×#518—31no—
63#5682C2×C311yescharacteristic, complemented
64#5545C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#476—31no—
68C3×#474—31no—
69C3×#463—21no—
70C3×#463—31no—
71C3×#463D311yescharacteristic, complemented
72C3×#463C2×C311yescharacteristic, complemented
73C3×#450—31no—
74C3×#447—31no—
75C3×#442—31no—
76C3×#440—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#433—31no—
80#5169C2×C311yescharacteristic, complemented
81Dic3×SD16C2×C311yescharacteristic, complemented
82#5156C2×C311yescharacteristic
83#5152C2×C311yescharacteristic, complemented
84#5057C2×C311yescharacteristic, complemented
85#5007C2×C311yescharacteristic, complemented
86#4842C2×C311yescharacteristic, complemented
87#4840C2×C311yescharacteristic, complemented
88#4817C2×C311yescharacteristic, complemented
89#4815C2×C311yescharacteristic, complemented
90#4779C2×C311yescharacteristic, complemented
91#4756C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C32×SD16—22no—
109C32×D8—22no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C22⋊C4—21no—
116C32×C42C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#215—22no—
121C3×#213—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141#3118—31noSylow
142C22×C3×D4—31no—
143C2×D3×D4C22×C311yescharacteristic
144C2×C3×SD16—21no—
145C2×C3×SD16—31no—
146C2×C3×SD16C2×D311yescharacteristic
147C2×C3×SD16C22×C311yescharacteristic
148C2×C3×D8—21no—
149C2×C3×D8—31no—
150C2×C3×D8C2×D311yescharacteristic
151C2×C3×D8C22×C311yescharacteristic
152C3×C4⋊Q8—31no—
153C3×#126—61no—
154C3×#124—21no—
155C3×#124—61no—
156C3×#124C2×D311yescharacteristic, complemented
157C3×#124C22×C311yescharacteristic, complemented
158C3×#123—61no—
159C3×C22⋊Q8—31no—
160C3×C22⋊Q8—61no—
161C3×#121—31no—
162C3×C4×Q8—31no—
163C3×C4×D4—21no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—31no—
167C3×C4×D4—31no—
168C3×C4×D4—61no—
169C3×C4×D4—61no—
170C3×C4×D4C2×D311yescharacteristic
171C3×C4×D4C22×C311yescharacteristic
172C3×#117—31no—
173C3×#117—31no—
174C2×C3×C22⋊C4—61no—
175C2×C3×C22⋊C4—61no—
176#946C22×C311yescharacteristic
177Q8×Dic3C22×C311yescharacteristic, complemented
178C2×#215C22×C311yescharacteristic
179#938C22×C311yescharacteristic
180D4×Dic3C22×C311yescharacteristic
181D4×Dic3C22×C311yescharacteristic, complemented
182C2×#213C22×C311yescharacteristic
183C4×#67—21no—
184C2×(C2×D3)⋊C4—21no—
185#893C22×C311yescharacteristic
186#892C22×C311yescharacteristic
187#886—21no—
188#885—21no—
189#67⋊C4—21no—
190D3×C22⋊C4—21no—
191#879—21no—
192#878—21no—
193C4×D12C22×C311yescharacteristic
194#872C22×C311yescharacteristic
195#869C22×C311yescharacteristic, complemented
196C3×#107—31no—
197C3×#107—31no—
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—21no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8C2×D311yescharacteristic, complemented
203C3×C4⋊C8C22×C311yescharacteristic, complemented
204C3×#103—21no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic, complemented
207C3×#103C22×C311yescharacteristic, complemented
208C3×#102—21no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102C2×D311yescharacteristic, complemented
215C3×#102C22×C311yescharacteristic, complemented
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×#97—31no—
219C3×C4×C8—31no—
220#835C22×C311yescharacteristic, complemented
221#832C22×C311yescharacteristic
222#832C22×C311yescharacteristic
223#832C22×C311yescharacteristic, complemented
224#821C22×C311yescharacteristic
225#821C22×C311yescharacteristic
226(C2×D3)⋊C8C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228#817C22×C311yescharacteristic, complemented
229#817C22×C311yescharacteristic, complemented
230#815C22×C311yescharacteristic, complemented
231C8×Dic3C22×C311yescharacteristic, complemented
232#807C22×C311yescharacteristic, complemented
233#807C22×C311yescharacteristic, complemented
234C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
235C23×C32—21no—
236C23×C32—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—81no—
240C22×C3×D3—81no—
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4—21no—
247C32×D4#4112yes—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—81no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C3×#67—24no—
255C3×#67—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270C3×Dic6—81no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—31no—
276#518—31no—
277#485—31no—
278#482—31no—
279#476—31no—
280#474—31no—
281#463—31no—
282#463C3×D311yescharacteristic, complemented
283#450—31no—
284#447—31no—
285#442—31no—
286#440—31no—
287C4×SD16—31no—
288C4×D8—31no—
289#433—31no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—21no—
293C2×C3×Q8—61no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C23×C311yescharacteristic
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—62no—
301C2×C3×D4—62no—
302C2×C3×D4—61no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C23×C311yescharacteristic
306C2×C3×D4C23×C311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—41no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C2×#67—21no—
316C2×#67—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319D3×D4—22no—
320D3×D4—22no—
321C2×D12C23×C311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3C23×C311yescharacteristic
325C2×Dic6—21no—
326C3×SD16—22no—
327C3×SD16—22no—
328C3×SD16—42no—
329C3×SD16—62no—
330C3×D8—22no—
331C3×D8—22no—
332C3×D8—42no—
333C3×D8—62no—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C23×C311yescharacteristic
341C2×C3×C8C23×C311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C23×C311yescharacteristic
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—41no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—21no—
372C3×C42—31no—
373C3×C42—61no—
374C3×C42—61no—
375C3×C42C22×D311yescharacteristic
376C3×C42C23×C311yescharacteristic
377#217—21no—
378#217—21no—
379#217—21no—
380#215—22no—
381#213—22no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4C3×D411yescharacteristic
387(C2×D3)⋊C4C3×D411yescharacteristic
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3C23×C311yescharacteristic
391C4⋊Dic3C23×C311yescharacteristic
392C4⋊Dic3C23×C311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4C3×D411yescharacteristic
395Dic3⋊C4C3×D411yescharacteristic
396C4×Dic3—21no—
397C4×Dic3—21no—
398C4×Dic3C23×C311yescharacteristic
399C2×C3⋊C8C23×C311yescharacteristic
400C2×C3⋊C8C23×C311yescharacteristic
401C22×C32—22no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—22no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—84no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×D4—31no—
428C2×SD16—31no—
429C2×SD16C2×C3×D311yescharacteristic
430C2×D8—31no—
431C2×D8C2×C3×D311yescharacteristic
432C4⋊Q8—31no—
433#126—61no—
434#124—61no—
435#124C2×C3×D311yescharacteristic, complemented
436#123—61no—
437C22⋊Q8—31no—
438C22⋊Q8—61no—
439#121—31no—
440C4×Q8—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—61no—
446C4×D4—61no—
447C4×D4C2×C3×D311yescharacteristic
448#117—31no—
449#117—31no—
450C2×C22⋊C4—61no—
451C2×C22⋊C4—61no—
452#107—31no—
453#107—31no—
454#106—31no—
455#106—31no—
456C4⋊C8—31no—
457C4⋊C8C2×C3×D311yescharacteristic, complemented
458#103—31no—
459#103C2×C3×D311yescharacteristic, complemented
460#102—31no—
461#102—31no—
462#102—31no—
463#102—31no—
464#102—31no—
465#102C2×C3×D311yescharacteristic, complemented
466C22⋊C8—31no—
467C22⋊C8—31no—
468#97—31no—
469C4×C8—31no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—31no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—64no—
478C23×C3—61no—
479C23×C3—241no—
480C23×C3—241no—
481C22×D3—21no—
482C22×D3—24no—
483C22×D3—81no—
484C22×D3—81no—
485C22×D3C2×C3×D411yescharacteristic
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—241no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—32no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—64no—
505C3×D4—61no—
506C3×D4—241no—
507C3×D4#23712yes—
508C3×D4C3×#4112yes—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—81no—
527C2×C3×C4—81no—
528C2×C3×C4—82no—
529C2×C3×C4—241no—
530C2×C3×C4—241no—
531C2×C3×C4—241no—
532C2×C3×C4—241no—
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C2×C3×D411yescharacteristic
536C2×C3×C4C2×C3×D411yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C24×C311yescharacteristic
539#67—24no—
540#67—81no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—81no—
545C2×Dic3—81no—
546C2×Dic3C2×C3×D411yescharacteristic
547C2×Dic3C2×C3×D411yescharacteristic
548C2×Dic3C2×C3×D411yescharacteristic
549D12—21no—
550D12C3×#4112yes—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—81no—
554C4×D3—81no—
555Dic6—81no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—41no—
561C3×C8—41no—
562C3×C8—61no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—21no—
566C2×C32—42no—
567C2×C32—81no—
568C2×C32#52511yescharacteristic
569C2×C32#57611yescharacteristic
570C2×C32#57711yescharacteristic
571C3×D3—41no—
572C3×D3—42no—
573C24—61no—
574C2×Q8—61no—
575C2×Q8C22×C3×D311yescharacteristic
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—62no—
579C2×D4—62no—
580C2×D4—61no—
581C2×D4C22×C3×D311yescharacteristic
582C2×D4C22×C3×D311yescharacteristic
583C22×C4—21no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589SD16—22no—
590SD16—62no—
591D8—22no—
592D8—62no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8C22×C3×D311yescharacteristic
596C2×C8C22×C3×D311yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4C22×C3×D311yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—31no—
610C22⋊C4—31no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C42—31no—
619C42—61no—
620C42—61no—
621C42C22×C3×D311yescharacteristic
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—62no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—244no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C22×C3×D411yescharacteristic
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—22no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—84no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—81no—
673C3×C4—81no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4C2×#23711yescharacteristic
678C3×C4D3×#4111yescharacteristic
679C3×C4C2×C3×#4111yescharacteristic
680C3×C4C2×C3×#4111yescharacteristic
681Dic3—21no—
682Dic3—21no—
683Dic3—21no—
684Dic3—41no—
685Dic3—41no—
686Dic3—41no—
687C32#311811yescharacteristic, complemented, Sylow
688C23—21no—
689C23—21no—
690C23—31no—
691C23—64no—
692C23—61no—
693C23—241no—
694C23—241no—
695Q8—21no—
696Q8—21no—
697Q8—241no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—32no—
702D4—64no—
703D4—61no—
704D4—241no—
705D4C3×#23712yes—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—81no—
717C2×C4—241no—
718C2×C4—241no—
719C2×C4—241no—
720C2×C4—241no—
721C2×C4C3×D3×D411yescharacteristic
722C2×C4C3×D3×D411yescharacteristic
723C2×C4C23×C3×D311yescharacteristic
724C8—21no—
725C8—21no—
726C8—61no—
727C8—61no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—42no—
732C2×C3—42no—
733C2×C3—82no—
734C2×C3—81no—
735C2×C3—81no—
736C2×C3—121no—
737C2×C3—122no—
738C2×C3—161no—
739C2×C3#560611yescharacteristic
740C2×C3#577011yescharacteristic
741C2×C3#577411yescharacteristic
742C2×C3C3×#52511yescharacteristic
743C2×C3C3×#57611yescharacteristic
744C2×C3C3×#57711yescharacteristic
745D3—41no—
746D3—42no—
747C22—22no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—61no—
754C22—61no—
755C22—61no—
756C22—62no—
757C22—121no—
758C22—121no—
759C22—244no—
760C22C2×C3×D3×D411yescharacteristic
761C4—21no—
762C4—21no—
763C4—41no—
764C4—41no—
765C4—61no—
766C4—61no—
767C4—61no—
768C4—121no—
769C4—121no—
770C4—121no—
771C4C2×C3×#23711yescharacteristic
772C4C3×D3×#4111yescharacteristic
773C3—21no—
774C3#8050911yescharacteristic, direct product factor
775C3C3×#311811yescharacteristic, complemented
776C2—42no—
777C2—81no—
778C2—121no—
779C2—122no—
780C2C3×#560611yescharacteristic
781C2C3×#577011yescharacteristic
782C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#463C2
socleC22×C32C22×D4
prime radicalC3×#5156C2
hypercenterC3×#463D3
hypocenterC3C3×#3118
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×#5682C2semidirect
2. C3×#5545C2semidirect
3. C32×#463C2semidirect
4. C3×#5169C2semidirect
5. C3×Dic3×SD16C2semidirect
7. C3×#5152C2semidirect
8. C3×#5057C2semidirect
9. C3×#5007C2semidirect
10. C3×#4842C2semidirect
11. C3×#4840C2semidirect
12. C3×#4817C2semidirect
13. C3×#4815C2semidirect
14. C3×#4779C2semidirect
15. C3×#4756C2semidirect
17. #80509C3direct (N × H)
21. C32×#124C22semidirect
24. C3×Q8×Dic3C22semidirect
28. C3×D4×Dic3C22semidirect
42. C3×#869C22semidirect
43. C32×C4⋊C8C22semidirect
44. C32×#103C22semidirect
45. C32×#102C22semidirect
46. C3×#835C22semidirect
49. C3×#832C22semidirect
54. C3×#817C22semidirect
55. C3×#817C22semidirect
56. C3×#815C22semidirect
57. C3×C8×Dic3C22semidirect
58. C3×#807C22semidirect
59. C3×#807C22semidirect
60. C3×C4⋊(C3⋊C8)C22semidirect
63. #5682C2×C3semidirect
64. #5545C2×C3semidirect
71. C3×#463D3semidirect
72. C3×#463C2×C3semidirect
80. #5169C2×C3semidirect
81. Dic3×SD16C2×C3semidirect
83. #5152C2×C3semidirect
84. #5057C2×C3semidirect
85. #5007C2×C3semidirect
86. #4842C2×C3semidirect
87. #4840C2×C3semidirect
88. #4817C2×C3semidirect
89. #4815C2×C3semidirect
90. #4779C2×C3semidirect
91. #4756C2×C3semidirect
156. C3×#124C2×D3semidirect
157. C3×#124C22×C3semidirect
177. Q8×Dic3C22×C3semidirect
181. D4×Dic3C22×C3semidirect
195. #869C22×C3semidirect
202. C3×C4⋊C8C2×D3semidirect
203. C3×C4⋊C8C22×C3semidirect
206. C3×#103C2×D3semidirect
207. C3×#103C22×C3semidirect
214. C3×#102C2×D3semidirect
215. C3×#102C22×C3semidirect
220. #835C22×C3semidirect
223. #832C22×C3semidirect
228. #817C22×C3semidirect
229. #817C22×C3semidirect
230. #815C22×C3semidirect
231. C8×Dic3C22×C3semidirect
232. #807C22×C3semidirect
233. #807C22×C3semidirect
234. C4⋊(C3⋊C8)C22×C3semidirect
282. #463C3×D3semidirect
435. #124C2×C3×D3semidirect
457. C4⋊C8C2×C3×D3semidirect
459. #103C2×C3×D3semidirect
465. #102C2×C3×D3semidirect
687. C32#3118semidirect
774. C3#80509direct (N × H)
775. C3C3×#3118semidirect

Maximal subgroups

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

subgroupindex
C3×#56822
C3×#55452
C32×#4632
C3×#51692
C3×Dic3×SD162
C3×#51562
C3×#51522
C3×#50572
C3×#50072
C3×#48422
C3×#48402
C3×#48172
C3×#48152
C3×#47792
C3×#47562
C3×#31183
#805093