Finite Group Databasebeta

← C3×#81352 #11872087

Subgroups — C3×#81352 #11872087

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5603C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3C32×#482C211yesmaximal, characteristic, complemented
4C3×#5036C211yesmaximal, characteristic
5C3×#4996C211yesmaximal, characteristic, complemented
6C3×#4890C211yesmaximal, characteristic, complemented
7C3×#4889C211yesmaximal, characteristic, complemented
8C3×#4870C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4787C211yesmaximal, characteristic, complemented
11C3×#4787C211yesmaximal, characteristic, complemented
12C3×#4785C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×#4731C211yesmaximal, characteristic, complemented
15C3×#4720C211yesmaximal, characteristic, complemented
16C3×#3118—31nomaximal
17#81352C311yesmaximal, characteristic, direct product factor
18C22×C3×D12C2211yescharacteristic
19C32×#121C2211yescharacteristic
20C32×#117C2211yescharacteristic
21C3×#936—21no—
22C3×#936C2211yescharacteristic, complemented
23C3×#935—21no—
24C3×D4×Dic3C2211yescharacteristic, complemented
25C2×C3×#213C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#893C2211yescharacteristic
35C3×#888C2211yescharacteristic, complemented
36C3×#887C2211yescharacteristic, complemented
37C3×D3×C22⋊C4—21no—
38C3×D3×C22⋊C4—21no—
39C3×#879—21no—
40C3×#878—21no—
41C3×C4×D12—21no—
42C3×C4×D12—21no—
43C32×#107C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45C32×#102C2211yescharacteristic, complemented
46C32×#102C2211yescharacteristic, complemented
47C32×C22⋊C8C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#815C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#808C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#542—31no—
62C3×#518—31no—
63#5603C2×C311yescharacteristic, complemented
64#5521C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—21no—
67C3×#482D311yescharacteristic, complemented
68C3×#482C2×C311yescharacteristic, complemented
69C3×#476—31no—
70C3×#474—31no—
71C3×#463—31no—
72C3×#463—31no—
73C3×#450—31no—
74C3×#447—31no—
75C3×#442—31no—
76C3×#440—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#433—31no—
80#5036C2×C311yescharacteristic
81#4996C2×C311yescharacteristic, complemented
82#4890C2×C311yescharacteristic, complemented
83#4889C2×C311yescharacteristic, complemented
84#4870C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4787C2×C311yescharacteristic, complemented
87#4787C2×C311yescharacteristic, complemented
88#4785C2×C311yescharacteristic, complemented
89#4756C2×C311yescharacteristic, complemented
90#4731C2×C311yescharacteristic, complemented
91#4720C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3×Dic3—21no—
97C2×C3×D12—21no—
98C2×C3×D12—22no—
99C2×C3×D12—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C22⋊C4—21no—
115C32×C42—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×#217D411yescharacteristic
122C3×#213—22no—
123C3×#213—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3D411yescharacteristic
129C3×C4⋊Dic3D411yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×#204—22no—
141#3118—31noSylow
142C22×C3×D4—31no—
143C22×D12C22×C311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C2×C3×D8—31no—
147C2×C3×D8—31no—
148C3×C4⋊Q8—31no—
149C3×#126—61no—
150C3×#124—31no—
151C3×#124—61no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C3×#121—21no—
156C3×#121C2×D311yescharacteristic
157C3×#121C22×C311yescharacteristic
158C3×C4×Q8—31no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4—61no—
166C3×#117—21no—
167C3×#117—31no—
168C3×#117C2×D311yescharacteristic
169C3×#117C22×C311yescharacteristic
170C2×C3×C22⋊C4—61no—
171C2×C3×C22⋊C4—61no—
172#936—21no—
173#936C22×C311yescharacteristic, complemented
174#935—21no—
175D4×Dic3C22×C311yescharacteristic, complemented
176C2×#213C22×C311yescharacteristic
177C2×#213C22×C311yescharacteristic
178#926C22×C311yescharacteristic
179#924C22×C311yescharacteristic
180C2×#204C22×C311yescharacteristic
181C2×#204C22×C311yescharacteristic
182#893C22×C311yescharacteristic
183#893C22×C311yescharacteristic
184#893C22×C311yescharacteristic
185#893C22×C311yescharacteristic
186#888C22×C311yescharacteristic, complemented
187#887C22×C311yescharacteristic, complemented
188D3×C22⋊C4—21no—
189D3×C22⋊C4—21no—
190#879—21no—
191#878—21no—
192C4×D12—21no—
193C4×D12—21no—
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic, complemented
197C3×#107C22×C311yescharacteristic, complemented
198C3×#106—21no—
199C3×#106—31no—
200C3×#106C2×D311yescharacteristic, complemented
201C3×#106C22×C311yescharacteristic, complemented
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—21no—
207C3×#102—21no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic, complemented
213C3×#102C2×D311yescharacteristic, complemented
214C3×#102C22×C311yescharacteristic, complemented
215C3×#102C22×C311yescharacteristic, complemented
216C3×C22⋊C8—21no—
217C3×C22⋊C8—31no—
218C3×C22⋊C8C2×D311yescharacteristic
219C3×C22⋊C8C22×C311yescharacteristic
220C3×#97—31no—
221C3×C4×C8—31no—
222#830C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224#821C22×C311yescharacteristic
225#815C22×C311yescharacteristic, complemented
226Dic3⋊C8C22×C311yescharacteristic, complemented
227Dic3⋊C8C22×C311yescharacteristic, complemented
228C8×Dic3C22×C311yescharacteristic, complemented
229#810C22×C311yescharacteristic, complemented
230#810C22×C311yescharacteristic, complemented
231#809C22×C311yescharacteristic
232#809C22×C311yescharacteristic
233#808C22×C311yescharacteristic, complemented
234#807C22×C311yescharacteristic, complemented
235C23×C32—21no—
236C23×C32C2×D411yescharacteristic
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—24no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C32×D4—21no—
243C32×D4—21no—
244C32×D4—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—24no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12#4112yes—
263C3×D12#4112yes—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×Dic6—21no—
269C3×Dic6—21no—
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#482C3×D311yescharacteristic, complemented
279#476—31no—
280#474—31no—
281#463—31no—
282#463—31no—
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—31no—
293C2×C3×Q8—61no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—41no—
300C2×C3×D4—62no—
301C2×C3×D4—62no—
302C2×C3×D4—61no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C23×C311yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C23×C311yescharacteristic
313C22×Dic3—21no—
314C2×D12—21no—
315C2×D12—22no—
316C2×D12—22no—
317C2×D12C23×C311yescharacteristic
318C2×D12C23×C311yescharacteristic
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×Dic6—21no—
324C2×Dic6C23×C311yescharacteristic
325C3×SD16—62no—
326C3×SD16—62no—
327C3×D8—62no—
328C3×D8—62no—
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—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C23×C311yescharacteristic
350C3×C4⋊C4C23×C311yescharacteristic
351C3×C4⋊C4C23×C311yescharacteristic
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—41no—
359C3×C22⋊C4—41no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C42—21no—
369C3×C42—21no—
370C3×C42—31no—
371C3×C42—31no—
372C3×C42—41no—
373C3×C42—61no—
374#217—21no—
375#217—21no—
376#217—21no—
377#217—21no—
378#217C3×D411yescharacteristic
379#217C3×D411yescharacteristic
380#213—22no—
381#213—22no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386C4⋊Dic3C3×D411yescharacteristic
387C4⋊Dic3C3×D411yescharacteristic
388C4⋊Dic3C23×C311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392C4×Dic3—21no—
393C4×Dic3C23×C311yescharacteristic
394C4×Dic3C23×C311yescharacteristic
395C2×C3⋊C8C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397#204—22no—
398#204—22no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—84no—
413C32×C4—21no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C22×D4—31no—
426C2×SD16—31no—
427C2×SD16—31no—
428C2×D8—31no—
429C2×D8—31no—
430C4⋊Q8—31no—
431#126—61no—
432#124—31no—
433#124—61no—
434#123—61no—
435C22⋊Q8—31no—
436C22⋊Q8—61no—
437#121C2×C3×D311yescharacteristic
438C4×Q8—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—31no—
444C4×D4—61no—
445C4×D4—61no—
446#117—31no—
447#117C2×C3×D311yescharacteristic
448C2×C22⋊C4—61no—
449C2×C22⋊C4—61no—
450#107—31no—
451#107C2×C3×D311yescharacteristic, complemented
452#106—31no—
453#106C2×C3×D311yescharacteristic, complemented
454C4⋊C8—31no—
455C4⋊C8—31no—
456#103—31no—
457#103—31no—
458#102—31no—
459#102—31no—
460#102—31no—
461#102—31no—
462#102C2×C3×D311yescharacteristic, complemented
463#102C2×C3×D311yescharacteristic, complemented
464C22⋊C8—31no—
465C22⋊C8C2×C3×D311yescharacteristic
466#97—31no—
467C4×C8—31no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—41no—
472C23×C3—64no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—241no—
476C23×C3—241no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×C3×D411yescharacteristic
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—24no—
482C22×D3—81no—
483C22×D3—81no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—241no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—32no—
492C3×D4—32no—
493C3×D4—41no—
494C3×D4—41no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—81no—
499C3×D4—81no—
500C3×D4—82no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—241no—
525C2×C3×C4—241no—
526C2×C3×C4—241no—
527C2×C3×C4—241no—
528C2×C3×C4—241no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×C3×D411yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C24×C311yescharacteristic
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—81no—
536C2×Dic3C2×C3×D411yescharacteristic
537C2×Dic3C2×C3×D411yescharacteristic
538C2×Dic3C2×C3×D411yescharacteristic
539C2×Dic3C2×C3×D411yescharacteristic
540D12—24no—
541D12—21no—
542D12—21no—
543D12C3×#4112yes—
544D12C3×#4112yes—
545C4×D3—81no—
546C4×D3—81no—
547C4×D3—81no—
548C4×D3—81no—
549Dic6—21no—
550Dic6—21no—
551Dic6—81no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—41no—
557C3×C8—41no—
558C3×C8—61no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C2×C32—41no—
563C2×C32—81no—
564C2×C32#52511yescharacteristic
565C2×C32#57611yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—42no—
568C3×D3—42no—
569C24—61no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×D4—21no—
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—62no—
576C2×D4—62no—
577C2×D4—61no—
578C2×D4C22×C3×D311yescharacteristic
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4C22×C3×D311yescharacteristic
585SD16—62no—
586SD16—62no—
587D8—62no—
588D8—62no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8C22×C3×D311yescharacteristic
592C2×C8C22×C3×D311yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4C22×C3×D311yescharacteristic
600C4⋊C4C22×C3×D311yescharacteristic
601C4⋊C4C22×C3×D311yescharacteristic
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C42—21no—
615C42—31no—
616C42—31no—
617C42—61no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—41no—
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—62no—
635C22×C3—62no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—244no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C22×C3×D411yescharacteristic
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—84no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—81no—
669C3×C4—81no—
670C3×C4—81no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4D3×#4111yescharacteristic
674C3×C4D3×#4111yescharacteristic
675C3×C4C2×C3×#4111yescharacteristic
676C3×C4C2×C3×#4111yescharacteristic
677Dic3—21no—
678Dic3—21no—
679Dic3—21no—
680Dic3—21no—
681Dic3—41no—
682Dic3—41no—
683C32#311811yescharacteristic, complemented, Sylow
684C23—21no—
685C23—64no—
686C23—61no—
687C23—61no—
688C23—241no—
689C23—241no—
690C23C3×D3×D411yescharacteristic
691Q8—61no—
692Q8—61no—
693Q8—241no—
694D4—21no—
695D4—21no—
696D4—32no—
697D4—32no—
698D4—64no—
699D4—61no—
700D4—61no—
701D4—81no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—241no—
714C2×C4—241no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—241no—
718C2×C4C3×D3×D411yescharacteristic
719C2×C4C23×C3×D311yescharacteristic
720C8—21no—
721C8—21no—
722C8—61no—
723C8—61no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—41no—
728C2×C3—41no—
729C2×C3—81no—
730C2×C3—81no—
731C2×C3—81no—
732C2×C3—122no—
733C2×C3—122no—
734C2×C3—161no—
735C2×C3#565611yescharacteristic
736C2×C3#577011yescharacteristic
737C2×C3#577411yescharacteristic
738C2×C3C3×#52511yescharacteristic
739C2×C3C3×#57611yescharacteristic
740C2×C3C3×#57711yescharacteristic
741D3—42no—
742D3—42no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—62no—
750C22—62no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—244no—
756C22C2×C3×D3×D411yescharacteristic
757C4—21no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—61no—
762C4—61no—
763C4—61no—
764C4—61no—
765C4—121no—
766C4—121no—
767C4C3×D3×#4111yescharacteristic
768C4C3×D3×#4111yescharacteristic
769C3—21no—
770C3#8135211yescharacteristic, direct product factor
771C3C3×#311811yescharacteristic, complemented
772C2—41no—
773C2—81no—
774C2—122no—
775C2—122no—
776C2C3×#565611yescharacteristic
777C2C3×#577011yescharacteristic
778C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#482C2
socleC22×C32C22×D4
prime radicalC3×#5036C2
hypercenterC3×#482D3
hypocenterC3C3×#3118
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#482

Complements

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

NH ≅ G/Ntype
1. C3×#5603C2semidirect
2. C3×#5521C2semidirect
3. C32×#482C2semidirect
5. C3×#4996C2semidirect
6. C3×#4890C2semidirect
7. C3×#4889C2semidirect
8. C3×#4870C2semidirect
9. C3×#4852C2semidirect
10. C3×#4787C2semidirect
11. C3×#4787C2semidirect
12. C3×#4785C2semidirect
13. C3×#4756C2semidirect
14. C3×#4731C2semidirect
15. C3×#4720C2semidirect
17. #81352C3direct (N × H)
22. C3×#936C22semidirect
24. C3×D4×Dic3C22semidirect
35. C3×#888C22semidirect
36. C3×#887C22semidirect
43. C32×#107C22semidirect
44. C32×#106C22semidirect
45. C32×#102C22semidirect
46. C32×#102C22semidirect
51. C3×#815C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. C3×#810C22semidirect
56. C3×#810C22semidirect
59. C3×#808C22semidirect
60. C3×#807C22semidirect
63. #5603C2×C3semidirect
64. #5521C2×C3semidirect
67. C3×#482D3semidirect
68. C3×#482C2×C3semidirect
81. #4996C2×C3semidirect
82. #4890C2×C3semidirect
83. #4889C2×C3semidirect
84. #4870C2×C3semidirect
85. #4852C2×C3semidirect
86. #4787C2×C3semidirect
87. #4787C2×C3semidirect
88. #4785C2×C3semidirect
89. #4756C2×C3semidirect
90. #4731C2×C3semidirect
91. #4720C2×C3semidirect
173. #936C22×C3semidirect
175. D4×Dic3C22×C3semidirect
186. #888C22×C3semidirect
187. #887C22×C3semidirect
196. C3×#107C2×D3semidirect
197. C3×#107C22×C3semidirect
200. C3×#106C2×D3semidirect
201. C3×#106C22×C3semidirect
212. C3×#102C2×D3semidirect
213. C3×#102C2×D3semidirect
214. C3×#102C22×C3semidirect
215. C3×#102C22×C3semidirect
225. #815C22×C3semidirect
226. Dic3⋊C8C22×C3semidirect
227. Dic3⋊C8C22×C3semidirect
228. C8×Dic3C22×C3semidirect
229. #810C22×C3semidirect
230. #810C22×C3semidirect
233. #808C22×C3semidirect
234. #807C22×C3semidirect
278. #482C3×D3semidirect
451. #107C2×C3×D3semidirect
453. #106C2×C3×D3semidirect
462. #102C2×C3×D3semidirect
463. #102C2×C3×D3semidirect
683. C32#3118semidirect
770. C3#81352direct (N × H)
771. C3C3×#3118semidirect

Maximal subgroups

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

subgroupindex
C3×#56032
C3×#55212
C32×#4822
C3×#50362
C3×#49962
C3×#48902
C3×#48892
C3×#48702
C3×#48522
C3×#47872
C3×#47852
C3×#47562
C3×#47312
C3×#47202
C3×#31183
#813523