Finite Group Databasebeta

← C3×#81354 #11872703

Subgroups — C3×#81354 #11872703

Order 1152.

889 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5619C211yesmaximal, characteristic, complemented
2C3×#5521C211yesmaximal, characteristic, complemented
3C32×#482C211yesmaximal, characteristic, complemented
4C3×#5036C211yesmaximal, characteristic, complemented
5C3×#5003C211yesmaximal, characteristic, complemented
6C3×#4891C211yesmaximal, characteristic, complemented
7C3×#4872C211yesmaximal, characteristic, complemented
8C3×#4871C211yesmaximal, characteristic, complemented
9C3×#4869C211yesmaximal, characteristic, complemented
10C3×#4786C211yesmaximal, characteristic, complemented
11C3×#4786C211yesmaximal, characteristic, complemented
12C3×#4785C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×#4732C211yesmaximal, characteristic, complemented
15C3×#4720C211yesmaximal, characteristic, complemented
16C3×#3122—31nomaximal
17#81354C311yesmaximal, characteristic, direct product factor
18C22×C3×D12C2211yescharacteristic
19C32×#121C2211yescharacteristic
20C32×#117C2211yescharacteristic
21C3×#940C2211yescharacteristic, complemented
22C3×#939—21no—
23C3×#938—21no—
24C3×D4×Dic3C2211yescharacteristic, complemented
25C2×C3×#213C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#930C2211yescharacteristic
28C3×#926C2211yescharacteristic
29C2×C3×D24C2211yescharacteristic
30C2×C3×D24C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#893C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#893C2211yescharacteristic
35C3×#893C2211yescharacteristic, complemented
36C3×#890C2211yescharacteristic, complemented
37C3×#886—21no—
38C3×#883—21no—
39C3×D3×C22⋊C4—21no—
40C3×D3×C22⋊C4—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×#809C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59C3×#808C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#540—31no—
62C3×#518—31no—
63#5619C2×C311yescharacteristic, complemented
64#5521C2×C311yescharacteristic, complemented
65C3×#482—21no—
66C3×#482—31no—
67C3×#482D311yescharacteristic, complemented
68C3×#482C2×C311yescharacteristic, complemented
69C3×#478—31no—
70C3×#478—31no—
71C3×#459—31no—
72C3×#459—31no—
73C3×#447—31no—
74C3×#447—31no—
75C3×#442—31no—
76C3×#442—31no—
77C3×C4×D8—31no—
78C3×C4×D8—31no—
79C3×#433—31no—
80#5036C2×C311yescharacteristic, complemented
81#5003C2×C311yescharacteristic, complemented
82#4891C2×C311yescharacteristic, complemented
83#4872C2×C311yescharacteristic, complemented
84#4871C2×C311yescharacteristic, complemented
85#4869C2×C311yescharacteristic, complemented
86#4786C2×C311yescharacteristic, complemented
87#4786C2×C311yescharacteristic, complemented
88#4785C2×C311yescharacteristic, complemented
89#4756C2×C311yescharacteristic, complemented
90#4732C2×C311yescharacteristic, complemented
91#4720C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C2×C3×D12—21no—
101C2×C3×D12—22no—
102C2×C3×D12—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C32×C42—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×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3D411yescharacteristic
132C3×C4⋊Dic3D411yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3C2311yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D24—22no—
140C3×D24—22no—
141#3122—31noSylow
142C22×C3×D4—31no—
143C22×D12C22×C311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C2×C3×D8—31no—
147C2×C3×D8—31no—
148C3×#127—31no—
149C3×#125—31no—
150C3×#123—61no—
151C3×#123—61no—
152C3×#121—21no—
153C3×#121—31no—
154C3×#121—61no—
155C3×#121—61no—
156C3×#121C2×D311yescharacteristic
157C3×#121C22×C311yescharacteristic
158C3×C4×D4—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#940C22×C311yescharacteristic, complemented
173#939—21no—
174#938—21no—
175D4×Dic3C22×C311yescharacteristic, complemented
176C2×#213C22×C311yescharacteristic
177C2×#213C22×C311yescharacteristic
178#930C22×C311yescharacteristic
179#926C22×C311yescharacteristic
180C2×D24C22×C311yescharacteristic
181C2×D24C22×C311yescharacteristic
182#893C22×C311yescharacteristic
183#893C22×C311yescharacteristic
184#893C22×C311yescharacteristic
185#893C22×C311yescharacteristic
186#893C22×C311yescharacteristic, complemented
187#890C22×C311yescharacteristic, complemented
188#886—21no—
189#883—21no—
190D3×C22⋊C4—21no—
191D3×C22⋊C4—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×#102—21no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102—31no—
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#809C22×C311yescharacteristic
230#809C22×C311yescharacteristic
231#809C22×C311yescharacteristic, complemented
232#809C22×C311yescharacteristic, complemented
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—21no—
241C22×C3×D3—81no—
242C22×C3×D3—81no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—81no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C3×#67—81no—
254C3×#67—81no—
255C3×#67—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—81no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—24no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12#4112yes—
268C3×D12#4112yes—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
271C3×C4×D3—81no—
272C3×C4×D3—81no—
273C3×C4×D3—81no—
274C32×C8—21no—
275C32×C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—31no—
279#518—31no—
280#482—31no—
281#482C3×D311yescharacteristic, complemented
282#478—31no—
283#478—31no—
284#459—31no—
285#459—31no—
286#447—31no—
287#447—31no—
288#442—31no—
289#442—31no—
290C4×D8—31no—
291C4×D8—31no—
292#433—31no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—41no—
302C2×C3×D4—62no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C23×C311yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C2×#67—21no—
320C2×#67—21no—
321C2×#67—21no—
322C22×Dic3—21no—
323C2×D12—21no—
324C2×D12—22no—
325C2×D12—22no—
326C2×D12C23×C311yescharacteristic
327C2×D12C23×C311yescharacteristic
328C2×D12C23×C311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C3×D8—62no—
335C3×D8—62no—
336C3×D8—62no—
337C3×D8—62no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C23×C311yescharacteristic
345C2×C3×C8C23×C311yescharacteristic
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C23×C311yescharacteristic
358C3×C4⋊C4C23×C311yescharacteristic
359C3×C4⋊C4C23×C311yescharacteristic
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—41no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—31no—
378C3×C42—31no—
379C3×C42—41no—
380#217—21no—
381#217C3×D411yescharacteristic
382#217C3×D411yescharacteristic
383#213—22no—
384#213—22no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3C3×D411yescharacteristic
393C4⋊Dic3C3×D411yescharacteristic
394C4⋊Dic3C23×C311yescharacteristic
395Dic3⋊C4—21no—
396C4×Dic3C23×C311yescharacteristic
397C4×Dic3C23×C311yescharacteristic
398C2×C3⋊C8C23×C311yescharacteristic
399C2×C3⋊C8C23×C311yescharacteristic
400D24—22no—
401D24—22no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32C22×D411yescharacteristic
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—84no—
419C32×C4—21no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C22×D4—31no—
431C2×D8—31no—
432C2×D8—31no—
433C2×D8—31no—
434C2×D8—31no—
435#127—31no—
436#125—31no—
437#123—61no—
438#123—61no—
439#121—31no—
440#121—61no—
441#121—61no—
442#121C2×C3×D311yescharacteristic
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—31no—
449C4×D4—61no—
450C4×D4—61no—
451#117—31no—
452#117C2×C3×D311yescharacteristic
453C2×C22⋊C4—61no—
454C2×C22⋊C4—61no—
455#107—31no—
456#107C2×C3×D311yescharacteristic, complemented
457#106—31no—
458#106C2×C3×D311yescharacteristic, complemented
459C4⋊C8—31no—
460C4⋊C8—31no—
461#102—31no—
462#102—31no—
463#102—31no—
464#102—31no—
465#102—31no—
466#102—31no—
467#102C2×C3×D311yescharacteristic, complemented
468#102C2×C3×D311yescharacteristic, complemented
469C22⋊C8—31no—
470C22⋊C8C2×C3×D311yescharacteristic
471#97—31no—
472C4×C8—31no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—41no—
477C23×C3—64no—
478C23×C3—61no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—241no—
482C23×C3—241no—
483C23×C3D3×D411yescharacteristic
484C23×C3C2×C3×D411yescharacteristic
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—24no—
488C22×D3—21no—
489C22×D3—81no—
490C22×D3—81no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—32no—
496C3×D4—32no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—64no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—81no—
505C3×D4—81no—
506C3×D4—82no—
507C3×D4—241no—
508C3×D4—241no—
509C3×D4—241no—
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—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—61no—
532C2×C3×C4—241no—
533C2×C3×C4—241no—
534C2×C3×C4—241no—
535C2×C3×C4—241no—
536C2×C3×C4—241no—
537C2×C3×C4—241no—
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4C2×C3×D411yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C24×C311yescharacteristic
542#67—81no—
543#67—81no—
544#67—81no—
545C2×Dic3—21no—
546C2×Dic3—81no—
547C2×Dic3C2×C3×D411yescharacteristic
548C2×Dic3C2×C3×D411yescharacteristic
549C2×Dic3C2×C3×D411yescharacteristic
550C2×Dic3C2×C3×D411yescharacteristic
551D12—24no—
552D12—21no—
553D12—21no—
554D12—21no—
555D12—21no—
556D12C3×#4112yes—
557D12C3×#4112yes—
558C4×D3—81no—
559C4×D3—81no—
560C4×D3—81no—
561C4×D3—81no—
562C4×D3—81no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—41no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32—41no—
574C2×C32—81no—
575C2×C32#52511yescharacteristic
576C2×C32#57611yescharacteristic
577C2×C32#57611yescharacteristic
578C3×D3—42no—
579C3×D3—42no—
580C3×D3—81no—
581C24—61no—
582C2×D4—21no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—62no—
587C2×D4—62no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4C22×C3×D311yescharacteristic
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—61no—
599C22×C4C22×C3×D311yescharacteristic
600D8—62no—
601D8—62no—
602D8—62no—
603D8—62no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8C22×C3×D311yescharacteristic
607C2×C8C22×C3×D311yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4C22×C3×D311yescharacteristic
614C4⋊C4C22×C3×D311yescharacteristic
615C4⋊C4C22×C3×D311yescharacteristic
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C42—21no—
628C42—31no—
629C42—31no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—62no—
647C22×C3—62no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—244no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C22×C3×D411yescharacteristic
661C2×D3—22no—
662C2×D3—22no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—84no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—81no—
687C3×C4—81no—
688C3×C4—81no—
689C3×C4—121no—
690C3×C4D3×#4111yescharacteristic
691C3×C4D3×#4111yescharacteristic
692C3×C4C2×C3×#4111yescharacteristic
693C3×C4C2×C3×#4111yescharacteristic
694Dic3—21no—
695Dic3—21no—
696Dic3—21no—
697Dic3—21no—
698Dic3—41no—
699C32#312211yescharacteristic, complemented, Sylow
700C23—21no—
701C23—64no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—241no—
706C23—241no—
707C23C3×D3×D411yescharacteristic
708D4—21no—
709D4—21no—
710D4—32no—
711D4—32no—
712D4—64no—
713D4—61no—
714D4—61no—
715D4—61no—
716D4—61no—
717D4—81no—
718D4—241no—
719D4—241no—
720D4—241no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—241no—
732C2×C4—241no—
733C2×C4—241no—
734C2×C4—241no—
735C2×C4—241no—
736C2×C4—241no—
737C2×C4C3×D3×D411yescharacteristic
738C2×C4C23×C3×D311yescharacteristic
739C8—21no—
740C8—21no—
741C8—61no—
742C8—61no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—41no—
747C2×C3—41no—
748C2×C3—81no—
749C2×C3—81no—
750C2×C3—81no—
751C2×C3—122no—
752C2×C3—122no—
753C2×C3—161no—
754C2×C3—241no—
755C2×C3#565611yescharacteristic
756C2×C3#576911yescharacteristic
757C2×C3#577411yescharacteristic
758C2×C3C3×#52511yescharacteristic
759C2×C3C3×#57611yescharacteristic
760C2×C3C3×#57611yescharacteristic
761D3—42no—
762D3—42no—
763D3—81no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—62no—
771C22—62no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—244no—
780C22C2×C3×D3×D411yescharacteristic
781C4—21no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—61no—
786C4—61no—
787C4—61no—
788C4—61no—
789C4—121no—
790C4C3×D3×#4111yescharacteristic
791C4C3×D3×#4111yescharacteristic
792C3—21no—
793C3#8135411yescharacteristic, direct product factor
794C3C3×#312211yescharacteristic, complemented
795C2—41no—
796C2—81no—
797C2—122no—
798C2—122no—
799C2—241no—
800C2C3×#565611yescharacteristic
801C2C3×#576911yescharacteristic
802C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#482C2
socleC22×C32C22×D4
hypercenterC3×#482D3
hypocenterC3C3×#3122
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×#5619C2semidirect
2. C3×#5521C2semidirect
3. C32×#482C2semidirect
4. C3×#5036C2semidirect
5. C3×#5003C2semidirect
6. C3×#4891C2semidirect
7. C3×#4872C2semidirect
8. C3×#4871C2semidirect
9. C3×#4869C2semidirect
10. C3×#4786C2semidirect
11. C3×#4786C2semidirect
12. C3×#4785C2semidirect
13. C3×#4756C2semidirect
14. C3×#4732C2semidirect
15. C3×#4720C2semidirect
17. #81354C3direct (N × H)
21. C3×#940C22semidirect
24. C3×D4×Dic3C22semidirect
35. C3×#893C22semidirect
36. C3×#890C22semidirect
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
57. C3×#809C22semidirect
58. C3×#809C22semidirect
59. C3×#808C22semidirect
60. C3×#807C22semidirect
63. #5619C2×C3semidirect
64. #5521C2×C3semidirect
67. C3×#482D3semidirect
68. C3×#482C2×C3semidirect
80. #5036C2×C3semidirect
81. #5003C2×C3semidirect
82. #4891C2×C3semidirect
83. #4872C2×C3semidirect
84. #4871C2×C3semidirect
85. #4869C2×C3semidirect
86. #4786C2×C3semidirect
87. #4786C2×C3semidirect
88. #4785C2×C3semidirect
89. #4756C2×C3semidirect
90. #4732C2×C3semidirect
91. #4720C2×C3semidirect
172. #940C22×C3semidirect
175. D4×Dic3C22×C3semidirect
186. #893C22×C3semidirect
187. #890C22×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
231. #809C22×C3semidirect
232. #809C22×C3semidirect
233. #808C22×C3semidirect
234. #807C22×C3semidirect
281. #482C3×D3semidirect
456. #107C2×C3×D3semidirect
458. #106C2×C3×D3semidirect
467. #102C2×C3×D3semidirect
468. #102C2×C3×D3semidirect
699. C32#3122semidirect
793. C3#81354direct (N × H)
794. C3C3×#3122semidirect

Maximal subgroups

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

subgroupindex
C3×#56192
C3×#55212
C32×#4822
C3×#50362
C3×#50032
C3×#48912
C3×#48722
C3×#48712
C3×#48692
C3×#47862
C3×#47852
C3×#47562
C3×#47322
C3×#47202
C3×#31223
#813543