Finite Group Databasebeta

← C3×#79592 #11870844

Subgroups — C3×#79592 #11870844

Order 1152.

975 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5557C211yesmaximal, characteristic, complemented
2C3×C4×D3×D4C211yesmaximal, characteristic, complemented
3C32×C4×D8C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic
5C3×#5153C211yesmaximal, characteristic, complemented
6C3×C4×#214C211yesmaximal, characteristic, complemented
7C3×C4×#213C211yesmaximal, characteristic, complemented
8C3×#4891C211yesmaximal, characteristic, complemented
9C3×#4884C211yesmaximal, characteristic, complemented
10C3×#4787C211yesmaximal, characteristic, complemented
11C3×#4777C211yesmaximal, characteristic, complemented
12C3×#4776C211yesmaximal, characteristic, complemented
13C3×#4763C211yesmaximal, characteristic, complemented
14C3×C4×#204C211yesmaximal, characteristic, complemented
15C3×#4685C211yesmaximal, characteristic, complemented
16C3×#3105—31nomaximal
17#79592C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×D4C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C2×C32×D8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic, complemented
23C3×#938C2211yescharacteristic
24C3×#936C2211yescharacteristic, complemented
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C3×C4×#67—21no—
29C3×C4×#67—21no—
30C3×#926—21no—
31C2×C3×#204C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×D3×C4⋊C4C2211yescharacteristic
35C3×#890C2211yescharacteristic, complemented
36C3×#883—21no—
37C3×#67⋊C4—21no—
38C3×D3×C22⋊C4—21no—
39C3×#879—21no—
40C3×C4×D12C2211yescharacteristic
41C3×C42×D3C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic, complemented
43C32×#107C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45C32×#102C2211yescharacteristic, complemented
46C32×C4×C8C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#817C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55C3×Dic3⋊C8C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60C3×C4×C3⋊C8C2211yescharacteristic, complemented
61C3×#529—31no—
62C2×C3×C4×D4—31no—
63#5557C2×C311yescharacteristic, complemented
64C4×D3×D4C2×C311yescharacteristic, complemented
65C3×#484—31no—
66C3×#481—31no—
67C3×#478—31no—
68C3×#478—31no—
69C3×#463—31no—
70C3×#463—31no—
71C3×#450—31no—
72C3×#447—31no—
73C3×C4×SD16—31no—
74C3×C4×SD16—31no—
75C3×C4×D8—21no—
76C3×C4×D8—31no—
77C3×C4×D8D311yescharacteristic, complemented
78C3×C4×D8C2×C311yescharacteristic, complemented
79C3×#431—31no—
80#5156C2×C311yescharacteristic
81#5153C2×C311yescharacteristic, complemented
82C4×#214C2×C311yescharacteristic, complemented
83C4×#213C2×C311yescharacteristic, complemented
84#4891C2×C311yescharacteristic, complemented
85#4884C2×C311yescharacteristic, complemented
86#4787C2×C311yescharacteristic, complemented
87#4777C2×C311yescharacteristic, complemented
88#4776C2×C311yescharacteristic, complemented
89#4763C2×C311yescharacteristic, complemented
90C4×#204C2×C311yescharacteristic, complemented
91#4685C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C22×C32×C4—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C3×D3×D4—22no—
101C3×D3×D4—22no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—44no—
107C2×C3×C4×D3D411yescharacteristic
108C2×C3×C4×D3D411yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C32×D8—22no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C22⋊C4—21no—
118C32×C42C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#214—22no—
124C3×#213—22no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3D411yescharacteristic
137C3×C4×Dic3D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×#204—22no—
142#3105—31noSylow
143C22×C3×D4—31no—
144C23×C3×C4—61no—
145C2×D3×D4C22×C311yescharacteristic
146C22×C4×D3—21no—
147C2×C3×SD16—31no—
148C2×C3×SD16—31no—
149C2×C3×D8—21no—
150C2×C3×D8—31no—
151C2×C3×D8C2×D311yescharacteristic
152C2×C3×D8C22×C311yescharacteristic
153C3×#126—61no—
154C3×#125—31no—
155C3×#124—31no—
156C3×#123—61no—
157C3×C22⋊Q8—31no—
158C3×#121—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—21no—
161C3×C4×D4—21no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C3×C4×D4—61no—
166C3×C4×D4—61no—
167C3×C4×D4—61no—
168C3×C4×D4C2×D311yescharacteristic
169C3×C4×D4C2×D311yescharacteristic, complemented
170C3×C4×D4C22×C311yescharacteristic
171C3×C4×D4C22×C311yescharacteristic, complemented
172C3×#117—61no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C22⋊C4—61no—
175C2×C3×C42—31no—
176#938C22×C311yescharacteristic
177#936C22×C311yescharacteristic, complemented
178D4×Dic3C22×C311yescharacteristic
179C2×#214C22×C311yescharacteristic
180C2×#213C22×C311yescharacteristic
181C4×#67—21no—
182C4×#67—21no—
183#926—21no—
184C2×#204C22×C311yescharacteristic
185#897C22×C311yescharacteristic
186#893C22×C311yescharacteristic
187D3×C4⋊C4C22×C311yescharacteristic
188#890C22×C311yescharacteristic, complemented
189#883—21no—
190#67⋊C4—21no—
191D3×C22⋊C4—21no—
192#879—21no—
193C4×D12C22×C311yescharacteristic
194C42×D3C22×C311yescharacteristic
195C4×Dic6C22×C311yescharacteristic, complemented
196C3×#107—21no—
197C3×#107—31no—
198C3×#107C2×D311yescharacteristic, complemented
199C3×#107C22×C311yescharacteristic, complemented
200C3×#106—31no—
201C3×#106—31no—
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
213C3×#102C2×D311yescharacteristic, complemented
214C3×#102C22×C311yescharacteristic
215C3×#102C22×C311yescharacteristic, complemented
216C3×C22⋊C8—31no—
217C3×C22⋊C8—31no—
218C3×C4×C8—21no—
219C3×C4×C8—31no—
220C3×C4×C8C2×D311yescharacteristic, complemented
221C3×C4×C8C22×C311yescharacteristic, complemented
222#832C22×C311yescharacteristic
223#832C22×C311yescharacteristic, complemented
224#821C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226(C2×D3)⋊C8C22×C311yescharacteristic
227#817C22×C311yescharacteristic, complemented
228#816C22×C311yescharacteristic, complemented
229Dic3⋊C8C22×C311yescharacteristic, complemented
230Dic3⋊C8C22×C311yescharacteristic, complemented
231#810C22×C311yescharacteristic, complemented
232#809C22×C311yescharacteristic
233#808C22×C311yescharacteristic, complemented
234#807C22×C311yescharacteristic, complemented
235C4×C3⋊C8C22×C311yescharacteristic, complemented
236C23×C32—21no—
237C23×C32—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—42no—
250C2×C32×C4—42no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C3×#67—24no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—22no—
266C3×C4×D3—22no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C32×C8—21no—
275C32×C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#529—31no—
279C2×C4×D4—31no—
280#484—31no—
281#481—31no—
282#478—31no—
283#478—31no—
284#463—31no—
285#463—31no—
286#450—31no—
287#447—31no—
288C4×SD16—31no—
289C4×SD16—31no—
290C4×D8—31no—
291C4×D8C3×D311yescharacteristic, complemented
292#431—31no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×Q8—31no—
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—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—41no—
315C22×C3×C4—41no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—124no—
321C2×#67—21no—
322C2×#67—21no—
323C22×Dic3—21no—
324D3×D4—22no—
325D3×D4—22no—
326C2×D12C23×C311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—44no—
331C2×C4×D3C3×D411yescharacteristic
332C2×C4×D3C3×D411yescharacteristic
333C2×C4×D3C23×C311yescharacteristic
334C2×Dic6C23×C311yescharacteristic
335C3×SD16—62no—
336C3×SD16—62no—
337C3×D8—24no—
338C3×D8—22no—
339C3×D8—22no—
340C3×D8—62no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
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—31no—
377C3×C42—31no—
378C3×C42—31no—
379C3×C42—61no—
380C3×C42C22×D311yescharacteristic
381C3×C42C23×C311yescharacteristic
382#217—21no—
383#217—21no—
384#217—21no—
385#217—21no—
386#214—22no—
387#213—22no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3C23×C311yescharacteristic
394C4⋊Dic3C23×C311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398C4×Dic3—21no—
399C4×Dic3C3×D411yescharacteristic
400C4×Dic3C3×D411yescharacteristic
401C4×Dic3C23×C311yescharacteristic
402C2×C3⋊C8C23×C311yescharacteristic
403C2×C3⋊C8C23×C311yescharacteristic
404#204—22no—
405C22×C32—22no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32C22×D411yescharacteristic
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—22no—
415C2×C3×D3—48no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3#13512yes—
419C32×C4—21no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4AGL(1,ℤ/8)12yes—
423C32×C4C2×#4111yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C22×D4—31no—
432C23×C4—61no—
433C2×SD16—31no—
434C2×SD16—31no—
435C2×D8—31no—
436C2×D8C2×C3×D311yescharacteristic
437#126—61no—
438#125—31no—
439#124—31no—
440#123—61no—
441C22⋊Q8—31no—
442#121—31no—
443C4×Q8—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—61no—
448C4×D4—61no—
449C4×D4—61no—
450C4×D4C2×C3×D311yescharacteristic
451C4×D4C2×C3×D311yescharacteristic, complemented
452#117—61no—
453C2×C4⋊C4—31no—
454C2×C22⋊C4—61no—
455C2×C42—31no—
456#107—31no—
457#107C2×C3×D311yescharacteristic, complemented
458#106—31no—
459#106—31no—
460C4⋊C8—31no—
461C4⋊C8—31no—
462#103—31no—
463#103—31no—
464#102—31no—
465#102—31no—
466#102—31no—
467#102—31no—
468#102C2×C3×D311yescharacteristic
469#102C2×C3×D311yescharacteristic, complemented
470C22⋊C8—31no—
471C22⋊C8—31no—
472C4×C8—31no—
473C4×C8C2×C3×D311yescharacteristic, complemented
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—64no—
482C23×C3—61no—
483C23×C3—122no—
484C23×C3—122no—
485C22×D3—24no—
486C22×D3—21no—
487C22×D3—42no—
488C22×D3—42no—
489C22×D3C2×C3×D411yescharacteristic
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—22no—
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—64no—
504C3×D4—61no—
505C3×D4—122no—
506C3×D4#23512yes—
507C3×D4C3×#4112yes—
508C2×C3×C4—21no—
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—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—42no—
521C2×C3×C4—42no—
522C2×C3×C4—42no—
523C2×C3×C4—42no—
524C2×C3×C4—62no—
525C2×C3×C4—62no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—82no—
532C2×C3×C4—82no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4—122no—
536C2×C3×C4—122no—
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4C2×C3×D411yescharacteristic
540C2×C3×C4C2×C3×D411yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C24×C311yescharacteristic
543#67—24no—
544#67—42no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—42no—
549C2×Dic3C2×C3×D411yescharacteristic
550C2×Dic3C2×C3×D411yescharacteristic
551C2×Dic3C2×C3×D411yescharacteristic
552D12—21no—
553D12C3×#4112yes—
554C4×D3—22no—
555C4×D3—22no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—42no—
559C4×D3—42no—
560C4×D3—42no—
561Dic6—21no—
562Dic6—21no—
563C3×C8—22no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—41no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32—42no—
574C2×C32—81no—
575C2×C32#52511yescharacteristic
576C2×C32C2×#13511yescharacteristic
577C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
578C3×D3—22no—
579C3×D3—42no—
580C24—61no—
581C2×Q8—31no—
582C2×D4—31no—
583C2×D4—61no—
584C2×D4—62no—
585C2×D4—62no—
586C2×D4—61no—
587C2×D4C22×C3×D311yescharacteristic
588C2×D4C22×C3×D311yescharacteristic
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—124no—
599SD16—62no—
600SD16—62no—
601D8—22no—
602D8—62no—
603C2×C8—31no—
604C2×C8—31no—
605C2×C8C22×C3×D311yescharacteristic
606C2×C8C22×C3×D311yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4C22×C3×D311yescharacteristic
615C4⋊C4C22×C3×D311yescharacteristic
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C42—31no—
626C42—31no—
627C42—31no—
628C42—61no—
629C42C22×C3×D311yescharacteristic
630C22×C3—22no—
631C22×C3—22no—
632C22×C3—21no—
633C22×C3—32no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—41no—
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—61no—
647C22×C3—61no—
648C22×C3—62no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—128no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C22×C3×D411yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—22no—
661C2×D3—48no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3C3×#13512yes—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—22no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4#91112yes—
684C3×C4C3×AGL(1,ℤ/8)12yes—
685C3×C4C2×#23511yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4C2×C3×#4111yescharacteristic
688C3×C4C2×C3×#4111yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—21no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695C32#310511yescharacteristic, complemented, Sylow
696C23—21no—
697C23—21no—
698C23—31no—
699C23—64no—
700C23—61no—
701C23—122no—
702C23—122no—
703Q8—61no—
704Q8—61no—
705D4—21no—
706D4—21no—
707D4—21no—
708D4—32no—
709D4—64no—
710D4—61no—
711D4—122no—
712D4C3×#23512yes—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—122no—
728C2×C4—122no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4C3×D3×D411yescharacteristic
732C2×C4C3×D3×D411yescharacteristic
733C2×C4C23×C3×D311yescharacteristic
734C8—21no—
735C8—21no—
736C8—61no—
737C8—61no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—42no—
742C2×C3—42no—
743C2×C3—62no—
744C2×C3—82no—
745C2×C3—82no—
746C2×C3—81no—
747C2×C3—81no—
748C2×C3—122no—
749C2×C3#554711yescharacteristic
750C2×C3C2×#91111yescharacteristic
751C2×C3D3×#13511yescharacteristic
752C2×C3C3×#52511yescharacteristic
753C2×C3C2×C3×#13511yescharacteristic
754C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
755D3—22no—
756D3—42no—
757C22—22no—
758C22—32no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—61no—
765C22—61no—
766C22—62no—
767C22—128no—
768C22—121no—
769C22—121no—
770C22C2×C3×D3×D411yescharacteristic
771C4—21no—
772C4—41no—
773C4—41no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4C3×#91112yes—
781C4C2×C3×#23511yescharacteristic
782C4C3×D3×#4111yescharacteristic
783C3—21no—
784C3#7959211yescharacteristic, direct product factor
785C3C3×#310511yescharacteristic, complemented
786C2—42no—
787C2—62no—
788C2—81no—
789C2—122no—
790C2C3×#554711yescharacteristic
791C2C2×C3×#91111yescharacteristic
792C2C3×D3×#13511yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×D8C2
socleC22×C32C22×D4
prime radicalC3×#5156C2
hypercenterC3×C4×D8D3
hypocenterC3C3×#3105
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×D8

Complements

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

NH ≅ G/Ntype
1. C3×#5557C2semidirect
2. C3×C4×D3×D4C2semidirect
3. C32×C4×D8C2semidirect
5. C3×#5153C2semidirect
6. C3×C4×#214C2semidirect
7. C3×C4×#213C2semidirect
8. C3×#4891C2semidirect
9. C3×#4884C2semidirect
10. C3×#4787C2semidirect
11. C3×#4777C2semidirect
12. C3×#4776C2semidirect
13. C3×#4763C2semidirect
14. C3×C4×#204C2semidirect
15. C3×#4685C2semidirect
17. #79592C3direct (N × H)
22. C32×C4×D4C22semidirect
24. C3×#936C22semidirect
35. C3×#890C22semidirect
42. C3×C4×Dic6C22semidirect
43. C32×#107C22semidirect
45. C32×#102C22semidirect
46. C32×C4×C8C22semidirect
48. C3×#832C22semidirect
52. C3×#817C22semidirect
53. C3×#816C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. C3×Dic3⋊C8C22semidirect
56. C3×#810C22semidirect
58. C3×#808C22semidirect
59. C3×#807C22semidirect
60. C3×C4×C3⋊C8C22semidirect
63. #5557C2×C3semidirect
64. C4×D3×D4C2×C3semidirect
77. C3×C4×D8D3semidirect
78. C3×C4×D8C2×C3semidirect
81. #5153C2×C3semidirect
82. C4×#214C2×C3semidirect
83. C4×#213C2×C3semidirect
84. #4891C2×C3semidirect
85. #4884C2×C3semidirect
86. #4787C2×C3semidirect
87. #4777C2×C3semidirect
88. #4776C2×C3semidirect
89. #4763C2×C3semidirect
90. C4×#204C2×C3semidirect
91. #4685C2×C3semidirect
169. C3×C4×D4C2×D3semidirect
171. C3×C4×D4C22×C3semidirect
177. #936C22×C3semidirect
188. #890C22×C3semidirect
195. C4×Dic6C22×C3semidirect
198. C3×#107C2×D3semidirect
199. C3×#107C22×C3semidirect
213. C3×#102C2×D3semidirect
215. C3×#102C22×C3semidirect
220. C3×C4×C8C2×D3semidirect
221. C3×C4×C8C22×C3semidirect
223. #832C22×C3semidirect
227. #817C22×C3semidirect
228. #816C22×C3semidirect
229. Dic3⋊C8C22×C3semidirect
230. Dic3⋊C8C22×C3semidirect
231. #810C22×C3semidirect
233. #808C22×C3semidirect
234. #807C22×C3semidirect
235. C4×C3⋊C8C22×C3semidirect
291. C4×D8C3×D3semidirect
451. C4×D4C2×C3×D3semidirect
457. #107C2×C3×D3semidirect
469. #102C2×C3×D3semidirect
473. C4×C8C2×C3×D3semidirect
695. C32#3105semidirect
784. C3#79592direct (N × H)
785. C3C3×#3105semidirect

Maximal subgroups

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

subgroupindex
C3×#55572
C3×C4×D3×D42
C32×C4×D82
C3×#51562
C3×#51532
C3×C4×#2142
C3×C4×#2132
C3×#48912
C3×#48842
C3×#47872
C3×#47772
C3×#47762
C3×#47632
C3×C4×#2042
C3×#46852
C3×#31053
#795923