Finite Group Databasebeta

← C3×D3×#417 #11857888

Subgroups — C3×D3×#417 #11857888

Order 1152.

1713 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2C2×C3×D3×M16C211yesmaximal, characteristic, complemented
3C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C32×#417C211yesmaximal, characteristic, complemented
5C3×#5232C211yesmaximal, characteristic, complemented
6C3×#5133C211yesmaximal, characteristic, complemented
7C3×#4966C211yesmaximal, characteristic, complemented
8C3×#4803C212yesmaximal, complemented
9C3×D3×#103C212yesmaximal, complemented
10C3×#4771C212yesmaximal, complemented
11C3×D3×#102C212yesmaximal, complemented
12C2×C3×#417—31nomaximal
13D3×#417C311yesmaximal, characteristic, direct product factor
14C2×C32×#41C2211yescharacteristic
15C3×D3×#41—24no—
16C3×D3×#41C418yescomplemented
17C2×C3×#239C2211yescharacteristic
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237—21no—
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4—21no—
22C2×C3×D3×D4C2211yescharacteristic
23C2×C3×#235—21no—
24C2×C3×#235C2211yescharacteristic
25C22×C3×C4×D3—21no—
26C22×C3×C4×D3—21no—
27C22×C3×C4×D3C2211yescharacteristic
28C2×C32×M16C2211yescharacteristic, complemented
29C2×C32×C4⋊C4C2211yescharacteristic, complemented
30C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
31C2×C3×Dic3⋊C4—21no—
32C2×C3×#208C2211yescharacteristic, complemented
33C3×D3×M16—24no—
34C2×C3×ΓL(1,𝔽25)C2212yescomplemented
35C2×C3×D3×C8C2212yes—
36C3×D3×C4⋊C4—21no—
37C3×D3×C4⋊C4—21no—
38C3×D3×C4⋊C4C2212yes—
39C3×D3×C4⋊C4C2212yescomplemented
40C32×#103C2212yescomplemented
41C32×#102C2212yescomplemented
42C3×#835C2212yescomplemented
43C3×#832C2212yescomplemented
44C3×#821C2212yescomplemented
45C3×#816C2212yescomplemented
46C3×#810C2212yescomplemented
47C3×#809C2212yescomplemented
48C22×C3×#41—31no—
49C2×D3×#41C2×C311yescharacteristic
50C22×C3×M16—31no—
51C22×C3×C4⋊C4—31no—
52C2×D3×M16C2×C311yescharacteristic, complemented
53C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
54C3×#417—21no—
55C3×#417—31no—
56C3×#417—31no—
57C3×#417—31no—
58C3×#417—32no—
59C3×#417—32no—
60C3×#417D311yescharacteristic, direct product factor
61C3×#417C2×C311yescharacteristic, complemented
62C2×C3×#103—32no—
63C2×C3×#102—32no—
64#5232C2×C311yescharacteristic, complemented
65#5133C2×C311yescharacteristic, complemented
66#4966C2×C311yescharacteristic, complemented
67#4803C2×C312yescomplemented
68D3×#103C2×C312yescomplemented
69#4771C2×C312yescomplemented
70D3×#102C2×C312yescomplemented
71C23×C3×D3—21no—
72C23×C3×D3D411yescharacteristic
73C32×#41—22no—
74C32×#41C2×C414yescomplemented
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4—21no—
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C22×C32×C4C2311yescharacteristic
81C2×C3×#67—21no—
82C2×C3×#67—21no—
83C2×C3×#67—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3D411yescharacteristic
87C3×#239—22no—
88C3×#239C2×C414yescomplemented
89C3×D3×Q8—22no—
90C3×D3×Q8C2×C414yescomplemented
91C3×#237—28no—
92C3×#237—22no—
93C3×#237C2×C414yescomplemented
94C3×D3×D4—28no—
95C3×D3×D4—22no—
96C3×D3×D4C2×C414yescomplemented
97C3×#235—22no—
98C3×#235—28no—
99C3×#235C2×C414yescomplemented
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—28no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—44no—
109C2×C3×C4×D3C2×C414yes—
110C2×C3×C4×D3D411yescharacteristic
111C2×C3×C4×D3D411yescharacteristic
112C2×C3×C4×D3D414yes—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6—21no—
116C2×C3×Dic6C2311yescharacteristic
117C32×M16—22no—
118C2×C32×C8C2312yes—
119C32×C4⋊C4—21no—
120C32×C4⋊C4C2312yes—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2312yes—
123C3×Dic3⋊C4—22no—
124C3×Dic3⋊C4—22no—
125C3×#208—22no—
126C2×C3×C3⋊C8C2312yes—
127C3×ΓL(1,𝔽25)—24no—
128C3×D3×C8—24no—
129C2×#417—31noSylow
130C2×C3×#41—21no—
131C2×C3×#41—38no—
132C2×C3×#41—31no—
133C2×C3×#41—31no—
134C2×C3×#41—31no—
135C2×C3×#41—61no—
136C2×C3×#41—61no—
137C2×C3×#41—64no—
138C2×C3×#41C2×D311yescharacteristic
139C2×C3×#41C22×C311yescharacteristic
140C22×C3×Q8—31no—
141C22×C3×D4—31no—
142C22×C3×D4—61no—
143C23×C3×C4—31no—
144C23×C3×C4—61no—
145C23×C3×C4—61no—
146D3×#41—24no—
147D3×#41C3×C418yescomplemented
148C2×#239C22×C311yescharacteristic
149C2×D3×Q8C22×C311yescharacteristic
150C2×#237—21no—
151C2×#237C22×C311yescharacteristic
152C2×D3×D4—21no—
153C2×D3×D4C22×C311yescharacteristic
154C2×#235—21no—
155C2×#235C22×C311yescharacteristic
156C22×C4×D3—21no—
157C22×C4×D3—21no—
158C22×C4×D3C22×C311yescharacteristic
159C2×C3×M16—21no—
160C2×C3×M16—31no—
161C2×C3×M16—32no—
162C2×C3×M16—64no—
163C2×C3×M16C2×D311yescharacteristic, complemented
164C2×C3×M16C22×C311yescharacteristic, complemented
165C22×C3×C8—32no—
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—32no—
169C2×C3×C4⋊C4—32no—
170C2×C3×C4⋊C4—61no—
171C2×C3×C4⋊C4—61no—
172C2×C3×C4⋊C4—61no—
173C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
174C2×C3×C4⋊C4C22×C311yescharacteristic, complemented
175C2×C4⋊Dic3C22×C311yescharacteristic, complemented
176C2×Dic3⋊C4—21no—
177C2×#208C22×C311yescharacteristic, complemented
178D3×M16—24no—
179C2×ΓL(1,𝔽25)C22×C312yescomplemented
180C2×D3×C8C22×C312yes—
181D3×C4⋊C4—21no—
182D3×C4⋊C4—21no—
183D3×C4⋊C4C22×C312yes—
184D3×C4⋊C4C22×C312yescomplemented
185C3×#103—22no—
186C3×#103—32no—
187C3×#103—32no—
188C3×#103—32no—
189C3×#103C2×D312yescomplemented
190C3×#103C22×C312yescomplemented
191C3×#102—22no—
192C3×#102—32no—
193C3×#102—32no—
194C3×#102—32no—
195C3×#102C2×D312yescomplemented
196C3×#102C22×C312yescomplemented
197#835C22×C312yescomplemented
198#832C22×C312yescomplemented
199#821C22×C312yescomplemented
200#816C22×C312yescomplemented
201#810C22×C312yescomplemented
202#809C22×C312yescomplemented
203C23×C32—21no—
204C23×C32C2×D411yescharacteristic
205C22×C3×D3—22no—
206C22×C3×D3—22no—
207C22×C3×D3—21no—
208C22×C3×D3—24no—
209C22×C3×D3—42no—
210C22×C3×D3—42no—
211C22×C3×D3C22⋊C414yes—
212C22×C3×D3C2×D411yescharacteristic
213C22×C3×D3C2×D411yescharacteristic
214C32×Q8—21no—
215C32×Q8C22×C412yescomplemented
216C32×D4—24no—
217C32×D4—21no—
218C32×D4C22×C412yescomplemented
219C2×C32×C4—21no—
220C2×C32×C4—24no—
221C2×C32×C4—22no—
222C2×C32×C4—42no—
223C2×C32×C4C22×C412yes—
224C2×C32×C4C2×D411yescharacteristic
225C2×C32×C4C2×D412yes—
226C2×C32×C4C2411yescharacteristic
227C3×#67—24no—
228C3×#67—24no—
229C3×#67—24no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—24no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—42no—
234C2×C3×Dic3C22⋊C414yes—
235C2×C3×Dic3C2×D411yescharacteristic
236C2×C3×Dic3C2×D411yescharacteristic
237C3×D12—24no—
238C3×D12—21no—
239C3×D12C22×C412yescomplemented
240C3×C4×D3—24no—
241C3×C4×D3—24no—
242C3×C4×D3—24no—
243C3×C4×D3—44no—
244C3×C4×D3—44no—
245C3×C4×D3C22⋊C414yes—
246C3×C4×D3C22⋊C414yes—
247C3×C4×D3C22×C412yes—
248C3×C4×D3C22×C412yes—
249C3×C4×D3C2×D412yes—
250C3×C4×D3C2×D412yes—
251C3×Dic6—21no—
252C3×Dic6—24no—
253C3×Dic6C22×C412yescomplemented
254C32×C8—22no—
255C3×C3⋊C8—22no—
256C22×#41—31no—
257C22×M16—31no—
258C22×C4⋊C4—31no—
259#417—31no—
260#417—31no—
261#417—31no—
262#417—32no—
263#417—32no—
264#417C3×D311yescharacteristic, direct product factor
265C2×#103—32no—
266C2×#102—32no—
267C24×C3—31no—
268C24×C3—61no—
269C23×D3—21no—
270C23×D3C3×D411yescharacteristic
271C3×#41—22no—
272C3×#41—22no—
273C3×#41—24no—
274C3×#41—34no—
275C3×#41—34no—
276C3×#41—34no—
277C3×#41—42no—
278C3×#41—68no—
279C3×#41—68no—
280C3×#41—62no—
281C3×#41—62no—
282C3×#41—62no—
283C3×#41C4×D314yescomplemented
284C3×#41C2×C3×C414yescomplemented
285C2×C3×Q8—21no—
286C2×C3×Q8—34no—
287C2×C3×Q8—31no—
288C2×C3×Q8—61no—
289C2×C3×Q8—62no—
290C2×C3×Q8C22×D311yescharacteristic
291C2×C3×Q8C23×C311yescharacteristic
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—34no—
296C2×C3×D4—31no—
297C2×C3×D4—41no—
298C2×C3×D4—61no—
299C2×C3×D4—62no—
300C2×C3×D4—61no—
301C2×C3×D4—68no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C23×C311yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—34no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—34no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—41no—
319C22×C3×C4—41no—
320C22×C3×C4—61no—
321C22×C3×C4—68no—
322C22×C3×C4—61no—
323C22×C3×C4—62no—
324C22×C3×C4—62no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—124no—
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C23×C311yescharacteristic
331C2×#67—21no—
332C2×#67—21no—
333C2×#67—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3C3×D411yescharacteristic
337#239—22no—
338#239C2×C3×C414yescomplemented
339D3×Q8—22no—
340D3×Q8C2×C3×C414yescomplemented
341#237—28no—
342#237—22no—
343#237C2×C3×C414yescomplemented
344D3×D4—28no—
345D3×D4—22no—
346D3×D4C2×C3×C414yescomplemented
347#235—22no—
348#235—28no—
349#235C2×C3×C414yescomplemented
350C2×D12—21no—
351C2×D12C23×C311yescharacteristic
352C2×C4×D3—21no—
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×C4×D3—28no—
356C2×C4×D3—22no—
357C2×C4×D3—22no—
358C2×C4×D3—44no—
359C2×C4×D3C2×C3×C414yes—
360C2×C4×D3C3×D411yescharacteristic
361C2×C4×D3C3×D411yescharacteristic
362C2×C4×D3C3×D414yes—
363C2×C4×D3C23×C311yescharacteristic
364C2×C4×D3C23×C311yescharacteristic
365C2×Dic6—21no—
366C2×Dic6C23×C311yescharacteristic
367C3×M16—22no—
368C3×M16—22no—
369C3×M16—42no—
370C3×M16—64no—
371C3×M16—62no—
372C2×C3×C8—22no—
373C2×C3×C8—32no—
374C2×C3×C8—64no—
375C2×C3×C8C22×D312yes—
376C2×C3×C8C23×C312yes—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—32no—
381C3×C4⋊C4—41no—
382C3×C4⋊C4—62no—
383C3×C4⋊C4—62no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4C22×D312yes—
386C3×C4⋊C4C23×C312yes—
387C4⋊Dic3—21no—
388C4⋊Dic3C23×C312yes—
389Dic3⋊C4—22no—
390Dic3⋊C4—22no—
391#208—22no—
392C2×C3⋊C8C23×C312yes—
393ΓL(1,𝔽25)—24no—
394D3×C8—24no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—22no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C2×C22⋊C412yes—
401C22×C32C22×D411yescharacteristic
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—28no—
405C2×C3×D3—22no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—48no—
409C2×C3×D3C2×C22⋊C412yes—
410C2×C3×D3C2×C22⋊C412yes—
411C2×C3×D3AGL(1,ℤ/8)12yes—
412C2×C3×D3#13712yes—
413C32×C4—22no—
414C32×C4—42no—
415C32×C4C2×C22⋊C412yes—
416C32×C4C23×C411yescharacteristic
417C32×C4C22×D411yescharacteristic
418C3×Dic3—22no—
419C3×Dic3—42no—
420C3×Dic3C2×C22⋊C412yes—
421C3×Dic3C2×C22⋊C412yes—
422C2×#41—38no—
423C2×#41—31no—
424C2×#41—31no—
425C2×#41—31no—
426C2×#41—61no—
427C2×#41—61no—
428C2×#41—64no—
429C2×#41C2×C3×D311yescharacteristic
430C22×Q8—31no—
431C22×D4—31no—
432C22×D4—61no—
433C23×C4—31no—
434C23×C4—61no—
435C23×C4—61no—
436C2×M16—31no—
437C2×M16—32no—
438C2×M16—64no—
439C2×M16C2×C3×D311yescharacteristic, complemented
440C22×C8—32no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—32no—
443C2×C4⋊C4—32no—
444C2×C4⋊C4—61no—
445C2×C4⋊C4—61no—
446C2×C4⋊C4—61no—
447C2×C4⋊C4C2×C3×D311yescharacteristic, complemented
448#103—32no—
449#103—32no—
450#103—32no—
451#103C2×C3×D312yescomplemented
452#102—32no—
453#102—32no—
454#102—32no—
455#102C2×C3×D312yescomplemented
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—31no—
460C23×C3—34no—
461C23×C3—31no—
462C23×C3—41no—
463C23×C3—62no—
464C23×C3—62no—
465C23×C3—64no—
466C23×C3—61no—
467C23×C3—122no—
468C23×C3—122no—
469C23×C3D3×D411yescharacteristic
470C23×C3C2×C3×D411yescharacteristic
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—21no—
474C22×D3—24no—
475C22×D3—42no—
476C22×D3—42no—
477C22×D3C3×C22⋊C414yes—
478C22×D3C2×C3×D411yescharacteristic
479C22×D3C2×C3×D411yescharacteristic
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—22no—
483C3×Q8—32no—
484C3×Q8—41no—
485C3×Q8—64no—
486C3×Q8—61no—
487C3×Q8C2×C4×D312yescomplemented
488C3×Q8C22×C3×C412yescomplemented
489C3×D4—24no—
490C3×D4—24no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—22no—
494C3×D4—32no—
495C3×D4—41no—
496C3×D4—44no—
497C3×D4—64no—
498C3×D4—64no—
499C3×D4—64no—
500C3×D4—64no—
501C3×D4—61no—
502C3×D4C2×C4×D312yescomplemented
503C3×D4C22×C3×C412yescomplemented
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—24no—
507C2×C3×C4—24no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—34no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—34no—
518C2×C3×C4—34no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—32no—
523C2×C3×C4—44no—
524C2×C3×C4—41no—
525C2×C3×C4—42no—
526C2×C3×C4—42no—
527C2×C3×C4—42no—
528C2×C3×C4—64no—
529C2×C3×C4—64no—
530C2×C3×C4—64no—
531C2×C3×C4—61no—
532C2×C3×C4—64no—
533C2×C3×C4—62no—
534C2×C3×C4—82no—
535C2×C3×C4—124no—
536C2×C3×C4—124no—
537C2×C3×C4—122no—
538C2×C3×C4C2×C4×D312yes—
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4D3×D412yes—
541C2×C3×C4C22×C3×C412yes—
542C2×C3×C4C2×C3×D411yescharacteristic
543C2×C3×C4C2×C3×D412yes—
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C24×C311yescharacteristic
546#67—24no—
547#67—24no—
548#67—24no—
549C2×Dic3—21no—
550C2×Dic3—24no—
551C2×Dic3—22no—
552C2×Dic3—42no—
553C2×Dic3C3×C22⋊C414yes—
554C2×Dic3C2×C3×D411yescharacteristic
555C2×Dic3C2×C3×D411yescharacteristic
556D12—24no—
557D12—21no—
558D12C22×C3×C412yescomplemented
559C4×D3—24no—
560C4×D3—24no—
561C4×D3—24no—
562C4×D3—44no—
563C4×D3—44no—
564C4×D3C3×C22⋊C414yes—
565C4×D3C3×C22⋊C414yes—
566C4×D3C22×C3×C412yes—
567C4×D3C22×C3×C412yes—
568C4×D3C2×C3×D412yes—
569C4×D3C2×C3×D412yes—
570Dic6—21no—
571Dic6—24no—
572Dic6C22×C3×C412yescomplemented
573C3×C8—22no—
574C3×C8—22no—
575C3×C8—42no—
576C3×C8—62no—
577C3⋊C8—22no—
578C2×C32—22no—
579C2×C32—42no—
580C2×C32C22×C22⋊C411yescharacteristic
581C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
582C2×C32C2×#13711yescharacteristic
583C3×D3—22no—
584C3×D3—42no—
585C3×D3#41714yesdirect product factor
586C24—31no—
587C24—61no—
588#41—22no—
589#41—34no—
590#41—34no—
591#41—34no—
592#41—68no—
593#41—68no—
594#41—62no—
595#41—62no—
596#41—62no—
597#41C3×C4×D314yescomplemented
598C2×Q8—34no—
599C2×Q8—31no—
600C2×Q8—61no—
601C2×Q8—62no—
602C2×Q8C22×C3×D311yescharacteristic
603C2×D4—21no—
604C2×D4—34no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—62no—
608C2×D4—61no—
609C2×D4—68no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4C22×C3×D311yescharacteristic
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—34no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—34no—
622C22×C4—61no—
623C22×C4—68no—
624C22×C4—61no—
625C22×C4—62no—
626C22×C4—62no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—124no—
631C22×C4C22×C3×D311yescharacteristic
632M16—22no—
633M16—64no—
634M16—62no—
635C2×C8—32no—
636C2×C8—64no—
637C2×C8C22×C3×D312yes—
638C4⋊C4—21no—
639C4⋊C4—32no—
640C4⋊C4—62no—
641C4⋊C4—62no—
642C4⋊C4—61no—
643C4⋊C4C22×C3×D312yes—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—32no—
653C22×C3—32no—
654C22×C3—32no—
655C22×C3—32no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—42no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—68no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—62no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—128no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3D3×C22⋊C412yes—
673C22×C3C2×C3×C22⋊C412yes—
674C22×C3C2×D3×D411yescharacteristic
675C22×C3C22×C3×D411yescharacteristic
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—28no—
679C2×D3—22no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—48no—
683C2×D3C2×C3×C22⋊C412yes—
684C2×D3C2×C3×C22⋊C412yes—
685C2×D3C3×AGL(1,ℤ/8)12yes—
686C2×D3C3×#13712yes—
687C3×C4—22no—
688C3×C4—22no—
689C3×C4—22no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—32no—
693C3×C4—32no—
694C3×C4—42no—
695C3×C4—42no—
696C3×C4—42no—
697C3×C4—62no—
698C3×C4—82no—
699C3×C4—122no—
700C3×C4D3×C22⋊C412yes—
701C3×C4C2×C3×C22⋊C412yes—
702C3×C4C22×C4×D311yescharacteristic
703C3×C4C2×D3×D411yescharacteristic
704C3×C4C23×C3×C411yescharacteristic
705C3×C4C22×C3×D411yescharacteristic
706Dic3—22no—
707Dic3—42no—
708Dic3C2×C3×C22⋊C412yes—
709Dic3C2×C3×C22⋊C412yes—
710C32C2×#41711yescharacteristic, complemented, Sylow
711C23—21no—
712C23—31no—
713C23—34no—
714C23—31no—
715C23—62no—
716C23—62no—
717C23—64no—
718C23—61no—
719C23—122no—
720C23—122no—
721C23C3×D3×D411yescharacteristic
722Q8—21no—
723Q8—32no—
724Q8—64no—
725Q8—61no—
726Q8C2×C3×C4×D312yescomplemented
727D4—24no—
728D4—21no—
729D4—32no—
730D4—64no—
731D4—64no—
732D4—64no—
733D4—64no—
734D4—61no—
735D4C2×C3×C4×D312yescomplemented
736C2×C4—21no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—34no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—34no—
743C2×C4—34no—
744C2×C4—32no—
745C2×C4—32no—
746C2×C4—32no—
747C2×C4—32no—
748C2×C4—42no—
749C2×C4—64no—
750C2×C4—64no—
751C2×C4—64no—
752C2×C4—61no—
753C2×C4—64no—
754C2×C4—62no—
755C2×C4—124no—
756C2×C4—124no—
757C2×C4—122no—
758C2×C4C2×C3×C4×D312yes—
759C2×C4C3×D3×D411yescharacteristic
760C2×C4C3×D3×D412yes—
761C2×C4C23×C3×D311yescharacteristic
762C8—22no—
763C8—62no—
764C2×C3—22no—
765C2×C3—22no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—34no—
770C2×C3—42no—
771C2×C3—42no—
772C2×C3—42no—
773C2×C3—62no—
774C2×C3—82no—
775C2×C3—122no—
776C2×C3C2×D3×C22⋊C411yescharacteristic
777C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
778C2×C3D3×#13711yescharacteristic
779C2×C3C22×C3×C22⋊C411yescharacteristic
780C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
781C2×C3C2×C3×#13711yescharacteristic
782D3—22no—
783D3—42no—
784D3C3×#41714yesdirect product factor
785C22—21no—
786C22—21no—
787C22—22no—
788C22—32no—
789C22—32no—
790C22—32no—
791C22—32no—
792C22—41no—
793C22—41no—
794C22—68no—
795C22—61no—
796C22—61no—
797C22—62no—
798C22—128no—
799C22—121no—
800C22—121no—
801C22C3×D3×C22⋊C412yes—
802C22C2×C3×D3×D411yescharacteristic
803C4—22no—
804C4—32no—
805C4—32no—
806C4—42no—
807C4—62no—
808C4—122no—
809C4C3×D3×C22⋊C412yes—
810C4C22×C3×C4×D311yescharacteristic
811C4C2×C3×D3×D411yescharacteristic
812C3—21no—
813C3D3×#41711yescharacteristic, direct product factor
814C3C2×C3×#41711yescharacteristic, complemented
815C2—22no—
816C2—34no—
817C2—42no—
818C2—62no—
819C2—122no—
820C2C2×C3×D3×C22⋊C411yescharacteristic
821C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
822C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#417C2
socleC22×C32C22×D4
prime radicalC2×C3×D3×#41C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#417D3
hypocenterC3C2×C3×#417
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#417

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×M16C2semidirect
3. C2×C3×D3×C4⋊C4C2semidirect
4. C32×#417C2semidirect
5. C3×#5232C2semidirect
6. C3×#5133C2semidirect
7. C3×#4966C2semidirect
8. C3×#4803C2semidirect
9. C3×D3×#103C2semidirect
10. C3×#4771C2semidirect
11. C3×D3×#102C2semidirect
13. D3×#417C3direct (N × H)
16. C3×D3×#41C4semidirect
28. C2×C32×M16C22semidirect
29. C2×C32×C4⋊C4C22semidirect
30. C2×C3×C4⋊Dic3C22semidirect
32. C2×C3×#208C22semidirect
34. C2×C3×ΓL(1,𝔽25)C22semidirect
39. C3×D3×C4⋊C4C22semidirect
40. C32×#103C22semidirect
41. C32×#102C22semidirect
42. C3×#835C22semidirect
43. C3×#832C22semidirect
44. C3×#821C22semidirect
45. C3×#816C22semidirect
46. C3×#810C22semidirect
47. C3×#809C22semidirect
52. C2×D3×M16C2×C3semidirect
53. C2×D3×C4⋊C4C2×C3semidirect
60. C3×#417D3direct (N × H)
61. C3×#417C2×C3semidirect
64. #5232C2×C3semidirect
65. #5133C2×C3semidirect
66. #4966C2×C3semidirect
67. #4803C2×C3semidirect
68. D3×#103C2×C3semidirect
69. #4771C2×C3semidirect
70. D3×#102C2×C3semidirect
74. C32×#41C2×C4semidirect
88. C3×#239C2×C4semidirect
90. C3×D3×Q8C2×C4semidirect
93. C3×#237C2×C4semidirect
96. C3×D3×D4C2×C4semidirect
99. C3×#235C2×C4semidirect
147. D3×#41C3×C4semidirect
163. C2×C3×M16C2×D3semidirect
164. C2×C3×M16C22×C3semidirect
173. C2×C3×C4⋊C4C2×D3semidirect
174. C2×C3×C4⋊C4C22×C3semidirect
175. C2×C4⋊Dic3C22×C3semidirect
177. C2×#208C22×C3semidirect
179. C2×ΓL(1,𝔽25)C22×C3semidirect
184. D3×C4⋊C4C22×C3semidirect
189. C3×#103C2×D3semidirect
190. C3×#103C22×C3semidirect
195. C3×#102C2×D3semidirect
196. C3×#102C22×C3semidirect
197. #835C22×C3semidirect
198. #832C22×C3semidirect
199. #821C22×C3semidirect
200. #816C22×C3semidirect
201. #810C22×C3semidirect
202. #809C22×C3semidirect
215. C32×Q8C22×C4semidirect
218. C32×D4C22×C4semidirect
239. C3×D12C22×C4semidirect
253. C3×Dic6C22×C4semidirect
264. #417C3×D3direct (N × H)
283. C3×#41C4×D3semidirect
284. C3×#41C2×C3×C4semidirect
338. #239C2×C3×C4semidirect
340. D3×Q8C2×C3×C4semidirect
343. #237C2×C3×C4semidirect
346. D3×D4C2×C3×C4semidirect
349. #235C2×C3×C4semidirect
439. C2×M16C2×C3×D3semidirect
447. C2×C4⋊C4C2×C3×D3semidirect
451. #103C2×C3×D3semidirect
455. #102C2×C3×D3semidirect
487. C3×Q8C2×C4×D3semidirect
488. C3×Q8C22×C3×C4semidirect
502. C3×D4C2×C4×D3semidirect
503. C3×D4C22×C3×C4semidirect
558. D12C22×C3×C4semidirect
572. Dic6C22×C3×C4semidirect
585. C3×D3#417direct (N × H)
597. #41C3×C4×D3semidirect
710. C32C2×#417semidirect
726. Q8C2×C3×C4×D3semidirect
735. D4C2×C3×C4×D3semidirect
784. D3C3×#417direct (N × H)
813. C3D3×#417direct (N × H)
814. C3C2×C3×#417semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×C3×D3×M162
C2×C3×D3×C4⋊C42
C32×#4172
C3×#52322
C3×#51332
C3×#49662
C3×#48032
C3×D3×#1032
C3×#47712
C3×D3×#1022
C2×C3×#4173
D3×#4173