Finite Group Databasebeta

← #13170785

Subgroups — #13170785

Order 1728.

2194 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89026C211yesmaximal, characteristic
2C2×D3×#624C212yesmaximal, complemented
3#11723691C211yesmaximal, characteristic, complemented
4#11723503C211yesmaximal, characteristic, complemented
5C4×#6289C211yesmaximal, characteristic, complemented
6C3×#63898C211yesmaximal, characteristic, complemented
7C3×#63894C211yesmaximal, characteristic, complemented
8C3×Dic3×D12C211yesmaximal, characteristic, complemented
9#11722936C212yesmaximal, complemented
10#11722930C212yesmaximal, complemented
11#11722906C212yesmaximal, complemented
12D4×#624—31nomaximal
13#10594605—31nomaximal
14C4×#3802—31nomaximal
15C22×D3×C3⋊D3C2212yes—
16C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C32×D12C2211yescharacteristic
19C2×#6294C2212yescomplemented
20C2×#6290C2212yes—
21C2×#6289C2212yes—
22C2×#6289C2211yescharacteristic
23C2×#6289C2211yescharacteristic
24#89026C418yescomplemented
25C2×C3×#624C2212yescomplemented
26C2×C3×D3×Dic3C2212yescomplemented
27C2×C3×D3×Dic3C2212yescomplemented
28D3×#624—28no—
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
31C32×C4⋊Dic3C2211yescharacteristic, complemented
32C32×C4×Dic3C2211yescharacteristic, complemented
33#88814C2212yescomplemented
34#88806C2212yescomplemented
35Dic3×C3⋊Dic3C2211yescharacteristic, complemented
36Dic3×C3⋊Dic3C2211yescharacteristic, complemented
37C3×#3722C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C2×D4×C3⋊D3—31no—
41C22×#624—32no—
42C2×#3802—31no—
43C2×#3802—31no—
44C2×#3802—61no—
45C2×C4×D32—32no—
46C2×C4×D32—32no—
47C4⋊C4×C3⋊D3—31no—
48C42×C3⋊D3—31no—
49C3×D4×Dic3—31no—
50C3×D4×Dic3—31no—
51C3×#893—31no—
52C3×#893—31no—
53C3×C4×D12—31no—
54C3×C4×D12—31no—
55#63974—32no—
56#63952—32no—
57#63952—32no—
58#63921—32no—
59#63921—32no—
60#63902—32no—
61C4×#625—32no—
62#63900—31no—
63#63900—31no—
64#63900—61no—
65#63898—31no—
66#63898D311yescharacteristic, complemented
67#63894—31no—
68#63894D311yescharacteristic, complemented
69Dic3×D12—31no—
70Dic3×D12D311yescharacteristic, complemented
71C4×#624—31no—
72C4×#624—31no—
73C4×#624—61no—
74#63879—32no—
75#63879—32no—
76C22×C3⋊(C3⋊D3)C2311yescharacteristic
77C22×C3×C3⋊D3C2312yes—
78C22×C32×D3C2312yes—
79C2×D3×C3⋊D3—24no—
80C2×D3×C3⋊D3—24no—
81C2×D3×C3⋊D3C2×C418yescomplemented
82C2×C33×C4C2311yescharacteristic
83C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
84C4×C3⋊(C3⋊D3)C2×C414yescomplemented
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C3×C4⋊(C3⋊D3)C2×C414yescomplemented
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2311yescharacteristic
91C2×C32×Dic3C2311yescharacteristic
92C32×D12C2×C414yescomplemented
93#6294—24no—
94#6290C2×C418yescomplemented
95#6289—24no—
96#6289—22no—
97#6289D414yescomplemented
98C3×#624—24no—
99C3×D3×Dic3—24no—
100C3×D3×Dic3—24no—
101C4×D3×D4—91no—
102C4×D3×D4—91no—
103C4×D3×D4—91no—
104C23×C3⋊D3—32no—
105C22×D32—32no—
106C22×D32—32no—
107C22×D32—62no—
108C2×C32×D4—31no—
109C2×#638—32no—
110D4×C3⋊D3—38no—
111C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
112C2×C4×C3⋊D3—31no—
113C2×C4×C3⋊D3—31no—
114C2×C4×C3⋊D3—31no—
115C2×C4×C3⋊D3—31no—
116C2×C4×C3⋊D3—32no—
117C2×C4×C3⋊D3—31no—
118C2×C4×C3⋊D3—61no—
119C2×C4×C3⋊D3—61no—
120C2×C4×C3⋊D3—61no—
121C2×C4×C3⋊D3—121no—
122C22×C3×Dic3—32no—
123C22×C3×Dic3—32no—
124C2×C3×D12—21no—
125C2×C3×D12—31no—
126C2×C3×D12—31no—
127C2×C3×D12—61no—
128C2×C3×D12C2×D311yescharacteristic
129C2×C3×D12C2×D311yescharacteristic
130C2×C3×C4×D3—32no—
131C2×C3×C4×D3—32no—
132C2×C3×C4×D3—32no—
133C2×C3×C4×D3—32no—
134C2×#625—32no—
135C2×#625—32no—
136C2×#625—62no—
137C2×#624—31no—
138C2×#624—31no—
139C2×#624—32no—
140C2×#624—32no—
141C2×#624—32no—
142C2×#624—31no—
143C2×#624—31no—
144C2×#624—68no—
145C2×#624—61no—
146C2×#624—61no—
147C2×#624—62no—
148C2×#624C2×D312yescomplemented
149C2×D3×Dic3—32no—
150C2×D3×Dic3—32no—
151C2×D3×Dic3C2×D312yescomplemented
152C2×D3×Dic3C2×D312yescomplemented
153#3802—38no—
154#3802—38no—
155#3802—68no—
156C4×D32—68no—
157C4×D32—68no—
158C32×C4⋊C4—31no—
159C32×C42—31no—
160C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
161#3750—32no—
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—31no—
164C4×C3⋊Dic3C2×D311yescharacteristic, complemented
165C3×#217—32no—
166C3×#217—32no—
167C3×(C2×D3)⋊C4—32no—
168C3×(C2×D3)⋊C4—32no—
169C3×(C2×D3)⋊C4—32no—
170C3×(C2×D3)⋊C4—32no—
171C3×C4⋊Dic3—21no—
172C3×C4⋊Dic3—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—61no—
175C3×C4⋊Dic3C2×D311yescharacteristic, complemented
176C3×C4⋊Dic3C2×D311yescharacteristic, complemented
177C3×C4×Dic3—21no—
178C3×C4×Dic3—31no—
179C3×C4×Dic3—31no—
180C3×C4×Dic3—61no—
181C3×C4×Dic3C2×D311yescharacteristic, complemented
182C3×C4×Dic3C2×D311yescharacteristic, complemented
183#3724—32no—
184#3724—32no—
185#3724—62no—
186#3722—32no—
187#3722C2×D312yescomplemented
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—32no—
190(C2×D3)⋊Dic3C2×D312yescomplemented
191(C2×D3)⋊Dic3C2×D312yescomplemented
192Dic32—31no—
193Dic32—31no—
194Dic32—31no—
195Dic32—31no—
196Dic32—61no—
197Dic32—61no—
198C22×C33C2411yescharacteristic
199C2×C3⋊(C3⋊D3)C22×C412yes—
200C2×C3⋊(C3⋊D3)C2×D412yes—
201C2×C3⋊(C3⋊D3)#4112yes—
202C2×C3×C3⋊D3—22no—
203C2×C3×C3⋊D3—22no—
204C2×C3×C3⋊D3C22×C414yescomplemented
205C2×C32×D3—22no—
206C2×C32×D3—22no—
207C2×C32×D3C22×C414yescomplemented
208D3×C3⋊D3—216no—
209C33×C4C22×C412yescomplemented
210C3⋊(C3⋊Dic3)C22×C412yescomplemented
211C3×C3⋊Dic3—22no—
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3C2×D412yescomplemented
214C32×Dic3—22no—
215C32×Dic3—21no—
216C32×Dic3C2×D412yescomplemented
217C2×D3×D4—91no—
218C2×D3×D4—91no—
219C2×D3×D4—91no—
220C2×D3×D4—181no—
221C22×C4×D3—92no—
222C22×C4×D3—92no—
223C22×C4×D3—92no—
224C3×C4×D4—91no—
225C3×C4×D4—91no—
226C3×C4×D4—91no—
227D4×Dic3—31no—
228D4×Dic3—31no—
229D4×Dic3—91no—
230C4×#67—92no—
231C4×#67—92no—
232C4×#67—92no—
233#893—31no—
234#893—31no—
235#893—91no—
236D3×C4⋊C4—91no—
237D3×C4⋊C4—91no—
238D3×C4⋊C4—91no—
239D3×C4⋊C4—181no—
240#67⋊C4—92no—
241#67⋊C4—92no—
242#67⋊C4—92no—
243D3×C22⋊C4—92no—
244D3×C22⋊C4—92no—
245D3×C22⋊C4—92no—
246C4×D12—31no—
247C4×D12—31no—
248C4×D12—91no—
249C42×D3—91no—
250C42×D3—91no—
251C42×D3—91no—
252C42×D3—181no—
253C23×C32—32no—
254C22×C3⋊D3—31no—
255C22×C3⋊D3—31no—
256C22×C3⋊D3—31no—
257C22×C3⋊D3—38no—
258C22×C3⋊D3—61no—
259C22×C3⋊D3—61no—
260C22×C3⋊D3—61no—
261C22×C3⋊D3—64no—
262C22×C3⋊D3—64no—
263C22×C3⋊D3—121no—
264C22×C3⋊D3C22×D312yes—
265C22×C3×D3—22no—
266C22×C3×D3—32no—
267C22×C3×D3—32no—
268C22×C3×D3—62no—
269C22×C3×D3C22×D312yes—
270C22×C3×D3C22×D312yes—
271C2×D32—38no—
272C2×D32—38no—
273C2×D32—68no—
274C2×D32—64no—
275C2×D32—64no—
276C2×D32—64no—
277C2×D32—64no—
278C2×D32—124no—
279C2×D32—124no—
280C32×D4—34no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—31no—
285C2×C32×C4—31no—
286C2×C32×C4—32no—
287C2×C32×C4—41no—
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291#638—38no—
292C2×C3⋊Dic3—31no—
293C2×C3⋊Dic3—31no—
294C2×C3⋊Dic3—31no—
295C2×C3⋊Dic3—61no—
296C2×C3⋊Dic3—61no—
297C2×C3⋊Dic3—61no—
298C2×C3⋊Dic3—121no—
299C2×C3⋊Dic3C22×D311yescharacteristic
300C2×C3⋊Dic3C22×D312yes—
301C2×C3⋊Dic3C22×D311yescharacteristic
302C4⋊(C3⋊D3)C4×D314yescomplemented
303C4×C3⋊D3—34no—
304C4×C3⋊D3—34no—
305C4×C3⋊D3—34no—
306C4×C3⋊D3—34no—
307C4×C3⋊D3—64no—
308C4×C3⋊D3—64no—
309C4×C3⋊D3—64no—
310C4×C3⋊D3—62no—
311C4×C3⋊D3—64no—
312C4×C3⋊D3—124no—
313C2×C3×Dic3—21no—
314C2×C3×Dic3—21no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—31no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—31no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—32no—
321C2×C3×Dic3—32no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—61no—
324C2×C3×Dic3—62no—
325C2×C3×Dic3—64no—
326C2×C3×Dic3—64no—
327C2×C3×Dic3C22×D311yescharacteristic
328C2×C3×Dic3C22×D311yescharacteristic
329C2×C3×Dic3C22×D312yes—
330C2×C3×Dic3C22×D312yes—
331C2×C3×Dic3C22×D311yescharacteristic
332C2×C3×Dic3C22×D311yescharacteristic
333C3×D12—24no—
334C3×D12—34no—
335C3×D12—34no—
336C3×D12—64no—
337C3×D12C4×D314yescomplemented
338C3×D12C4×D314yescomplemented
339C3×C4×D3—64no—
340C3×C4×D3—64no—
341C3×C4×D3—64no—
342C3×C4×D3—64no—
343#625—38no—
344#625—38no—
345#625—68no—
346#624—24no—
347#624—34no—
348#624—34no—
349#624—64no—
350#624—64no—
351#624—62no—
352#624—62no—
353#624—64no—
354#624—64no—
355#624—64no—
356#624—124no—
357D3×Dic3—24no—
358D3×Dic3—24no—
359D3×Dic3—64no—
360D3×Dic3—64no—
361C2×C4×D4—271noSylow
362C2×C33C23×C411yescharacteristic
363C2×C33C22×D411yescharacteristic
364C2×C33C2×#4111yescharacteristic
365C3⋊(C3⋊D3)C4×D414yescomplemented
366C3×C3⋊D3—24no—
367C32×D3—24no—
368C23×D3—92no—
369C23×D3—92no—
370C23×D3—92no—
371C23×D3—182no—
372C2×C3×D4—31no—
373C2×C3×D4—31no—
374C2×C3×D4—61no—
375C2×C3×D4—91no—
376C22×C3×C4—92no—
377C22×C3×C4—92no—
378C22×C3×C4—92no—
379C2×#67—92no—
380C2×#67—92no—
381C2×#67—92no—
382C2×#67—182no—
383C22×Dic3—32no—
384C22×Dic3—32no—
385C22×Dic3—92no—
386D3×D4—98no—
387D3×D4—98no—
388D3×D4—98no—
389D3×D4—188no—
390C2×D12—31no—
391C2×D12—31no—
392C2×D12—61no—
393C2×D12D3211yescharacteristic
394C2×C4×D3—32no—
395C2×C4×D3—32no—
396C2×C4×D3—32no—
397C2×C4×D3—32no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3—92no—
407C2×C4×D3—92no—
408C2×C4×D3—92no—
409C2×C4×D3—92no—
410C2×C4×D3—91no—
411C2×C4×D3—92no—
412C2×C4×D3—181no—
413C2×C4×D3—181no—
414C2×C4×D3—181no—
415C2×C4×D3—181no—
416C2×C4×D3—181no—
417C2×C4×D3—182no—
418C2×C4×D3—188no—
419C2×C4×D3—188no—
420C2×C4×D3—188no—
421C2×C4×D3—361no—
422C3×C4⋊C4—31no—
423C3×C4⋊C4—31no—
424C3×C4⋊C4—61no—
425C3×C4⋊C4—91no—
426C3×C22⋊C4—92no—
427C3×C22⋊C4—92no—
428C3×C22⋊C4—92no—
429C3×C42—31no—
430C3×C42—31no—
431C3×C42—61no—
432C3×C42—91no—
433#217—32no—
434#217—32no—
435#217—92no—
436(C2×D3)⋊C4—32no—
437(C2×D3)⋊C4—32no—
438(C2×D3)⋊C4—32no—
439(C2×D3)⋊C4—32no—
440(C2×D3)⋊C4—92no—
441(C2×D3)⋊C4—92no—
442C4⋊Dic3—31no—
443C4⋊Dic3—31no—
444C4⋊Dic3—61no—
445C4⋊Dic3D3211yescharacteristic, complemented
446Dic3⋊C4—92no—
447Dic3⋊C4—92no—
448Dic3⋊C4—92no—
449Dic3⋊C4—182no—
450C4×Dic3—31no—
451C4×Dic3—31no—
452C4×Dic3—61no—
453C4×Dic3—91no—
454C4×Dic3—91no—
455C4×Dic3—91no—
456C4×Dic3—91no—
457C4×Dic3—91no—
458C4×Dic3—91no—
459C4×Dic3—181no—
460C4×Dic3—181no—
461C4×Dic3D3211yescharacteristic, complemented
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—34no—
466C22×C32—41no—
467C22×C32—62no—
468C22×C32—62no—
469C22×C32C23×D311yescharacteristic
470C22×C32C23×D311yescharacteristic
471C22×C32C23×D311yescharacteristic
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3—32no—
475C2×C3⋊D3—32no—
476C2×C3⋊D3—32no—
477C2×C3⋊D3—32no—
478C2×C3⋊D3—32no—
479C2×C3⋊D3—32no—
480C2×C3⋊D3—32no—
481C2×C3⋊D3—32no—
482C2×C3⋊D3—32no—
483C2×C3⋊D3—62no—
484C2×C3⋊D3—62no—
485C2×C3⋊D3—62no—
486C2×C3⋊D3—62no—
487C2×C3⋊D3—62no—
488C2×C3⋊D3—62no—
489C2×C3⋊D3—62no—
490C2×C3⋊D3—62no—
491C2×C3⋊D3—62no—
492C2×C3⋊D3—616no—
493C2×C3⋊D3—122no—
494C2×C3⋊D3—122no—
495C2×C3⋊D3—122no—
496C2×C3⋊D3C2×C4×D314yescomplemented
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—22no—
501C2×C3×D3—24no—
502C2×C3×D3—34no—
503C2×C3×D3—34no—
504C2×C3×D3—42no—
505C2×C3×D3—42no—
506C2×C3×D3—64no—
507C2×C3×D3—62no—
508C2×C3×D3—62no—
509C2×C3×D3—62no—
510C2×C3×D3—62no—
511C2×C3×D3—122no—
512C2×C3×D3—122no—
513C2×C3×D3C2×C4×D314yescomplemented
514C2×C3×D3C2×C4×D314yescomplemented
515D32—616no—
516D32—616no—
517D32—1216no—
518C32×C4—22no—
519C32×C4—22no—
520C32×C4—22no—
521C32×C4—32no—
522C32×C4—42no—
523C32×C4—61no—
524C32×C4—62no—
525C32×C4C2×C4×D312yescomplemented
526C32×C4C2×C4×D312yescomplemented
527C32×C4C2×C4×D312yescomplemented
528C3⋊Dic3—21no—
529C3⋊Dic3—22no—
530C3⋊Dic3—32no—
531C3⋊Dic3—32no—
532C3⋊Dic3—32no—
533C3⋊Dic3—62no—
534C3⋊Dic3—62no—
535C3⋊Dic3—62no—
536C3⋊Dic3—122no—
537C3⋊Dic3D3×D412yescomplemented
538C3×Dic3—22no—
539C3×Dic3—22no—
540C3×Dic3—22no—
541C3×Dic3—21no—
542C3×Dic3—21no—
543C3×Dic3—22no—
544C3×Dic3—32no—
545C3×Dic3—32no—
546C3×Dic3—42no—
547C3×Dic3—62no—
548C3×Dic3—62no—
549C3×Dic3—62no—
550C3×Dic3—62no—
551C3×Dic3—61no—
552C3×Dic3—61no—
553C3×Dic3—122no—
554C3×Dic3D3×D412yescomplemented
555C3×Dic3D3×D412yescomplemented
556C22×D4—271no—
557C23×C4—272no—
558C4×D4—91no—
559C4×D4—91no—
560C4×D4—91no—
561C4×D4—271no—
562C4×D4—272no—
563C4×D4—272no—
564C2×C4⋊C4—271no—
565C2×C22⋊C4—272no—
566C2×C42—271no—
567C33C2×C4×D411yescharacteristic, complemented, Sylow
568C23×C3—32no—
569C23×C3—32no—
570C23×C3—62no—
571C23×C3—92no—
572C22×D3—32no—
573C22×D3—32no—
574C22×D3—62no—
575C22×D3—98no—
576C22×D3—98no—
577C22×D3—91no—
578C22×D3—91no—
579C22×D3—91no—
580C22×D3—98no—
581C22×D3—188no—
582C22×D3—181no—
583C22×D3—181no—
584C22×D3—181no—
585C22×D3—184no—
586C22×D3—184no—
587C22×D3—184no—
588C22×D3—184no—
589C22×D3—184no—
590C22×D3—184no—
591C22×D3—361no—
592C22×D3—364no—
593C22×D3—364no—
594C22×D3C2×D3212yes—
595C3×D4—34no—
596C3×D4—34no—
597C3×D4—64no—
598C3×D4—94no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—31no—
603C2×C3×C4—31no—
604C2×C3×C4—31no—
605C2×C3×C4—31no—
606C2×C3×C4—32no—
607C2×C3×C4—32no—
608C2×C3×C4—41no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—62no—
612C2×C3×C4—91no—
613C2×C3×C4—91no—
614C2×C3×C4—92no—
615C2×C3×C4—184no—
616C2×C3×C4—184no—
617C2×C3×C4—184no—
618C2×C3×C4C2×D3211yescharacteristic
619C2×C3×C4C2×D3211yescharacteristic
620C2×C3×C4C2×D3211yescharacteristic
621#67—98no—
622#67—98no—
623#67—98no—
624#67—188no—
625C2×Dic3—31no—
626C2×Dic3—31no—
627C2×Dic3—31no—
628C2×Dic3—31no—
629C2×Dic3—32no—
630C2×Dic3—32no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—62no—
634C2×Dic3—64no—
635C2×Dic3—64no—
636C2×Dic3—91no—
637C2×Dic3—91no—
638C2×Dic3—91no—
639C2×Dic3—181no—
640C2×Dic3—181no—
641C2×Dic3—181no—
642C2×Dic3—184no—
643C2×Dic3—361no—
644C2×Dic3C2×D3211yescharacteristic
645C2×Dic3C2×D3212yes—
646C2×Dic3C2×D3211yescharacteristic
647D12—34no—
648D12—34no—
649D12—64no—
650D12#62414yescomplemented
651C4×D3—64no—
652C4×D3—64no—
653C4×D3—64no—
654C4×D3—64no—
655C4×D3—94no—
656C4×D3—94no—
657C4×D3—94no—
658C4×D3—94no—
659C4×D3—94no—
660C4×D3—94no—
661C4×D3—184no—
662C4×D3—184no—
663C4×D3—184no—
664C4×D3—184no—
665C4×D3—182no—
666C4×D3—184no—
667C4×D3—184no—
668C4×D3—182no—
669C4×D3—182no—
670C4×D3—184no—
671C4×D3—184no—
672C4×D3—184no—
673C4×D3—184no—
674C4×D3—364no—
675C4×D3—364no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—21no—
681C2×C32—21no—
682C2×C32—21no—
683C2×C32—21no—
684C2×C32—21no—
685C2×C32—41no—
686C2×C32—41no—
687C2×C32—41no—
688C2×C32—64no—
689C2×C32C22×C4×D311yescharacteristic
690C2×C32C22×C4×D311yescharacteristic
691C2×C32C22×C4×D311yescharacteristic
692C2×C32C2×D3×D411yescharacteristic
693C2×C32C2×D3×D411yescharacteristic
694C2×C32C2×D3×D411yescharacteristic
695C2×C32D3×#4111yescharacteristic
696C2×C32D3×#4111yescharacteristic
697C2×C32D3×#4111yescharacteristic
698C3⋊D3—24no—
699C3⋊D3—34no—
700C3⋊D3—34no—
701C3⋊D3—34no—
702C3⋊D3—64no—
703C3⋊D3—64no—
704C3⋊D3—64no—
705C3⋊D3—124no—
706C3×D3—24no—
707C3×D3—24no—
708C3×D3—44no—
709C3×D3—64no—
710C3×D3—64no—
711C3×D3—124no—
712C24—272no—
713C2×D4—31no—
714C2×D4—91no—
715C2×D4—278no—
716C2×D4—272no—
717C22×C4—92no—
718C22×C4—92no—
719C22×C4—92no—
720C22×C4—271no—
721C22×C4—271no—
722C22×C4—272no—
723C22×C4—272no—
724C22×C4—271no—
725C22×C4—548no—
726C4⋊C4—31no—
727C4⋊C4—91no—
728C4⋊C4—272no—
729C22⋊C4—92no—
730C22⋊C4—92no—
731C22⋊C4—92no—
732C22⋊C4—272no—
733C42—31no—
734C42—91no—
735C42—271no—
736C42—271no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—34no—
741C22×C3—34no—
742C22×C3—41no—
743C22×C3—64no—
744C22×C3—62no—
745C22×C3—62no—
746C22×C3—62no—
747C22×C3—62no—
748C22×C3—94no—
749C22×C3—122no—
750C22×C3—122no—
751C22×C3—182no—
752C22×C3—182no—
753C22×C3C22×D3211yescharacteristic
754C22×C3C22×D3211yescharacteristic
755C22×C3C22×D3211yescharacteristic
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—34no—
759C2×D3—34no—
760C2×D3—64no—
761C2×D3—62no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—92no—
766C2×D3—92no—
767C2×D3—92no—
768C2×D3—92no—
769C2×D3—92no—
770C2×D3—92no—
771C2×D3—92no—
772C2×D3—92no—
773C2×D3—92no—
774C2×D3—122no—
775C2×D3—122no—
776C2×D3—182no—
777C2×D3—182no—
778C2×D3—182no—
779C2×D3—182no—
780C2×D3—182no—
781C2×D3—182no—
782C2×D3—182no—
783C2×D3—182no—
784C2×D3—182no—
785C2×D3—1816no—
786C2×D3—1816no—
787C2×D3—1816no—
788C2×D3—362no—
789C2×D3—362no—
790C2×D3—362no—
791C2×D3—3616no—
792C2×D3C2×#62414yescomplemented
793C3×C4—22no—
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—32no—
797C3×C4—32no—
798C3×C4—42no—
799C3×C4—62no—
800C3×C4—62no—
801C3×C4—62no—
802C3×C4—62no—
803C3×C4—61no—
804C3×C4—61no—
805C3×C4—92no—
806C3×C4—122no—
807C3×C4—181no—
808C3×C4—182no—
809C3×C4C4×D3212yescomplemented
810C3×C4C4×D3212yescomplemented
811C3×C4C2×#62412yescomplemented
812Dic3—21no—
813Dic3—22no—
814Dic3—32no—
815Dic3—32no—
816Dic3—62no—
817Dic3—62no—
818Dic3—62no—
819Dic3—62no—
820Dic3—61no—
821Dic3—61no—
822Dic3—92no—
823Dic3—92no—
824Dic3—92no—
825Dic3—122no—
826Dic3—182no—
827Dic3—182no—
828Dic3—182no—
829Dic3—362no—
830Dic3#380212yescomplemented
831C32—21no—
832C32—21no—
833C32—21no—
834C32—41no—
835C32C4×D3×D411yescharacteristic, complemented
836C32C4×D3×D411yescharacteristic, complemented
837C32C4×D3×D411yescharacteristic, complemented
838C23—32no—
839C23—92no—
840C23—278no—
841C23—271no—
842C23—544no—
843C23—544no—
844D4—34no—
845D4—94no—
846D4—278no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—32no—
850C2×C4—91no—
851C2×C4—91no—
852C2×C4—92no—
853C2×C4—184no—
854C2×C4—184no—
855C2×C4—184no—
856C2×C4—274no—
857C2×C4—271no—
858C2×C4—274no—
859C2×C4—544no—
860C2×C4—542no—
861C2×C4—544no—
862C2×C4D3311yescharacteristic
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—21no—
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—41no—
873C2×C3—41no—
874C2×C3—41no—
875C2×C3—64no—
876C2×C3—64no—
877C2×C3—124no—
878C2×C3—184no—
879C2×C3C2×C4×D3211yescharacteristic
880C2×C3C2×C4×D3211yescharacteristic
881C2×C3C2×#380211yescharacteristic
882C2×C3#6430611yescharacteristic
883C2×C3D32×D411yescharacteristic
884C2×C3D32×D411yescharacteristic
885C2×C3#6431211yescharacteristic
886C2×C3#6431911yescharacteristic
887C2×C3C22×#62411yescharacteristic
888D3—24no—
889D3—64no—
890D3—64no—
891D3—94no—
892D3—94no—
893D3—94no—
894D3—124no—
895D3—184no—
896D3—184no—
897D3—184no—
898D3—364no—
899C22—34no—
900C22—62no—
901C22—62no—
902C22—94no—
903C22—182no—
904C22—182no—
905C22—272no—
906C22—272no—
907C22—272no—
908C22—5416no—
909C22C2×D3311yescharacteristic
910C4—32no—
911C4—61no—
912C4—62no—
913C4—92no—
914C4—181no—
915C4—182no—
916C4—272no—
917C4D3×#62412yescomplemented
918C3—21no—
919C3—21no—
920C3—21no—
921C3—41no—
922C3C4×#380211yescharacteristic, complemented
923C3#1059460511yescharacteristic, complemented
924C3D4×#62411yescharacteristic, complemented
925C2—64no—
926C2—184no—
927C2—274no—
928C2#1172437611yescharacteristic
929C2D3×#380211yescharacteristic
930C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×#89026C2
hypercenterC2×C4D33
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#624C2semidirect
3. #11723691C2semidirect
4. #11723503C2semidirect
5. C4×#6289C2semidirect
6. C3×#63898C2semidirect
7. C3×#63894C2semidirect
8. C3×Dic3×D12C2semidirect
9. #11722936C2semidirect
10. #11722930C2semidirect
11. #11722906C2semidirect
19. C2×#6294C22semidirect
24. #89026C4semidirect
25. C2×C3×#624C22semidirect
26. C2×C3×D3×Dic3C22semidirect
27. C2×C3×D3×Dic3C22semidirect
29. C3×C4⋊(C3⋊Dic3)C22semidirect
30. C3×C4×C3⋊Dic3C22semidirect
31. C32×C4⋊Dic3C22semidirect
32. C32×C4×Dic3C22semidirect
33. #88814C22semidirect
34. #88806C22semidirect
35. Dic3×C3⋊Dic3C22semidirect
36. Dic3×C3⋊Dic3C22semidirect
37. C3×#3722C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
66. #63898D3semidirect
68. #63894D3semidirect
70. Dic3×D12D3semidirect
81. C2×D3×C3⋊D3C2×C4semidirect
84. C4×C3⋊(C3⋊D3)C2×C4semidirect
88. C3×C4⋊(C3⋊D3)C2×C4semidirect
92. C32×D12C2×C4semidirect
94. #6290C2×C4semidirect
97. #6289D4semidirect
148. C2×#624C2×D3semidirect
151. C2×D3×Dic3C2×D3semidirect
152. C2×D3×Dic3C2×D3semidirect
160. C4⋊(C3⋊Dic3)C2×D3semidirect
164. C4×C3⋊Dic3C2×D3semidirect
175. C3×C4⋊Dic3C2×D3semidirect
176. C3×C4⋊Dic3C2×D3semidirect
181. C3×C4×Dic3C2×D3semidirect
182. C3×C4×Dic3C2×D3semidirect
187. #3722C2×D3semidirect
190. (C2×D3)⋊Dic3C2×D3semidirect
191. (C2×D3)⋊Dic3C2×D3semidirect
204. C2×C3×C3⋊D3C22×C4semidirect
207. C2×C32×D3C22×C4semidirect
209. C33×C4C22×C4semidirect
210. C3⋊(C3⋊Dic3)C22×C4semidirect
213. C3×C3⋊Dic3C2×D4semidirect
216. C32×Dic3C2×D4semidirect
302. C4⋊(C3⋊D3)C4×D3semidirect
337. C3×D12C4×D3semidirect
338. C3×D12C4×D3semidirect
365. C3⋊(C3⋊D3)C4×D4semidirect
445. C4⋊Dic3D32semidirect
461. C4×Dic3D32semidirect
496. C2×C3⋊D3C2×C4×D3semidirect
513. C2×C3×D3C2×C4×D3semidirect
514. C2×C3×D3C2×C4×D3semidirect
525. C32×C4C2×C4×D3semidirect
526. C32×C4C2×C4×D3semidirect
527. C32×C4C2×C4×D3semidirect
537. C3⋊Dic3D3×D4semidirect
554. C3×Dic3D3×D4semidirect
555. C3×Dic3D3×D4semidirect
567. C33C2×C4×D4semidirect
650. D12#624semidirect
792. C2×D3C2×#624semidirect
809. C3×C4C4×D32semidirect
810. C3×C4C4×D32semidirect
811. C3×C4C2×#624semidirect
830. Dic3#3802semidirect
835. C32C4×D3×D4semidirect
836. C32C4×D3×D4semidirect
837. C32C4×D3×D4semidirect
917. C4D3×#624semidirect
922. C3C4×#3802semidirect
923. C3#10594605semidirect
924. C3D4×#624semidirect

Maximal subgroups

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

subgroupindex
C2×#890262
C2×D3×#6242
#117236912
#117235032
C4×#62892
C3×#638982
C3×#638942
C3×Dic3×D122
#117229362
#117229302
#117229062
D4×#6243
#105946053
C4×#38023