Finite Group Databasebeta

← D3×#63891 #13170730

Subgroups — D3×#63891 #13170730

Order 1728.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#625C211yesmaximal, characteristic
2C2×D32×Dic3C211yesmaximal, characteristic, complemented
3#11723690C211yesmaximal, characteristic, complemented
4#11723523C211yesmaximal, characteristic, complemented
5#11723480C211yesmaximal, characteristic, complemented
6D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7C3×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8C3×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
9C3×#63891C211yesmaximal, characteristic, complemented
10#11722998C211yesmaximal, characteristic, complemented
11#11722997C211yesmaximal, characteristic, complemented
12#11722989C211yesmaximal, characteristic, complemented
13#11722988C211yesmaximal, characteristic, complemented
14D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
16C2×#63891—31nomaximal
17D3×#886—31nomaximal
18D3×#883—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C22×C3×D32C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×#6295C2211yescharacteristic
23C2×#6294C2211yescharacteristic, complemented
24C2×#6290C2211yescharacteristic
25C2×#6290C2211yescharacteristic
26C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C2×D3×C3⋊Dic3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
30C2×C3×#625C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic, complemented
34D3×#625—24no—
35D32×Dic3—24no—
36C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
37C3×#3752C2211yescharacteristic, complemented
38C3×#3752C2211yescharacteristic, complemented
39C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88807C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88803C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50C3×Dic3⋊Dic3C2211yescharacteristic, complemented
51C3×#3722C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×D3×#67—31no—
57C2×D3×#67—31no—
58C22×#625—31no—
59C22×D3×Dic3—31no—
60C22×D3×Dic3—31no—
61C2×C4×D32—31no—
62C2×C4⋊(C3⋊Dic3)—31no—
63#64095—31no—
64#64092—31no—
65C2×C3×(C2×D3)⋊C4—31no—
66C2×C3×(C2×D3)⋊C4—31no—
67C3×#886—31no—
68C3×#883—31no—
69C3×D3×C22⋊C4—31no—
70C3×D3×C22⋊C4—31no—
71#63975—31no—
72#63969—31no—
73D3×#217—31no—
74#63966—31no—
75C2×Dic3⋊Dic3—31no—
76#63962—31no—
77C2×(C2×D3)⋊Dic3—31no—
78D3×(C2×D3)⋊C4—31no—
79D3×(C2×D3)⋊C4D311yescharacteristic, complemented
80D3×(C2×D3)⋊C4D311yescharacteristic, complemented
81#63905—31no—
82#63891—31no—
83#63891—31no—
84#63891—31no—
85#63891—31no—
86#63891—31no—
87#63891—31no—
88#63891—31no—
89#63891—31no—
90#63891—31no—
91#63891—31no—
92#63891—61no—
93#63891—61no—
94#63891D311yescharacteristic, direct product factor
95#63890—31no—
96#63890—31no—
97D3×C4⋊Dic3—31no—
98D3×C4⋊Dic3—31no—
99D3×C4⋊Dic3—31no—
100D3×C4⋊Dic3—61no—
101D3×Dic3⋊C4—31no—
102#63854—31no—
103#63853—31no—
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C2×C3×D32—22no—
110C2×C3×D32—22no—
111C2×C3×D32—22no—
112C2×C3×D32—22no—
113C2×C3×D32—22no—
114C2×C3×D32D414yes—
115C2×C33×C4C2311yescharacteristic
116C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C2×C3×C3⋊Dic3C2311yescharacteristic
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C32×C4×D3—22no—
126#6295—22no—
127#6294—22no—
128#6290—22no—
129#6290—22no—
130Dic3×C3⋊D3—22no—
131D3×C3⋊Dic3—22no—
132D3×C3⋊Dic3—22no—
133D3×C3⋊Dic3—22no—
134C3×#625—22no—
135C3×D3×Dic3—22no—
136C3×D3×Dic3—22no—
137C3×D3×Dic3—22no—
138D3×#123—91no—
139C2×#886—91no—
140C2×#883—91no—
141C23×C3×D3—31no—
142C23×C3×D3—31no—
143C23×C3×D3—31no—
144C23×C3×D3—31no—
145C22×D32C2×D311yescharacteristic
146C22×D32C2×D311yescharacteristic
147C22×C32×C4—31no—
148C2×#638—31no—
149C2×#638—31no—
150C22×C3⋊Dic3—31no—
151C22×C3⋊Dic3—31no—
152C22×C3⋊Dic3—31no—
153C2×C4×C3⋊D3—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C2×C3×C4×D3—21no—
160C2×C3×C4×D3—31no—
161C2×C3×C4×D3—31no—
162C2×C3×C4×D3—31no—
163C2×C3×C4×D3C2×D311yescharacteristic
164C2×C3×C4×D3C2×D311yescharacteristic
165D3×#67—64no—
166D3×#67—64no—
167C2×#626—31no—
168C2×#626—31no—
169C2×#625—31no—
170C2×#625—31no—
171C2×#625—31no—
172C2×#625—31no—
173C2×#625—31no—
174C2×#625—64no—
175C2×#625—61no—
176C2×#625—61no—
177C2×#625C2×D311yescharacteristic
178C2×#624—31no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—31no—
185C2×D3×Dic3—31no—
186C2×D3×Dic3—31no—
187C2×D3×Dic3—31no—
188C2×D3×Dic3—31no—
189C2×D3×Dic3—64no—
190C2×D3×Dic3—64no—
191C2×D3×Dic3—61no—
192C2×D3×Dic3—61no—
193C2×D3×Dic3—61no—
194C2×D3×Dic3—61no—
195C2×D3×Dic3C2×D311yescharacteristic
196C2×D3×Dic3C2×D311yescharacteristic
197C2×D3×Dic3C2×D311yescharacteristic, complemented
198C4×D32—64no—
199C32×C22⋊C4—31no—
200C32×C22⋊C4—31no—
201#3757—31no—
202#3752—31no—
203#3752C2×D311yescharacteristic, complemented
204#3752C2×D311yescharacteristic, complemented
205C4⋊(C3⋊Dic3)—31no—
206C4⋊(C3⋊Dic3)—31no—
207C4⋊(C3⋊Dic3)—31no—
208C4⋊(C3⋊Dic3)—31no—
209C4⋊(C3⋊Dic3)—31no—
210C4⋊(C3⋊Dic3)—31no—
211C4⋊(C3⋊Dic3)—61no—
212C4⋊(C3⋊Dic3)—61no—
213C4⋊(C3⋊Dic3)—61no—
214C4⋊(C3⋊Dic3)—121no—
215C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
216#3750—31no—
217C3×#217—31no—
218C3×#217—31no—
219C3×#217—31no—
220C3×(C2×D3)⋊C4—21no—
221C3×(C2×D3)⋊C4—21no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×(C2×D3)⋊C4—31no—
228C3×(C2×D3)⋊C4—31no—
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×(C2×D3)⋊C4—61no—
234C3×(C2×D3)⋊C4—61no—
235C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
236C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
237C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
238C3×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
239C3×C4⋊Dic3—31no—
240C3×C4⋊Dic3—31no—
241C3×C4⋊Dic3—31no—
242C3×C4⋊Dic3—61no—
243C3×Dic3⋊C4—31no—
244#3724—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—61no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3—61no—
258Dic3⋊Dic3—61no—
259Dic3⋊Dic3C2×D311yescharacteristic, complemented
260#3722—31no—
261#3722C2×D311yescharacteristic, complemented
262#3722C2×D311yescharacteristic, complemented
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
272(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
273(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
274C22×C33C2411yescharacteristic
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3C2×D412yes—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3—21no—
285C2×C32×D3—21no—
286C2×C32×D3C2×D412yes—
287C2×C32×D3C2×D412yes—
288C2×C32×D3#4112yes—
289C2×C32×D3#4112yes—
290C3×D32—28no—
291C3×D32—44no—
292C33×C4—21no—
293C3⋊(C3⋊Dic3)—21no—
294C3⋊(C3⋊Dic3)—21no—
295C3×C3⋊Dic3—21no—
296C3×C3⋊Dic3—21no—
297C3×C3⋊Dic3—21no—
298C3×C3⋊Dic3—21no—
299C32×Dic3—21no—
300C32×Dic3—21no—
301C32×Dic3—21no—
302C22×#67—91no—
303C22×#67—91no—
304C23×Dic3—91no—
305C2×D3×D4—91no—
306C22×C4×D3—91no—
307C22×C4×D3—91no—
308C3×#123—91no—
309C2×C3×C22⋊C4—91no—
310C2×C3×C22⋊C4—91no—
311C2×#217—91no—
312#935—91no—
313#929—91no—
314C2×(C2×D3)⋊C4—31no—
315C2×(C2×D3)⋊C4—31no—
316C2×(C2×D3)⋊C4—91no—
317C2×C4⋊Dic3—91no—
318C2×C4⋊Dic3—91no—
319C2×C4⋊Dic3—91no—
320C2×C4⋊Dic3—181no—
321C2×Dic3⋊C4—91no—
322#894—91no—
323#894—91no—
324D3×C4⋊C4—91no—
325D3×C4⋊C4—91no—
326#886—31no—
327#886—91no—
328#886—91no—
329#886—91no—
330#886—91no—
331#886—91no—
332#886—91no—
333#886—91no—
334#886—91no—
335#886—181no—
336#883—31no—
337#883—91no—
338#883—91no—
339#883—91no—
340#883—91no—
341#883—91no—
342#883—91no—
343#883—91no—
344#883—91no—
345#883—91no—
346#883—181no—
347D3×C22⋊C4—31no—
348D3×C22⋊C4—31no—
349D3×C22⋊C4—91no—
350C23×C32—31no—
351C23×C32—31no—
352C23×C32—31no—
353C22×C3⋊D3C22×D311yescharacteristic
354C22×C3⋊D3C22×D311yescharacteristic
355C22×C3×D3—21no—
356C22×C3×D3—21no—
357C22×C3×D3—21no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—34no—
361C22×C3×D3—34no—
362C22×C3×D3—31no—
363C22×C3×D3—31no—
364C22×C3×D3—61no—
365C22×C3×D3—61no—
366C22×C3×D3—62no—
367C22×C3×D3—62no—
368C22×C3×D3—62no—
369C22×C3×D3—62no—
370C22×C3×D3—62no—
371C22×C3×D3—62no—
372C22×C3×D3—62no—
373C22×C3×D3—62no—
374C22×C3×D3—62no—
375C22×C3×D3—62no—
376C22×C3×D3C22×D311yescharacteristic
377C22×C3×D3C22×D311yescharacteristic
378C22×C3×D3C22×D311yescharacteristic
379C22×C3×D3C22×D311yescharacteristic
380C22×C3×D3C22×D311yescharacteristic
381C22×C3×D3C22×D311yescharacteristic
382C2×D32—22no—
383C2×D32—22no—
384C2×D32—22no—
385C2×D32—22no—
386C2×D32—22no—
387C2×D32D1214yes—
388C2×C32×C4—21no—
389C2×C32×C4—21no—
390C2×C32×C4—21no—
391C2×C32×C4—31no—
392C2×C32×C4—31no—
393C2×C32×C4—31no—
394C2×C32×C4—41no—
395C2×C32×C4—62no—
396C2×C32×C4C22×D311yescharacteristic
397C2×C32×C4C22×D311yescharacteristic
398C2×C32×C4C22×D311yescharacteristic
399#638—62no—
400#638—62no—
401C2×C3⋊Dic3—31no—
402C2×C3⋊Dic3—31no—
403C2×C3⋊Dic3—31no—
404C2×C3⋊Dic3—31no—
405C2×C3⋊Dic3—31no—
406C2×C3⋊Dic3—31no—
407C2×C3⋊Dic3—61no—
408C2×C3⋊Dic3—61no—
409C2×C3⋊Dic3—61no—
410C2×C3⋊Dic3—61no—
411C2×C3⋊Dic3—61no—
412C2×C3⋊Dic3—61no—
413C2×C3⋊Dic3—62no—
414C2×C3⋊Dic3—62no—
415C2×C3⋊Dic3—62no—
416C2×C3⋊Dic3—121no—
417C2×C3⋊Dic3—121no—
418C2×C3⋊Dic3C22×D311yescharacteristic
419C2×C3⋊Dic3C22×D311yescharacteristic
420C2×C3⋊Dic3C22×D311yescharacteristic
421C2×C3⋊Dic3C22×D311yescharacteristic
422C4×C3⋊D3—62no—
423C3×#67—62no—
424C3×#67—62no—
425C2×C3×Dic3—21no—
426C2×C3×Dic3—21no—
427C2×C3×Dic3—21no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—31no—
435C2×C3×Dic3—31no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—61no—
439C2×C3×Dic3—61no—
440C2×C3×Dic3—62no—
441C2×C3×Dic3—62no—
442C2×C3×Dic3—62no—
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C3×C4×D3—24no—
450C3×C4×D3—22no—
451C3×C4×D3—22no—
452C3×C4×D3—62no—
453C3×C4×D3—62no—
454C3×C4×D3—62no—
455#626—62no—
456#626—62no—
457#625—22no—
458#625—62no—
459#625—62no—
460#625—62no—
461#625—62no—
462#625—62no—
463#625—122no—
464#625—122no—
465#624—62no—
466D3×Dic3—22no—
467D3×Dic3—22no—
468D3×Dic3—22no—
469D3×Dic3—62no—
470D3×Dic3—62no—
471D3×Dic3—62no—
472D3×Dic3—62no—
473D3×Dic3—62no—
474D3×Dic3—62no—
475D3×Dic3—62no—
476D3×Dic3—62no—
477D3×Dic3—62no—
478D3×Dic3—62no—
479D3×Dic3—122no—
480D3×Dic3—122no—
481D3×Dic3—122no—
482D3×Dic3—122no—
483C2×#123—271noSylow
484C2×C33C22×D411yescharacteristic
485C2×C33C2×#4111yescharacteristic
486C2×C33C2×#4111yescharacteristic
487C3×C3⋊D3—22no—
488C3×C3⋊D3—41no—
489C32×D3—22no—
490C32×D3—41no—
491C32×D3#12314yescomplemented
492C24×C3—91no—
493C24×C3—91no—
494C23×D3—31no—
495C23×D3—31no—
496C23×D3—31no—
497C23×D3—31no—
498C2×C3×D4—91no—
499C22×C3×C4—31no—
500C22×C3×C4—31no—
501C22×C3×C4—61no—
502C22×C3×C4—91no—
503C22×C3×C4—91no—
504C22×C3×C4—91no—
505C2×#67—31no—
506C2×#67—31no—
507C2×#67—91no—
508C2×#67—91no—
509C2×#67—91no—
510C2×#67—91no—
511C2×#67—91no—
512C2×#67—91no—
513C2×#67—91no—
514C2×#67—91no—
515C2×#67—181no—
516C2×#67—181no—
517C2×#67—184no—
518C2×#67—184no—
519C22×Dic3—31no—
520C22×Dic3—31no—
521C22×Dic3—31no—
522C22×Dic3—91no—
523C22×Dic3—91no—
524C22×Dic3—91no—
525C22×Dic3—91no—
526C22×Dic3—91no—
527C22×Dic3—91no—
528C22×Dic3—91no—
529C22×Dic3—91no—
530C22×Dic3—181no—
531C22×Dic3—181no—
532C22×Dic3—181no—
533C22×Dic3—184no—
534D3×D4—184no—
535C2×D12—91no—
536C2×C4×D3—31no—
537C2×C4×D3—31no—
538C2×C4×D3—31no—
539C2×C4×D3—91no—
540C2×C4×D3—91no—
541C2×C4×D3—91no—
542C2×C4×D3—91no—
543C2×C4×D3—91no—
544C2×C4×D3—91no—
545C2×C4×D3—91no—
546C2×C4×D3—181no—
547C2×C4×D3—184no—
548C2×C4×D3—184no—
549C2×C4×D3D3211yescharacteristic
550C3×C4⋊C4—91no—
551C3×C4⋊C4—91no—
552C3×C22⋊C4—31no—
553C3×C22⋊C4—31no—
554C3×C22⋊C4—31no—
555C3×C22⋊C4—31no—
556C3×C22⋊C4—61no—
557C3×C22⋊C4—61no—
558C3×C22⋊C4—91no—
559C3×C22⋊C4—91no—
560C3×C22⋊C4—91no—
561C3×C22⋊C4—91no—
562C3×C22⋊C4—91no—
563C3×C22⋊C4—91no—
564C3×C22⋊C4—91no—
565#217—31no—
566#217—31no—
567#217—31no—
568#217—91no—
569#217—91no—
570#217—91no—
571#217—91no—
572#217—181no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—31no—
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—31no—
577(C2×D3)⋊C4—31no—
578(C2×D3)⋊C4—31no—
579(C2×D3)⋊C4—31no—
580(C2×D3)⋊C4—31no—
581(C2×D3)⋊C4—31no—
582(C2×D3)⋊C4—31no—
583(C2×D3)⋊C4—31no—
584(C2×D3)⋊C4—61no—
585(C2×D3)⋊C4—61no—
586(C2×D3)⋊C4—91no—
587(C2×D3)⋊C4—91no—
588(C2×D3)⋊C4—91no—
589(C2×D3)⋊C4—91no—
590(C2×D3)⋊C4—91no—
591(C2×D3)⋊C4—181no—
592(C2×D3)⋊C4D3211yescharacteristic, complemented
593(C2×D3)⋊C4D3211yescharacteristic, complemented
594C4⋊Dic3—31no—
595C4⋊Dic3—31no—
596C4⋊Dic3—31no—
597C4⋊Dic3—61no—
598C4⋊Dic3—91no—
599C4⋊Dic3—91no—
600C4⋊Dic3—91no—
601C4⋊Dic3—91no—
602C4⋊Dic3—91no—
603C4⋊Dic3—91no—
604C4⋊Dic3—91no—
605C4⋊Dic3—91no—
606C4⋊Dic3—91no—
607C4⋊Dic3—91no—
608C4⋊Dic3—91no—
609C4⋊Dic3—181no—
610C4⋊Dic3—181no—
611C4⋊Dic3—181no—
612C4⋊Dic3—181no—
613C4⋊Dic3—181no—
614C4⋊Dic3—181no—
615C4⋊Dic3—361no—
616Dic3⋊C4—31no—
617Dic3⋊C4—91no—
618Dic3⋊C4—91no—
619Dic3⋊C4—91no—
620Dic3⋊C4—91no—
621Dic3⋊C4—91no—
622Dic3⋊C4—91no—
623Dic3⋊C4—91no—
624Dic3⋊C4—181no—
625C22×C32—21no—
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—32no—
629C22×C32—32no—
630C22×C32—32no—
631C22×C32—32no—
632C22×C32—41no—
633C22×C32—61no—
634C22×C32—61no—
635C22×C32—61no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32C23×D311yescharacteristic
639C22×C32C23×D311yescharacteristic
640C22×C32C23×D311yescharacteristic
641C2×C3⋊D3—21no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3—21no—
644C2×C3⋊D3—21no—
645C2×C3⋊D3—21no—
646C2×C3⋊D3C2×D1212yes—
647C2×C3×D3—21no—
648C2×C3×D3—21no—
649C2×C3×D3—21no—
650C2×C3×D3—21no—
651C2×C3×D3—21no—
652C2×C3×D3—21no—
653C2×C3×D3—21no—
654C2×C3×D3—21no—
655C2×C3×D3—21no—
656C2×C3×D3—21no—
657C2×C3×D3—22no—
658C2×C3×D3—22no—
659C2×C3×D3—22no—
660C2×C3×D3—22no—
661C2×C3×D3—32no—
662C2×C3×D3—32no—
663C2×C3×D3—41no—
664C2×C3×D3—41no—
665C2×C3×D3—41no—
666C2×C3×D3—41no—
667C2×C3×D3—41no—
668C2×C3×D3—62no—
669C2×C3×D3—68no—
670C2×C3×D3—61no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—61no—
674C2×C3×D3—68no—
675C2×C3×D3—61no—
676C2×C3×D3—61no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—61no—
681C2×C3×D3—121no—
682C2×C3×D3—121no—
683C2×C3×D3—121no—
684C2×C3×D3—121no—
685C2×C3×D3—121no—
686C2×C3×D3—124no—
687C2×C3×D3—124no—
688C2×C3×D3C2×D1212yes—
689C2×C3×D3C2×D1212yes—
690C2×C3×D3#23512yes—
691C2×C3×D3D3×D412yes—
692C2×C3×D3D3×D412yes—
693C2×C3×D3#23712yes—
694C2×C3×D3#23712yes—
695C2×C3×D3#23712yes—
696D32—28no—
697D32—44no—
698C32×C4—21no—
699C32×C4—22no—
700C32×C4—21no—
701C32×C4—21no—
702C32×C4—41no—
703C32×C4—41no—
704C32×C4—42no—
705C32×C4—61no—
706C32×C4—61no—
707C32×C4—61no—
708C3⋊Dic3—21no—
709C3⋊Dic3—21no—
710C3⋊Dic3—21no—
711C3⋊Dic3—21no—
712C3⋊Dic3—61no—
713C3⋊Dic3—61no—
714C3⋊Dic3—61no—
715C3⋊Dic3—61no—
716C3⋊Dic3—61no—
717C3⋊Dic3—61no—
718C3⋊Dic3—121no—
719C3⋊Dic3—121no—
720C3⋊Dic3—121no—
721C3⋊Dic3—121no—
722C3⋊Dic3—121no—
723C3⋊Dic3—121no—
724C3⋊Dic3—241no—
725C3⋊Dic3—241no—
726C3×Dic3—22no—
727C3×Dic3—21no—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—21no—
732C3×Dic3—21no—
733C3×Dic3—41no—
734C3×Dic3—41no—
735C3×Dic3—61no—
736C3×Dic3—61no—
737C3×Dic3—61no—
738C3×Dic3—61no—
739C3×Dic3—61no—
740C3×Dic3—61no—
741C3×Dic3—61no—
742C3×Dic3—61no—
743C3×Dic3—121no—
744C3×Dic3—121no—
745C3×Dic3—121no—
746C3×Dic3—121no—
747C22×D4—271no—
748C23×C4—271no—
749#123—91no—
750#123—271no—
751#123—271no—
752#123—271no—
753#123—271no—
754#123—271no—
755#123—271no—
756#123—271no—
757C2×C4⋊C4—271no—
758C2×C4⋊C4—271no—
759C2×C22⋊C4—91no—
760C2×C22⋊C4—91no—
761C2×C22⋊C4—271no—
762C33C2×#12311yescharacteristic, complemented, Sylow
763C23×C3—31no—
764C23×C3—31no—
765C23×C3—31no—
766C23×C3—31no—
767C23×C3—31no—
768C23×C3—31no—
769C23×C3—61no—
770C23×C3—61no—
771C23×C3—61no—
772C23×C3—94no—
773C23×C3—91no—
774C23×C3—91no—
775C23×C3—182no—
776C23×C3—182no—
777C23×C3—182no—
778C23×C3—182no—
779C23×C3—182no—
780C22×D3—31no—
781C22×D3—31no—
782C22×D3—34no—
783C22×D3—34no—
784C22×D3—31no—
785C22×D3—31no—
786C22×D3—61no—
787C22×D3—61no—
788C22×D3—62no—
789C22×D3—62no—
790C22×D3—62no—
791C22×D3—62no—
792C22×D3—62no—
793C22×D3—62no—
794C22×D3—62no—
795C22×D3—62no—
796C22×D3—62no—
797C22×D3—62no—
798C22×D3C2×D3211yescharacteristic
799C22×D3C2×D3211yescharacteristic
800C22×D3C2×D3211yescharacteristic
801C3×D4—182no—
802C2×C3×C4—21no—
803C2×C3×C4—21no—
804C2×C3×C4—21no—
805C2×C3×C4—31no—
806C2×C3×C4—31no—
807C2×C3×C4—31no—
808C2×C3×C4—31no—
809C2×C3×C4—31no—
810C2×C3×C4—31no—
811C2×C3×C4—41no—
812C2×C3×C4—61no—
813C2×C3×C4—61no—
814C2×C3×C4—61no—
815C2×C3×C4—62no—
816C2×C3×C4—62no—
817C2×C3×C4—64no—
818C2×C3×C4—91no—
819C2×C3×C4—91no—
820C2×C3×C4—91no—
821C2×C3×C4—91no—
822C2×C3×C4—182no—
823C2×C3×C4—182no—
824C2×C3×C4—182no—
825C2×C3×C4C2×D3211yescharacteristic
826C2×C3×C4C2×D3211yescharacteristic
827C2×C3×C4C2×D3211yescharacteristic
828#67—62no—
829#67—62no—
830#67—182no—
831#67—182no—
832#67—182no—
833#67—182no—
834#67—182no—
835#67—182no—
836#67—182no—
837#67—182no—
838#67—362no—
839#67—362no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—31no—
843C2×Dic3—31no—
844C2×Dic3—31no—
845C2×Dic3—31no—
846C2×Dic3—31no—
847C2×Dic3—31no—
848C2×Dic3—61no—
849C2×Dic3—61no—
850C2×Dic3—61no—
851C2×Dic3—61no—
852C2×Dic3—62no—
853C2×Dic3—62no—
854C2×Dic3—62no—
855C2×Dic3—91no—
856C2×Dic3—91no—
857C2×Dic3—91no—
858C2×Dic3—91no—
859C2×Dic3—91no—
860C2×Dic3—91no—
861C2×Dic3—181no—
862C2×Dic3—181no—
863C2×Dic3—181no—
864C2×Dic3—181no—
865C2×Dic3—181no—
866C2×Dic3—181no—
867C2×Dic3—182no—
868C2×Dic3—182no—
869C2×Dic3—182no—
870C2×Dic3—182no—
871C2×Dic3—182no—
872C2×Dic3—182no—
873C2×Dic3—182no—
874C2×Dic3—182no—
875C2×Dic3—361no—
876C2×Dic3—361no—
877C2×Dic3—362no—
878C2×Dic3—362no—
879C2×Dic3—362no—
880C2×Dic3C2×D3211yescharacteristic
881C2×Dic3C2×D3211yescharacteristic
882C2×Dic3C2×D3211yescharacteristic
883D12—182no—
884C4×D3—22no—
885C4×D3—62no—
886C4×D3—62no—
887C4×D3—62no—
888C4×D3—182no—
889C4×D3—182no—
890C4×D3—182no—
891C4×D3—182no—
892C4×D3—182no—
893C4×D3—182no—
894C4×D3—182no—
895C4×D3—362no—
896C2×C32—21no—
897C2×C32—21no—
898C2×C32—21no—
899C2×C32—21no—
900C2×C32—21no—
901C2×C32—21no—
902C2×C32—21no—
903C2×C32—21no—
904C2×C32—21no—
905C2×C32—34no—
906C2×C32—41no—
907C2×C32—41no—
908C2×C32—41no—
909C2×C32—62no—
910C2×C32—121no—
911C2×C32C22×D1211yescharacteristic
912C2×C32C2×#23511yescharacteristic
913C2×C32C2×D3×D411yescharacteristic
914C2×C32C2×D3×D411yescharacteristic
915C2×C32C2×#23711yescharacteristic
916C2×C32C2×#23711yescharacteristic
917C2×C32C2×#23711yescharacteristic
918C2×C32D3×#4111yescharacteristic
919C2×C32D3×#4111yescharacteristic
920C3⋊D3—22no—
921C3⋊D3—41no—
922C3×D3—22no—
923C3×D3—22no—
924C3×D3—24no—
925C3×D3—42no—
926C3×D3—41no—
927C3×D3—41no—
928C3×D3—62no—
929C3×D3—62no—
930C3×D3—81no—
931C3×D3—122no—
932C3×D3—121no—
933C3×D3—121no—
934C3×D3—241no—
935C3×D3#88314yescomplemented
936C3×D3#88614yescomplemented
937C24—91no—
938C24—91no—
939C2×D4—91no—
940C2×D4—271no—
941C2×D4—271no—
942C2×D4—271no—
943C2×D4—544no—
944C22×C4—31no—
945C22×C4—91no—
946C22×C4—91no—
947C22×C4—91no—
948C22×C4—271no—
949C22×C4—271no—
950C22×C4—271no—
951C22×C4—271no—
952C22×C4—271no—
953C22×C4—544no—
954C4⋊C4—91no—
955C4⋊C4—91no—
956C4⋊C4—271no—
957C4⋊C4—271no—
958C4⋊C4—271no—
959C4⋊C4—271no—
960C4⋊C4—271no—
961C4⋊C4—271no—
962C22⋊C4—31no—
963C22⋊C4—31no—
964C22⋊C4—91no—
965C22⋊C4—91no—
966C22⋊C4—91no—
967C22⋊C4—91no—
968C22⋊C4—91no—
969C22⋊C4—91no—
970C22⋊C4—91no—
971C22⋊C4—271no—
972C22⋊C4—271no—
973C22⋊C4—271no—
974C22×C3—21no—
975C22×C3—21no—
976C22×C3—21no—
977C22×C3—32no—
978C22×C3—32no—
979C22×C3—32no—
980C22×C3—32no—
981C22×C3—32no—
982C22×C3—32no—
983C22×C3—32no—
984C22×C3—32no—
985C22×C3—41no—
986C22×C3—62no—
987C22×C3—62no—
988C22×C3—62no—
989C22×C3—62no—
990C22×C3—61no—
991C22×C3—61no—
992C22×C3—61no—
993C22×C3—61no—
994C22×C3—61no—
995C22×C3—61no—
996C22×C3—61no—
997C22×C3—61no—
998C22×C3—61no—
999C22×C3—61no—
1000C22×C3—92no—
1001C22×C3—121no—
1002C22×C3—121no—
1003C22×C3—121no—
1004C22×C3—121no—
1005C22×C3—121no—
1006C22×C3—188no—
1007C22×C3—181no—
1008C22×C3—181no—
1009C22×C3—181no—
1010C22×C3—181no—
1011C22×C3—181no—
1012C22×C3—364no—
1013C22×C3C22×D3211yescharacteristic
1014C22×C3C22×D3211yescharacteristic
1015C22×C3C22×D3211yescharacteristic
1016C2×D3—21no—
1017C2×D3—21no—
1018C2×D3—21no—
1019C2×D3—21no—
1020C2×D3—21no—
1021C2×D3—32no—
1022C2×D3—32no—
1023C2×D3—62no—
1024C2×D3—68no—
1025C2×D3—61no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—68no—
1030C2×D3—61no—
1031C2×D3—61no—
1032C2×D3—61no—
1033C2×D3—61no—
1034C2×D3—61no—
1035C2×D3—61no—
1036C2×D3—121no—
1037C2×D3—121no—
1038C2×D3—121no—
1039C2×D3—121no—
1040C2×D3—121no—
1041C2×D3—124no—
1042C2×D3—124no—
1043C2×D3#379512yes—
1044C2×D3D3×D1212yes—
1045C2×D3D3×D1212yes—
1046C2×D3#380512yes—
1047C3×C4—22no—
1048C3×C4—21no—
1049C3×C4—21no—
1050C3×C4—21no—
1051C3×C4—41no—
1052C3×C4—41no—
1053C3×C4—42no—
1054C3×C4—62no—
1055C3×C4—61no—
1056C3×C4—61no—
1057C3×C4—61no—
1058C3×C4—61no—
1059C3×C4—61no—
1060C3×C4—61no—
1061C3×C4—121no—
1062C3×C4—121no—
1063C3×C4—181no—
1064C3×C4—181no—
1065C3×C4—181no—
1066C3×C4—181no—
1067Dic3—21no—
1068Dic3—21no—
1069Dic3—21no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—61no—
1073Dic3—61no—
1074Dic3—61no—
1075Dic3—61no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—121no—
1079Dic3—121no—
1080Dic3—121no—
1081Dic3—121no—
1082Dic3—181no—
1083Dic3—181no—
1084Dic3—181no—
1085Dic3—181no—
1086Dic3—181no—
1087Dic3—181no—
1088Dic3—361no—
1089Dic3—361no—
1090Dic3—361no—
1091Dic3—361no—
1092Dic3—361no—
1093Dic3—361no—
1094Dic3—721no—
1095Dic3—721no—
1096C32—21no—
1097C32—21no—
1098C32—21no—
1099C32—41no—
1100C32C2×#88311yescharacteristic, complemented
1101C32C2×#88611yescharacteristic, complemented
1102C32D3×#12311yescharacteristic, complemented
1103C23—31no—
1104C23—31no—
1105C23—31no—
1106C23—94no—
1107C23—91no—
1108C23—91no—
1109C23—182no—
1110C23—182no—
1111C23—182no—
1112C23—182no—
1113C23—182no—
1114D4—182no—
1115D4—542no—
1116D4—542no—
1117D4—542no—
1118C2×C4—31no—
1119C2×C4—31no—
1120C2×C4—31no—
1121C2×C4—62no—
1122C2×C4—91no—
1123C2×C4—91no—
1124C2×C4—91no—
1125C2×C4—91no—
1126C2×C4—182no—
1127C2×C4—182no—
1128C2×C4—182no—
1129C2×C4—271no—
1130C2×C4—271no—
1131C2×C4—542no—
1132C2×C4—542no—
1133C2×C4—542no—
1134C2×C4—542no—
1135C2×C4—542no—
1136C2×C4D3311yescharacteristic
1137C2×C3—21no—
1138C2×C3—21no—
1139C2×C3—21no—
1140C2×C3—21no—
1141C2×C3—21no—
1142C2×C3—21no—
1143C2×C3—21no—
1144C2×C3—21no—
1145C2×C3—21no—
1146C2×C3—34no—
1147C2×C3—34no—
1148C2×C3—41no—
1149C2×C3—41no—
1150C2×C3—41no—
1151C2×C3—64no—
1152C2×C3—62no—
1153C2×C3—62no—
1154C2×C3—122no—
1155C2×C3—121no—
1156C2×C3—121no—
1157C2×C3—182no—
1158C2×C3—241no—
1159C2×C3—361no—
1160C2×C3C2×#379511yescharacteristic
1161C2×C3C2×D3×D1211yescharacteristic
1162C2×C3C2×D3×D1211yescharacteristic
1163C2×C3D3×#23511yescharacteristic
1164C2×C3D32×D411yescharacteristic
1165C2×C3D3×#23711yescharacteristic
1166C2×C3D3×#23711yescharacteristic
1167C2×C3D3×#23711yescharacteristic
1168C2×C3C2×#380511yescharacteristic
1169D3—22no—
1170D3—41no—
1171D3—62no—
1172D3—62no—
1173D3—122no—
1174D3—121no—
1175D3—121no—
1176D3—241no—
1177D3#6389114yesdirect product factor
1178C22—32no—
1179C22—32no—
1180C22—32no—
1181C22—32no—
1182C22—61no—
1183C22—61no—
1184C22—61no—
1185C22—61no—
1186C22—61no—
1187C22—92no—
1188C22—188no—
1189C22—181no—
1190C22—181no—
1191C22—181no—
1192C22—181no—
1193C22—181no—
1194C22—364no—
1195C22C2×D3311yescharacteristic
1196C4—21no—
1197C4—61no—
1198C4—61no—
1199C4—61no—
1200C4—181no—
1201C4—181no—
1202C4—181no—
1203C4—181no—
1204C4—541no—
1205C4—541no—
1206C3—21no—
1207C3—21no—
1208C3—21no—
1209C3—41no—
1210C3D3×#88311yescharacteristic, complemented
1211C3D3×#88611yescharacteristic, complemented
1212C3C2×#6389111yescharacteristic, complemented
1213C2—34no—
1214C2—62no—
1215C2—121no—
1216C2—182no—
1217C2—361no—
1218C2D3×#379511yescharacteristic
1219C2D32×D1211yescharacteristic
1220C2D3×#380511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC2×D3×#625C2
hypercenterC2×C4D33
hypocenterC33C2×#123
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×D32×Dic3C2semidirect
3. #11723690C2semidirect
4. #11723523C2semidirect
5. #11723480C2semidirect
6. D3×C4⋊(C3⋊Dic3)C2semidirect
7. C3×D3×(C2×D3)⋊C4C2semidirect
8. C3×D3×(C2×D3)⋊C4C2semidirect
9. C3×#63891C2semidirect
10. #11722998C2semidirect
11. #11722997C2semidirect
12. #11722989C2semidirect
13. #11722988C2semidirect
14. D3×Dic3⋊Dic3C2semidirect
15. D3×(C2×D3)⋊Dic3C2semidirect
23. C2×#6294C22semidirect
26. C2×Dic3×C3⋊D3C22semidirect
29. C2×D3×C3⋊Dic3C22semidirect
33. C2×C3×D3×Dic3C22semidirect
36. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
37. C3×#3752C22semidirect
38. C3×#3752C22semidirect
39. C3×C4⋊(C3⋊Dic3)C22semidirect
40. C32×(C2×D3)⋊C4C22semidirect
41. C32×(C2×D3)⋊C4C22semidirect
42. #88815C22semidirect
43. #88814C22semidirect
44. #88807C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
48. #88803C22semidirect
49. (C2×D3)⋊(C3⋊Dic3)C22semidirect
50. C3×Dic3⋊Dic3C22semidirect
51. C3×#3722C22semidirect
52. C3×#3722C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×(C2×D3)⋊Dic3C22semidirect
79. D3×(C2×D3)⋊C4D3semidirect
80. D3×(C2×D3)⋊C4D3semidirect
94. #63891D3direct (N × H)
197. C2×D3×Dic3C2×D3semidirect
203. #3752C2×D3semidirect
204. #3752C2×D3semidirect
215. C4⋊(C3⋊Dic3)C2×D3semidirect
235. C3×(C2×D3)⋊C4C2×D3semidirect
236. C3×(C2×D3)⋊C4C2×D3semidirect
237. C3×(C2×D3)⋊C4C2×D3semidirect
238. C3×(C2×D3)⋊C4C2×D3semidirect
259. Dic3⋊Dic3C2×D3semidirect
261. #3722C2×D3semidirect
262. #3722C2×D3semidirect
271. (C2×D3)⋊Dic3C2×D3semidirect
272. (C2×D3)⋊Dic3C2×D3semidirect
273. (C2×D3)⋊Dic3C2×D3semidirect
491. C32×D3#123semidirect
592. (C2×D3)⋊C4D32semidirect
593. (C2×D3)⋊C4D32semidirect
762. C33C2×#123semidirect
935. C3×D3#883semidirect
936. C3×D3#886semidirect
1100. C32C2×#883semidirect
1101. C32C2×#886semidirect
1102. C32D3×#123semidirect
1177. D3#63891direct (N × H)
1210. C3D3×#883semidirect
1211. C3D3×#886semidirect
1212. C3C2×#63891semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6252
C2×D32×Dic32
#117236902
#117235232
#117234802
D3×C4⋊(C3⋊Dic3)2
C3×D3×(C2×D3)⋊C42
C3×#638912
#117229982
#117229972
#117229892
#117229882
D3×Dic3⋊Dic32
D3×(C2×D3)⋊Dic32
C2×#638913
D3×#8863
D3×#8833