Finite Group Databasebeta

← D3×#64092 #13175918

Subgroups — D3×#64092 #13175918

Order 1728.

2364 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#638C211yesmaximal, characteristic
2C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
3#11723924C211yesmaximal, characteristic, complemented
4C3×#64092C211yesmaximal, characteristic, complemented
5C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6#11723628C211yesmaximal, characteristic, complemented
7#11723621C211yesmaximal, characteristic, complemented
8D3×#3757C211yesmaximal, characteristic, complemented
9D3×#3752C211yesmaximal, characteristic, complemented
10#11723523C211yesmaximal, characteristic, complemented
11#11723518C211yesmaximal, characteristic, complemented
12D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
13D3×#3750C211yesmaximal, characteristic, complemented
14#11723422C211yesmaximal, characteristic, complemented
15#11723420C211yesmaximal, characteristic, complemented
16C2×#64092—31nomaximal
17D3×#883—34nomaximal
18C23×C32×D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26D3×#638—24no—
27C2×#6291C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×#6289C2211yescharacteristic, complemented
30C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
31C2×D3×C3⋊Dic3C2211yescharacteristic
32C2×D3×C3⋊Dic3C2211yescharacteristic
33C2×D3×C3⋊Dic3C2211yescharacteristic
34C4×D3×C3⋊D3—24no—
35C33×C22⋊C4C2211yescharacteristic, complemented
36#88864C2211yescharacteristic, complemented
37#88859C2211yescharacteristic, complemented
38C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
39#88857C2211yescharacteristic, complemented
40C3×#3757C2211yescharacteristic, complemented
41C3×#3752C2211yescharacteristic, complemented
42C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C22×#638—31no—
56C22×C4×C3⋊D3—31no—
57C2×D3×#67—34no—
58C2×C4×D32—34no—
59C2×C32×C22⋊C4—31no—
60C2×#3757—31no—
61C2×#3752—31no—
62C2×C4⋊(C3⋊Dic3)—31no—
63C2×#3750—31no—
64#64092—31no—
65#64092—31no—
66#64092—31no—
67#64092—31no—
68#64092—31no—
69#64092—31no—
70#64092—31no—
71#64092—34no—
72#64092—64no—
73#64092D311yescharacteristic, direct product factor
74C3×#883—34no—
75C3×D3×C22⋊C4D314yescomplemented
76#63975—34no—
77#63969—34no—
78D3×#217—34no—
79D3×(C2×D3)⋊C4—34no—
80#63905—34no—
81#63891—34no—
82D3×C4⋊Dic3—34no—
83D3×Dic3⋊C4—34no—
84#63854—34no—
85#63853—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3—22no—
90C22×C32×D3—22no—
91C22×C32×D3—22no—
92C22×C32×D3C2311yescharacteristic
93C22×C32×D3C2311yescharacteristic
94C2×D3×C3⋊D3—22no—
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3D414yes—
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99#6312—22no—
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C4×C3⋊(C3⋊D3)—22no—
104C3×#638—22no—
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C3×C4×C3⋊D3—22no—
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C32×C4×D3—22no—
112C32×C4×D3—22no—
113#6291—22no—
114#6290—22no—
115#6289—22no—
116Dic3×C3⋊D3—22no—
117D3×C3⋊Dic3—22no—
118D3×C3⋊Dic3—22no—
119D3×C3⋊Dic3—22no—
120D3×#123—91no—
121C2×#883—94no—
122C24×C32—31no—
123C23×C3⋊D3—31no—
124C23×C3×D3C2×D314yes—
125C22×D32—34no—
126C22×C32×C4—31no—
127C22×C32×C4—31no—
128C2×#638—31no—
129C2×#638—34no—
130C2×#638—31no—
131C2×#638—31no—
132C2×#638—64no—
133C2×#638—64no—
134C2×#638C2×D311yescharacteristic
135C22×C3⋊Dic3—31no—
136C22×C3⋊Dic3—31no—
137C22×C3⋊Dic3—31no—
138C2×C4×C3⋊D3—31no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—34no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—64no—
143C2×C4×C3⋊D3—64no—
144C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
145C2×C3×#67—34no—
146C2×C3×C4×D3—34no—
147C2×C3×C4×D3C2×D314yes—
148C2×C3×C4×D3C2×D314yes—
149D3×#67—616no—
150C2×#626—34no—
151C2×#625—34no—
152C2×#624—34no—
153C2×D3×Dic3—34no—
154C2×D3×Dic3—34no—
155C2×D3×Dic3—34no—
156C2×D3×Dic3—34no—
157C4×D32—616no—
158C32×C22⋊C4—24no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4—31no—
161C32×C22⋊C4—31no—
162C32×C22⋊C4C2×D314yescomplemented
163C32×C22⋊C4C2×D311yescharacteristic, complemented
164#3757—31no—
165#3757—34no—
166#3757—31no—
167#3757—31no—
168#3757—64no—
169#3757C2×D311yescharacteristic, complemented
170#3752—31no—
171#3752—31no—
172#3752—34no—
173#3752—31no—
174#3752—64no—
175#3752C2×D311yescharacteristic, complemented
176C4⋊(C3⋊Dic3)—31no—
177C4⋊(C3⋊Dic3)—34no—
178C4⋊(C3⋊Dic3)—31no—
179C4⋊(C3⋊Dic3)—31no—
180C4⋊(C3⋊Dic3)—64no—
181C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
182#3750—31no—
183#3750—34no—
184#3750—31no—
185#3750—31no—
186#3750—64no—
187#3750C2×D311yescharacteristic, complemented
188C3×#217—34no—
189C3×#217C2×D314yescomplemented
190C3×(C2×D3)⋊C4—34no—
191C3×(C2×D3)⋊C4C2×D314yescomplemented
192C3×(C2×D3)⋊C4C2×D314yescomplemented
193C3×C4⋊Dic3—34no—
194C3×Dic3⋊C4—34no—
195#3724—34no—
196Dic3⋊Dic3—34no—
197Dic3⋊Dic3—34no—
198Dic3⋊Dic3—34no—
199#3722—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33—21no—
206C22×C33C2411yescharacteristic
207C2×C3⋊(C3⋊D3)—21no—
208C2×C3⋊(C3⋊D3)—21no—
209C2×C3⋊(C3⋊D3)C2×D412yes—
210C2×C3×C3⋊D3—21no—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3C2×D412yes—
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
216C2×C32×D3—44no—
217C2×C32×D3C2×D412yes—
218C2×C32×D3#4112yes—
219C2×C32×D3#4112yes—
220D3×C3⋊D3—28no—
221C33×C4—21no—
222C33×C4—21no—
223C3⋊(C3⋊Dic3)—21no—
224C3⋊(C3⋊Dic3)—21no—
225C3⋊(C3⋊Dic3)—21no—
226C3×C3⋊Dic3—21no—
227C3×C3⋊Dic3—21no—
228C3×C3⋊Dic3—21no—
229C32×Dic3—21no—
230C32×Dic3—21no—
231C22×#67—94no—
232C2×D3×D4—91no—
233C22×C4×D3—94no—
234C22×C4×D3—91no—
235C3×#123—91no—
236C2×C3×C22⋊C4—34no—
237C2×#217—94no—
238#935—91no—
239#929—91no—
240C2×(C2×D3)⋊C4—94no—
241C2×C4⋊Dic3—94no—
242C2×Dic3⋊C4—94no—
243#894—91no—
244#894—91no—
245D3×C4⋊C4—91no—
246D3×C4⋊C4—91no—
247#886—91no—
248#883—34no—
249#883—94no—
250#883—94no—
251#883—94no—
252#883—94no—
253#883—94no—
254#883—94no—
255#883—94no—
256#883—91no—
257#883—91no—
258#883—184no—
259D3×C22⋊C4—91no—
260D3×C22⋊C4—91no—
261D3×C22⋊C4C3⋊D311yescharacteristic, complemented
262C23×C32—24no—
263C23×C32—31no—
264C23×C32—31no—
265C23×C32—62no—
266C23×C32—62no—
267C23×C32—62no—
268C23×C32C22×D314yes—
269C23×C32C22×D311yescharacteristic
270C22×C3⋊D3—31no—
271C22×C3⋊D3—34no—
272C22×C3⋊D3—34no—
273C22×C3⋊D3—64no—
274C22×C3⋊D3—62no—
275C22×C3⋊D3—62no—
276C22×C3⋊D3C22×D311yescharacteristic
277C22×C3×D3—28no—
278C22×C3×D3—28no—
279C22×C3×D3—28no—
280C22×C3×D3—34no—
281C22×C3×D3C22×D314yes—
282C22×C3×D3C22×D314yes—
283C2×D32—316no—
284C2×D32—68no—
285C2×D32—68no—
286C2×C32×C4—24no—
287C2×C32×C4—24no—
288C2×C32×C4—31no—
289C2×C32×C4—31no—
290C2×C32×C4—62no—
291C2×C32×C4—62no—
292C2×C32×C4C22×D314yes—
293C2×C32×C4C22×D314yes—
294C2×C32×C4C22×D311yescharacteristic
295C2×C32×C4C22×D311yescharacteristic
296#638—22no—
297#638—62no—
298#638—62no—
299#638—62no—
300#638—68no—
301#638—128no—
302C2×C3⋊Dic3—31no—
303C2×C3⋊Dic3—31no—
304C2×C3⋊Dic3—31no—
305C2×C3⋊Dic3—34no—
306C2×C3⋊Dic3—34no—
307C2×C3⋊Dic3—34no—
308C2×C3⋊Dic3—64no—
309C2×C3⋊Dic3—64no—
310C2×C3⋊Dic3—64no—
311C2×C3⋊Dic3—62no—
312C2×C3⋊Dic3—62no—
313C2×C3⋊Dic3—62no—
314C2×C3⋊Dic3C22×D311yescharacteristic
315C2×C3⋊Dic3C22×D311yescharacteristic
316C2×C3⋊Dic3C22×D311yescharacteristic
317C4×C3⋊D3—22no—
318C4×C3⋊D3—62no—
319C4×C3⋊D3—62no—
320C4×C3⋊D3—62no—
321C4×C3⋊D3—68no—
322C4×C3⋊D3—128no—
323C3×#67—68no—
324C2×C3×Dic3—34no—
325C2×C3×Dic3—34no—
326C2×C3×Dic3—34no—
327C2×C3×Dic3C22×D314yes—
328C2×C3×Dic3C22×D314yes—
329C3×C4×D3—28no—
330C3×C4×D3—28no—
331C3×C4×D3—68no—
332#626—68no—
333#625—68no—
334#624—68no—
335D3×Dic3—68no—
336D3×Dic3—68no—
337D3×Dic3—68no—
338D3×Dic3—68no—
339C2×#123—271noSylow
340C2×C33—41no—
341C2×C33C22×D411yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C3⋊(C3⋊D3)—22no—
345C3×C3⋊D3—22no—
346C32×D3—41no—
347C32×D3#12314yescomplemented
348C24×C3—34no—
349C23×D3—94no—
350C23×D3—91no—
351C23×D3C2×C3⋊D311yescharacteristic
352C2×C3×D4—91no—
353C22×C3×C4—34no—
354C22×C3×C4—34no—
355C22×C3×C4—91no—
356C2×#67—34no—
357C2×#67—94no—
358C2×#67—94no—
359C2×#67—94no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—184no—
363C2×#67—1816no—
364C22×Dic3—94no—
365C22×Dic3—94no—
366C22×Dic3—94no—
367C22×Dic3—91no—
368D3×D4—184no—
369C2×D12—91no—
370C2×C4×D3—34no—
371C2×C4×D3—94no—
372C2×C4×D3—94no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—94no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—184no—
380C2×C4×D3—184no—
381C2×C4×D3—1816no—
382C2×C4×D3C2×C3⋊D311yescharacteristic
383C2×C4×D3C2×C3⋊D311yescharacteristic
384C3×C4⋊C4—91no—
385C3×C4⋊C4—91no—
386C3×C22⋊C4—24no—
387C3×C22⋊C4—34no—
388C3×C22⋊C4—34no—
389C3×C22⋊C4—34no—
390C3×C22⋊C4—91no—
391C3×C22⋊C4—91no—
392C3×C22⋊C4D3214yescomplemented
393C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
394#217—34no—
395#217—94no—
396#217—94no—
397#217—94no—
398#217—91no—
399#217—91no—
400#217—184no—
401#217C2×C3⋊D311yescharacteristic, complemented
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—94no—
404(C2×D3)⋊C4—94no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—94no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—184no—
411(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
412(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
413C4⋊Dic3—34no—
414C4⋊Dic3—94no—
415C4⋊Dic3—94no—
416C4⋊Dic3—94no—
417C4⋊Dic3—91no—
418C4⋊Dic3—91no—
419C4⋊Dic3—184no—
420Dic3⋊C4—34no—
421Dic3⋊C4—94no—
422Dic3⋊C4—94no—
423Dic3⋊C4—94no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—91no—
428Dic3⋊C4—184no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—24no—
433C22×C32—24no—
434C22×C32—24no—
435C22×C32—24no—
436C22×C32—32no—
437C22×C32—32no—
438C22×C32—32no—
439C22×C32—44no—
440C22×C32—44no—
441C22×C32—44no—
442C22×C32—61no—
443C22×C32—61no—
444C22×C32—61no—
445C22×C32—124no—
446C22×C32C23×D314yes—
447C22×C32C23×D311yescharacteristic
448C2×C3⋊D3—21no—
449C2×C3⋊D3—21no—
450C2×C3⋊D3—32no—
451C2×C3⋊D3—38no—
452C2×C3⋊D3—68no—
453C2×C3⋊D3—68no—
454C2×C3⋊D3—61no—
455C2×C3⋊D3—61no—
456C2×C3⋊D3—64no—
457C2×C3⋊D3—64no—
458C2×C3⋊D3—124no—
459C2×C3⋊D3—124no—
460C2×C3⋊D3D3×D412yes—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—24no—
464C2×C3×D3—38no—
465C2×C3×D3—416no—
466C2×C3×D3—64no—
467C2×C3×D3—64no—
468C2×C3×D3#23518yes—
469C2×C3×D3D3×D418yes—
470C2×C3×D3#23718yes—
471D32—632no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—24no—
475C32×C4—24no—
476C32×C4—44no—
477C32×C4—44no—
478C32×C4—61no—
479C32×C4—61no—
480C3⋊Dic3—21no—
481C3⋊Dic3—21no—
482C3⋊Dic3—21no—
483C3⋊Dic3—61no—
484C3⋊Dic3—61no—
485C3⋊Dic3—61no—
486C3⋊Dic3—64no—
487C3⋊Dic3—64no—
488C3⋊Dic3—64no—
489C3⋊Dic3—124no—
490C3⋊Dic3—124no—
491C3⋊Dic3—124no—
492C3×Dic3—24no—
493C3×Dic3—24no—
494C3×Dic3—64no—
495C3×Dic3—64no—
496C3×Dic3—64no—
497C22×D4—271no—
498C23×C4—271no—
499#123—91no—
500#123—271no—
501#123—271no—
502#123—271no—
503#123—271no—
504#123—271no—
505#123—271no—
506#123—271no—
507C2×C4⋊C4—271no—
508C2×C4⋊C4—271no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—271no—
511C2×C22⋊C4—271no—
512C33C2×#12311yescharacteristic, complemented, Sylow
513C23×C3—24no—
514C23×C3—34no—
515C23×C3—34no—
516C23×C3—68no—
517C23×C3—68no—
518C23×C3—68no—
519C23×C3—91no—
520C23×C3C2×D3214yes—
521C23×C3C22×C3⋊D311yescharacteristic
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—34no—
526C22×D3—916no—
527C22×D3—94no—
528C22×D3—91no—
529C22×D3—94no—
530C22×D3—184no—
531C22×D3—188no—
532C22×D3—188no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3C22×C3⋊D311yescharacteristic
536C22×D3C22×C3⋊D311yescharacteristic
537C3×D4—182no—
538C2×C3×C4—24no—
539C2×C3×C4—24no—
540C2×C3×C4—34no—
541C2×C3×C4—34no—
542C2×C3×C4—68no—
543C2×C3×C4—68no—
544C2×C3×C4—91no—
545C2×C3×C4—91no—
546C2×C3×C4—91no—
547C2×C3×C4—182no—
548C2×C3×C4C2×D3214yes—
549C2×C3×C4C2×D3214yes—
550C2×C3×C4C22×C3⋊D311yescharacteristic
551C2×C3×C4C22×C3⋊D311yescharacteristic
552#67—68no—
553#67—188no—
554#67—182no—
555#67—188no—
556#67—182no—
557#67—188no—
558#67—368no—
559C2×Dic3—34no—
560C2×Dic3—34no—
561C2×Dic3—34no—
562C2×Dic3—94no—
563C2×Dic3—94no—
564C2×Dic3—94no—
565C2×Dic3—91no—
566C2×Dic3—91no—
567C2×Dic3—91no—
568C2×Dic3—184no—
569C2×Dic3—184no—
570C2×Dic3—184no—
571C2×Dic3—182no—
572C2×Dic3—188no—
573C2×Dic3—188no—
574C2×Dic3—188no—
575C2×Dic3C22×C3⋊D311yescharacteristic
576C2×Dic3C22×C3⋊D311yescharacteristic
577D12—182no—
578C4×D3—22no—
579C4×D3—22no—
580C4×D3—68no—
581C4×D3—182no—
582C4×D3—188no—
583C4×D3—182no—
584C4×D3—188no—
585C4×D3—188no—
586C4×D3—182no—
587C4×D3—182no—
588C4×D3—182no—
589C4×D3—368no—
590C2×C32—24no—
591C2×C32—24no—
592C2×C32—24no—
593C2×C32—34no—
594C2×C32—41no—
595C2×C32—44no—
596C2×C32—84no—
597C2×C32—121no—
598C2×C32C2×#23514yes—
599C2×C32C2×D3×D414yes—
600C2×C32C2×D3×D411yescharacteristic
601C2×C32C2×#23714yes—
602C2×C32D3×#4111yescharacteristic
603C2×C32D3×#4111yescharacteristic
604C3⋊D3—22no—
605C3⋊D3—62no—
606C3⋊D3—68no—
607C3⋊D3—128no—
608C3×D3—44no—
609C3×D3—68no—
610C3×D3#883116yescomplemented
611C24—31no—
612C24—271no—
613C2×D4—91no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—544no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—91no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—544no—
628C4⋊C4—91no—
629C4⋊C4—91no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C4⋊C4—271no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—91no—
640C22⋊C4—91no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4D3×C3⋊D311yescharacteristic, complemented
648C22×C3—24no—
649C22×C3—24no—
650C22×C3—24no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—24no—
655C22×C3—38no—
656C22×C3—38no—
657C22×C3—38no—
658C22×C3—44no—
659C22×C3—44no—
660C22×C3—44no—
661C22×C3—64no—
662C22×C3—64no—
663C22×C3—64no—
664C22×C3—92no—
665C22×C3—1216no—
666C22×C3—181no—
667C22×C3—181no—
668C22×C3C22×D3214yes—
669C22×C3C23×C3⋊D311yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—38no—
674C2×D3—44no—
675C2×D3—64no—
676C2×D3—64no—
677C2×D3—98no—
678C2×D3—92no—
679C2×D3—188no—
680C2×D3—1832no—
681C2×D3—184no—
682C2×D3—184no—
683C2×D3—181no—
684C2×D3—181no—
685C2×D3—188no—
686C2×D3—364no—
687C2×D3—364no—
688C2×D3#382812yes—
689C2×D3D4×C3⋊D312yes—
690C2×D3#383012yes—
691C3×C4—24no—
692C3×C4—24no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—44no—
696C3×C4—44no—
697C3×C4—64no—
698C3×C4—64no—
699C3×C4—181no—
700C3×C4—181no—
701C3×C4—181no—
702Dic3—21no—
703Dic3—21no—
704Dic3—64no—
705Dic3—64no—
706Dic3—64no—
707Dic3—184no—
708Dic3—184no—
709Dic3—184no—
710Dic3—181no—
711Dic3—181no—
712Dic3—181no—
713Dic3—364no—
714Dic3—364no—
715Dic3—364no—
716C32—24no—
717C32C2×#88314yescomplemented
718C32D3×#12311yescharacteristic, complemented
719C23—31no—
720C23—31no—
721C23—62no—
722C23—62no—
723C23—62no—
724C23—91no—
725C23—274no—
726C23—271no—
727C23—542no—
728C23—542no—
729C23C2×D3×C3⋊D311yescharacteristic
730D4—182no—
731D4—542no—
732D4—542no—
733D4—542no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—91no—
739C2×C4—91no—
740C2×C4—91no—
741C2×C4—182no—
742C2×C4—271no—
743C2×C4—271no—
744C2×C4—271no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4—542no—
748C2×C4—542no—
749C2×C4—542no—
750C2×C4—542no—
751C2×C4C2×D3×C3⋊D311yescharacteristic
752C2×C4C2×D3×C3⋊D311yescharacteristic
753C2×C3—24no—
754C2×C3—24no—
755C2×C3—24no—
756C2×C3—316no—
757C2×C3—41no—
758C2×C3—44no—
759C2×C3—84no—
760C2×C3—124no—
761C2×C3—182no—
762C2×C3D3×#23514yes—
763C2×C3D32×D414yes—
764C2×C3D3×#23714yes—
765C2×C3C2×#382811yescharacteristic
766C2×C3C2×D4×C3⋊D311yescharacteristic
767C2×C3C2×#383011yescharacteristic
768D3—41no—
769D3—68no—
770D3—182no—
771D3—188no—
772D3—368no—
773D3#6409214yesdirect product factor
774C22—21no—
775C22—21no—
776C22—21no—
777C22—32no—
778C22—32no—
779C22—32no—
780C22—61no—
781C22—61no—
782C22—61no—
783C22—92no—
784C22—124no—
785C22—181no—
786C22—181no—
787C22—272no—
788C22—548no—
789C22—541no—
790C22—541no—
791C22C22×D3×C3⋊D311yescharacteristic
792C4—21no—
793C4—21no—
794C4—61no—
795C4—61no—
796C4—181no—
797C4—181no—
798C4—181no—
799C4—541no—
800C4—541no—
801C4—541no—
802C3—24no—
803C3D3×#88314yescomplemented
804C3C2×#6409211yescharacteristic, complemented
805C2—34no—
806C2—41no—
807C2—121no—
808C2—182no—
809C2—542no—
810C2D3×#382811yescharacteristic
811C2D3×D4×C3⋊D311yescharacteristic
812C2D3×#383011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radicalC2×D3×#638C2
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33C2×#123
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×C3⋊D3C2semidirect
3. #11723924C2semidirect
4. C3×#64092C2semidirect
5. C32×D3×C22⋊C4C2semidirect
6. #11723628C2semidirect
7. #11723621C2semidirect
8. D3×#3757C2semidirect
9. D3×#3752C2semidirect
10. #11723523C2semidirect
11. #11723518C2semidirect
12. D3×C4⋊(C3⋊Dic3)C2semidirect
13. D3×#3750C2semidirect
14. #11723422C2semidirect
15. #11723420C2semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×C4×C3⋊D3C22semidirect
29. C2×#6289C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
35. C33×C22⋊C4C22semidirect
36. #88864C22semidirect
37. #88859C22semidirect
38. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
39. #88857C22semidirect
40. C3×#3757C22semidirect
41. C3×#3752C22semidirect
42. C3×C4⋊(C3⋊Dic3)C22semidirect
43. C3×#3750C22semidirect
44. C32×#217C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×(C2×D3)⋊C4C22semidirect
47. #88807C22semidirect
48. #88806C22semidirect
49. Dic3⋊(C3⋊Dic3)C22semidirect
50. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88804C22semidirect
52. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
73. #64092D3direct (N × H)
75. C3×D3×C22⋊C4D3semidirect
144. C2×C4×C3⋊D3C2×D3semidirect
162. C32×C22⋊C4C2×D3semidirect
163. C32×C22⋊C4C2×D3semidirect
169. #3757C2×D3semidirect
175. #3752C2×D3semidirect
181. C4⋊(C3⋊Dic3)C2×D3semidirect
187. #3750C2×D3semidirect
189. C3×#217C2×D3semidirect
191. C3×(C2×D3)⋊C4C2×D3semidirect
192. C3×(C2×D3)⋊C4C2×D3semidirect
261. D3×C22⋊C4C3⋊D3semidirect
347. C32×D3#123semidirect
392. C3×C22⋊C4D32semidirect
393. C3×C22⋊C4C2×C3⋊D3semidirect
401. #217C2×C3⋊D3semidirect
411. (C2×D3)⋊C4C2×C3⋊D3semidirect
412. (C2×D3)⋊C4C2×C3⋊D3semidirect
512. C33C2×#123semidirect
610. C3×D3#883semidirect
647. C22⋊C4D3×C3⋊D3semidirect
717. C32C2×#883semidirect
718. C32D3×#123semidirect
773. D3#64092direct (N × H)
803. C3D3×#883semidirect
804. C3C2×#64092semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
C2×C4×D3×C3⋊D32
#117239242
C3×#640922
C32×D3×C22⋊C42
#117236282
#117236212
D3×#37572
D3×#37522
#117235232
#117235182
D3×C4⋊(C3⋊Dic3)2
D3×#37502
#117234222
#117234202
C2×#640923
D3×#8833