Finite Group Databasebeta

← D3×#64103 #13176531

Subgroups — D3×#64103 #13176531

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×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
3#11723935C211yesmaximal, characteristic, complemented
4C3×#64103C211yesmaximal, characteristic, complemented
5C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
6D3×#3752C211yesmaximal, characteristic, complemented
7D3×#3752C211yesmaximal, characteristic, complemented
8D3×#3752C211yesmaximal, characteristic, complemented
9#11723504C211yesmaximal, characteristic, complemented
10#11723498C211yesmaximal, characteristic, complemented
11#11723493C211yesmaximal, characteristic, complemented
12#11723488C211yesmaximal, characteristic, complemented
13D3×#3750C211yesmaximal, characteristic, complemented
14#11723421C211yesmaximal, characteristic, complemented
15#11723417C211yesmaximal, characteristic, complemented
16C2×#64103—31nomaximal
17D3×#894—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic
29C2×#6289C2211yescharacteristic, complemented
30C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
31C2×D3×C3⋊Dic3C2211yescharacteristic
32C2×D3×C3⋊Dic3C2211yescharacteristic
33D3×C4⋊(C3⋊D3)—24no—
34C4×D3×C3⋊D3—24no—
35C33×C4⋊C4C2211yescharacteristic, complemented
36#88859C2211yescharacteristic, complemented
37#88859C2211yescharacteristic, complemented
38#88859C2211yescharacteristic, complemented
39#88857C2211yescharacteristic, complemented
40C3×#3752C2211yescharacteristic, complemented
41C3×#3752C2211yescharacteristic, complemented
42C3×#3752C2211yescharacteristic, complemented
43C3×#3750C2211yescharacteristic, complemented
44C32×C4⋊Dic3C2211yescharacteristic, complemented
45C32×Dic3⋊C4C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54#88803C2211yescharacteristic, complemented
55C22×C4⋊(C3⋊D3)—31no—
56C22×C4×C3⋊D3—31no—
57C2×D3×D12—34no—
58C2×C4×D32—34no—
59C2×C32×C4⋊C4—31no—
60C2×#3752—31no—
61C2×#3752—31no—
62C2×#3752—31no—
63C2×#3750—31no—
64#64103—31no—
65#64103—31no—
66#64103—31no—
67#64103—31no—
68#64103—31no—
69#64103—31no—
70#64103—31no—
71#64103—34no—
72#64103—64no—
73#64103D311yescharacteristic, direct product factor
74C3×#894—34no—
75C3×D3×C4⋊C4D314yescomplemented
76D3×(C2×D3)⋊C4—34no—
77D3×(C2×D3)⋊C4—34no—
78D3×(C2×D3)⋊C4—34no—
79#63897—34no—
80#63890—34no—
81#63884—34no—
82D3×Dic3⋊C4—34no—
83#63854—34no—
84#63853—34no—
85#63850—34no—
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C3×C3⋊D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C2×D3×C3⋊D3—22no—
92C2×D3×C3⋊D3—22no—
93C2×D3×C3⋊D3—22no—
94C2×D3×C3⋊D3—22no—
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3D414yes—
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C4⋊(C3⋊(C3⋊D3))—22no—
103C4×C3⋊(C3⋊D3)—22no—
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C3×C4⋊(C3⋊D3)—22no—
107C3×C4×C3⋊D3—22no—
108C2×C32×Dic3C2311yescharacteristic
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C32×C4×D3—22no—
112C32×C4×D3—22no—
113C32×C4×D3—22no—
114#6292—22no—
115#6292—22no—
116#6289—22no—
117Dic3×C3⋊D3—22no—
118D3×C3⋊Dic3—22no—
119D3×C3⋊Dic3—22no—
120D3×#123—91no—
121C2×#894—94no—
122C23×C3⋊D3—31no—
123C23×C3⋊D3—31no—
124C22×D32—34no—
125C22×D32—34no—
126C22×C32×C4—31no—
127C22×C32×C4—31no—
128C22×C32×C4—31no—
129C22×C3⋊Dic3—31no—
130C22×C3⋊Dic3—31no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4⋊(C3⋊D3)—31no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4⋊(C3⋊D3)—34no—
135C2×C4⋊(C3⋊D3)—64no—
136C2×C4⋊(C3⋊D3)—64no—
137C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
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×D12—34no—
146C2×C3×C4×D3—34no—
147C2×C3×C4×D3C2×D314yes—
148C2×C3×C4×D3C2×D314yes—
149C2×C3×C4×D3C2×D314yes—
150C2×#626—34no—
151C2×#626—34no—
152C2×#624—34no—
153C2×D3×Dic3—34no—
154C2×D3×Dic3—34no—
155C2×D3×Dic3—34no—
156D3×D12—616no—
157C4×D32—616no—
158C32×C4⋊C4—24no—
159C32×C4⋊C4—31no—
160C32×C4⋊C4—31no—
161C32×C4⋊C4—31no—
162C32×C4⋊C4C2×D314yescomplemented
163C32×C4⋊C4C2×D311yescharacteristic, complemented
164#3752—31no—
165#3752—31no—
166#3752—31no—
167#3752—31no—
168#3752—31no—
169#3752—31no—
170#3752—34no—
171#3752—34no—
172#3752—34no—
173#3752—31no—
174#3752—31no—
175#3752—31no—
176#3752—64no—
177#3752—64no—
178#3752—64no—
179#3752C2×D311yescharacteristic, complemented
180#3752C2×D311yescharacteristic, complemented
181#3752C2×D311yescharacteristic, complemented
182#3750—31no—
183#3750—34no—
184#3750—31no—
185#3750—31no—
186#3750—64no—
187#3750C2×D311yescharacteristic, complemented
188C3×(C2×D3)⋊C4—34no—
189C3×(C2×D3)⋊C4—34no—
190C3×(C2×D3)⋊C4—34no—
191C3×C4⋊Dic3C2×D314yescomplemented
192C3×Dic3⋊C4—34no—
193C3×Dic3⋊C4C2×D314yescomplemented
194C3×Dic3⋊C4C2×D314yescomplemented
195#3724—34no—
196Dic3⋊Dic3—34no—
197#3722—34no—
198#3722—34no—
199#3722—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203C22×C33C2411yescharacteristic
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3⋊(C3⋊D3)—21no—
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⋊D3—21no—
213C2×C3×C3⋊D3—21no—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3C2×D412yes—
216C2×C32×D3C2×D412yes—
217C2×C32×D3#4112yes—
218C2×C32×D3#4112yes—
219D3×C3⋊D3—28no—
220D3×C3⋊D3—44no—
221C33×C4—21no—
222C33×C4—21no—
223C33×C4—21no—
224C3⋊(C3⋊Dic3)—21no—
225C3⋊(C3⋊Dic3)—21no—
226C3×C3⋊Dic3—21no—
227C3×C3⋊Dic3—21no—
228C32×Dic3—21no—
229C32×Dic3—21no—
230C32×Dic3—21no—
231C2×D3×D4—91no—
232C22×D12—94no—
233C22×C4×D3—94no—
234C22×C4×D3—91no—
235C3×#123—91no—
236C2×C3×C4⋊C4—34no—
237#935—91no—
238#929—91no—
239C2×(C2×D3)⋊C4—94no—
240C2×(C2×D3)⋊C4—94no—
241C2×(C2×D3)⋊C4—94no—
242C2×Dic3⋊C4—94no—
243#894—34no—
244#894—94no—
245#894—94no—
246#894—94no—
247#894—94no—
248#894—94no—
249#894—94no—
250#894—94no—
251#894—91no—
252#894—91no—
253#894—184no—
254D3×C4⋊C4—91no—
255D3×C4⋊C4C3⋊D311yescharacteristic, complemented
256#886—91no—
257#883—91no—
258#883—91no—
259D3×C22⋊C4—91no—
260D3×C22⋊C4—91no—
261D3×C22⋊C4—91no—
262C23×C32—31no—
263C22×C3⋊D3—31no—
264C22×C3⋊D3—34no—
265C22×C3⋊D3—31no—
266C22×C3⋊D3—34no—
267C22×C3⋊D3—34no—
268C22×C3⋊D3—64no—
269C22×C3⋊D3—64no—
270C22×C3⋊D3—62no—
271C22×C3⋊D3—62no—
272C22×C3⋊D3—62no—
273C22×C3⋊D3—62no—
274C22×C3⋊D3—62no—
275C22×C3⋊D3C22×D311yescharacteristic
276C22×C3⋊D3C22×D311yescharacteristic
277C22×C3×D3—34no—
278C22×C3×D3—34no—
279C22×C3×D3C22×D314yes—
280C2×D32—316no—
281C2×D32—68no—
282C2×D32—68no—
283C2×D32—68no—
284C2×D32—68no—
285C2×D32—68no—
286C2×C32×C4—24no—
287C2×C32×C4—24no—
288C2×C32×C4—24no—
289C2×C32×C4—31no—
290C2×C32×C4—31no—
291C2×C32×C4—31no—
292C2×C32×C4—62no—
293C2×C32×C4—62no—
294C2×C32×C4—62no—
295C2×C32×C4C22×D314yes—
296C2×C32×C4C22×D314yes—
297C2×C32×C4C22×D314yes—
298C2×C32×C4C22×D311yescharacteristic
299C2×C32×C4C22×D311yescharacteristic
300C2×C32×C4C22×D311yescharacteristic
301C2×C3⋊Dic3—31no—
302C2×C3⋊Dic3—31no—
303C2×C3⋊Dic3—34no—
304C2×C3⋊Dic3—34no—
305C2×C3⋊Dic3—64no—
306C2×C3⋊Dic3—64no—
307C2×C3⋊Dic3—62no—
308C2×C3⋊Dic3—62no—
309C2×C3⋊Dic3C22×D311yescharacteristic
310C2×C3⋊Dic3C22×D311yescharacteristic
311C4⋊(C3⋊D3)—22no—
312C4⋊(C3⋊D3)—62no—
313C4⋊(C3⋊D3)—62no—
314C4⋊(C3⋊D3)—62no—
315C4⋊(C3⋊D3)—68no—
316C4⋊(C3⋊D3)—128no—
317C4×C3⋊D3—22no—
318C4×C3⋊D3—62no—
319C4×C3⋊D3—62no—
320C4×C3⋊D3—62no—
321C4×C3⋊D3—68no—
322C4×C3⋊D3—128no—
323C2×C3×Dic3—34no—
324C2×C3×Dic3—34no—
325C2×C3×Dic3C22×D314yes—
326C2×C3×Dic3C22×D314yes—
327C2×C3×Dic3C22×D314yes—
328C3×D12—68no—
329C3×C4×D3—28no—
330C3×C4×D3—28no—
331C3×C4×D3—28no—
332C3×C4×D3—68no—
333#626—68no—
334#626—68no—
335#624—68no—
336D3×Dic3—68no—
337D3×Dic3—68no—
338D3×Dic3—68no—
339C2×#123—271noSylow
340C2×C33C22×D411yescharacteristic
341C2×C33C2×#4111yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C3⋊(C3⋊D3)—22no—
344C3⋊(C3⋊D3)—41no—
345C3×C3⋊D3—22no—
346C3×C3⋊D3—41no—
347C32×D3#12314yescomplemented
348C23×D3—94no—
349C23×D3—94no—
350C23×D3—91no—
351C23×D3—91no—
352C2×C3×D4—91no—
353C22×C3×C4—34no—
354C22×C3×C4—34no—
355C22×C3×C4—34no—
356C22×C3×C4—91no—
357C2×#67—91no—
358C2×#67—91no—
359C22×Dic3—94no—
360C22×Dic3—94no—
361C22×Dic3—91no—
362D3×D4—184no—
363C2×D12—34no—
364C2×D12—94no—
365C2×D12—94no—
366C2×D12—94no—
367C2×D12—91no—
368C2×D12—184no—
369C2×D12—1816no—
370C2×C4×D3—34no—
371C2×C4×D3—94no—
372C2×C4×D3—94no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—94no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—184no—
379C2×C4×D3—184no—
380C2×C4×D3—1816no—
381C2×C4×D3C2×C3⋊D311yescharacteristic
382C2×C4×D3C2×C3⋊D311yescharacteristic
383C2×C4×D3C2×C3⋊D311yescharacteristic
384C3×C4⋊C4—24no—
385C3×C4⋊C4—34no—
386C3×C4⋊C4—34no—
387C3×C4⋊C4—34no—
388C3×C4⋊C4—91no—
389C3×C4⋊C4D3214yescomplemented
390C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
391C3×C22⋊C4—91no—
392C3×C22⋊C4—91no—
393C3×C22⋊C4—91no—
394#217—91no—
395#217—91no—
396#217—91no—
397(C2×D3)⋊C4—34no—
398(C2×D3)⋊C4—34no—
399(C2×D3)⋊C4—34no—
400(C2×D3)⋊C4—94no—
401(C2×D3)⋊C4—94no—
402(C2×D3)⋊C4—94no—
403(C2×D3)⋊C4—94no—
404(C2×D3)⋊C4—94no—
405(C2×D3)⋊C4—94no—
406(C2×D3)⋊C4—94no—
407(C2×D3)⋊C4—94no—
408(C2×D3)⋊C4—94no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4—91no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—184no—
416(C2×D3)⋊C4—184no—
417(C2×D3)⋊C4—184no—
418C4⋊Dic3—91no—
419C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
420Dic3⋊C4—34no—
421Dic3⋊C4—94no—
422Dic3⋊C4—94no—
423Dic3⋊C4—94no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—184no—
427Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
428Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
429C22×C32—24no—
430C22×C32—32no—
431C22×C32—32no—
432C22×C32—32no—
433C22×C32C23×D314yes—
434C22×C32C23×D311yescharacteristic
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3—21no—
440C2×C3⋊D3—32no—
441C2×C3⋊D3—38no—
442C2×C3⋊D3—68no—
443C2×C3⋊D3—68no—
444C2×C3⋊D3—61no—
445C2×C3⋊D3—61no—
446C2×C3⋊D3—61no—
447C2×C3⋊D3—61no—
448C2×C3⋊D3—61no—
449C2×C3⋊D3—64no—
450C2×C3⋊D3—64no—
451C2×C3⋊D3—64no—
452C2×C3⋊D3—64no—
453C2×C3⋊D3—64no—
454C2×C3⋊D3—124no—
455C2×C3⋊D3—124no—
456C2×C3⋊D3—124no—
457C2×C3⋊D3—124no—
458C2×C3⋊D3—124no—
459C2×C3⋊D3—124no—
460C2×C3⋊D3D3×D412yes—
461C2×C3×D3—38no—
462C2×C3×D3—64no—
463C2×C3×D3—64no—
464C2×C3×D3—64no—
465C2×C3×D3—64no—
466C2×C3×D3—64no—
467C2×C3×D3#23518yes—
468C2×C3×D3D3×D418yes—
469C2×C3×D3#23918yes—
470D32—632no—
471D32—1216no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—21no—
475C32×C4—24no—
476C32×C4—24no—
477C32×C4—24no—
478C32×C4—44no—
479C32×C4—44no—
480C32×C4—44no—
481C32×C4—61no—
482C32×C4—61no—
483C32×C4—61no—
484C3⋊Dic3—21no—
485C3⋊Dic3—21no—
486C3⋊Dic3—61no—
487C3⋊Dic3—61no—
488C3⋊Dic3—64no—
489C3⋊Dic3—64no—
490C3⋊Dic3—124no—
491C3⋊Dic3—124no—
492C3×Dic3—24no—
493C3×Dic3—24no—
494C3×Dic3—24no—
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—31no—
508C2×C4⋊C4—271no—
509C2×C22⋊C4—271no—
510C2×C22⋊C4—271no—
511C2×C22⋊C4—271no—
512C33C2×#12311yescharacteristic, complemented, Sylow
513C23×C3—34no—
514C23×C3—91no—
515C23×C3—91no—
516C22×D3—34no—
517C22×D3—34no—
518C22×D3—916no—
519C22×D3—94no—
520C22×D3—91no—
521C22×D3—94no—
522C22×D3—94no—
523C22×D3—91no—
524C22×D3—184no—
525C22×D3—184no—
526C22×D3—188no—
527C22×D3—188no—
528C22×D3—188no—
529C22×D3—188no—
530C22×D3—188no—
531C22×D3—182no—
532C22×D3—182no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3—182no—
536C22×D3C22×C3⋊D311yescharacteristic
537C3×D4—182no—
538C2×C3×C4—24no—
539C2×C3×C4—24no—
540C2×C3×C4—24no—
541C2×C3×C4—34no—
542C2×C3×C4—34no—
543C2×C3×C4—34no—
544C2×C3×C4—68no—
545C2×C3×C4—68no—
546C2×C3×C4—68no—
547C2×C3×C4—91no—
548C2×C3×C4—91no—
549C2×C3×C4—182no—
550C2×C3×C4C2×D3214yes—
551C2×C3×C4C2×D3214yes—
552C2×C3×C4C2×D3214yes—
553C2×C3×C4C22×C3⋊D311yescharacteristic
554C2×C3×C4C22×C3⋊D311yescharacteristic
555C2×C3×C4C22×C3⋊D311yescharacteristic
556#67—182no—
557#67—182no—
558C2×Dic3—34no—
559C2×Dic3—34no—
560C2×Dic3—94no—
561C2×Dic3—94no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—184no—
565C2×Dic3—184no—
566C2×Dic3—182no—
567C2×Dic3—188no—
568C2×Dic3—188no—
569C2×Dic3C22×C3⋊D311yescharacteristic
570C2×Dic3C22×C3⋊D311yescharacteristic
571C2×Dic3C22×C3⋊D311yescharacteristic
572D12—68no—
573D12—182no—
574D12—188no—
575D12—188no—
576D12—188no—
577D12—368no—
578C4×D3—22no—
579C4×D3—22no—
580C4×D3—22no—
581C4×D3—68no—
582C4×D3—182no—
583C4×D3—188no—
584C4×D3—182no—
585C4×D3—188no—
586C4×D3—188no—
587C4×D3—182no—
588C4×D3—182no—
589C4×D3—368no—
590C2×C32—24no—
591C2×C32—24no—
592C2×C32—24no—
593C2×C32—34no—
594C2×C32C2×#23514yes—
595C2×C32C2×D3×D414yes—
596C2×C32C2×D3×D411yescharacteristic
597C2×C32C2×#23914yes—
598C2×C32D3×#4111yescharacteristic
599C2×C32D3×#4111yescharacteristic
600C3⋊D3—22no—
601C3⋊D3—41no—
602C3⋊D3—62no—
603C3⋊D3—68no—
604C3⋊D3—128no—
605C3⋊D3—121no—
606C3⋊D3—124no—
607C3⋊D3—244no—
608C3×D3—68no—
609C3×D3—124no—
610C3×D3#894116yescomplemented
611C24—271no—
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—31no—
621C22×C4—91no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—271no—
627C22×C4—544no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—91no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4—271no—
635C4⋊C4D3×C3⋊D311yescharacteristic, complemented
636C22⋊C4—91no—
637C22⋊C4—91no—
638C22⋊C4—91no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22⋊C4—271no—
648C22×C3—24no—
649C22×C3—38no—
650C22×C3—38no—
651C22×C3—38no—
652C22×C3—92no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3—181no—
656C22×C3—181no—
657C22×C3—181no—
658C22×C3C22×D3214yes—
659C22×C3C23×C3⋊D311yescharacteristic
660C2×D3—38no—
661C2×D3—64no—
662C2×D3—64no—
663C2×D3—64no—
664C2×D3—64no—
665C2×D3—64no—
666C2×D3—98no—
667C2×D3—92no—
668C2×D3—188no—
669C2×D3—1832no—
670C2×D3—184no—
671C2×D3—184no—
672C2×D3—181no—
673C2×D3—181no—
674C2×D3—188no—
675C2×D3—184no—
676C2×D3—184no—
677C2×D3—184no—
678C2×D3—181no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—364no—
682C2×D3—364no—
683C2×D3—364no—
684C2×D3—364no—
685C2×D3—364no—
686C2×D3—3616no—
687C2×D3—364no—
688C2×D3#382812yes—
689C2×D3D4×C3⋊D312yes—
690C2×D3#383212yes—
691C3×C4—24no—
692C3×C4—24no—
693C3×C4—24no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—44no—
698C3×C4—44no—
699C3×C4—44no—
700C3×C4—64no—
701C3×C4—64no—
702C3×C4—64no—
703C3×C4—181no—
704C3×C4—181no—
705Dic3—21no—
706Dic3—21no—
707Dic3—21no—
708Dic3—64no—
709Dic3—64no—
710Dic3—184no—
711Dic3—184no—
712Dic3—181no—
713Dic3—181no—
714Dic3—364no—
715Dic3—364no—
716C32—24no—
717C32C2×#89414yescomplemented
718C32D3×#12311yescharacteristic, complemented
719C23—31no—
720C23—91no—
721C23—91no—
722C23—274no—
723C23—271no—
724C23—271no—
725C23—542no—
726C23—542no—
727C23—542no—
728C23—542no—
729C23—542no—
730D4—182no—
731D4—542no—
732D4—542no—
733D4—542no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—91no—
741C2×C4—91no—
742C2×C4—182no—
743C2×C4—271no—
744C2×C4—271no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4—542no—
748C2×C4—542no—
749C2×C4—542no—
750C2×C4C2×D3×C3⋊D311yescharacteristic
751C2×C4C2×D3×C3⋊D311yescharacteristic
752C2×C4C2×D3×C3⋊D311yescharacteristic
753C2×C3—24no—
754C2×C3—24no—
755C2×C3—24no—
756C2×C3—316no—
757C2×C3—182no—
758C2×C3—361no—
759C2×C3D3×#23514yes—
760C2×C3D32×D414yes—
761C2×C3D3×#23914yes—
762C2×C3C2×#382811yescharacteristic
763C2×C3C2×D4×C3⋊D311yescharacteristic
764C2×C3C2×#383211yescharacteristic
765D3—68no—
766D3—124no—
767D3—188no—
768D3—182no—
769D3—368no—
770D3—364no—
771D3—361no—
772D3—724no—
773D3#6410314yesdirect product factor
774C22—32no—
775C22—32no—
776C22—32no—
777C22—92no—
778C22—181no—
779C22—181no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—272no—
784C22—548no—
785C22—541no—
786C22—541no—
787C22—541no—
788C22—541no—
789C22—541no—
790C22—1084no—
791C22C22×D3×C3⋊D311yescharacteristic
792C4—21no—
793C4—21no—
794C4—21no—
795C4—61no—
796C4—61no—
797C4—61no—
798C4—181no—
799C4—181no—
800C4—541no—
801C4—541no—
802C3—24no—
803C3D3×#89414yescomplemented
804C3C2×#6410311yescharacteristic, complemented
805C2—34no—
806C2—182no—
807C2—361no—
808C2—542no—
809C2—1081no—
810C2D3×#382811yescharacteristic
811C2D3×D4×C3⋊D311yescharacteristic
812C2D3×#383211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC2×D3×C4⋊(C3⋊D3)C2
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33C2×#123
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×C3⋊D3C2semidirect
3. #11723935C2semidirect
4. C3×#64103C2semidirect
5. C32×D3×C4⋊C4C2semidirect
6. D3×#3752C2semidirect
7. D3×#3752C2semidirect
8. D3×#3752C2semidirect
9. #11723504C2semidirect
10. #11723498C2semidirect
11. #11723493C2semidirect
12. #11723488C2semidirect
13. D3×#3750C2semidirect
14. #11723421C2semidirect
15. #11723417C2semidirect
21. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×C4×C3⋊D3C22semidirect
29. C2×#6289C22semidirect
30. C2×Dic3×C3⋊D3C22semidirect
35. C33×C4⋊C4C22semidirect
36. #88859C22semidirect
37. #88859C22semidirect
38. #88859C22semidirect
39. #88857C22semidirect
40. C3×#3752C22semidirect
41. C3×#3752C22semidirect
42. C3×#3752C22semidirect
43. C3×#3750C22semidirect
44. C32×C4⋊Dic3C22semidirect
45. C32×Dic3⋊C4C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. #88807C22semidirect
48. #88806C22semidirect
49. #88804C22semidirect
50. #88804C22semidirect
51. #88804C22semidirect
52. #88803C22semidirect
53. #88803C22semidirect
54. #88803C22semidirect
73. #64103D3direct (N × H)
75. C3×D3×C4⋊C4D3semidirect
144. C2×C4×C3⋊D3C2×D3semidirect
162. C32×C4⋊C4C2×D3semidirect
163. C32×C4⋊C4C2×D3semidirect
179. #3752C2×D3semidirect
180. #3752C2×D3semidirect
181. #3752C2×D3semidirect
187. #3750C2×D3semidirect
191. C3×C4⋊Dic3C2×D3semidirect
193. C3×Dic3⋊C4C2×D3semidirect
194. C3×Dic3⋊C4C2×D3semidirect
255. D3×C4⋊C4C3⋊D3semidirect
347. C32×D3#123semidirect
389. C3×C4⋊C4D32semidirect
390. C3×C4⋊C4C2×C3⋊D3semidirect
419. C4⋊Dic3C2×C3⋊D3semidirect
427. Dic3⋊C4C2×C3⋊D3semidirect
428. Dic3⋊C4C2×C3⋊D3semidirect
512. C33C2×#123semidirect
610. C3×D3#894semidirect
635. C4⋊C4D3×C3⋊D3semidirect
717. C32C2×#894semidirect
718. C32D3×#123semidirect
773. D3#64103direct (N × H)
803. C3D3×#894semidirect
804. C3C2×#64103semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊(C3⋊D3)2
C2×C4×D3×C3⋊D32
#117239352
C3×#641032
C32×D3×C4⋊C42
D3×#37522
#117235042
#117234982
#117234932
#117234882
D3×#37502
#117234212
#117234172
C2×#641033
D3×#8943