Finite Group Databasebeta

← D3×#64107 #13176583

Subgroups — D3×#64107 #13176583

Order 1728.

1716 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723939C211yesmaximal, characteristic, complemented
2C3×#64107C211yesmaximal, characteristic, complemented
3C32×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4D3×#3752C211yesmaximal, characteristic
5D3×#3752C211yesmaximal, characteristic
6D3×#3752C211yesmaximal, characteristic
7D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
8D3×#3750C211yesmaximal, characteristic, complemented
9C4×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
10#11723446C211yesmaximal, characteristic, complemented
11#11723433C211yesmaximal, characteristic, complemented
12#11723411C211yesmaximal, characteristic, complemented
13#11723408C211yesmaximal, characteristic, complemented
14#11723407C211yesmaximal, characteristic, complemented
15#11723403C211yesmaximal, characteristic, complemented
16C2×#64107—31nomaximal
17D3×#898—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×C32×C4×D3C2211yescharacteristic
22C2×D3×C3⋊Dic3C2211yescharacteristic
23C2×D3×C3⋊Dic3C2211yescharacteristic
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C33×C4⋊C4C2211yescharacteristic, complemented
26#88859C2211yescharacteristic
27#88859C2211yescharacteristic
28#88859C2211yescharacteristic
29C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
30#88857C2211yescharacteristic, complemented
31C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
32C3×#3752C2211yescharacteristic
33C3×#3752C2211yescharacteristic
34C3×#3752C2211yescharacteristic
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C3×#3750C2211yescharacteristic, complemented
37C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
38C32×C4⋊Dic3C2211yescharacteristic, complemented
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40C32×Dic3⋊C4C2211yescharacteristic, complemented
41#88807C2211yescharacteristic, complemented
42#88806C2211yescharacteristic, complemented
43Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52Dic3×C3⋊Dic3C2211yescharacteristic, complemented
53C2×C32×C4⋊C4—31no—
54C2×#3752—31no—
55C2×#3752—31no—
56C2×#3752—31no—
57C2×C4⋊(C3⋊Dic3)—31no—
58C2×#3750—31no—
59C2×C4×C3⋊Dic3—31no—
60#64107—31no—
61#64107—31no—
62#64107—31no—
63#64107—31no—
64#64107—31no—
65#64107—31no—
66#64107—31no—
67#64107—34no—
68#64107—64no—
69#64107D311yescharacteristic, direct product factor
70C3×#898—34no—
71C3×D3×C4⋊C4D314yescomplemented
72D3×(C2×D3)⋊C4—34no—
73D3×(C2×D3)⋊C4—34no—
74D3×(C2×D3)⋊C4—34no—
75D3×C4⋊Dic3—34no—
76D3×Dic3⋊C4—34no—
77C4×D3×Dic3—34no—
78#63868—34no—
79#63862—34no—
80#63861—34no—
81#63858—34no—
82#63848—34no—
83#63848—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C2×D3×C3⋊D3—22no—
88C2×D3×C3⋊D3—22no—
89C2×D3×C3⋊D3—22no—
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C33×C4C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
96C2×C3×C3⋊Dic3C2311yescharacteristic
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C32×Dic3C2311yescharacteristic
100C2×C32×Dic3C2311yescharacteristic
101C2×C32×Dic3C2311yescharacteristic
102C32×C4×D3—22no—
103C32×C4×D3—22no—
104C32×C4×D3—22no—
105D3×C3⋊Dic3—22no—
106D3×C3⋊Dic3—22no—
107D3×C3⋊Dic3—22no—
108D3×#126—91no—
109C2×#898—94no—
110C23×C3⋊D3—31no—
111C22×D32—34no—
112C22×C32×C4—31no—
113C22×C32×C4—31no—
114C22×C32×C4—31no—
115C22×C3⋊Dic3—31no—
116C22×C3⋊Dic3—31no—
117C22×C3⋊Dic3—31no—
118C2×C3×C4×D3C2×D314yes—
119C2×C3×C4×D3C2×D314yes—
120C2×C3×C4×D3C2×D314yes—
121C2×D3×Dic3—34no—
122C2×D3×Dic3—34no—
123C2×D3×Dic3—34no—
124C32×C4⋊C4—24no—
125C32×C4⋊C4—31no—
126C32×C4⋊C4—31no—
127C32×C4⋊C4—31no—
128C32×C4⋊C4C2×D314yescomplemented
129C32×C4⋊C4C2×D311yescharacteristic, complemented
130#3752—31no—
131#3752—31no—
132#3752—31no—
133#3752—31no—
134#3752—31no—
135#3752—31no—
136#3752—34no—
137#3752—34no—
138#3752—34no—
139#3752—31no—
140#3752—31no—
141#3752—31no—
142#3752—64no—
143#3752—64no—
144#3752—64no—
145#3752C2×D311yescharacteristic
146#3752C2×D311yescharacteristic
147#3752C2×D311yescharacteristic
148C4⋊(C3⋊Dic3)—31no—
149C4⋊(C3⋊Dic3)—34no—
150C4⋊(C3⋊Dic3)—31no—
151C4⋊(C3⋊Dic3)—31no—
152C4⋊(C3⋊Dic3)—64no—
153C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
154#3750—31no—
155#3750—34no—
156#3750—31no—
157#3750—31no—
158#3750—64no—
159#3750C2×D311yescharacteristic, complemented
160C4×C3⋊Dic3—31no—
161C4×C3⋊Dic3—34no—
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—31no—
164C4×C3⋊Dic3—64no—
165C4×C3⋊Dic3C2×D311yescharacteristic, complemented
166C3×(C2×D3)⋊C4—34no—
167C3×(C2×D3)⋊C4—34no—
168C3×(C2×D3)⋊C4—34no—
169C3×C4⋊Dic3—34no—
170C3×C4⋊Dic3C2×D314yescomplemented
171C3×Dic3⋊C4—34no—
172C3×Dic3⋊C4C2×D314yescomplemented
173C3×Dic3⋊C4C2×D314yescomplemented
174C3×C4×Dic3—34no—
175#3724—34no—
176Dic3⋊Dic3—34no—
177Dic3⋊Dic3—34no—
178Dic3⋊Dic3—34no—
179#3722—34no—
180#3722—34no—
181#3722—34no—
182(C2×D3)⋊Dic3—34no—
183(C2×D3)⋊Dic3—34no—
184(C2×D3)⋊Dic3—34no—
185Dic32—34no—
186Dic32—34no—
187C22×C33C2411yescharacteristic
188C2×C3⋊(C3⋊D3)—21no—
189C2×C3⋊(C3⋊D3)—21no—
190C2×C3⋊(C3⋊D3)—21no—
191C2×C3×C3⋊D3—21no—
192C2×C3×C3⋊D3—21no—
193C2×C3×C3⋊D3—21no—
194C2×C32×D3#4112yes—
195C2×C32×D3#4112yes—
196C2×C32×D3#4112yes—
197D3×C3⋊D3—44no—
198C33×C4—21no—
199C33×C4—21no—
200C33×C4—21no—
201C3⋊(C3⋊Dic3)—21no—
202C3⋊(C3⋊Dic3)—21no—
203C3⋊(C3⋊Dic3)—21no—
204C3×C3⋊Dic3—21no—
205C3×C3⋊Dic3—21no—
206C3×C3⋊Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3—21no—
209C32×Dic3—21no—
210C3×#126—91no—
211C2×C3×C4⋊C4—34no—
212C2×(C2×D3)⋊C4—94no—
213C2×(C2×D3)⋊C4—94no—
214C2×(C2×D3)⋊C4—94no—
215C2×C4⋊Dic3—94no—
216C2×Dic3⋊C4—94no—
217C2×C4×Dic3—94no—
218#898—34no—
219#898—94no—
220#898—94no—
221#898—94no—
222#898—94no—
223#898—94no—
224#898—94no—
225#898—94no—
226#898—91no—
227#898—91no—
228#898—91no—
229#898—184no—
230D3×C4⋊C4—91no—
231D3×C4⋊C4—91no—
232D3×C4⋊C4C3⋊D311yescharacteristic, complemented
233D3×C22⋊C4—91no—
234D3×C22⋊C4—91no—
235D3×C22⋊C4—91no—
236#879—91no—
237#879—91no—
238#879—91no—
239#876—91no—
240C42×D3—91no—
241C23×C32—31no—
242C22×C3⋊D3—31no—
243C22×C3⋊D3—34no—
244C22×C3⋊D3—64no—
245C22×C3⋊D3—62no—
246C22×C3⋊D3—62no—
247C22×C3⋊D3—62no—
248C22×C3⋊D3C22×D311yescharacteristic
249C22×C3×D3—34no—
250C22×C3×D3C22×D314yes—
251C2×D32—68no—
252C2×D32—68no—
253C2×D32—68no—
254C2×C32×C4—24no—
255C2×C32×C4—24no—
256C2×C32×C4—24no—
257C2×C32×C4—31no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—62no—
261C2×C32×C4—62no—
262C2×C32×C4—62no—
263C2×C32×C4C22×D314yes—
264C2×C32×C4C22×D314yes—
265C2×C32×C4C22×D314yes—
266C2×C32×C4C22×D311yescharacteristic
267C2×C32×C4C22×D311yescharacteristic
268C2×C32×C4C22×D311yescharacteristic
269C2×C3⋊Dic3—31no—
270C2×C3⋊Dic3—31no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—34no—
273C2×C3⋊Dic3—34no—
274C2×C3⋊Dic3—34no—
275C2×C3⋊Dic3—64no—
276C2×C3⋊Dic3—64no—
277C2×C3⋊Dic3—64no—
278C2×C3⋊Dic3—62no—
279C2×C3⋊Dic3—62no—
280C2×C3⋊Dic3—62no—
281C2×C3⋊Dic3C22×D311yescharacteristic
282C2×C3⋊Dic3C22×D311yescharacteristic
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3×Dic3—34no—
285C2×C3×Dic3—34no—
286C2×C3×Dic3—34no—
287C2×C3×Dic3C22×D314yes—
288C2×C3×Dic3C22×D314yes—
289C2×C3×Dic3C22×D314yes—
290C3×C4×D3—28no—
291C3×C4×D3—28no—
292C3×C4×D3—28no—
293D3×Dic3—68no—
294D3×Dic3—68no—
295D3×Dic3—68no—
296C2×#126—271noSylow
297C2×C33C2×#4111yescharacteristic
298C2×C33C2×#4111yescharacteristic
299C2×C33C2×#4111yescharacteristic
300C3⋊(C3⋊D3)—41no—
301C3×C3⋊D3—41no—
302C32×D3#12614yescomplemented
303C23×D3—94no—
304C23×D3—91no—
305C22×C3×C4—34no—
306C22×C3×C4—34no—
307C22×C3×C4—34no—
308C22×Dic3—94no—
309C22×Dic3—94no—
310C22×Dic3—94no—
311C2×C4×D3—91no—
312C2×C4×D3—91no—
313C2×C4×D3—91no—
314C2×C4×D3C2×C3⋊D311yescharacteristic
315C2×C4×D3C2×C3⋊D311yescharacteristic
316C2×C4×D3C2×C3⋊D311yescharacteristic
317C3×C4⋊C4—24no—
318C3×C4⋊C4—34no—
319C3×C4⋊C4—34no—
320C3×C4⋊C4—34no—
321C3×C4⋊C4—91no—
322C3×C4⋊C4—91no—
323C3×C4⋊C4D3214yescomplemented
324C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
325C3×C22⋊C4—91no—
326C3×C22⋊C4—91no—
327C3×C22⋊C4—91no—
328C3×C42—91no—
329#217—91no—
330#217—91no—
331#217—91no—
332(C2×D3)⋊C4—34no—
333(C2×D3)⋊C4—34no—
334(C2×D3)⋊C4—34no—
335(C2×D3)⋊C4—94no—
336(C2×D3)⋊C4—94no—
337(C2×D3)⋊C4—94no—
338(C2×D3)⋊C4—94no—
339(C2×D3)⋊C4—94no—
340(C2×D3)⋊C4—94no—
341(C2×D3)⋊C4—94no—
342(C2×D3)⋊C4—94no—
343(C2×D3)⋊C4—94no—
344(C2×D3)⋊C4—91no—
345(C2×D3)⋊C4—91no—
346(C2×D3)⋊C4—91no—
347(C2×D3)⋊C4—91no—
348(C2×D3)⋊C4—91no—
349(C2×D3)⋊C4—91no—
350(C2×D3)⋊C4—184no—
351(C2×D3)⋊C4—184no—
352(C2×D3)⋊C4—184no—
353C4⋊Dic3—34no—
354C4⋊Dic3—94no—
355C4⋊Dic3—94no—
356C4⋊Dic3—94no—
357C4⋊Dic3—91no—
358C4⋊Dic3—91no—
359C4⋊Dic3—184no—
360C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
361Dic3⋊C4—34no—
362Dic3⋊C4—94no—
363Dic3⋊C4—94no—
364Dic3⋊C4—94no—
365Dic3⋊C4—91no—
366Dic3⋊C4—91no—
367Dic3⋊C4—91no—
368Dic3⋊C4—91no—
369Dic3⋊C4—184no—
370Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
371Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
372C4×Dic3—34no—
373C4×Dic3—94no—
374C4×Dic3—94no—
375C4×Dic3—94no—
376C4×Dic3—91no—
377C4×Dic3—91no—
378C4×Dic3—91no—
379C4×Dic3—184no—
380C22×C32—24no—
381C22×C32—32no—
382C22×C32—32no—
383C22×C32—32no—
384C22×C32C23×D314yes—
385C22×C32C23×D311yescharacteristic
386C2×C3⋊D3—21no—
387C2×C3⋊D3—21no—
388C2×C3⋊D3—21no—
389C2×C3⋊D3—61no—
390C2×C3⋊D3—61no—
391C2×C3⋊D3—61no—
392C2×C3⋊D3—64no—
393C2×C3⋊D3—64no—
394C2×C3⋊D3—64no—
395C2×C3⋊D3—124no—
396C2×C3⋊D3—124no—
397C2×C3⋊D3—124no—
398C2×C3⋊D3—124no—
399C2×C3×D3—64no—
400C2×C3×D3—64no—
401C2×C3×D3—64no—
402C2×C3×D3#23518yes—
403C2×C3×D3#23718yes—
404C2×C3×D3#23918yes—
405D32—1216no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—24no—
410C32×C4—24no—
411C32×C4—24no—
412C32×C4—44no—
413C32×C4—44no—
414C32×C4—44no—
415C32×C4—61no—
416C32×C4—61no—
417C32×C4—61no—
418C3⋊Dic3—21no—
419C3⋊Dic3—21no—
420C3⋊Dic3—21no—
421C3⋊Dic3—61no—
422C3⋊Dic3—61no—
423C3⋊Dic3—61no—
424C3⋊Dic3—64no—
425C3⋊Dic3—64no—
426C3⋊Dic3—64no—
427C3⋊Dic3—124no—
428C3⋊Dic3—124no—
429C3⋊Dic3—124no—
430C3×Dic3—24no—
431C3×Dic3—24no—
432C3×Dic3—24no—
433C3×Dic3—64no—
434C3×Dic3—64no—
435C3×Dic3—64no—
436#126—91no—
437#126—271no—
438#126—271no—
439#126—271no—
440#126—271no—
441#126—271no—
442#126—271no—
443#126—271no—
444C2×C4⋊C4—31no—
445C2×C4⋊C4—271no—
446C2×C4⋊C4—271no—
447C2×C22⋊C4—271no—
448C2×C22⋊C4—271no—
449C2×C22⋊C4—271no—
450C2×C42—271no—
451C33C2×#12611yescharacteristic, complemented, Sylow
452C23×C3—34no—
453C23×C3—91no—
454C22×D3—34no—
455C22×D3—94no—
456C22×D3—91no—
457C22×D3—184no—
458C22×D3—188no—
459C22×D3—188no—
460C22×D3—188no—
461C22×D3—182no—
462C22×D3—182no—
463C22×D3—182no—
464C22×D3C22×C3⋊D311yescharacteristic
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—24no—
468C2×C3×C4—34no—
469C2×C3×C4—34no—
470C2×C3×C4—34no—
471C2×C3×C4—68no—
472C2×C3×C4—68no—
473C2×C3×C4—68no—
474C2×C3×C4—91no—
475C2×C3×C4—91no—
476C2×C3×C4—91no—
477C2×C3×C4C2×D3214yes—
478C2×C3×C4C2×D3214yes—
479C2×C3×C4C2×D3214yes—
480C2×C3×C4C22×C3⋊D311yescharacteristic
481C2×C3×C4C22×C3⋊D311yescharacteristic
482C2×C3×C4C22×C3⋊D311yescharacteristic
483C2×Dic3—34no—
484C2×Dic3—34no—
485C2×Dic3—34no—
486C2×Dic3—94no—
487C2×Dic3—94no—
488C2×Dic3—94no—
489C2×Dic3—91no—
490C2×Dic3—91no—
491C2×Dic3—91no—
492C2×Dic3—184no—
493C2×Dic3—184no—
494C2×Dic3—184no—
495C2×Dic3—188no—
496C2×Dic3—188no—
497C2×Dic3—188no—
498C2×Dic3C22×C3⋊D311yescharacteristic
499C2×Dic3C22×C3⋊D311yescharacteristic
500C2×Dic3C22×C3⋊D311yescharacteristic
501C4×D3—22no—
502C4×D3—22no—
503C4×D3—22no—
504C4×D3—182no—
505C4×D3—182no—
506C4×D3—182no—
507C2×C32—24no—
508C2×C32—24no—
509C2×C32—24no—
510C2×C32—34no—
511C2×C32C2×#23514yes—
512C2×C32C2×#23714yes—
513C2×C32C2×#23914yes—
514C2×C32D3×#4111yescharacteristic
515C2×C32D3×#4111yescharacteristic
516C2×C32D3×#4111yescharacteristic
517C3⋊D3—41no—
518C3⋊D3—121no—
519C3⋊D3—124no—
520C3⋊D3—244no—
521C3×D3—124no—
522C3×D3#898116yescomplemented
523C24—271no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—31no—
527C22×C4—271no—
528C22×C4—271no—
529C22×C4—271no—
530C4⋊C4—31no—
531C4⋊C4—31no—
532C4⋊C4—31no—
533C4⋊C4—91no—
534C4⋊C4—91no—
535C4⋊C4—271no—
536C4⋊C4—271no—
537C4⋊C4—271no—
538C4⋊C4—271no—
539C4⋊C4—271no—
540C4⋊C4—271no—
541C4⋊C4D3×C3⋊D311yescharacteristic, complemented
542C22⋊C4—91no—
543C22⋊C4—91no—
544C22⋊C4—91no—
545C22⋊C4—271no—
546C22⋊C4—271no—
547C22⋊C4—271no—
548C22⋊C4—271no—
549C22⋊C4—271no—
550C22⋊C4—271no—
551C22⋊C4—271no—
552C22⋊C4—271no—
553C22⋊C4—271no—
554C42—91no—
555C42—271no—
556C42—271no—
557C42—271no—
558C22×C3—24no—
559C22×C3—38no—
560C22×C3—38no—
561C22×C3—38no—
562C22×C3—181no—
563C22×C3—181no—
564C22×C3—181no—
565C22×C3C22×D3214yes—
566C22×C3C23×C3⋊D311yescharacteristic
567C2×D3—64no—
568C2×D3—64no—
569C2×D3—64no—
570C2×D3—184no—
571C2×D3—184no—
572C2×D3—184no—
573C2×D3—181no—
574C2×D3—181no—
575C2×D3—181no—
576C2×D3—364no—
577C2×D3—364no—
578C2×D3—364no—
579C2×D3—3616no—
580C2×D3—364no—
581C2×D3#382812yes—
582C2×D3#383012yes—
583C2×D3#383212yes—
584C3×C4—24no—
585C3×C4—24no—
586C3×C4—24no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—44no—
591C3×C4—44no—
592C3×C4—44no—
593C3×C4—64no—
594C3×C4—64no—
595C3×C4—64no—
596C3×C4—181no—
597C3×C4—181no—
598C3×C4—181no—
599Dic3—21no—
600Dic3—21no—
601Dic3—21no—
602Dic3—64no—
603Dic3—64no—
604Dic3—64no—
605Dic3—184no—
606Dic3—184no—
607Dic3—184no—
608Dic3—181no—
609Dic3—181no—
610Dic3—181no—
611Dic3—364no—
612Dic3—364no—
613Dic3—364no—
614C32—24no—
615C32C2×#89814yescomplemented
616C32D3×#12611yescharacteristic, complemented
617C23—31no—
618C23—91no—
619C23—271no—
620C23—542no—
621C23—542no—
622C23—542no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—62no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—91no—
630C2×C4—91no—
631C2×C4—91no—
632C2×C4—271no—
633C2×C4—271no—
634C2×C4—271no—
635C2×C4—542no—
636C2×C4—542no—
637C2×C4—542no—
638C2×C4C2×D3×C3⋊D311yescharacteristic
639C2×C4C2×D3×C3⋊D311yescharacteristic
640C2×C4C2×D3×C3⋊D311yescharacteristic
641C2×C3—24no—
642C2×C3—24no—
643C2×C3—24no—
644C2×C3—316no—
645C2×C3—361no—
646C2×C3D3×#23514yes—
647C2×C3D3×#23714yes—
648C2×C3D3×#23914yes—
649C2×C3C2×#382811yescharacteristic
650C2×C3C2×#383011yescharacteristic
651C2×C3C2×#383211yescharacteristic
652D3—124no—
653D3—364no—
654D3—361no—
655D3—724no—
656D3#6410714yesdirect product factor
657C22—32no—
658C22—32no—
659C22—32no—
660C22—181no—
661C22—181no—
662C22—181no—
663C22—541no—
664C22—541no—
665C22—541no—
666C22—1084no—
667C22C22×D3×C3⋊D311yescharacteristic
668C4—21no—
669C4—21no—
670C4—21no—
671C4—61no—
672C4—61no—
673C4—61no—
674C4—181no—
675C4—181no—
676C4—181no—
677C4—541no—
678C4—541no—
679C4—541no—
680C3—24no—
681C3D3×#89814yescomplemented
682C3C2×#6410711yescharacteristic, complemented
683C2—34no—
684C2—361no—
685C2—1081no—
686C2D3×#382811yescharacteristic
687C2D3×#383011yescharacteristic
688C2D3×#383211yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC22×D3×C3⋊D3C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33C2×#126
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723939C2semidirect
2. C3×#64107C2semidirect
3. C32×D3×C4⋊C4C2semidirect
7. D3×C4⋊(C3⋊Dic3)C2semidirect
8. D3×#3750C2semidirect
9. C4×D3×C3⋊Dic3C2semidirect
10. #11723446C2semidirect
11. #11723433C2semidirect
12. #11723411C2semidirect
13. #11723408C2semidirect
14. #11723407C2semidirect
15. #11723403C2semidirect
25. C33×C4⋊C4C22semidirect
29. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
30. #88857C22semidirect
31. C4×C3⋊(C3⋊Dic3)C22semidirect
35. C3×C4⋊(C3⋊Dic3)C22semidirect
36. C3×#3750C22semidirect
37. C3×C4×C3⋊Dic3C22semidirect
38. C32×C4⋊Dic3C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. C32×Dic3⋊C4C22semidirect
41. #88807C22semidirect
42. #88806C22semidirect
43. Dic3⋊(C3⋊Dic3)C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. Dic3×C3⋊Dic3C22semidirect
69. #64107D3direct (N × H)
71. C3×D3×C4⋊C4D3semidirect
128. C32×C4⋊C4C2×D3semidirect
129. C32×C4⋊C4C2×D3semidirect
153. C4⋊(C3⋊Dic3)C2×D3semidirect
159. #3750C2×D3semidirect
165. C4×C3⋊Dic3C2×D3semidirect
170. C3×C4⋊Dic3C2×D3semidirect
172. C3×Dic3⋊C4C2×D3semidirect
173. C3×Dic3⋊C4C2×D3semidirect
232. D3×C4⋊C4C3⋊D3semidirect
302. C32×D3#126semidirect
323. C3×C4⋊C4D32semidirect
324. C3×C4⋊C4C2×C3⋊D3semidirect
360. C4⋊Dic3C2×C3⋊D3semidirect
370. Dic3⋊C4C2×C3⋊D3semidirect
371. Dic3⋊C4C2×C3⋊D3semidirect
451. C33C2×#126semidirect
522. C3×D3#898semidirect
541. C4⋊C4D3×C3⋊D3semidirect
615. C32C2×#898semidirect
616. C32D3×#126semidirect
656. D3#64107direct (N × H)
681. C3D3×#898semidirect
682. C3C2×#64107semidirect

Maximal subgroups

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

subgroupindex
#117239392
C3×#641072
C32×D3×C4⋊C42
D3×#37522
D3×C4⋊(C3⋊Dic3)2
D3×#37502
C4×D3×C3⋊Dic32
#117234462
#117234332
#117234112
#117234082
#117234072
#117234032
C2×#641073
D3×#8983