Finite Group Databasebeta

← D3×C22⋊C4×C3⋊D3 #13175907

Subgroups — D3×C22⋊C4×C3⋊D3 #13175907

Order 1728.

4572 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×C3⋊D3C211yesmaximal, characteristic
2C2×C4×D3×C3⋊D3C212yesmaximal, complemented
3C22⋊C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
5C32×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6#11723627C211yesmaximal, characteristic, complemented
7C3⋊D3×#217C211yesmaximal, characteristic, complemented
8D3×#3757C211yesmaximal, characteristic, complemented
9#11723539C212yesmaximal, complemented
10C3⋊D3×(C2×D3)⋊C4C212yesmaximal, complemented
11D3×#3752C212yesmaximal, complemented
12C2×C22⋊C4×C3⋊D3—31nomaximal
13D32×C22⋊C4—34nomaximal
14C23×C3⋊(C3⋊D3)C2211yescharacteristic
15C23×C3×C3⋊D3C2211yescharacteristic
16C23×C32×D3C2211yescharacteristic
17C22×D3×C3⋊D3—28no—
18C22×D3×C3⋊D3C418yescomplemented
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C22×D3×C3⋊D3C2211yescharacteristic
22C22×D3×C3⋊D3C2211yescharacteristic
23C2×C4×C3⋊(C3⋊D3)C2212yescomplemented
24C2×C3×C4×C3⋊D3C2212yescomplemented
25C2×C32×C4×D3C2212yescomplemented
26C2×#6289C2212yescomplemented
27C2×Dic3×C3⋊D3C2212yescomplemented
28C2×D3×C3⋊Dic3C2212yescomplemented
29C4×D3×C3⋊D3—28no—
30C33×C22⋊C4C2211yescharacteristic, complemented
31#88864C2211yescharacteristic, complemented
32#88859C2212yescomplemented
33C3×#3757C2211yescharacteristic, complemented
34C3×#3752C2212yescomplemented
35C32×#217C2211yescharacteristic, complemented
36C32×(C2×D3)⋊C4C2212yescomplemented
37#88804C2212yescomplemented
38#88803C2212yescomplemented
39(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
40C24×C3⋊D3—31no—
41C23×D32—34no—
42C22×C4×C3⋊D3—32no—
43C2×C4×D32—38no—
44C2×C32×C22⋊C4—31no—
45C2×#3757—31no—
46C2×#3752—32no—
47C22⋊C4×C3⋊D3—32no—
48C22⋊C4×C3⋊D3—31no—
49C22⋊C4×C3⋊D3—31no—
50C22⋊C4×C3⋊D3—32no—
51C22⋊C4×C3⋊D3—34no—
52C22⋊C4×C3⋊D3—31no—
53C22⋊C4×C3⋊D3—64no—
54C22⋊C4×C3⋊D3D311yescharacteristic, direct product factor
55C3×D3×C22⋊C4—34no—
56C3×D3×C22⋊C4D314yescomplemented
57#63974—34no—
58D3×#217—34no—
59D3×#217—34no—
60#63921—38no—
61D3×(C2×D3)⋊C4—38no—
62D3×(C2×D3)⋊C4—38no—
63C23×C33C2311yescharacteristic
64C22×C3⋊(C3⋊D3)—24no—
65C22×C3⋊(C3⋊D3)C2×C414yescomplemented
66C22×C3⋊(C3⋊D3)C2311yescharacteristic
67C22×C3⋊(C3⋊D3)C2311yescharacteristic
68C22×C3×C3⋊D3—24no—
69C22×C3×C3⋊D3C2×C414yescomplemented
70C22×C3×C3⋊D3C2311yescharacteristic
71C22×C3×C3⋊D3C2311yescharacteristic
72C22×C32×D3—24no—
73C22×C32×D3C2×C414yescomplemented
74C22×C32×D3C2311yescharacteristic
75C22×C32×D3C2311yescharacteristic
76C2×D3×C3⋊D3—24no—
77C2×D3×C3⋊D3—24no—
78C2×D3×C3⋊D3—24no—
79C2×D3×C3⋊D3—232no—
80C2×D3×C3⋊D3C2×C414yes—
81C2×D3×C3⋊D3C2×C414yescomplemented
82C2×D3×C3⋊D3C2×C414yescomplemented
83C2×D3×C3⋊D3C2×C414yescomplemented
84C2×D3×C3⋊D3D418yes—
85C2×C33×C4C2312yescomplemented
86C2×C3⋊(C3⋊Dic3)C2312yescomplemented
87C4×C3⋊(C3⋊D3)—24no—
88C2×C3×C3⋊Dic3C2312yescomplemented
89C3×C4×C3⋊D3—24no—
90C2×C32×Dic3C2312yescomplemented
91C32×C4×D3—24no—
92#6289—24no—
93Dic3×C3⋊D3—24no—
94D3×C3⋊Dic3—24no—
95C2×D3×C22⋊C4—94no—
96C2×D3×C22⋊C4—91no—
97C24×C32—31no—
98C23×C3⋊D3—31no—
99C23×C3⋊D3—31no—
100C23×C3⋊D3—34no—
101C23×C3⋊D3—38no—
102C23×C3⋊D3—31no—
103C23×C3⋊D3—31no—
104C23×C3⋊D3—31no—
105C23×C3⋊D3—68no—
106C23×C3⋊D3—64no—
107C23×C3⋊D3C2×D311yescharacteristic
108C23×C3×D3—34no—
109C23×C3×D3C2×D314yes—
110C22×D32—34no—
111C22×D32—332no—
112C22×D32—34no—
113C22×D32—34no—
114C22×D32—34no—
115C22×D32—632no—
116C22×C32×C4—32no—
117C22×C3⋊Dic3—32no—
118C2×C4×C3⋊D3—32no—
119C2×C4×C3⋊D3—32no—
120C2×C4×C3⋊D3—38no—
121C2×C4×C3⋊D3—32no—
122C2×C4×C3⋊D3—68no—
123C2×C4×C3⋊D3—68no—
124C2×C4×C3⋊D3C2×D312yescomplemented
125C2×C3×C4×D3—38no—
126C2×C3×C4×D3C2×D318yescomplemented
127C2×#624—38no—
128C2×D3×Dic3—38no—
129C2×D3×Dic3—38no—
130C4×D32—632no—
131C32×C22⋊C4—24no—
132C32×C22⋊C4—31no—
133C32×C22⋊C4—32no—
134C32×C22⋊C4C2×D314yescomplemented
135C32×C22⋊C4C2×D311yescharacteristic, complemented
136#3757—31no—
137#3757—34no—
138#3757—32no—
139#3757—64no—
140#3757C2×D311yescharacteristic, complemented
141#3752—32no—
142#3752—32no—
143#3752—38no—
144#3752—32no—
145#3752—68no—
146#3752C2×D312yescomplemented
147C3×#217—34no—
148C3×#217C2×D314yescomplemented
149C3×(C2×D3)⋊C4—38no—
150C3×(C2×D3)⋊C4C2×D318yescomplemented
151#3722—38no—
152(C2×D3)⋊Dic3—38no—
153(C2×D3)⋊Dic3—38no—
154C22×C33—22no—
155C22×C33C22×C412yescomplemented
156C22×C33C2411yescharacteristic
157C2×C3⋊(C3⋊D3)—22no—
158C2×C3⋊(C3⋊D3)—28no—
159C2×C3⋊(C3⋊D3)C22×C412yes—
160C2×C3⋊(C3⋊D3)C22×C412yescomplemented
161C2×C3⋊(C3⋊D3)C2×D414yes—
162C2×C3×C3⋊D3—22no—
163C2×C3×C3⋊D3—28no—
164C2×C3×C3⋊D3C22×C412yes—
165C2×C3×C3⋊D3C22×C412yescomplemented
166C2×C3×C3⋊D3C2×D414yes—
167C2×C32×D3—22no—
168C2×C32×D3—28no—
169C2×C32×D3C22×C412yes—
170C2×C32×D3C22×C412yescomplemented
171C2×C32×D3C2×D414yes—
172D3×C3⋊D3—28no—
173D3×C3⋊D3—28no—
174D3×C3⋊D3—28no—
175D3×C3⋊D3C22⋊C4116yesdirect product factor
176C33×C4—22no—
177C3⋊(C3⋊Dic3)—22no—
178C3×C3⋊Dic3—22no—
179C32×Dic3—22no—
180C24×D3—94no—
181C24×D3—91no—
182C22×C4×D3—98no—
183C22×C4×D3—92no—
184C2×C3×C22⋊C4—34no—
185C2×C3×C22⋊C4—91no—
186C2×#217—94no—
187C2×#217—91no—
188C2×(C2×D3)⋊C4—98no—
189C2×(C2×D3)⋊C4—92no—
190D3×C22⋊C4—34no—
191D3×C22⋊C4—98no—
192D3×C22⋊C4—94no—
193D3×C22⋊C4—98no—
194D3×C22⋊C4—94no—
195D3×C22⋊C4—91no—
196D3×C22⋊C4—92no—
197D3×C22⋊C4—94no—
198D3×C22⋊C4—91no—
199D3×C22⋊C4—91no—
200D3×C22⋊C4—92no—
201D3×C22⋊C4—184no—
202D3×C22⋊C4C3⋊D311yescharacteristic, direct product factor
203C23×C32—24no—
204C23×C32—31no—
205C23×C32—34no—
206C23×C32—31no—
207C23×C32—64no—
208C23×C32C22×D314yes—
209C23×C32C22×D311yescharacteristic
210C22×C3⋊D3—24no—
211C22×C3⋊D3—31no—
212C22×C3⋊D3—34no—
213C22×C3⋊D3—38no—
214C22×C3⋊D3—34no—
215C22×C3⋊D3—31no—
216C22×C3⋊D3—34no—
217C22×C3⋊D3—34no—
218C22×C3⋊D3—34no—
219C22×C3⋊D3—34no—
220C22×C3⋊D3—316no—
221C22×C3⋊D3—34no—
222C22×C3⋊D3—64no—
223C22×C3⋊D3—64no—
224C22×C3⋊D3—616no—
225C22×C3⋊D3—64no—
226C22×C3⋊D3—632no—
227C22×C3⋊D3—64no—
228C22×C3⋊D3—64no—
229C22×C3⋊D3—64no—
230C22×C3⋊D3—616no—
231C22×C3⋊D3—1216no—
232C22×C3⋊D3C4×D314yescomplemented
233C22×C3⋊D3C22×D311yescharacteristic
234C22×C3⋊D3C22×D311yescharacteristic
235C22×C3×D3—216no—
236C22×C3×D3—34no—
237C22×C3×D3—316no—
238C22×C3×D3—34no—
239C22×C3×D3—616no—
240C22×C3×D3C4×D3116yescomplemented
241C22×C3×D3C22×D314yes—
242C22×C3×D3C22×D314yes—
243C2×D32—316no—
244C2×D32—332no—
245C2×D32—316no—
246C2×D32—316no—
247C2×D32—316no—
248C2×D32—6128no—
249C2×D32—616no—
250C2×D32—616no—
251C2×D32—616no—
252C2×C32×C4—28no—
253C2×C32×C4—32no—
254C2×C32×C4—64no—
255C2×C32×C4C22×D318yescomplemented
256C2×C32×C4C22×D312yescomplemented
257C2×C3⋊Dic3—32no—
258C2×C3⋊Dic3—38no—
259C2×C3⋊Dic3—68no—
260C2×C3⋊Dic3—64no—
261C2×C3⋊Dic3C22×D312yescomplemented
262C4×C3⋊D3—24no—
263C4×C3⋊D3—64no—
264C4×C3⋊D3—64no—
265C4×C3⋊D3—64no—
266C4×C3⋊D3—616no—
267C4×C3⋊D3—1216no—
268C2×C3×Dic3—38no—
269C2×C3×Dic3C22×D318yescomplemented
270C3×C4×D3—216no—
271C3×C4×D3—616no—
272#624—616no—
273D3×Dic3—616no—
274D3×Dic3—616no—
275C22×C22⋊C4—271noSylow
276C2×C33—22no—
277C2×C33C23×C411yescharacteristic
278C2×C33C22×D412yes—
279C3⋊(C3⋊D3)—22no—
280C3⋊(C3⋊D3)C2×C22⋊C414yescomplemented
281C3×C3⋊D3—22no—
282C3×C3⋊D3C2×C22⋊C414yescomplemented
283C32×D3—22no—
284C32×D3C2×C22⋊C414yescomplemented
285C24×C3—34no—
286C24×C3—91no—
287C23×D3—34no—
288C23×D3—94no—
289C23×D3—94no—
290C23×D3—94no—
291C23×D3—94no—
292C23×D3—932no—
293C23×D3—91no—
294C23×D3—94no—
295C23×D3—91no—
296C23×D3—98no—
297C23×D3—91no—
298C23×D3—91no—
299C23×D3—91no—
300C23×D3—184no—
301C23×D3—188no—
302C23×D3—1832no—
303C23×D3C2×C3⋊D311yescharacteristic
304C22×C3×C4—38no—
305C22×C3×C4—92no—
306C22×Dic3—98no—
307C22×Dic3—92no—
308C2×C4×D3—38no—
309C2×C4×D3—98no—
310C2×C4×D3—98no—
311C2×C4×D3—92no—
312C2×C4×D3—98no—
313C2×C4×D3—92no—
314C2×C4×D3—92no—
315C2×C4×D3—188no—
316C2×C4×D3—188no—
317C2×C4×D3—1832no—
318C2×C4×D3C2×C3⋊D312yescomplemented
319C3×C22⋊C4—24no—
320C3×C22⋊C4—34no—
321C3×C22⋊C4—38no—
322C3×C22⋊C4—91no—
323C3×C22⋊C4—92no—
324C3×C22⋊C4D3214yescomplemented
325C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
326#217—34no—
327#217—98no—
328#217—94no—
329#217—91no—
330#217—92no—
331#217—184no—
332#217C2×C3⋊D311yescharacteristic, complemented
333(C2×D3)⋊C4—38no—
334(C2×D3)⋊C4—98no—
335(C2×D3)⋊C4—98no—
336(C2×D3)⋊C4—92no—
337(C2×D3)⋊C4—98no—
338(C2×D3)⋊C4—92no—
339(C2×D3)⋊C4—92no—
340(C2×D3)⋊C4—188no—
341(C2×D3)⋊C4C2×C3⋊D312yescomplemented
342C22×C32—22no—
343C22×C32—24no—
344C22×C32—28no—
345C22×C32—28no—
346C22×C32—32no—
347C22×C32—34no—
348C22×C32—32no—
349C22×C32—48no—
350C22×C32—68no—
351C22×C32—62no—
352C22×C32C2×C4×D318yescomplemented
353C22×C32C2×C4×D312yescomplemented
354C22×C32C23×D314yes—
355C22×C32C23×D311yescharacteristic
356C2×C3⋊D3—22no—
357C2×C3⋊D3—28no—
358C2×C3⋊D3—32no—
359C2×C3⋊D3—34no—
360C2×C3⋊D3—316no—
361C2×C3⋊D3—32no—
362C2×C3⋊D3—38no—
363C2×C3⋊D3—316no—
364C2×C3⋊D3—38no—
365C2×C3⋊D3—68no—
366C2×C3⋊D3—616no—
367C2×C3⋊D3—68no—
368C2×C3⋊D3—68no—
369C2×C3⋊D3—68no—
370C2×C3⋊D3—68no—
371C2×C3⋊D3—62no—
372C2×C3⋊D3—68no—
373C2×C3⋊D3—632no—
374C2×C3⋊D3—68no—
375C2×C3⋊D3—1232no—
376C2×C3⋊D3—128no—
377C2×C3⋊D3C2×C4×D312yes—
378C2×C3⋊D3C2×C4×D312yescomplemented
379C2×C3⋊D3D3×D414yes—
380C2×C3×D3—28no—
381C2×C3×D3—232no—
382C2×C3×D3—38no—
383C2×C3×D3—316no—
384C2×C3×D3—38no—
385C2×C3×D3—632no—
386C2×C3×D3—68no—
387C2×C3×D3C2×C4×D318yes—
388C2×C3×D3C2×C4×D318yescomplemented
389C2×C3×D3D3×D4116yes—
390D32—364no—
391D32—632no—
392D32—632no—
393D32—632no—
394C32×C4—22no—
395C32×C4—28no—
396C32×C4—48no—
397C32×C4—62no—
398C3⋊Dic3—22no—
399C3⋊Dic3—62no—
400C3⋊Dic3—68no—
401C3⋊Dic3—128no—
402C3×Dic3—28no—
403C3×Dic3—68no—
404C25—271no—
405C23×C4—272no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—271no—
409C2×C22⋊C4—272no—
410C2×C22⋊C4—272no—
411C2×C22⋊C4—271no—
412C2×C22⋊C4—272no—
413C2×C22⋊C4—271no—
414C2×C22⋊C4—271no—
415C33C22×C22⋊C411yescharacteristic, complemented, Sylow
416C23×C3—24no—
417C23×C3—34no—
418C23×C3—34no—
419C23×C3—316no—
420C23×C3—616no—
421C23×C3—91no—
422C23×C3—91no—
423C23×C3—94no—
424C23×C3—184no—
425C23×C3C2×D3214yes—
426C23×C3C22×C3⋊D311yescharacteristic
427C22×D3—24no—
428C22×D3—34no—
429C22×D3—34no—
430C22×D3—316no—
431C22×D3—616no—
432C22×D3—932no—
433C22×D3—916no—
434C22×D3—916no—
435C22×D3—916no—
436C22×D3—916no—
437C22×D3—94no—
438C22×D3—91no—
439C22×D3—94no—
440C22×D3—98no—
441C22×D3—94no—
442C22×D3—91no—
443C22×D3—916no—
444C22×D3—94no—
445C22×D3—94no—
446C22×D3—94no—
447C22×D3—94no—
448C22×D3—184no—
449C22×D3—184no—
450C22×D3—1816no—
451C22×D3—184no—
452C22×D3—1832no—
453C22×D3—184no—
454C22×D3—1816no—
455C22×D3—18128no—
456C22×D3—1816no—
457C22×D3—1816no—
458C22×D3—184no—
459C22×D3—1816no—
460C22×D3—184no—
461C22×D3—3616no—
462C22×D3C4×C3⋊D314yescomplemented
463C22×D3C22×C3⋊D311yescharacteristic
464C22×D3C22×C3⋊D311yescharacteristic
465C2×C3×C4—28no—
466C2×C3×C4—38no—
467C2×C3×C4—616no—
468C2×C3×C4—92no—
469C2×C3×C4—184no—
470C2×C3×C4C2×D3218yescomplemented
471C2×C3×C4C22×C3⋊D312yescomplemented
472C2×Dic3—38no—
473C2×Dic3—98no—
474C2×Dic3—92no—
475C2×Dic3—188no—
476C2×Dic3—184no—
477C2×Dic3—1816no—
478C2×Dic3C22×C3⋊D312yescomplemented
479C4×D3—24no—
480C4×D3—616no—
481C4×D3—184no—
482C4×D3—1816no—
483C4×D3—184no—
484C4×D3—1816no—
485C4×D3—1816no—
486C4×D3—184no—
487C4×D3—3616no—
488C2×C32—22no—
489C2×C32—24no—
490C2×C32—28no—
491C2×C32—28no—
492C2×C32—34no—
493C2×C32—48no—
494C2×C32—62no—
495C2×C32C22×C4×D314yes—
496C2×C32C22×C4×D311yescharacteristic
497C2×C32C2×D3×D418yes—
498C2×C32C2×D3×D412yes—
499C3⋊D3—22no—
500C3⋊D3—34no—
501C3⋊D3—316no—
502C3⋊D3—616no—
503C3⋊D3—62no—
504C3⋊D3—68no—
505C3⋊D3—128no—
506C3⋊D3D3×C22⋊C414yesdirect product factor
507C3×D3—28no—
508C3×D3—316no—
509C3×D3—68no—
510C3×D3D3×C22⋊C4116yescomplemented
511C24—31no—
512C24—91no—
513C24—271no—
514C24—271no—
515C24—271no—
516C24—271no—
517C24—278no—
518C24—271no—
519C24—548no—
520C22×C4—32no—
521C22×C4—92no—
522C22×C4—272no—
523C22×C4—272no—
524C22×C4—272no—
525C22×C4—272no—
526C22×C4—548no—
527C22⋊C4—31no—
528C22⋊C4—32no—
529C22⋊C4—91no—
530C22⋊C4—92no—
531C22⋊C4—272no—
532C22⋊C4—272no—
533C22⋊C4—272no—
534C22⋊C4—271no—
535C22⋊C4—272no—
536C22⋊C4D3×C3⋊D311yescharacteristic, direct product factor
537C22×C3—28no—
538C22×C3—22no—
539C22×C3—24no—
540C22×C3—28no—
541C22×C3—38no—
542C22×C3—316no—
543C22×C3—38no—
544C22×C3—48no—
545C22×C3—632no—
546C22×C3—68no—
547C22×C3—92no—
548C22×C3—94no—
549C22×C3—92no—
550C22×C3—188no—
551C22×C3—182no—
552C22×C3C4×D3218yescomplemented
553C22×C3C2×C4×C3⋊D312yescomplemented
554C22×C3C22×D3214yes—
555C22×C3C23×C3⋊D311yescharacteristic
556C2×D3—22no—
557C2×D3—28no—
558C2×D3—38no—
559C2×D3—316no—
560C2×D3—38no—
561C2×D3—632no—
562C2×D3—68no—
563C2×D3—964no—
564C2×D3—98no—
565C2×D3—916no—
566C2×D3—92no—
567C2×D3—94no—
568C2×D3—916no—
569C2×D3—98no—
570C2×D3—92no—
571C2×D3—1816no—
572C2×D3—188no—
573C2×D3—188no—
574C2×D3—188no—
575C2×D3—188no—
576C2×D3—1832no—
577C2×D3—1832no—
578C2×D3—1832no—
579C2×D3—188no—
580C2×D3—1832no—
581C2×D3—188no—
582C2×D3—182no—
583C2×D3—188no—
584C2×D3—3632no—
585C2×D3—368no—
586C2×D3C2×C4×C3⋊D312yes—
587C2×D3C2×C4×C3⋊D312yescomplemented
588C2×D3D4×C3⋊D314yes—
589C3×C4—28no—
590C3×C4—22no—
591C3×C4—48no—
592C3×C4—68no—
593C3×C4—182no—
594Dic3—22no—
595Dic3—68no—
596Dic3—188no—
597Dic3—182no—
598Dic3—368no—
599C32—24no—
600C32C2×D3×C22⋊C414yescomplemented
601C32C2×D3×C22⋊C411yescharacteristic, complemented
602C23—31no—
603C23—31no—
604C23—34no—
605C23—64no—
606C23—91no—
607C23—91no—
608C23—94no—
609C23—184no—
610C23—278no—
611C23—274no—
612C23—274no—
613C23—274no—
614C23—274no—
615C23—271no—
616C23—271no—
617C23—274no—
618C23—544no—
619C23—544no—
620C23—544no—
621C23—5432no—
622C23—544no—
623C23C2×D3×C3⋊D311yescharacteristic
624C2×C4—32no—
625C2×C4—64no—
626C2×C4—92no—
627C2×C4—184no—
628C2×C4—272no—
629C2×C4—544no—
630C2×C4—544no—
631C2×C4—544no—
632C2×C4—544no—
633C2×C4C2×D3×C3⋊D312yescomplemented
634C2×C3—22no—
635C2×C3—28no—
636C2×C3—24no—
637C2×C3—28no—
638C2×C3—316no—
639C2×C3—48no—
640C2×C3—68no—
641C2×C3—94no—
642C2×C3—182no—
643C2×C3C2×C4×D3214yes—
644C2×C3D32×D418yes—
645C2×C3C22×C4×C3⋊D311yescharacteristic
646C2×C3C2×D4×C3⋊D312yes—
647D3—22no—
648D3—316no—
649D3—68no—
650D3—94no—
651D3—916no—
652D3—1816no—
653D3—182no—
654D3—188no—
655D3—368no—
656D3C22⋊C4×C3⋊D314yesdirect product factor
657C22—22no—
658C22—32no—
659C22—34no—
660C22—32no—
661C22—68no—
662C22—62no—
663C22—92no—
664C22—94no—
665C22—92no—
666C22—188no—
667C22—182no—
668C22—2716no—
669C22—272no—
670C22—274no—
671C22—272no—
672C22—548no—
673C22—548no—
674C22—548no—
675C22—548no—
676C22—542no—
677C22C4×D3×C3⋊D312yescomplemented
678C22C22×D3×C3⋊D311yescharacteristic
679C4—22no—
680C4—62no—
681C4—182no—
682C4—542no—
683C3—24no—
684C3D32×C22⋊C414yescomplemented
685C3C2×C22⋊C4×C3⋊D311yescharacteristic, complemented
686C2—22no—
687C2—34no—
688C2—62no—
689C2—94no—
690C2—182no—
691C2—274no—
692C2—542no—
693C2C2×C4×D3×C3⋊D311yescharacteristic
694C2D3×D4×C3⋊D312yes—
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutatorC2×C33C23×C4
FittingC33×C22⋊C4C22
socle, cosocleC22×C33C24
prime radicalC23×D3×C3⋊D3C2
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33C22×C22⋊C4
LCSG ▷ C2×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. C22⋊C4×C3⋊(C3⋊D3)C2semidirect
4. C3×C22⋊C4×C3⋊D3C2semidirect
5. C32×D3×C22⋊C4C2semidirect
6. #11723627C2semidirect
7. C3⋊D3×#217C2semidirect
8. D3×#3757C2semidirect
9. #11723539C2semidirect
10. C3⋊D3×(C2×D3)⋊C4C2semidirect
11. D3×#3752C2semidirect
18. C22×D3×C3⋊D3C4semidirect
23. C2×C4×C3⋊(C3⋊D3)C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
25. C2×C32×C4×D3C22semidirect
26. C2×#6289C22semidirect
27. C2×Dic3×C3⋊D3C22semidirect
28. C2×D3×C3⋊Dic3C22semidirect
30. C33×C22⋊C4C22semidirect
31. #88864C22semidirect
32. #88859C22semidirect
33. C3×#3757C22semidirect
34. C3×#3752C22semidirect
35. C32×#217C22semidirect
36. C32×(C2×D3)⋊C4C22semidirect
37. #88804C22semidirect
38. #88803C22semidirect
39. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. C22⋊C4×C3⋊D3D3direct (N × H)
56. C3×D3×C22⋊C4D3semidirect
65. C22×C3⋊(C3⋊D3)C2×C4semidirect
69. C22×C3×C3⋊D3C2×C4semidirect
73. C22×C32×D3C2×C4semidirect
81. C2×D3×C3⋊D3C2×C4semidirect
82. C2×D3×C3⋊D3C2×C4semidirect
83. C2×D3×C3⋊D3C2×C4semidirect
85. C2×C33×C4C23semidirect
86. C2×C3⋊(C3⋊Dic3)C23semidirect
88. C2×C3×C3⋊Dic3C23semidirect
90. C2×C32×Dic3C23semidirect
124. C2×C4×C3⋊D3C2×D3semidirect
126. C2×C3×C4×D3C2×D3semidirect
134. C32×C22⋊C4C2×D3semidirect
135. C32×C22⋊C4C2×D3semidirect
140. #3757C2×D3semidirect
146. #3752C2×D3semidirect
148. C3×#217C2×D3semidirect
150. C3×(C2×D3)⋊C4C2×D3semidirect
155. C22×C33C22×C4semidirect
160. C2×C3⋊(C3⋊D3)C22×C4semidirect
165. C2×C3×C3⋊D3C22×C4semidirect
170. C2×C32×D3C22×C4semidirect
175. D3×C3⋊D3C22⋊C4direct (N × H)
202. D3×C22⋊C4C3⋊D3direct (N × H)
232. C22×C3⋊D3C4×D3semidirect
240. C22×C3×D3C4×D3semidirect
255. C2×C32×C4C22×D3semidirect
256. C2×C32×C4C22×D3semidirect
261. C2×C3⋊Dic3C22×D3semidirect
269. C2×C3×Dic3C22×D3semidirect
280. C3⋊(C3⋊D3)C2×C22⋊C4semidirect
282. C3×C3⋊D3C2×C22⋊C4semidirect
284. C32×D3C2×C22⋊C4semidirect
318. C2×C4×D3C2×C3⋊D3semidirect
324. C3×C22⋊C4D32semidirect
325. C3×C22⋊C4C2×C3⋊D3semidirect
332. #217C2×C3⋊D3semidirect
341. (C2×D3)⋊C4C2×C3⋊D3semidirect
352. C22×C32C2×C4×D3semidirect
353. C22×C32C2×C4×D3semidirect
378. C2×C3⋊D3C2×C4×D3semidirect
388. C2×C3×D3C2×C4×D3semidirect
415. C33C22×C22⋊C4semidirect
462. C22×D3C4×C3⋊D3semidirect
470. C2×C3×C4C2×D32semidirect
471. C2×C3×C4C22×C3⋊D3semidirect
478. C2×Dic3C22×C3⋊D3semidirect
506. C3⋊D3D3×C22⋊C4direct (N × H)
510. C3×D3D3×C22⋊C4semidirect
536. C22⋊C4D3×C3⋊D3direct (N × H)
552. C22×C3C4×D32semidirect
553. C22×C3C2×C4×C3⋊D3semidirect
587. C2×D3C2×C4×C3⋊D3semidirect
600. C32C2×D3×C22⋊C4semidirect
601. C32C2×D3×C22⋊C4semidirect
633. C2×C4C2×D3×C3⋊D3semidirect
656. D3C22⋊C4×C3⋊D3direct (N × H)
677. C22C4×D3×C3⋊D3semidirect
684. C3D32×C22⋊C4semidirect
685. C3C2×C22⋊C4×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
C23×D3×C3⋊D32
C2×C4×D3×C3⋊D32
C22⋊C4×C3⋊(C3⋊D3)2
C3×C22⋊C4×C3⋊D32
C32×D3×C22⋊C42
#117236272
C3⋊D3×#2172
D3×#37572
#117235392
C3⋊D3×(C2×D3)⋊C42
D3×#37522
C2×C22⋊C4×C3⋊D33
D32×C22⋊C43