Finite Group Databasebeta

← C3⋊D3×#5152 #72245075

Subgroups — C3⋊D3×#5152 #72245075

Order 3456.

4176 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D8×C3⋊D3C211yesmaximal, characteristic
2D4×Dic3×C3⋊D3C212yesmaximal, complemented
3#13163789C211yesmaximal, characteristic, complemented
4C32×#5152C211yesmaximal, characteristic, complemented
5#13160922C212yesmaximal, complemented
6#13160917C212yesmaximal, complemented
7C3⋊D3×#832C212yesmaximal, complemented
8#13159701C211yesmaximal, characteristic, complemented
9#13159688C211yesmaximal, characteristic, complemented
10C3⋊D3×#817C211yesmaximal, characteristic, complemented
11C3⋊D3×#815C211yesmaximal, characteristic, complemented
12D3×#5152—34nomaximal
13C3⋊D3×#442—31nomaximal
14C2×C3×D4×C3⋊D3C2212yes—
15C22×Dic3×C3⋊D3—22no—
16C2×C33×D8C2211yescharacteristic
17D4×C3⋊(C3⋊Dic3)C2212yescomplemented
18C2×C3×#3753C2212yes—
19C3×D8×C3⋊D3C418yescomplemented
20C2×C3×#3745C2211yescharacteristic
21C2×C3×C8×C3⋊D3C2211yescharacteristic
22C32×D4×Dic3C2212yescomplemented
23#11723626—22no—
24C3⋊D3×#217—22no—
25Dic3×#638—22no—
26#11723501C2212yescomplemented
27C3⋊D3×C4⋊Dic3C2212yes—
28Dic3×C4⋊(C3⋊D3)C2212yescomplemented
29C4×Dic3×C3⋊D3C2211yescharacteristic
30C2×C3⋊D3×C3⋊C8C2211yescharacteristic
31#11722202C2212yescomplemented
32#11722187C2211yescharacteristic, complemented
33#11722185C2211yescharacteristic, complemented
34C32×#832C2212yescomplemented
35C32×#817C2211yescharacteristic, complemented
36C32×#815C2211yescharacteristic, complemented
37#11722054C2212yescomplemented
38#11722034C2212yescomplemented
39#11722033C2212yescomplemented
40#11722021C2211yescharacteristic, complemented
41#11722019C2211yescharacteristic, complemented
42C2×D8×C3⋊D3D311yescharacteristic
43C4×D4×C3⋊D3—32no—
44C2×C3×D3×D8—34no—
45D3×D4×Dic3—38no—
46C32×#442—31no—
47#10592851—31no—
48#10592851—34no—
49#10592851—64no—
50#10592713—32no—
51#10592568—31no—
52C3⋊D3×#106—31no—
53#10592484—32no—
54C3⋊D3×#102—32no—
55#10592410—31no—
56C3⋊D3×#97—31no—
57C3×#5152D314yescomplemented
58#10591436—38no—
59#10591430—38no—
60D3×#832—38no—
61#10590781—34no—
62#10590771—34no—
63D3×#817—34no—
64D3×#815—34no—
65C23×C3×C3⋊D3—22no—
66C2×C33×D4C2312yes—
67C22×C3⋊(C3⋊Dic3)—22no—
68C2×C3×#638—22no—
69C3×D4×C3⋊D3—24no—
70C3×D4×C3⋊D3C2×C418yescomplemented
71C2×C3×C4⋊(C3⋊D3)C2312yes—
72C2×C3×C4×C3⋊D3C2311yescharacteristic
73C22×C32×Dic3—22no—
74C2×Dic3×C3⋊D3—22no—
75C2×Dic3×C3⋊D3—22no—
76C2×Dic3×C3⋊D3—22no—
77C2×Dic3×C3⋊D3—48no—
78C2×Dic3×C3⋊D3D412yes—
79C33×D8C2×C414yescomplemented
80C2×C33×C8C2311yescharacteristic
81#88864—22no—
82C4⋊(C3⋊(C3⋊Dic3))C2312yes—
83C4×C3⋊(C3⋊Dic3)C2311yescharacteristic
84C2×C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
85C3×#3753C2×C418yescomplemented
86C2×C3×C3⋊(C3⋊C8)C2311yescharacteristic
87C3×#3745C2×C414yescomplemented
88C3×C8×C3⋊D3C2×C414yescomplemented
89C32×#217—22no—
90C32×C4⋊Dic3C2312yes—
91C32×C4×Dic3C2311yescharacteristic
92C2×C32×C3⋊C8C2311yescharacteristic
93#88807—22no—
94#88803—22no—
95#88803—22no—
96Dic3×C3⋊Dic3D412yes—
97C3⋊D3×C3⋊C8—22no—
98C2×#5152—91no—
99D3×#442—94no—
100C2×D4×C3⋊D3C2×D312yes—
101C22×C4×C3⋊D3—62no—
102C2×C3×D3×D4—38no—
103C22×D3×Dic3—68no—
104C2×C32×D8—24no—
105C2×C32×D8C2×D314yes—
106C2×C32×D8C2×D311yescharacteristic
107C32×C4×D4—32no—
108D4×C3⋊Dic3—32no—
109D4×C3⋊Dic3—38no—
110D4×C3⋊Dic3—68no—
111C2×#3753C2×D312yes—
112C4×#638—62no—
113D8×C3⋊D3Dic318yescomplemented
114C2×#3745C2×D311yescharacteristic
115C2×C8×C3⋊D3—31no—
116C2×C8×C3⋊D3C2×D311yescharacteristic
117#64102—32no—
118C4⋊C4×C3⋊D3—32no—
119#64090—62no—
120C22⋊C4×C3⋊D3—62no—
121C4×C4⋊(C3⋊D3)—32no—
122C42×C3⋊D3—31no—
123C3×D4×Dic3C2×D318yescomplemented
124C2×C3×#213—38no—
125C3×D3×D8—332no—
126C2×C3×D24—34no—
127C2×C3×D3×C8—34no—
128#67⋊Dic3—68no—
129Dic3×#67—68no—
130D3×#217—68no—
131#63898—38no—
132Dic3×D12—38no—
133D3×C4⋊Dic3—38no—
134C4×D3×Dic3—34no—
135C2×D3×C3⋊C8—34no—
136C32×#106—31no—
137C32×#102—32no—
138C32×#97—31no—
139#63659—32no—
140#63659—38no—
141#63659—68no—
142#63648—32no—
143#63644—31no—
144#63644—34no—
145#63644—64no—
146#63642—31no—
147#63642—31no—
148#63642—34no—
149#63642—64no—
150#63636—32no—
151#63635—32no—
152#63630—31no—
153C3×#832C2×D318yescomplemented
154C3×#817C2×D314yescomplemented
155C3×#815C2×D314yescomplemented
156#63573—38no—
157#63563—38no—
158#63562—38no—
159#63555—34no—
160#63554—34no—
161C23×C33—22no—
162C22×C3×C3⋊D3—22no—
163C22×C3×C3⋊D3—28no—
164C22×C3×C3⋊D3—44no—
165C22×C3×C3⋊D3—44no—
166C22×C3×C3⋊D3C2×D411yescharacteristic
167C33×D4—22no—
168C33×D4C22×C414yescomplemented
169C2×C33×C4C2411yescharacteristic
170C2×C3⋊(C3⋊Dic3)—22no—
171C2×C3⋊(C3⋊Dic3)—44no—
172C2×C3⋊(C3⋊Dic3)C2×D412yes—
173C3×#638—28no—
174C2×C3×C3⋊Dic3C2×D411yescharacteristic
175C3×C4⋊(C3⋊D3)—22no—
176C3×C4⋊(C3⋊D3)C22×C414yescomplemented
177C3×C4×C3⋊D3C22×C412yes—
178C3×C4×C3⋊D3#4112yes—
179C2×C32×Dic3—22no—
180C2×C32×Dic3—44no—
181C2×C32×Dic3C2×D412yes—
182Dic3×C3⋊D3—24no—
183Dic3×C3⋊D3—44no—
184Dic3×C3⋊D3—44no—
185Dic3×C3⋊D3—44no—
186C33×C8C22×C412yescomplemented
187C3⋊(C3⋊(C3⋊C8))—21no—
188C3×C3⋊(C3⋊C8)C22×C412yescomplemented
189C32×C3⋊C8—21no—
190C22×C3×D8—91no—
191C2×D4×Dic3—92no—
192C2×D3×D8—34no—
193C4×D3×D4—98no—
194C3×#442—34no—
195C2×#832—92no—
196#5152—94no—
197#5152—91no—
198#5152—92no—
199#5152—92no—
200#5152—91no—
201#5152—91no—
202#5152—184no—
203#5152C3⋊D311yescharacteristic, direct product factor
204C2×#817—91no—
205C2×#815—91no—
206#5014—98no—
207#4869—94no—
208D3×#106—94no—
209#4785—98no—
210D3×#102—98no—
211#4711—94no—
212D3×#97—94no—
213C23×C3⋊D3—22no—
214C23×C3×D3—68no—
215C2×C32×D4—28no—
216C2×C32×D4C22×D318yes—
217C2×C32×D4C22×D312yes—
218C22×C32×C4—62no—
219C2×#638—22no—
220C22×C3⋊Dic3—62no—
221C22×C3⋊Dic3—68no—
222C22×C3⋊Dic3—128no—
223D4×C3⋊D3—24no—
224D4×C3⋊D3C2×Dic318yescomplemented
225C2×C4⋊(C3⋊D3)C22×D312yes—
226C2×C4×C3⋊D3—32no—
227C2×C4×C3⋊D3—62no—
228C2×C4×C3⋊D3—62no—
229C2×C4×C3⋊D3—62no—
230C2×C4×C3⋊D3—128no—
231C2×C4×C3⋊D3C22×D311yescharacteristic
232C2×C3×#67—68no—
233C22×C3×Dic3—28no—
234C3×D3×D4—332no—
235C3×D3×D4—616no—
236C2×C3×D12—38no—
237C2×C3×C4×D3—34no—
238C2×D3×Dic3—38no—
239C2×D3×Dic3—68no—
240C2×D3×Dic3—68no—
241C2×D3×Dic3—68no—
242C2×D3×Dic3—1232no—
243C32×D8—216no—
244C32×D8C4×D3116yescomplemented
245C32×D8C2×Dic314yescomplemented
246C2×C32×C8—24no—
247C2×C32×C8—31no—
248C2×C32×C8C22×D314yes—
249C2×C32×C8C22×D311yescharacteristic
250C32×C4⋊C4—32no—
251C32×C22⋊C4—62no—
252C32×C42—31no—
253#3757—62no—
254#3757—68no—
255#3757—128no—
256#3753C2×Dic318yescomplemented
257#3752—62no—
258#3752—62no—
259C4⋊(C3⋊Dic3)—32no—
260C4⋊(C3⋊Dic3)—38no—
261C4⋊(C3⋊Dic3)—68no—
262#3750—62no—
263C4×C3⋊Dic3—31no—
264C4×C3⋊Dic3—34no—
265C4×C3⋊Dic3—32no—
266C4×C3⋊Dic3—64no—
267C2×C3⋊(C3⋊C8)—31no—
268C2×C3⋊(C3⋊C8)—34no—
269C2×C3⋊(C3⋊C8)—64no—
270C2×C3⋊(C3⋊C8)C22×D311yescharacteristic
271#3745C2×Dic314yescomplemented
272C8×C3⋊D3—62no—
273C8×C3⋊D3C2×Dic314yescomplemented
274C3×#217—28no—
275C3×#213—332no—
276C3×C4⋊Dic3C22×D318yes—
277C3×C4×Dic3C22×D314yes—
278C2×C3×C3⋊C8—34no—
279C2×C3×C3⋊C8C22×D314yes—
280C3×D24—316no—
281C3×D3×C8—316no—
282Dic3⋊Dic3—68no—
283(C2×D3)⋊Dic3—68no—
284(C2×D3)⋊Dic3—68no—
285Dic32—38no—
286D3×C3⋊C8—68no—
287C2×#442—271noSylow
288C22×C33—24no—
289C22×C33—42no—
290C22×C33—42no—
291C22×C33C22×D411yescharacteristic
292C2×C3×C3⋊D3—24no—
293C2×C3×C3⋊D3—42no—
294C2×C3×C3⋊D3—42no—
295C2×C3×C3⋊D3—416no—
296C2×C3×C3⋊D3C4×D412yes—
297C2×C3×C3⋊D3AGL(1,ℤ/8)14yes—
298C33×C4C23×C411yescharacteristic
299C33×C4C2×#4111yescharacteristic
300C3⋊(C3⋊Dic3)—22no—
301C3⋊(C3⋊Dic3)—42no—
302C3×C3⋊Dic3C4×D412yes—
303C32×Dic3—22no—
304C32×Dic3—42no—
305C22×C3×D4—92no—
306C23×Dic3—182no—
307C2×D3×D4—38no—
308C22×C4×D3—188no—
309C2×C3×D8—24no—
310C2×C3×D8—92no—
311C2×C3×D8—98no—
312C2×C3×D8—91no—
313C2×C3×D8D3214yes—
314C2×C3×D8C2×C3⋊D311yescharacteristic
315C22×C3×C8—91no—
316C3×C4×D4—38no—
317C2×#217—182no—
318D4×Dic3—98no—
319D4×Dic3—92no—
320D4×Dic3—92no—
321D4×Dic3—92no—
322D4×Dic3—188no—
323D4×Dic3—182no—
324D4×Dic3—182no—
325D4×Dic3C2×C3⋊D312yescomplemented
326C2×#213—38no—
327C4×#67—188no—
328C2×C4⋊Dic3—92no—
329C2×C4×Dic3—91no—
330C22×C3⋊C8—91no—
331D3×D8—332no—
332C2×D24—34no—
333C2×D3×C8—34no—
334C2×D3×C8—94no—
335#893—98no—
336D3×C4⋊C4—98no—
337#67⋊C4—188no—
338D3×C22⋊C4—188no—
339C4×D12—98no—
340C42×D3—94no—
341C3×#106—34no—
342C3×#102—38no—
343C3×#97—34no—
344#832—98no—
345#832—92no—
346#832—92no—
347#832—92no—
348#832—188no—
349#832C2×C3⋊D312yescomplemented
350#821—98no—
351#817—94no—
352#817—91no—
353#817—92no—
354#817—184no—
355#817C2×C3⋊D311yescharacteristic, complemented
356#815—94no—
357#815—94no—
358#815—91no—
359#815—91no—
360#815—91no—
361#815—184no—
362#815C2×C3⋊D311yescharacteristic, complemented
363#809—98no—
364#808—98no—
365#803—94no—
366C23×C32—22no—
367C23×C32—28no—
368C23×C32—48no—
369C22×C3⋊D3—22no—
370C22×C3⋊D3—28no—
371C22×C3⋊D3—44no—
372C22×C3⋊D3—44no—
373C22×C3⋊D3D3×D411yescharacteristic
374C22×C3×D3—34no—
375C22×C3×D3—632no—
376C22×C3×D3—68no—
377C22×C3×D3—1216no—
378C22×C3×D3—1216no—
379C32×D4—22no—
380C32×D4—216no—
381C32×D4—28no—
382C32×D4—48no—
383C32×D4C2×C4×D3116yescomplemented
384C32×D4C22×Dic314yescomplemented
385C2×C32×C4—24no—
386C2×C32×C4—32no—
387C2×C32×C4—62no—
388C2×C32×C4—124no—
389C2×C32×C4C23×D314yes—
390C2×C32×C4C23×D311yescharacteristic
391#638—28no—
392C2×C3⋊Dic3—32no—
393C2×C3⋊Dic3—38no—
394C2×C3⋊Dic3—68no—
395C2×C3⋊Dic3—62no—
396C2×C3⋊Dic3—68no—
397C2×C3⋊Dic3—128no—
398C2×C3⋊Dic3—124no—
399C2×C3⋊Dic3—1216no—
400C2×C3⋊Dic3—2416no—
401C2×C3⋊Dic3D3×D411yescharacteristic
402C4⋊(C3⋊D3)—22no—
403C4⋊(C3⋊D3)C22×Dic314yescomplemented
404C4×C3⋊D3—64no—
405C4×C3⋊D3—124no—
406C4×C3⋊D3—124no—
407C4×C3⋊D3—124no—
408C4×C3⋊D3#23712yes—
409C4×C3⋊D3C22×Dic312yes—
410C3×#67—632no—
411C2×C3×Dic3—28no—
412C2×C3×Dic3—34no—
413C2×C3×Dic3—416no—
414C2×C3×Dic3D3×D418yes—
415C3×D12—316no—
416C3×D12—68no—
417C3×C4×D3—38no—
418C3×C4×D3—38no—
419D3×Dic3—616no—
420D3×Dic3—1216no—
421D3×Dic3—1216no—
422D3×Dic3—1216no—
423C32×C8—28no—
424C32×C8—61no—
425C32×C8C2×C4×D318yescomplemented
426C32×C8C22×Dic312yescomplemented
427C3⋊(C3⋊C8)—61no—
428C3⋊(C3⋊C8)—64no—
429C3⋊(C3⋊C8)—124no—
430C3⋊(C3⋊C8)C22×Dic312yescomplemented
431C3×C3⋊C8—24no—
432C3×C3⋊C8—38no—
433C22×D8—91no—
434C2×C4×D4—272no—
435#442—31no—
436#442—271no—
437#442—272no—
438#442—271no—
439#442—272no—
440#442—271no—
441C2×#106—271no—
442C2×#102—272no—
443C2×#97—271no—
444C2×C33—44no—
445C2×C33C2×C4×D411yescharacteristic
446C2×C33C2×AGL(1,ℤ/8)12yes—
447C3×C3⋊D3—44no—
448C3×C3⋊D3#44214yescomplemented
449C24×C3—182no—
450C23×D3—68no—
451C2×C3×D4—28no—
452C2×C3×D4—98no—
453C2×C3×D4—92no—
454C2×C3×D4—184no—
455C2×C3×D4—182no—
456C2×C3×D4C2×D3218yes—
457C2×C3×D4C22×C3⋊D312yes—
458C22×C3×C4—68no—
459C22×C3×C4—91no—
460C2×#67—68no—
461C22×Dic3—22no—
462C22×Dic3—92no—
463C22×Dic3—182no—
464C22×Dic3—182no—
465C22×Dic3—188no—
466C22×Dic3—182no—
467C22×Dic3—182no—
468C22×Dic3—368no—
469C22×Dic3—368no—
470D3×D4—332no—
471D3×D4—616no—
472C2×D12—38no—
473C2×C4×D3—34no—
474C2×C4×D3—98no—
475C2×C4×D3—188no—
476C2×C4×D3—188no—
477C2×C4×D3—188no—
478C2×C4×D3—3632no—
479C3×D8—216no—
480C3×D8—98no—
481C3×D8—94no—
482C3×D8D3×Dic3116yescomplemented
483C3×D8C4×C3⋊D314yescomplemented
484C2×C3×C8—24no—
485C2×C3×C8—34no—
486C2×C3×C8—91no—
487C2×C3×C8—94no—
488C2×C3×C8C2×D3214yes—
489C2×C3×C8C22×C3⋊D311yescharacteristic
490C3×C4⋊C4—38no—
491C3×C22⋊C4—68no—
492C3×C42—34no—
493#217—22no—
494#217—182no—
495#217—188no—
496#217—182no—
497#217—182no—
498#217—368no—
499#213—332no—
500(C2×D3)⋊C4—188no—
501(C2×D3)⋊C4—188no—
502C4⋊Dic3—98no—
503C4⋊Dic3—92no—
504C4⋊Dic3—188no—
505C4⋊Dic3—182no—
506C4⋊Dic3C22×C3⋊D312yes—
507Dic3⋊C4—188no—
508C4×Dic3—98no—
509C4×Dic3—94no—
510C4×Dic3—91no—
511C4×Dic3—92no—
512C4×Dic3—184no—
513C4×Dic3C22×C3⋊D311yescharacteristic
514C2×C3⋊C8—34no—
515C2×C3⋊C8—94no—
516C2×C3⋊C8—91no—
517C2×C3⋊C8—184no—
518C2×C3⋊C8—182no—
519C2×C3⋊C8C22×C3⋊D311yescharacteristic
520D24—316no—
521D3×C8—316no—
522D3×C8—188no—
523C22×C32—24no—
524C22×C32—24no—
525C22×C32—216no—
526C22×C32—416no—
527C22×C32—42no—
528C22×C32—42no—
529C22×C32—48no—
530C22×C32—48no—
531C22×C32—88no—
532C22×C32—88no—
533C22×C32C2×D3×D414yes—
534C22×C32C2×D3×D411yescharacteristic
535C2×C3⋊D3—24no—
536C2×C3⋊D3—42no—
537C2×C3⋊D3—42no—
538C2×C3⋊D3—416no—
539C2×C3⋊D3#91114yes—
540C2×C3⋊D3D4×Dic312yes—
541C2×C3×D3—316no—
542C2×C3×D3—38no—
543C2×C3×D3—616no—
544C2×C3×D3—1264no—
545C2×C3×D3—128no—
546C2×C3×D3—128no—
547C32×C4—24no—
548C32×C4—24no—
549C32×C4—62no—
550C32×C4—122no—
551C32×C4C22×C4×D314yes—
552C32×C4C2×#23711yescharacteristic
553C32×C4D3×#4114yes—
554C32×C4C23×Dic311yescharacteristic
555C3⋊Dic3—62no—
556C3⋊Dic3—68no—
557C3⋊Dic3—128no—
558C3⋊Dic3—122no—
559C3⋊Dic3—128no—
560C3⋊Dic3—248no—
561C3⋊Dic3D4×Dic312yes—
562C3×Dic3—28no—
563C3×Dic3—38no—
564C3×Dic3—48no—
565C22×D4—92no—
566C23×C4—542no—
567C2×D8—92no—
568C2×D8—98no—
569C2×D8—91no—
570C2×D8D3×C3⋊D311yescharacteristic
571C22×C8—91no—
572C22×C8—271no—
573C4×D4—32no—
574C4×D4—272no—
575C4×D4—272no—
576C4×D4—272no—
577C4×D4—542no—
578C4×D4—542no—
579C2×C4⋊C4—272no—
580C2×C22⋊C4—542no—
581C2×C42—271no—
582#106—31no—
583#106—272no—
584#106—271no—
585#102—32no—
586#102—272no—
587#102—272no—
588#102—272no—
589#97—31no—
590#97—271no—
591#97—271no—
592#97—271no—
593C33C2×#44211yescharacteristic, complemented, Sylow
594C23×C3—28no—
595C23×C3—22no—
596C23×C3—48no—
597C23×C3—91no—
598C23×C3—188no—
599C23×C3—182no—
600C23×C3—364no—
601C23×C3—364no—
602C22×D3—34no—
603C22×D3—632no—
604C22×D3—68no—
605C22×D3—1216no—
606C22×D3—1216no—
607C3×D4—28no—
608C3×D4—22no—
609C3×D4—216no—
610C3×D4—48no—
611C3×D4—94no—
612C3×D4—188no—
613C3×D4—182no—
614C3×D4C2×D3×Dic3116yescomplemented
615C3×D4C2×C4×C3⋊D314yescomplemented
616C2×C3×C4—24no—
617C2×C3×C4—38no—
618C2×C3×C4—68no—
619C2×C3×C4—91no—
620C2×C3×C4—92no—
621C2×C3×C4—92no—
622C2×C3×C4—1216no—
623C2×C3×C4C22×D3214yes—
624C2×C3×C4C23×C3⋊D311yescharacteristic
625#67—632no—
626C2×Dic3—22no—
627C2×Dic3—34no—
628C2×Dic3—44no—
629C2×Dic3—98no—
630C2×Dic3—92no—
631C2×Dic3—188no—
632C2×Dic3—184no—
633C2×Dic3—188no—
634C2×Dic3—182no—
635C2×Dic3—368no—
636C2×Dic3—364no—
637C2×Dic3—364no—
638C2×Dic3—364no—
639C2×Dic3—364no—
640C2×Dic3—3616no—
641C2×Dic3—7216no—
642C2×Dic3D4×C3⋊D312yes—
643D12—316no—
644D12—68no—
645C4×D3—38no—
646C4×D3—38no—
647C4×D3—1816no—
648C4×D3—3616no—
649C4×D3—3616no—
650C4×D3—3616no—
651C3×C8—28no—
652C3×C8—64no—
653C3×C8—92no—
654C3×C8C2×D3×Dic318yescomplemented
655C3×C8C2×C4×C3⋊D312yescomplemented
656C3⋊C8—21no—
657C3⋊C8—38no—
658C3⋊C8—184no—
659C3⋊C8—181no—
660C3⋊C8—364no—
661C2×C32—24no—
662C2×C32—28no—
663C2×C32—44no—
664C2×C32—416no—
665C2×C32—816no—
666C2×C32C4×D3×D414yes—
667C2×C32C2×#91112yes—
668C2×C32D3×AGL(1,ℤ/8)18yes—
669C2×C32C2×D4×Dic311yescharacteristic
670C3⋊D3—44no—
671C3⋊D3#515214yesdirect product factor
672C3×D3—316no—
673C3×D3—1216no—
674C24—182no—
675C2×D4—98no—
676C2×D4—92no—
677C2×D4—184no—
678C2×D4—182no—
679C2×D4C2×D3×C3⋊D312yes—
680C22×C4—62no—
681C22×C4—91no—
682C22×C4—272no—
683C22×C4—542no—
684C22×C4—542no—
685C22×C4—542no—
686C22×C4—542no—
687C22×C4—1088no—
688D8—98no—
689D8—94no—
690D8Dic3×C3⋊D314yescomplemented
691C2×C8—31no—
692C2×C8—91no—
693C2×C8—94no—
694C2×C8—271no—
695C2×C8—542no—
696C2×C8C2×D3×C3⋊D311yescharacteristic
697C4⋊C4—32no—
698C4⋊C4—272no—
699C4⋊C4—542no—
700C22⋊C4—62no—
701C22⋊C4—542no—
702C22⋊C4—542no—
703C22⋊C4—542no—
704C42—31no—
705C42—272no—
706C42—271no—
707C22×C3—216no—
708C22×C3—24no—
709C22×C3—24no—
710C22×C3—416no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—48no—
714C22×C3—48no—
715C22×C3—88no—
716C22×C3—88no—
717C22×C3—94no—
718C22×C3—92no—
719C22×C3—184no—
720C22×C3—3616no—
721C22×C3—362no—
722C22×C3—362no—
723C22×C3D32×D414yes—
724C22×C3C2×D4×C3⋊D311yescharacteristic
725C2×D3—38no—
726C2×D3—316no—
727C2×D3—616no—
728C2×D3—1264no—
729C2×D3—128no—
730C2×D3—128no—
731C3×C4—24no—
732C3×C4—24no—
733C3×C4—68no—
734C3×C4—92no—
735C3×C4—128no—
736C3×C4D3×#23714yes—
737C3×C4C22×D3×Dic314yes—
738C3×C4C22×C4×C3⋊D311yescharacteristic
739C3×C4#41×C3⋊D311yescharacteristic
740Dic3—22no—
741Dic3—38no—
742Dic3—42no—
743Dic3—182no—
744Dic3—188no—
745Dic3—368no—
746Dic3—362no—
747Dic3—368no—
748Dic3—728no—
749C32—24no—
750C32D3×#44214yescomplemented
751C32C2×#515211yescharacteristic, complemented
752C23—22no—
753C23—91no—
754C23—188no—
755C23—182no—
756C23—364no—
757C23—364no—
758D4—22no—
759D4—94no—
760D4—188no—
761D4—182no—
762D4C2×Dic3×C3⋊D314yescomplemented
763C2×C4—32no—
764C2×C4—62no—
765C2×C4—91no—
766C2×C4—92no—
767C2×C4—92no—
768C2×C4—124no—
769C2×C4—272no—
770C2×C4—544no—
771C2×C4—542no—
772C2×C4—1084no—
773C2×C4—1084no—
774C2×C4—1084no—
775C2×C4—1084no—
776C2×C4C22×D3×C3⋊D311yescharacteristic
777C8—61no—
778C8—92no—
779C8—541no—
780C8C2×Dic3×C3⋊D312yescomplemented
781C2×C3—24no—
782C2×C3—28no—
783C2×C3—44no—
784C2×C3—416no—
785C2×C3—816no—
786C2×C3—94no—
787C2×C3—364no—
788C2×C3D3×#91118yes—
789C2×C3D3×D4×Dic314yes—
790C2×C3C4×D4×C3⋊D311yescharacteristic
791C2×C3C3⋊D3×AGL(1,ℤ/8)12yes—
792D3—316no—
793D3—1216no—
794C22—24no—
795C22—42no—
796C22—42no—
797C22—92no—
798C22—94no—
799C22—184no—
800C22—3616no—
801C22—362no—
802C22—362no—
803C22D3×D4×C3⋊D311yescharacteristic
804C4—62no—
805C4—92no—
806C4—122no—
807C4—542no—
808C4—1082no—
809C4C3⋊D3×#23711yescharacteristic
810C4C22×Dic3×C3⋊D311yescharacteristic
811C3—24no—
812C3C3⋊D3×#44211yescharacteristic, complemented
813C3D3×#515214yescomplemented
814C2—44no—
815C2—94no—
816C2—364no—
817C2C3⋊D3×#91112yes—
818C2D4×Dic3×C3⋊D311yescharacteristic
subgroupG/H
centerC22D3×D4×C3⋊D3
commutatorC33×C4C23×C4
FrattiniC2×C4C22×D3×C3⋊D3
FittingC2×C33×D8C22
socleC22×C33C22×D4
prime radicalC2×C3×D8×C3⋊D3C2
cosocleC2×C33×C4C24
hypercenterC2×D8D3×C3⋊D3
hypocenterC33C2×#442
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. D4×Dic3×C3⋊D3C2semidirect
3. #13163789C2semidirect
4. C32×#5152C2semidirect
5. #13160922C2semidirect
6. #13160917C2semidirect
7. C3⋊D3×#832C2semidirect
8. #13159701C2semidirect
9. #13159688C2semidirect
10. C3⋊D3×#817C2semidirect
11. C3⋊D3×#815C2semidirect
17. D4×C3⋊(C3⋊Dic3)C22semidirect
19. C3×D8×C3⋊D3C4semidirect
22. C32×D4×Dic3C22semidirect
26. #11723501C22semidirect
28. Dic3×C4⋊(C3⋊D3)C22semidirect
31. #11722202C22semidirect
32. #11722187C22semidirect
33. #11722185C22semidirect
34. C32×#832C22semidirect
35. C32×#817C22semidirect
36. C32×#815C22semidirect
37. #11722054C22semidirect
38. #11722034C22semidirect
39. #11722033C22semidirect
40. #11722021C22semidirect
41. #11722019C22semidirect
57. C3×#5152D3semidirect
70. C3×D4×C3⋊D3C2×C4semidirect
79. C33×D8C2×C4semidirect
85. C3×#3753C2×C4semidirect
87. C3×#3745C2×C4semidirect
88. C3×C8×C3⋊D3C2×C4semidirect
113. D8×C3⋊D3Dic3semidirect
123. C3×D4×Dic3C2×D3semidirect
153. C3×#832C2×D3semidirect
154. C3×#817C2×D3semidirect
155. C3×#815C2×D3semidirect
168. C33×D4C22×C4semidirect
176. C3×C4⋊(C3⋊D3)C22×C4semidirect
186. C33×C8C22×C4semidirect
188. C3×C3⋊(C3⋊C8)C22×C4semidirect
203. #5152C3⋊D3direct (N × H)
224. D4×C3⋊D3C2×Dic3semidirect
244. C32×D8C4×D3semidirect
245. C32×D8C2×Dic3semidirect
256. #3753C2×Dic3semidirect
271. #3745C2×Dic3semidirect
273. C8×C3⋊D3C2×Dic3semidirect
325. D4×Dic3C2×C3⋊D3semidirect
349. #832C2×C3⋊D3semidirect
355. #817C2×C3⋊D3semidirect
362. #815C2×C3⋊D3semidirect
383. C32×D4C2×C4×D3semidirect
384. C32×D4C22×Dic3semidirect
403. C4⋊(C3⋊D3)C22×Dic3semidirect
425. C32×C8C2×C4×D3semidirect
426. C32×C8C22×Dic3semidirect
430. C3⋊(C3⋊C8)C22×Dic3semidirect
448. C3×C3⋊D3#442semidirect
482. C3×D8D3×Dic3semidirect
483. C3×D8C4×C3⋊D3semidirect
593. C33C2×#442semidirect
614. C3×D4C2×D3×Dic3semidirect
615. C3×D4C2×C4×C3⋊D3semidirect
654. C3×C8C2×D3×Dic3semidirect
655. C3×C8C2×C4×C3⋊D3semidirect
671. C3⋊D3#5152direct (N × H)
690. D8Dic3×C3⋊D3semidirect
750. C32D3×#442semidirect
751. C32C2×#5152semidirect
762. D4C2×Dic3×C3⋊D3semidirect
780. C8C2×Dic3×C3⋊D3semidirect
812. C3C3⋊D3×#442semidirect
813. C3D3×#5152semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D8×C3⋊D32
D4×Dic3×C3⋊D32
#131637892
C32×#51522
#131609222
#131609172
C3⋊D3×#8322
#131597012
#131596882
C3⋊D3×#8172
C3⋊D3×#8152
D3×#51523
C3⋊D3×#4423