Finite Group Databasebeta

← #13167989

Subgroups — #13167989

Order 1728.

1646 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D12C211yesmaximal, characteristic
2#11723691C211yesmaximal, characteristic, complemented
3#11723501C211yesmaximal, characteristic, complemented
4#11723499C211yesmaximal, characteristic, complemented
5#11723423C211yesmaximal, characteristic, complemented
6C3×#63898C211yesmaximal, characteristic, complemented
7C3×#63841C211yesmaximal, characteristic, complemented
8#11722928C212yesmaximal, complemented
9Dic3×#626C212yesmaximal, complemented
10#11722902C212yesmaximal, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal, complemented
12#10595215—31nomaximal
13#10594982—31nomaximal
14#10594604—31nomaximal
15C22×C3×D32C2212yes—
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C32×D12C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×#6294C2212yescomplemented
20C2×Dic3×C3⋊D3C2212yescomplemented
21C2×D3×C3⋊Dic3C2212yescomplemented
22C2×C3×#626C2212yes—
23C2×C3×D3×Dic3C2212yescomplemented
24C3×D3×D12C418yescomplemented
25C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
27C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
28C32×C4⋊Dic3C2211yescharacteristic, complemented
29#88814C2212yescomplemented
30Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
32#88803C2212yescomplemented
33(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
34(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
35(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×Dic32C2212yescomplemented
39C2×C3×D3×D4—31no—
40C22×C3×D12—31no—
41C2×D3×D12D311yescharacteristic
42D4×C3⋊Dic3—31no—
43#64135—31no—
44#64102—31no—
45C3×D4×Dic3—31no—
46C3×#926—31no—
47C3×#893—31no—
48C3×#892—31no—
49#67⋊Dic3—32no—
50Dic3×#67—32no—
51D3×#217—32no—
52D3×#217—32no—
53D3×#217—32no—
54C2×(C2×D3)⋊Dic3—32no—
55#63921—32no—
56D3×(C2×D3)⋊C4—32no—
57C4×#626—32no—
58#63898—31no—
59#63898—31no—
60#63898—31no—
61#63898—31no—
62#63898—31no—
63#63898—61no—
64#63898—61no—
65#63898D311yescharacteristic, complemented
66#63894—31no—
67Dic3×D12—32no—
68Dic3×D12—31no—
69Dic3×D12—32no—
70#63880—32no—
71#63855—31no—
72#63855—31no—
73#63855—61no—
74#63841D311yescharacteristic, complemented
75C22×C3×C3⋊D3C2312yes—
76C22×C32×D3C2311yescharacteristic
77C22×C32×D3C2312yes—
78C2×C3×D32—42no—
79C2×C3×D32—42no—
80C2×C3×D32C2×C418yescomplemented
81C2×C33×C4C2311yescharacteristic
82C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
83C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C3×C4⋊(C3⋊D3)C2×C414yescomplemented
88C2×C32×Dic3C2312yes—
89C2×C32×Dic3C2311yescharacteristic
90C32×D12C2×C414yescomplemented
91C32×C4×D3C2×C414yescomplemented
92#6294—42no—
93Dic3×C3⋊D3—42no—
94D3×C3⋊Dic3—42no—
95C3×#626C2×C418yescomplemented
96C3×D3×Dic3—42no—
97#5798—91no—
98#5545—91no—
99#5521—91no—
100C23×C3×D3—32no—
101C23×C3×D3—32no—
102C22×D32C2×D312yes—
103C2×C32×D4—31no—
104C22×C32×C4—31no—
105C22×C3⋊Dic3—32no—
106C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
107C2×C4×C3⋊D3—32no—
108C2×C3×#67—32no—
109C22×C3×Dic3—32no—
110C3×D3×D4—38no—
111C2×C3×D12—21no—
112C2×C3×D12—32no—
113C2×C3×D12—31no—
114C2×C3×D12—31no—
115C2×C3×D12—38no—
116C2×C3×D12—61no—
117C2×C3×D12C2×D311yescharacteristic
118C2×C3×D12C2×D311yescharacteristic
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3—32no—
121C2×C3×C4×D3C2×D311yescharacteristic
122C2×C3×C4×D3C2×D311yescharacteristic
123C2×#626C2×D312yes—
124C2×#624—32no—
125C2×D3×Dic3—32no—
126C2×D3×Dic3—32no—
127C2×D3×Dic3—32no—
128C2×D3×Dic3—32no—
129C2×D3×Dic3—32no—
130C2×D3×Dic3—32no—
131C2×D3×Dic3—62no—
132C2×D3×Dic3—62no—
133C2×D3×Dic3C2×D312yescomplemented
134D3×D12Dic318yescomplemented
135C32×C4⋊C4—31no—
136#3757—31no—
137#3757—31no—
138#3757—32no—
139#3752—32no—
140C4⋊(C3⋊Dic3)—31no—
141C4⋊(C3⋊Dic3)—31no—
142C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
143C4×C3⋊Dic3—31no—
144C4×C3⋊Dic3—31no—
145C4×C3⋊Dic3—31no—
146C4×C3⋊Dic3—61no—
147C4×C3⋊Dic3—61no—
148C4×C3⋊Dic3—61no—
149C4×C3⋊Dic3—121no—
150C4×C3⋊Dic3C2×D311yescharacteristic, complemented
151C3×#217—32no—
152C3×#217—32no—
153C3×(C2×D3)⋊C4—32no—
154C3×(C2×D3)⋊C4—32no—
155C3×C4⋊Dic3—21no—
156C3×C4⋊Dic3—31no—
157C3×C4⋊Dic3—31no—
158C3×C4⋊Dic3—61no—
159C3×C4⋊Dic3C2×D311yescharacteristic, complemented
160C3×C4⋊Dic3C2×D311yescharacteristic, complemented
161C3×C4×Dic3—31no—
162C3×C4×Dic3—31no—
163C3×C4×Dic3—32no—
164C3×C4×Dic3—32no—
165C3×C4×Dic3—61no—
166Dic3⋊Dic3—31no—
167Dic3⋊Dic3—31no—
168Dic3⋊Dic3—31no—
169Dic3⋊Dic3—31no—
170Dic3⋊Dic3—61no—
171Dic3⋊Dic3—61no—
172#3722—32no—
173(C2×D3)⋊Dic3—31no—
174(C2×D3)⋊Dic3—31no—
175(C2×D3)⋊Dic3—31no—
176(C2×D3)⋊Dic3—31no—
177(C2×D3)⋊Dic3—32no—
178(C2×D3)⋊Dic3—32no—
179(C2×D3)⋊Dic3—32no—
180(C2×D3)⋊Dic3—32no—
181(C2×D3)⋊Dic3—32no—
182(C2×D3)⋊Dic3—32no—
183(C2×D3)⋊Dic3—62no—
184(C2×D3)⋊Dic3—61no—
185(C2×D3)⋊Dic3—61no—
186(C2×D3)⋊Dic3—62no—
187(C2×D3)⋊Dic3C2×D312yes—
188(C2×D3)⋊Dic3C2×D312yescomplemented
189Dic32C2×D312yescomplemented
190C22×C33C2411yescharacteristic
191C2×C3×C3⋊D3—22no—
192C2×C3×C3⋊D3—22no—
193C2×C3×C3⋊D3C22×C414yes—
194C2×C32×D3—22no—
195C2×C32×D3—22no—
196C2×C32×D3—21no—
197C2×C32×D3—21no—
198C2×C32×D3C22×C414yes—
199C2×C32×D3C22×C412yes—
200C3×D32—48no—
201C33×C4C22×C412yes—
202C3⋊(C3⋊Dic3)—21no—
203C3⋊(C3⋊Dic3)—21no—
204C3×C3⋊Dic3—21no—
205C3×C3⋊Dic3—22no—
206C3×C3⋊Dic3—21no—
207C32×Dic3—22no—
208C32×Dic3C22×C412yes—
209C22×C3×D4—91no—
210C2×D3×D4—31no—
211C22×D12—31no—
212C3×C4×D4—91no—
213C3×#117—91no—
214C2×#217—92no—
215C2×#217—92no—
216D4×Dic3—31no—
217D4×Dic3—91no—
218D4×Dic3—92no—
219D4×Dic3—92no—
220D4×Dic3—91no—
221D4×Dic3—91no—
222D4×Dic3—91no—
223D4×Dic3—181no—
224C4×#67—92no—
225C2×(C2×D3)⋊C4—92no—
226#926—31no—
227#926—91no—
228#926—91no—
229#926—181no—
230#893—31no—
231#893—91no—
232#893—91no—
233#893—91no—
234#893—91no—
235#893—181no—
236#892—31no—
237#67⋊C4—92no—
238D3×C22⋊C4—92no—
239D3×C22⋊C4—92no—
240D3×C22⋊C4—92no—
241C4×D12—91no—
242C4×D12—92no—
243C4×D12—92no—
244#872—91no—
245C23×C32—31no—
246C23×C32—32no—
247C22×C3⋊D3C22×D312yes—
248C22×C3×D3—21no—
249C22×C3×D3—22no—
250C22×C3×D3—32no—
251C22×C3×D3—32no—
252C22×C3×D3—38no—
253C22×C3×D3—38no—
254C22×C3×D3—62no—
255C22×C3×D3—122no—
256C22×C3×D3—122no—
257C22×C3×D3—122no—
258C22×C3×D3—122no—
259C22×C3×D3C22×D311yescharacteristic
260C22×C3×D3C22×D312yes—
261C22×C3×D3C22×D311yescharacteristic
262C22×C3×D3C22×D312yes—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32C2×Dic318yescomplemented
266C32×D4—34no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—31no—
271C2×C32×C4—34no—
272C2×C32×C4—32no—
273C2×C32×C4—41no—
274C2×C32×C4C22×D311yescharacteristic
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C3⋊Dic3—31no—
278C2×C3⋊Dic3—31no—
279C2×C3⋊Dic3—31no—
280C2×C3⋊Dic3—31no—
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—61no—
284C2×C3⋊Dic3—61no—
285C2×C3⋊Dic3—61no—
286C2×C3⋊Dic3—61no—
287C2×C3⋊Dic3—61no—
288C2×C3⋊Dic3—61no—
289C2×C3⋊Dic3—121no—
290C2×C3⋊Dic3—121no—
291C2×C3⋊Dic3—122no—
292C2×C3⋊Dic3C22×D312yes—
293C2×C3⋊Dic3C22×D311yescharacteristic
294C2×C3⋊Dic3C22×D311yescharacteristic
295C4⋊(C3⋊D3)C2×Dic314yescomplemented
296C4×C3⋊D3—122no—
297C3×#67—38no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—32no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—32no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—61no—
307C2×C3×Dic3—61no—
308C2×C3×Dic3—62no—
309C2×C3×Dic3—122no—
310C2×C3×Dic3C22×D312yes—
311C2×C3×Dic3C22×D312yes—
312C2×C3×Dic3C22×D311yescharacteristic
313C2×C3×Dic3C22×D311yescharacteristic
314C3×D12—24no—
315C3×D12—38no—
316C3×D12—34no—
317C3×D12—34no—
318C3×D12—64no—
319C3×D12C4×D314yescomplemented
320C3×D12C2×Dic314yescomplemented
321C3×C4×D3—24no—
322C3×C4×D3—122no—
323C3×C4×D3C4×D314yescomplemented
324C3×C4×D3C2×Dic314yescomplemented
325#626C2×Dic318yescomplemented
326#624—122no—
327D3×Dic3—42no—
328D3×Dic3—122no—
329D3×Dic3—122no—
330D3×Dic3—124no—
331D3×Dic3—122no—
332D3×Dic3—122no—
333D3×Dic3—122no—
334D3×Dic3—122no—
335D3×Dic3—124no—
336#518—271noSylow
337C2×C33C23×C411yescharacteristic
338C2×C33H(5,𝔽2)11yescharacteristic
339C2×C33H(5,𝔽2)11yescharacteristic
340C3×C3⋊D3—24no—
341C32×D3—22no—
342C32×D3—24no—
343C24×C3—92no—
344C23×D3—32no—
345C23×D3—32no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—61no—
349C2×C3×D4—98no—
350C2×C3×D4—92no—
351C2×C3×D4—91no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—61no—
355C22×C3×C4—92no—
356C2×#67—32no—
357C22×Dic3—32no—
358C22×Dic3—92no—
359C22×Dic3—92no—
360C22×Dic3—92no—
361C22×Dic3—92no—
362C22×Dic3—182no—
363D3×D4—38no—
364C2×D12—32no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—38no—
368C2×D12—61no—
369C2×D12D3211yescharacteristic
370C2×C4×D3—32no—
371C2×C4×D3—92no—
372C2×C4×D3—92no—
373C2×C4×D3—92no—
374C2×C4×D3—92no—
375C2×C4×D3—92no—
376C2×C4×D3—182no—
377C2×C4×D3D3211yescharacteristic
378C3×C4⋊C4—31no—
379C3×C4⋊C4—31no—
380C3×C4⋊C4—61no—
381C3×C4⋊C4—91no—
382C3×C22⋊C4—92no—
383C3×C22⋊C4—92no—
384C3×C42—92no—
385C3×C42—91no—
386#217—32no—
387#217—32no—
388#217—92no—
389#217—91no—
390#217—91no—
391#217—92no—
392#217—91no—
393#217—91no—
394#217—92no—
395#217—92no—
396#217—181no—
397#217—181no—
398#217—182no—
399(C2×D3)⋊C4—32no—
400(C2×D3)⋊C4—32no—
401(C2×D3)⋊C4—92no—
402(C2×D3)⋊C4—92no—
403(C2×D3)⋊C4—92no—
404(C2×D3)⋊C4—92no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—92no—
408(C2×D3)⋊C4—182no—
409C4⋊Dic3—31no—
410C4⋊Dic3—31no—
411C4⋊Dic3—61no—
412C4⋊Dic3—91no—
413C4⋊Dic3—91no—
414C4⋊Dic3—91no—
415C4⋊Dic3—91no—
416C4⋊Dic3—181no—
417C4⋊Dic3—181no—
418C4⋊Dic3D3211yescharacteristic, complemented
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421C4×Dic3—31no—
422C4×Dic3—31no—
423C4×Dic3—32no—
424C4×Dic3—32no—
425C4×Dic3—61no—
426C4×Dic3—91no—
427C4×Dic3—91no—
428C4×Dic3—91no—
429C4×Dic3—181no—
430C4×Dic3—181no—
431C4×Dic3—181no—
432C4×Dic3—361no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—21no—
436C22×C32—34no—
437C22×C32—32no—
438C22×C32—41no—
439C22×C32—61no—
440C22×C32—62no—
441C22×C32—62no—
442C22×C32—61no—
443C22×C32C23×D311yescharacteristic
444C22×C32C23×D311yescharacteristic
445C22×C32C23×D311yescharacteristic
446C2×C3⋊D3—22no—
447C2×C3⋊D3—22no—
448C2×C3⋊D3C22×Dic314yes—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—22no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—22no—
458C2×C3×D3—24no—
459C2×C3×D3—34no—
460C2×C3×D3—34no—
461C2×C3×D3—42no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—42no—
465C2×C3×D3—64no—
466C2×C3×D3—62no—
467C2×C3×D3—62no—
468C2×C3×D3—62no—
469C2×C3×D3—62no—
470C2×C3×D3—122no—
471C2×C3×D3—122no—
472C2×C3×D3—128no—
473C2×C3×D3—128no—
474C2×C3×D3C2×C4×D312yes—
475C2×C3×D3C2×C4×D314yes—
476C2×C3×D3C22×Dic314yes—
477C2×C3×D3C22×Dic312yes—
478D32—48no—
479C32×C4—22no—
480C32×C4—22no—
481C32×C4—22no—
482C32×C4—32no—
483C32×C4—42no—
484C32×C4—62no—
485C32×C4C2×C4×D312yes—
486C32×C4C2×C4×D312yes—
487C32×C4C22×Dic312yes—
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3⋊Dic3—22no—
491C3⋊Dic3—61no—
492C3⋊Dic3—61no—
493C3⋊Dic3—62no—
494C3⋊Dic3—62no—
495C3⋊Dic3—61no—
496C3⋊Dic3—61no—
497C3⋊Dic3—61no—
498C3⋊Dic3—61no—
499C3⋊Dic3—121no—
500C3⋊Dic3—121no—
501C3⋊Dic3—121no—
502C3⋊Dic3—121no—
503C3⋊Dic3—122no—
504C3⋊Dic3—122no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—42no—
509C3×Dic3—62no—
510C3×Dic3—61no—
511C3×Dic3—61no—
512C3×Dic3—61no—
513C3×Dic3—62no—
514C3×Dic3—61no—
515C3×Dic3—122no—
516C3×Dic3—121no—
517C3×Dic3—121no—
518C3×Dic3C2×C4×D312yes—
519C3×Dic3C22×Dic312yes—
520C22×D4—91no—
521C4×D4—91no—
522C4×D4—272no—
523C4×D4—271no—
524C4×D4—272no—
525C4×D4—271no—
526C4×D4—271no—
527#117—91no—
528#117—271no—
529C2×C22⋊C4—272no—
530C2×C22⋊C4—272no—
531C33#51811yescharacteristic, complemented, Sylow
532C23×C3—31no—
533C23×C3—32no—
534C23×C3—31no—
535C23×C3—32no—
536C23×C3—61no—
537C23×C3—62no—
538C23×C3—98no—
539C23×C3—92no—
540C23×C3—362no—
541C23×C3—362no—
542C22×D3—32no—
543C22×D3—32no—
544C22×D3—38no—
545C22×D3—38no—
546C22×D3—62no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3C2×D3211yescharacteristic
552C22×D3C2×D3212yes—
553C3×D4—34no—
554C3×D4—34no—
555C3×D4—64no—
556C3×D4—98no—
557C3×D4—94no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—34no—
564C2×C3×C4—34no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—41no—
568C2×C3×C4—64no—
569C2×C3×C4—61no—
570C2×C3×C4—62no—
571C2×C3×C4—91no—
572C2×C3×C4—91no—
573C2×C3×C4—92no—
574C2×C3×C4—362no—
575C2×C3×C4C2×D3211yescharacteristic
576C2×C3×C4C2×D3211yescharacteristic
577C2×C3×C4C2×D3211yescharacteristic
578#67—38no—
579C2×Dic3—32no—
580C2×Dic3—32no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—62no—
588C2×Dic3—91no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—122no—
595C2×Dic3—181no—
596C2×Dic3—181no—
597C2×Dic3—181no—
598C2×Dic3—181no—
599C2×Dic3—181no—
600C2×Dic3—181no—
601C2×Dic3—361no—
602C2×Dic3—361no—
603C2×Dic3—362no—
604C2×Dic3—362no—
605C2×Dic3—362no—
606C2×Dic3—362no—
607C2×Dic3—364no—
608C2×Dic3C2×D3212yes—
609C2×Dic3C2×D3211yescharacteristic
610D12—38no—
611D12—34no—
612D12—34no—
613D12—64no—
614D12D3×Dic314yescomplemented
615C4×D3—122no—
616C4×D3—362no—
617C4×D3—362no—
618C4×D3—362no—
619C4×D3—362no—
620C4×D3—364no—
621C4×D3—362no—
622C4×D3D3×Dic314yescomplemented
623C2×C32—21no—
624C2×C32—21no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—21no—
629C2×C32—21no—
630C2×C32—21no—
631C2×C32—21no—
632C2×C32—41no—
633C2×C32—41no—
634C2×C32—41no—
635C2×C32—64no—
636C2×C32—62no—
637C2×C32C22×C4×D311yescharacteristic
638C2×C32C22×C4×D311yescharacteristic
639C2×C32#100411yescharacteristic
640C2×C32#100411yescharacteristic
641C2×C32#100411yescharacteristic
642C2×C32#100911yescharacteristic
643C2×C32#100911yescharacteristic
644C2×C32#100911yescharacteristic
645C2×C32C23×Dic311yescharacteristic
646C3⋊D3—24no—
647C3×D3—22no—
648C3×D3—22no—
649C3×D3—24no—
650C3×D3—24no—
651C3×D3—44no—
652C3×D3—42no—
653C3×D3—64no—
654C3×D3—64no—
655C3×D3—124no—
656C24—92no—
657C2×D4—31no—
658C2×D4—98no—
659C2×D4—92no—
660C2×D4—91no—
661C22×C4—31no—
662C22×C4—92no—
663C22×C4—272no—
664C22×C4—272no—
665C22×C4—272no—
666C4⋊C4—31no—
667C4⋊C4—91no—
668C4⋊C4—271no—
669C4⋊C4—271no—
670C22⋊C4—92no—
671C22⋊C4—92no—
672C22⋊C4—272no—
673C22⋊C4—272no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—272no—
677C42—92no—
678C42—91no—
679C42—271no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—32no—
684C22×C3—34no—
685C22×C3—34no—
686C22×C3—32no—
687C22×C3—41no—
688C22×C3—62no—
689C22×C3—64no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—61no—
693C22×C3—62no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—62no—
697C22×C3—61no—
698C22×C3—94no—
699C22×C3—122no—
700C22×C3—122no—
701C22×C3—121no—
702C22×C3—121no—
703C22×C3—182no—
704C22×C3—182no—
705C22×C3—368no—
706C22×C3C22×D3211yescharacteristic
707C22×C3C22×D3211yescharacteristic
708C22×C3C22×D3211yescharacteristic
709C2×D3—21no—
710C2×D3—21no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—34no—
714C2×D3—34no—
715C2×D3—64no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—122no—
721C2×D3—122no—
722C2×D3—128no—
723C2×D3—128no—
724C2×D3C2×D3×Dic312yes—
725C2×D3C2×D3×Dic314yes—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—32no—
730C3×C4—32no—
731C3×C4—42no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—122no—
736C3×C4—181no—
737C3×C4—181no—
738C3×C4—182no—
739C3×C4C4×D3212yes—
740C3×C4C2×D3×Dic312yes—
741C3×C4C2×D3×Dic312yes—
742Dic3—22no—
743Dic3—62no—
744Dic3—61no—
745Dic3—61no—
746Dic3—61no—
747Dic3—62no—
748Dic3—61no—
749Dic3—122no—
750Dic3—121no—
751Dic3—121no—
752Dic3—182no—
753Dic3—182no—
754Dic3—181no—
755Dic3—181no—
756Dic3—181no—
757Dic3—181no—
758Dic3—181no—
759Dic3—181no—
760Dic3—361no—
761Dic3—361no—
762Dic3—361no—
763Dic3—361no—
764Dic3—362no—
765Dic3—362no—
766Dic3C2×D3×Dic312yes—
767C32—21no—
768C32—21no—
769C32—21no—
770C32—41no—
771C32#552111yescharacteristic, complemented
772C32#554511yescharacteristic, complemented
773C32#579811yescharacteristic, complemented
774C23—31no—
775C23—32no—
776C23—98no—
777C23—92no—
778C23—362no—
779C23—362no—
780D4—34no—
781D4—98no—
782D4—94no—
783C2×C4—31no—
784C2×C4—34no—
785C2×C4—32no—
786C2×C4—91no—
787C2×C4—92no—
788C2×C4—91no—
789C2×C4—271no—
790C2×C4—271no—
791C2×C4—362no—
792C2×C4—1082no—
793C2×C4—1082no—
794C2×C4—1082no—
795C2×C4D3311yescharacteristic
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—41no—
806C2×C3—41no—
807C2×C3—41no—
808C2×C3—62no—
809C2×C3—64no—
810C2×C3—62no—
811C2×C3—64no—
812C2×C3—122no—
813C2×C3—124no—
814C2×C3—184no—
815C2×C3C2×C4×D3211yescharacteristic
816C2×C3#6430711yescharacteristic
817C2×C3#6430711yescharacteristic
818C2×C3#6431311yescharacteristic
819C2×C3#6431411yescharacteristic
820C2×C3#6431411yescharacteristic
821C2×C3#6432011yescharacteristic
822C2×C3C22×D3×Dic311yescharacteristic
823C2×C3C22×D3×Dic311yescharacteristic
824D3—24no—
825D3—22no—
826D3—64no—
827D3—64no—
828D3—124no—
829C22—32no—
830C22—34no—
831C22—62no—
832C22—61no—
833C22—62no—
834C22—61no—
835C22—94no—
836C22—182no—
837C22—182no—
838C22—368no—
839C22C2×D3311yescharacteristic
840C4—32no—
841C4—62no—
842C4—181no—
843C4—181no—
844C4—182no—
845C4—541no—
846C4—541no—
847C4D32×Dic312yes—
848C3—21no—
849C3—21no—
850C3—21no—
851C3—41no—
852C3#1059460411yescharacteristic, complemented
853C3#1059498211yescharacteristic, complemented
854C3#1059521511yescharacteristic, complemented
855C2—62no—
856C2—64no—
857C2—184no—
858C2#1172438111yescharacteristic
859C2#1172438511yescharacteristic
860C2C2×D32×Dic311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×C3×D3×D12C2
hypercenterC2×C4D33
hypocenterC33#518
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. #11723691C2semidirect
3. #11723501C2semidirect
4. #11723499C2semidirect
5. #11723423C2semidirect
6. C3×#63898C2semidirect
7. C3×#63841C2semidirect
8. #11722928C2semidirect
9. Dic3×#626C2semidirect
10. #11722902C2semidirect
11. D3×(C2×D3)⋊Dic3C2semidirect
19. C2×#6294C22semidirect
20. C2×Dic3×C3⋊D3C22semidirect
21. C2×D3×C3⋊Dic3C22semidirect
23. C2×C3×D3×Dic3C22semidirect
24. C3×D3×D12C4semidirect
25. C4×C3⋊(C3⋊Dic3)C22semidirect
26. C3×C4⋊(C3⋊Dic3)C22semidirect
27. C3×C4×C3⋊Dic3C22semidirect
28. C32×C4⋊Dic3C22semidirect
29. #88814C22semidirect
30. Dic3⋊(C3⋊Dic3)C22semidirect
31. Dic3⋊(C3⋊Dic3)C22semidirect
32. #88803C22semidirect
35. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×Dic32C22semidirect
65. #63898D3semidirect
74. #63841D3semidirect
80. C2×C3×D32C2×C4semidirect
87. C3×C4⋊(C3⋊D3)C2×C4semidirect
90. C32×D12C2×C4semidirect
91. C32×C4×D3C2×C4semidirect
95. C3×#626C2×C4semidirect
133. C2×D3×Dic3C2×D3semidirect
134. D3×D12Dic3semidirect
142. C4⋊(C3⋊Dic3)C2×D3semidirect
150. C4×C3⋊Dic3C2×D3semidirect
159. C3×C4⋊Dic3C2×D3semidirect
160. C3×C4⋊Dic3C2×D3semidirect
188. (C2×D3)⋊Dic3C2×D3semidirect
189. Dic32C2×D3semidirect
265. C2×D32C2×Dic3semidirect
295. C4⋊(C3⋊D3)C2×Dic3semidirect
319. C3×D12C4×D3semidirect
320. C3×D12C2×Dic3semidirect
323. C3×C4×D3C4×D3semidirect
324. C3×C4×D3C2×Dic3semidirect
325. #626C2×Dic3semidirect
418. C4⋊Dic3D32semidirect
531. C33#518semidirect
614. D12D3×Dic3semidirect
622. C4×D3D3×Dic3semidirect
771. C32#5521semidirect
772. C32#5545semidirect
773. C32#5798semidirect
852. C3#10594604semidirect
853. C3#10594982semidirect
854. C3#10595215semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D122
#117236912
#117235012
#117234992
#117234232
C3×#638982
C3×#638412
#117229282
Dic3×#6262
#117229022
D3×(C2×D3)⋊Dic32
#105952153
#105949823
#105946043