Finite Group Databasebeta

← #13169239

Subgroups — #13169239

Order 1728.

1830 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2#11723691C211yesmaximal, characteristic, complemented
3#11723494C211yesmaximal, characteristic, complemented
4#11723484C211yesmaximal, characteristic, complemented
5C3×#63894C211yesmaximal, characteristic, complemented
6C3×#63855C211yesmaximal, characteristic, complemented
7C3×#63841C211yesmaximal, characteristic, complemented
8#11722937C212yesmaximal, complemented
9#11722933C212yesmaximal, complemented
10#11722906C212yesmaximal, complemented
11#11722904C212yesmaximal, complemented
12#10594996—31nomaximal
13#10594604—31nomaximal
14#10593994—31nomaximal
15C22×D3×C3⋊D3C2212yes—
16C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×#6294C2212yescomplemented
20C2×#6292C2212yes—
21C2×#6289C2212yescomplemented
22C2×#6289C2212yescomplemented
23D3×C4⋊(C3⋊D3)C418yescomplemented
24C2×C3×#624C2212yescomplemented
25C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
26C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C32×C4⋊Dic3C2211yescharacteristic, complemented
28C32×C4×Dic3C2211yescharacteristic, complemented
29#88814C2212yescomplemented
30#88804C2212yescomplemented
31#88804C2212yescomplemented
32C3×Dic3⋊Dic3C2211yescharacteristic, complemented
33C3×Dic3⋊Dic3C2211yescharacteristic, complemented
34C3×#3722C2212yescomplemented
35C3×(C2×D3)⋊Dic3C2211yescharacteristic
36C3×(C2×D3)⋊Dic3C2212yes—
37C3×(C2×D3)⋊Dic3C2211yescharacteristic
38C3×Dic32C2212yescomplemented
39C22×C4⋊(C3⋊D3)—31no—
40C2×D3×D12—31no—
41C2×D3×D12—31no—
42C2×D3×D12—61no—
43#64102—31no—
44C4×C4⋊(C3⋊D3)—31no—
45C3×#926—31no—
46C3×#926—31no—
47C3×#893—31no—
48C3×#892—31no—
49C3×C4×D12—31no—
50C3×#872—31no—
51#63974—32no—
52#63974—32no—
53#63921—32no—
54#63921—32no—
55D3×(C2×D3)⋊C4—32no—
56D3×(C2×D3)⋊C4—32no—
57#63904—32no—
58C4×#626—32no—
59#63898—31no—
60#63894—31no—
61#63894—32no—
62#63894—31no—
63#63894—31no—
64#63894—31no—
65#63894—31no—
66#63894—32no—
67#63894—61no—
68#63894—61no—
69#63894D311yescharacteristic, complemented
70Dic3×D12—31no—
71#63881—32no—
72#63880—32no—
73#63855D311yescharacteristic, complemented
74#63841D311yescharacteristic, complemented
75C22×C3⋊(C3⋊D3)C2312yes—
76C22×C3×C3⋊D3C2312yes—
77C22×C32×D3C2311yescharacteristic
78C2×D3×C3⋊D3—42no—
79C2×D3×C3⋊D3—42no—
80C2×D3×C3⋊D3C2×C418yescomplemented
81C2×C33×C4C2311yescharacteristic
82C4⋊(C3⋊(C3⋊D3))C2×C414yescomplemented
83C2×C3×C3⋊Dic3C2311yescharacteristic
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2312yes—
86C3×C4⋊(C3⋊D3)C2×C414yescomplemented
87C2×C32×Dic3C2311yescharacteristic
88C2×C32×Dic3C2312yes—
89C2×C32×Dic3C2311yescharacteristic
90C2×C32×Dic3C2311yescharacteristic
91C32×C4×D3C2×C414yescomplemented
92#6294—42no—
93#6292C2×C418yescomplemented
94#6289—42no—
95#6289—42no—
96C3×#624—42no—
97#5545—91no—
98#5521—91no—
99#5521—91no—
100C23×C3⋊D3—32no—
101C22×D32—32no—
102C22×D32—32no—
103C22×D32—62no—
104C22×C32×C4—31no—
105C2×C4⋊(C3⋊D3)—32no—
106C2×C4⋊(C3⋊D3)—31no—
107C2×C4⋊(C3⋊D3)—31no—
108C2×C4⋊(C3⋊D3)—31no—
109C2×C4⋊(C3⋊D3)—38no—
110C2×C4⋊(C3⋊D3)—61no—
111C2×C4⋊(C3⋊D3)—61no—
112C2×C4⋊(C3⋊D3)—61no—
113C2×C4⋊(C3⋊D3)—121no—
114C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
115C2×C4×C3⋊D3—32no—
116C2×C4×C3⋊D3—32no—
117C2×C3×D12—31no—
118C2×C3×D12—31no—
119C2×C3×D12—61no—
120C2×C3×C4×D3—21no—
121C2×C3×C4×D3—32no—
122C2×C3×C4×D3—32no—
123C2×C3×C4×D3C2×D311yescharacteristic
124C2×C3×C4×D3C2×D311yescharacteristic
125C2×#626—32no—
126C2×#626—32no—
127C2×#626—62no—
128C2×#624—32no—
129C2×#624—32no—
130C2×#624—32no—
131C2×#624—32no—
132C2×#624—32no—
133C2×#624—62no—
134C2×#624—62no—
135C2×#624C2×D312yescomplemented
136C2×D3×Dic3—32no—
137C2×D3×Dic3—32no—
138D3×D12—38no—
139D3×D12—38no—
140D3×D12—68no—
141C32×C4⋊C4—31no—
142C32×C42—31no—
143#3752—32no—
144#3752—32no—
145C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
146C4×C3⋊Dic3C2×D311yescharacteristic, complemented
147C3×#217—31no—
148C3×#217—32no—
149C3×#217—31no—
150C3×(C2×D3)⋊C4—32no—
151C3×(C2×D3)⋊C4—31no—
152C3×(C2×D3)⋊C4—31no—
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—31no—
159C3×C4⋊Dic3—31no—
160C3×C4⋊Dic3—61no—
161C3×C4⋊Dic3C2×D311yescharacteristic, complemented
162C3×C4⋊Dic3C2×D311yescharacteristic, complemented
163C3×Dic3⋊C4—31no—
164C3×Dic3⋊C4—31no—
165C3×C4×Dic3—21no—
166C3×C4×Dic3—31no—
167C3×C4×Dic3—31no—
168C3×C4×Dic3—32no—
169C3×C4×Dic3—32no—
170C3×C4×Dic3—61no—
171C3×C4×Dic3C2×D311yescharacteristic, complemented
172C3×C4×Dic3C2×D311yescharacteristic, complemented
173Dic3⋊Dic3C2×D311yescharacteristic, complemented
174Dic3⋊Dic3C2×D311yescharacteristic, complemented
175#3722—32no—
176#3722—32no—
177#3722—32no—
178#3722—32no—
179#3722—32no—
180#3722—62no—
181#3722—62no—
182#3722C2×D312yescomplemented
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—32no—
185(C2×D3)⋊Dic3C2×D312yes—
186(C2×D3)⋊Dic3C2×D311yescharacteristic
187(C2×D3)⋊Dic3C2×D311yescharacteristic
188Dic32C2×D312yescomplemented
189C22×C33C2411yescharacteristic
190C2×C3⋊(C3⋊D3)—22no—
191C2×C3⋊(C3⋊D3)—22no—
192C2×C3⋊(C3⋊D3)C22×C414yes—
193C2×C3×C3⋊D3—22no—
194C2×C3×C3⋊D3—22no—
195C2×C3×C3⋊D3C22×C414yes—
196C2×C32×D3—21no—
197C2×C32×D3—21no—
198C2×C32×D3C22×C412yes—
199D3×C3⋊D3—48no—
200C33×C4C22×C412yes—
201C3×C3⋊Dic3—21no—
202C3×C3⋊Dic3—22no—
203C3×C3⋊Dic3—21no—
204C32×Dic3—21no—
205C32×Dic3—21no—
206C32×Dic3—22no—
207C32×Dic3C22×C412yes—
208C2×D3×D4—91no—
209C22×D12—91no—
210C22×D12—91no—
211C22×D12—181no—
212C3×C4×D4—91no—
213C3×#117—91no—
214C3×#117—91no—
215D4×Dic3—91no—
216C4×#67—92no—
217C2×(C2×D3)⋊C4—92no—
218#926—31no—
219#926—31no—
220#893—31no—
221#893—92no—
222#893—91no—
223#893—91no—
224#893—92no—
225#893—91no—
226#893—91no—
227#893—181no—
228#892—31no—
229#67⋊C4—92no—
230D3×C22⋊C4—92no—
231D3×C22⋊C4—92no—
232D3×C22⋊C4—92no—
233D3×C22⋊C4—92no—
234D3×C22⋊C4—92no—
235C4×D12—31no—
236C4×D12—92no—
237C4×D12—91no—
238C4×D12—91no—
239C4×D12—92no—
240C4×D12—91no—
241C4×D12—91no—
242C4×D12—181no—
243#872—31no—
244C23×C32—31no—
245C22×C3⋊D3—32no—
246C22×C3⋊D3—32no—
247C22×C3⋊D3—32no—
248C22×C3⋊D3—38no—
249C22×C3⋊D3—62no—
250C22×C3⋊D3—62no—
251C22×C3⋊D3—62no—
252C22×C3⋊D3—122no—
253C22×C3⋊D3—122no—
254C22×C3⋊D3—122no—
255C22×C3⋊D3C22×D312yes—
256C22×C3×D3—21no—
257C22×C3×D3—32no—
258C22×C3×D3—32no—
259C22×C3×D3—62no—
260C22×C3×D3C22×D311yescharacteristic
261C22×C3×D3C22×D311yescharacteristic
262C2×D32—38no—
263C2×D32—38no—
264C2×D32—68no—
265C2×D32—122no—
266C2×D32—122no—
267C2×D32—122no—
268C2×D32—122no—
269C2×D32—124no—
270C2×D32—124no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—31no—
275C2×C32×C4—34no—
276C2×C32×C4—32no—
277C2×C32×C4—31no—
278C2×C32×C4—31no—
279C2×C32×C4—41no—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282C2×C32×C4C22×D311yescharacteristic
283C2×C3⋊Dic3C22×D312yes—
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C4⋊(C3⋊D3)—38no—
287C4⋊(C3⋊D3)—34no—
288C4⋊(C3⋊D3)—34no—
289C4⋊(C3⋊D3)—34no—
290C4⋊(C3⋊D3)—64no—
291C4⋊(C3⋊D3)—64no—
292C4⋊(C3⋊D3)—64no—
293C4⋊(C3⋊D3)—124no—
294C4⋊(C3⋊D3)C4×D314yescomplemented
295C4×C3⋊D3—122no—
296C4×C3⋊D3—122no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—32no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—31no—
305C2×C3×Dic3—32no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—61no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—62no—
310C2×C3×Dic3C22×D312yes—
311C2×C3×Dic3C22×D311yescharacteristic
312C2×C3×Dic3C22×D311yescharacteristic
313C2×C3×Dic3C22×D311yescharacteristic
314C2×C3×Dic3C22×D312yes—
315C2×C3×Dic3C22×D311yescharacteristic
316C2×C3×Dic3C22×D311yescharacteristic
317C2×C3×Dic3C22×D311yescharacteristic
318C3×D12—34no—
319C3×D12—34no—
320C3×D12—64no—
321C3×C4×D3—24no—
322C3×C4×D3—122no—
323C3×C4×D3—122no—
324C3×C4×D3C4×D314yescomplemented
325C3×C4×D3C4×D314yescomplemented
326#626—38no—
327#626—38no—
328#626—68no—
329#624—42no—
330#624—122no—
331#624—122no—
332#624—122no—
333#624—122no—
334#624—124no—
335#624—124no—
336#624—122no—
337D3×Dic3—122no—
338D3×Dic3—122no—
339#518—271noSylow
340C2×C33C23×C411yescharacteristic
341C2×C33H(5,𝔽2)11yescharacteristic
342C2×C33H(5,𝔽2)11yescharacteristic
343C3⋊(C3⋊D3)—24no—
344C3×C3⋊D3—24no—
345C32×D3—22no—
346C23×D3—92no—
347C23×D3—92no—
348C23×D3—92no—
349C23×D3—182no—
350C2×C3×D4—91no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—61no—
354C22×C3×C4—92no—
355C2×#67—92no—
356C22×Dic3—92no—
357D3×D4—98no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—61no—
361C2×D12—98no—
362C2×D12—98no—
363C2×D12—92no—
364C2×D12—92no—
365C2×D12—91no—
366C2×D12—91no—
367C2×D12—91no—
368C2×D12—188no—
369C2×D12—181no—
370C2×D12—181no—
371C2×D12—181no—
372C2×D12—182no—
373C2×D12—361no—
374C2×C4×D3—32no—
375C2×C4×D3—32no—
376C2×C4×D3—92no—
377C2×C4×D3—92no—
378C2×C4×D3—92no—
379C2×C4×D3—92no—
380C2×C4×D3—92no—
381C2×C4×D3—92no—
382C2×C4×D3—92no—
383C2×C4×D3—92no—
384C2×C4×D3—182no—
385C2×C4×D3—182no—
386C2×C4×D3D3211yescharacteristic
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—61no—
390C3×C4⋊C4—91no—
391C3×C4⋊C4—91no—
392C3×C4⋊C4—91no—
393C3×C22⋊C4—92no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—92no—
396C3×C22⋊C4—91no—
397C3×C42—31no—
398C3×C42—31no—
399C3×C42—61no—
400C3×C42—92no—
401C3×C42—91no—
402#217—32no—
403#217—31no—
404#217—31no—
405#217—92no—
406(C2×D3)⋊C4—31no—
407(C2×D3)⋊C4—31no—
408(C2×D3)⋊C4—32no—
409(C2×D3)⋊C4—32no—
410(C2×D3)⋊C4—32no—
411(C2×D3)⋊C4—92no—
412(C2×D3)⋊C4—92no—
413(C2×D3)⋊C4—92no—
414(C2×D3)⋊C4—92no—
415(C2×D3)⋊C4—92no—
416(C2×D3)⋊C4—92no—
417(C2×D3)⋊C4—92no—
418(C2×D3)⋊C4—92no—
419(C2×D3)⋊C4—182no—
420(C2×D3)⋊C4—182no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426C4⋊Dic3D3211yescharacteristic, complemented
427Dic3⋊C4—31no—
428Dic3⋊C4—31no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—32no—
432C4×Dic3—32no—
433C4×Dic3—61no—
434C4×Dic3D3211yescharacteristic, complemented
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—21no—
438C22×C32—32no—
439C22×C32—41no—
440C22×C32—61no—
441C22×C32—61no—
442C22×C32C23×D311yescharacteristic
443C22×C32C23×D311yescharacteristic
444C22×C32C23×D311yescharacteristic
445C2×C3⋊D3—22no—
446C2×C3⋊D3—22no—
447C2×C3⋊D3—34no—
448C2×C3⋊D3—34no—
449C2×C3⋊D3—34no—
450C2×C3⋊D3—64no—
451C2×C3⋊D3—64no—
452C2×C3⋊D3—64no—
453C2×C3⋊D3—62no—
454C2×C3⋊D3—62no—
455C2×C3⋊D3—62no—
456C2×C3⋊D3—62no—
457C2×C3⋊D3—62no—
458C2×C3⋊D3—62no—
459C2×C3⋊D3—124no—
460C2×C3⋊D3—122no—
461C2×C3⋊D3—122no—
462C2×C3⋊D3—122no—
463C2×C3⋊D3—122no—
464C2×C3⋊D3—122no—
465C2×C3⋊D3—122no—
466C2×C3⋊D3—128no—
467C2×C3⋊D3—242no—
468C2×C3⋊D3—242no—
469C2×C3⋊D3C2×C4×D314yes—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—22no—
477C2×C3×D3—34no—
478C2×C3×D3—34no—
479C2×C3×D3—64no—
480C2×C3×D3—62no—
481C2×C3×D3—62no—
482C2×C3×D3—62no—
483C2×C3×D3—62no—
484C2×C3×D3—122no—
485C2×C3×D3—122no—
486C2×C3×D3C2×C4×D312yes—
487C2×C3×D3C2×C4×D312yes—
488D32—128no—
489D32—128no—
490D32—1216no—
491C32×C4—22no—
492C32×C4—22no—
493C32×C4—22no—
494C32×C4—32no—
495C32×C4—42no—
496C32×C4—61no—
497C32×C4—61no—
498C32×C4—62no—
499C32×C4C2×C4×D312yes—
500C32×C4C2×C4×D312yes—
501C32×C4C2×C4×D312yes—
502C3⋊Dic3—21no—
503C3⋊Dic3—21no—
504C3⋊Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—21no—
507C3×Dic3—22no—
508C3×Dic3—21no—
509C3×Dic3—21no—
510C3×Dic3—22no—
511C3×Dic3—21no—
512C3×Dic3—22no—
513C3×Dic3—42no—
514C3×Dic3—41no—
515C3×Dic3—62no—
516C3×Dic3—61no—
517C3×Dic3—61no—
518C3×Dic3—62no—
519C3×Dic3—61no—
520C3×Dic3—61no—
521C3×Dic3—62no—
522C3×Dic3—122no—
523C3×Dic3—121no—
524C3×Dic3C2×C4×D312yes—
525C3×Dic3C2×C4×D312yes—
526C22×D4—271no—
527C4×D4—91no—
528C4×D4—271no—
529C4×D4—272no—
530C4×D4—271no—
531C4×D4—272no—
532C4×D4—271no—
533#117—91no—
534#117—91no—
535C2×C22⋊C4—272no—
536C2×C22⋊C4—272no—
537C33#51811yescharacteristic, complemented, Sylow
538C23×C3—31no—
539C23×C3—31no—
540C23×C3—61no—
541C23×C3—92no—
542C22×D3—32no—
543C22×D3—32no—
544C22×D3—62no—
545C22×D3—98no—
546C22×D3—98no—
547C22×D3—92no—
548C22×D3—92no—
549C22×D3—92no—
550C22×D3—98no—
551C22×D3—188no—
552C22×D3—182no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—362no—
556C22×D3—362no—
557C22×D3—362no—
558C22×D3—362no—
559C22×D3—362no—
560C22×D3—362no—
561C22×D3—362no—
562C22×D3—364no—
563C22×D3—364no—
564C22×D3C2×D3211yescharacteristic
565C3×D4—94no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—34no—
572C2×C3×C4—34no—
573C2×C3×C4—32no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—32no—
578C2×C3×C4—31no—
579C2×C3×C4—41no—
580C2×C3×C4—64no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—62no—
585C2×C3×C4—92no—
586C2×C3×C4—91no—
587C2×C3×C4—91no—
588C2×C3×C4—362no—
589C2×C3×C4C2×D3211yescharacteristic
590C2×C3×C4C2×D3211yescharacteristic
591C2×C3×C4C2×D3211yescharacteristic
592#67—98no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—32no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—32no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—62no—
602C2×Dic3—362no—
603C2×Dic3C2×D3212yes—
604C2×Dic3C2×D3211yescharacteristic
605C2×Dic3C2×D3211yescharacteristic
606C2×Dic3C2×D3211yescharacteristic
607D12—34no—
608D12—34no—
609D12—64no—
610D12—98no—
611D12—98no—
612D12—94no—
613D12—94no—
614D12—94no—
615D12—184no—
616D12—184no—
617D12—184no—
618D12—188no—
619D12—364no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—362no—
623C4×D3—362no—
624C4×D3—362no—
625C4×D3—362no—
626C4×D3—362no—
627C4×D3—362no—
628C4×D3—364no—
629C4×D3—362no—
630C4×D3—362no—
631C4×D3—364no—
632C4×D3#62414yescomplemented
633C2×C32—21no—
634C2×C32—21no—
635C2×C32—21no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—21no—
639C2×C32—21no—
640C2×C32—21no—
641C2×C32—21no—
642C2×C32—41no—
643C2×C32—41no—
644C2×C32—41no—
645C2×C32—62no—
646C2×C32C22×C4×D311yescharacteristic
647C2×C32C22×C4×D311yescharacteristic
648C2×C32C22×C4×D311yescharacteristic
649C2×C32#100411yescharacteristic
650C2×C32#100911yescharacteristic
651C2×C32#100911yescharacteristic
652C2×C32#100911yescharacteristic
653C2×C32#100911yescharacteristic
654C2×C32#100911yescharacteristic
655C3⋊D3—24no—
656C3⋊D3—64no—
657C3⋊D3—64no—
658C3⋊D3—64no—
659C3⋊D3—124no—
660C3⋊D3—124no—
661C3⋊D3—124no—
662C3⋊D3—244no—
663C3×D3—24no—
664C3×D3—22no—
665C3×D3—22no—
666C3×D3—64no—
667C3×D3—64no—
668C3×D3—124no—
669C24—272no—
670C2×D4—91no—
671C2×D4—278no—
672C2×D4—272no—
673C2×D4—271no—
674C22×C4—31no—
675C22×C4—92no—
676C22×C4—272no—
677C22×C4—272no—
678C22×C4—272no—
679C4⋊C4—31no—
680C4⋊C4—91no—
681C4⋊C4—91no—
682C4⋊C4—91no—
683C22⋊C4—92no—
684C22⋊C4—91no—
685C22⋊C4—91no—
686C22⋊C4—92no—
687C22⋊C4—272no—
688C22⋊C4—272no—
689C22⋊C4—272no—
690C42—31no—
691C42—92no—
692C42—91no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—32no—
697C22×C3—32no—
698C22×C3—41no—
699C22×C3—62no—
700C22×C3—62no—
701C22×C3—62no—
702C22×C3—61no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—61no—
706C22×C3—94no—
707C22×C3—182no—
708C22×C3—182no—
709C22×C3C22×D3211yescharacteristic
710C22×C3C22×D3211yescharacteristic
711C22×C3C22×D3211yescharacteristic
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—34no—
715C2×D3—34no—
716C2×D3—64no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—94no—
722C2×D3—94no—
723C2×D3—94no—
724C2×D3—122no—
725C2×D3—122no—
726C2×D3—184no—
727C2×D3—184no—
728C2×D3—184no—
729C2×D3—182no—
730C2×D3—182no—
731C2×D3—182no—
732C2×D3—182no—
733C2×D3—182no—
734C2×D3—182no—
735C2×D3—364no—
736C2×D3—362no—
737C2×D3—362no—
738C2×D3—362no—
739C2×D3—362no—
740C2×D3—362no—
741C2×D3—362no—
742C2×D3—368no—
743C2×D3—368no—
744C2×D3—368no—
745C2×D3—3616no—
746C2×D3—722no—
747C2×D3—722no—
748C2×D3C2×#62412yes—
749C3×C4—22no—
750C3×C4—22no—
751C3×C4—22no—
752C3×C4—32no—
753C3×C4—32no—
754C3×C4—42no—
755C3×C4—62no—
756C3×C4—62no—
757C3×C4—62no—
758C3×C4—61no—
759C3×C4—62no—
760C3×C4—61no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—122no—
764C3×C4—121no—
765C3×C4—182no—
766C3×C4—181no—
767C3×C4—181no—
768C3×C4C4×D3212yes—
769C3×C4C4×D3212yes—
770C3×C4C2×#62412yes—
771Dic3—21no—
772Dic3—21no—
773Dic3—22no—
774Dic3—62no—
775Dic3—61no—
776Dic3—61no—
777Dic3—61no—
778Dic3—62no—
779Dic3—61no—
780Dic3—62no—
781Dic3—122no—
782Dic3—121no—
783Dic3C2×#62412yes—
784C32—21no—
785C32—21no—
786C32—21no—
787C32—41no—
788C32#552111yescharacteristic, complemented
789C32#552111yescharacteristic, complemented
790C32#554511yescharacteristic, complemented
791C23—31no—
792C23—92no—
793C23—278no—
794C23—272no—
795C23—1082no—
796C23—1082no—
797D4—94no—
798D4—278no—
799D4—274no—
800C2×C4—31no—
801C2×C4—34no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—32no—
805C2×C4—91no—
806C2×C4—92no—
807C2×C4—91no—
808C2×C4—362no—
809C2×C4—1082no—
810C2×C4—1082no—
811C2×C4—1082no—
812C2×C4D3311yescharacteristic
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—41no—
823C2×C3—41no—
824C2×C3—41no—
825C2×C3—64no—
826C2×C3—62no—
827C2×C3—62no—
828C2×C3—184no—
829C2×C3C2×C4×D3211yescharacteristic
830C2×C3C2×C4×D3211yescharacteristic
831C2×C3#6430711yescharacteristic
832C2×C3#6430811yescharacteristic
833C2×C3#6430811yescharacteristic
834C2×C3#6430811yescharacteristic
835C2×C3#6431411yescharacteristic
836C2×C3#6432011yescharacteristic
837C2×C3C22×#62411yescharacteristic
838D3—22no—
839D3—64no—
840D3—64no—
841D3—124no—
842D3—184no—
843D3—184no—
844D3—184no—
845D3—364no—
846D3—364no—
847D3—364no—
848D3—724no—
849C22—32no—
850C22—61no—
851C22—61no—
852C22—94no—
853C22—182no—
854C22—182no—
855C22—274no—
856C22—542no—
857C22—542no—
858C22—1088no—
859C22C2×D3311yescharacteristic
860C4—32no—
861C4—61no—
862C4—62no—
863C4—61no—
864C4—181no—
865C4—182no—
866C4—181no—
867C4D3×#62412yes—
868C3—21no—
869C3—21no—
870C3—21no—
871C3—41no—
872C3#1059399411yescharacteristic, complemented
873C3#1059460411yescharacteristic, complemented
874C3#1059499611yescharacteristic, complemented
875C2—62no—
876C2—184no—
877C2—544no—
878C2#1172438411yescharacteristic
879C2#1172439011yescharacteristic
880C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC2×C33×C4C23
socle, cosocleC22×C33C24
prime radicalC2×D3×C4⋊(C3⋊D3)C2
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. #11723494C2semidirect
4. #11723484C2semidirect
5. C3×#63894C2semidirect
6. C3×#63855C2semidirect
7. C3×#63841C2semidirect
8. #11722937C2semidirect
9. #11722933C2semidirect
10. #11722906C2semidirect
11. #11722904C2semidirect
19. C2×#6294C22semidirect
21. C2×#6289C22semidirect
22. C2×#6289C22semidirect
23. D3×C4⋊(C3⋊D3)C4semidirect
24. C2×C3×#624C22semidirect
25. C3×C4⋊(C3⋊Dic3)C22semidirect
26. C3×C4×C3⋊Dic3C22semidirect
27. C32×C4⋊Dic3C22semidirect
28. C32×C4×Dic3C22semidirect
29. #88814C22semidirect
30. #88804C22semidirect
31. #88804C22semidirect
32. C3×Dic3⋊Dic3C22semidirect
33. C3×Dic3⋊Dic3C22semidirect
34. C3×#3722C22semidirect
38. C3×Dic32C22semidirect
69. #63894D3semidirect
73. #63855D3semidirect
74. #63841D3semidirect
80. C2×D3×C3⋊D3C2×C4semidirect
82. C4⋊(C3⋊(C3⋊D3))C2×C4semidirect
86. C3×C4⋊(C3⋊D3)C2×C4semidirect
91. C32×C4×D3C2×C4semidirect
93. #6292C2×C4semidirect
135. C2×#624C2×D3semidirect
145. C4⋊(C3⋊Dic3)C2×D3semidirect
146. C4×C3⋊Dic3C2×D3semidirect
161. C3×C4⋊Dic3C2×D3semidirect
162. C3×C4⋊Dic3C2×D3semidirect
171. C3×C4×Dic3C2×D3semidirect
172. C3×C4×Dic3C2×D3semidirect
173. Dic3⋊Dic3C2×D3semidirect
174. Dic3⋊Dic3C2×D3semidirect
182. #3722C2×D3semidirect
188. Dic32C2×D3semidirect
294. C4⋊(C3⋊D3)C4×D3semidirect
324. C3×C4×D3C4×D3semidirect
325. C3×C4×D3C4×D3semidirect
426. C4⋊Dic3D32semidirect
434. C4×Dic3D32semidirect
537. C33#518semidirect
632. C4×D3#624semidirect
788. C32#5521semidirect
789. C32#5521semidirect
790. C32#5545semidirect
872. C3#10593994semidirect
873. C3#10594604semidirect
874. C3#10594996semidirect

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
#117236912
#117234942
#117234842
C3×#638942
C3×#638552
C3×#638412
#117229372
#117229332
#117229062
#117229042
#105949963
#105946043
#105939943