Finite Group Databasebeta

← #13168076

Subgroups — #13168076

Order 1728.

1630 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D12C211yesmaximal, characteristic, complemented
2C2×C3×#3796C211yesmaximal, characteristic, complemented
3#11723696C211yesmaximal, characteristic, complemented
4C4×#6290C211yesmaximal, characteristic, complemented
5#11723499C211yesmaximal, characteristic, complemented
6#11723436C211yesmaximal, characteristic, complemented
7C3×#63856C211yesmaximal, characteristic, complemented
8#11722986C212yesmaximal, complemented
9#11722955C212yesmaximal, complemented
10#11722947C212yesmaximal, complemented
11D3×(C2×D3)⋊Dic3C212yesmaximal, complemented
12#10595427—31nomaximal
13#10595244—31nomaximal
14#10594889—31nomaximal
15C22×C3×D32C2212yes—
16C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
18C2×C32×D12C2211yescharacteristic
19C2×C32×C4×D3C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic, complemented
21C2×#6295C2212yescomplemented
22C2×#6290C2211yescharacteristic
23C2×D3×C3⋊Dic3C2212yescomplemented
24C2×C3×#626C2212yes—
25C2×C3×#626C2212yescomplemented
26C2×C3×D3×Dic3C2212yescomplemented
27C3×D3×D12—24no—
28C3×#3796—24no—
29C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31#88814C2212yescomplemented
32#88806C2211yescharacteristic, complemented
33#88803C2212yescomplemented
34#88803C2212yescomplemented
35#88803C2211yescharacteristic, complemented
36(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38C3×#3724C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yes—
40C2×C3×#239—31no—
41C2×C3×#237—31no—
42C2×C3×D3×D4—31no—
43C22×C3×D12—31no—
44C2×D3×D12D311yescharacteristic, complemented
45C2×#3796D311yescharacteristic, complemented
46#64156—31no—
47D4×C3⋊Dic3—31no—
48C4×#638—31no—
49C3×#946—31no—
50C3×#924—31no—
51#63980—32no—
52#63977—32no—
53#63976—32no—
54D3×#217—32no—
55#63961—32no—
56C2×(C2×D3)⋊Dic3—32no—
57#63922—32no—
58D3×(C2×D3)⋊C4—32no—
59#63916—31no—
60#63909—31no—
61#63908—31no—
62C4×#625—31no—
63C4×#625—31no—
64C4×#625—61no—
65#63898—31no—
66#63898—31no—
67#63898—61no—
68#63886—32no—
69#63886—32no—
70#63884—32no—
71#63863—31no—
72#63863—31no—
73#63863—61no—
74#63856D311yescharacteristic, complemented
75#63850—32no—
76C22×C3×C3⋊D3C2312yes—
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3C2312yes—
79C22×C32×D3C2311yescharacteristic
80C2×C3×D32—24no—
81C2×C3×D32—24no—
82C2×C3×D32—42no—
83C2×C33×C4C2311yescharacteristic
84C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
85C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C3×C4⋊(C3⋊D3)—22no—
89C3×C4×C3⋊D3—22no—
90C2×C32×Dic3C2312yes—
91C2×C32×Dic3C2311yescharacteristic
92C32×D12D414yescomplemented
93C32×C4×D3—22no—
94C32×Dic6—22no—
95#6295—42no—
96#6290—22no—
97D3×C3⋊Dic3—42no—
98C3×#626—24no—
99C3×#626—24no—
100C3×D3×Dic3—24no—
101#5829—91no—
102#5806—91no—
103#5630—91no—
104C23×C3×D3—32no—
105C23×C3×D3—32no—
106C22×D32C2×D312yes—
107C2×C32×Q8—31no—
108C2×C32×D4—31no—
109C22×C32×C4—31no—
110C2×#638—31no—
111C22×C3⋊Dic3—32no—
112C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
113C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
114C2×C3×#67—32no—
115C2×C3×#67—32no—
116C22×C3×Dic3—32no—
117C3×#239—64no—
118C3×#237—64no—
119C3×D3×D4—64no—
120C2×C3×D12—21no—
121C2×C3×D12—32no—
122C2×C3×D12—32no—
123C2×C3×D12—31no—
124C2×C3×D12—31no—
125C2×C3×D12—64no—
126C2×C3×D12—61no—
127C2×C3×D12C2×D311yescharacteristic
128C2×C3×D12C2×D311yescharacteristic
129C2×C3×C4×D3—21no—
130C2×C3×C4×D3—32no—
131C2×C3×C4×D3—31no—
132C2×C3×C4×D3—31no—
133C2×C3×C4×D3—61no—
134C2×C3×C4×D3C2×D311yescharacteristic
135C2×C3×C4×D3C2×D311yescharacteristic
136C2×C3×Dic6—21no—
137C2×C3×Dic6C2×D311yescharacteristic, complemented
138C2×C3×Dic6C2×D311yescharacteristic, complemented
139C2×#626—32no—
140C2×#626—32no—
141C2×#626C2×D312yes—
142C2×#626C2×D312yescomplemented
143C2×#625—31no—
144C2×#625—31no—
145C2×#625—32no—
146C2×#625—61no—
147C2×D3×Dic3—32no—
148C2×D3×Dic3—32no—
149C2×D3×Dic3—62no—
150C2×D3×Dic3C2×D312yescomplemented
151D3×D12—24no—
152#3796—24no—
153#3757—31no—
154#3757—32no—
155#3752—32no—
156#3752—31no—
157#3752—32no—
158C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
159#3750—31no—
160C4×C3⋊Dic3—31no—
161C4×C3⋊Dic3—31no—
162C4×C3⋊Dic3—31no—
163C4×C3⋊Dic3—61no—
164C4×C3⋊Dic3—61no—
165C4×C3⋊Dic3—61no—
166C4×C3⋊Dic3—121no—
167C3×#217—32no—
168C3×(C2×D3)⋊C4—32no—
169C3×C4⋊Dic3—31no—
170C3×C4⋊Dic3—31no—
171C3×C4⋊Dic3—61no—
172C3×Dic3⋊C4—32no—
173C3×Dic3⋊C4—32no—
174#3724—31no—
175#3724—31no—
176#3724—61no—
177#3724C2×D312yescomplemented
178#3722—32no—
179(C2×D3)⋊Dic3—32no—
180(C2×D3)⋊Dic3—32no—
181(C2×D3)⋊Dic3—31no—
182(C2×D3)⋊Dic3—31no—
183(C2×D3)⋊Dic3—32no—
184(C2×D3)⋊Dic3—32no—
185(C2×D3)⋊Dic3—32no—
186(C2×D3)⋊Dic3—32no—
187(C2×D3)⋊Dic3—32no—
188(C2×D3)⋊Dic3—32no—
189(C2×D3)⋊Dic3—31no—
190(C2×D3)⋊Dic3—31no—
191(C2×D3)⋊Dic3—62no—
192(C2×D3)⋊Dic3—62no—
193(C2×D3)⋊Dic3—61no—
194(C2×D3)⋊Dic3—62no—
195(C2×D3)⋊Dic3—61no—
196(C2×D3)⋊Dic3C2×D312yes—
197C22×C33C2411yescharacteristic
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—22no—
200C2×C3×C3⋊D3—21no—
201C2×C3×C3⋊D3—22no—
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—22no—
204C2×C32×D3—21no—
205C2×C32×D3—22no—
206C2×C32×D3—22no—
207C2×C32×D3—21no—
208C2×C32×D3C2×D414yes—
209C2×C32×D3#4112yescomplemented
210C3×D32—48no—
211C33×C4C2×D412yes—
212C3⋊(C3⋊Dic3)—21no—
213C3⋊(C3⋊Dic3)—21no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—22no—
216C32×Dic3—22no—
217C32×Dic3—21no—
218C2×C3×#41—91no—
219C22×C3×D4—91no—
220C2×#239—31no—
221C2×#237—31no—
222C2×D3×D4—31no—
223C22×D12—31no—
224C3×C22⋊Q8—91no—
225#953—92no—
226C2×#217—92no—
227#947—91no—
228#947—91no—
229#947—181no—
230#946—31no—
231#939—92no—
232#939—92no—
233#938—91no—
234#937—92no—
235#936—91no—
236#935—92no—
237D4×Dic3—91no—
238D4×Dic3—91no—
239D4×Dic3—181no—
240#930—91no—
241#929—92no—
242C4×#67—91no—
243C4×#67—91no—
244C4×#67—91no—
245C4×#67—181no—
246C2×(C2×D3)⋊C4—92no—
247#924—31no—
248#895—91no—
249#895—92no—
250#894—92no—
251#893—91no—
252#882—92no—
253D3×C22⋊C4—92no—
254C23×C32—31no—
255C23×C32—32no—
256C22×C3⋊D3C22×D312yes—
257C22×C3⋊D3C22×D311yescharacteristic
258C22×C3×D3—22no—
259C22×C3×D3—21no—
260C22×C3×D3—32no—
261C22×C3×D3—32no—
262C22×C3×D3—31no—
263C22×C3×D3—31no—
264C22×C3×D3—61no—
265C22×C3×D3—62no—
266C22×C3×D3—64no—
267C22×C3×D3—64no—
268C22×C3×D3—64no—
269C22×C3×D3—64no—
270C22×C3×D3—122no—
271C22×C3×D3—122no—
272C22×C3×D3C22×D311yescharacteristic
273C22×C3×D3C22×D311yescharacteristic
274C22×C3×D3C22×D312yes—
275C22×C3×D3C22×D312yes—
276C2×D32—24no—
277C2×D32—24no—
278C2×D32—42no—
279C32×Q8—62no—
280C32×D4—34no—
281C2×C32×C4—21no—
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4—31no—
285C2×C32×C4—32no—
286C2×C32×C4—41no—
287C2×C32×C4—62no—
288C2×C32×C4C22×D311yescharacteristic
289C2×C32×C4C22×D311yescharacteristic
290C2×C32×C4C22×D311yescharacteristic
291#638—62no—
292C2×C3⋊Dic3—31no—
293C2×C3⋊Dic3—31no—
294C2×C3⋊Dic3—31no—
295C2×C3⋊Dic3—31no—
296C2×C3⋊Dic3—31no—
297C2×C3⋊Dic3—31no—
298C2×C3⋊Dic3—61no—
299C2×C3⋊Dic3—61no—
300C2×C3⋊Dic3—61no—
301C2×C3⋊Dic3—61no—
302C2×C3⋊Dic3—61no—
303C2×C3⋊Dic3—61no—
304C2×C3⋊Dic3—121no—
305C2×C3⋊Dic3—121no—
306C2×C3⋊Dic3—122no—
307C2×C3⋊Dic3C22×D311yescharacteristic
308C2×C3⋊Dic3C22×D312yes—
309C4⋊(C3⋊D3)—22no—
310C4×C3⋊D3—22no—
311C3×#67—64no—
312C3×#67—64no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—21no—
315C2×C3×Dic3—31no—
316C2×C3×Dic3—32no—
317C2×C3×Dic3—31no—
318C2×C3×Dic3—32no—
319C2×C3×Dic3—61no—
320C2×C3×Dic3—62no—
321C2×C3×Dic3—64no—
322C2×C3×Dic3C22×D312yes—
323C2×C3×Dic3C22×D312yes—
324C2×C3×Dic3C22×D311yescharacteristic
325C2×C3×Dic3C22×D311yescharacteristic
326C3×D12—24no—
327C3×D12—64no—
328C3×D12—64no—
329C3×D12—62no—
330C3×D12—62no—
331C3×D12—122no—
332C3×D12#6714yescomplemented
333C3×D12#6714yescomplemented
334C3×C4×D3—22no—
335C3×C4×D3—22no—
336C3×C4×D3—42no—
337C3×C4×D3—64no—
338C3×C4×D3—62no—
339C3×C4×D3—62no—
340C3×C4×D3—122no—
341C3×Dic6—22no—
342C3×Dic6—22no—
343C3×Dic6—42no—
344#626—24no—
345#626—24no—
346#626—122no—
347#626—122no—
348#625—64no—
349#625—62no—
350#625—62no—
351#625—122no—
352D3×Dic3—24no—
353D3×Dic3—122no—
354D3×Dic3—122no—
355D3×Dic3—124no—
356#546—271noSylow
357C2×C33C22×D411yescharacteristic
358C2×C33C2×#4111yescharacteristic
359C2×C33H(5,𝔽2)11yescharacteristic
360C3×C3⋊D3—41no—
361C3×C3⋊D3—42no—
362C32×D3—22no—
363C32×D3—24no—
364C24×C3—92no—
365C23×D3—32no—
366C23×D3—32no—
367C3×#41—184no—
368C2×C3×Q8—31no—
369C2×C3×Q8—31no—
370C2×C3×Q8—61no—
371C2×C3×D4—31no—
372C2×C3×D4—31no—
373C2×C3×D4—61no—
374C2×C3×D4—92no—
375C2×C3×D4—92no—
376C2×C3×D4—91no—
377C2×C3×D4—184no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—61no—
381C22×C3×C4—92no—
382C22×C3×C4—91no—
383C2×#67—32no—
384C2×#67—32no—
385C2×#67—92no—
386C2×#67—92no—
387C2×#67—91no—
388C2×#67—91no—
389C2×#67—91no—
390C2×#67—181no—
391C22×Dic3—32no—
392C22×Dic3—92no—
393C22×Dic3—92no—
394C22×Dic3—182no—
395#239—64no—
396#237—64no—
397D3×D4—64no—
398C2×D12—32no—
399C2×D12—32no—
400C2×D12—31no—
401C2×D12—31no—
402C2×D12—61no—
403C2×D12—64no—
404C2×D12—92no—
405C2×D12D3211yescharacteristic
406C2×C4×D3—32no—
407C2×C4×D3—31no—
408C2×C4×D3—31no—
409C2×C4×D3—61no—
410C2×C4×D3—92no—
411C2×C4×D3D3211yescharacteristic
412C2×Dic6D3211yescharacteristic, complemented
413C3×C4⋊C4—92no—
414C3×C4⋊C4—91no—
415C3×C22⋊C4—92no—
416#217—32no—
417#217—92no—
418#217—91no—
419#217—91no—
420#217—92no—
421#217—92no—
422#217—91no—
423#217—92no—
424#217—92no—
425#217—181no—
426#217—182no—
427(C2×D3)⋊C4—32no—
428(C2×D3)⋊C4—92no—
429(C2×D3)⋊C4—92no—
430(C2×D3)⋊C4—92no—
431(C2×D3)⋊C4—92no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—92no—
434(C2×D3)⋊C4—91no—
435(C2×D3)⋊C4—92no—
436(C2×D3)⋊C4—92no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—181no—
439(C2×D3)⋊C4—182no—
440(C2×D3)⋊C4—182no—
441C4⋊Dic3—31no—
442C4⋊Dic3—31no—
443C4⋊Dic3—61no—
444Dic3⋊C4—32no—
445Dic3⋊C4—32no—
446Dic3⋊C4—91no—
447Dic3⋊C4—91no—
448Dic3⋊C4—91no—
449Dic3⋊C4—181no—
450C4×Dic3—91no—
451C4×Dic3—91no—
452C4×Dic3—91no—
453C4×Dic3—181no—
454C4×Dic3—181no—
455C4×Dic3—181no—
456C4×Dic3—361no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—34no—
461C22×C32—32no—
462C22×C32—41no—
463C22×C32—62no—
464C22×C32—62no—
465C22×C32—61no—
466C22×C32—61no—
467C22×C32C23×D311yescharacteristic
468C22×C32C23×D311yescharacteristic
469C22×C32C23×D311yescharacteristic
470C2×C3⋊D3—21no—
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—22no—
476C2×C3×D3—21no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—21no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—22no—
485C2×C3×D3—24no—
486C2×C3×D3—42no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—42no—
490C2×C3×D3—62no—
491C2×C3×D3—61no—
492C2×C3×D3—62no—
493C2×C3×D3—61no—
494C2×C3×D3—61no—
495C2×C3×D3—61no—
496C2×C3×D3—62no—
497C2×C3×D3—62no—
498C2×C3×D3—61no—
499C2×C3×D3—62no—
500C2×C3×D3—62no—
501C2×C3×D3—61no—
502C2×C3×D3—62no—
503C2×C3×D3—121no—
504C2×C3×D3—121no—
505C2×C3×D3—122no—
506C2×C3×D3—122no—
507C2×C3×D3—122no—
508C2×C3×D3—128no—
509C2×C3×D3—128no—
510C2×C3×D3#23712yescomplemented
511C2×C3×D3#23912yescomplemented
512C2×C3×D3C2×#6714yes—
513C2×C3×D3C2×#6714yes—
514D32—48no—
515C32×C4—22no—
516C32×C4—22no—
517C32×C4—22no—
518C32×C4—42no—
519C32×C4—62no—
520C32×C4—61no—
521C32×C4D3×D412yes—
522C32×C4C2×#6712yes—
523C32×C4C2×#6712yes—
524C3⋊Dic3—22no—
525C3⋊Dic3—21no—
526C3⋊Dic3—61no—
527C3⋊Dic3—61no—
528C3⋊Dic3—62no—
529C3⋊Dic3—62no—
530C3⋊Dic3—61no—
531C3⋊Dic3—61no—
532C3⋊Dic3—61no—
533C3⋊Dic3—61no—
534C3⋊Dic3—121no—
535C3⋊Dic3—121no—
536C3⋊Dic3—121no—
537C3⋊Dic3—121no—
538C3⋊Dic3—122no—
539C3⋊Dic3—122no—
540C3×Dic3—22no—
541C3×Dic3—21no—
542C3×Dic3—22no—
543C3×Dic3—21no—
544C3×Dic3—42no—
545C3×Dic3—41no—
546C3×Dic3—61no—
547C3×Dic3—62no—
548C3×Dic3—62no—
549C3×Dic3—61no—
550C3×Dic3—122no—
551C3×Dic3—121no—
552C2×#41—91no—
553C22×D4—91no—
554#124—271no—
555#123—272no—
556C22⋊Q8—91no—
557#121—271no—
558#121—272no—
559#120—272no—
560C4×D4—271no—
561C4×D4—271no—
562C2×C22⋊C4—272no—
563C33#54611yescharacteristic, complemented, Sylow
564C23×C3—31no—
565C23×C3—31no—
566C23×C3—32no—
567C23×C3—32no—
568C23×C3—62no—
569C23×C3—61no—
570C23×C3—92no—
571C23×C3—91no—
572C23×C3—184no—
573C23×C3—184no—
574C23×C3—362no—
575C22×D3—32no—
576C22×D3—32no—
577C22×D3—31no—
578C22×D3—31no—
579C22×D3—61no—
580C22×D3—62no—
581C22×D3—64no—
582C22×D3—64no—
583C22×D3—64no—
584C22×D3—64no—
585C22×D3—122no—
586C22×D3—122no—
587C22×D3C2×D3211yescharacteristic
588C22×D3C2×D3212yes—
589C3×Q8—62no—
590C3×Q8—62no—
591C3×Q8—122no—
592C3×D4—34no—
593C3×D4—34no—
594C3×D4—64no—
595C3×D4—184no—
596C3×D4—184no—
597C3×D4—182no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—31no—
602C2×C3×C4—32no—
603C2×C3×C4—31no—
604C2×C3×C4—32no—
605C2×C3×C4—41no—
606C2×C3×C4—61no—
607C2×C3×C4—62no—
608C2×C3×C4—62no—
609C2×C3×C4—62no—
610C2×C3×C4—91no—
611C2×C3×C4—92no—
612C2×C3×C4—122no—
613C2×C3×C4—184no—
614C2×C3×C4—182no—
615C2×C3×C4C2×D3211yescharacteristic
616C2×C3×C4C2×D3211yescharacteristic
617C2×C3×C4C2×D3211yescharacteristic
618#67—64no—
619#67—64no—
620#67—182no—
621#67—182no—
622#67—184no—
623#67—182no—
624#67—362no—
625#67—362no—
626C2×Dic3—32no—
627C2×Dic3—32no—
628C2×Dic3—31no—
629C2×Dic3—31no—
630C2×Dic3—61no—
631C2×Dic3—62no—
632C2×Dic3—64no—
633C2×Dic3—91no—
634C2×Dic3—91no—
635C2×Dic3—91no—
636C2×Dic3—91no—
637C2×Dic3—91no—
638C2×Dic3—91no—
639C2×Dic3—181no—
640C2×Dic3—181no—
641C2×Dic3—181no—
642C2×Dic3—181no—
643C2×Dic3—181no—
644C2×Dic3—181no—
645C2×Dic3—361no—
646C2×Dic3—361no—
647C2×Dic3—362no—
648C2×Dic3—362no—
649C2×Dic3—364no—
650C2×Dic3C2×D3211yescharacteristic
651C2×Dic3C2×D3212yes—
652D12—64no—
653D12—64no—
654D12—62no—
655D12—62no—
656D12—122no—
657D12—362no—
658D12#62514yescomplemented
659C4×D3—22no—
660C4×D3—64no—
661C4×D3—62no—
662C4×D3—62no—
663C4×D3—122no—
664C4×D3—362no—
665Dic6—22no—
666C2×C32—21no—
667C2×C32—21no—
668C2×C32—21no—
669C2×C32—21no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32—41no—
676C2×C32—41no—
677C2×C32—41no—
678C2×C32—62no—
679C2×C32—64no—
680C2×C32C2×D3×D411yescharacteristic
681C2×C32C2×#23711yescharacteristic
682C2×C32#100411yescharacteristic
683C2×C32C2×#23911yescharacteristic
684C2×C32D3×#4111yescharacteristic
685C2×C32#100911yescharacteristic
686C2×C32#100911yescharacteristic
687C2×C32C22×#6711yescharacteristic
688C2×C32C22×#6711yescharacteristic
689C3⋊D3—41no—
690C3⋊D3—42no—
691C3×D3—22no—
692C3×D3—24no—
693C3×D3—24no—
694C3×D3—22no—
695C3×D3—42no—
696C3×D3—44no—
697C3×D3—122no—
698C3×D3—121no—
699C3×D3—122no—
700C3×D3—121no—
701C3×D3—122no—
702C3×D3—242no—
703C24—92no—
704#41—184no—
705C2×Q8—31no—
706C2×D4—31no—
707C2×D4—92no—
708C2×D4—92no—
709C2×D4—91no—
710C2×D4—184no—
711C2×D4—272no—
712C2×D4—271no—
713C22×C4—31no—
714C22×C4—92no—
715C22×C4—91no—
716C22×C4—272no—
717C4⋊C4—92no—
718C4⋊C4—91no—
719C4⋊C4—271no—
720C22⋊C4—92no—
721C22⋊C4—272no—
722C22⋊C4—271no—
723C22⋊C4—272no—
724C22⋊C4—272no—
725C22⋊C4—271no—
726C22⋊C4—272no—
727C42—271no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—32no—
732C22×C3—32no—
733C22×C3—34no—
734C22×C3—34no—
735C22×C3—41no—
736C22×C3—62no—
737C22×C3—64no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—61no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—122no—
747C22×C3—121no—
748C22×C3—122no—
749C22×C3—121no—
750C22×C3—181no—
751C22×C3—181no—
752C22×C3—182no—
753C22×C3—182no—
754C22×C3—181no—
755C22×C3—182no—
756C22×C3—368no—
757C22×C3C22×D3211yescharacteristic
758C22×C3C22×D3211yescharacteristic
759C22×C3C22×D3211yescharacteristic
760C2×D3—21no—
761C2×D3—22no—
762C2×D3—22no—
763C2×D3—21no—
764C2×D3—62no—
765C2×D3—62no—
766C2×D3—62no—
767C2×D3—61no—
768C2×D3—62no—
769C2×D3—61no—
770C2×D3—62no—
771C2×D3—61no—
772C2×D3—61no—
773C2×D3—61no—
774C2×D3—62no—
775C2×D3—61no—
776C2×D3—62no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—122no—
780C2×D3—122no—
781C2×D3—122no—
782C2×D3—128no—
783C2×D3—128no—
784C2×D3#379612yescomplemented
785C2×D3C2×#62514yes—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—22no—
789C3×C4—42no—
790C3×C4—62no—
791C3×C4—61no—
792C3×C4—61no—
793C3×C4—62no—
794C3×C4—121no—
795C3×C4—122no—
796C3×C4—182no—
797C3×C4—181no—
798C3×C4C2×#62512yes—
799C3×C4D3×#6712yes—
800C3×C4D3×#6712yes—
801Dic3—22no—
802Dic3—21no—
803Dic3—62no—
804Dic3—62no—
805Dic3—61no—
806Dic3—61no—
807Dic3—121no—
808Dic3—122no—
809Dic3—182no—
810Dic3—182no—
811Dic3—181no—
812Dic3—181no—
813Dic3—181no—
814Dic3—181no—
815Dic3—181no—
816Dic3—181no—
817Dic3—361no—
818Dic3—361no—
819Dic3—361no—
820Dic3—361no—
821Dic3—362no—
822Dic3—362no—
823C32—21no—
824C32—21no—
825C32—21no—
826C32—41no—
827C32#563011yescharacteristic, complemented
828C32#580611yescharacteristic, complemented
829C32#582911yescharacteristic, complemented
830C23—31no—
831C23—32no—
832C23—92no—
833C23—91no—
834C23—184no—
835C23—184no—
836C23—362no—
837Q8—62no—
838D4—34no—
839D4—184no—
840D4—184no—
841D4—182no—
842D4—542no—
843D4—1082no—
844C2×C4—32no—
845C2×C4—31no—
846C2×C4—62no—
847C2×C4—92no—
848C2×C4—91no—
849C2×C4—184no—
850C2×C4—182no—
851C2×C4—271no—
852C2×C4—271no—
853C2×C4—1082no—
854C2×C4D3311yescharacteristic
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—21no—
864C2×C3—41no—
865C2×C3—41no—
866C2×C3—41no—
867C2×C3—64no—
868C2×C3—62no—
869C2×C3—64no—
870C2×C3—62no—
871C2×C3—122no—
872C2×C3—124no—
873C2×C3—361no—
874C2×C3—362no—
875C2×C3C2×#379611yescharacteristic
876C2×C3#6430711yescharacteristic
877C2×C3D3×#23711yescharacteristic
878C2×C3#6431411yescharacteristic
879C2×C3D3×#23911yescharacteristic
880C2×C3#6432011yescharacteristic
881C2×C3C22×#62511yescharacteristic
882C2×C3C2×D3×#6711yescharacteristic
883C2×C3C2×D3×#6711yescharacteristic
884D3—22no—
885D3—24no—
886D3—122no—
887D3—122no—
888D3—121no—
889D3—122no—
890D3—121no—
891D3—242no—
892C22—32no—
893C22—34no—
894C22—62no—
895C22—62no—
896C22—61no—
897C22—61no—
898C22—181no—
899C22—182no—
900C22—181no—
901C22—182no—
902C22—181no—
903C22—182no—
904C22—368no—
905C22C2×D3311yescharacteristic
906C4—61no—
907C4—62no—
908C4—182no—
909C4—181no—
910C4—541no—
911C4—541no—
912C4D3×#62512yes—
913C3—21no—
914C3—21no—
915C3—21no—
916C3—41no—
917C3#1059488911yescharacteristic, complemented
918C3#1059524411yescharacteristic, complemented
919C3#1059542711yescharacteristic, complemented
920C2—62no—
921C2—64no—
922C2—362no—
923C2—361no—
924C2D3×#379611yescharacteristic
925C2#1172438511yescharacteristic
926C2C2×D3×#62511yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
hypercenterC2×C4D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×D12C2semidirect
2. C2×C3×#3796C2semidirect
3. #11723696C2semidirect
4. C4×#6290C2semidirect
5. #11723499C2semidirect
6. #11723436C2semidirect
7. C3×#63856C2semidirect
8. #11722986C2semidirect
9. #11722955C2semidirect
10. #11722947C2semidirect
11. D3×(C2×D3)⋊Dic3C2semidirect
17. C2×C3×C4×C3⋊D3C22semidirect
20. C2×C32×Dic6C22semidirect
21. C2×#6295C22semidirect
23. C2×D3×C3⋊Dic3C22semidirect
25. C2×C3×#626C22semidirect
26. C2×C3×D3×Dic3C22semidirect
29. C4×C3⋊(C3⋊Dic3)C22semidirect
30. C3×C4⋊(C3⋊Dic3)C22semidirect
31. #88814C22semidirect
32. #88806C22semidirect
33. #88803C22semidirect
34. #88803C22semidirect
35. #88803C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. C3×#3724C22semidirect
44. C2×D3×D12D3semidirect
45. C2×#3796D3semidirect
74. #63856D3semidirect
92. C32×D12D4semidirect
113. C2×C4×C3⋊D3C2×D3semidirect
137. C2×C3×Dic6C2×D3semidirect
138. C2×C3×Dic6C2×D3semidirect
142. C2×#626C2×D3semidirect
150. C2×D3×Dic3C2×D3semidirect
158. C4⋊(C3⋊Dic3)C2×D3semidirect
177. #3724C2×D3semidirect
209. C2×C32×D3#41semidirect
332. C3×D12#67semidirect
333. C3×D12#67semidirect
412. C2×Dic6D32semidirect
510. C2×C3×D3#237semidirect
511. C2×C3×D3#239semidirect
563. C33#546semidirect
658. D12#625semidirect
784. C2×D3#3796semidirect
827. C32#5630semidirect
828. C32#5806semidirect
829. C32#5829semidirect
917. C3#10594889semidirect
918. C3#10595244semidirect
919. C3#10595427semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D122
C2×C3×#37962
#117236962
C4×#62902
#117234992
#117234362
C3×#638562
#117229862
#117229552
#117229472
D3×(C2×D3)⋊Dic32
#105954273
#105952443
#105948893