Finite Group Databasebeta

← #13178670

Subgroups — #13178670

Order 1728.

1884 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#11723727C212yesmaximal, complemented
5#11723720C212yesmaximal, complemented
6C2×#88814C212yesmaximal, complemented
7#11723717C212yesmaximal, complemented
8#11723696C211yesmaximal, characteristic, complemented
9C4×#6295C211yesmaximal, characteristic, complemented
10#11723677C211yesmaximal, characteristic, complemented
11#11723674C211yesmaximal, characteristic, complemented
12#10595254—31nomaximal
13#10595246—31nomaximal
14#10595244—31nomaximal
15C23×C3×C3⋊D3C2212yes—
16C2×C33×D4C2211yescharacteristic
17C2×C3×#638C2212yes—
18C2×C3×#638C2212yescomplemented
19C22×C3×C3⋊Dic3C2212yescomplemented
20C22×C3×C3⋊Dic3C2212yescomplemented
21C3×#3830—24no—
22C3×D4×C3⋊D3—24no—
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×C3×#634C2211yescharacteristic, complemented
27C2×#6295C2211yescharacteristic
28C2×#6295C2212yescomplemented
29C3×#3757C2212yescomplemented
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
31C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
32#88815C2212yescomplemented
33#88815C2211yescharacteristic, complemented
34#88814C2212yes—
35#88814C2211yescharacteristic
36#88814C2212yescomplemented
37#88814C2212yescomplemented
38#88814C2211yescharacteristic, complemented
39#88814C2212yescomplemented
40C2×#3830D311yescharacteristic, complemented
41C2×D4×C3⋊D3D311yescharacteristic, complemented
42C2×C3×#237—31no—
43C2×C3×#237—31no—
44C2×C3×#237—61no—
45C2×C3×D3×D4—31no—
46C2×C3×D3×D4—31no—
47C2×C3×D3×D4—61no—
48D4×C3⋊Dic3D311yescharacteristic, complemented
49C3×D4×Dic3—31no—
50C3×D4×Dic3—31no—
51C3×D4×Dic3—61no—
52#63981—32no—
53#63980—32no—
54#63978—32no—
55#63978—32no—
56#63977—32no—
57#63976—32no—
58#63966—32no—
59C2×#3722—32no—
60#63962—32no—
61#63961—32no—
62C2×(C2×D3)⋊Dic3—32no—
63C2×(C2×D3)⋊Dic3—32no—
64#63916—31no—
65#63909—31no—
66#63908—31no—
67C4×#626—31no—
68C4×#626—31no—
69C4×#625—31no—
70#63871—31no—
71#63864—31no—
72#63863—31no—
73#63860—31no—
74#63857—31no—
75#63856—31no—
76C23×C33C2312yes—
77C22×C3×C3⋊D3—24no—
78C22×C3×C3⋊D3—24no—
79C22×C3×C3⋊D3—42no—
80C22×C3×C3⋊D3C2312yes—
81C22×C3×C3⋊D3C2311yescharacteristic
82C22×C3×C3⋊D3C2311yescharacteristic
83C33×D4D414yescomplemented
84C2×C33×C4C2311yescharacteristic
85C3×#638—24no—
86C3×#638—24no—
87C2×C3×C3⋊Dic3—24no—
88C2×C3×C3⋊Dic3—42no—
89C2×C3×C3⋊Dic3C2311yescharacteristic
90C2×C3×C3⋊Dic3C2311yescharacteristic
91C2×C3×C3⋊Dic3C2312yes—
92C2×C3×C3⋊Dic3C2312yes—
93C2×C3×C3⋊Dic3C2311yescharacteristic
94C2×C3×C3⋊Dic3C2311yescharacteristic
95C3×C4⋊(C3⋊D3)—22no—
96C3×C4×C3⋊D3—22no—
97C3×C4×C3⋊D3—22no—
98C3×#634—22no—
99#6295—22no—
100#6295—42no—
101#5829—91no—
102#5806—91no—
103#5554—91no—
104C23×C3⋊D3C2×D312yes—
105C23×C3×D3—32no—
106C23×C3×D3—32no—
107C23×C3×D3—62no—
108C2×C32×D4—21no—
109C2×C32×D4—21no—
110C2×C32×D4—21no—
111C2×C32×D4—41no—
112C2×C32×D4C2×D311yescharacteristic
113C2×C32×D4C2×D311yescharacteristic
114C2×C32×D4C2×D311yescharacteristic
115C2×#638C2×D312yes—
116C2×#638C2×D312yescomplemented
117C22×C3⋊Dic3C2×D312yescomplemented
118C22×C3⋊Dic3C2×D312yescomplemented
119#3830—24no—
120D4×C3⋊D3—24no—
121C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
122C2×C4×C3⋊D3C2×D311yescharacteristic
123C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
124C2×#634C2×D311yescharacteristic, complemented
125C2×C3×#67—32no—
126C2×C3×#67—32no—
127C2×C3×#67—32no—
128C2×C3×#67—32no—
129C2×C3×#67—62no—
130C2×C3×#67—62no—
131C22×C3×Dic3—32no—
132C22×C3×Dic3—32no—
133C22×C3×Dic3—32no—
134C22×C3×Dic3—32no—
135C22×C3×Dic3—62no—
136C22×C3×Dic3—62no—
137C3×#237—68no—
138C3×#237—64no—
139C3×#237—64no—
140C3×D3×D4—68no—
141C3×D3×D4—64no—
142C3×D3×D4—64no—
143C2×C3×D12—31no—
144C2×C3×D12—31no—
145C2×C3×D12—61no—
146C2×C3×C4×D3—31no—
147C2×C3×C4×D3—31no—
148C2×C3×C4×D3—31no—
149C2×C3×C4×D3—31no—
150C2×C3×C4×D3—61no—
151C2×C3×C4×D3—61no—
152C2×C3×Dic6—31no—
153C2×C3×Dic6—31no—
154C2×C3×Dic6—61no—
155C2×#626—31no—
156C2×#626—31no—
157C2×#626—32no—
158C2×#626—32no—
159C2×#625—31no—
160C2×#625—32no—
161#3757C2×D312yescomplemented
162C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
163C4×C3⋊Dic3C2×D311yescharacteristic, complemented
164C3×#217—32no—
165C3×#217—32no—
166C3×#217—62no—
167C3×C4⋊Dic3—31no—
168C3×C4⋊Dic3—31no—
169C3×C4⋊Dic3—61no—
170C3×C4×Dic3—31no—
171C3×C4×Dic3—31no—
172C3×C4×Dic3—61no—
173#3724—32no—
174#3724—31no—
175Dic3⋊Dic3—32no—
176Dic3⋊Dic3—32no—
177Dic3⋊Dic3—31no—
178Dic3⋊Dic3—31no—
179#3722—32no—
180#3722—32no—
181#3722—32no—
182#3722—31no—
183#3722—31no—
184#3722—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—32no—
190(C2×D3)⋊Dic3—32no—
191(C2×D3)⋊Dic3—31no—
192(C2×D3)⋊Dic3—31no—
193(C2×D3)⋊Dic3—31no—
194(C2×D3)⋊Dic3—31no—
195(C2×D3)⋊Dic3—32no—
196(C2×D3)⋊Dic3—32no—
197C22×C33—22no—
198C22×C33—22no—
199C22×C33C2×D414yes—
200C22×C33C2411yescharacteristic
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—21no—
204C2×C3×C3⋊D3—22no—
205C2×C3×C3⋊D3—21no—
206C2×C3×C3⋊D3—22no—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—22no—
209C2×C3×C3⋊D3—48no—
210C2×C3×C3⋊D3#4112yescomplemented
211C33×C4C2×D412yes—
212C3×C3⋊Dic3—22no—
213C3×C3⋊Dic3—21no—
214C3×C3⋊Dic3—21no—
215C3×C3⋊Dic3—21no—
216C3×C3⋊Dic3—21no—
217C3×C3⋊Dic3—22no—
218C2×C3×#41—91no—
219C22×C3×D4—91no—
220C2×#237—31no—
221C2×#237—31no—
222C2×#237—61no—
223C2×D3×D4—31no—
224C2×D3×D4—31no—
225C2×D3×D4—61no—
226C3×C4×D4—91no—
227#953—92no—
228C2×#217—92no—
229#947—91no—
230#946—91no—
231#939—92no—
232#939—92no—
233#938—91no—
234#937—92no—
235#936—91no—
236#935—92no—
237D4×Dic3—31no—
238D4×Dic3—31no—
239D4×Dic3—61no—
240#930—91no—
241#930—92no—
242#929—92no—
243C4×#67—91no—
244C4×#67—91no—
245C2×(C2×D3)⋊C4—92no—
246C2×(C2×D3)⋊C4—92no—
247#924—91no—
248#897—91no—
249#895—91no—
250#886—92no—
251#882—92no—
252#875—91no—
253C4×D12—91no—
254C23×C32—22no—
255C23×C32—22no—
256C23×C32—22no—
257C23×C32—42no—
258C23×C32C22×D312yes—
259C23×C32C22×D312yes—
260C23×C32C22×D312yes—
261C22×C3⋊D3—24no—
262C22×C3⋊D3—24no—
263C22×C3⋊D3—42no—
264C22×C3⋊D3C22×D312yes—
265C22×C3⋊D3C22×D311yescharacteristic
266C22×C3⋊D3C22×D311yescharacteristic
267C22×C3×D3—31no—
268C22×C3×D3—31no—
269C22×C3×D3—32no—
270C22×C3×D3—32no—
271C22×C3×D3—31no—
272C22×C3×D3—31no—
273C22×C3×D3—61no—
274C22×C3×D3—62no—
275C22×C3×D3—61no—
276C22×C3×D3—64no—
277C22×C3×D3—64no—
278C22×C3×D3—68no—
279C22×C3×D3—64no—
280C22×C3×D3—64no—
281C22×C3×D3—124no—
282C22×C3×D3—122no—
283C22×C3×D3—122no—
284C22×C3×D3—124no—
285C32×D4—24no—
286C32×D4—24no—
287C32×D4—24no—
288C32×D4—44no—
289C32×D4D1214yescomplemented
290C32×D4#6714yescomplemented
291C32×D4#6714yescomplemented
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4—41no—
296C2×C32×C4C22×D311yescharacteristic
297C2×C32×C4C22×D311yescharacteristic
298C2×C32×C4C22×D311yescharacteristic
299#638—24no—
300#638—24no—
301C2×C3⋊Dic3—24no—
302C2×C3⋊Dic3—42no—
303C2×C3⋊Dic3C22×D311yescharacteristic
304C2×C3⋊Dic3C22×D312yes—
305C2×C3⋊Dic3C22×D311yescharacteristic
306C2×C3⋊Dic3C22×D311yescharacteristic
307C2×C3⋊Dic3C22×D312yes—
308C2×C3⋊Dic3C22×D311yescharacteristic
309C4⋊(C3⋊D3)—22no—
310C4×C3⋊D3—22no—
311C4×C3⋊D3—22no—
312#634—22no—
313C3×#67—68no—
314C3×#67—68no—
315C3×#67—64no—
316C3×#67—64no—
317C3×#67—64no—
318C3×#67—64no—
319C2×C3×Dic3—31no—
320C2×C3×Dic3—32no—
321C2×C3×Dic3—31no—
322C2×C3×Dic3—31no—
323C2×C3×Dic3—32no—
324C2×C3×Dic3—31no—
325C2×C3×Dic3—31no—
326C2×C3×Dic3—32no—
327C2×C3×Dic3—31no—
328C2×C3×Dic3—31no—
329C2×C3×Dic3—32no—
330C2×C3×Dic3—31no—
331C2×C3×Dic3—61no—
332C2×C3×Dic3—62no—
333C2×C3×Dic3—61no—
334C2×C3×Dic3—61no—
335C2×C3×Dic3—61no—
336C2×C3×Dic3—62no—
337C2×C3×Dic3—68no—
338C2×C3×Dic3—64no—
339C2×C3×Dic3—64no—
340C2×C3×Dic3—122no—
341C2×C3×Dic3—122no—
342C2×C3×Dic3—124no—
343C3×D12—64no—
344C3×D12—62no—
345C3×D12—62no—
346C3×C4×D3—64no—
347C3×C4×D3—64no—
348C3×C4×D3—62no—
349C3×C4×D3—62no—
350C3×C4×D3—62no—
351C3×C4×D3—62no—
352C3×Dic6—64no—
353C3×Dic6—62no—
354C3×Dic6—62no—
355#626—62no—
356#626—62no—
357#626—122no—
358#626—122no—
359#625—62no—
360#625—122no—
361#546—271noSylow
362C2×C33—24no—
363C2×C33C22×D411yescharacteristic
364C2×C33C2×#4111yescharacteristic
365C2×C33H(5,𝔽2)11yescharacteristic
366C3×C3⋊D3—22no—
367C3×C3⋊D3—41no—
368C3×C3⋊D3—42no—
369C24×C3—92no—
370C23×D3—32no—
371C23×D3—32no—
372C23×D3—62no—
373C3×#41—184no—
374C2×C3×Q8—91no—
375C2×C3×D4—21no—
376C2×C3×D4—21no—
377C2×C3×D4—21no—
378C2×C3×D4—41no—
379C2×C3×D4—92no—
380C2×C3×D4—92no—
381C2×C3×D4—91no—
382C2×C3×D4—184no—
383C2×C3×D4D3211yescharacteristic
384C2×C3×D4D3211yescharacteristic
385C2×C3×D4D3211yescharacteristic
386C22×C3×C4—92no—
387C22×C3×C4—92no—
388C22×C3×C4—91no—
389C22×C3×C4—91no—
390C2×#67—32no—
391C2×#67—32no—
392C2×#67—32no—
393C2×#67—32no—
394C2×#67—62no—
395C2×#67—62no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—92no—
399C2×#67—92no—
400C22×Dic3—32no—
401C22×Dic3—32no—
402C22×Dic3—32no—
403C22×Dic3—32no—
404C22×Dic3—62no—
405C22×Dic3—62no—
406#237—68no—
407#237—64no—
408#237—64no—
409D3×D4—68no—
410D3×D4—64no—
411D3×D4—64no—
412C2×D12—31no—
413C2×D12—31no—
414C2×D12—61no—
415C2×D12—91no—
416C2×D12—92no—
417C2×C4×D3—31no—
418C2×C4×D3—31no—
419C2×C4×D3—31no—
420C2×C4×D3—31no—
421C2×C4×D3—61no—
422C2×C4×D3—61no—
423C2×Dic6—31no—
424C2×Dic6—31no—
425C2×Dic6—61no—
426C3×C4⋊C4—91no—
427C3×C22⋊C4—92no—
428C3×C42—91no—
429#217—32no—
430#217—32no—
431#217—62no—
432#217—92no—
433#217—91no—
434#217—91no—
435#217—92no—
436#217—92no—
437#217—92no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—92no—
441(C2×D3)⋊C4—92no—
442(C2×D3)⋊C4—92no—
443(C2×D3)⋊C4—92no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—92no—
446(C2×D3)⋊C4—92no—
447(C2×D3)⋊C4—92no—
448(C2×D3)⋊C4—91no—
449(C2×D3)⋊C4—92no—
450C4⋊Dic3—31no—
451C4⋊Dic3—31no—
452C4⋊Dic3—61no—
453C4⋊Dic3—91no—
454C4⋊Dic3—92no—
455Dic3⋊C4—92no—
456Dic3⋊C4—91no—
457Dic3⋊C4—91no—
458Dic3⋊C4—92no—
459C4×Dic3—31no—
460C4×Dic3—31no—
461C4×Dic3—61no—
462C22×C32—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—21no—
469C22×C32—21no—
470C22×C32—21no—
471C22×C32—24no—
472C22×C32—24no—
473C22×C32—24no—
474C22×C32—41no—
475C22×C32—44no—
476C22×C32—42no—
477C22×C32—42no—
478C22×C32—42no—
479C22×C32—42no—
480C22×C32—42no—
481C22×C32—42no—
482C22×C32—82no—
483C22×C32—82no—
484C22×C32C2×D1214yes—
485C22×C32C2×#6714yes—
486C22×C32C2×#6714yes—
487C22×C32C23×D311yescharacteristic
488C22×C32C23×D311yescharacteristic
489C22×C32C23×D311yescharacteristic
490C2×C3⋊D3—21no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—21no—
497C2×C3⋊D3—21no—
498C2×C3⋊D3—48no—
499C2×C3⋊D3#23712yescomplemented
500C2×C3×D3—32no—
501C2×C3×D3—32no—
502C2×C3×D3—62no—
503C2×C3×D3—62no—
504C2×C3×D3—62no—
505C2×C3×D3—61no—
506C2×C3×D3—61no—
507C2×C3×D3—61no—
508C2×C3×D3—61no—
509C2×C3×D3—62no—
510C2×C3×D3—64no—
511C2×C3×D3—61no—
512C2×C3×D3—62no—
513C2×C3×D3—61no—
514C2×C3×D3—61no—
515C2×C3×D3—62no—
516C2×C3×D3—61no—
517C2×C3×D3—61no—
518C2×C3×D3—62no—
519C2×C3×D3—62no—
520C2×C3×D3—62no—
521C2×C3×D3—61no—
522C2×C3×D3—62no—
523C2×C3×D3—121no—
524C2×C3×D3—121no—
525C2×C3×D3—122no—
526C2×C3×D3—122no—
527C2×C3×D3—128no—
528C2×C3×D3—128no—
529C2×C3×D3—1216no—
530C32×C4—22no—
531C32×C4—22no—
532C32×C4—22no—
533C32×C4—42no—
534C32×C4C2×D1212yes—
535C32×C4C2×#6712yes—
536C32×C4C2×#6712yes—
537C3⋊Dic3—21no—
538C3⋊Dic3—22no—
539C3⋊Dic3—21no—
540C3⋊Dic3—21no—
541C3⋊Dic3—22no—
542C3⋊Dic3—21no—
543C3×Dic3—64no—
544C3×Dic3—62no—
545C3×Dic3—62no—
546C3×Dic3—62no—
547C3×Dic3—62no—
548C3×Dic3—61no—
549C3×Dic3—61no—
550C3×Dic3—61no—
551C3×Dic3—62no—
552C3×Dic3—61no—
553C3×Dic3—61no—
554C3×Dic3—62no—
555C3×Dic3—61no—
556C3×Dic3—62no—
557C3×Dic3—61no—
558C3×Dic3—61no—
559C3×Dic3—121no—
560C3×Dic3—122no—
561C2×#41—91no—
562C22×D4—91no—
563#124—271no—
564#123—272no—
565C22⋊Q8—271no—
566#121—271no—
567#121—272no—
568#120—272no—
569C4×D4—91no—
570C4×D4—271no—
571C2×C22⋊C4—272no—
572C33#54611yescharacteristic, complemented, Sylow
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—22no—
576C23×C3—42no—
577C23×C3—91no—
578C23×C3—92no—
579C23×C3—91no—
580C23×C3—184no—
581C23×C3—184no—
582C23×C3—362no—
583C23×C3C2×D3212yes—
584C23×C3C2×D3212yes—
585C23×C3C2×D3212yes—
586C22×D3—31no—
587C22×D3—31no—
588C22×D3—32no—
589C22×D3—32no—
590C22×D3—31no—
591C22×D3—31no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—62no—
595C22×D3—64no—
596C22×D3—64no—
597C22×D3—68no—
598C22×D3—64no—
599C22×D3—64no—
600C22×D3—124no—
601C22×D3—122no—
602C22×D3—122no—
603C22×D3—124no—
604C3×Q8—182no—
605C3×D4—24no—
606C3×D4—24no—
607C3×D4—24no—
608C3×D4—44no—
609C3×D4—184no—
610C3×D4—184no—
611C3×D4—182no—
612C3×D4#62514yescomplemented
613C3×D4#62614yescomplemented
614C3×D4#62614yescomplemented
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—41no—
619C2×C3×C4—91no—
620C2×C3×C4—91no—
621C2×C3×C4—92no—
622C2×C3×C4—91no—
623C2×C3×C4—92no—
624C2×C3×C4—91no—
625C2×C3×C4—184no—
626C2×C3×C4—182no—
627C2×C3×C4—182no—
628C2×C3×C4—362no—
629C2×C3×C4C2×D3211yescharacteristic
630C2×C3×C4C2×D3211yescharacteristic
631C2×C3×C4C2×D3211yescharacteristic
632#67—68no—
633#67—68no—
634#67—64no—
635#67—64no—
636#67—64no—
637#67—64no—
638#67—182no—
639#67—182no—
640#67—362no—
641#67—362no—
642C2×Dic3—31no—
643C2×Dic3—31no—
644C2×Dic3—31no—
645C2×Dic3—31no—
646C2×Dic3—31no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—31no—
651C2×Dic3—31no—
652C2×Dic3—32no—
653C2×Dic3—31no—
654C2×Dic3—61no—
655C2×Dic3—62no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—62no—
660C2×Dic3—68no—
661C2×Dic3—64no—
662C2×Dic3—64no—
663C2×Dic3—122no—
664C2×Dic3—122no—
665C2×Dic3—124no—
666D12—64no—
667D12—62no—
668D12—62no—
669D12—182no—
670D12—362no—
671C4×D3—64no—
672C4×D3—64no—
673C4×D3—62no—
674C4×D3—62no—
675C4×D3—62no—
676C4×D3—62no—
677Dic6—64no—
678Dic6—62no—
679Dic6—62no—
680C2×C32—24no—
681C2×C32—24no—
682C2×C32—24no—
683C2×C32—21no—
684C2×C32—21no—
685C2×C32—21no—
686C2×C32—21no—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—21no—
690C2×C32—21no—
691C2×C32—21no—
692C2×C32—41no—
693C2×C32—41no—
694C2×C32—41no—
695C2×C32—44no—
696C2×C32—44no—
697C2×C32—44no—
698C2×C32—84no—
699C2×C32C22×D1211yescharacteristic
700C2×C32C2×#23711yescharacteristic
701C2×C32#100411yescharacteristic
702C2×C32#100411yescharacteristic
703C2×C32D3×#4111yescharacteristic
704C2×C32D3×#4111yescharacteristic
705C2×C32#100911yescharacteristic
706C2×C32C22×#6711yescharacteristic
707C2×C32C22×#6711yescharacteristic
708C3⋊D3—22no—
709C3⋊D3—42no—
710C3⋊D3—41no—
711C3×D3—64no—
712C3×D3—62no—
713C3×D3—62no—
714C3×D3—122no—
715C3×D3—124no—
716C3×D3—121no—
717C3×D3—121no—
718C3×D3—122no—
719C3×D3—122no—
720C24—92no—
721#41—184no—
722C2×Q8—91no—
723C2×D4—92no—
724C2×D4—92no—
725C2×D4—91no—
726C2×D4—184no—
727C2×D4—271no—
728C2×D4—272no—
729C2×D4#111311yescharacteristic
730C22×C4—92no—
731C22×C4—92no—
732C22×C4—91no—
733C22×C4—91no—
734C4⋊C4—91no—
735C4⋊C4—271no—
736C4⋊C4—272no—
737C22⋊C4—92no—
738C22⋊C4—271no—
739C22⋊C4—272no—
740C22⋊C4—272no—
741C22⋊C4—272no—
742C22⋊C4—271no—
743C22⋊C4—272no—
744C42—91no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—24no—
755C22×C3—24no—
756C22×C3—24no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—42no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—41no—
764C22×C3—44no—
765C22×C3—82no—
766C22×C3—82no—
767C22×C3—92no—
768C22×C3—181no—
769C22×C3—181no—
770C22×C3—181no—
771C22×C3—182no—
772C22×C3—181no—
773C22×C3—182no—
774C22×C3—181no—
775C22×C3—182no—
776C22×C3—368no—
777C22×C3C2×#62514yes—
778C22×C3C2×#62614yes—
779C22×C3C2×#62614yes—
780C22×C3C22×D3211yescharacteristic
781C22×C3C22×D3211yescharacteristic
782C22×C3C22×D3211yescharacteristic
783C2×D3—32no—
784C2×D3—32no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—61no—
789C2×D3—61no—
790C2×D3—61no—
791C2×D3—61no—
792C2×D3—62no—
793C2×D3—64no—
794C2×D3—61no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—61no—
798C2×D3—62no—
799C2×D3—61no—
800C2×D3—62no—
801C2×D3—61no—
802C2×D3—61no—
803C2×D3—62no—
804C2×D3—61no—
805C2×D3—62no—
806C2×D3—122no—
807C2×D3—122no—
808C2×D3—121no—
809C2×D3—121no—
810C2×D3—128no—
811C2×D3—128no—
812C2×D3—1216no—
813C3×C4—22no—
814C3×C4—22no—
815C3×C4—22no—
816C3×C4—42no—
817C3×C4—181no—
818C3×C4—182no—
819C3×C4—181no—
820C3×C4—181no—
821C3×C4—181no—
822C3×C4—182no—
823C3×C4C2×#62512yes—
824C3×C4C2×#62612yes—
825C3×C4C2×#62612yes—
826Dic3—64no—
827Dic3—62no—
828Dic3—62no—
829Dic3—62no—
830Dic3—61no—
831Dic3—61no—
832Dic3—61no—
833Dic3—62no—
834Dic3—61no—
835Dic3—62no—
836Dic3—62no—
837Dic3—61no—
838Dic3—61no—
839Dic3—62no—
840Dic3—61no—
841Dic3—61no—
842Dic3—122no—
843Dic3—121no—
844C32—21no—
845C32—21no—
846C32—21no—
847C32—41no—
848C32#555411yescharacteristic, complemented
849C32#580611yescharacteristic, complemented
850C32#582911yescharacteristic, complemented
851C23—91no—
852C23—92no—
853C23—91no—
854C23—184no—
855C23—184no—
856C23—362no—
857C23C2×#111312yes—
858Q8—182no—
859D4—184no—
860D4—184no—
861D4—182no—
862D4—542no—
863D4—1082no—
864D4#629514yescomplemented
865C2×C4—91no—
866C2×C4—91no—
867C2×C4—92no—
868C2×C4—91no—
869C2×C4—92no—
870C2×C4—91no—
871C2×C4—184no—
872C2×C4—182no—
873C2×C4—182no—
874C2×C4—362no—
875C2×C4C2×#111311yescharacteristic
876C2×C3—24no—
877C2×C3—24no—
878C2×C3—24no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—44no—
889C2×C3—44no—
890C2×C3—44no—
891C2×C3—41no—
892C2×C3—41no—
893C2×C3—41no—
894C2×C3—84no—
895C2×C3—182no—
896C2×C3—361no—
897C2×C3—362no—
898C2×C3D3×#23711yescharacteristic
899C2×C3D3×#23711yescharacteristic
900C2×C3#6431211yescharacteristic
901C2×C3#6431311yescharacteristic
902C2×C3#6431411yescharacteristic
903C2×C3#6431411yescharacteristic
904C2×C3C22×#62511yescharacteristic
905C2×C3C22×#62611yescharacteristic
906C2×C3C22×#62611yescharacteristic
907D3—64no—
908D3—62no—
909D3—62no—
910D3—124no—
911D3—122no—
912D3—122no—
913D3—121no—
914D3—122no—
915D3—121no—
916C22—22no—
917C22—22no—
918C22—92no—
919C22—181no—
920C22—181no—
921C22—181no—
922C22—182no—
923C22—181no—
924C22—182no—
925C22—181no—
926C22—182no—
927C22—368no—
928C22C2×#629514yes—
929C22C22×#111311yescharacteristic
930C4—181no—
931C4—181no—
932C4—182no—
933C4—181no—
934C4—181no—
935C4—182no—
936C4C2×#629512yes—
937C3—21no—
938C3—21no—
939C3—21no—
940C3—41no—
941C3#1059524411yescharacteristic, complemented
942C3#1059524611yescharacteristic, complemented
943C3#1059525411yescharacteristic, complemented
944C2—24no—
945C2—182no—
946C2—362no—
947C2—361no—
948C2#1172462211yescharacteristic
949C2#1172462311yescharacteristic
950C2C22×#629511yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3830C2semidirect
2. C2×C3×D4×C3⋊D3C2semidirect
3. C3×D4×C3⋊Dic3C2semidirect
4. #11723727C2semidirect
5. #11723720C2semidirect
6. C2×#88814C2semidirect
7. #11723717C2semidirect
8. #11723696C2semidirect
9. C4×#6295C2semidirect
10. #11723677C2semidirect
11. #11723674C2semidirect
18. C2×C3×#638C22semidirect
19. C22×C3×C3⋊Dic3C22semidirect
20. C22×C3×C3⋊Dic3C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
26. C2×C3×#634C22semidirect
28. C2×#6295C22semidirect
29. C3×#3757C22semidirect
30. C3×C4⋊(C3⋊Dic3)C22semidirect
31. C3×C4×C3⋊Dic3C22semidirect
32. #88815C22semidirect
33. #88815C22semidirect
36. #88814C22semidirect
37. #88814C22semidirect
38. #88814C22semidirect
39. #88814C22semidirect
40. C2×#3830D3semidirect
41. C2×D4×C3⋊D3D3semidirect
48. D4×C3⋊Dic3D3semidirect
83. C33×D4D4semidirect
116. C2×#638C2×D3semidirect
117. C22×C3⋊Dic3C2×D3semidirect
118. C22×C3⋊Dic3C2×D3semidirect
123. C2×C4×C3⋊D3C2×D3semidirect
124. C2×#634C2×D3semidirect
161. #3757C2×D3semidirect
162. C4⋊(C3⋊Dic3)C2×D3semidirect
163. C4×C3⋊Dic3C2×D3semidirect
210. C2×C3×C3⋊D3#41semidirect
289. C32×D4D12semidirect
290. C32×D4#67semidirect
291. C32×D4#67semidirect
499. C2×C3⋊D3#237semidirect
572. C33#546semidirect
612. C3×D4#625semidirect
613. C3×D4#626semidirect
614. C3×D4#626semidirect
848. C32#5554semidirect
849. C32#5806semidirect
850. C32#5829semidirect
864. D4#6295semidirect
941. C3#10595244semidirect
942. C3#10595246semidirect
943. C3#10595254semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38302
C2×C3×D4×C3⋊D32
C3×D4×C3⋊Dic32
#117237272
#117237202
C2×#888142
#117237172
#117236962
C4×#62952
#117236772
#117236742
#105952543
#105952463
#105952443