Finite Group Databasebeta

← #13178664

Subgroups — #13178664

Order 1728.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×#6295C211yesmaximal, characteristic, complemented
3C3×#64146C211yesmaximal, characteristic, complemented
4C3×#64144C211yesmaximal, characteristic, complemented
5#11723727C212yesmaximal, complemented
6#11723727C211yesmaximal, characteristic, complemented
7#11723725C212yesmaximal, complemented
8#11723723C211yesmaximal, characteristic, complemented
9#11723720C211yesmaximal, characteristic, complemented
10#11723694C212yesmaximal, complemented
11#11723687C212yesmaximal, complemented
12#10595242—31nomaximal
13#10595234—31nomaximal
14#10595230—31nomaximal
15C23×C3×C3⋊D3C2211yescharacteristic
16C23×C3×C3⋊D3C2211yescharacteristic, complemented
17C23×C3×C3⋊D3C2211yescharacteristic, complemented
18C2×C33×D4C2211yescharacteristic
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic, complemented
21C2×C3×#638C2212yescomplemented
22C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
23C3×D4×C3⋊D3—24no—
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26C2×#6295—24no—
27C2×#6295C2212yes—
28C2×#6295C2212yescomplemented
29C2×#6295C2212yescomplemented
30C2×#6294C2212yescomplemented
31C3×#3757C2211yescharacteristic, complemented
32C3×#3757C2212yescomplemented
33C3×#3757C2211yescharacteristic, complemented
34C3×#3752C2212yescomplemented
35C3×#3750C2212yescomplemented
36#88815C2212yescomplemented
37#88814C2212yescomplemented
38#88814C2212yescomplemented
39#88814C2212yescomplemented
40C2×D4×C3⋊D3D311yescharacteristic, complemented
41C2×C3×D3×D4—31no—
42C2×C3×D3×D4—31no—
43C2×C3×D3×D4—61no—
44C22×#626—31no—
45C22×#626—31no—
46C22×#625—31no—
47#64146D311yescharacteristic, complemented
48#64144D311yescharacteristic, complemented
49C3×#937—31no—
50C3×#937—31no—
51C3×#937—61no—
52C3×#935—31no—
53C3×#935—31no—
54C3×#935—61no—
55#63981—31no—
56#63981—32no—
57#63977—31no—
58#63977—32no—
59#63976—31no—
60#63976—32no—
61#63974—31no—
62#63971—32no—
63#63970—32no—
64D3×#217—31no—
65D3×#217—31no—
66#63966—31no—
67#63962—31no—
68#63961—31no—
69#63958—32no—
70#63910—32no—
71#63905—32no—
72#63886—32no—
73#63885—32no—
74#63853—32no—
75#63850—32no—
76C23×C33C2311yescharacteristic
77C23×C33C2311yescharacteristic
78C22×C3×C3⋊D3—22no—
79C22×C3×C3⋊D3—22no—
80C22×C3×C3⋊D3—42no—
81C22×C3×C3⋊D3—42no—
82C22×C3×C3⋊D3—42no—
83C22×C3×C3⋊D3D414yescomplemented
84C22×C3×C3⋊D3C2312yes—
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C33×D4—22no—
89C2×C33×C4C2311yescharacteristic
90C3×#638—22no—
91C3×#638—22no—
92C3×#638—42no—
93C2×C3×C3⋊Dic3—22no—
94C2×C3×C3⋊Dic3C2312yes—
95C2×C3×C3⋊Dic3C2312yes—
96C2×C3×C3⋊Dic3C2312yes—
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C3×C4⋊(C3⋊D3)—22no—
99C3×C4×C3⋊D3—22no—
100#6295—24no—
101#6295—24no—
102#6295—42no—
103#6294—42no—
104#5804—91no—
105#5653—91no—
106#5589—91no—
107C23×C3⋊D3C2×D311yescharacteristic
108C23×C3⋊D3C2×D311yescharacteristic, complemented
109C23×C3⋊D3C2×D311yescharacteristic, complemented
110C23×C3×D3—31no—
111C23×C3×D3—31no—
112C23×C3×D3—31no—
113C23×C3×D3—31no—
114C23×C3×D3—31no—
115C23×C3×D3—31no—
116C23×C3×D3—61no—
117C23×C3×D3—61no—
118C23×C3×D3—61no—
119C2×C32×D4—21no—
120C2×C32×D4—21no—
121C2×C32×D4—21no—
122C2×C32×D4—41no—
123C2×C32×D4C2×D311yescharacteristic
124C2×C32×D4C2×D311yescharacteristic
125C2×C32×D4C2×D311yescharacteristic
126C2×#638C2×D311yescharacteristic
127C2×#638C2×D311yescharacteristic, complemented
128C2×#638C2×D312yescomplemented
129C22×C3⋊Dic3C2×D311yescharacteristic, complemented
130D4×C3⋊D3—24no—
131C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
132C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67—32no—
138C2×C3×#67—32no—
139C2×C3×#67—61no—
140C2×C3×#67—61no—
141C2×C3×#67—62no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C22×C3×Dic3—61no—
145C3×D3×D4—64no—
146C3×D3×D4—64no—
147C3×D3×D4—68no—
148C2×C3×D12—31no—
149C2×C3×D12—31no—
150C2×C3×D12—61no—
151C2×C3×C4×D3—31no—
152C2×C3×C4×D3—31no—
153C2×C3×C4×D3—61no—
154C2×#626—32no—
155C2×#626—32no—
156C2×#626—32no—
157C2×#626—32no—
158C2×#626—32no—
159C2×#626—32no—
160C2×#626—64no—
161C2×#626—64no—
162C2×#625—32no—
163C2×#625—32no—
164C2×#625—32no—
165C2×#625—64no—
166C2×#624—32no—
167C2×D3×Dic3—32no—
168C2×D3×Dic3—32no—
169#3757C2×D311yescharacteristic, complemented
170#3757C2×D312yescomplemented
171#3757C2×D311yescharacteristic, complemented
172#3752C2×D312yescomplemented
173#3750C2×D312yescomplemented
174C3×#217—32no—
175C3×#217—31no—
176C3×#217—32no—
177C3×#217—31no—
178C3×#217—31no—
179C3×#217—31no—
180C3×#217—61no—
181C3×#217—62no—
182C3×#217—61no—
183C3×(C2×D3)⋊C4—32no—
184C3×(C2×D3)⋊C4—32no—
185C3×(C2×D3)⋊C4—62no—
186C3×Dic3⋊C4—32no—
187C3×Dic3⋊C4—32no—
188C3×Dic3⋊C4—62no—
189#3724—32no—
190Dic3⋊Dic3—32no—
191Dic3⋊Dic3—32no—
192#3722—32no—
193#3722—32no—
194#3722—32no—
195(C2×D3)⋊Dic3—32no—
196(C2×D3)⋊Dic3—32no—
197(C2×D3)⋊Dic3—32no—
198(C2×D3)⋊Dic3—32no—
199(C2×D3)⋊Dic3—32no—
200(C2×D3)⋊Dic3—32no—
201C22×C33—22no—
202C22×C33—21no—
203C22×C33—22no—
204C22×C33C2×D412yes—
205C22×C33C2411yescharacteristic
206C2×C3×C3⋊D3—22no—
207C2×C3×C3⋊D3—22no—
208C2×C3×C3⋊D3—21no—
209C2×C3×C3⋊D3—22no—
210C2×C3×C3⋊D3—22no—
211C2×C3×C3⋊D3—22no—
212C2×C3×C3⋊D3—22no—
213C2×C3×C3⋊D3—44no—
214C2×C3×C3⋊D3—44no—
215C2×C3×C3⋊D3—44no—
216C2×C3×C3⋊D3C2×D412yes—
217C2×C3×C3⋊D3C2×D412yes—
218C33×C4—21no—
219C3×C3⋊Dic3—21no—
220C3×C3⋊Dic3—22no—
221C3×C3⋊Dic3—22no—
222C3×C3⋊Dic3—22no—
223C22×C3×D4—91no—
224C22×#67—91no—
225C22×#67—91no—
226C2×D3×D4—31no—
227C2×D3×D4—31no—
228C2×D3×D4—61no—
229C22×D12—91no—
230C3×#123—91no—
231C3×#120—91no—
232#953—92no—
233#953—91no—
234C2×#217—91no—
235#939—92no—
236#939—92no—
237#938—92no—
238#937—31no—
239#937—31no—
240#937—61no—
241#937—91no—
242#937—92no—
243#935—31no—
244#935—31no—
245#935—61no—
246#935—91no—
247#929—92no—
248#929—91no—
249#895—92no—
250#894—92no—
251#886—91no—
252#884—92no—
253#884—92no—
254#883—92no—
255#882—92no—
256#882—91no—
257D3×C22⋊C4—91no—
258D3×C22⋊C4—91no—
259C23×C32—21no—
260C23×C32—21no—
261C23×C32—21no—
262C23×C32—21no—
263C23×C32—21no—
264C23×C32—21no—
265C23×C32—41no—
266C23×C32—41no—
267C23×C32C22×D311yescharacteristic
268C23×C32C22×D311yescharacteristic
269C23×C32C22×D311yescharacteristic
270C23×C32C22×D311yescharacteristic
271C23×C32C22×D311yescharacteristic
272C23×C32C22×D311yescharacteristic
273C22×C3⋊D3—22no—
274C22×C3⋊D3—22no—
275C22×C3⋊D3—42no—
276C22×C3⋊D3—42no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3#6714yescomplemented
279C22×C3⋊D3C22×D311yescharacteristic
280C22×C3⋊D3C22×D312yes—
281C22×C3⋊D3C22×D311yescharacteristic
282C22×C3⋊D3C22×D311yescharacteristic
283C22×C3×D3—31no—
284C22×C3×D3—31no—
285C22×C3×D3—31no—
286C22×C3×D3—31no—
287C22×C3×D3—34no—
288C22×C3×D3—34no—
289C22×C3×D3—31no—
290C22×C3×D3—31no—
291C22×C3×D3—32no—
292C22×C3×D3—32no—
293C22×C3×D3—61no—
294C22×C3×D3—62no—
295C22×C3×D3—64no—
296C22×C3×D3—61no—
297C22×C3×D3—61no—
298C22×C3×D3—62no—
299C22×C3×D3—62no—
300C22×C3×D3—64no—
301C22×C3×D3—62no—
302C22×C3×D3—62no—
303C22×C3×D3—122no—
304C22×C3×D3—122no—
305C22×C3×D3—122no—
306C22×C3×D3—122no—
307C22×C3×D3—122no—
308C22×C3×D3—122no—
309C22×C3×D3—122no—
310C22×C3×D3—124no—
311C22×C3×D3—124no—
312C22×C3×D3—124no—
313C32×D4—22no—
314C32×D4—24no—
315C32×D4—22no—
316C32×D4—22no—
317C32×D4—42no—
318C32×D4—42no—
319C32×D4—44no—
320C2×C32×C4—21no—
321C2×C32×C4—21no—
322C2×C32×C4—21no—
323C2×C32×C4—41no—
324C2×C32×C4C22×D311yescharacteristic
325C2×C32×C4C22×D311yescharacteristic
326C2×C32×C4C22×D311yescharacteristic
327#638—22no—
328#638—22no—
329#638—42no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3C22×D311yescharacteristic
332C2×C3⋊Dic3C22×D312yes—
333C2×C3⋊Dic3C22×D312yes—
334C2×C3⋊Dic3C22×D312yes—
335C4⋊(C3⋊D3)—22no—
336C4×C3⋊D3—22no—
337C3×#67—62no—
338C3×#67—62no—
339C3×#67—64no—
340C3×#67—64no—
341C3×#67—62no—
342C3×#67—62no—
343C3×#67—122no—
344C3×#67—122no—
345C3×#67—124no—
346C2×C3×Dic3—31no—
347C2×C3×Dic3—32no—
348C2×C3×Dic3—32no—
349C2×C3×Dic3—32no—
350C2×C3×Dic3—32no—
351C2×C3×Dic3—32no—
352C2×C3×Dic3—31no—
353C2×C3×Dic3—32no—
354C2×C3×Dic3—61no—
355C2×C3×Dic3—62no—
356C2×C3×Dic3—62no—
357C2×C3×Dic3—62no—
358C2×C3×Dic3—62no—
359C2×C3×Dic3—62no—
360C2×C3×Dic3—122no—
361C3×D12—62no—
362C3×D12—62no—
363C3×D12—64no—
364C3×C4×D3—62no—
365C3×C4×D3—62no—
366C3×C4×D3—64no—
367#626—64no—
368#626—64no—
369#626—64no—
370#626—64no—
371#626—122no—
372#626—122no—
373#625—64no—
374#625—64no—
375#625—122no—
376#624—122no—
377D3×Dic3—122no—
378D3×Dic3—122no—
379#534—271noSylow
380C2×C33—22no—
381C2×C33—41no—
382C2×C33C22×D411yescharacteristic
383C2×C33H(5,𝔽2)12yes—
384C3×C3⋊D3—22no—
385C3×C3⋊D3—22no—
386C3×C3⋊D3—42no—
387C3×C3⋊D3—41no—
388C24×C3—91no—
389C24×C3—91no—
390C24×C3—91no—
391C23×D3—31no—
392C23×D3—31no—
393C23×D3—31no—
394C23×D3—31no—
395C23×D3—31no—
396C23×D3—31no—
397C23×D3—61no—
398C23×D3—61no—
399C23×D3—61no—
400C2×C3×D4—21no—
401C2×C3×D4—21no—
402C2×C3×D4—21no—
403C2×C3×D4—41no—
404C2×C3×D4—91no—
405C2×C3×D4—91no—
406C2×C3×D4—92no—
407C2×C3×D4—91no—
408C2×C3×D4—184no—
409C2×C3×D4D3211yescharacteristic
410C2×C3×D4D3211yescharacteristic
411C2×C3×D4D3211yescharacteristic
412C22×C3×C4—91no—
413C22×C3×C4—91no—
414C2×#67—31no—
415C2×#67—31no—
416C2×#67—31no—
417C2×#67—31no—
418C2×#67—32no—
419C2×#67—32no—
420C2×#67—61no—
421C2×#67—61no—
422C2×#67—62no—
423C2×#67—92no—
424C2×#67—92no—
425C2×#67—92no—
426C2×#67—92no—
427C2×#67—92no—
428C2×#67—92no—
429C2×#67—184no—
430C2×#67—184no—
431C22×Dic3—31no—
432C22×Dic3—31no—
433C22×Dic3—61no—
434C22×Dic3—92no—
435D3×D4—64no—
436D3×D4—64no—
437D3×D4—68no—
438C2×D12—31no—
439C2×D12—31no—
440C2×D12—61no—
441C2×D12—92no—
442C2×D12—92no—
443C2×D12—92no—
444C2×D12—184no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—61no—
448C2×C4×D3—92no—
449C2×C4×D3—92no—
450C3×C4⋊C4—92no—
451C3×C22⋊C4—91no—
452C3×C22⋊C4—91no—
453C3×C22⋊C4—92no—
454C3×C22⋊C4—92no—
455#217—31no—
456#217—31no—
457#217—32no—
458#217—31no—
459#217—32no—
460#217—31no—
461#217—61no—
462#217—62no—
463#217—61no—
464#217—92no—
465#217—92no—
466#217—92no—
467(C2×D3)⋊C4—32no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—62no—
470(C2×D3)⋊C4—92no—
471(C2×D3)⋊C4—92no—
472(C2×D3)⋊C4—92no—
473(C2×D3)⋊C4—92no—
474(C2×D3)⋊C4—92no—
475(C2×D3)⋊C4—92no—
476C4⋊Dic3—92no—
477Dic3⋊C4—32no—
478Dic3⋊C4—32no—
479Dic3⋊C4—62no—
480Dic3⋊C4—92no—
481Dic3⋊C4—92no—
482C22×C32—21no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—21no—
488C22×C32—21no—
489C22×C32—22no—
490C22×C32—22no—
491C22×C32—22no—
492C22×C32—21no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—22no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—41no—
499C22×C32—42no—
500C22×C32—41no—
501C22×C32—41no—
502C22×C32—42no—
503C22×C32—42no—
504C22×C32—42no—
505C22×C32—42no—
506C22×C32—42no—
507C22×C32—42no—
508C22×C32—42no—
509C22×C32—82no—
510C22×C32—82no—
511C22×C32D3×D412yes—
512C22×C32D3×D412yes—
513C22×C32C2×#6712yes—
514C22×C32C23×D311yescharacteristic
515C22×C32C23×D311yescharacteristic
516C22×C32C23×D311yescharacteristic
517C2×C3⋊D3—22no—
518C2×C3⋊D3—22no—
519C2×C3⋊D3—21no—
520C2×C3⋊D3—22no—
521C2×C3⋊D3—22no—
522C2×C3⋊D3—22no—
523C2×C3⋊D3—22no—
524C2×C3⋊D3—44no—
525C2×C3⋊D3—44no—
526C2×C3⋊D3—44no—
527C2×C3⋊D3C2×#6712yes—
528C2×C3⋊D3C2×#6712yes—
529C2×C3×D3—32no—
530C2×C3×D3—32no—
531C2×C3×D3—32no—
532C2×C3×D3—32no—
533C2×C3×D3—62no—
534C2×C3×D3—62no—
535C2×C3×D3—64no—
536C2×C3×D3—62no—
537C2×C3×D3—62no—
538C2×C3×D3—62no—
539C2×C3×D3—62no—
540C2×C3×D3—62no—
541C2×C3×D3—64no—
542C2×C3×D3—62no—
543C2×C3×D3—61no—
544C2×C3×D3—61no—
545C2×C3×D3—62no—
546C2×C3×D3—62no—
547C2×C3×D3—62no—
548C2×C3×D3—62no—
549C2×C3×D3—62no—
550C2×C3×D3—62no—
551C2×C3×D3—62no—
552C2×C3×D3—122no—
553C2×C3×D3—122no—
554C2×C3×D3—122no—
555C2×C3×D3—122no—
556C2×C3×D3—124no—
557C2×C3×D3—124no—
558C2×C3×D3—128no—
559C2×C3×D3—128no—
560C2×C3×D3—124no—
561C2×C3×D3—124no—
562C2×C3×D3—124no—
563C2×C3×D3—124no—
564C2×C3×D3—128no—
565C32×C4—21no—
566C32×C4—22no—
567C32×C4—21no—
568C32×C4—21no—
569C32×C4—41no—
570C32×C4—41no—
571C32×C4—42no—
572C3⋊Dic3—21no—
573C3⋊Dic3—22no—
574C3⋊Dic3—22no—
575C3⋊Dic3—22no—
576C3×Dic3—62no—
577C3×Dic3—62no—
578C3×Dic3—61no—
579C3×Dic3—61no—
580C3×Dic3—62no—
581C3×Dic3—62no—
582C3×Dic3—62no—
583C3×Dic3—62no—
584C3×Dic3—62no—
585C3×Dic3—122no—
586C3×Dic3—122no—
587C3×Dic3—122no—
588C22×D4—91no—
589C22×D4—271no—
590#123—91no—
591#123—272no—
592#123—271no—
593#121—272no—
594#121—272no—
595#120—91no—
596#120—271no—
597#120—272no—
598C2×C22⋊C4—271no—
599C33#53411yescharacteristic, complemented, Sylow
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—41no—
607C23×C3—41no—
608C23×C3—91no—
609C23×C3—91no—
610C23×C3—94no—
611C23×C3—91no—
612C23×C3—92no—
613C23×C3—182no—
614C23×C3—182no—
615C23×C3—362no—
616C23×C3—362no—
617C23×C3—362no—
618C23×C3C2×D3211yescharacteristic
619C23×C3C2×D3211yescharacteristic
620C23×C3C2×D3211yescharacteristic
621C23×C3C2×D3211yescharacteristic
622C23×C3C2×D3211yescharacteristic
623C23×C3C2×D3211yescharacteristic
624C22×D3—31no—
625C22×D3—31no—
626C22×D3—31no—
627C22×D3—31no—
628C22×D3—34no—
629C22×D3—34no—
630C22×D3—32no—
631C22×D3—32no—
632C22×D3—31no—
633C22×D3—31no—
634C22×D3—61no—
635C22×D3—64no—
636C22×D3—62no—
637C22×D3—61no—
638C22×D3—61no—
639C22×D3—62no—
640C22×D3—62no—
641C22×D3—64no—
642C22×D3—62no—
643C22×D3—62no—
644C22×D3—122no—
645C22×D3—122no—
646C22×D3—122no—
647C22×D3—122no—
648C22×D3—122no—
649C22×D3—122no—
650C22×D3—122no—
651C22×D3—124no—
652C22×D3—124no—
653C22×D3—124no—
654C3×D4—24no—
655C3×D4—22no—
656C3×D4—22no—
657C3×D4—22no—
658C3×D4—42no—
659C3×D4—42no—
660C3×D4—44no—
661C3×D4—182no—
662C3×D4—182no—
663C3×D4—182no—
664C3×D4—362no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—41no—
669C2×C3×C4—91no—
670C2×C3×C4—92no—
671C2×C3×C4—92no—
672C2×C3×C4—92no—
673C2×C3×C4—182no—
674C2×C3×C4—182no—
675C2×C3×C4C2×D3211yescharacteristic
676C2×C3×C4C2×D3211yescharacteristic
677C2×C3×C4C2×D3211yescharacteristic
678#67—62no—
679#67—62no—
680#67—64no—
681#67—64no—
682#67—62no—
683#67—62no—
684#67—122no—
685#67—122no—
686#67—124no—
687#67—184no—
688#67—184no—
689#67—184no—
690#67—184no—
691#67—362no—
692#67—362no—
693C2×Dic3—32no—
694C2×Dic3—32no—
695C2×Dic3—32no—
696C2×Dic3—32no—
697C2×Dic3—31no—
698C2×Dic3—32no—
699C2×Dic3—32no—
700C2×Dic3—31no—
701C2×Dic3—61no—
702C2×Dic3—62no—
703C2×Dic3—62no—
704C2×Dic3—62no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—122no—
708C2×Dic3—362no—
709D12—62no—
710D12—62no—
711D12—64no—
712D12—184no—
713D12—184no—
714D12—362no—
715C4×D3—62no—
716C4×D3—62no—
717C4×D3—64no—
718C4×D3—362no—
719C4×D3—362no—
720C2×C32—22no—
721C2×C32—22no—
722C2×C32—22no—
723C2×C32—22no—
724C2×C32—22no—
725C2×C32—22no—
726C2×C32—21no—
727C2×C32—21no—
728C2×C32—21no—
729C2×C32—41no—
730C2×C32—42no—
731C2×C32—42no—
732C2×C32—42no—
733C2×C32—42no—
734C2×C32—41no—
735C2×C32—42no—
736C2×C32—41no—
737C2×C32—41no—
738C2×C32—82no—
739C2×C32—81no—
740C2×C32—81no—
741C2×C32—82no—
742C2×C32C2×D3×D411yescharacteristic
743C2×C32C2×D3×D411yescharacteristic
744C2×C32#100412yes—
745C2×C32#100412yes—
746C2×C32#100912yes—
747C2×C32C22×#6711yescharacteristic
748C3⋊D3—22no—
749C3⋊D3—22no—
750C3⋊D3—41no—
751C3⋊D3—42no—
752C3×D3—64no—
753C3×D3—62no—
754C3×D3—62no—
755C3×D3—62no—
756C3×D3—62no—
757C3×D3—122no—
758C3×D3—124no—
759C3×D3—122no—
760C3×D3—121no—
761C3×D3—122no—
762C3×D3—122no—
763C3×D3—121no—
764C24—91no—
765C24—91no—
766C24—91no—
767C2×D4—91no—
768C2×D4—91no—
769C2×D4—92no—
770C2×D4—91no—
771C2×D4—184no—
772C2×D4—272no—
773C2×D4—272no—
774C2×D4—272no—
775C2×D4—544no—
776C2×D4#111311yescharacteristic
777C22×C4—91no—
778C22×C4—91no—
779C22×C4—272no—
780C4⋊C4—92no—
781C4⋊C4—272no—
782C22⋊C4—91no—
783C22⋊C4—91no—
784C22⋊C4—92no—
785C22⋊C4—92no—
786C22⋊C4—272no—
787C22⋊C4—272no—
788C22⋊C4—272no—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—22no—
795C22×C3—22no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—42no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—42no—
813C22×C3—42no—
814C22×C3—41no—
815C22×C3—42no—
816C22×C3—82no—
817C22×C3—82no—
818C22×C3—92no—
819C22×C3—92no—
820C22×C3—182no—
821C22×C3—182no—
822C22×C3—182no—
823C22×C3—182no—
824C22×C3—182no—
825C22×C3—182no—
826C22×C3—181no—
827C22×C3—364no—
828C22×C3—364no—
829C22×C3—364no—
830C22×C3D3×#6712yes—
831C22×C3D3×#6712yes—
832C22×C3#381112yes—
833C22×C3C22×D3211yescharacteristic
834C22×C3C22×D3211yescharacteristic
835C22×C3C22×D3211yescharacteristic
836C2×D3—32no—
837C2×D3—32no—
838C2×D3—32no—
839C2×D3—32no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—64no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—64no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—61no—
856C2×D3—61no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—122no—
860C2×D3—122no—
861C2×D3—122no—
862C2×D3—122no—
863C2×D3—124no—
864C2×D3—124no—
865C2×D3—128no—
866C2×D3—128no—
867C2×D3—124no—
868C2×D3—124no—
869C2×D3—124no—
870C2×D3—124no—
871C2×D3—128no—
872C3×C4—22no—
873C3×C4—21no—
874C3×C4—21no—
875C3×C4—21no—
876C3×C4—41no—
877C3×C4—41no—
878C3×C4—42no—
879C3×C4—182no—
880C3×C4—182no—
881C3×C4—182no—
882C3×C4—181no—
883Dic3—62no—
884Dic3—62no—
885Dic3—62no—
886Dic3—62no—
887Dic3—62no—
888Dic3—61no—
889Dic3—61no—
890Dic3—62no—
891Dic3—62no—
892Dic3—122no—
893Dic3—122no—
894Dic3—122no—
895C32—21no—
896C32—21no—
897C32—21no—
898C32—41no—
899C32#558911yescharacteristic, complemented
900C32#565311yescharacteristic, complemented
901C32#580411yescharacteristic, complemented
902C23—91no—
903C23—91no—
904C23—94no—
905C23—92no—
906C23—91no—
907C23—182no—
908C23—182no—
909C23—362no—
910C23—362no—
911C23—362no—
912C23C2×#111311yescharacteristic
913C23C2×#111311yescharacteristic
914D4—22no—
915D4—182no—
916D4—182no—
917D4—182no—
918D4—362no—
919D4—544no—
920D4—544no—
921D4—1082no—
922C2×C4—92no—
923C2×C4—92no—
924C2×C4—92no—
925C2×C4—91no—
926C2×C4—182no—
927C2×C4—182no—
928C2×C4—1082no—
929C2×C4C2×#111311yescharacteristic
930C2×C3—22no—
931C2×C3—22no—
932C2×C3—22no—
933C2×C3—22no—
934C2×C3—22no—
935C2×C3—22no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—42no—
940C2×C3—42no—
941C2×C3—42no—
942C2×C3—42no—
943C2×C3—41no—
944C2×C3—41no—
945C2×C3—41no—
946C2×C3—42no—
947C2×C3—41no—
948C2×C3—82no—
949C2×C3—81no—
950C2×C3—81no—
951C2×C3—82no—
952C2×C3—182no—
953C2×C3—182no—
954C2×C3—362no—
955C2×C3—361no—
956C2×C3#6431312yes—
957C2×C3#6431412yes—
958C2×C3#6431412yes—
959C2×C3C2×D3×#6711yescharacteristic
960C2×C3C2×D3×#6711yescharacteristic
961C2×C3C2×#381111yescharacteristic
962D3—64no—
963D3—62no—
964D3—62no—
965D3—62no—
966D3—62no—
967D3—122no—
968D3—122no—
969D3—124no—
970D3—121no—
971D3—122no—
972D3—121no—
973D3—122no—
974C22—22no—
975C22—22no—
976C22—21no—
977C22—92no—
978C22—92no—
979C22—182no—
980C22—182no—
981C22—182no—
982C22—182no—
983C22—182no—
984C22—181no—
985C22—182no—
986C22—364no—
987C22—364no—
988C22—364no—
989C22#8904912yes—
990C22C22×#111311yescharacteristic
991C4—21no—
992C4—182no—
993C4—182no—
994C4—181no—
995C4—182no—
996C3—21no—
997C3—21no—
998C3—21no—
999C3—41no—
1000C3#1059523011yescharacteristic, complemented
1001C3#1059523411yescharacteristic, complemented
1002C3#1059524211yescharacteristic, complemented
1003C2—22no—
1004C2—41no—
1005C2—182no—
1006C2—182no—
1007C2—362no—
1008C2—361no—
1009C2#1172462312yes—
1010C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#534
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×D4×C3⋊D3C2semidirect
2. C22×#6295C2semidirect
3. C3×#64146C2semidirect
4. C3×#64144C2semidirect
5. #11723727C2semidirect
6. #11723727C2semidirect
7. #11723725C2semidirect
8. #11723723C2semidirect
9. #11723720C2semidirect
10. #11723694C2semidirect
11. #11723687C2semidirect
16. C23×C3×C3⋊D3C22semidirect
17. C23×C3×C3⋊D3C22semidirect
20. C2×C3×#638C22semidirect
21. C2×C3×#638C22semidirect
22. C22×C3×C3⋊Dic3C22semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
28. C2×#6295C22semidirect
29. C2×#6295C22semidirect
30. C2×#6294C22semidirect
31. C3×#3757C22semidirect
32. C3×#3757C22semidirect
33. C3×#3757C22semidirect
34. C3×#3752C22semidirect
35. C3×#3750C22semidirect
36. #88815C22semidirect
37. #88814C22semidirect
38. #88814C22semidirect
39. #88814C22semidirect
40. C2×D4×C3⋊D3D3semidirect
47. #64146D3semidirect
48. #64144D3semidirect
83. C22×C3×C3⋊D3D4semidirect
108. C23×C3⋊D3C2×D3semidirect
109. C23×C3⋊D3C2×D3semidirect
127. C2×#638C2×D3semidirect
128. C2×#638C2×D3semidirect
129. C22×C3⋊Dic3C2×D3semidirect
131. C2×C4⋊(C3⋊D3)C2×D3semidirect
132. C2×C4×C3⋊D3C2×D3semidirect
169. #3757C2×D3semidirect
170. #3757C2×D3semidirect
171. #3757C2×D3semidirect
172. #3752C2×D3semidirect
173. #3750C2×D3semidirect
278. C22×C3⋊D3#67semidirect
599. C33#534semidirect
899. C32#5589semidirect
900. C32#5653semidirect
901. C32#5804semidirect
1000. C3#10595230semidirect
1001. C3#10595234semidirect
1002. C3#10595242semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C22×#62952
C3×#641462
C3×#641442
#117237272
#117237252
#117237232
#117237202
#117236942
#117236872
#105952423
#105952343
#105952303