Finite Group Databasebeta

← #13172284

Subgroups — #13172284

Order 1728.

1758 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#67C211yesmaximal, characteristic, complemented
2C22×C3×#625C211yesmaximal, characteristic, complemented
3#11723720C211yesmaximal, characteristic, complemented
4#11723629C211yesmaximal, characteristic, complemented
5D3×#3757C211yesmaximal, characteristic, complemented
6#11723602C211yesmaximal, characteristic, complemented
7C3×#63976C211yesmaximal, characteristic, complemented
8#11722985C212yesmaximal, complemented
9#11722954C212yesmaximal, complemented
10#11722953C212yesmaximal, complemented
11#11722946C212yesmaximal, complemented
12#10595524—31nomaximal
13#10595518—31nomaximal
14#10595230—31nomaximal
15C23×C32×D3C2211yescharacteristic
16C23×C32×D3C2211yescharacteristic, complemented
17C22×C3×D32C2211yescharacteristic, complemented
18C2×C3×#638C2211yescharacteristic
19C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
20C2×C32×#67C2211yescharacteristic
21C2×#6290C2212yescomplemented
22C2×D3×C3⋊Dic3C2212yescomplemented
23C3×D3×#67—24no—
24C2×C3×#626C2211yescharacteristic, complemented
25C2×C3×#625—24no—
26C2×C3×#625C2212yes—
27C2×C3×#625C2212yescomplemented
28C2×C3×#625C2211yescharacteristic, complemented
29C2×C3×#625C2212yescomplemented
30C2×C3×D3×Dic3C2211yescharacteristic, complemented
31#88864C2211yescharacteristic, complemented
32C3×#3757C2211yescharacteristic, complemented
33#88815C2212yescomplemented
34#88814C2212yescomplemented
35#88806C2212yescomplemented
36(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
37(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
38(C2×D3)⋊(C3⋊Dic3)C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C22×C3×#67—31no—
41C22×C3×#67—31no—
42C22×C3×#67—31no—
43C2×C3×D3×D4—31no—
44C2×D3×#67D311yescharacteristic, complemented
45C22×#625D311yescharacteristic, complemented
46#64162—31no—
47C2×#3757—31no—
48#64144—31no—
49C3×#953—31no—
50C3×#937—31no—
51#63983—32no—
52#63980—32no—
53#63980—32no—
54#63976—32no—
55#63976—32no—
56#63976—31no—
57#63976—31no—
58#63976—61no—
59#63976D311yescharacteristic, complemented
60#63971—32no—
61#63970—32no—
62#63970—32no—
63#63969—32no—
64D3×#217—31no—
65D3×#217—31no—
66D3×#217—61no—
67#63966—31no—
68#63962—31no—
69#63961—31no—
70#63961—31no—
71#63961—31no—
72#63961—32no—
73#63961—61no—
74#63905—32no—
75#63885—32no—
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3—22no—
79C22×C32×D3—42no—
80C22×C32×D3—42no—
81C22×C32×D3D414yescomplemented
82C22×C32×D3C2311yescharacteristic
83C22×C32×D3C2312yes—
84C22×C32×D3C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C2×C3×D32—22no—
87C2×C3×D32—42no—
88C2×C3⋊(C3⋊Dic3)C2312yes—
89C3×#638—22no—
90C2×C3×C3⋊Dic3—22no—
91C2×C3×C3⋊Dic3C2312yes—
92C2×C3×C3⋊Dic3C2311yescharacteristic
93C2×C3×C3⋊Dic3C2312yes—
94C32×#67—22no—
95C2×C32×Dic3C2311yescharacteristic
96#6290—42no—
97D3×C3⋊Dic3—42no—
98C3×#626—22no—
99C3×#625—24no—
100C3×#625—24no—
101C3×#625—22no—
102C3×#625—42no—
103C3×D3×Dic3—22no—
104#5804—91no—
105#5804—91no—
106#5589—91no—
107C24×C32—31no—
108C24×C32—31no—
109C23×C3×D3—21no—
110C23×C3×D3—21no—
111C23×C3×D3—31no—
112C23×C3×D3—31no—
113C23×C3×D3C2×D311yescharacteristic
114C23×C3×D3C2×D311yescharacteristic
115C23×C3×D3C2×D311yescharacteristic, complemented
116C23×C3×D3C2×D311yescharacteristic, complemented
117C22×D32C2×D311yescharacteristic, complemented
118C2×C32×D4—31no—
119C2×#638—32no—
120C2×#638C2×D311yescharacteristic
121C22×C3⋊Dic3—32no—
122C22×C3⋊Dic3C2×D311yescharacteristic, complemented
123C2×C3×#67—21no—
124C2×C3×#67—31no—
125C2×C3×#67—31no—
126C2×C3×#67—31no—
127C2×C3×#67—32no—
128C2×C3×#67—32no—
129C2×C3×#67—32no—
130C2×C3×#67—31no—
131C2×C3×#67—32no—
132C2×C3×#67—32no—
133C2×C3×#67—32no—
134C2×C3×#67—31no—
135C2×C3×#67—64no—
136C2×C3×#67—64no—
137C2×C3×#67—64no—
138C2×C3×#67—61no—
139C2×C3×#67C2×D311yescharacteristic
140C2×C3×#67C2×D311yescharacteristic
141C22×C3×Dic3—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—31no—
144C22×C3×Dic3—61no—
145C3×D3×D4—64no—
146C2×C3×D12—31no—
147C2×C3×C4×D3—31no—
148D3×#67—24no—
149C2×#626C2×D311yescharacteristic, complemented
150C2×#625—24no—
151C2×#625—32no—
152C2×#625—32no—
153C2×#625—62no—
154C2×#625C2×D312yes—
155C2×#625C2×D312yescomplemented
156C2×#625C2×D311yescharacteristic, complemented
157C2×#625C2×D312yescomplemented
158C2×D3×Dic3—32no—
159C2×D3×Dic3—32no—
160C2×D3×Dic3—62no—
161C2×D3×Dic3C2×D311yescharacteristic, complemented
162#3757—31no—
163#3757—31no—
164#3757—31no—
165#3757—32no—
166#3757—32no—
167#3757—32no—
168#3757—61no—
169#3757—61no—
170#3757—61no—
171#3757—121no—
172#3757C2×D311yescharacteristic, complemented
173#3750—32no—
174C3×#217—31no—
175C3×#217—31no—
176C3×#217—32no—
177C3×#217—61no—
178C3×(C2×D3)⋊C4—32no—
179#3724—32no—
180#3724—32no—
181#3724—32no—
182#3724—62no—
183Dic3⋊Dic3—32no—
184Dic3⋊Dic3—32no—
185#3722—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—32no—
192(C2×D3)⋊Dic3—32no—
193(C2×D3)⋊Dic3—32no—
194(C2×D3)⋊Dic3—62no—
195(C2×D3)⋊Dic3—62no—
196(C2×D3)⋊Dic3—62no—
197(C2×D3)⋊Dic3C2×D312yescomplemented
198C22×C33—22no—
199C22×C33C2×D412yes—
200C22×C33C2411yescharacteristic
201C2×C3×C3⋊D3—21no—
202C2×C3×C3⋊D3—22no—
203C2×C32×D3—22no—
204C2×C32×D3—22no—
205C2×C32×D3—22no—
206C2×C32×D3—21no—
207C2×C32×D3—22no—
208C2×C32×D3—22no—
209C2×C32×D3—22no—
210C2×C32×D3—44no—
211C2×C32×D3—44no—
212C2×C32×D3C2×D412yes—
213C2×C32×D3C2×D412yes—
214C3×D32—44no—
215C3⋊(C3⋊Dic3)—22no—
216C3×C3⋊Dic3—21no—
217C3×C3⋊Dic3—22no—
218C3×C3⋊Dic3—22no—
219C32×Dic3—21no—
220C22×C3×D4—91no—
221C22×C3×D4—91no—
222C22×#67—31no—
223C22×#67—31no—
224C22×#67—31no—
225C2×D3×D4—31no—
226C3×#120—91no—
227#953—31no—
228#953—92no—
229#953—91no—
230#953—91no—
231#953—181no—
232C2×#217—91no—
233C2×#217—91no—
234C2×#217—181no—
235#939—92no—
236#939—92no—
237#939—92no—
238#939—92no—
239#938—92no—
240#937—31no—
241#937—92no—
242#937—92no—
243#937—91no—
244#935—91no—
245#935—92no—
246#935—91no—
247#935—91no—
248#935—181no—
249#929—92no—
250#929—91no—
251#929—91no—
252#886—91no—
253#884—92no—
254#883—92no—
255D3×C22⋊C4—91no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32—31no—
260C23×C32—31no—
261C23×C32—34no—
262C23×C32—31no—
263C23×C32—32no—
264C23×C32—41no—
265C23×C32—62no—
266C23×C32—122no—
267C23×C32—122no—
268C23×C32C22×D311yescharacteristic
269C23×C32C22×D311yescharacteristic
270C23×C32C22×D311yescharacteristic
271C22×C3⋊D3C22×D311yescharacteristic
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—24no—
275C22×C3×D3—21no—
276C22×C3×D3—21no—
277C22×C3×D3—22no—
278C22×C3×D3—21no—
279C22×C3×D3—31no—
280C22×C3×D3—31no—
281C22×C3×D3—42no—
282C22×C3×D3—42no—
283C22×C3×D3—42no—
284C22×C3×D3—42no—
285C22×C3×D3—42no—
286C22×C3×D3—44no—
287C22×C3×D3—44no—
288C22×C3×D3—61no—
289C22×C3×D3—62no—
290C22×C3×D3—62no—
291C22×C3×D3—122no—
292C22×C3×D3—122no—
293C22×C3×D3#6714yescomplemented
294C22×C3×D3#6714yescomplemented
295C22×C3×D3C22×D311yescharacteristic
296C22×C3×D3C22×D311yescharacteristic
297C22×C3×D3C22×D312yes—
298C22×C3×D3C22×D312yes—
299C22×C3×D3C22×D311yescharacteristic
300C22×C3×D3C22×D311yescharacteristic
301C22×C3×D3C22×D311yescharacteristic
302C22×C3×D3C22×D311yescharacteristic
303C2×D32—22no—
304C2×D32—42no—
305C32×D4—62no—
306C2×C32×C4—31no—
307#638—22no—
308#638—122no—
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3—32no—
311C2×C3⋊Dic3—32no—
312C2×C3⋊Dic3—32no—
313C2×C3⋊Dic3—62no—
314C2×C3⋊Dic3—62no—
315C2×C3⋊Dic3—62no—
316C2×C3⋊Dic3—122no—
317C2×C3⋊Dic3—122no—
318C2×C3⋊Dic3C22×D312yes—
319C2×C3⋊Dic3C22×D312yes—
320C2×C3⋊Dic3C22×D311yescharacteristic
321C3×#67—22no—
322C3×#67—22no—
323C3×#67—42no—
324C3×#67—62no—
325C3×#67—62no—
326C3×#67—64no—
327C3×#67—64no—
328C3×#67—62no—
329C3×#67—62no—
330C3×#67—62no—
331C3×#67—64no—
332C3×#67—64no—
333C3×#67—122no—
334C3×#67—122no—
335C3×#67—122no—
336C2×C3×Dic3—21no—
337C2×C3×Dic3—31no—
338C2×C3×Dic3—32no—
339C2×C3×Dic3—31no—
340C2×C3×Dic3—32no—
341C2×C3×Dic3—32no—
342C2×C3×Dic3—32no—
343C2×C3×Dic3—61no—
344C2×C3×Dic3—62no—
345C2×C3×Dic3—62no—
346C2×C3×Dic3—62no—
347C2×C3×Dic3—62no—
348C2×C3×Dic3—62no—
349C2×C3×Dic3—122no—
350C2×C3×Dic3C22×D311yescharacteristic
351C2×C3×Dic3C22×D311yescharacteristic
352C3×D12—62no—
353C3×C4×D3—62no—
354#626—22no—
355#625—24no—
356#625—24no—
357#625—22no—
358#625—42no—
359#625—122no—
360#625—122no—
361#625—124no—
362D3×Dic3—22no—
363D3×Dic3—122no—
364D3×Dic3—122no—
365D3×Dic3—124no—
366#534—271noSylow
367C2×C33—22no—
368C2×C33C22×D411yescharacteristic
369C2×C33H(5,𝔽2)12yes—
370C3×C3⋊D3—41no—
371C32×D3—22no—
372C32×D3—22no—
373C32×D3—42no—
374C32×D3—41no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—31no—
379C24×C3—61no—
380C24×C3—61no—
381C24×C3—91no—
382C23×D3—31no—
383C23×D3—31no—
384C23×D3D3211yescharacteristic
385C23×D3D3211yescharacteristic, complemented
386C2×C3×D4—31no—
387C2×C3×D4—31no—
388C2×C3×D4—61no—
389C2×C3×D4—91no—
390C2×C3×D4—92no—
391C2×C3×D4—92no—
392C2×C3×D4—91no—
393C2×C3×D4—91no—
394C2×C3×D4—92no—
395C2×C3×D4—184no—
396C2×C3×D4—184no—
397C22×C3×C4—91no—
398C22×C3×C4—91no—
399C2×#67—31no—
400C2×#67—31no—
401C2×#67—32no—
402C2×#67—32no—
403C2×#67—32no—
404C2×#67—31no—
405C2×#67—32no—
406C2×#67—31no—
407C2×#67—32no—
408C2×#67—32no—
409C2×#67—31no—
410C2×#67—61no—
411C2×#67—64no—
412C2×#67—64no—
413C2×#67—64no—
414C2×#67—92no—
415C2×#67—92no—
416C2×#67—92no—
417C2×#67—182no—
418C2×#67D3211yescharacteristic
419C22×Dic3—31no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—61no—
423C22×Dic3—92no—
424C22×Dic3—92no—
425C22×Dic3—182no—
426D3×D4—64no—
427C2×D12—31no—
428C2×C4×D3—31no—
429C2×C4×D3—92no—
430C3×C22⋊C4—92no—
431C3×C22⋊C4—91no—
432#217—31no—
433#217—31no—
434#217—32no—
435#217—61no—
436#217—92no—
437#217—92no—
438#217—92no—
439#217—92no—
440#217—92no—
441#217—92no—
442#217—92no—
443#217—91no—
444#217—91no—
445#217—91no—
446#217—182no—
447#217—182no—
448#217—182no—
449#217—181no—
450#217—181no—
451#217—181no—
452#217—361no—
453(C2×D3)⋊C4—32no—
454(C2×D3)⋊C4—92no—
455(C2×D3)⋊C4—92no—
456(C2×D3)⋊C4—92no—
457(C2×D3)⋊C4—92no—
458(C2×D3)⋊C4—92no—
459C4⋊Dic3—92no—
460Dic3⋊C4—92no—
461Dic3⋊C4—92no—
462Dic3⋊C4—92no—
463Dic3⋊C4—92no—
464Dic3⋊C4—92no—
465Dic3⋊C4—182no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—21no—
470C22×C32—21no—
471C22×C32—21no—
472C22×C32—22no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—32no—
476C22×C32—32no—
477C22×C32—41no—
478C22×C32—42no—
479C22×C32—42no—
480C22×C32—42no—
481C22×C32—42no—
482C22×C32—62no—
483C22×C32—62no—
484C22×C32—62no—
485C22×C32—62no—
486C22×C32—62no—
487C22×C32—62no—
488C22×C32—61no—
489C22×C32—82no—
490C22×C32—124no—
491C22×C32—124no—
492C22×C32D3×D412yes—
493C22×C32C2×#6712yes—
494C22×C32C2×#6712yes—
495C22×C32C23×D311yescharacteristic
496C22×C32C23×D311yescharacteristic
497C22×C32C23×D311yescharacteristic
498C2×C3⋊D3—22no—
499C2×C3⋊D3—21no—
500C2×C3×D3—24no—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—24no—
506C2×C3×D3—21no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—21no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—42no—
519C2×C3×D3—42no—
520C2×C3×D3—42no—
521C2×C3×D3—41no—
522C2×C3×D3—42no—
523C2×C3×D3—44no—
524C2×C3×D3—44no—
525C2×C3×D3—48no—
526C2×C3×D3—44no—
527C2×C3×D3—44no—
528C2×C3×D3—48no—
529C2×C3×D3—61no—
530C2×C3×D3—62no—
531C2×C3×D3—62no—
532C2×C3×D3—61no—
533C2×C3×D3—122no—
534C2×C3×D3—121no—
535C2×C3×D3—124no—
536C2×C3×D3—124no—
537C2×C3×D3C2×#6712yes—
538C2×C3×D3C2×#6712yes—
539C2×C3×D3C2×#6712yes—
540C2×C3×D3C2×#6712yes—
541D32—44no—
542C32×C4—61no—
543C3⋊Dic3—22no—
544C3⋊Dic3—21no—
545C3⋊Dic3—22no—
546C3⋊Dic3—62no—
547C3⋊Dic3—62no—
548C3⋊Dic3—62no—
549C3⋊Dic3—122no—
550C3⋊Dic3—122no—
551C3⋊Dic3—122no—
552C3⋊Dic3—242no—
553C3×Dic3—21no—
554C3×Dic3—21no—
555C3×Dic3—41no—
556C3×Dic3—61no—
557C3×Dic3—62no—
558C3×Dic3—62no—
559C3×Dic3—62no—
560C3×Dic3—61no—
561C3×Dic3—62no—
562C3×Dic3—122no—
563C3×Dic3—122no—
564C3×Dic3—121no—
565C22×D4—91no—
566C22×D4—91no—
567#123—272no—
568#123—271no—
569#123—271no—
570#121—272no—
571#121—272no—
572#120—91no—
573#120—272no—
574#120—271no—
575C2×C22⋊C4—271no—
576C33#53411yescharacteristic, complemented, Sylow
577C23×C3—21no—
578C23×C3—21no—
579C23×C3—21no—
580C23×C3—31no—
581C23×C3—31no—
582C23×C3—31no—
583C23×C3—31no—
584C23×C3—34no—
585C23×C3—34no—
586C23×C3—32no—
587C23×C3—31no—
588C23×C3—31no—
589C23×C3—32no—
590C23×C3—41no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—62no—
594C23×C3—64no—
595C23×C3—61no—
596C23×C3—62no—
597C23×C3—62no—
598C23×C3—91no—
599C23×C3—122no—
600C23×C3—122no—
601C23×C3—122no—
602C23×C3—122no—
603C23×C3—122no—
604C23×C3—124no—
605C23×C3—124no—
606C23×C3—182no—
607C23×C3—362no—
608C23×C3C2×D3211yescharacteristic
609C23×C3C2×D3211yescharacteristic
610C23×C3C2×D3211yescharacteristic
611C22×D3—22no—
612C22×D3—31no—
613C22×D3—31no—
614C22×D3—42no—
615C22×D3—42no—
616C22×D3—61no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—122no—
620C22×D3—122no—
621C22×D3#62514yescomplemented
622C22×D3C2×D3212yes—
623C22×D3C2×D3211yescharacteristic
624C22×D3C2×D3211yescharacteristic
625C22×D3C2×D3211yescharacteristic
626C3×D4—62no—
627C3×D4—62no—
628C3×D4—122no—
629C3×D4—182no—
630C3×D4—184no—
631C3×D4—182no—
632C3×D4—184no—
633C3×D4—182no—
634C3×D4—362no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—61no—
638C2×C3×C4—92no—
639C2×C3×C4—91no—
640C2×C3×C4—92no—
641C2×C3×C4—182no—
642C2×C3×C4—182no—
643#67—22no—
644#67—62no—
645#67—62no—
646#67—64no—
647#67—64no—
648#67—62no—
649#67—62no—
650#67—62no—
651#67—64no—
652#67—64no—
653#67—122no—
654#67—122no—
655#67—122no—
656#67—362no—
657#67—362no—
658#67—362no—
659#67—364no—
660C2×Dic3—31no—
661C2×Dic3—32no—
662C2×Dic3—32no—
663C2×Dic3—32no—
664C2×Dic3—32no—
665C2×Dic3—31no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—61no—
669C2×Dic3—62no—
670C2×Dic3—62no—
671C2×Dic3—62no—
672C2×Dic3—92no—
673C2×Dic3—92no—
674C2×Dic3—92no—
675C2×Dic3—122no—
676C2×Dic3—182no—
677C2×Dic3—182no—
678C2×Dic3—182no—
679C2×Dic3—362no—
680C2×Dic3—362no—
681C2×Dic3—362no—
682C2×Dic3—364no—
683C2×Dic3C2×D3211yescharacteristic
684D12—62no—
685C4×D3—62no—
686C4×D3—362no—
687C2×C32—22no—
688C2×C32—22no—
689C2×C32—22no—
690C2×C32—22no—
691C2×C32—21no—
692C2×C32—21no—
693C2×C32—21no—
694C2×C32—22no—
695C2×C32—22no—
696C2×C32—41no—
697C2×C32—42no—
698C2×C32—42no—
699C2×C32—42no—
700C2×C32—42no—
701C2×C32—62no—
702C2×C32—62no—
703C2×C32—82no—
704C2×C32—122no—
705C2×C32—121no—
706C2×C32C2×D3×D411yescharacteristic
707C2×C32#100412yes—
708C2×C32#100412yes—
709C2×C32#100412yes—
710C2×C32C22×#6711yescharacteristic
711C2×C32C22×#6711yescharacteristic
712C3⋊D3—41no—
713C3×D3—24no—
714C3×D3—22no—
715C3×D3—22no—
716C3×D3—22no—
717C3×D3—22no—
718C3×D3—42no—
719C3×D3—44no—
720C3×D3—41no—
721C3×D3—42no—
722C3×D3—42no—
723C3×D3—41no—
724C3×D3—81no—
725C3×D3—121no—
726C3×D3—121no—
727C3×D3—241no—
728C24—31no—
729C24—31no—
730C24—91no—
731C2×D4—31no—
732C2×D4—91no—
733C2×D4—92no—
734C2×D4—92no—
735C2×D4—91no—
736C2×D4—91no—
737C2×D4—92no—
738C2×D4—184no—
739C2×D4—184no—
740C2×D4—272no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—272no—
744C4⋊C4—272no—
745C4⋊C4—272no—
746C22⋊C4—92no—
747C22⋊C4—91no—
748C22⋊C4—272no—
749C22⋊C4—272no—
750C22⋊C4—272no—
751C22⋊C4—272no—
752C22⋊C4—271no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—32no—
763C22×C3—32no—
764C22×C3—32no—
765C22×C3—32no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—41no—
770C22×C3—42no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—64no—
774C22×C3—64no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—62no—
779C22×C3—62no—
780C22×C3—62no—
781C22×C3—62no—
782C22×C3—61no—
783C22×C3—61no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—82no—
790C22×C3—122no—
791C22×C3—122no—
792C22×C3—122no—
793C22×C3—121no—
794C22×C3—122no—
795C22×C3—124no—
796C22×C3—124no—
797C22×C3—124no—
798C22×C3—124no—
799C22×C3—128no—
800C22×C3—128no—
801C22×C3—181no—
802C22×C3—182no—
803C22×C3—364no—
804C22×C3C2×#62512yes—
805C22×C3D3×#6712yes—
806C22×C3D3×#6712yes—
807C22×C3C22×D3211yescharacteristic
808C22×C3C22×D3211yescharacteristic
809C22×C3C22×D3211yescharacteristic
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—21no—
814C2×D3—22no—
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—44no—
818C2×D3—44no—
819C2×D3—62no—
820C2×D3—61no—
821C2×D3—61no—
822C2×D3—62no—
823C2×D3—121no—
824C2×D3—122no—
825C2×D3—124no—
826C2×D3—124no—
827C2×D3C2×#62512yes—
828C2×D3C2×#62512yes—
829C3×C4—61no—
830C3×C4—61no—
831C3×C4—121no—
832C3×C4—182no—
833C3×C4—181no—
834C3×C4—182no—
835Dic3—21no—
836Dic3—62no—
837Dic3—61no—
838Dic3—62no—
839Dic3—61no—
840Dic3—62no—
841Dic3—62no—
842Dic3—122no—
843Dic3—122no—
844Dic3—121no—
845Dic3—182no—
846Dic3—182no—
847Dic3—182no—
848Dic3—362no—
849Dic3—362no—
850Dic3—362no—
851Dic3—722no—
852C32—21no—
853C32—21no—
854C32—21no—
855C32—41no—
856C32#558911yescharacteristic, complemented
857C32#580411yescharacteristic, complemented
858C32#580411yescharacteristic, complemented
859C23—31no—
860C23—31no—
861C23—34no—
862C23—32no—
863C23—31no—
864C23—62no—
865C23—91no—
866C23—122no—
867C23—122no—
868C23—182no—
869C23—362no—
870C23D3311yescharacteristic
871D4—62no—
872D4—182no—
873D4—184no—
874D4—182no—
875D4—184no—
876D4—182no—
877D4—362no—
878D4—1082no—
879C2×C4—31no—
880C2×C4—92no—
881C2×C4—92no—
882C2×C4—91no—
883C2×C4—182no—
884C2×C4—182no—
885C2×C4—272no—
886C2×C4—1082no—
887C2×C3—22no—
888C2×C3—22no—
889C2×C3—22no—
890C2×C3—21no—
891C2×C3—21no—
892C2×C3—21no—
893C2×C3—22no—
894C2×C3—22no—
895C2×C3—22no—
896C2×C3—42no—
897C2×C3—42no—
898C2×C3—42no—
899C2×C3—41no—
900C2×C3—42no—
901C2×C3—64no—
902C2×C3—62no—
903C2×C3—62no—
904C2×C3—62no—
905C2×C3—62no—
906C2×C3—82no—
907C2×C3—122no—
908C2×C3—124no—
909C2×C3—122no—
910C2×C3—121no—
911C2×C3—122no—
912C2×C3—121no—
913C2×C3—241no—
914C2×C3—361no—
915C2×C3#6431312yes—
916C2×C3C22×#62511yescharacteristic
917C2×C3C2×D3×#6711yescharacteristic
918C2×C3C2×D3×#6711yescharacteristic
919C2×C3#6433012yes—
920C2×C3#6433012yes—
921D3—22no—
922D3—22no—
923D3—41no—
924D3—42no—
925D3—121no—
926D3—121no—
927D3—241no—
928C22—22no—
929C22—32no—
930C22—32no—
931C22—62no—
932C22—62no—
933C22—61no—
934C22—62no—
935C22—62no—
936C22—62no—
937C22—62no—
938C22—124no—
939C22—124no—
940C22—181no—
941C22—182no—
942C22—364no—
943C22D3×#62512yes—
944C22C2×D3311yescharacteristic
945C4—61no—
946C4—181no—
947C4—182no—
948C4—182no—
949C4—542no—
950C3—21no—
951C3—21no—
952C3—21no—
953C3—41no—
954C3#1059523011yescharacteristic, complemented
955C3#1059551811yescharacteristic, complemented
956C3#1059552411yescharacteristic, complemented
957C2—22no—
958C2—62no—
959C2—62no—
960C2—122no—
961C2—121no—
962C2—361no—
963C2C2×D3×#62511yescharacteristic
964C2#1172441412yes—
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#534
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#67C2semidirect
2. C22×C3×#625C2semidirect
3. #11723720C2semidirect
4. #11723629C2semidirect
5. D3×#3757C2semidirect
6. #11723602C2semidirect
7. C3×#63976C2semidirect
8. #11722985C2semidirect
9. #11722954C2semidirect
10. #11722953C2semidirect
11. #11722946C2semidirect
16. C23×C32×D3C22semidirect
17. C22×C3×D32C22semidirect
19. C22×C3×C3⋊Dic3C22semidirect
21. C2×#6290C22semidirect
22. C2×D3×C3⋊Dic3C22semidirect
24. C2×C3×#626C22semidirect
27. C2×C3×#625C22semidirect
28. C2×C3×#625C22semidirect
29. C2×C3×#625C22semidirect
30. C2×C3×D3×Dic3C22semidirect
31. #88864C22semidirect
32. C3×#3757C22semidirect
33. #88815C22semidirect
34. #88814C22semidirect
35. #88806C22semidirect
36. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. (C2×D3)⋊(C3⋊Dic3)C22semidirect
38. (C2×D3)⋊(C3⋊Dic3)C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
44. C2×D3×#67D3semidirect
45. C22×#625D3semidirect
59. #63976D3semidirect
81. C22×C32×D3D4semidirect
115. C23×C3×D3C2×D3semidirect
116. C23×C3×D3C2×D3semidirect
117. C22×D32C2×D3semidirect
122. C22×C3⋊Dic3C2×D3semidirect
149. C2×#626C2×D3semidirect
155. C2×#625C2×D3semidirect
156. C2×#625C2×D3semidirect
157. C2×#625C2×D3semidirect
161. C2×D3×Dic3C2×D3semidirect
172. #3757C2×D3semidirect
197. (C2×D3)⋊Dic3C2×D3semidirect
293. C22×C3×D3#67semidirect
294. C22×C3×D3#67semidirect
385. C23×D3D32semidirect
576. C33#534semidirect
621. C22×D3#625semidirect
856. C32#5589semidirect
857. C32#5804semidirect
858. C32#5804semidirect
954. C3#10595230semidirect
955. C3#10595518semidirect
956. C3#10595524semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#672
C22×C3×#6252
#117237202
#117236292
D3×#37572
#117236022
C3×#639762
#117229852
#117229542
#117229532
#117229462
#105955243
#105955183
#105952303