Finite Group Databasebeta

← #13172662

Subgroups — #13172662

Order 1728.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3805C211yesmaximal, characteristic, complemented
2C2×D3×#626C211yesmaximal, characteristic, complemented
3#11723717C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723635C211yesmaximal, characteristic, complemented
6#11723633C211yesmaximal, characteristic, complemented
7C3×#63983C211yesmaximal, characteristic, complemented
8C3×#63979C211yesmaximal, characteristic, complemented
9#11723003C211yesmaximal, characteristic, complemented
10#11723001C211yesmaximal, characteristic, complemented
11#11722960C211yesmaximal, characteristic, complemented
12#11722958C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722946C211yesmaximal, characteristic, complemented
15#11722913C211yesmaximal, characteristic, complemented
16#10595303—31nomaximal
17#10595286—31nomaximal
18#10595238—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C3×D32C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic, complemented
23C2×C3×#638C2211yescharacteristic, complemented
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C2×C32×#67C2211yescharacteristic, complemented
27C2×C32×#67C2211yescharacteristic, complemented
28C2×#6295C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6291C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic, complemented
33C2×C3×#627C2211yescharacteristic, complemented
34C2×C3×#626C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic, complemented
36C2×C3×#625C2211yescharacteristic
37C2×C3×#625C2211yescharacteristic, complemented
38C3×#3805—24no—
39C2×C3×D3×Dic3C2211yescharacteristic
40C2×C3×D3×Dic3C2211yescharacteristic, complemented
41D3×#626—24no—
42#88815C2211yescharacteristic, complemented
43#88814C2211yescharacteristic, complemented
44#88814C2211yescharacteristic, complemented
45#88807C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88803C2211yescharacteristic, complemented
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52C3×#3722C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×C3×#237—31no—
57C2×C3×#237—31no—
58C2×D3×#67—31no—
59C22×#626—31no—
60C2×#3805D311yescharacteristic, complemented
61C2×D3×D12—31no—
62#64149—31no—
63#64148—31no—
64#64146—31no—
65C3×#940—31no—
66C3×#940—31no—
67C3×#937—31no—
68C3×#937—31no—
69#63983—31no—
70#63983—31no—
71#63983—31no—
72#63983—31no—
73#63983—61no—
74#63983D311yescharacteristic, complemented
75#63981—31no—
76#63980—31no—
77#63979—31no—
78#63979—31no—
79#63979—61no—
80#63979D311yescharacteristic, complemented
81#63978—31no—
82#63978—31no—
83#63978—31no—
84#63978—31no—
85#63978—31no—
86#63978—31no—
87#63978—61no—
88#63976—31no—
89#63976—31no—
90#63971—31no—
91#63959—31no—
92#63955—31no—
93#63922—31no—
94#63907—31no—
95#63907—31no—
96#63906—31no—
97#63906—31no—
98#63885—31no—
99#63877—31no—
100#63864—31no—
101#63863—31no—
102#63855—31no—
103#63852—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C22×C32×D3C2311yescharacteristic
111C2×D3×C3⋊D3—22no—
112C2×D3×C3⋊D3—41no—
113C2×D3×C3⋊D3—41no—
114C2×C3×D32—22no—
115C2×C3×D32—41no—
116C2×C3×D32—41no—
117#6312—41no—
118C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
119C3×#638—41no—
120C3×#638—41no—
121C2×C3×C3⋊Dic3—22no—
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C2×C3×C3⋊Dic3C2311yescharacteristic
126C32×#67—22no—
127C32×#67—22no—
128C32×#67—41no—
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131C2×C32×Dic3C2311yescharacteristic
132#6295—22no—
133#6292—22no—
134#6291—22no—
135#6291—41no—
136#6290—41no—
137C3×#627—22no—
138C3×#626—22no—
139C3×#626—41no—
140C3×#625—22no—
141C3×#625—41no—
142C3×D3×Dic3—22no—
143C3×D3×Dic3D414yescomplemented
144#5830—91no—
145#5715—91no—
146#5592—91no—
147C23×C3⋊D3—31no—
148C23×C3×D3—31no—
149C23×C3×D3—31no—
150C22×D32—31no—
151C22×D32—31no—
152C22×D32—61no—
153C22×D32C2×D311yescharacteristic
154C2×C32×D4—31no—
155C2×C32×D4—31no—
156C2×C32×D4—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—31no—
161C2×#638—31no—
162C2×#638—31no—
163C2×#638—61no—
164C2×#638—61no—
165C2×#638—61no—
166C2×#638—121no—
167C2×#638C2×D311yescharacteristic, complemented
168C2×#638C2×D311yescharacteristic, complemented
169C22×C3⋊Dic3C2×D311yescharacteristic, complemented
170C2×C4⋊(C3⋊D3)—31no—
171C2×C3×#67—21no—
172C2×C3×#67—21no—
173C2×C3×#67—21no—
174C2×C3×#67—31no—
175C2×C3×#67—31no—
176C2×C3×#67—31no—
177C2×C3×#67—31no—
178C2×C3×#67—31no—
179C2×C3×#67—31no—
180C2×C3×#67—31no—
181C2×C3×#67—31no—
182C2×C3×#67—31no—
183C2×C3×#67—31no—
184C2×C3×#67—61no—
185C2×C3×#67—61no—
186C2×C3×#67C2×D311yescharacteristic
187C2×C3×#67C2×D311yescharacteristic
188C2×C3×#67C2×D311yescharacteristic, complemented
189C2×C3×#67C2×D311yescharacteristic, complemented
190C2×C3×#67C2×D311yescharacteristic, complemented
191C2×C3×#67C2×D311yescharacteristic, complemented
192C22×C3×Dic3—31no—
193C22×C3×Dic3—31no—
194C22×C3×Dic3—31no—
195C22×C3×Dic3—31no—
196C22×C3×Dic3—61no—
197C3×#237—64no—
198C3×#237—64no—
199C2×C3×D12—31no—
200C2×C3×D12—31no—
201C2×C3×C4×D3—31no—
202C2×C3×C4×D3—31no—
203C2×C3×Dic6—31no—
204C2×C3×Dic6—31no—
205D3×#67—64no—
206C2×#627C2×D311yescharacteristic, complemented
207C2×#626—31no—
208C2×#626—31no—
209C2×#626—31no—
210C2×#626—31no—
211C2×#626—31no—
212C2×#626—31no—
213C2×#626—31no—
214C2×#626—31no—
215C2×#626—64no—
216C2×#626—61no—
217C2×#626—61no—
218C2×#626—61no—
219C2×#626C2×D311yescharacteristic
220C2×#626C2×D311yescharacteristic, complemented
221C2×#625—31no—
222C2×#625—31no—
223C2×#625—31no—
224C2×#625—61no—
225C2×#625C2×D311yescharacteristic
226C2×#625C2×D311yescharacteristic, complemented
227#3805—24no—
228C2×D3×Dic3C2×D311yescharacteristic
229C2×D3×Dic3C2×D311yescharacteristic, complemented
230D3×D12—64no—
231#3757—31no—
232#3757—31no—
233#3752—31no—
234#3752—31no—
235#3752—31no—
236#3750—31no—
237C4×C3⋊Dic3—31no—
238C3×#217—31no—
239C3×#217—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×(C2×D3)⋊C4—31no—
243C3×(C2×D3)⋊C4—31no—
244C3×C4×Dic3—31no—
245C3×C4×Dic3—31no—
246#3724—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—61no—
252#3722—31no—
253#3722—31no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—31no—
258#3722—61no—
259#3722—61no—
260#3722C2×D311yescharacteristic, complemented
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—61no—
272(C2×D3)⋊Dic3—61no—
273(C2×D3)⋊Dic3—61no—
274(C2×D3)⋊Dic3C2×D311yescharacteristic
275(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
276Dic32—31no—
277Dic32—31no—
278Dic32—61no—
279Dic32C2×D311yescharacteristic, complemented
280C22×C33—21no—
281C22×C33—21no—
282C22×C33—21no—
283C22×C33C2411yescharacteristic
284C2×C3⋊(C3⋊D3)—21no—
285C2×C3⋊(C3⋊D3)—21no—
286C2×C3⋊(C3⋊D3)—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3—21no—
292C2×C3×C3⋊D3—21no—
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3—21no—
296C2×C32×D3—21no—
297C2×C32×D3—21no—
298C2×C32×D3—21no—
299C2×C32×D3—21no—
300C2×C32×D3—21no—
301C2×C32×D3C2×D412yes—
302D3×C3⋊D3—44no—
303C3×D32—44no—
304C3⋊(C3⋊Dic3)—21no—
305C3×C3⋊Dic3—21no—
306C3×C3⋊Dic3—21no—
307C3×C3⋊Dic3—21no—
308C3×C3⋊Dic3C2×D412yes—
309C32×Dic3—21no—
310C32×Dic3—21no—
311C32×Dic3C2×D412yes—
312C2×C3×#41—91no—
313C22×#67—91no—
314C2×#237—31no—
315C2×#237—31no—
316C2×D3×D4—91no—
317C22×D12—91no—
318C3×#127—91no—
319C3×#120—91no—
320#953—91no—
321#947—91no—
322#947—91no—
323#940—31no—
324#940—31no—
325#940—91no—
326#940—91no—
327#940—91no—
328#940—181no—
329#939—91no—
330#939—91no—
331#939—91no—
332#939—91no—
333#939—91no—
334#939—91no—
335#939—181no—
336#937—31no—
337#937—31no—
338#937—91no—
339#937—91no—
340#937—91no—
341#937—91no—
342#937—91no—
343#937—91no—
344#937—91no—
345#937—181no—
346#936—91no—
347#930—91no—
348#930—91no—
349#930—91no—
350#930—91no—
351#926—91no—
352#885—91no—
353#885—91no—
354#884—91no—
355#884—91no—
356#882—91no—
357#877—91no—
358#875—91no—
359#872—91no—
360C23×C32—21no—
361C23×C32—21no—
362C23×C32—21no—
363C23×C32—31no—
364C23×C32—31no—
365C23×C32—31no—
366C23×C32—41no—
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C23×C32C22×D311yescharacteristic
370C22×C3⋊D3—31no—
371C22×C3⋊D3—31no—
372C22×C3⋊D3—31no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—61no—
375C22×C3⋊D3—61no—
376C22×C3⋊D3—62no—
377C22×C3⋊D3—121no—
378C22×C3⋊D3—121no—
379C22×C3⋊D3—121no—
380C22×C3⋊D3C22×D311yescharacteristic
381C22×C3⋊D3C22×D311yescharacteristic
382C22×C3×D3—21no—
383C22×C3×D3—21no—
384C22×C3×D3—21no—
385C22×C3×D3—31no—
386C22×C3×D3—31no—
387C22×C3×D3—31no—
388C22×C3×D3—31no—
389C22×C3×D3—61no—
390C22×C3×D3—61no—
391C22×C3×D3—62no—
392C22×C3×D3—62no—
393C22×C3×D3—121no—
394C22×C3×D3—121no—
395C22×C3×D3—121no—
396C22×C3×D3—121no—
397C22×C3×D3C22×D311yescharacteristic
398C22×C3×D3C22×D311yescharacteristic
399C22×C3×D3C22×D311yescharacteristic
400C22×C3×D3C22×D311yescharacteristic
401C22×C3×D3C22×D311yescharacteristic
402C22×C3×D3C22×D311yescharacteristic
403C2×D32—22no—
404C2×D32—41no—
405C2×D32—41no—
406C2×D32—62no—
407C2×D32—62no—
408C2×D32—122no—
409C2×D32—121no—
410C2×D32—121no—
411C2×D32—121no—
412C2×D32—121no—
413C2×D32—122no—
414C2×D32—122no—
415C32×D4—62no—
416C32×D4—62no—
417C32×D4—121no—
418C2×C32×C4—31no—
419C2×C32×C4—31no—
420C2×C32×C4—31no—
421#638—41no—
422#638—41no—
423#638—62no—
424#638—121no—
425#638—121no—
426#638—121no—
427#638—121no—
428#638—121no—
429#638—122no—
430#638—122no—
431#638—122no—
432#638—124no—
433C2×C3⋊Dic3—22no—
434C2×C3⋊Dic3—31no—
435C2×C3⋊Dic3—31no—
436C2×C3⋊Dic3—31no—
437C2×C3⋊Dic3—61no—
438C2×C3⋊Dic3—61no—
439C2×C3⋊Dic3—61no—
440C2×C3⋊Dic3—121no—
441C2×C3⋊Dic3C22×D311yescharacteristic
442C2×C3⋊Dic3C22×D311yescharacteristic
443C2×C3⋊Dic3C22×D311yescharacteristic
444C2×C3⋊Dic3C22×D311yescharacteristic
445C4⋊(C3⋊D3)—62no—
446C3×#67—22no—
447C3×#67—22no—
448C3×#67—22no—
449C3×#67—22no—
450C3×#67—42no—
451C3×#67—42no—
452C3×#67—41no—
453C3×#67—41no—
454C3×#67—42no—
455C3×#67—62no—
456C3×#67—62no—
457C3×#67—62no—
458C3×#67—121no—
459C3×#67—121no—
460C3×#67—121no—
461C3×#67—121no—
462C3×#67—121no—
463C3×#67—121no—
464C3×#67—121no—
465C3×#67—122no—
466C3×#67—122no—
467C2×C3×Dic3—21no—
468C2×C3×Dic3—21no—
469C2×C3×Dic3—21no—
470C2×C3×Dic3—31no—
471C2×C3×Dic3—31no—
472C2×C3×Dic3—34no—
473C2×C3×Dic3—31no—
474C2×C3×Dic3—31no—
475C2×C3×Dic3—31no—
476C2×C3×Dic3—31no—
477C2×C3×Dic3—31no—
478C2×C3×Dic3—31no—
479C2×C3×Dic3—61no—
480C2×C3×Dic3—61no—
481C2×C3×Dic3—61no—
482C2×C3×Dic3—61no—
483C2×C3×Dic3—62no—
484C2×C3×Dic3—62no—
485C2×C3×Dic3—62no—
486C2×C3×Dic3—122no—
487C2×C3×Dic3C22×D311yescharacteristic
488C2×C3×Dic3C22×D311yescharacteristic
489C2×C3×Dic3C22×D311yescharacteristic
490C2×C3×Dic3C22×D311yescharacteristic
491C2×C3×Dic3C22×D311yescharacteristic
492C2×C3×Dic3C22×D311yescharacteristic
493C3×D12—62no—
494C3×D12—121no—
495C3×C4×D3—34no—
496C3×C4×D3—62no—
497C3×Dic6—62no—
498C3×Dic6—62no—
499#627—22no—
500#626—22no—
501#626—41no—
502#626—62no—
503#626—62no—
504#626—62no—
505#626—62no—
506#626—62no—
507#626—62no—
508#626—122no—
509#626—122no—
510#626—121no—
511#626—121no—
512#626—122no—
513#625—22no—
514#625—41no—
515#625—62no—
516#625—121no—
517#625—121no—
518#625—122no—
519D3×Dic3—22no—
520D3×Dic3#6714yescomplemented
521#535—271noSylow
522C2×C33—41no—
523C2×C33C22×D411yescharacteristic
524C2×C33H(5,𝔽2)11yescharacteristic
525C2×C33H(5,𝔽2)11yescharacteristic
526C3⋊(C3⋊D3)—41no—
527C3×C3⋊D3—41no—
528C3×C3⋊D3—41no—
529C32×D3—22no—
530C32×D3—41no—
531C32×D3—41no—
532C24×C3—91no—
533C23×D3—31no—
534C23×D3—31no—
535C23×D3—91no—
536C23×D3—91no—
537C23×D3—91no—
538C23×D3—181no—
539C3×#41—184no—
540C2×C3×Q8—91no—
541C2×C3×D4—31no—
542C2×C3×D4—31no—
543C2×C3×D4—31no—
544C2×C3×D4—31no—
545C2×C3×D4—31no—
546C2×C3×D4—31no—
547C2×C3×D4—61no—
548C2×C3×D4—61no—
549C2×C3×D4—61no—
550C2×C3×D4—91no—
551C2×C3×D4—91no—
552C2×C3×D4—91no—
553C2×C3×D4—91no—
554C2×C3×D4—91no—
555C2×C3×D4—91no—
556C22×C3×C4—91no—
557C22×C3×C4—91no—
558C22×C3×C4—91no—
559C2×#67—31no—
560C2×#67—31no—
561C2×#67—31no—
562C2×#67—31no—
563C2×#67—31no—
564C2×#67—31no—
565C2×#67—31no—
566C2×#67—31no—
567C2×#67—31no—
568C2×#67—31no—
569C2×#67—61no—
570C2×#67—61no—
571C2×#67—91no—
572C2×#67—91no—
573C2×#67—91no—
574C2×#67—91no—
575C2×#67—91no—
576C2×#67—91no—
577C2×#67—91no—
578C2×#67—91no—
579C2×#67—91no—
580C2×#67—91no—
581C2×#67—91no—
582C2×#67—91no—
583C2×#67—91no—
584C2×#67—181no—
585C2×#67—181no—
586C2×#67—181no—
587C2×#67—181no—
588C2×#67—181no—
589C2×#67—181no—
590C2×#67—184no—
591C2×#67—361no—
592C2×#67D3211yescharacteristic
593C2×#67D3211yescharacteristic, complemented
594C2×#67D3211yescharacteristic, complemented
595C22×Dic3—31no—
596C22×Dic3—31no—
597C22×Dic3—31no—
598C22×Dic3—31no—
599C22×Dic3—61no—
600#237—64no—
601#237—64no—
602D3×D4—184no—
603C2×D12—31no—
604C2×D12—31no—
605C2×D12—91no—
606C2×D12—91no—
607C2×D12—91no—
608C2×D12—91no—
609C2×D12—91no—
610C2×D12—181no—
611C2×D12—184no—
612C2×C4×D3—31no—
613C2×C4×D3—31no—
614C2×Dic6—31no—
615C2×Dic6—31no—
616C3×C22⋊C4—91no—
617C3×C22⋊C4—91no—
618C3×C22⋊C4—91no—
619C3×C42—91no—
620#217—31no—
621#217—31no—
622#217—91no—
623#217—91no—
624#217—91no—
625#217—91no—
626#217—91no—
627#217—91no—
628#217—91no—
629#217—181no—
630#217—181no—
631(C2×D3)⋊C4—31no—
632(C2×D3)⋊C4—31no—
633(C2×D3)⋊C4—31no—
634(C2×D3)⋊C4—31no—
635(C2×D3)⋊C4—91no—
636(C2×D3)⋊C4—91no—
637(C2×D3)⋊C4—91no—
638(C2×D3)⋊C4—91no—
639(C2×D3)⋊C4—91no—
640(C2×D3)⋊C4—91no—
641(C2×D3)⋊C4—91no—
642(C2×D3)⋊C4—91no—
643(C2×D3)⋊C4—91no—
644(C2×D3)⋊C4—91no—
645(C2×D3)⋊C4—91no—
646(C2×D3)⋊C4—91no—
647(C2×D3)⋊C4—91no—
648(C2×D3)⋊C4—91no—
649(C2×D3)⋊C4—181no—
650(C2×D3)⋊C4—181no—
651(C2×D3)⋊C4—181no—
652C4⋊Dic3—91no—
653C4⋊Dic3—91no—
654Dic3⋊C4—91no—
655Dic3⋊C4—91no—
656Dic3⋊C4—91no—
657Dic3⋊C4—91no—
658Dic3⋊C4—181no—
659C4×Dic3—31no—
660C4×Dic3—31no—
661C4×Dic3—91no—
662C4×Dic3—91no—
663C4×Dic3—91no—
664C4×Dic3—181no—
665C22×C32—21no—
666C22×C32—22no—
667C22×C32—21no—
668C22×C32—21no—
669C22×C32—21no—
670C22×C32—21no—
671C22×C32—21no—
672C22×C32—21no—
673C22×C32—21no—
674C22×C32—21no—
675C22×C32—21no—
676C22×C32—21no—
677C22×C32—21no—
678C22×C32—32no—
679C22×C32—41no—
680C22×C32—41no—
681C22×C32—41no—
682C22×C32—42no—
683C22×C32—41no—
684C22×C32—41no—
685C22×C32—41no—
686C22×C32—41no—
687C22×C32—41no—
688C22×C32—41no—
689C22×C32—61no—
690C22×C32—61no—
691C22×C32—61no—
692C22×C32—61no—
693C22×C32—61no—
694C22×C32—61no—
695C22×C32—61no—
696C22×C32—61no—
697C22×C32—81no—
698C22×C32—81no—
699C22×C32C23×D311yescharacteristic
700C22×C32C23×D311yescharacteristic
701C22×C32C23×D311yescharacteristic
702C2×C3⋊D3—21no—
703C2×C3⋊D3—21no—
704C2×C3⋊D3—21no—
705C2×C3⋊D3—21no—
706C2×C3⋊D3—21no—
707C2×C3⋊D3—21no—
708C2×C3⋊D3—61no—
709C2×C3⋊D3—62no—
710C2×C3⋊D3—61no—
711C2×C3⋊D3—61no—
712C2×C3⋊D3—61no—
713C2×C3⋊D3—61no—
714C2×C3⋊D3—61no—
715C2×C3⋊D3—61no—
716C2×C3⋊D3—61no—
717C2×C3⋊D3—61no—
718C2×C3⋊D3—121no—
719C2×C3⋊D3—121no—
720C2×C3⋊D3—122no—
721C2×C3⋊D3—121no—
722C2×C3⋊D3—121no—
723C2×C3⋊D3—121no—
724C2×C3⋊D3—121no—
725C2×C3⋊D3—121no—
726C2×C3⋊D3—121no—
727C2×C3⋊D3—124no—
728C2×C3⋊D3—241no—
729C2×C3⋊D3—241no—
730C2×C3×D3—21no—
731C2×C3×D3—21no—
732C2×C3×D3—21no—
733C2×C3×D3—21no—
734C2×C3×D3—21no—
735C2×C3×D3—21no—
736C2×C3×D3—21no—
737C2×C3×D3—21no—
738C2×C3×D3—21no—
739C2×C3×D3—21no—
740C2×C3×D3—21no—
741C2×C3×D3—21no—
742C2×C3×D3—21no—
743C2×C3×D3—21no—
744C2×C3×D3—21no—
745C2×C3×D3—21no—
746C2×C3×D3—22no—
747C2×C3×D3—41no—
748C2×C3×D3—41no—
749C2×C3×D3—41no—
750C2×C3×D3—41no—
751C2×C3×D3—41no—
752C2×C3×D3—41no—
753C2×C3×D3—41no—
754C2×C3×D3—41no—
755C2×C3×D3—62no—
756C2×C3×D3—61no—
757C2×C3×D3—61no—
758C2×C3×D3—61no—
759C2×C3×D3—61no—
760C2×C3×D3—61no—
761C2×C3×D3—61no—
762C2×C3×D3—61no—
763C2×C3×D3—61no—
764C2×C3×D3—61no—
765C2×C3×D3—61no—
766C2×C3×D3—61no—
767C2×C3×D3—61no—
768C2×C3×D3—121no—
769C2×C3×D3—121no—
770C2×C3×D3—121no—
771C2×C3×D3—121no—
772C2×C3×D3—121no—
773C2×C3×D3—124no—
774C2×C3×D3—124no—
775C2×C3×D3D3×D412yes—
776C2×C3×D3C2×#6712yes—
777D32—44no—
778D32—124no—
779D32—124no—
780D32—128no—
781C32×C4—32no—
782C32×C4—61no—
783C32×C4—61no—
784C3⋊Dic3—21no—
785C3⋊Dic3—21no—
786C3⋊Dic3—21no—
787C3⋊Dic3—61no—
788C3⋊Dic3—62no—
789C3⋊Dic3—61no—
790C3⋊Dic3—61no—
791C3⋊Dic3—121no—
792C3⋊Dic3—121no—
793C3⋊Dic3—122no—
794C3⋊Dic3C2×#6712yes—
795C3×Dic3—21no—
796C3×Dic3—21no—
797C3×Dic3—21no—
798C3×Dic3—21no—
799C3×Dic3—22no—
800C3×Dic3—32no—
801C3×Dic3—32no—
802C3×Dic3—41no—
803C3×Dic3—41no—
804C3×Dic3—62no—
805C3×Dic3—62no—
806C3×Dic3—61no—
807C3×Dic3—61no—
808C3×Dic3—61no—
809C3×Dic3—61no—
810C3×Dic3—61no—
811C3×Dic3—61no—
812C3×Dic3—121no—
813C3×Dic3—121no—
814C3×Dic3D3×D412yes—
815C3×Dic3C2×#6712yes—
816C2×#41—91no—
817C22×D4—271no—
818#127—91no—
819#127—271no—
820#124—271no—
821#124—271no—
822#121—271no—
823#121—271no—
824#121—271no—
825#121—271no—
826#120—91no—
827#120—271no—
828#120—271no—
829#120—271no—
830#117—271no—
831C33#53511yescharacteristic, complemented, Sylow
832C23×C3—21no—
833C23×C3—21no—
834C23×C3—21no—
835C23×C3—31no—
836C23×C3—31no—
837C23×C3—31no—
838C23×C3—31no—
839C23×C3—31no—
840C23×C3—31no—
841C23×C3—41no—
842C23×C3—61no—
843C23×C3—61no—
844C23×C3—61no—
845C23×C3—91no—
846C23×C3—91no—
847C23×C3—182no—
848C23×C3—361no—
849C23×C3—361no—
850C23×C3C2×D3211yescharacteristic
851C23×C3C2×D3211yescharacteristic
852C23×C3C2×D3211yescharacteristic
853C22×D3—31no—
854C22×D3—31no—
855C22×D3—31no—
856C22×D3—31no—
857C22×D3—61no—
858C22×D3—61no—
859C22×D3—62no—
860C22×D3—62no—
861C22×D3—91no—
862C22×D3—91no—
863C22×D3—91no—
864C22×D3—121no—
865C22×D3—121no—
866C22×D3—121no—
867C22×D3—121no—
868C22×D3—181no—
869C22×D3—181no—
870C22×D3—181no—
871C22×D3—182no—
872C22×D3—182no—
873C22×D3—182no—
874C22×D3—361no—
875C22×D3—362no—
876C22×D3—361no—
877C22×D3—361no—
878C22×D3—361no—
879C22×D3—361no—
880C22×D3—361no—
881C22×D3—361no—
882C22×D3—362no—
883C22×D3—362no—
884C22×D3C2×D3211yescharacteristic
885C22×D3C2×D3211yescharacteristic
886C22×D3C2×D3211yescharacteristic
887C3×Q8—182no—
888C3×D4—62no—
889C3×D4—62no—
890C3×D4—62no—
891C3×D4—62no—
892C3×D4—122no—
893C3×D4—122no—
894C3×D4—121no—
895C3×D4—121no—
896C3×D4—122no—
897C3×D4—182no—
898C3×D4—182no—
899C3×D4—361no—
900C3×D4—361no—
901C3×D4—361no—
902C3×D4—361no—
903C2×C3×C4—31no—
904C2×C3×C4—31no—
905C2×C3×C4—31no—
906C2×C3×C4—31no—
907C2×C3×C4—31no—
908C2×C3×C4—31no—
909C2×C3×C4—61no—
910C2×C3×C4—61no—
911C2×C3×C4—61no—
912C2×C3×C4—94no—
913C2×C3×C4—91no—
914C2×C3×C4—91no—
915C2×C3×C4—91no—
916C2×C3×C4—91no—
917C2×C3×C4—182no—
918C2×C3×C4—182no—
919#67—22no—
920#67—22no—
921#67—41no—
922#67—62no—
923#67—62no—
924#67—62no—
925#67—121no—
926#67—121no—
927#67—121no—
928#67—121no—
929#67—121no—
930#67—121no—
931#67—121no—
932#67—122no—
933#67—122no—
934#67—182no—
935#67—182no—
936#67—182no—
937#67—182no—
938#67—182no—
939#67—362no—
940#67—361no—
941#67—361no—
942#67—362no—
943#67—361no—
944#67—361no—
945#67—361no—
946#67—362no—
947#67—361no—
948#67—361no—
949#67—361no—
950#67—362no—
951#67—362no—
952#67—362no—
953#67—364no—
954C2×Dic3—31no—
955C2×Dic3—31no—
956C2×Dic3—34no—
957C2×Dic3—31no—
958C2×Dic3—31no—
959C2×Dic3—31no—
960C2×Dic3—31no—
961C2×Dic3—31no—
962C2×Dic3—31no—
963C2×Dic3—61no—
964C2×Dic3—61no—
965C2×Dic3—61no—
966C2×Dic3—61no—
967C2×Dic3—62no—
968C2×Dic3—62no—
969C2×Dic3—62no—
970C2×Dic3—91no—
971C2×Dic3—91no—
972C2×Dic3—91no—
973C2×Dic3—122no—
974C2×Dic3—181no—
975C2×Dic3—181no—
976C2×Dic3—181no—
977C2×Dic3—361no—
978C2×Dic3C2×D3211yescharacteristic
979C2×Dic3C2×D3211yescharacteristic
980C2×Dic3C2×D3211yescharacteristic
981D12—62no—
982D12—121no—
983D12—182no—
984D12—182no—
985D12—182no—
986D12—182no—
987D12—362no—
988D12—361no—
989C4×D3—34no—
990C4×D3—62no—
991Dic6—62no—
992Dic6—62no—
993C2×C32—21no—
994C2×C32—21no—
995C2×C32—21no—
996C2×C32—21no—
997C2×C32—21no—
998C2×C32—21no—
999C2×C32—21no—
1000C2×C32—21no—
1001C2×C32—21no—
1002C2×C32—41no—
1003C2×C32—41no—
1004C2×C32—41no—
1005C2×C32—41no—
1006C2×C32—42no—
1007C2×C32—41no—
1008C2×C32—41no—
1009C2×C32—62no—
1010C2×C32—81no—
1011C2×C32—81no—
1012C2×C32—82no—
1013C2×C32—121no—
1014C2×C32—121no—
1015C2×C32C2×D3×D411yescharacteristic
1016C2×C32C2×D3×D411yescharacteristic
1017C2×C32#100411yescharacteristic
1018C2×C32#100411yescharacteristic
1019C2×C32#100411yescharacteristic
1020C2×C32#100411yescharacteristic
1021C2×C32#100911yescharacteristic
1022C2×C32#100911yescharacteristic
1023C2×C32C22×#6711yescharacteristic
1024C3⋊D3—41no—
1025C3⋊D3—41no—
1026C3⋊D3—121no—
1027C3⋊D3—122no—
1028C3⋊D3—121no—
1029C3⋊D3—121no—
1030C3⋊D3—241no—
1031C3⋊D3—241no—
1032C3⋊D3—242no—
1033C3×D3—22no—
1034C3×D3—22no—
1035C3×D3—42no—
1036C3×D3—41no—
1037C3×D3—41no—
1038C3×D3—41no—
1039C3×D3—41no—
1040C3×D3—81no—
1041C3×D3—81no—
1042C3×D3—122no—
1043C3×D3—121no—
1044C3×D3—121no—
1045C3×D3—121no—
1046C3×D3—121no—
1047C3×D3—241no—
1048C24—91no—
1049C24—271no—
1050#41—184no—
1051C2×Q8—91no—
1052C2×D4—31no—
1053C2×D4—31no—
1054C2×D4—31no—
1055C2×D4—91no—
1056C2×D4—91no—
1057C2×D4—91no—
1058C2×D4—91no—
1059C2×D4—91no—
1060C2×D4—91no—
1061C2×D4—271no—
1062C2×D4—271no—
1063C2×D4—271no—
1064C2×D4—271no—
1065C2×D4—271no—
1066C2×D4—271no—
1067C2×D4—544no—
1068C22×C4—91no—
1069C22×C4—91no—
1070C22×C4—91no—
1071C4⋊C4—271no—
1072C4⋊C4—271no—
1073C22⋊C4—91no—
1074C22⋊C4—91no—
1075C22⋊C4—91no—
1076C22⋊C4—271no—
1077C22⋊C4—271no—
1078C22⋊C4—271no—
1079C22⋊C4—271no—
1080C22⋊C4—271no—
1081C22⋊C4—271no—
1082C22⋊C4—271no—
1083C42—91no—
1084C42—271no—
1085C22×C3—22no—
1086C22×C3—21no—
1087C22×C3—21no—
1088C22×C3—21no—
1089C22×C3—21no—
1090C22×C3—21no—
1091C22×C3—21no—
1092C22×C3—21no—
1093C22×C3—21no—
1094C22×C3—21no—
1095C22×C3—21no—
1096C22×C3—21no—
1097C22×C3—21no—
1098C22×C3—32no—
1099C22×C3—32no—
1100C22×C3—41no—
1101C22×C3—41no—
1102C22×C3—41no—
1103C22×C3—41no—
1104C22×C3—41no—
1105C22×C3—41no—
1106C22×C3—41no—
1107C22×C3—41no—
1108C22×C3—42no—
1109C22×C3—41no—
1110C22×C3—62no—
1111C22×C3—61no—
1112C22×C3—61no—
1113C22×C3—61no—
1114C22×C3—61no—
1115C22×C3—61no—
1116C22×C3—61no—
1117C22×C3—61no—
1118C22×C3—61no—
1119C22×C3—61no—
1120C22×C3—61no—
1121C22×C3—61no—
1122C22×C3—61no—
1123C22×C3—61no—
1124C22×C3—61no—
1125C22×C3—61no—
1126C22×C3—61no—
1127C22×C3—81no—
1128C22×C3—81no—
1129C22×C3—121no—
1130C22×C3—121no—
1131C22×C3—121no—
1132C22×C3—121no—
1133C22×C3—121no—
1134C22×C3—121no—
1135C22×C3—121no—
1136C22×C3—121no—
1137C22×C3—181no—
1138C22×C3—181no—
1139C22×C3—181no—
1140C22×C3—181no—
1141C22×C3—181no—
1142C22×C3—181no—
1143C22×C3—364no—
1144C22×C3C22×D3211yescharacteristic
1145C22×C3C22×D3211yescharacteristic
1146C22×C3C22×D3211yescharacteristic
1147C2×D3—21no—
1148C2×D3—21no—
1149C2×D3—21no—
1150C2×D3—21no—
1151C2×D3—21no—
1152C2×D3—21no—
1153C2×D3—21no—
1154C2×D3—21no—
1155C2×D3—62no—
1156C2×D3—61no—
1157C2×D3—61no—
1158C2×D3—61no—
1159C2×D3—61no—
1160C2×D3—61no—
1161C2×D3—61no—
1162C2×D3—61no—
1163C2×D3—61no—
1164C2×D3—61no—
1165C2×D3—61no—
1166C2×D3—61no—
1167C2×D3—61no—
1168C2×D3—121no—
1169C2×D3—121no—
1170C2×D3—121no—
1171C2×D3—121no—
1172C2×D3—121no—
1173C2×D3—124no—
1174C2×D3—124no—
1175C2×D3—182no—
1176C2×D3—181no—
1177C2×D3—181no—
1178C2×D3—181no—
1179C2×D3—181no—
1180C2×D3—181no—
1181C2×D3—181no—
1182C2×D3—181no—
1183C2×D3—181no—
1184C2×D3—181no—
1185C2×D3—361no—
1186C2×D3—361no—
1187C2×D3—361no—
1188C2×D3—361no—
1189C2×D3—361no—
1190C2×D3—361no—
1191C2×D3—361no—
1192C2×D3—361no—
1193C2×D3—362no—
1194C2×D3—364no—
1195C2×D3—364no—
1196C2×D3—364no—
1197C2×D3—368no—
1198C2×D3—721no—
1199C2×D3—721no—
1200C2×D3D3×#6712yes—
1201C3×C4—32no—
1202C3×C4—32no—
1203C3×C4—62no—
1204C3×C4—61no—
1205C3×C4—61no—
1206C3×C4—61no—
1207C3×C4—61no—
1208C3×C4—92no—
1209C3×C4—121no—
1210C3×C4—121no—
1211C3×C4—181no—
1212C3×C4—181no—
1213C3×C4—181no—
1214Dic3—21no—
1215Dic3—21no—
1216Dic3—32no—
1217Dic3—32no—
1218Dic3—62no—
1219Dic3—62no—
1220Dic3—61no—
1221Dic3—61no—
1222Dic3—61no—
1223Dic3—61no—
1224Dic3—61no—
1225Dic3—61no—
1226Dic3—121no—
1227Dic3—121no—
1228Dic3—182no—
1229Dic3—181no—
1230Dic3—181no—
1231Dic3—181no—
1232Dic3—361no—
1233Dic3—361no—
1234Dic3—362no—
1235Dic3D3×#6712yes—
1236C32—21no—
1237C32—21no—
1238C32—21no—
1239C32—41no—
1240C32#559211yescharacteristic, complemented
1241C32#571511yescharacteristic, complemented
1242C32#583011yescharacteristic, complemented
1243C23—31no—
1244C23—31no—
1245C23—31no—
1246C23—91no—
1247C23—91no—
1248C23—182no—
1249C23—271no—
1250C23—361no—
1251C23—361no—
1252C23—542no—
1253C23—1081no—
1254C23—1081no—
1255C23D3311yescharacteristic
1256Q8—182no—
1257D4—62no—
1258D4—62no—
1259D4—121no—
1260D4—182no—
1261D4—182no—
1262D4—361no—
1263D4—361no—
1264D4—361no—
1265D4—361no—
1266D4—542no—
1267D4—542no—
1268D4—542no—
1269D4—1081no—
1270D4—1081no—
1271D4—1081no—
1272C2×C4—31no—
1273C2×C4—31no—
1274C2×C4—31no—
1275C2×C4—94no—
1276C2×C4—91no—
1277C2×C4—91no—
1278C2×C4—91no—
1279C2×C4—91no—
1280C2×C4—182no—
1281C2×C4—182no—
1282C2×C4—271no—
1283C2×C3—21no—
1284C2×C3—21no—
1285C2×C3—21no—
1286C2×C3—21no—
1287C2×C3—21no—
1288C2×C3—21no—
1289C2×C3—21no—
1290C2×C3—21no—
1291C2×C3—21no—
1292C2×C3—42no—
1293C2×C3—41no—
1294C2×C3—41no—
1295C2×C3—41no—
1296C2×C3—41no—
1297C2×C3—41no—
1298C2×C3—41no—
1299C2×C3—62no—
1300C2×C3—62no—
1301C2×C3—81no—
1302C2×C3—81no—
1303C2×C3—82no—
1304C2×C3—122no—
1305C2×C3—121no—
1306C2×C3—121no—
1307C2×C3—121no—
1308C2×C3—121no—
1309C2×C3—241no—
1310C2×C3—241no—
1311C2×C3—361no—
1312C2×C3—361no—
1313C2×C3D32×D411yescharacteristic
1314C2×C3#6431311yescharacteristic
1315C2×C3#6431411yescharacteristic
1316C2×C3#6431411yescharacteristic
1317C2×C3#6431411yescharacteristic
1318C2×C3#6431411yescharacteristic
1319C2×C3C2×D3×#6711yescharacteristic
1320C2×C3C2×D3×#6711yescharacteristic
1321C2×C3#6433011yescharacteristic
1322D3—22no—
1323D3—41no—
1324D3—41no—
1325D3—122no—
1326D3—121no—
1327D3—121no—
1328D3—121no—
1329D3—121no—
1330D3—241no—
1331D3—362no—
1332D3—361no—
1333D3—361no—
1334D3—361no—
1335D3—721no—
1336D3—721no—
1337D3—722no—
1338C22—21no—
1339C22—21no—
1340C22—21no—
1341C22—32no—
1342C22—61no—
1343C22—61no—
1344C22—61no—
1345C22—61no—
1346C22—61no—
1347C22—61no—
1348C22—61no—
1349C22—61no—
1350C22—181no—
1351C22—181no—
1352C22—181no—
1353C22—181no—
1354C22—181no—
1355C22—181no—
1356C22—364no—
1357C22—541no—
1358C22—541no—
1359C22—541no—
1360C22—1084no—
1361C22C2×D3311yescharacteristic
1362C4—32no—
1363C4—61no—
1364C4—61no—
1365C4—92no—
1366C4—181no—
1367C4—181no—
1368C4—181no—
1369C4—541no—
1370C3—21no—
1371C3—21no—
1372C3—21no—
1373C3—41no—
1374C3#1059523811yescharacteristic, complemented
1375C3#1059528611yescharacteristic, complemented
1376C3#1059530311yescharacteristic, complemented
1377C2—41no—
1378C2—62no—
1379C2—121no—
1380C2—121no—
1381C2—361no—
1382C2—361no—
1383C2—1081no—
1384C2#1172441611yescharacteristic
1385C2#1172441911yescharacteristic
1386C2D32×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#535
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3805C2semidirect
2. C2×D3×#626C2semidirect
3. #11723717C2semidirect
4. #11723643C2semidirect
5. #11723635C2semidirect
6. #11723633C2semidirect
7. C3×#63983C2semidirect
8. C3×#63979C2semidirect
9. #11723003C2semidirect
10. #11723001C2semidirect
11. #11722960C2semidirect
12. #11722958C2semidirect
13. #11722949C2semidirect
14. #11722946C2semidirect
15. #11722913C2semidirect
21. C2×#6312C22semidirect
22. C2×C3×#638C22semidirect
23. C2×C3×#638C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
26. C2×C32×#67C22semidirect
27. C2×C32×#67C22semidirect
31. C2×#6291C22semidirect
32. C2×#6290C22semidirect
33. C2×C3×#627C22semidirect
35. C2×C3×#626C22semidirect
37. C2×C3×#625C22semidirect
40. C2×C3×D3×Dic3C22semidirect
42. #88815C22semidirect
43. #88814C22semidirect
44. #88814C22semidirect
45. #88807C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
48. #88803C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
60. C2×#3805D3semidirect
74. #63983D3semidirect
80. #63979D3semidirect
143. C3×D3×Dic3D4semidirect
167. C2×#638C2×D3semidirect
168. C2×#638C2×D3semidirect
169. C22×C3⋊Dic3C2×D3semidirect
188. C2×C3×#67C2×D3semidirect
189. C2×C3×#67C2×D3semidirect
190. C2×C3×#67C2×D3semidirect
191. C2×C3×#67C2×D3semidirect
206. C2×#627C2×D3semidirect
220. C2×#626C2×D3semidirect
226. C2×#625C2×D3semidirect
229. C2×D3×Dic3C2×D3semidirect
260. #3722C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
279. Dic32C2×D3semidirect
520. D3×Dic3#67semidirect
593. C2×#67D32semidirect
594. C2×#67D32semidirect
831. C33#535semidirect
1240. C32#5592semidirect
1241. C32#5715semidirect
1242. C32#5830semidirect
1374. C3#10595238semidirect
1375. C3#10595286semidirect
1376. C3#10595303semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38052
C2×D3×#6262
#117237172
#117236432
#117236352
#117236332
C3×#639832
C3×#639792
#117230032
#117230012
#117229602
#117229582
#117229492
#117229462
#117229132
#105953033
#105952863
#105952383