Finite Group Databasebeta

← #13172689

Subgroups — #13172689

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×#3804C211yesmaximal, characteristic, complemented
2C2×#88955C211yesmaximal, characteristic, complemented
3#11723729C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723633C211yesmaximal, characteristic, complemented
6#11723632C211yesmaximal, characteristic, complemented
7C3×#63979C211yesmaximal, characteristic, complemented
8C3×#63978C211yesmaximal, characteristic, complemented
9#11723003C211yesmaximal, characteristic, complemented
10#11723001C211yesmaximal, characteristic, complemented
11#11722959C211yesmaximal, characteristic, complemented
12#11722956C211yesmaximal, characteristic, complemented
13#11722951C211yesmaximal, characteristic, complemented
14#11722949C211yesmaximal, characteristic, complemented
15#11722915C211yesmaximal, characteristic, complemented
16#10595303—31nomaximal
17#10595299—31nomaximal
18#10595064—31nomaximal
19C22×#1113C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C2×C32×#67C2211yescharacteristic, complemented
27C22×C32×Dic3C2211yescharacteristic, complemented
28C2×#6292C2211yescharacteristic
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic, complemented
31C2×#6290C2211yescharacteristic, complemented
32C2×C3×#627C2211yescharacteristic, complemented
33C2×C3×#626C2211yescharacteristic
34C2×C3×#626C2211yescharacteristic
35C2×C3×#626C2211yescharacteristic
36C2×C3×#626C2211yescharacteristic, complemented
37C2×C3×#625C2211yescharacteristic, complemented
38C2×C3×#624C2211yescharacteristic
39C3×#3804—24no—
40C2×C3×D3×Dic3C2211yescharacteristic, complemented
41#88955—24no—
42#88814C2211yescharacteristic
43#88814C2211yescharacteristic, complemented
44#88814C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51Dic3×C3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic, complemented
54C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×C3×#237—31no—
57C2×C3×#235—31no—
58C2×#3811—31no—
59C2×#3804D311yescharacteristic, complemented
60C2×D3×D12—31no—
61C2×D3×D12—31no—
62#64149—31no—
63#64146—31no—
64#64139—31no—
65C3×#940—31no—
66C3×#940—31no—
67C3×#939—31no—
68C3×#930—31no—
69#63983—31no—
70#63983—31no—
71#63983—31no—
72#63983—31no—
73#63983—31no—
74#63983—31no—
75#63983—31no—
76#63983—61no—
77#63981—31no—
78#63979—31no—
79#63979—31no—
80#63979—61no—
81#63979D311yescharacteristic, complemented
82#63978—31no—
83#63978—31no—
84#63978—31no—
85#63978—31no—
86#63978—61no—
87#63978D311yescharacteristic, complemented
88#63970—31no—
89#63959—31no—
90#63922—31no—
91#63922—31no—
92#63922—31no—
93#63909—31no—
94#63908—31no—
95#63907—31no—
96#63907—31no—
97#63886—31no—
98#63864—31no—
99#63863—31no—
100#63855—31no—
101#63852—31no—
102#63841—31no—
103#63836—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C22×C32×D3C2311yescharacteristic
111C2×#1113—22no—
112C2×#1113—41no—
113C2×#1113—41no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116C2×D3×C3⋊D3—41no—
117#6312—41no—
118C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
119C3×#638—22no—
120C3×#638—41no—
121C3×#638—41no—
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C2×C3×C3⋊Dic3C2311yescharacteristic
125C32×#67—22no—
126C32×#67—41no—
127C2×C32×Dic3—22no—
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131C2×C32×Dic3C2311yescharacteristic
132#6292—22no—
133#6292—22no—
134#6291—41no—
135#6290—41no—
136C3×#627—22no—
137C3×#626—22no—
138C3×#626—22no—
139C3×#626—22no—
140C3×#626—41no—
141C3×#625—41no—
142C3×#624D414yescomplemented
143C3×D3×Dic3—22no—
144#5830—91no—
145#5715—91no—
146#5607—91no—
147C23×C3⋊D3—31no—
148C22×D32—31no—
149C22×D32—31no—
150C22×D32—31no—
151C22×D32—31no—
152C22×D32—31no—
153C22×D32—61no—
154C2×C32×D4—31no—
155C2×C32×D4—31no—
156C22×C32×C4—31no—
157C2×#638—31no—
158C2×#638—31no—
159C2×#638—31no—
160C2×#638—31no—
161C2×#638—31no—
162C2×#638—61no—
163C2×#638—61no—
164C2×#638—61no—
165C2×#638—121no—
166C2×#638C2×D311yescharacteristic
167C2×#638C2×D311yescharacteristic, complemented
168C2×#638C2×D311yescharacteristic, complemented
169C2×C4⋊(C3⋊D3)—31no—
170C2×C4⋊(C3⋊D3)—31no—
171C2×C3×#67—21no—
172C2×C3×#67—21no—
173C2×C3×#67—31no—
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—31no—
185C2×C3×#67—61no—
186C2×C3×#67—61no—
187C2×C3×#67—61no—
188C2×C3×#67C2×D311yescharacteristic, complemented
189C2×C3×#67C2×D311yescharacteristic, complemented
190C2×C3×#67C2×D311yescharacteristic, complemented
191C2×C3×#67C2×D311yescharacteristic, complemented
192C22×C3×Dic3—21no—
193C22×C3×Dic3—31no—
194C22×C3×Dic3C2×D311yescharacteristic, complemented
195C22×C3×Dic3C2×D311yescharacteristic, complemented
196C3×#237—64no—
197C3×#235—64no—
198C2×C3×D12—31no—
199C2×C3×D12—31no—
200C2×C3×D12—31no—
201C2×C3×D12—31no—
202C2×C3×C4×D3—31no—
203C2×C3×C4×D3—31no—
204C2×C3×C4×D3—31no—
205C2×C3×Dic6—31no—
206C2×C3×Dic6—31no—
207#3811—64no—
208C2×#627C2×D311yescharacteristic, complemented
209C2×#626—31no—
210C2×#626—31no—
211C2×#626—31no—
212C2×#626—31no—
213C2×#626—31no—
214C2×#626—31no—
215C2×#626—61no—
216C2×#626—61no—
217C2×#626—61no—
218C2×#626C2×D311yescharacteristic
219C2×#626C2×D311yescharacteristic
220C2×#626C2×D311yescharacteristic
221C2×#626C2×D311yescharacteristic, complemented
222C2×#625—31no—
223C2×#625—31no—
224C2×#625—61no—
225C2×#625C2×D311yescharacteristic, complemented
226C2×#624C2×D311yescharacteristic
227#3804—24no—
228C2×D3×Dic3C2×D311yescharacteristic, complemented
229D3×D12—64no—
230D3×D12—64no—
231#3757—31no—
232#3752—31no—
233#3752—31no—
234#3752—31no—
235#3752—31no—
236C4⋊(C3⋊Dic3)—31no—
237C4×C3⋊Dic3—31no—
238C3×#217—31no—
239C3×(C2×D3)⋊C4—31no—
240C3×(C2×D3)⋊C4—31no—
241C3×(C2×D3)⋊C4—31no—
242C3×C4⋊Dic3—31no—
243C3×Dic3⋊C4—31no—
244C3×C4×Dic3—31no—
245C3×C4×Dic3—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—61no—
249Dic3⋊Dic3C2×D311yescharacteristic, complemented
250#3722—31no—
251#3722—31no—
252#3722—31no—
253#3722—31no—
254#3722—31no—
255#3722—31no—
256#3722—31no—
257#3722—61no—
258#3722—61no—
259#3722C2×D311yescharacteristic, complemented
260(C2×D3)⋊Dic3—31no—
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—31no—
272(C2×D3)⋊Dic3—61no—
273(C2×D3)⋊Dic3—61no—
274(C2×D3)⋊Dic3—61no—
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×C3×C3⋊D3—21no—
294C2×C3×C3⋊D3—21no—
295C2×C3×C3⋊D3C2×D412yes—
296C2×C32×D3—21no—
297C2×C32×D3—21no—
298C2×C32×D3—21no—
299C2×C32×D3—21no—
300C2×C32×D3—21no—
301C2×C32×D3—21no—
302#1113—44no—
303D3×C3⋊D3—44no—
304C3⋊(C3⋊Dic3)—21no—
305C3×C3⋊Dic3—21no—
306C3×C3⋊Dic3—21no—
307C3×C3⋊Dic3—21no—
308C32×Dic3—21no—
309C32×Dic3—21no—
310C32×Dic3C2×D412yes—
311C32×Dic3C2×D412yes—
312C2×C3×#41—91no—
313C2×#237—31no—
314C2×D3×D4—91no—
315C2×D3×D4—91no—
316C2×#235—31no—
317C22×D12—91no—
318C3×#127—91no—
319C3×#121—91no—
320#947—91no—
321#947—91no—
322#940—31no—
323#940—31no—
324#940—91no—
325#940—91no—
326#940—91no—
327#940—181no—
328#939—31no—
329#939—91no—
330#939—91no—
331#939—91no—
332#938—91no—
333#937—91no—
334#937—91no—
335#937—91no—
336#937—91no—
337#937—91no—
338#937—91no—
339#937—91no—
340#937—91no—
341#937—91no—
342#937—91no—
343#937—181no—
344#936—91no—
345#930—31no—
346#930—91no—
347#930—91no—
348#930—91no—
349#930—91no—
350#930—181no—
351#926—91no—
352#895—91no—
353#892—91no—
354#885—91no—
355#885—91no—
356#882—91no—
357#882—91no—
358#875—91no—
359#872—91no—
360C23×C32—21no—
361C23×C32—21no—
362C23×C32—21no—
363C23×C32—31no—
364C23×C32—31no—
365C23×C32—41no—
366C23×C32C22×D311yescharacteristic
367C23×C32C22×D311yescharacteristic
368C23×C32C22×D311yescharacteristic
369C22×C3⋊D3—31no—
370C22×C3⋊D3—31no—
371C22×C3⋊D3—31no—
372C22×C3⋊D3—61no—
373C22×C3⋊D3—61no—
374C22×C3⋊D3—61no—
375C22×C3⋊D3—62no—
376C22×C3⋊D3—121no—
377C22×C3⋊D3—121no—
378C22×C3⋊D3—121no—
379C22×C3⋊D3C22×D311yescharacteristic
380C22×C3⋊D3C22×D311yescharacteristic
381C22×C3⋊D3C22×D311yescharacteristic
382C22×C3×D3—21no—
383C22×C3×D3—21no—
384C22×C3×D3—31no—
385C22×C3×D3—31no—
386C22×C3×D3—31no—
387C22×C3×D3—31no—
388C22×C3×D3—31no—
389C22×C3×D3—31no—
390C22×C3×D3—61no—
391C22×C3×D3—61no—
392C22×C3×D3—61no—
393C22×C3×D3C22×D311yescharacteristic
394C22×C3×D3C22×D311yescharacteristic
395C22×C3×D3C22×D311yescharacteristic
396C22×C3×D3C22×D311yescharacteristic
397C2×D32—62no—
398C2×D32—62no—
399C2×D32—62no—
400C2×D32—62no—
401C2×D32—62no—
402C2×D32—122no—
403C2×D32—121no—
404C2×D32—121no—
405C2×D32—121no—
406C2×D32—121no—
407C2×D32—122no—
408C2×D32—122no—
409C2×D32—121no—
410C2×D32—121no—
411C2×D32—121no—
412C2×D32—121no—
413C2×D32—121no—
414C2×D32—121no—
415C32×D4—62no—
416C32×D4—121no—
417C2×C32×C4—31no—
418C2×C32×C4—31no—
419C2×C32×C4—31no—
420C2×C32×C4—31no—
421C2×C32×C4—62no—
422#638—22no—
423#638—41no—
424#638—41no—
425#638—121no—
426#638—121no—
427#638—121no—
428#638—121no—
429#638—121no—
430#638—122no—
431#638—122no—
432#638—122no—
433#638—124no—
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
444C4⋊(C3⋊D3)—62no—
445C4⋊(C3⋊D3)—62no—
446C3×#67—22no—
447C3×#67—22no—
448C3×#67—42no—
449C3×#67—41no—
450C3×#67—41no—
451C3×#67—42no—
452C3×#67—62no—
453C3×#67—62no—
454C3×#67—62no—
455C3×#67—62no—
456C3×#67—62no—
457C3×#67—122no—
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—22no—
468C2×C3×Dic3—22no—
469C2×C3×Dic3—21no—
470C2×C3×Dic3—21no—
471C2×C3×Dic3—21no—
472C2×C3×Dic3—21no—
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—42no—
480C2×C3×Dic3—61no—
481C2×C3×Dic3—61no—
482C2×C3×Dic3—61no—
483C2×C3×Dic3—62no—
484C2×C3×Dic3C22×D311yescharacteristic
485C2×C3×Dic3C22×D311yescharacteristic
486C2×C3×Dic3C22×D311yescharacteristic
487C2×C3×Dic3C22×D311yescharacteristic
488C2×C3×Dic3C22×D311yescharacteristic
489C2×C3×Dic3C22×D311yescharacteristic
490C2×C3×Dic3C22×D311yescharacteristic
491C2×C3×Dic3C22×D311yescharacteristic
492C3×D12—62no—
493C3×D12—62no—
494C3×D12—62no—
495C3×D12—121no—
496C3×C4×D3—34no—
497C3×C4×D3—34no—
498C3×C4×D3—62no—
499C3×Dic6—62no—
500C3×Dic6—62no—
501#627—22no—
502#626—22no—
503#626—22no—
504#626—22no—
505#626—41no—
506#626—62no—
507#626—62no—
508#626—62no—
509#626—62no—
510#626—122no—
511#626—122no—
512#626—121no—
513#626—121no—
514#626—122no—
515#625—41no—
516#625—121no—
517#625—121no—
518#625—122no—
519#624#6714yescomplemented
520D3×Dic3—22no—
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—22no—
528C3×C3⋊D3—41no—
529C3×C3⋊D3—41no—
530C32×D3—41no—
531C32×D3—41no—
532C23×D3—91no—
533C23×D3—91no—
534C23×D3—91no—
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—61no—
546C2×C3×D4—61no—
547C2×C3×D4—91no—
548C2×C3×D4—91no—
549C2×C3×D4—91no—
550C2×C3×D4—91no—
551C2×C3×D4—91no—
552C2×C3×D4—91no—
553C2×C3×D4—91no—
554C2×C3×D4—91no—
555C22×C3×C4—31no—
556C22×C3×C4—31no—
557C22×C3×C4—61no—
558C22×C3×C4—91no—
559C22×C3×C4—91no—
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—31no—
570C2×#67—31no—
571C2×#67—31no—
572C2×#67—61no—
573C2×#67—61no—
574C2×#67—61no—
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—91no—
585C2×#67—181no—
586C2×#67—181no—
587C2×#67—181no—
588C2×#67—181no—
589C2×#67—181no—
590C2×#67—361no—
591C2×#67D3211yescharacteristic, complemented
592C2×#67D3211yescharacteristic, complemented
593C22×Dic3—31no—
594C22×Dic3D3211yescharacteristic, complemented
595#237—64no—
596D3×D4—184no—
597D3×D4—184no—
598#235—64no—
599C2×D12—31no—
600C2×D12—31no—
601C2×D12—31no—
602C2×D12—31no—
603C2×D12—91no—
604C2×D12—91no—
605C2×D12—91no—
606C2×D12—91no—
607C2×D12—91no—
608C2×D12—181no—
609C2×D12—181no—
610C2×D12—184no—
611C2×C4×D3—31no—
612C2×C4×D3—31no—
613C2×C4×D3—31no—
614C2×Dic6—31no—
615C2×Dic6—31no—
616C3×C4⋊C4—91no—
617C3×C22⋊C4—91no—
618C3×C22⋊C4—91no—
619C3×C42—91no—
620#217—31no—
621#217—91no—
622#217—91no—
623#217—91no—
624#217—91no—
625#217—91no—
626#217—91no—
627#217—91no—
628#217—181no—
629(C2×D3)⋊C4—31no—
630(C2×D3)⋊C4—31no—
631(C2×D3)⋊C4—31no—
632(C2×D3)⋊C4—91no—
633(C2×D3)⋊C4—91no—
634(C2×D3)⋊C4—91no—
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—
652(C2×D3)⋊C4—181no—
653C4⋊Dic3—31no—
654C4⋊Dic3—91no—
655C4⋊Dic3—91no—
656C4⋊Dic3—181no—
657Dic3⋊C4—31no—
658Dic3⋊C4—91no—
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—41no—
679C22×C32—41no—
680C22×C32—41no—
681C22×C32—42no—
682C22×C32—41no—
683C22×C32—41no—
684C22×C32—41no—
685C22×C32—41no—
686C22×C32—41no—
687C22×C32—41no—
688C22×C32—61no—
689C22×C32—61no—
690C22×C32—61no—
691C22×C32—61no—
692C22×C32—61no—
693C22×C32—61no—
694C22×C32—81no—
695C22×C32—81no—
696C22×C32C23×D311yescharacteristic
697C22×C32C23×D311yescharacteristic
698C22×C32C23×D311yescharacteristic
699C2×C3⋊D3—21no—
700C2×C3⋊D3—21no—
701C2×C3⋊D3—21no—
702C2×C3⋊D3—21no—
703C2×C3⋊D3—21no—
704C2×C3⋊D3—21no—
705C2×C3⋊D3—21no—
706C2×C3⋊D3—21no—
707C2×C3⋊D3—61no—
708C2×C3⋊D3—62no—
709C2×C3⋊D3—61no—
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—121no—
718C2×C3⋊D3—121no—
719C2×C3⋊D3—122no—
720C2×C3⋊D3—121no—
721C2×C3⋊D3—121no—
722C2×C3⋊D3—121no—
723C2×C3⋊D3—121no—
724C2×C3⋊D3—121no—
725C2×C3⋊D3—121no—
726C2×C3⋊D3—124no—
727C2×C3⋊D3—241no—
728C2×C3⋊D3—241no—
729C2×C3⋊D3C2×#6712yes—
730C2×C3×D3—22no—
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—32no—
744C2×C3×D3—32no—
745C2×C3×D3—41no—
746C2×C3×D3—41no—
747C2×C3×D3—41no—
748C2×C3×D3—41no—
749C2×C3×D3—41no—
750C2×C3×D3—62no—
751C2×C3×D3—61no—
752C2×C3×D3—61no—
753C2×C3×D3—61no—
754C2×C3×D3—61no—
755C2×C3×D3—61no—
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—121no—
768C2×C3×D3—121no—
769C2×C3×D3—121no—
770C2×C3×D3—121no—
771C2×C3×D3—121no—
772C2×C3×D3—121no—
773C2×C3×D3—121no—
774C2×C3×D3—121no—
775D32—124no—
776D32—124no—
777D32—128no—
778D32—124no—
779D32—124no—
780D32—124no—
781C32×C4—32no—
782C32×C4—32no—
783C32×C4—61no—
784C32×C4—61no—
785C3⋊Dic3—21no—
786C3⋊Dic3—21no—
787C3⋊Dic3—21no—
788C3⋊Dic3—61no—
789C3⋊Dic3—62no—
790C3⋊Dic3—61no—
791C3⋊Dic3—61no—
792C3⋊Dic3—121no—
793C3⋊Dic3—121no—
794C3⋊Dic3—122no—
795C3×Dic3—21no—
796C3×Dic3—21no—
797C3×Dic3—21no—
798C3×Dic3—21no—
799C3×Dic3—22no—
800C3×Dic3—22no—
801C3×Dic3—41no—
802C3×Dic3—41no—
803C3×Dic3—62no—
804C3×Dic3—61no—
805C3×Dic3—61no—
806C3×Dic3—61no—
807C3×Dic3—61no—
808C3×Dic3—61no—
809C3×Dic3—61no—
810C3×Dic3—121no—
811C3×Dic3—121no—
812C3×Dic3D3×D412yes—
813C3×Dic3D3×D412yes—
814C3×Dic3C2×#6712yes—
815C3×Dic3C2×#6712yes—
816C2×#41—91no—
817C22×D4—271no—
818#127—91no—
819#127—271no—
820#124—271no—
821#124—271no—
822#121—91no—
823#121—271no—
824#121—271no—
825#121—271no—
826#120—271no—
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—41no—
840C23×C3—61no—
841C23×C3—61no—
842C23×C3—91no—
843C23×C3—91no—
844C23×C3—91no—
845C23×C3C2×D3211yescharacteristic
846C23×C3C2×D3211yescharacteristic
847C23×C3C2×D3211yescharacteristic
848C22×D3—31no—
849C22×D3—31no—
850C22×D3—31no—
851C22×D3—31no—
852C22×D3—31no—
853C22×D3—31no—
854C22×D3—61no—
855C22×D3—61no—
856C22×D3—61no—
857C22×D3—91no—
858C22×D3—91no—
859C22×D3—91no—
860C22×D3—181no—
861C22×D3—181no—
862C22×D3—181no—
863C22×D3—182no—
864C22×D3—182no—
865C22×D3—182no—
866C22×D3—182no—
867C22×D3—182no—
868C22×D3—182no—
869C22×D3—361no—
870C22×D3—362no—
871C22×D3—361no—
872C22×D3—361no—
873C22×D3—361no—
874C22×D3—361no—
875C22×D3—361no—
876C22×D3—361no—
877C22×D3—361no—
878C22×D3—361no—
879C22×D3—361no—
880C22×D3—361no—
881C22×D3—361no—
882C22×D3—361no—
883C22×D3—362no—
884C22×D3—362no—
885C22×D3C2×D3211yescharacteristic
886C22×D3C2×D3211yescharacteristic
887C3×Q8—182no—
888C3×D4—62no—
889C3×D4—62no—
890C3×D4—122no—
891C3×D4—121no—
892C3×D4—121no—
893C3×D4—122no—
894C3×D4—182no—
895C3×D4—182no—
896C3×D4—182no—
897C3×D4—182no—
898C3×D4—361no—
899C3×D4—361no—
900C3×D4—361no—
901C3×D4—361no—
902C2×C3×C4—31no—
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—31no—
910C2×C3×C4—61no—
911C2×C3×C4—61no—
912C2×C3×C4—61no—
913C2×C3×C4—61no—
914C2×C3×C4—62no—
915C2×C3×C4—62no—
916C2×C3×C4—94no—
917C2×C3×C4—91no—
918C2×C3×C4—91no—
919C2×C3×C4—91no—
920C2×C3×C4—122no—
921C2×C3×C4—182no—
922#67—22no—
923#67—41no—
924#67—62no—
925#67—62no—
926#67—62no—
927#67—62no—
928#67—62no—
929#67—122no—
930#67—121no—
931#67—121no—
932#67—121no—
933#67—121no—
934#67—121no—
935#67—121no—
936#67—121no—
937#67—122no—
938#67—122no—
939#67—182no—
940#67—182no—
941#67—361no—
942#67—361no—
943#67—362no—
944#67—361no—
945#67—361no—
946#67—361no—
947#67—362no—
948#67—361no—
949#67—361no—
950#67—361no—
951#67—362no—
952#67—362no—
953#67—362no—
954#67—364no—
955C2×Dic3—22no—
956C2×Dic3—31no—
957C2×Dic3—31no—
958C2×Dic3—31no—
959C2×Dic3—31no—
960C2×Dic3—31no—
961C2×Dic3—31no—
962C2×Dic3—61no—
963C2×Dic3—61no—
964C2×Dic3—61no—
965C2×Dic3—62no—
966C2×Dic3—91no—
967C2×Dic3—91no—
968C2×Dic3—91no—
969C2×Dic3—181no—
970C2×Dic3—181no—
971C2×Dic3—181no—
972C2×Dic3—361no—
973C2×Dic3C2×D3211yescharacteristic
974C2×Dic3C2×D3211yescharacteristic
975C2×Dic3C2×D3211yescharacteristic
976C2×Dic3C2×D3211yescharacteristic
977D12—62no—
978D12—62no—
979D12—62no—
980D12—121no—
981D12—182no—
982D12—182no—
983D12—182no—
984D12—182no—
985D12—362no—
986D12—362no—
987D12—361no—
988C4×D3—34no—
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—81no—
1010C2×C32—81no—
1011C2×C32—82no—
1012C2×C32—121no—
1013C2×C32—121no—
1014C2×C32C2×D3×D411yescharacteristic
1015C2×C32C2×D3×D411yescharacteristic
1016C2×C32#100411yescharacteristic
1017C2×C32#100411yescharacteristic
1018C2×C32#100411yescharacteristic
1019C2×C32#100911yescharacteristic
1020C2×C32#100911yescharacteristic
1021C2×C32#100911yescharacteristic
1022C2×C32C22×#6711yescharacteristic
1023C3⋊D3—22no—
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—42no—
1034C3×D3—41no—
1035C3×D3—41no—
1036C3×D3—41no—
1037C3×D3—41no—
1038C3×D3—62no—
1039C3×D3—62no—
1040C3×D3—81no—
1041C3×D3—122no—
1042C3×D3—121no—
1043C3×D3—121no—
1044C3×D3—121no—
1045C3×D3—121no—
1046C3×D3—241no—
1047C3×D3—241no—
1048C24—271no—
1049C24—271no—
1050#41—184no—
1051C2×Q8—91no—
1052C2×D4—31no—
1053C2×D4—31no—
1054C2×D4—91no—
1055C2×D4—91no—
1056C2×D4—91no—
1057C2×D4—91no—
1058C2×D4—91no—
1059C2×D4—91no—
1060C2×D4—91no—
1061C2×D4—91no—
1062C2×D4—271no—
1063C2×D4—271no—
1064C2×D4—271no—
1065C2×D4—271no—
1066C2×D4—271no—
1067C2×D4—544no—
1068C22×C4—31no—
1069C22×C4—91no—
1070C22×C4—91no—
1071C4⋊C4—91no—
1072C4⋊C4—271no—
1073C22⋊C4—91no—
1074C22⋊C4—91no—
1075C22⋊C4—271no—
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—41no—
1099C22×C3—41no—
1100C22×C3—41no—
1101C22×C3—41no—
1102C22×C3—41no—
1103C22×C3—41no—
1104C22×C3—41no—
1105C22×C3—41no—
1106C22×C3—42no—
1107C22×C3—41no—
1108C22×C3—62no—
1109C22×C3—61no—
1110C22×C3—61no—
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—81no—
1122C22×C3—81no—
1123C22×C3—92no—
1124C22×C3—121no—
1125C22×C3—121no—
1126C22×C3—121no—
1127C22×C3—121no—
1128C22×C3—121no—
1129C22×C3—181no—
1130C22×C3—181no—
1131C22×C3—181no—
1132C22×C3—181no—
1133C22×C3—181no—
1134C22×C3—181no—
1135C22×C3—181no—
1136C22×C3—181no—
1137C22×C3C22×D3211yescharacteristic
1138C22×C3C22×D3211yescharacteristic
1139C22×C3C22×D3211yescharacteristic
1140C2×D3—21no—
1141C2×D3—21no—
1142C2×D3—21no—
1143C2×D3—21no—
1144C2×D3—21no—
1145C2×D3—21no—
1146C2×D3—32no—
1147C2×D3—32no—
1148C2×D3—62no—
1149C2×D3—61no—
1150C2×D3—61no—
1151C2×D3—61no—
1152C2×D3—61no—
1153C2×D3—61no—
1154C2×D3—61no—
1155C2×D3—61no—
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—121no—
1166C2×D3—121no—
1167C2×D3—121no—
1168C2×D3—121no—
1169C2×D3—121no—
1170C2×D3—121no—
1171C2×D3—121no—
1172C2×D3—121no—
1173C2×D3—182no—
1174C2×D3—181no—
1175C2×D3—181no—
1176C2×D3—181no—
1177C2×D3—181no—
1178C2×D3—181no—
1179C2×D3—181no—
1180C2×D3—181no—
1181C2×D3—181no—
1182C2×D3—181no—
1183C2×D3—361no—
1184C2×D3—361no—
1185C2×D3—361no—
1186C2×D3—361no—
1187C2×D3—361no—
1188C2×D3—361no—
1189C2×D3—361no—
1190C2×D3—361no—
1191C2×D3—362no—
1192C2×D3—364no—
1193C2×D3—364no—
1194C2×D3—364no—
1195C2×D3—364no—
1196C2×D3—364no—
1197C2×D3—364no—
1198C2×D3—368no—
1199C2×D3—721no—
1200C2×D3—721no—
1201C3×C4—32no—
1202C3×C4—32no—
1203C3×C4—32no—
1204C3×C4—32no—
1205C3×C4—62no—
1206C3×C4—62no—
1207C3×C4—61no—
1208C3×C4—61no—
1209C3×C4—61no—
1210C3×C4—61no—
1211C3×C4—121no—
1212C3×C4—121no—
1213C3×C4—181no—
1214C3×C4—181no—
1215C3×C4—181no—
1216Dic3—21no—
1217Dic3—21no—
1218Dic3—62no—
1219Dic3—61no—
1220Dic3—61no—
1221Dic3—61no—
1222Dic3—61no—
1223Dic3—61no—
1224Dic3—61no—
1225Dic3—121no—
1226Dic3—121no—
1227Dic3—182no—
1228Dic3—181no—
1229Dic3—181no—
1230Dic3—181no—
1231Dic3—361no—
1232Dic3—361no—
1233Dic3—362no—
1234Dic3D3×#6712yes—
1235Dic3D3×#6712yes—
1236C32—21no—
1237C32—21no—
1238C32—21no—
1239C32—41no—
1240C32#560711yescharacteristic, complemented
1241C32#571511yescharacteristic, complemented
1242C32#583011yescharacteristic, complemented
1243C23—31no—
1244C23—31no—
1245C23—91no—
1246C23—91no—
1247C23—91no—
1248C23—271no—
1249C23—542no—
1250C23—542no—
1251C23—1081no—
1252C23—1081no—
1253C23—1081no—
1254C23—1081no—
1255C23D3311yescharacteristic
1256Q8—182no—
1257D4—62no—
1258D4—121no—
1259D4—182no—
1260D4—182no—
1261D4—182no—
1262D4—182no—
1263D4—361no—
1264D4—361no—
1265D4—361no—
1266D4—361no—
1267D4—542no—
1268D4—542no—
1269D4—1081no—
1270D4—1081no—
1271D4—1081no—
1272C2×C4—31no—
1273C2×C4—31no—
1274C2×C4—31no—
1275C2×C4—31no—
1276C2×C4—62no—
1277C2×C4—94no—
1278C2×C4—91no—
1279C2×C4—91no—
1280C2×C4—91no—
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—81no—
1300C2×C3—81no—
1301C2×C3—82no—
1302C2×C3—122no—
1303C2×C3—121no—
1304C2×C3—121no—
1305C2×C3—121no—
1306C2×C3—121no—
1307C2×C3—182no—
1308C2×C3—241no—
1309C2×C3—361no—
1310C2×C3—361no—
1311C2×C3#6430711yescharacteristic
1312C2×C3#6430811yescharacteristic
1313C2×C3D32×D411yescharacteristic
1314C2×C3#6431411yescharacteristic
1315C2×C3#6431411yescharacteristic
1316C2×C3#6431411yescharacteristic
1317C2×C3C2×D3×#6711yescharacteristic
1318C2×C3C2×D3×#6711yescharacteristic
1319C2×C3#6433011yescharacteristic
1320D3—41no—
1321D3—41no—
1322D3—62no—
1323D3—62no—
1324D3—122no—
1325D3—121no—
1326D3—121no—
1327D3—121no—
1328D3—121no—
1329D3—241no—
1330D3—241no—
1331D3—362no—
1332D3—361no—
1333D3—361no—
1334D3—361no—
1335D3—721no—
1336D3—721no—
1337D3—722no—
1338C22—21no—
1339C22—21no—
1340C22—21no—
1341C22—61no—
1342C22—61no—
1343C22—61no—
1344C22—61no—
1345C22—61no—
1346C22—61no—
1347C22—92no—
1348C22—181no—
1349C22—181no—
1350C22—181no—
1351C22—181no—
1352C22—181no—
1353C22—181no—
1354C22—181no—
1355C22—181no—
1356C22—541no—
1357C22—541no—
1358C22—541no—
1359C22—1084no—
1360C22—1084no—
1361C22C2×D3311yescharacteristic
1362C4—32no—
1363C4—32no—
1364C4—61no—
1365C4—61no—
1366C4—181no—
1367C4—181no—
1368C4—181no—
1369C4—541no—
1370C3—21no—
1371C3—21no—
1372C3—21no—
1373C3—41no—
1374C3#1059506411yescharacteristic, complemented
1375C3#1059529911yescharacteristic, complemented
1376C3#1059530311yescharacteristic, complemented
1377C2—41no—
1378C2—121no—
1379C2—121no—
1380C2—182no—
1381C2—361no—
1382C2—361no—
1383C2—1081no—
1384C2#1172441811yescharacteristic
1385C2#1172442011yescharacteristic
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×#3804C2semidirect
2. C2×#88955C2semidirect
3. #11723729C2semidirect
4. #11723643C2semidirect
5. #11723633C2semidirect
6. #11723632C2semidirect
7. C3×#63979C2semidirect
8. C3×#63978C2semidirect
9. #11723003C2semidirect
10. #11723001C2semidirect
11. #11722959C2semidirect
12. #11722956C2semidirect
13. #11722951C2semidirect
14. #11722949C2semidirect
15. #11722915C2semidirect
21. C2×#6312C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×#638C22semidirect
25. C2×C32×#67C22semidirect
26. C2×C32×#67C22semidirect
27. C22×C32×Dic3C22semidirect
30. C2×#6291C22semidirect
31. C2×#6290C22semidirect
32. C2×C3×#627C22semidirect
36. C2×C3×#626C22semidirect
37. C2×C3×#625C22semidirect
40. C2×C3×D3×Dic3C22semidirect
43. #88814C22semidirect
44. #88814C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
49. #88803C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. Dic3×C3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
53. C3×#3722C22semidirect
54. C3×(C2×D3)⋊Dic3C22semidirect
55. C3×Dic32C22semidirect
59. C2×#3804D3semidirect
81. #63979D3semidirect
87. #63978D3semidirect
142. C3×#624D4semidirect
167. C2×#638C2×D3semidirect
168. C2×#638C2×D3semidirect
188. C2×C3×#67C2×D3semidirect
189. C2×C3×#67C2×D3semidirect
190. C2×C3×#67C2×D3semidirect
191. C2×C3×#67C2×D3semidirect
194. C22×C3×Dic3C2×D3semidirect
195. C22×C3×Dic3C2×D3semidirect
208. C2×#627C2×D3semidirect
221. C2×#626C2×D3semidirect
225. C2×#625C2×D3semidirect
228. C2×D3×Dic3C2×D3semidirect
249. Dic3⋊Dic3C2×D3semidirect
259. #3722C2×D3semidirect
275. (C2×D3)⋊Dic3C2×D3semidirect
279. Dic32C2×D3semidirect
519. #624#67semidirect
591. C2×#67D32semidirect
592. C2×#67D32semidirect
594. C22×Dic3D32semidirect
831. C33#535semidirect
1240. C32#5607semidirect
1241. C32#5715semidirect
1242. C32#5830semidirect
1374. C3#10595064semidirect
1375. C3#10595299semidirect
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×#38042
C2×#889552
#117237292
#117236432
#117236332
#117236322
C3×#639792
C3×#639782
#117230032
#117230012
#117229592
#117229562
#117229512
#117229492
#117229152
#105953033
#105952993
#105950643