Finite Group Databasebeta

← #13172292

Subgroups — #13172292

Order 1728.

1308 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723717C211yesmaximal, characteristic, complemented
2#11723631C211yesmaximal, characteristic, complemented
3#11723615C211yesmaximal, characteristic, complemented
4#11723602C211yesmaximal, characteristic, complemented
5C3×#63983C211yesmaximal, characteristic, complemented
6C3×#63980C211yesmaximal, characteristic, complemented
7C3×#63979C211yesmaximal, characteristic, complemented
8#11723023C211yesmaximal, characteristic, complemented
9#11723020C211yesmaximal, characteristic, complemented
10#11722991C211yesmaximal, characteristic, complemented
11#11722989C211yesmaximal, characteristic, complemented
12#11722967C211yesmaximal, characteristic, complemented
13#11722954C211yesmaximal, characteristic, complemented
14#11722947C211yesmaximal, characteristic, complemented
15#11722946C211yesmaximal, characteristic, complemented
16#10595313—31nomaximal
17#10595259—31nomaximal
18#10595258—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic, complemented
22C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic
25C2×C32×#67C2211yescharacteristic, complemented
26C2×#6295C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
30C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
31C2×C3×#626C2211yescharacteristic
32C2×C3×#626C2211yescharacteristic, complemented
33C2×C3×#625C2211yescharacteristic
34C2×C3×#625C2211yescharacteristic
35#88864C2211yescharacteristic, complemented
36#88815C2211yescharacteristic, complemented
37#88814C2211yescharacteristic
38#88814C2211yescharacteristic, complemented
39#88807C2211yescharacteristic, complemented
40#88806C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43#88803C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47C3×#3724C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64148—31no—
55#64147—31no—
56#64144—31no—
57C3×#940—31no—
58C3×#940—31no—
59C3×#939—31no—
60C3×#939—31no—
61C3×#937—31no—
62C3×#937—31no—
63#63983—31no—
64#63983D311yescharacteristic, complemented
65#63980—31no—
66#63980—31no—
67#63980D311yescharacteristic, complemented
68#63979D311yescharacteristic, complemented
69#63978—31no—
70#63978—31no—
71#63977—31no—
72#63976—31no—
73#63976—31no—
74#63976—31no—
75#63971—31no—
76#63971—31no—
77#63970—31no—
78#63970—31no—
79#63970—31no—
80#63970—31no—
81#63970—61no—
82#63970—61no—
83#63969—31no—
84#63969—31no—
85#63962—31no—
86#63961—31no—
87#63961—31no—
88#63961—61no—
89#63956—31no—
90#63922—31no—
91#63912—31no—
92#63891—31no—
93#63885—31no—
94#63885—31no—
95#63884—31no—
96#63868—31no—
97#63861—31no—
98#63859—31no—
99#63859—31no—
100#63859—31no—
101#63853—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C2×C3×D32—41no—
109C2×C3×D32—41no—
110C2×C3×D32—41no—
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113C3×#638—41no—
114C3×#638—41no—
115C2×C3×C3⋊Dic3—41no—
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C3×C3⋊Dic3C2311yescharacteristic
120C32×#67—41no—
121C32×#67—41no—
122C32×#67—41no—
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125C2×C32×Dic3C2311yescharacteristic
126#6295—41no—
127#6290—41no—
128#6290—41no—
129Dic3×C3⋊D3—41no—
130D3×C3⋊Dic3—41no—
131C3×#626—41no—
132C3×#626—41no—
133C3×#625—41no—
134C3×#625—41no—
135#5720—91no—
136#5620—91no—
137#5595—91no—
138C23×C3×D3—31no—
139C23×C3×D3—31no—
140C22×D32C2×D311yescharacteristic
141C2×C32×D4—31no—
142C2×C32×D4—31no—
143C2×C32×D4—31no—
144C2×#638—31no—
145C2×#638—31no—
146C2×#638C2×D311yescharacteristic
147C2×#638C2×D311yescharacteristic, complemented
148C22×C3⋊Dic3—31no—
149C22×C3⋊Dic3C2×D311yescharacteristic, complemented
150C2×C4×C3⋊D3—31no—
151C2×C3×#67—21no—
152C2×C3×#67—21no—
153C2×C3×#67—21no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—61no—
165C2×C3×#67—61no—
166C2×C3×#67C2×D311yescharacteristic
167C2×C3×#67C2×D311yescharacteristic
168C2×C3×#67C2×D311yescharacteristic
169C2×C3×#67C2×D311yescharacteristic
170C2×C3×#67C2×D311yescharacteristic, complemented
171C2×C3×#67C2×D311yescharacteristic, complemented
172C22×C3×Dic3—31no—
173C22×C3×Dic3—31no—
174C22×C3×Dic3—61no—
175C2×C3×D12—31no—
176C2×C3×D12—31no—
177C2×#626—31no—
178C2×#626—31no—
179C2×#626C2×D311yescharacteristic
180C2×#626C2×D311yescharacteristic, complemented
181C2×#625—31no—
182C2×#625—31no—
183C2×#625—31no—
184C2×#625—31no—
185C2×#625—31no—
186C2×#625—61no—
187C2×#625—61no—
188C2×#625C2×D311yescharacteristic
189C2×#625C2×D311yescharacteristic
190C2×D3×Dic3—31no—
191C2×D3×Dic3—31no—
192C2×D3×Dic3—31no—
193C2×D3×Dic3—31no—
194C2×D3×Dic3—61no—
195C2×D3×Dic3—61no—
196#3757—31no—
197#3757—31no—
198#3757—31no—
199#3757—31no—
200#3757—31no—
201#3757—31no—
202#3757—61no—
203#3757—61no—
204#3757—61no—
205#3757—121no—
206#3752—31no—
207C4⋊(C3⋊Dic3)—31no—
208#3750—31no—
209#3750—31no—
210#3750—31no—
211C3×#217—31no—
212C3×#217—31no—
213C3×#217—31no—
214C3×#217—31no—
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×Dic3⋊C4—31no—
222C3×Dic3⋊C4—31no—
223C3×C4×Dic3—31no—
224C3×C4×Dic3—31no—
225#3724—31no—
226#3724—31no—
227#3724—31no—
228#3724—31no—
229#3724—31no—
230#3724—61no—
231#3724—61no—
232#3724C2×D311yescharacteristic, complemented
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic3⋊Dic3—31no—
239Dic3⋊Dic3—61no—
240Dic3⋊Dic3—61no—
241#3722—31no—
242#3722—31no—
243#3722C2×D311yescharacteristic
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—31no—
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—61no—
257(C2×D3)⋊Dic3—61no—
258(C2×D3)⋊Dic3—61no—
259(C2×D3)⋊Dic3—61no—
260(C2×D3)⋊Dic3C2×D311yescharacteristic
261(C2×D3)⋊Dic3C2×D311yescharacteristic
262(C2×D3)⋊Dic3C2×D311yescharacteristic
263(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
264Dic32C2×D311yescharacteristic, complemented
265C22×C33—21no—
266C22×C33—21no—
267C22×C33—21no—
268C22×C33C2411yescharacteristic
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C3×C3⋊D3—21no—
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C2×C32×D3—21no—
279C2×C32×D3—21no—
280C2×C32×D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C3×D32—44no—
285C3⋊(C3⋊Dic3)—21no—
286C3⋊(C3⋊Dic3)—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C3×C3⋊Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C3×#127—91no—
295C3×#121—91no—
296C3×#120—91no—
297#953—91no—
298#953—91no—
299#940—31no—
300#940—31no—
301#939—31no—
302#939—31no—
303#939—91no—
304#939—91no—
305#939—91no—
306#939—91no—
307#939—91no—
308#939—91no—
309#939—91no—
310#939—91no—
311#939—181no—
312#938—91no—
313#938—91no—
314#938—91no—
315#938—181no—
316#937—31no—
317#937—31no—
318#937—91no—
319#937—91no—
320#937—91no—
321#935—91no—
322#935—91no—
323#935—91no—
324#935—91no—
325#935—181no—
326#930—91no—
327#929—91no—
328#898—91no—
329#894—91no—
330#886—91no—
331#884—91no—
332#884—91no—
333#884—91no—
334#883—91no—
335#883—91no—
336#882—91no—
337#879—91no—
338#879—91no—
339#879—91no—
340#876—91no—
341#876—91no—
342C23×C32—21no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—31no—
346C23×C32—31no—
347C23×C32—31no—
348C23×C32—41no—
349C23×C32C22×D311yescharacteristic
350C23×C32C22×D311yescharacteristic
351C23×C32C22×D311yescharacteristic
352C22×C3⋊D3C22×D311yescharacteristic
353C22×C3⋊D3C22×D311yescharacteristic
354C22×C3×D3—21no—
355C22×C3×D3—21no—
356C22×C3×D3—21no—
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—61no—
362C22×C3×D3—61no—
363C22×C3×D3—121no—
364C22×C3×D3—121no—
365C22×C3×D3—121no—
366C22×C3×D3—121no—
367C22×C3×D3—121no—
368C22×C3×D3—121no—
369C22×C3×D3C22×D311yescharacteristic
370C22×C3×D3C22×D311yescharacteristic
371C22×C3×D3C22×D311yescharacteristic
372C22×C3×D3C22×D311yescharacteristic
373C22×C3×D3C22×D311yescharacteristic
374C22×C3×D3C22×D311yescharacteristic
375C2×D32—41no—
376C2×D32—41no—
377C2×D32—41no—
378C32×D4—121no—
379C32×D4—121no—
380C32×D4—121no—
381C2×C32×C4—31no—
382C2×C32×C4—31no—
383C2×C32×C4—31no—
384#638—41no—
385#638—41no—
386#638—121no—
387#638—121no—
388C2×C3⋊Dic3—31no—
389C2×C3⋊Dic3—31no—
390C2×C3⋊Dic3—31no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—31no—
393C2×C3⋊Dic3—31no—
394C2×C3⋊Dic3—41no—
395C2×C3⋊Dic3—61no—
396C2×C3⋊Dic3—61no—
397C2×C3⋊Dic3—61no—
398C2×C3⋊Dic3—61no—
399C2×C3⋊Dic3—61no—
400C2×C3⋊Dic3—61no—
401C2×C3⋊Dic3—121no—
402C2×C3⋊Dic3—121no—
403C2×C3⋊Dic3—121no—
404C2×C3⋊Dic3C22×D311yescharacteristic
405C2×C3⋊Dic3C22×D311yescharacteristic
406C2×C3⋊Dic3C22×D311yescharacteristic
407C2×C3⋊Dic3C22×D311yescharacteristic
408C4×C3⋊D3—121no—
409C3×#67—41no—
410C3×#67—41no—
411C3×#67—41no—
412C3×#67—41no—
413C3×#67—41no—
414C3×#67—41no—
415C3×#67—42no—
416C3×#67—42no—
417C3×#67—42no—
418C3×#67—121no—
419C3×#67—121no—
420C3×#67—121no—
421C3×#67—121no—
422C3×#67—121no—
423C3×#67—121no—
424C3×#67—121no—
425C3×#67—121no—
426C3×#67—121no—
427C3×#67—121no—
428C3×#67—122no—
429C3×#67—122no—
430C2×C3×Dic3—21no—
431C2×C3×Dic3—21no—
432C2×C3×Dic3—21no—
433C2×C3×Dic3—31no—
434C2×C3×Dic3—31no—
435C2×C3×Dic3—31no—
436C2×C3×Dic3—31no—
437C2×C3×Dic3—31no—
438C2×C3×Dic3—31no—
439C2×C3×Dic3—31no—
440C2×C3×Dic3—31no—
441C2×C3×Dic3—61no—
442C2×C3×Dic3—61no—
443C2×C3×Dic3—61no—
444C2×C3×Dic3—61no—
445C2×C3×Dic3—121no—
446C2×C3×Dic3—121no—
447C2×C3×Dic3—122no—
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C2×C3×Dic3C22×D311yescharacteristic
451C2×C3×Dic3C22×D311yescharacteristic
452C2×C3×Dic3C22×D311yescharacteristic
453C2×C3×Dic3C22×D311yescharacteristic
454C3×D12—121no—
455C3×D12—121no—
456#626—41no—
457#626—41no—
458#626—121no—
459#626—121no—
460#625—41no—
461#625—41no—
462#625—121no—
463#625—121no—
464#625—121no—
465#625—121no—
466#625—121no—
467#625—122no—
468#625—122no—
469D3×Dic3—121no—
470D3×Dic3—121no—
471D3×Dic3—122no—
472D3×Dic3—121no—
473D3×Dic3—121no—
474D3×Dic3—122no—
475#560—271noSylow
476C2×C33—41no—
477C2×C33H(5,𝔽2)11yescharacteristic
478C2×C33H(5,𝔽2)11yescharacteristic
479C2×C33H(5,𝔽2)11yescharacteristic
480C3×C3⋊D3—41no—
481C3×C3⋊D3—41no—
482C32×D3—41no—
483C32×D3—41no—
484C32×D3—41no—
485C24×C3—91no—
486C23×D3—31no—
487C23×D3—31no—
488C2×C3×D4—31no—
489C2×C3×D4—31no—
490C2×C3×D4—31no—
491C2×C3×D4—31no—
492C2×C3×D4—31no—
493C2×C3×D4—31no—
494C2×C3×D4—61no—
495C2×C3×D4—61no—
496C2×C3×D4—61no—
497C2×C3×D4—91no—
498C2×C3×D4—91no—
499C2×C3×D4—91no—
500C2×C3×D4—91no—
501C2×C3×D4—91no—
502C2×C3×D4—91no—
503C22×C3×C4—91no—
504C2×#67—31no—
505C2×#67—31no—
506C2×#67—31no—
507C2×#67—31no—
508C2×#67—31no—
509C2×#67—31no—
510C2×#67—31no—
511C2×#67—31no—
512C2×#67—31no—
513C2×#67—31no—
514C2×#67—61no—
515C2×#67—61no—
516C2×#67—91no—
517C2×#67—91no—
518C2×#67—91no—
519C2×#67—91no—
520C2×#67—91no—
521C2×#67—91no—
522C2×#67—91no—
523C2×#67—91no—
524C2×#67—181no—
525C2×#67—181no—
526C2×#67D3211yescharacteristic
527C2×#67D3211yescharacteristic
528C2×#67D3211yescharacteristic, complemented
529C22×Dic3—31no—
530C22×Dic3—31no—
531C22×Dic3—61no—
532C22×Dic3—91no—
533C22×Dic3—91no—
534C22×Dic3—91no—
535C22×Dic3—181no—
536C2×D12—31no—
537C2×D12—31no—
538C2×D12—91no—
539C2×C4×D3—91no—
540C2×C4×D3—91no—
541C2×C4×D3—91no—
542C2×C4×D3—181no—
543C3×C4⋊C4—91no—
544C3×C22⋊C4—91no—
545C3×C22⋊C4—91no—
546C3×C22⋊C4—91no—
547C3×C22⋊C4—91no—
548C3×C22⋊C4—91no—
549C3×C42—91no—
550#217—31no—
551#217—31no—
552#217—31no—
553#217—31no—
554#217—91no—
555#217—91no—
556#217—91no—
557#217—91no—
558#217—91no—
559#217—91no—
560#217—91no—
561#217—91no—
562#217—91no—
563#217—91no—
564#217—91no—
565#217—91no—
566#217—181no—
567#217—181no—
568#217—181no—
569#217—181no—
570#217—181no—
571#217—181no—
572#217—361no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—31no—
575(C2×D3)⋊C4—31no—
576(C2×D3)⋊C4—31no—
577(C2×D3)⋊C4—31no—
578(C2×D3)⋊C4—31no—
579(C2×D3)⋊C4—91no—
580(C2×D3)⋊C4—91no—
581(C2×D3)⋊C4—91no—
582(C2×D3)⋊C4—91no—
583(C2×D3)⋊C4—91no—
584(C2×D3)⋊C4—91no—
585(C2×D3)⋊C4—91no—
586(C2×D3)⋊C4—91no—
587(C2×D3)⋊C4—91no—
588(C2×D3)⋊C4—181no—
589C4⋊Dic3—91no—
590C4⋊Dic3—91no—
591C4⋊Dic3—91no—
592C4⋊Dic3—91no—
593C4⋊Dic3—181no—
594Dic3⋊C4—31no—
595Dic3⋊C4—31no—
596Dic3⋊C4—91no—
597Dic3⋊C4—91no—
598Dic3⋊C4—91no—
599Dic3⋊C4—91no—
600Dic3⋊C4—91no—
601Dic3⋊C4—91no—
602Dic3⋊C4—91no—
603Dic3⋊C4—91no—
604Dic3⋊C4—91no—
605Dic3⋊C4—91no—
606Dic3⋊C4—91no—
607Dic3⋊C4—181no—
608Dic3⋊C4—181no—
609Dic3⋊C4—181no—
610C4×Dic3—31no—
611C4×Dic3—31no—
612C22×C32—21no—
613C22×C32—22no—
614C22×C32—21no—
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—21no—
625C22×C32—41no—
626C22×C32—41no—
627C22×C32—41no—
628C22×C32—42no—
629C22×C32—41no—
630C22×C32—41no—
631C22×C32—41no—
632C22×C32—41no—
633C22×C32—41no—
634C22×C32—41no—
635C22×C32—61no—
636C22×C32—61no—
637C22×C32—61no—
638C22×C32—61no—
639C22×C32—61no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32—61no—
643C22×C32—61no—
644C22×C32—81no—
645C22×C32—81no—
646C22×C32C23×D311yescharacteristic
647C22×C32C23×D311yescharacteristic
648C22×C32C23×D311yescharacteristic
649C2×C3⋊D3—21no—
650C2×C3⋊D3—21no—
651C2×C3⋊D3—21no—
652C2×C3⋊D3—21no—
653C2×C3⋊D3—21no—
654C2×C3⋊D3—21no—
655C2×C3×D3—22no—
656C2×C3×D3—21no—
657C2×C3×D3—21no—
658C2×C3×D3—21no—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—21no—
664C2×C3×D3—21no—
665C2×C3×D3—21no—
666C2×C3×D3—21no—
667C2×C3×D3—21no—
668C2×C3×D3—21no—
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—21no—
673C2×C3×D3—21no—
674C2×C3×D3—41no—
675C2×C3×D3—41no—
676C2×C3×D3—41no—
677C2×C3×D3—41no—
678C2×C3×D3—41no—
679C2×C3×D3—41no—
680C2×C3×D3—41no—
681C2×C3×D3—41no—
682C2×C3×D3—62no—
683C2×C3×D3—61no—
684C2×C3×D3—61no—
685C2×C3×D3—61no—
686C2×C3×D3—61no—
687C2×C3×D3—61no—
688C2×C3×D3—61no—
689C2×C3×D3—61no—
690C2×C3×D3—61no—
691C2×C3×D3—61no—
692C2×C3×D3—61no—
693C2×C3×D3—61no—
694C2×C3×D3—61no—
695C2×C3×D3—121no—
696C2×C3×D3—121no—
697C2×C3×D3—121no—
698C2×C3×D3—121no—
699C2×C3×D3—121no—
700C2×C3×D3—124no—
701C2×C3×D3—124no—
702D32—44no—
703C32×C4—61no—
704C32×C4—61no—
705C32×C4—61no—
706C3⋊Dic3—21no—
707C3⋊Dic3—21no—
708C3⋊Dic3—21no—
709C3⋊Dic3—21no—
710C3⋊Dic3—61no—
711C3⋊Dic3—61no—
712C3⋊Dic3—61no—
713C3⋊Dic3—61no—
714C3⋊Dic3—61no—
715C3⋊Dic3—61no—
716C3⋊Dic3—121no—
717C3⋊Dic3—121no—
718C3⋊Dic3—121no—
719C3⋊Dic3—121no—
720C3⋊Dic3—121no—
721C3⋊Dic3—121no—
722C3⋊Dic3—241no—
723C3⋊Dic3—241no—
724C3×Dic3—22no—
725C3×Dic3—21no—
726C3×Dic3—21no—
727C3×Dic3—21no—
728C3×Dic3—21no—
729C3×Dic3—21no—
730C3×Dic3—21no—
731C3×Dic3—41no—
732C3×Dic3—41no—
733C3×Dic3—62no—
734C3×Dic3—61no—
735C3×Dic3—61no—
736C3×Dic3—61no—
737C3×Dic3—61no—
738C3×Dic3—61no—
739C3×Dic3—61no—
740C3×Dic3—61no—
741C3×Dic3—61no—
742C3×Dic3—121no—
743C3×Dic3—121no—
744C3×Dic3—121no—
745#127—91no—
746#126—271no—
747#126—271no—
748#123—271no—
749#123—271no—
750#123—271no—
751#121—91no—
752#121—271no—
753#121—271no—
754#121—271no—
755#121—271no—
756#121—271no—
757#120—91no—
758#120—271no—
759#120—271no—
760C33#56011yescharacteristic, complemented, Sylow
761C23×C3—21no—
762C23×C3—21no—
763C23×C3—21no—
764C23×C3—31no—
765C23×C3—31no—
766C23×C3—31no—
767C23×C3—31no—
768C23×C3—31no—
769C23×C3—31no—
770C23×C3—41no—
771C23×C3—61no—
772C23×C3—61no—
773C23×C3—61no—
774C23×C3—91no—
775C23×C3—91no—
776C23×C3—361no—
777C23×C3—361no—
778C23×C3—361no—
779C23×C3C2×D3211yescharacteristic
780C23×C3C2×D3211yescharacteristic
781C23×C3C2×D3211yescharacteristic
782C22×D3—31no—
783C22×D3—31no—
784C22×D3—31no—
785C22×D3—31no—
786C22×D3—61no—
787C22×D3—61no—
788C22×D3—121no—
789C22×D3—121no—
790C22×D3—121no—
791C22×D3—121no—
792C22×D3—121no—
793C22×D3—121no—
794C22×D3C2×D3211yescharacteristic
795C22×D3C2×D3211yescharacteristic
796C22×D3C2×D3211yescharacteristic
797C3×D4—121no—
798C3×D4—121no—
799C3×D4—121no—
800C3×D4—121no—
801C3×D4—121no—
802C3×D4—121no—
803C3×D4—122no—
804C3×D4—122no—
805C3×D4—122no—
806C3×D4—361no—
807C3×D4—361no—
808C3×D4—361no—
809C3×D4—361no—
810C3×D4—361no—
811C3×D4—361no—
812C2×C3×C4—31no—
813C2×C3×C4—31no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—31no—
817C2×C3×C4—31no—
818C2×C3×C4—61no—
819C2×C3×C4—61no—
820C2×C3×C4—61no—
821C2×C3×C4—91no—
822C2×C3×C4—91no—
823C2×C3×C4—91no—
824C2×C3×C4—91no—
825C2×C3×C4—361no—
826#67—41no—
827#67—41no—
828#67—41no—
829#67—121no—
830#67—121no—
831#67—121no—
832#67—121no—
833#67—121no—
834#67—121no—
835#67—121no—
836#67—121no—
837#67—121no—
838#67—121no—
839#67—122no—
840#67—122no—
841#67—361no—
842#67—361no—
843#67—361no—
844#67—361no—
845#67—361no—
846#67—361no—
847#67—361no—
848#67—361no—
849#67—362no—
850#67—362no—
851C2×Dic3—31no—
852C2×Dic3—31no—
853C2×Dic3—31no—
854C2×Dic3—31no—
855C2×Dic3—31no—
856C2×Dic3—31no—
857C2×Dic3—31no—
858C2×Dic3—31no—
859C2×Dic3—61no—
860C2×Dic3—61no—
861C2×Dic3—61no—
862C2×Dic3—61no—
863C2×Dic3—91no—
864C2×Dic3—91no—
865C2×Dic3—91no—
866C2×Dic3—91no—
867C2×Dic3—91no—
868C2×Dic3—91no—
869C2×Dic3—121no—
870C2×Dic3—121no—
871C2×Dic3—122no—
872C2×Dic3—181no—
873C2×Dic3—181no—
874C2×Dic3—181no—
875C2×Dic3—181no—
876C2×Dic3—181no—
877C2×Dic3—181no—
878C2×Dic3—361no—
879C2×Dic3—361no—
880C2×Dic3—361no—
881C2×Dic3—361no—
882C2×Dic3—361no—
883C2×Dic3—362no—
884C2×Dic3C2×D3211yescharacteristic
885C2×Dic3C2×D3211yescharacteristic
886C2×Dic3C2×D3211yescharacteristic
887D12—121no—
888D12—121no—
889D12—361no—
890C4×D3—361no—
891C4×D3—361no—
892C4×D3—361no—
893C4×D3—362no—
894C2×C32—21no—
895C2×C32—21no—
896C2×C32—21no—
897C2×C32—21no—
898C2×C32—21no—
899C2×C32—21no—
900C2×C32—21no—
901C2×C32—21no—
902C2×C32—21no—
903C2×C32—41no—
904C2×C32—41no—
905C2×C32—41no—
906C2×C32—41no—
907C2×C32—42no—
908C2×C32—41no—
909C2×C32—41no—
910C2×C32—81no—
911C2×C32—81no—
912C2×C32—82no—
913C2×C32—121no—
914C2×C32—121no—
915C2×C32—121no—
916C2×C32#100411yescharacteristic
917C2×C32#100411yescharacteristic
918C2×C32#100411yescharacteristic
919C2×C32#100411yescharacteristic
920C2×C32#100411yescharacteristic
921C2×C32#100411yescharacteristic
922C2×C32#100411yescharacteristic
923C2×C32#100411yescharacteristic
924C2×C32#100911yescharacteristic
925C3⋊D3—41no—
926C3⋊D3—41no—
927C3×D3—42no—
928C3×D3—41no—
929C3×D3—41no—
930C3×D3—41no—
931C3×D3—41no—
932C3×D3—41no—
933C3×D3—41no—
934C3×D3—81no—
935C3×D3—81no—
936C3×D3—122no—
937C3×D3—121no—
938C3×D3—121no—
939C3×D3—121no—
940C3×D3—121no—
941C3×D3—241no—
942C24—91no—
943C2×D4—31no—
944C2×D4—31no—
945C2×D4—31no—
946C2×D4—91no—
947C2×D4—91no—
948C2×D4—91no—
949C2×D4—91no—
950C2×D4—91no—
951C2×D4—91no—
952C2×D4—271no—
953C2×D4—271no—
954C2×D4—271no—
955C22×C4—91no—
956C22×C4—271no—
957C22×C4—271no—
958C4⋊C4—91no—
959C4⋊C4—271no—
960C4⋊C4—271no—
961C4⋊C4—271no—
962C4⋊C4—271no—
963C4⋊C4—271no—
964C22⋊C4—91no—
965C22⋊C4—91no—
966C22⋊C4—91no—
967C22⋊C4—91no—
968C22⋊C4—91no—
969C22⋊C4—271no—
970C22⋊C4—271no—
971C22⋊C4—271no—
972C22⋊C4—271no—
973C22⋊C4—271no—
974C22⋊C4—271no—
975C22⋊C4—271no—
976C42—91no—
977C22×C3—22no—
978C22×C3—21no—
979C22×C3—21no—
980C22×C3—21no—
981C22×C3—21no—
982C22×C3—21no—
983C22×C3—21no—
984C22×C3—21no—
985C22×C3—21no—
986C22×C3—21no—
987C22×C3—21no—
988C22×C3—21no—
989C22×C3—21no—
990C22×C3—41no—
991C22×C3—41no—
992C22×C3—41no—
993C22×C3—41no—
994C22×C3—41no—
995C22×C3—41no—
996C22×C3—41no—
997C22×C3—41no—
998C22×C3—42no—
999C22×C3—41no—
1000C22×C3—62no—
1001C22×C3—61no—
1002C22×C3—61no—
1003C22×C3—61no—
1004C22×C3—61no—
1005C22×C3—61no—
1006C22×C3—61no—
1007C22×C3—61no—
1008C22×C3—61no—
1009C22×C3—61no—
1010C22×C3—61no—
1011C22×C3—61no—
1012C22×C3—61no—
1013C22×C3—61no—
1014C22×C3—61no—
1015C22×C3—61no—
1016C22×C3—61no—
1017C22×C3—61no—
1018C22×C3—61no—
1019C22×C3—81no—
1020C22×C3—81no—
1021C22×C3—121no—
1022C22×C3—121no—
1023C22×C3—121no—
1024C22×C3—121no—
1025C22×C3—121no—
1026C22×C3—121no—
1027C22×C3—121no—
1028C22×C3—121no—
1029C22×C3—181no—
1030C22×C3—181no—
1031C22×C3—181no—
1032C22×C3—181no—
1033C22×C3—181no—
1034C22×C3—181no—
1035C22×C3—364no—
1036C22×C3C22×D3211yescharacteristic
1037C22×C3C22×D3211yescharacteristic
1038C22×C3C22×D3211yescharacteristic
1039C2×D3—21no—
1040C2×D3—21no—
1041C2×D3—21no—
1042C2×D3—21no—
1043C2×D3—21no—
1044C2×D3—21no—
1045C2×D3—21no—
1046C2×D3—21no—
1047C2×D3—21no—
1048C2×D3—62no—
1049C2×D3—61no—
1050C2×D3—61no—
1051C2×D3—61no—
1052C2×D3—61no—
1053C2×D3—61no—
1054C2×D3—61no—
1055C2×D3—61no—
1056C2×D3—61no—
1057C2×D3—61no—
1058C2×D3—61no—
1059C2×D3—61no—
1060C2×D3—61no—
1061C2×D3—121no—
1062C2×D3—121no—
1063C2×D3—121no—
1064C2×D3—121no—
1065C2×D3—121no—
1066C2×D3—124no—
1067C2×D3—124no—
1068C3×C4—62no—
1069C3×C4—61no—
1070C3×C4—61no—
1071C3×C4—61no—
1072C3×C4—61no—
1073C3×C4—61no—
1074C3×C4—61no—
1075C3×C4—121no—
1076C3×C4—121no—
1077C3×C4—181no—
1078C3×C4—181no—
1079C3×C4—181no—
1080C3×C4—181no—
1081Dic3—21no—
1082Dic3—21no—
1083Dic3—21no—
1084Dic3—62no—
1085Dic3—61no—
1086Dic3—61no—
1087Dic3—61no—
1088Dic3—61no—
1089Dic3—61no—
1090Dic3—61no—
1091Dic3—61no—
1092Dic3—61no—
1093Dic3—121no—
1094Dic3—121no—
1095Dic3—121no—
1096Dic3—181no—
1097Dic3—181no—
1098Dic3—181no—
1099Dic3—181no—
1100Dic3—181no—
1101Dic3—181no—
1102Dic3—361no—
1103Dic3—361no—
1104Dic3—361no—
1105Dic3—361no—
1106Dic3—361no—
1107Dic3—361no—
1108Dic3—721no—
1109Dic3—721no—
1110C32—21no—
1111C32—21no—
1112C32—21no—
1113C32—41no—
1114C32#559511yescharacteristic, complemented
1115C32#562011yescharacteristic, complemented
1116C32#572011yescharacteristic, complemented
1117C23—31no—
1118C23—31no—
1119C23—31no—
1120C23—91no—
1121C23—91no—
1122C23—361no—
1123C23—361no—
1124C23—361no—
1125C23D3311yescharacteristic
1126D4—121no—
1127D4—121no—
1128D4—121no—
1129D4—361no—
1130D4—361no—
1131D4—361no—
1132D4—361no—
1133D4—361no—
1134D4—361no—
1135D4—1081no—
1136D4—1081no—
1137D4—1081no—
1138C2×C4—31no—
1139C2×C4—31no—
1140C2×C4—31no—
1141C2×C4—91no—
1142C2×C4—91no—
1143C2×C4—91no—
1144C2×C4—91no—
1145C2×C4—271no—
1146C2×C4—271no—
1147C2×C4—361no—
1148C2×C4—1081no—
1149C2×C4—1081no—
1150C2×C3—21no—
1151C2×C3—21no—
1152C2×C3—21no—
1153C2×C3—21no—
1154C2×C3—21no—
1155C2×C3—21no—
1156C2×C3—21no—
1157C2×C3—21no—
1158C2×C3—21no—
1159C2×C3—42no—
1160C2×C3—41no—
1161C2×C3—41no—
1162C2×C3—41no—
1163C2×C3—41no—
1164C2×C3—41no—
1165C2×C3—41no—
1166C2×C3—81no—
1167C2×C3—81no—
1168C2×C3—82no—
1169C2×C3—122no—
1170C2×C3—121no—
1171C2×C3—121no—
1172C2×C3—121no—
1173C2×C3—121no—
1174C2×C3—121no—
1175C2×C3—121no—
1176C2×C3—241no—
1177C2×C3—241no—
1178C2×C3—361no—
1179C2×C3—361no—
1180C2×C3#6431311yescharacteristic
1181C2×C3#6431311yescharacteristic
1182C2×C3#6431311yescharacteristic
1183C2×C3#6431311yescharacteristic
1184C2×C3#6431411yescharacteristic
1185C2×C3#6431411yescharacteristic
1186C2×C3#6433011yescharacteristic
1187C2×C3#6433011yescharacteristic
1188C2×C3#6433011yescharacteristic
1189D3—41no—
1190D3—41no—
1191D3—41no—
1192D3—122no—
1193D3—121no—
1194D3—121no—
1195D3—121no—
1196D3—121no—
1197D3—241no—
1198C22—21no—
1199C22—21no—
1200C22—21no—
1201C22—61no—
1202C22—61no—
1203C22—61no—
1204C22—61no—
1205C22—61no—
1206C22—61no—
1207C22—61no—
1208C22—61no—
1209C22—61no—
1210C22—181no—
1211C22—181no—
1212C22—181no—
1213C22—181no—
1214C22—181no—
1215C22—181no—
1216C22—364no—
1217C22C2×D3311yescharacteristic
1218C4—61no—
1219C4—61no—
1220C4—61no—
1221C4—181no—
1222C4—181no—
1223C4—181no—
1224C4—181no—
1225C4—541no—
1226C4—541no—
1227C3—21no—
1228C3—21no—
1229C3—21no—
1230C3—41no—
1231C3#1059525811yescharacteristic, complemented
1232C3#1059525911yescharacteristic, complemented
1233C3#1059531311yescharacteristic, complemented
1234C2—41no—
1235C2—121no—
1236C2—121no—
1237C2—121no—
1238C2—361no—
1239C2—361no—
1240C2#1172441411yescharacteristic
1241C2#1172441511yescharacteristic
1242C2#1172441611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#560
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723717C2semidirect
2. #11723631C2semidirect
3. #11723615C2semidirect
4. #11723602C2semidirect
5. C3×#63983C2semidirect
6. C3×#63980C2semidirect
7. C3×#63979C2semidirect
8. #11723023C2semidirect
9. #11723020C2semidirect
10. #11722991C2semidirect
11. #11722989C2semidirect
12. #11722967C2semidirect
13. #11722954C2semidirect
14. #11722947C2semidirect
15. #11722946C2semidirect
21. C2×C3×#638C22semidirect
22. C22×C3×C3⋊Dic3C22semidirect
25. C2×C32×#67C22semidirect
29. C2×Dic3×C3⋊D3C22semidirect
30. C2×D3×C3⋊Dic3C22semidirect
32. C2×C3×#626C22semidirect
35. #88864C22semidirect
36. #88815C22semidirect
38. #88814C22semidirect
39. #88807C22semidirect
40. #88806C22semidirect
41. #88806C22semidirect
42. Dic3⋊(C3⋊Dic3)C22semidirect
47. C3×#3724C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
64. #63983D3semidirect
67. #63980D3semidirect
68. #63979D3semidirect
147. C2×#638C2×D3semidirect
149. C22×C3⋊Dic3C2×D3semidirect
170. C2×C3×#67C2×D3semidirect
171. C2×C3×#67C2×D3semidirect
180. C2×#626C2×D3semidirect
232. #3724C2×D3semidirect
263. (C2×D3)⋊Dic3C2×D3semidirect
264. Dic32C2×D3semidirect
528. C2×#67D32semidirect
760. C33#560semidirect
1114. C32#5595semidirect
1115. C32#5620semidirect
1116. C32#5720semidirect
1231. C3#10595258semidirect
1232. C3#10595259semidirect
1233. C3#10595313semidirect

Maximal subgroups

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

subgroupindex
#117237172
#117236312
#117236152
#117236022
C3×#639832
C3×#639802
C3×#639792
#117230232
#117230202
#117229912
#117229892
#117229672
#117229542
#117229472
#117229462
#105953133
#105952593
#105952583