Finite Group Databasebeta

← #13172080

Subgroups — #13172080

Order 1728.

1320 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723724C211yesmaximal, characteristic, complemented
2#11723615C211yesmaximal, characteristic, complemented
3D3×#3757C211yesmaximal, characteristic, complemented
4#11723596C211yesmaximal, characteristic, complemented
5C3×#63977C211yesmaximal, characteristic, complemented
6C3×#63976C211yesmaximal, characteristic, complemented
7C3×#63959C211yesmaximal, characteristic, complemented
8#11723020C211yesmaximal, characteristic, complemented
9#11723001C211yesmaximal, characteristic, complemented
10#11722989C211yesmaximal, characteristic, complemented
11#11722976C211yesmaximal, characteristic, complemented
12#11722965C211yesmaximal, characteristic, complemented
13#11722954C211yesmaximal, characteristic, complemented
14#11722928C211yesmaximal, characteristic, complemented
15#11722925C211yesmaximal, characteristic, complemented
16#10595508—31nomaximal
17#10595184—31nomaximal
18#10594122—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×#6294C2211yescharacteristic, complemented
23C2×#6290C2211yescharacteristic, complemented
24C2×D3×C3⋊Dic3C2211yescharacteristic
25C2×D3×C3⋊Dic3C2211yescharacteristic
26C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
27C2×C3×#627C2211yescharacteristic, complemented
28C2×C3×#626C2211yescharacteristic
29C2×C3×#626C2211yescharacteristic
30C2×C3×#625C2211yescharacteristic
31C2×C3×#625C2211yescharacteristic
32#88864C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C32×#217C2211yescharacteristic
36#88815C2211yescharacteristic, complemented
37#88815C2211yescharacteristic, complemented
38#88814C2211yescharacteristic, complemented
39#88807C2211yescharacteristic, complemented
40#88807C2211yescharacteristic, complemented
41#88806C2211yescharacteristic, complemented
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
43#88803C2211yescharacteristic, complemented
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47C3×(C2×D3)⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54C2×#3757—31no—
55#64148—31no—
56#64088—31no—
57C3×#953—31no—
58C3×#953—31no—
59C3×#937—31no—
60C3×#936—31no—
61C3×#885—31no—
62C3×#882—31no—
63#63982—31no—
64#63980—31no—
65#63977D311yescharacteristic, complemented
66#63976D311yescharacteristic, complemented
67#63975—31no—
68#67⋊Dic3—31no—
69#67⋊Dic3—31no—
70#67⋊Dic3—31no—
71#63971—31no—
72#63970—31no—
73#63970—31no—
74#63970—31no—
75#63970—61no—
76#63969—31no—
77#63969—31no—
78#63969—31no—
79D3×#217—31no—
80D3×#217—31no—
81D3×#217—61no—
82#63962—31no—
83#63959—31no—
84#63959D311yescharacteristic, complemented
85#63958—31no—
86#63956—31no—
87#63956—31no—
88#63956—31no—
89#63956—61no—
90#63907—31no—
91#63902—31no—
92Dic3×D12—31no—
93#63891—31no—
94#63887—31no—
95#63887—31no—
96#63885—31no—
97#63885—31no—
98#63880—31no—
99#63863—31no—
100#63859—31no—
101#63859—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C32×D3—22no—
105C22×C32×D3—41no—
106C22×C32×D3—41no—
107C22×C32×D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C3×#638—41no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C32×#67—41no—
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6294—41no—
123#6290—41no—
124D3×C3⋊Dic3—41no—
125D3×C3⋊Dic3—41no—
126D3×C3⋊Dic3—41no—
127C3×#627—41no—
128C3×#626—22no—
129C3×#626—41no—
130C3×#625—22no—
131C3×#625—41no—
132#5678—91no—
133#5593—91no—
134#5593—91no—
135C24×C32—31no—
136C23×C3×D3—21no—
137C23×C3×D3C2×D311yescharacteristic
138C23×C3×D3C2×D311yescharacteristic
139C2×C32×D4—31no—
140C2×#638—31no—
141C2×#638C2×D311yescharacteristic
142C22×C3⋊Dic3—31no—
143C22×C3⋊Dic3—31no—
144C22×C3⋊Dic3—31no—
145C2×C3×#67—21no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—31no—
154C2×C3×#67—61no—
155C2×C3×#67C2×D311yescharacteristic
156C2×C3×#67C2×D311yescharacteristic
157C2×C3×D12—31no—
158C2×C3×D12—31no—
159C2×C3×Dic6—31no—
160C2×C3×Dic6—31no—
161C2×#627C2×D311yescharacteristic, complemented
162C2×#626C2×D311yescharacteristic
163C2×#626C2×D311yescharacteristic
164C2×#625—31no—
165C2×#625—31no—
166C2×#625—61no—
167C2×#625C2×D311yescharacteristic
168C2×#625C2×D311yescharacteristic
169C2×#624—31no—
170C2×D3×Dic3—31no—
171C2×D3×Dic3—31no—
172C2×D3×Dic3—31no—
173C2×D3×Dic3—31no—
174C2×D3×Dic3—31no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—61no—
179C2×D3×Dic3—61no—
180C2×D3×Dic3—61no—
181C32×C22⋊C4—31no—
182#3757—31no—
183#3757—31no—
184#3757—31no—
185#3757—31no—
186#3757—31no—
187#3757—61no—
188#3757—61no—
189#3757—61no—
190#3757—121no—
191#3757C2×D311yescharacteristic
192#3757C2×D311yescharacteristic
193#3752—31no—
194C4⋊(C3⋊Dic3)—31no—
195#3750—31no—
196#3750—31no—
197#3750—31no—
198C4×C3⋊Dic3—31no—
199C3×#217—21no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×#217—31no—
204C3×#217—31no—
205C3×#217—31no—
206C3×#217—31no—
207C3×#217—31no—
208C3×#217—31no—
209C3×#217—31no—
210C3×#217—61no—
211C3×#217—61no—
212C3×#217C2×D311yescharacteristic
213C3×#217C2×D311yescharacteristic
214C3×(C2×D3)⋊C4—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×C4×Dic3—31no—
221C3×C4×Dic3—31no—
222#3724—31no—
223#3724—31no—
224#3724—31no—
225#3724—31no—
226#3724—61no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—61no—
238Dic3⋊Dic3—61no—
239Dic3⋊Dic3—61no—
240#3722—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
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—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic
255(C2×D3)⋊Dic3C2×D311yescharacteristic
256(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
257(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic, complemented
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
265C22×C33C2411yescharacteristic
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—21no—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—44no—
278C2×C32×D3#4112yes—
279C3⋊(C3⋊Dic3)—21no—
280C3⋊(C3⋊Dic3)—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×C3⋊Dic3—21no—
285C3×C3⋊Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#124—91no—
290C3×#120—91no—
291C3×#120—91no—
292#953—31no—
293#953—31no—
294C2×#217—91no—
295C2×#217—91no—
296C2×#217—181no—
297#947—91no—
298#946—91no—
299#939—91no—
300#939—91no—
301#939—91no—
302#939—91no—
303#939—91no—
304#939—181no—
305#938—91no—
306#938—91no—
307#937—31no—
308#936—31no—
309#936—91no—
310#935—91no—
311#935—91no—
312D4×Dic3—91no—
313D4×Dic3—91no—
314#886—91no—
315#885—31no—
316#885—91no—
317#884—91no—
318#884—91no—
319#883—91no—
320#883—91no—
321#883—91no—
322#882—31no—
323#67⋊C4—91no—
324#67⋊C4—91no—
325#67⋊C4—91no—
326D3×C22⋊C4—91no—
327#879—91no—
328#879—91no—
329#879—91no—
330#879—91no—
331#879—91no—
332#879—181no—
333#878—91no—
334#878—91no—
335#876—91no—
336C4×D12—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—31no—
341C23×C32—31no—
342C23×C32—31no—
343C23×C32—41no—
344C23×C32—62no—
345C23×C32—121no—
346C23×C32—121no—
347C23×C32C22×D311yescharacteristic
348C23×C32C22×D311yescharacteristic
349C23×C32C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—24no—
352C22×C3×D3—22no—
353C22×C3×D3—22no—
354C22×C3×D3—21no—
355C22×C3×D3—21no—
356C22×C3×D3—21no—
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—41no—
360C22×C3×D3—41no—
361C22×C3×D3—41no—
362C22×C3×D3—41no—
363C22×C3×D3—42no—
364C22×C3×D3—42no—
365C22×C3×D3—61no—
366C22×C3×D3C22×D311yescharacteristic
367C22×C3×D3C22×D311yescharacteristic
368C22×C3×D3C22×D311yescharacteristic
369C22×C3×D3C22×D311yescharacteristic
370C22×C3×D3C22×D311yescharacteristic
371C22×C3×D3C22×D311yescharacteristic
372C32×D4—121no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376#638—41no—
377#638—121no—
378C2×C3⋊Dic3—31no—
379C2×C3⋊Dic3—31no—
380C2×C3⋊Dic3—31no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—61no—
385C2×C3⋊Dic3—61no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—121no—
391C2×C3⋊Dic3—121no—
392C2×C3⋊Dic3—121no—
393C2×C3⋊Dic3—121no—
394C2×C3⋊Dic3—121no—
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C3×#67—41no—
401C3×#67—41no—
402C3×#67—42no—
403C3×#67—62no—
404C3×#67—62no—
405C3×#67—62no—
406C3×#67—121no—
407C3×#67—121no—
408C3×#67—121no—
409C3×#67—121no—
410C3×#67—121no—
411C3×#67—122no—
412C2×C3×Dic3—21no—
413C2×C3×Dic3—21no—
414C2×C3×Dic3—21no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C3×D12—62no—
437C3×D12—121no—
438C3×Dic6—121no—
439C3×Dic6—121no—
440#627—41no—
441#626—22no—
442#626—41no—
443#625—22no—
444#625—41no—
445#625—121no—
446#625—121no—
447#625—122no—
448#624—121no—
449D3×Dic3—121no—
450D3×Dic3—121no—
451D3×Dic3—121no—
452D3×Dic3—121no—
453D3×Dic3—121no—
454D3×Dic3—121no—
455D3×Dic3—121no—
456D3×Dic3—121no—
457D3×Dic3—122no—
458D3×Dic3—122no—
459D3×Dic3—122no—
460#538—271noSylow
461C2×C33—41no—
462C2×C33C2×#4111yescharacteristic
463C2×C33H(5,𝔽2)11yescharacteristic
464C2×C33H(5,𝔽2)11yescharacteristic
465C3×C3⋊D3—41no—
466C32×D3—22no—
467C32×D3—41no—
468C32×D3—41no—
469C24×C3—31no—
470C24×C3—31no—
471C24×C3—61no—
472C23×D3D3211yescharacteristic
473C2×C3×Q8—91no—
474C2×C3×D4—31no—
475C2×C3×D4—31no—
476C2×C3×D4—61no—
477C2×C3×D4—91no—
478C2×C3×D4—91no—
479C2×C3×D4—91no—
480C2×C3×D4—91no—
481C2×C3×D4—91no—
482C2×#67—31no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—61no—
491C2×#67—91no—
492C2×#67—91no—
493C2×#67—91no—
494C2×#67—181no—
495C2×#67D3211yescharacteristic
496C22×Dic3—91no—
497C22×Dic3—91no—
498C22×Dic3—91no—
499C22×Dic3—91no—
500C22×Dic3—91no—
501C22×Dic3—91no—
502C22×Dic3—91no—
503C22×Dic3—181no—
504C22×Dic3—181no—
505C22×Dic3—181no—
506C2×D12—31no—
507C2×D12—31no—
508C2×C4×D3—91no—
509C2×C4×D3—91no—
510C2×C4×D3—91no—
511C2×C4×D3—91no—
512C2×C4×D3—91no—
513C2×Dic6—31no—
514C2×Dic6—31no—
515C3×C22⋊C4—31no—
516C3×C22⋊C4—31no—
517C3×C22⋊C4—61no—
518C3×C22⋊C4—91no—
519C3×C22⋊C4—91no—
520C3×C22⋊C4—91no—
521C3×C22⋊C4—91no—
522C3×C22⋊C4—91no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C42—91no—
527#217—31no—
528#217—31no—
529#217—31no—
530#217—31no—
531#217—31no—
532#217—31no—
533#217—31no—
534#217—31no—
535#217—31no—
536#217—31no—
537#217—61no—
538#217—61no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217—91no—
547#217—91no—
548#217—181no—
549#217—181no—
550#217—181no—
551#217—181no—
552#217—181no—
553#217—361no—
554#217D3211yescharacteristic
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—31no—
560(C2×D3)⋊C4—31no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—181no—
568C4⋊Dic3—91no—
569C4⋊Dic3—91no—
570C4⋊Dic3—91no—
571C4⋊Dic3—91no—
572C4⋊Dic3—91no—
573C4⋊Dic3—91no—
574C4⋊Dic3—181no—
575Dic3⋊C4—91no—
576Dic3⋊C4—91no—
577Dic3⋊C4—91no—
578Dic3⋊C4—91no—
579Dic3⋊C4—91no—
580Dic3⋊C4—91no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—181no—
588Dic3⋊C4—181no—
589Dic3⋊C4—181no—
590C4×Dic3—31no—
591C4×Dic3—31no—
592C4×Dic3—91no—
593C4×Dic3—91no—
594C4×Dic3—91no—
595C4×Dic3—181no—
596C22×C32—21no—
597C22×C32—22no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—32no—
610C22×C32—41no—
611C22×C32—41no—
612C22×C32—41no—
613C22×C32—42no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—41no—
620C22×C32—61no—
621C22×C32—61no—
622C22×C32—61no—
623C22×C32—61no—
624C22×C32—61no—
625C22×C32—61no—
626C22×C32—61no—
627C22×C32—61no—
628C22×C32—81no—
629C22×C32—81no—
630C22×C32—124no—
631C22×C32C23×D311yescharacteristic
632C22×C32C23×D311yescharacteristic
633C22×C32C23×D311yescharacteristic
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3×D3—22no—
638C2×C3×D3—22no—
639C2×C3×D3—21no—
640C2×C3×D3—21no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—22no—
644C2×C3×D3—22no—
645C2×C3×D3—21no—
646C2×C3×D3—21no—
647C2×C3×D3—21no—
648C2×C3×D3—21no—
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—21no—
656C2×C3×D3—21no—
657C2×C3×D3—22no—
658C2×C3×D3—41no—
659C2×C3×D3—41no—
660C2×C3×D3—41no—
661C2×C3×D3—41no—
662C2×C3×D3—48no—
663C2×C3×D3—44no—
664C2×C3×D3—44no—
665C2×C3×D3—61no—
666C2×C3×D3—61no—
667C2×C3×D3—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—121no—
672C2×C3×D3—121no—
673C2×C3×D3—121no—
674C2×C3×D3#23712yes—
675C2×C3×D3#23712yes—
676C32×C4—61no—
677C32×C4—61no—
678C32×C4—61no—
679C3⋊Dic3—21no—
680C3⋊Dic3—21no—
681C3⋊Dic3—21no—
682C3⋊Dic3—21no—
683C3⋊Dic3—21no—
684C3⋊Dic3—61no—
685C3⋊Dic3—61no—
686C3⋊Dic3—61no—
687C3⋊Dic3—61no—
688C3⋊Dic3—61no—
689C3⋊Dic3—61no—
690C3⋊Dic3—121no—
691C3⋊Dic3—121no—
692C3⋊Dic3—121no—
693C3⋊Dic3—121no—
694C3⋊Dic3—121no—
695C3⋊Dic3—121no—
696C3⋊Dic3—241no—
697C3⋊Dic3—241no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—41no—
705C3×Dic3—41no—
706C3×Dic3—41no—
707C3×Dic3—62no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3—121no—
721C3×Dic3—121no—
722#126—271no—
723#126—271no—
724#124—91no—
725#124—271no—
726#123—271no—
727#123—271no—
728C22⋊Q8—271no—
729#121—271no—
730#121—271no—
731#121—271no—
732#120—91no—
733#120—91no—
734C4×D4—271no—
735C4×D4—271no—
736C2×C22⋊C4—271no—
737C33#53811yescharacteristic, complemented, Sylow
738C23×C3—21no—
739C23×C3—21no—
740C23×C3—21no—
741C23×C3—31no—
742C23×C3—31no—
743C23×C3—31no—
744C23×C3—31no—
745C23×C3—31no—
746C23×C3—31no—
747C23×C3—41no—
748C23×C3—61no—
749C23×C3—61no—
750C23×C3—61no—
751C23×C3—62no—
752C23×C3—62no—
753C23×C3—64no—
754C23×C3—91no—
755C23×C3—121no—
756C23×C3—121no—
757C23×C3—121no—
758C23×C3—121no—
759C23×C3—122no—
760C23×C3—122no—
761C23×C3C2×D3211yescharacteristic
762C23×C3C2×D3211yescharacteristic
763C23×C3C2×D3211yescharacteristic
764C22×D3—22no—
765C22×D3—31no—
766C22×D3—31no—
767C22×D3—41no—
768C22×D3—41no—
769C22×D3—61no—
770C22×D3C2×D3211yescharacteristic
771C22×D3C2×D3211yescharacteristic
772C22×D3C2×D3211yescharacteristic
773C3×Q8—361no—
774C3×D4—121no—
775C3×D4—121no—
776C3×D4—122no—
777C3×D4—182no—
778C3×D4—182no—
779C3×D4—361no—
780C3×D4—361no—
781C3×D4—361no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—31no—
785C2×C3×C4—31no—
786C2×C3×C4—31no—
787C2×C3×C4—31no—
788C2×C3×C4—61no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—91no—
796#67—41no—
797#67—62no—
798#67—62no—
799#67—62no—
800#67—121no—
801#67—121no—
802#67—121no—
803#67—121no—
804#67—121no—
805#67—122no—
806#67—361no—
807#67—361no—
808#67—361no—
809#67—362no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—61no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—61no—
825C2×Dic3—91no—
826C2×Dic3—91no—
827C2×Dic3—91no—
828C2×Dic3—91no—
829C2×Dic3—91no—
830C2×Dic3—91no—
831C2×Dic3—181no—
832C2×Dic3—181no—
833C2×Dic3—181no—
834C2×Dic3—181no—
835C2×Dic3—181no—
836C2×Dic3—181no—
837C2×Dic3—361no—
838C2×Dic3—361no—
839C2×Dic3—361no—
840C2×Dic3—361no—
841C2×Dic3—361no—
842C2×Dic3—361no—
843C2×Dic3—361no—
844C2×Dic3—361no—
845C2×Dic3—361no—
846C2×Dic3—362no—
847C2×Dic3—362no—
848C2×Dic3—362no—
849C2×Dic3C2×D3211yescharacteristic
850C2×Dic3C2×D3211yescharacteristic
851C2×Dic3C2×D3211yescharacteristic
852D12—62no—
853D12—121no—
854C4×D3—361no—
855C4×D3—361no—
856C4×D3—361no—
857C4×D3—361no—
858C4×D3—361no—
859Dic6—121no—
860Dic6—121no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—21no—
869C2×C32—21no—
870C2×C32—41no—
871C2×C32—41no—
872C2×C32—41no—
873C2×C32—41no—
874C2×C32—42no—
875C2×C32—41no—
876C2×C32—41no—
877C2×C32—62no—
878C2×C32—81no—
879C2×C32—81no—
880C2×C32—82no—
881C2×C32—121no—
882C2×C32—121no—
883C2×C32C2×#23711yescharacteristic
884C2×C32C2×#23711yescharacteristic
885C2×C32#100411yescharacteristic
886C2×C32#100411yescharacteristic
887C2×C32#100411yescharacteristic
888C2×C32#100411yescharacteristic
889C2×C32#100411yescharacteristic
890C2×C32D3×#4111yescharacteristic
891C2×C32#100911yescharacteristic
892C3⋊D3—41no—
893C3×D3—24no—
894C3×D3—22no—
895C3×D3—22no—
896C3×D3—42no—
897C3×D3—42no—
898C3×D3—41no—
899C3×D3—41no—
900C3×D3—41no—
901C3×D3—41no—
902C3×D3—121no—
903C3×D3—121no—
904C3×D3—241no—
905C24—31no—
906C2×Q8—91no—
907C2×D4—31no—
908C2×D4—91no—
909C2×D4—91no—
910C2×D4—91no—
911C2×D4—91no—
912C2×D4—91no—
913C2×D4—271no—
914C22×C4—271no—
915C22×C4—271no—
916C22×C4—271no—
917C22×C4—271no—
918C4⋊C4—271no—
919C4⋊C4—271no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C4⋊C4—271no—
923C4⋊C4—271no—
924C22⋊C4—31no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—91no—
930C22⋊C4—91no—
931C22⋊C4—91no—
932C22⋊C4—91no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C42—91no—
939C42—271no—
940C22×C3—22no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—32no—
954C22×C3—32no—
955C22×C3—41no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3—41no—
961C22×C3—41no—
962C22×C3—41no—
963C22×C3—42no—
964C22×C3—41no—
965C22×C3—62no—
966C22×C3—62no—
967C22×C3—62no—
968C22×C3—62no—
969C22×C3—62no—
970C22×C3—61no—
971C22×C3—61no—
972C22×C3—61no—
973C22×C3—61no—
974C22×C3—61no—
975C22×C3—61no—
976C22×C3—61no—
977C22×C3—61no—
978C22×C3—61no—
979C22×C3—61no—
980C22×C3—61no—
981C22×C3—61no—
982C22×C3—61no—
983C22×C3—61no—
984C22×C3—61no—
985C22×C3—61no—
986C22×C3—81no—
987C22×C3—81no—
988C22×C3—121no—
989C22×C3—121no—
990C22×C3—121no—
991C22×C3—121no—
992C22×C3—128no—
993C22×C3—124no—
994C22×C3—124no—
995C22×C3—181no—
996C22×C3—181no—
997C22×C3—181no—
998C22×C3C22×D3211yescharacteristic
999C22×C3C22×D3211yescharacteristic
1000C22×C3C22×D3211yescharacteristic
1001C2×D3—21no—
1002C2×D3—21no—
1003C2×D3—21no—
1004C2×D3—21no—
1005C2×D3—21no—
1006C2×D3—21no—
1007C2×D3—21no—
1008C2×D3—21no—
1009C2×D3—44no—
1010C2×D3—61no—
1011C2×D3—61no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—121no—
1017C2×D3—121no—
1018C2×D3—121no—
1019C2×D3#380512yes—
1020C3×C4—61no—
1021C3×C4—61no—
1022C3×C4—61no—
1023C3×C4—61no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—121no—
1027C3×C4—121no—
1028C3×C4—121no—
1029C3×C4—181no—
1030C3×C4—181no—
1031C3×C4—181no—
1032C3×C4—181no—
1033C3×C4—181no—
1034Dic3—21no—
1035Dic3—21no—
1036Dic3—21no—
1037Dic3—62no—
1038Dic3—61no—
1039Dic3—61no—
1040Dic3—61no—
1041Dic3—61no—
1042Dic3—61no—
1043Dic3—61no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—121no—
1049Dic3—121no—
1050Dic3—121no—
1051Dic3—121no—
1052Dic3—181no—
1053Dic3—181no—
1054Dic3—181no—
1055Dic3—181no—
1056Dic3—181no—
1057Dic3—181no—
1058Dic3—361no—
1059Dic3—361no—
1060Dic3—361no—
1061Dic3—361no—
1062Dic3—361no—
1063Dic3—361no—
1064Dic3—721no—
1065Dic3—721no—
1066C32—21no—
1067C32—21no—
1068C32—21no—
1069C32—41no—
1070C32#559311yescharacteristic, complemented
1071C32#559311yescharacteristic, complemented
1072C32#567811yescharacteristic, complemented
1073C23—31no—
1074C23—31no—
1075C23—31no—
1076C23—62no—
1077C23—91no—
1078C23—121no—
1079C23—121no—
1080C23D3311yescharacteristic
1081Q8—361no—
1082D4—121no—
1083D4—182no—
1084D4—182no—
1085D4—361no—
1086D4—361no—
1087D4—361no—
1088D4—1081no—
1089C2×C4—31no—
1090C2×C4—31no—
1091C2×C4—31no—
1092C2×C4—91no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—91no—
1096C2×C4—91no—
1097C2×C4—271no—
1098C2×C4—271no—
1099C2×C4—1081no—
1100C2×C4—1081no—
1101C2×C4—1081no—
1102C2×C4—1081no—
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—21no—
1111C2×C3—21no—
1112C2×C3—42no—
1113C2×C3—41no—
1114C2×C3—41no—
1115C2×C3—41no—
1116C2×C3—41no—
1117C2×C3—41no—
1118C2×C3—41no—
1119C2×C3—64no—
1120C2×C3—62no—
1121C2×C3—62no—
1122C2×C3—81no—
1123C2×C3—81no—
1124C2×C3—82no—
1125C2×C3—122no—
1126C2×C3—122no—
1127C2×C3—121no—
1128C2×C3—121no—
1129C2×C3—121no—
1130C2×C3—121no—
1131C2×C3—361no—
1132C2×C3#6430711yescharacteristic
1133C2×C3D3×#23711yescharacteristic
1134C2×C3D3×#23711yescharacteristic
1135C2×C3#6431311yescharacteristic
1136C2×C3#6431411yescharacteristic
1137C2×C3C2×#380511yescharacteristic
1138C2×C3#6433011yescharacteristic
1139C2×C3#6433011yescharacteristic
1140C2×C3#6433011yescharacteristic
1141D3—22no—
1142D3—41no—
1143D3—41no—
1144D3—121no—
1145D3—121no—
1146D3—241no—
1147C22—21no—
1148C22—21no—
1149C22—21no—
1150C22—32no—
1151C22—61no—
1152C22—61no—
1153C22—61no—
1154C22—61no—
1155C22—61no—
1156C22—61no—
1157C22—61no—
1158C22—61no—
1159C22—124no—
1160C22—181no—
1161C22—181no—
1162C22—181no—
1163C22C2×D3311yescharacteristic
1164C4—61no—
1165C4—61no—
1166C4—61no—
1167C4—181no—
1168C4—181no—
1169C4—181no—
1170C4—181no—
1171C4—181no—
1172C4—541no—
1173C4—541no—
1174C3—21no—
1175C3—21no—
1176C3—21no—
1177C3—41no—
1178C3#1059412211yescharacteristic, complemented
1179C3#1059518411yescharacteristic, complemented
1180C3#1059550811yescharacteristic, complemented
1181C2—41no—
1182C2—62no—
1183C2—121no—
1184C2—121no—
1185C2—361no—
1186C2D3×#380511yescharacteristic
1187C2#1172441411yescharacteristic
1188C2#1172441811yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723724C2semidirect
2. #11723615C2semidirect
3. D3×#3757C2semidirect
4. #11723596C2semidirect
5. C3×#63977C2semidirect
6. C3×#63976C2semidirect
7. C3×#63959C2semidirect
8. #11723020C2semidirect
9. #11723001C2semidirect
10. #11722989C2semidirect
11. #11722976C2semidirect
12. #11722965C2semidirect
13. #11722954C2semidirect
14. #11722928C2semidirect
15. #11722925C2semidirect
22. C2×#6294C22semidirect
23. C2×#6290C22semidirect
26. C2×D3×C3⋊Dic3C22semidirect
27. C2×C3×#627C22semidirect
36. #88815C22semidirect
37. #88815C22semidirect
38. #88814C22semidirect
39. #88807C22semidirect
40. #88807C22semidirect
41. #88806C22semidirect
42. Dic3⋊(C3⋊Dic3)C22semidirect
43. #88803C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
51. C3×(C2×D3)⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×Dic32C22semidirect
65. #63977D3semidirect
66. #63976D3semidirect
84. #63959D3semidirect
161. C2×#627C2×D3semidirect
256. (C2×D3)⋊Dic3C2×D3semidirect
257. (C2×D3)⋊Dic3C2×D3semidirect
261. Dic32C2×D3semidirect
737. C33#538semidirect
1070. C32#5593semidirect
1071. C32#5593semidirect
1072. C32#5678semidirect
1178. C3#10594122semidirect
1179. C3#10595184semidirect
1180. C3#10595508semidirect

Maximal subgroups

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

subgroupindex
#117237242
#117236152
D3×#37572
#117235962
C3×#639772
C3×#639762
C3×#639592
#117230202
#117230012
#117229892
#117229762
#117229652
#117229542
#117229282
#117229252
#105955083
#105951843
#105941223