Finite Group Databasebeta

← #13172031

Subgroups — #13172031

Order 1728.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723717C211yesmaximal, characteristic, complemented
2#11723643C211yesmaximal, characteristic, complemented
3#11723624C211yesmaximal, characteristic, complemented
4#11723608C211yesmaximal, characteristic, complemented
5C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#63971C211yesmaximal, characteristic, complemented
7C3×#63953C211yesmaximal, characteristic, complemented
8#11723023C211yesmaximal, characteristic, complemented
9#11723021C211yesmaximal, characteristic, complemented
10#11723003C211yesmaximal, characteristic, complemented
11#11722997C211yesmaximal, characteristic, complemented
12#11722969C211yesmaximal, characteristic, complemented
13#11722950C211yesmaximal, characteristic, complemented
14Dic3×#626C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10595221—31nomaximal
17#10594301—31nomaximal
18#10594298—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic, complemented
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×#6295C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
28C2×C3×#627C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32C32×#217C2211yescharacteristic, complemented
33C32×#217C2211yescharacteristic, complemented
34#88815C2211yescharacteristic, complemented
35#88814C2211yescharacteristic
36#88814C2211yescharacteristic, complemented
37#88806C2211yescharacteristic, complemented
38Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88804C2211yescharacteristic
43#88804C2211yescharacteristic
44#88803C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46C3×#3724C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×#3722C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×#3722C2211yescharacteristic, complemented
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic, complemented
53C3×Dic32C2211yescharacteristic, complemented
54#64146—31no—
55#64095—31no—
56#64093—31no—
57C3×#939—31no—
58C3×D4×Dic3—31no—
59C3×#885—31no—
60C3×#885—31no—
61C3×#884—31no—
62C3×#67⋊C4—31no—
63#63983—31no—
64#63983—31no—
65#63983—61no—
66#63981—31no—
67#63980—31no—
68#63978—31no—
69#63978—31no—
70#67⋊Dic3D311yescharacteristic, complemented
71Dic3×#67—31no—
72#63971—31no—
73#63971—31no—
74#63971—61no—
75#63971D311yescharacteristic, complemented
76#63966—31no—
77#63966—31no—
78#63966—61no—
79#63964—31no—
80C2×#3722—31no—
81#63953D311yescharacteristic, complemented
82#63923—31no—
83#63922—31no—
84D3×(C2×D3)⋊C4—31no—
85D3×(C2×D3)⋊C4—31no—
86#63907—31no—
87C4×#626—31no—
88Dic3×D12—31no—
89#63891—31no—
90#63890—31no—
91#63887—31no—
92#63868—31no—
93#63868—31no—
94#63868—31no—
95#63864—31no—
96#63861—31no—
97#63859—31no—
98#63856—31no—
99#63853—31no—
100#63852—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×D3×C3⋊D3—41no—
110#6312—41no—
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C3×#638—41no—
113C3×#638—41no—
114C2×C3×C3⋊Dic3—41no—
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C32×#67—22no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6295—41no—
126#6292—41no—
127Dic3×C3⋊D3—41no—
128C3×#627—41no—
129C3×#626—22no—
130C3×D3×Dic3—41no—
131C3×D3×Dic3—41no—
132#5678—91no—
133#5617—91no—
134#5560—91no—
135C23×C3⋊D3—31no—
136C22×D32—31no—
137C22×D32—31no—
138C22×D32—61no—
139C2×C32×D4—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—61no—
144C2×#638—61no—
145C2×#638—61no—
146C2×#638—121no—
147C2×#638C2×D311yescharacteristic
148C2×#638C2×D311yescharacteristic, complemented
149C22×C3⋊Dic3C2×D311yescharacteristic, complemented
150C2×C4⋊(C3⋊D3)—31no—
151C2×C4×C3⋊D3—31no—
152C2×C3×#67—21no—
153C2×C3×#67—31no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—61no—
159C2×C3×#67—61no—
160C2×C3×#67C2×D311yescharacteristic
161C2×C3×#67C2×D311yescharacteristic
162C22×C3×Dic3—31no—
163C22×C3×Dic3—31no—
164C22×C3×Dic3—31no—
165C22×C3×Dic3—31no—
166C22×C3×Dic3—61no—
167C2×C3×D12—31no—
168C2×C3×C4×D3—31no—
169C2×C3×C4×D3—31no—
170C2×C3×Dic6—31no—
171C2×C3×Dic6—31no—
172C2×#627C2×D311yescharacteristic, complemented
173C2×#626—31no—
174C2×#626—31no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—61no—
178C2×#626C2×D311yescharacteristic
179C2×#625—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—61no—
183C2×D3×Dic3C2×D311yescharacteristic
184C2×D3×Dic3C2×D311yescharacteristic
185C32×C22⋊C4—31no—
186C32×C22⋊C4—31no—
187#3757—31no—
188#3752—31no—
189#3752—31no—
190#3752—31no—
191#3752—31no—
192#3752—31no—
193C4⋊(C3⋊Dic3)—31no—
194C4⋊(C3⋊Dic3)—31no—
195#3750—31no—
196C3×#217—21no—
197C3×#217—21no—
198C3×#217—31no—
199C3×#217C2×D311yescharacteristic, complemented
200C3×#217C2×D311yescharacteristic, complemented
201C3×#217C2×D311yescharacteristic, complemented
202C3×#217C2×D311yescharacteristic, complemented
203C3×(C2×D3)⋊C4—31no—
204C3×(C2×D3)⋊C4—31no—
205C3×(C2×D3)⋊C4—31no—
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×C4⋊Dic3—31no—
211C3×Dic3⋊C4—31no—
212C3×Dic3⋊C4—31no—
213C3×Dic3⋊C4—31no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—31no—
218#3724—31no—
219#3724—31no—
220#3724—31no—
221#3724—61no—
222#3724C2×D311yescharacteristic, complemented
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—61no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3C2×D311yescharacteristic, complemented
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—31no—
238#3722—31no—
239#3722—31no—
240#3722—31no—
241#3722—31no—
242#3722—61no—
243#3722—61no—
244#3722—61no—
245#3722—61no—
246#3722C2×D311yescharacteristic
247#3722C2×D311yescharacteristic
248#3722C2×D311yescharacteristic, complemented
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—31no—
257(C2×D3)⋊Dic3—61no—
258(C2×D3)⋊Dic3—61no—
259(C2×D3)⋊Dic3C2×D311yescharacteristic
260Dic32C2×D311yescharacteristic, complemented
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×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#4112yes—
278D3×C3⋊D3—44no—
279C3⋊(C3⋊Dic3)—21no—
280C3×C3⋊Dic3—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#124—91no—
290C3×#121—91no—
291C3×C4×D4—91no—
292#947—91no—
293#946—91no—
294#939—31no—
295#939—91no—
296#939—91no—
297#939—91no—
298#937—91no—
299#937—91no—
300#937—91no—
301#937—91no—
302#937—181no—
303D4×Dic3—31no—
304D4×Dic3—91no—
305#930—91no—
306#929—91no—
307C4×#67—91no—
308C2×(C2×D3)⋊C4—91no—
309C2×(C2×D3)⋊C4—91no—
310#924—91no—
311#898—91no—
312#898—91no—
313#898—91no—
314#894—91no—
315#886—91no—
316#886—91no—
317#886—91no—
318#886—181no—
319#885—31no—
320#885—31no—
321#885—91no—
322#884—31no—
323#884—91no—
324#884—91no—
325#884—181no—
326#883—91no—
327#882—91no—
328#882—91no—
329#67⋊C4—31no—
330D3×C22⋊C4—91no—
331#879—91no—
332#878—91no—
333#876—91no—
334#876—91no—
335#875—91no—
336C4×D12—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—31no—
341C23×C32—41no—
342C23×C32C22×D311yescharacteristic
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C22×C3⋊D3—31no—
346C22×C3⋊D3—31no—
347C22×C3⋊D3—31no—
348C22×C3⋊D3—61no—
349C22×C3⋊D3—61no—
350C22×C3⋊D3—61no—
351C22×C3⋊D3—62no—
352C22×C3⋊D3—121no—
353C22×C3⋊D3—121no—
354C22×C3⋊D3—121no—
355C22×C3⋊D3C22×D311yescharacteristic
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3×D3—21no—
358C22×C3×D3—31no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—31no—
362C22×C3×D3—61no—
363C22×C3×D3—61no—
364C22×C3×D3C22×D311yescharacteristic
365C22×C3×D3C22×D311yescharacteristic
366C2×D32—62no—
367C2×D32—62no—
368C2×D32—122no—
369C2×D32—121no—
370C2×D32—121no—
371C2×D32—121no—
372C2×D32—121no—
373C2×D32—122no—
374C2×D32—122no—
375C32×D4—62no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381#638—41no—
382#638—41no—
383#638—121no—
384#638—121no—
385#638—121no—
386#638—122no—
387#638—122no—
388#638—122no—
389#638—124no—
390C2×C3⋊Dic3—31no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—31no—
393C2×C3⋊Dic3—41no—
394C2×C3⋊Dic3—61no—
395C2×C3⋊Dic3—61no—
396C2×C3⋊Dic3—61no—
397C2×C3⋊Dic3—121no—
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C2×C3⋊Dic3C22×D311yescharacteristic
401C2×C3⋊Dic3C22×D311yescharacteristic
402C4⋊(C3⋊D3)—121no—
403C4×C3⋊D3—121no—
404C3×#67—22no—
405C3×#67—22no—
406C3×#67—42no—
407C3×#67—62no—
408C3×#67—121no—
409C3×#67—121no—
410C3×#67—121no—
411C3×#67—121no—
412C3×#67—122no—
413C3×#67—122no—
414C2×C3×Dic3—21no—
415C2×C3×Dic3—21no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—21no—
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—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—61no—
430C2×C3×Dic3—61no—
431C2×C3×Dic3—121no—
432C2×C3×Dic3—121no—
433C2×C3×Dic3—121no—
434C2×C3×Dic3—121no—
435C2×C3×Dic3—122no—
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C3×D12—62no—
447C3×C4×D3—121no—
448C3×C4×D3—121no—
449C3×Dic6—121no—
450C3×Dic6—121no—
451#627—41no—
452#626—22no—
453#626—121no—
454#626—121no—
455#626—122no—
456#626—121no—
457#626—121no—
458#625—121no—
459D3×Dic3—41no—
460D3×Dic3—41no—
461D3×Dic3—121no—
462D3×Dic3—121no—
463D3×Dic3—122no—
464#538—271noSylow
465C2×C33—41no—
466C2×C33C2×#4111yescharacteristic
467C2×C33H(5,𝔽2)11yescharacteristic
468C2×C33H(5,𝔽2)11yescharacteristic
469C3⋊(C3⋊D3)—41no—
470C3×C3⋊D3—41no—
471C3×C3⋊D3—41no—
472C32×D3—22no—
473C23×D3—91no—
474C23×D3—91no—
475C23×D3—91no—
476C23×D3—181no—
477C2×C3×Q8—91no—
478C2×C3×D4—31no—
479C2×C3×D4—31no—
480C2×C3×D4—61no—
481C2×C3×D4—91no—
482C2×C3×D4—91no—
483C2×C3×D4—91no—
484C22×C3×C4—91no—
485C22×C3×C4—91no—
486C22×C3×C4—91no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—31no—
491C2×#67—31no—
492C2×#67—61no—
493C2×#67—61no—
494C2×#67—91no—
495C2×#67—91no—
496C2×#67—91no—
497C2×#67—91no—
498C2×#67—91no—
499C2×#67—91no—
500C2×#67—181no—
501C2×#67—181no—
502C2×#67—181no—
503C2×#67—361no—
504C2×#67D3211yescharacteristic
505C22×Dic3—31no—
506C22×Dic3—31no—
507C22×Dic3—31no—
508C22×Dic3—31no—
509C22×Dic3—61no—
510C22×Dic3—91no—
511C2×D12—31no—
512C2×D12—91no—
513C2×D12—91no—
514C2×D12—91no—
515C2×D12—181no—
516C2×C4×D3—31no—
517C2×C4×D3—31no—
518C2×C4×D3—91no—
519C2×C4×D3—91no—
520C2×C4×D3—181no—
521C2×Dic6—31no—
522C2×Dic6—31no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C22⋊C4—31no—
526C3×C22⋊C4—31no—
527C3×C22⋊C4—31no—
528C3×C22⋊C4—31no—
529C3×C22⋊C4—61no—
530C3×C22⋊C4—61no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4—91no—
535C3×C42—91no—
536C3×C42—91no—
537#217—31no—
538#217—91no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—181no—
544#217D3211yescharacteristic, complemented
545#217D3211yescharacteristic, complemented
546(C2×D3)⋊C4—31no—
547(C2×D3)⋊C4—31no—
548(C2×D3)⋊C4—31no—
549(C2×D3)⋊C4—31no—
550(C2×D3)⋊C4—31no—
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—91no—
554(C2×D3)⋊C4—91no—
555(C2×D3)⋊C4—91no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
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—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—181no—
573(C2×D3)⋊C4—181no—
574(C2×D3)⋊C4—181no—
575(C2×D3)⋊C4—181no—
576(C2×D3)⋊C4—181no—
577C4⋊Dic3—31no—
578C4⋊Dic3—91no—
579C4⋊Dic3—91no—
580C4⋊Dic3—91no—
581C4⋊Dic3—91no—
582C4⋊Dic3—91no—
583C4⋊Dic3—181no—
584C4⋊Dic3—181no—
585Dic3⋊C4—31no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—91no—
591Dic3⋊C4—91no—
592Dic3⋊C4—91no—
593Dic3⋊C4—91no—
594Dic3⋊C4—91no—
595Dic3⋊C4—181no—
596C4×Dic3—31no—
597C4×Dic3—31no—
598C4×Dic3—31no—
599C4×Dic3—31no—
600C22×C32—21no—
601C22×C32—22no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—21no—
612C22×C32—21no—
613C22×C32—32no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—42no—
618C22×C32—41no—
619C22×C32—41no—
620C22×C32—41no—
621C22×C32—41no—
622C22×C32—41no—
623C22×C32—41no—
624C22×C32—61no—
625C22×C32—61no—
626C22×C32—81no—
627C22×C32—81no—
628C22×C32C23×D311yescharacteristic
629C22×C32C23×D311yescharacteristic
630C22×C32C23×D311yescharacteristic
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—61no—
638C2×C3⋊D3—62no—
639C2×C3⋊D3—61no—
640C2×C3⋊D3—61no—
641C2×C3⋊D3—61no—
642C2×C3⋊D3—61no—
643C2×C3⋊D3—61no—
644C2×C3⋊D3—61no—
645C2×C3⋊D3—61no—
646C2×C3⋊D3—61no—
647C2×C3⋊D3—121no—
648C2×C3⋊D3—121no—
649C2×C3⋊D3—122no—
650C2×C3⋊D3—121no—
651C2×C3⋊D3—121no—
652C2×C3⋊D3—121no—
653C2×C3⋊D3—121no—
654C2×C3⋊D3—121no—
655C2×C3⋊D3—121no—
656C2×C3⋊D3—124no—
657C2×C3⋊D3—241no—
658C2×C3⋊D3—241no—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—22no—
664C2×C3×D3—41no—
665C2×C3×D3—41no—
666C2×C3×D3—62no—
667C2×C3×D3—62no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—61no—
674C2×C3×D3—61no—
675C2×C3×D3—61no—
676C2×C3×D3—61no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—61no—
680C2×C3×D3—121no—
681C2×C3×D3—121no—
682C2×C3×D3—121no—
683C2×C3×D3—121no—
684C2×C3×D3#23512yes—
685C2×C3×D3#23712yes—
686D32—124no—
687D32—124no—
688D32—128no—
689C32×C4—61no—
690C32×C4—61no—
691C32×C4—61no—
692C32×C4—61no—
693C32×C4—61no—
694C3⋊Dic3—21no—
695C3⋊Dic3—21no—
696C3⋊Dic3—21no—
697C3⋊Dic3—21no—
698C3⋊Dic3—61no—
699C3⋊Dic3—62no—
700C3⋊Dic3—61no—
701C3⋊Dic3—61no—
702C3⋊Dic3—121no—
703C3⋊Dic3—121no—
704C3⋊Dic3—122no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—21no—
712C3×Dic3—21no—
713C3×Dic3—21no—
714C3×Dic3—21no—
715C3×Dic3—41no—
716C3×Dic3—41no—
717C3×Dic3—41no—
718C3×Dic3—41no—
719C3×Dic3—41no—
720C3×Dic3—61no—
721C3×Dic3—61no—
722C3×Dic3—61no—
723C3×Dic3—61no—
724C3×Dic3—61no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727C3×Dic3—61no—
728C3×Dic3—121no—
729C3×Dic3—121no—
730C3×Dic3—121no—
731C3×Dic3—121no—
732#126—271no—
733#126—271no—
734#124—91no—
735#124—271no—
736#123—271no—
737#123—271no—
738C22⋊Q8—271no—
739#121—91no—
740#121—271no—
741#121—271no—
742#120—271no—
743#120—271no—
744C4×D4—91no—
745C4×D4—271no—
746C2×C22⋊C4—271no—
747C33#53811yescharacteristic, complemented, Sylow
748C23×C3—21no—
749C23×C3—21no—
750C23×C3—21no—
751C23×C3—31no—
752C23×C3—31no—
753C23×C3—41no—
754C23×C3—61no—
755C23×C3—91no—
756C23×C3—91no—
757C23×C3C2×D3211yescharacteristic
758C23×C3C2×D3211yescharacteristic
759C23×C3C2×D3211yescharacteristic
760C22×D3—31no—
761C22×D3—31no—
762C22×D3—31no—
763C22×D3—31no—
764C22×D3—61no—
765C22×D3—61no—
766C22×D3—91no—
767C22×D3—91no—
768C22×D3—91no—
769C22×D3—181no—
770C22×D3—181no—
771C22×D3—181no—
772C22×D3—182no—
773C22×D3—182no—
774C22×D3—182no—
775C22×D3—361no—
776C22×D3—362no—
777C22×D3—361no—
778C22×D3—361no—
779C22×D3—361no—
780C22×D3—361no—
781C22×D3—361no—
782C22×D3—361no—
783C22×D3—362no—
784C22×D3—362no—
785C22×D3C2×D3211yescharacteristic
786C3×Q8—361no—
787C3×D4—62no—
788C3×D4—62no—
789C3×D4—122no—
790C3×D4—182no—
791C3×D4—361no—
792C3×D4—361no—
793C2×C3×C4—31no—
794C2×C3×C4—31no—
795C2×C3×C4—31no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—31no—
802C2×C3×C4—31no—
803C2×C3×C4—61no—
804C2×C3×C4—61no—
805C2×C3×C4—61no—
806C2×C3×C4—61no—
807C2×C3×C4—61no—
808C2×C3×C4—91no—
809C2×C3×C4—91no—
810C2×C3×C4—91no—
811C2×C3×C4—91no—
812C2×C3×C4—361no—
813C2×C3×C4—361no—
814C2×C3×C4—361no—
815#67—22no—
816#67—62no—
817#67—121no—
818#67—121no—
819#67—121no—
820#67—121no—
821#67—122no—
822#67—122no—
823#67—361no—
824#67—361no—
825#67—361no—
826#67—361no—
827#67—361no—
828#67—361no—
829#67—362no—
830#67—362no—
831#67—362no—
832#67—364no—
833C2×Dic3—31no—
834C2×Dic3—31no—
835C2×Dic3—31no—
836C2×Dic3—31no—
837C2×Dic3—31no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—31no—
841C2×Dic3—61no—
842C2×Dic3—61no—
843C2×Dic3—61no—
844C2×Dic3—61no—
845C2×Dic3—91no—
846C2×Dic3—91no—
847C2×Dic3—91no—
848C2×Dic3—121no—
849C2×Dic3—121no—
850C2×Dic3—121no—
851C2×Dic3—121no—
852C2×Dic3—122no—
853C2×Dic3—181no—
854C2×Dic3—181no—
855C2×Dic3—181no—
856C2×Dic3—361no—
857C2×Dic3—361no—
858C2×Dic3C2×D3211yescharacteristic
859C2×Dic3C2×D3211yescharacteristic
860C2×Dic3C2×D3211yescharacteristic
861C2×Dic3C2×D3211yescharacteristic
862C2×Dic3C2×D3211yescharacteristic
863D12—62no—
864D12—361no—
865D12—361no—
866D12—362no—
867D12—361no—
868C4×D3—121no—
869C4×D3—121no—
870C4×D3—361no—
871C4×D3—361no—
872C4×D3—362no—
873Dic6—121no—
874Dic6—121no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—21no—
880C2×C32—21no—
881C2×C32—21no—
882C2×C32—21no—
883C2×C32—21no—
884C2×C32—41no—
885C2×C32—41no—
886C2×C32—41no—
887C2×C32—41no—
888C2×C32—42no—
889C2×C32—41no—
890C2×C32—41no—
891C2×C32—62no—
892C2×C32—81no—
893C2×C32—81no—
894C2×C32—82no—
895C2×C32C2×#23511yescharacteristic
896C2×C32C2×#23711yescharacteristic
897C2×C32#100411yescharacteristic
898C2×C32#100411yescharacteristic
899C2×C32#100411yescharacteristic
900C2×C32D3×#4111yescharacteristic
901C2×C32#100911yescharacteristic
902C2×C32#100911yescharacteristic
903C2×C32#100911yescharacteristic
904C3⋊D3—41no—
905C3⋊D3—41no—
906C3⋊D3—121no—
907C3⋊D3—122no—
908C3⋊D3—121no—
909C3⋊D3—121no—
910C3⋊D3—241no—
911C3⋊D3—241no—
912C3⋊D3—242no—
913C3×D3—22no—
914C3×D3—22no—
915C3×D3—42no—
916C3×D3—122no—
917C3×D3—122no—
918C3×D3—121no—
919C3×D3—121no—
920C3×D3—121no—
921C3×D3—121no—
922C24—271no—
923C2×Q8—91no—
924C2×D4—31no—
925C2×D4—91no—
926C2×D4—91no—
927C2×D4—91no—
928C2×D4—271no—
929C2×D4—271no—
930C2×D4—271no—
931C22×C4—91no—
932C22×C4—91no—
933C22×C4—91no—
934C22×C4—271no—
935C4⋊C4—91no—
936C4⋊C4—91no—
937C4⋊C4—271no—
938C4⋊C4—271no—
939C4⋊C4—271no—
940C4⋊C4—271no—
941C22⋊C4—31no—
942C22⋊C4—31no—
943C22⋊C4—91no—
944C22⋊C4—91no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—271no—
948C22⋊C4—271no—
949C22⋊C4—271no—
950C22⋊C4—271no—
951C22⋊C4—271no—
952C22⋊C4—271no—
953C22⋊C4—271no—
954C22⋊C4—271no—
955C42—91no—
956C42—91no—
957C22×C3—22no—
958C22×C3—21no—
959C22×C3—21no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—32no—
971C22×C3—32no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3—41no—
979C22×C3—41no—
980C22×C3—42no—
981C22×C3—41no—
982C22×C3—62no—
983C22×C3—61no—
984C22×C3—61no—
985C22×C3—61no—
986C22×C3—61no—
987C22×C3—81no—
988C22×C3—81no—
989C22×C3—121no—
990C22×C3—121no—
991C22×C3—181no—
992C22×C3—181no—
993C22×C3—181no—
994C22×C3—181no—
995C22×C3—181no—
996C22×C3—181no—
997C22×C3C22×D3211yescharacteristic
998C22×C3C22×D3211yescharacteristic
999C22×C3C22×D3211yescharacteristic
1000C2×D3—21no—
1001C2×D3—21no—
1002C2×D3—62no—
1003C2×D3—62no—
1004C2×D3—61no—
1005C2×D3—61no—
1006C2×D3—61no—
1007C2×D3—61no—
1008C2×D3—61no—
1009C2×D3—61no—
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—121no—
1020C2×D3—182no—
1021C2×D3—181no—
1022C2×D3—181no—
1023C2×D3—181no—
1024C2×D3—181no—
1025C2×D3—181no—
1026C2×D3—181no—
1027C2×D3—181no—
1028C2×D3—181no—
1029C2×D3—181no—
1030C2×D3—361no—
1031C2×D3—361no—
1032C2×D3—361no—
1033C2×D3—361no—
1034C2×D3—361no—
1035C2×D3—361no—
1036C2×D3—361no—
1037C2×D3—361no—
1038C2×D3—362no—
1039C2×D3—364no—
1040C2×D3—364no—
1041C2×D3—364no—
1042C2×D3—368no—
1043C2×D3—721no—
1044C2×D3—721no—
1045C2×D3#380412yes—
1046C3×C4—61no—
1047C3×C4—61no—
1048C3×C4—61no—
1049C3×C4—61no—
1050C3×C4—61no—
1051C3×C4—61no—
1052C3×C4—61no—
1053C3×C4—61no—
1054C3×C4—61no—
1055C3×C4—61no—
1056C3×C4—121no—
1057C3×C4—121no—
1058C3×C4—121no—
1059C3×C4—121no—
1060C3×C4—121no—
1061C3×C4—181no—
1062C3×C4—181no—
1063C3×C4—181no—
1064C3×C4—181no—
1065Dic3—21no—
1066Dic3—21no—
1067Dic3—21no—
1068Dic3—21no—
1069Dic3—21no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—61no—
1073Dic3—61no—
1074Dic3—61no—
1075Dic3—61no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—121no—
1079Dic3—121no—
1080Dic3—121no—
1081Dic3—121no—
1082Dic3—182no—
1083Dic3—181no—
1084Dic3—181no—
1085Dic3—181no—
1086Dic3—361no—
1087Dic3—361no—
1088Dic3—362no—
1089C32—21no—
1090C32—21no—
1091C32—21no—
1092C32—41no—
1093C32#556011yescharacteristic, complemented
1094C32#561711yescharacteristic, complemented
1095C32#567811yescharacteristic, complemented
1096C23—31no—
1097C23—91no—
1098C23—91no—
1099C23—271no—
1100C23—542no—
1101C23—1081no—
1102C23—1081no—
1103C23D3311yescharacteristic
1104Q8—361no—
1105D4—62no—
1106D4—182no—
1107D4—361no—
1108D4—361no—
1109D4—1081no—
1110D4—1081no—
1111D4—1081no—
1112C2×C4—31no—
1113C2×C4—31no—
1114C2×C4—31no—
1115C2×C4—31no—
1116C2×C4—31no—
1117C2×C4—91no—
1118C2×C4—91no—
1119C2×C4—91no—
1120C2×C4—91no—
1121C2×C4—271no—
1122C2×C4—361no—
1123C2×C4—361no—
1124C2×C4—361no—
1125C2×C4—1081no—
1126C2×C3—21no—
1127C2×C3—21no—
1128C2×C3—21no—
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—42no—
1136C2×C3—41no—
1137C2×C3—41no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—41no—
1142C2×C3—62no—
1143C2×C3—62no—
1144C2×C3—81no—
1145C2×C3—81no—
1146C2×C3—82no—
1147C2×C3—122no—
1148C2×C3—361no—
1149C2×C3—361no—
1150C2×C3D3×#23511yescharacteristic
1151C2×C3#6430811yescharacteristic
1152C2×C3D3×#23711yescharacteristic
1153C2×C3#6431311yescharacteristic
1154C2×C3#6431411yescharacteristic
1155C2×C3#6431411yescharacteristic
1156C2×C3#6431411yescharacteristic
1157C2×C3#6431411yescharacteristic
1158C2×C3C2×#380411yescharacteristic
1159D3—22no—
1160D3—122no—
1161D3—122no—
1162D3—121no—
1163D3—121no—
1164D3—121no—
1165D3—121no—
1166D3—362no—
1167D3—361no—
1168D3—361no—
1169D3—361no—
1170D3—721no—
1171D3—721no—
1172D3—722no—
1173C22—21no—
1174C22—21no—
1175C22—21no—
1176C22—32no—
1177C22—61no—
1178C22—61no—
1179C22—181no—
1180C22—181no—
1181C22—181no—
1182C22—181no—
1183C22—181no—
1184C22—181no—
1185C22—541no—
1186C22—541no—
1187C22—541no—
1188C22—1084no—
1189C22C2×D3311yescharacteristic
1190C4—61no—
1191C4—61no—
1192C4—61no—
1193C4—61no—
1194C4—61no—
1195C4—181no—
1196C4—181no—
1197C4—181no—
1198C4—181no—
1199C4—541no—
1200C3—21no—
1201C3—21no—
1202C3—21no—
1203C3—41no—
1204C3#1059429811yescharacteristic, complemented
1205C3#1059430111yescharacteristic, complemented
1206C3#1059522111yescharacteristic, complemented
1207C2—41no—
1208C2—62no—
1209C2—361no—
1210C2—361no—
1211C2—1081no—
1212C2D3×#380411yescharacteristic
1213C2#1172441611yescharacteristic
1214C2#1172442011yescharacteristic
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. #11723717C2semidirect
2. #11723643C2semidirect
3. #11723624C2semidirect
4. #11723608C2semidirect
5. C3×#67⋊Dic3C2semidirect
6. C3×#63971C2semidirect
7. C3×#63953C2semidirect
8. #11723023C2semidirect
9. #11723021C2semidirect
10. #11723003C2semidirect
11. #11722997C2semidirect
12. #11722969C2semidirect
13. #11722950C2semidirect
14. Dic3×#626C2semidirect
15. D3×#3722C2semidirect
22. C2×C3×#638C22semidirect
23. C22×C3×C3⋊Dic3C22semidirect
27. C2×Dic3×C3⋊D3C22semidirect
28. C2×C3×#627C22semidirect
32. C32×#217C22semidirect
33. C32×#217C22semidirect
34. #88815C22semidirect
36. #88814C22semidirect
37. #88806C22semidirect
38. Dic3⋊(C3⋊Dic3)C22semidirect
39. Dic3⋊(C3⋊Dic3)C22semidirect
46. C3×#3724C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
50. C3×#3722C22semidirect
52. C3×Dic32C22semidirect
53. C3×Dic32C22semidirect
70. #67⋊Dic3D3semidirect
75. #63971D3semidirect
81. #63953D3semidirect
148. C2×#638C2×D3semidirect
149. C22×C3⋊Dic3C2×D3semidirect
172. C2×#627C2×D3semidirect
199. C3×#217C2×D3semidirect
200. C3×#217C2×D3semidirect
201. C3×#217C2×D3semidirect
202. C3×#217C2×D3semidirect
222. #3724C2×D3semidirect
231. Dic3⋊Dic3C2×D3semidirect
248. #3722C2×D3semidirect
260. Dic32C2×D3semidirect
261. Dic32C2×D3semidirect
544. #217D32semidirect
545. #217D32semidirect
747. C33#538semidirect
1093. C32#5560semidirect
1094. C32#5617semidirect
1095. C32#5678semidirect
1204. C3#10594298semidirect
1205. C3#10594301semidirect
1206. C3#10595221semidirect

Maximal subgroups

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

subgroupindex
#117237172
#117236432
#117236242
#117236082
C3×#67⋊Dic32
C3×#639712
C3×#639532
#117230232
#117230212
#117230032
#117229972
#117229692
#117229502
Dic3×#6262
D3×#37222
#105952213
#105943013
#105942983