Finite Group Databasebeta

← #13171730

Subgroups — #13171730

Order 1728.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3804C211yesmaximal, characteristic
2#11723726C211yesmaximal, characteristic, complemented
3#11723626C211yesmaximal, characteristic, complemented
4#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5C2×Dic3×C3⋊Dic3C211yesmaximal, characteristic, complemented
6C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63955C211yesmaximal, characteristic, complemented
8#11722941C211yesmaximal, characteristic, complemented
9#11722940C211yesmaximal, characteristic, complemented
10#11722929C211yesmaximal, characteristic, complemented
11#11722927C211yesmaximal, characteristic, complemented
12#11722915C211yesmaximal, characteristic, complemented
13#11722913C211yesmaximal, characteristic, complemented
14Dic3×#624C211yesmaximal, characteristic, complemented
15D3×Dic32C211yesmaximal, characteristic, complemented
16Dic3×#237—31nomaximal
17#10594958—31nomaximal
18#10594048—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C2×C3×#627C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#624C2211yescharacteristic
30C3×#3804C418yescomplemented
31C2×C3×D3×Dic3C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C32×#217C2211yescharacteristic
35#88815C2211yescharacteristic
36#88814C2211yescharacteristic
37#88813C2211yescharacteristic
38#88807C2211yescharacteristic
39Dic3⋊(C3⋊Dic3)C2211yescharacteristic
40#88803C2211yescharacteristic
41(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic
47Dic3×C3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C3×Dic32C2211yescharacteristic
55C2×C3×#237—31no—
56C2×C3×#235—31no—
57C2×#3804D311yescharacteristic
58D4×C3⋊Dic3—31no—
59C2×C4×C3⋊Dic3—31no—
60#64090—31no—
61C3×D4×Dic3—31no—
62C3×#926—31no—
63C3×#67⋊C4—31no—
64C3×#877—31no—
65#67⋊Dic3—31no—
66#67⋊Dic3—31no—
67#67⋊Dic3—31no—
68#67⋊Dic3—31no—
69#67⋊Dic3—31no—
70#67⋊Dic3—31no—
71#67⋊Dic3—61no—
72#67⋊Dic3—61no—
73#67⋊Dic3D311yescharacteristic, complemented
74Dic3×#67—31no—
75Dic3×#67—31no—
76#63955—31no—
77#63955D311yescharacteristic, complemented
78C2×Dic32—31no—
79C2×Dic32—31no—
80C2×Dic32—31no—
81C2×Dic32—61no—
82#63952—31no—
83#63904—31no—
84#63898—31no—
85#63898—31no—
86C4×#624—31no—
87#63881—31no—
88#63877—31no—
89C4×D3×Dic3—31no—
90C4×D3×Dic3—31no—
91C4×D3×Dic3—31no—
92C4×D3×Dic3—31no—
93#63855—31no—
94#63855—31no—
95#63843—31no—
96#63843—31no—
97#63843—31no—
98Dic3×Dic6—31no—
99#63841—31no—
100#63838—31no—
101#63837—31no—
102#63836—31no—
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)—22no—
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C3×#638C2×C414yescomplemented
110C2×C3×C3⋊Dic3—22no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C32×#67C2×C414yescomplemented
117C2×C32×Dic3C2×C414yescomplemented
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6294—22no—
124Dic3×C3⋊D3—22no—
125D3×C3⋊Dic3—22no—
126C3×#627C2×C414yescomplemented
127C3×#626C2×C414yescomplemented
128C3×#624C2×C414yescomplemented
129C3×D3×Dic3—22no—
130C3×D3×Dic3C2×C414yescomplemented
131Dic3×#41—91no—
132C4×#237—91no—
133#5522—91no—
134C2×C32×D4—31no—
135C22×C32×C4—31no—
136C2×#638C2×D311yescharacteristic
137C22×C3⋊Dic3—31no—
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3—31no—
141C22×C3⋊Dic3—61no—
142C22×C3⋊Dic3—61no—
143C22×C3⋊Dic3—61no—
144C22×C3⋊Dic3—121no—
145C22×C3⋊Dic3C2×D311yescharacteristic
146C2×C4×C3⋊D3—31no—
147C2×C3×#67—21no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—61no—
152C2×C3×#67C2×D311yescharacteristic
153C2×C3×#67C2×D311yescharacteristic
154C22×C3×Dic3—21no—
155C22×C3×Dic3—31no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—61no—
160C22×C3×Dic3C2×D311yescharacteristic
161C22×C3×Dic3C2×D311yescharacteristic
162C3×#237—38no—
163C3×#235—38no—
164C2×C3×D12—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×C3×C4×D3—31no—
169C2×C3×Dic6—31no—
170C2×C3×Dic6—31no—
171C2×#627C2×D311yescharacteristic
172C2×#626C2×D311yescharacteristic
173C2×#624—31no—
174C2×#624C2×D311yescharacteristic
175#3804Dic318yescomplemented
176C2×D3×Dic3—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—61no—
183C2×D3×Dic3—61no—
184C2×D3×Dic3C2×D311yescharacteristic
185C2×D3×Dic3C2×D311yescharacteristic
186C32×C22⋊C4—31no—
187#3757—31no—
188#3757C2×D311yescharacteristic
189#3752—31no—
190C4⋊(C3⋊Dic3)—31no—
191#3750—31no—
192C4×C3⋊Dic3—31no—
193C4×C3⋊Dic3—31no—
194C4×C3⋊Dic3—31no—
195C4×C3⋊Dic3—31no—
196C4×C3⋊Dic3—31no—
197C4×C3⋊Dic3—31no—
198C3×#217—21no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—61no—
203C3×#217C2×D311yescharacteristic
204C3×#217C2×D311yescharacteristic
205C3×(C2×D3)⋊C4—31no—
206C3×C4⋊Dic3—31no—
207C3×C4⋊Dic3—31no—
208C3×C4⋊Dic3—31no—
209C3×Dic3⋊C4—31no—
210C3×Dic3⋊C4—31no—
211C3×Dic3⋊C4—31no—
212C3×C4×Dic3—31no—
213C3×C4×Dic3—31no—
214C3×C4×Dic3—31no—
215C3×C4×Dic3—31no—
216C3×C4×Dic3—31no—
217C3×C4×Dic3—31no—
218#3724—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—61no—
226Dic3⋊Dic3—61no—
227Dic3⋊Dic3C2×D311yescharacteristic
228Dic3⋊Dic3C2×D311yescharacteristic
229Dic3⋊Dic3C2×D311yescharacteristic
230#3722—31no—
231(C2×D3)⋊Dic3—31no—
232(C2×D3)⋊Dic3—31no—
233(C2×D3)⋊Dic3—31no—
234(C2×D3)⋊Dic3—31no—
235(C2×D3)⋊Dic3—31no—
236(C2×D3)⋊Dic3—31no—
237(C2×D3)⋊Dic3—61no—
238(C2×D3)⋊Dic3—61no—
239(C2×D3)⋊Dic3C2×D311yescharacteristic
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—61no—
256Dic32—61no—
257Dic32—61no—
258Dic32—61no—
259Dic32—61no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic
262Dic32C2×D311yescharacteristic
263Dic32C2×D311yescharacteristic
264C22×C33—21no—
265C22×C33—21no—
266C22×C33C22×C412yes—
267C22×C33C2411yescharacteristic
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3C22×C412yes—
271C2×C32×D3—21no—
272C2×C32×D3—21no—
273C2×C32×D3C22×C412yes—
274C3⋊(C3⋊Dic3)—21no—
275C3⋊(C3⋊Dic3)#4112yescomplemented
276C3×C3⋊Dic3—21no—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3C22×C412yes—
280C3×C3⋊Dic3#4112yescomplemented
281C32×Dic3—21no—
282C32×Dic3—21no—
283C32×Dic3C22×C412yes—
284C32×Dic3C22×C412yes—
285C32×Dic3C22×C412yes—
286C2×C3×#41—91no—
287C2×#237—31no—
288C2×#235—31no—
289C3×C4×D4—91no—
290C3×#117—91no—
291Q8×Dic3—91no—
292Q8×Dic3—91no—
293D4×Dic3—31no—
294D4×Dic3—91no—
295D4×Dic3—91no—
296D4×Dic3—91no—
297D4×Dic3—91no—
298D4×Dic3—91no—
299D4×Dic3—91no—
300D4×Dic3—181no—
301C4×#67—91no—
302C4×#67—91no—
303#926—31no—
304#926—91no—
305#926—91no—
306C2×C4×Dic3—91no—
307C2×C4×Dic3—91no—
308C2×C4×Dic3—91no—
309C2×C4×Dic3—91no—
310C2×C4×Dic3—91no—
311C2×C4×Dic3—91no—
312C2×C4×Dic3—181no—
313#893—91no—
314#893—91no—
315#892—91no—
316#887—91no—
317#887—91no—
318#887—91no—
319#67⋊C4—31no—
320#67⋊C4—91no—
321#67⋊C4—91no—
322#67⋊C4—91no—
323#67⋊C4—91no—
324#67⋊C4—91no—
325#67⋊C4—181no—
326#877—31no—
327#877—91no—
328#872—91no—
329#872—91no—
330C42×D3—91no—
331C42×D3—91no—
332C42×D3—91no—
333C4×Dic6—91no—
334C23×C32—21no—
335C23×C32—21no—
336C23×C32—21no—
337C23×C32—31no—
338C23×C32—41no—
339C23×C32C22×D311yescharacteristic
340C23×C32C22×D311yescharacteristic
341C23×C32C22×D311yescharacteristic
342C22×C3⋊D3C22×D311yescharacteristic
343C22×C3×D3—21no—
344C22×C3×D3—31no—
345C22×C3×D3—31no—
346C22×C3×D3—61no—
347C22×C3×D3C22×D311yescharacteristic
348C22×C3×D3C22×D311yescharacteristic
349C32×D4—34no—
350C2×C32×C4—34no—
351C2×C32×C4—31no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356#638C2×Dic314yescomplemented
357C2×C3⋊Dic3—22no—
358C2×C3⋊Dic3—31no—
359C2×C3⋊Dic3—31no—
360C2×C3⋊Dic3—31no—
361C2×C3⋊Dic3—31no—
362C2×C3⋊Dic3—31no—
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—61no—
365C2×C3⋊Dic3—61no—
366C2×C3⋊Dic3—61no—
367C2×C3⋊Dic3—61no—
368C2×C3⋊Dic3—61no—
369C2×C3⋊Dic3—61no—
370C2×C3⋊Dic3—62no—
371C2×C3⋊Dic3—62no—
372C2×C3⋊Dic3—62no—
373C2×C3⋊Dic3—62no—
374C2×C3⋊Dic3—64no—
375C2×C3⋊Dic3—121no—
376C2×C3⋊Dic3—121no—
377C2×C3⋊Dic3—122no—
378C2×C3⋊Dic3—122no—
379C2×C3⋊Dic3—124no—
380C2×C3⋊Dic3C22×D311yescharacteristic
381C2×C3⋊Dic3C22×D311yescharacteristic
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C4×C3⋊D3—62no—
386C3×#67—24no—
387C3×#67—34no—
388C3×#67—34no—
389C3×#67—34no—
390C3×#67—64no—
391C3×#67C4×D314yescomplemented
392C3×#67C2×Dic314yescomplemented
393C2×C3×Dic3—24no—
394C2×C3×Dic3—21no—
395C2×C3×Dic3—21no—
396C2×C3×Dic3—21no—
397C2×C3×Dic3—21no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—31no—
400C2×C3×Dic3—31no—
401C2×C3×Dic3—31no—
402C2×C3×Dic3—31no—
403C2×C3×Dic3—34no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—61no—
411C2×C3×Dic3—61no—
412C2×C3×Dic3—61no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—62no—
416C2×C3×Dic3—62no—
417C2×C3×Dic3—62no—
418C2×C3×Dic3—64no—
419C2×C3×Dic3C4×D314yescomplemented
420C2×C3×Dic3C2×Dic314yescomplemented
421C2×C3×Dic3C22×D311yescharacteristic
422C2×C3×Dic3C22×D311yescharacteristic
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C3×D12—34no—
432C3×C4×D3—34no—
433C3×C4×D3—34no—
434C3×C4×D3—34no—
435C3×C4×D3—62no—
436C3×Dic6—34no—
437C3×Dic6—34no—
438#627C2×Dic314yescomplemented
439#626C2×Dic314yescomplemented
440#624—62no—
441#624C2×Dic314yescomplemented
442D3×Dic3—22no—
443D3×Dic3—62no—
444D3×Dic3—62no—
445D3×Dic3—62no—
446D3×Dic3—62no—
447D3×Dic3—62no—
448D3×Dic3—62no—
449D3×Dic3—122no—
450D3×Dic3—122no—
451D3×Dic3C2×Dic314yescomplemented
452C4×#41—271noSylow
453C2×C33—22no—
454C2×C33C23×C411yescharacteristic
455C2×C33C2×#4111yescharacteristic
456C2×C33C2×#4111yescharacteristic
457C3×C3⋊D3—22no—
458C32×D3—22no—
459C3×#41—98no—
460C2×C3×Q8—91no—
461C2×C3×D4—31no—
462C2×C3×D4—31no—
463C2×C3×D4—61no—
464C2×C3×D4—91no—
465C2×C3×D4—91no—
466C22×C3×C4—31no—
467C22×C3×C4—31no—
468C22×C3×C4—61no—
469C22×C3×C4—91no—
470C22×C3×C4—91no—
471C22×C3×C4—91no—
472C22×C3×C4—91no—
473C2×#67—31no—
474C2×#67—31no—
475C2×#67—31no—
476C2×#67—61no—
477C2×#67D3211yescharacteristic
478C22×Dic3—31no—
479C22×Dic3—31no—
480C22×Dic3—31no—
481C22×Dic3—31no—
482C22×Dic3—61no—
483C22×Dic3—91no—
484C22×Dic3—91no—
485C22×Dic3—91no—
486C22×Dic3—91no—
487C22×Dic3—91no—
488C22×Dic3—91no—
489C22×Dic3—91no—
490C22×Dic3—181no—
491C22×Dic3—181no—
492C22×Dic3—181no—
493C22×Dic3—181no—
494C22×Dic3—361no—
495C22×Dic3D3211yescharacteristic
496#237—38no—
497#235—38no—
498C2×D12—31no—
499C2×C4×D3—31no—
500C2×C4×D3—31no—
501C2×C4×D3—31no—
502C2×C4×D3—31no—
503C2×C4×D3—91no—
504C2×C4×D3—91no—
505C2×C4×D3—91no—
506C2×C4×D3—91no—
507C2×C4×D3—91no—
508C2×C4×D3—181no—
509C2×Dic6—31no—
510C2×Dic6—31no—
511C3×C4⋊C4—91no—
512C3×C4⋊C4—91no—
513C3×C4⋊C4—91no—
514C3×C22⋊C4—31no—
515C3×C22⋊C4—31no—
516C3×C22⋊C4—61no—
517C3×C22⋊C4—91no—
518C3×C22⋊C4—91no—
519C3×C42—91no—
520C3×C42—91no—
521C3×C42—91no—
522#217—31no—
523#217—31no—
524#217—31no—
525#217—61no—
526#217—91no—
527#217—91no—
528#217—91no—
529#217—91no—
530#217—181no—
531#217D3211yescharacteristic
532(C2×D3)⋊C4—31no—
533(C2×D3)⋊C4—91no—
534(C2×D3)⋊C4—91no—
535(C2×D3)⋊C4—91no—
536(C2×D3)⋊C4—91no—
537(C2×D3)⋊C4—91no—
538(C2×D3)⋊C4—181no—
539C4⋊Dic3—31no—
540C4⋊Dic3—31no—
541C4⋊Dic3—31no—
542C4⋊Dic3—91no—
543C4⋊Dic3—91no—
544C4⋊Dic3—91no—
545C4⋊Dic3—91no—
546C4⋊Dic3—181no—
547Dic3⋊C4—31no—
548Dic3⋊C4—31no—
549Dic3⋊C4—31no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—91no—
555Dic3⋊C4—181no—
556C4×Dic3—31no—
557C4×Dic3—31no—
558C4×Dic3—31no—
559C4×Dic3—31no—
560C4×Dic3—31no—
561C4×Dic3—31no—
562C4×Dic3—91no—
563C4×Dic3—91no—
564C4×Dic3—91no—
565C4×Dic3—91no—
566C4×Dic3—91no—
567C4×Dic3—91no—
568C4×Dic3—91no—
569C4×Dic3—91no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C4×Dic3—91no—
582C4×Dic3—91no—
583C4×Dic3—181no—
584C4×Dic3—181no—
585C4×Dic3—181no—
586C4×Dic3—181no—
587C4×Dic3—181no—
588C4×Dic3—181no—
589C22×C32—21no—
590C22×C32—21no—
591C22×C32—22no—
592C22×C32—22no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—21no—
596C22×C32—21no—
597C22×C32—21no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—22no—
601C22×C32—22no—
602C22×C32—22no—
603C22×C32—32no—
604C22×C32—42no—
605C22×C32—41no—
606C22×C32—41no—
607C22×C32—41no—
608C22×C32—41no—
609C22×C32—41no—
610C22×C32—42no—
611C22×C32—42no—
612C22×C32—61no—
613C22×C32—61no—
614C22×C32C2×C4×D312yes—
615C22×C32C2×C4×D312yes—
616C22×C32C22×Dic312yes—
617C22×C32C23×D311yescharacteristic
618C22×C32C23×D311yescharacteristic
619C22×C32C23×D311yescharacteristic
620C2×C3⋊D3—21no—
621C2×C3⋊D3—21no—
622C2×C3⋊D3C22×Dic312yes—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—21no—
627C2×C3×D3—22no—
628C2×C3×D3—32no—
629C2×C3×D3—32no—
630C2×C3×D3—41no—
631C2×C3×D3—41no—
632C2×C3×D3—62no—
633C2×C3×D3—61no—
634C2×C3×D3—61no—
635C2×C3×D3—61no—
636C2×C3×D3—61no—
637C2×C3×D3—121no—
638C2×C3×D3—121no—
639C2×C3×D3C2×C4×D312yes—
640C2×C3×D3C22×Dic312yes—
641C32×C4—32no—
642C32×C4—32no—
643C32×C4—32no—
644C32×C4—61no—
645C32×C4—61no—
646C3⋊Dic3—21no—
647C3⋊Dic3—21no—
648C3⋊Dic3—21no—
649C3⋊Dic3—32no—
650C3⋊Dic3—32no—
651C3⋊Dic3—32no—
652C3⋊Dic3—62no—
653C3⋊Dic3—62no—
654C3⋊Dic3—62no—
655C3⋊Dic3—61no—
656C3⋊Dic3—62no—
657C3⋊Dic3—61no—
658C3⋊Dic3—61no—
659C3⋊Dic3—122no—
660C3⋊Dic3—121no—
661C3⋊Dic3—121no—
662C3⋊Dic3—122no—
663C3⋊Dic3#23712yescomplemented
664C3⋊Dic3C22×Dic312yes—
665C3×Dic3—21no—
666C3×Dic3—21no—
667C3×Dic3—21no—
668C3×Dic3—21no—
669C3×Dic3—22no—
670C3×Dic3—22no—
671C3×Dic3—22no—
672C3×Dic3—32no—
673C3×Dic3—32no—
674C3×Dic3—32no—
675C3×Dic3—32no—
676C3×Dic3—41no—
677C3×Dic3—41no—
678C3×Dic3—62no—
679C3×Dic3—62no—
680C3×Dic3—62no—
681C3×Dic3—61no—
682C3×Dic3—61no—
683C3×Dic3—61no—
684C3×Dic3—61no—
685C3×Dic3—61no—
686C3×Dic3—61no—
687C3×Dic3—121no—
688C3×Dic3—121no—
689C3×Dic3C2×C4×D312yes—
690C3×Dic3C2×C4×D312yes—
691C3×Dic3C2×C4×D312yes—
692C3×Dic3C22×Dic312yes—
693C3×Dic3C22×Dic312yes—
694C3×Dic3C22×Dic312yes—
695C2×#41—91no—
696C4×Q8—271no—
697C4×Q8—271no—
698C4×D4—91no—
699C4×D4—271no—
700C4×D4—271no—
701C4×D4—271no—
702C4×D4—271no—
703C4×D4—271no—
704#117—91no—
705#117—271no—
706#117—271no—
707C2×C42—271no—
708C2×C42—271no—
709C2×C42—271no—
710C33C4×#4111yescharacteristic, complemented, Sylow
711C23×C3—21no—
712C23×C3—21no—
713C23×C3—21no—
714C23×C3—31no—
715C23×C3—31no—
716C23×C3—41no—
717C23×C3—61no—
718C23×C3—91no—
719C23×C3C2×D3211yescharacteristic
720C23×C3C2×D3211yescharacteristic
721C23×C3C2×D3211yescharacteristic
722C22×D3—31no—
723C22×D3—31no—
724C22×D3—61no—
725C22×D3C2×D3211yescharacteristic
726C3×Q8—94no—
727C3×D4—34no—
728C3×D4—34no—
729C3×D4—64no—
730C3×D4—94no—
731C3×D4—94no—
732C2×C3×C4—31no—
733C2×C3×C4—31no—
734C2×C3×C4—31no—
735C2×C3×C4—31no—
736C2×C3×C4—31no—
737C2×C3×C4—31no—
738C2×C3×C4—34no—
739C2×C3×C4—34no—
740C2×C3×C4—31no—
741C2×C3×C4—31no—
742C2×C3×C4—31no—
743C2×C3×C4—31no—
744C2×C3×C4—61no—
745C2×C3×C4—61no—
746C2×C3×C4—61no—
747C2×C3×C4—64no—
748C2×C3×C4—61no—
749C2×C3×C4—61no—
750C2×C3×C4—94no—
751C2×C3×C4—94no—
752C2×C3×C4—91no—
753C2×C3×C4—91no—
754C2×C3×C4—91no—
755C2×C3×C4—91no—
756C2×C3×C4—91no—
757C2×C3×C4—182no—
758C2×C3×C4—182no—
759#67—34no—
760#67—34no—
761#67—34no—
762#67—64no—
763#67D3×Dic314yescomplemented
764C2×Dic3—31no—
765C2×Dic3—31no—
766C2×Dic3—31no—
767C2×Dic3—31no—
768C2×Dic3—34no—
769C2×Dic3—31no—
770C2×Dic3—31no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—61no—
776C2×Dic3—61no—
777C2×Dic3—61no—
778C2×Dic3—61no—
779C2×Dic3—61no—
780C2×Dic3—62no—
781C2×Dic3—62no—
782C2×Dic3—62no—
783C2×Dic3—64no—
784C2×Dic3—91no—
785C2×Dic3—91no—
786C2×Dic3—91no—
787C2×Dic3—91no—
788C2×Dic3—91no—
789C2×Dic3—91no—
790C2×Dic3—181no—
791C2×Dic3—181no—
792C2×Dic3—181no—
793C2×Dic3—181no—
794C2×Dic3—181no—
795C2×Dic3—181no—
796C2×Dic3—182no—
797C2×Dic3—182no—
798C2×Dic3—182no—
799C2×Dic3—182no—
800C2×Dic3—182no—
801C2×Dic3—182no—
802C2×Dic3—182no—
803C2×Dic3—184no—
804C2×Dic3—361no—
805C2×Dic3—361no—
806C2×Dic3—362no—
807C2×Dic3—362no—
808C2×Dic3—362no—
809C2×Dic3—364no—
810C2×Dic3D3×Dic314yescomplemented
811C2×Dic3C2×D3211yescharacteristic
812C2×Dic3C2×D3211yescharacteristic
813C2×Dic3C2×D3211yescharacteristic
814C2×Dic3C2×D3211yescharacteristic
815C2×Dic3C2×D3211yescharacteristic
816D12—34no—
817C4×D3—34no—
818C4×D3—34no—
819C4×D3—34no—
820C4×D3—62no—
821C4×D3—182no—
822C4×D3—182no—
823C4×D3—182no—
824C4×D3—182no—
825C4×D3—182no—
826C4×D3—362no—
827Dic6—34no—
828Dic6—34no—
829C2×C32—22no—
830C2×C32—24no—
831C2×C32—22no—
832C2×C32—22no—
833C2×C32—21no—
834C2×C32—21no—
835C2×C32—21no—
836C2×C32—21no—
837C2×C32—21no—
838C2×C32—21no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—21no—
842C2×C32—41no—
843C2×C32—41no—
844C2×C32—41no—
845C2×C32—42no—
846C2×C32—42no—
847C2×C32—44no—
848C2×C32—62no—
849C2×C32C22×C4×D311yescharacteristic
850C2×C32C22×C4×D311yescharacteristic
851C2×C32C2×#23711yescharacteristic
852C2×C32D3×#4111yescharacteristic
853C2×C32D3×#4111yescharacteristic
854C2×C32D3×#4111yescharacteristic
855C2×C32D3×#4111yescharacteristic
856C2×C32D3×#4111yescharacteristic
857C2×C32C23×Dic311yescharacteristic
858C3⋊D3—22no—
859C3×D3—22no—
860C3×D3—22no—
861C3×D3—42no—
862C3×D3—62no—
863C3×D3—62no—
864C3×D3—122no—
865#41—98no—
866C2×Q8—91no—
867C2×D4—31no—
868C2×D4—91no—
869C2×D4—91no—
870C22×C4—31no—
871C22×C4—91no—
872C22×C4—91no—
873C22×C4—91no—
874C22×C4—91no—
875C22×C4—271no—
876C22×C4—271no—
877C22×C4—271no—
878C22×C4—271no—
879C4⋊C4—91no—
880C4⋊C4—91no—
881C4⋊C4—91no—
882C4⋊C4—271no—
883C4⋊C4—271no—
884C4⋊C4—271no—
885C22⋊C4—31no—
886C22⋊C4—91no—
887C22⋊C4—91no—
888C22⋊C4—271no—
889C22⋊C4—271no—
890C22⋊C4—271no—
891C42—91no—
892C42—91no—
893C42—91no—
894C42—271no—
895C42—271no—
896C42—271no—
897C42—271no—
898C42—271no—
899C42—271no—
900C42—271no—
901C22×C3—22no—
902C22×C3—22no—
903C22×C3—21no—
904C22×C3—21no—
905C22×C3—21no—
906C22×C3—21no—
907C22×C3—21no—
908C22×C3—21no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—22no—
913C22×C3—22no—
914C22×C3—22no—
915C22×C3—32no—
916C22×C3—32no—
917C22×C3—41no—
918C22×C3—41no—
919C22×C3—41no—
920C22×C3—41no—
921C22×C3—42no—
922C22×C3—42no—
923C22×C3—41no—
924C22×C3—42no—
925C22×C3—62no—
926C22×C3—61no—
927C22×C3—61no—
928C22×C3—61no—
929C22×C3—61no—
930C22×C3—92no—
931C22×C3—121no—
932C22×C3—121no—
933C22×C3—181no—
934C22×C3—181no—
935C22×C3C4×D3212yes—
936C22×C3C2×D3×Dic312yes—
937C22×C3C2×D3×Dic312yes—
938C22×C3C22×D3211yescharacteristic
939C22×C3C22×D3211yescharacteristic
940C22×C3C22×D3211yescharacteristic
941C2×D3—21no—
942C2×D3—21no—
943C2×D3—32no—
944C2×D3—32no—
945C2×D3—62no—
946C2×D3—61no—
947C2×D3—61no—
948C2×D3—61no—
949C2×D3—61no—
950C2×D3—121no—
951C2×D3—121no—
952C2×D3C2×D3×Dic312yes—
953C3×C4—32no—
954C3×C4—32no—
955C3×C4—32no—
956C3×C4—32no—
957C3×C4—32no—
958C3×C4—32no—
959C3×C4—62no—
960C3×C4—62no—
961C3×C4—62no—
962C3×C4—61no—
963C3×C4—61no—
964C3×C4—61no—
965C3×C4—61no—
966C3×C4—92no—
967C3×C4—92no—
968C3×C4—121no—
969C3×C4—121no—
970C3×C4—181no—
971C3×C4—181no—
972C3×C4—181no—
973Dic3—21no—
974Dic3—21no—
975Dic3—32no—
976Dic3—32no—
977Dic3—32no—
978Dic3—32no—
979Dic3—62no—
980Dic3—62no—
981Dic3—62no—
982Dic3—61no—
983Dic3—61no—
984Dic3—61no—
985Dic3—61no—
986Dic3—61no—
987Dic3—61no—
988Dic3—92no—
989Dic3—92no—
990Dic3—92no—
991Dic3—121no—
992Dic3—121no—
993Dic3—182no—
994Dic3—182no—
995Dic3—182no—
996Dic3—182no—
997Dic3—181no—
998Dic3—181no—
999Dic3—181no—
1000Dic3—362no—
1001Dic3—361no—
1002Dic3—361no—
1003Dic3—362no—
1004Dic3C2×D3×Dic312yes—
1005Dic3C2×D3×Dic312yes—
1006Dic3C2×D3×Dic312yes—
1007C32—21no—
1008C32—21no—
1009C32—21no—
1010C32—41no—
1011C32#552211yescharacteristic, complemented
1012C32C4×#23711yescharacteristic, complemented
1013C32Dic3×#4111yescharacteristic, complemented
1014C23—31no—
1015C23—91no—
1016C23D3311yescharacteristic
1017Q8—94no—
1018D4—34no—
1019D4—94no—
1020D4—94no—
1021C2×C4—31no—
1022C2×C4—31no—
1023C2×C4—31no—
1024C2×C4—34no—
1025C2×C4—31no—
1026C2×C4—31no—
1027C2×C4—94no—
1028C2×C4—94no—
1029C2×C4—91no—
1030C2×C4—91no—
1031C2×C4—91no—
1032C2×C4—91no—
1033C2×C4—91no—
1034C2×C4—182no—
1035C2×C4—182no—
1036C2×C4—271no—
1037C2×C4—271no—
1038C2×C4—542no—
1039C2×C4—542no—
1040C2×C4—542no—
1041C2×C4—542no—
1042C2×C3—24no—
1043C2×C3—22no—
1044C2×C3—22no—
1045C2×C3—22no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—42no—
1056C2×C3—42no—
1057C2×C3—44no—
1058C2×C3—41no—
1059C2×C3—41no—
1060C2×C3—41no—
1061C2×C3—62no—
1062C2×C3—62no—
1063C2×C3—122no—
1064C2×C3—182no—
1065C2×C3C2×C4×D3211yescharacteristic
1066C2×C3#6430611yescharacteristic
1067C2×C3#6430611yescharacteristic
1068C2×C3D3×#23711yescharacteristic
1069C2×C3D3×#23711yescharacteristic
1070C2×C3#6431211yescharacteristic
1071C2×C3#6431211yescharacteristic
1072C2×C3C22×D3×Dic311yescharacteristic
1073C2×C3C22×D3×Dic311yescharacteristic
1074D3—22no—
1075D3—62no—
1076D3—62no—
1077D3—122no—
1078C22—21no—
1079C22—21no—
1080C22—32no—
1081C22—61no—
1082C22—61no—
1083C22—92no—
1084C22—181no—
1085C22—181no—
1086C22D32×Dic312yes—
1087C22C2×D3311yescharacteristic
1088C4—32no—
1089C4—32no—
1090C4—32no—
1091C4—61no—
1092C4—61no—
1093C4—92no—
1094C4—92no—
1095C4—181no—
1096C4—181no—
1097C4—181no—
1098C4—272no—
1099C4—541no—
1100C3—21no—
1101C3—21no—
1102C3—21no—
1103C3—41no—
1104C3#1059404811yescharacteristic, complemented
1105C3#1059495811yescharacteristic, complemented
1106C3Dic3×#23711yescharacteristic, complemented
1107C2—22no—
1108C2—62no—
1109C2—182no—
1110C2C2×D32×Dic311yescharacteristic
1111C2#1172440711yescharacteristic
1112C2#1172441111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC23×C33C23
socle, cosocleC22×C33C24
prime radicalC2×C3×#3804C2
hypercenterC23D33
hypocenterC33C4×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723726C2semidirect
3. #11723626C2semidirect
4. #67⋊(C3⋊Dic3)C2semidirect
5. C2×Dic3×C3⋊Dic3C2semidirect
6. C3×#67⋊Dic3C2semidirect
7. C3×#63955C2semidirect
8. #11722941C2semidirect
9. #11722940C2semidirect
10. #11722929C2semidirect
11. #11722927C2semidirect
12. #11722915C2semidirect
13. #11722913C2semidirect
14. Dic3×#624C2semidirect
15. D3×Dic32C2semidirect
30. C3×#3804C4semidirect
73. #67⋊Dic3D3semidirect
77. #63955D3semidirect
109. C3×#638C2×C4semidirect
116. C32×#67C2×C4semidirect
117. C2×C32×Dic3C2×C4semidirect
126. C3×#627C2×C4semidirect
127. C3×#626C2×C4semidirect
128. C3×#624C2×C4semidirect
130. C3×D3×Dic3C2×C4semidirect
175. #3804Dic3semidirect
275. C3⋊(C3⋊Dic3)#41semidirect
280. C3×C3⋊Dic3#41semidirect
356. #638C2×Dic3semidirect
391. C3×#67C4×D3semidirect
392. C3×#67C2×Dic3semidirect
419. C2×C3×Dic3C4×D3semidirect
420. C2×C3×Dic3C2×Dic3semidirect
438. #627C2×Dic3semidirect
439. #626C2×Dic3semidirect
441. #624C2×Dic3semidirect
451. D3×Dic3C2×Dic3semidirect
663. C3⋊Dic3#237semidirect
710. C33C4×#41semidirect
763. #67D3×Dic3semidirect
810. C2×Dic3D3×Dic3semidirect
1011. C32#5522semidirect
1012. C32C4×#237semidirect
1013. C32Dic3×#41semidirect
1104. C3#10594048semidirect
1105. C3#10594958semidirect
1106. C3Dic3×#237semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38042
#117237262
#117236262
#67⋊(C3⋊Dic3)2
C2×Dic3×C3⋊Dic32
C3×#67⋊Dic32
C3×#639552
#117229412
#117229402
#117229292
#117229272
#117229152
#117229132
Dic3×#6242
D3×Dic322
Dic3×#2373
#105949583
#105940483