Finite Group Databasebeta

← C3×#10595062 #13174659

Subgroups — C3×#10595062 #13174659

Order 1728.

1830 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×D12C211yesmaximal, characteristic, complemented
2C2×C3×D3×#67C211yesmaximal, characteristic, complemented
3C3×#64138C211yesmaximal, characteristic, complemented
4C32×#929C211yesmaximal, characteristic, complemented
5C3×#63977C211yesmaximal, characteristic, complemented
6C3×#63976C211yesmaximal, characteristic, complemented
7C3×D3×#217C211yesmaximal, characteristic, complemented
8C3×#63922C212yesmaximal, complemented
9C3×#63886C212yesmaximal, complemented
10C3×#63885C212yesmaximal, complemented
11C3×#63884C212yesmaximal, complemented
12C3×#5804—31nomaximal
13C3×#5653—31nomaximal
14#10595062C311yesmaximal, characteristic, direct product factor
15C23×C32×D3C2211yescharacteristic
16C23×C32×D3C2211yescharacteristic, complemented
17C22×C3×D32C2211yescharacteristic, complemented
18C22×C33×C4C2211yescharacteristic, complemented
19C2×C3×#638C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×D12—24no—
22C2×C32×D12C2212yes—
23C2×C32×D12C2212yescomplemented
24C3×D3×#67—24no—
25C2×C3×#626C2211yescharacteristic, complemented
26C2×C3×#626C2212yescomplemented
27C2×C3×#625C2211yescharacteristic, complemented
28C2×C3×#625C2212yescomplemented
29C2×C3×D3×Dic3C2211yescharacteristic, complemented
30C2×C3×D3×Dic3C2212yescomplemented
31C3×#3757C2211yescharacteristic, complemented
32C3×#3752C2212yescomplemented
33C3×#3750C2212yescomplemented
34C32×#217C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2212yescomplemented
36C32×Dic3⋊C4C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C22×C32×D4—31no—
41C22×C3×#67—31no—
42C2×C3×D3×D4—31no—
43C22×C3×D12—21no—
44C22×C3×D12D311yescharacteristic, complemented
45C22×C3×D12C2×C311yescharacteristic, complemented
46C2×D3×#67C2×C311yescharacteristic, complemented
47C32×#123—31no—
48#64138C2×C311yescharacteristic, complemented
49C3×#953—31no—
50C3×#953—31no—
51C2×C3×#217—31no—
52C3×#939—32no—
53C3×#939—32no—
54C3×#937—32no—
55C3×#937—31no—
56C3×#935—32no—
57C3×#929—21no—
58C3×#929—31no—
59C3×#929—31no—
60C3×#929—61no—
61C3×#929D311yescharacteristic, complemented
62C3×#929C2×C311yescharacteristic, complemented
63C3×#895—32no—
64C3×#894—32no—
65C3×#884—32no—
66C3×#882—32no—
67C3×#882—31no—
68C3×D3×C22⋊C4—31no—
69#63977C2×C311yescharacteristic, complemented
70#63976C2×C311yescharacteristic, complemented
71D3×#217C2×C311yescharacteristic, complemented
72#63922C2×C312yescomplemented
73#63886C2×C312yescomplemented
74#63885C2×C312yescomplemented
75#63884C2×C312yescomplemented
76C23×C33C2311yescharacteristic
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C32×D3—22no—
79C22×C32×D3—42no—
80C22×C32×D3—42no—
81C22×C32×D3D414yescomplemented
82C22×C32×D3C2311yescharacteristic
83C22×C32×D3C2312yes—
84C22×C32×D3C2311yescharacteristic
85C22×C32×D3C2311yescharacteristic
86C2×C3×D32—22no—
87C2×C3×D32—42no—
88C2×C33×C4—22no—
89C2×C33×C4C2312yes—
90C3×#638—22no—
91C2×C3×C3⋊Dic3C2311yescharacteristic
92C2×C3×C3⋊Dic3C2312yes—
93C32×#67—22no—
94C2×C32×Dic3C2312yes—
95C2×C32×Dic3C2311yescharacteristic
96C32×D12—24no—
97C32×D12—24no—
98C3×#626—22no—
99C3×#626—42no—
100C3×#625—22no—
101C3×#625—42no—
102C3×D3×Dic3—22no—
103C3×D3×Dic3—42no—
104C3×#534—91no—
105#5804—31no—
106#5653—31no—
107C24×C32—31no—
108C24×C32—31no—
109C23×C3×D3—21no—
110C23×C3×D3—21no—
111C23×C3×D3—31no—
112C23×C3×D3—31no—
113C23×C3×D3C2×D311yescharacteristic
114C23×C3×D3C2×D311yescharacteristic, complemented
115C23×C3×D3C22×C311yescharacteristic
116C23×C3×D3C22×C311yescharacteristic, complemented
117C22×D32C22×C311yescharacteristic, complemented
118C2×C32×D4—31no—
119C2×C32×D4—32no—
120C2×C32×D4—32no—
121C2×C32×D4—64no—
122C22×C32×C4—21no—
123C22×C32×C4—21no—
124C22×C32×C4—21no—
125C22×C32×C4—41no—
126C22×C32×C4C2×D311yescharacteristic, complemented
127C22×C32×C4C2×D311yescharacteristic, complemented
128C22×C32×C4C22×C311yescharacteristic, complemented
129C2×#638C22×C311yescharacteristic
130C2×C3×#67—21no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C2×C3×#67—32no—
136C2×C3×#67—32no—
137C2×C3×#67—31no—
138C2×C3×#67—32no—
139C2×C3×#67—64no—
140C2×C3×#67—61no—
141C2×C3×#67C2×D311yescharacteristic
142C2×C3×#67C22×C311yescharacteristic
143C22×C3×Dic3—31no—
144C22×C3×Dic3—32no—
145C3×D3×D4—64no—
146C2×C3×D12—28no—
147C2×C3×D12—22no—
148C2×C3×D12—22no—
149C2×C3×D12—24no—
150C2×C3×D12—24no—
151C2×C3×D12—31no—
152C2×C3×D12—32no—
153C2×C3×D12C2×D312yes—
154C2×C3×D12C2×D312yescomplemented
155C2×C3×D12C22×C312yes—
156C2×C3×D12C22×C312yescomplemented
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3—32no—
159D3×#67—24no—
160C2×#626C22×C311yescharacteristic, complemented
161C2×#626C22×C312yescomplemented
162C2×#625C22×C311yescharacteristic, complemented
163C2×#625C22×C312yescomplemented
164C2×D3×Dic3C22×C311yescharacteristic, complemented
165C2×D3×Dic3C22×C312yescomplemented
166C32×C4⋊C4—32no—
167C32×C22⋊C4—31no—
168C32×C22⋊C4—32no—
169#3757C22×C311yescharacteristic, complemented
170#3752C22×C312yescomplemented
171#3750C22×C312yescomplemented
172C3×#217—21no—
173C3×#217—31no—
174C3×#217—31no—
175C3×#217—32no—
176C3×#217—32no—
177C3×#217—32no—
178C3×#217—61no—
179C3×#217C2×D311yescharacteristic, complemented
180C3×#217C22×C311yescharacteristic, complemented
181C3×(C2×D3)⋊C4—22no—
182C3×(C2×D3)⋊C4—32no—
183C3×(C2×D3)⋊C4—32no—
184C3×(C2×D3)⋊C4—32no—
185C3×(C2×D3)⋊C4—32no—
186C3×(C2×D3)⋊C4—32no—
187C3×(C2×D3)⋊C4—62no—
188C3×(C2×D3)⋊C4C2×D312yescomplemented
189C3×(C2×D3)⋊C4C22×C312yescomplemented
190C3×Dic3⋊C4—22no—
191C3×Dic3⋊C4—32no—
192C3×Dic3⋊C4—32no—
193C3×Dic3⋊C4—62no—
194C3×Dic3⋊C4C2×D312yescomplemented
195C3×Dic3⋊C4C22×C312yescomplemented
196(C2×D3)⋊Dic3C22×C312yescomplemented
197(C2×D3)⋊Dic3C22×C312yescomplemented
198(C2×D3)⋊Dic3C22×C312yescomplemented
199C22×C33—22no—
200C22×C33C2×D412yes—
201C22×C33C2411yescharacteristic
202C2×C3×C3⋊D3—21no—
203C2×C3×C3⋊D3—22no—
204C2×C32×D3—22no—
205C2×C32×D3—22no—
206C2×C32×D3—22no—
207C2×C32×D3—21no—
208C2×C32×D3—22no—
209C2×C32×D3—22no—
210C2×C32×D3—22no—
211C2×C32×D3—44no—
212C2×C32×D3—44no—
213C2×C32×D3C2×D412yes—
214C2×C32×D3C2×D412yes—
215C3×D32—44no—
216C33×C4—22no—
217C3×C3⋊Dic3—21no—
218C3×C3⋊Dic3—22no—
219C32×Dic3—21no—
220C32×Dic3—22no—
221C22×C3×D4—31no—
222C22×C3×D4—31no—
223C22×C3×D4—61no—
224C22×C3×D4—91no—
225C22×#67—31no—
226C2×D3×D4—31no—
227C22×D12C3×D311yescharacteristic, complemented
228C3×#123—31no—
229C3×#123—31no—
230C3×#123—61no—
231C3×#123—92no—
232C3×#123—91no—
233C3×#121—92no—
234C3×#121—92no—
235C3×#120—92no—
236C3×#120—91no—
237C3×#120—91no—
238C2×C3×C22⋊C4—91no—
239#953—31no—
240#953—31no—
241C2×#217—31no—
242#939—32no—
243#939—32no—
244#937—31no—
245#937—32no—
246#935—32no—
247#929—31no—
248#929—31no—
249#929—61no—
250#929C3×D311yescharacteristic, complemented
251#895—32no—
252#894—32no—
253#884—32no—
254#882—31no—
255#882—32no—
256D3×C22⋊C4—31no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32—21no—
260C23×C32—31no—
261C23×C32—31no—
262C23×C32—34no—
263C23×C32—31no—
264C23×C32—32no—
265C23×C32—41no—
266C23×C32—62no—
267C23×C32—122no—
268C23×C32—122no—
269C23×C32C22×D311yescharacteristic
270C23×C32C22×D311yescharacteristic
271C23×C32C23×C311yescharacteristic
272C22×C3⋊D3C23×C311yescharacteristic
273C22×C3×D3—24no—
274C22×C3×D3—22no—
275C22×C3×D3—22no—
276C22×C3×D3—24no—
277C22×C3×D3—22no—
278C22×C3×D3—21no—
279C22×C3×D3—21no—
280C22×C3×D3—21no—
281C22×C3×D3—31no—
282C22×C3×D3—31no—
283C22×C3×D3—42no—
284C22×C3×D3—42no—
285C22×C3×D3—42no—
286C22×C3×D3—42no—
287C22×C3×D3—44no—
288C22×C3×D3—44no—
289C22×C3×D3—61no—
290C22×C3×D3—62no—
291C22×C3×D3—62no—
292C22×C3×D3—122no—
293C22×C3×D3—122no—
294C22×C3×D3#6714yescomplemented
295C22×C3×D3C3×D414yescomplemented
296C22×C3×D3C22×D311yescharacteristic
297C22×C3×D3C22×D312yes—
298C22×C3×D3C22×D311yescharacteristic
299C22×C3×D3C22×D311yescharacteristic
300C22×C3×D3C23×C311yescharacteristic
301C22×C3×D3C23×C312yes—
302C22×C3×D3C23×C311yescharacteristic
303C22×C3×D3C23×C311yescharacteristic
304C2×D32—22no—
305C2×D32—42no—
306C32×D4—64no—
307C32×D4—64no—
308C32×D4—62no—
309C2×C32×C4—22no—
310C2×C32×C4—24no—
311C2×C32×C4—22no—
312C2×C32×C4—22no—
313C2×C32×C4—22no—
314C2×C32×C4—22no—
315C2×C32×C4—22no—
316C2×C32×C4—32no—
317C2×C32×C4—31no—
318C2×C32×C4—42no—
319C2×C32×C4—42no—
320C2×C32×C4—42no—
321C2×C32×C4—44no—
322C2×C32×C4C22×D312yes—
323C2×C32×C4C22×D312yes—
324C2×C32×C4C23×C312yes—
325#638—22no—
326C2×C3⋊Dic3C23×C311yescharacteristic
327C2×C3⋊Dic3C23×C312yes—
328C3×#67—22no—
329C3×#67—22no—
330C3×#67—42no—
331C3×#67—62no—
332C3×#67—62no—
333C3×#67—62no—
334C3×#67—62no—
335C3×#67—62no—
336C3×#67—122no—
337C3×#67—122no—
338C3×#67—122no—
339C3×#67—122no—
340C2×C3×Dic3—21no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—31no—
343C2×C3×Dic3—31no—
344C2×C3×Dic3—32no—
345C2×C3×Dic3—32no—
346C2×C3×Dic3—61no—
347C2×C3×Dic3—62no—
348C2×C3×Dic3—62no—
349C2×C3×Dic3—122no—
350C2×C3×Dic3C22×D311yescharacteristic
351C2×C3×Dic3C22×D312yes—
352C2×C3×Dic3C23×C311yescharacteristic
353C2×C3×Dic3C23×C312yes—
354C3×D12—28no—
355C3×D12—28no—
356C3×D12—24no—
357C3×D12—24no—
358C3×D12—24no—
359C3×D12—24no—
360C3×D12—62no—
361C3×D12—122no—
362C3×C4×D3—62no—
363C3×C4×D3—122no—
364#626—22no—
365#626—42no—
366#625—22no—
367#625—42no—
368D3×Dic3—22no—
369D3×Dic3—42no—
370#534—91noSylow
371C2×C33—22no—
372C2×C33C22×D411yescharacteristic
373C2×C33H(5,𝔽2)12yes—
374C3×C3⋊D3—41no—
375C32×D3—22no—
376C32×D3—22no—
377C32×D3—42no—
378C32×D3—41no—
379C24×C3—31no—
380C24×C3—31no—
381C24×C3—31no—
382C24×C3—31no—
383C24×C3—61no—
384C24×C3—61no—
385C24×C3—91no—
386C23×D3—31no—
387C23×D3—31no—
388C23×D3C2×C3×D311yescharacteristic
389C23×D3C2×C3×D311yescharacteristic, complemented
390C2×C3×D4—31no—
391C2×C3×D4—31no—
392C2×C3×D4—32no—
393C2×C3×D4—32no—
394C2×C3×D4—32no—
395C2×C3×D4—32no—
396C2×C3×D4—62no—
397C2×C3×D4—62no—
398C2×C3×D4—61no—
399C2×C3×D4—64no—
400C2×C3×D4—64no—
401C2×C3×D4—68no—
402C2×C3×D4—91no—
403C2×C3×D4—92no—
404C2×C3×D4—91no—
405C2×C3×D4—91no—
406C2×C3×D4—92no—
407C2×C3×D4—184no—
408C22×C3×C4—21no—
409C22×C3×C4—21no—
410C22×C3×C4—21no—
411C22×C3×C4—41no—
412C22×C3×C4—91no—
413C22×C3×C4—92no—
414C22×C3×C4D3211yescharacteristic, complemented
415C22×C3×C4C2×C3×D311yescharacteristic, complemented
416C22×C3×C4C2×C3×D311yescharacteristic, complemented
417C2×#67—31no—
418C2×#67—31no—
419C2×#67—31no—
420C2×#67—31no—
421C2×#67—32no—
422C2×#67—32no—
423C2×#67—31no—
424C2×#67—32no—
425C2×#67—61no—
426C2×#67—64no—
427C2×#67C2×C3×D311yescharacteristic
428C22×Dic3—31no—
429C22×Dic3—32no—
430D3×D4—64no—
431C2×D12—24no—
432C2×D12—31no—
433C2×D12—32no—
434C2×D12C2×C3×D312yes—
435C2×D12C2×C3×D312yescomplemented
436C2×C4×D3—31no—
437C2×C4×D3—32no—
438C3×C4⋊C4—32no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—62no—
441C3×C4⋊C4—92no—
442C3×C22⋊C4—31no—
443C3×C22⋊C4—31no—
444C3×C22⋊C4—32no—
445C3×C22⋊C4—32no—
446C3×C22⋊C4—62no—
447C3×C22⋊C4—61no—
448C3×C22⋊C4—92no—
449C3×C22⋊C4—92no—
450C3×C22⋊C4—92no—
451C3×C22⋊C4—91no—
452C3×C22⋊C4—92no—
453#217—31no—
454#217—31no—
455#217—32no—
456#217—32no—
457#217—32no—
458#217—61no—
459#217C2×C3×D311yescharacteristic, complemented
460(C2×D3)⋊C4—32no—
461(C2×D3)⋊C4—32no—
462(C2×D3)⋊C4—32no—
463(C2×D3)⋊C4—32no—
464(C2×D3)⋊C4—32no—
465(C2×D3)⋊C4—62no—
466(C2×D3)⋊C4C2×C3×D312yescomplemented
467Dic3⋊C4—32no—
468Dic3⋊C4—32no—
469Dic3⋊C4—62no—
470Dic3⋊C4C2×C3×D312yescomplemented
471C22×C32—22no—
472C22×C32—24no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—32no—
482C22×C32—32no—
483C22×C32—42no—
484C22×C32—41no—
485C22×C32—42no—
486C22×C32—42no—
487C22×C32—44no—
488C22×C32—62no—
489C22×C32—62no—
490C22×C32—62no—
491C22×C32—62no—
492C22×C32—62no—
493C22×C32—62no—
494C22×C32—61no—
495C22×C32—124no—
496C22×C32—124no—
497C22×C32D3×D412yes—
498C22×C32C2×#6712yes—
499C22×C32C2×C3×D412yes—
500C22×C32C23×D311yescharacteristic
501C22×C32C23×D311yescharacteristic
502C22×C32C24×C311yescharacteristic
503C2×C3⋊D3—21no—
504C2×C3⋊D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—24no—
510C2×C3×D3—21no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—21no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—42no—
523C2×C3×D3—42no—
524C2×C3×D3—42no—
525C2×C3×D3—42no—
526C2×C3×D3—41no—
527C2×C3×D3—42no—
528C2×C3×D3—44no—
529C2×C3×D3—44no—
530C2×C3×D3—48no—
531C2×C3×D3—48no—
532C2×C3×D3—44no—
533C2×C3×D3—44no—
534C2×C3×D3—61no—
535C2×C3×D3—62no—
536C2×C3×D3—62no—
537C2×C3×D3—61no—
538C2×C3×D3—121no—
539C2×C3×D3—122no—
540C2×C3×D3—124no—
541C2×C3×D3—124no—
542C2×C3×D3C2×#6712yes—
543C2×C3×D3C2×#6712yes—
544C2×C3×D3C2×C3×D412yes—
545C2×C3×D3C2×C3×D412yes—
546D32—44no—
547C32×C4—22no—
548C32×C4—24no—
549C32×C4—22no—
550C32×C4—22no—
551C32×C4—42no—
552C32×C4—42no—
553C32×C4—44no—
554C32×C4—62no—
555C32×C4—61no—
556C3⋊Dic3—21no—
557C3⋊Dic3—22no—
558C3×Dic3—21no—
559C3×Dic3—22no—
560C3×Dic3—21no—
561C3×Dic3—22no—
562C3×Dic3—42no—
563C3×Dic3—41no—
564C3×Dic3—61no—
565C3×Dic3—62no—
566C3×Dic3—62no—
567C3×Dic3—61no—
568C3×Dic3—122no—
569C3×Dic3—121no—
570C22×D4—31no—
571C22×D4—91no—
572#123—31no—
573#123—92no—
574#123—91no—
575#121—92no—
576#121—92no—
577#120—92no—
578#120—91no—
579#120—91no—
580C2×C22⋊C4—91no—
581C33#53411yescharacteristic, complemented, Sylow
582C23×C3—21no—
583C23×C3—21no—
584C23×C3—21no—
585C23×C3—31no—
586C23×C3—31no—
587C23×C3—31no—
588C23×C3—31no—
589C23×C3—34no—
590C23×C3—34no—
591C23×C3—31no—
592C23×C3—32no—
593C23×C3—32no—
594C23×C3—31no—
595C23×C3—41no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—64no—
599C23×C3—62no—
600C23×C3—61no—
601C23×C3—64no—
602C23×C3—62no—
603C23×C3—62no—
604C23×C3—91no—
605C23×C3—122no—
606C23×C3—122no—
607C23×C3—122no—
608C23×C3—122no—
609C23×C3—124no—
610C23×C3—124no—
611C23×C3—182no—
612C23×C3—362no—
613C23×C3C2×D3211yescharacteristic
614C23×C3C22×C3×D311yescharacteristic
615C23×C3C22×C3×D311yescharacteristic
616C22×D3—22no—
617C22×D3—31no—
618C22×D3—31no—
619C22×D3—42no—
620C22×D3—42no—
621C22×D3—61no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—122no—
625C22×D3—122no—
626C22×D3C3×#6714yescomplemented
627C22×D3C22×C3×D312yes—
628C22×D3C22×C3×D311yescharacteristic
629C22×D3C22×C3×D311yescharacteristic
630C22×D3C22×C3×D311yescharacteristic
631C3×D4—64no—
632C3×D4—64no—
633C3×D4—64no—
634C3×D4—64no—
635C3×D4—68no—
636C3×D4—68no—
637C3×D4—62no—
638C3×D4—62no—
639C3×D4—122no—
640C3×D4—182no—
641C3×D4—182no—
642C3×D4—182no—
643C3×D4—362no—
644C3×D4—362no—
645C2×C3×C4—24no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—32no—
653C2×C3×C4—31no—
654C2×C3×C4—32no—
655C2×C3×C4—31no—
656C2×C3×C4—42no—
657C2×C3×C4—42no—
658C2×C3×C4—44no—
659C2×C3×C4—42no—
660C2×C3×C4—62no—
661C2×C3×C4—61no—
662C2×C3×C4—92no—
663C2×C3×C4—91no—
664C2×C3×C4—182no—
665C2×C3×C4—362no—
666C2×C3×C4C2×D3212yes—
667C2×C3×C4C22×C3×D312yes—
668C2×C3×C4C22×C3×D312yes—
669#67—22no—
670#67—62no—
671#67—62no—
672#67—62no—
673#67—62no—
674#67—62no—
675#67—122no—
676#67—122no—
677#67—122no—
678#67—122no—
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—32no—
682C2×Dic3—32no—
683C2×Dic3—61no—
684C2×Dic3—62no—
685C2×Dic3—62no—
686C2×Dic3—122no—
687C2×Dic3C22×C3×D311yescharacteristic
688C2×Dic3C22×C3×D312yes—
689D12—24no—
690D12—24no—
691D12—62no—
692D12—122no—
693C4×D3—62no—
694C4×D3—122no—
695C2×C32—22no—
696C2×C32—24no—
697C2×C32—22no—
698C2×C32—22no—
699C2×C32—22no—
700C2×C32—21no—
701C2×C32—21no—
702C2×C32—22no—
703C2×C32—22no—
704C2×C32—21no—
705C2×C32—41no—
706C2×C32—42no—
707C2×C32—42no—
708C2×C32—42no—
709C2×C32—44no—
710C2×C32—62no—
711C2×C32—62no—
712C2×C32—122no—
713C2×C32—121no—
714C2×C32C2×D3×D411yescharacteristic
715C2×C32#100412yes—
716C2×C32#100912yes—
717C2×C32C22×#6711yescharacteristic
718C2×C32C22×C3×D411yescharacteristic
719C2×C32C3×H(5,𝔽2)12yes—
720C3⋊D3—41no—
721C3×D3—22no—
722C3×D3—22no—
723C3×D3—22no—
724C3×D3—22no—
725C3×D3—42no—
726C3×D3—42no—
727C3×D3—44no—
728C3×D3—41no—
729C3×D3—42no—
730C3×D3—41no—
731C3×D3—42no—
732C3×D3—81no—
733C3×D3—121no—
734C3×D3—121no—
735C3×D3—241no—
736C24—31no—
737C24—31no—
738C24—91no—
739C2×D4—31no—
740C2×D4—32no—
741C2×D4—32no—
742C2×D4—64no—
743C2×D4—91no—
744C2×D4—92no—
745C2×D4—91no—
746C2×D4—91no—
747C2×D4—92no—
748C2×D4—184no—
749C22×C4—91no—
750C22×C4—92no—
751C22×C4C3×D3211yescharacteristic, complemented
752C4⋊C4—32no—
753C4⋊C4—92no—
754C22⋊C4—31no—
755C22⋊C4—32no—
756C22⋊C4—92no—
757C22⋊C4—92no—
758C22⋊C4—92no—
759C22⋊C4—91no—
760C22⋊C4—92no—
761C22×C3—24no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—32no—
772C22×C3—32no—
773C22×C3—32no—
774C22×C3—32no—
775C22×C3—42no—
776C22×C3—42no—
777C22×C3—44no—
778C22×C3—41no—
779C22×C3—42no—
780C22×C3—62no—
781C22×C3—62no—
782C22×C3—64no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—61no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—61no—
797C22×C3—122no—
798C22×C3—122no—
799C22×C3—122no—
800C22×C3—122no—
801C22×C3—121no—
802C22×C3—122no—
803C22×C3—124no—
804C22×C3—124no—
805C22×C3—128no—
806C22×C3—128no—
807C22×C3—124no—
808C22×C3—124no—
809C22×C3—182no—
810C22×C3—181no—
811C22×C3—364no—
812C22×C3D3×#6712yes—
813C22×C3C3×D3×D412yes—
814C22×C3C2×C3×#6712yes—
815C22×C3C22×D3211yescharacteristic
816C22×C3C23×C3×D311yescharacteristic
817C22×C3C23×C3×D311yescharacteristic
818C2×D3—22no—
819C2×D3—22no—
820C2×D3—21no—
821C2×D3—22no—
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—44no—
826C2×D3—44no—
827C2×D3—61no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—61no—
831C2×D3—121no—
832C2×D3—122no—
833C2×D3—124no—
834C2×D3—124no—
835C2×D3C2×C3×#6712yes—
836C2×D3C2×C3×#6712yes—
837C3×C4—24no—
838C3×C4—22no—
839C3×C4—22no—
840C3×C4—22no—
841C3×C4—42no—
842C3×C4—42no—
843C3×C4—44no—
844C3×C4—62no—
845C3×C4—61no—
846C3×C4—62no—
847C3×C4—61no—
848C3×C4—121no—
849C3×C4—122no—
850C3×C4—182no—
851C3×C4—181no—
852Dic3—21no—
853Dic3—22no—
854Dic3—61no—
855Dic3—62no—
856Dic3—62no—
857Dic3—61no—
858Dic3—121no—
859Dic3—122no—
860C32—21no—
861C32—21no—
862C32—21no—
863C32—41no—
864C32#565311yescharacteristic, complemented
865C32#580411yescharacteristic, complemented
866C32C3×#53411yescharacteristic, complemented
867C23—31no—
868C23—31no—
869C23—34no—
870C23—31no—
871C23—32no—
872C23—62no—
873C23—91no—
874C23—122no—
875C23—122no—
876C23—182no—
877C23—362no—
878C23C2×C3×D3211yescharacteristic
879D4—64no—
880D4—64no—
881D4—62no—
882D4—182no—
883D4—182no—
884D4—182no—
885D4—362no—
886D4—362no—
887C2×C4—22no—
888C2×C4—32no—
889C2×C4—31no—
890C2×C4—92no—
891C2×C4—91no—
892C2×C4—182no—
893C2×C4—362no—
894C2×C4C2×C3×D3212yes—
895C2×C3—24no—
896C2×C3—22no—
897C2×C3—22no—
898C2×C3—22no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—22no—
903C2×C3—22no—
904C2×C3—22no—
905C2×C3—42no—
906C2×C3—42no—
907C2×C3—44no—
908C2×C3—41no—
909C2×C3—42no—
910C2×C3—62no—
911C2×C3—62no—
912C2×C3—62no—
913C2×C3—62no—
914C2×C3—122no—
915C2×C3—122no—
916C2×C3—124no—
917C2×C3—121no—
918C2×C3—122no—
919C2×C3—122no—
920C2×C3—121no—
921C2×C3—241no—
922C2×C3—361no—
923C2×C3#6430712yes—
924C2×C3C2×D3×#6711yescharacteristic
925C2×C3C2×C3×D3×D411yescharacteristic
926C2×C3C3×#100412yes—
927C2×C3C3×#100912yes—
928C2×C3C22×C3×#6711yescharacteristic
929D3—22no—
930D3—22no—
931D3—42no—
932D3—41no—
933D3—121no—
934D3—121no—
935D3—241no—
936C22—22no—
937C22—32no—
938C22—32no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—61no—
943C22—62no—
944C22—62no—
945C22—62no—
946C22—124no—
947C22—124no—
948C22—181no—
949C22—182no—
950C22—364no—
951C22C3×D3×#6712yes—
952C22C22×C3×D3211yescharacteristic
953C4—22no—
954C4—61no—
955C4—62no—
956C4—181no—
957C4—182no—
958C3—21no—
959C3—21no—
960C3—21no—
961C3—41no—
962C3#1059506211yescharacteristic, direct product factor
963C3C3×#565311yescharacteristic, complemented
964C3C3×#580411yescharacteristic, complemented
965C2—22no—
966C2—62no—
967C2—62no—
968C2—122no—
969C2—121no—
970C2—361no—
971C2C3×#6430712yes—
972C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×D12C2semidirect
2. C2×C3×D3×#67C2semidirect
3. C3×#64138C2semidirect
4. C32×#929C2semidirect
5. C3×#63977C2semidirect
6. C3×#63976C2semidirect
7. C3×D3×#217C2semidirect
8. C3×#63922C2semidirect
9. C3×#63886C2semidirect
10. C3×#63885C2semidirect
11. C3×#63884C2semidirect
14. #10595062C3direct (N × H)
16. C23×C32×D3C22semidirect
17. C22×C3×D32C22semidirect
18. C22×C33×C4C22semidirect
23. C2×C32×D12C22semidirect
25. C2×C3×#626C22semidirect
26. C2×C3×#626C22semidirect
27. C2×C3×#625C22semidirect
28. C2×C3×#625C22semidirect
29. C2×C3×D3×Dic3C22semidirect
30. C2×C3×D3×Dic3C22semidirect
31. C3×#3757C22semidirect
32. C3×#3752C22semidirect
33. C3×#3750C22semidirect
34. C32×#217C22semidirect
35. C32×(C2×D3)⋊C4C22semidirect
36. C32×Dic3⋊C4C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
44. C22×C3×D12D3semidirect
45. C22×C3×D12C2×C3semidirect
46. C2×D3×#67C2×C3semidirect
48. #64138C2×C3semidirect
61. C3×#929D3semidirect
62. C3×#929C2×C3semidirect
69. #63977C2×C3semidirect
70. #63976C2×C3semidirect
71. D3×#217C2×C3semidirect
72. #63922C2×C3semidirect
73. #63886C2×C3semidirect
74. #63885C2×C3semidirect
75. #63884C2×C3semidirect
81. C22×C32×D3D4semidirect
114. C23×C3×D3C2×D3semidirect
116. C23×C3×D3C22×C3semidirect
117. C22×D32C22×C3semidirect
126. C22×C32×C4C2×D3semidirect
127. C22×C32×C4C2×D3semidirect
128. C22×C32×C4C22×C3semidirect
154. C2×C3×D12C2×D3semidirect
156. C2×C3×D12C22×C3semidirect
160. C2×#626C22×C3semidirect
161. C2×#626C22×C3semidirect
162. C2×#625C22×C3semidirect
163. C2×#625C22×C3semidirect
164. C2×D3×Dic3C22×C3semidirect
165. C2×D3×Dic3C22×C3semidirect
169. #3757C22×C3semidirect
170. #3752C22×C3semidirect
171. #3750C22×C3semidirect
179. C3×#217C2×D3semidirect
180. C3×#217C22×C3semidirect
188. C3×(C2×D3)⋊C4C2×D3semidirect
189. C3×(C2×D3)⋊C4C22×C3semidirect
194. C3×Dic3⋊C4C2×D3semidirect
195. C3×Dic3⋊C4C22×C3semidirect
196. (C2×D3)⋊Dic3C22×C3semidirect
197. (C2×D3)⋊Dic3C22×C3semidirect
198. (C2×D3)⋊Dic3C22×C3semidirect
227. C22×D12C3×D3semidirect
250. #929C3×D3semidirect
294. C22×C3×D3#67semidirect
295. C22×C3×D3C3×D4semidirect
389. C23×D3C2×C3×D3semidirect
414. C22×C3×C4D32semidirect
415. C22×C3×C4C2×C3×D3semidirect
416. C22×C3×C4C2×C3×D3semidirect
435. C2×D12C2×C3×D3semidirect
459. #217C2×C3×D3semidirect
466. (C2×D3)⋊C4C2×C3×D3semidirect
470. Dic3⋊C4C2×C3×D3semidirect
581. C33#534semidirect
626. C22×D3C3×#67semidirect
751. C22×C4C3×D32semidirect
864. C32#5653semidirect
865. C32#5804semidirect
866. C32C3×#534semidirect
962. C3#10595062direct (N × H)
963. C3C3×#5653semidirect
964. C3C3×#5804semidirect

Maximal subgroups

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

subgroupindex
C22×C32×D122
C2×C3×D3×#672
C3×#641382
C32×#9292
C3×#639772
C3×#639762
C3×D3×#2172
C3×#639222
C3×#638862
C3×#638852
C3×#638842
C3×#58043
C3×#56533
#105950623