Finite Group Databasebeta

← C3×#10595230 #13174793

Subgroups — C3×#10595230 #13174793

Order 1728.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic, complemented
2C22×C3×#625C211yesmaximal, characteristic, complemented
3C3×#64144C211yesmaximal, characteristic, complemented
4C32×#937C211yesmaximal, characteristic, complemented
5C3×#63976C212yesmaximal, complemented
6C3×#63976C211yesmaximal, characteristic, complemented
7C3×#63970C212yesmaximal, complemented
8C3×D3×#217C211yesmaximal, characteristic, complemented
9C3×#63962C211yesmaximal, characteristic, complemented
10C3×#63905C212yesmaximal, complemented
11C3×#63885C212yesmaximal, complemented
12C3×#5804—31nomaximal
13C3×#5589—31nomaximal
14#10595230C311yesmaximal, characteristic, direct product factor
15C23×C32×D3C2211yescharacteristic
16C23×C32×D3C2211yescharacteristic, complemented
17C23×C32×D3C2211yescharacteristic, complemented
18C2×C33×D4C2211yescharacteristic
19C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
20C2×C32×#67C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic, complemented
22C2×C32×#67C2212yescomplemented
23C32×D3×D4—24no—
24C2×C32×D12C2211yescharacteristic, complemented
25C2×C32×C4×D3C2211yescharacteristic, complemented
26C2×C3×#625—24no—
27C2×C3×#625C2212yes—
28C2×C3×#625C2212yescomplemented
29C2×C3×#625C2212yescomplemented
30C2×C3×D3×Dic3C2212yescomplemented
31C3×#3757C2211yescharacteristic, complemented
32C3×#3757C2212yescomplemented
33C3×#3750C2212yescomplemented
34C32×#217C2211yescharacteristic, complemented
35C32×(C2×D3)⋊C4C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C22×C32×D4—31no—
41C22×C3×#67—31no—
42C22×C3×#67—31no—
43C2×C3×D3×D4—21no—
44C2×C3×D3×D4D311yescharacteristic, complemented
45C2×C3×D3×D4C2×C311yescharacteristic, complemented
46C22×#625C2×C311yescharacteristic, complemented
47C32×#120—31no—
48#64144C2×C311yescharacteristic, complemented
49C3×#953—31no—
50C3×#953—32no—
51C2×C3×#217—31no—
52C3×#939—32no—
53C3×#939—32no—
54C3×#938—32no—
55C3×#937—21no—
56C3×#937—31no—
57C3×#937—32no—
58C3×#937D311yescharacteristic, complemented
59C3×#937C2×C311yescharacteristic, complemented
60C3×#935—31no—
61C3×#935—31no—
62C3×#935—31no—
63C3×#935—61no—
64C3×#929—32no—
65C3×#886—31no—
66C3×#884—32no—
67C3×#883—32no—
68C3×D3×C22⋊C4—31no—
69#63976C2×C312yescomplemented
70#63976C2×C311yescharacteristic, complemented
71#63970C2×C312yescomplemented
72D3×#217C2×C311yescharacteristic, complemented
73#63962C2×C311yescharacteristic, complemented
74#63905C2×C312yescomplemented
75#63885C2×C312yescomplemented
76C23×C33C2311yescharacteristic
77C23×C33C2311yescharacteristic
78C22×C32×D3—22no—
79C22×C32×D3—22no—
80C22×C32×D3—42no—
81C22×C32×D3—42no—
82C22×C32×D3—42no—
83C22×C32×D3D414yescomplemented
84C22×C32×D3C2312yes—
85C22×C32×D3C2311yescharacteristic
86C22×C32×D3C2311yescharacteristic
87C22×C32×D3C2311yescharacteristic
88C33×D4—22no—
89C2×C33×C4C2311yescharacteristic
90C2×C3×C3⋊Dic3—22no—
91C2×C3×C3⋊Dic3C2312yes—
92C2×C3×C3⋊Dic3C2312yes—
93C32×#67—22no—
94C32×#67—22no—
95C32×#67—42no—
96C2×C32×Dic3C2312yes—
97C2×C32×Dic3C2311yescharacteristic
98C32×D12—22no—
99C32×C4×D3—22no—
100C3×#625—24no—
101C3×#625—24no—
102C3×#625—42no—
103C3×D3×Dic3—42no—
104C3×#534—91no—
105#5804—31no—
106#5589—31no—
107C24×C32—31no—
108C24×C32—31no—
109C24×C32—31no—
110C23×C3×D3—21no—
111C23×C3×D3—21no—
112C23×C3×D3—21no—
113C23×C3×D3C2×D311yescharacteristic
114C23×C3×D3C2×D311yescharacteristic, complemented
115C23×C3×D3C2×D311yescharacteristic, complemented
116C23×C3×D3C22×C311yescharacteristic
117C23×C3×D3C22×C311yescharacteristic, complemented
118C23×C3×D3C22×C311yescharacteristic, complemented
119C2×C32×D4—21no—
120C2×C32×D4—21no—
121C2×C32×D4—21no—
122C2×C32×D4—31no—
123C2×C32×D4—31no—
124C2×C32×D4—32no—
125C2×C32×D4—31no—
126C2×C32×D4—41no—
127C2×C32×D4—64no—
128C2×C32×D4C2×D311yescharacteristic
129C2×C32×D4C2×D311yescharacteristic
130C2×C32×D4C22×C311yescharacteristic
131C22×C32×C4—31no—
132C22×C3⋊Dic3C22×C311yescharacteristic, complemented
133C2×C3×#67—21no—
134C2×C3×#67—21no—
135C2×C3×#67—22no—
136C2×C3×#67—32no—
137C2×C3×#67—32no—
138C2×C3×#67—32no—
139C2×C3×#67—32no—
140C2×C3×#67—32no—
141C2×C3×#67—32no—
142C2×C3×#67—64no—
143C2×C3×#67—64no—
144C2×C3×#67C2×D311yescharacteristic
145C2×C3×#67C2×D311yescharacteristic, complemented
146C2×C3×#67C2×D312yescomplemented
147C2×C3×#67C22×C311yescharacteristic
148C2×C3×#67C22×C311yescharacteristic, complemented
149C2×C3×#67C22×C312yescomplemented
150C22×C3×Dic3—31no—
151C22×C3×Dic3—31no—
152C22×C3×Dic3—32no—
153C22×C3×Dic3—61no—
154C3×D3×D4—28no—
155C3×D3×D4—24no—
156C3×D3×D4—24no—
157C2×C3×D12—21no—
158C2×C3×D12C2×D311yescharacteristic, complemented
159C2×C3×D12C22×C311yescharacteristic, complemented
160C2×C3×C4×D3—21no—
161C2×C3×C4×D3—32no—
162C2×C3×C4×D3C2×D311yescharacteristic, complemented
163C2×C3×C4×D3C22×C311yescharacteristic, complemented
164C2×#625—24no—
165C2×#625C22×C312yes—
166C2×#625C22×C312yescomplemented
167C2×#625C22×C312yescomplemented
168C2×D3×Dic3C22×C312yescomplemented
169C32×C22⋊C4—31no—
170C32×C22⋊C4—32no—
171#3757C22×C311yescharacteristic, complemented
172#3757C22×C312yescomplemented
173#3750C22×C312yescomplemented
174C3×#217—21no—
175C3×#217—31no—
176C3×#217—32no—
177C3×#217—31no—
178C3×#217—32no—
179C3×#217—32no—
180C3×#217—32no—
181C3×#217—32no—
182C3×#217—61no—
183C3×#217—62no—
184C3×#217C2×D311yescharacteristic, complemented
185C3×#217C22×C311yescharacteristic, complemented
186C3×(C2×D3)⋊C4—22no—
187C3×(C2×D3)⋊C4—32no—
188C3×(C2×D3)⋊C4—32no—
189C3×(C2×D3)⋊C4—32no—
190C3×(C2×D3)⋊C4C2×D312yescomplemented
191C3×(C2×D3)⋊C4C22×C312yescomplemented
192C3×C4⋊Dic3—32no—
193C3×Dic3⋊C4—32no—
194C3×Dic3⋊C4—32no—
195C3×Dic3⋊C4—32no—
196C3×Dic3⋊C4—62no—
197Dic3⋊Dic3C22×C312yescomplemented
198(C2×D3)⋊Dic3C22×C312yescomplemented
199(C2×D3)⋊Dic3C22×C312yescomplemented
200(C2×D3)⋊Dic3C22×C312yescomplemented
201C22×C33—22no—
202C22×C33—21no—
203C22×C33—22no—
204C22×C33C2×D412yes—
205C22×C33C2411yescharacteristic
206C2×C32×D3—22no—
207C2×C32×D3—22no—
208C2×C32×D3—21no—
209C2×C32×D3—22no—
210C2×C32×D3—22no—
211C2×C32×D3—22no—
212C2×C32×D3—22no—
213C2×C32×D3—44no—
214C2×C32×D3—44no—
215C2×C32×D3—44no—
216C2×C32×D3C2×D412yes—
217C2×C32×D3C2×D412yes—
218C33×C4—21no—
219C3×C3⋊Dic3—22no—
220C3×C3⋊Dic3—22no—
221C32×Dic3—21no—
222C32×Dic3—22no—
223C22×C3×D4—31no—
224C22×C3×D4—31no—
225C22×C3×D4—61no—
226C22×C3×D4—91no—
227C22×#67—31no—
228C22×#67—31no—
229C2×D3×D4C3×D311yescharacteristic, complemented
230C3×#123—92no—
231C3×#123—91no—
232C3×#123—91no—
233C3×#121—92no—
234C3×#121—92no—
235C3×#120—31no—
236C3×#120—31no—
237C3×#120—61no—
238C3×#120—92no—
239C3×#120—91no—
240C2×C3×C22⋊C4—91no—
241#953—31no—
242#953—32no—
243C2×#217—31no—
244#939—32no—
245#939—32no—
246#938—32no—
247#937—31no—
248#937—32no—
249#937C3×D311yescharacteristic, complemented
250#935—31no—
251#935—31no—
252#935—31no—
253#935—61no—
254#929—32no—
255#886—31no—
256#884—32no—
257#883—32no—
258D3×C22⋊C4—31no—
259C23×C32—21no—
260C23×C32—21no—
261C23×C32—21no—
262C23×C32—21no—
263C23×C32—21no—
264C23×C32—21no—
265C23×C32—31no—
266C23×C32—31no—
267C23×C32—34no—
268C23×C32—31no—
269C23×C32—32no—
270C23×C32—41no—
271C23×C32—41no—
272C23×C32—62no—
273C23×C32—62no—
274C23×C32—122no—
275C23×C32—122no—
276C23×C32—122no—
277C23×C32C22×D311yescharacteristic
278C23×C32C22×D311yescharacteristic
279C23×C32C22×D311yescharacteristic
280C23×C32C22×D311yescharacteristic
281C23×C32C23×C311yescharacteristic
282C23×C32C23×C311yescharacteristic
283C22×C3×D3—24no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—24no—
289C22×C3×D3—21no—
290C22×C3×D3—22no—
291C22×C3×D3—21no—
292C22×C3×D3—21no—
293C22×C3×D3—42no—
294C22×C3×D3—42no—
295C22×C3×D3—42no—
296C22×C3×D3—42no—
297C22×C3×D3—42no—
298C22×C3×D3—42no—
299C22×C3×D3—42no—
300C22×C3×D3—44no—
301C22×C3×D3—44no—
302C22×C3×D3—44no—
303C22×C3×D3#6714yescomplemented
304C22×C3×D3C3×D414yescomplemented
305C22×C3×D3C22×D311yescharacteristic
306C22×C3×D3C22×D312yes—
307C22×C3×D3C22×D311yescharacteristic
308C22×C3×D3C22×D311yescharacteristic
309C22×C3×D3C23×C311yescharacteristic
310C22×C3×D3C23×C312yes—
311C22×C3×D3C23×C311yescharacteristic
312C22×C3×D3C23×C311yescharacteristic
313C32×D4—22no—
314C32×D4—24no—
315C32×D4—22no—
316C32×D4—22no—
317C32×D4—42no—
318C32×D4—42no—
319C32×D4—44no—
320C32×D4—62no—
321C32×D4—62no—
322C32×D4—62no—
323C32×D4—122no—
324C2×C32×C4—21no—
325C2×C32×C4—21no—
326C2×C32×C4—21no—
327C2×C32×C4—31no—
328C2×C32×C4—32no—
329C2×C32×C4—41no—
330C2×C32×C4—62no—
331C2×C32×C4C22×D311yescharacteristic
332C2×C32×C4C22×D311yescharacteristic
333C2×C32×C4C23×C311yescharacteristic
334C2×C3⋊Dic3—22no—
335C2×C3⋊Dic3C23×C312yes—
336C2×C3⋊Dic3C23×C312yes—
337C3×#67—24no—
338C3×#67—24no—
339C3×#67—22no—
340C3×#67—22no—
341C3×#67—22no—
342C3×#67—22no—
343C3×#67—42no—
344C3×#67—42no—
345C3×#67—44no—
346C3×#67—64no—
347C3×#67—64no—
348C3×#67—64no—
349C3×#67—64no—
350C3×#67—122no—
351C3×#67—122no—
352C2×C3×Dic3—21no—
353C2×C3×Dic3—22no—
354C2×C3×Dic3—32no—
355C2×C3×Dic3—32no—
356C2×C3×Dic3—32no—
357C2×C3×Dic3—32no—
358C2×C3×Dic3—62no—
359C2×C3×Dic3—62no—
360C2×C3×Dic3—62no—
361C2×C3×Dic3—62no—
362C2×C3×Dic3—122no—
363C2×C3×Dic3—122no—
364C2×C3×Dic3C22×D312yes—
365C2×C3×Dic3C22×D311yescharacteristic
366C2×C3×Dic3C23×C311yescharacteristic
367C2×C3×Dic3C23×C312yes—
368C3×D12—24no—
369C3×D12—22no—
370C3×D12—22no—
371C3×C4×D3—24no—
372C3×C4×D3—22no—
373C3×C4×D3—22no—
374C3×C4×D3—122no—
375#625—24no—
376#625—24no—
377#625—42no—
378D3×Dic3—42no—
379#534—91noSylow
380C2×C33—22no—
381C2×C33—41no—
382C2×C33C22×D411yescharacteristic
383C2×C33H(5,𝔽2)12yes—
384C32×D3—22no—
385C32×D3—22no—
386C32×D3—41no—
387C32×D3—42no—
388C24×C3—31no—
389C24×C3—31no—
390C24×C3—31no—
391C24×C3—31no—
392C24×C3—31no—
393C24×C3—31no—
394C24×C3—61no—
395C24×C3—61no—
396C24×C3—61no—
397C23×D3C2×C3×D311yescharacteristic
398C23×D3C2×C3×D311yescharacteristic, complemented
399C23×D3C2×C3×D311yescharacteristic, complemented
400C2×C3×D4—21no—
401C2×C3×D4—21no—
402C2×C3×D4—21no—
403C2×C3×D4—31no—
404C2×C3×D4—31no—
405C2×C3×D4—31no—
406C2×C3×D4—31no—
407C2×C3×D4—32no—
408C2×C3×D4—32no—
409C2×C3×D4—31no—
410C2×C3×D4—31no—
411C2×C3×D4—41no—
412C2×C3×D4—61no—
413C2×C3×D4—61no—
414C2×C3×D4—61no—
415C2×C3×D4—62no—
416C2×C3×D4—64no—
417C2×C3×D4—64no—
418C2×C3×D4—68no—
419C2×C3×D4—92no—
420C2×C3×D4—92no—
421C2×C3×D4—92no—
422C2×C3×D4—184no—
423C2×C3×D4D3211yescharacteristic
424C2×C3×D4C2×C3×D311yescharacteristic
425C2×C3×D4C2×C3×D311yescharacteristic
426C22×C3×C4—31no—
427C22×C3×C4—31no—
428C22×C3×C4—61no—
429C22×C3×C4—92no—
430C22×C3×C4—91no—
431C2×#67—32no—
432C2×#67—32no—
433C2×#67—32no—
434C2×#67—32no—
435C2×#67—32no—
436C2×#67—32no—
437C2×#67—64no—
438C2×#67—64no—
439C2×#67C2×C3×D311yescharacteristic
440C2×#67C2×C3×D311yescharacteristic, complemented
441C2×#67C2×C3×D312yescomplemented
442C22×Dic3—31no—
443C22×Dic3—31no—
444C22×Dic3—32no—
445C22×Dic3—61no—
446D3×D4—24no—
447C2×D12C2×C3×D311yescharacteristic, complemented
448C2×C4×D3—32no—
449C2×C4×D3C2×C3×D311yescharacteristic, complemented
450C3×C4⋊C4—92no—
451C3×C4⋊C4—92no—
452C3×C22⋊C4—31no—
453C3×C22⋊C4—31no—
454C3×C22⋊C4—32no—
455C3×C22⋊C4—32no—
456C3×C22⋊C4—62no—
457C3×C22⋊C4—61no—
458C3×C22⋊C4—92no—
459C3×C22⋊C4—92no—
460C3×C22⋊C4—92no—
461C3×C22⋊C4—91no—
462C3×C22⋊C4—92no—
463#217—31no—
464#217—32no—
465#217—31no—
466#217—32no—
467#217—32no—
468#217—32no—
469#217—32no—
470#217—61no—
471#217—62no—
472#217C2×C3×D311yescharacteristic, complemented
473(C2×D3)⋊C4—32no—
474(C2×D3)⋊C4—32no—
475(C2×D3)⋊C4—32no—
476(C2×D3)⋊C4C2×C3×D312yescomplemented
477C4⋊Dic3—32no—
478Dic3⋊C4—32no—
479Dic3⋊C4—32no—
480Dic3⋊C4—32no—
481Dic3⋊C4—62no—
482C22×C32—21no—
483C22×C32—22no—
484C22×C32—22no—
485C22×C32—22no—
486C22×C32—22no—
487C22×C32—22no—
488C22×C32—22no—
489C22×C32—21no—
490C22×C32—21no—
491C22×C32—22no—
492C22×C32—21no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—22no—
496C22×C32—22no—
497C22×C32—22no—
498C22×C32—32no—
499C22×C32—32no—
500C22×C32—41no—
501C22×C32—42no—
502C22×C32—41no—
503C22×C32—41no—
504C22×C32—42no—
505C22×C32—42no—
506C22×C32—42no—
507C22×C32—42no—
508C22×C32—42no—
509C22×C32—42no—
510C22×C32—42no—
511C22×C32—62no—
512C22×C32—61no—
513C22×C32—62no—
514C22×C32—62no—
515C22×C32—62no—
516C22×C32—62no—
517C22×C32—62no—
518C22×C32—82no—
519C22×C32—82no—
520C22×C32—124no—
521C22×C32—124no—
522C22×C32—124no—
523C22×C32D3×D412yes—
524C22×C32C2×#6712yes—
525C22×C32C2×C3×D412yes—
526C22×C32C23×D311yescharacteristic
527C22×C32C23×D311yescharacteristic
528C22×C32C24×C311yescharacteristic
529C2×C3×D3—24no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D3—22no—
533C2×C3×D3—22no—
534C2×C3×D3—22no—
535C2×C3×D3—24no—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—21no—
541C2×C3×D3—22no—
542C2×C3×D3—21no—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3—42no—
549C2×C3×D3—42no—
550C2×C3×D3—42no—
551C2×C3×D3—42no—
552C2×C3×D3—44no—
553C2×C3×D3—44no—
554C2×C3×D3—48no—
555C2×C3×D3—48no—
556C2×C3×D3—44no—
557C2×C3×D3—44no—
558C2×C3×D3—44no—
559C2×C3×D3—44no—
560C2×C3×D3—48no—
561C2×C3×D3C2×#6712yes—
562C2×C3×D3C2×#6712yes—
563C2×C3×D3C2×C3×D412yes—
564C2×C3×D3C2×C3×D412yes—
565C32×C4—21no—
566C32×C4—22no—
567C32×C4—21no—
568C32×C4—21no—
569C32×C4—41no—
570C32×C4—41no—
571C32×C4—42no—
572C32×C4—61no—
573C32×C4—62no—
574C3⋊Dic3—22no—
575C3⋊Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—21no—
579C3×Dic3—21no—
580C3×Dic3—22no—
581C3×Dic3—42no—
582C3×Dic3—62no—
583C3×Dic3—62no—
584C3×Dic3—62no—
585C3×Dic3—62no—
586C3×Dic3—122no—
587C3×Dic3—122no—
588C22×D4—31no—
589C22×D4—91no—
590#123—92no—
591#123—91no—
592#123—91no—
593#121—92no—
594#121—92no—
595#120—31no—
596#120—92no—
597#120—91no—
598C2×C22⋊C4—91no—
599C33#53411yescharacteristic, complemented, Sylow
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—31no—
607C23×C3—31no—
608C23×C3—31no—
609C23×C3—31no—
610C23×C3—34no—
611C23×C3—34no—
612C23×C3—32no—
613C23×C3—31no—
614C23×C3—31no—
615C23×C3—32no—
616C23×C3—41no—
617C23×C3—41no—
618C23×C3—61no—
619C23×C3—62no—
620C23×C3—61no—
621C23×C3—64no—
622C23×C3—61no—
623C23×C3—62no—
624C23×C3—62no—
625C23×C3—64no—
626C23×C3—62no—
627C23×C3—62no—
628C23×C3—122no—
629C23×C3—122no—
630C23×C3—122no—
631C23×C3—122no—
632C23×C3—122no—
633C23×C3—122no—
634C23×C3—122no—
635C23×C3—124no—
636C23×C3—124no—
637C23×C3—124no—
638C23×C3C2×D3211yescharacteristic
639C23×C3C2×D3211yescharacteristic
640C23×C3C22×C3×D311yescharacteristic
641C23×C3C22×C3×D311yescharacteristic
642C23×C3C22×C3×D311yescharacteristic
643C23×C3C22×C3×D311yescharacteristic
644C22×D3—22no—
645C22×D3—22no—
646C22×D3—42no—
647C22×D3—42no—
648C22×D3—42no—
649C22×D3C3×#6714yescomplemented
650C22×D3C22×C3×D311yescharacteristic
651C22×D3C22×C3×D312yes—
652C22×D3C22×C3×D311yescharacteristic
653C22×D3C22×C3×D311yescharacteristic
654C3×D4—24no—
655C3×D4—22no—
656C3×D4—22no—
657C3×D4—22no—
658C3×D4—42no—
659C3×D4—42no—
660C3×D4—44no—
661C3×D4—62no—
662C3×D4—62no—
663C3×D4—64no—
664C3×D4—62no—
665C3×D4—62no—
666C3×D4—64no—
667C3×D4—64no—
668C3×D4—62no—
669C3×D4—62no—
670C3×D4—122no—
671C3×D4—122no—
672C3×D4—124no—
673C3×D4—184no—
674C3×D4—184no—
675C3×D4—362no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—32no—
680C2×C3×C4—31no—
681C2×C3×C4—31no—
682C2×C3×C4—32no—
683C2×C3×C4—41no—
684C2×C3×C4—61no—
685C2×C3×C4—62no—
686C2×C3×C4—62no—
687C2×C3×C4—62no—
688C2×C3×C4—64no—
689C2×C3×C4—92no—
690C2×C3×C4—92no—
691C2×C3×C4—182no—
692C2×C3×C4—362no—
693C2×C3×C4C2×D3211yescharacteristic
694C2×C3×C4C22×C3×D311yescharacteristic
695C2×C3×C4C22×C3×D311yescharacteristic
696#67—22no—
697#67—22no—
698#67—42no—
699#67—64no—
700#67—64no—
701#67—64no—
702#67—64no—
703#67—122no—
704#67—122no—
705C2×Dic3—32no—
706C2×Dic3—32no—
707C2×Dic3—32no—
708C2×Dic3—32no—
709C2×Dic3—62no—
710C2×Dic3—62no—
711C2×Dic3—62no—
712C2×Dic3—62no—
713C2×Dic3—122no—
714C2×Dic3—122no—
715C2×Dic3C22×C3×D312yes—
716C2×Dic3C22×C3×D311yescharacteristic
717D12—22no—
718C4×D3—22no—
719C4×D3—122no—
720C2×C32—22no—
721C2×C32—22no—
722C2×C32—22no—
723C2×C32—22no—
724C2×C32—21no—
725C2×C32—21no—
726C2×C32—22no—
727C2×C32—22no—
728C2×C32—21no—
729C2×C32—41no—
730C2×C32—42no—
731C2×C32—42no—
732C2×C32—42no—
733C2×C32—42no—
734C2×C32—41no—
735C2×C32—42no—
736C2×C32—41no—
737C2×C32—41no—
738C2×C32—62no—
739C2×C32—62no—
740C2×C32—82no—
741C2×C32—81no—
742C2×C32—81no—
743C2×C32—82no—
744C2×C32—122no—
745C2×C32—121no—
746C2×C32C2×D3×D411yescharacteristic
747C2×C32#100412yes—
748C2×C32#100412yes—
749C2×C32C22×#6711yescharacteristic
750C2×C32C22×C3×D411yescharacteristic
751C2×C32C3×H(5,𝔽2)12yes—
752C3×D3—24no—
753C3×D3—22no—
754C3×D3—22no—
755C3×D3—22no—
756C3×D3—22no—
757C3×D3—42no—
758C3×D3—42no—
759C3×D3—44no—
760C3×D3—41no—
761C3×D3—42no—
762C3×D3—41no—
763C3×D3—42no—
764C24—31no—
765C24—31no—
766C24—31no—
767C2×D4—31no—
768C2×D4—31no—
769C2×D4—32no—
770C2×D4—31no—
771C2×D4—64no—
772C2×D4—92no—
773C2×D4—92no—
774C2×D4—92no—
775C2×D4—184no—
776C2×D4C3×D3211yescharacteristic
777C22×C4—31no—
778C22×C4—92no—
779C22×C4—91no—
780C4⋊C4—92no—
781C4⋊C4—92no—
782C22⋊C4—31no—
783C22⋊C4—32no—
784C22⋊C4—92no—
785C22⋊C4—92no—
786C22⋊C4—92no—
787C22⋊C4—91no—
788C22⋊C4—92no—
789C22×C3—22no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—21no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—32no—
806C22×C3—32no—
807C22×C3—32no—
808C22×C3—32no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—42no—
812C22×C3—42no—
813C22×C3—41no—
814C22×C3—41no—
815C22×C3—42no—
816C22×C3—42no—
817C22×C3—42no—
818C22×C3—41no—
819C22×C3—42no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—64no—
823C22×C3—62no—
824C22×C3—64no—
825C22×C3—62no—
826C22×C3—62no—
827C22×C3—62no—
828C22×C3—62no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—61no—
833C22×C3—62no—
834C22×C3—61no—
835C22×C3—62no—
836C22×C3—62no—
837C22×C3—62no—
838C22×C3—62no—
839C22×C3—82no—
840C22×C3—82no—
841C22×C3—122no—
842C22×C3—122no—
843C22×C3—122no—
844C22×C3—122no—
845C22×C3—124no—
846C22×C3—124no—
847C22×C3—124no—
848C22×C3—124no—
849C22×C3—128no—
850C22×C3—128no—
851C22×C3—124no—
852C22×C3—124no—
853C22×C3—128no—
854C22×C3D3×#6712yes—
855C22×C3C3×D3×D412yes—
856C22×C3C2×C3×#6712yes—
857C22×C3C22×D3211yescharacteristic
858C22×C3C23×C3×D311yescharacteristic
859C22×C3C23×C3×D311yescharacteristic
860C2×D3—22no—
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—22no—
864C2×D3—22no—
865C2×D3—22no—
866C2×D3—21no—
867C2×D3—44no—
868C2×D3—44no—
869C2×D3—44no—
870C2×D3C2×C3×#6712yes—
871C2×D3C2×C3×#6712yes—
872C3×C4—22no—
873C3×C4—21no—
874C3×C4—21no—
875C3×C4—21no—
876C3×C4—41no—
877C3×C4—41no—
878C3×C4—42no—
879C3×C4—62no—
880C3×C4—62no—
881C3×C4—61no—
882C3×C4—61no—
883C3×C4—62no—
884C3×C4—122no—
885C3×C4—182no—
886C3×C4—182no—
887Dic3—22no—
888Dic3—21no—
889Dic3—62no—
890Dic3—62no—
891Dic3—62no—
892Dic3—62no—
893Dic3—122no—
894Dic3—122no—
895C32—21no—
896C32—21no—
897C32—21no—
898C32—41no—
899C32#558911yescharacteristic, complemented
900C32#580411yescharacteristic, complemented
901C32C3×#53411yescharacteristic, complemented
902C23—31no—
903C23—31no—
904C23—34no—
905C23—32no—
906C23—31no—
907C23—62no—
908C23—62no—
909C23—122no—
910C23—122no—
911C23—122no—
912C23C2×C3×D3211yescharacteristic
913C23C2×C3×D3211yescharacteristic
914D4—22no—
915D4—62no—
916D4—62no—
917D4—62no—
918D4—122no—
919D4—184no—
920D4—184no—
921D4—362no—
922C2×C4—32no—
923C2×C4—31no—
924C2×C4—62no—
925C2×C4—92no—
926C2×C4—92no—
927C2×C4—182no—
928C2×C4—362no—
929C2×C4C2×C3×D3211yescharacteristic
930C2×C3—22no—
931C2×C3—22no—
932C2×C3—22no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—22no—
937C2×C3—22no—
938C2×C3—22no—
939C2×C3—42no—
940C2×C3—42no—
941C2×C3—42no—
942C2×C3—42no—
943C2×C3—41no—
944C2×C3—41no—
945C2×C3—41no—
946C2×C3—41no—
947C2×C3—42no—
948C2×C3—64no—
949C2×C3—62no—
950C2×C3—62no—
951C2×C3—62no—
952C2×C3—62no—
953C2×C3—82no—
954C2×C3—81no—
955C2×C3—81no—
956C2×C3—82no—
957C2×C3—122no—
958C2×C3—122no—
959C2×C3—124no—
960C2×C3—122no—
961C2×C3—121no—
962C2×C3—122no—
963C2×C3—121no—
964C2×C3#6431312yes—
965C2×C3C2×D3×#6711yescharacteristic
966C2×C3C2×C3×D3×D411yescharacteristic
967C2×C3C3×#100412yes—
968C2×C3C3×#100412yes—
969C2×C3C22×C3×#6711yescharacteristic
970D3—22no—
971D3—22no—
972D3—41no—
973D3—42no—
974C22—22no—
975C22—21no—
976C22—22no—
977C22—32no—
978C22—32no—
979C22—62no—
980C22—62no—
981C22—61no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—124no—
987C22—124no—
988C22—124no—
989C22C3×D3×#6712yes—
990C22C22×C3×D3211yescharacteristic
991C4—21no—
992C4—61no—
993C4—62no—
994C4—182no—
995C4—182no—
996C3—21no—
997C3—21no—
998C3—21no—
999C3—41no—
1000C3#1059523011yescharacteristic, direct product factor
1001C3C3×#558911yescharacteristic, complemented
1002C3C3×#580411yescharacteristic, complemented
1003C2—22no—
1004C2—41no—
1005C2—62no—
1006C2—62no—
1007C2—121no—
1008C2—122no—
1009C2C3×#6431312yes—
1010C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×D3×D4C2semidirect
2. C22×C3×#625C2semidirect
3. C3×#64144C2semidirect
4. C32×#937C2semidirect
5. C3×#63976C2semidirect
6. C3×#63976C2semidirect
7. C3×#63970C2semidirect
8. C3×D3×#217C2semidirect
9. C3×#63962C2semidirect
10. C3×#63905C2semidirect
11. C3×#63885C2semidirect
14. #10595230C3direct (N × H)
16. C23×C32×D3C22semidirect
17. C23×C32×D3C22semidirect
19. C22×C3×C3⋊Dic3C22semidirect
21. C2×C32×#67C22semidirect
22. C2×C32×#67C22semidirect
24. C2×C32×D12C22semidirect
25. C2×C32×C4×D3C22semidirect
28. C2×C3×#625C22semidirect
29. C2×C3×#625C22semidirect
30. C2×C3×D3×Dic3C22semidirect
31. C3×#3757C22semidirect
32. C3×#3757C22semidirect
33. C3×#3750C22semidirect
34. C32×#217C22semidirect
35. C32×(C2×D3)⋊C4C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
44. C2×C3×D3×D4D3semidirect
45. C2×C3×D3×D4C2×C3semidirect
46. C22×#625C2×C3semidirect
48. #64144C2×C3semidirect
58. C3×#937D3semidirect
59. C3×#937C2×C3semidirect
69. #63976C2×C3semidirect
70. #63976C2×C3semidirect
71. #63970C2×C3semidirect
72. D3×#217C2×C3semidirect
73. #63962C2×C3semidirect
74. #63905C2×C3semidirect
75. #63885C2×C3semidirect
83. C22×C32×D3D4semidirect
114. C23×C3×D3C2×D3semidirect
115. C23×C3×D3C2×D3semidirect
117. C23×C3×D3C22×C3semidirect
118. C23×C3×D3C22×C3semidirect
132. C22×C3⋊Dic3C22×C3semidirect
145. C2×C3×#67C2×D3semidirect
146. C2×C3×#67C2×D3semidirect
148. C2×C3×#67C22×C3semidirect
149. C2×C3×#67C22×C3semidirect
158. C2×C3×D12C2×D3semidirect
159. C2×C3×D12C22×C3semidirect
162. C2×C3×C4×D3C2×D3semidirect
163. C2×C3×C4×D3C22×C3semidirect
166. C2×#625C22×C3semidirect
167. C2×#625C22×C3semidirect
168. C2×D3×Dic3C22×C3semidirect
171. #3757C22×C3semidirect
172. #3757C22×C3semidirect
173. #3750C22×C3semidirect
184. C3×#217C2×D3semidirect
185. C3×#217C22×C3semidirect
190. C3×(C2×D3)⋊C4C2×D3semidirect
191. C3×(C2×D3)⋊C4C22×C3semidirect
197. Dic3⋊Dic3C22×C3semidirect
198. (C2×D3)⋊Dic3C22×C3semidirect
199. (C2×D3)⋊Dic3C22×C3semidirect
200. (C2×D3)⋊Dic3C22×C3semidirect
229. C2×D3×D4C3×D3semidirect
249. #937C3×D3semidirect
303. C22×C3×D3#67semidirect
304. C22×C3×D3C3×D4semidirect
398. C23×D3C2×C3×D3semidirect
399. C23×D3C2×C3×D3semidirect
440. C2×#67C2×C3×D3semidirect
441. C2×#67C2×C3×D3semidirect
447. C2×D12C2×C3×D3semidirect
449. C2×C4×D3C2×C3×D3semidirect
472. #217C2×C3×D3semidirect
476. (C2×D3)⋊C4C2×C3×D3semidirect
599. C33#534semidirect
649. C22×D3C3×#67semidirect
899. C32#5589semidirect
900. C32#5804semidirect
901. C32C3×#534semidirect
1000. C3#10595230direct (N × H)
1001. C3C3×#5589semidirect
1002. C3C3×#5804semidirect

Maximal subgroups

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

subgroupindex
C2×C32×D3×D42
C22×C3×#6252
C3×#641442
C32×#9372
C3×#639762
C3×#639702
C3×D3×#2172
C3×#639622
C3×#639052
C3×#638852
C3×#58043
C3×#55893
#105952303