Finite Group Databasebeta

← C3×D3×#935 #13174706

Subgroups — C3×D3×#935 #13174706

Order 1728.

1814 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×D3×D4C211yesmaximal, characteristic
2C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
3C3×#64144C211yesmaximal, characteristic, complemented
4C32×#935C211yesmaximal, characteristic, complemented
5C3×#63969C212yesmaximal, complemented
6C3×D3×#217C211yesmaximal, characteristic, complemented
7C3×D3×#217C212yesmaximal, complemented
8C3×#63962C211yesmaximal, characteristic, complemented
9C3×#63961C211yesmaximal, characteristic, complemented
10C3×#63884C212yesmaximal, complemented
11C3×D3×Dic3⋊C4C212yesmaximal, complemented
12C2×C3×#935—31nomaximal
13C3×D3×#123—31nomaximal
14D3×#935C311yesmaximal, characteristic, direct product factor
15C23×C32×D3C2211yescharacteristic
16C23×C32×D3C2211yescharacteristic
17C2×C33×D4C2211yescharacteristic
18C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
19C2×C32×#67C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C22×C32×Dic3C2211yescharacteristic, complemented
22C32×D3×D4—24no—
23C2×C32×D12C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic
25C2×C3×D3×Dic3—24no—
26C2×C3×D3×Dic3C2212yes—
27C2×C3×D3×Dic3C2212yes—
28C2×C3×D3×Dic3C2212yescomplemented
29C3×#3757C2211yescharacteristic, complemented
30C3×#3757C2212yescomplemented
31C3×#3750C2212yescomplemented
32C32×#217C2211yescharacteristic, complemented
33C32×#217C2212yescomplemented
34C32×Dic3⋊C4C2212yescomplemented
35C3×#3724C2212yescomplemented
36C3×Dic3⋊Dic3C2212yescomplemented
37C3×(C2×D3)⋊Dic3C2212yescomplemented
38C3×(C2×D3)⋊Dic3C2212yescomplemented
39C3×(C2×D3)⋊Dic3C2212yescomplemented
40C22×C32×D4—31no—
41C23×C3×Dic3—31no—
42C2×C3×D3×D4—21no—
43C2×C3×D3×D4D311yescharacteristic
44C2×C3×D3×D4C2×C311yescharacteristic
45C22×C3×C4×D3—31no—
46C22×D3×Dic3C2×C311yescharacteristic, complemented
47C32×#123—31no—
48#64144C2×C311yescharacteristic, complemented
49C2×C3×#217—31no—
50C2×C3×#217—32no—
51C3×#935—21no—
52C3×#935—31no—
53C3×#935—31no—
54C3×#935—31no—
55C3×#935—31no—
56C3×#935—32no—
57C3×#935—32no—
58C3×#935—61no—
59C3×#935D311yescharacteristic, direct product factor
60C3×#935C2×C311yescharacteristic, complemented
61C3×#929—31no—
62C2×C3×Dic3⋊C4—32no—
63C3×#894—32no—
64C3×D3×C4⋊C4—32no—
65C3×#886—31no—
66C3×#883—32no—
67C3×D3×C22⋊C4—32no—
68C3×D3×C22⋊C4—31no—
69#63969C2×C312yescomplemented
70D3×#217C2×C312yescomplemented
71D3×#217C2×C311yescharacteristic, complemented
72#63962C2×C311yescharacteristic, complemented
73#63961C2×C311yescharacteristic, complemented
74#63884C2×C312yescomplemented
75D3×Dic3⋊C4C2×C312yescomplemented
76C23×C33C2311yescharacteristic
77C23×C33C2311yescharacteristic
78C22×C32×D3—24no—
79C22×C32×D3—22no—
80C22×C32×D3—24no—
81C22×C32×D3D414yes—
82C22×C32×D3C2311yescharacteristic
83C22×C32×D3C2311yescharacteristic
84C22×C32×D3C2311yescharacteristic
85C33×D4—22no—
86C2×C33×C4C2311yescharacteristic
87C2×C3×C3⋊Dic3—22no—
88C2×C3×C3⋊Dic3C2312yes—
89C2×C3×C3⋊Dic3C2312yes—
90C32×#67—22no—
91C32×#67—22no—
92C2×C32×Dic3—22no—
93C2×C32×Dic3C2312yes—
94C2×C32×Dic3C2312yes—
95C2×C32×Dic3C2311yescharacteristic
96C32×D12—22no—
97C32×C4×D3—22no—
98C3×D3×Dic3—24no—
99C3×D3×Dic3—24no—
100C3×D3×Dic3—24no—
101C2×C3×#123—91no—
102C2×#935—31no—
103D3×#123—31no—
104C24×C32—31no—
105C24×C32—31no—
106C23×C3×D3—21no—
107C23×C3×D3—21no—
108C23×C3×D3C2×D311yescharacteristic
109C23×C3×D3C2×D311yescharacteristic
110C23×C3×D3C22×C311yescharacteristic
111C23×C3×D3C22×C311yescharacteristic
112C2×C32×D4—21no—
113C2×C32×D4—21no—
114C2×C32×D4—21no—
115C2×C32×D4—31no—
116C2×C32×D4—31no—
117C2×C32×D4—31no—
118C2×C32×D4—41no—
119C2×C32×D4—64no—
120C2×C32×D4C2×D311yescharacteristic
121C2×C32×D4C2×D311yescharacteristic
122C2×C32×D4C22×C311yescharacteristic
123C22×C32×C4—31no—
124C22×C32×C4—31no—
125C22×C3⋊Dic3C22×C311yescharacteristic, complemented
126C2×C3×#67—21no—
127C2×C3×#67—21no—
128C2×C3×#67C2×D311yescharacteristic
129C2×C3×#67C2×D311yescharacteristic
130C2×C3×#67C22×C311yescharacteristic
131C2×C3×#67C22×C311yescharacteristic
132C22×C3×Dic3—21no—
133C22×C3×Dic3—31no—
134C22×C3×Dic3—31no—
135C22×C3×Dic3—32no—
136C22×C3×Dic3—32no—
137C22×C3×Dic3—32no—
138C22×C3×Dic3—64no—
139C22×C3×Dic3—61no—
140C22×C3×Dic3C2×D311yescharacteristic, complemented
141C22×C3×Dic3C22×C311yescharacteristic, complemented
142C3×D3×D4—28no—
143C3×D3×D4—24no—
144C3×D3×D4—24no—
145C2×C3×D12—21no—
146C2×C3×D12C2×D311yescharacteristic
147C2×C3×D12C22×C311yescharacteristic
148C2×C3×C4×D3—21no—
149C2×C3×C4×D3—32no—
150C2×C3×C4×D3—32no—
151C2×C3×C4×D3—32no—
152C2×C3×C4×D3—64no—
153C2×C3×C4×D3C2×D311yescharacteristic
154C2×C3×C4×D3C22×C311yescharacteristic
155C2×D3×Dic3—24no—
156C2×D3×Dic3C22×C312yes—
157C2×D3×Dic3C22×C312yes—
158C2×D3×Dic3C22×C312yescomplemented
159C32×C4⋊C4—32no—
160C32×C22⋊C4—32no—
161C32×C22⋊C4—31no—
162#3757C22×C311yescharacteristic, complemented
163#3757C22×C312yescomplemented
164#3750C22×C312yescomplemented
165C3×#217—21no—
166C3×#217—22no—
167C3×#217—32no—
168C3×#217—31no—
169C3×#217—31no—
170C3×#217—32no—
171C3×#217—32no—
172C3×#217—32no—
173C3×#217—32no—
174C3×#217—61no—
175C3×#217—62no—
176C3×#217C2×D311yescharacteristic, complemented
177C3×#217C2×D312yescomplemented
178C3×#217C22×C311yescharacteristic, complemented
179C3×#217C22×C312yescomplemented
180C3×(C2×D3)⋊C4—32no—
181C3×(C2×D3)⋊C4—32no—
182C3×(C2×D3)⋊C4—32no—
183C3×C4⋊Dic3—32no—
184C3×Dic3⋊C4—22no—
185C3×Dic3⋊C4—32no—
186C3×Dic3⋊C4—32no—
187C3×Dic3⋊C4—32no—
188C3×Dic3⋊C4—32no—
189C3×Dic3⋊C4—32no—
190C3×Dic3⋊C4—62no—
191C3×Dic3⋊C4C2×D312yescomplemented
192C3×Dic3⋊C4C22×C312yescomplemented
193#3724C22×C312yescomplemented
194Dic3⋊Dic3C22×C312yescomplemented
195(C2×D3)⋊Dic3C22×C312yescomplemented
196(C2×D3)⋊Dic3C22×C312yescomplemented
197(C2×D3)⋊Dic3C22×C312yescomplemented
198C22×C33—22no—
199C22×C33—21no—
200C22×C33—22no—
201C22×C33C2×D412yes—
202C22×C33C2411yescharacteristic
203C2×C32×D3—22no—
204C2×C32×D3—28no—
205C2×C32×D3—21no—
206C2×C32×D3—22no—
207C2×C32×D3—44no—
208C2×C32×D3C2×D412yes—
209C2×C32×D3C2×D412yes—
210C2×C32×D3#4114yes—
211C33×C4—21no—
212C3×C3⋊Dic3—22no—
213C3×C3⋊Dic3—22no—
214C32×Dic3—21no—
215C32×Dic3—22no—
216C32×Dic3—22no—
217C22×C3×D4—31no—
218C22×C3×D4—31no—
219C22×C3×D4—61no—
220C23×C3×C4—91no—
221C23×Dic3—31no—
222C2×D3×D4C3×D311yescharacteristic
223C22×C4×D3—31no—
224C3×#123—31no—
225C3×#123—31no—
226C3×#123—61no—
227C3×#123—92no—
228C3×#123—91no—
229C3×#123—92no—
230C3×#123—91no—
231C3×#123—91no—
232C2×C3×C4⋊C4—92no—
233C2×C3×C22⋊C4—91no—
234C2×C3×C22⋊C4—92no—
235C2×#217—31no—
236C2×#217—32no—
237#935—31no—
238#935—31no—
239#935—31no—
240#935—31no—
241#935—32no—
242#935—32no—
243#935—61no—
244#935C3×D311yescharacteristic, direct product factor
245#929—31no—
246C2×Dic3⋊C4—32no—
247#894—32no—
248D3×C4⋊C4—32no—
249#886—31no—
250#883—32no—
251D3×C22⋊C4—31no—
252D3×C22⋊C4—32no—
253C23×C32—21no—
254C23×C32—21no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32—31no—
260C23×C32—34no—
261C23×C32—31no—
262C23×C32—31no—
263C23×C32—41no—
264C23×C32—41no—
265C23×C32—62no—
266C23×C32—64no—
267C23×C32—64no—
268C23×C32C22×D311yescharacteristic
269C23×C32C22×D311yescharacteristic
270C23×C32C22×D311yescharacteristic
271C23×C32C22×D311yescharacteristic
272C23×C32C23×C311yescharacteristic
273C23×C32C23×C311yescharacteristic
274C22×C3×D3—24no—
275C22×C3×D3—24no—
276C22×C3×D3—24no—
277C22×C3×D3—24no—
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—24no—
281C22×C3×D3—24no—
282C22×C3×D3—21no—
283C22×C3×D3—21no—
284C22×C3×D3—21no—
285C22×C3×D3—44no—
286C22×C3×D3—44no—
287C22×C3×D3#6714yes—
288C22×C3×D3C3×D414yes—
289C22×C3×D3C22×D311yescharacteristic
290C22×C3×D3C22×D311yescharacteristic
291C22×C3×D3C22×D311yescharacteristic
292C22×C3×D3C23×C311yescharacteristic
293C22×C3×D3C23×C311yescharacteristic
294C22×C3×D3C23×C311yescharacteristic
295C32×D4—22no—
296C32×D4—24no—
297C32×D4—22no—
298C32×D4—22no—
299C32×D4—42no—
300C32×D4—42no—
301C32×D4—44no—
302C32×D4—62no—
303C32×D4—62no—
304C32×D4—62no—
305C2×C32×C4—21no—
306C2×C32×C4—21no—
307C2×C32×C4—21no—
308C2×C32×C4—31no—
309C2×C32×C4—32no—
310C2×C32×C4—32no—
311C2×C32×C4—41no—
312C2×C32×C4—62no—
313C2×C32×C4—62no—
314C2×C32×C4C22×D311yescharacteristic
315C2×C32×C4C22×D311yescharacteristic
316C2×C32×C4C23×C311yescharacteristic
317C2×C3⋊Dic3—22no—
318C2×C3⋊Dic3C23×C312yes—
319C2×C3⋊Dic3C23×C312yes—
320C3×#67—24no—
321C3×#67—24no—
322C3×#67—22no—
323C3×#67—22no—
324C3×#67—22no—
325C3×#67—22no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—21no—
329C2×C3×Dic3—22no—
330C2×C3×Dic3—22no—
331C2×C3×Dic3—32no—
332C2×C3×Dic3—32no—
333C2×C3×Dic3—32no—
334C2×C3×Dic3—32no—
335C2×C3×Dic3—42no—
336C2×C3×Dic3—62no—
337C2×C3×Dic3—62no—
338C2×C3×Dic3—64no—
339C2×C3×Dic3—64no—
340C2×C3×Dic3—64no—
341C2×C3×Dic3—62no—
342C2×C3×Dic3—62no—
343C2×C3×Dic3—122no—
344C2×C3×Dic3C22×D311yescharacteristic
345C2×C3×Dic3C22×D312yes—
346C2×C3×Dic3C22×D312yes—
347C2×C3×Dic3C23×C312yes—
348C2×C3×Dic3C23×C312yes—
349C2×C3×Dic3C23×C311yescharacteristic
350C3×D12—24no—
351C3×D12—22no—
352C3×D12—22no—
353C3×C4×D3—24no—
354C3×C4×D3—22no—
355C3×C4×D3—22no—
356C3×C4×D3—64no—
357C3×C4×D3—64no—
358C3×C4×D3—64no—
359D3×Dic3—24no—
360D3×Dic3—24no—
361D3×Dic3—24no—
362C2×#123—91noSylow
363C2×C33—22no—
364C2×C33—41no—
365C2×C33C22×D411yescharacteristic
366C2×C33C2×#4112yes—
367C32×D3—22no—
368C32×D3—41no—
369C32×D3#12314yescomplemented
370C24×C3—31no—
371C24×C3—31no—
372C24×C3—31no—
373C24×C3—31no—
374C24×C3—61no—
375C24×C3—61no—
376C23×D3C2×C3×D311yescharacteristic
377C23×D3C2×C3×D311yescharacteristic
378C2×C3×D4—21no—
379C2×C3×D4—21no—
380C2×C3×D4—21no—
381C2×C3×D4—31no—
382C2×C3×D4—31no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—31no—
387C2×C3×D4—41no—
388C2×C3×D4—61no—
389C2×C3×D4—61no—
390C2×C3×D4—61no—
391C2×C3×D4—64no—
392C2×C3×D4—64no—
393C2×C3×D4—68no—
394C2×C3×D4D3211yescharacteristic
395C2×C3×D4C2×C3×D311yescharacteristic
396C2×C3×D4C2×C3×D311yescharacteristic
397C22×C3×C4—31no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—61no—
402C22×C3×C4—61no—
403C22×C3×C4—92no—
404C22×C3×C4—92no—
405C22×C3×C4—92no—
406C22×C3×C4—91no—
407C22×C3×C4—184no—
408C2×#67C2×C3×D311yescharacteristic
409C2×#67C2×C3×D311yescharacteristic
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—32no—
413C22×Dic3—32no—
414C22×Dic3—32no—
415C22×Dic3—61no—
416C22×Dic3—64no—
417C22×Dic3C2×C3×D311yescharacteristic, complemented
418D3×D4—24no—
419C2×D12C2×C3×D311yescharacteristic
420C2×C4×D3—32no—
421C2×C4×D3—32no—
422C2×C4×D3—32no—
423C2×C4×D3—64no—
424C2×C4×D3C2×C3×D311yescharacteristic
425C3×C4⋊C4—32no—
426C3×C4⋊C4—32no—
427C3×C4⋊C4—62no—
428C3×C4⋊C4—92no—
429C3×C4⋊C4—92no—
430C3×C4⋊C4—92no—
431C3×C22⋊C4—31no—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—32no—
434C3×C22⋊C4—31no—
435C3×C22⋊C4—61no—
436C3×C22⋊C4—62no—
437C3×C22⋊C4—92no—
438C3×C22⋊C4—92no—
439C3×C22⋊C4—92no—
440C3×C22⋊C4—91no—
441C3×C22⋊C4—92no—
442#217—32no—
443#217—31no—
444#217—31no—
445#217—32no—
446#217—32no—
447#217—32no—
448#217—32no—
449#217—61no—
450#217—62no—
451#217C2×C3×D311yescharacteristic, complemented
452#217C2×C3×D312yescomplemented
453(C2×D3)⋊C4—32no—
454(C2×D3)⋊C4—32no—
455(C2×D3)⋊C4—32no—
456C4⋊Dic3—32no—
457Dic3⋊C4—32no—
458Dic3⋊C4—32no—
459Dic3⋊C4—32no—
460Dic3⋊C4—32no—
461Dic3⋊C4—32no—
462Dic3⋊C4—62no—
463Dic3⋊C4C2×C3×D312yescomplemented
464C22×C32—21no—
465C22×C32—22no—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—21no—
472C22×C32—21no—
473C22×C32—22no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—22no—
478C22×C32—22no—
479C22×C32—22no—
480C22×C32—32no—
481C22×C32—34no—
482C22×C32—32no—
483C22×C32—41no—
484C22×C32—42no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—42no—
488C22×C32—42no—
489C22×C32—42no—
490C22×C32—42no—
491C22×C32—42no—
492C22×C32—42no—
493C22×C32—42no—
494C22×C32—61no—
495C22×C32—68no—
496C22×C32—62no—
497C22×C32—62no—
498C22×C32—82no—
499C22×C32—82no—
500C22×C32—124no—
501C22×C32D3×D412yes—
502C22×C32C2×#6712yes—
503C22×C32C2×C3×D412yes—
504C22×C32C23×D311yescharacteristic
505C22×C32C23×D311yescharacteristic
506C22×C32C24×C311yescharacteristic
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—28no—
510C2×C3×D3—28no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—21no—
514C2×C3×D3—21no—
515C2×C3×D3—22no—
516C2×C3×D3—24no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—48no—
520C2×C3×D3—42no—
521C2×C3×D3—42no—
522C2×C3×D3—48no—
523C2×C3×D3—44no—
524C2×C3×D3—44no—
525C2×C3×D3#23714yes—
526C2×C3×D3C2×#6712yes—
527C2×C3×D3C2×#6712yes—
528C2×C3×D3C2×C3×D412yes—
529C2×C3×D3C2×C3×D412yes—
530C2×C3×D3C3×#4114yes—
531C32×C4—21no—
532C32×C4—22no—
533C32×C4—21no—
534C32×C4—21no—
535C32×C4—41no—
536C32×C4—41no—
537C32×C4—42no—
538C32×C4—61no—
539C32×C4—62no—
540C32×C4—62no—
541C3⋊Dic3—22no—
542C3⋊Dic3—22no—
543C3×Dic3—22no—
544C3×Dic3—22no—
545C3×Dic3—22no—
546C3×Dic3—21no—
547C3×Dic3—22no—
548C3×Dic3—21no—
549C3×Dic3—22no—
550C3×Dic3—42no—
551C3×Dic3—42no—
552C3×Dic3—62no—
553C3×Dic3—62no—
554C3×Dic3—62no—
555C3×Dic3—62no—
556C3×Dic3—122no—
557C3×Dic3—122no—
558C22×D4—31no—
559C23×C4—91no—
560#123—31no—
561#123—92no—
562#123—91no—
563#123—92no—
564#123—91no—
565#123—91no—
566C2×C4⋊C4—92no—
567C2×C22⋊C4—91no—
568C2×C22⋊C4—92no—
569C33C2×#12311yescharacteristic, complemented, Sylow
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—21no—
575C23×C3—21no—
576C23×C3—31no—
577C23×C3—31no—
578C23×C3—31no—
579C23×C3—31no—
580C23×C3—34no—
581C23×C3—34no—
582C23×C3—31no—
583C23×C3—31no—
584C23×C3—41no—
585C23×C3—41no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—64no—
589C23×C3—61no—
590C23×C3—64no—
591C23×C3—64no—
592C23×C3—62no—
593C23×C3—62no—
594C23×C3—64no—
595C23×C3—64no—
596C23×C3—64no—
597C23×C3—124no—
598C23×C3—124no—
599C23×C3C2×D3211yescharacteristic
600C23×C3C2×D3211yescharacteristic
601C23×C3C22×C3×D311yescharacteristic
602C23×C3C22×C3×D311yescharacteristic
603C23×C3C22×C3×D311yescharacteristic
604C23×C3C22×C3×D311yescharacteristic
605C22×D3—24no—
606C22×D3—24no—
607C22×D3—22no—
608C22×D3C3×#6714yes—
609C22×D3C22×C3×D311yescharacteristic
610C22×D3C22×C3×D311yescharacteristic
611C22×D3C22×C3×D311yescharacteristic
612C3×D4—24no—
613C3×D4—22no—
614C3×D4—22no—
615C3×D4—22no—
616C3×D4—42no—
617C3×D4—42no—
618C3×D4—44no—
619C3×D4—62no—
620C3×D4—62no—
621C3×D4—64no—
622C3×D4—62no—
623C3×D4—62no—
624C3×D4—64no—
625C3×D4—64no—
626C3×D4—62no—
627C3×D4—62no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—31no—
634C2×C3×C4—31no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—41no—
638C2×C3×C4—61no—
639C2×C3×C4—62no—
640C2×C3×C4—62no—
641C2×C3×C4—62no—
642C2×C3×C4—62no—
643C2×C3×C4—64no—
644C2×C3×C4—62no—
645C2×C3×C4—62no—
646C2×C3×C4—92no—
647C2×C3×C4—92no—
648C2×C3×C4—122no—
649C2×C3×C4—184no—
650C2×C3×C4—184no—
651C2×C3×C4—184no—
652C2×C3×C4—182no—
653C2×C3×C4C2×D3211yescharacteristic
654C2×C3×C4C22×C3×D311yescharacteristic
655C2×C3×C4C22×C3×D311yescharacteristic
656#67—22no—
657#67—22no—
658C2×Dic3—22no—
659C2×Dic3—32no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—32no—
663C2×Dic3—62no—
664C2×Dic3—62no—
665C2×Dic3—64no—
666C2×Dic3—64no—
667C2×Dic3—64no—
668C2×Dic3—62no—
669C2×Dic3—62no—
670C2×Dic3—122no—
671C2×Dic3C22×C3×D311yescharacteristic
672C2×Dic3C22×C3×D312yes—
673C2×Dic3C22×C3×D312yes—
674D12—22no—
675C4×D3—22no—
676C4×D3—64no—
677C4×D3—64no—
678C4×D3—64no—
679C2×C32—22no—
680C2×C32—22no—
681C2×C32—22no—
682C2×C32—22no—
683C2×C32—21no—
684C2×C32—21no—
685C2×C32—22no—
686C2×C32—22no—
687C2×C32—21no—
688C2×C32—34no—
689C2×C32—41no—
690C2×C32—42no—
691C2×C32—42no—
692C2×C32—42no—
693C2×C32—42no—
694C2×C32—41no—
695C2×C32—42no—
696C2×C32—41no—
697C2×C32—41no—
698C2×C32—62no—
699C2×C32—82no—
700C2×C32—81no—
701C2×C32—81no—
702C2×C32—82no—
703C2×C32—121no—
704C2×C32C2×D3×D411yescharacteristic
705C2×C32C2×#23712yes—
706C2×C32D3×#4112yes—
707C2×C32C22×#6711yescharacteristic
708C2×C32C22×C3×D411yescharacteristic
709C2×C32C2×C3×#4112yes—
710C3×D3—22no—
711C3×D3—22no—
712C3×D3—24no—
713C3×D3—42no—
714C3×D3—42no—
715C3×D3—41no—
716C3×D3—41no—
717C3×D3#93514yesdirect product factor
718C3×D3C3×#12314yescomplemented
719C24—31no—
720C24—31no—
721C2×D4—31no—
722C2×D4—31no—
723C2×D4—31no—
724C2×D4—64no—
725C2×D4C3×D3211yescharacteristic
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—92no—
729C22×C4—92no—
730C22×C4—92no—
731C22×C4—91no—
732C22×C4—184no—
733C4⋊C4—32no—
734C4⋊C4—92no—
735C4⋊C4—92no—
736C4⋊C4—92no—
737C22⋊C4—31no—
738C22⋊C4—32no—
739C22⋊C4—92no—
740C22⋊C4—92no—
741C22⋊C4—92no—
742C22⋊C4—91no—
743C22⋊C4—92no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—34no—
761C22×C3—32no—
762C22×C3—32no—
763C22×C3—34no—
764C22×C3—32no—
765C22×C3—32no—
766C22×C3—42no—
767C22×C3—42no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3—42no—
775C22×C3—41no—
776C22×C3—42no—
777C22×C3—62no—
778C22×C3—64no—
779C22×C3—62no—
780C22×C3—68no—
781C22×C3—68no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—61no—
787C22×C3—61no—
788C22×C3—62no—
789C22×C3—82no—
790C22×C3—82no—
791C22×C3—122no—
792C22×C3—122no—
793C22×C3—128no—
794C22×C3—124no—
795C22×C3—124no—
796C22×C3—128no—
797C22×C3D3×#6712yes—
798C22×C3C3×D3×D412yes—
799C22×C3C2×C3×#6712yes—
800C22×C3C22×D3211yescharacteristic
801C22×C3C23×C3×D311yescharacteristic
802C22×C3C23×C3×D311yescharacteristic
803C2×D3—22no—
804C2×D3—28no—
805C2×D3—22no—
806C2×D3—21no—
807C2×D3—44no—
808C2×D3C3×#23714yes—
809C2×D3C2×C3×#6712yes—
810C2×D3C2×C3×#6712yes—
811C3×C4—22no—
812C3×C4—21no—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—41no—
816C3×C4—41no—
817C3×C4—42no—
818C3×C4—62no—
819C3×C4—62no—
820C3×C4—62no—
821C3×C4—61no—
822C3×C4—61no—
823C3×C4—62no—
824C3×C4—62no—
825C3×C4—122no—
826C3×C4—122no—
827C3×C4—182no—
828C3×C4—182no—
829Dic3—22no—
830Dic3—22no—
831Dic3—21no—
832Dic3—62no—
833Dic3—62no—
834Dic3—62no—
835Dic3—62no—
836Dic3—122no—
837Dic3—122no—
838C32—21no—
839C32—21no—
840C32—21no—
841C32—41no—
842C32D3×#12311yescharacteristic, complemented
843C32C2×#93511yescharacteristic, complemented
844C32C2×C3×#12311yescharacteristic, complemented
845C23—31no—
846C23—31no—
847C23—34no—
848C23—31no—
849C23—64no—
850C23—62no—
851C23—64no—
852C23C2×C3×D3211yescharacteristic
853C23C2×C3×D3211yescharacteristic
854D4—22no—
855D4—62no—
856D4—62no—
857D4—62no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—31no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—92no—
864C2×C4—92no—
865C2×C4—184no—
866C2×C4—184no—
867C2×C4—184no—
868C2×C4—182no—
869C2×C4C2×C3×D3211yescharacteristic
870C2×C3—22no—
871C2×C3—22no—
872C2×C3—22no—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—22no—
877C2×C3—22no—
878C2×C3—22no—
879C2×C3—34no—
880C2×C3—34no—
881C2×C3—42no—
882C2×C3—42no—
883C2×C3—42no—
884C2×C3—42no—
885C2×C3—41no—
886C2×C3—41no—
887C2×C3—41no—
888C2×C3—41no—
889C2×C3—42no—
890C2×C3—64no—
891C2×C3—62no—
892C2×C3—62no—
893C2×C3—82no—
894C2×C3—81no—
895C2×C3—81no—
896C2×C3—82no—
897C2×C3—122no—
898C2×C3—122no—
899C2×C3—121no—
900C2×C3—121no—
901C2×C3D3×#23712yes—
902C2×C3C2×D3×#6711yescharacteristic
903C2×C3C2×C3×D3×D411yescharacteristic
904C2×C3C2×C3×#23712yes—
905C2×C3C3×D3×#4112yes—
906C2×C3C22×C3×#6711yescharacteristic
907D3—22no—
908D3—41no—
909D3C3×#93514yesdirect product factor
910C22—22no—
911C22—21no—
912C22—22no—
913C22—32no—
914C22—34no—
915C22—32no—
916C22—68no—
917C22—62no—
918C22—61no—
919C22—62no—
920C22—124no—
921C22C3×D3×#6712yes—
922C22C22×C3×D3211yescharacteristic
923C4—21no—
924C4—62no—
925C4—61no—
926C4—62no—
927C4—182no—
928C4—182no—
929C3—21no—
930C3—21no—
931C3—21no—
932C3—41no—
933C3D3×#93511yescharacteristic, direct product factor
934C3C3×D3×#12311yescharacteristic, complemented
935C3C2×C3×#93511yescharacteristic, complemented
936C2—22no—
937C2—34no—
938C2—41no—
939C2—62no—
940C2—121no—
941C2C3×D3×#23712yes—
942C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
prime radicalC2×C32×D3×D4C2
hypercenterC2×C3×D4D32
hypocenterC32C2×C3×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×D3×Dic3C2semidirect
3. C3×#64144C2semidirect
4. C32×#935C2semidirect
5. C3×#63969C2semidirect
6. C3×D3×#217C2semidirect
7. C3×D3×#217C2semidirect
8. C3×#63962C2semidirect
9. C3×#63961C2semidirect
10. C3×#63884C2semidirect
11. C3×D3×Dic3⋊C4C2semidirect
14. D3×#935C3direct (N × H)
18. C22×C3×C3⋊Dic3C22semidirect
21. C22×C32×Dic3C22semidirect
28. C2×C3×D3×Dic3C22semidirect
29. C3×#3757C22semidirect
30. C3×#3757C22semidirect
31. C3×#3750C22semidirect
32. C32×#217C22semidirect
33. C32×#217C22semidirect
34. C32×Dic3⋊C4C22semidirect
35. C3×#3724C22semidirect
36. C3×Dic3⋊Dic3C22semidirect
37. C3×(C2×D3)⋊Dic3C22semidirect
38. C3×(C2×D3)⋊Dic3C22semidirect
39. C3×(C2×D3)⋊Dic3C22semidirect
46. C22×D3×Dic3C2×C3semidirect
48. #64144C2×C3semidirect
59. C3×#935D3direct (N × H)
60. C3×#935C2×C3semidirect
69. #63969C2×C3semidirect
70. D3×#217C2×C3semidirect
71. D3×#217C2×C3semidirect
72. #63962C2×C3semidirect
73. #63961C2×C3semidirect
74. #63884C2×C3semidirect
75. D3×Dic3⋊C4C2×C3semidirect
125. C22×C3⋊Dic3C22×C3semidirect
140. C22×C3×Dic3C2×D3semidirect
141. C22×C3×Dic3C22×C3semidirect
158. C2×D3×Dic3C22×C3semidirect
162. #3757C22×C3semidirect
163. #3757C22×C3semidirect
164. #3750C22×C3semidirect
176. C3×#217C2×D3semidirect
177. C3×#217C2×D3semidirect
178. C3×#217C22×C3semidirect
179. C3×#217C22×C3semidirect
191. C3×Dic3⋊C4C2×D3semidirect
192. C3×Dic3⋊C4C22×C3semidirect
193. #3724C22×C3semidirect
194. Dic3⋊Dic3C22×C3semidirect
195. (C2×D3)⋊Dic3C22×C3semidirect
196. (C2×D3)⋊Dic3C22×C3semidirect
197. (C2×D3)⋊Dic3C22×C3semidirect
244. #935C3×D3direct (N × H)
369. C32×D3#123semidirect
417. C22×Dic3C2×C3×D3semidirect
451. #217C2×C3×D3semidirect
452. #217C2×C3×D3semidirect
463. Dic3⋊C4C2×C3×D3semidirect
569. C33C2×#123semidirect
717. C3×D3#935direct (N × H)
718. C3×D3C3×#123semidirect
842. C32D3×#123semidirect
843. C32C2×#935semidirect
844. C32C2×C3×#123semidirect
909. D3C3×#935direct (N × H)
933. C3D3×#935direct (N × H)
934. C3C3×D3×#123semidirect
935. C3C2×C3×#935semidirect

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×D3×Dic32
C3×#641442
C32×#9352
C3×#639692
C3×D3×#2172
C3×#639622
C3×#639612
C3×#638842
C3×D3×Dic3⋊C42
C2×C3×#9353
C3×D3×#1233
D3×#9353