Finite Group Databasebeta

← C3×D3×#930 #13174660

Subgroups — C3×D3×#930 #13174660

Order 1728.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic, complemented
2C2×C3×D3×#67C212yesmaximal, complemented
3C2×C3×D3×D12C211yesmaximal, characteristic, complemented
4C3×#64139C211yesmaximal, characteristic, complemented
5C32×#930C211yesmaximal, characteristic, complemented
6C3×#63978C212yesmaximal, complemented
7C3×D3×(C2×D3)⋊C4C212yesmaximal, complemented
8C3×#63909C211yesmaximal, characteristic, complemented
9C3×#63908C211yesmaximal, characteristic, complemented
10C3×#63906C212yesmaximal, complemented
11C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12C2×C3×#930—31nomaximal
13C3×D3×#121—31nomaximal
14D3×#930C311yesmaximal, characteristic, direct product factor
15C23×C32×D3C2211yescharacteristic
16C22×C3×D32C2212yes—
17C22×C33×C4C2211yescharacteristic, complemented
18C2×C3×#638C2212yescomplemented
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
20C2×C32×#67C2212yescomplemented
21C22×C32×Dic3C2211yescharacteristic, complemented
22C2×C32×D12C2211yescharacteristic, complemented
23C2×C32×C4×D3—24no—
24C2×C32×C4×D3C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic, complemented
27C2×C32×C4×D3C2211yescharacteristic, complemented
28C3×D3×#67—28no—
29C2×C3×#626C2212yescomplemented
30C2×C3×#626C2212yescomplemented
31C2×C3×#625C2212yescomplemented
32C2×C3×D3×Dic3C2212yes—
33C3×D3×D12—24no—
34C3×#3752C2212yescomplemented
35C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C32×(C2×D3)⋊C4C2212yescomplemented
37C32×C4⋊Dic3C2211yescharacteristic, complemented
38C3×Dic3⋊Dic3C2212yescomplemented
39C3×#3722C2212yescomplemented
40C3×(C2×D3)⋊Dic3C2212yescomplemented
41C23×C32×C4—31no—
42C22×C3×#67—32no—
43C2×C3×D3×D4—31no—
44C2×C3×D3×D4—32no—
45C22×C3×D12—31no—
46C22×C3×C4×D3—21no—
47C22×C3×C4×D3D311yescharacteristic, complemented
48C22×C3×C4×D3C2×C311yescharacteristic, complemented
49C2×D3×#67C2×C312yescomplemented
50C2×D3×D12C2×C311yescharacteristic, complemented
51C32×#121—31no—
52#64139C2×C311yescharacteristic, complemented
53C3×#939—32no—
54C3×#938—31no—
55C3×#930—21no—
56C3×#930—31no—
57C3×#930—31no—
58C3×#930—32no—
59C3×#930—31no—
60C3×#930—32no—
61C3×#930—31no—
62C3×#930—61no—
63C3×#930D311yescharacteristic, direct product factor
64C3×#930C2×C311yescharacteristic, complemented
65C2×C3×(C2×D3)⋊C4—32no—
66C2×C3×C4⋊Dic3—31no—
67C3×#895—31no—
68C3×D3×C4⋊C4—31no—
69C3×#884—32no—
70C3×D3×C22⋊C4—32no—
71#63978C2×C312yescomplemented
72D3×(C2×D3)⋊C4C2×C312yescomplemented
73#63909C2×C311yescharacteristic, complemented
74#63908C2×C311yescharacteristic, complemented
75#63906C2×C312yescomplemented
76D3×C4⋊Dic3C2×C311yescharacteristic, complemented
77C23×C33C2311yescharacteristic
78C22×C3×C3⋊D3C2312yes—
79C22×C32×D3—22no—
80C22×C32×D3—22no—
81C22×C32×D3D414yescomplemented
82C22×C32×D3C2312yes—
83C22×C32×D3C2311yescharacteristic
84C22×C32×D3C2311yescharacteristic
85C2×C3×D32—24no—
86C2×C3×D32—24no—
87C2×C3×D32—24no—
88C2×C33×C4—22no—
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C3×#638—24no—
92C2×C3×C3⋊Dic3C2312yes—
93C3×C4⋊(C3⋊D3)—22no—
94C32×#67—24no—
95C2×C32×Dic3—22no—
96C2×C32×Dic3C2312yes—
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C32×D12—22no—
100C32×C4×D3—22no—
101C32×C4×D3—22no—
102C32×C4×D3—22no—
103C32×C4×D3D414yescomplemented
104C3×#626—24no—
105C3×#626—24no—
106C3×#625—24no—
107C3×D3×Dic3—24no—
108C2×C3×#121—91no—
109C2×#930—31no—
110D3×#121—31no—
111C24×C32—31no—
112C23×C3×D3—21no—
113C23×C3×D3—32no—
114C23×C3×D3—32no—
115C23×C3×D3C2×D311yescharacteristic
116C23×C3×D3C22×C311yescharacteristic
117C22×D32C22×C312yes—
118C2×C32×D4—32no—
119C2×C32×D4—31no—
120C22×C32×C4—21no—
121C22×C32×C4—21no—
122C22×C32×C4—21no—
123C22×C32×C4—31no—
124C22×C32×C4—31no—
125C22×C32×C4—31no—
126C22×C32×C4—31no—
127C22×C32×C4—31no—
128C22×C32×C4—41no—
129C22×C32×C4—64no—
130C22×C32×C4C2×D311yescharacteristic, complemented
131C22×C32×C4C2×D311yescharacteristic, complemented
132C22×C32×C4C22×C311yescharacteristic, complemented
133C2×#638C22×C312yescomplemented
134C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
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—68no—
143C2×C3×#67—62no—
144C2×C3×#67C2×D312yescomplemented
145C2×C3×#67C22×C312yescomplemented
146C22×C3×Dic3—21no—
147C22×C3×Dic3—32no—
148C22×C3×Dic3C2×D311yescharacteristic, complemented
149C22×C3×Dic3C22×C311yescharacteristic, complemented
150C3×D3×D4—68no—
151C3×D3×D4—64no—
152C2×C3×D12—21no—
153C2×C3×D12—32no—
154C2×C3×D12—32no—
155C2×C3×D12—31no—
156C2×C3×D12—31no—
157C2×C3×D12—64no—
158C2×C3×D12—61no—
159C2×C3×D12C2×D311yescharacteristic, complemented
160C2×C3×D12C22×C311yescharacteristic, complemented
161C2×C3×C4×D3—28no—
162C2×C3×C4×D3—21no—
163C2×C3×C4×D3—21no—
164C2×C3×C4×D3—21no—
165C2×C3×C4×D3—21no—
166C2×C3×C4×D3—24no—
167C2×C3×C4×D3—24no—
168C2×C3×C4×D3—32no—
169C2×C3×C4×D3C2×D311yescharacteristic
170C2×C3×C4×D3C2×D311yescharacteristic
171C2×C3×C4×D3C2×D311yescharacteristic, complemented
172C2×C3×C4×D3C2×D311yescharacteristic, complemented
173C2×C3×C4×D3C22×C311yescharacteristic
174C2×C3×C4×D3C22×C311yescharacteristic
175C2×C3×C4×D3C22×C311yescharacteristic, complemented
176C2×C3×C4×D3C22×C311yescharacteristic, complemented
177D3×#67—28no—
178C2×#626C22×C312yescomplemented
179C2×#626C22×C312yescomplemented
180C2×#625C22×C312yescomplemented
181C2×D3×Dic3C22×C312yes—
182D3×D12—24no—
183C32×C4⋊C4—31no—
184C32×C22⋊C4—32no—
185#3752C22×C312yescomplemented
186C4⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
187C3×#217—32no—
188C3×(C2×D3)⋊C4—22no—
189C3×(C2×D3)⋊C4—32no—
190C3×(C2×D3)⋊C4—32no—
191C3×(C2×D3)⋊C4—32no—
192C3×(C2×D3)⋊C4—32no—
193C3×(C2×D3)⋊C4—32no—
194C3×(C2×D3)⋊C4—62no—
195C3×(C2×D3)⋊C4C2×D312yescomplemented
196C3×(C2×D3)⋊C4C22×C312yescomplemented
197C3×C4⋊Dic3—21no—
198C3×C4⋊Dic3—31no—
199C3×C4⋊Dic3—31no—
200C3×C4⋊Dic3—32no—
201C3×C4⋊Dic3—61no—
202C3×C4⋊Dic3C2×D311yescharacteristic, complemented
203C3×C4⋊Dic3C22×C311yescharacteristic, complemented
204C3×Dic3⋊C4—32no—
205Dic3⋊Dic3C22×C312yescomplemented
206#3722C22×C312yescomplemented
207(C2×D3)⋊Dic3C22×C312yescomplemented
208C22×C33—21no—
209C22×C33—21no—
210C22×C33C2×D412yescomplemented
211C22×C33C2411yescharacteristic
212C2×C3×C3⋊D3—22no—
213C2×C3×C3⋊D3—22no—
214C2×C3×C3⋊D3—22no—
215C2×C32×D3—21no—
216C2×C32×D3—21no—
217C2×C32×D3—28no—
218C2×C32×D3—22no—
219C2×C32×D3—22no—
220C2×C32×D3—22no—
221C2×C32×D3C2×D412yes—
222C2×C32×D3C2×D412yes—
223C2×C32×D3C2×D412yescomplemented
224C2×C32×D3#4112yes—
225C3×D32—48no—
226C33×C4—21no—
227C33×C4C2×D412yescomplemented
228C3×C3⋊Dic3—22no—
229C32×Dic3—21no—
230C32×Dic3—22no—
231C32×Dic3C2×D412yescomplemented
232C22×C3×D4—91no—
233C22×C3×D4—92no—
234C23×C3×C4—31no—
235C23×C3×C4—31no—
236C23×C3×C4—61no—
237C22×#67—32no—
238C2×D3×D4—32no—
239C2×D3×D4—31no—
240C22×D12—31no—
241C22×C4×D3C3×D311yescharacteristic, complemented
242C3×#121—31no—
243C3×#121—31no—
244C3×#121—61no—
245C3×#121—92no—
246C3×#121—91no—
247C3×#121—91no—
248C3×#121—92no—
249C3×#121—91no—
250C2×C3×C4⋊C4—91no—
251C2×C3×C22⋊C4—92no—
252#939—32no—
253#938—31no—
254#930—31no—
255#930—31no—
256#930—32no—
257#930—31no—
258#930—32no—
259#930—31no—
260#930—61no—
261#930C3×D311yescharacteristic, direct product factor
262C2×(C2×D3)⋊C4—32no—
263C2×C4⋊Dic3—31no—
264#895—31no—
265D3×C4⋊C4—31no—
266#884—32no—
267D3×C22⋊C4—32no—
268C23×C32—21no—
269C23×C32—21no—
270C23×C32—21no—
271C23×C32—31no—
272C23×C32—34no—
273C23×C32—31no—
274C23×C32—32no—
275C23×C32—41no—
276C23×C32—62no—
277C23×C32—62no—
278C23×C32C22×D311yescharacteristic
279C23×C32C22×D311yescharacteristic
280C23×C32C23×C311yescharacteristic
281C22×C3⋊D3C23×C312yes—
282C22×C3×D3—24no—
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—21no—
291C22×C3×D3—22no—
292C22×C3×D3—32no—
293C22×C3×D3—32no—
294C22×C3×D3—62no—
295C22×C3×D3—64no—
296C22×C3×D3—64no—
297C22×C3×D3—64no—
298C22×C3×D3—64no—
299C22×C3×D3—64no—
300C22×C3×D3—64no—
301C22×C3×D3D1214yescomplemented
302C22×C3×D3C3×D414yescomplemented
303C22×C3×D3C22×D312yes—
304C22×C3×D3C22×D311yescharacteristic
305C22×C3×D3C22×D311yescharacteristic
306C22×C3×D3C23×C312yes—
307C22×C3×D3C23×C311yescharacteristic
308C22×C3×D3C23×C311yescharacteristic
309C2×D32—24no—
310C2×D32—24no—
311C2×D32—24no—
312C32×D4—64no—
313C32×D4—62no—
314C2×C32×C4—22no—
315C2×C32×C4—24no—
316C2×C32×C4—22no—
317C2×C32×C4—22no—
318C2×C32×C4—21no—
319C2×C32×C4—21no—
320C2×C32×C4—21no—
321C2×C32×C4—21no—
322C2×C32×C4—21no—
323C2×C32×C4—21no—
324C2×C32×C4—31no—
325C2×C32×C4—34no—
326C2×C32×C4—32no—
327C2×C32×C4—31no—
328C2×C32×C4—41no—
329C2×C32×C4—41no—
330C2×C32×C4—42no—
331C2×C32×C4—42no—
332C2×C32×C4—44no—
333C2×C32×C4—62no—
334C2×C32×C4—62no—
335C2×C32×C4—62no—
336C2×C32×C4—62no—
337C2×C32×C4C22×D311yescharacteristic
338C2×C32×C4C22×D311yescharacteristic
339C2×C32×C4C22×D311yescharacteristic
340C2×C32×C4C22×D311yescharacteristic
341C2×C32×C4C23×C311yescharacteristic
342C2×C32×C4C23×C311yescharacteristic
343#638—24no—
344C2×C3⋊Dic3C23×C312yes—
345C4⋊(C3⋊D3)—22no—
346C3×#67—24no—
347C3×#67—24no—
348C3×#67—44no—
349C3×#67—64no—
350C3×#67—64no—
351C3×#67—64no—
352C3×#67—64no—
353C3×#67—64no—
354C3×#67—64no—
355C3×#67—124no—
356C2×C3×Dic3—24no—
357C2×C3×Dic3—22no—
358C2×C3×Dic3—22no—
359C2×C3×Dic3—21no—
360C2×C3×Dic3—21no—
361C2×C3×Dic3—22no—
362C2×C3×Dic3—32no—
363C2×C3×Dic3—32no—
364C2×C3×Dic3—62no—
365C2×C3×Dic3—64no—
366C2×C3×Dic3C22×D312yes—
367C2×C3×Dic3C22×D311yescharacteristic
368C2×C3×Dic3C22×D311yescharacteristic
369C2×C3×Dic3C23×C311yescharacteristic
370C2×C3×Dic3C23×C312yes—
371C2×C3×Dic3C23×C311yescharacteristic
372C3×D12—22no—
373C3×D12—22no—
374C3×D12—42no—
375C3×D12—64no—
376C3×D12—64no—
377C3×D12—62no—
378C3×D12—62no—
379C3×D12—122no—
380C3×C4×D3—24no—
381C3×C4×D3—24no—
382C3×C4×D3—24no—
383C3×C4×D3—22no—
384C3×C4×D3—22no—
385C3×C4×D3—22no—
386C3×C4×D3—22no—
387C3×C4×D3—22no—
388C3×C4×D3—22no—
389C3×C4×D3—24no—
390C3×C4×D3—64no—
391C3×C4×D3#6714yescomplemented
392C3×C4×D3C3×D414yescomplemented
393#626—24no—
394#626—24no—
395#625—24no—
396D3×Dic3—24no—
397C2×#121—91noSylow
398C2×C33—22no—
399C2×C33C22×D411yescharacteristic
400C2×C33C22×D411yescharacteristic
401C2×C33C2×#4111yescharacteristic
402C3×C3⋊D3—42no—
403C32×D3—22no—
404C32×D3—42no—
405C32×D3#12114yescomplemented
406C24×C3—31no—
407C24×C3—31no—
408C24×C3—61no—
409C24×C3—92no—
410C23×D3—32no—
411C23×D3—32no—
412C23×D3C2×C3×D311yescharacteristic
413C2×C3×D4—32no—
414C2×C3×D4—32no—
415C2×C3×D4—31no—
416C2×C3×D4—31no—
417C2×C3×D4—61no—
418C2×C3×D4—62no—
419C2×C3×D4—92no—
420C2×C3×D4—92no—
421C2×C3×D4—92no—
422C2×C3×D4—92no—
423C2×C3×D4—91no—
424C2×C3×D4—184no—
425C2×C3×D4—188no—
426C22×C3×C4—21no—
427C22×C3×C4—21no—
428C22×C3×C4—21no—
429C22×C3×C4—31no—
430C22×C3×C4—31no—
431C22×C3×C4—31no—
432C22×C3×C4—31no—
433C22×C3×C4—31no—
434C22×C3×C4—31no—
435C22×C3×C4—31no—
436C22×C3×C4—31no—
437C22×C3×C4—31no—
438C22×C3×C4—31no—
439C22×C3×C4—41no—
440C22×C3×C4—61no—
441C22×C3×C4—61no—
442C22×C3×C4—61no—
443C22×C3×C4—61no—
444C22×C3×C4—61no—
445C22×C3×C4—64no—
446C22×C3×C4—64no—
447C22×C3×C4—68no—
448C22×C3×C4—92no—
449C22×C3×C4D3211yescharacteristic, complemented
450C22×C3×C4C2×C3×D311yescharacteristic, complemented
451C22×C3×C4C2×C3×D311yescharacteristic, complemented
452C2×#67—32no—
453C2×#67—32no—
454C2×#67—32no—
455C2×#67—32no—
456C2×#67—32no—
457C2×#67—32no—
458C2×#67—62no—
459C2×#67—68no—
460C2×#67C2×C3×D312yescomplemented
461C22×Dic3—32no—
462C22×Dic3C2×C3×D311yescharacteristic, complemented
463D3×D4—68no—
464D3×D4—64no—
465C2×D12—32no—
466C2×D12—32no—
467C2×D12—31no—
468C2×D12—31no—
469C2×D12—61no—
470C2×D12—64no—
471C2×D12C2×C3×D311yescharacteristic, complemented
472C2×C4×D3—24no—
473C2×C4×D3—32no—
474C2×C4×D3C2×C3×D311yescharacteristic
475C2×C4×D3C2×C3×D311yescharacteristic
476C2×C4×D3C2×C3×D311yescharacteristic, complemented
477C2×C4×D3C2×C3×D311yescharacteristic, complemented
478C3×C4⋊C4—31no—
479C3×C4⋊C4—31no—
480C3×C4⋊C4—61no—
481C3×C4⋊C4—92no—
482C3×C4⋊C4—91no—
483C3×C22⋊C4—32no—
484C3×C22⋊C4—32no—
485C3×C22⋊C4—62no—
486C3×C22⋊C4—92no—
487C3×C22⋊C4—92no—
488C3×C22⋊C4—92no—
489#217—32no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—32no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—62no—
496(C2×D3)⋊C4C2×C3×D312yescomplemented
497C4⋊Dic3—31no—
498C4⋊Dic3—31no—
499C4⋊Dic3—32no—
500C4⋊Dic3—61no—
501C4⋊Dic3C2×C3×D311yescharacteristic, complemented
502Dic3⋊C4—32no—
503C22×C32—21no—
504C22×C32—21no—
505C22×C32—22no—
506C22×C32—22no—
507C22×C32—21no—
508C22×C32—21no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—21no—
514C22×C32—22no—
515C22×C32—22no—
516C22×C32—22no—
517C22×C32—32no—
518C22×C32—32no—
519C22×C32—32no—
520C22×C32—32no—
521C22×C32—42no—
522C22×C32—41no—
523C22×C32—41no—
524C22×C32—41no—
525C22×C32—41no—
526C22×C32—41no—
527C22×C32—42no—
528C22×C32—42no—
529C22×C32—68no—
530C22×C32—61no—
531C22×C32—61no—
532C22×C32—62no—
533C22×C32—62no—
534C22×C32—62no—
535C22×C32C2×D1212yescomplemented
536C22×C32D3×D412yescomplemented
537C22×C32C2×C3×D412yescomplemented
538C22×C32C23×D311yescharacteristic
539C22×C32C23×D311yescharacteristic
540C22×C32C24×C311yescharacteristic
541C2×C3⋊D3—22no—
542C2×C3⋊D3—22no—
543C2×C3⋊D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—216no—
547C2×C3×D3—21no—
548C2×C3×D3—21no—
549C2×C3×D3—21no—
550C2×C3×D3—21no—
551C2×C3×D3—28no—
552C2×C3×D3—28no—
553C2×C3×D3—22no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—42no—
564C2×C3×D3—42no—
565C2×C3×D3—42no—
566C2×C3×D3—62no—
567C2×C3×D3—62no—
568C2×C3×D3—62no—
569C2×C3×D3—62no—
570C2×C3×D3—62no—
571C2×C3×D3—62no—
572C2×C3×D3—122no—
573C2×C3×D3—122no—
574C2×C3×D3—122no—
575C2×C3×D3—128no—
576C2×C3×D3—128no—
577C2×C3×D3C2×D1212yes—
578C2×C3×D3C2×D1212yescomplemented
579C2×C3×D3#23512yes—
580C2×C3×D3C2×#6712yes—
581C2×C3×D3C2×C3×D412yes—
582C2×C3×D3C2×C3×D412yes—
583C2×C3×D3C2×C3×D412yescomplemented
584C2×C3×D3C3×#4112yes—
585D32—48no—
586C32×C4—21no—
587C32×C4—22no—
588C32×C4—21no—
589C32×C4—21no—
590C32×C4—22no—
591C32×C4—22no—
592C32×C4—22no—
593C32×C4—32no—
594C32×C4—42no—
595C32×C4—41no—
596C32×C4—41no—
597C32×C4—42no—
598C32×C4—61no—
599C32×C4—62no—
600C32×C4D3×D412yescomplemented
601C32×C4C2×#6712yescomplemented
602C32×C4C2×C3×D412yescomplemented
603C3⋊Dic3—22no—
604C3×Dic3—22no—
605C3×Dic3—22no—
606C3×Dic3—21no—
607C3×Dic3—22no—
608C3×Dic3—21no—
609C3×Dic3—22no—
610C3×Dic3—42no—
611C3×Dic3—62no—
612C3×Dic3—62no—
613C3×Dic3—122no—
614C3×Dic3C2×#6712yescomplemented
615C3×Dic3C2×C3×D412yescomplemented
616C22×D4—91no—
617C22×D4—92no—
618C23×C4—31no—
619#121—31no—
620#121—92no—
621#121—91no—
622#121—91no—
623#121—92no—
624#121—91no—
625C2×C4⋊C4—91no—
626C2×C22⋊C4—92no—
627C33C2×#12111yescharacteristic, complemented, Sylow
628C23×C3—21no—
629C23×C3—21no—
630C23×C3—21no—
631C23×C3—31no—
632C23×C3—31no—
633C23×C3—31no—
634C23×C3—31no—
635C23×C3—34no—
636C23×C3—34no—
637C23×C3—32no—
638C23×C3—32no—
639C23×C3—41no—
640C23×C3—61no—
641C23×C3—61no—
642C23×C3—64no—
643C23×C3—62no—
644C23×C3—62no—
645C23×C3—62no—
646C23×C3—62no—
647C23×C3—62no—
648C23×C3—64no—
649C23×C3—64no—
650C23×C3—92no—
651C23×C3—184no—
652C23×C3—184no—
653C23×C3—184no—
654C23×C3C2×D3211yescharacteristic
655C23×C3C22×C3×D311yescharacteristic
656C23×C3C22×C3×D311yescharacteristic
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—32no—
660C22×D3—32no—
661C22×D3—62no—
662C22×D3—64no—
663C22×D3—64no—
664C22×D3—64no—
665C22×D3—64no—
666C22×D3—64no—
667C22×D3—64no—
668C22×D3C3×D1214yescomplemented
669C22×D3C22×C3×D312yes—
670C22×D3C22×C3×D311yescharacteristic
671C22×D3C22×C3×D311yescharacteristic
672C3×D4—64no—
673C3×D4—64no—
674C3×D4—62no—
675C3×D4—62no—
676C3×D4—122no—
677C3×D4—124no—
678C3×D4—184no—
679C3×D4—184no—
680C3×D4—184no—
681C3×D4—184no—
682C3×D4—182no—
683C2×C3×C4—24no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—22no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—31no—
694C2×C3×C4—31no—
695C2×C3×C4—34no—
696C2×C3×C4—34no—
697C2×C3×C4—32no—
698C2×C3×C4—31no—
699C2×C3×C4—32no—
700C2×C3×C4—31no—
701C2×C3×C4—42no—
702C2×C3×C4—42no—
703C2×C3×C4—44no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—64no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—62no—
710C2×C3×C4—62no—
711C2×C3×C4—62no—
712C2×C3×C4—62no—
713C2×C3×C4—62no—
714C2×C3×C4—64no—
715C2×C3×C4—64no—
716C2×C3×C4—64no—
717C2×C3×C4—62no—
718C2×C3×C4—62no—
719C2×C3×C4—64no—
720C2×C3×C4—62no—
721C2×C3×C4—62no—
722C2×C3×C4—92no—
723C2×C3×C4—184no—
724C2×C3×C4C2×D3211yescharacteristic
725C2×C3×C4C2×D3211yescharacteristic
726C2×C3×C4C22×C3×D311yescharacteristic
727C2×C3×C4C22×C3×D311yescharacteristic
728C2×C3×C4C22×C3×D311yescharacteristic
729C2×C3×C4C22×C3×D311yescharacteristic
730#67—24no—
731#67—64no—
732#67—64no—
733#67—64no—
734#67—64no—
735#67—64no—
736#67—64no—
737#67—124no—
738C2×Dic3—22no—
739C2×Dic3—32no—
740C2×Dic3—32no—
741C2×Dic3—62no—
742C2×Dic3—64no—
743C2×Dic3C22×C3×D312yes—
744C2×Dic3C22×C3×D311yescharacteristic
745C2×Dic3C22×C3×D311yescharacteristic
746D12—22no—
747D12—64no—
748D12—64no—
749D12—62no—
750D12—62no—
751D12—122no—
752C4×D3—22no—
753C4×D3—22no—
754C4×D3—22no—
755C4×D3—64no—
756C4×D3C3×#6714yescomplemented
757C2×C32—22no—
758C2×C32—24no—
759C2×C32—22no—
760C2×C32—22no—
761C2×C32—21no—
762C2×C32—21no—
763C2×C32—21no—
764C2×C32—21no—
765C2×C32—21no—
766C2×C32—21no—
767C2×C32—21no—
768C2×C32—21no—
769C2×C32—21no—
770C2×C32—34no—
771C2×C32—41no—
772C2×C32—41no—
773C2×C32—41no—
774C2×C32—42no—
775C2×C32—42no—
776C2×C32—44no—
777C2×C32—62no—
778C2×C32—122no—
779C2×C32C22×D1211yescharacteristic
780C2×C32C2×#23511yescharacteristic
781C2×C32C2×D3×D411yescharacteristic
782C2×C32C2×D3×D411yescharacteristic
783C2×C32D3×#4111yescharacteristic
784C2×C32C22×#6711yescharacteristic
785C2×C32C22×C3×D411yescharacteristic
786C2×C32C22×C3×D411yescharacteristic
787C2×C32C2×C3×#4111yescharacteristic
788C3⋊D3—42no—
789C3×D3—24no—
790C3×D3—22no—
791C3×D3—22no—
792C3×D3—24no—
793C3×D3—42no—
794C3×D3—42no—
795C3×D3—82no—
796C3×D3—122no—
797C3×D3—122no—
798C3×D3—242no—
799C3×D3#93014yesdirect product factor
800C3×D3C3×#12114yescomplemented
801C24—31no—
802C24—92no—
803C2×D4—32no—
804C2×D4—31no—
805C2×D4—92no—
806C2×D4—92no—
807C2×D4—92no—
808C2×D4—92no—
809C2×D4—91no—
810C2×D4—184no—
811C2×D4—188no—
812C22×C4—31no—
813C22×C4—31no—
814C22×C4—31no—
815C22×C4—31no—
816C22×C4—31no—
817C22×C4—64no—
818C22×C4—92no—
819C22×C4C3×D3211yescharacteristic, complemented
820C4⋊C4—31no—
821C4⋊C4—92no—
822C4⋊C4—91no—
823C22⋊C4—32no—
824C22⋊C4—92no—
825C22⋊C4—92no—
826C22⋊C4—92no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—21no—
830C22×C3—21no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—21no—
834C22×C3—21no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—32no—
842C22×C3—32no—
843C22×C3—32no—
844C22×C3—32no—
845C22×C3—32no—
846C22×C3—32no—
847C22×C3—32no—
848C22×C3—32no—
849C22×C3—41no—
850C22×C3—41no—
851C22×C3—41no—
852C22×C3—41no—
853C22×C3—42no—
854C22×C3—42no—
855C22×C3—41no—
856C22×C3—42no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—62no—
860C22×C3—62no—
861C22×C3—68no—
862C22×C3—68no—
863C22×C3—62no—
864C22×C3—616no—
865C22×C3—62no—
866C22×C3—61no—
867C22×C3—61no—
868C22×C3—61no—
869C22×C3—61no—
870C22×C3—62no—
871C22×C3—62no—
872C22×C3—62no—
873C22×C3—62no—
874C22×C3—62no—
875C22×C3—62no—
876C22×C3—122no—
877C22×C3—122no—
878C22×C3—122no—
879C22×C3—182no—
880C22×C3—182no—
881C22×C3—182no—
882C22×C3—368no—
883C22×C3D3×D1212yescomplemented
884C22×C3C2×C3×D1212yescomplemented
885C22×C3C3×D3×D412yescomplemented
886C22×C3C22×D3211yescharacteristic
887C22×C3C23×C3×D311yescharacteristic
888C22×C3C23×C3×D311yescharacteristic
889C2×D3—21no—
890C2×D3—21no—
891C2×D3—28no—
892C2×D3—22no—
893C2×D3—22no—
894C2×D3—22no—
895C2×D3—62no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—62no—
899C2×D3—62no—
900C2×D3—62no—
901C2×D3—122no—
902C2×D3—122no—
903C2×D3—122no—
904C2×D3—128no—
905C2×D3—128no—
906C2×D3C2×C3×D1212yes—
907C2×D3C2×C3×D1212yescomplemented
908C2×D3C3×#23512yes—
909C2×D3C2×C3×#6712yes—
910C3×C4—22no—
911C3×C4—21no—
912C3×C4—21no—
913C3×C4—21no—
914C3×C4—22no—
915C3×C4—22no—
916C3×C4—22no—
917C3×C4—32no—
918C3×C4—32no—
919C3×C4—41no—
920C3×C4—41no—
921C3×C4—42no—
922C3×C4—42no—
923C3×C4—62no—
924C3×C4—62no—
925C3×C4—62no—
926C3×C4—61no—
927C3×C4—62no—
928C3×C4—61no—
929C3×C4—122no—
930C3×C4—182no—
931C3×C4D3×#6712yescomplemented
932C3×C4C3×D3×D412yescomplemented
933C3×C4C2×C3×#6712yescomplemented
934Dic3—22no—
935Dic3—21no—
936Dic3—62no—
937Dic3—62no—
938Dic3—122no—
939Dic3C2×C3×#6712yescomplemented
940C32—21no—
941C32—21no—
942C32—21no—
943C32—41no—
944C32D3×#12111yescharacteristic, complemented
945C32C2×#93011yescharacteristic, complemented
946C32C2×C3×#12111yescharacteristic, complemented
947C23—31no—
948C23—31no—
949C23—34no—
950C23—32no—
951C23—62no—
952C23—62no—
953C23—92no—
954C23—184no—
955C23—184no—
956C23—184no—
957C23C2×C3×D3211yescharacteristic
958D4—64no—
959D4—62no—
960D4—184no—
961D4—184no—
962D4—184no—
963D4—184no—
964D4—182no—
965C2×C4—22no—
966C2×C4—31no—
967C2×C4—34no—
968C2×C4—32no—
969C2×C4—31no—
970C2×C4—62no—
971C2×C4—62no—
972C2×C4—62no—
973C2×C4—62no—
974C2×C4—92no—
975C2×C4—184no—
976C2×C4C2×C3×D3211yescharacteristic
977C2×C4C2×C3×D3211yescharacteristic
978C2×C3—24no—
979C2×C3—22no—
980C2×C3—22no—
981C2×C3—22no—
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—21no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—34no—
992C2×C3—34no—
993C2×C3—42no—
994C2×C3—42no—
995C2×C3—44no—
996C2×C3—41no—
997C2×C3—41no—
998C2×C3—41no—
999C2×C3—64no—
1000C2×C3—64no—
1001C2×C3—62no—
1002C2×C3—62no—
1003C2×C3—122no—
1004C2×C3—122no—
1005C2×C3—242no—
1006C2×C3—362no—
1007C2×C3C2×D3×D1211yescharacteristic
1008C2×C3D3×#23511yescharacteristic
1009C2×C3C2×D3×#6711yescharacteristic
1010C2×C3C22×C3×D1211yescharacteristic
1011C2×C3C2×C3×#23511yescharacteristic
1012C2×C3C2×C3×D3×D411yescharacteristic
1013C2×C3C2×C3×D3×D411yescharacteristic
1014C2×C3C3×D3×#4111yescharacteristic
1015C2×C3C22×C3×#6711yescharacteristic
1016D3—22no—
1017D3—42no—
1018D3—122no—
1019D3—122no—
1020D3—242no—
1021D3C3×#93014yesdirect product factor
1022C22—21no—
1023C22—21no—
1024C22—32no—
1025C22—32no—
1026C22—32no—
1027C22—32no—
1028C22—68no—
1029C22—61no—
1030C22—61no—
1031C22—62no—
1032C22—62no—
1033C22—62no—
1034C22—182no—
1035C22—182no—
1036C22—182no—
1037C22—368no—
1038C22C3×D3×D1212yescomplemented
1039C22C22×C3×D3211yescharacteristic
1040C4—21no—
1041C4—32no—
1042C4—61no—
1043C4—62no—
1044C4—182no—
1045C4C3×D3×#6712yescomplemented
1046C3—21no—
1047C3—21no—
1048C3—21no—
1049C3—41no—
1050C3D3×#93011yescharacteristic, direct product factor
1051C3C3×D3×#12111yescharacteristic, complemented
1052C3C2×C3×#93011yescharacteristic, complemented
1053C2—22no—
1054C2—34no—
1055C2—62no—
1056C2—122no—
1057C2—362no—
1058C2C2×C3×D3×D1211yescharacteristic
1059C2C3×D3×#23511yescharacteristic
1060C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#121
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×C4×D3C2semidirect
2. C2×C3×D3×#67C2semidirect
3. C2×C3×D3×D12C2semidirect
4. C3×#64139C2semidirect
5. C32×#930C2semidirect
6. C3×#63978C2semidirect
7. C3×D3×(C2×D3)⋊C4C2semidirect
8. C3×#63909C2semidirect
9. C3×#63908C2semidirect
10. C3×#63906C2semidirect
11. C3×D3×C4⋊Dic3C2semidirect
14. D3×#930C3direct (N × H)
17. C22×C33×C4C22semidirect
18. C2×C3×#638C22semidirect
19. C2×C3×C4⋊(C3⋊D3)C22semidirect
20. C2×C32×#67C22semidirect
21. C22×C32×Dic3C22semidirect
22. C2×C32×D12C22semidirect
26. C2×C32×C4×D3C22semidirect
27. C2×C32×C4×D3C22semidirect
29. C2×C3×#626C22semidirect
30. C2×C3×#626C22semidirect
31. C2×C3×#625C22semidirect
34. C3×#3752C22semidirect
35. C3×C4⋊(C3⋊Dic3)C22semidirect
36. C32×(C2×D3)⋊C4C22semidirect
37. C32×C4⋊Dic3C22semidirect
38. C3×Dic3⋊Dic3C22semidirect
39. C3×#3722C22semidirect
40. C3×(C2×D3)⋊Dic3C22semidirect
47. C22×C3×C4×D3D3semidirect
48. C22×C3×C4×D3C2×C3semidirect
49. C2×D3×#67C2×C3semidirect
50. C2×D3×D12C2×C3semidirect
52. #64139C2×C3semidirect
63. C3×#930D3direct (N × H)
64. C3×#930C2×C3semidirect
71. #63978C2×C3semidirect
72. D3×(C2×D3)⋊C4C2×C3semidirect
73. #63909C2×C3semidirect
74. #63908C2×C3semidirect
75. #63906C2×C3semidirect
76. D3×C4⋊Dic3C2×C3semidirect
81. C22×C32×D3D4semidirect
103. C32×C4×D3D4semidirect
130. C22×C32×C4C2×D3semidirect
131. C22×C32×C4C2×D3semidirect
132. C22×C32×C4C22×C3semidirect
133. C2×#638C22×C3semidirect
134. C2×C4⋊(C3⋊D3)C22×C3semidirect
144. C2×C3×#67C2×D3semidirect
145. C2×C3×#67C22×C3semidirect
148. C22×C3×Dic3C2×D3semidirect
149. C22×C3×Dic3C22×C3semidirect
159. C2×C3×D12C2×D3semidirect
160. C2×C3×D12C22×C3semidirect
171. C2×C3×C4×D3C2×D3semidirect
172. C2×C3×C4×D3C2×D3semidirect
175. C2×C3×C4×D3C22×C3semidirect
176. C2×C3×C4×D3C22×C3semidirect
178. C2×#626C22×C3semidirect
179. C2×#626C22×C3semidirect
180. C2×#625C22×C3semidirect
185. #3752C22×C3semidirect
186. C4⋊(C3⋊Dic3)C22×C3semidirect
195. C3×(C2×D3)⋊C4C2×D3semidirect
196. C3×(C2×D3)⋊C4C22×C3semidirect
202. C3×C4⋊Dic3C2×D3semidirect
203. C3×C4⋊Dic3C22×C3semidirect
205. Dic3⋊Dic3C22×C3semidirect
206. #3722C22×C3semidirect
207. (C2×D3)⋊Dic3C22×C3semidirect
210. C22×C33C2×D4semidirect
223. C2×C32×D3C2×D4semidirect
227. C33×C4C2×D4semidirect
231. C32×Dic3C2×D4semidirect
241. C22×C4×D3C3×D3semidirect
261. #930C3×D3direct (N × H)
301. C22×C3×D3D12semidirect
302. C22×C3×D3C3×D4semidirect
391. C3×C4×D3#67semidirect
392. C3×C4×D3C3×D4semidirect
405. C32×D3#121semidirect
449. C22×C3×C4D32semidirect
450. C22×C3×C4C2×C3×D3semidirect
451. C22×C3×C4C2×C3×D3semidirect
460. C2×#67C2×C3×D3semidirect
462. C22×Dic3C2×C3×D3semidirect
471. C2×D12C2×C3×D3semidirect
476. C2×C4×D3C2×C3×D3semidirect
477. C2×C4×D3C2×C3×D3semidirect
496. (C2×D3)⋊C4C2×C3×D3semidirect
501. C4⋊Dic3C2×C3×D3semidirect
535. C22×C32C2×D12semidirect
536. C22×C32D3×D4semidirect
537. C22×C32C2×C3×D4semidirect
578. C2×C3×D3C2×D12semidirect
583. C2×C3×D3C2×C3×D4semidirect
600. C32×C4D3×D4semidirect
601. C32×C4C2×#67semidirect
602. C32×C4C2×C3×D4semidirect
614. C3×Dic3C2×#67semidirect
615. C3×Dic3C2×C3×D4semidirect
627. C33C2×#121semidirect
668. C22×D3C3×D12semidirect
756. C4×D3C3×#67semidirect
799. C3×D3#930direct (N × H)
800. C3×D3C3×#121semidirect
819. C22×C4C3×D32semidirect
883. C22×C3D3×D12semidirect
884. C22×C3C2×C3×D12semidirect
885. C22×C3C3×D3×D4semidirect
907. C2×D3C2×C3×D12semidirect
931. C3×C4D3×#67semidirect
932. C3×C4C3×D3×D4semidirect
933. C3×C4C2×C3×#67semidirect
939. Dic3C2×C3×#67semidirect
944. C32D3×#121semidirect
945. C32C2×#930semidirect
946. C32C2×C3×#121semidirect
1021. D3C3×#930direct (N × H)
1038. C22C3×D3×D12semidirect
1045. C4C3×D3×#67semidirect
1050. C3D3×#930direct (N × H)
1051. C3C3×D3×#121semidirect
1052. C3C2×C3×#930semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4×D32
C2×C3×D3×#672
C2×C3×D3×D122
C3×#641392
C32×#9302
C3×#639782
C3×D3×(C2×D3)⋊C42
C3×#639092
C3×#639082
C3×#639062
C3×D3×C4⋊Dic32
C2×C3×#9303
C3×D3×#1213
D3×#9303