Finite Group Databasebeta

← C2×C3×D3×(C2×D3)⋊C4 #13174650

Subgroups — C2×C3×D3×(C2×D3)⋊C4 #13174650

Order 1728.

3250 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D32C211yesmaximal, characteristic
2C22×C32×C4×D3C211yesmaximal, characteristic, complemented
3C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
4C2×C3×#3752C211yesmaximal, characteristic, complemented
5C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C2×C3×#3722C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8C3×D3×(C2×D3)⋊C4C218yesmaximal, direct product factor
9C22×C3×(C2×D3)⋊C4—31nomaximal
10C2×C3×D3×C22⋊C4—31nomaximal
11C2×D3×(C2×D3)⋊C4C311yesmaximal, characteristic, direct product factor
12C23×C3×C3⋊D3C2211yescharacteristic
13C23×C32×D3C2211yescharacteristic
14C23×C32×D3C2211yescharacteristic
15C22×C3×D32—24no—
16C22×C3×D32—24no—
17C22×C3×D32C418yescomplemented
18C22×C3×D32C2214yes—
19C22×C33×C4C2211yescharacteristic, complemented
20C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
21C22×C32×Dic3C2211yescharacteristic, complemented
22C22×C32×Dic3C2211yescharacteristic, complemented
23C2×C32×C4×D3—24no—
24C2×C32×C4×D3C2214yescomplemented
25C2×C3×D3×Dic3—24no—
26C2×C3×D3×Dic3C2214yescomplemented
27C3×#3752C2214yescomplemented
28C32×(C2×D3)⋊C4C2214yescomplemented
29C3×#3722C2214yescomplemented
30C3×(C2×D3)⋊Dic3C2214yescomplemented
31C24×C3×D3—31no—
32C24×C3×D3—31no—
33C23×D32C2×C311yescharacteristic
34C23×C32×C4—31no—
35C23×C3×Dic3—31no—
36C22×C3×C4×D3—21no—
37C22×C3×C4×D3—31no—
38C22×C3×C4×D3D311yescharacteristic, complemented
39C22×C3×C4×D3C2×C311yescharacteristic, complemented
40C22×D3×Dic3C2×C311yescharacteristic, complemented
41C2×C32×C22⋊C4—31no—
42C2×#3752C2×C311yescharacteristic, complemented
43C2×C3×#217—31no—
44C2×C3×(C2×D3)⋊C4—21no—
45C2×C3×(C2×D3)⋊C4—31no—
46C2×C3×(C2×D3)⋊C4—31no—
47C2×C3×(C2×D3)⋊C4—31no—
48C2×C3×(C2×D3)⋊C4—31no—
49C2×C3×(C2×D3)⋊C4—38no—
50C2×C3×(C2×D3)⋊C4—31no—
51C2×C3×(C2×D3)⋊C4—61no—
52C2×C3×(C2×D3)⋊C4D311yescharacteristic, direct product factor
53C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
54C3×D3×C22⋊C4—38no—
55C2×#3722C2×C311yescharacteristic, complemented
56C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
57D3×(C2×D3)⋊C4C2×C318yesdirect product factor
58C23×C33C2311yescharacteristic
59C22×C3×C3⋊D3—22no—
60C22×C3×C3⋊D3—22no—
61C22×C3×C3⋊D3C2×C414yescomplemented
62C22×C3×C3⋊D3C2312yes—
63C22×C32×D3—22no—
64C22×C32×D3—22no—
65C22×C32×D3C2×C414yes—
66C22×C32×D3C2×C414yescomplemented
67C22×C32×D3D414yes—
68C22×C32×D3D414yes—
69C22×C32×D3C2312yes—
70C22×C32×D3C2312yes—
71C2×C3×D32—232no—
72C2×C3×D32—28no—
73C2×C3×D32—28no—
74C2×C3×D32C2×C4116yescomplemented
75C2×C33×C4—22no—
76C2×C33×C4C2312yescomplemented
77C2×C3×C3⋊Dic3—22no—
78C2×C3×C3⋊Dic3C2312yescomplemented
79C2×C32×Dic3—22no—
80C2×C32×Dic3—22no—
81C2×C32×Dic3C2312yescomplemented
82C2×C32×Dic3C2312yescomplemented
83C32×C4×D3—28no—
84C3×D3×Dic3—28no—
85C22×C3×C22⋊C4—91no—
86C22×(C2×D3)⋊C4—31no—
87C2×D3×C22⋊C4—31no—
88C24×C32—31no—
89C24×C32—31no—
90C23×C3⋊D3C22×C311yescharacteristic
91C23×C3×D3—21no—
92C23×C3×D3—21no—
93C23×C3×D3—31no—
94C23×C3×D3—31no—
95C23×C3×D3—38no—
96C23×C3×D3—38no—
97C23×C3×D3—34no—
98C23×C3×D3—34no—
99C23×C3×D3—64no—
100C23×C3×D3—64no—
101C23×C3×D3—64no—
102C23×C3×D3—64no—
103C23×C3×D3—61no—
104C23×C3×D3C2×D311yescharacteristic
105C23×C3×D3C2×D311yescharacteristic
106C23×C3×D3C22×C311yescharacteristic
107C23×C3×D3C22×C311yescharacteristic
108C22×D32—24no—
109C22×D32—24no—
110C22×D32C3×C418yescomplemented
111C22×D32C22×C314yes—
112C22×C32×C4—21no—
113C22×C32×C4—21no—
114C22×C32×C4—21no—
115C22×C32×C4—31no—
116C22×C32×C4—31no—
117C22×C32×C4—34no—
118C22×C32×C4—41no—
119C22×C32×C4—64no—
120C22×C32×C4C2×D311yescharacteristic, complemented
121C22×C32×C4C2×D311yescharacteristic, complemented
122C22×C32×C4C22×C311yescharacteristic, complemented
123C22×C3⋊Dic3C22×C311yescharacteristic, complemented
124C22×C3×Dic3—21no—
125C22×C3×Dic3—21no—
126C22×C3×Dic3—31no—
127C22×C3×Dic3—31no—
128C22×C3×Dic3—34no—
129C22×C3×Dic3—64no—
130C22×C3×Dic3—61no—
131C22×C3×Dic3C2×D311yescharacteristic, complemented
132C22×C3×Dic3C2×D311yescharacteristic, complemented
133C22×C3×Dic3C22×C311yescharacteristic, complemented
134C22×C3×Dic3C22×C311yescharacteristic, complemented
135C2×C3×C4×D3—28no—
136C2×C3×C4×D3—24no—
137C2×C3×C4×D3—24no—
138C2×C3×C4×D3—24no—
139C2×C3×C4×D3—34no—
140C2×C3×C4×D3—64no—
141C2×C3×C4×D3C2×D314yescomplemented
142C2×C3×C4×D3C22×C314yescomplemented
143C2×D3×Dic3—24no—
144C2×D3×Dic3C22×C314yescomplemented
145C32×C22⋊C4—34no—
146#3752C22×C314yescomplemented
147C3×#217—34no—
148C3×(C2×D3)⋊C4—24no—
149C3×(C2×D3)⋊C4—34no—
150C3×(C2×D3)⋊C4—34no—
151C3×(C2×D3)⋊C4—34no—
152C3×(C2×D3)⋊C4—34no—
153C3×(C2×D3)⋊C4—34no—
154C3×(C2×D3)⋊C4—64no—
155C3×(C2×D3)⋊C4C2×D314yesdirect product factor
156C3×(C2×D3)⋊C4C22×C314yescomplemented
157#3722C22×C314yescomplemented
158(C2×D3)⋊Dic3C22×C314yescomplemented
159C22×C33C22×C412yes—
160C22×C33C2×D412yes—
161C22×C33C2×D412yes—
162C22×C33C2411yescharacteristic
163C2×C3×C3⋊D3—28no—
164C2×C3×C3⋊D3—22no—
165C2×C3×C3⋊D3—22no—
166C2×C3×C3⋊D3C22×C414yescomplemented
167C2×C32×D3—28no—
168C2×C32×D3—22no—
169C2×C32×D3—22no—
170C2×C32×D3C22⋊C4116yescomplemented
171C2×C32×D3C22×C414yes—
172C2×C32×D3C22×C414yescomplemented
173C2×C32×D3C2×D414yes—
174C2×C32×D3C2×D414yes—
175C3×D32—232no—
176C33×C4—22no—
177C3×C3⋊Dic3—22no—
178C32×Dic3—22no—
179C32×Dic3—22no—
180C25×C3—91no—
181C24×D3—31no—
182C24×D3—31no—
183C23×C3×C4—31no—
184C23×C3×C4—31no—
185C23×C3×C4—61no—
186C23×C3×C4—91no—
187C23×Dic3—31no—
188C22×C4×D3—31no—
189C22×C4×D3C3×D311yescharacteristic, complemented
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—61no—
193C2×C3×C22⋊C4—98no—
194C2×C3×C22⋊C4—91no—
195C2×C3×C22⋊C4—91no—
196C2×C3×C22⋊C4—91no—
197C2×#217—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—38no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4C3×D311yescharacteristic, direct product factor
206D3×C22⋊C4—38no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—34no—
211C23×C32—34no—
212C23×C32—34no—
213C23×C32—32no—
214C23×C32—34no—
215C23×C32—32no—
216C23×C32—41no—
217C23×C32—62no—
218C23×C32—62no—
219C23×C32C22×D311yescharacteristic
220C23×C32C22×D311yescharacteristic
221C23×C32C23×C311yescharacteristic
222C22×C3⋊D3—22no—
223C22×C3⋊D3—22no—
224C22×C3⋊D3C2×C3×C414yescomplemented
225C22×C3⋊D3C23×C312yes—
226C22×C3×D3—22no—
227C22×C3×D3—22no—
228C22×C3×D3—22no—
229C22×C3×D3—22no—
230C22×C3×D3—24no—
231C22×C3×D3—24no—
232C22×C3×D3—24no—
233C22×C3×D3—24no—
234C22×C3×D3—22no—
235C22×C3×D3—22no—
236C22×C3×D3—34no—
237C22×C3×D3—34no—
238C22×C3×D3—32no—
239C22×C3×D3—32no—
240C22×C3×D3—316no—
241C22×C3×D3—316no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—62no—
245C22×C3×D3—64no—
246C22×C3×D3—632no—
247C22×C3×D3—68no—
248C22×C3×D3—68no—
249C22×C3×D3—62no—
250C22×C3×D3—62no—
251C22×C3×D3—62no—
252C22×C3×D3—62no—
253C22×C3×D3—632no—
254C22×C3×D3—68no—
255C22×C3×D3—68no—
256C22×C3×D3—122no—
257C22×C3×D3—122no—
258C22×C3×D3C4×D314yes—
259C22×C3×D3C4×D314yescomplemented
260C22×C3×D3D1214yes—
261C22×C3×D3#6714yes—
262C22×C3×D3C2×C3×C414yes—
263C22×C3×D3C2×C3×C414yescomplemented
264C22×C3×D3C3×D414yes—
265C22×C3×D3C3×D414yes—
266C22×C3×D3C22×D312yes—
267C22×C3×D3C22×D312yes—
268C22×C3×D3C23×C312yes—
269C22×C3×D3C23×C312yes—
270C2×D32—232no—
271C2×D32—28no—
272C2×D32—28no—
273C2×D32C2×C3×C4116yescomplemented
274C2×C32×C4—22no—
275C2×C32×C4—24no—
276C2×C32×C4—22no—
277C2×C32×C4—22no—
278C2×C32×C4—22no—
279C2×C32×C4—22no—
280C2×C32×C4—22no—
281C2×C32×C4—32no—
282C2×C32×C4—32no—
283C2×C32×C4—42no—
284C2×C32×C4—42no—
285C2×C32×C4—42no—
286C2×C32×C4—44no—
287C2×C32×C4—68no—
288C2×C32×C4—62no—
289C2×C32×C4—62no—
290C2×C32×C4C22×D312yescomplemented
291C2×C32×C4C22×D312yescomplemented
292C2×C32×C4C23×C312yescomplemented
293C2×C3⋊Dic3—22no—
294C2×C3⋊Dic3C23×C312yescomplemented
295C2×C3×Dic3—24no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—32no—
303C2×C3×Dic3—32no—
304C2×C3×Dic3—42no—
305C2×C3×Dic3—62no—
306C2×C3×Dic3—68no—
307C2×C3×Dic3—62no—
308C2×C3×Dic3—62no—
309C2×C3×Dic3—122no—
310C2×C3×Dic3C22×D312yescomplemented
311C2×C3×Dic3C22×D312yescomplemented
312C2×C3×Dic3C23×C312yescomplemented
313C2×C3×Dic3C23×C312yescomplemented
314C3×C4×D3—216no—
315C3×C4×D3—28no—
316C3×C4×D3—28no—
317C3×C4×D3—68no—
318D3×Dic3—28no—
319C22×C22⋊C4—91noSylow
320C2×C33C2×C22⋊C414yescomplemented
321C2×C33C23×C411yescharacteristic
322C2×C33C22×D411yescharacteristic
323C2×C33C22×D411yescharacteristic
324C3×C3⋊D3—24no—
325C32×D3—24no—
326C32×D3C2×C22⋊C418yescomplemented
327C24×C3—31no—
328C24×C3—31no—
329C24×C3—31no—
330C24×C3—31no—
331C24×C3—61no—
332C24×C3—61no—
333C24×C3—98no—
334C24×C3—94no—
335C24×C3—91no—
336C24×C3—184no—
337C24×C3—184no—
338C23×D3—31no—
339C23×D3—31no—
340C23×D3—38no—
341C23×D3—38no—
342C23×D3—34no—
343C23×D3—34no—
344C23×D3—61no—
345C23×D3—64no—
346C23×D3—64no—
347C23×D3—64no—
348C23×D3—64no—
349C23×D3C2×C3×D311yescharacteristic
350C23×D3C2×C3×D311yescharacteristic
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—34no—
359C22×C3×C4—34no—
360C22×C3×C4—41no—
361C22×C3×C4—64no—
362C22×C3×C4—61no—
363C22×C3×C4—61no—
364C22×C3×C4—64no—
365C22×C3×C4—64no—
366C22×C3×C4—68no—
367C22×C3×C4—94no—
368C22×C3×C4—91no—
369C22×C3×C4—184no—
370C22×C3×C4D3211yescharacteristic, complemented
371C22×C3×C4C2×C3×D311yescharacteristic, complemented
372C22×C3×C4C2×C3×D311yescharacteristic, complemented
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—34no—
376C22×Dic3—61no—
377C22×Dic3—64no—
378C22×Dic3C2×C3×D311yescharacteristic, complemented
379C22×Dic3C2×C3×D311yescharacteristic, complemented
380C2×C4×D3—24no—
381C2×C4×D3—34no—
382C2×C4×D3—64no—
383C2×C4×D3C2×C3×D314yescomplemented
384C3×C22⋊C4—34no—
385C3×C22⋊C4—34no—
386C3×C22⋊C4—64no—
387C3×C22⋊C4—94no—
388C3×C22⋊C4—94no—
389C3×C22⋊C4—94no—
390#217—34no—
391(C2×D3)⋊C4—34no—
392(C2×D3)⋊C4—34no—
393(C2×D3)⋊C4—34no—
394(C2×D3)⋊C4—34no—
395(C2×D3)⋊C4—34no—
396(C2×D3)⋊C4—64no—
397(C2×D3)⋊C4C2×C3×D314yesdirect product factor
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—22no—
402C22×C32—22no—
403C22×C32—22no—
404C22×C32—22no—
405C22×C32—22no—
406C22×C32—22no—
407C22×C32—22no—
408C22×C32—22no—
409C22×C32—22no—
410C22×C32—316no—
411C22×C32—34no—
412C22×C32—34no—
413C22×C32—34no—
414C22×C32—34no—
415C22×C32—42no—
416C22×C32—42no—
417C22×C32—42no—
418C22×C32—41no—
419C22×C32—68no—
420C22×C32—62no—
421C22×C32—62no—
422C22×C32C2×C4×D312yes—
423C22×C32C2×C4×D312yes—
424C22×C32C2×D1212yes—
425C22×C32D3×D412yes—
426C22×C32D3×D412yes—
427C22×C32C2×#6712yes—
428C22×C32C22×C3×C412yes—
429C22×C32C2×C3×D412yes—
430C22×C32C2×C3×D412yes—
431C22×C32C23×D311yescharacteristic
432C22×C32C23×D311yescharacteristic
433C22×C32C24×C311yescharacteristic
434C2×C3⋊D3—28no—
435C2×C3⋊D3—22no—
436C2×C3⋊D3—22no—
437C2×C3⋊D3C22×C3×C414yescomplemented
438C2×C3×D3—28no—
439C2×C3×D3—28no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—22no—
444C2×C3×D3—216no—
445C2×C3×D3—24no—
446C2×C3×D3—24no—
447C2×C3×D3—24no—
448C2×C3×D3—24no—
449C2×C3×D3—34no—
450C2×C3×D3—34no—
451C2×C3×D3—48no—
452C2×C3×D3—42no—
453C2×C3×D3—42no—
454C2×C3×D3—64no—
455C2×C3×D3—632no—
456C2×C3×D3—68no—
457C2×C3×D3—68no—
458C2×C3×D3—62no—
459C2×C3×D3—62no—
460C2×C3×D3—62no—
461C2×C3×D3—62no—
462C2×C3×D3—632no—
463C2×C3×D3—122no—
464C2×C3×D3—122no—
465C2×C3×D3—128no—
466C2×C3×D3(C2×D3)⋊C4116yesdirect product factor
467C2×C3×D3C3×C22⋊C4116yescomplemented
468C2×C3×D3C2×C4×D314yes—
469C2×C3×D3C2×C4×D314yescomplemented
470C2×C3×D3C2×D1214yes—
471C2×C3×D3C2×#6714yes—
472C2×C3×D3C22×C3×C414yes—
473C2×C3×D3C22×C3×C414yescomplemented
474C2×C3×D3C2×C3×D414yes—
475C2×C3×D3C2×C3×D414yes—
476D32—232no—
477C32×C4—22no—
478C32×C4—24no—
479C32×C4—22no—
480C32×C4—22no—
481C32×C4—42no—
482C32×C4—42no—
483C32×C4—44no—
484C32×C4—62no—
485C32×C4—62no—
486C3⋊Dic3—22no—
487C3×Dic3—24no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—42no—
493C3×Dic3—62no—
494C3×Dic3—62no—
495C3×Dic3—122no—
496C25—91no—
497C23×C4—31no—
498C23×C4—91no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—98no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C33C22×C22⋊C411yescharacteristic, complemented, Sylow
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—32no—
509C23×C3—32no—
510C23×C3—34no—
511C23×C3—34no—
512C23×C3—34no—
513C23×C3—34no—
514C23×C3—34no—
515C23×C3—34no—
516C23×C3—32no—
517C23×C3—32no—
518C23×C3—34no—
519C23×C3—34no—
520C23×C3—41no—
521C23×C3—62no—
522C23×C3—64no—
523C23×C3—64no—
524C23×C3—64no—
525C23×C3—62no—
526C23×C3—64no—
527C23×C3—62no—
528C23×C3—62no—
529C23×C3—62no—
530C23×C3—62no—
531C23×C3—916no—
532C23×C3—92no—
533C23×C3—94no—
534C23×C3—122no—
535C23×C3—122no—
536C23×C3—188no—
537C23×C3—188no—
538C23×C3—1832no—
539C23×C3—182no—
540C23×C3—182no—
541C23×C3C2×D3211yescharacteristic
542C23×C3C22×C3×D311yescharacteristic
543C23×C3C22×C3×D311yescharacteristic
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—32no—
547C22×D3—32no—
548C22×D3—34no—
549C22×D3—34no—
550C22×D3—316no—
551C22×D3—316no—
552C22×D3—64no—
553C22×D3—62no—
554C22×D3—632no—
555C22×D3—68no—
556C22×D3—68no—
557C22×D3—62no—
558C22×D3—62no—
559C22×D3—62no—
560C22×D3—62no—
561C22×D3—632no—
562C22×D3—68no—
563C22×D3—68no—
564C22×D3—122no—
565C22×D3—122no—
566C22×D3C3×C4×D314yes—
567C22×D3C3×C4×D314yescomplemented
568C22×D3C3×D1214yes—
569C22×D3C3×#6714yes—
570C22×D3C22×C3×D312yes—
571C22×D3C22×C3×D312yes—
572C2×C3×C4—24no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—42no—
584C2×C3×C4—42no—
585C2×C3×C4—44no—
586C2×C3×C4—42no—
587C2×C3×C4—62no—
588C2×C3×C4—62no—
589C2×C3×C4—68no—
590C2×C3×C4—68no—
591C2×C3×C4—616no—
592C2×C3×C4—64no—
593C2×C3×C4—62no—
594C2×C3×C4—62no—
595C2×C3×C4—62no—
596C2×C3×C4—62no—
597C2×C3×C4—92no—
598C2×C3×C4—122no—
599C2×C3×C4—188no—
600C2×C3×C4—182no—
601C2×C3×C4C2×D3212yescomplemented
602C2×C3×C4C22×C3×D312yescomplemented
603C2×C3×C4C22×C3×D312yescomplemented
604C2×Dic3—22no—
605C2×Dic3—22no—
606C2×Dic3—32no—
607C2×Dic3—32no—
608C2×Dic3—62no—
609C2×Dic3—68no—
610C2×Dic3—62no—
611C2×Dic3—62no—
612C2×Dic3—122no—
613C2×Dic3C22×C3×D312yescomplemented
614C2×Dic3C22×C3×D312yescomplemented
615C4×D3—28no—
616C4×D3—68no—
617C2×C32—24no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—24no—
621C2×C32—21no—
622C2×C32—21no—
623C2×C32—21no—
624C2×C32—21no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—21no—
628C2×C32—24no—
629C2×C32—38no—
630C2×C32—44no—
631C2×C32—41no—
632C2×C32—41no—
633C2×C32—41no—
634C2×C32—64no—
635C2×C32D3×C22⋊C414yescomplemented
636C2×C32C2×(C2×D3)⋊C414yescomplemented
637C2×C32C2×C3×C22⋊C414yescomplemented
638C2×C32C22×C4×D311yescharacteristic
639C2×C32C22×C4×D311yescharacteristic
640C2×C32C22×D1211yescharacteristic
641C2×C32C2×D3×D411yescharacteristic
642C2×C32C2×D3×D411yescharacteristic
643C2×C32C22×#6711yescharacteristic
644C2×C32C23×C3×C411yescharacteristic
645C2×C32C22×C3×D411yescharacteristic
646C2×C32C22×C3×D411yescharacteristic
647C3⋊D3—24no—
648C3×D3—24no—
649C3×D3—24no—
650C3×D3—28no—
651C3×D3—44no—
652C3×D3—64no—
653C3×D3—64no—
654C3×D3—124no—
655C3×D3C2×(C2×D3)⋊C418yesdirect product factor
656C3×D3C2×C3×C22⋊C418yescomplemented
657C24—31no—
658C24—31no—
659C24—94no—
660C24—98no—
661C24—91no—
662C24—184no—
663C24—184no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—34no—
667C22×C4—64no—
668C22×C4—94no—
669C22×C4—91no—
670C22×C4—184no—
671C22×C4C3×D3211yescharacteristic, complemented
672C22⋊C4—34no—
673C22⋊C4—94no—
674C22⋊C4—94no—
675C22⋊C4—94no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—22no—
680C22×C3—22no—
681C22×C3—22no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—316no—
689C22×C3—34no—
690C22×C3—34no—
691C22×C3—34no—
692C22×C3—34no—
693C22×C3—34no—
694C22×C3—34no—
695C22×C3—316no—
696C22×C3—34no—
697C22×C3—34no—
698C22×C3—41no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—42no—
702C22×C3—64no—
703C22×C3—616no—
704C22×C3—64no—
705C22×C3—64no—
706C22×C3—64no—
707C22×C3—62no—
708C22×C3—68no—
709C22×C3—62no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3—68no—
713C22×C3—94no—
714C22×C3—122no—
715C22×C3—128no—
716C22×C3—122no—
717C22×C3—1832no—
718C22×C3—182no—
719C22×C3—182no—
720C22×C3—188no—
721C22×C3C4×D3212yes—
722C22×C3D3×D1212yes—
723C22×C3D3×#6712yes—
724C22×C3C2×C3×C4×D312yes—
725C22×C3C2×C3×C4×D312yes—
726C22×C3C2×C3×D1212yes—
727C22×C3C3×D3×D412yes—
728C22×C3C3×D3×D412yes—
729C22×C3C2×C3×#6712yes—
730C22×C3C22×D3211yescharacteristic
731C22×C3C23×C3×D311yescharacteristic
732C22×C3C23×C3×D311yescharacteristic
733C2×D3—28no—
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—34no—
737C2×D3—34no—
738C2×D3—64no—
739C2×D3—632no—
740C2×D3—68no—
741C2×D3—68no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—632no—
747C2×D3—122no—
748C2×D3—128no—
749C2×D3—122no—
750C2×D3C3×(C2×D3)⋊C4116yesdirect product factor
751C2×D3C2×C3×C4×D314yes—
752C2×D3C2×C3×C4×D314yescomplemented
753C2×D3C2×C3×D1214yes—
754C2×D3C2×C3×#6714yes—
755C3×C4—24no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—42no—
760C3×C4—42no—
761C3×C4—44no—
762C3×C4—64no—
763C3×C4—62no—
764C3×C4—62no—
765C3×C4—62no—
766C3×C4—62no—
767C3×C4—122no—
768C3×C4—182no—
769Dic3—22no—
770Dic3—22no—
771Dic3—62no—
772Dic3—62no—
773Dic3—122no—
774C32—21no—
775C32—21no—
776C32—21no—
777C32—41no—
778C32C2×D3×C22⋊C411yescharacteristic, complemented
779C32C22×(C2×D3)⋊C411yescharacteristic, complemented
780C32C22×C3×C22⋊C411yescharacteristic, complemented
781C23—32no—
782C23—34no—
783C23—34no—
784C23—34no—
785C23—32no—
786C23—34no—
787C23—62no—
788C23—62no—
789C23—916no—
790C23—92no—
791C23—94no—
792C23—188no—
793C23—1832no—
794C23—188no—
795C23—182no—
796C23—182no—
797C23C2×C3×D3211yescharacteristic
798C2×C4—22no—
799C2×C4—32no—
800C2×C4—32no—
801C2×C4—68no—
802C2×C4—62no—
803C2×C4—62no—
804C2×C4—92no—
805C2×C4—188no—
806C2×C4—182no—
807C2×C4C2×C3×D3212yescomplemented
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—24no—
812C2×C3—24no—
813C2×C3—24no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—38no—
821C2×C3—38no—
822C2×C3—41no—
823C2×C3—44no—
824C2×C3—41no—
825C2×C3—41no—
826C2×C3—68no—
827C2×C3—64no—
828C2×C3—64no—
829C2×C3—124no—
830C2×C3—184no—
831C2×C3D3×(C2×D3)⋊C414yesdirect product factor
832C2×C3C3×D3×C22⋊C414yescomplemented
833C2×C3C2×C3×(C2×D3)⋊C414yescomplemented
834C2×C3C2×C4×D3211yescharacteristic
835C2×C3C2×D3×D1211yescharacteristic
836C2×C3C2×D3×#6711yescharacteristic
837C2×C3C22×C3×C4×D311yescharacteristic
838C2×C3C22×C3×C4×D311yescharacteristic
839C2×C3C22×C3×D1211yescharacteristic
840C2×C3C2×C3×D3×D411yescharacteristic
841C2×C3C2×C3×D3×D411yescharacteristic
842C2×C3C22×C3×#6711yescharacteristic
843D3—24no—
844D3—64no—
845D3—64no—
846D3—124no—
847D3C2×C3×(C2×D3)⋊C418yesdirect product factor
848C22—34no—
849C22—316no—
850C22—34no—
851C22—34no—
852C22—34no—
853C22—62no—
854C22—68no—
855C22—62no—
856C22—94no—
857C22—1832no—
858C22—182no—
859C22—188no—
860C22—182no—
861C22C3×C4×D3212yes—
862C22C3×D3×D1212yes—
863C22C3×D3×#6712yes—
864C22C22×C3×D3211yescharacteristic
865C4—22no—
866C4—62no—
867C4—62no—
868C4—182no—
869C3—21no—
870C3—21no—
871C3—21no—
872C3—41no—
873C3C2×D3×(C2×D3)⋊C411yescharacteristic, direct product factor
874C3C2×C3×D3×C22⋊C411yescharacteristic, complemented
875C3C22×C3×(C2×D3)⋊C411yescharacteristic, complemented
876C2—38no—
877C2—64no—
878C2—184no—
879C2C3×D3×(C2×D3)⋊C414yesdirect product factor
880C2C2×C3×C4×D3211yescharacteristic
881C2C2×C3×D3×D1211yescharacteristic
882C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C3×D32C2
cosocleC22×C32C24×C3
hypercenterC22×C3×C4D32
hypocenterC32C22×C3×C22⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C22×C32×C4×D3C2semidirect
3. C22×C3×D3×Dic3C2semidirect
4. C2×C3×#3752C2semidirect
5. C2×C32×(C2×D3)⋊C4C2semidirect
6. C2×C3×#3722C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. C3×D3×(C2×D3)⋊C4C2direct (N × H)
11. C2×D3×(C2×D3)⋊C4C3direct (N × H)
17. C22×C3×D32C4semidirect
19. C22×C33×C4C22semidirect
20. C22×C3×C3⋊Dic3C22semidirect
21. C22×C32×Dic3C22semidirect
22. C22×C32×Dic3C22semidirect
24. C2×C32×C4×D3C22semidirect
26. C2×C3×D3×Dic3C22semidirect
27. C3×#3752C22semidirect
28. C32×(C2×D3)⋊C4C22semidirect
29. C3×#3722C22semidirect
30. C3×(C2×D3)⋊Dic3C22semidirect
38. C22×C3×C4×D3D3semidirect
39. C22×C3×C4×D3C2×C3semidirect
40. C22×D3×Dic3C2×C3semidirect
42. C2×#3752C2×C3semidirect
52. C2×C3×(C2×D3)⋊C4D3direct (N × H)
53. C2×C3×(C2×D3)⋊C4C2×C3semidirect
55. C2×#3722C2×C3semidirect
56. C2×(C2×D3)⋊Dic3C2×C3semidirect
57. D3×(C2×D3)⋊C4C2×C3direct (N × H)
61. C22×C3×C3⋊D3C2×C4semidirect
66. C22×C32×D3C2×C4semidirect
74. C2×C3×D32C2×C4semidirect
76. C2×C33×C4C23semidirect
78. C2×C3×C3⋊Dic3C23semidirect
81. C2×C32×Dic3C23semidirect
82. C2×C32×Dic3C23semidirect
110. C22×D32C3×C4semidirect
120. C22×C32×C4C2×D3semidirect
121. C22×C32×C4C2×D3semidirect
122. C22×C32×C4C22×C3semidirect
123. C22×C3⋊Dic3C22×C3semidirect
131. C22×C3×Dic3C2×D3semidirect
132. C22×C3×Dic3C2×D3semidirect
133. C22×C3×Dic3C22×C3semidirect
134. C22×C3×Dic3C22×C3semidirect
141. C2×C3×C4×D3C2×D3semidirect
142. C2×C3×C4×D3C22×C3semidirect
144. C2×D3×Dic3C22×C3semidirect
146. #3752C22×C3semidirect
155. C3×(C2×D3)⋊C4C2×D3direct (N × H)
156. C3×(C2×D3)⋊C4C22×C3semidirect
157. #3722C22×C3semidirect
158. (C2×D3)⋊Dic3C22×C3semidirect
166. C2×C3×C3⋊D3C22×C4semidirect
170. C2×C32×D3C22⋊C4semidirect
172. C2×C32×D3C22×C4semidirect
189. C22×C4×D3C3×D3semidirect
205. C2×(C2×D3)⋊C4C3×D3direct (N × H)
224. C22×C3⋊D3C2×C3×C4semidirect
259. C22×C3×D3C4×D3semidirect
263. C22×C3×D3C2×C3×C4semidirect
273. C2×D32C2×C3×C4semidirect
290. C2×C32×C4C22×D3semidirect
291. C2×C32×C4C22×D3semidirect
292. C2×C32×C4C23×C3semidirect
294. C2×C3⋊Dic3C23×C3semidirect
310. C2×C3×Dic3C22×D3semidirect
311. C2×C3×Dic3C22×D3semidirect
312. C2×C3×Dic3C23×C3semidirect
313. C2×C3×Dic3C23×C3semidirect
320. C2×C33C2×C22⋊C4semidirect
326. C32×D3C2×C22⋊C4semidirect
370. C22×C3×C4D32semidirect
371. C22×C3×C4C2×C3×D3semidirect
372. C22×C3×C4C2×C3×D3semidirect
378. C22×Dic3C2×C3×D3semidirect
379. C22×Dic3C2×C3×D3semidirect
383. C2×C4×D3C2×C3×D3semidirect
397. (C2×D3)⋊C4C2×C3×D3direct (N × H)
437. C2×C3⋊D3C22×C3×C4semidirect
466. C2×C3×D3(C2×D3)⋊C4direct (N × H)
467. C2×C3×D3C3×C22⋊C4semidirect
469. C2×C3×D3C2×C4×D3semidirect
473. C2×C3×D3C22×C3×C4semidirect
504. C33C22×C22⋊C4semidirect
567. C22×D3C3×C4×D3semidirect
601. C2×C3×C4C2×D32semidirect
602. C2×C3×C4C22×C3×D3semidirect
603. C2×C3×C4C22×C3×D3semidirect
613. C2×Dic3C22×C3×D3semidirect
614. C2×Dic3C22×C3×D3semidirect
635. C2×C32D3×C22⋊C4semidirect
636. C2×C32C2×(C2×D3)⋊C4semidirect
637. C2×C32C2×C3×C22⋊C4semidirect
655. C3×D3C2×(C2×D3)⋊C4direct (N × H)
656. C3×D3C2×C3×C22⋊C4semidirect
671. C22×C4C3×D32semidirect
750. C2×D3C3×(C2×D3)⋊C4direct (N × H)
752. C2×D3C2×C3×C4×D3semidirect
778. C32C2×D3×C22⋊C4semidirect
779. C32C22×(C2×D3)⋊C4semidirect
780. C32C22×C3×C22⋊C4semidirect
807. C2×C4C2×C3×D32semidirect
831. C2×C3D3×(C2×D3)⋊C4direct (N × H)
832. C2×C3C3×D3×C22⋊C4semidirect
833. C2×C3C2×C3×(C2×D3)⋊C4semidirect
847. D3C2×C3×(C2×D3)⋊C4direct (N × H)
873. C3C2×D3×(C2×D3)⋊C4direct (N × H)
874. C3C2×C3×D3×C22⋊C4semidirect
875. C3C22×C3×(C2×D3)⋊C4semidirect
879. C2C3×D3×(C2×D3)⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D322
C22×C32×C4×D32
C22×C3×D3×Dic32
C2×C3×#37522
C2×C32×(C2×D3)⋊C42
C2×C3×#37222
C2×C3×(C2×D3)⋊Dic32
C3×D3×(C2×D3)⋊C42
C22×C3×(C2×D3)⋊C43
C2×C3×D3×C22⋊C43
C2×D3×(C2×D3)⋊C43