Finite Group Databasebeta

← C2×C3×D3×Dic3⋊C4 #13174436

Subgroups — C2×C3×D3×Dic3⋊C4 #13174436

Order 1728.

2146 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic
2C22×C3×D3×Dic3C211yesmaximal, characteristic
3C22×C3×D3×Dic3C211yesmaximal, characteristic
4C2×C3×#3750C211yesmaximal, characteristic, complemented
5C2×C32×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C2×C3×#3724C211yesmaximal, characteristic, complemented
7C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8C3×D3×Dic3⋊C4C218yesmaximal, direct product factor
9C22×C3×Dic3⋊C4—31nomaximal
10C2×C3×D3×C4⋊C4—31nomaximal
11C2×D3×Dic3⋊C4C311yesmaximal, characteristic, direct product factor
12C23×C32×D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×C32×C4×D3—24no—
20C2×C32×C4×D3C2214yes—
21C2×C3×D3×Dic3—24no—
22C2×C3×D3×Dic3C418yescomplemented
23C2×C3×D3×Dic3C2214yes—
24C2×C3×D3×Dic3C2214yes—
25C3×#3750C2214yescomplemented
26C32×Dic3⋊C4C2214yescomplemented
27C3×#3724C2214yescomplemented
28C3×Dic3⋊Dic3C2214yescomplemented
29C23×C32×C4—31no—
30C23×C3×Dic3—31no—
31C23×C3×Dic3—31no—
32C22×C3×C4×D3—21no—
33C22×C3×C4×D3—31no—
34C22×C3×C4×D3—31no—
35C22×C3×C4×D3D311yescharacteristic
36C22×C3×C4×D3C2×C311yescharacteristic
37C22×D3×Dic3C2×C311yescharacteristic
38C22×D3×Dic3C2×C311yescharacteristic
39C2×C32×C4⋊C4—31no—
40C2×#3750C2×C311yescharacteristic, complemented
41C2×C3×C4⋊Dic3—31no—
42C2×C3×Dic3⋊C4—21no—
43C2×C3×Dic3⋊C4—31no—
44C2×C3×Dic3⋊C4—31no—
45C2×C3×Dic3⋊C4—31no—
46C2×C3×Dic3⋊C4—31no—
47C2×C3×Dic3⋊C4—31no—
48C2×C3×Dic3⋊C4—38no—
49C2×C3×Dic3⋊C4—61no—
50C2×C3×Dic3⋊C4D311yescharacteristic, direct product factor
51C2×C3×Dic3⋊C4C2×C311yescharacteristic, complemented
52C3×D3×C4⋊C4—38no—
53C2×#3724C2×C311yescharacteristic, complemented
54C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
55D3×Dic3⋊C4C2×C318yesdirect product factor
56C23×C33C2311yescharacteristic
57C22×C32×D3C2×C414yes—
58C22×C32×D3D414yes—
59C22×C32×D3Q814yes—
60C22×C32×D3C2312yes—
61C2×C33×C4—22no—
62C2×C33×C4C2312yes—
63C2×C3×C3⋊Dic3—22no—
64C2×C3×C3⋊Dic3C2×C414yescomplemented
65C2×C3×C3⋊Dic3C2312yes—
66C2×C3×C3⋊Dic3C2312yes—
67C2×C32×Dic3—22no—
68C2×C32×Dic3—22no—
69C2×C32×Dic3C2×C414yescomplemented
70C2×C32×Dic3C2312yes—
71C2×C32×Dic3C2312yes—
72C2×C32×Dic3C2312yes—
73C32×C4×D3—28no—
74C3×D3×Dic3—28no—
75C3×D3×Dic3C2×C4116yescomplemented
76C22×C3×C4⋊C4—91no—
77C22×Dic3⋊C4—31no—
78C2×D3×C4⋊C4—31no—
79C24×C32—31no—
80C23×C3×D3—21no—
81C23×C3×D3C2×D311yescharacteristic
82C23×C3×D3C22×C311yescharacteristic
83C22×C32×C4—21no—
84C22×C32×C4—21no—
85C22×C32×C4—21no—
86C22×C32×C4—31no—
87C22×C32×C4—31no—
88C22×C32×C4—31no—
89C22×C32×C4—34no—
90C22×C32×C4—41no—
91C22×C32×C4—64no—
92C22×C32×C4C2×D311yescharacteristic
93C22×C32×C4C2×D311yescharacteristic
94C22×C32×C4C22×C311yescharacteristic
95C22×C3⋊Dic3C22×C311yescharacteristic
96C22×C3⋊Dic3C22×C311yescharacteristic
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—38no—
103C22×C3×Dic3—34no—
104C22×C3×Dic3—31no—
105C22×C3×Dic3—31no—
106C22×C3×Dic3—34no—
107C22×C3×Dic3—64no—
108C22×C3×Dic3—61no—
109C22×C3×Dic3—61no—
110C22×C3×Dic3C2×D311yescharacteristic
111C22×C3×Dic3C2×D311yescharacteristic
112C22×C3×Dic3C2×D311yescharacteristic
113C22×C3×Dic3C22×C311yescharacteristic
114C22×C3×Dic3C22×C311yescharacteristic
115C22×C3×Dic3C22×C311yescharacteristic
116C2×C3×C4×D3—28no—
117C2×C3×C4×D3—24no—
118C2×C3×C4×D3—24no—
119C2×C3×C4×D3—24no—
120C2×C3×C4×D3—38no—
121C2×C3×C4×D3—34no—
122C2×C3×C4×D3—34no—
123C2×C3×C4×D3—64no—
124C2×C3×C4×D3C2×D314yes—
125C2×C3×C4×D3C22×C314yes—
126C2×D3×Dic3—24no—
127C2×D3×Dic3C3×C418yescomplemented
128C2×D3×Dic3C22×C314yes—
129C2×D3×Dic3C22×C314yes—
130C32×C4⋊C4—34no—
131#3750C22×C314yescomplemented
132C3×C4⋊Dic3—34no—
133C3×Dic3⋊C4—24no—
134C3×Dic3⋊C4—34no—
135C3×Dic3⋊C4—34no—
136C3×Dic3⋊C4—34no—
137C3×Dic3⋊C4—34no—
138C3×Dic3⋊C4—34no—
139C3×Dic3⋊C4—64no—
140C3×Dic3⋊C4C2×D314yesdirect product factor
141C3×Dic3⋊C4C22×C314yescomplemented
142#3724C22×C314yescomplemented
143Dic3⋊Dic3C22×C314yescomplemented
144C22×C33C22×C412yes—
145C22×C33C2×D412yes—
146C22×C33C2×Q812yes—
147C22×C33C2411yescharacteristic
148C2×C32×D3C4⋊C4116yescomplemented
149C2×C32×D3C22×C414yes—
150C2×C32×D3C2×D414yes—
151C2×C32×D3C2×Q814yes—
152C33×C4—22no—
153C3×C3⋊Dic3—22no—
154C3×C3⋊Dic3C22×C414yescomplemented
155C32×Dic3—22no—
156C32×Dic3—22no—
157C32×Dic3C22×C414yescomplemented
158C23×C3×C4—31no—
159C23×C3×C4—31no—
160C23×C3×C4—61no—
161C23×C3×C4—91no—
162C23×C3×C4—91no—
163C23×Dic3—31no—
164C23×Dic3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3C3×D311yescharacteristic
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—61no—
171C2×C3×C4⋊C4—98no—
172C2×C3×C4⋊C4—91no—
173C2×C3×C4⋊C4—91no—
174C2×C3×C4⋊C4—91no—
175C2×C4⋊Dic3—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—38no—
182C2×Dic3⋊C4—61no—
183C2×Dic3⋊C4C3×D311yescharacteristic, direct product factor
184D3×C4⋊C4—38no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—21no—
188C23×C32—34no—
189C23×C32—34no—
190C23×C32—34no—
191C23×C32—32no—
192C23×C32—41no—
193C23×C32C22×D311yescharacteristic
194C23×C32C22×D311yescharacteristic
195C23×C32C23×C311yescharacteristic
196C22×C3×D3—24no—
197C22×C3×D3—24no—
198C22×C3×D3—24no—
199C22×C3×D3—22no—
200C22×C3×D3Dic614yes—
201C22×C3×D3C4×D314yes—
202C22×C3×D3#6714yes—
203C22×C3×D3C2×C3×C414yes—
204C22×C3×D3C3×D414yes—
205C22×C3×D3C3×Q814yes—
206C22×C3×D3C22×D312yes—
207C22×C3×D3C23×C312yes—
208C2×C32×C4—22no—
209C2×C32×C4—24no—
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—22no—
214C2×C32×C4—22no—
215C2×C32×C4—34no—
216C2×C32×C4—32no—
217C2×C32×C4—32no—
218C2×C32×C4—32no—
219C2×C32×C4—42no—
220C2×C32×C4—42no—
221C2×C32×C4—42no—
222C2×C32×C4—44no—
223C2×C32×C4—68no—
224C2×C32×C4—62no—
225C2×C32×C4—62no—
226C2×C32×C4C22×D312yes—
227C2×C32×C4C22×D312yes—
228C2×C32×C4C23×C312yes—
229C2×C3⋊Dic3—22no—
230C2×C3⋊Dic3C2×C3×C414yescomplemented
231C2×C3⋊Dic3C23×C312yes—
232C2×C3⋊Dic3C23×C312yes—
233C2×C3×Dic3—24no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3—22no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3—22no—
242C2×C3×Dic3—34no—
243C2×C3×Dic3—34no—
244C2×C3×Dic3—32no—
245C2×C3×Dic3—32no—
246C2×C3×Dic3—316no—
247C2×C3×Dic3—32no—
248C2×C3×Dic3—32no—
249C2×C3×Dic3—42no—
250C2×C3×Dic3—62no—
251C2×C3×Dic3—64no—
252C2×C3×Dic3—62no—
253C2×C3×Dic3—68no—
254C2×C3×Dic3—62no—
255C2×C3×Dic3—62no—
256C2×C3×Dic3—122no—
257C2×C3×Dic3C4×D314yescomplemented
258C2×C3×Dic3C2×C3×C414yescomplemented
259C2×C3×Dic3C22×D312yes—
260C2×C3×Dic3C22×D312yes—
261C2×C3×Dic3C22×D312yes—
262C2×C3×Dic3C23×C312yes—
263C2×C3×Dic3C23×C312yes—
264C2×C3×Dic3C23×C312yes—
265C3×C4×D3—216no—
266C3×C4×D3—28no—
267C3×C4×D3—28no—
268C3×C4×D3—316no—
269C3×C4×D3—68no—
270D3×Dic3—28no—
271D3×Dic3C2×C3×C4116yescomplemented
272C22×C4⋊C4—91noSylow
273C2×C33C2×C4⋊C414yescomplemented
274C2×C33C23×C411yescharacteristic
275C2×C33C22×D411yescharacteristic
276C2×C33C22×Q811yescharacteristic
277C32×D3C2×C4⋊C418yescomplemented
278C24×C3—31no—
279C24×C3—31no—
280C24×C3—61no—
281C23×D3C2×C3×D311yescharacteristic
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—34no—
292C22×C3×C4—34no—
293C22×C3×C4—41no—
294C22×C3×C4—64no—
295C22×C3×C4—61no—
296C22×C3×C4—61no—
297C22×C3×C4—61no—
298C22×C3×C4—64no—
299C22×C3×C4—64no—
300C22×C3×C4—68no—
301C22×C3×C4—94no—
302C22×C3×C4—98no—
303C22×C3×C4—94no—
304C22×C3×C4—91no—
305C22×C3×C4—91no—
306C22×C3×C4—184no—
307C22×C3×C4D3211yescharacteristic
308C22×C3×C4C2×C3×D311yescharacteristic
309C22×C3×C4C2×C3×D311yescharacteristic
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—38no—
313C22×Dic3—34no—
314C22×Dic3—31no—
315C22×Dic3—31no—
316C22×Dic3—34no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—64no—
320C22×Dic3C2×C3×D311yescharacteristic
321C22×Dic3C2×C3×D311yescharacteristic
322C22×Dic3C2×C3×D311yescharacteristic
323C2×C4×D3—24no—
324C2×C4×D3—38no—
325C2×C4×D3—34no—
326C2×C4×D3—34no—
327C2×C4×D3—64no—
328C2×C4×D3C2×C3×D314yes—
329C3×C4⋊C4—34no—
330C3×C4⋊C4—34no—
331C3×C4⋊C4—64no—
332C3×C4⋊C4—94no—
333C3×C4⋊C4—94no—
334C3×C4⋊C4—94no—
335C4⋊Dic3—34no—
336Dic3⋊C4—34no—
337Dic3⋊C4—34no—
338Dic3⋊C4—34no—
339Dic3⋊C4—34no—
340Dic3⋊C4—34no—
341Dic3⋊C4—64no—
342Dic3⋊C4C2×C3×D314yesdirect product factor
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—22no—
347C22×C32—22no—
348C22×C32—22no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—316no—
356C22×C32—34no—
357C22×C32—34no—
358C22×C32—34no—
359C22×C32—42no—
360C22×C32—42no—
361C22×C32—42no—
362C22×C32—41no—
363C22×C32C2×Dic612yes—
364C22×C32C2×C4×D312yes—
365C22×C32C2×C4×D312yes—
366C22×C32D3×D412yes—
367C22×C32D3×Q812yes—
368C22×C32C2×#6712yes—
369C22×C32C22×C3×C412yes—
370C22×C32C2×C3×D412yes—
371C22×C32C2×C3×Q812yes—
372C22×C32C23×D311yescharacteristic
373C22×C32C23×D311yescharacteristic
374C22×C32C24×C311yescharacteristic
375C2×C3×D3—216no—
376C2×C3×D3—24no—
377C2×C3×D3—24no—
378C2×C3×D3—24no—
379C2×C3×D3Dic3⋊C4116yesdirect product factor
380C2×C3×D3C3×C4⋊C4116yescomplemented
381C2×C3×D3C2×Dic614yes—
382C2×C3×D3C2×C4×D314yes—
383C2×C3×D3C2×#6714yes—
384C2×C3×D3C22×C3×C414yes—
385C2×C3×D3C2×C3×D414yes—
386C2×C3×D3C2×C3×Q814yes—
387C32×C4—22no—
388C32×C4—24no—
389C32×C4—22no—
390C32×C4—22no—
391C32×C4—34no—
392C32×C4—42no—
393C32×C4—42no—
394C32×C4—44no—
395C32×C4—62no—
396C32×C4—62no—
397C3⋊Dic3—22no—
398C3⋊Dic3C22×C3×C414yescomplemented
399C3×Dic3—24no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—24no—
405C3×Dic3—34no—
406C3×Dic3—34no—
407C3×Dic3—42no—
408C3×Dic3—64no—
409C3×Dic3—62no—
410C3×Dic3—62no—
411C3×Dic3—122no—
412C3×Dic3C2×C4×D314yescomplemented
413C3×Dic3C22×C3×C414yescomplemented
414C23×C4—31no—
415C23×C4—91no—
416C23×C4—91no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—98no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4—91no—
422C33C22×C4⋊C411yescharacteristic, complemented, Sylow
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—32no—
427C23×C3—32no—
428C23×C3—34no—
429C23×C3—34no—
430C23×C3—34no—
431C23×C3—34no—
432C23×C3—34no—
433C23×C3—34no—
434C23×C3—41no—
435C23×C3—62no—
436C23×C3—64no—
437C23×C3—64no—
438C23×C3—64no—
439C23×C3C2×D3211yescharacteristic
440C23×C3C22×C3×D311yescharacteristic
441C23×C3C22×C3×D311yescharacteristic
442C22×D3C3×Dic614yes—
443C22×D3C3×C4×D314yes—
444C22×D3C3×#6714yes—
445C22×D3C22×C3×D312yes—
446C2×C3×C4—24no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—34no—
456C2×C3×C4—34no—
457C2×C3×C4—32no—
458C2×C3×C4—32no—
459C2×C3×C4—32no—
460C2×C3×C4—32no—
461C2×C3×C4—42no—
462C2×C3×C4—42no—
463C2×C3×C4—44no—
464C2×C3×C4—42no—
465C2×C3×C4—62no—
466C2×C3×C4—64no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—68no—
470C2×C3×C4—68no—
471C2×C3×C4—616no—
472C2×C3×C4—64no—
473C2×C3×C4—62no—
474C2×C3×C4—62no—
475C2×C3×C4—62no—
476C2×C3×C4—62no—
477C2×C3×C4—916no—
478C2×C3×C4—92no—
479C2×C3×C4—94no—
480C2×C3×C4—92no—
481C2×C3×C4—122no—
482C2×C3×C4—188no—
483C2×C3×C4—182no—
484C2×C3×C4C2×D3212yes—
485C2×C3×C4C22×C3×D312yes—
486C2×C3×C4C22×C3×D312yes—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—32no—
490C2×Dic3—32no—
491C2×Dic3—34no—
492C2×Dic3—34no—
493C2×Dic3—316no—
494C2×Dic3—32no—
495C2×Dic3—32no—
496C2×Dic3—64no—
497C2×Dic3—62no—
498C2×Dic3—62no—
499C2×Dic3—68no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—122no—
503C2×Dic3C3×C4×D314yescomplemented
504C2×Dic3C22×C3×D312yes—
505C2×Dic3C22×C3×D312yes—
506C2×Dic3C22×C3×D312yes—
507C4×D3—28no—
508C4×D3—316no—
509C4×D3—68no—
510C2×C32—24no—
511C2×C32—21no—
512C2×C32—24no—
513C2×C32—21no—
514C2×C32—21no—
515C2×C32—21no—
516C2×C32—21no—
517C2×C32—21no—
518C2×C32—21no—
519C2×C32—21no—
520C2×C32—21no—
521C2×C32—24no—
522C2×C32—38no—
523C2×C32—44no—
524C2×C32—41no—
525C2×C32—41no—
526C2×C32—41no—
527C2×C32D3×C4⋊C414yescomplemented
528C2×C32C2×Dic3⋊C414yescomplemented
529C2×C32C2×C3×C4⋊C414yescomplemented
530C2×C32C22×Dic611yescharacteristic
531C2×C32C22×C4×D311yescharacteristic
532C2×C32C22×C4×D311yescharacteristic
533C2×C32C2×D3×D411yescharacteristic
534C2×C32C2×D3×Q811yescharacteristic
535C2×C32C22×#6711yescharacteristic
536C2×C32C23×C3×C411yescharacteristic
537C2×C32C22×C3×D411yescharacteristic
538C2×C32C22×C3×Q811yescharacteristic
539C3×D3—28no—
540C3×D3C2×Dic3⋊C418yesdirect product factor
541C3×D3C2×C3×C4⋊C418yescomplemented
542C24—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—34no—
547C22×C4—64no—
548C22×C4—94no—
549C22×C4—98no—
550C22×C4—94no—
551C22×C4—91no—
552C22×C4—91no—
553C22×C4—184no—
554C22×C4C3×D3211yescharacteristic
555C4⋊C4—34no—
556C4⋊C4—94no—
557C4⋊C4—94no—
558C4⋊C4—94no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—316no—
572C22×C3—34no—
573C22×C3—34no—
574C22×C3—34no—
575C22×C3—34no—
576C22×C3—34no—
577C22×C3—34no—
578C22×C3—316no—
579C22×C3—41no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—64no—
584C22×C3—616no—
585C22×C3—64no—
586C22×C3—64no—
587C22×C3D3×Dic612yes—
588C22×C3C4×D3212yes—
589C22×C3D3×#6712yes—
590C22×C3C2×C3×Dic612yes—
591C22×C3C2×C3×C4×D312yes—
592C22×C3C2×C3×C4×D312yes—
593C22×C3C3×D3×D412yes—
594C22×C3C3×D3×Q812yes—
595C22×C3C2×C3×#6712yes—
596C22×C3C22×D3211yescharacteristic
597C22×C3C23×C3×D311yescharacteristic
598C22×C3C23×C3×D311yescharacteristic
599C2×D3C3×Dic3⋊C4116yesdirect product factor
600C2×D3C2×C3×Dic614yes—
601C2×D3C2×C3×C4×D314yes—
602C2×D3C2×C3×#6714yes—
603C3×C4—24no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—34no—
608C3×C4—34no—
609C3×C4—42no—
610C3×C4—42no—
611C3×C4—44no—
612C3×C4—64no—
613C3×C4—64no—
614C3×C4—62no—
615C3×C4—62no—
616C3×C4—62no—
617C3×C4—62no—
618C3×C4—94no—
619C3×C4—122no—
620C3×C4—182no—
621Dic3—22no—
622Dic3—22no—
623Dic3—34no—
624Dic3—34no—
625Dic3—64no—
626Dic3—62no—
627Dic3—62no—
628Dic3—122no—
629Dic3C2×C3×C4×D314yescomplemented
630C32—21no—
631C32—21no—
632C32—21no—
633C32—41no—
634C32C2×D3×C4⋊C411yescharacteristic, complemented
635C32C22×Dic3⋊C411yescharacteristic, complemented
636C32C22×C3×C4⋊C411yescharacteristic, complemented
637C23—32no—
638C23—34no—
639C23—34no—
640C23—34no—
641C23C2×C3×D3211yescharacteristic
642C2×C4—22no—
643C2×C4—32no—
644C2×C4—34no—
645C2×C4—32no—
646C2×C4—32no—
647C2×C4—68no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—916no—
651C2×C4—92no—
652C2×C4—94no—
653C2×C4—92no—
654C2×C4—188no—
655C2×C4—182no—
656C2×C4C2×C3×D3212yes—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—24no—
661C2×C3—24no—
662C2×C3—24no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—38no—
670C2×C3—38no—
671C2×C3—41no—
672C2×C3—44no—
673C2×C3—41no—
674C2×C3—41no—
675C2×C3—68no—
676C2×C3D3×Dic3⋊C414yesdirect product factor
677C2×C3C3×D3×C4⋊C414yescomplemented
678C2×C3C2×C3×Dic3⋊C414yescomplemented
679C2×C3C2×D3×Dic611yescharacteristic
680C2×C3C2×C4×D3211yescharacteristic
681C2×C3C2×D3×#6711yescharacteristic
682C2×C3C22×C3×Dic611yescharacteristic
683C2×C3C22×C3×C4×D311yescharacteristic
684C2×C3C22×C3×C4×D311yescharacteristic
685C2×C3C2×C3×D3×D411yescharacteristic
686C2×C3C2×C3×D3×Q811yescharacteristic
687C2×C3C22×C3×#6711yescharacteristic
688D3C2×C3×Dic3⋊C418yesdirect product factor
689C22—34no—
690C22—316no—
691C22—34no—
692C22—34no—
693C22C3×D3×Dic612yes—
694C22C3×C4×D3212yes—
695C22C3×D3×#6712yes—
696C22C22×C3×D3211yescharacteristic
697C4—22no—
698C4—34no—
699C4—62no—
700C4—62no—
701C4—94no—
702C4—182no—
703C3—21no—
704C3—21no—
705C3—21no—
706C3—41no—
707C3C2×D3×Dic3⋊C411yescharacteristic, direct product factor
708C3C2×C3×D3×C4⋊C411yescharacteristic, complemented
709C3C22×C3×Dic3⋊C411yescharacteristic, complemented
710C2—38no—
711C2C3×D3×Dic3⋊C414yesdirect product factor
712C2C2×C3×D3×Dic611yescharacteristic
713C2C2×C3×C4×D3211yescharacteristic
714C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC2×C32C23×C3×C4
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
cosocleC22×C32C24×C3
hypercenterC22×C3×C4D32
hypocenterC32C22×C3×C4⋊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
4. C2×C3×#3750C2semidirect
5. C2×C32×Dic3⋊C4C2semidirect
6. C2×C3×#3724C2semidirect
7. C2×C3×Dic3⋊Dic3C2semidirect
8. C3×D3×Dic3⋊C4C2direct (N × H)
11. C2×D3×Dic3⋊C4C3direct (N × H)
22. C2×C3×D3×Dic3C4semidirect
25. C3×#3750C22semidirect
26. C32×Dic3⋊C4C22semidirect
27. C3×#3724C22semidirect
28. C3×Dic3⋊Dic3C22semidirect
40. C2×#3750C2×C3semidirect
50. C2×C3×Dic3⋊C4D3direct (N × H)
51. C2×C3×Dic3⋊C4C2×C3semidirect
53. C2×#3724C2×C3semidirect
54. C2×Dic3⋊Dic3C2×C3semidirect
55. D3×Dic3⋊C4C2×C3direct (N × H)
64. C2×C3×C3⋊Dic3C2×C4semidirect
69. C2×C32×Dic3C2×C4semidirect
75. C3×D3×Dic3C2×C4semidirect
127. C2×D3×Dic3C3×C4semidirect
131. #3750C22×C3semidirect
140. C3×Dic3⋊C4C2×D3direct (N × H)
141. C3×Dic3⋊C4C22×C3semidirect
142. #3724C22×C3semidirect
143. Dic3⋊Dic3C22×C3semidirect
148. C2×C32×D3C4⋊C4semidirect
154. C3×C3⋊Dic3C22×C4semidirect
157. C32×Dic3C22×C4semidirect
183. C2×Dic3⋊C4C3×D3direct (N × H)
230. C2×C3⋊Dic3C2×C3×C4semidirect
257. C2×C3×Dic3C4×D3semidirect
258. C2×C3×Dic3C2×C3×C4semidirect
271. D3×Dic3C2×C3×C4semidirect
273. C2×C33C2×C4⋊C4semidirect
277. C32×D3C2×C4⋊C4semidirect
342. Dic3⋊C4C2×C3×D3direct (N × H)
379. C2×C3×D3Dic3⋊C4direct (N × H)
380. C2×C3×D3C3×C4⋊C4semidirect
398. C3⋊Dic3C22×C3×C4semidirect
412. C3×Dic3C2×C4×D3semidirect
413. C3×Dic3C22×C3×C4semidirect
422. C33C22×C4⋊C4semidirect
503. C2×Dic3C3×C4×D3semidirect
527. C2×C32D3×C4⋊C4semidirect
528. C2×C32C2×Dic3⋊C4semidirect
529. C2×C32C2×C3×C4⋊C4semidirect
540. C3×D3C2×Dic3⋊C4direct (N × H)
541. C3×D3C2×C3×C4⋊C4semidirect
599. C2×D3C3×Dic3⋊C4direct (N × H)
629. Dic3C2×C3×C4×D3semidirect
634. C32C2×D3×C4⋊C4semidirect
635. C32C22×Dic3⋊C4semidirect
636. C32C22×C3×C4⋊C4semidirect
676. C2×C3D3×Dic3⋊C4direct (N × H)
677. C2×C3C3×D3×C4⋊C4semidirect
678. C2×C3C2×C3×Dic3⋊C4semidirect
688. D3C2×C3×Dic3⋊C4direct (N × H)
707. C3C2×D3×Dic3⋊C4direct (N × H)
708. C3C2×C3×D3×C4⋊C4semidirect
709. C3C22×C3×Dic3⋊C4semidirect
711. C2C3×D3×Dic3⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4×D32
C22×C3×D3×Dic32
C2×C3×#37502
C2×C32×Dic3⋊C42
C2×C3×#37242
C2×C3×Dic3⋊Dic32
C3×D3×Dic3⋊C42
C22×C3×Dic3⋊C43
C2×C3×D3×C4⋊C43
C2×D3×Dic3⋊C43