Finite Group Databasebeta

← C2×C3×#63854 #13174597

Subgroups — C2×C3×#63854 #13174597

Order 1728.

1778 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#626C211yesmaximal, characteristic
2C22×C3×#624C211yesmaximal, characteristic, complemented
3C2×C3×#3752C211yesmaximal, characteristic, complemented
4C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C2×C32×C4⋊Dic3C211yesmaximal, characteristic, complemented
6C2×C3×#3724C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#63854C218yesmaximal, direct product factor
9C2×C3×#894—31nomaximal
10C2×C3×#883—31nomaximal
11C2×#63854C311yesmaximal, characteristic, direct product factor
12C23×C3×C3⋊D3C2211yescharacteristic
13C23×C32×D3C2211yescharacteristic
14C22×C33×C4C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×C3×#626—24no—
20C2×C3×#626C2214yes—
21C2×C3×#624—24no—
22C2×C3×#624C2214yescomplemented
23C3×#3752C2214yescomplemented
24C32×(C2×D3)⋊C4C2214yescomplemented
25C32×C4⋊Dic3C2214yescomplemented
26C3×#3724C2214yescomplemented
27C3×(C2×D3)⋊Dic3C2214yescomplemented
28C22×C3×#67—31no—
29C22×C3×D12—31no—
30C22×C3×C4×D3—31no—
31C22×C3×C4×D3—31no—
32C22×#626C2×C311yescharacteristic
33C22×#624C2×C311yescharacteristic, complemented
34C2×C32×C4⋊C4—31no—
35C2×C32×C22⋊C4—31no—
36C2×#3752C2×C311yescharacteristic, complemented
37C2×C3×#217—31no—
38C2×C3×(C2×D3)⋊C4—21no—
39C2×C3×(C2×D3)⋊C4—31no—
40C2×C3×(C2×D3)⋊C4—31no—
41C2×C3×(C2×D3)⋊C4—31no—
42C2×C3×(C2×D3)⋊C4—61no—
43C2×C3×(C2×D3)⋊C4D311yescharacteristic, complemented
44C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
45C2×C3×C4⋊Dic3—21no—
46C2×C3×C4⋊Dic3D311yescharacteristic, complemented
47C2×C3×C4⋊Dic3C2×C311yescharacteristic, complemented
48C2×C3×Dic3⋊C4—31no—
49C2×C3×Dic3⋊C4—31no—
50C3×#894—38no—
51C3×#883—38no—
52C2×#3724C2×C311yescharacteristic, complemented
53C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
54#63854C2×C318yesdirect product factor
55C23×C33C2311yescharacteristic
56C22×C3×C3⋊D3—22no—
57C22×C3×C3⋊D3—22no—
58C22×C3×C3⋊D3D414yes—
59C22×C3×C3⋊D3C2312yes—
60C22×C32×D3—22no—
61C22×C32×D3—22no—
62C22×C32×D3—22no—
63C22×C32×D3C2312yes—
64C2×C33×C4—22no—
65C2×C33×C4C2312yes—
66C2×C3×C3⋊Dic3—22no—
67C2×C3×C3⋊Dic3C2312yes—
68C2×C32×Dic3—22no—
69C2×C32×Dic3—22no—
70C2×C32×Dic3—22no—
71C2×C32×Dic3C2312yes—
72C2×C32×Dic3C2312yes—
73C2×C32×Dic3C2312yes—
74C3×#626—28no—
75C3×#624—28no—
76C2×C3×#123—91no—
77C2×#894—31no—
78C2×#883—31no—
79C24×C32—31no—
80C23×C3⋊D3C22×C311yescharacteristic
81C23×C3×D3—21no—
82C23×C3×D3—31no—
83C23×C3×D3—31no—
84C23×C3×D3—61no—
85C23×C3×D3C2×D311yescharacteristic
86C23×C3×D3C22×C311yescharacteristic
87C22×C32×C4—21no—
88C22×C32×C4—21no—
89C22×C32×C4—21no—
90C22×C32×C4—31no—
91C22×C32×C4—31no—
92C22×C32×C4—31no—
93C22×C32×C4—41no—
94C22×C32×C4C2×D311yescharacteristic
95C22×C32×C4C2×D311yescharacteristic
96C22×C32×C4C22×C311yescharacteristic
97C22×C3⋊Dic3C22×C311yescharacteristic
98C2×C3×#67—34no—
99C2×C3×#67—64no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—31no—
104C22×C3×Dic3—31no—
105C22×C3×Dic3—61no—
106C22×C3×Dic3C2×D311yescharacteristic
107C22×C3×Dic3C2×D311yescharacteristic
108C22×C3×Dic3C2×D311yescharacteristic
109C22×C3×Dic3C22×C311yescharacteristic
110C22×C3×Dic3C22×C311yescharacteristic
111C22×C3×Dic3C22×C311yescharacteristic
112C2×C3×D12—34no—
113C2×C3×D12—64no—
114C2×C3×C4×D3—34no—
115C2×C3×C4×D3—34no—
116C2×C3×C4×D3—64no—
117C2×C3×C4×D3—64no—
118C2×#626—24no—
119C2×#626C22×C314yes—
120C2×#624—24no—
121C2×#624C22×C314yescomplemented
122C32×C4⋊C4—34no—
123C32×C22⋊C4—34no—
124#3752C22×C314yescomplemented
125C3×#217—34no—
126C3×(C2×D3)⋊C4—24no—
127C3×(C2×D3)⋊C4—34no—
128C3×(C2×D3)⋊C4—34no—
129C3×(C2×D3)⋊C4—34no—
130C3×(C2×D3)⋊C4—64no—
131C3×(C2×D3)⋊C4C2×D314yescomplemented
132C3×(C2×D3)⋊C4C22×C314yescomplemented
133C3×C4⋊Dic3—24no—
134C3×C4⋊Dic3C2×D314yescomplemented
135C3×C4⋊Dic3C22×C314yescomplemented
136C3×Dic3⋊C4—34no—
137C3×Dic3⋊C4—34no—
138#3724C22×C314yescomplemented
139(C2×D3)⋊Dic3C22×C314yescomplemented
140C22×C33C2×D412yes—
141C22×C33#4112yes—
142C22×C33#4112yes—
143C22×C33C2411yescharacteristic
144C2×C3×C3⋊D3—28no—
145C2×C3×C3⋊D3—22no—
146C2×C3×C3⋊D3—22no—
147C2×C3×C3⋊D3C2×D414yes—
148C2×C32×D3—22no—
149C2×C32×D3—22no—
150C2×C32×D3—22no—
151C2×C32×D3—44no—
152C33×C4—22no—
153C3×C3⋊Dic3—22no—
154C32×Dic3—22no—
155C32×Dic3—22no—
156C32×Dic3—22no—
157C22×C3×D4—91no—
158C23×C3×C4—91no—
159C22×#67—31no—
160C22×D12—31no—
161C22×C4×D3—31no—
162C22×C4×D3—31no—
163C3×#123—98no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—61no—
167C2×C3×C4⋊C4—91no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—61no—
171C2×C3×C22⋊C4—91no—
172C2×C3×C22⋊C4—91no—
173C2×#217—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—61no—
178C2×(C2×D3)⋊C4C3×D311yescharacteristic, complemented
179C2×C4⋊Dic3C3×D311yescharacteristic, complemented
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182#894—38no—
183#883—38no—
184C23×C32—21no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—32no—
188C23×C32—41no—
189C23×C32—62no—
190C23×C32—62no—
191C23×C32—62no—
192C23×C32C22×D311yescharacteristic
193C23×C32C22×D311yescharacteristic
194C23×C32C23×C311yescharacteristic
195C22×C3⋊D3—22no—
196C22×C3⋊D3—22no—
197C22×C3⋊D3C3×D414yes—
198C22×C3⋊D3C23×C312yes—
199C22×C3×D3—24no—
200C22×C3×D3—22no—
201C22×C3×D3—22no—
202C22×C3×D3—22no—
203C22×C3×D3—22no—
204C22×C3×D3—22no—
205C22×C3×D3—22no—
206C22×C3×D3—22no—
207C22×C3×D3—34no—
208C22×C3×D3—34no—
209C22×C3×D3—32no—
210C22×C3×D3—32no—
211C22×C3×D3—42no—
212C22×C3×D3—42no—
213C22×C3×D3—62no—
214C22×C3×D3—64no—
215C22×C3×D3—62no—
216C22×C3×D3—62no—
217C22×C3×D3—62no—
218C22×C3×D3—62no—
219C22×C3×D3—122no—
220C22×C3×D3—122no—
221C22×C3×D3C22×D312yes—
222C22×C3×D3C23×C312yes—
223C2×C32×C4—22no—
224C2×C32×C4—24no—
225C2×C32×C4—22no—
226C2×C32×C4—22no—
227C2×C32×C4—22no—
228C2×C32×C4—22no—
229C2×C32×C4—22no—
230C2×C32×C4—32no—
231C2×C32×C4—32no—
232C2×C32×C4—32no—
233C2×C32×C4—42no—
234C2×C32×C4—42no—
235C2×C32×C4—42no—
236C2×C32×C4—44no—
237C2×C32×C4—62no—
238C2×C32×C4—62no—
239C2×C32×C4—62no—
240C2×C32×C4C22×D312yes—
241C2×C32×C4C22×D312yes—
242C2×C32×C4C23×C312yes—
243C2×C3⋊Dic3—22no—
244C2×C3⋊Dic3C23×C312yes—
245C3×#67—68no—
246C2×C3×Dic3—22no—
247C2×C3×Dic3—22no—
248C2×C3×Dic3—22no—
249C2×C3×Dic3—22no—
250C2×C3×Dic3—22no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—22no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—32no—
256C2×C3×Dic3—32no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3—62no—
261C2×C3×Dic3—62no—
262C2×C3×Dic3—62no—
263C2×C3×Dic3—122no—
264C2×C3×Dic3C22×D312yes—
265C2×C3×Dic3C22×D312yes—
266C2×C3×Dic3C22×D312yes—
267C2×C3×Dic3C23×C312yes—
268C2×C3×Dic3C23×C312yes—
269C2×C3×Dic3C23×C312yes—
270C3×D12—68no—
271C3×C4×D3—68no—
272C3×C4×D3—68no—
273#626—28no—
274#624—28no—
275C2×#123—91noSylow
276C2×C33#12314yescomplemented
277C2×C33C22×D411yescharacteristic
278C2×C33C2×#4111yescharacteristic
279C2×C33C2×#4111yescharacteristic
280C3×C3⋊D3—24no—
281C32×D3—42no—
282C24×C3—31no—
283C24×C3—31no—
284C24×C3—61no—
285C24×C3—91no—
286C23×D3—31no—
287C23×D3—31no—
288C23×D3—61no—
289C23×D3C2×C3×D311yescharacteristic
290C2×C3×D4—94no—
291C2×C3×D4—184no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—41no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—94no—
306C22×C3×C4—91no—
307C22×C3×C4—184no—
308C22×C3×C4D3211yescharacteristic
309C22×C3×C4C2×C3×D311yescharacteristic
310C22×C3×C4C2×C3×D311yescharacteristic
311C2×#67—34no—
312C2×#67—64no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—61no—
316C22×Dic3C2×C3×D311yescharacteristic
317C22×Dic3C2×C3×D311yescharacteristic
318C22×Dic3C2×C3×D311yescharacteristic
319C2×D12—34no—
320C2×D12—64no—
321C2×C4×D3—34no—
322C2×C4×D3—34no—
323C2×C4×D3—64no—
324C2×C4×D3—64no—
325C3×C4⋊C4—34no—
326C3×C4⋊C4—34no—
327C3×C4⋊C4—64no—
328C3×C4⋊C4—94no—
329C3×C22⋊C4—34no—
330C3×C22⋊C4—34no—
331C3×C22⋊C4—64no—
332C3×C22⋊C4—94no—
333C3×C22⋊C4—94no—
334#217—34no—
335(C2×D3)⋊C4—34no—
336(C2×D3)⋊C4—34no—
337(C2×D3)⋊C4—34no—
338(C2×D3)⋊C4—64no—
339(C2×D3)⋊C4C2×C3×D314yescomplemented
340C4⋊Dic3C2×C3×D314yescomplemented
341Dic3⋊C4—34no—
342Dic3⋊C4—34no—
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—42no—
356C22×C32—42no—
357C22×C32—42no—
358C22×C32—41no—
359C22×C32—62no—
360C22×C32—62no—
361C22×C32—62no—
362C22×C32—124no—
363C22×C32#23512yes—
364C22×C32#23512yes—
365C22×C32D3×D412yes—
366C22×C32D3×D412yes—
367C22×C32#23712yes—
368C22×C32#23912yes—
369C22×C32C2×C3×D412yes—
370C22×C32C3×#4112yes—
371C22×C32C3×#4112yes—
372C22×C32C23×D311yescharacteristic
373C22×C32C23×D311yescharacteristic
374C22×C32C24×C311yescharacteristic
375C2×C3⋊D3—28no—
376C2×C3⋊D3—22no—
377C2×C3⋊D3—22no—
378C2×C3⋊D3C2×C3×D414yes—
379C2×C3×D3—24no—
380C2×C3×D3—22no—
381C2×C3×D3—22no—
382C2×C3×D3—22no—
383C2×C3×D3—22no—
384C2×C3×D3—22no—
385C2×C3×D3—22no—
386C2×C3×D3—34no—
387C2×C3×D3—34no—
388C2×C3×D3—42no—
389C2×C3×D3—42no—
390C2×C3×D3—48no—
391C2×C3×D3—44no—
392C2×C3×D3—44no—
393C2×C3×D3—64no—
394C2×C3×D3—68no—
395C2×C3×D3—68no—
396C2×C3×D3—62no—
397C2×C3×D3—62no—
398C2×C3×D3—62no—
399C2×C3×D3—62no—
400C2×C3×D3—122no—
401C2×C3×D3—122no—
402C2×C3×D3—128no—
403C32×C4—22no—
404C32×C4—24no—
405C32×C4—22no—
406C32×C4—22no—
407C32×C4—42no—
408C32×C4—42no—
409C32×C4—44no—
410C32×C4—62no—
411C32×C4—62no—
412C32×C4—62no—
413C3⋊Dic3—22no—
414C3×Dic3—22no—
415C3×Dic3—22no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—42no—
421C3×Dic3—42no—
422C3×Dic3—42no—
423C3×Dic3—62no—
424C3×Dic3—62no—
425C3×Dic3—122no—
426C22×D4—91no—
427C23×C4—91no—
428#123—98no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—91no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—91no—
433C2×C22⋊C4—91no—
434C33C2×#12311yescharacteristic, complemented, Sylow
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—32no—
439C23×C3—32no—
440C23×C3—41no—
441C23×C3—62no—
442C23×C3—64no—
443C23×C3—62no—
444C23×C3—62no—
445C23×C3—62no—
446C23×C3—62no—
447C23×C3—62no—
448C23×C3—62no—
449C23×C3—92no—
450C23×C3—94no—
451C23×C3—122no—
452C23×C3—122no—
453C23×C3—182no—
454C23×C3—182no—
455C23×C3C2×D3211yescharacteristic
456C23×C3C22×C3×D311yescharacteristic
457C23×C3C22×C3×D311yescharacteristic
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—32no—
462C22×D3—32no—
463C22×D3—34no—
464C22×D3—34no—
465C22×D3—64no—
466C22×D3—62no—
467C22×D3—62no—
468C22×D3—62no—
469C22×D3—62no—
470C22×D3—62no—
471C22×D3—122no—
472C22×D3—122no—
473C22×D3C22×C3×D312yes—
474C3×D4—188no—
475C2×C3×C4—24no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—42no—
489C2×C3×C4—42no—
490C2×C3×C4—44no—
491C2×C3×C4—42no—
492C2×C3×C4—62no—
493C2×C3×C4—62no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—62no—
501C2×C3×C4—92no—
502C2×C3×C4—122no—
503C2×C3×C4—122no—
504C2×C3×C4—122no—
505C2×C3×C4—188no—
506C2×C3×C4—182no—
507C2×C3×C4C2×D3212yes—
508C2×C3×C4C22×C3×D312yes—
509C2×C3×C4C22×C3×D312yes—
510#67—68no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—22no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—62no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—122no—
520C2×Dic3C22×C3×D312yes—
521C2×Dic3C22×C3×D312yes—
522C2×Dic3C22×C3×D312yes—
523D12—68no—
524C4×D3—68no—
525C4×D3—68no—
526C2×C32—24no—
527C2×C32—24no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—24no—
538C2×C32—44no—
539C2×C32—41no—
540C2×C32—41no—
541C2×C32—41no—
542C2×C32—122no—
543C2×C32#88314yescomplemented
544C2×C32#89414yescomplemented
545C2×C32C3×#12314yescomplemented
546C2×C32C2×#23511yescharacteristic
547C2×C32C2×#23511yescharacteristic
548C2×C32C2×D3×D411yescharacteristic
549C2×C32C2×D3×D411yescharacteristic
550C2×C32C2×#23711yescharacteristic
551C2×C32C2×#23911yescharacteristic
552C2×C32C22×C3×D411yescharacteristic
553C2×C32C2×C3×#4111yescharacteristic
554C2×C32C2×C3×#4111yescharacteristic
555C3⋊D3—24no—
556C3×D3—44no—
557C3×D3—42no—
558C3×D3—42no—
559C3×D3—64no—
560C3×D3—64no—
561C3×D3—124no—
562C24—31no—
563C24—91no—
564C2×D4—94no—
565C2×D4—184no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—94no—
570C22×C4—91no—
571C22×C4—184no—
572C22×C4C3×D3211yescharacteristic
573C4⋊C4—34no—
574C4⋊C4—94no—
575C22⋊C4—34no—
576C22⋊C4—94no—
577C22⋊C4—94no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—41no—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—64no—
595C22×C3—62no—
596C22×C3—62no—
597C22×C3—62no—
598C22×C3—62no—
599C22×C3—62no—
600C22×C3—62no—
601C22×C3—94no—
602C22×C3—122no—
603C22×C3—122no—
604C22×C3—128no—
605C22×C3—124no—
606C22×C3—124no—
607C22×C3—182no—
608C22×C3—182no—
609C22×C3—188no—
610C22×C3#379912yes—
611C22×C3#380212yes—
612C22×C3#380412yes—
613C22×C3C3×#23512yes—
614C22×C3C3×#23512yes—
615C22×C3C3×D3×D412yes—
616C22×C3C3×D3×D412yes—
617C22×C3C3×#23712yes—
618C22×C3C3×#23912yes—
619C22×C3C22×D3211yescharacteristic
620C22×C3C23×C3×D311yescharacteristic
621C22×C3C23×C3×D311yescharacteristic
622C2×D3—22no—
623C2×D3—22no—
624C2×D3—22no—
625C2×D3—34no—
626C2×D3—34no—
627C2×D3—44no—
628C2×D3—64no—
629C2×D3—68no—
630C2×D3—68no—
631C2×D3—62no—
632C2×D3—62no—
633C2×D3—62no—
634C2×D3—62no—
635C2×D3—122no—
636C2×D3—128no—
637C2×D3—122no—
638C3×C4—24no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—44no—
645C3×C4—62no—
646C3×C4—62no—
647C3×C4—62no—
648C3×C4—62no—
649C3×C4—62no—
650C3×C4—62no—
651C3×C4—122no—
652C3×C4—122no—
653C3×C4—122no—
654C3×C4—182no—
655Dic3—22no—
656Dic3—22no—
657Dic3—22no—
658Dic3—62no—
659Dic3—62no—
660Dic3—122no—
661C32—21no—
662C32—21no—
663C32—21no—
664C32—41no—
665C32C2×#88311yescharacteristic, complemented
666C32C2×#89411yescharacteristic, complemented
667C32C2×C3×#12311yescharacteristic, complemented
668C23—32no—
669C23—62no—
670C23—62no—
671C23—62no—
672C23—92no—
673C23—94no—
674C23—182no—
675C23—182no—
676C23C2×C3×D3211yescharacteristic
677D4—188no—
678C2×C4—22no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—92no—
686C2×C4—188no—
687C2×C4—182no—
688C2×C4C2×C3×D3212yes—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—24no—
693C2×C3—24no—
694C2×C3—24no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—41no—
702C2×C3—44no—
703C2×C3—41no—
704C2×C3—41no—
705C2×C3—124no—
706C2×C3—122no—
707C2×C3—122no—
708C2×C3—184no—
709C2×C3#6385414yesdirect product factor
710C2×C3C3×#88314yescomplemented
711C2×C3C3×#89414yescomplemented
712C2×C3C2×#379911yescharacteristic
713C2×C3C2×#380211yescharacteristic
714C2×C3C2×#380411yescharacteristic
715C2×C3C2×C3×#23511yescharacteristic
716C2×C3C2×C3×#23511yescharacteristic
717C2×C3C2×C3×D3×D411yescharacteristic
718C2×C3C2×C3×D3×D411yescharacteristic
719C2×C3C2×C3×#23711yescharacteristic
720C2×C3C2×C3×#23911yescharacteristic
721D3—42no—
722D3—64no—
723D3—64no—
724D3—124no—
725C22—62no—
726C22—62no—
727C22—62no—
728C22—94no—
729C22—124no—
730C22—182no—
731C22—188no—
732C22—182no—
733C22C3×#379912yes—
734C22C3×#380212yes—
735C22C3×#380412yes—
736C22C22×C3×D3211yescharacteristic
737C4—22no—
738C4—62no—
739C4—62no—
740C4—62no—
741C4—182no—
742C3—21no—
743C3—21no—
744C3—21no—
745C3—41no—
746C3C2×#6385411yescharacteristic, direct product factor
747C3C2×C3×#88311yescharacteristic, complemented
748C3C2×C3×#89411yescharacteristic, complemented
749C2—122no—
750C2—184no—
751C2C3×#6385414yesdirect product factor
752C2C2×C3×#379911yescharacteristic
753C2C2×C3×#380211yescharacteristic
754C2C2×C3×#380411yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC22×C3×#626C2
hypercenterC22×C3×C4D32
hypocenterC32C2×C3×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#624C2semidirect
3. C2×C3×#3752C2semidirect
4. C2×C32×(C2×D3)⋊C4C2semidirect
5. C2×C32×C4⋊Dic3C2semidirect
6. C2×C3×#3724C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. C3×#63854C2direct (N × H)
11. C2×#63854C3direct (N × H)
22. C2×C3×#624C22semidirect
23. C3×#3752C22semidirect
24. C32×(C2×D3)⋊C4C22semidirect
25. C32×C4⋊Dic3C22semidirect
26. C3×#3724C22semidirect
27. C3×(C2×D3)⋊Dic3C22semidirect
33. C22×#624C2×C3semidirect
36. C2×#3752C2×C3semidirect
43. C2×C3×(C2×D3)⋊C4D3semidirect
44. C2×C3×(C2×D3)⋊C4C2×C3semidirect
46. C2×C3×C4⋊Dic3D3semidirect
47. C2×C3×C4⋊Dic3C2×C3semidirect
52. C2×#3724C2×C3semidirect
53. C2×(C2×D3)⋊Dic3C2×C3semidirect
54. #63854C2×C3direct (N × H)
121. C2×#624C22×C3semidirect
124. #3752C22×C3semidirect
131. C3×(C2×D3)⋊C4C2×D3semidirect
132. C3×(C2×D3)⋊C4C22×C3semidirect
134. C3×C4⋊Dic3C2×D3semidirect
135. C3×C4⋊Dic3C22×C3semidirect
138. #3724C22×C3semidirect
139. (C2×D3)⋊Dic3C22×C3semidirect
178. C2×(C2×D3)⋊C4C3×D3semidirect
179. C2×C4⋊Dic3C3×D3semidirect
276. C2×C33#123semidirect
339. (C2×D3)⋊C4C2×C3×D3semidirect
340. C4⋊Dic3C2×C3×D3semidirect
434. C33C2×#123semidirect
543. C2×C32#883semidirect
544. C2×C32#894semidirect
545. C2×C32C3×#123semidirect
665. C32C2×#883semidirect
666. C32C2×#894semidirect
667. C32C2×C3×#123semidirect
709. C2×C3#63854direct (N × H)
710. C2×C3C3×#883semidirect
711. C2×C3C3×#894semidirect
746. C3C2×#63854direct (N × H)
747. C3C2×C3×#883semidirect
748. C3C2×C3×#894semidirect
751. C2C3×#63854direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6262
C22×C3×#6242
C2×C3×#37522
C2×C32×(C2×D3)⋊C42
C2×C32×C4⋊Dic32
C2×C3×#37242
C2×C3×(C2×D3)⋊Dic32
C3×#638542
C2×C3×#8943
C2×C3×#8833
C2×#638543