Finite Group Databasebeta

← C3×#10595298 #13174701

Subgroups — C3×#10595298 #13174701

Order 1728.

2182 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#3811C211yesmaximal, characteristic, complemented
3C2×C3×#3811C211yesmaximal, characteristic, complemented
4C22×C3×#624C211yesmaximal, characteristic, complemented
5C32×#939C212yesmaximal, complemented
6C3×#63978C212yesmaximal, complemented
7C3×#63974C211yesmaximal, characteristic, complemented
8C3×#63958C212yesmaximal, complemented
9C3×#63921C211yesmaximal, characteristic, complemented
10C3×#63910C212yesmaximal, complemented
11C3×#63883C211yesmaximal, characteristic, complemented
12C3×D3×#121—32nomaximal
13#10595298C311yesmaximal, characteristic, direct product factor
14C23×C3×C3⋊D3C2211yescharacteristic
15C23×C3×C3⋊D3C2211yescharacteristic
16C22×C3×D32C2211yescharacteristic
17C2×C33×D4C2211yescharacteristic, complemented
18C2×C3×#638C2211yescharacteristic, complemented
19C2×C3×#638C2211yescharacteristic, complemented
20C3×D4×C3⋊D3—24no—
21C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C32×#67C2212yescomplemented
24C2×C32×#67C2212yescomplemented
25C22×C32×Dic3C2212yescomplemented
26C3×#3811—24no—
27C3×#3811—24no—
28C2×C3×#626C2212yescomplemented
29C2×C3×#626C2212yescomplemented
30C2×C3×#624—24no—
31C2×C3×#624C2211yescharacteristic
32C2×C3×#624C2211yescharacteristic
33C2×C3×#624C2211yescharacteristic
34C2×C3×#624C2212yescomplemented
35C32×#217C2212yescomplemented
36C32×(C2×D3)⋊C4C2212yescomplemented
37C32×Dic3⋊C4C2212yescomplemented
38C3×Dic3⋊Dic3C2212yescomplemented
39C3×#3722C2212yescomplemented
40C3×(C2×D3)⋊Dic3C2212yescomplemented
41C2×D4×C3⋊D3C2×C311yescharacteristic, complemented
42C2×C3×D3×D4—32no—
43C2×C3×D3×D4—32no—
44C2×C3×D3×D4—32no—
45C2×C3×D3×D4—61no—
46C22×C3×C4×D3—32no—
47C2×#3811C2×C311yescharacteristic, complemented
48C2×#3811C2×C311yescharacteristic, complemented
49C22×#624C2×C311yescharacteristic, complemented
50C32×#121—32no—
51C3×#939—22no—
52C3×#939—32no—
53C3×#939D312yescomplemented
54C3×#939C2×C312yescomplemented
55C3×#938—32no—
56C3×#930—32no—
57C3×#895—32no—
58C3×D3×C4⋊C4—32no—
59C3×#884—32no—
60C3×#884—32no—
61C3×D3×C22⋊C4—32no—
62C3×D3×C22⋊C4—32no—
63#63978C2×C312yescomplemented
64#63974C2×C311yescharacteristic, complemented
65#63958C2×C312yescomplemented
66#63921C2×C311yescharacteristic, complemented
67#63910C2×C312yescomplemented
68#63883C2×C311yescharacteristic, complemented
69C23×C33C2311yescharacteristic
70C23×C33C2311yescharacteristic
71C22×C3×C3⋊D3—22no—
72C22×C3×C3⋊D3—22no—
73C22×C3×C3⋊D3—22no—
74C22×C3×C3⋊D3—22no—
75C22×C3×C3⋊D3—22no—
76C22×C3×C3⋊D3D414yescomplemented
77C22×C3×C3⋊D3C2311yescharacteristic
78C22×C3×C3⋊D3C2311yescharacteristic
79C22×C3×C3⋊D3C2311yescharacteristic
80C22×C32×D3C2312yes—
81C2×C3×D32—22no—
82C2×C3×D32—22no—
83C2×C3×D32—22no—
84C33×D4—22no—
85C2×C33×C4C2311yescharacteristic
86C3×#638—22no—
87C3×#638—22no—
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C3×C4⋊(C3⋊D3)—22no—
90C3×C4×C3⋊D3—22no—
91C32×#67—24no—
92C32×#67—24no—
93C2×C32×Dic3—24no—
94C2×C32×Dic3C2312yes—
95C2×C32×Dic3C2312yes—
96C2×C32×Dic3C2312yes—
97C3×#626—24no—
98C3×#626—24no—
99C3×#624—22no—
100C3×#624—22no—
101C3×#624—24no—
102C3×#624D414yescomplemented
103C2×C3×#121—91no—
104D3×#121—32no—
105C23×C3⋊D3C22×C311yescharacteristic
106C23×C3⋊D3C22×C311yescharacteristic
107C23×C3×D3—32no—
108C23×C3×D3—32no—
109C23×C3×D3—32no—
110C23×C3×D3—61no—
111C23×C3×D3—61no—
112C22×D32C22×C311yescharacteristic
113C2×C32×D4—21no—
114C2×C32×D4—22no—
115C2×C32×D4—32no—
116C2×C32×D4—32no—
117C2×C32×D4—41no—
118C2×C32×D4C2×D312yescomplemented
119C2×C32×D4C22×C311yescharacteristic, complemented
120C22×C32×C4—32no—
121C2×#638C22×C311yescharacteristic, complemented
122C2×#638C22×C311yescharacteristic, complemented
123D4×C3⋊D3—24no—
124C2×C4⋊(C3⋊D3)C22×C311yescharacteristic, complemented
125C2×C4×C3⋊D3C22×C311yescharacteristic
126C2×C3×#67—22no—
127C2×C3×#67—22no—
128C2×C3×#67—32no—
129C2×C3×#67—32no—
130C2×C3×#67—32no—
131C2×C3×#67—32no—
132C2×C3×#67—61no—
133C2×C3×#67—61no—
134C2×C3×#67C2×D312yescomplemented
135C2×C3×#67C2×D312yescomplemented
136C2×C3×#67C22×C312yescomplemented
137C2×C3×#67C22×C312yescomplemented
138C22×C3×Dic3—22no—
139C22×C3×Dic3C2×D312yescomplemented
140C22×C3×Dic3C22×C312yescomplemented
141C3×D3×D4—68no—
142C3×D3×D4—68no—
143C3×D3×D4—68no—
144C3×D3×D4—68no—
145C2×C3×D12—32no—
146C2×C3×D12—32no—
147C2×C3×D12—32no—
148C2×C3×D12—61no—
149C2×C3×C4×D3—32no—
150C2×C3×C4×D3—32no—
151C2×C3×C4×D3—32no—
152C2×C3×C4×D3—32no—
153C2×C3×C4×D3—32no—
154C2×C3×C4×D3—32no—
155C2×C3×C4×D3—68no—
156C2×C3×C4×D3—61no—
157#3811—24no—
158#3811—24no—
159C2×#626C22×C312yescomplemented
160C2×#626C22×C312yescomplemented
161C2×#624—24no—
162C2×#624C22×C311yescharacteristic
163C2×#624C22×C311yescharacteristic
164C2×#624C22×C311yescharacteristic
165C2×#624C22×C312yescomplemented
166C32×C4⋊C4—32no—
167C32×C22⋊C4—32no—
168C32×C22⋊C4—32no—
169C3×#217—22no—
170C3×#217—32no—
171C3×#217C2×D312yescomplemented
172C3×#217C22×C312yescomplemented
173C3×(C2×D3)⋊C4—22no—
174C3×(C2×D3)⋊C4—32no—
175C3×(C2×D3)⋊C4—32no—
176C3×(C2×D3)⋊C4—32no—
177C3×(C2×D3)⋊C4C2×D312yescomplemented
178C3×(C2×D3)⋊C4C22×C312yescomplemented
179C3×C4⋊Dic3—32no—
180C3×Dic3⋊C4—22no—
181C3×Dic3⋊C4—32no—
182C3×Dic3⋊C4C2×D312yescomplemented
183C3×Dic3⋊C4C22×C312yescomplemented
184Dic3⋊Dic3C22×C312yescomplemented
185#3722C22×C312yescomplemented
186(C2×D3)⋊Dic3C22×C312yescomplemented
187C22×C33—21no—
188C22×C33—21no—
189C22×C33—21no—
190C22×C33—21no—
191C22×C33—21no—
192C22×C33C2×D412yescomplemented
193C22×C33C2411yescharacteristic
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C3×C3⋊D3—28no—
197C2×C3×C3⋊D3—21no—
198C2×C3×C3⋊D3—21no—
199C2×C3×C3⋊D3—21no—
200C2×C3×C3⋊D3—44no—
201C2×C3×C3⋊D3C2×D412yes—
202C2×C3×C3⋊D3C2×D412yes—
203C2×C3×C3⋊D3C2×D412yescomplemented
204C2×C3×C3⋊D3#4112yes—
205C2×C32×D3—22no—
206C2×C32×D3—22no—
207C2×C32×D3—22no—
208C3×D32—44no—
209C33×C4—21no—
210C3×C3⋊Dic3—21no—
211C32×Dic3—22no—
212C32×Dic3—22no—
213C32×Dic3C2×D414yescomplemented
214C22×C3×D4—91no—
215C22×C3×D4—91no—
216C22×C3×D4—91no—
217C23×C3×C4—91no—
218C2×D3×D4—32no—
219C2×D3×D4—32no—
220C2×D3×D4—32no—
221C2×D3×D4—61no—
222C22×C4×D3—32no—
223C3×#121—32no—
224C3×#121—32no—
225C3×#121—62no—
226C3×#121—92no—
227C3×#121—92no—
228C3×#121—92no—
229C2×C3×C4⋊C4—91no—
230C2×C3×C22⋊C4—91no—
231C2×C3×C22⋊C4—91no—
232#939—32no—
233#939C3×D312yescomplemented
234#938—32no—
235#930—32no—
236#895—32no—
237D3×C4⋊C4—32no—
238#884—32no—
239#884—32no—
240D3×C22⋊C4—32no—
241D3×C22⋊C4—32no—
242C23×C32—21no—
243C23×C32—21no—
244C23×C32—22no—
245C23×C32—22no—
246C23×C32—32no—
247C23×C32—41no—
248C23×C32—41no—
249C23×C32C22×D312yes—
250C23×C32C22×D312yes—
251C23×C32C23×C311yescharacteristic
252C23×C32C23×C311yescharacteristic
253C22×C3⋊D3—22no—
254C22×C3⋊D3—22no—
255C22×C3⋊D3—22no—
256C22×C3⋊D3—22no—
257C22×C3⋊D3—22no—
258C22×C3⋊D3C3×D414yescomplemented
259C22×C3⋊D3C23×C311yescharacteristic
260C22×C3⋊D3C23×C311yescharacteristic
261C22×C3⋊D3C23×C311yescharacteristic
262C22×C3×D3—22no—
263C22×C3×D3—32no—
264C22×C3×D3—38no—
265C22×C3×D3—32no—
266C22×C3×D3—32no—
267C22×C3×D3—61no—
268C22×C3×D3—64no—
269C22×C3×D3—61no—
270C22×C3×D3—61no—
271C22×C3×D3—64no—
272C22×C3×D3—64no—
273C22×C3×D3—64no—
274C22×C3×D3—64no—
275C22×C3×D3—64no—
276C22×C3×D3—64no—
277C22×C3×D3—64no—
278C22×C3×D3—64no—
279C22×C3×D3—64no—
280C22×C3×D3—122no—
281C22×C3×D3—122no—
282C22×C3×D3—122no—
283C22×C3×D3—122no—
284C22×C3×D3C22×D312yes—
285C22×C3×D3C23×C312yes—
286C2×D32—22no—
287C2×D32—22no—
288C2×D32—22no—
289C32×D4—22no—
290C32×D4—24no—
291C32×D4—24no—
292C32×D4—44no—
293C32×D4—44no—
294C32×D4—64no—
295C32×D4—64no—
296C2×C32×C4—21no—
297C2×C32×C4—22no—
298C2×C32×C4—32no—
299C2×C32×C4—32no—
300C2×C32×C4—32no—
301C2×C32×C4—41no—
302C2×C32×C4—64no—
303C2×C32×C4C22×D312yes—
304C2×C32×C4C23×C311yescharacteristic
305#638—22no—
306#638—22no—
307C2×C3⋊Dic3C23×C311yescharacteristic
308C4⋊(C3⋊D3)—22no—
309C4×C3⋊D3—22no—
310C3×#67—24no—
311C3×#67—24no—
312C3×#67—24no—
313C3×#67—24no—
314C3×#67—44no—
315C3×#67—44no—
316C3×#67—64no—
317C3×#67—64no—
318C3×#67—64no—
319C3×#67—64no—
320C3×#67—64no—
321C3×#67—64no—
322C2×C3×Dic3—24no—
323C2×C3×Dic3—24no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—22no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—32no—
328C2×C3×Dic3—44no—
329C2×C3×Dic3—61no—
330C2×C3×Dic3C22×D312yes—
331C2×C3×Dic3C22×D312yes—
332C2×C3×Dic3C22×D312yes—
333C2×C3×Dic3C23×C312yes—
334C2×C3×Dic3C23×C312yes—
335C2×C3×Dic3C23×C312yes—
336C3×D12—64no—
337C3×D12—64no—
338C3×D12—64no—
339C3×D12—64no—
340C3×C4×D3—38no—
341C3×C4×D3—64no—
342C3×C4×D3—64no—
343C3×C4×D3—64no—
344C3×C4×D3—64no—
345C3×C4×D3—64no—
346C3×C4×D3—64no—
347#626—24no—
348#626—24no—
349#624—22no—
350#624—22no—
351#624—24no—
352#624C3×D414yescomplemented
353C2×#121—91noSylow
354C2×C33—22no—
355C2×C33—41no—
356C2×C33C22×D411yescharacteristic
357C2×C33C22×D411yescharacteristic
358C2×C33C2×#4111yescharacteristic
359C3×C3⋊D3—22no—
360C3×C3⋊D3—41no—
361C3×C3⋊D3#12114yescomplemented
362C32×D3—42no—
363C24×C3—91no—
364C24×C3—91no—
365C24×C3—91no—
366C23×D3—32no—
367C23×D3—32no—
368C23×D3—32no—
369C23×D3—61no—
370C23×D3—61no—
371C2×C3×D4—21no—
372C2×C3×D4—22no—
373C2×C3×D4—32no—
374C2×C3×D4—32no—
375C2×C3×D4—32no—
376C2×C3×D4—32no—
377C2×C3×D4—41no—
378C2×C3×D4—62no—
379C2×C3×D4—62no—
380C2×C3×D4—92no—
381C2×C3×D4—92no—
382C2×C3×D4—91no—
383C2×C3×D4—91no—
384C2×C3×D4—91no—
385C2×C3×D4—184no—
386C2×C3×D4—184no—
387C2×C3×D4—184no—
388C2×C3×D4D3211yescharacteristic, complemented
389C2×C3×D4C2×C3×D312yescomplemented
390C22×C3×C4—32no—
391C22×C3×C4—32no—
392C22×C3×C4—62no—
393C22×C3×C4—91no—
394C22×C3×C4—91no—
395C22×C3×C4—91no—
396C22×C3×C4—92no—
397C22×C3×C4—91no—
398C22×C3×C4—184no—
399C2×#67—32no—
400C2×#67—32no—
401C2×#67—32no—
402C2×#67—32no—
403C2×#67—61no—
404C2×#67—61no—
405C2×#67C2×C3×D312yescomplemented
406C2×#67C2×C3×D312yescomplemented
407C22×Dic3C2×C3×D312yescomplemented
408D3×D4—68no—
409D3×D4—68no—
410D3×D4—68no—
411D3×D4—68no—
412C2×D12—32no—
413C2×D12—32no—
414C2×D12—32no—
415C2×D12—61no—
416C2×C4×D3—32no—
417C2×C4×D3—32no—
418C2×C4×D3—32no—
419C2×C4×D3—32no—
420C2×C4×D3—32no—
421C2×C4×D3—32no—
422C2×C4×D3—61no—
423C2×C4×D3—68no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4—32no—
426C3×C4⋊C4—62no—
427C3×C4⋊C4—92no—
428C3×C22⋊C4—32no—
429C3×C22⋊C4—32no—
430C3×C22⋊C4—32no—
431C3×C22⋊C4—32no—
432C3×C22⋊C4—62no—
433C3×C22⋊C4—62no—
434C3×C22⋊C4—92no—
435C3×C22⋊C4—92no—
436#217—32no—
437#217C2×C3×D312yescomplemented
438(C2×D3)⋊C4—32no—
439(C2×D3)⋊C4—32no—
440(C2×D3)⋊C4—32no—
441(C2×D3)⋊C4C2×C3×D312yescomplemented
442C4⋊Dic3—32no—
443Dic3⋊C4—32no—
444Dic3⋊C4C2×C3×D312yescomplemented
445C22×C32—21no—
446C22×C32—22no—
447C22×C32—22no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—22no—
451C22×C32—22no—
452C22×C32—22no—
453C22×C32—22no—
454C22×C32—21no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—22no—
458C22×C32—22no—
459C22×C32—24no—
460C22×C32—41no—
461C22×C32—42no—
462C22×C32—42no—
463C22×C32—42no—
464C22×C32—42no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32—42no—
470C22×C32—42no—
471C22×C32—42no—
472C22×C32—62no—
473C22×C32—62no—
474C22×C32—62no—
475C22×C32—81no—
476C22×C32—81no—
477C22×C32—81no—
478C22×C32—81no—
479C22×C32D3×D414yescomplemented
480C22×C32C2×C3×D412yescomplemented
481C22×C32C23×D312yes—
482C22×C32C24×C311yescharacteristic
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—21no—
486C2×C3⋊D3—28no—
487C2×C3⋊D3—21no—
488C2×C3⋊D3—21no—
489C2×C3⋊D3—44no—
490C2×C3⋊D3C2×C3×D412yes—
491C2×C3⋊D3C2×C3×D412yes—
492C2×C3⋊D3C2×C3×D412yescomplemented
493C2×C3⋊D3C3×#4112yes—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—34no—
501C2×C3×D3—34no—
502C2×C3×D3—34no—
503C2×C3×D3—34no—
504C2×C3×D3—42no—
505C2×C3×D3—42no—
506C2×C3×D3—42no—
507C2×C3×D3—62no—
508C2×C3×D3—62no—
509C2×C3×D3—62no—
510C2×C3×D3—62no—
511C2×C3×D3—616no—
512C2×C3×D3—62no—
513C2×C3×D3—62no—
514C2×C3×D3—62no—
515C2×C3×D3—62no—
516C2×C3×D3—62no—
517C2×C3×D3—62no—
518C2×C3×D3—128no—
519C2×C3×D3—121no—
520C2×C3×D3—121no—
521C2×C3×D3—121no—
522C2×C3×D3—121no—
523C2×C3×D3—128no—
524C2×C3×D3—128no—
525C2×C3×D3—128no—
526D32—44no—
527C32×C4—21no—
528C32×C4—22no—
529C32×C4—22no—
530C32×C4—34no—
531C32×C4—42no—
532C32×C4—42no—
533C32×C4—62no—
534C32×C4—62no—
535C3⋊Dic3—21no—
536C3×Dic3—22no—
537C3×Dic3—22no—
538C3×Dic3—22no—
539C3×Dic3—22no—
540C3×Dic3—24no—
541C3×Dic3—42no—
542C3×Dic3—42no—
543C3×Dic3—62no—
544C3×Dic3—62no—
545C3×Dic3D3×D414yescomplemented
546C3×Dic3C2×C3×D414yescomplemented
547C22×D4—91no—
548C22×D4—91no—
549C22×D4—91no—
550C23×C4—91no—
551#121—32no—
552#121—92no—
553#121—92no—
554#121—92no—
555C2×C4⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C33C2×#12111yescharacteristic, complemented, Sylow
559C23×C3—22no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—22no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—41no—
566C23×C3—41no—
567C23×C3—62no—
568C23×C3—91no—
569C23×C3—91no—
570C23×C3—94no—
571C23×C3—91no—
572C23×C3—182no—
573C23×C3—182no—
574C23×C3—182no—
575C23×C3—182no—
576C23×C3—182no—
577C23×C3—182no—
578C23×C3—182no—
579C23×C3—182no—
580C23×C3C2×D3211yescharacteristic
581C23×C3C2×D3211yescharacteristic
582C23×C3C22×C3×D312yes—
583C23×C3C22×C3×D312yes—
584C22×D3—32no—
585C22×D3—32no—
586C22×D3—38no—
587C22×D3—32no—
588C22×D3—61no—
589C22×D3—64no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—64no—
593C22×D3—64no—
594C22×D3—64no—
595C22×D3—64no—
596C22×D3—64no—
597C22×D3—64no—
598C22×D3—64no—
599C22×D3—64no—
600C22×D3—64no—
601C22×D3—122no—
602C22×D3—122no—
603C22×D3—122no—
604C22×D3—122no—
605C22×D3C22×C3×D312yes—
606C3×D4—24no—
607C3×D4—22no—
608C3×D4—24no—
609C3×D4—44no—
610C3×D4—44no—
611C3×D4—64no—
612C3×D4—64no—
613C3×D4—64no—
614C3×D4—64no—
615C3×D4—124no—
616C3×D4—124no—
617C3×D4—182no—
618C3×D4—184no—
619C3×D4—184no—
620C3×D4—182no—
621C3×D4—182no—
622C2×C3×C4—21no—
623C2×C3×C4—22no—
624C2×C3×C4—32no—
625C2×C3×C4—32no—
626C2×C3×C4—32no—
627C2×C3×C4—32no—
628C2×C3×C4—32no—
629C2×C3×C4—32no—
630C2×C3×C4—41no—
631C2×C3×C4—62no—
632C2×C3×C4—62no—
633C2×C3×C4—62no—
634C2×C3×C4—64no—
635C2×C3×C4—64no—
636C2×C3×C4—94no—
637C2×C3×C4—91no—
638C2×C3×C4—124no—
639C2×C3×C4—182no—
640C2×C3×C4—184no—
641C2×C3×C4—182no—
642C2×C3×C4—182no—
643C2×C3×C4C2×D3211yescharacteristic
644C2×C3×C4C22×C3×D312yes—
645#67—24no—
646#67—24no—
647#67—64no—
648#67—64no—
649#67—64no—
650#67—64no—
651#67—64no—
652#67—64no—
653C2×Dic3—24no—
654C2×Dic3—32no—
655C2×Dic3—61no—
656C2×Dic3C22×C3×D312yes—
657C2×Dic3C22×C3×D312yes—
658C2×Dic3C22×C3×D312yes—
659D12—64no—
660D12—64no—
661D12—64no—
662D12—64no—
663C4×D3—38no—
664C4×D3—64no—
665C4×D3—64no—
666C4×D3—64no—
667C4×D3—64no—
668C4×D3—64no—
669C4×D3—64no—
670C2×C32—22no—
671C2×C32—24no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32—22no—
676C2×C32—22no—
677C2×C32—22no—
678C2×C32—41no—
679C2×C32—41no—
680C2×C32—41no—
681C2×C32—42no—
682C2×C32—44no—
683C2×C32—41no—
684C2×C32—42no—
685C2×C32—42no—
686C2×C32—82no—
687C2×C32—82no—
688C2×C32—82no—
689C2×C32—122no—
690C2×C32C2×D3×D412yes—
691C2×C32C2×D3×D412yes—
692C2×C32D3×#4112yes—
693C2×C32C22×C3×D411yescharacteristic
694C2×C32C22×C3×D411yescharacteristic
695C2×C32C2×C3×#4111yescharacteristic
696C3⋊D3—22no—
697C3⋊D3—41no—
698C3⋊D3C3×#12114yescomplemented
699C3×D3—38no—
700C3×D3—42no—
701C3×D3—42no—
702C3×D3—64no—
703C3×D3—64no—
704C3×D3—82no—
705C3×D3—122no—
706C3×D3—122no—
707C3×D3—122no—
708C24—91no—
709C24—91no—
710C24—91no—
711C2×D4—32no—
712C2×D4—32no—
713C2×D4—92no—
714C2×D4—92no—
715C2×D4—91no—
716C2×D4—91no—
717C2×D4—91no—
718C2×D4—184no—
719C2×D4—184no—
720C2×D4—184no—
721C2×D4C3×D3211yescharacteristic, complemented
722C22×C4—32no—
723C22×C4—91no—
724C22×C4—91no—
725C22×C4—91no—
726C22×C4—92no—
727C22×C4—91no—
728C22×C4—184no—
729C4⋊C4—32no—
730C4⋊C4—92no—
731C22⋊C4—32no—
732C22⋊C4—32no—
733C22⋊C4—92no—
734C22⋊C4—92no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—21no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—24no—
750C22×C3—42no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—42no—
759C22×C3—42no—
760C22×C3—41no—
761C22×C3—42no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—62no—
767C22×C3—62no—
768C22×C3—81no—
769C22×C3—81no—
770C22×C3—81no—
771C22×C3—81no—
772C22×C3—92no—
773C22×C3—92no—
774C22×C3—92no—
775C22×C3—92no—
776C22×C3—122no—
777C22×C3—122no—
778C22×C3—122no—
779C22×C3—188no—
780C22×C3—181no—
781C22×C3—181no—
782C22×C3—181no—
783C22×C3—181no—
784C22×C3—181no—
785C22×C3—364no—
786C22×C3—364no—
787C22×C3#381112yescomplemented
788C22×C3C3×D3×D414yescomplemented
789C22×C3C22×D3211yescharacteristic
790C22×C3C23×C3×D312yes—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—34no—
795C2×D3—34no—
796C2×D3—34no—
797C2×D3—34no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—616no—
803C2×D3—62no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—62no—
807C2×D3—62no—
808C2×D3—62no—
809C2×D3—128no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—121no—
813C2×D3—121no—
814C2×D3—128no—
815C2×D3—128no—
816C2×D3—128no—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—22no—
820C3×C4—34no—
821C3×C4—34no—
822C3×C4—42no—
823C3×C4—42no—
824C3×C4—64no—
825C3×C4—62no—
826C3×C4—62no—
827C3×C4—62no—
828C3×C4—62no—
829C3×C4—122no—
830C3×C4—122no—
831C3×C4—181no—
832Dic3—22no—
833Dic3—22no—
834Dic3—62no—
835Dic3—62no—
836Dic3C3×D3×D414yescomplemented
837C32—22no—
838C32—21no—
839C32—41no—
840C32D3×#12112yescomplemented
841C32C2×C3×#12111yescharacteristic, complemented
842C23—32no—
843C23—91no—
844C23—91no—
845C23—94no—
846C23—91no—
847C23—182no—
848C23—182no—
849C23—182no—
850C23—182no—
851C23—182no—
852C23—182no—
853C23—182no—
854C23—182no—
855C23C2×C3×D3211yescharacteristic
856C23C2×C3×D3211yescharacteristic
857D4—22no—
858D4—64no—
859D4—64no—
860D4—182no—
861D4—184no—
862D4—184no—
863D4—182no—
864D4—182no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—64no—
869C2×C4—94no—
870C2×C4—91no—
871C2×C4—182no—
872C2×C4—184no—
873C2×C4—182no—
874C2×C4—182no—
875C2×C4C2×C3×D3211yescharacteristic
876C2×C3—24no—
877C2×C3—22no—
878C2×C3—21no—
879C2×C3—22no—
880C2×C3—22no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—22no—
884C2×C3—42no—
885C2×C3—44no—
886C2×C3—42no—
887C2×C3—42no—
888C2×C3—41no—
889C2×C3—41no—
890C2×C3—41no—
891C2×C3—41no—
892C2×C3—82no—
893C2×C3—82no—
894C2×C3—82no—
895C2×C3—94no—
896C2×C3—122no—
897C2×C3—122no—
898C2×C3—182no—
899C2×C3—242no—
900C2×C3—361no—
901C2×C3D32×D411yescharacteristic
902C2×C3#6431211yescharacteristic
903C2×C3C2×#381111yescharacteristic
904C2×C3C2×C3×D3×D412yes—
905C2×C3C2×C3×D3×D412yes—
906C2×C3C3×D3×#4112yes—
907D3—38no—
908D3—42no—
909D3—64no—
910D3—64no—
911D3—122no—
912D3—122no—
913D3—122no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—62no—
920C22—62no—
921C22—62no—
922C22—92no—
923C22—92no—
924C22—92no—
925C22—92no—
926C22—188no—
927C22—181no—
928C22—181no—
929C22—181no—
930C22—181no—
931C22—181no—
932C22—364no—
933C22—364no—
934C22C3×#381112yescomplemented
935C22C22×C3×D3211yescharacteristic
936C4—21no—
937C4—34no—
938C4—62no—
939C4—62no—
940C4—181no—
941C3—21no—
942C3—22no—
943C3—41no—
944C3#1059529811yescharacteristic, direct product factor
945C3C3×D3×#12112yescomplemented
946C2—22no—
947C2—41no—
948C2—94no—
949C2—122no—
950C2—182no—
951C2—361no—
952C2C3×D32×D411yescharacteristic
953C2C3×#6431211yescharacteristic
954C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C2×C3×#121
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C3⋊D3C2semidirect
2. C2×C3×#3811C2semidirect
3. C2×C3×#3811C2semidirect
4. C22×C3×#624C2semidirect
5. C32×#939C2semidirect
6. C3×#63978C2semidirect
7. C3×#63974C2semidirect
8. C3×#63958C2semidirect
9. C3×#63921C2semidirect
10. C3×#63910C2semidirect
11. C3×#63883C2semidirect
13. #10595298C3direct (N × H)
17. C2×C33×D4C22semidirect
18. C2×C3×#638C22semidirect
19. C2×C3×#638C22semidirect
21. C2×C3×C4⋊(C3⋊D3)C22semidirect
23. C2×C32×#67C22semidirect
24. C2×C32×#67C22semidirect
25. C22×C32×Dic3C22semidirect
28. C2×C3×#626C22semidirect
29. C2×C3×#626C22semidirect
34. C2×C3×#624C22semidirect
35. C32×#217C22semidirect
36. C32×(C2×D3)⋊C4C22semidirect
37. C32×Dic3⋊C4C22semidirect
38. C3×Dic3⋊Dic3C22semidirect
39. C3×#3722C22semidirect
40. C3×(C2×D3)⋊Dic3C22semidirect
41. C2×D4×C3⋊D3C2×C3semidirect
47. C2×#3811C2×C3semidirect
48. C2×#3811C2×C3semidirect
49. C22×#624C2×C3semidirect
53. C3×#939D3semidirect
54. C3×#939C2×C3semidirect
63. #63978C2×C3semidirect
64. #63974C2×C3semidirect
65. #63958C2×C3semidirect
66. #63921C2×C3semidirect
67. #63910C2×C3semidirect
68. #63883C2×C3semidirect
76. C22×C3×C3⋊D3D4semidirect
102. C3×#624D4semidirect
118. C2×C32×D4C2×D3semidirect
119. C2×C32×D4C22×C3semidirect
121. C2×#638C22×C3semidirect
122. C2×#638C22×C3semidirect
124. C2×C4⋊(C3⋊D3)C22×C3semidirect
134. C2×C3×#67C2×D3semidirect
135. C2×C3×#67C2×D3semidirect
136. C2×C3×#67C22×C3semidirect
137. C2×C3×#67C22×C3semidirect
139. C22×C3×Dic3C2×D3semidirect
140. C22×C3×Dic3C22×C3semidirect
159. C2×#626C22×C3semidirect
160. C2×#626C22×C3semidirect
165. C2×#624C22×C3semidirect
171. C3×#217C2×D3semidirect
172. C3×#217C22×C3semidirect
177. C3×(C2×D3)⋊C4C2×D3semidirect
178. C3×(C2×D3)⋊C4C22×C3semidirect
182. C3×Dic3⋊C4C2×D3semidirect
183. C3×Dic3⋊C4C22×C3semidirect
184. Dic3⋊Dic3C22×C3semidirect
185. #3722C22×C3semidirect
186. (C2×D3)⋊Dic3C22×C3semidirect
192. C22×C33C2×D4semidirect
203. C2×C3×C3⋊D3C2×D4semidirect
213. C32×Dic3C2×D4semidirect
233. #939C3×D3semidirect
258. C22×C3⋊D3C3×D4semidirect
352. #624C3×D4semidirect
361. C3×C3⋊D3#121semidirect
388. C2×C3×D4D32semidirect
389. C2×C3×D4C2×C3×D3semidirect
405. C2×#67C2×C3×D3semidirect
406. C2×#67C2×C3×D3semidirect
407. C22×Dic3C2×C3×D3semidirect
437. #217C2×C3×D3semidirect
441. (C2×D3)⋊C4C2×C3×D3semidirect
444. Dic3⋊C4C2×C3×D3semidirect
479. C22×C32D3×D4semidirect
480. C22×C32C2×C3×D4semidirect
492. C2×C3⋊D3C2×C3×D4semidirect
545. C3×Dic3D3×D4semidirect
546. C3×Dic3C2×C3×D4semidirect
558. C33C2×#121semidirect
698. C3⋊D3C3×#121semidirect
721. C2×D4C3×D32semidirect
787. C22×C3#3811semidirect
788. C22×C3C3×D3×D4semidirect
836. Dic3C3×D3×D4semidirect
840. C32D3×#121semidirect
841. C32C2×C3×#121semidirect
934. C22C3×#3811semidirect
944. C3#10595298direct (N × H)
945. C3C3×D3×#121semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C3⋊D32
C2×C3×#38112
C22×C3×#6242
C32×#9392
C3×#639782
C3×#639742
C3×#639582
C3×#639212
C3×#639102
C3×#638832
C3×D3×#1213
#105952983