Finite Group Databasebeta

← C3×#10591382 #13158388

Subgroups — C3×#10591382 #13158388

Order 1728.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4×D3C211yesmaximal, characteristic, complemented
2C22×C3×#626C211yesmaximal, characteristic
3C2×C3×#3752C211yesmaximal, characteristic, complemented
4C2×C3×#3722C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
6C32×C3⋊#95C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8C3×#5213—31nomaximal
9C3×#4665—31nomaximal
10#10591382C311yesmaximal, characteristic, direct product factor
11C23×C3×C3⋊D3C2211yescharacteristic
12C23×C32×D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C32×C4×D3—22no—
19C2×C32×C4×D3—22no—
20C2×C32×C4×D3—22no—
21C2×C3×#626—22no—
22C2×C3×#626—22no—
23C2×C3×#626C414yescomplemented
24C3×#3752—22no—
25C3×#3722—22no—
26C3×(C2×D3)⋊Dic3—22no—
27C23×C32×C4—31no—
28C22×C3×#67—31no—
29C22×C3×D12—31no—
30C22×C3×C4×D3—21no—
31C22×C3×C4×D3D311yescharacteristic, complemented
32C22×C3×C4×D3C2×C311yescharacteristic, complemented
33C22×#626C2×C311yescharacteristic
34C2×#3752C2×C311yescharacteristic, complemented
35C2×C3×#217—31no—
36C2×C3×(C2×D3)⋊C4—31no—
37C2×C3×(C2×D3)⋊C4—31no—
38C2×C3×(C2×D3)⋊C4—31no—
39C2×C3×(C2×D3)⋊C4—31no—
40C2×C3×(C2×D3)⋊C4—31no—
41C2×C3×(C2×D3)⋊C4—61no—
42C2×#3722C2×C311yescharacteristic, complemented
43C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
44C32×#95—31no—
45C3×C3⋊#95—21no—
46C3×C3⋊#95—31no—
47C3×C3⋊#95—31no—
48C3×C3⋊#95D311yescharacteristic, complemented
49C3×C3⋊#95C2×C311yescharacteristic, complemented
50#63579C2×C311yescharacteristic, complemented
51C23×C33C2311yescharacteristic
52C22×C3×C3⋊D3—21no—
53C22×C3×C3⋊D3—21no—
54C22×C3×C3⋊D3—21no—
55C22×C3×C3⋊D3—21no—
56C22×C3×C3⋊D3—21no—
57C22×C3×C3⋊D3—21no—
58C22×C3×C3⋊D3C2×C412yescomplemented
59C22×C32×D3—21no—
60C22×C32×D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3—21no—
63C22×C32×D3C2×C412yes—
64C22×C32×D3D412yes—
65C22×C32×D3D412yes—
66C2×C33×C4—21no—
67C2×C33×C4—21no—
68C2×C33×C4D412yescomplemented
69C2×C3×C3⋊Dic3—21no—
70C2×C3×C3⋊Dic3—21no—
71C2×C3×C3⋊Dic3—21no—
72C2×C32×Dic3—21no—
73C2×C32×Dic3—21no—
74C2×C32×Dic3—21no—
75C2×C32×Dic3—21no—
76C2×C32×Dic3—21no—
77C2×C32×Dic3—21no—
78C2×C32×Dic3—21no—
79C2×C32×Dic3C2×C412yescomplemented
80C2×C32×Dic3D412yescomplemented
81C32×C4×D3—28no—
82C3×#626—28no—
83C3×#386—91no—
84#5213—31no—
85#4665—31no—
86C24×C32—31no—
87C23×C3⋊D3C22×C311yescharacteristic
88C23×C3×D3—21no—
89C23×C3×D3—31no—
90C23×C3×D3—31no—
91C23×C3×D3—61no—
92C23×C3×D3C2×D311yescharacteristic
93C23×C3×D3C22×C311yescharacteristic
94C22×C32×C4—21no—
95C22×C32×C4—21no—
96C22×C32×C4—21no—
97C22×C32×C4—31no—
98C22×C32×C4—31no—
99C22×C32×C4—31no—
100C22×C32×C4—41no—
101C22×C32×C4—62no—
102C22×C32×C4—62no—
103C22×C32×C4—62no—
104C22×C32×C4C2×D311yescharacteristic
105C22×C32×C4C2×D311yescharacteristic
106C22×C32×C4C22×C311yescharacteristic
107C22×C3⋊Dic3C22×C311yescharacteristic
108C2×C3×#67—34no—
109C2×C3×#67—62no—
110C2×C3×#67—62no—
111C22×C3×Dic3—21no—
112C22×C3×Dic3—21no—
113C22×C3×Dic3—21no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—61no—
117C22×C3×Dic3C2×D311yescharacteristic
118C22×C3×Dic3C2×D311yescharacteristic
119C22×C3×Dic3C2×D311yescharacteristic
120C22×C3×Dic3C22×C311yescharacteristic
121C22×C3×Dic3C22×C311yescharacteristic
122C22×C3×Dic3C22×C311yescharacteristic
123C2×C3×D12—34no—
124C2×C3×D12—62no—
125C2×C3×D12—62no—
126C2×C3×C4×D3—24no—
127C2×C3×C4×D3—24no—
128C2×C3×C4×D3—24no—
129C2×C3×C4×D3—22no—
130C2×C3×C4×D3—22no—
131C2×C3×C4×D3—22no—
132C2×C3×C4×D3—22no—
133C2×C3×C4×D3—22no—
134C2×C3×C4×D3—22no—
135C2×#626—22no—
136C2×#626—22no—
137C2×#626C3×C414yescomplemented
138#3752—22no—
139C3×#217—62no—
140C3×(C2×D3)⋊C4—62no—
141C3×(C2×D3)⋊C4—64no—
142C3×(C2×D3)⋊C4—62no—
143C3×(C2×D3)⋊C4—62no—
144C3×(C2×D3)⋊C4—62no—
145C3×(C2×D3)⋊C4—62no—
146#3722—22no—
147(C2×D3)⋊Dic3—22no—
148C22×C33C22×C411yescharacteristic
149C22×C33C2×D411yescharacteristic
150C22×C33C2×D411yescharacteristic
151C22×C33C2×D411yescharacteristic
152C22×C33C2×D411yescharacteristic
153C22×C33#4111yescharacteristic
154C22×C33#4111yescharacteristic
155C2×C3×C3⋊D3—22no—
156C2×C3×C3⋊D3—22no—
157C2×C3×C3⋊D3—22no—
158C2×C3×C3⋊D3—41no—
159C2×C3×C3⋊D3—41no—
160C2×C3×C3⋊D3—41no—
161C2×C3×C3⋊D3—41no—
162C2×C32×D3—22no—
163C2×C32×D3—22no—
164C2×C32×D3—22no—
165C2×C32×D3—22no—
166C2×C32×D3—22no—
167C2×C32×D3—22no—
168C2×C32×D3C22⋊C414yescomplemented
169C33×C4—22no—
170C3×C3⋊Dic3—41no—
171C32×Dic3—22no—
172C32×Dic3—22no—
173C32×Dic3—41no—
174C22×C3×D4—91no—
175C23×C3×C4—31no—
176C23×C3×C4—31no—
177C23×C3×C4—61no—
178C22×#67—31no—
179C22×D12—31no—
180C22×C4×D3C3×D311yescharacteristic, complemented
181C2×C3×C22⋊C4—91no—
182C2×C3×C22⋊C4—91no—
183C2×C3×C22⋊C4—91no—
184C2×#217—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—61no—
191C3×#95—31no—
192C3×#95—31no—
193C3×#95—61no—
194C3×#95—91no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95C3×D311yescharacteristic, complemented
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—32no—
202C23×C32—32no—
203C23×C32—32no—
204C23×C32—41no—
205C23×C32—61no—
206C23×C32—61no—
207C23×C32—61no—
208C23×C32—61no—
209C23×C32C22×D311yescharacteristic
210C23×C32C22×D311yescharacteristic
211C23×C32C23×C311yescharacteristic
212C22×C3⋊D3—21no—
213C22×C3⋊D3—21no—
214C22×C3⋊D3—21no—
215C22×C3⋊D3—21no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3C2×C3×C412yescomplemented
219C22×C3×D3—22no—
220C22×C3×D3—22no—
221C22×C3×D3—22no—
222C22×C3×D3—22no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—22no—
232C22×C3×D3—22no—
233C22×C3×D3—22no—
234C22×C3×D3—32no—
235C22×C3×D3—32no—
236C22×C3×D3—62no—
237C22×C3×D3—62no—
238C22×C3×D3—62no—
239C22×C3×D3—61no—
240C22×C3×D3—61no—
241C22×C3×D3—61no—
242C22×C3×D3—61no—
243C22×C3×D3—61no—
244C22×C3×D3—61no—
245C22×C3×D3—61no—
246C22×C3×D3—61no—
247C22×C3×D3—61no—
248C22×C3×D3—61no—
249C22×C3×D3—61no—
250C22×C3×D3—61no—
251C22×C3×D3—121no—
252C22×C3×D3—121no—
253C22×C3×D3—121no—
254C22×C3×D3—121no—
255C22×C3×D3C4×D312yes—
256C22×C3×D3D1212yes—
257C22×C3×D3#6712yes—
258C22×C3×D3C2×C3×C412yes—
259C22×C3×D3C3×D412yes—
260C22×C3×D3C3×D412yes—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—22no—
264C2×C32×C4—22no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—22no—
270C2×C32×C4—22no—
271C2×C32×C4—22no—
272C2×C32×C4—32no—
273C2×C32×C4—32no—
274C2×C32×C4—42no—
275C2×C32×C4—41no—
276C2×C32×C4—41no—
277C2×C32×C4—41no—
278C2×C32×C4—41no—
279C2×C32×C4—42no—
280C2×C32×C4—42no—
281C2×C32×C4—68no—
282C2×C32×C4—61no—
283C2×C32×C4—61no—
284C2×C32×C4—61no—
285C2×C32×C4—61no—
286C2×C32×C4—61no—
287C2×C32×C4—61no—
288C2×C32×C4—61no—
289C2×C32×C4D1212yescomplemented
290C2×C32×C4#6712yescomplemented
291C2×C32×C4C3×D412yescomplemented
292C2×C3⋊Dic3—21no—
293C2×C3⋊Dic3—21no—
294C2×C3⋊Dic3—21no—
295C3×#67—68no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—41no—
316C2×C3×Dic3—41no—
317C2×C3×Dic3—41no—
318C2×C3×Dic3—41no—
319C2×C3×Dic3—62no—
320C2×C3×Dic3—61no—
321C2×C3×Dic3—61no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—61no—
324C2×C3×Dic3—61no—
325C2×C3×Dic3—61no—
326C2×C3×Dic3—121no—
327C2×C3×Dic3—121no—
328C2×C3×Dic3C4×D312yescomplemented
329C2×C3×Dic3#6712yescomplemented
330C2×C3×Dic3C2×C3×C412yescomplemented
331C2×C3×Dic3C3×D412yescomplemented
332C3×D12—68no—
333C3×C4×D3—216no—
334C3×C4×D3—28no—
335C3×C4×D3—28no—
336#626—28no—
337#386—91noSylow
338C2×C33C2×C22⋊C411yescharacteristic
339C2×C33C4×D411yescharacteristic
340C2×C33C4×D411yescharacteristic
341C2×C33#12011yescharacteristic
342C2×C33#12111yescharacteristic
343C2×C33#12111yescharacteristic
344C2×C33#12311yescharacteristic
345C3×C3⋊D3—42no—
346C32×D3—24no—
347C24×C3—31no—
348C24×C3—31no—
349C24×C3—61no—
350C24×C3—91no—
351C23×D3—31no—
352C23×D3—31no—
353C23×D3—61no—
354C23×D3C2×C3×D311yescharacteristic
355C2×C3×D4—94no—
356C2×C3×D4—182no—
357C2×C3×D4—182no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—41no—
368C22×C3×C4—61no—
369C22×C3×C4—61no—
370C22×C3×C4—61no—
371C22×C3×C4—62no—
372C22×C3×C4—62no—
373C22×C3×C4—62no—
374C22×C3×C4—62no—
375C22×C3×C4—64no—
376C22×C3×C4—64no—
377C22×C3×C4—64no—
378C22×C3×C4—62no—
379C22×C3×C4—62no—
380C22×C3×C4—91no—
381C22×C3×C4D3211yescharacteristic
382C22×C3×C4C2×C3×D311yescharacteristic
383C22×C3×C4C2×C3×D311yescharacteristic
384C2×#67—34no—
385C2×#67—62no—
386C2×#67—62no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—61no—
390C22×Dic3C2×C3×D311yescharacteristic
391C22×Dic3C2×C3×D311yescharacteristic
392C22×Dic3C2×C3×D311yescharacteristic
393C2×D12—34no—
394C2×D12—62no—
395C2×D12—62no—
396C2×C4×D3—22no—
397C2×C4×D3—22no—
398C2×C4×D3—22no—
399C3×C22⋊C4—182no—
400C3×C22⋊C4—182no—
401C3×C22⋊C4—182no—
402#217—62no—
403(C2×D3)⋊C4—62no—
404(C2×D3)⋊C4—64no—
405(C2×D3)⋊C4—62no—
406(C2×D3)⋊C4—62no—
407(C2×D3)⋊C4—62no—
408(C2×D3)⋊C4—62no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—34no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32—62no—
439C22×C32—62no—
440C22×C32—62no—
441C22×C32—62no—
442C22×C32—62no—
443C22×C32—62no—
444C22×C32C2×C4×D311yescharacteristic
445C22×C32C2×C4×D311yescharacteristic
446C22×C32C2×D1211yescharacteristic
447C22×C32C2×D1211yescharacteristic
448C22×C32#23511yescharacteristic
449C22×C32#23511yescharacteristic
450C22×C32#23511yescharacteristic
451C22×C32D3×D411yescharacteristic
452C22×C32D3×D411yescharacteristic
453C22×C32D3×D411yescharacteristic
454C22×C32#23911yescharacteristic
455C22×C32C2×#6711yescharacteristic
456C22×C32C2×#6711yescharacteristic
457C22×C32C2×#6711yescharacteristic
458C22×C32C22×C3×C411yescharacteristic
459C22×C32C2×C3×D411yescharacteristic
460C22×C32C2×C3×D411yescharacteristic
461C22×C32C2×C3×D411yescharacteristic
462C22×C32C2×C3×D411yescharacteristic
463C22×C32C3×#4111yescharacteristic
464C22×C32C3×#4111yescharacteristic
465C2×C3⋊D3—22no—
466C2×C3⋊D3—22no—
467C2×C3⋊D3—22no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3×D3—24no—
473C2×C3×D3—24no—
474C2×C3×D3—24no—
475C2×C3×D3—24no—
476C2×C3×D3—24no—
477C2×C3×D3—24no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—24no—
491C2×C3×D3—64no—
492C2×C3×D3—62no—
493C2×C3×D3—62no—
494C2×C3×D3—62no—
495C2×C3×D3—62no—
496C2×C3×D3—62no—
497C2×C3×D3—62no—
498C2×C3×D3—122no—
499C2×C3×D3—122no—
500C2×C3×D3—122no—
501C2×C3×D3—122no—
502C2×C3×D3—122no—
503C2×C3×D3—122no—
504C2×C3×D3—121no—
505C2×C3×D3—121no—
506C2×C3×D3—121no—
507C2×C3×D3—121no—
508C2×C3×D3—121no—
509C2×C3×D3—121no—
510C2×C3×D3—121no—
511C2×C3×D3—121no—
512C2×C3×D3(C2×D3)⋊C414yescomplemented
513C2×C3×D3C3×C22⋊C414yescomplemented
514C32×C4—22no—
515C32×C4—24no—
516C32×C4—22no—
517C32×C4—22no—
518C32×C4—42no—
519C32×C4—42no—
520C32×C4—44no—
521C32×C4—62no—
522C32×C4—62no—
523C32×C4—121no—
524C3⋊Dic3—41no—
525C3×Dic3—24no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—42no—
531C3×Dic3—42no—
532C3×Dic3—41no—
533C3×Dic3—41no—
534C3×Dic3—122no—
535C3×Dic3—121no—
536C3×Dic3—121no—
537C22×D4—91no—
538C23×C4—31no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542#95—31no—
543#95—91no—
544C33#38611yescharacteristic, complemented, Sylow
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—32no—
549C23×C3—32no—
550C23×C3—32no—
551C23×C3—32no—
552C23×C3—32no—
553C23×C3—32no—
554C23×C3—41no—
555C23×C3—62no—
556C23×C3—62no—
557C23×C3—62no—
558C23×C3—62no—
559C23×C3—62no—
560C23×C3—62no—
561C23×C3—62no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—92no—
571C23×C3—181no—
572C23×C3—181no—
573C23×C3—181no—
574C23×C3—181no—
575C23×C3—181no—
576C23×C3—181no—
577C23×C3C2×D3211yescharacteristic
578C23×C3C22×C3×D311yescharacteristic
579C23×C3C22×C3×D311yescharacteristic
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—32no—
585C22×D3—32no—
586C22×D3—62no—
587C22×D3—62no—
588C22×D3—62no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—61no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—121no—
602C22×D3—121no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3C3×C4×D312yes—
606C22×D3C3×D1212yes—
607C22×D3C3×#6712yes—
608C3×D4—188no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—32no—
621C2×C3×C4—32no—
622C2×C3×C4—32no—
623C2×C3×C4—32no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—42no—
629C2×C3×C4—42no—
630C2×C3×C4—42no—
631C2×C3×C4—62no—
632C2×C3×C4—62no—
633C2×C3×C4—616no—
634C2×C3×C4—68no—
635C2×C3×C4—68no—
636C2×C3×C4—62no—
637C2×C3×C4—62no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—61no—
644C2×C3×C4—61no—
645C2×C3×C4—61no—
646C2×C3×C4—62no—
647C2×C3×C4—61no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—121no—
654C2×C3×C4—121no—
655C2×C3×C4—121no—
656C2×C3×C4—121no—
657C2×C3×C4—181no—
658C2×C3×C4—181no—
659C2×C3×C4—181no—
660C2×C3×C4#62612yescomplemented
661C2×C3×C4C3×D1212yescomplemented
662C2×C3×C4C3×#6712yescomplemented
663#67—68no—
664C2×Dic3—21no—
665C2×Dic3—21no—
666C2×Dic3—21no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—21no—
670C2×Dic3—21no—
671C2×Dic3—62no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—121no—
679C2×Dic3—121no—
680C2×Dic3C3×C4×D312yescomplemented
681C2×Dic3C3×#6712yescomplemented
682D12—68no—
683C4×D3—28no—
684C2×C32—21no—
685C2×C32—21no—
686C2×C32—21no—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—21no—
690C2×C32—21no—
691C2×C32—21no—
692C2×C32—21no—
693C2×C32—21no—
694C2×C32—21no—
695C2×C32—21no—
696C2×C32—21no—
697C2×C32—21no—
698C2×C32—21no—
699C2×C32—21no—
700C2×C32—21no—
701C2×C32—21no—
702C2×C32—21no—
703C2×C32—21no—
704C2×C32—21no—
705C2×C32—41no—
706C2×C32—41no—
707C2×C32—41no—
708C2×C32—41no—
709C2×C32—41no—
710C2×C32—41no—
711C2×C32—41no—
712C2×C32—64no—
713C2×C32C4×D1211yescharacteristic
714C2×C32D3×C22⋊C411yescharacteristic
715C2×C32#88211yescharacteristic
716C2×C32#88411yescharacteristic
717C2×C32#89311yescharacteristic
718C2×C32#89411yescharacteristic
719C2×C32#89511yescharacteristic
720C2×C32C2×(C2×D3)⋊C411yescharacteristic
721C2×C32C4×#6711yescharacteristic
722C2×C32C4×#6711yescharacteristic
723C2×C32#92911yescharacteristic
724C2×C32#93011yescharacteristic
725C2×C32#93011yescharacteristic
726C2×C32#95311yescharacteristic
727C2×C32C2×C3×C22⋊C411yescharacteristic
728C2×C32C3×C4×D411yescharacteristic
729C2×C32C3×C4×D411yescharacteristic
730C2×C32C3×#12011yescharacteristic
731C2×C32C3×#12111yescharacteristic
732C2×C32C3×#12111yescharacteristic
733C2×C32C3×#12311yescharacteristic
734C3⋊D3—42no—
735C3×D3—28no—
736C3×D3—24no—
737C3×D3—24no—
738C3×D3—124no—
739C3×D3—122no—
740C3×D3—122no—
741C24—31no—
742C24—91no—
743C2×D4—94no—
744C2×D4—182no—
745C2×D4—182no—
746C22×C4—31no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—62no—
750C22×C4—62no—
751C22×C4—62no—
752C22×C4—91no—
753C22×C4C3×D3211yescharacteristic
754C22⋊C4—182no—
755C22⋊C4—182no—
756C22⋊C4—182no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—21no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—34no—
779C22×C3—34no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—64no—
788C22×C3—64no—
789C22×C3—64no—
790C22×C3—64no—
791C22×C3—64no—
792C22×C3—64no—
793C22×C3—64no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—182no—
807C22×C3—182no—
808C22×C3—182no—
809C22×C3—361no—
810C22×C3—361no—
811C22×C3—361no—
812C22×C3—361no—
813C22×C3#379811yescharacteristic
814C22×C3#379911yescharacteristic
815C22×C3C4×D3211yescharacteristic
816C22×C3D3×D1211yescharacteristic
817C22×C3C2×#62611yescharacteristic
818C22×C3D3×#6711yescharacteristic
819C22×C3D3×#6711yescharacteristic
820C22×C3C2×C3×C4×D311yescharacteristic
821C22×C3C2×C3×C4×D311yescharacteristic
822C22×C3C2×C3×D1211yescharacteristic
823C22×C3C2×C3×D1211yescharacteristic
824C22×C3C3×#23511yescharacteristic
825C22×C3C3×#23511yescharacteristic
826C22×C3C3×#23511yescharacteristic
827C22×C3C3×D3×D411yescharacteristic
828C22×C3C3×D3×D411yescharacteristic
829C22×C3C3×D3×D411yescharacteristic
830C22×C3C3×#23911yescharacteristic
831C22×C3C2×C3×#6711yescharacteristic
832C22×C3C2×C3×#6711yescharacteristic
833C22×C3C2×C3×#6711yescharacteristic
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—64no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—122no—
848C2×D3—122no—
849C2×D3—122no—
850C2×D3—122no—
851C2×D3—122no—
852C2×D3—122no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—121no—
858C2×D3—121no—
859C2×D3—121no—
860C2×D3—121no—
861C2×D3C3×(C2×D3)⋊C414yescomplemented
862C3×C4—24no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—22no—
866C3×C4—42no—
867C3×C4—42no—
868C3×C4—44no—
869C3×C4—64no—
870C3×C4—62no—
871C3×C4—62no—
872C3×C4—62no—
873C3×C4—62no—
874C3×C4—122no—
875C3×C4—122no—
876C3×C4—121no—
877C3×C4—121no—
878C3×C4—361no—
879Dic3—22no—
880Dic3—22no—
881Dic3—41no—
882Dic3—122no—
883Dic3—121no—
884Dic3—121no—
885C32—21no—
886C32—21no—
887C32—21no—
888C32—41no—
889C32#466511yescharacteristic, complemented
890C32#521311yescharacteristic, complemented
891C32C3×#38611yescharacteristic, complemented
892C23—32no—
893C23—32no—
894C23—32no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—92no—
900C23—181no—
901C23—181no—
902C23—181no—
903C23—181no—
904C23—181no—
905C23—181no—
906C23C2×C3×D3211yescharacteristic
907D4—188no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—32no—
911C2×C4—32no—
912C2×C4—68no—
913C2×C4—61no—
914C2×C4—61no—
915C2×C4—61no—
916C2×C4—61no—
917C2×C4—61no—
918C2×C4—61no—
919C2×C4—61no—
920C2×C4—181no—
921C2×C4—181no—
922C2×C4—181no—
923C2×C4C3×#62612yescomplemented
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—21no—
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—41no—
946C2×C3—41no—
947C2×C3—41no—
948C2×C3—41no—
949C2×C3—41no—
950C2×C3—41no—
951C2×C3—41no—
952C2×C3—68no—
953C2×C3—64no—
954C2×C3—64no—
955C2×C3—362no—
956C2×C3#6385011yescharacteristic
957C2×C3C4×#62611yescharacteristic
958C2×C3#6390411yescharacteristic
959C2×C3#6390611yescharacteristic
960C2×C3#6390911yescharacteristic
961C2×C3D3×(C2×D3)⋊C411yescharacteristic
962C2×C3#6397711yescharacteristic
963C2×C3C3×C4×D1211yescharacteristic
964C2×C3C3×D3×C22⋊C411yescharacteristic
965C2×C3C3×#88211yescharacteristic
966C2×C3C3×#88411yescharacteristic
967C2×C3C3×#89311yescharacteristic
968C2×C3C3×#89411yescharacteristic
969C2×C3C3×#89511yescharacteristic
970C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
971C2×C3C3×C4×#6711yescharacteristic
972C2×C3C3×C4×#6711yescharacteristic
973C2×C3C3×#92911yescharacteristic
974C2×C3C3×#93011yescharacteristic
975C2×C3C3×#93011yescharacteristic
976C2×C3C3×#95311yescharacteristic
977D3—24no—
978D3—124no—
979D3—122no—
980D3—122no—
981C22—34no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—62no—
988C22—182no—
989C22—182no—
990C22—182no—
991C22—361no—
992C22—361no—
993C22—361no—
994C22—361no—
995C22C3×#379811yescharacteristic
996C22C3×#379911yescharacteristic
997C22C3×C4×D3211yescharacteristic
998C22C3×D3×D1211yescharacteristic
999C22C2×C3×#62611yescharacteristic
1000C22C3×D3×#6711yescharacteristic
1001C22C3×D3×#6711yescharacteristic
1002C4—22no—
1003C4—62no—
1004C4—62no—
1005C4—121no—
1006C4—361no—
1007C3—21no—
1008C3—21no—
1009C3—21no—
1010C3—41no—
1011C3#1059138211yescharacteristic, direct product factor
1012C3C3×#466511yescharacteristic, complemented
1013C3C3×#521311yescharacteristic, complemented
1014C2—64no—
1015C2—362no—
1016C2C3×#6385011yescharacteristic
1017C2C3×C4×#62611yescharacteristic
1018C2C3×#6390411yescharacteristic
1019C2C3×#6390611yescharacteristic
1020C2C3×#6390911yescharacteristic
1021C2C3×D3×(C2×D3)⋊C411yescharacteristic
1022C2C3×#6397711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC22×C3×#626C2
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#386
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4×D3C2semidirect
3. C2×C3×#3752C2semidirect
4. C2×C3×#3722C2semidirect
5. C2×C3×(C2×D3)⋊Dic3C2semidirect
6. C32×C3⋊#95C2semidirect
7. C3×#63579C2semidirect
10. #10591382C3direct (N × H)
23. C2×C3×#626C4semidirect
31. C22×C3×C4×D3D3semidirect
32. C22×C3×C4×D3C2×C3semidirect
34. C2×#3752C2×C3semidirect
42. C2×#3722C2×C3semidirect
43. C2×(C2×D3)⋊Dic3C2×C3semidirect
48. C3×C3⋊#95D3semidirect
49. C3×C3⋊#95C2×C3semidirect
50. #63579C2×C3semidirect
58. C22×C3×C3⋊D3C2×C4semidirect
68. C2×C33×C4D4semidirect
79. C2×C32×Dic3C2×C4semidirect
80. C2×C32×Dic3D4semidirect
137. C2×#626C3×C4semidirect
168. C2×C32×D3C22⋊C4semidirect
180. C22×C4×D3C3×D3semidirect
197. C3⋊#95C3×D3semidirect
218. C22×C3⋊D3C2×C3×C4semidirect
289. C2×C32×C4D12semidirect
290. C2×C32×C4#67semidirect
291. C2×C32×C4C3×D4semidirect
328. C2×C3×Dic3C4×D3semidirect
329. C2×C3×Dic3#67semidirect
330. C2×C3×Dic3C2×C3×C4semidirect
331. C2×C3×Dic3C3×D4semidirect
512. C2×C3×D3(C2×D3)⋊C4semidirect
513. C2×C3×D3C3×C22⋊C4semidirect
544. C33#386semidirect
660. C2×C3×C4#626semidirect
661. C2×C3×C4C3×D12semidirect
662. C2×C3×C4C3×#67semidirect
680. C2×Dic3C3×C4×D3semidirect
681. C2×Dic3C3×#67semidirect
861. C2×D3C3×(C2×D3)⋊C4semidirect
889. C32#4665semidirect
890. C32#5213semidirect
891. C32C3×#386semidirect
923. C2×C4C3×#626semidirect
1011. C3#10591382direct (N × H)
1012. C3C3×#4665semidirect
1013. C3C3×#5213semidirect

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×#6262
C2×C3×#37522
C2×C3×#37222
C2×C3×(C2×D3)⋊Dic32
C32×C3⋊#952
C3×#635792
C3×#52133
C3×#46653
#105913823