Finite Group Databasebeta

← C3×#10591368 #13158377

Subgroups — C3×#10591368 #13158377

Order 1728.

1402 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
1C22×C3×D3×Dic3C211yesmaximal, characteristic
2C2×C3×C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
5C2×C3×Dic32C211yesmaximal, characteristic, complemented
6C32×C3⋊#95C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8C3×Dic3×C22⋊C4—31nomaximal
9C3×#4666—31nomaximal
10#10591368C311yesmaximal, characteristic, direct product factor
11C23×C32×D3C2211yescharacteristic
12C22×C33×C4C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C3×D3×Dic3—22no—
19C2×C3×D3×Dic3—22no—
20C2×C3×D3×Dic3C414yescomplemented
21C3×C4×C3⋊Dic3—22no—
22C32×(C2×D3)⋊C4C414yescomplemented
23C3×(C2×D3)⋊Dic3C414yescomplemented
24C3×Dic32—22no—
25C23×C3×Dic3—31no—
26C22×C3×C4×D3—31no—
27C22×D3×Dic3C2×C311yescharacteristic
28C2×C32×C22⋊C4—31no—
29C2×C4×C3⋊Dic3C2×C311yescharacteristic, complemented
30C2×C3×#217—31no—
31C2×C3×(C2×D3)⋊C4—21no—
32C2×C3×(C2×D3)⋊C4—31no—
33C2×C3×(C2×D3)⋊C4D311yescharacteristic
34C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
35C2×C3×C4×Dic3—31no—
36C2×C3×C4×Dic3—31no—
37C2×C3×C4×Dic3—31no—
38C2×C3×C4×Dic3—31no—
39C2×C3×C4×Dic3—61no—
40C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
41C2×Dic32C2×C311yescharacteristic, complemented
42C32×#95—31no—
43C3×C3⋊#95—21no—
44C3×C3⋊#95—31no—
45C3×C3⋊#95—31no—
46C3×C3⋊#95D311yescharacteristic, complemented
47C3×C3⋊#95C2×C311yescharacteristic, complemented
48#63579C2×C311yescharacteristic, complemented
49C23×C33C2311yescharacteristic
50C22×C32×D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3—21no—
54C22×C32×D3C2×C412yes—
55C22×C32×D3C2×C412yes—
56C22×C32×D3C2×C412yes—
57C2×C33×C4—21no—
58C2×C33×C4—21no—
59C2×C33×C4C2×C412yescomplemented
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3C2×C412yes—
63C2×C3×C3⋊Dic3C2×C412yescomplemented
64C2×C3×C3⋊Dic3D412yes—
65C2×C3×C3⋊Dic3D412yes—
66C2×C32×Dic3—21no—
67C2×C32×Dic3—21no—
68C2×C32×Dic3—21no—
69C2×C32×Dic3—21no—
70C2×C32×Dic3—21no—
71C2×C32×Dic3—21no—
72C2×C32×Dic3C2×C412yes—
73C2×C32×Dic3C2×C412yescomplemented
74C2×C32×Dic3C2×C412yescomplemented
75C3×D3×Dic3—28no—
76C3×C4×C22⋊C4—91no—
77Dic3×C22⋊C4—31no—
78#4666—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—41no—
90C22×C32×C4C2×D311yescharacteristic
91C22×C32×C4C2×D311yescharacteristic
92C22×C32×C4C22×C311yescharacteristic
93C22×C3⋊Dic3C22×C311yescharacteristic
94C22×C3⋊Dic3C22×C311yescharacteristic
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—34no—
103C22×C3×Dic3—62no—
104C22×C3×Dic3—62no—
105C22×C3×Dic3—61no—
106C22×C3×Dic3—61no—
107C22×C3×Dic3C2×D311yescharacteristic
108C22×C3×Dic3C2×D311yescharacteristic
109C22×C3×Dic3C2×D311yescharacteristic
110C22×C3×Dic3C22×C311yescharacteristic
111C22×C3×Dic3C22×C311yescharacteristic
112C22×C3×Dic3C22×C311yescharacteristic
113C2×C3×C4×D3—34no—
114C2×C3×C4×D3—62no—
115C2×C3×C4×D3—62no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3C3×C414yescomplemented
119C32×C22⋊C4—34no—
120C4×C3⋊Dic3—22no—
121C3×#217—34no—
122C3×(C2×D3)⋊C4—24no—
123C3×(C2×D3)⋊C4—34no—
124C3×(C2×D3)⋊C4Dic314yescomplemented
125C3×(C2×D3)⋊C4C3×C414yescomplemented
126C3×C4×Dic3—62no—
127C3×C4×Dic3—62no—
128C3×C4×Dic3—62no—
129C3×C4×Dic3—62no—
130C3×C4×Dic3—64no—
131(C2×D3)⋊Dic3C3×C414yescomplemented
132Dic32—22no—
133C22×C33C22×C411yescharacteristic
134C22×C33C22×C411yescharacteristic
135C22×C33C22×C411yescharacteristic
136C22×C33C2×D411yescharacteristic
137C22×C33C2×D411yescharacteristic
138C22×C33#4111yescharacteristic
139C22×C33#4111yescharacteristic
140C2×C32×D3—22no—
141C2×C32×D3—22no—
142C2×C32×D3—22no—
143C2×C32×D3—22no—
144C2×C32×D3—22no—
145C2×C32×D3—22no—
146C2×C32×D3C4214yescomplemented
147C33×C4—22no—
148C3×C3⋊Dic3—22no—
149C3×C3⋊Dic3C22⋊C414yescomplemented
150C32×Dic3—22no—
151C32×Dic3—22no—
152C32×Dic3—22no—
153C23×C3×C4—91no—
154C23×Dic3—31no—
155C22×C4×D3—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—61no—
159C2×C3×C22⋊C4—91no—
160C2×C3×C42—91no—
161C2×C3×C42—91no—
162C2×#217—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4C3×D311yescharacteristic
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—61no—
170C3×#95—31no—
171C3×#95—31no—
172C3×#95—61no—
173C3×#95—91no—
174C3⋊#95—31no—
175C3⋊#95—31no—
176C3⋊#95C3×D311yescharacteristic, complemented
177C23×C32—21no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—32no—
181C23×C32—32no—
182C23×C32—32no—
183C23×C32—41no—
184C23×C32—61no—
185C23×C32—61no—
186C23×C32—61no—
187C23×C32—61no—
188C23×C32C22×D311yescharacteristic
189C23×C32C22×D311yescharacteristic
190C23×C32C23×C311yescharacteristic
191C22×C3×D3—21no—
192C22×C3×D3—21no—
193C22×C3×D3—21no—
194C22×C3×D3—21no—
195C22×C3×D3—21no—
196C22×C3×D3—21no—
197C22×C3×D3—21no—
198C22×C3×D3—21no—
199C22×C3×D3—22no—
200C22×C3×D3—22no—
201C22×C3×D3—22no—
202C22×C3×D3—41no—
203C22×C3×D3—41no—
204C22×C3×D3—41no—
205C22×C3×D3—41no—
206C22×C3×D3C4×D312yes—
207C22×C3×D3C4×D312yes—
208C22×C3×D3C2×Dic312yes—
209C22×C3×D3C2×C3×C412yes—
210C22×C3×D3C2×C3×C412yes—
211C22×C3×D3C2×C3×C412yes—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—22no—
221C2×C32×C4—22no—
222C2×C32×C4—22no—
223C2×C32×C4—32no—
224C2×C32×C4—32no—
225C2×C32×C4—32no—
226C2×C32×C4—42no—
227C2×C32×C4—41no—
228C2×C32×C4—41no—
229C2×C32×C4—41no—
230C2×C32×C4—41no—
231C2×C32×C4—42no—
232C2×C32×C4—42no—
233C2×C32×C4—61no—
234C2×C32×C4—61no—
235C2×C32×C4—61no—
236C2×C32×C4—61no—
237C2×C32×C4—61no—
238C2×C32×C4—61no—
239C2×C32×C4C4×D312yescomplemented
240C2×C32×C4C2×Dic312yescomplemented
241C2×C32×C4C2×C3×C412yescomplemented
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3C2×C3×C412yes—
245C2×C3⋊Dic3C2×C3×C412yescomplemented
246C2×C3⋊Dic3C3×D412yes—
247C2×C3⋊Dic3C3×D412yes—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—22no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—32no—
270C2×C3×Dic3—32no—
271C2×C3×Dic3—41no—
272C2×C3×Dic3—41no—
273C2×C3×Dic3—41no—
274C2×C3×Dic3—41no—
275C2×C3×Dic3—41no—
276C2×C3×Dic3—41no—
277C2×C3×Dic3—62no—
278C2×C3×Dic3—62no—
279C2×C3×Dic3—62no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—68no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3C4×D312yes—
289C2×C3×Dic3C4×D312yescomplemented
290C2×C3×Dic3C2×Dic312yescomplemented
291C2×C3×Dic3C2×C3×C412yes—
292C2×C3×Dic3C2×C3×C412yescomplemented
293C2×C3×Dic3C2×C3×C412yescomplemented
294C3×C4×D3—68no—
295D3×Dic3—28no—
296C4×C22⋊C4—91noSylow
297C2×C33C2×C4211yescharacteristic
298C2×C33C2×C22⋊C411yescharacteristic
299C2×C33#11711yescharacteristic
300C2×C33C4×D411yescharacteristic
301C2×C33C4×D411yescharacteristic
302C2×C33C4×D411yescharacteristic
303C2×C33C4×D411yescharacteristic
304C32×D3—24no—
305C24×C3—31no—
306C24×C3—31no—
307C24×C3—61no—
308C23×D3C2×C3×D311yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—41no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4—61no—
322C22×C3×C4—94no—
323C22×C3×C4—91no—
324C22×C3×C4—91no—
325C22×C3×C4—182no—
326C22×C3×C4—182no—
327C22×C3×C4D3211yescharacteristic
328C22×C3×C4C2×C3×D311yescharacteristic
329C22×C3×C4C2×C3×D311yescharacteristic
330C22×Dic3—31no—
331C22×Dic3—31no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—34no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—62no—
338C22×Dic3—62no—
339C22×Dic3C2×C3×D311yescharacteristic
340C22×Dic3C2×C3×D311yescharacteristic
341C22×Dic3C2×C3×D311yescharacteristic
342C2×C4×D3—34no—
343C2×C4×D3—62no—
344C2×C4×D3—62no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—64no—
348C3×C22⋊C4—94no—
349C3×C42—182no—
350C3×C42—182no—
351#217—34no—
352(C2×D3)⋊C4—34no—
353(C2×D3)⋊C4C3×Dic314yescomplemented
354C4×Dic3—62no—
355C4×Dic3—62no—
356C4×Dic3—62no—
357C4×Dic3—62no—
358C4×Dic3—64no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—34no—
381C22×C32—41no—
382C22×C32—41no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—62no—
389C22×C32—62no—
390C22×C32—62no—
391C22×C32—62no—
392C22×C32—62no—
393C22×C32—62no—
394C22×C32C2×C4×D311yescharacteristic
395C22×C32C2×C4×D311yescharacteristic
396C22×C32C2×C4×D311yescharacteristic
397C22×C32C2×C4×D311yescharacteristic
398C22×C32C2×C4×D311yescharacteristic
399C22×C32D3×D411yescharacteristic
400C22×C32D3×D411yescharacteristic
401C22×C32D3×D411yescharacteristic
402C22×C32D3×D411yescharacteristic
403C22×C32#23711yescharacteristic
404C22×C32#23711yescharacteristic
405C22×C32#23711yescharacteristic
406C22×C32#23911yescharacteristic
407C22×C32C22×Dic311yescharacteristic
408C22×C32C22×C3×C411yescharacteristic
409C22×C32C22×C3×C411yescharacteristic
410C22×C32C22×C3×C411yescharacteristic
411C22×C32C2×C3×D411yescharacteristic
412C22×C32C2×C3×D411yescharacteristic
413C22×C32C3×#4111yescharacteristic
414C22×C32C3×#4111yescharacteristic
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—24no—
428C2×C3×D3—42no—
429C2×C3×D3—42no—
430C2×C3×D3—42no—
431C2×C3×D3—42no—
432C2×C3×D3—42no—
433C2×C3×D3—42no—
434C2×C3×D3C4×Dic314yescomplemented
435C2×C3×D3C3×C4214yescomplemented
436C32×C4—22no—
437C32×C4—24no—
438C32×C4—22no—
439C32×C4—22no—
440C32×C4—42no—
441C32×C4—42no—
442C32×C4—44no—
443C32×C4—62no—
444C32×C4—62no—
445C32×C4—62no—
446C3⋊Dic3—22no—
447C3⋊Dic3C3×C22⋊C414yescomplemented
448C3×Dic3—22no—
449C3×Dic3—22no—
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—34no—
455C3×Dic3—34no—
456C3×Dic3—42no—
457C3×Dic3—42no—
458C3×Dic3—42no—
459C3×Dic3—64no—
460C3×Dic3—64no—
461C3×Dic3—62no—
462C3×Dic3—62no—
463C23×C4—91no—
464C2×C22⋊C4—31no—
465C2×C22⋊C4—91no—
466C2×C42—91no—
467C2×C42—91no—
468#95—31no—
469#95—91no—
470C33C4×C22⋊C411yescharacteristic, complemented, Sylow
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—32no—
475C23×C3—32no—
476C23×C3—32no—
477C23×C3—32no—
478C23×C3—32no—
479C23×C3—32no—
480C23×C3—41no—
481C23×C3—62no—
482C23×C3—62no—
483C23×C3—62no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—121no—
493C23×C3—121no—
494C23×C3—121no—
495C23×C3—121no—
496C23×C3C2×D3211yescharacteristic
497C23×C3C22×C3×D311yescharacteristic
498C23×C3C22×C3×D311yescharacteristic
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3C3×C4×D312yes—
504C22×D3C3×C4×D312yes—
505C22×D3C2×C3×Dic312yes—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—32no—
518C2×C3×C4—32no—
519C2×C3×C4—32no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—32no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—42no—
528C2×C3×C4—42no—
529C2×C3×C4—42no—
530C2×C3×C4—62no—
531C2×C3×C4—62no—
532C2×C3×C4—62no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—92no—
546C2×C3×C4—92no—
547C2×C3×C4—92no—
548C2×C3×C4—92no—
549C2×C3×C4—121no—
550C2×C3×C4—121no—
551C2×C3×C4—121no—
552C2×C3×C4—121no—
553C2×C3×C4—121no—
554C2×C3×C4—121no—
555C2×C3×C4—188no—
556C2×C3×C4—181no—
557C2×C3×C4—181no—
558C2×C3×C4D3×Dic312yescomplemented
559C2×C3×C4C3×C4×D312yescomplemented
560C2×C3×C4C2×C3×Dic312yescomplemented
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—32no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—32no—
571C2×Dic3—32no—
572C2×Dic3—32no—
573C2×Dic3—32no—
574C2×Dic3—32no—
575C2×Dic3—62no—
576C2×Dic3—62no—
577C2×Dic3—62no—
578C2×Dic3—62no—
579C2×Dic3—68no—
580C2×Dic3—62no—
581C2×Dic3—62no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3C3×C4×D312yes—
587C2×Dic3C3×C4×D312yescomplemented
588C2×Dic3C2×C3×Dic312yescomplemented
589C4×D3—68no—
590C2×C32—21no—
591C2×C32—21no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—21no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—21no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—41no—
612C2×C32—41no—
613C2×C32—41no—
614C2×C32—41no—
615C2×C32—41no—
616C2×C32—41no—
617C2×C32—41no—
618C2×C32—64no—
619C2×C32C42×D311yescharacteristic
620C2×C32#87711yescharacteristic
621C2×C32D3×C22⋊C411yescharacteristic
622C2×C32D3×C22⋊C411yescharacteristic
623C2×C32#67⋊C411yescharacteristic
624C2×C32#67⋊C411yescharacteristic
625C2×C32#67⋊C411yescharacteristic
626C2×C32#67⋊C411yescharacteristic
627C2×C32#89211yescharacteristic
628C2×C32#89311yescharacteristic
629C2×C32#89311yescharacteristic
630C2×C32C2×C4×Dic311yescharacteristic
631C2×C32D4×Dic311yescharacteristic
632C2×C32D4×Dic311yescharacteristic
633C2×C32C2×C3×C4211yescharacteristic
634C2×C32C2×C3×C22⋊C411yescharacteristic
635C2×C32C3×#11711yescharacteristic
636C2×C32C3×C4×D411yescharacteristic
637C2×C32C3×C4×D411yescharacteristic
638C2×C32C3×C4×D411yescharacteristic
639C2×C32C3×C4×D411yescharacteristic
640C3×D3—24no—
641C3×D3—24no—
642C3×D3—44no—
643C24—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—94no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—182no—
651C22×C4—182no—
652C22×C4C3×D3211yescharacteristic
653C22⋊C4—34no—
654C22⋊C4—94no—
655C42—182no—
656C42—182no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—34no—
679C22×C3—34no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—64no—
688C22×C3—62no—
689C22×C3—62no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—62no—
695C22×C3—62no—
696C22×C3—62no—
697C22×C3—62no—
698C22×C3—62no—
699C22×C3—62no—
700C22×C3—122no—
701C22×C3—122no—
702C22×C3—122no—
703C22×C3—122no—
704C22×C3—122no—
705C22×C3—122no—
706C22×C3#379611yescharacteristic
707C22×C3C4×D3211yescharacteristic
708C22×C3C4×D3211yescharacteristic
709C22×C3#380211yescharacteristic
710C22×C3C2×D3×Dic311yescharacteristic
711C22×C3#380511yescharacteristic
712C22×C3#381111yescharacteristic
713C22×C3C2×C3×C4×D311yescharacteristic
714C22×C3C2×C3×C4×D311yescharacteristic
715C22×C3C2×C3×C4×D311yescharacteristic
716C22×C3C2×C3×C4×D311yescharacteristic
717C22×C3C2×C3×C4×D311yescharacteristic
718C22×C3C3×D3×D411yescharacteristic
719C22×C3C3×D3×D411yescharacteristic
720C22×C3C3×D3×D411yescharacteristic
721C22×C3C3×D3×D411yescharacteristic
722C22×C3C3×#23711yescharacteristic
723C22×C3C3×#23711yescharacteristic
724C22×C3C3×#23711yescharacteristic
725C22×C3C3×#23911yescharacteristic
726C22×C3C22×C3×Dic311yescharacteristic
727C2×D3—22no—
728C2×D3—22no—
729C2×D3—22no—
730C2×D3—22no—
731C2×D3—22no—
732C2×D3—22no—
733C2×D3C3×C4×Dic314yescomplemented
734C3×C4—24no—
735C3×C4—22no—
736C3×C4—22no—
737C3×C4—22no—
738C3×C4—42no—
739C3×C4—42no—
740C3×C4—44no—
741C3×C4—62no—
742C3×C4—62no—
743C3×C4—62no—
744C3×C4—62no—
745C3×C4—62no—
746C3×C4—62no—
747C3×C4—94no—
748C3×C4—122no—
749C3×C4—122no—
750C3×C4—122no—
751C3×C4—182no—
752Dic3—22no—
753Dic3—22no—
754Dic3—22no—
755Dic3—34no—
756Dic3—34no—
757Dic3—64no—
758Dic3—64no—
759Dic3—62no—
760Dic3—62no—
761C32—21no—
762C32—21no—
763C32—21no—
764C32—41no—
765C32#466611yescharacteristic, complemented
766C32Dic3×C22⋊C411yescharacteristic, complemented
767C32C3×C4×C22⋊C411yescharacteristic, complemented
768C23—32no—
769C23—32no—
770C23—32no—
771C23—61no—
772C23—61no—
773C23—61no—
774C23—61no—
775C23C2×C3×D3211yescharacteristic
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—32no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—92no—
788C2×C4—92no—
789C2×C4—92no—
790C2×C4—92no—
791C2×C4—188no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4C3×D3×Dic312yescomplemented
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—41no—
817C2×C3—41no—
818C2×C3—41no—
819C2×C3—41no—
820C2×C3—41no—
821C2×C3—41no—
822C2×C3—41no—
823C2×C3—64no—
824C2×C3—64no—
825C2×C3—124no—
826C2×C3C4×D3×Dic311yescharacteristic
827C2×C3#6387811yescharacteristic
828C2×C3#6388111yescharacteristic
829C2×C3#6389811yescharacteristic
830C2×C3#6390211yescharacteristic
831C2×C3#6392111yescharacteristic
832C2×C3#67⋊Dic311yescharacteristic
833C2×C3C3×C42×D311yescharacteristic
834C2×C3C3×#87711yescharacteristic
835C2×C3C3×D3×C22⋊C411yescharacteristic
836C2×C3C3×D3×C22⋊C411yescharacteristic
837C2×C3C3×#67⋊C411yescharacteristic
838C2×C3C3×#67⋊C411yescharacteristic
839C2×C3C3×#67⋊C411yescharacteristic
840C2×C3C3×#67⋊C411yescharacteristic
841C2×C3C3×#89211yescharacteristic
842C2×C3C3×#89311yescharacteristic
843C2×C3C3×#89311yescharacteristic
844C2×C3C2×C3×C4×Dic311yescharacteristic
845C2×C3C3×D4×Dic311yescharacteristic
846C2×C3C3×D4×Dic311yescharacteristic
847D3—24no—
848C22—34no—
849C22—62no—
850C22—62no—
851C22—62no—
852C22—62no—
853C22—62no—
854C22—62no—
855C22C3×#379611yescharacteristic
856C22C3×C4×D3211yescharacteristic
857C22C3×C4×D3211yescharacteristic
858C22C3×#380211yescharacteristic
859C22C2×C3×D3×Dic311yescharacteristic
860C22C3×#380511yescharacteristic
861C22C3×#381111yescharacteristic
862C4—22no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—94no—
867C4—182no—
868C3—21no—
869C3—21no—
870C3—21no—
871C3—41no—
872C3#1059136811yescharacteristic, direct product factor
873C3C3×#466611yescharacteristic, complemented
874C3C3×Dic3×C22⋊C411yescharacteristic, complemented
875C2—64no—
876C2C3×C4×D3×Dic311yescharacteristic
877C2C3×#6387811yescharacteristic
878C2C3×#6388111yescharacteristic
879C2C3×#6389811yescharacteristic
880C2C3×#6390211yescharacteristic
881C2C3×#6392111yescharacteristic
882C2C3×#67⋊Dic311yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC2×C32C2×C3×C42
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×C4×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. C2×C3×C4×C3⋊Dic3C2semidirect
5. C2×C3×Dic32C2semidirect
6. C32×C3⋊#95C2semidirect
7. C3×#63579C2semidirect
10. #10591368C3direct (N × H)
20. C2×C3×D3×Dic3C4semidirect
22. C32×(C2×D3)⋊C4C4semidirect
23. C3×(C2×D3)⋊Dic3C4semidirect
29. C2×C4×C3⋊Dic3C2×C3semidirect
41. C2×Dic32C2×C3semidirect
46. C3×C3⋊#95D3semidirect
47. C3×C3⋊#95C2×C3semidirect
48. #63579C2×C3semidirect
59. C2×C33×C4C2×C4semidirect
63. C2×C3×C3⋊Dic3C2×C4semidirect
73. C2×C32×Dic3C2×C4semidirect
74. C2×C32×Dic3C2×C4semidirect
118. C2×D3×Dic3C3×C4semidirect
124. C3×(C2×D3)⋊C4Dic3semidirect
125. C3×(C2×D3)⋊C4C3×C4semidirect
131. (C2×D3)⋊Dic3C3×C4semidirect
146. C2×C32×D3C42semidirect
149. C3×C3⋊Dic3C22⋊C4semidirect
176. C3⋊#95C3×D3semidirect
239. C2×C32×C4C4×D3semidirect
240. C2×C32×C4C2×Dic3semidirect
241. C2×C32×C4C2×C3×C4semidirect
245. C2×C3⋊Dic3C2×C3×C4semidirect
289. C2×C3×Dic3C4×D3semidirect
290. C2×C3×Dic3C2×Dic3semidirect
292. C2×C3×Dic3C2×C3×C4semidirect
293. C2×C3×Dic3C2×C3×C4semidirect
353. (C2×D3)⋊C4C3×Dic3semidirect
434. C2×C3×D3C4×Dic3semidirect
435. C2×C3×D3C3×C42semidirect
447. C3⋊Dic3C3×C22⋊C4semidirect
470. C33C4×C22⋊C4semidirect
558. C2×C3×C4D3×Dic3semidirect
559. C2×C3×C4C3×C4×D3semidirect
560. C2×C3×C4C2×C3×Dic3semidirect
587. C2×Dic3C3×C4×D3semidirect
588. C2×Dic3C2×C3×Dic3semidirect
733. C2×D3C3×C4×Dic3semidirect
765. C32#4666semidirect
766. C32Dic3×C22⋊C4semidirect
767. C32C3×C4×C22⋊C4semidirect
794. C2×C4C3×D3×Dic3semidirect
872. C3#10591368direct (N × H)
873. C3C3×#4666semidirect
874. C3C3×Dic3×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×Dic32
C2×C3×C4×C3⋊Dic32
C2×C32×(C2×D3)⋊C42
C2×C3×(C2×D3)⋊Dic32
C2×C3×Dic322
C32×C3⋊#952
C3×#635792
C3×Dic3×C22⋊C43
C3×#46663
#105913683