Finite Group Databasebeta

← C3×#10591390 #13158399

Subgroups — C3×#10591390 #13158399

Order 1728.

1346 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#625C211yesmaximal, characteristic
2C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
3C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63658C211yesmaximal, characteristic, complemented
8C3×#4961—31nomaximal
9C3×#4959—31nomaximal
10#10591390C311yesmaximal, characteristic, direct product factor
11C23×C32×D3C2211yescharacteristic
12C23×C32×D3C2211yescharacteristic
13C22×C33×C4C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C3×#625—22no—
19C2×C3×#625—22no—
20C2×C3×#625—22no—
21C32×(C2×D3)⋊C4—22no—
22C32×(C2×D3)⋊C4—22no—
23C3×Dic3⋊Dic3—22no—
24C3×(C2×D3)⋊Dic3—22no—
25C3×(C2×D3)⋊Dic3—22no—
26C22×C3×#67—31no—
27C22×C3×#67—31no—
28C22×#625C2×C311yescharacteristic
29C2×C32×C22⋊C4—31no—
30C2×C32×C22⋊C4—31no—
31C2×C3×#217—31no—
32C2×C3×#217—31no—
33C2×C3×(C2×D3)⋊C4—21no—
34C2×C3×(C2×D3)⋊C4—21no—
35C2×C3×(C2×D3)⋊C4—31no—
36C2×C3×(C2×D3)⋊C4—31no—
37C2×C3×(C2×D3)⋊C4D311yescharacteristic, complemented
38C2×C3×(C2×D3)⋊C4D311yescharacteristic, complemented
39C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
40C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
41C2×C3×C4⋊Dic3—31no—
42C2×C3×Dic3⋊C4—31no—
43C2×Dic3⋊Dic3C2×C311yescharacteristic, complemented
44C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
45C2×(C2×D3)⋊Dic3C2×C311yescharacteristic, complemented
46#63658C2×C311yescharacteristic, complemented
47C3×C3⋊#95—31no—
48C3×C3⋊#95—31no—
49C3×C3⋊#95—61no—
50C23×C33C2311yescharacteristic
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3—21no—
54C22×C32×D3—21no—
55C22×C32×D3—21no—
56C22×C32×D3—21no—
57C22×C32×D3—21no—
58C22×C32×D3—21no—
59C22×C32×D3—21no—
60C22×C32×D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3—21no—
63C22×C32×D3D412yes—
64C22×C32×D3D412yes—
65C2×C33×C4—21no—
66C2×C33×C4—21no—
67C2×C33×C4—21no—
68C2×C3×C3⋊Dic3—21no—
69C2×C3×C3⋊Dic3—21no—
70C2×C3×C3⋊Dic3—21no—
71C2×C3×C3⋊Dic3—21no—
72C2×C3×C3⋊Dic3—21no—
73C2×C3×C3⋊Dic3D412yes—
74C2×C32×Dic3—21no—
75C2×C32×Dic3—21no—
76C2×C32×Dic3—21no—
77C2×C32×Dic3—21no—
78C2×C32×Dic3—21no—
79C2×C32×Dic3D412yescomplemented
80C3×#625—28no—
81C3×#394—91no—
82#4961—31no—
83#4959—31no—
84C24×C32—31no—
85C24×C32—31no—
86C23×C3×D3—21no—
87C23×C3×D3—21no—
88C23×C3×D3C2×D311yescharacteristic
89C23×C3×D3C2×D311yescharacteristic
90C23×C3×D3C22×C311yescharacteristic
91C23×C3×D3C22×C311yescharacteristic
92C22×C32×C4—21no—
93C22×C32×C4—21no—
94C22×C32×C4—21no—
95C22×C32×C4—31no—
96C22×C32×C4—31no—
97C22×C32×C4—41no—
98C22×C32×C4C2×D311yescharacteristic
99C22×C32×C4C2×D311yescharacteristic
100C22×C32×C4C22×C311yescharacteristic
101C22×C3⋊Dic3C22×C311yescharacteristic
102C22×C3⋊Dic3C22×C311yescharacteristic
103C2×C3×#67—62no—
104C2×C3×#67—62no—
105C2×C3×#67—62no—
106C2×C3×#67—62no—
107C2×C3×#67—62no—
108C2×C3×#67—62no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—21no—
111C22×C3×Dic3—31no—
112C22×C3×Dic3—31no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—61no—
116C22×C3×Dic3—61no—
117C22×C3×Dic3C2×D311yescharacteristic
118C22×C3×Dic3C2×D311yescharacteristic
119C22×C3×Dic3C22×C311yescharacteristic
120C22×C3×Dic3C22×C311yescharacteristic
121C2×#625—22no—
122C2×#625—22no—
123C2×#625—22no—
124C32×C22⋊C4—62no—
125C32×C22⋊C4—62no—
126C3×#217—62no—
127C3×#217—62no—
128C3×(C2×D3)⋊C4—24no—
129C3×(C2×D3)⋊C4—24no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—62no—
135C3×(C2×D3)⋊C4—62no—
136C3×C4⋊Dic3—62no—
137C3×Dic3⋊C4—62no—
138Dic3⋊Dic3—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141C22×C33C2×D411yescharacteristic
142C22×C33C2×D411yescharacteristic
143C22×C33C2×D411yescharacteristic
144C22×C33C2×D411yescharacteristic
145C22×C33#4111yescharacteristic
146C22×C33#4111yescharacteristic
147C22×C33#4111yescharacteristic
148C2×C32×D3—22no—
149C2×C32×D3—22no—
150C2×C32×D3—22no—
151C2×C32×D3—22no—
152C2×C32×D3—22no—
153C2×C32×D3—22no—
154C2×C32×D3—41no—
155C2×C32×D3—41no—
156C2×C32×D3—41no—
157C2×C32×D3—41no—
158C2×C32×D3—41no—
159C2×C32×D3—41no—
160C2×C32×D3—41no—
161C2×C32×D3—41no—
162C33×C4—41no—
163C3×C3⋊Dic3—22no—
164C3×C3⋊Dic3—41no—
165C32×Dic3—22no—
166C32×Dic3—41no—
167C22×C3×D4—91no—
168C22×#67—31no—
169C22×#67—31no—
170C2×C3×C4⋊C4—91no—
171C2×C3×C22⋊C4—31no—
172C2×C3×C22⋊C4—31no—
173C2×C3×C22⋊C4—31no—
174C2×C3×C22⋊C4—31no—
175C2×C3×C22⋊C4—61no—
176C2×C3×C22⋊C4—61no—
177C2×C3×C22⋊C4—91no—
178C2×C3×C22⋊C4—91no—
179C2×#217—31no—
180C2×#217—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4C3×D311yescharacteristic, complemented
184C2×(C2×D3)⋊C4C3×D311yescharacteristic, complemented
185C2×C4⋊Dic3—31no—
186C2×Dic3⋊C4—31no—
187C3×#95—91no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—61no—
191C23×C32—21no—
192C23×C32—21no—
193C23×C32—21no—
194C23×C32—32no—
195C23×C32—32no—
196C23×C32—41no—
197C23×C32—61no—
198C23×C32—61no—
199C23×C32—61no—
200C23×C32—61no—
201C23×C32—61no—
202C23×C32—61no—
203C23×C32—61no—
204C23×C32—61no—
205C23×C32—61no—
206C23×C32—61no—
207C23×C32—61no—
208C23×C32—61no—
209C23×C32C22×D311yescharacteristic
210C23×C32C22×D311yescharacteristic
211C23×C32C23×C311yescharacteristic
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3—22no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
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—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—22no—
241C22×C3×D3—22no—
242C22×C3×D3—41no—
243C22×C3×D3—41no—
244C22×C3×D3—41no—
245C22×C3×D3—41no—
246C22×C3×D3—41no—
247C22×C3×D3—41no—
248C22×C3×D3—41no—
249C22×C3×D3—41no—
250C22×C3×D3D1212yes—
251C22×C3×D3#6712yes—
252C22×C3×D3C3×D412yes—
253C22×C3×D3C3×D412yes—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—22no—
258C2×C32×C4—22no—
259C2×C32×C4—22no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—32no—
267C2×C32×C4—41no—
268C2×C32×C4—41no—
269C2×C32×C4—41no—
270C2×C32×C4—41no—
271C2×C32×C4—41no—
272C2×C32×C4—41no—
273C2×C32×C4—42no—
274C2×C32×C4—42no—
275C2×C32×C4—42no—
276C2×C32×C4—61no—
277C2×C32×C4—61no—
278C2×C32×C4—61no—
279C2×C32×C4—61no—
280C2×C32×C4—61no—
281C2×C3⋊Dic3—21no—
282C2×C3⋊Dic3—21no—
283C2×C3⋊Dic3—21no—
284C2×C3⋊Dic3—21no—
285C2×C3⋊Dic3—21no—
286C2×C3⋊Dic3C3×D412yes—
287C3×#67—68no—
288C3×#67—68no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—32no—
302C2×C3×Dic3—32no—
303C2×C3×Dic3—41no—
304C2×C3×Dic3—41no—
305C2×C3×Dic3—41no—
306C2×C3×Dic3—41no—
307C2×C3×Dic3—62no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—61no—
310C2×C3×Dic3—61no—
311C2×C3×Dic3—61no—
312C2×C3×Dic3—62no—
313C2×C3×Dic3—61no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—61no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—61no—
319C2×C3×Dic3—121no—
320C2×C3×Dic3—121no—
321C2×C3×Dic3—121no—
322C2×C3×Dic3—121no—
323C2×C3×Dic3#6712yescomplemented
324C2×C3×Dic3C3×D412yescomplemented
325#625—28no—
326#394—91noSylow
327C2×C33#12011yescharacteristic
328C2×C33#12111yescharacteristic
329C2×C33#12111yescharacteristic
330C2×C33#12111yescharacteristic
331C2×C33#12311yescharacteristic
332C2×C33#12311yescharacteristic
333C2×C33#12411yescharacteristic
334C32×D3—42no—
335C32×D3—42no—
336C24×C3—31no—
337C24×C3—31no—
338C24×C3—31no—
339C24×C3—31no—
340C24×C3—61no—
341C24×C3—61no—
342C23×D3C2×C3×D311yescharacteristic
343C23×D3C2×C3×D311yescharacteristic
344C2×C3×D4—182no—
345C2×C3×D4—182no—
346C2×C3×D4—182no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—41no—
355C22×C3×C4—61no—
356C22×C3×C4—61no—
357C22×C3×C4—91no—
358C22×C3×C4—91no—
359C22×C3×C4D3211yescharacteristic
360C22×C3×C4C2×C3×D311yescharacteristic
361C22×C3×C4C2×C3×D311yescharacteristic
362C2×#67—62no—
363C2×#67—62no—
364C2×#67—62no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—61no—
373C22×Dic3—61no—
374C22×Dic3C2×C3×D311yescharacteristic
375C22×Dic3C2×C3×D311yescharacteristic
376C3×C4⋊C4—182no—
377C3×C22⋊C4—62no—
378C3×C22⋊C4—62no—
379C3×C22⋊C4—62no—
380C3×C22⋊C4—62no—
381C3×C22⋊C4—64no—
382C3×C22⋊C4—64no—
383C3×C22⋊C4—182no—
384C3×C22⋊C4—182no—
385#217—62no—
386#217—62no—
387(C2×D3)⋊C4—22no—
388(C2×D3)⋊C4—22no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—62no—
391C4⋊Dic3—62no—
392Dic3⋊C4—62no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—62no—
422C22×C32—62no—
423C22×C32—62no—
424C22×C32—62no—
425C22×C32—62no—
426C22×C32—62no—
427C22×C32—121no—
428C22×C32—121no—
429C22×C32—121no—
430C22×C32—121no—
431C22×C32—121no—
432C22×C32—121no—
433C22×C32—121no—
434C22×C32—121no—
435C22×C32C2×D1211yescharacteristic
436C22×C32#23511yescharacteristic
437C22×C32#23511yescharacteristic
438C22×C32#23511yescharacteristic
439C22×C32D3×D411yescharacteristic
440C22×C32D3×D411yescharacteristic
441C22×C32D3×D411yescharacteristic
442C22×C32D3×D411yescharacteristic
443C22×C32D3×D411yescharacteristic
444C22×C32#23711yescharacteristic
445C22×C32#23711yescharacteristic
446C22×C32#23711yescharacteristic
447C22×C32C2×#6711yescharacteristic
448C22×C32C2×#6711yescharacteristic
449C22×C32C2×C3×D411yescharacteristic
450C22×C32C2×C3×D411yescharacteristic
451C22×C32C2×C3×D411yescharacteristic
452C22×C32C2×C3×D411yescharacteristic
453C22×C32C3×#4111yescharacteristic
454C22×C32C3×#4111yescharacteristic
455C22×C32C3×#4111yescharacteristic
456C2×C3×D3—24no—
457C2×C3×D3—24no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—22no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
470C2×C3×D3—42no—
471C2×C3×D3—42no—
472C2×C3×D3—42no—
473C2×C3×D3—42no—
474C2×C3×D3—42no—
475C2×C3×D3—42no—
476C2×C3×D3—42no—
477C2×C3×D3—42no—
478C2×C3×D3—42no—
479C2×C3×D3—42no—
480C2×C3×D3—42no—
481C2×C3×D3—42no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3—41no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496C2×C3×D3—41no—
497C2×C3×D3—41no—
498C32×C4—42no—
499C32×C4—42no—
500C32×C4—42no—
501C32×C4—44no—
502C32×C4—41no—
503C32×C4—41no—
504C32×C4—41no—
505C32×C4—62no—
506C32×C4—121no—
507C3⋊Dic3—22no—
508C3⋊Dic3—41no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—42no—
512C3×Dic3—42no—
513C3×Dic3—41no—
514C3×Dic3—41no—
515C3×Dic3—62no—
516C3×Dic3—62no—
517C3×Dic3—122no—
518C3×Dic3—122no—
519C3×Dic3—121no—
520C3×Dic3—121no—
521C22×D4—91no—
522C2×C4⋊C4—91no—
523C2×C22⋊C4—31no—
524C2×C22⋊C4—31no—
525C2×C22⋊C4—91no—
526C2×C22⋊C4—91no—
527#95—91no—
528C33#39411yescharacteristic, complemented, Sylow
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—32no—
533C23×C3—32no—
534C23×C3—32no—
535C23×C3—32no—
536C23×C3—41no—
537C23×C3—62no—
538C23×C3—62no—
539C23×C3—62no—
540C23×C3—62no—
541C23×C3—62no—
542C23×C3—62no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—121no—
568C23×C3—121no—
569C23×C3—121no—
570C23×C3—121no—
571C23×C3—121no—
572C23×C3—121no—
573C23×C3—121no—
574C23×C3—121no—
575C23×C3C2×D3211yescharacteristic
576C23×C3C22×C3×D311yescharacteristic
577C23×C3C22×C3×D311yescharacteristic
578C22×D3—21no—
579C22×D3—21no—
580C22×D3—21no—
581C22×D3—21no—
582C22×D3—21no—
583C22×D3—21no—
584C22×D3—21no—
585C22×D3—21no—
586C22×D3—21no—
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3C3×D1212yes—
591C22×D3C3×#6712yes—
592C3×D4—188no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—32no—
606C2×C3×C4—32no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—42no—
614C2×C3×C4—42no—
615C2×C3×C4—42no—
616C2×C3×C4—62no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—62no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—92no—
629C2×C3×C4—121no—
630C2×C3×C4—121no—
631C2×C3×C4—121no—
632C2×C3×C4—121no—
633C2×C3×C4—181no—
634C2×C3×C4—181no—
635C2×C3×C4—181no—
636C2×C3×C4—181no—
637C2×C3×C4—181no—
638#67—68no—
639#67—68no—
640C2×Dic3—21no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—62no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—62no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3—121no—
662C2×Dic3—121no—
663C2×Dic3C3×#6712yescomplemented
664C2×C32—21no—
665C2×C32—21no—
666C2×C32—21no—
667C2×C32—21no—
668C2×C32—21no—
669C2×C32—21no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32—21no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—21no—
681C2×C32—21no—
682C2×C32—21no—
683C2×C32—21no—
684C2×C32—21no—
685C2×C32—41no—
686C2×C32—41no—
687C2×C32—41no—
688C2×C32—41no—
689C2×C32—41no—
690C2×C32—41no—
691C2×C32—41no—
692C2×C32—122no—
693C2×C32—122no—
694C2×C32#88211yescharacteristic
695C2×C32#88311yescharacteristic
696C2×C32#88311yescharacteristic
697C2×C32#88411yescharacteristic
698C2×C32#88411yescharacteristic
699C2×C32#88511yescharacteristic
700C2×C32#88511yescharacteristic
701C2×C32#88611yescharacteristic
702C2×C32#92911yescharacteristic
703C2×C32#93011yescharacteristic
704C2×C32#93711yescharacteristic
705C2×C32#93811yescharacteristic
706C2×C32#93911yescharacteristic
707C2×C32#93911yescharacteristic
708C2×C32C3×#12011yescharacteristic
709C2×C32C3×#12111yescharacteristic
710C2×C32C3×#12111yescharacteristic
711C2×C32C3×#12111yescharacteristic
712C2×C32C3×#12311yescharacteristic
713C2×C32C3×#12311yescharacteristic
714C2×C32C3×#12411yescharacteristic
715C3×D3—44no—
716C3×D3—44no—
717C3×D3—42no—
718C3×D3—42no—
719C3×D3—42no—
720C3×D3—42no—
721C24—31no—
722C24—31no—
723C2×D4—182no—
724C2×D4—182no—
725C2×D4—182no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—91no—
729C22×C4—91no—
730C22×C4C3×D3211yescharacteristic
731C4⋊C4—182no—
732C22⋊C4—62no—
733C22⋊C4—62no—
734C22⋊C4—182no—
735C22⋊C4—182no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—41no—
764C22×C3—64no—
765C22×C3—64no—
766C22×C3—62no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—122no—
779C22×C3—122no—
780C22×C3—122no—
781C22×C3—122no—
782C22×C3—122no—
783C22×C3—122no—
784C22×C3—122no—
785C22×C3—122no—
786C22×C3—122no—
787C22×C3—122no—
788C22×C3—122no—
789C22×C3—122no—
790C22×C3—121no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3—121no—
796C22×C3—121no—
797C22×C3—121no—
798C22×C3—121no—
799C22×C3—121no—
800C22×C3—121no—
801C22×C3—121no—
802C22×C3—121no—
803C22×C3—121no—
804C22×C3—121no—
805C22×C3—121no—
806C22×C3#379511yescharacteristic
807C22×C3#379811yescharacteristic
808C22×C3D3×D1211yescharacteristic
809C22×C3#380211yescharacteristic
810C22×C3#380511yescharacteristic
811C22×C3D3×#6711yescharacteristic
812C22×C3D3×#6711yescharacteristic
813C22×C3C2×C3×D1211yescharacteristic
814C22×C3C3×#23511yescharacteristic
815C22×C3C3×#23511yescharacteristic
816C22×C3C3×#23511yescharacteristic
817C22×C3C3×D3×D411yescharacteristic
818C22×C3C3×D3×D411yescharacteristic
819C22×C3C3×D3×D411yescharacteristic
820C22×C3C3×D3×D411yescharacteristic
821C22×C3C3×D3×D411yescharacteristic
822C22×C3C3×#23711yescharacteristic
823C22×C3C3×#23711yescharacteristic
824C22×C3C3×#23711yescharacteristic
825C22×C3C2×C3×#6711yescharacteristic
826C22×C3C2×C3×#6711yescharacteristic
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—41no—
841C3×C4—42no—
842C3×C4—42no—
843C3×C4—42no—
844C3×C4—44no—
845C3×C4—41no—
846C3×C4—41no—
847C3×C4—41no—
848C3×C4—62no—
849C3×C4—62no—
850C3×C4—122no—
851C3×C4—122no—
852C3×C4—121no—
853C3×C4—121no—
854C3×C4—182no—
855C3×C4—361no—
856Dic3—22no—
857Dic3—41no—
858Dic3—62no—
859Dic3—62no—
860Dic3—122no—
861Dic3—122no—
862Dic3—121no—
863Dic3—121no—
864C32—21no—
865C32—21no—
866C32—21no—
867C32—41no—
868C32#495911yescharacteristic, complemented
869C32#496111yescharacteristic, complemented
870C32C3×#39411yescharacteristic, complemented
871C23—32no—
872C23—32no—
873C23—61no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—61no—
879C23—61no—
880C23—61no—
881C23—61no—
882C23—61no—
883C23—61no—
884C23—61no—
885C23C2×C3×D3211yescharacteristic
886D4—188no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—32no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—92no—
897C2×C4—181no—
898C2×C4—181no—
899C2×C4—181no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—41no—
926C2×C3—41no—
927C2×C3—41no—
928C2×C3—41no—
929C2×C3—41no—
930C2×C3—124no—
931C2×C3—124no—
932C2×C3—122no—
933C2×C3—122no—
934C2×C3—122no—
935C2×C3—122no—
936C2×C3#6388511yescharacteristic
937C2×C3#6389111yescharacteristic
938C2×C3#6390511yescharacteristic
939C2×C3#6390611yescharacteristic
940C2×C3#6391511yescharacteristic
941C2×C3#6392211yescharacteristic
942C2×C3#6397011yescharacteristic
943C2×C3C3×#88211yescharacteristic
944C2×C3C3×#88311yescharacteristic
945C2×C3C3×#88311yescharacteristic
946C2×C3C3×#88411yescharacteristic
947C2×C3C3×#88411yescharacteristic
948C2×C3C3×#88511yescharacteristic
949C2×C3C3×#88511yescharacteristic
950C2×C3C3×#88611yescharacteristic
951C2×C3C3×#92911yescharacteristic
952C2×C3C3×#93011yescharacteristic
953C2×C3C3×#93711yescharacteristic
954C2×C3C3×#93811yescharacteristic
955C2×C3C3×#93911yescharacteristic
956C2×C3C3×#93911yescharacteristic
957D3—42no—
958D3—42no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22—121no—
969C22—121no—
970C22—121no—
971C22—121no—
972C22—121no—
973C22C3×#379511yescharacteristic
974C22C3×#379811yescharacteristic
975C22C3×D3×D1211yescharacteristic
976C22C3×#380211yescharacteristic
977C22C3×#380511yescharacteristic
978C22C3×D3×#6711yescharacteristic
979C22C3×D3×#6711yescharacteristic
980C4—41no—
981C4—62no—
982C4—121no—
983C4—182no—
984C4—361no—
985C3—21no—
986C3—21no—
987C3—21no—
988C3—41no—
989C3#1059139011yescharacteristic, direct product factor
990C3C3×#495911yescharacteristic, complemented
991C3C3×#496111yescharacteristic, complemented
992C2—122no—
993C2—122no—
994C2C3×#6388511yescharacteristic
995C2C3×#6389111yescharacteristic
996C2C3×#6390511yescharacteristic
997C2C3×#6390611yescharacteristic
998C2C3×#6391511yescharacteristic
999C2C3×#6392211yescharacteristic
1000C2C3×#6397011yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC22×C3×#625C2
hypercenterC22×C3×C4D32
hypocenterC32C3×#394
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C32×(C2×D3)⋊C4C2semidirect
3. C2×C32×(C2×D3)⋊C4C2semidirect
4. C2×C3×Dic3⋊Dic3C2semidirect
5. C2×C3×(C2×D3)⋊Dic3C2semidirect
6. C2×C3×(C2×D3)⋊Dic3C2semidirect
7. C3×#63658C2semidirect
10. #10591390C3direct (N × H)
37. C2×C3×(C2×D3)⋊C4D3semidirect
38. C2×C3×(C2×D3)⋊C4D3semidirect
39. C2×C3×(C2×D3)⋊C4C2×C3semidirect
40. C2×C3×(C2×D3)⋊C4C2×C3semidirect
43. C2×Dic3⋊Dic3C2×C3semidirect
44. C2×(C2×D3)⋊Dic3C2×C3semidirect
45. C2×(C2×D3)⋊Dic3C2×C3semidirect
46. #63658C2×C3semidirect
79. C2×C32×Dic3D4semidirect
183. C2×(C2×D3)⋊C4C3×D3semidirect
184. C2×(C2×D3)⋊C4C3×D3semidirect
323. C2×C3×Dic3#67semidirect
324. C2×C3×Dic3C3×D4semidirect
528. C33#394semidirect
663. C2×Dic3C3×#67semidirect
868. C32#4959semidirect
869. C32#4961semidirect
870. C32C3×#394semidirect
989. C3#10591390direct (N × H)
990. C3C3×#4959semidirect
991. C3C3×#4961semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6252
C2×C32×(C2×D3)⋊C42
C2×C3×Dic3⋊Dic32
C2×C3×(C2×D3)⋊Dic32
C3×#636582
C3×#49613
C3×#49593
#105913903