Finite Group Databasebeta

← C3×#10591362 #13158372

Subgroups — C3×#10591362 #13158372

Order 1728.

1210 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Dic3C211yesmaximal, characteristic
2C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
4C3×#63658C211yesmaximal, characteristic, complemented
5C32×C3⋊#95C211yesmaximal, characteristic, complemented
6C3×#63579C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8C3×#4943—31nomaximal
9C3×#4664—31nomaximal
10#10591362C311yesmaximal, 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
21C32×(C2×D3)⋊C4—22no—
22C3×(C2×D3)⋊Dic3—22no—
23C23×C3×Dic3—31no—
24C22×C3×C4×D3—31no—
25C22×D3×Dic3C2×C311yescharacteristic
26C2×C32×C22⋊C4—31no—
27C2×C3×#217—31no—
28C2×C3×(C2×D3)⋊C4—21no—
29C2×C3×(C2×D3)⋊C4—31no—
30C2×C3×(C2×D3)⋊C4D311yescharacteristic
31C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
32C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
33C32×#95—31no—
34#63658C2×C311yescharacteristic, complemented
35C3×C3⋊#95—21no—
36C3×C3⋊#95—31no—
37C3×C3⋊#95—31no—
38C3×C3⋊#95—31no—
39C3×C3⋊#95—31no—
40C3×C3⋊#95—31no—
41C3×C3⋊#95—31no—
42C3×C3⋊#95—61no—
43C3×C3⋊#95D311yescharacteristic, complemented
44C3×C3⋊#95C2×C311yescharacteristic, complemented
45#63579C2×C311yescharacteristic, complemented
46#63579C2×C311yescharacteristic, complemented
47C23×C33C2311yescharacteristic
48C22×C32×D3—21no—
49C22×C32×D3—21no—
50C22×C32×D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3C2×C412yes—
53C22×C32×D3D412yes—
54C22×C32×D3D412yes—
55C2×C33×C4—21no—
56C2×C33×C4—21no—
57C2×C33×C4—21no—
58C2×C3×C3⋊Dic3—21no—
59C2×C3×C3⋊Dic3—21no—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3C2×C412yes—
64C2×C32×Dic3—21no—
65C2×C32×Dic3—21no—
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—
73C3×D3×Dic3—28no—
74C3×#381—91no—
75#4943—31no—
76#4664—31no—
77C24×C32—31no—
78C23×C3×D3—21no—
79C23×C3×D3C2×D311yescharacteristic
80C23×C3×D3C22×C311yescharacteristic
81C22×C32×C4—21no—
82C22×C32×C4—21no—
83C22×C32×C4—21no—
84C22×C32×C4—31no—
85C22×C32×C4—31no—
86C22×C32×C4—31no—
87C22×C32×C4—41no—
88C22×C32×C4C2×D311yescharacteristic
89C22×C32×C4C2×D311yescharacteristic
90C22×C32×C4C22×C311yescharacteristic
91C22×C3⋊Dic3C22×C311yescharacteristic
92C22×C3⋊Dic3C22×C311yescharacteristic
93C22×C3×Dic3—21no—
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—34no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—62no—
102C22×C3×Dic3—62no—
103C22×C3×Dic3—61no—
104C22×C3×Dic3—61no—
105C22×C3×Dic3C2×D311yescharacteristic
106C22×C3×Dic3C2×D311yescharacteristic
107C22×C3×Dic3C2×D311yescharacteristic
108C22×C3×Dic3C22×C311yescharacteristic
109C22×C3×Dic3C22×C311yescharacteristic
110C22×C3×Dic3C22×C311yescharacteristic
111C2×C3×C4×D3—34no—
112C2×C3×C4×D3—62no—
113C2×C3×C4×D3—62no—
114C2×D3×Dic3—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3C3×C414yescomplemented
117C32×C22⋊C4—62no—
118C3×#217—62no—
119C3×(C2×D3)⋊C4—24no—
120C3×(C2×D3)⋊C4—22no—
121C3×(C2×D3)⋊C4—22no—
122C3×(C2×D3)⋊C4—62no—
123(C2×D3)⋊Dic3—22no—
124C22×C33C22×C411yescharacteristic
125C22×C33C2×D411yescharacteristic
126C22×C33C2×D411yescharacteristic
127C22×C33#4111yescharacteristic
128C22×C33#4111yescharacteristic
129C22×C33#4111yescharacteristic
130C22×C33#4111yescharacteristic
131C2×C32×D3—22no—
132C2×C32×D3—22no—
133C2×C32×D3—22no—
134C2×C32×D3—22no—
135C2×C32×D3—22no—
136C2×C32×D3—22no—
137C2×C32×D3C22⋊C414yes—
138C33×C4—41no—
139C3×C3⋊Dic3—22no—
140C3×C3⋊Dic3—41no—
141C32×Dic3—22no—
142C32×Dic3—41no—
143C32×Dic3—41no—
144C23×C3×C4—91no—
145C23×Dic3—31no—
146C22×C4×D3—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—61no—
150C2×C3×C22⋊C4—91no—
151C2×#217—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4C3×D311yescharacteristic
154C3×#95—31no—
155C3×#95—31no—
156C3×#95—61no—
157C3×#95—91no—
158C3×#95—91no—
159C3×#95—91no—
160C3⋊#95—31no—
161C3⋊#95—31no—
162C3⋊#95—31no—
163C3⋊#95—31no—
164C3⋊#95—31no—
165C3⋊#95—31no—
166C3⋊#95—61no—
167C3⋊#95C3×D311yescharacteristic, complemented
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—32no—
172C23×C32—32no—
173C23×C32—32no—
174C23×C32—41no—
175C23×C32—61no—
176C23×C32—61no—
177C23×C32—61no—
178C23×C32—61no—
179C23×C32C22×D311yescharacteristic
180C23×C32C22×D311yescharacteristic
181C23×C32C23×C311yescharacteristic
182C22×C3×D3—21no—
183C22×C3×D3—21no—
184C22×C3×D3—21no—
185C22×C3×D3—21no—
186C22×C3×D3—21no—
187C22×C3×D3—21no—
188C22×C3×D3—21no—
189C22×C3×D3—21no—
190C22×C3×D3—22no—
191C22×C3×D3—22no—
192C22×C3×D3—22no—
193C22×C3×D3—41no—
194C22×C3×D3—41no—
195C22×C3×D3—41no—
196C22×C3×D3—41no—
197C22×C3×D3C4×D312yes—
198C22×C3×D3D1212yes—
199C22×C3×D3#6712yes—
200C22×C3×D3C2×C3×C412yes—
201C22×C3×D3C3×D412yes—
202C22×C3×D3C3×D412yes—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—21no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—22no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—32no—
216C2×C32×C4—41no—
217C2×C32×C4—41no—
218C2×C32×C4—41no—
219C2×C32×C4—41no—
220C2×C32×C4—41no—
221C2×C32×C4—41no—
222C2×C32×C4—42no—
223C2×C32×C4—42no—
224C2×C32×C4—42no—
225C2×C32×C4—61no—
226C2×C32×C4—61no—
227C2×C32×C4—61no—
228C2×C32×C4—61no—
229C2×C32×C4—61no—
230C2×C32×C4—61no—
231C2×C32×C4—61no—
232C2×C32×C4—61no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—21no—
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3C2×C3×C412yes—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—22no—
244C2×C3×Dic3—22no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
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—22no—
258C2×C3×Dic3—32no—
259C2×C3×Dic3—32no—
260C2×C3×Dic3—41no—
261C2×C3×Dic3—41no—
262C2×C3×Dic3—41no—
263C2×C3×Dic3—41no—
264C2×C3×Dic3—41no—
265C2×C3×Dic3—41no—
266C2×C3×Dic3—62no—
267C2×C3×Dic3—68no—
268C2×C3×Dic3—61no—
269C2×C3×Dic3—61no—
270C2×C3×Dic3—61no—
271C2×C3×Dic3—61no—
272C2×C3×Dic3—62no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—121no—
280C2×C3×Dic3—121no—
281C2×C3×Dic3—121no—
282C2×C3×Dic3—121no—
283C2×C3×Dic3C4×D312yes—
284C2×C3×Dic3C2×C3×C412yes—
285C3×C4×D3—68no—
286D3×Dic3—28no—
287#381—91noSylow
288C2×C33C2×C22⋊C411yescharacteristic
289C2×C33#11711yescharacteristic
290C2×C33#11711yescharacteristic
291C2×C33#12311yescharacteristic
292C2×C33#12311yescharacteristic
293C2×C33#12311yescharacteristic
294C2×C33#12311yescharacteristic
295C32×D3—24no—
296C24×C3—31no—
297C24×C3—31no—
298C24×C3—61no—
299C23×D3C2×C3×D311yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—41no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—94no—
314C22×C3×C4—91no—
315C22×C3×C4—91no—
316C22×C3×C4—182no—
317C22×C3×C4—182no—
318C22×C3×C4D3211yescharacteristic
319C22×C3×C4C2×C3×D311yescharacteristic
320C22×C3×C4C2×C3×D311yescharacteristic
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—34no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—61no—
327C22×Dic3—61no—
328C22×Dic3—62no—
329C22×Dic3—62no—
330C22×Dic3C2×C3×D311yescharacteristic
331C22×Dic3C2×C3×D311yescharacteristic
332C22×Dic3C2×C3×D311yescharacteristic
333C2×C4×D3—34no—
334C2×C4×D3—62no—
335C2×C4×D3—62no—
336C3×C22⋊C4—62no—
337C3×C22⋊C4—62no—
338C3×C22⋊C4—64no—
339C3×C22⋊C4—182no—
340#217—62no—
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—62no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—21no—
350C22×C32—21no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C32—21no—
354C22×C32—21no—
355C22×C32—21no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32—21no—
359C22×C32—21no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—21no—
364C22×C32—34no—
365C22×C32—41no—
366C22×C32—41no—
367C22×C32—41no—
368C22×C32—41no—
369C22×C32—41no—
370C22×C32—41no—
371C22×C32—41no—
372C22×C32—62no—
373C22×C32—62no—
374C22×C32—62no—
375C22×C32—62no—
376C22×C32—62no—
377C22×C32—62no—
378C22×C32C2×C4×D311yescharacteristic
379C22×C32C2×C4×D311yescharacteristic
380C22×C32C2×D1211yescharacteristic
381C22×C32#23511yescharacteristic
382C22×C32#23511yescharacteristic
383C22×C32D3×D411yescharacteristic
384C22×C32D3×D411yescharacteristic
385C22×C32#23711yescharacteristic
386C22×C32#23711yescharacteristic
387C22×C32#23711yescharacteristic
388C22×C32#23711yescharacteristic
389C22×C32#23711yescharacteristic
390C22×C32#23911yescharacteristic
391C22×C32C2×#6711yescharacteristic
392C22×C32C22×C3×C411yescharacteristic
393C22×C32C2×C3×D411yescharacteristic
394C22×C32C2×C3×D411yescharacteristic
395C22×C32C3×#4111yescharacteristic
396C22×C32C3×#4111yescharacteristic
397C22×C32C3×#4111yescharacteristic
398C22×C32C3×#4111yescharacteristic
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—22no—
403C2×C3×D3—22no—
404C2×C3×D3—22no—
405C2×C3×D3—22no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—24no—
412C2×C3×D3—42no—
413C2×C3×D3—42no—
414C2×C3×D3—42no—
415C2×C3×D3—42no—
416C2×C3×D3—42no—
417C2×C3×D3—42no—
418C2×C3×D3(C2×D3)⋊C414yes—
419C2×C3×D3C3×C22⋊C414yes—
420C32×C4—42no—
421C32×C4—42no—
422C32×C4—42no—
423C32×C4—44no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4—62no—
428C32×C4—121no—
429C32×C4—121no—
430C3⋊Dic3—22no—
431C3⋊Dic3—41no—
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—42no—
435C3×Dic3—42no—
436C3×Dic3—42no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—62no—
442C3×Dic3—62no—
443C3×Dic3—122no—
444C3×Dic3—122no—
445C3×Dic3—121no—
446C3×Dic3—121no—
447C23×C4—91no—
448C2×C22⋊C4—31no—
449C2×C22⋊C4—91no—
450#95—31no—
451#95—91no—
452#95—91no—
453#95—91no—
454C33#38111yescharacteristic, complemented, Sylow
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—32no—
459C23×C3—32no—
460C23×C3—32no—
461C23×C3—32no—
462C23×C3—32no—
463C23×C3—32no—
464C23×C3—41no—
465C23×C3—62no—
466C23×C3—62no—
467C23×C3—62no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—61no—
476C23×C3—121no—
477C23×C3—121no—
478C23×C3—121no—
479C23×C3—121no—
480C23×C3C2×D3211yescharacteristic
481C23×C3C22×C3×D311yescharacteristic
482C23×C3C22×C3×D311yescharacteristic
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3C3×C4×D312yes—
488C22×D3C3×D1212yes—
489C22×D3C3×#6712yes—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—42no—
511C2×C3×C4—42no—
512C2×C3×C4—42no—
513C2×C3×C4—62no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—62no—
519C2×C3×C4—62no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—92no—
533C2×C3×C4—121no—
534C2×C3×C4—121no—
535C2×C3×C4—121no—
536C2×C3×C4—121no—
537C2×C3×C4—121no—
538C2×C3×C4—121no—
539C2×C3×C4—188no—
540C2×C3×C4—181no—
541C2×C3×C4—181no—
542C2×C3×C4—181no—
543C2×C3×C4—181no—
544C2×C3×C4—181no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—62no—
556C2×Dic3—68no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—62no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—121no—
569C2×Dic3—121no—
570C2×Dic3—121no—
571C2×Dic3—121no—
572C2×Dic3C3×C4×D312yes—
573C4×D3—68no—
574C2×C32—21no—
575C2×C32—21no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32—21no—
580C2×C32—21no—
581C2×C32—21no—
582C2×C32—21no—
583C2×C32—21no—
584C2×C32—21no—
585C2×C32—21no—
586C2×C32—21no—
587C2×C32—21no—
588C2×C32—21no—
589C2×C32—21no—
590C2×C32—21no—
591C2×C32—21no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—41no—
596C2×C32—41no—
597C2×C32—41no—
598C2×C32—41no—
599C2×C32—41no—
600C2×C32—41no—
601C2×C32—41no—
602C2×C32—64no—
603C2×C32#87211yescharacteristic
604C2×C32#87711yescharacteristic
605C2×C32#87711yescharacteristic
606C2×C32D3×C22⋊C411yescharacteristic
607C2×C32#88311yescharacteristic
608C2×C32#88311yescharacteristic
609C2×C32#88611yescharacteristic
610C2×C32#88611yescharacteristic
611C2×C32#89211yescharacteristic
612C2×C32#89411yescharacteristic
613C2×C32#89411yescharacteristic
614C2×C32C2×(C2×D3)⋊C411yescharacteristic
615C2×C32#93511yescharacteristic
616C2×C32#93511yescharacteristic
617C2×C32C2×C3×C22⋊C411yescharacteristic
618C2×C32C3×#11711yescharacteristic
619C2×C32C3×#11711yescharacteristic
620C2×C32C3×#12311yescharacteristic
621C2×C32C3×#12311yescharacteristic
622C2×C32C3×#12311yescharacteristic
623C2×C32C3×#12311yescharacteristic
624C3×D3—24no—
625C3×D3—24no—
626C3×D3—44no—
627C24—31no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—94no—
632C22×C4—91no—
633C22×C4—91no—
634C22×C4—182no—
635C22×C4—182no—
636C22×C4C3×D3211yescharacteristic
637C22⋊C4—62no—
638C22⋊C4—182no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—34no—
661C22×C3—34no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—64no—
670C22×C3—62no—
671C22×C3—62no—
672C22×C3—62no—
673C22×C3—62no—
674C22×C3—62no—
675C22×C3—62no—
676C22×C3—62no—
677C22×C3—62no—
678C22×C3—62no—
679C22×C3—62no—
680C22×C3—62no—
681C22×C3—62no—
682C22×C3—122no—
683C22×C3—122no—
684C22×C3—122no—
685C22×C3—122no—
686C22×C3—122no—
687C22×C3—122no—
688C22×C3#379511yescharacteristic
689C22×C3#379611yescharacteristic
690C22×C3C4×D3211yescharacteristic
691C22×C3D3×D1211yescharacteristic
692C22×C3#380411yescharacteristic
693C22×C3#380511yescharacteristic
694C22×C3D3×#6711yescharacteristic
695C22×C3C2×C3×C4×D311yescharacteristic
696C22×C3C2×C3×C4×D311yescharacteristic
697C22×C3C2×C3×D1211yescharacteristic
698C22×C3C3×#23511yescharacteristic
699C22×C3C3×#23511yescharacteristic
700C22×C3C3×D3×D411yescharacteristic
701C22×C3C3×D3×D411yescharacteristic
702C22×C3C3×#23711yescharacteristic
703C22×C3C3×#23711yescharacteristic
704C22×C3C3×#23711yescharacteristic
705C22×C3C3×#23711yescharacteristic
706C22×C3C3×#23711yescharacteristic
707C22×C3C3×#23911yescharacteristic
708C22×C3C2×C3×#6711yescharacteristic
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—22no—
715C2×D3C3×(C2×D3)⋊C414yes—
716C3×C4—42no—
717C3×C4—42no—
718C3×C4—42no—
719C3×C4—44no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—62no—
724C3×C4—62no—
725C3×C4—122no—
726C3×C4—122no—
727C3×C4—122no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4—121no—
732C3×C4—182no—
733C3×C4—361no—
734Dic3—22no—
735Dic3—41no—
736Dic3—41no—
737Dic3—62no—
738Dic3—62no—
739Dic3—122no—
740Dic3—122no—
741Dic3—121no—
742Dic3—121no—
743C32—21no—
744C32—21no—
745C32—21no—
746C32—41no—
747C32#466411yescharacteristic, complemented
748C32#494311yescharacteristic, complemented
749C32C3×#38111yescharacteristic, complemented
750C23—32no—
751C23—32no—
752C23—32no—
753C23—61no—
754C23—61no—
755C23—61no—
756C23—61no—
757C23C2×C3×D3211yescharacteristic
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—32no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—92no—
771C2×C4—188no—
772C2×C4—181no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—41no—
799C2×C3—41no—
800C2×C3—41no—
801C2×C3—41no—
802C2×C3—41no—
803C2×C3—41no—
804C2×C3—41no—
805C2×C3—64no—
806C2×C3—64no—
807C2×C3—124no—
808C2×C3#6387711yescharacteristic
809C2×C3#6387811yescharacteristic
810C2×C3#6388411yescharacteristic
811C2×C3#6389011yescharacteristic
812C2×C3#6389111yescharacteristic
813C2×C3D3×(C2×D3)⋊C411yescharacteristic
814C2×C3#6396911yescharacteristic
815C2×C3C3×#87211yescharacteristic
816C2×C3C3×#87711yescharacteristic
817C2×C3C3×#87711yescharacteristic
818C2×C3C3×D3×C22⋊C411yescharacteristic
819C2×C3C3×#88311yescharacteristic
820C2×C3C3×#88311yescharacteristic
821C2×C3C3×#88611yescharacteristic
822C2×C3C3×#88611yescharacteristic
823C2×C3C3×#89211yescharacteristic
824C2×C3C3×#89411yescharacteristic
825C2×C3C3×#89411yescharacteristic
826C2×C3C2×C3×(C2×D3)⋊C411yescharacteristic
827C2×C3C3×#93511yescharacteristic
828C2×C3C3×#93511yescharacteristic
829D3—24no—
830C22—34no—
831C22—62no—
832C22—62no—
833C22—62no—
834C22—62no—
835C22—62no—
836C22—62no—
837C22C3×#379511yescharacteristic
838C22C3×#379611yescharacteristic
839C22C3×C4×D3211yescharacteristic
840C22C3×D3×D1211yescharacteristic
841C22C3×#380411yescharacteristic
842C22C3×#380511yescharacteristic
843C22C3×D3×#6711yescharacteristic
844C4—41no—
845C4—62no—
846C4—121no—
847C4—121no—
848C4—182no—
849C4—361no—
850C3—21no—
851C3—21no—
852C3—21no—
853C3—41no—
854C3#1059136211yescharacteristic, direct product factor
855C3C3×#466411yescharacteristic, complemented
856C3C3×#494311yescharacteristic, complemented
857C2—64no—
858C2C3×#6387711yescharacteristic
859C2C3×#6387811yescharacteristic
860C2C3×#6388411yescharacteristic
861C2C3×#6389011yescharacteristic
862C2C3×#6389111yescharacteristic
863C2C3×D3×(C2×D3)⋊C411yescharacteristic
864C2C3×#6396911yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#381
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
4. C3×#63658C2semidirect
5. C32×C3⋊#95C2semidirect
6. C3×#63579C2semidirect
7. C3×#63579C2semidirect
10. #10591362C3direct (N × H)
20. C2×C3×D3×Dic3C4semidirect
34. #63658C2×C3semidirect
43. C3×C3⋊#95D3semidirect
44. C3×C3⋊#95C2×C3semidirect
45. #63579C2×C3semidirect
46. #63579C2×C3semidirect
116. C2×D3×Dic3C3×C4semidirect
167. C3⋊#95C3×D3semidirect
454. C33#381semidirect
747. C32#4664semidirect
748. C32#4943semidirect
749. C32C3×#381semidirect
854. C3#10591362direct (N × H)
855. C3C3×#4664semidirect
856. C3C3×#4943semidirect

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×C32×(C2×D3)⋊C42
C2×C3×(C2×D3)⋊Dic32
C3×#636582
C32×C3⋊#952
C3×#635792
C3×#49433
C3×#46643
#105913623