Finite Group Databasebeta

← C3×#10591293 #13158412

Subgroups — C3×#10591293 #13158412

Order 1728.

1146 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#627C211yesmaximal, characteristic, complemented
2C2×C32×(C2×D3)⋊C4C211yesmaximal, characteristic
3C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
4C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
5C3×#63658C211yesmaximal, characteristic, complemented
6C32×C3⋊#95C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8C3×#4947—31nomaximal
9C3×#4673—31nomaximal
10#10591293C311yesmaximal, 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×#627—22no—
19C2×C3×#627—22no—
20C2×C3×#627—22no—
21C32×(C2×D3)⋊C4—22no—
22C3×(C2×D3)⋊Dic3—22no—
23C3×(C2×D3)⋊Dic3—22no—
24C22×C3×Dic6—31no—
25C22×C3×Dic6—31no—
26C22×#627C2×C311yescharacteristic, complemented
27C2×C32×C22⋊C4—31no—
28C2×C3×#217—31no—
29C2×C3×#217—31no—
30C2×C3×(C2×D3)⋊C4—21no—
31C2×C3×(C2×D3)⋊C4—31no—
32C2×C3×(C2×D3)⋊C4—31no—
33C2×C3×(C2×D3)⋊C4D311yescharacteristic
34C2×C3×(C2×D3)⋊C4C2×C311yescharacteristic
35C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
36C2×(C2×D3)⋊Dic3C2×C311yescharacteristic
37C32×#95—31no—
38#63658C2×C311yescharacteristic, complemented
39C3×C3⋊#95—21no—
40C3×C3⋊#95—31no—
41C3×C3⋊#95—31no—
42C3×C3⋊#95—31no—
43C3×C3⋊#95—31no—
44C3×C3⋊#95—61no—
45C3×C3⋊#95D311yescharacteristic, complemented
46C3×C3⋊#95C2×C311yescharacteristic, complemented
47#63579C2×C311yescharacteristic, complemented
48C23×C33C2311yescharacteristic
49C22×C32×D3—21no—
50C22×C32×D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3—21no—
54C22×C32×D3—21no—
55C22×C32×D3Q812yescomplemented
56C2×C33×C4—21no—
57C2×C33×C4—21no—
58C2×C33×C4—21no—
59C2×C3×C3⋊Dic3—21no—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3—21no—
64C2×C3×C3⋊Dic3D412yes—
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×Dic3D412yes—
73C2×C32×Dic3D412yes—
74C3×#627—28no—
75C3×#393—91no—
76#4947—31no—
77#4673—31no—
78C24×C32—31no—
79C23×C3×D3—21no—
80C23×C3×D3C2×D311yescharacteristic
81C23×C3×D3C22×C311yescharacteristic
82C22×C32×C4—21no—
83C22×C32×C4—21no—
84C22×C32×C4—21no—
85C22×C32×C4—31no—
86C22×C32×C4—31no—
87C22×C32×C4—31no—
88C22×C32×C4—41no—
89C22×C32×C4C2×D311yescharacteristic
90C22×C32×C4C2×D311yescharacteristic
91C22×C32×C4C22×C311yescharacteristic
92C22×C3⋊Dic3C22×C311yescharacteristic
93C22×C3⋊Dic3C22×C311yescharacteristic
94C22×C3×Dic3—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—61no—
102C22×C3×Dic3—61no—
103C22×C3×Dic3C2×D311yescharacteristic
104C22×C3×Dic3C2×D311yescharacteristic
105C22×C3×Dic3C2×D311yescharacteristic
106C22×C3×Dic3C22×C311yescharacteristic
107C22×C3×Dic3C22×C311yescharacteristic
108C22×C3×Dic3C22×C311yescharacteristic
109C2×C3×Dic6—62no—
110C2×C3×Dic6—62no—
111C2×C3×Dic6—62no—
112C2×C3×Dic6—62no—
113C2×C3×Dic6—62no—
114C2×C3×Dic6—62no—
115C2×#627—22no—
116C2×#627—22no—
117C2×#627—22no—
118C32×C22⋊C4—62no—
119C3×#217—62no—
120C3×#217—62no—
121C3×(C2×D3)⋊C4—24no—
122C3×(C2×D3)⋊C4—22no—
123C3×(C2×D3)⋊C4—22no—
124C3×(C2×D3)⋊C4—62no—
125C3×(C2×D3)⋊C4—62no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—22no—
128C22×C33C2×D411yescharacteristic
129C22×C33C2×D411yescharacteristic
130C22×C33C2×D411yescharacteristic
131C22×C33C2×Q811yescharacteristic
132C22×C33#4111yescharacteristic
133C22×C33#4111yescharacteristic
134C22×C33#4111yescharacteristic
135C2×C32×D3—22no—
136C2×C32×D3—22no—
137C2×C32×D3—22no—
138C2×C32×D3—41no—
139C2×C32×D3—41no—
140C2×C32×D3—41no—
141C2×C32×D3—41no—
142C33×C4—41no—
143C3×C3⋊Dic3—22no—
144C3×C3⋊Dic3—41no—
145C32×Dic3—22no—
146C32×Dic3—22no—
147C32×Dic3—41no—
148C22×C3×Q8—91no—
149C22×Dic6—31no—
150C22×Dic6—31no—
151C2×C3×C22⋊C4—31no—
152C2×C3×C22⋊C4—31no—
153C2×C3×C22⋊C4—61no—
154C2×C3×C22⋊C4—91no—
155C2×C3×C22⋊C4—91no—
156C2×#217—31no—
157C2×#217—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4C3×D311yescharacteristic
161C3×#95—31no—
162C3×#95—31no—
163C3×#95—61no—
164C3×#95—91no—
165C3×#95—91no—
166C3⋊#95—31no—
167C3⋊#95—31no—
168C3⋊#95—31no—
169C3⋊#95—31no—
170C3⋊#95—61no—
171C3⋊#95C3×D311yescharacteristic, complemented
172C23×C32—21no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—32no—
176C23×C32—41no—
177C23×C32—61no—
178C23×C32—61no—
179C23×C32—61no—
180C23×C32—61no—
181C23×C32—61no—
182C23×C32—61no—
183C23×C32C22×D311yescharacteristic
184C23×C32C22×D311yescharacteristic
185C23×C32C23×C311yescharacteristic
186C22×C3×D3—22no—
187C22×C3×D3—22no—
188C22×C3×D3—21no—
189C22×C3×D3—21no—
190C22×C3×D3—21no—
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—21no—
200C22×C3×D3—22no—
201C22×C3×D3—41no—
202C22×C3×D3—41no—
203C22×C3×D3—41no—
204C22×C3×D3—41no—
205C22×C3×D3Dic612yescomplemented
206C22×C3×D3C3×Q812yescomplemented
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—32no—
220C2×C32×C4—32no—
221C2×C32×C4—41no—
222C2×C32×C4—41no—
223C2×C32×C4—41no—
224C2×C32×C4—41no—
225C2×C32×C4—41no—
226C2×C32×C4—41no—
227C2×C32×C4—42no—
228C2×C32×C4—42no—
229C2×C32×C4—42no—
230C2×C32×C4—61no—
231C2×C32×C4—61no—
232C2×C32×C4—61no—
233C2×C32×C4—61no—
234C2×C32×C4—61no—
235C2×C32×C4—61no—
236C2×C32×C4—61no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3C3×D412yes—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
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—22no—
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—22no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—32no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—41no—
263C2×C3×Dic3—41no—
264C2×C3×Dic3—41no—
265C2×C3×Dic3—41no—
266C2×C3×Dic3—41no—
267C2×C3×Dic3—41no—
268C2×C3×Dic3—62no—
269C2×C3×Dic3—61no—
270C2×C3×Dic3—61no—
271C2×C3×Dic3—61no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—62no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—121no—
281C2×C3×Dic3—121no—
282C2×C3×Dic3—121no—
283C2×C3×Dic3—121no—
284C2×C3×Dic3D1212yes—
285C2×C3×Dic3#6712yes—
286C2×C3×Dic3C3×D412yes—
287C2×C3×Dic3C3×D412yes—
288C3×Dic6—68no—
289C3×Dic6—68no—
290#627—28no—
291#393—91noSylow
292C2×C33#12011yescharacteristic
293C2×C33C22⋊Q811yescharacteristic
294C2×C33C22⋊Q811yescharacteristic
295C2×C33C22⋊Q811yescharacteristic
296C2×C33#12411yescharacteristic
297C2×C33#12411yescharacteristic
298C2×C33#12411yescharacteristic
299C32×D3—42no—
300C24×C3—31no—
301C24×C3—31no—
302C24×C3—61no—
303C23×D3C2×C3×D311yescharacteristic
304C2×C3×Q8—182no—
305C2×C3×Q8—182no—
306C2×C3×Q8—182no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—41no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—91no—
321C22×C3×C4—91no—
322C22×C3×C4D3211yescharacteristic
323C22×C3×C4C2×C3×D311yescharacteristic
324C22×C3×C4C2×C3×D311yescharacteristic
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3C2×C3×D311yescharacteristic
332C22×Dic3C2×C3×D311yescharacteristic
333C22×Dic3C2×C3×D311yescharacteristic
334C2×Dic6—62no—
335C2×Dic6—62no—
336C2×Dic6—62no—
337C2×Dic6—62no—
338C2×Dic6—62no—
339C2×Dic6—62no—
340C3×C22⋊C4—62no—
341C3×C22⋊C4—62no—
342C3×C22⋊C4—64no—
343C3×C22⋊C4—182no—
344C3×C22⋊C4—182no—
345#217—62no—
346#217—62no—
347(C2×D3)⋊C4—22no—
348(C2×D3)⋊C4—62no—
349(C2×D3)⋊C4—62no—
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—21no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—41no—
372C22×C32—41no—
373C22×C32—41no—
374C22×C32—41no—
375C22×C32—41no—
376C22×C32—41no—
377C22×C32—41no—
378C22×C32—62no—
379C22×C32—62no—
380C22×C32—62no—
381C22×C32—121no—
382C22×C32—121no—
383C22×C32—121no—
384C22×C32—121no—
385C22×C32C2×Dic611yescharacteristic
386C22×C32C2×D1211yescharacteristic
387C22×C32#23511yescharacteristic
388C22×C32#23511yescharacteristic
389C22×C32#23511yescharacteristic
390C22×C32D3×D411yescharacteristic
391C22×C32D3×D411yescharacteristic
392C22×C32D3×D411yescharacteristic
393C22×C32D3×D411yescharacteristic
394C22×C32#23711yescharacteristic
395C22×C32#23711yescharacteristic
396C22×C32#23711yescharacteristic
397C22×C32D3×Q811yescharacteristic
398C22×C32C2×#6711yescharacteristic
399C22×C32C2×C3×D411yescharacteristic
400C22×C32C2×C3×D411yescharacteristic
401C22×C32C2×C3×D411yescharacteristic
402C22×C32C2×C3×Q811yescharacteristic
403C22×C32C3×#4111yescharacteristic
404C22×C32C3×#4111yescharacteristic
405C22×C32C3×#4111yescharacteristic
406C2×C3×D3—24no—
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—22no—
412C2×C3×D3—22no—
413C2×C3×D3—42no—
414C2×C3×D3—42no—
415C2×C3×D3—42no—
416C2×C3×D3—42no—
417C2×C3×D3—42no—
418C2×C3×D3—42no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C32×C4—42no—
428C32×C4—42no—
429C32×C4—42no—
430C32×C4—44no—
431C32×C4—41no—
432C32×C4—41no—
433C32×C4—41no—
434C32×C4—62no—
435C32×C4—62no—
436C32×C4—121no—
437C3⋊Dic3—22no—
438C3⋊Dic3—41no—
439C3×Dic3—22no—
440C3×Dic3—22no—
441C3×Dic3—22no—
442C3×Dic3—22no—
443C3×Dic3—42no—
444C3×Dic3—42no—
445C3×Dic3—42no—
446C3×Dic3—41no—
447C3×Dic3—41no—
448C3×Dic3—62no—
449C3×Dic3—62no—
450C3×Dic3—122no—
451C3×Dic3—122no—
452C3×Dic3—121no—
453C3×Dic3—121no—
454C22×Q8—91no—
455C2×C22⋊C4—31no—
456C2×C22⋊C4—91no—
457C2×C22⋊C4—91no—
458#95—31no—
459#95—91no—
460#95—91no—
461C33#39311yescharacteristic, complemented, Sylow
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—32no—
466C23×C3—32no—
467C23×C3—41no—
468C23×C3—62no—
469C23×C3—62no—
470C23×C3—62no—
471C23×C3—61no—
472C23×C3—61no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—61no—
476C23×C3—61no—
477C23×C3—61no—
478C23×C3—61no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—121no—
484C23×C3—121no—
485C23×C3—121no—
486C23×C3—121no—
487C23×C3C2×D3211yescharacteristic
488C23×C3C22×C3×D311yescharacteristic
489C23×C3C22×C3×D311yescharacteristic
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3C3×Dic612yescomplemented
497C3×Q8—188no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—32no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—42no—
521C2×C3×C4—42no—
522C2×C3×C4—42no—
523C2×C3×C4—62no—
524C2×C3×C4—62no—
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—61no—
533C2×C3×C4—62no—
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—92no—
541C2×C3×C4—121no—
542C2×C3×C4—121no—
543C2×C3×C4—121no—
544C2×C3×C4—121no—
545C2×C3×C4—121no—
546C2×C3×C4—121no—
547C2×C3×C4—181no—
548C2×C3×C4—181no—
549C2×C3×C4—181no—
550C2×C3×C4—181no—
551C2×C3×C4—181no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—32no—
560C2×Dic3—32no—
561C2×Dic3—62no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—62no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—121no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—121no—
577C2×Dic3C3×D1212yes—
578C2×Dic3C3×#6712yes—
579Dic6—68no—
580Dic6—68no—
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—21no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—21no—
602C2×C32—41no—
603C2×C32—41no—
604C2×C32—41no—
605C2×C32—41no—
606C2×C32—41no—
607C2×C32—41no—
608C2×C32—41no—
609C2×C32—122no—
610C2×C32#87511yescharacteristic
611C2×C32#87811yescharacteristic
612C2×C32#87811yescharacteristic
613C2×C32#88211yescharacteristic
614C2×C32#88511yescharacteristic
615C2×C32#88511yescharacteristic
616C2×C32#88511yescharacteristic
617C2×C32#88511yescharacteristic
618C2×C32#89611yescharacteristic
619C2×C32#89611yescharacteristic
620C2×C32#89711yescharacteristic
621C2×C32#92411yescharacteristic
622C2×C32#93611yescharacteristic
623C2×C32#93711yescharacteristic
624C2×C32C3×#12011yescharacteristic
625C2×C32C3×C22⋊Q811yescharacteristic
626C2×C32C3×C22⋊Q811yescharacteristic
627C2×C32C3×C22⋊Q811yescharacteristic
628C2×C32C3×#12411yescharacteristic
629C2×C32C3×#12411yescharacteristic
630C2×C32C3×#12411yescharacteristic
631C3×D3—44no—
632C3×D3—42no—
633C3×D3—42no—
634C24—31no—
635C2×Q8—182no—
636C2×Q8—182no—
637C2×Q8—182no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—91no—
642C22×C4—91no—
643C22×C4C3×D3211yescharacteristic
644C22⋊C4—62no—
645C22⋊C4—182no—
646C22⋊C4—182no—
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—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—64no—
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—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3D3×Dic611yescharacteristic
697C22×C3#379811yescharacteristic
698C22×C3D3×D1211yescharacteristic
699C22×C3#380211yescharacteristic
700C22×C3#380411yescharacteristic
701C22×C3#380511yescharacteristic
702C22×C3D3×#6711yescharacteristic
703C22×C3C2×C3×Dic611yescharacteristic
704C22×C3C2×C3×D1211yescharacteristic
705C22×C3C3×#23511yescharacteristic
706C22×C3C3×#23511yescharacteristic
707C22×C3C3×#23511yescharacteristic
708C22×C3C3×D3×D411yescharacteristic
709C22×C3C3×D3×D411yescharacteristic
710C22×C3C3×D3×D411yescharacteristic
711C22×C3C3×D3×D411yescharacteristic
712C22×C3C3×#23711yescharacteristic
713C22×C3C3×#23711yescharacteristic
714C22×C3C3×#23711yescharacteristic
715C22×C3C3×D3×Q811yescharacteristic
716C22×C3C2×C3×#6711yescharacteristic
717C2×D3—22no—
718C2×D3—22no—
719C2×D3—22no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—44no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—122no—
736C3×C4—122no—
737C3×C4—122no—
738C3×C4—121no—
739C3×C4—121no—
740C3×C4—182no—
741C3×C4—361no—
742Dic3—22no—
743Dic3—22no—
744Dic3—41no—
745Dic3—62no—
746Dic3—62no—
747Dic3—122no—
748Dic3—122no—
749Dic3—121no—
750Dic3—121no—
751C32—21no—
752C32—21no—
753C32—21no—
754C32—41no—
755C32#467311yescharacteristic, complemented
756C32#494711yescharacteristic, complemented
757C32C3×#39311yescharacteristic, complemented
758C23—32no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23—61no—
763C23—61no—
764C23—61no—
765C23C2×C3×D3211yescharacteristic
766Q8—188no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—92no—
780C2×C4—181no—
781C2×C4—181no—
782C2×C4—181no—
783C2×C4—181no—
784C2×C4—181no—
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—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—41no—
807C2×C3—41no—
808C2×C3—41no—
809C2×C3—41no—
810C2×C3—41no—
811C2×C3—41no—
812C2×C3—41no—
813C2×C3—124no—
814C2×C3—122no—
815C2×C3—122no—
816C2×C3#6385111yescharacteristic
817C2×C3#6385211yescharacteristic
818C2×C3#6389311yescharacteristic
819C2×C3#6389911yescharacteristic
820C2×C3#6391511yescharacteristic
821C2×C3#6392211yescharacteristic
822C2×C3#6395911yescharacteristic
823C2×C3C3×#87511yescharacteristic
824C2×C3C3×#87811yescharacteristic
825C2×C3C3×#87811yescharacteristic
826C2×C3C3×#88211yescharacteristic
827C2×C3C3×#88511yescharacteristic
828C2×C3C3×#88511yescharacteristic
829C2×C3C3×#88511yescharacteristic
830C2×C3C3×#88511yescharacteristic
831C2×C3C3×#89611yescharacteristic
832C2×C3C3×#89611yescharacteristic
833C2×C3C3×#89711yescharacteristic
834C2×C3C3×#92411yescharacteristic
835C2×C3C3×#93611yescharacteristic
836C2×C3C3×#93711yescharacteristic
837D3—42no—
838C22—62no—
839C22—62no—
840C22—62no—
841C22—121no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22C3×D3×Dic611yescharacteristic
846C22C3×#379811yescharacteristic
847C22C3×D3×D1211yescharacteristic
848C22C3×#380211yescharacteristic
849C22C3×#380411yescharacteristic
850C22C3×#380511yescharacteristic
851C22C3×D3×#6711yescharacteristic
852C4—41no—
853C4—62no—
854C4—62no—
855C4—121no—
856C4—182no—
857C4—361no—
858C3—21no—
859C3—21no—
860C3—21no—
861C3—41no—
862C3#1059129311yescharacteristic, direct product factor
863C3C3×#467311yescharacteristic, complemented
864C3C3×#494711yescharacteristic, complemented
865C2—122no—
866C2C3×#6385111yescharacteristic
867C2C3×#6385211yescharacteristic
868C2C3×#6389311yescharacteristic
869C2C3×#6389911yescharacteristic
870C2C3×#6391511yescharacteristic
871C2C3×#6392211yescharacteristic
872C2C3×#6395911yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socleC23×C33C23
prime radicalC23×C32×D3C22
hypercenterC22×C3×C4D32
hypocenterC32C3×#393
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#627C2semidirect
5. C3×#63658C2semidirect
6. C32×C3⋊#95C2semidirect
7. C3×#63579C2semidirect
10. #10591293C3direct (N × H)
26. C22×#627C2×C3semidirect
38. #63658C2×C3semidirect
45. C3×C3⋊#95D3semidirect
46. C3×C3⋊#95C2×C3semidirect
47. #63579C2×C3semidirect
55. C22×C32×D3Q8semidirect
171. C3⋊#95C3×D3semidirect
205. C22×C3×D3Dic6semidirect
206. C22×C3×D3C3×Q8semidirect
461. C33#393semidirect
496. C22×D3C3×Dic6semidirect
755. C32#4673semidirect
756. C32#4947semidirect
757. C32C3×#393semidirect
862. C3#10591293direct (N × H)
863. C3C3×#4673semidirect
864. C3C3×#4947semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6272
C2×C32×(C2×D3)⋊C42
C2×C3×(C2×D3)⋊Dic32
C3×#636582
C32×C3⋊#952
C3×#635792
C3×#49473
C3×#46733
#105912933