Finite Group Databasebeta

← C3×#10591261 #13158182

Subgroups — C3×#10591261 #13158182

Order 1728.

1106 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×Dic6C211yesmaximal, characteristic
2C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
3C2×C3×Dic32C211yesmaximal, characteristic
4C3×#63658C211yesmaximal, characteristic
5C32×C3⋊#95C211yesmaximal, characteristic
6C3×#63579C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8C3×#5229—31nomaximal
9C3×#4646—31nomaximal
10#10591261C311yesmaximal, characteristic, direct product factor
11C22×C33×C4C2211yescharacteristic
12C22×C3×C3⋊Dic3C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C32×Dic3C2211yescharacteristic
15C22×C32×Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C32×Dic6—22no—
19C2×C32×Dic6—22no—
20C2×C32×Dic6C414yescomplemented
21C3×Dic3⋊Dic3—22no—
22C3×Dic32—22no—
23C22×C32×Q8—31no—
24C22×C3×Dic6—21no—
25C22×C3×Dic6D311yescharacteristic
26C22×C3×Dic6C2×C311yescharacteristic
27C2×C3×C4⋊Dic3—31no—
28C2×C3×Dic3⋊C4—31no—
29C2×C3×C4×Dic3—31no—
30C2×C3×C4×Dic3—31no—
31C2×Dic3⋊Dic3C2×C311yescharacteristic
32C2×Dic32C2×C311yescharacteristic
33C32×#95—31no—
34#63658C2×C311yescharacteristic
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
44C3×C3⋊#95C2×C311yescharacteristic
45#63579C2×C311yescharacteristic
46#63579C2×C311yescharacteristic
47C23×C33C2311yescharacteristic
48C2×C33×C4—21no—
49C2×C33×C4—21no—
50C2×C33×C4C2×C412yes—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3—21no—
53C2×C3×C3⋊Dic3—21no—
54C2×C3×C3⋊Dic3—21no—
55C2×C3×C3⋊Dic3—21no—
56C2×C3×C3⋊Dic3Q812yescomplemented
57C2×C32×Dic3—21no—
58C2×C32×Dic3—21no—
59C2×C32×Dic3—21no—
60C2×C32×Dic3—21no—
61C2×C32×Dic3—21no—
62C2×C32×Dic3—21no—
63C2×C32×Dic3—21no—
64C2×C32×Dic3C2×C412yes—
65C2×C32×Dic3C2×C412yes—
66C2×C32×Dic3D412yes—
67C2×C32×Dic3D412yes—
68C2×C32×Dic3Q812yescomplemented
69C32×Dic6—28no—
70C3×#391—91no—
71#5229—31no—
72#4646—31no—
73C2×C32×Q8—34no—
74C2×C32×Q8—62no—
75C2×C32×Q8—62no—
76C22×C32×C4—21no—
77C22×C32×C4—21no—
78C22×C32×C4—21no—
79C22×C32×C4—31no—
80C22×C32×C4—31no—
81C22×C32×C4—31no—
82C22×C32×C4—31no—
83C22×C32×C4—41no—
84C22×C32×C4C2×D311yescharacteristic
85C22×C32×C4C2×D311yescharacteristic
86C22×C32×C4C22×C311yescharacteristic
87C22×C3⋊Dic3C22×C311yescharacteristic
88C22×C3⋊Dic3C22×C311yescharacteristic
89C22×C3×Dic3—21no—
90C22×C3×Dic3—21no—
91C22×C3×Dic3—21no—
92C22×C3×Dic3—21no—
93C22×C3×Dic3—31no—
94C22×C3×Dic3—31no—
95C22×C3×Dic3—31no—
96C22×C3×Dic3—31no—
97C22×C3×Dic3—61no—
98C22×C3×Dic3—61no—
99C22×C3×Dic3C2×D311yescharacteristic
100C22×C3×Dic3C2×D311yescharacteristic
101C22×C3×Dic3C2×D311yescharacteristic
102C22×C3×Dic3C2×D311yescharacteristic
103C22×C3×Dic3C22×C311yescharacteristic
104C22×C3×Dic3C22×C311yescharacteristic
105C22×C3×Dic3C22×C311yescharacteristic
106C22×C3×Dic3C22×C311yescharacteristic
107C2×C3×Dic6—24no—
108C2×C3×Dic6—24no—
109C2×C3×Dic6—24no—
110C2×C3×Dic6—22no—
111C2×C3×Dic6—22no—
112C2×C3×Dic6—22no—
113C2×C3×Dic6—22no—
114C2×C3×Dic6Dic314yescomplemented
115C2×C3×Dic6C3×C414yescomplemented
116C3×C4⋊Dic3—62no—
117C3×Dic3⋊C4—62no—
118C3×C4×Dic3—62no—
119C3×C4×Dic3—62no—
120Dic3⋊Dic3—22no—
121Dic32—22no—
122C22×C33C22×C411yescharacteristic
123C22×C33C2×D411yescharacteristic
124C22×C33C2×D411yescharacteristic
125C22×C33C2×Q811yescharacteristic
126C22×C33C2×Q811yescharacteristic
127C22×C33#4111yescharacteristic
128C22×C33#4111yescharacteristic
129C33×C4—22no—
130C3×C3⋊Dic3—22no—
131C3×C3⋊Dic3—41no—
132C32×Dic3—22no—
133C32×Dic3—22no—
134C32×Dic3—41no—
135C32×Dic3C22⋊C414yes—
136C22×C3×Q8—31no—
137C22×C3×Q8—31no—
138C22×C3×Q8—61no—
139C22×Dic6C3×D311yescharacteristic
140C2×C3×C4⋊C4—91no—
141C2×C3×C42—91no—
142C2×C4⋊Dic3—31no—
143C2×Dic3⋊C4—31no—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—31no—
146C3×#95—31no—
147C3×#95—31no—
148C3×#95—61no—
149C3×#95—91no—
150C3×#95—91no—
151C3×#95—91no—
152C3⋊#95—31no—
153C3⋊#95—31no—
154C3⋊#95—31no—
155C3⋊#95—31no—
156C3⋊#95—31no—
157C3⋊#95—31no—
158C3⋊#95—61no—
159C3⋊#95C3×D311yescharacteristic
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—41no—
164C23×C32C22×D311yescharacteristic
165C23×C32C22×D311yescharacteristic
166C23×C32C23×C311yescharacteristic
167C32×Q8—68no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—32no—
180C2×C32×C4—32no—
181C2×C32×C4—32no—
182C2×C32×C4—32no—
183C2×C32×C4—32no—
184C2×C32×C4—42no—
185C2×C32×C4—41no—
186C2×C32×C4—41no—
187C2×C32×C4—41no—
188C2×C32×C4—41no—
189C2×C32×C4—42no—
190C2×C32×C4—42no—
191C2×C32×C4—61no—
192C2×C32×C4—61no—
193C2×C32×C4—61no—
194C2×C32×C4—61no—
195C2×C32×C4—61no—
196C2×C32×C4—61no—
197C2×C32×C4—61no—
198C2×C32×C4C4×D312yes—
199C2×C32×C4C2×Dic312yes—
200C2×C32×C4C2×C3×C412yes—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3C3×Q812yescomplemented
207C2×C3×Dic3—22no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—21no—
212C2×C3×Dic3—21no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—21no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—21no—
223C2×C3×Dic3—21no—
224C2×C3×Dic3—22no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—32no—
230C2×C3×Dic3—32no—
231C2×C3×Dic3—41no—
232C2×C3×Dic3—41no—
233C2×C3×Dic3—41no—
234C2×C3×Dic3—41no—
235C2×C3×Dic3—62no—
236C2×C3×Dic3—61no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3—61no—
239C2×C3×Dic3—61no—
240C2×C3×Dic3—62no—
241C2×C3×Dic3—61no—
242C2×C3×Dic3—61no—
243C2×C3×Dic3—61no—
244C2×C3×Dic3—61no—
245C2×C3×Dic3—61no—
246C2×C3×Dic3—61no—
247C2×C3×Dic3—121no—
248C2×C3×Dic3—121no—
249C2×C3×Dic3—121no—
250C2×C3×Dic3—121no—
251C2×C3×Dic3Dic612yescomplemented
252C2×C3×Dic3C2×Dic312yes—
253C2×C3×Dic3C2×Dic312yes—
254C2×C3×Dic3#6712yes—
255C2×C3×Dic3#6712yes—
256C2×C3×Dic3C2×C3×C412yes—
257C2×C3×Dic3C2×C3×C412yes—
258C2×C3×Dic3C3×D412yes—
259C2×C3×Dic3C3×D412yes—
260C2×C3×Dic3C3×Q812yescomplemented
261C3×Dic6—216no—
262C3×Dic6—28no—
263C3×Dic6—28no—
264#391—91noSylow
265C2×C33C2×C22⋊C411yescharacteristic
266C2×C33C4×Q811yescharacteristic
267C2×C33C4×Q811yescharacteristic
268C2×C33C22⋊Q811yescharacteristic
269C2×C33C22⋊Q811yescharacteristic
270C2×C33#12411yescharacteristic
271C2×C33C4⋊Q811yescharacteristic
272C2×C3×Q8—34no—
273C2×C3×Q8—34no—
274C2×C3×Q8—64no—
275C2×C3×Q8—62no—
276C2×C3×Q8—62no—
277C2×C3×Q8—62no—
278C2×C3×Q8—62no—
279C2×C3×Q8—64no—
280C2×C3×Q8—64no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—41no—
293C22×C3×C4—61no—
294C22×C3×C4—61no—
295C22×C3×C4—61no—
296C22×C3×C4—61no—
297C22×C3×C4—91no—
298C22×C3×C4—91no—
299C22×C3×C4D3211yescharacteristic
300C22×C3×C4C2×C3×D311yescharacteristic
301C22×C3×C4C2×C3×D311yescharacteristic
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3C2×C3×D311yescharacteristic
309C22×Dic3C2×C3×D311yescharacteristic
310C22×Dic3C2×C3×D311yescharacteristic
311C22×Dic3C2×C3×D311yescharacteristic
312C2×Dic6—22no—
313C2×Dic6—22no—
314C2×Dic6C3×Dic314yescomplemented
315C3×C4⋊C4—182no—
316C3×C42—182no—
317C4⋊Dic3—62no—
318Dic3⋊C4—62no—
319C4×Dic3—62no—
320C4×Dic3—62no—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—21no—
332C22×C32—21no—
333C22×C32—21no—
334C22×C32—21no—
335C22×C32—21no—
336C22×C32—21no—
337C22×C32—21no—
338C22×C32—21no—
339C22×C32—21no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32—41no—
343C22×C32—41no—
344C22×C32—41no—
345C22×C32—41no—
346C22×C32—41no—
347C22×C32—41no—
348C22×C32—41no—
349C22×C32C2×Dic611yescharacteristic
350C22×C32C2×C4×D311yescharacteristic
351C22×C32#23511yescharacteristic
352C22×C32D3×D411yescharacteristic
353C22×C32D3×D411yescharacteristic
354C22×C32#23711yescharacteristic
355C22×C32D3×Q811yescharacteristic
356C22×C32D3×Q811yescharacteristic
357C22×C32D3×Q811yescharacteristic
358C22×C32#23911yescharacteristic
359C22×C32#23911yescharacteristic
360C22×C32C22×Dic311yescharacteristic
361C22×C32C2×#6711yescharacteristic
362C22×C32C2×#6711yescharacteristic
363C22×C32C22×C3×C411yescharacteristic
364C22×C32C2×C3×D411yescharacteristic
365C22×C32C2×C3×D411yescharacteristic
366C22×C32C2×C3×Q811yescharacteristic
367C22×C32C2×C3×Q811yescharacteristic
368C22×C32C3×#4111yescharacteristic
369C22×C32C3×#4111yescharacteristic
370C32×C4—22no—
371C32×C4—24no—
372C32×C4—22no—
373C32×C4—22no—
374C32×C4—34no—
375C32×C4—42no—
376C32×C4—42no—
377C32×C4—44no—
378C32×C4—62no—
379C32×C4—62no—
380C32×C4—121no—
381C3⋊Dic3—22no—
382C3⋊Dic3—41no—
383C3×Dic3—24no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—24no—
389C3×Dic3—42no—
390C3×Dic3—42no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3—62no—
394C3×Dic3—62no—
395C3×Dic3—122no—
396C3×Dic3—122no—
397C3×Dic3—121no—
398C3×Dic3—121no—
399C3×Dic3#21714yes—
400C3×Dic3C3×C22⋊C414yes—
401C22×Q8—31no—
402C2×C4⋊C4—91no—
403C2×C42—91no—
404#95—31no—
405#95—91no—
406#95—91no—
407#95—91no—
408C33#39111yescharacteristic, complemented, Sylow
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—41no—
413C23×C3C2×D3211yescharacteristic
414C23×C3C22×C3×D311yescharacteristic
415C23×C3C22×C3×D311yescharacteristic
416C3×Q8—68no—
417C3×Q8—68no—
418C3×Q8—616no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—32no—
431C2×C3×C4—32no—
432C2×C3×C4—32no—
433C2×C3×C4—32no—
434C2×C3×C4—32no—
435C2×C3×C4—32no—
436C2×C3×C4—32no—
437C2×C3×C4—32no—
438C2×C3×C4—32no—
439C2×C3×C4—32no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—42no—
447C2×C3×C4—62no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—62no—
451C2×C3×C4—62no—
452C2×C3×C4—62no—
453C2×C3×C4—62no—
454C2×C3×C4—61no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—62no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—92no—
470C2×C3×C4—121no—
471C2×C3×C4—121no—
472C2×C3×C4—121no—
473C2×C3×C4—121no—
474C2×C3×C4—181no—
475C2×C3×C4—181no—
476C2×C3×C4—181no—
477C2×C3×C4—181no—
478C2×C3×C4—181no—
479C2×C3×C4D3×Dic312yes—
480C2×C3×C4C3×C4×D312yes—
481C2×C3×C4C2×C3×Dic312yes—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—32no—
490C2×Dic3—32no—
491C2×Dic3—62no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—62no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—121no—
504C2×Dic3—121no—
505C2×Dic3—121no—
506C2×Dic3—121no—
507C2×Dic3C3×Dic612yescomplemented
508C2×Dic3C2×C3×Dic312yes—
509C2×Dic3C2×C3×Dic312yes—
510C2×Dic3C3×#6712yes—
511C2×Dic3C3×#6712yes—
512Dic6—28no—
513C2×C32—21no—
514C2×C32—21no—
515C2×C32—21no—
516C2×C32—21no—
517C2×C32—21no—
518C2×C32—21no—
519C2×C32—21no—
520C2×C32—21no—
521C2×C32—21no—
522C2×C32—21no—
523C2×C32—21no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—41no—
535C2×C32—41no—
536C2×C32—41no—
537C2×C32—41no—
538C2×C32—41no—
539C2×C32—41no—
540C2×C32—41no—
541C2×C32C4×Dic611yescharacteristic
542C2×C32#87811yescharacteristic
543C2×C32D3×C22⋊C411yescharacteristic
544C2×C32#88511yescharacteristic
545C2×C32#88711yescharacteristic
546C2×C32#88811yescharacteristic
547C2×C32#89611yescharacteristic
548C2×C32#94411yescharacteristic
549C2×C32Q8×Dic311yescharacteristic
550C2×C32Q8×Dic311yescharacteristic
551C2×C32#94611yescharacteristic
552C2×C32#94611yescharacteristic
553C2×C32#94711yescharacteristic
554C2×C32C2×#21711yescharacteristic
555C2×C32C2×C3×C22⋊C411yescharacteristic
556C2×C32C3×C4×Q811yescharacteristic
557C2×C32C3×C4×Q811yescharacteristic
558C2×C32C3×C22⋊Q811yescharacteristic
559C2×C32C3×C22⋊Q811yescharacteristic
560C2×C32C3×#12411yescharacteristic
561C2×C32C3×C4⋊Q811yescharacteristic
562C2×Q8—34no—
563C2×Q8—62no—
564C2×Q8—62no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—91no—
570C22×C4—91no—
571C22×C4C3×D3211yescharacteristic
572C4⋊C4—182no—
573C42—182no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—21no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3D3×Dic611yescharacteristic
603C22×C3#379611yescharacteristic
604C22×C3#379711yescharacteristic
605C22×C3#379911yescharacteristic
606C22×C3C2×D3×Dic311yescharacteristic
607C22×C3D3×#6711yescharacteristic
608C22×C3D3×#6711yescharacteristic
609C22×C3C2×C3×Dic611yescharacteristic
610C22×C3C2×C3×C4×D311yescharacteristic
611C22×C3C3×#23511yescharacteristic
612C22×C3C3×D3×D411yescharacteristic
613C22×C3C3×D3×D411yescharacteristic
614C22×C3C3×#23711yescharacteristic
615C22×C3C3×D3×Q811yescharacteristic
616C22×C3C3×D3×Q811yescharacteristic
617C22×C3C3×D3×Q811yescharacteristic
618C22×C3C3×#23911yescharacteristic
619C22×C3C3×#23911yescharacteristic
620C22×C3C22×C3×Dic311yescharacteristic
621C22×C3C2×C3×#6711yescharacteristic
622C22×C3C2×C3×#6711yescharacteristic
623C3×C4—24no—
624C3×C4—22no—
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—34no—
628C3×C4—34no—
629C3×C4—42no—
630C3×C4—42no—
631C3×C4—44no—
632C3×C4—64no—
633C3×C4—64no—
634C3×C4—62no—
635C3×C4—62no—
636C3×C4—62no—
637C3×C4—62no—
638C3×C4—122no—
639C3×C4—122no—
640C3×C4—121no—
641C3×C4—121no—
642C3×C4—182no—
643C3×C4—361no—
644Dic3—22no—
645Dic3—22no—
646Dic3—41no—
647Dic3—62no—
648Dic3—62no—
649Dic3—122no—
650Dic3—122no—
651Dic3—121no—
652Dic3—121no—
653Dic3C3×#21714yes—
654C32—21no—
655C32—21no—
656C32—21no—
657C32—41no—
658C32#464611yescharacteristic, complemented
659C32#522911yescharacteristic, complemented
660C32C3×#39111yescharacteristic, complemented
661C23C2×C3×D3211yescharacteristic
662Q8—68no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—92no—
678C2×C4—181no—
679C2×C4—181no—
680C2×C4—181no—
681C2×C4—181no—
682C2×C4—181no—
683C2×C4C3×D3×Dic312yes—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—21no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—41no—
708C2×C3—41no—
709C2×C3—41no—
710C2×C3—41no—
711C2×C3—41no—
712C2×C3#6383911yescharacteristic
713C2×C3Dic3×Dic611yescharacteristic
714C2×C3#6384311yescharacteristic
715C2×C3#6388711yescharacteristic
716C2×C3#6388811yescharacteristic
717C2×C3#6390711yescharacteristic
718C2×C3D3×#21711yescharacteristic
719C2×C3C3×C4×Dic611yescharacteristic
720C2×C3C3×#87811yescharacteristic
721C2×C3C3×D3×C22⋊C411yescharacteristic
722C2×C3C3×#88511yescharacteristic
723C2×C3C3×#88711yescharacteristic
724C2×C3C3×#88811yescharacteristic
725C2×C3C3×#89611yescharacteristic
726C2×C3C3×#94411yescharacteristic
727C2×C3C3×Q8×Dic311yescharacteristic
728C2×C3C3×Q8×Dic311yescharacteristic
729C2×C3C3×#94611yescharacteristic
730C2×C3C3×#94611yescharacteristic
731C2×C3C3×#94711yescharacteristic
732C2×C3C2×C3×#21711yescharacteristic
733C22C3×D3×Dic611yescharacteristic
734C22C3×#379611yescharacteristic
735C22C3×#379711yescharacteristic
736C22C3×#379911yescharacteristic
737C22C2×C3×D3×Dic311yescharacteristic
738C22C3×D3×#6711yescharacteristic
739C22C3×D3×#6711yescharacteristic
740C4—22no—
741C4—34no—
742C4—62no—
743C4—62no—
744C4—121no—
745C4—182no—
746C4—361no—
747C3—21no—
748C3—21no—
749C3—21no—
750C3—41no—
751C3#1059126111yescharacteristic, direct product factor
752C3C3×#464611yescharacteristic, complemented
753C3C3×#522911yescharacteristic, complemented
754C2C3×#6383911yescharacteristic
755C2C3×Dic3×Dic611yescharacteristic
756C2C3×#6384311yescharacteristic
757C2C3×#6388711yescharacteristic
758C2C3×#6388811yescharacteristic
759C2C3×#6390711yescharacteristic
760C2C3×D3×#21711yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#391
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
10. #10591261C3direct (N × H)
20. C2×C32×Dic6C4semidirect
56. C2×C3×C3⋊Dic3Q8semidirect
68. C2×C32×Dic3Q8semidirect
114. C2×C3×Dic6Dic3semidirect
115. C2×C3×Dic6C3×C4semidirect
206. C2×C3⋊Dic3C3×Q8semidirect
251. C2×C3×Dic3Dic6semidirect
260. C2×C3×Dic3C3×Q8semidirect
314. C2×Dic6C3×Dic3semidirect
408. C33#391semidirect
507. C2×Dic3C3×Dic6semidirect
658. C32#4646semidirect
659. C32#5229semidirect
660. C32C3×#391semidirect
751. C3#10591261direct (N × H)
752. C3C3×#4646semidirect
753. C3C3×#5229semidirect

Maximal subgroups

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

subgroupindex
C22×C32×Dic62
C2×C3×Dic3⋊Dic32
C2×C3×Dic322
C3×#636582
C32×C3⋊#952
C3×#635792
C3×#52293
C3×#46463
#105912613