Finite Group Databasebeta

← C3×#10591342 #13158274

Subgroups — C3×#10591342 #13158274

Order 1728.

930 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3750C211yesmaximal, characteristic
2C2×C32×C4⋊Dic3C211yesmaximal, characteristic
3C2×C32×Dic3⋊C4C211yesmaximal, characteristic
4C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic
5C3×#63579C211yesmaximal, characteristic
6C3×#63579C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8C3×#4982—31nomaximal
9C3×#4981—31nomaximal
10#10591342C311yesmaximal, 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
18C3×#3750—22no—
19C32×C4⋊Dic3—22no—
20C32×Dic3⋊C4—22no—
21C3×Dic3⋊Dic3—22no—
22C2×C32×C4⋊C4—31no—
23C2×C32×C4⋊C4—31no—
24C2×#3750C2×C311yescharacteristic
25C2×C3×C4⋊Dic3—21no—
26C2×C3×C4⋊Dic3—31no—
27C2×C3×C4⋊Dic3D311yescharacteristic
28C2×C3×C4⋊Dic3C2×C311yescharacteristic
29C2×C3×Dic3⋊C4—21no—
30C2×C3×Dic3⋊C4—31no—
31C2×C3×Dic3⋊C4—31no—
32C2×C3×Dic3⋊C4—31no—
33C2×C3×Dic3⋊C4—61no—
34C2×C3×Dic3⋊C4D311yescharacteristic
35C2×C3×Dic3⋊C4C2×C311yescharacteristic
36C2×Dic3⋊Dic3C2×C311yescharacteristic
37C3×C3⋊#95—31no—
38C3×C3⋊#95—31no—
39C3×C3⋊#95—31no—
40C3×C3⋊#95—31no—
41C3×C3⋊#95—31no—
42C3×C3⋊#95—31no—
43#63579C2×C311yescharacteristic
44#63579C2×C311yescharacteristic
45#63579C2×C311yescharacteristic
46C23×C33C2311yescharacteristic
47C2×C33×C4—21no—
48C2×C33×C4—21no—
49C2×C33×C4D412yes—
50C2×C3×C3⋊Dic3—21no—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3—21no—
53C2×C3×C3⋊Dic3—21no—
54C2×C3×C3⋊Dic3—21no—
55C2×C3×C3⋊Dic3Q812yes—
56C2×C32×Dic3—21no—
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×Dic3—21no—
65C2×C32×Dic3—21no—
66C2×C32×Dic3D412yes—
67C2×C32×Dic3Q812yes—
68C3×#398—91no—
69#4982—31no—
70#4981—31no—
71C22×C32×C4—21no—
72C22×C32×C4—21no—
73C22×C32×C4—21no—
74C22×C32×C4—31no—
75C22×C32×C4—31no—
76C22×C32×C4—31no—
77C22×C32×C4—31no—
78C22×C32×C4—41no—
79C22×C32×C4C2×D311yescharacteristic
80C22×C32×C4C2×D311yescharacteristic
81C22×C32×C4C22×C311yescharacteristic
82C22×C3⋊Dic3C22×C311yescharacteristic
83C22×C3⋊Dic3C22×C311yescharacteristic
84C22×C3×Dic3—21no—
85C22×C3×Dic3—21no—
86C22×C3×Dic3—21no—
87C22×C3×Dic3—21no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—31no—
90C22×C3×Dic3—31no—
91C22×C3×Dic3—31no—
92C22×C3×Dic3—61no—
93C22×C3×Dic3—61no—
94C22×C3×Dic3C2×D311yescharacteristic
95C22×C3×Dic3C2×D311yescharacteristic
96C22×C3×Dic3C2×D311yescharacteristic
97C22×C3×Dic3C2×D311yescharacteristic
98C22×C3×Dic3C22×C311yescharacteristic
99C22×C3×Dic3C22×C311yescharacteristic
100C22×C3×Dic3C22×C311yescharacteristic
101C22×C3×Dic3C22×C311yescharacteristic
102C32×C4⋊C4—62no—
103C32×C4⋊C4—62no—
104#3750—22no—
105C3×C4⋊Dic3—24no—
106C3×C4⋊Dic3—22no—
107C3×C4⋊Dic3—22no—
108C3×C4⋊Dic3—62no—
109C3×Dic3⋊C4—24no—
110C3×Dic3⋊C4—22no—
111C3×Dic3⋊C4—22no—
112C3×Dic3⋊C4—64no—
113C3×Dic3⋊C4—62no—
114C3×Dic3⋊C4—62no—
115C3×Dic3⋊C4—62no—
116Dic3⋊Dic3—22no—
117C22×C33C2×D411yescharacteristic
118C22×C33C2×D411yescharacteristic
119C22×C33C2×Q811yescharacteristic
120C22×C33C2×Q811yescharacteristic
121C22×C33#4111yescharacteristic
122C22×C33#4111yescharacteristic
123C22×C33#4111yescharacteristic
124C33×C4—22no—
125C3×C3⋊Dic3—22no—
126C3×C3⋊Dic3—41no—
127C32×Dic3—22no—
128C32×Dic3—22no—
129C32×Dic3—41no—
130C32×Dic3—41no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—61no—
136C2×C3×C4⋊C4—61no—
137C2×C3×C4⋊C4—91no—
138C2×C3×C4⋊C4—91no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3C3×D311yescharacteristic
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—61no—
145C2×Dic3⋊C4C3×D311yescharacteristic
146C3×#95—91no—
147C3×#95—91no—
148C3×#95—91no—
149C3⋊#95—31no—
150C3⋊#95—31no—
151C3⋊#95—31no—
152C3⋊#95—31no—
153C3⋊#95—31no—
154C3⋊#95—31no—
155C23×C32—21no—
156C23×C32—21no—
157C23×C32—21no—
158C23×C32—41no—
159C23×C32C22×D311yescharacteristic
160C23×C32C22×D311yescharacteristic
161C23×C32C23×C311yescharacteristic
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—32no—
174C2×C32×C4—32no—
175C2×C32×C4—42no—
176C2×C32×C4—41no—
177C2×C32×C4—41no—
178C2×C32×C4—41no—
179C2×C32×C4—41no—
180C2×C32×C4—42no—
181C2×C32×C4—42no—
182C2×C32×C4—61no—
183C2×C32×C4—61no—
184C2×C32×C4—61no—
185C2×C32×C4—61no—
186C2×C32×C4—61no—
187C2×C32×C4—61no—
188C2×C32×C4—61no—
189C2×C32×C4—61no—
190C2×C32×C4—61no—
191C2×C32×C4—61no—
192C2×C32×C4D1212yes—
193C2×C32×C4#6712yes—
194C2×C32×C4C3×D412yes—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3C3×Q812yes—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3—21no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—22no—
212C2×C3×Dic3—22no—
213C2×C3×Dic3—21no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—21no—
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—21no—
225C2×C3×Dic3—22no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—32no—
228C2×C3×Dic3—32no—
229C2×C3×Dic3—41no—
230C2×C3×Dic3—41no—
231C2×C3×Dic3—41no—
232C2×C3×Dic3—41no—
233C2×C3×Dic3—41no—
234C2×C3×Dic3—41no—
235C2×C3×Dic3—62no—
236C2×C3×Dic3—62no—
237C2×C3×Dic3—62no—
238C2×C3×Dic3—61no—
239C2×C3×Dic3—61no—
240C2×C3×Dic3—61no—
241C2×C3×Dic3—61no—
242C2×C3×Dic3—62no—
243C2×C3×Dic3—61no—
244C2×C3×Dic3—61no—
245C2×C3×Dic3—61no—
246C2×C3×Dic3—61no—
247C2×C3×Dic3—61no—
248C2×C3×Dic3—61no—
249C2×C3×Dic3—121no—
250C2×C3×Dic3—121no—
251C2×C3×Dic3Dic612yes—
252C2×C3×Dic3#6712yes—
253C2×C3×Dic3C3×D412yes—
254C2×C3×Dic3C3×Q812yes—
255#398—91noSylow
256C2×C33#12111yescharacteristic
257C2×C33C22⋊Q811yescharacteristic
258C2×C33C22⋊Q811yescharacteristic
259C2×C33#12311yescharacteristic
260C2×C33#12511yescharacteristic
261C2×C33#12511yescharacteristic
262C2×C33C4⋊Q811yescharacteristic
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—31no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—31no—
270C22×C3×C4—31no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—41no—
275C22×C3×C4—61no—
276C22×C3×C4—61no—
277C22×C3×C4—61no—
278C22×C3×C4—61no—
279C22×C3×C4—91no—
280C22×C3×C4—91no—
281C22×C3×C4D3211yescharacteristic
282C22×C3×C4C2×C3×D311yescharacteristic
283C22×C3×C4C2×C3×D311yescharacteristic
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—61no—
289C22×Dic3—61no—
290C22×Dic3C2×C3×D311yescharacteristic
291C22×Dic3C2×C3×D311yescharacteristic
292C22×Dic3C2×C3×D311yescharacteristic
293C22×Dic3C2×C3×D311yescharacteristic
294C3×C4⋊C4—62no—
295C3×C4⋊C4—62no—
296C3×C4⋊C4—64no—
297C3×C4⋊C4—64no—
298C3×C4⋊C4—62no—
299C3×C4⋊C4—62no—
300C3×C4⋊C4—182no—
301C3×C4⋊C4—182no—
302C4⋊Dic3—22no—
303C4⋊Dic3—62no—
304Dic3⋊C4—22no—
305Dic3⋊C4—64no—
306Dic3⋊C4—62no—
307Dic3⋊C4—62no—
308Dic3⋊C4—62no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—21no—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—21no—
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—41no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32—41no—
334C22×C32—41no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32C2×Dic611yescharacteristic
338C22×C32C2×D1211yescharacteristic
339C22×C32#23511yescharacteristic
340C22×C32#23511yescharacteristic
341C22×C32D3×D411yescharacteristic
342C22×C32#23711yescharacteristic
343C22×C32#23711yescharacteristic
344C22×C32#23711yescharacteristic
345C22×C32D3×Q811yescharacteristic
346C22×C32D3×Q811yescharacteristic
347C22×C32D3×Q811yescharacteristic
348C22×C32#23911yescharacteristic
349C22×C32C2×#6711yescharacteristic
350C22×C32C2×#6711yescharacteristic
351C22×C32C2×C3×D411yescharacteristic
352C22×C32C2×C3×D411yescharacteristic
353C22×C32C2×C3×Q811yescharacteristic
354C22×C32C2×C3×Q811yescharacteristic
355C22×C32C3×#4111yescharacteristic
356C22×C32C3×#4111yescharacteristic
357C22×C32C3×#4111yescharacteristic
358C32×C4—22no—
359C32×C4—24no—
360C32×C4—22no—
361C32×C4—22no—
362C32×C4—42no—
363C32×C4—42no—
364C32×C4—44no—
365C32×C4—62no—
366C32×C4—62no—
367C32×C4—121no—
368C32×C4—121no—
369C3⋊Dic3—22no—
370C3⋊Dic3—41no—
371C3×Dic3—24no—
372C3×Dic3—22no—
373C3×Dic3—22no—
374C3×Dic3—22no—
375C3×Dic3—22no—
376C3×Dic3—42no—
377C3×Dic3—42no—
378C3×Dic3—42no—
379C3×Dic3—41no—
380C3×Dic3—41no—
381C3×Dic3—41no—
382C3×Dic3—41no—
383C3×Dic3—64no—
384C3×Dic3—62no—
385C3×Dic3—62no—
386C3×Dic3—122no—
387C3×Dic3—121no—
388C3×Dic3—121no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—91no—
392C2×C4⋊C4—91no—
393#95—91no—
394#95—91no—
395#95—91no—
396C33#39811yescharacteristic, complemented, Sylow
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—41no—
401C23×C3C2×D3211yescharacteristic
402C23×C3C22×C3×D311yescharacteristic
403C23×C3C22×C3×D311yescharacteristic
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—32no—
418C2×C3×C4—32no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—62no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—61no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—61no—
436C2×C3×C4—61no—
437C2×C3×C4—61no—
438C2×C3×C4—62no—
439C2×C3×C4—62no—
440C2×C3×C4—61no—
441C2×C3×C4—61no—
442C2×C3×C4—61no—
443C2×C3×C4—61no—
444C2×C3×C4—61no—
445C2×C3×C4—61no—
446C2×C3×C4—61no—
447C2×C3×C4—61no—
448C2×C3×C4—61no—
449C2×C3×C4—61no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—92no—
453C2×C3×C4—121no—
454C2×C3×C4—121no—
455C2×C3×C4—121no—
456C2×C3×C4—121no—
457C2×C3×C4—121no—
458C2×C3×C4—121no—
459C2×C3×C4—181no—
460C2×C3×C4—181no—
461C2×C3×C4—181no—
462C2×C3×C4—181no—
463C2×C3×C4—181no—
464C2×C3×C4#62612yes—
465C2×C3×C4C3×D1212yes—
466C2×C3×C4C3×#6712yes—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—32no—
478C2×Dic3—32no—
479C2×Dic3—62no—
480C2×Dic3—62no—
481C2×Dic3—62no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—62no—
487C2×Dic3—61no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—121no—
494C2×Dic3—121no—
495C2×Dic3C3×Dic612yes—
496C2×Dic3C3×#6712yes—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—21no—
510C2×C32—21no—
511C2×C32—21no—
512C2×C32—21no—
513C2×C32—21no—
514C2×C32—21no—
515C2×C32—21no—
516C2×C32—21no—
517C2×C32—21no—
518C2×C32—41no—
519C2×C32—41no—
520C2×C32—41no—
521C2×C32—41no—
522C2×C32—41no—
523C2×C32—41no—
524C2×C32—41no—
525C2×C32#88811yescharacteristic
526C2×C32#88911yescharacteristic
527C2×C32#88911yescharacteristic
528C2×C32#88911yescharacteristic
529C2×C32#89011yescharacteristic
530C2×C32#89411yescharacteristic
531C2×C32#89711yescharacteristic
532C2×C32#89711yescharacteristic
533C2×C32#92411yescharacteristic
534C2×C32#93011yescharacteristic
535C2×C32#93511yescharacteristic
536C2×C32#93911yescharacteristic
537C2×C32#94411yescharacteristic
538C2×C32#94611yescharacteristic
539C2×C32C3×#12111yescharacteristic
540C2×C32C3×C22⋊Q811yescharacteristic
541C2×C32C3×C22⋊Q811yescharacteristic
542C2×C32C3×#12311yescharacteristic
543C2×C32C3×#12511yescharacteristic
544C2×C32C3×#12511yescharacteristic
545C2×C32C3×C4⋊Q811yescharacteristic
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—91no—
551C22×C4—91no—
552C22×C4C3×D3211yescharacteristic
553C4⋊C4—62no—
554C4⋊C4—62no—
555C4⋊C4—182no—
556C4⋊C4—182no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3D3×Dic611yescharacteristic
586C22×C3#379511yescharacteristic
587C22×C3#379611yescharacteristic
588C22×C3#379711yescharacteristic
589C22×C3#380411yescharacteristic
590C22×C3C2×#62611yescharacteristic
591C22×C3D3×#6711yescharacteristic
592C22×C3C2×C3×Dic611yescharacteristic
593C22×C3C2×C3×D1211yescharacteristic
594C22×C3C3×#23511yescharacteristic
595C22×C3C3×#23511yescharacteristic
596C22×C3C3×D3×D411yescharacteristic
597C22×C3C3×#23711yescharacteristic
598C22×C3C3×#23711yescharacteristic
599C22×C3C3×#23711yescharacteristic
600C22×C3C3×D3×Q811yescharacteristic
601C22×C3C3×D3×Q811yescharacteristic
602C22×C3C3×D3×Q811yescharacteristic
603C22×C3C3×#23911yescharacteristic
604C22×C3C2×C3×#6711yescharacteristic
605C22×C3C2×C3×#6711yescharacteristic
606C3×C4—24no—
607C3×C4—22no—
608C3×C4—22no—
609C3×C4—22no—
610C3×C4—42no—
611C3×C4—42no—
612C3×C4—44no—
613C3×C4—64no—
614C3×C4—62no—
615C3×C4—62no—
616C3×C4—62no—
617C3×C4—62no—
618C3×C4—122no—
619C3×C4—122no—
620C3×C4—122no—
621C3×C4—121no—
622C3×C4—121no—
623C3×C4—121no—
624C3×C4—121no—
625C3×C4—182no—
626C3×C4—361no—
627Dic3—22no—
628Dic3—22no—
629Dic3—41no—
630Dic3—41no—
631Dic3—64no—
632Dic3—62no—
633Dic3—62no—
634Dic3—122no—
635Dic3—121no—
636Dic3—121no—
637C32—21no—
638C32—21no—
639C32—21no—
640C32—41no—
641C32#498111yescharacteristic, complemented
642C32#498211yescharacteristic, complemented
643C32C3×#39811yescharacteristic, complemented
644C23C2×C3×D3211yescharacteristic
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—32no—
648C2×C4—32no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—92no—
660C2×C4—181no—
661C2×C4—181no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4C3×#62612yes—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—41no—
688C2×C3—41no—
689C2×C3—41no—
690C2×C3—41no—
691C2×C3—41no—
692C2×C3—41no—
693C2×C3—41no—
694C2×C3#6383911yescharacteristic
695C2×C3#6384611yescharacteristic
696C2×C3#6384711yescharacteristic
697C2×C3#6385711yescharacteristic
698C2×C3#6387111yescharacteristic
699C2×C3#6388411yescharacteristic
700C2×C3#6397811yescharacteristic
701C2×C3C3×#88811yescharacteristic
702C2×C3C3×#88911yescharacteristic
703C2×C3C3×#88911yescharacteristic
704C2×C3C3×#88911yescharacteristic
705C2×C3C3×#89011yescharacteristic
706C2×C3C3×#89411yescharacteristic
707C2×C3C3×#89711yescharacteristic
708C2×C3C3×#89711yescharacteristic
709C2×C3C3×#92411yescharacteristic
710C2×C3C3×#93011yescharacteristic
711C2×C3C3×#93511yescharacteristic
712C2×C3C3×#93911yescharacteristic
713C2×C3C3×#94411yescharacteristic
714C2×C3C3×#94611yescharacteristic
715C22C3×D3×Dic611yescharacteristic
716C22C3×#379511yescharacteristic
717C22C3×#379611yescharacteristic
718C22C3×#379711yescharacteristic
719C22C3×#380411yescharacteristic
720C22C2×C3×#62611yescharacteristic
721C22C3×D3×#6711yescharacteristic
722C4—22no—
723C4—62no—
724C4—62no—
725C4—121no—
726C4—121no—
727C4—182no—
728C4—361no—
729C3—21no—
730C3—21no—
731C3—21no—
732C3—41no—
733C3#1059134211yescharacteristic, direct product factor
734C3C3×#498111yescharacteristic, complemented
735C3C3×#498211yescharacteristic, complemented
736C2C3×#6383911yescharacteristic
737C2C3×#6384611yescharacteristic
738C2C3×#6384711yescharacteristic
739C2C3×#6385711yescharacteristic
740C2C3×#6387111yescharacteristic
741C2C3×#6388411yescharacteristic
742C2C3×#6397811yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutator, cosocleC23×C32C23×C3
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
hypercenterC22×C3×C4D32
hypocenterC32C3×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
10. #10591342C3direct (N × H)
396. C33#398semidirect
641. C32#4981semidirect
642. C32#4982semidirect
643. C32C3×#398semidirect
733. C3#10591342direct (N × H)
734. C3C3×#4981semidirect
735. C3C3×#4982semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37502
C2×C32×C4⋊Dic32
C2×C32×Dic3⋊C42
C2×C3×Dic3⋊Dic32
C3×#635792
C3×#49823
C3×#49813
#105913423