Finite Group Databasebeta

← C3×#10591248 #13158180

Subgroups — C3×#10591248 #13158180

Order 1728.

834 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Dic32C211yesmaximal, characteristic
2C3×#63658C211yesmaximal, characteristic
3C32×C3⋊#95C211yesmaximal, characteristic
4C32×C3⋊#95C211yesmaximal, characteristic
5C3×#63579C211yesmaximal, characteristic
6C3×#63579C211yesmaximal, characteristic
7C3×#63579C211yesmaximal, characteristic
8C3×#4651—31nomaximal
9C3×#4651—31nomaximal
10#10591248C311yesmaximal, 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×Dic32C414yescomplemented
19C2×C3×C4×Dic3—31no—
20C2×C3×C4×Dic3—31no—
21C2×Dic32C2×C311yescharacteristic
22C32×#95—31no—
23C32×#95—31no—
24#63658C2×C311yescharacteristic
25C3×C3⋊#95—21no—
26C3×C3⋊#95—21no—
27C3×C3⋊#95—31no—
28C3×C3⋊#95—31no—
29C3×C3⋊#95—31no—
30C3×C3⋊#95—31no—
31C3×C3⋊#95—31no—
32C3×C3⋊#95—31no—
33C3×C3⋊#95—31no—
34C3×C3⋊#95—31no—
35C3×C3⋊#95—61no—
36C3×C3⋊#95D311yescharacteristic
37C3×C3⋊#95D311yescharacteristic
38C3×C3⋊#95C2×C311yescharacteristic
39C3×C3⋊#95C2×C311yescharacteristic
40#63579C2×C311yescharacteristic
41#63579C2×C311yescharacteristic
42#63579C2×C311yescharacteristic
43C23×C33C2311yescharacteristic
44C2×C33×C4—21no—
45C2×C33×C4—21no—
46C2×C33×C4—21no—
47C2×C3×C3⋊Dic3—21no—
48C2×C3×C3⋊Dic3—21no—
49C2×C3×C3⋊Dic3—21no—
50C2×C3×C3⋊Dic3—21no—
51C2×C3×C3⋊Dic3—21no—
52C2×C3×C3⋊Dic3C2×C412yes—
53C2×C32×Dic3—21no—
54C2×C32×Dic3—21no—
55C2×C32×Dic3—21no—
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×Dic3C2×C412yes—
64C2×C32×Dic3C2×C412yes—
65C3×#383—91no—
66#4651—31no—
67#4651—31no—
68C22×C32×C4—21no—
69C22×C32×C4—21no—
70C22×C32×C4—21no—
71C22×C32×C4—31no—
72C22×C32×C4—31no—
73C22×C32×C4—31no—
74C22×C32×C4—31no—
75C22×C32×C4—41no—
76C22×C32×C4C2×D311yescharacteristic
77C22×C32×C4C2×D311yescharacteristic
78C22×C32×C4C22×C311yescharacteristic
79C22×C3⋊Dic3C22×C311yescharacteristic
80C22×C3⋊Dic3C22×C311yescharacteristic
81C22×C3×Dic3—21no—
82C22×C3×Dic3—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85C22×C3×Dic3—31no—
86C22×C3×Dic3—31no—
87C22×C3×Dic3—31no—
88C22×C3×Dic3—31no—
89C22×C3×Dic3—61no—
90C22×C3×Dic3—61no—
91C22×C3×Dic3C2×D311yescharacteristic
92C22×C3×Dic3C2×D311yescharacteristic
93C22×C3×Dic3C2×D311yescharacteristic
94C22×C3×Dic3C2×D311yescharacteristic
95C22×C3×Dic3C22×C311yescharacteristic
96C22×C3×Dic3C22×C311yescharacteristic
97C22×C3×Dic3C22×C311yescharacteristic
98C22×C3×Dic3C22×C311yescharacteristic
99C3×C4×Dic3—34no—
100C3×C4×Dic3—34no—
101Dic32C3×C414yescomplemented
102C22×C33C22×C411yescharacteristic
103C22×C33#4111yescharacteristic
104C22×C33#4111yescharacteristic
105C22×C33#4111yescharacteristic
106C22×C33#4111yescharacteristic
107C22×C33#4111yescharacteristic
108C22×C33#4111yescharacteristic
109C33×C4—41no—
110C3×C3⋊Dic3—22no—
111C3×C3⋊Dic3—41no—
112C32×Dic3—22no—
113C32×Dic3—22no—
114C32×Dic3—41no—
115C32×Dic3—41no—
116C2×C3×C42—91no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C3×#95—31no—
120C3×#95—31no—
121C3×#95—31no—
122C3×#95—31no—
123C3×#95—61no—
124C3×#95—61no—
125C3×#95—91no—
126C3×#95—91no—
127C3×#95—91no—
128C3×#95—91no—
129C3⋊#95—31no—
130C3⋊#95—31no—
131C3⋊#95—31no—
132C3⋊#95—31no—
133C3⋊#95—31no—
134C3⋊#95—31no—
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—61no—
138C3⋊#95C3×D311yescharacteristic
139C3⋊#95C3×D311yescharacteristic
140C23×C32—21no—
141C23×C32—21no—
142C23×C32—21no—
143C23×C32—41no—
144C23×C32C22×D311yescharacteristic
145C23×C32C22×D311yescharacteristic
146C23×C32C23×C311yescharacteristic
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—21no—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—32no—
160C2×C32×C4—32no—
161C2×C32×C4—41no—
162C2×C32×C4—41no—
163C2×C32×C4—41no—
164C2×C32×C4—41no—
165C2×C32×C4—41no—
166C2×C32×C4—41no—
167C2×C32×C4—42no—
168C2×C32×C4—42no—
169C2×C32×C4—42no—
170C2×C32×C4—61no—
171C2×C32×C4—61no—
172C2×C32×C4—61no—
173C2×C32×C4—61no—
174C2×C32×C4—61no—
175C2×C32×C4—61no—
176C2×C32×C4—61no—
177C2×C32×C4—61no—
178C2×C32×C4—61no—
179C2×C32×C4—61no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3C2×C3×C412yes—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—21no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—32no—
211C2×C3×Dic3—32no—
212C2×C3×Dic3—41no—
213C2×C3×Dic3—41no—
214C2×C3×Dic3—41no—
215C2×C3×Dic3—41no—
216C2×C3×Dic3—41no—
217C2×C3×Dic3—41no—
218C2×C3×Dic3—41no—
219C2×C3×Dic3—41no—
220C2×C3×Dic3—62no—
221C2×C3×Dic3—61no—
222C2×C3×Dic3—61no—
223C2×C3×Dic3—61no—
224C2×C3×Dic3—61no—
225C2×C3×Dic3—62no—
226C2×C3×Dic3—61no—
227C2×C3×Dic3—61no—
228C2×C3×Dic3—61no—
229C2×C3×Dic3—61no—
230C2×C3×Dic3—61no—
231C2×C3×Dic3—61no—
232C2×C3×Dic3—121no—
233C2×C3×Dic3—121no—
234C2×C3×Dic3—121no—
235C2×C3×Dic3—121no—
236C2×C3×Dic3C4×D312yes—
237C2×C3×Dic3C4×D312yes—
238C2×C3×Dic3C2×C3×C412yes—
239C2×C3×Dic3C2×C3×C412yes—
240#383—91noSylow
241C2×C33#11711yescharacteristic
242C2×C33#11711yescharacteristic
243C2×C33#11711yescharacteristic
244C2×C33#12611yescharacteristic
245C2×C33#12611yescharacteristic
246C2×C33#12611yescharacteristic
247C2×C33#12611yescharacteristic
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4—31no—
255C22×C3×C4—31no—
256C22×C3×C4—31no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—41no—
260C22×C3×C4—61no—
261C22×C3×C4—61no—
262C22×C3×C4—61no—
263C22×C3×C4—61no—
264C22×C3×C4—91no—
265C22×C3×C4—91no—
266C22×C3×C4D3211yescharacteristic
267C22×C3×C4C2×C3×D311yescharacteristic
268C22×C3×C4C2×C3×D311yescharacteristic
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—31no—
273C22×Dic3—61no—
274C22×Dic3—61no—
275C22×Dic3C2×C3×D311yescharacteristic
276C22×Dic3C2×C3×D311yescharacteristic
277C22×Dic3C2×C3×D311yescharacteristic
278C22×Dic3C2×C3×D311yescharacteristic
279C3×C42—94no—
280C4×Dic3—34no—
281C4×Dic3—34no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32—21no—
286C22×C32—21no—
287C22×C32—21no—
288C22×C32—21no—
289C22×C32—21no—
290C22×C32—21no—
291C22×C32—21no—
292C22×C32—21no—
293C22×C32—21no—
294C22×C32—21no—
295C22×C32—21no—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32—21no—
299C22×C32—21no—
300C22×C32—21no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32—41no—
304C22×C32—41no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32C2×C4×D311yescharacteristic
311C22×C32C2×C4×D311yescharacteristic
312C22×C32#23511yescharacteristic
313C22×C32#23511yescharacteristic
314C22×C32#23511yescharacteristic
315C22×C32#23511yescharacteristic
316C22×C32#23711yescharacteristic
317C22×C32#23711yescharacteristic
318C22×C32#23711yescharacteristic
319C22×C32#23711yescharacteristic
320C22×C32#23711yescharacteristic
321C22×C32#23711yescharacteristic
322C22×C32#23911yescharacteristic
323C22×C32#23911yescharacteristic
324C22×C32C22×C3×C411yescharacteristic
325C22×C32C3×#4111yescharacteristic
326C22×C32C3×#4111yescharacteristic
327C22×C32C3×#4111yescharacteristic
328C22×C32C3×#4111yescharacteristic
329C22×C32C3×#4111yescharacteristic
330C22×C32C3×#4111yescharacteristic
331C32×C4—42no—
332C32×C4—42no—
333C32×C4—42no—
334C32×C4—44no—
335C32×C4—41no—
336C32×C4—41no—
337C32×C4—41no—
338C32×C4—62no—
339C32×C4—62no—
340C32×C4—121no—
341C32×C4—121no—
342C3⋊Dic3—22no—
343C3⋊Dic3—41no—
344C3×Dic3—22no—
345C3×Dic3—22no—
346C3×Dic3—22no—
347C3×Dic3—22no—
348C3×Dic3—42no—
349C3×Dic3—42no—
350C3×Dic3—42no—
351C3×Dic3—42no—
352C3×Dic3—41no—
353C3×Dic3—41no—
354C3×Dic3—41no—
355C3×Dic3—41no—
356C3×Dic3—62no—
357C3×Dic3—62no—
358C3×Dic3—122no—
359C3×Dic3—122no—
360C3×Dic3—121no—
361C3×Dic3—121no—
362C2×C42—91no—
363#95—31no—
364#95—31no—
365#95—91no—
366#95—91no—
367#95—91no—
368#95—91no—
369C33#38311yescharacteristic, complemented, Sylow
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—41no—
374C23×C3C2×D3211yescharacteristic
375C23×C3C22×C3×D311yescharacteristic
376C23×C3C22×C3×D311yescharacteristic
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—32no—
390C2×C3×C4—32no—
391C2×C3×C4—32no—
392C2×C3×C4—32no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—61no—
409C2×C3×C4—61no—
410C2×C3×C4—61no—
411C2×C3×C4—61no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—61no—
421C2×C3×C4—61no—
422C2×C3×C4—61no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—61no—
426C2×C3×C4—92no—
427C2×C3×C4—121no—
428C2×C3×C4—121no—
429C2×C3×C4—121no—
430C2×C3×C4—121no—
431C2×C3×C4—121no—
432C2×C3×C4—121no—
433C2×C3×C4—121no—
434C2×C3×C4—121no—
435C2×C3×C4—181no—
436C2×C3×C4—181no—
437C2×C3×C4—181no—
438C2×C3×C4—181no—
439C2×C3×C4—181no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—32no—
451C2×Dic3—32no—
452C2×Dic3—62no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455C2×Dic3—61no—
456C2×Dic3—61no—
457C2×Dic3—62no—
458C2×Dic3—61no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—61no—
462C2×Dic3—61no—
463C2×Dic3—61no—
464C2×Dic3—121no—
465C2×Dic3—121no—
466C2×Dic3—121no—
467C2×Dic3—121no—
468C2×Dic3C3×C4×D312yes—
469C2×Dic3C3×C4×D312yes—
470C2×C32—21no—
471C2×C32—21no—
472C2×C32—21no—
473C2×C32—21no—
474C2×C32—21no—
475C2×C32—21no—
476C2×C32—21no—
477C2×C32—21no—
478C2×C32—21no—
479C2×C32—21no—
480C2×C32—21no—
481C2×C32—21no—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—21no—
488C2×C32—21no—
489C2×C32—21no—
490C2×C32—21no—
491C2×C32—41no—
492C2×C32—41no—
493C2×C32—41no—
494C2×C32—41no—
495C2×C32—41no—
496C2×C32—41no—
497C2×C32—41no—
498C2×C32#87211yescharacteristic
499C2×C32#87211yescharacteristic
500C2×C32#87711yescharacteristic
501C2×C32#87711yescharacteristic
502C2×C32#87911yescharacteristic
503C2×C32#87911yescharacteristic
504C2×C32#87911yescharacteristic
505C2×C32#87911yescharacteristic
506C2×C32#89211yescharacteristic
507C2×C32#89211yescharacteristic
508C2×C32#89811yescharacteristic
509C2×C32#89811yescharacteristic
510C2×C32#89811yescharacteristic
511C2×C32#89811yescharacteristic
512C2×C32C3×#11711yescharacteristic
513C2×C32C3×#11711yescharacteristic
514C2×C32C3×#11711yescharacteristic
515C2×C32C3×#12611yescharacteristic
516C2×C32C3×#12611yescharacteristic
517C2×C32C3×#12611yescharacteristic
518C2×C32C3×#12611yescharacteristic
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4C3×D3211yescharacteristic
526C42—94no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—21no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—41no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3#379511yescharacteristic
556C22×C3#379611yescharacteristic
557C22×C3#379911yescharacteristic
558C22×C3C4×D3211yescharacteristic
559C22×C3#380411yescharacteristic
560C22×C3#380411yescharacteristic
561C22×C3#380511yescharacteristic
562C22×C3C2×C3×C4×D311yescharacteristic
563C22×C3C2×C3×C4×D311yescharacteristic
564C22×C3C3×#23511yescharacteristic
565C22×C3C3×#23511yescharacteristic
566C22×C3C3×#23511yescharacteristic
567C22×C3C3×#23511yescharacteristic
568C22×C3C3×#23711yescharacteristic
569C22×C3C3×#23711yescharacteristic
570C22×C3C3×#23711yescharacteristic
571C22×C3C3×#23711yescharacteristic
572C22×C3C3×#23711yescharacteristic
573C22×C3C3×#23711yescharacteristic
574C22×C3C3×#23911yescharacteristic
575C22×C3C3×#23911yescharacteristic
576C3×C4—42no—
577C3×C4—42no—
578C3×C4—42no—
579C3×C4—44no—
580C3×C4—41no—
581C3×C4—41no—
582C3×C4—41no—
583C3×C4—62no—
584C3×C4—62no—
585C3×C4—62no—
586C3×C4—62no—
587C3×C4—122no—
588C3×C4—122no—
589C3×C4—122no—
590C3×C4—122no—
591C3×C4—121no—
592C3×C4—121no—
593C3×C4—121no—
594C3×C4—121no—
595C3×C4—182no—
596C3×C4—361no—
597Dic3—22no—
598Dic3—22no—
599Dic3—41no—
600Dic3—41no—
601Dic3—62no—
602Dic3—62no—
603Dic3—122no—
604Dic3—122no—
605Dic3—121no—
606Dic3—121no—
607C32—21no—
608C32—21no—
609C32—21no—
610C32—41no—
611C32#465111yescharacteristic, complemented
612C32#465111yescharacteristic, complemented
613C32C3×#38311yescharacteristic, complemented
614C23C2×C3×D3211yescharacteristic
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—32no—
619C2×C4—32no—
620C2×C4—61no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—92no—
631C2×C4—181no—
632C2×C4—181no—
633C2×C4—181no—
634C2×C4—181no—
635C2×C4—181no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—41no—
658C2×C3—41no—
659C2×C3—41no—
660C2×C3—41no—
661C2×C3—41no—
662C2×C3—41no—
663C2×C3—41no—
664C2×C3#6383611yescharacteristic
665C2×C3#6384811yescharacteristic
666C2×C3#6385811yescharacteristic
667C2×C3#6386111yescharacteristic
668C2×C3#6387711yescharacteristic
669C2×C3#6387811yescharacteristic
670C2×C3#6395611yescharacteristic
671C2×C3C3×#87211yescharacteristic
672C2×C3C3×#87211yescharacteristic
673C2×C3C3×#87711yescharacteristic
674C2×C3C3×#87711yescharacteristic
675C2×C3C3×#87911yescharacteristic
676C2×C3C3×#87911yescharacteristic
677C2×C3C3×#87911yescharacteristic
678C2×C3C3×#87911yescharacteristic
679C2×C3C3×#89211yescharacteristic
680C2×C3C3×#89211yescharacteristic
681C2×C3C3×#89811yescharacteristic
682C2×C3C3×#89811yescharacteristic
683C2×C3C3×#89811yescharacteristic
684C2×C3C3×#89811yescharacteristic
685C22C3×#379511yescharacteristic
686C22C3×#379611yescharacteristic
687C22C3×#379911yescharacteristic
688C22C3×C4×D3211yescharacteristic
689C22C3×#380411yescharacteristic
690C22C3×#380411yescharacteristic
691C22C3×#380511yescharacteristic
692C4—41no—
693C4—62no—
694C4—62no—
695C4—121no—
696C4—121no—
697C4—182no—
698C4—361no—
699C3—21no—
700C3—21no—
701C3—21no—
702C3—41no—
703C3#1059124811yescharacteristic, direct product factor
704C3C3×#465111yescharacteristic, complemented
705C3C3×#465111yescharacteristic, complemented
706C2C3×#6383611yescharacteristic
707C2C3×#6384811yescharacteristic
708C2C3×#6385811yescharacteristic
709C2C3×#6386111yescharacteristic
710C2C3×#6387711yescharacteristic
711C2C3×#6387811yescharacteristic
712C2C3×#6395611yescharacteristic
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×#383
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. #10591248C3direct (N × H)
18. C3×Dic32C4semidirect
101. Dic32C3×C4semidirect
369. C33#383semidirect
611. C32#4651semidirect
612. C32#4651semidirect
613. C32C3×#383semidirect
703. C3#10591248direct (N × H)
704. C3C3×#4651semidirect
705. C3C3×#4651semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Dic322
C3×#636582
C32×C3⋊#952
C3×#635792
C3×#46513
#105912483