Finite Group Databasebeta

← C3×#16641 #10635248

Subgroups — C3×#16641 #10635248

Order 768.

1050 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#400C211yesmaximal, characteristic
2C2×C3×#387C211yesmaximal, characteristic
3C3×#1445C211yesmaximal, characteristic
4C3×#1445C211yesmaximal, characteristic
5C3×#1445C211yesmaximal, characteristic
6C3×#1444C211yesmaximal, characteristic
7C3×#1443C211yesmaximal, characteristic
8C3×#1443C211yesmaximal, characteristic
9C3×#1442C211yesmaximal, characteristic
10C3×#1442C211yesmaximal, characteristic
11C3×#1442C211yesmaximal, characteristic
12C3×#1442C211yesmaximal, characteristic
13C3×#1441C211yesmaximal, characteristic
14C3×#1436C211yesmaximal, characteristic
15C3×#1436C211yesmaximal, characteristic
16#16641C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×C4⋊C4C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C42C2211yescharacteristic
24C3×#400—24no—
25C3×#387—24no—
26C2×C3×#95C2211yescharacteristic
27C2×C3×#95C2211yescharacteristic
28C2×C3×#95C2211yescharacteristic
29C2×C3×#95C2211yescharacteristic
30C2×C3×#95C2211yescharacteristic
31C2×C3×#95C2211yescharacteristic
32C2×C3×#95C2211yescharacteristic
33C2×C3×#95C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3×#95C2211yescharacteristic
45C2×C3×#95C2211yescharacteristic
46C2×C3×#95C2211yescharacteristic
47C2×C3×#95C2211yescharacteristic
48C2×C3×#95C2211yescharacteristic
49C2×C3×#95C2211yescharacteristic
50C2×C3×#95C2211yescharacteristic
51C2×C3×#95C2211yescharacteristic
52C2×C3×#95C2211yescharacteristic
53C2×C3×#95C2211yescharacteristic
54C2×#400C2×C311yescharacteristic
55C2×#387C2×C311yescharacteristic
56#1445C2×C311yescharacteristic
57#1445C2×C311yescharacteristic
58#1445C2×C311yescharacteristic
59#1444C2×C311yescharacteristic
60#1443C2×C311yescharacteristic
61#1443C2×C311yescharacteristic
62#1442C2×C311yescharacteristic
63#1442C2×C311yescharacteristic
64#1442C2×C311yescharacteristic
65#1442C2×C311yescharacteristic
66#1441C2×C311yescharacteristic
67#1436C2×C311yescharacteristic
68#1436C2×C311yescharacteristic
69C23×C3×C4C2311yescharacteristic
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C23×C3×C4C2311yescharacteristic
75C23×C3×C4C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—22no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4—22no—
91C2×C3×C4⋊C4—22no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C4⋊C4—41no—
94C2×C3×C4⋊C4—41no—
95C2×C3×C4⋊C4—41no—
96C2×C3×C4⋊C4—41no—
97C2×C3×C4⋊C4—41no—
98C2×C3×C4⋊C4—41no—
99C2×C3×C4⋊C4—41no—
100C2×C3×C4⋊C4—41no—
101C2×C3×C4⋊C4D414yes—
102C2×C3×C42—22no—
103C2×C3×C42—41no—
104C2×C3×C42—41no—
105C3×#95—22no—
106C3×#95—22no—
107C3×#95—22no—
108C3×#95—22no—
109C3×#95—22no—
110C3×#95—22no—
111C3×#95—22no—
112C3×#95—22no—
113C3×#95—22no—
114C3×#95—22no—
115C3×#95—22no—
116C3×#95—22no—
117C3×#95—22no—
118C3×#95—22no—
119C3×#95—22no—
120C3×#95—22no—
121C3×#95—22no—
122C3×#95—22no—
123C3×#95—22no—
124C3×#95—22no—
125C3×#95—41no—
126C3×#95—41no—
127C3×#95—41no—
128C3×#95—41no—
129C3×#95—41no—
130C3×#95—41no—
131C3×#95—41no—
132C3×#95—41no—
133C22×C4⋊C4C22×C311yescharacteristic
134C22×C4⋊C4C22×C311yescharacteristic
135C22×C4⋊C4C22×C311yescharacteristic
136C22×C4⋊C4C22×C311yescharacteristic
137C22×C4⋊C4C22×C311yescharacteristic
138C22×C4⋊C4C22×C311yescharacteristic
139C22×C42C22×C311yescharacteristic
140#400—24no—
141#387—24no—
142C2×#95C22×C311yescharacteristic
143C2×#95C22×C311yescharacteristic
144C2×#95C22×C311yescharacteristic
145C2×#95C22×C311yescharacteristic
146C2×#95C22×C311yescharacteristic
147C2×#95C22×C311yescharacteristic
148C2×#95C22×C311yescharacteristic
149C2×#95C22×C311yescharacteristic
150C2×#95C22×C311yescharacteristic
151C2×#95C22×C311yescharacteristic
152C2×#95C22×C311yescharacteristic
153C2×#95C22×C311yescharacteristic
154C2×#95C22×C311yescharacteristic
155C2×#95C22×C311yescharacteristic
156C2×#95C22×C311yescharacteristic
157C2×#95C22×C311yescharacteristic
158C2×#95C22×C311yescharacteristic
159C2×#95C22×C311yescharacteristic
160C2×#95C22×C311yescharacteristic
161C2×#95C22×C311yescharacteristic
162C2×#95C22×C311yescharacteristic
163C2×#95C22×C311yescharacteristic
164C2×#95C22×C311yescharacteristic
165C2×#95C22×C311yescharacteristic
166C2×#95C22×C311yescharacteristic
167C2×#95C22×C311yescharacteristic
168C2×#95C22×C311yescharacteristic
169C2×#95C22×C311yescharacteristic
170C24×C3C2411yescharacteristic
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4C2×D412yes—
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×D412yes—
270C22×C3×C4#4112yes—
271C22×C3×C4#4112yes—
272C22×C3×C4#4112yes—
273C22×C3×C4#4112yes—
274C22×C3×C4#4112yes—
275C22×C3×C4#4112yes—
276C3×C4⋊C4—28no—
277C3×C4⋊C4—44no—
278C3×C4⋊C4—44no—
279C3×C4⋊C4—44no—
280C3×C4⋊C4—44no—
281C3×C4⋊C4—44no—
282C3×C42—44no—
283C23×C4C23×C311yescharacteristic
284C23×C4C23×C311yescharacteristic
285C23×C4C23×C311yescharacteristic
286C23×C4C23×C311yescharacteristic
287C23×C4C23×C311yescharacteristic
288C23×C4C23×C311yescharacteristic
289C23×C4C23×C311yescharacteristic
290C23×C4C23×C311yescharacteristic
291C23×C4C23×C311yescharacteristic
292C23×C4C23×C311yescharacteristic
293C23×C4C23×C311yescharacteristic
294C23×C4C23×C311yescharacteristic
295C23×C4C23×C311yescharacteristic
296C23×C4C23×C311yescharacteristic
297C23×C4C23×C311yescharacteristic
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4C3×D414yes—
316C2×C42—22no—
317C2×C42—41no—
318C2×C42—41no—
319#95—22no—
320#95—22no—
321#95—22no—
322#95—22no—
323#95—22no—
324#95—22no—
325#95—22no—
326#95—22no—
327#95—22no—
328#95—22no—
329#95—22no—
330#95—22no—
331#95—22no—
332#95—22no—
333#95—22no—
334#95—22no—
335#95—22no—
336#95—22no—
337#95—22no—
338#95—22no—
339#95—41no—
340#95—41no—
341#95—41no—
342#95—41no—
343#95—41no—
344#95—41no—
345#95—41no—
346#95—41no—
347C23×C3C22×D411yescharacteristic
348C23×C3C2×#4111yescharacteristic
349C23×C3C2×#4111yescharacteristic
350C23×C3C2×#4111yescharacteristic
351C23×C3C2×#4111yescharacteristic
352C23×C3C2×#4111yescharacteristic
353C23×C3C2×#4111yescharacteristic
354C23×C3H(5,𝔽2)11yescharacteristic
355C23×C3H(5,𝔽2)11yescharacteristic
356C23×C3H(5,𝔽2)11yescharacteristic
357C23×C32−1+411yescharacteristic
358C23×C32−1+411yescharacteristic
359C23×C32−1+411yescharacteristic
360C23×C32−1+411yescharacteristic
361C23×C32−1+411yescharacteristic
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
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—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C24C24×C311yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4C2×C3×D412yes—
565C22×C4C2×C3×D412yes—
566C22×C4C2×C3×D412yes—
567C22×C4C3×#4112yes—
568C22×C4C3×#4112yes—
569C22×C4C3×#4112yes—
570C22×C4C3×#4112yes—
571C22×C4C3×#4112yes—
572C22×C4C3×#4112yes—
573C4⋊C4—28no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C42—44no—
580C22×C3#52511yescharacteristic
581C22×C3#52911yescharacteristic
582C22×C3#52911yescharacteristic
583C22×C3#53411yescharacteristic
584C22×C3#53611yescharacteristic
585C22×C3#53811yescharacteristic
586C22×C3#53911yescharacteristic
587C22×C3#53911yescharacteristic
588C22×C3#53911yescharacteristic
589C22×C3#53911yescharacteristic
590C22×C3#53911yescharacteristic
591C22×C3#54111yescharacteristic
592C22×C3#54111yescharacteristic
593C22×C3#54111yescharacteristic
594C22×C3#54111yescharacteristic
595C22×C3#54211yescharacteristic
596C22×C3#54211yescharacteristic
597C22×C3#54211yescharacteristic
598C22×C3#54211yescharacteristic
599C22×C3#54711yescharacteristic
600C22×C3#54711yescharacteristic
601C22×C3#54811yescharacteristic
602C22×C3#55011yescharacteristic
603C22×C3#55111yescharacteristic
604C22×C3#55111yescharacteristic
605C22×C3#55211yescharacteristic
606C22×C3#55211yescharacteristic
607C22×C3#55211yescharacteristic
608C22×C3#55611yescharacteristic
609C22×C3#55611yescharacteristic
610C22×C3#55911yescharacteristic
611C22×C3#56211yescharacteristic
612C22×C3#56311yescharacteristic
613C22×C3#56311yescharacteristic
614C22×C3#56411yescharacteristic
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—81no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4—81no—
630C23C22×C3×D411yescharacteristic
631C23C2×C3×#4111yescharacteristic
632C23C2×C3×#4111yescharacteristic
633C23C2×C3×#4111yescharacteristic
634C23C2×C3×#4111yescharacteristic
635C23C2×C3×#4111yescharacteristic
636C23C2×C3×#4111yescharacteristic
637C23C3×H(5,𝔽2)11yescharacteristic
638C23C3×H(5,𝔽2)11yescharacteristic
639C23C3×H(5,𝔽2)11yescharacteristic
640C23C3×2−1+411yescharacteristic
641C23C3×2−1+411yescharacteristic
642C23C3×2−1+411yescharacteristic
643C23C3×2−1+411yescharacteristic
644C23C3×2−1+411yescharacteristic
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C3#246911yescharacteristic
751C2×C3#247911yescharacteristic
752C2×C3#257511yescharacteristic
753C2×C3#263811yescharacteristic
754C2×C3#265211yescharacteristic
755C2×C3#265511yescharacteristic
756C2×C3#271911yescharacteristic
757C2×C3#272111yescharacteristic
758C2×C3#272411yescharacteristic
759C2×C3#273011yescharacteristic
760C2×C3#274511yescharacteristic
761C2×C3#275811yescharacteristic
762C2×C3#276711yescharacteristic
763C2×C3#279811yescharacteristic
764C2×C3#283911yescharacteristic
765C22C3×#52511yescharacteristic
766C22C3×#52911yescharacteristic
767C22C3×#52911yescharacteristic
768C22C3×#53411yescharacteristic
769C22C3×#53611yescharacteristic
770C22C3×#53811yescharacteristic
771C22C3×#53911yescharacteristic
772C22C3×#53911yescharacteristic
773C22C3×#53911yescharacteristic
774C22C3×#53911yescharacteristic
775C22C3×#53911yescharacteristic
776C22C3×#54111yescharacteristic
777C22C3×#54111yescharacteristic
778C22C3×#54111yescharacteristic
779C22C3×#54111yescharacteristic
780C22C3×#54211yescharacteristic
781C22C3×#54211yescharacteristic
782C22C3×#54211yescharacteristic
783C22C3×#54211yescharacteristic
784C22C3×#54711yescharacteristic
785C22C3×#54711yescharacteristic
786C22C3×#54811yescharacteristic
787C22C3×#55011yescharacteristic
788C22C3×#55111yescharacteristic
789C22C3×#55111yescharacteristic
790C22C3×#55211yescharacteristic
791C22C3×#55211yescharacteristic
792C22C3×#55211yescharacteristic
793C22C3×#55611yescharacteristic
794C22C3×#55611yescharacteristic
795C22C3×#55911yescharacteristic
796C22C3×#56211yescharacteristic
797C22C3×#56311yescharacteristic
798C22C3×#56311yescharacteristic
799C22C3×#56411yescharacteristic
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4—81no—
813C4—81no—
814C4—81no—
815C3#1664111yescharacteristic, direct product factor, Sylow
816C2C3×#246911yescharacteristic
817C2C3×#247911yescharacteristic
818C2C3×#257511yescharacteristic
819C2C3×#263811yescharacteristic
820C2C3×#265211yescharacteristic
821C2C3×#265511yescharacteristic
822C2C3×#271911yescharacteristic
823C2C3×#272111yescharacteristic
824C2C3×#272411yescharacteristic
825C2C3×#273011yescharacteristic
826C2C3×#274511yescharacteristic
827C2C3×#275811yescharacteristic
828C2C3×#276711yescharacteristic
829C2C3×#279811yescharacteristic
830C2C3×#283911yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3C24
commutator, Frattini, cosocleC24C24×C3
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C3 ◁ G

Complements

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

NH ≅ G/Ntype
16. #16641C3direct (N × H)
815. C3#16641direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4002
C2×C3×#3872
C3×#14452
C3×#14442
C3×#14432
C3×#14422
C3×#14412
C3×#14362
#166413