Finite Group Databasebeta

← C3×#30444 #10649051

Subgroups — C3×#30444 #10649051

Order 768.

1466 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#493C211yesmaximal, characteristic, complemented
2C2×C3×#459C211yesmaximal, characteristic, complemented
3C2×C3×#447C211yesmaximal, characteristic, complemented
4C2×C3×#447C211yesmaximal, characteristic, complemented
5C3×#2433C211yesmaximal, characteristic, complemented
6C3×#2428C211yesmaximal, characteristic, complemented
7C3×#2054C211yesmaximal, characteristic, complemented
8C3×#2041C211yesmaximal, characteristic, complemented
9C3×#2011C211yesmaximal, characteristic, complemented
10C3×#2011C211yesmaximal, characteristic, complemented
11C3×#1999C211yesmaximal, characteristic, complemented
12C3×#1999C211yesmaximal, characteristic, complemented
13C3×#1934C211yesmaximal, characteristic, complemented
14C3×#1923C211yesmaximal, characteristic, complemented
15C3×#1879C211yesmaximal, characteristic, complemented
16#30444C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C22×C3×D8C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C22×C3×D8C2211yescharacteristic, complemented
23C22×C3×D8C2211yescharacteristic, complemented
24C2×C3×#127C2211yescharacteristic
25C2×C3×#127C2211yescharacteristic
26C2×C3×#127C2211yescharacteristic, complemented
27C2×C3×#121—21no—
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#120—21no—
32C2×C3×#120—21no—
33C2×C3×C4×D4C2211yescharacteristic, complemented
34C3×#493—24no—
35C3×#459—24no—
36C3×#447—24no—
37C3×#447—24no—
38C2×C3×C4⋊C8C2211yescharacteristic, complemented
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic, complemented
44C2×C3×#102C2211yescharacteristic, complemented
45C2×C3×#102C2211yescharacteristic, complemented
46C2×C3×#102C2211yescharacteristic, complemented
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×C3×C4×C8C2211yescharacteristic, complemented
50C3×#394—21no—
51C3×#392—21no—
52C3×#392—21no—
53C3×#392—21no—
54C3×#390C2211yescharacteristic
55C3×#390C2211yescharacteristic
56C3×#390C2211yescharacteristic, complemented
57C3×#389C2211yescharacteristic, complemented
58C3×#386—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62C3×#336C2211yescharacteristic, complemented
63C3×#336C2211yescharacteristic, complemented
64C2×#493C2×C311yescharacteristic, complemented
65C2×#459C2×C311yescharacteristic, complemented
66C2×#447C2×C311yescharacteristic, complemented
67C2×#447C2×C311yescharacteristic, complemented
68#2433C2×C311yescharacteristic, complemented
69#2428C2×C311yescharacteristic, complemented
70#2054C2×C311yescharacteristic, complemented
71#2041C2×C311yescharacteristic, complemented
72#2011C2×C311yescharacteristic, complemented
73#2011C2×C311yescharacteristic, complemented
74#1999C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic, complemented
76#1934C2×C311yescharacteristic, complemented
77#1923C2×C311yescharacteristic, complemented
78#1879C2×C311yescharacteristic, complemented
79C25×C3—21no—
80C22×C3×D4—22no—
81C22×C3×D4—22no—
82C22×C3×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4—21no—
85C22×C3×D4—21no—
86C22×C3×D4—21no—
87C22×C3×D4—21no—
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4—41no—
93C22×C3×D4—41no—
94C22×C3×D4—41no—
95C22×C3×D4—41no—
96C22×C3×D4C2311yescharacteristic
97C22×C3×D4C2311yescharacteristic
98C22×C3×D4C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C23×C3×C4—21no—
102C23×C3×C4C2311yescharacteristic
103C2×C3×D8—22no—
104C2×C3×D8—22no—
105C2×C3×D8—22no—
106C2×C3×D8—22no—
107C2×C3×D8—22no—
108C2×C3×D8—22no—
109C2×C3×D8—22no—
110C2×C3×D8—22no—
111C2×C3×D8—41no—
112C2×C3×D8—41no—
113C2×C3×D8—41no—
114C2×C3×D8—41no—
115C2×C3×D8—41no—
116C2×C3×D8—41no—
117C2×C3×D8—41no—
118C2×C3×D8—41no—
119C2×C3×D8—41no—
120C2×C3×D8D414yescomplemented
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C22×C3×C8C2311yescharacteristic
124C22×C3×C8C2311yescharacteristic
125C3×#127—22no—
126C3×#127—22no—
127C3×#127—22no—
128C3×#127—41no—
129C3×#127—41no—
130C3×#127—41no—
131C3×#121—22no—
132C3×#121—22no—
133C3×#121—41no—
134C3×#121—41no—
135C3×#121—41no—
136C3×#121—41no—
137C3×#121—44no—
138C3×#120—44no—
139C3×#120—44no—
140C3×C4×D4—22no—
141C3×C4×D4—41no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4D411yescharacteristic
157C2×C3×C22⋊C4D411yescharacteristic
158C2×C3×C42C2311yescharacteristic
159C2×C3×C42C2311yescharacteristic
160C3×C4⋊C8—22no—
161C3×#102—22no—
162C3×#102—22no—
163C3×#102—22no—
164C3×#102—22no—
165C3×#102—41no—
166C3×#102—41no—
167C3×#102—41no—
168C3×#102D414yescomplemented
169C3×C22⋊C8—22no—
170C3×C22⋊C8—22no—
171C3×C4×C8—22no—
172C3×#95—21no—
173C3×#95D411yescharacteristic
174C3×#95D411yescharacteristic
175C23×D4C22×C311yescharacteristic
176C22×D8C22×C311yescharacteristic
177C22×D8C22×C311yescharacteristic
178C22×D8C22×C311yescharacteristic
179C22×D8C22×C311yescharacteristic
180C22×D8C22×C311yescharacteristic, complemented
181C22×D8C22×C311yescharacteristic, complemented
182C2×#127C22×C311yescharacteristic
183C2×#127C22×C311yescharacteristic
184C2×#127C22×C311yescharacteristic, complemented
185C2×#121—21no—
186C2×#121C22×C311yescharacteristic
187C2×#121C22×C311yescharacteristic
188C2×#121C22×C311yescharacteristic
189C2×#120—21no—
190C2×#120—21no—
191C2×C4×D4C22×C311yescharacteristic, complemented
192#493—24no—
193#459—24no—
194#447—24no—
195#447—24no—
196C2×C4⋊C8C22×C311yescharacteristic, complemented
197C2×#102C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×#102C22×C311yescharacteristic
200C2×#102C22×C311yescharacteristic
201C2×#102C22×C311yescharacteristic, complemented
202C2×#102C22×C311yescharacteristic, complemented
203C2×#102C22×C311yescharacteristic, complemented
204C2×#102C22×C311yescharacteristic, complemented
205C2×C22⋊C8C22×C311yescharacteristic
206C2×C22⋊C8C22×C311yescharacteristic
207C2×C4×C8C22×C311yescharacteristic, complemented
208#394—21no—
209#392—21no—
210#392—21no—
211#392—21no—
212#390C22×C311yescharacteristic
213#390C22×C311yescharacteristic
214#390C22×C311yescharacteristic, complemented
215#389C22×C311yescharacteristic, complemented
216#386—21no—
217C4×C22⋊C4C22×C311yescharacteristic
218#340C22×C311yescharacteristic, complemented
219#340C22×C311yescharacteristic, complemented
220#336C22×C311yescharacteristic, complemented
221#336C22×C311yescharacteristic, complemented
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—42no—
228C24×C3—42no—
229C24×C3—42no—
230C24×C3—42no—
231C24×C3—42no—
232C24×C3—81no—
233C24×C3—81no—
234C24×C3C2×D411yescharacteristic
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4—42no—
265C2×C3×D4—42no—
266C2×C3×D4—42no—
267C2×C3×D4—42no—
268C2×C3×D4—42no—
269C2×C3×D4—42no—
270C2×C3×D4—42no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4—44no—
274C2×C3×D4—44no—
275C2×C3×D4—44no—
276C2×C3×D4—44no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—42no—
280C2×C3×D4—42no—
281C2×C3×D4—42no—
282C2×C3×D4—42no—
283C2×C3×D4—42no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4—42no—
287C2×C3×D4—42no—
288C2×C3×D4—81no—
289C2×C3×D4—81no—
290C2×C3×D4—81no—
291C2×C3×D4—81no—
292C2×C3×D4—81no—
293C2×C3×D4—81no—
294C2×C3×D4—81no—
295C2×C3×D4—81no—
296C2×C3×D4C2×D412yes—
297C2×C3×D4C2×D412yes—
298C2×C3×D4C2×D412yes—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—42no—
309C22×C3×C4—42no—
310C22×C3×C4—81no—
311C22×C3×C4C2×D411yescharacteristic
312C22×C3×C4C2×D411yescharacteristic
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2×D411yescharacteristic
315C22×C3×C4C2×D411yescharacteristic
316C22×C3×C4C2411yescharacteristic
317C3×D8—44no—
318C3×D8—44no—
319C3×D8—44no—
320C3×D8—44no—
321C3×D8—44no—
322C3×D8—44no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8C2×D412yes—
334C2×C3×C8C2×D412yes—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—42no—
341C3×C4⋊C4C2×D412yes—
342C3×C22⋊C4—22no—
343C3×C22⋊C4—42no—
344C3×C22⋊C4—42no—
345C3×C22⋊C4—42no—
346C3×C22⋊C4—42no—
347C3×C22⋊C4—42no—
348C3×C22⋊C4—42no—
349C3×C22⋊C4—42no—
350C3×C22⋊C4—42no—
351C3×C22⋊C4—42no—
352C3×C22⋊C4—81no—
353C3×C22⋊C4D814yescomplemented
354C3×C42—21no—
355C3×C42—21no—
356C3×C42—21no—
357C3×C42—21no—
358C25—21no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—21no—
362C22×D4—21no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4—21no—
370C22×D4—21no—
371C22×D4—41no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4—41no—
375C22×D4C23×C311yescharacteristic
376C22×D4C23×C311yescharacteristic
377C22×D4C23×C311yescharacteristic
378C22×D4C23×C311yescharacteristic
379C22×D4C23×C311yescharacteristic
380C23×C4—21no—
381C23×C4C23×C311yescharacteristic
382C2×D8—22no—
383C2×D8—22no—
384C2×D8—22no—
385C2×D8—22no—
386C2×D8—22no—
387C2×D8—22no—
388C2×D8—22no—
389C2×D8—22no—
390C2×D8—41no—
391C2×D8—41no—
392C2×D8—41no—
393C2×D8—41no—
394C2×D8—41no—
395C2×D8—41no—
396C2×D8—41no—
397C2×D8—41no—
398C2×D8—41no—
399C2×D8C3×D414yescomplemented
400C22×C8C23×C311yescharacteristic
401C22×C8C23×C311yescharacteristic
402C22×C8C23×C311yescharacteristic
403C22×C8C23×C311yescharacteristic
404#127—22no—
405#127—22no—
406#127—22no—
407#127—41no—
408#127—41no—
409#127—41no—
410#121—22no—
411#121—22no—
412#121—41no—
413#121—41no—
414#121—41no—
415#121—41no—
416#121—44no—
417#120—44no—
418#120—44no—
419C4×D4—22no—
420C4×D4—41no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4C23×C311yescharacteristic
423C2×C4⋊C4C23×C311yescharacteristic
424C2×C4⋊C4C23×C311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4C3×D411yescharacteristic
436C2×C22⋊C4C3×D411yescharacteristic
437C2×C42C23×C311yescharacteristic
438C2×C42C23×C311yescharacteristic
439C4⋊C8—22no—
440#102—22no—
441#102—22no—
442#102—22no—
443#102—22no—
444#102—41no—
445#102—41no—
446#102—41no—
447#102C3×D414yescomplemented
448C22⋊C8—22no—
449C22⋊C8—22no—
450C4×C8—22no—
451#95—21no—
452#95C3×D411yescharacteristic
453#95C3×D411yescharacteristic
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—48no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—41no—
494C23×C3—41no—
495C23×C3—41no—
496C23×C3—84no—
497C23×C3—84no—
498C23×C3—84no—
499C23×C3—84no—
500C23×C3—84no—
501C23×C3—84no—
502C23×C3C2×D812yes—
503C23×C3C22×D411yescharacteristic
504C3×D4—22no—
505C3×D4—22no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—22no—
510C3×D4—48no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—41no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—41no—
525C3×D4—84no—
526C3×D4—84no—
527C3×D4—84no—
528C3×D4—84no—
529C3×D4—84no—
530C3×D4—84no—
531C3×D4—84no—
532C3×D4—84no—
533C3×D4—84no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—22no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—84no—
560C2×C3×C4C2×D812yes—
561C2×C3×C4C2×D812yes—
562C2×C3×C4AGL(1,ℤ/8)12yes—
563C2×C3×C4C22×D411yescharacteristic
564C2×C3×C4C22×D411yescharacteristic
565C2×C3×C4H(5,𝔽2)11yescharacteristic
566C2×C3×C4H(5,𝔽2)11yescharacteristic
567C2×C3×C4H(5,𝔽2)11yescharacteristic
568C2×C3×C4H(5,𝔽2)11yescharacteristic
569C3×C8—22no—
570C3×C8—22no—
571C3×C8—41no—
572C3×C8—41no—
573C24—21no—
574C24—21no—
575C24—21no—
576C24—21no—
577C24—21no—
578C24—42no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—81no—
584C24—81no—
585C24C2×C3×D411yescharacteristic
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—81no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4C2×C3×D412yes—
648C2×D4C2×C3×D412yes—
649C2×D4C2×C3×D412yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4C2×C3×D411yescharacteristic
663C22×C4C2×C3×D411yescharacteristic
664C22×C4C2×C3×D411yescharacteristic
665C22×C4C2×C3×D411yescharacteristic
666C22×C4C2×C3×D411yescharacteristic
667C22×C4C24×C311yescharacteristic
668D8—44no—
669D8—44no—
670D8—44no—
671D8—44no—
672D8—44no—
673D8—44no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8C2×C3×D412yes—
685C2×C8C2×C3×D412yes—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4C2×C3×D412yes—
693C22⋊C4—22no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4C3×D814yescomplemented
705C42—21no—
706C42—21no—
707C42—21no—
708C42—21no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—816no—
726C22×C3—81no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—81no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—81no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—81no—
737C22×C3—81no—
738C22×C3—81no—
739C22×C3—81no—
740C22×C3—81no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3—81no—
752C22×C3#53511yescharacteristic
753C22×C3D4211yescharacteristic
754C22×C3D4211yescharacteristic
755C22×C3C22×D811yescharacteristic
756C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
757C22×C3#57611yescharacteristic
758C22×C3#57611yescharacteristic
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—41no—
763C3×C4—41no—
764C3×C4—42no—
765C3×C4—81no—
766C3×C4—81no—
767C3×C4#53411yescharacteristic
768C3×C4#53511yescharacteristic
769C3×C4D4211yescharacteristic
770C3×C4#56011yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—48no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C3×D812yes—
820C23C22×C3×D411yescharacteristic
821D4—22no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—22no—
826D4—22no—
827D4—48no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4—84no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—84no—
877C2×C4C2×C3×D812yes—
878C2×C4C2×C3×D812yes—
879C2×C4C3×AGL(1,ℤ/8)12yes—
880C2×C4C22×C3×D411yescharacteristic
881C2×C4C22×C3×D411yescharacteristic
882C2×C4C3×H(5,𝔽2)11yescharacteristic
883C2×C4C3×H(5,𝔽2)11yescharacteristic
884C2×C4C3×H(5,𝔽2)11yescharacteristic
885C2×C4C3×H(5,𝔽2)11yescharacteristic
886C8—22no—
887C8—22no—
888C8—41no—
889C8—41no—
890C2×C3—42no—
891C2×C3—82no—
892C2×C3—82no—
893C2×C3—82no—
894C2×C3—161no—
895C2×C3—161no—
896C2×C3#266911yescharacteristic
897C2×C3#320511yescharacteristic
898C2×C3#322011yescharacteristic
899C2×C3#326411yescharacteristic
900C2×C3#327411yescharacteristic
901C2×C3D4×D811yescharacteristic
902C2×C3D4×D811yescharacteristic
903C22—22no—
904C22—22no—
905C22—22no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—816no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—81no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22C3×#53511yescharacteristic
947C22C3×D4211yescharacteristic
948C22C3×D4211yescharacteristic
949C22C22×C3×D811yescharacteristic
950C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
951C22C3×#57611yescharacteristic
952C22C3×#57611yescharacteristic
953C4—22no—
954C4—22no—
955C4—22no—
956C4—41no—
957C4—41no—
958C4—42no—
959C4—81no—
960C4—81no—
961C4C3×#53411yescharacteristic
962C4C3×#53511yescharacteristic
963C4C3×D4211yescharacteristic
964C4C3×#56011yescharacteristic
965C3#3044411yescharacteristic, direct product factor, Sylow
966C2—42no—
967C2—82no—
968C2—82no—
969C2—82no—
970C2—161no—
971C2—161no—
972C2C3×#266911yescharacteristic
973C2C3×#320511yescharacteristic
974C2C3×#322011yescharacteristic
975C2C3×#326411yescharacteristic
976C2C3×#327411yescharacteristic
977C2C3×D4×D811yescharacteristic
978C2C3×D4×D811yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#493C2semidirect
2. C2×C3×#459C2semidirect
3. C2×C3×#447C2semidirect
4. C2×C3×#447C2semidirect
5. C3×#2433C2semidirect
6. C3×#2428C2semidirect
7. C3×#2054C2semidirect
8. C3×#2041C2semidirect
9. C3×#2011C2semidirect
10. C3×#2011C2semidirect
11. C3×#1999C2semidirect
12. C3×#1999C2semidirect
13. C3×#1934C2semidirect
14. C3×#1923C2semidirect
15. C3×#1879C2semidirect
16. #30444C3direct (N × H)
22. C22×C3×D8C22semidirect
23. C22×C3×D8C22semidirect
26. C2×C3×#127C22semidirect
33. C2×C3×C4×D4C22semidirect
38. C2×C3×C4⋊C8C22semidirect
43. C2×C3×#102C22semidirect
44. C2×C3×#102C22semidirect
45. C2×C3×#102C22semidirect
46. C2×C3×#102C22semidirect
49. C2×C3×C4×C8C22semidirect
56. C3×#390C22semidirect
57. C3×#389C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. C3×#336C22semidirect
63. C3×#336C22semidirect
64. C2×#493C2×C3semidirect
65. C2×#459C2×C3semidirect
66. C2×#447C2×C3semidirect
67. C2×#447C2×C3semidirect
68. #2433C2×C3semidirect
69. #2428C2×C3semidirect
70. #2054C2×C3semidirect
71. #2041C2×C3semidirect
72. #2011C2×C3semidirect
73. #2011C2×C3semidirect
74. #1999C2×C3semidirect
75. #1999C2×C3semidirect
76. #1934C2×C3semidirect
77. #1923C2×C3semidirect
78. #1879C2×C3semidirect
120. C2×C3×D8D4semidirect
168. C3×#102D4semidirect
180. C22×D8C22×C3semidirect
181. C22×D8C22×C3semidirect
184. C2×#127C22×C3semidirect
191. C2×C4×D4C22×C3semidirect
196. C2×C4⋊C8C22×C3semidirect
201. C2×#102C22×C3semidirect
202. C2×#102C22×C3semidirect
203. C2×#102C22×C3semidirect
204. C2×#102C22×C3semidirect
207. C2×C4×C8C22×C3semidirect
214. #390C22×C3semidirect
215. #389C22×C3semidirect
218. #340C22×C3semidirect
219. #340C22×C3semidirect
220. #336C22×C3semidirect
221. #336C22×C3semidirect
353. C3×C22⋊C4D8semidirect
399. C2×D8C3×D4semidirect
447. #102C3×D4semidirect
704. C22⋊C4C3×D8semidirect
965. C3#30444direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4932
C2×C3×#4592
C2×C3×#4472
C3×#24332
C3×#24282
C3×#20542
C3×#20412
C3×#20112
C3×#19992
C3×#19342
C3×#19232
C3×#18792
#304443