Finite Group Databasebeta

← C3×#30452 #10649059

Subgroups — C3×#30452 #10649059

Order 768.

1250 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#495C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×C3×#450C211yesmaximal, characteristic, complemented
4C2×C3×#447C211yesmaximal, characteristic
5C3×#2435C211yesmaximal, characteristic, complemented
6C3×#2427C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8C3×#2042C211yesmaximal, characteristic, complemented
9C3×#2015C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#2001C211yesmaximal, characteristic, complemented
12C3×#2000C211yesmaximal, characteristic, complemented
13C3×#1934C211yesmaximal, characteristic, complemented
14C3×#1923C211yesmaximal, characteristic, complemented
15C3×#1879C211yesmaximal, characteristic, complemented
16#30452C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic, complemented
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic, complemented
22C22×C3×D8C2211yescharacteristic
23C22×C3×D8C2211yescharacteristic
24C2×C3×#124C2211yescharacteristic
25C2×C3×#124C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic, complemented
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic, complemented
31C3×#495—24no—
32C3×#463—24no—
33C3×#450—24no—
34C3×#447—24no—
35C2×C3×C4⋊C8C2211yescharacteristic, complemented
36C2×C3×#103C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#103C2211yescharacteristic, complemented
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic, complemented
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C4×C8C2211yescharacteristic, complemented
47C3×#397—21no—
48C3×#394—21no—
49C3×#394—21no—
50C3×#394—21no—
51C3×#391C2211yescharacteristic, complemented
52C3×#390C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#389C2211yescharacteristic, complemented
55C3×#386—21no—
56C3×#380—21no—
57C3×#379—21no—
58C3×#379—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62C3×#336C2211yescharacteristic, complemented
63C3×#336C2211yescharacteristic, complemented
64C2×#495C2×C311yescharacteristic, complemented
65C2×#463C2×C311yescharacteristic, complemented
66C2×#450C2×C311yescharacteristic, complemented
67C2×#447C2×C311yescharacteristic
68#2435C2×C311yescharacteristic, complemented
69#2427C2×C311yescharacteristic, complemented
70#2055C2×C311yescharacteristic, complemented
71#2042C2×C311yescharacteristic, complemented
72#2015C2×C311yescharacteristic, complemented
73#2012C2×C311yescharacteristic, complemented
74#2001C2×C311yescharacteristic, complemented
75#2000C2×C311yescharacteristic, complemented
76#1934C2×C311yescharacteristic, complemented
77#1923C2×C311yescharacteristic, complemented
78#1879C2×C311yescharacteristic, complemented
79C25×C3—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4—22no—
83C22×C3×D4—22no—
84C22×C3×D4—21no—
85C22×C3×D4—21no—
86C22×C3×D4—41no—
87C22×C3×D4—41no—
88C22×C3×D4—41no—
89C22×C3×D4—41no—
90C22×C3×D4C2311yescharacteristic
91C22×C3×D4C2311yescharacteristic
92C22×C3×D4C2311yescharacteristic
93C23×C3×C4—21no—
94C23×C3×C4C2311yescharacteristic
95C2×C3×Q16—22no—
96C2×C3×Q16—41no—
97C2×C3×Q16—41no—
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—41no—
104C2×C3×SD16—41no—
105C2×C3×SD16—41no—
106C2×C3×SD16—41no—
107C2×C3×D8—22no—
108C2×C3×D8—22no—
109C2×C3×D8—41no—
110C2×C3×D8—41no—
111C2×C3×D8—41no—
112C2×C3×D8D414yes—
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C3×#124—22no—
118C3×#124—22no—
119C3×#124—22no—
120C3×#124—41no—
121C3×#124—41no—
122C3×#124—41no—
123C3×C22⋊Q8—22no—
124C3×C22⋊Q8—41no—
125C3×C22⋊Q8—41no—
126C3×C22⋊Q8—41no—
127C3×#121—22no—
128C3×#121—41no—
129C3×C4×D4—22no—
130C3×C4×D4—41no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—21no—
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⋊C4D411yescharacteristic
152C2×C3×C22⋊C4D411yescharacteristic
153C2×C3×C42C2311yescharacteristic
154C2×C3×C42C2311yescharacteristic
155C3×C4⋊C8—22no—
156C3×#103—22no—
157C3×#103—41no—
158C3×#103—41no—
159C3×#102—22no—
160C3×#102—22no—
161C3×#102—22no—
162C3×#102—41no—
163C3×#102D414yescomplemented
164C3×C22⋊C8—22no—
165C3×C22⋊C8—22no—
166C3×C4×C8—22no—
167C3×#95—21no—
168C3×#95—21no—
169C3×#95—21no—
170C3×#95D411yescharacteristic
171C3×#95D411yescharacteristic
172C23×D4C22×C311yescharacteristic
173C22×Q16C22×C311yescharacteristic, complemented
174C22×SD16C22×C311yescharacteristic
175C22×SD16C22×C311yescharacteristic
176C22×SD16C22×C311yescharacteristic, complemented
177C22×D8C22×C311yescharacteristic
178C22×D8C22×C311yescharacteristic
179C2×#124C22×C311yescharacteristic
180C2×#124C22×C311yescharacteristic
181C2×#124C22×C311yescharacteristic, complemented
182C2×C22⋊Q8C22×C311yescharacteristic
183C2×C22⋊Q8C22×C311yescharacteristic
184C2×#121C22×C311yescharacteristic
185C2×C4×D4C22×C311yescharacteristic, complemented
186#495—24no—
187#463—24no—
188#450—24no—
189#447—24no—
190C2×C4⋊C8C22×C311yescharacteristic, complemented
191C2×#103C22×C311yescharacteristic, complemented
192C2×#103C22×C311yescharacteristic, complemented
193C2×#103C22×C311yescharacteristic, complemented
194C2×#102C22×C311yescharacteristic
195C2×#102C22×C311yescharacteristic
196C2×#102C22×C311yescharacteristic
197C2×#102C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic, complemented
199C2×C22⋊C8C22×C311yescharacteristic
200C2×C22⋊C8C22×C311yescharacteristic
201C2×C4×C8C22×C311yescharacteristic, complemented
202#397—21no—
203#394—21no—
204#394—21no—
205#394—21no—
206#391C22×C311yescharacteristic, complemented
207#390C22×C311yescharacteristic
208#390C22×C311yescharacteristic
209#389C22×C311yescharacteristic, complemented
210#386—21no—
211#380—21no—
212#379—21no—
213#379—21no—
214C4×C22⋊C4C22×C311yescharacteristic
215#340C22×C311yescharacteristic, complemented
216#340C22×C311yescharacteristic, complemented
217#336C22×C311yescharacteristic, complemented
218#336C22×C311yescharacteristic, complemented
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—42no—
223C24×C3—42no—
224C24×C3—42no—
225C24×C3—42no—
226C24×C3—42no—
227C24×C3—81no—
228C24×C3—81no—
229C24×C3C2×D411yescharacteristic
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—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—42no—
258C2×C3×D4—42no—
259C2×C3×D4—42no—
260C2×C3×D4—44no—
261C2×C3×D4—44no—
262C2×C3×D4—44no—
263C2×C3×D4—44no—
264C2×C3×D4—42no—
265C2×C3×D4—42no—
266C2×C3×D4—81no—
267C2×C3×D4C2×D412yes—
268C2×C3×D4C2×D412yes—
269C2×C3×D4C2×D412yes—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—42no—
282C22×C3×C4—42no—
283C22×C3×C4—81no—
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2×D411yescharacteristic
286C22×C3×C4C2×D411yescharacteristic
287C22×C3×C4C2×D411yescharacteristic
288C22×C3×C4C2×D411yescharacteristic
289C22×C3×C4C2411yescharacteristic
290C3×Q16—44no—
291C3×SD16—44no—
292C3×SD16—44no—
293C3×SD16—44no—
294C3×D8—44no—
295C3×D8—44no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8C2×D412yes—
307C2×C3×C8C2×D412yes—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—42no—
314C3×C4⋊C4—42no—
315C3×C4⋊C4—81no—
316C3×C4⋊C4C2×D412yes—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—41no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—42no—
322C3×C22⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C22⋊C4—42no—
325C3×C22⋊C4—42no—
326C3×C22⋊C4—42no—
327C3×C22⋊C4—42no—
328C3×C22⋊C4—42no—
329C3×C22⋊C4—81no—
330C3×C22⋊C4—81no—
331C3×C22⋊C4—81no—
332C3×C22⋊C4—81no—
333C3×C42—21no—
334C3×C42—21no—
335C3×C42—21no—
336C3×C42—21no—
337C25—21no—
338C22×Q8C23×C311yescharacteristic
339C22×Q8C23×C311yescharacteristic
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—41no—
345C22×D4—41no—
346C22×D4—41no—
347C22×D4—41no—
348C22×D4C23×C311yescharacteristic
349C22×D4C23×C311yescharacteristic
350C22×D4C23×C311yescharacteristic
351C23×C4—21no—
352C23×C4C23×C311yescharacteristic
353C2×Q16—22no—
354C2×Q16—41no—
355C2×Q16—41no—
356C2×SD16—22no—
357C2×SD16—22no—
358C2×SD16—22no—
359C2×SD16—22no—
360C2×SD16—22no—
361C2×SD16—41no—
362C2×SD16—41no—
363C2×SD16—41no—
364C2×SD16—41no—
365C2×D8—22no—
366C2×D8—22no—
367C2×D8—41no—
368C2×D8—41no—
369C2×D8—41no—
370C2×D8C3×D414yes—
371C22×C8C23×C311yescharacteristic
372C22×C8C23×C311yescharacteristic
373C22×C8C23×C311yescharacteristic
374C22×C8C23×C311yescharacteristic
375#124—22no—
376#124—22no—
377#124—22no—
378#124—41no—
379#124—41no—
380#124—41no—
381C22⋊Q8—22no—
382C22⋊Q8—41no—
383C22⋊Q8—41no—
384C22⋊Q8—41no—
385#121—22no—
386#121—41no—
387C4×D4—22no—
388C4×D4—41no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C23×C311yescharacteristic
393C2×C4⋊C4C23×C311yescharacteristic
394C2×C4⋊C4C23×C311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4C3×D411yescharacteristic
410C2×C22⋊C4C3×D411yescharacteristic
411C2×C42C23×C311yescharacteristic
412C2×C42C23×C311yescharacteristic
413C4⋊C8—22no—
414#103—22no—
415#103—41no—
416#103—41no—
417#102—22no—
418#102—22no—
419#102—22no—
420#102—41no—
421#102C3×D414yescomplemented
422C22⋊C8—22no—
423C22⋊C8—22no—
424C4×C8—22no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95C3×D411yescharacteristic
429#95C3×D411yescharacteristic
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—48no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—84no—
459C23×C3—84no—
460C23×C3—84no—
461C23×C3—84no—
462C23×C3—84no—
463C23×C3—84no—
464C23×C3#13512yes—
465C23×C3C22×D411yescharacteristic
466C3×Q8—41no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×Q8—41no—
470C3×Q8—41no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×D4—22no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—22no—
478C3×D4—22no—
479C3×D4—22no—
480C3×D4—48no—
481C3×D4—41no—
482C3×D4—41no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—84no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—84no—
523C2×C3×C4C22×D411yescharacteristic
524C2×C3×C4C22×D411yescharacteristic
525C2×C3×C4H(5,𝔽2)11yescharacteristic
526C2×C3×C4H(5,𝔽2)11yescharacteristic
527C2×C3×C4H(5,𝔽2)11yescharacteristic
528C2×C3×C4H(5,𝔽2)11yescharacteristic
529C3×C8—22no—
530C3×C8—22no—
531C3×C8—41no—
532C3×C8—41no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—42no—
537C24—42no—
538C24—42no—
539C24—42no—
540C24—42no—
541C24—81no—
542C24—81no—
543C24C2×C3×D411yescharacteristic
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4C2×C3×D412yes—
582C2×D4C2×C3×D412yes—
583C2×D4C2×C3×D412yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—81no—
598C22×C4C2×C3×D411yescharacteristic
599C22×C4C2×C3×D411yescharacteristic
600C22×C4C2×C3×D411yescharacteristic
601C22×C4C2×C3×D411yescharacteristic
602C22×C4C2×C3×D411yescharacteristic
603C22×C4C24×C311yescharacteristic
604Q16—44no—
605SD16—44no—
606SD16—44no—
607SD16—44no—
608D8—44no—
609D8—44no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8C2×C3×D412yes—
621C2×C8C2×C3×D412yes—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—81no—
630C4⋊C4C2×C3×D412yes—
631C22⋊C4—22no—
632C22⋊C4—41no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—816no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3#53511yescharacteristic
681C22×C3D4211yescharacteristic
682C22×C3D4211yescharacteristic
683C22×C3C2×#13511yescharacteristic
684C22×C3#57511yescharacteristic
685C22×C3#57611yescharacteristic
686C22×C3#57711yescharacteristic
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—42no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—81no—
694C3×C4—81no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4#53411yescharacteristic
698C3×C4#53511yescharacteristic
699C3×C4D4211yescharacteristic
700C3×C4#56011yescharacteristic
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23C3×#13512yes—
736C23C22×C3×D411yescharacteristic
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745D4—22no—
746D4—22no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—84no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—84no—
794C2×C4C22×C3×D411yescharacteristic
795C2×C4C22×C3×D411yescharacteristic
796C2×C4C3×H(5,𝔽2)11yescharacteristic
797C2×C4C3×H(5,𝔽2)11yescharacteristic
798C2×C4C3×H(5,𝔽2)11yescharacteristic
799C2×C4C3×H(5,𝔽2)11yescharacteristic
800C8—22no—
801C8—22no—
802C8—41no—
803C8—41no—
804C2×C3—42no—
805C2×C3—82no—
806C2×C3—82no—
807C2×C3—82no—
808C2×C3#266911yescharacteristic
809C2×C3#321111yescharacteristic
810C2×C3#322411yescharacteristic
811C2×C3#326711yescharacteristic
812C2×C3#327311yescharacteristic
813C2×C3#328011yescharacteristic
814C2×C3#328211yescharacteristic
815C22—22no—
816C22—22no—
817C22—22no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—816no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22C3×#53511yescharacteristic
845C22C3×D4211yescharacteristic
846C22C3×D4211yescharacteristic
847C22C2×C3×#13511yescharacteristic
848C22C3×#57511yescharacteristic
849C22C3×#57611yescharacteristic
850C22C3×#57711yescharacteristic
851C4—41no—
852C4—41no—
853C4—41no—
854C4—42no—
855C4—41no—
856C4—41no—
857C4—81no—
858C4—81no—
859C4—81no—
860C4—81no—
861C4C3×#53411yescharacteristic
862C4C3×#53511yescharacteristic
863C4C3×D4211yescharacteristic
864C4C3×#56011yescharacteristic
865C3#3045211yescharacteristic, direct product factor, Sylow
866C2—42no—
867C2—82no—
868C2—82no—
869C2—82no—
870C2C3×#266911yescharacteristic
871C2C3×#321111yescharacteristic
872C2C3×#322411yescharacteristic
873C2C3×#326711yescharacteristic
874C2C3×#327311yescharacteristic
875C2C3×#328011yescharacteristic
876C2C3×#328211yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#447C2
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×#495C2semidirect
2. C2×C3×#463C2semidirect
3. C2×C3×#450C2semidirect
5. C3×#2435C2semidirect
6. C3×#2427C2semidirect
7. C3×#2055C2semidirect
8. C3×#2042C2semidirect
9. C3×#2015C2semidirect
10. C3×#2012C2semidirect
11. C3×#2001C2semidirect
12. C3×#2000C2semidirect
13. C3×#1934C2semidirect
14. C3×#1923C2semidirect
15. C3×#1879C2semidirect
16. #30452C3direct (N × H)
18. C22×C3×Q16C22semidirect
21. C22×C3×SD16C22semidirect
26. C2×C3×#124C22semidirect
30. C2×C3×C4×D4C22semidirect
35. C2×C3×C4⋊C8C22semidirect
36. C2×C3×#103C22semidirect
37. C2×C3×#103C22semidirect
38. C2×C3×#103C22semidirect
43. C2×C3×#102C22semidirect
46. C2×C3×C4×C8C22semidirect
51. C3×#391C22semidirect
54. C3×#389C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. C3×#336C22semidirect
63. C3×#336C22semidirect
64. C2×#495C2×C3semidirect
65. C2×#463C2×C3semidirect
66. C2×#450C2×C3semidirect
68. #2435C2×C3semidirect
69. #2427C2×C3semidirect
70. #2055C2×C3semidirect
71. #2042C2×C3semidirect
72. #2015C2×C3semidirect
73. #2012C2×C3semidirect
74. #2001C2×C3semidirect
75. #2000C2×C3semidirect
76. #1934C2×C3semidirect
77. #1923C2×C3semidirect
78. #1879C2×C3semidirect
163. C3×#102D4semidirect
173. C22×Q16C22×C3semidirect
176. C22×SD16C22×C3semidirect
181. C2×#124C22×C3semidirect
185. C2×C4×D4C22×C3semidirect
190. C2×C4⋊C8C22×C3semidirect
191. C2×#103C22×C3semidirect
192. C2×#103C22×C3semidirect
193. C2×#103C22×C3semidirect
198. C2×#102C22×C3semidirect
201. C2×C4×C8C22×C3semidirect
206. #391C22×C3semidirect
209. #389C22×C3semidirect
215. #340C22×C3semidirect
216. #340C22×C3semidirect
217. #336C22×C3semidirect
218. #336C22×C3semidirect
421. #102C3×D4semidirect
865. C3#30452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4952
C2×C3×#4632
C2×C3×#4502
C2×C3×#4472
C3×#24352
C3×#24272
C3×#20552
C3×#20422
C3×#20152
C3×#20122
C3×#20012
C3×#20002
C3×#19342
C3×#19232
C3×#18792
#304523