Finite Group Databasebeta

← C3×#24383 #10642990

Subgroups — C3×#24383 #10642990

Order 768.

1600 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic
2C2×C3×#467C211yesmaximal, characteristic, complemented
3C2×C3×#465C211yesmaximal, characteristic, complemented
4C2×C3×#452C211yesmaximal, characteristic, complemented
5C22×C3×C22⋊C8C211yesmaximal, characteristic, complemented
6C3×#2848C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8C3×#2033C211yesmaximal, characteristic, complemented
9C3×#2001C211yesmaximal, characteristic, complemented
10C3×#2000C211yesmaximal, characteristic, complemented
11C3×#1893C211yesmaximal, characteristic, complemented
12C3×#1892C211yesmaximal, characteristic, complemented
13C3×#1873C211yesmaximal, characteristic, complemented
14C3×#1854C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#24383C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic, complemented
20C22×C3×SD16C2211yescharacteristic, complemented
21C23×C3×C8C2211yescharacteristic
22C23×C3×C8C2211yescharacteristic
23C3×#525—24no—
24C3×#525—24no—
25C2×C3×#123—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×C22⋊Q8C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×#121C2211yescharacteristic
33C2×C3×#120—21no—
34C2×C3×C4×D4—21no—
35C2×C3×C4×D4—21no—
36C2×C3×#117C2211yescharacteristic
37C3×#467—24no—
38C3×#465—24no—
39C3×#452—24no—
40C2×C3×#107C2211yescharacteristic, complemented
41C2×C3×#106C2211yescharacteristic, complemented
42C2×C3×#103C2211yescharacteristic, complemented
43C2×C3×#103C2211yescharacteristic, complemented
44C2×C3×#103C2211yescharacteristic, complemented
45C2×C3×#103C2211yescharacteristic, complemented
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic, complemented
48C2×C3×#102C2211yescharacteristic, complemented
49C2×C3×#102C2211yescharacteristic, complemented
50C2×C3×C22⋊C8—24no—
51C2×C3×C22⋊C8C2211yescharacteristic
52C2×C3×C22⋊C8C2211yescharacteristic
53C2×C3×C22⋊C8C2211yescharacteristic
54C2×C3×C22⋊C8C2211yescharacteristic
55C3×#385—21no—
56C3×#385—21no—
57C3×#385—21no—
58C3×#380C2211yescharacteristic
59C3×#380C2211yescharacteristic
60C3×#380C2211yescharacteristic
61C3×#379—21no—
62C3×#340C2211yescharacteristic, complemented
63C3×#340C2211yescharacteristic, complemented
64C3×#340C2211yescharacteristic, complemented
65C3×#340C2211yescharacteristic, complemented
66C2×#525C2×C311yescharacteristic
67C2×#467C2×C311yescharacteristic, complemented
68C2×#465C2×C311yescharacteristic, complemented
69C2×#452C2×C311yescharacteristic, complemented
70C22×C22⋊C8C2×C311yescharacteristic, complemented
71#2848C2×C311yescharacteristic, complemented
72#2035C2×C311yescharacteristic, complemented
73#2033C2×C311yescharacteristic, complemented
74#2001C2×C311yescharacteristic, complemented
75#2000C2×C311yescharacteristic, complemented
76#1893C2×C311yescharacteristic, complemented
77#1892C2×C311yescharacteristic, complemented
78#1873C2×C311yescharacteristic, complemented
79#1854C2×C311yescharacteristic, complemented
80#1788C2×C311yescharacteristic, complemented
81C25×C3D411yescharacteristic
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—41no—
87C2×C3×#41—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×Q8C2311yescharacteristic
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4C2311yescharacteristic
94C23×C3×C4—22no—
95C23×C3×C4—22no—
96C23×C3×C4—22no—
97C23×C3×C4—21no—
98C23×C3×C4—22no—
99C23×C3×C4—41no—
100C23×C3×C4—41no—
101C23×C3×C4D411yescharacteristic
102C23×C3×C4D411yescharacteristic
103C23×C3×C4D411yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16—41no—
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—41no—
113C22×C3×C8—22no—
114C22×C3×C8—22no—
115C22×C3×C8—22no—
116C22×C3×C8—22no—
117C22×C3×C8—41no—
118C22×C3×C8—41no—
119C22×C3×C8C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C3×#123—28no—
124C3×C22⋊Q8—22no—
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8—22no—
127C3×C22⋊Q8—22no—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—22no—
130C3×C22⋊Q8—22no—
131C3×C22⋊Q8—41no—
132C3×C22⋊Q8—41no—
133C3×C22⋊Q8D414yes—
134C3×#121—22no—
135C3×#121—22no—
136C3×#121—22no—
137C3×#121D414yes—
138C3×#120—28no—
139C3×C4×D4—28no—
140C3×C4×D4—28no—
141C3×#117—22no—
142C3×#117—22no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4—21no—
145C2×C3×C4⋊C4—21no—
146C2×C3×C4⋊C4—21no—
147C2×C3×C4⋊C4—21no—
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C4⋊C4C2311yescharacteristic
150C2×C3×C4⋊C4C2311yescharacteristic
151C2×C3×C4⋊C4C2311yescharacteristic
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—21no—
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—21no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—21no—
162C2×C3×C22⋊C4—21no—
163C2×C3×C22⋊C4—21no—
164C2×C3×C42—21no—
165C3×#107—22no—
166C3×#106—22no—
167C3×#103—22no—
168C3×#103—22no—
169C3×#103—22no—
170C3×#103—22no—
171C3×#103—41no—
172C3×#102—22no—
173C3×#102—22no—
174C3×#102—41no—
175C3×C22⋊C8—22no—
176C3×C22⋊C8—22no—
177C3×C22⋊C8—22no—
178C3×C22⋊C8D414yescomplemented
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—21no—
182C22×#41C22×C311yescharacteristic
183C24×C4C22×C311yescharacteristic
184C22×Q16C22×C311yescharacteristic, complemented
185C22×SD16C22×C311yescharacteristic, complemented
186C23×C8C22×C311yescharacteristic
187C23×C8C22×C311yescharacteristic
188#525—24no—
189#525—24no—
190C2×#123—21no—
191C2×C22⋊Q8C22×C311yescharacteristic
192C2×C22⋊Q8C22×C311yescharacteristic
193C2×C22⋊Q8C22×C311yescharacteristic
194C2×C22⋊Q8C22×C311yescharacteristic
195C2×C22⋊Q8C22×C311yescharacteristic
196C2×#121C22×C311yescharacteristic
197C2×#121C22×C311yescharacteristic
198C2×#120—21no—
199C2×C4×D4—21no—
200C2×C4×D4—21no—
201C2×#117C22×C311yescharacteristic
202#467—24no—
203#465—24no—
204#452—24no—
205C2×#107C22×C311yescharacteristic, complemented
206C2×#106C22×C311yescharacteristic, complemented
207C2×#103C22×C311yescharacteristic, complemented
208C2×#103C22×C311yescharacteristic, complemented
209C2×#103C22×C311yescharacteristic, complemented
210C2×#103C22×C311yescharacteristic, complemented
211C2×#103C22×C311yescharacteristic, complemented
212C2×#102C22×C311yescharacteristic, complemented
213C2×#102C22×C311yescharacteristic, complemented
214C2×#102C22×C311yescharacteristic, complemented
215C2×C22⋊C8—24no—
216C2×C22⋊C8C22×C311yescharacteristic
217C2×C22⋊C8C22×C311yescharacteristic
218C2×C22⋊C8C22×C311yescharacteristic
219C2×C22⋊C8C22×C311yescharacteristic
220#385—21no—
221#385—21no—
222#385—21no—
223#380C22×C311yescharacteristic
224#380C22×C311yescharacteristic
225#380C22×C311yescharacteristic
226#379—21no—
227#340C22×C311yescharacteristic, complemented
228#340C22×C311yescharacteristic, complemented
229#340C22×C311yescharacteristic, complemented
230#340C22×C311yescharacteristic, complemented
231C24×C3—22no—
232C24×C3—22no—
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—21no—
237C24×C3—41no—
238C24×C3—41no—
239C24×C3C2×D411yescharacteristic
240C24×C3C2×D411yescharacteristic
241C24×C3C2×D411yescharacteristic
242C3×#41—44no—
243C3×#41—44no—
244C3×#41—44no—
245C3×#41—44no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—21no—
255C2×C3×Q8—21no—
256C2×C3×Q8—21no—
257C2×C3×Q8C2×D412yes—
258C2×C3×D4—24no—
259C2×C3×D4—24no—
260C2×C3×D4—24no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
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×D4C2×D412yes—
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—24no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—41no—
302C22×C3×C4—41no—
303C22×C3×C4—41no—
304C22×C3×C4—44no—
305C22×C3×C4—44no—
306C22×C3×C4—44no—
307C22×C3×C4—44no—
308C22×C3×C4—42no—
309C22×C3×C4—42no—
310C22×C3×C4C2×D411yescharacteristic
311C22×C3×C4C2×D411yescharacteristic
312C22×C3×C4C2×D412yes—
313C22×C3×C4C2×D412yes—
314C22×C3×C4C2×D411yescharacteristic
315C22×C3×C4C2×D412yes—
316C22×C3×C4#4112yes—
317C22×C3×C4C2411yescharacteristic
318C3×Q16—44no—
319C3×SD16—44no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
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—44no—
331C2×C3×C8—44no—
332C2×C3×C8C2×D412yes—
333C2×C3×C8C2×D412yes—
334C3×C4⋊C4—24no—
335C3×C4⋊C4—24no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—42no—
345C3×C4⋊C4—42no—
346C3×C4⋊C4—42no—
347C3×C4⋊C4C2×D412yes—
348C3×C4⋊C4C2×D412yes—
349C3×C22⋊C4—24no—
350C3×C22⋊C4—24no—
351C3×C22⋊C4—24no—
352C3×C22⋊C4—24no—
353C3×C22⋊C4—24no—
354C3×C22⋊C4—42no—
355C3×C22⋊C4—42no—
356C3×C22⋊C4—42no—
357C3×C22⋊C4—42no—
358C3×C22⋊C4—42no—
359C3×C22⋊C4—42no—
360C3×C42—24no—
361C25C3×D411yescharacteristic
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—41no—
367C2×#41—41no—
368C22×Q8C23×C311yescharacteristic
369C22×Q8C23×C311yescharacteristic
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—21no—
373C22×D4C23×C311yescharacteristic
374C23×C4—21no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—41no—
380C23×C4—41no—
381C23×C4C3×D411yescharacteristic
382C23×C4C3×D411yescharacteristic
383C23×C4C3×D411yescharacteristic
384C23×C4C23×C311yescharacteristic
385C23×C4C23×C311yescharacteristic
386C23×C4C23×C311yescharacteristic
387C2×Q16—22no—
388C2×Q16—22no—
389C2×Q16—41no—
390C2×SD16—22no—
391C2×SD16—22no—
392C2×SD16—41no—
393C22×C8—22no—
394C22×C8—22no—
395C22×C8—22no—
396C22×C8—22no—
397C22×C8—41no—
398C22×C8—41no—
399C22×C8C23×C311yescharacteristic
400C22×C8C23×C311yescharacteristic
401C22×C8C23×C311yescharacteristic
402C22×C8C23×C311yescharacteristic
403#123—28no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—41no—
412C22⋊Q8—41no—
413C22⋊Q8C3×D414yes—
414#121—22no—
415#121—22no—
416#121—22no—
417#121C3×D414yes—
418#120—28no—
419C4×D4—28no—
420C4×D4—28no—
421#117—22no—
422#117—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4C23×C311yescharacteristic
429C2×C4⋊C4C23×C311yescharacteristic
430C2×C4⋊C4C23×C311yescharacteristic
431C2×C4⋊C4C23×C311yescharacteristic
432C2×C4⋊C4C23×C311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C42—21no—
445#107—22no—
446#106—22no—
447#103—22no—
448#103—22no—
449#103—22no—
450#103—22no—
451#103—41no—
452#102—22no—
453#102—22no—
454#102—41no—
455C22⋊C8—22no—
456C22⋊C8—22no—
457C22⋊C8—22no—
458C22⋊C8C3×D414yescomplemented
459#95—21no—
460#95—21no—
461#95—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—28no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—22no—
480C23×C3—44no—
481C23×C3—44no—
482C23×C3—44no—
483C23×C3—44no—
484C23×C3—44no—
485C23×C3—44no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3#12012yes—
493C23×C3#12112yes—
494C23×C3#13512yes—
495C23×C3#13512yes—
496C23×C3#13712yes—
497C23×C3C22×D411yescharacteristic
498C3×Q8—22no—
499C3×Q8—22no—
500C3×Q8—41no—
501C3×Q8—41no—
502C3×Q8—41no—
503C3×Q8—41no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—48no—
509C3×D4—48no—
510C3×D4—48no—
511C3×D4—41no—
512C3×D4—41no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—21no—
528C2×C3×C4—22no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—44no—
532C2×C3×C4—44no—
533C2×C3×C4—44no—
534C2×C3×C4—48no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
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#12012yes—
558C2×C3×C4#12112yes—
559C2×C3×C4C22×D411yescharacteristic
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C22×D411yescharacteristic
562C2×C3×C4C2×#4111yescharacteristic
563C2×C3×C4H(5,𝔽2)11yescharacteristic
564C2×C3×C4H(5,𝔽2)11yescharacteristic
565C3×C8—22no—
566C3×C8—22no—
567C3×C8—41no—
568C3×C8—41no—
569C24—22no—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—21no—
575C24—41no—
576C24—41no—
577C24C2×C3×D411yescharacteristic
578C24C2×C3×D411yescharacteristic
579C24C2×C3×D411yescharacteristic
580#41—44no—
581#41—44no—
582#41—44no—
583#41—44no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×C3×D412yes—
596C2×D4—24no—
597C2×D4—24no—
598C2×D4—24no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4C2×C3×D412yes—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4C2×C3×D411yescharacteristic
649C22×C4C2×C3×D411yescharacteristic
650C22×C4C2×C3×D412yes—
651C22×C4C2×C3×D412yes—
652C22×C4C2×C3×D411yescharacteristic
653C22×C4C2×C3×D412yes—
654C22×C4C3×#4112yes—
655C22×C4C24×C311yescharacteristic
656Q16—44no—
657SD16—44no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—44no—
669C2×C8—44no—
670C2×C8C2×C3×D412yes—
671C2×C8C2×C3×D412yes—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—42no—
685C4⋊C4C2×C3×D412yes—
686C4⋊C4C2×C3×D412yes—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C42—24no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—416no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—81no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—81no—
727C22×C3#45214yescomplemented
728C22×C3C2×#12011yescharacteristic
729C22×C3C2×#12111yescharacteristic
730C22×C3#53411yescharacteristic
731C22×C3C2×#13511yescharacteristic
732C22×C3C2×#13511yescharacteristic
733C22×C3C2×#13711yescharacteristic
734C22×C3#57511yescharacteristic
735C3×C4—22no—
736C3×C4—22no—
737C3×C4—41no—
738C3×C4—42no—
739C3×C4—42no—
740C3×C4—42no—
741C3×C4—81no—
742C3×C4—81no—
743C3×C4—81no—
744C3×C4—81no—
745C3×C4D4211yescharacteristic
746C3×C4D4211yescharacteristic
747C3×C4#54611yescharacteristic
748C3×C4#54611yescharacteristic
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—28no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—22no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23C3×#12012yes—
780C23C3×#12112yes—
781C23C3×#13512yes—
782C23C3×#13512yes—
783C23C3×#13712yes—
784C23C22×C3×D411yescharacteristic
785Q8—22no—
786Q8—22no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792Q8—41no—
793D4—22no—
794D4—22no—
795D4—48no—
796D4—48no—
797D4—48no—
798D4—41no—
799D4—41no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—48no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4C3×#12012yes—
845C2×C4C3×#12112yes—
846C2×C4C22×C3×D411yescharacteristic
847C2×C4C22×C3×D411yescharacteristic
848C2×C4C22×C3×D411yescharacteristic
849C2×C4C2×C3×#4111yescharacteristic
850C2×C4C3×H(5,𝔽2)11yescharacteristic
851C2×C4C3×H(5,𝔽2)11yescharacteristic
852C8—22no—
853C8—22no—
854C8—41no—
855C8—41no—
856C2×C3—24no—
857C2×C3—42no—
858C2×C3—42no—
859C2×C3—82no—
860C2×C3#241011yescharacteristic
861C2×C3C2×#45211yescharacteristic
862C2×C3#300211yescharacteristic
863C2×C3#305011yescharacteristic
864C2×C3#305611yescharacteristic
865C2×C3#319011yescharacteristic
866C2×C3#319111yescharacteristic
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—416no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22C3×#45214yescomplemented
896C22C2×C3×#12011yescharacteristic
897C22C2×C3×#12111yescharacteristic
898C22C3×#53411yescharacteristic
899C22C2×C3×#13511yescharacteristic
900C22C2×C3×#13511yescharacteristic
901C22C2×C3×#13711yescharacteristic
902C22C3×#57511yescharacteristic
903C4—22no—
904C4—22no—
905C4—41no—
906C4—42no—
907C4—42no—
908C4—42no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4—81no—
913C4C3×D4211yescharacteristic
914C4C3×D4211yescharacteristic
915C4C3×#54611yescharacteristic
916C4C3×#54611yescharacteristic
917C3#2438311yescharacteristic, direct product factor, Sylow
918C2—24no—
919C2—42no—
920C2—42no—
921C2—82no—
922C2C3×#241011yescharacteristic
923C2C2×C3×#45211yescharacteristic
924C2C3×#300211yescharacteristic
925C2C3×#305011yescharacteristic
926C2C3×#305611yescharacteristic
927C2C3×#319011yescharacteristic
928C2C3×#319111yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#467C2semidirect
3. C2×C3×#465C2semidirect
4. C2×C3×#452C2semidirect
5. C22×C3×C22⋊C8C2semidirect
6. C3×#2848C2semidirect
7. C3×#2035C2semidirect
8. C3×#2033C2semidirect
9. C3×#2001C2semidirect
10. C3×#2000C2semidirect
11. C3×#1893C2semidirect
12. C3×#1892C2semidirect
13. C3×#1873C2semidirect
14. C3×#1854C2semidirect
15. C3×#1788C2semidirect
16. #24383C3direct (N × H)
19. C22×C3×Q16C22semidirect
20. C22×C3×SD16C22semidirect
40. C2×C3×#107C22semidirect
41. C2×C3×#106C22semidirect
42. C2×C3×#103C22semidirect
43. C2×C3×#103C22semidirect
44. C2×C3×#103C22semidirect
45. C2×C3×#103C22semidirect
46. C2×C3×#103C22semidirect
47. C2×C3×#102C22semidirect
48. C2×C3×#102C22semidirect
49. C2×C3×#102C22semidirect
62. C3×#340C22semidirect
63. C3×#340C22semidirect
64. C3×#340C22semidirect
65. C3×#340C22semidirect
67. C2×#467C2×C3semidirect
68. C2×#465C2×C3semidirect
69. C2×#452C2×C3semidirect
70. C22×C22⋊C8C2×C3semidirect
71. #2848C2×C3semidirect
72. #2035C2×C3semidirect
73. #2033C2×C3semidirect
74. #2001C2×C3semidirect
75. #2000C2×C3semidirect
76. #1893C2×C3semidirect
77. #1892C2×C3semidirect
78. #1873C2×C3semidirect
79. #1854C2×C3semidirect
80. #1788C2×C3semidirect
178. C3×C22⋊C8D4semidirect
184. C22×Q16C22×C3semidirect
185. C22×SD16C22×C3semidirect
205. C2×#107C22×C3semidirect
206. C2×#106C22×C3semidirect
207. C2×#103C22×C3semidirect
208. C2×#103C22×C3semidirect
209. C2×#103C22×C3semidirect
210. C2×#103C22×C3semidirect
211. C2×#103C22×C3semidirect
212. C2×#102C22×C3semidirect
213. C2×#102C22×C3semidirect
214. C2×#102C22×C3semidirect
227. #340C22×C3semidirect
228. #340C22×C3semidirect
229. #340C22×C3semidirect
230. #340C22×C3semidirect
458. C22⋊C8C3×D4semidirect
727. C22×C3#452semidirect
895. C22C3×#452semidirect
917. C3#24383direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C2×C3×#4672
C2×C3×#4652
C2×C3×#4522
C22×C3×C22⋊C82
C3×#28482
C3×#20352
C3×#20332
C3×#20012
C3×#20002
C3×#18932
C3×#18922
C3×#18732
C3×#18542
C3×#17882
#243833