Finite Group Databasebeta

← C3×#24396 #10643003

Subgroups — C3×#24396 #10643003

Order 768.

1444 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#536C211yesmaximal, characteristic, complemented
2C2×C3×#468C211yesmaximal, characteristic, complemented
3C2×C3×#465C211yesmaximal, characteristic, complemented
4C2×C3×#448C211yesmaximal, characteristic, complemented
5C2×C3×#408C211yesmaximal, characteristic, complemented
6C3×#2615C211yesmaximal, characteristic
7C3×#2036C211yesmaximal, characteristic, complemented
8C3×#2035C211yesmaximal, characteristic, complemented
9C3×#2000C211yesmaximal, characteristic, complemented
10C3×#2000C211yesmaximal, characteristic, complemented
11C3×#1894C211yesmaximal, characteristic, complemented
12C3×#1892C211yesmaximal, characteristic, complemented
13C3×#1875C211yesmaximal, characteristic, complemented
14C3×#1854C211yesmaximal, characteristic, complemented
15C3×#1787C211yesmaximal, characteristic, complemented
16#24396C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×M16C2211yescharacteristic
22C23×C3×C8C2211yescharacteristic
23C3×#536—24no—
24C3×#536—24no—
25C2×C3×C4⋊Q8—21no—
26C2×C3×#124—21no—
27C2×C3×#123—21no—
28C2×C3×#123—21no—
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×C22⋊Q8C2211yescharacteristic
31C2×C3×C22⋊Q8C2211yescharacteristic
32C2×C3×C22⋊Q8C2211yescharacteristic
33C2×C3×#121C2211yescharacteristic
34C2×C3×#121C2211yescharacteristic
35C2×C3×#121C2211yescharacteristic
36C2×C3×#117C2211yescharacteristic
37C3×#468—24no—
38C3×#465—24no—
39C3×#448—24no—
40C2×C3×#107C2211yescharacteristic
41C2×C3×#106C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×#103C2211yescharacteristic
47C2×C3×#103C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C3×#408—24no—
51C2×C3×C22⋊C8C2211yescharacteristic
52C2×C3×C22⋊C8C2211yescharacteristic
53C2×C3×C22⋊C8C2211yescharacteristic
54C2×C3×C22⋊C8C2211yescharacteristic
55C3×#393—21no—
56C3×#392—21no—
57C3×#392—21no—
58C3×#392—21no—
59C3×#380C2211yescharacteristic
60C3×#380C2211yescharacteristic
61C3×#380C2211yescharacteristic
62C3×#340C2211yescharacteristic
63C3×#340C2211yescharacteristic
64C3×#340C2211yescharacteristic
65C3×#340C2211yescharacteristic
66C2×#536C2×C311yescharacteristic, complemented
67C2×#468C2×C311yescharacteristic, complemented
68C2×#465C2×C311yescharacteristic, complemented
69C2×#448C2×C311yescharacteristic, complemented
70C2×#408C2×C311yescharacteristic, complemented
71#2615C2×C311yescharacteristic
72#2036C2×C311yescharacteristic, complemented
73#2035C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#2000C2×C311yescharacteristic, complemented
76#1894C2×C311yescharacteristic, complemented
77#1892C2×C311yescharacteristic, complemented
78#1875C2×C311yescharacteristic, complemented
79#1854C2×C311yescharacteristic, complemented
80#1787C2×C311yescharacteristic, complemented
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—41no—
86C2×C3×#41—41no—
87C22×C3×Q8—22no—
88C22×C3×Q8—22no—
89C22×C3×Q8—21no—
90C22×C3×Q8—22no—
91C22×C3×Q8—22no—
92C22×C3×Q8—41no—
93C22×C3×Q8—41no—
94C22×C3×Q8D411yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×Q8C2311yescharacteristic
97C22×C3×D4—21no—
98C22×C3×D4—21no—
99C22×C3×D4—21no—
100C22×C3×D4D411yescharacteristic
101C22×C3×D4D411yescharacteristic
102C22×C3×D4D411yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4—21no—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C2×C3×SD16—22no—
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—41no—
113C2×C3×SD16—41no—
114C2×C3×M16—22no—
115C2×C3×M16—22no—
116C2×C3×M16—41no—
117C22×C3×C8—22no—
118C22×C3×C8—22no—
119C22×C3×C8—41no—
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C22×C3×C8C2311yescharacteristic
124C3×C4⋊Q8—28no—
125C3×#124—28no—
126C3×#123—28no—
127C3×#123—28no—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—22no—
130C3×C22⋊Q8—22no—
131C3×C22⋊Q8—22no—
132C3×C22⋊Q8—22no—
133C3×C22⋊Q8—22no—
134C3×C22⋊Q8D414yescomplemented
135C3×C22⋊Q8D414yescomplemented
136C3×#121—22no—
137C3×#121—22no—
138C3×#121—22no—
139C3×#121—22no—
140C3×#121—41no—
141C3×#121—41no—
142C3×#117—22no—
143C3×#117—22no—
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×#103—41no—
173C3×#102—22no—
174C3×#102—22no—
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
183C23×Q8C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic
186C22×M16C22×C311yescharacteristic
187C23×C8C22×C311yescharacteristic
188#536—24no—
189#536—24no—
190C2×C4⋊Q8—21no—
191C2×#124—21no—
192C2×#123—21no—
193C2×#123—21no—
194C2×C22⋊Q8C22×C311yescharacteristic
195C2×C22⋊Q8C22×C311yescharacteristic
196C2×C22⋊Q8C22×C311yescharacteristic
197C2×C22⋊Q8C22×C311yescharacteristic
198C2×#121C22×C311yescharacteristic
199C2×#121C22×C311yescharacteristic
200C2×#121C22×C311yescharacteristic
201C2×#117C22×C311yescharacteristic
202#468—24no—
203#465—24no—
204#448—24no—
205C2×#107C22×C311yescharacteristic
206C2×#106C22×C311yescharacteristic
207C2×#103C22×C311yescharacteristic
208C2×#103C22×C311yescharacteristic
209C2×#103C22×C311yescharacteristic
210C2×#103C22×C311yescharacteristic
211C2×#103C22×C311yescharacteristic
212C2×#103C22×C311yescharacteristic
213C2×#102C22×C311yescharacteristic
214C2×#102C22×C311yescharacteristic
215#408—24no—
216C2×C22⋊C8C22×C311yescharacteristic
217C2×C22⋊C8C22×C311yescharacteristic
218C2×C22⋊C8C22×C311yescharacteristic
219C2×C22⋊C8C22×C311yescharacteristic
220#393—21no—
221#392—21no—
222#392—21no—
223#392—21no—
224#380C22×C311yescharacteristic
225#380C22×C311yescharacteristic
226#380C22×C311yescharacteristic
227#340C22×C311yescharacteristic
228#340C22×C311yescharacteristic
229#340C22×C311yescharacteristic
230#340C22×C311yescharacteristic
231C24×C3—21no—
232C24×C3C2×D411yescharacteristic
233C24×C3C2×D411yescharacteristic
234C24×C3C2×D411yescharacteristic
235C3×#41—44no—
236C3×#41—44no—
237C3×#41—44no—
238C3×#41—44no—
239C2×C3×Q8—24no—
240C2×C3×Q8—22no—
241C2×C3×Q8—22no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
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—41no—
253C2×C3×Q8—44no—
254C2×C3×Q8—44no—
255C2×C3×Q8—44no—
256C2×C3×Q8—44no—
257C2×C3×Q8—42no—
258C2×C3×Q8—42no—
259C2×C3×Q8C2×D412yes—
260C2×C3×Q8C2×D412yes—
261C2×C3×D4—22no—
262C2×C3×D4—22no—
263C2×C3×D4—22no—
264C2×C3×D4—22no—
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—21no—
273C2×C3×D4—41no—
274C2×C3×D4—41no—
275C2×C3×D4—41no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—81no—
280C2×C3×D4—81no—
281C2×C3×D4—81no—
282C2×C3×D4—81no—
283C2×C3×D4—81no—
284C2×C3×D4—81no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—24no—
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—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—42no—
308C22×C3×C4—42no—
309C22×C3×C4C2×D411yescharacteristic
310C22×C3×C4C2×D411yescharacteristic
311C22×C3×C4C2×D412yes—
312C22×C3×C4C2×D412yes—
313C22×C3×C4C2×D411yescharacteristic
314C22×C3×C4C2×D412yes—
315C22×C3×C4#4112yes—
316C22×C3×C4C2411yescharacteristic
317C3×SD16—44no—
318C3×SD16—44no—
319C3×M16—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×C8C2×D412yes—
332C2×C3×C8C2×D412yes—
333C3×C4⋊C4—24no—
334C3×C4⋊C4—24no—
335C3×C4⋊C4—24no—
336C3×C4⋊C4—24no—
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—21no—
345C3×C4⋊C4C2×D412yes—
346C3×C4⋊C4C2×D412yes—
347C3×C22⋊C4—24no—
348C3×C22⋊C4—24no—
349C3×C22⋊C4—24no—
350C3×C22⋊C4—24no—
351C3×C22⋊C4—24no—
352C3×C22⋊C4—42no—
353C3×C22⋊C4—42no—
354C3×C22⋊C4—42no—
355C3×C22⋊C4—81no—
356C3×C22⋊C4—81no—
357C3×C22⋊C4—81no—
358C3×C42—24no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—22no—
362C2×#41—22no—
363C2×#41—41no—
364C2×#41—41no—
365C22×Q8—22no—
366C22×Q8—22no—
367C22×Q8—21no—
368C22×Q8—22no—
369C22×Q8—22no—
370C22×Q8—41no—
371C22×Q8—41no—
372C22×Q8C3×D411yescharacteristic
373C22×Q8C23×C311yescharacteristic
374C22×Q8C23×C311yescharacteristic
375C22×D4—21no—
376C22×D4—21no—
377C22×D4—21no—
378C22×D4C3×D411yescharacteristic
379C22×D4C3×D411yescharacteristic
380C22×D4C3×D411yescharacteristic
381C22×D4C23×C311yescharacteristic
382C23×C4—21no—
383C23×C4C23×C311yescharacteristic
384C23×C4C23×C311yescharacteristic
385C23×C4C23×C311yescharacteristic
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16—41no—
391C2×SD16—41no—
392C2×M16—22no—
393C2×M16—22no—
394C2×M16—41no—
395C22×C8—22no—
396C22×C8—22no—
397C22×C8—41no—
398C22×C8C23×C311yescharacteristic
399C22×C8C23×C311yescharacteristic
400C22×C8C23×C311yescharacteristic
401C22×C8C23×C311yescharacteristic
402C4⋊Q8—28no—
403#124—28no—
404#123—28no—
405#123—28no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8C3×D414yescomplemented
413C22⋊Q8C3×D414yescomplemented
414#121—22no—
415#121—22no—
416#121—22no—
417#121—22no—
418#121—41no—
419#121—41no—
420#117—22no—
421#117—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4C23×C311yescharacteristic
427C2×C4⋊C4C23×C311yescharacteristic
428C2×C4⋊C4C23×C311yescharacteristic
429C2×C4⋊C4C23×C311yescharacteristic
430C2×C4⋊C4C23×C311yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
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×C42—21no—
443#107—22no—
444#106—22no—
445#103—22no—
446#103—22no—
447#103—22no—
448#103—22no—
449#103—41no—
450#103—41no—
451#102—22no—
452#102—22no—
453C22⋊C8—22no—
454C22⋊C8—22no—
455C22⋊C8—22no—
456C22⋊C8C3×D414yescomplemented
457#95—21no—
458#95—21no—
459#95—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
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—41no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3#12012yes—
487C23×C3#12112yes—
488C23×C3C22×D411yescharacteristic
489C3×Q8—22no—
490C3×Q8—22no—
491C3×Q8—22no—
492C3×Q8—22no—
493C3×Q8—44no—
494C3×Q8—48no—
495C3×Q8—41no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×D4—44no—
500C3×D4—44no—
501C3×D4—44no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4—84no—
507C3×D4—84no—
508C3×D4—84no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
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—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—48no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
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#12012yes—
551C2×C3×C4#12112yes—
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C22×D411yescharacteristic
554C2×C3×C4C22×D411yescharacteristic
555C2×C3×C4C2×#4111yescharacteristic
556C2×C3×C4H(5,𝔽2)11yescharacteristic
557C2×C3×C4H(5,𝔽2)11yescharacteristic
558C3×C8—22no—
559C3×C8—22no—
560C3×C8—41no—
561C3×C8—41no—
562C24—21no—
563C24C2×C3×D411yescharacteristic
564C24C2×C3×D411yescharacteristic
565C24C2×C3×D411yescharacteristic
566#41—44no—
567#41—44no—
568#41—44no—
569#41—44no—
570C2×Q8—24no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—41no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—44no—
588C2×Q8—42no—
589C2×Q8—42no—
590C2×Q8C2×C3×D412yes—
591C2×Q8C2×C3×D412yes—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—81no—
615C2×D4—81no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—24no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
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—42no—
639C22×C4—42no—
640C22×C4C2×C3×D411yescharacteristic
641C22×C4C2×C3×D411yescharacteristic
642C22×C4C2×C3×D412yes—
643C22×C4C2×C3×D412yes—
644C22×C4C2×C3×D411yescharacteristic
645C22×C4C2×C3×D412yes—
646C22×C4C3×#4112yes—
647C22×C4C24×C311yescharacteristic
648SD16—44no—
649SD16—44no—
650M16—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—44no—
662C2×C8C2×C3×D412yes—
663C2×C8C2×C3×D412yes—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—24no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4C2×C3×D412yes—
677C4⋊C4C2×C3×D412yes—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—24no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—81no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3C2×#12011yescharacteristic
719C22×C3C2×#12111yescharacteristic
720C22×C3#53411yescharacteristic
721C22×C3#57711yescharacteristic
722C22×C3#57711yescharacteristic
723C22×C3#57711yescharacteristic
724C22×C3#57811yescharacteristic
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—41no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—42no—
732C3×C4—81no—
733C3×C4—81no—
734C3×C4—81no—
735C3×C4D4211yescharacteristic
736C3×C4D4211yescharacteristic
737C3×C4#54611yescharacteristic
738C3×C4#54611yescharacteristic
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23C3×#12012yes—
766C23C3×#12112yes—
767C23C22×C3×D411yescharacteristic
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—22no—
772Q8—44no—
773Q8—48no—
774Q8—41no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778D4—44no—
779D4—44no—
780D4—44no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—84no—
786D4—84no—
787D4—84no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—48no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4C3×#12012yes—
830C2×C4C3×#12112yes—
831C2×C4C22×C3×D411yescharacteristic
832C2×C4C22×C3×D411yescharacteristic
833C2×C4C22×C3×D411yescharacteristic
834C2×C4C2×C3×#4111yescharacteristic
835C2×C4C3×H(5,𝔽2)11yescharacteristic
836C2×C4C3×H(5,𝔽2)11yescharacteristic
837C8—22no—
838C8—22no—
839C8—41no—
840C8—41no—
841C2×C3—42no—
842C2×C3—42no—
843C2×C3—81no—
844C2×C3—161no—
845C2×C3#241011yescharacteristic
846C2×C3#301011yescharacteristic
847C2×C3#301311yescharacteristic
848C2×C3#305711yescharacteristic
849C2×C3#306311yescharacteristic
850C2×C3#320011yescharacteristic
851C2×C3#320111yescharacteristic
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22C2×C3×#12011yescharacteristic
881C22C2×C3×#12111yescharacteristic
882C22C3×#53411yescharacteristic
883C22C3×#57711yescharacteristic
884C22C3×#57711yescharacteristic
885C22C3×#57711yescharacteristic
886C22C3×#57811yescharacteristic
887C4—22no—
888C4—22no—
889C4—41no—
890C4—42no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4C3×D4211yescharacteristic
898C4C3×D4211yescharacteristic
899C4C3×#54611yescharacteristic
900C4C3×#54611yescharacteristic
901C3#2439611yescharacteristic, direct product factor, Sylow
902C2—42no—
903C2—42no—
904C2—81no—
905C2—161no—
906C2C3×#241011yescharacteristic
907C2C3×#301011yescharacteristic
908C2C3×#301311yescharacteristic
909C2C3×#305711yescharacteristic
910C2C3×#306311yescharacteristic
911C2C3×#320011yescharacteristic
912C2C3×#320111yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#536C2semidirect
2. C2×C3×#468C2semidirect
3. C2×C3×#465C2semidirect
4. C2×C3×#448C2semidirect
5. C2×C3×#408C2semidirect
7. C3×#2036C2semidirect
8. C3×#2035C2semidirect
9. C3×#2000C2semidirect
10. C3×#2000C2semidirect
11. C3×#1894C2semidirect
12. C3×#1892C2semidirect
13. C3×#1875C2semidirect
14. C3×#1854C2semidirect
15. C3×#1787C2semidirect
16. #24396C3direct (N × H)
66. C2×#536C2×C3semidirect
67. C2×#468C2×C3semidirect
68. C2×#465C2×C3semidirect
69. C2×#448C2×C3semidirect
70. C2×#408C2×C3semidirect
72. #2036C2×C3semidirect
73. #2035C2×C3semidirect
74. #2000C2×C3semidirect
75. #2000C2×C3semidirect
76. #1894C2×C3semidirect
77. #1892C2×C3semidirect
78. #1875C2×C3semidirect
79. #1854C2×C3semidirect
80. #1787C2×C3semidirect
134. C3×C22⋊Q8D4semidirect
135. C3×C22⋊Q8D4semidirect
178. C3×C22⋊C8D4semidirect
412. C22⋊Q8C3×D4semidirect
413. C22⋊Q8C3×D4semidirect
456. C22⋊C8C3×D4semidirect
901. C3#24396direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5362
C2×C3×#4682
C2×C3×#4652
C2×C3×#4482
C2×C3×#4082
C3×#26152
C3×#20362
C3×#20352
C3×#20002
C3×#18942
C3×#18922
C3×#18752
C3×#18542
C3×#17872
#243963