Finite Group Databasebeta

← C3×#24219 #10642826

Subgroups — C3×#24219 #10642826

Order 768.

1420 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#536C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×C3×#461C211yesmaximal, characteristic, complemented
4C2×C3×#449C211yesmaximal, characteristic
5C2×C3×#448C211yesmaximal, characteristic, complemented
6C3×#2324C211yesmaximal, characteristic, complemented
7C3×#2043C211yesmaximal, characteristic, complemented
8C3×#2042C211yesmaximal, characteristic, complemented
9C3×#2013C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#1983C211yesmaximal, characteristic, complemented
12C3×#1981C211yesmaximal, characteristic, complemented
13C3×#1798C211yesmaximal, characteristic, complemented
14C3×#1788C211yesmaximal, characteristic, complemented
15C3×#1787C211yesmaximal, characteristic, complemented
16#24219C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×D8C2211yescharacteristic
23C3×#536—24no—
24C3×#536—24no—
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×C4⋊Q8C2211yescharacteristic
27C2×C3×#124C2211yescharacteristic
28C2×C3×#124C2211yescharacteristic
29C2×C3×#123—21no—
30C2×C3×#123—21no—
31C2×C3×C22⋊Q8—21no—
32C2×C3×C22⋊Q8—21no—
33C2×C3×#121C2211yescharacteristic
34C2×C3×C4×D4C2211yescharacteristic
35C2×C3×#117C2211yescharacteristic
36C3×#463—24no—
37C3×#461—24no—
38C3×#449—24no—
39C3×#448—24no—
40C2×C3×C4⋊C8C2211yescharacteristic
41C2×C3×C4⋊C8C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×#103C2211yescharacteristic
47C2×C3×#103C2211yescharacteristic
48C2×C3×#103C2211yescharacteristic
49C2×C3×#103C2211yescharacteristic
50C2×C3×#103C2211yescharacteristic
51C2×C3×#102C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×C3×#102C2211yescharacteristic
54C2×C3×C22⋊C8C2211yescharacteristic
55C2×C3×C22⋊C8C2211yescharacteristic
56C3×#390—21no—
57C3×#390C2211yescharacteristic
58C3×#389C2211yescharacteristic
59C3×#388—21no—
60C3×#386—21no—
61C3×#385—21no—
62C3×#380C2211yescharacteristic
63C3×C4×C4⋊C4C2211yescharacteristic
64C3×#336C2211yescharacteristic
65C3×#336C2211yescharacteristic
66C2×#536C2×C311yescharacteristic, complemented
67C2×#463C2×C311yescharacteristic, complemented
68C2×#461C2×C311yescharacteristic, complemented
69C2×#449C2×C311yescharacteristic
70C2×#448C2×C311yescharacteristic, complemented
71#2324C2×C311yescharacteristic, complemented
72#2043C2×C311yescharacteristic, complemented
73#2042C2×C311yescharacteristic, complemented
74#2013C2×C311yescharacteristic, complemented
75#2012C2×C311yescharacteristic, complemented
76#1983C2×C311yescharacteristic, complemented
77#1981C2×C311yescharacteristic, complemented
78#1798C2×C311yescharacteristic, complemented
79#1788C2×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×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×Q8C2311yescharacteristic
97C22×C3×D4—21no—
98C22×C3×D4—21no—
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C23×C3×C4—21no—
102C23×C3×C4—21no—
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C2×C3×SD16—22no—
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C2×C3×SD16—22no—
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—41no—
112C2×C3×SD16—41no—
113C2×C3×SD16—41no—
114C2×C3×D8—22no—
115C2×C3×D8—22no—
116C2×C3×D8—41no—
117C22×C3×C8C2311yescharacteristic
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C3×C4⋊Q8—22no—
122C3×C4⋊Q8—22no—
123C3×C4⋊Q8—22no—
124C3×C4⋊Q8D414yescomplemented
125C3×#124—22no—
126C3×#124—22no—
127C3×#124—22no—
128C3×#124D414yescomplemented
129C3×#123—28no—
130C3×#123—28no—
131C3×C22⋊Q8—28no—
132C3×C22⋊Q8—28no—
133C3×#121—22no—
134C3×#121D414yes—
135C3×C4×D4—22no—
136C3×C4×D4—22no—
137C3×#117—22no—
138C3×#117—22no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4D411yescharacteristic
145C2×C3×C4⋊C4D411yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4D411yescharacteristic
159C2×C3×C22⋊C4D411yescharacteristic
160C2×C3×C42—21no—
161C2×C3×C42C2311yescharacteristic
162C2×C3×C42C2311yescharacteristic
163C3×C4⋊C8—22no—
164C3×C4⋊C8—22no—
165C3×#103—22no—
166C3×#103—22no—
167C3×#103—22no—
168C3×#103—22no—
169C3×#103—22no—
170C3×#103—22no—
171C3×#103—41no—
172C3×#103—41no—
173C3×#103—41no—
174C3×#102—22no—
175C3×#102—22no—
176C3×#102—41no—
177C3×C22⋊C8—22no—
178C3×C22⋊C8—22no—
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—21no—
182C22×#41C22×C311yescharacteristic
183C23×Q8C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187C22×D8C22×C311yescharacteristic
188#536—24no—
189#536—24no—
190C2×C4⋊Q8C22×C311yescharacteristic
191C2×C4⋊Q8C22×C311yescharacteristic
192C2×#124C22×C311yescharacteristic
193C2×#124C22×C311yescharacteristic
194C2×#123—21no—
195C2×#123—21no—
196C2×C22⋊Q8—21no—
197C2×C22⋊Q8—21no—
198C2×#121C22×C311yescharacteristic
199C2×C4×D4C22×C311yescharacteristic
200C2×#117C22×C311yescharacteristic
201#463—24no—
202#461—24no—
203#449—24no—
204#448—24no—
205C2×C4⋊C8C22×C311yescharacteristic
206C2×C4⋊C8C22×C311yescharacteristic
207C2×#103C22×C311yescharacteristic
208C2×#103C22×C311yescharacteristic
209C2×#103C22×C311yescharacteristic
210C2×#103C22×C311yescharacteristic
211C2×#103C22×C311yescharacteristic
212C2×#103C22×C311yescharacteristic
213C2×#103C22×C311yescharacteristic
214C2×#103C22×C311yescharacteristic
215C2×#103C22×C311yescharacteristic
216C2×#102C22×C311yescharacteristic
217C2×#102C22×C311yescharacteristic
218C2×#102C22×C311yescharacteristic
219C2×C22⋊C8C22×C311yescharacteristic
220C2×C22⋊C8C22×C311yescharacteristic
221#390—21no—
222#390C22×C311yescharacteristic
223#389C22×C311yescharacteristic
224#388—21no—
225#386—21no—
226#385—21no—
227#380C22×C311yescharacteristic
228C4×C4⋊C4C22×C311yescharacteristic
229#336C22×C311yescharacteristic
230#336C22×C311yescharacteristic
231C24×C3—21no—
232C24×C3—21no—
233C24×C3C2×D411yescharacteristic
234C3×#41—44no—
235C3×#41—44no—
236C3×#41—44no—
237C3×#41—44no—
238C2×C3×Q8—24no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
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—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—44no—
255C2×C3×Q8—44no—
256C2×C3×Q8—44no—
257C2×C3×Q8—44no—
258C2×C3×Q8—42no—
259C2×C3×Q8—42no—
260C2×C3×Q8C2×D412yes—
261C2×C3×Q8C2×D412yes—
262C2×C3×Q8C2×D412yes—
263C2×C3×D4—24no—
264C2×C3×D4—24no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
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—21no—
274C2×C3×D4—21no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—81no—
278C2×C3×D4—81no—
279C2×C3×D4C2×D412yes—
280C2×C3×D4C2×D412yes—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—24no—
286C22×C3×C4—24no—
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—42no—
294C22×C3×C4—42no—
295C22×C3×C4—42no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4—81no—
299C22×C3×C4—81no—
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2×D412yes—
306C22×C3×C4#4112yes—
307C22×C3×C4C2411yescharacteristic
308C3×SD16—44no—
309C3×SD16—44no—
310C3×SD16—44no—
311C3×D8—44no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4—24no—
326C3×C4⋊C4—24no—
327C3×C4⋊C4—24no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—81no—
336C3×C4⋊C4C2×D412yes—
337C3×C22⋊C4—24no—
338C3×C22⋊C4—24no—
339C3×C22⋊C4—24no—
340C3×C22⋊C4—24no—
341C3×C22⋊C4—22no—
342C3×C22⋊C4—22no—
343C3×C22⋊C4—24no—
344C3×C22⋊C4—42no—
345C3×C22⋊C4—81no—
346C3×C22⋊C4—81no—
347C3×C22⋊C4—81no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—81no—
351C3×C42C2×D412yes—
352C3×C42C2×D412yes—
353C2×#41—22no—
354C2×#41—22no—
355C2×#41—22no—
356C2×#41—22no—
357C2×#41—41no—
358C2×#41—41no—
359C22×Q8—22no—
360C22×Q8—22no—
361C22×Q8—21no—
362C22×Q8—22no—
363C22×Q8—22no—
364C22×Q8—41no—
365C22×Q8—41no—
366C22×Q8C23×C311yescharacteristic
367C22×Q8C23×C311yescharacteristic
368C22×Q8C23×C311yescharacteristic
369C22×D4—21no—
370C22×D4—21no—
371C22×D4C23×C311yescharacteristic
372C22×D4C23×C311yescharacteristic
373C23×C4—21no—
374C23×C4—21no—
375C23×C4—21no—
376C23×C4C23×C311yescharacteristic
377C2×SD16—22no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—41no—
384C2×SD16—41no—
385C2×SD16—41no—
386C2×D8—22no—
387C2×D8—22no—
388C2×D8—41no—
389C22×C8C23×C311yescharacteristic
390C22×C8C23×C311yescharacteristic
391C22×C8C23×C311yescharacteristic
392C22×C8C23×C311yescharacteristic
393C4⋊Q8—22no—
394C4⋊Q8—22no—
395C4⋊Q8—22no—
396C4⋊Q8C3×D414yescomplemented
397#124—22no—
398#124—22no—
399#124—22no—
400#124C3×D414yescomplemented
401#123—28no—
402#123—28no—
403C22⋊Q8—28no—
404C22⋊Q8—28no—
405#121—22no—
406#121C3×D414yes—
407C4×D4—22no—
408C4×D4—22no—
409#117—22no—
410#117—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4C3×D411yescharacteristic
417C2×C4⋊C4C3×D411yescharacteristic
418C2×C4⋊C4C23×C311yescharacteristic
419C2×C4⋊C4C23×C311yescharacteristic
420C2×C4⋊C4C23×C311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4C3×D411yescharacteristic
431C2×C22⋊C4C3×D411yescharacteristic
432C2×C42—21no—
433C2×C42C23×C311yescharacteristic
434C2×C42C23×C311yescharacteristic
435C4⋊C8—22no—
436C4⋊C8—22no—
437#103—22no—
438#103—22no—
439#103—22no—
440#103—22no—
441#103—22no—
442#103—22no—
443#103—41no—
444#103—41no—
445#103—41no—
446#102—22no—
447#102—22no—
448#102—41no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451#95—21no—
452#95—21no—
453#95—21no—
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—41no—
463C23×C3—41no—
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#12112yes—
475C23×C3C22×D411yescharacteristic
476C3×Q8—22no—
477C3×Q8—22no—
478C3×Q8—22no—
479C3×Q8—22no—
480C3×Q8—22no—
481C3×Q8—22no—
482C3×Q8—48no—
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×D4—22no—
490C3×D4—22no—
491C3×D4—22no—
492C3×D4—22no—
493C3×D4—48no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—84no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—48no—
520C2×C3×C4—48no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
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—84no—
536C2×C3×C4#12012yes—
537C2×C3×C4#12012yes—
538C2×C3×C4#12112yes—
539C2×C3×C4C22×D411yescharacteristic
540C2×C3×C4C22×D411yescharacteristic
541C2×C3×C4C22×D411yescharacteristic
542C2×C3×C4C2×#4111yescharacteristic
543C2×C3×C4H(5,𝔽2)11yescharacteristic
544C2×C3×C4H(5,𝔽2)11yescharacteristic
545C3×C8—41no—
546C3×C8—41no—
547C3×C8—41no—
548C3×C8—41no—
549C24—21no—
550C24—21no—
551C24C2×C3×D411yescharacteristic
552#41—44no—
553#41—44no—
554#41—44no—
555#41—44no—
556C2×Q8—24no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—44no—
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—42no—
577C2×Q8—42no—
578C2×Q8C2×C3×D412yes—
579C2×Q8C2×C3×D412yes—
580C2×Q8C2×C3×D412yes—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4C2×C3×D412yes—
598C2×D4C2×C3×D412yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4C2×C3×D411yescharacteristic
619C22×C4C2×C3×D411yescharacteristic
620C22×C4C2×C3×D411yescharacteristic
621C22×C4C2×C3×D411yescharacteristic
622C22×C4C2×C3×D411yescharacteristic
623C22×C4C2×C3×D412yes—
624C22×C4C3×#4112yes—
625C22×C4C24×C311yescharacteristic
626SD16—44no—
627SD16—44no—
628SD16—44no—
629D8—44no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—81no—
654C4⋊C4C2×C3×D412yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—24no—
662C22⋊C4—42no—
663C22⋊C4—81no—
664C22⋊C4—81no—
665C22⋊C4—81no—
666C42—21no—
667C42—21no—
668C42—81no—
669C42C2×C3×D412yes—
670C42C2×C3×D412yes—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3C2×#12011yescharacteristic
693C22×C3C2×#12111yescharacteristic
694C22×C3#53511yescharacteristic
695C22×C3#57711yescharacteristic
696C22×C3#57711yescharacteristic
697C22×C3#57711yescharacteristic
698C22×C3#57811yescharacteristic
699C3×C4—22no—
700C3×C4—22no—
701C3×C4—22no—
702C3×C4—42no—
703C3×C4—42no—
704C3×C4—42no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—42no—
708C3×C4—81no—
709C3×C4—81no—
710C3×C4D4211yescharacteristic
711C3×C4D4211yescharacteristic
712C3×C4#54611yescharacteristic
713C3×C4#54611yescharacteristic
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—22no—
721C23—22no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23C3×#12112yes—
735C23C22×C3×D411yescharacteristic
736Q8—22no—
737Q8—22no—
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—48no—
743Q8—41no—
744Q8—41no—
745Q8—41no—
746Q8—41no—
747Q8—41no—
748Q8—41no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—48no—
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—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—48no—
780C2×C4—48no—
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—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4C3×#12012yes—
797C2×C4C3×#12012yes—
798C2×C4C3×#12112yes—
799C2×C4C22×C3×D411yescharacteristic
800C2×C4C22×C3×D411yescharacteristic
801C2×C4C22×C3×D411yescharacteristic
802C2×C4C2×C3×#4111yescharacteristic
803C2×C4C3×H(5,𝔽2)11yescharacteristic
804C2×C4C3×H(5,𝔽2)11yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C2×C3—42no—
810C2×C3—82no—
811C2×C3—82no—
812C2×C3#240811yescharacteristic
813C2×C3#301011yescharacteristic
814C2×C3#301311yescharacteristic
815C2×C3#304211yescharacteristic
816C2×C3#304611yescharacteristic
817C2×C3#322111yescharacteristic
818C2×C3#322511yescharacteristic
819C22—22no—
820C22—22no—
821C22—22no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22C2×C3×#12011yescharacteristic
841C22C2×C3×#12111yescharacteristic
842C22C3×#53511yescharacteristic
843C22C3×#57711yescharacteristic
844C22C3×#57711yescharacteristic
845C22C3×#57711yescharacteristic
846C22C3×#57811yescharacteristic
847C4—22no—
848C4—22no—
849C4—22no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—81no—
857C4—81no—
858C4C3×D4211yescharacteristic
859C4C3×D4211yescharacteristic
860C4C3×#54611yescharacteristic
861C4C3×#54611yescharacteristic
862C3#2421911yescharacteristic, direct product factor, Sylow
863C2—42no—
864C2—82no—
865C2—82no—
866C2C3×#240811yescharacteristic
867C2C3×#301011yescharacteristic
868C2C3×#301311yescharacteristic
869C2C3×#304211yescharacteristic
870C2C3×#304611yescharacteristic
871C2C3×#322111yescharacteristic
872C2C3×#322511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#536C2semidirect
2. C2×C3×#463C2semidirect
3. C2×C3×#461C2semidirect
5. C2×C3×#448C2semidirect
6. C3×#2324C2semidirect
7. C3×#2043C2semidirect
8. C3×#2042C2semidirect
9. C3×#2013C2semidirect
10. C3×#2012C2semidirect
11. C3×#1983C2semidirect
12. C3×#1981C2semidirect
13. C3×#1798C2semidirect
14. C3×#1788C2semidirect
15. C3×#1787C2semidirect
16. #24219C3direct (N × H)
66. C2×#536C2×C3semidirect
67. C2×#463C2×C3semidirect
68. C2×#461C2×C3semidirect
70. C2×#448C2×C3semidirect
71. #2324C2×C3semidirect
72. #2043C2×C3semidirect
73. #2042C2×C3semidirect
74. #2013C2×C3semidirect
75. #2012C2×C3semidirect
76. #1983C2×C3semidirect
77. #1981C2×C3semidirect
78. #1798C2×C3semidirect
79. #1788C2×C3semidirect
80. #1787C2×C3semidirect
124. C3×C4⋊Q8D4semidirect
128. C3×#124D4semidirect
396. C4⋊Q8C3×D4semidirect
400. #124C3×D4semidirect
862. C3#24219direct (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×#4632
C2×C3×#4612
C2×C3×#4492
C2×C3×#4482
C3×#23242
C3×#20432
C3×#20422
C3×#20132
C3×#20122
C3×#19832
C3×#19812
C3×#17982
C3×#17882
C3×#17872
#242193