Finite Group Databasebeta

← C3×#30419 #10649026

Subgroups — C3×#30419 #10649026

Order 768.

1024 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#468C211yesmaximal, characteristic, complemented
2C2×C3×#448C211yesmaximal, characteristic, complemented
3C3×#2535C211yesmaximal, characteristic
4C3×#2409C211yesmaximal, characteristic, complemented
5C3×#2097C211yesmaximal, characteristic, complemented
6C3×#2076C211yesmaximal, characteristic, complemented
7C3×#2074C211yesmaximal, characteristic, complemented
8C3×#2035C211yesmaximal, characteristic, complemented
9C3×#2034C211yesmaximal, characteristic, complemented
10C3×#2000C211yesmaximal, characteristic, complemented
11C3×#1894C211yesmaximal, characteristic, complemented
12C3×#1877C211yesmaximal, characteristic, complemented
13C3×#1877C211yesmaximal, characteristic, complemented
14C3×#1870C211yesmaximal, characteristic, complemented
15C3×#1787C211yesmaximal, characteristic, complemented
16#30419C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×C3×#121C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C3×#468—24no—
28C3×#448—24no—
29C2×C3×#107C2211yescharacteristic
30C2×C3×#106C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic
42C3×#397—21no—
43C3×#395—21no—
44C3×#393—21no—
45C3×#392—21no—
46C3×#391C2211yescharacteristic
47C3×#391C2211yescharacteristic
48C3×#386—21no—
49C3×#386—21no—
50C3×#386—21no—
51C3×#385—21no—
52C3×#382C2211yescharacteristic
53C3×#380C2211yescharacteristic
54C3×#380C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#468C2×C311yescharacteristic, complemented
63C2×#448C2×C311yescharacteristic, complemented
64#2535C2×C311yescharacteristic
65#2409C2×C311yescharacteristic, complemented
66#2097C2×C311yescharacteristic, complemented
67#2076C2×C311yescharacteristic, complemented
68#2074C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2034C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1894C2×C311yescharacteristic, complemented
73#1877C2×C311yescharacteristic, complemented
74#1877C2×C311yescharacteristic, complemented
75#1870C2×C311yescharacteristic, complemented
76#1787C2×C311yescharacteristic, complemented
77C22×C3×Q8—21no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—41no—
81C22×C3×Q8—41no—
82C22×C3×Q8—41no—
83C22×C3×Q8—41no—
84C22×C3×Q8C2311yescharacteristic
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4—21no—
88C22×C3×D4D411yescharacteristic
89C22×C3×D4C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C2×C3×SD16—22no—
95C2×C3×SD16—22no—
96C2×C3×SD16—41no—
97C2×C3×SD16—41no—
98C2×C3×SD16—41no—
99C2×C3×SD16D414yescomplemented
100C2×C3×M16—22no—
101C2×C3×M16—41no—
102C2×C3×M16—41no—
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—41no—
110C3×C22⋊Q8—41no—
111C3×#121—22no—
112C3×#121—22no—
113C3×#121—41no—
114C3×#121—41no—
115C3×C4×D4—41no—
116C3×C4×D4—41no—
117C3×C4×D4—41no—
118C3×C4×D4—41no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4D411yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4D411yescharacteristic
136C2×C3×C22⋊C4D411yescharacteristic
137C2×C3×C42C2311yescharacteristic
138C3×#107—22no—
139C3×#106—41no—
140C3×#103—22no—
141C3×#103—22no—
142C3×#103—22no—
143C3×#103—41no—
144C3×#103—41no—
145C3×#103—41no—
146C3×#102—22no—
147C3×#102—41no—
148C3×C22⋊C8—22no—
149C3×C22⋊C8—41no—
150C3×C22⋊C8—41no—
151C3×#95—21no—
152C3×#95—21no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C23×Q8C22×C311yescharacteristic
161C22×SD16C22×C311yescharacteristic
162C22×SD16C22×C311yescharacteristic
163C22×M16C22×C311yescharacteristic
164C2×C22⋊Q8C22×C311yescharacteristic
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×#121C22×C311yescharacteristic
167C2×#121C22×C311yescharacteristic
168C2×C4×D4C22×C311yescharacteristic
169C2×C4×D4C22×C311yescharacteristic
170#468—24no—
171#448—24no—
172C2×#107C22×C311yescharacteristic
173C2×#106C22×C311yescharacteristic
174C2×#103C22×C311yescharacteristic
175C2×#103C22×C311yescharacteristic
176C2×#103C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#103C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×C22⋊C8C22×C311yescharacteristic
183C2×C22⋊C8C22×C311yescharacteristic
184C2×C22⋊C8C22×C311yescharacteristic
185#397—21no—
186#395—21no—
187#393—21no—
188#392—21no—
189#391C22×C311yescharacteristic
190#391C22×C311yescharacteristic
191#386—21no—
192#386—21no—
193#386—21no—
194#385—21no—
195#382C22×C311yescharacteristic
196#380C22×C311yescharacteristic
197#380C22×C311yescharacteristic
198#380C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#340C22×C311yescharacteristic
202#340C22×C311yescharacteristic
203#336C22×C311yescharacteristic
204#336C22×C311yescharacteristic
205C24×C3—21no—
206C24×C3C2×D411yescharacteristic
207C24×C3C2×D411yescharacteristic
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—42no—
219C2×C3×Q8—42no—
220C2×C3×Q8—42no—
221C2×C3×Q8—44no—
222C2×C3×Q8—44no—
223C2×C3×Q8—44no—
224C2×C3×Q8—44no—
225C2×C3×Q8C2×D412yes—
226C2×C3×Q8#4112yes—
227C2×C3×D4—22no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—41no—
234C2×C3×D4—41no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—81no—
240C2×C3×D4—81no—
241C2×C3×D4C2×D412yes—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—42no—
262C22×C3×C4—42no—
263C22×C3×C4—42no—
264C22×C3×C4—42no—
265C22×C3×C4—81no—
266C22×C3×C4—81no—
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2×D411yescharacteristic
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2411yescharacteristic
272C3×SD16—44no—
273C3×SD16—44no—
274C3×M16—44no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8C2×D412yes—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—41no—
298C3×C4⋊C4—42no—
299C3×C4⋊C4—42no—
300C3×C22⋊C4—41no—
301C3×C22⋊C4—41no—
302C3×C22⋊C4—42no—
303C3×C22⋊C4—42no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—42no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—81no—
309C3×C22⋊C4—81no—
310C3×C42—21no—
311C3×C42—21no—
312C22×Q8—21no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—41no—
316C22×Q8—41no—
317C22×Q8—41no—
318C22×Q8—41no—
319C22×Q8C23×C311yescharacteristic
320C22×Q8C23×C311yescharacteristic
321C22×D4—21no—
322C22×D4—21no—
323C22×D4C3×D411yescharacteristic
324C22×D4C23×C311yescharacteristic
325C23×C4—21no—
326C23×C4—21no—
327C23×C4C23×C311yescharacteristic
328C23×C4C23×C311yescharacteristic
329C2×SD16—22no—
330C2×SD16—22no—
331C2×SD16—41no—
332C2×SD16—41no—
333C2×SD16—41no—
334C2×SD16C3×D414yescomplemented
335C2×M16—22no—
336C2×M16—41no—
337C2×M16—41no—
338C22×C8C23×C311yescharacteristic
339C22×C8C23×C311yescharacteristic
340C22×C8C23×C311yescharacteristic
341C22×C8C23×C311yescharacteristic
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—41no—
345C22⋊Q8—41no—
346#121—22no—
347#121—22no—
348#121—41no—
349#121—41no—
350C4×D4—41no—
351C4×D4—41no—
352C4×D4—41no—
353C4×D4—41no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4C3×D411yescharacteristic
357C2×C4⋊C4C23×C311yescharacteristic
358C2×C4⋊C4C23×C311yescharacteristic
359C2×C4⋊C4C23×C311yescharacteristic
360C2×C4⋊C4C23×C311yescharacteristic
361C2×C4⋊C4C23×C311yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4C3×D411yescharacteristic
371C2×C22⋊C4C3×D411yescharacteristic
372C2×C42C23×C311yescharacteristic
373#107—22no—
374#106—41no—
375#103—22no—
376#103—22no—
377#103—22no—
378#103—41no—
379#103—41no—
380#103—41no—
381#102—22no—
382#102—41no—
383C22⋊C8—22no—
384C22⋊C8—41no—
385C22⋊C8—41no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—22no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3#13712yes—
416C23×C3C22×D411yescharacteristic
417C3×Q8—22no—
418C3×Q8—22no—
419C3×Q8—22no—
420C3×Q8—22no—
421C3×Q8—48no—
422C3×Q8—41no—
423C3×Q8—41no—
424C3×Q8—41no—
425C3×Q8—41no—
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—44no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—84no—
432C3×D4—84no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—48no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—84no—
476C2×C3×C4C22×D411yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4H(5,𝔽2)11yescharacteristic
479C2×C3×C4H(5,𝔽2)11yescharacteristic
480C2×C3×C4H(5,𝔽2)11yescharacteristic
481C2×C3×C4H(5,𝔽2)11yescharacteristic
482C3×C8—22no—
483C3×C8—41no—
484C3×C8—41no—
485C3×C8—41no—
486C24—21no—
487C24C2×C3×D411yescharacteristic
488C24C2×C3×D411yescharacteristic
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8C2×C3×D412yes—
507C2×Q8C3×#4112yes—
508C2×D4—22no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4—81no—
521C2×D4—81no—
522C2×D4C2×C3×D412yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4C2×C3×D411yescharacteristic
549C22×C4C2×C3×D411yescharacteristic
550C22×C4C2×C3×D411yescharacteristic
551C22×C4C2×C3×D411yescharacteristic
552C22×C4C24×C311yescharacteristic
553SD16—44no—
554SD16—44no—
555M16—44no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8C2×C3×D412yes—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—41no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C42—21no—
592C42—21no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—42no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—42no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3—81no—
613C22×C3—81no—
614C22×C3#53411yescharacteristic
615C22×C3D4211yescharacteristic
616C22×C3#54611yescharacteristic
617C22×C3C2×#13711yescharacteristic
618C22×C3#57511yescharacteristic
619C22×C3#57711yescharacteristic
620C22×C3#57711yescharacteristic
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—42no—
624C3×C4—42no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4—81no—
630C3×C4—81no—
631C3×C4—81no—
632C3×C4#53411yescharacteristic
633C3×C4#53811yescharacteristic
634C3×C4#54611yescharacteristic
635C3×C4#56011yescharacteristic
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23C3×#13712yes—
657C23C22×C3×D411yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—48no—
663Q8—41no—
664Q8—41no—
665Q8—41no—
666Q8—41no—
667D4—22no—
668D4—22no—
669D4—44no—
670D4—41no—
671D4—41no—
672D4—84no—
673D4—84no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—48no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4C22×C3×D411yescharacteristic
718C2×C4C2×C3×#4111yescharacteristic
719C2×C4C3×H(5,𝔽2)11yescharacteristic
720C2×C4C3×H(5,𝔽2)11yescharacteristic
721C2×C4C3×H(5,𝔽2)11yescharacteristic
722C2×C4C3×H(5,𝔽2)11yescharacteristic
723C8—22no—
724C8—41no—
725C8—41no—
726C8—41no—
727C2×C3—42no—
728C2×C3—81no—
729C2×C3—82no—
730C2×C3#266811yescharacteristic
731C2×C3#319611yescharacteristic
732C2×C3#320011yescharacteristic
733C2×C3#326611yescharacteristic
734C2×C3#327511yescharacteristic
735C2×C3#332011yescharacteristic
736C2×C3#332611yescharacteristic
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—41no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—41no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22C3×#53411yescharacteristic
759C22C3×D4211yescharacteristic
760C22C3×#54611yescharacteristic
761C22C2×C3×#13711yescharacteristic
762C22C3×#57511yescharacteristic
763C22C3×#57711yescharacteristic
764C22C3×#57711yescharacteristic
765C4—41no—
766C4—41no—
767C4—42no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4—81no—
775C4—81no—
776C4C3×#53411yescharacteristic
777C4C3×#53811yescharacteristic
778C4C3×#54611yescharacteristic
779C4C3×#56011yescharacteristic
780C3#3041911yescharacteristic, direct product factor, Sylow
781C2—42no—
782C2—81no—
783C2—82no—
784C2C3×#266811yescharacteristic
785C2C3×#319611yescharacteristic
786C2C3×#320011yescharacteristic
787C2C3×#326611yescharacteristic
788C2C3×#327511yescharacteristic
789C2C3×#332011yescharacteristic
790C2C3×#332611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2535C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#468C2semidirect
2. C2×C3×#448C2semidirect
4. C3×#2409C2semidirect
5. C3×#2097C2semidirect
6. C3×#2076C2semidirect
7. C3×#2074C2semidirect
8. C3×#2035C2semidirect
9. C3×#2034C2semidirect
10. C3×#2000C2semidirect
11. C3×#1894C2semidirect
12. C3×#1877C2semidirect
13. C3×#1877C2semidirect
14. C3×#1870C2semidirect
15. C3×#1787C2semidirect
16. #30419C3direct (N × H)
62. C2×#468C2×C3semidirect
63. C2×#448C2×C3semidirect
65. #2409C2×C3semidirect
66. #2097C2×C3semidirect
67. #2076C2×C3semidirect
68. #2074C2×C3semidirect
69. #2035C2×C3semidirect
70. #2034C2×C3semidirect
71. #2000C2×C3semidirect
72. #1894C2×C3semidirect
73. #1877C2×C3semidirect
74. #1877C2×C3semidirect
75. #1870C2×C3semidirect
76. #1787C2×C3semidirect
99. C2×C3×SD16D4semidirect
334. C2×SD16C3×D4semidirect
780. C3#30419direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4682
C2×C3×#4482
C3×#25352
C3×#24092
C3×#20972
C3×#20762
C3×#20742
C3×#20352
C3×#20342
C3×#20002
C3×#18942
C3×#18772
C3×#18702
C3×#17872
#304193