Finite Group Databasebeta

← C3×#30456 #10649063

Subgroups — C3×#30456 #10649063

Order 768.

1332 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#492C211yesmaximal, characteristic, complemented
2C2×C3×#460C211yesmaximal, characteristic, complemented
3C2×C3×#450C211yesmaximal, characteristic, complemented
4C2×C3×#450C211yesmaximal, characteristic, complemented
5C3×#2433C211yesmaximal, characteristic
6C3×#2429C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8C3×#2041C211yesmaximal, characteristic, complemented
9C3×#2014C211yesmaximal, characteristic, complemented
10C3×#2013C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#2000C211yesmaximal, characteristic, complemented
13C3×#1934C211yesmaximal, characteristic, complemented
14C3×#1923C211yesmaximal, characteristic, complemented
15C3×#1880C211yesmaximal, characteristic, complemented
16#30456C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic, complemented
23C22×C3×SD16C2211yescharacteristic, complemented
24C2×C3×C4⋊Q8C2211yescharacteristic, complemented
25C2×C3×#127C2211yescharacteristic
26C2×C3×#127C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#120—21no—
31C2×C3×#120—21no—
32C2×C3×C4×Q8C2211yescharacteristic, complemented
33C3×#492—24no—
34C3×#460—24no—
35C3×#450—24no—
36C3×#450—24no—
37C2×C3×C4⋊C8C2211yescharacteristic, complemented
38C2×C3×#103C2211yescharacteristic, complemented
39C2×C3×#103C2211yescharacteristic, complemented
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic, complemented
45C2×C3×#102C2211yescharacteristic, complemented
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C4×C8C2211yescharacteristic, complemented
49C3×#398—21no—
50C3×#396—21no—
51C3×#392—21no—
52C3×#392—21no—
53C3×#391C2211yescharacteristic, complemented
54C3×#390C2211yescharacteristic
55C3×#390C2211yescharacteristic
56C3×#389—21no—
57C3×#389C2211yescharacteristic, complemented
58C3×#388—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62C3×#336C2211yescharacteristic, complemented
63C3×#336C2211yescharacteristic, complemented
64C2×#492C2×C311yescharacteristic, complemented
65C2×#460C2×C311yescharacteristic, complemented
66C2×#450C2×C311yescharacteristic, complemented
67C2×#450C2×C311yescharacteristic, complemented
68#2433C2×C311yescharacteristic
69#2429C2×C311yescharacteristic, complemented
70#2055C2×C311yescharacteristic, complemented
71#2041C2×C311yescharacteristic, complemented
72#2014C2×C311yescharacteristic, complemented
73#2013C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#2000C2×C311yescharacteristic, complemented
76#1934C2×C311yescharacteristic, complemented
77#1923C2×C311yescharacteristic, complemented
78#1880C2×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—21no—
87C22×C3×D4—21no—
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4—41no—
91C22×C3×D4—41no—
92C22×C3×D4—41no—
93C22×C3×D4—41no—
94C22×C3×D4C2311yescharacteristic
95C22×C3×D4C2311yescharacteristic
96C22×C3×D4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—22no—
105C2×C3×SD16—22no—
106C2×C3×SD16—41no—
107C2×C3×SD16—41no—
108C2×C3×SD16—41no—
109C2×C3×SD16—41no—
110C2×C3×SD16—41no—
111C2×C3×SD16—41no—
112C2×C3×SD16—41no—
113C2×C3×SD16—41no—
114C2×C3×SD16—41no—
115C2×C3×SD16D414yescomplemented
116C22×C3×C8C2311yescharacteristic
117C22×C3×C8C2311yescharacteristic
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C3×C4⋊Q8—22no—
121C3×C4⋊Q8—41no—
122C3×#127—22no—
123C3×#127—22no—
124C3×#127—41no—
125C3×#127—41no—
126C3×C22⋊Q8—22no—
127C3×C22⋊Q8—22no—
128C3×C22⋊Q8—41no—
129C3×C22⋊Q8—41no—
130C3×#121—41no—
131C3×#121—41no—
132C3×#120—44no—
133C3×#120—44no—
134C3×C4×Q8—22no—
135C3×C4×Q8—41no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4C2311yescharacteristic
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
152C2×C3×C22⋊C4D411yescharacteristic
153C2×C3×C22⋊C4D411yescharacteristic
154C2×C3×C42—21no—
155C2×C3×C42C2311yescharacteristic
156C2×C3×C42C2311yescharacteristic
157C3×C4⋊C8—22no—
158C3×#103—41no—
159C3×#103—41no—
160C3×#102—22no—
161C3×#102—22no—
162C3×#102—22no—
163C3×#102—22no—
164C3×#102—41no—
165C3×#102D414yescomplemented
166C3×C22⋊C8—22no—
167C3×C22⋊C8—22no—
168C3×C4×C8—22no—
169C3×#95—21no—
170C3×#95—21no—
171C3×#95—21no—
172C3×#95D411yescharacteristic
173C3×#95D411yescharacteristic
174C23×D4C22×C311yescharacteristic
175C22×SD16C22×C311yescharacteristic
176C22×SD16C22×C311yescharacteristic
177C22×SD16C22×C311yescharacteristic
178C22×SD16C22×C311yescharacteristic
179C22×SD16C22×C311yescharacteristic, complemented
180C22×SD16C22×C311yescharacteristic, complemented
181C2×C4⋊Q8C22×C311yescharacteristic, complemented
182C2×#127C22×C311yescharacteristic
183C2×#127C22×C311yescharacteristic
184C2×C22⋊Q8C22×C311yescharacteristic
185C2×C22⋊Q8C22×C311yescharacteristic
186C2×#121C22×C311yescharacteristic
187C2×#120—21no—
188C2×#120—21no—
189C2×C4×Q8C22×C311yescharacteristic, complemented
190#492—24no—
191#460—24no—
192#450—24no—
193#450—24no—
194C2×C4⋊C8C22×C311yescharacteristic, complemented
195C2×#103C22×C311yescharacteristic, complemented
196C2×#103C22×C311yescharacteristic, complemented
197C2×#102C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×#102C22×C311yescharacteristic
200C2×#102C22×C311yescharacteristic
201C2×#102C22×C311yescharacteristic, complemented
202C2×#102C22×C311yescharacteristic, complemented
203C2×C22⋊C8C22×C311yescharacteristic
204C2×C22⋊C8C22×C311yescharacteristic
205C2×C4×C8C22×C311yescharacteristic, complemented
206#398—21no—
207#396—21no—
208#392—21no—
209#392—21no—
210#391C22×C311yescharacteristic, complemented
211#390C22×C311yescharacteristic
212#390C22×C311yescharacteristic
213#389—21no—
214#389C22×C311yescharacteristic, complemented
215#388—21no—
216C4×C22⋊C4C22×C311yescharacteristic
217#340C22×C311yescharacteristic, complemented
218#340C22×C311yescharacteristic, complemented
219#336C22×C311yescharacteristic, complemented
220#336C22×C311yescharacteristic, complemented
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3—42no—
225C24×C3—42no—
226C24×C3—42no—
227C24×C3—42no—
228C24×C3—42no—
229C24×C3—81no—
230C24×C3—81no—
231C24×C3C2×D411yescharacteristic
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×Q8—21no—
243C2×C3×Q8C2×D412yes—
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—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4—42no—
265C2×C3×D4—42no—
266C2×C3×D4—42no—
267C2×C3×D4—42no—
268C2×C3×D4—44no—
269C2×C3×D4—44no—
270C2×C3×D4—44no—
271C2×C3×D4—44no—
272C2×C3×D4—42no—
273C2×C3×D4—42no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—81no—
279C2×C3×D4—81no—
280C2×C3×D4—81no—
281C2×C3×D4—81no—
282C2×C3×D4C2×D412yes—
283C2×C3×D4C2×D412yes—
284C22×C3×C4—21no—
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—21no—
294C22×C3×C4—21no—
295C22×C3×C4C2×D411yescharacteristic
296C22×C3×C4C2×D411yescharacteristic
297C22×C3×C4C2×D411yescharacteristic
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2411yescharacteristic
301C3×SD16—44no—
302C3×SD16—44no—
303C3×SD16—44no—
304C3×SD16—44no—
305C3×SD16—44no—
306C3×SD16—44no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8C2×D412yes—
318C2×C3×C8C2×D412yes—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—42no—
325C3×C4⋊C4—42no—
326C3×C4⋊C4—42no—
327C3×C4⋊C4—42no—
328C3×C4⋊C4—42no—
329C3×C4⋊C4—42no—
330C3×C4⋊C4C2×D412yes—
331C3×C22⋊C4—22no—
332C3×C22⋊C4—42no—
333C3×C22⋊C4—42no—
334C3×C22⋊C4—42no—
335C3×C22⋊C4—42no—
336C3×C22⋊C4—42no—
337C3×C22⋊C4—42no—
338C3×C22⋊C4—42no—
339C3×C22⋊C4SD1614yescomplemented
340C3×C42—21no—
341C3×C42—21no—
342C3×C42—21no—
343C3×C42—21no—
344C3×C42—42no—
345C25—21no—
346C22×Q8C23×C311yescharacteristic
347C22×Q8C23×C311yescharacteristic
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—21no—
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—41no—
357C22×D4—41no—
358C22×D4—41no—
359C22×D4—41no—
360C22×D4C23×C311yescharacteristic
361C22×D4C23×C311yescharacteristic
362C22×D4C23×C311yescharacteristic
363C23×C4C23×C311yescharacteristic
364C2×SD16—22no—
365C2×SD16—22no—
366C2×SD16—22no—
367C2×SD16—22no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16—22no—
371C2×SD16—22no—
372C2×SD16—41no—
373C2×SD16—41no—
374C2×SD16—41no—
375C2×SD16—41no—
376C2×SD16—41no—
377C2×SD16—41no—
378C2×SD16—41no—
379C2×SD16—41no—
380C2×SD16—41no—
381C2×SD16C3×D414yescomplemented
382C22×C8C23×C311yescharacteristic
383C22×C8C23×C311yescharacteristic
384C22×C8C23×C311yescharacteristic
385C22×C8C23×C311yescharacteristic
386C4⋊Q8—22no—
387C4⋊Q8—41no—
388#127—22no—
389#127—22no—
390#127—41no—
391#127—41no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—41no—
395C22⋊Q8—41no—
396#121—41no—
397#121—41no—
398#120—44no—
399#120—44no—
400C4×Q8—22no—
401C4×Q8—41no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4C23×C311yescharacteristic
409C2×C4⋊C4C23×C311yescharacteristic
410C2×C4⋊C4C23×C311yescharacteristic
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4C3×D411yescharacteristic
419C2×C22⋊C4C3×D411yescharacteristic
420C2×C42—21no—
421C2×C42C23×C311yescharacteristic
422C2×C42C23×C311yescharacteristic
423C4⋊C8—22no—
424#103—41no—
425#103—41no—
426#102—22no—
427#102—22no—
428#102—22no—
429#102—22no—
430#102—41no—
431#102C3×D414yescomplemented
432C22⋊C8—22no—
433C22⋊C8—22no—
434C4×C8—22no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95C3×D411yescharacteristic
439#95C3×D411yescharacteristic
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—48no—
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—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—84no—
469C23×C3—84no—
470C23×C3—84no—
471C23×C3—84no—
472C23×C3—84no—
473C23×C3—84no—
474C23×C3C2×SD1612yes—
475C23×C3C22×D411yescharacteristic
476C3×Q8—22no—
477C3×Q8—22no—
478C3×Q8—41no—
479C3×Q8—41no—
480C3×Q8—41no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×D4—22no—
485C3×D4—22no—
486C3×D4—22no—
487C3×D4—22no—
488C3×D4—48no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—41no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—84no—
498C3×D4—84no—
499C3×D4—84no—
500C3×D4—84no—
501C3×D4—84no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
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—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×C4C2×SD1612yes—
534C2×C3×C4C2×SD1612yes—
535C2×C3×C4AGL(1,ℤ/8)12yes—
536C2×C3×C4C22×D411yescharacteristic
537C2×C3×C4C22×D411yescharacteristic
538C2×C3×C4H(5,𝔽2)11yescharacteristic
539C2×C3×C4H(5,𝔽2)11yescharacteristic
540C2×C3×C4H(5,𝔽2)11yescharacteristic
541C2×C3×C4H(5,𝔽2)11yescharacteristic
542C3×C8—22no—
543C3×C8—22no—
544C3×C8—41no—
545C3×C8—41no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—42no—
554C24—81no—
555C24—81no—
556C24C2×C3×D411yescharacteristic
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×Q8C2×C3×D412yes—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—44no—
594C2×D4—44no—
595C2×D4—44no—
596C2×D4—44no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—81no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4C2×C3×D412yes—
608C2×D4C2×C3×D412yes—
609C22×C4—21no—
610C22×C4—21no—
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—21no—
620C22×C4C2×C3×D411yescharacteristic
621C22×C4C2×C3×D411yescharacteristic
622C22×C4C2×C3×D411yescharacteristic
623C22×C4C2×C3×D411yescharacteristic
624C22×C4C2×C3×D411yescharacteristic
625C22×C4C24×C311yescharacteristic
626SD16—44no—
627SD16—44no—
628SD16—44no—
629SD16—44no—
630SD16—44no—
631SD16—44no—
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—
642C2×C8C2×C3×D412yes—
643C2×C8C2×C3×D412yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4C2×C3×D412yes—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4C3×SD1614yescomplemented
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—42no—
670C22×C3—22no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—816no—
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×C3—81no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3#53511yescharacteristic
700C22×C3D4211yescharacteristic
701C22×C3D4211yescharacteristic
702C22×C3C22×SD1611yescharacteristic
703C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
704C22×C3#57711yescharacteristic
705C22×C3#57711yescharacteristic
706C3×C4—22no—
707C3×C4—22no—
708C3×C4—22no—
709C3×C4—41no—
710C3×C4—42no—
711C3×C4—41no—
712C3×C4—42no—
713C3×C4—81no—
714C3×C4—81no—
715C3×C4—81no—
716C3×C4#53411yescharacteristic
717C3×C4#53511yescharacteristic
718C3×C4D4211yescharacteristic
719C3×C4#56011yescharacteristic
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—48no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—84no—
749C23—84no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23C2×C3×SD1612yes—
755C23C22×C3×D411yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—41no—
759Q8—41no—
760Q8—41no—
761Q8—41no—
762Q8—41no—
763Q8—41no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4—84no—
779D4—84no—
780D4—84no—
781D4—84no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4C2×C3×SD1612yes—
814C2×C4C2×C3×SD1612yes—
815C2×C4C3×AGL(1,ℤ/8)12yes—
816C2×C4C22×C3×D411yescharacteristic
817C2×C4C22×C3×D411yescharacteristic
818C2×C4C3×H(5,𝔽2)11yescharacteristic
819C2×C4C3×H(5,𝔽2)11yescharacteristic
820C2×C4C3×H(5,𝔽2)11yescharacteristic
821C2×C4C3×H(5,𝔽2)11yescharacteristic
822C8—22no—
823C8—22no—
824C8—41no—
825C8—41no—
826C2×C3—42no—
827C2×C3—82no—
828C2×C3—82no—
829C2×C3—161no—
830C2×C3#266911yescharacteristic
831C2×C3#320811yescharacteristic
832C2×C3#322211yescharacteristic
833C2×C3#326511yescharacteristic
834C2×C3#327211yescharacteristic
835C2×C3D4×SD1611yescharacteristic
836C2×C3D4×SD1611yescharacteristic
837C22—22no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22C3×#53511yescharacteristic
867C22C3×D4211yescharacteristic
868C22C3×D4211yescharacteristic
869C22C22×C3×SD1611yescharacteristic
870C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
871C22C3×#57711yescharacteristic
872C22C3×#57711yescharacteristic
873C4—22no—
874C4—22no—
875C4—22no—
876C4—41no—
877C4—42no—
878C4—41no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4C3×#53411yescharacteristic
884C4C3×#53511yescharacteristic
885C4C3×D4211yescharacteristic
886C4C3×#56011yescharacteristic
887C3#3045611yescharacteristic, direct product factor, Sylow
888C2—42no—
889C2—82no—
890C2—82no—
891C2—161no—
892C2C3×#266911yescharacteristic
893C2C3×#320811yescharacteristic
894C2C3×#322211yescharacteristic
895C2C3×#326511yescharacteristic
896C2C3×#327211yescharacteristic
897C2C3×D4×SD1611yescharacteristic
898C2C3×D4×SD1611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2433C2
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×#492C2semidirect
2. C2×C3×#460C2semidirect
3. C2×C3×#450C2semidirect
4. C2×C3×#450C2semidirect
6. C3×#2429C2semidirect
7. C3×#2055C2semidirect
8. C3×#2041C2semidirect
9. C3×#2014C2semidirect
10. C3×#2013C2semidirect
11. C3×#2000C2semidirect
12. C3×#2000C2semidirect
13. C3×#1934C2semidirect
14. C3×#1923C2semidirect
15. C3×#1880C2semidirect
16. #30456C3direct (N × H)
22. C22×C3×SD16C22semidirect
23. C22×C3×SD16C22semidirect
24. C2×C3×C4⋊Q8C22semidirect
32. C2×C3×C4×Q8C22semidirect
37. C2×C3×C4⋊C8C22semidirect
38. C2×C3×#103C22semidirect
39. C2×C3×#103C22semidirect
44. C2×C3×#102C22semidirect
45. C2×C3×#102C22semidirect
48. C2×C3×C4×C8C22semidirect
53. C3×#391C22semidirect
57. C3×#389C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. C3×#336C22semidirect
63. C3×#336C22semidirect
64. C2×#492C2×C3semidirect
65. C2×#460C2×C3semidirect
66. C2×#450C2×C3semidirect
67. C2×#450C2×C3semidirect
69. #2429C2×C3semidirect
70. #2055C2×C3semidirect
71. #2041C2×C3semidirect
72. #2014C2×C3semidirect
73. #2013C2×C3semidirect
74. #2000C2×C3semidirect
75. #2000C2×C3semidirect
76. #1934C2×C3semidirect
77. #1923C2×C3semidirect
78. #1880C2×C3semidirect
115. C2×C3×SD16D4semidirect
165. C3×#102D4semidirect
179. C22×SD16C22×C3semidirect
180. C22×SD16C22×C3semidirect
181. C2×C4⋊Q8C22×C3semidirect
189. C2×C4×Q8C22×C3semidirect
194. C2×C4⋊C8C22×C3semidirect
195. C2×#103C22×C3semidirect
196. C2×#103C22×C3semidirect
201. C2×#102C22×C3semidirect
202. C2×#102C22×C3semidirect
205. C2×C4×C8C22×C3semidirect
210. #391C22×C3semidirect
214. #389C22×C3semidirect
217. #340C22×C3semidirect
218. #340C22×C3semidirect
219. #336C22×C3semidirect
220. #336C22×C3semidirect
339. C3×C22⋊C4SD16semidirect
381. C2×SD16C3×D4semidirect
431. #102C3×D4semidirect
664. C22⋊C4C3×SD16semidirect
887. C3#30456direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4922
C2×C3×#4602
C2×C3×#4502
C3×#24332
C3×#24292
C3×#20552
C3×#20412
C3×#20142
C3×#20132
C3×#20002
C3×#19342
C3×#19232
C3×#18802
#304563