Finite Group Databasebeta

← C3×#30460 #10649067

Subgroups — C3×#30460 #10649067

Order 768.

1374 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#496C211yesmaximal, characteristic, complemented
2C2×C3×#459C211yesmaximal, characteristic, complemented
3C2×C3×#450C211yesmaximal, characteristic, complemented
4C2×C3×#447C211yesmaximal, characteristic, complemented
5C3×#2433C211yesmaximal, characteristic, complemented
6C3×#2427C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8C3×#2041C211yesmaximal, characteristic, complemented
9C3×#2014C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#1999C211yesmaximal, characteristic, complemented
13C3×#1936C211yesmaximal, characteristic, complemented
14C3×#1924C211yesmaximal, characteristic, complemented
15C3×#1879C211yesmaximal, characteristic, complemented
16#30460C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic, complemented
21C22×C3×D8C2211yescharacteristic
22C22×C3×D8C2211yescharacteristic
23C22×C3×D8C2211yescharacteristic, complemented
24C2×C3×#127C2211yescharacteristic
25C2×C3×#127C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic, complemented
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#120—21no—
31C2×C3×#120—21no—
32C2×C3×C4×D4C2211yescharacteristic, complemented
33C3×#496—24no—
34C3×#459—24no—
35C3×#450—24no—
36C3×#447—24no—
37C2×C3×C4⋊C8C2211yescharacteristic, complemented
38C2×C3×#103C2211yescharacteristic, complemented
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic, complemented
44C2×C3×#102C2211yescharacteristic, complemented
45C2×C3×#102C2211yescharacteristic, complemented
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×#97C2211yescharacteristic, complemented
49C3×#397—21no—
50C3×#394—21no—
51C3×#392—21no—
52C3×#392—21no—
53C3×#391C2211yescharacteristic, complemented
54C3×#390C2211yescharacteristic
55C3×#390C2211yescharacteristic
56C3×#389C2211yescharacteristic, complemented
57C3×#386—21no—
58C3×#380—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62C3×#336C2211yescharacteristic, complemented
63C3×#336C2211yescharacteristic, complemented
64C2×#496C2×C311yescharacteristic, complemented
65C2×#459C2×C311yescharacteristic, complemented
66C2×#450C2×C311yescharacteristic, complemented
67C2×#447C2×C311yescharacteristic, complemented
68#2433C2×C311yescharacteristic, complemented
69#2427C2×C311yescharacteristic, complemented
70#2055C2×C311yescharacteristic, complemented
71#2041C2×C311yescharacteristic, complemented
72#2014C2×C311yescharacteristic, complemented
73#2012C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic, complemented
76#1936C2×C311yescharacteristic, complemented
77#1924C2×C311yescharacteristic, complemented
78#1879C2×C311yescharacteristic, complemented
79C25×C3—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—22no—
82C22×C3×D4—22no—
83C22×C3×D4—21no—
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
97C22×C3×D4C2311yescharacteristic
98C23×C3×C4—21no—
99C23×C3×C4C2311yescharacteristic
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—41no—
105C2×C3×SD16—41no—
106C2×C3×SD16—41no—
107C2×C3×SD16—41no—
108C2×C3×SD16—41no—
109C2×C3×D8—22no—
110C2×C3×D8—22no—
111C2×C3×D8—22no—
112C2×C3×D8—22no—
113C2×C3×D8—41no—
114C2×C3×D8—41no—
115C2×C3×D8—41no—
116C2×C3×D8—41no—
117C2×C3×D8D414yescomplemented
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2311yescharacteristic
122C3×#127—22no—
123C3×#127—22no—
124C3×#127—41no—
125C3×#127—41no—
126C3×#124—22no—
127C3×#124—41no—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—41no—
130C3×#121—22no—
131C3×#121—41no—
132C3×#121—41no—
133C3×#121—41no—
134C3×#120—44no—
135C3×#120—44no—
136C3×C4×D4—22no—
137C3×C4×D4—41no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4C2311yescharacteristic
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C4⋊C4C2311yescharacteristic
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
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⋊C4—21no—
153C2×C3×C22⋊C4D411yescharacteristic
154C2×C3×C22⋊C4D411yescharacteristic
155C2×C3×C42C2311yescharacteristic
156C2×C3×C42C2311yescharacteristic
157C3×C4⋊C8—22no—
158C3×#103—41no—
159C3×#102—22no—
160C3×#102—22no—
161C3×#102—22no—
162C3×#102—22no—
163C3×#102—41no—
164C3×#102—41no—
165C3×#102D414yescomplemented
166C3×C22⋊C8—22no—
167C3×C22⋊C8—22no—
168C3×#97—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, complemented
178C22×D8C22×C311yescharacteristic
179C22×D8C22×C311yescharacteristic
180C22×D8C22×C311yescharacteristic, complemented
181C2×#127C22×C311yescharacteristic
182C2×#127C22×C311yescharacteristic
183C2×#124C22×C311yescharacteristic, complemented
184C2×C22⋊Q8C22×C311yescharacteristic
185C2×#121C22×C311yescharacteristic
186C2×#121C22×C311yescharacteristic
187C2×#120—21no—
188C2×#120—21no—
189C2×C4×D4C22×C311yescharacteristic, complemented
190#496—24no—
191#459—24no—
192#450—24no—
193#447—24no—
194C2×C4⋊C8C22×C311yescharacteristic, complemented
195C2×#103C22×C311yescharacteristic, complemented
196C2×#102C22×C311yescharacteristic
197C2×#102C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×#102C22×C311yescharacteristic
200C2×#102C22×C311yescharacteristic, complemented
201C2×#102C22×C311yescharacteristic, complemented
202C2×#102C22×C311yescharacteristic, complemented
203C2×C22⋊C8C22×C311yescharacteristic
204C2×C22⋊C8C22×C311yescharacteristic
205C2×#97C22×C311yescharacteristic, complemented
206#397—21no—
207#394—21no—
208#392—21no—
209#392—21no—
210#391C22×C311yescharacteristic, complemented
211#390C22×C311yescharacteristic
212#390C22×C311yescharacteristic
213#389C22×C311yescharacteristic, complemented
214#386—21no—
215#380—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—21no—
225C24×C3—42no—
226C24×C3—42no—
227C24×C3—42no—
228C24×C3—42no—
229C24×C3—42no—
230C24×C3—81no—
231C24×C3—81no—
232C24×C3C2×D411yescharacteristic
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×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
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—42no—
269C2×C3×D4—42no—
270C2×C3×D4—44no—
271C2×C3×D4—44no—
272C2×C3×D4—44no—
273C2×C3×D4—44no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—42no—
280C2×C3×D4—81no—
281C2×C3×D4—81no—
282C2×C3×D4—81no—
283C2×C3×D4—81no—
284C2×C3×D4—81no—
285C2×C3×D4C2×D412yes—
286C2×C3×D4C2×D412yes—
287C2×C3×D4C2×D412yes—
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×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—42no—
299C22×C3×C4—42no—
300C22×C3×C4—81no—
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2411yescharacteristic
307C3×SD16—44no—
308C3×SD16—44no—
309C3×SD16—44no—
310C3×D8—44no—
311C3×D8—44no—
312C3×D8—44no—
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×C8C2×D412yes—
324C2×C3×C8C2×D412yes—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—42no—
331C3×C4⋊C4—81no—
332C3×C4⋊C4C2×D412yes—
333C3×C22⋊C4—22no—
334C3×C22⋊C4—22no—
335C3×C22⋊C4—42no—
336C3×C22⋊C4—42no—
337C3×C22⋊C4—42no—
338C3×C22⋊C4—42no—
339C3×C22⋊C4—42no—
340C3×C22⋊C4—42no—
341C3×C22⋊C4—42no—
342C3×C22⋊C4—42no—
343C3×C22⋊C4—42no—
344C3×C22⋊C4—42no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—21no—
349C25—21no—
350C22×Q8C23×C311yescharacteristic
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4—41no—
363C22×D4—41no—
364C22×D4C23×C311yescharacteristic
365C22×D4C23×C311yescharacteristic
366C22×D4C23×C311yescharacteristic
367C22×D4C23×C311yescharacteristic
368C23×C4—21no—
369C23×C4C23×C311yescharacteristic
370C2×SD16—22no—
371C2×SD16—22no—
372C2×SD16—22no—
373C2×SD16—22no—
374C2×SD16—41no—
375C2×SD16—41no—
376C2×SD16—41no—
377C2×SD16—41no—
378C2×SD16—41no—
379C2×D8—22no—
380C2×D8—22no—
381C2×D8—22no—
382C2×D8—22no—
383C2×D8—41no—
384C2×D8—41no—
385C2×D8—41no—
386C2×D8—41no—
387C2×D8C3×D414yescomplemented
388C22×C8C23×C311yescharacteristic
389C22×C8C23×C311yescharacteristic
390C22×C8C23×C311yescharacteristic
391C22×C8C23×C311yescharacteristic
392#127—22no—
393#127—22no—
394#127—41no—
395#127—41no—
396#124—22no—
397#124—41no—
398C22⋊Q8—22no—
399C22⋊Q8—41no—
400#121—22no—
401#121—41no—
402#121—41no—
403#121—41no—
404#120—44no—
405#120—44no—
406C4×D4—22no—
407C4×D4—41no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4C23×C311yescharacteristic
411C2×C4⋊C4C23×C311yescharacteristic
412C2×C4⋊C4C23×C311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4C3×D411yescharacteristic
424C2×C22⋊C4C3×D411yescharacteristic
425C2×C42C23×C311yescharacteristic
426C2×C42C23×C311yescharacteristic
427C4⋊C8—22no—
428#103—41no—
429#102—22no—
430#102—22no—
431#102—22no—
432#102—22no—
433#102—41no—
434#102—41no—
435#102C3×D414yescomplemented
436C22⋊C8—22no—
437C22⋊C8—22no—
438#97—22no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95C3×D411yescharacteristic
443#95C3×D411yescharacteristic
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—48no—
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—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—84no—
480C23×C3—84no—
481C23×C3—84no—
482C23×C3—84no—
483C23×C3—84no—
484C23×C3—84no—
485C23×C3AGL(1,ℤ/8)12yes—
486C23×C3C22×D411yescharacteristic
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×D4—22no—
492C3×D4—22no—
493C3×D4—22no—
494C3×D4—22no—
495C3×D4—22no—
496C3×D4—22no—
497C3×D4—48no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4—41no—
507C3×D4—41no—
508C3×D4—84no—
509C3×D4—84no—
510C3×D4—84no—
511C3×D4—84no—
512C3×D4—84no—
513C3×D4—84no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—22no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
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—84no—
545C2×C3×C4AGL(1,ℤ/8)12yes—
546C2×C3×C4C22×D411yescharacteristic
547C2×C3×C4C22×D411yescharacteristic
548C2×C3×C4H(5,𝔽2)11yescharacteristic
549C2×C3×C4H(5,𝔽2)11yescharacteristic
550C2×C3×C4H(5,𝔽2)11yescharacteristic
551C2×C3×C4H(5,𝔽2)11yescharacteristic
552C3×C8—22no—
553C3×C8—22no—
554C3×C8—41no—
555C3×C8—41no—
556C24—21no—
557C24—21no—
558C24—21no—
559C24—21no—
560C24—42no—
561C24—42no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—81no—
566C24—81no—
567C24C2×C3×D411yescharacteristic
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—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—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—44no—
606C2×D4—44no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4—81no—
620C2×D4C2×C3×D412yes—
621C2×D4C2×C3×D412yes—
622C2×D4C2×C3×D412yes—
623C22×C4—21no—
624C22×C4—21no—
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—42no—
634C22×C4—42no—
635C22×C4—81no—
636C22×C4C2×C3×D411yescharacteristic
637C22×C4C2×C3×D411yescharacteristic
638C22×C4C2×C3×D411yescharacteristic
639C22×C4C2×C3×D411yescharacteristic
640C22×C4C2×C3×D411yescharacteristic
641C22×C4C24×C311yescharacteristic
642SD16—44no—
643SD16—44no—
644SD16—44no—
645D8—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×C3×D412yes—
659C2×C8C2×C3×D412yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—42no—
666C4⋊C4—81no—
667C4⋊C4C2×C3×D412yes—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—21no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—42no—
692C22×C3—42no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3—42no—
696C22×C3—42no—
697C22×C3—42no—
698C22×C3—42no—
699C22×C3—42no—
700C22×C3—816no—
701C22×C3—81no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—81no—
711C22×C3—81no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—81no—
720C22×C3#53511yescharacteristic
721C22×C3D4211yescharacteristic
722C22×C3D4211yescharacteristic
723C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
724C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
725C22×C3#57611yescharacteristic
726C22×C3#57711yescharacteristic
727C3×C4—22no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—42no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—81no—
734C3×C4—81no—
735C3×C4—81no—
736C3×C4#53411yescharacteristic
737C3×C4#53511yescharacteristic
738C3×C4D4211yescharacteristic
739C3×C4#56011yescharacteristic
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—48no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—84no—
776C23—84no—
777C23—84no—
778C23—84no—
779C23—84no—
780C23—84no—
781C23C3×AGL(1,ℤ/8)12yes—
782C23C22×C3×D411yescharacteristic
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—22no—
793D4—48no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—41no—
804D4—84no—
805D4—84no—
806D4—84no—
807D4—84no—
808D4—84no—
809D4—84no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—21no—
824C2×C4—21no—
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—84no—
841C2×C4C3×AGL(1,ℤ/8)12yes—
842C2×C4C22×C3×D411yescharacteristic
843C2×C4C22×C3×D411yescharacteristic
844C2×C4C3×H(5,𝔽2)11yescharacteristic
845C2×C4C3×H(5,𝔽2)11yescharacteristic
846C2×C4C3×H(5,𝔽2)11yescharacteristic
847C2×C4C3×H(5,𝔽2)11yescharacteristic
848C8—22no—
849C8—22no—
850C8—41no—
851C8—41no—
852C2×C3—42no—
853C2×C3—82no—
854C2×C3—82no—
855C2×C3—82no—
856C2×C3—161no—
857C2×C3#266911yescharacteristic
858C2×C3#321711yescharacteristic
859C2×C3#322411yescharacteristic
860C2×C3#326411yescharacteristic
861C2×C3#326411yescharacteristic
862C2×C3#326511yescharacteristic
863C2×C3#327211yescharacteristic
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—816no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22C3×#53511yescharacteristic
901C22C3×D4211yescharacteristic
902C22C3×D4211yescharacteristic
903C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
904C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
905C22C3×#57611yescharacteristic
906C22C3×#57711yescharacteristic
907C4—22no—
908C4—41no—
909C4—41no—
910C4—42no—
911C4—41no—
912C4—41no—
913C4—81no—
914C4—81no—
915C4—81no—
916C4C3×#53411yescharacteristic
917C4C3×#53511yescharacteristic
918C4C3×D4211yescharacteristic
919C4C3×#56011yescharacteristic
920C3#3046011yescharacteristic, direct product factor, Sylow
921C2—42no—
922C2—82no—
923C2—82no—
924C2—82no—
925C2—161no—
926C2C3×#266911yescharacteristic
927C2C3×#321711yescharacteristic
928C2C3×#322411yescharacteristic
929C2C3×#326411yescharacteristic
930C2C3×#326411yescharacteristic
931C2C3×#326511yescharacteristic
932C2C3×#327211yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
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×#496C2semidirect
2. C2×C3×#459C2semidirect
3. C2×C3×#450C2semidirect
4. C2×C3×#447C2semidirect
5. C3×#2433C2semidirect
6. C3×#2427C2semidirect
7. C3×#2055C2semidirect
8. C3×#2041C2semidirect
9. C3×#2014C2semidirect
10. C3×#2012C2semidirect
11. C3×#2000C2semidirect
12. C3×#1999C2semidirect
13. C3×#1936C2semidirect
14. C3×#1924C2semidirect
15. C3×#1879C2semidirect
16. #30460C3direct (N × H)
20. C22×C3×SD16C22semidirect
23. C22×C3×D8C22semidirect
26. C2×C3×#124C22semidirect
32. C2×C3×C4×D4C22semidirect
37. C2×C3×C4⋊C8C22semidirect
38. C2×C3×#103C22semidirect
43. C2×C3×#102C22semidirect
44. C2×C3×#102C22semidirect
45. C2×C3×#102C22semidirect
48. C2×C3×#97C22semidirect
53. C3×#391C22semidirect
56. C3×#389C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. C3×#336C22semidirect
63. C3×#336C22semidirect
64. C2×#496C2×C3semidirect
65. C2×#459C2×C3semidirect
66. C2×#450C2×C3semidirect
67. C2×#447C2×C3semidirect
68. #2433C2×C3semidirect
69. #2427C2×C3semidirect
70. #2055C2×C3semidirect
71. #2041C2×C3semidirect
72. #2014C2×C3semidirect
73. #2012C2×C3semidirect
74. #2000C2×C3semidirect
75. #1999C2×C3semidirect
76. #1936C2×C3semidirect
77. #1924C2×C3semidirect
78. #1879C2×C3semidirect
117. C2×C3×D8D4semidirect
165. C3×#102D4semidirect
177. C22×SD16C22×C3semidirect
180. C22×D8C22×C3semidirect
183. C2×#124C22×C3semidirect
189. C2×C4×D4C22×C3semidirect
194. C2×C4⋊C8C22×C3semidirect
195. C2×#103C22×C3semidirect
200. C2×#102C22×C3semidirect
201. C2×#102C22×C3semidirect
202. C2×#102C22×C3semidirect
205. C2×#97C22×C3semidirect
210. #391C22×C3semidirect
213. #389C22×C3semidirect
217. #340C22×C3semidirect
218. #340C22×C3semidirect
219. #336C22×C3semidirect
220. #336C22×C3semidirect
387. C2×D8C3×D4semidirect
435. #102C3×D4semidirect
920. C3#30460direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4962
C2×C3×#4592
C2×C3×#4502
C2×C3×#4472
C3×#24332
C3×#24272
C3×#20552
C3×#20412
C3×#20142
C3×#20122
C3×#20002
C3×#19992
C3×#19362
C3×#19242
C3×#18792
#304603