Finite Group Databasebeta

← C3×#25736 #10644343

Subgroups — C3×#25736 #10644343

Order 768.

1700 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#535C211yesmaximal, characteristic, complemented
2C2×C3×#496C211yesmaximal, characteristic, complemented
3C2×C3×#495C211yesmaximal, characteristic, complemented
4C2×C3×#452C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic, complemented
6C2×C3×#450C211yesmaximal, characteristic, complemented
7C2×C3×#447C211yesmaximal, characteristic, complemented
8C3×#2620C211yesmaximal, characteristic, complemented
9C3×#2015C211yesmaximal, characteristic, complemented
10C3×#2014C211yesmaximal, characteristic, complemented
11C3×#2012C211yesmaximal, characteristic, complemented
12C3×#2011C211yesmaximal, characteristic, complemented
13C3×#1959C211yesmaximal, characteristic, complemented
14C3×#1957C211yesmaximal, characteristic, complemented
15C3×#1750C211yesmaximal, characteristic, complemented
16#25736C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic, complemented
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic, complemented
23C22×C3×SD16C2211yescharacteristic, complemented
24C22×C3×D8C2211yescharacteristic
25C22×C3×D8C2211yescharacteristic
26C22×C3×D8C2211yescharacteristic, complemented
27C3×#535—24no—
28C3×#535—24no—
29C2×C3×#127C2211yescharacteristic
30C2×C3×#127C2211yescharacteristic
31C2×C3×#124C2211yescharacteristic
32C2×C3×#124C2211yescharacteristic
33C2×C3×#124C2211yescharacteristic, complemented
34C2×C3×C22⋊Q8C2211yescharacteristic
35C2×C3×#121—22no—
36C2×C3×#121C2211yescharacteristic
37C2×C3×#120—22no—
38C2×C3×#117C2211yescharacteristic
39C3×#496—24no—
40C3×#495—24no—
41C3×#452—24no—
42C3×#450—24no—
43C3×#449—24no—
44C3×#447—24no—
45C2×C3×#103C2211yescharacteristic, complemented
46C2×C3×#103C2211yescharacteristic, complemented
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×#102C2211yescharacteristic
51C2×C3×#102C2211yescharacteristic, complemented
52C2×C3×#102C2211yescharacteristic, complemented
53C2×C3×C22⋊C8C2211yescharacteristic
54C2×C3×C22⋊C8C2211yescharacteristic
55C2×C3×#97C2211yescharacteristic, complemented
56C2×C3×C4×C8C2211yescharacteristic, complemented
57C3×#396—22no—
58C3×#394—22no—
59C3×#391C2211yescharacteristic, complemented
60C3×#390C2211yescharacteristic, complemented
61C3×#384C2211yescharacteristic, complemented
62C3×#336C2211yescharacteristic, complemented
63C3×#336C2211yescharacteristic, complemented
64C2×#535C2×C311yescharacteristic, complemented
65C2×#496C2×C311yescharacteristic, complemented
66C2×#495C2×C311yescharacteristic, complemented
67C2×#452C2×C311yescharacteristic, complemented
68C2×#449C2×C311yescharacteristic, complemented
69C2×#450C2×C311yescharacteristic, complemented
70C2×#447C2×C311yescharacteristic, complemented
71#2620C2×C311yescharacteristic, complemented
72#2015C2×C311yescharacteristic, complemented
73#2014C2×C311yescharacteristic, complemented
74#2012C2×C311yescharacteristic, complemented
75#2011C2×C311yescharacteristic, complemented
76#1959C2×C311yescharacteristic, complemented
77#1957C2×C311yescharacteristic, complemented
78#1750C2×C311yescharacteristic, complemented
79C25×C3—21no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—41no—
85C2×C3×#41—41no—
86C22×C3×Q8C2311yescharacteristic
87C22×C3×Q8C2311yescharacteristic
88C22×C3×D4—21no—
89C22×C3×D4—22no—
90C22×C3×D4—22no—
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4—22no—
94C22×C3×D4—22no—
95C22×C3×D4—22no—
96C22×C3×D4—22no—
97C22×C3×D4—41no—
98C22×C3×D4—41no—
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C2×C3×Q16—22no—
106C2×C3×Q16—22no—
107C2×C3×Q16—41no—
108C2×C3×SD16—22no—
109C2×C3×SD16—22no—
110C2×C3×SD16—22no—
111C2×C3×SD16—22no—
112C2×C3×SD16—22no—
113C2×C3×SD16—22no—
114C2×C3×SD16—22no—
115C2×C3×SD16—22no—
116C2×C3×SD16—41no—
117C2×C3×SD16—41no—
118C2×C3×SD16—41no—
119C2×C3×SD16—41no—
120C2×C3×D8—22no—
121C2×C3×D8—22no—
122C2×C3×D8—22no—
123C2×C3×D8—22no—
124C2×C3×D8—22no—
125C2×C3×D8—22no—
126C2×C3×D8—41no—
127C2×C3×D8—41no—
128C2×C3×D8—41no—
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C22×C3×C8C2311yescharacteristic
132C22×C3×C8C2311yescharacteristic
133C3×#127—22no—
134C3×#127—22no—
135C3×#127—22no—
136C3×#127D414yescomplemented
137C3×#124—22no—
138C3×#124—22no—
139C3×#124—22no—
140C3×#124—22no—
141C3×#124—22no—
142C3×#124D414yescomplemented
143C3×C22⋊Q8—22no—
144C3×C22⋊Q8—22no—
145C3×#121—216no—
146C3×#121—22no—
147C3×#121—22no—
148C3×#120—216no—
149C3×#117—22no—
150C3×#117—22no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4—22no—
153C2×C3×C4⋊C4D412yes—
154C2×C3×C4⋊C4C2311yescharacteristic
155C2×C3×C4⋊C4C2311yescharacteristic
156C2×C3×C22⋊C4—22no—
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—22no—
162C2×C3×C22⋊C4D412yes—
163C2×C3×C42C2311yescharacteristic
164C2×C3×C42C2311yescharacteristic
165C3×#103—22no—
166C3×#103—22no—
167C3×#102—22no—
168C3×#102—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—22no—
173C3×C22⋊C8D414yescomplemented
174C3×C22⋊C8D414yescomplemented
175C3×#97—22no—
176C3×C4×C8—22no—
177C3×#95—22no—
178C22×#41C22×C311yescharacteristic
179C23×D4C22×C311yescharacteristic
180C22×Q16C22×C311yescharacteristic, complemented
181C22×SD16C22×C311yescharacteristic
182C22×SD16C22×C311yescharacteristic
183C22×SD16C22×C311yescharacteristic, complemented
184C22×SD16C22×C311yescharacteristic, complemented
185C22×D8C22×C311yescharacteristic
186C22×D8C22×C311yescharacteristic
187C22×D8C22×C311yescharacteristic, complemented
188#535—24no—
189#535—24no—
190C2×#127C22×C311yescharacteristic
191C2×#127C22×C311yescharacteristic
192C2×#124C22×C311yescharacteristic
193C2×#124C22×C311yescharacteristic
194C2×#124C22×C311yescharacteristic, complemented
195C2×C22⋊Q8C22×C311yescharacteristic
196C2×#121—22no—
197C2×#121C22×C311yescharacteristic
198C2×#120—22no—
199C2×#117C22×C311yescharacteristic
200#496—24no—
201#495—24no—
202#452—24no—
203#450—24no—
204#449—24no—
205#447—24no—
206C2×#103C22×C311yescharacteristic, complemented
207C2×#103C22×C311yescharacteristic, complemented
208C2×#102C22×C311yescharacteristic
209C2×#102C22×C311yescharacteristic
210C2×#102C22×C311yescharacteristic
211C2×#102C22×C311yescharacteristic
212C2×#102C22×C311yescharacteristic, complemented
213C2×#102C22×C311yescharacteristic, complemented
214C2×C22⋊C8C22×C311yescharacteristic
215C2×C22⋊C8C22×C311yescharacteristic
216C2×#97C22×C311yescharacteristic, complemented
217C2×C4×C8C22×C311yescharacteristic, complemented
218#396—22no—
219#394—22no—
220#391C22×C311yescharacteristic, complemented
221#390C22×C311yescharacteristic, complemented
222#384C22×C311yescharacteristic, complemented
223#336C22×C311yescharacteristic, complemented
224#336C22×C311yescharacteristic, complemented
225C24×C3—24no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—42no—
231C24×C3—42no—
232C24×C3—82no—
233C24×C3—82no—
234C24×C3C2×D411yescharacteristic
235C3×#41—44no—
236C3×#41—44no—
237C3×#41—44no—
238C3×#41—44no—
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×Q8C2×D412yes—
251C2×C3×D4—24no—
252C2×C3×D4—24no—
253C2×C3×D4—28no—
254C2×C3×D4—28no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
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—21no—
276C2×C3×D4—44no—
277C2×C3×D4—44no—
278C2×C3×D4—44no—
279C2×C3×D4—44no—
280C2×C3×D4—42no—
281C2×C3×D4—42no—
282C2×C3×D4—42no—
283C2×C3×D4—42no—
284C2×C3×D4—42no—
285C2×C3×D4—82no—
286C2×C3×D4—82no—
287C2×C3×D4—82no—
288C2×C3×D4—82no—
289C2×C3×D4—82no—
290C2×C3×D4C2×D412yes—
291C2×C3×D4C2×D412yes—
292C2×C3×D4C2×D412yes—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—24no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—42no—
303C22×C3×C4—42no—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2×D412yes—
309C22×C3×C4C2411yescharacteristic
310C3×Q16—44no—
311C3×SD16—44no—
312C3×SD16—44no—
313C3×SD16—44no—
314C3×SD16—44no—
315C3×D8—44no—
316C3×D8—44no—
317C3×D8—44no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
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×C8C2×D412yes—
327C2×C3×C8C2×D412yes—
328C2×C3×C8C2×D412yes—
329C2×C3×C8C2×D412yes—
330C3×C4⋊C4—24no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—42no—
336C3×C4⋊C4—82no—
337C3×C22⋊C4—28no—
338C3×C22⋊C4—28no—
339C3×C22⋊C4—24no—
340C3×C22⋊C4—42no—
341C3×C22⋊C4—44no—
342C3×C22⋊C4—42no—
343C3×C22⋊C4—82no—
344C3×C42—21no—
345C3×C42—21no—
346C3×C42C2×D412yes—
347C3×C42C2×D412yes—
348C25—21no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—41no—
354C2×#41—41no—
355C22×Q8C23×C311yescharacteristic
356C22×Q8C23×C311yescharacteristic
357C22×D4—21no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—41no—
367C22×D4—41no—
368C22×D4C23×C311yescharacteristic
369C22×D4C23×C311yescharacteristic
370C22×D4C23×C311yescharacteristic
371C22×D4C23×C311yescharacteristic
372C23×C4—21no—
373C23×C4C23×C311yescharacteristic
374C2×Q16—22no—
375C2×Q16—22no—
376C2×Q16—41no—
377C2×SD16—22no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—41no—
386C2×SD16—41no—
387C2×SD16—41no—
388C2×SD16—41no—
389C2×D8—22no—
390C2×D8—22no—
391C2×D8—22no—
392C2×D8—22no—
393C2×D8—22no—
394C2×D8—22no—
395C2×D8—41no—
396C2×D8—41no—
397C2×D8—41no—
398C22×C8C23×C311yescharacteristic
399C22×C8C23×C311yescharacteristic
400C22×C8C23×C311yescharacteristic
401C22×C8C23×C311yescharacteristic
402#127—22no—
403#127—22no—
404#127—22no—
405#127C3×D414yescomplemented
406#124—22no—
407#124—22no—
408#124—22no—
409#124—22no—
410#124—22no—
411#124C3×D414yescomplemented
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414#121—216no—
415#121—22no—
416#121—22no—
417#120—216no—
418#117—22no—
419#117—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4C3×D412yes—
423C2×C4⋊C4C23×C311yescharacteristic
424C2×C4⋊C4C23×C311yescharacteristic
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4C3×D412yes—
432C2×C42C23×C311yescharacteristic
433C2×C42C23×C311yescharacteristic
434#103—22no—
435#103—22no—
436#102—22no—
437#102—22no—
438#102—22no—
439#102—22no—
440#102—22no—
441#102—22no—
442C22⋊C8C3×D414yescomplemented
443C22⋊C8C3×D414yescomplemented
444#97—22no—
445C4×C8—22no—
446#95—22no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—48no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—42no—
462C23×C3—42no—
463C23×C3—42no—
464C23×C3—42no—
465C23×C3—42no—
466C23×C3—42no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—42no—
471C23×C3—42no—
472C23×C3—84no—
473C23×C3—84no—
474C23×C3—88no—
475C23×C3—88no—
476C23×C3#12712yes—
477C23×C3C22×D411yescharacteristic
478C3×Q8—22no—
479C3×Q8—22no—
480C3×Q8—41no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—41no—
486C3×D4—22no—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—22no—
490C3×D4—22no—
491C3×D4—22no—
492C3×D4—48no—
493C3×D4—48no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—41no—
504C3×D4—88no—
505C3×D4—88no—
506C3×D4—84no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
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—48no—
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—42no—
528C2×C3×C4—42no—
529C2×C3×C4#12014yes—
530C2×C3×C4#12712yes—
531C2×C3×C4C22×D411yescharacteristic
532C2×C3×C4C22×D411yescharacteristic
533C2×C3×C4C22×D411yescharacteristic
534C2×C3×C4C22×D411yescharacteristic
535C2×C3×C4H(5,𝔽2)11yescharacteristic
536C2×C3×C4H(5,𝔽2)11yescharacteristic
537C3×C8—22no—
538C3×C8—22no—
539C3×C8—22no—
540C3×C8—22no—
541C24—24no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—82no—
549C24—82no—
550C24C2×C3×D411yescharacteristic
551#41—44no—
552#41—44no—
553#41—44no—
554#41—44no—
555C2×Q8—21no—
556C2×Q8—21no—
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×Q8C2×C3×D412yes—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—28no—
570C2×D4—28no—
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—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—44no—
593C2×D4—44no—
594C2×D4—44no—
595C2×D4—44no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—82no—
602C2×D4—82no—
603C2×D4—82no—
604C2×D4—82no—
605C2×D4—82no—
606C2×D4C2×C3×D412yes—
607C2×D4C2×C3×D412yes—
608C2×D4C2×C3×D412yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4C2×C3×D412yes—
621C22×C4C2×C3×D412yes—
622C22×C4C2×C3×D411yescharacteristic
623C22×C4C2×C3×D412yes—
624C22×C4C2×C3×D412yes—
625C22×C4C24×C311yescharacteristic
626Q16—44no—
627SD16—44no—
628SD16—44no—
629SD16—44no—
630SD16—44no—
631D8—44no—
632D8—44no—
633D8—44no—
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—
644C2×C8C2×C3×D412yes—
645C2×C8C2×C3×D412yes—
646C4⋊C4—24no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—42no—
652C4⋊C4—82no—
653C22⋊C4—28no—
654C22⋊C4—28no—
655C22⋊C4—24no—
656C22⋊C4—42no—
657C22⋊C4—44no—
658C22⋊C4—42no—
659C22⋊C4—82no—
660C42—21no—
661C42—21no—
662C42C2×C3×D412yes—
663C42C2×C3×D412yes—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—42no—
668C22×C3—42no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—44no—
673C22×C3—44no—
674C22×C3—44no—
675C22×C3—816no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3—81no—
682C22×C3—82no—
683C22×C3—82no—
684C22×C3—82no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—81no—
688C22×C3—82no—
689C22×C3—82no—
690C22×C3C2×#12011yescharacteristic
691C22×C3C2×#12711yescharacteristic
692C22×C3#53511yescharacteristic
693C22×C3#57612yes—
694C22×C3#57712yes—
695C3×C4—22no—
696C3×C4—24no—
697C3×C4—42no—
698C3×C4—42no—
699C3×C4—81no—
700C3×C4—81no—
701C3×C4—81no—
702C3×C4D4211yescharacteristic
703C3×C4D4211yescharacteristic
704C3×C4D4211yescharacteristic
705C3×C4D4211yescharacteristic
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—48no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—84no—
732C23—84no—
733C23—88no—
734C23—88no—
735C23C3×#12712yes—
736C23C22×C3×D411yescharacteristic
737Q8—22no—
738Q8—22no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—41no—
745D4—22no—
746D4—22no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—48no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—88no—
764D4—88no—
765D4—84no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—48no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4C3×#12014yes—
789C2×C4C3×#12712yes—
790C2×C4C22×C3×D411yescharacteristic
791C2×C4C22×C3×D411yescharacteristic
792C2×C4C22×C3×D411yescharacteristic
793C2×C4C22×C3×D411yescharacteristic
794C2×C4C3×H(5,𝔽2)11yescharacteristic
795C2×C4C3×H(5,𝔽2)11yescharacteristic
796C8—22no—
797C8—22no—
798C8—22no—
799C8—22no—
800C2×C3—42no—
801C2×C3—82no—
802C2×C3—82no—
803C2×C3—82no—
804C2×C3—161no—
805C2×C3#243311yescharacteristic
806C2×C3#301212yes—
807C2×C3#315411yescharacteristic
808C2×C3#315511yescharacteristic
809C2×C3#322412yes—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—816no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—82no—
835C22—82no—
836C22C2×C3×#12011yescharacteristic
837C22C2×C3×#12711yescharacteristic
838C22C3×#53511yescharacteristic
839C22C3×#57612yes—
840C22C3×#57712yes—
841C4—22no—
842C4—24no—
843C4—42no—
844C4—42no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C3×D4211yescharacteristic
849C4C3×D4211yescharacteristic
850C4C3×D4211yescharacteristic
851C4C3×D4211yescharacteristic
852C3#2573611yescharacteristic, direct product factor, Sylow
853C2—42no—
854C2—82no—
855C2—82no—
856C2—82no—
857C2—161no—
858C2C3×#243311yescharacteristic
859C2C3×#301212yes—
860C2C3×#315411yescharacteristic
861C2C3×#315511yescharacteristic
862C2C3×#322412yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
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×#535C2semidirect
2. C2×C3×#496C2semidirect
3. C2×C3×#495C2semidirect
4. C2×C3×#452C2semidirect
5. C2×C3×#449C2semidirect
6. C2×C3×#450C2semidirect
7. C2×C3×#447C2semidirect
8. C3×#2620C2semidirect
9. C3×#2015C2semidirect
10. C3×#2014C2semidirect
11. C3×#2012C2semidirect
12. C3×#2011C2semidirect
13. C3×#1959C2semidirect
14. C3×#1957C2semidirect
15. C3×#1750C2semidirect
16. #25736C3direct (N × H)
19. C22×C3×Q16C22semidirect
22. C22×C3×SD16C22semidirect
23. C22×C3×SD16C22semidirect
26. C22×C3×D8C22semidirect
33. C2×C3×#124C22semidirect
45. C2×C3×#103C22semidirect
46. C2×C3×#103C22semidirect
51. C2×C3×#102C22semidirect
52. C2×C3×#102C22semidirect
55. C2×C3×#97C22semidirect
56. C2×C3×C4×C8C22semidirect
59. C3×#391C22semidirect
60. C3×#390C22semidirect
61. C3×#384C22semidirect
62. C3×#336C22semidirect
63. C3×#336C22semidirect
64. C2×#535C2×C3semidirect
65. C2×#496C2×C3semidirect
66. C2×#495C2×C3semidirect
67. C2×#452C2×C3semidirect
68. C2×#449C2×C3semidirect
69. C2×#450C2×C3semidirect
70. C2×#447C2×C3semidirect
71. #2620C2×C3semidirect
72. #2015C2×C3semidirect
73. #2014C2×C3semidirect
74. #2012C2×C3semidirect
75. #2011C2×C3semidirect
76. #1959C2×C3semidirect
77. #1957C2×C3semidirect
78. #1750C2×C3semidirect
136. C3×#127D4semidirect
142. C3×#124D4semidirect
173. C3×C22⋊C8D4semidirect
174. C3×C22⋊C8D4semidirect
180. C22×Q16C22×C3semidirect
183. C22×SD16C22×C3semidirect
184. C22×SD16C22×C3semidirect
187. C22×D8C22×C3semidirect
194. C2×#124C22×C3semidirect
206. C2×#103C22×C3semidirect
207. C2×#103C22×C3semidirect
212. C2×#102C22×C3semidirect
213. C2×#102C22×C3semidirect
216. C2×#97C22×C3semidirect
217. C2×C4×C8C22×C3semidirect
220. #391C22×C3semidirect
221. #390C22×C3semidirect
222. #384C22×C3semidirect
223. #336C22×C3semidirect
224. #336C22×C3semidirect
405. #127C3×D4semidirect
411. #124C3×D4semidirect
442. C22⋊C8C3×D4semidirect
443. C22⋊C8C3×D4semidirect
852. C3#25736direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5352
C2×C3×#4962
C2×C3×#4952
C2×C3×#4522
C2×C3×#4492
C2×C3×#4502
C2×C3×#4472
C3×#26202
C3×#20152
C3×#20142
C3×#20122
C3×#20112
C3×#19592
C3×#19572
C3×#17502
#257363