Finite Group Databasebeta

← C3×#25793 #10644400

Subgroups — C3×#25793 #10644400

Order 768.

1688 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
2C2×C3×#496C211yesmaximal, characteristic, complemented
3C2×C3×#495C211yesmaximal, characteristic, complemented
4C2×C3×#468C211yesmaximal, characteristic, complemented
5C2×C3×#452C211yesmaximal, characteristic, complemented
6C2×C3×#447C211yesmaximal, characteristic, complemented
7C3×#2435C211yesmaximal, characteristic, complemented
8C3×#2431C211yesmaximal, characteristic, complemented
9C3×#2015C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#2012C211yesmaximal, characteristic, complemented
12C3×#2011C211yesmaximal, characteristic, complemented
13C3×#1973C211yesmaximal, characteristic, complemented
14C3×#1970C211yesmaximal, characteristic, complemented
15C3×#1753C211yesmaximal, characteristic, complemented
16#25793C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×D4C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)—24no—
20C2×C3×AGL(1,ℤ/8)—24no—
21C2×C3×AGL(1,ℤ/8)—24no—
22C22×C3×Q16C2211yescharacteristic, complemented
23C22×C3×SD16C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic, complemented
26C22×C3×SD16C2211yescharacteristic, complemented
27C22×C3×D8C2211yescharacteristic
28C22×C3×D8C2211yescharacteristic
29C22×C3×D8C2211yescharacteristic
30C22×C3×D8C2211yescharacteristic
31C22×C3×M16C2211yescharacteristic
32C2×C3×#127C2211yescharacteristic, complemented
33C2×C3×#124C2211yescharacteristic
34C2×C3×#124C2211yescharacteristic
35C2×C3×#124C2211yescharacteristic, complemented
36C2×C3×C22⋊Q8C2211yescharacteristic
37C2×C3×#121C2211yescharacteristic
38C3×#496—24no—
39C3×#495—24no—
40C3×#468—24no—
41C3×#452—24no—
42C3×#447—24no—
43C2×C3×#107C2211yescharacteristic, complemented
44C2×C3×#103C2211yescharacteristic, complemented
45C2×C3×#103C2211yescharacteristic, complemented
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic, complemented
49C2×C3×#102C2211yescharacteristic, complemented
50C2×C3×C22⋊C8C2211yescharacteristic
51C2×C3×#97C2211yescharacteristic, complemented
52C2×C3×C4×C8C2211yescharacteristic, complemented
53C3×#394—22no—
54C3×#392—22no—
55C3×#391C2211yescharacteristic, complemented
56C3×#390C2211yescharacteristic
57C3×#390C2211yescharacteristic
58C3×#390C2211yescharacteristic, complemented
59C3×#386—22no—
60C3×#379—22no—
61C3×C4×C22⋊C4C2211yescharacteristic
62C3×#336C2211yescharacteristic, complemented
63C3×#336C2211yescharacteristic, complemented
64C22×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
65C2×#496C2×C311yescharacteristic, complemented
66C2×#495C2×C311yescharacteristic, complemented
67C2×#468C2×C311yescharacteristic, complemented
68C2×#452C2×C311yescharacteristic, complemented
69C2×#447C2×C311yescharacteristic, complemented
70#2435C2×C311yescharacteristic, complemented
71#2431C2×C311yescharacteristic, complemented
72#2015C2×C311yescharacteristic, complemented
73#2012C2×C311yescharacteristic, complemented
74#2012C2×C311yescharacteristic, complemented
75#2011C2×C311yescharacteristic, complemented
76#1973C2×C311yescharacteristic, complemented
77#1970C2×C311yescharacteristic, complemented
78#1753C2×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—22no—
89C22×C3×D4—22no—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4—22no—
93C22×C3×D4—22no—
94C22×C3×D4—21no—
95C22×C3×D4—22no—
96C22×C3×D4—41no—
97C22×C3×D4—41no—
98C22×C3×D4C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C23×C3×C4—21no—
103C23×C3×C4C2311yescharacteristic
104C3×AGL(1,ℤ/8)—232no—
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—22no—
117C2×C3×SD16—22no—
118C2×C3×SD16—41no—
119C2×C3×SD16D414yescomplemented
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—22no—
127C2×C3×D8—22no—
128C2×C3×D8—22no—
129C2×C3×D8—41no—
130C2×C3×D8—41no—
131C2×C3×D8D414yescomplemented
132C2×C3×M16—22no—
133C2×C3×M16—22no—
134C2×C3×M16D414yescomplemented
135C22×C3×C8C2311yescharacteristic
136C22×C3×C8C2311yescharacteristic
137C22×C3×C8C2311yescharacteristic
138C22×C3×C8C2311yescharacteristic
139C3×#127—22no—
140C3×#127—41no—
141C3×#124—22no—
142C3×#124—22no—
143C3×#124—22no—
144C3×#124—41no—
145C3×#124—41no—
146C3×#124—41no—
147C3×C22⋊Q8—22no—
148C3×C22⋊Q8—22no—
149C3×#121—22no—
150C3×#121—22no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C4⋊C4C2311yescharacteristic
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—22no—
156C2×C3×C22⋊C4—22no—
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—22no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4—22no—
161C2×C3×C22⋊C4—22no—
162C2×C3×C22⋊C4D412yes—
163C2×C3×C42C2311yescharacteristic
164C2×C3×C42C2311yescharacteristic
165C3×#107—22no—
166C3×#103—22no—
167C3×#103—22no—
168C3×#102—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×C22⋊C8D414yescomplemented
173C3×#97—22no—
174C3×C4×C8—22no—
175C3×#95—22no—
176C3×#95D412yes—
177C22×#41C22×C311yescharacteristic
178C23×D4C22×C311yescharacteristic
179C2×AGL(1,ℤ/8)—24no—
180C2×AGL(1,ℤ/8)—24no—
181C2×AGL(1,ℤ/8)—24no—
182C22×Q16C22×C311yescharacteristic, complemented
183C22×SD16C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic, complemented
186C22×SD16C22×C311yescharacteristic, complemented
187C22×D8C22×C311yescharacteristic
188C22×D8C22×C311yescharacteristic
189C22×D8C22×C311yescharacteristic
190C22×D8C22×C311yescharacteristic
191C22×M16C22×C311yescharacteristic
192C2×#127C22×C311yescharacteristic, complemented
193C2×#124C22×C311yescharacteristic
194C2×#124C22×C311yescharacteristic
195C2×#124C22×C311yescharacteristic, complemented
196C2×C22⋊Q8C22×C311yescharacteristic
197C2×#121C22×C311yescharacteristic
198#496—24no—
199#495—24no—
200#468—24no—
201#452—24no—
202#447—24no—
203C2×#107C22×C311yescharacteristic, complemented
204C2×#103C22×C311yescharacteristic, complemented
205C2×#103C22×C311yescharacteristic, complemented
206C2×#102C22×C311yescharacteristic
207C2×#102C22×C311yescharacteristic
208C2×#102C22×C311yescharacteristic, complemented
209C2×#102C22×C311yescharacteristic, complemented
210C2×C22⋊C8C22×C311yescharacteristic
211C2×#97C22×C311yescharacteristic, complemented
212C2×C4×C8C22×C311yescharacteristic, complemented
213#394—22no—
214#392—22no—
215#391C22×C311yescharacteristic, complemented
216#390C22×C311yescharacteristic
217#390C22×C311yescharacteristic
218#390C22×C311yescharacteristic, complemented
219#386—22no—
220#379—22no—
221C4×C22⋊C4C22×C311yescharacteristic
222#336C22×C311yescharacteristic, complemented
223#336C22×C311yescharacteristic, complemented
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—42no—
229C24×C3—42no—
230C24×C3—44no—
231C24×C3—42no—
232C24×C3—82no—
233C24×C3C2×D411yescharacteristic
234C3×#41—28no—
235C3×#41—44no—
236C3×#41—44no—
237C3×#41—44no—
238C2×C3×Q8—21no—
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×Q8C2×D412yes—
250C2×C3×D4—28no—
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—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—44no—
273C2×C3×D4—44no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
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—82no—
285C2×C3×D4—82no—
286C2×C3×D4C2×D412yes—
287C2×C3×D4C2×D412yes—
288C2×C3×D4C2×D412yes—
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—42no—
298C22×C3×C4—42no—
299C22×C3×C4—42no—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D412yes—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2411yescharacteristic
306C3×Q16—44no—
307C3×SD16—28no—
308C3×SD16—28no—
309C3×SD16—44no—
310C3×SD16—44no—
311C3×D8—28no—
312C3×D8—28no—
313C3×D8—44no—
314C3×D8—44no—
315C3×M16—28no—
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×C8C2×D412yes—
323C2×C3×C8C2×D412yes—
324C2×C3×C8C2×D412yes—
325C2×C3×C8C2×D412yes—
326C2×C3×C8C2×D412yes—
327C2×C3×C8C2×D412yes—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—42no—
333C3×C22⋊C4—42no—
334C3×C22⋊C4—44no—
335C3×C22⋊C4—44no—
336C3×C22⋊C4—44no—
337C3×C22⋊C4—42no—
338C3×C22⋊C4—42no—
339C3×C22⋊C4—82no—
340C3×C22⋊C4—82no—
341C3×C22⋊C4—82no—
342C3×C42—21no—
343C3×C42—21no—
344C3×C42—21no—
345C3×C42—21no—
346C25—21no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—41no—
352C2×#41—41no—
353C22×Q8C23×C311yescharacteristic
354C22×Q8C23×C311yescharacteristic
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—21no—
362C22×D4—22no—
363C22×D4—41no—
364C22×D4—41no—
365C22×D4C23×C311yescharacteristic
366C22×D4C23×C311yescharacteristic
367C22×D4C23×C311yescharacteristic
368C22×D4C23×C311yescharacteristic
369C23×C4—21no—
370C23×C4C23×C311yescharacteristic
371AGL(1,ℤ/8)—232no—
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—41no—
375C2×SD16—22no—
376C2×SD16—22no—
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×SD16C3×D414yescomplemented
387C2×D8—22no—
388C2×D8—22no—
389C2×D8—22no—
390C2×D8—22no—
391C2×D8—22no—
392C2×D8—22no—
393C2×D8—22no—
394C2×D8—22no—
395C2×D8—22no—
396C2×D8—41no—
397C2×D8—41no—
398C2×D8C3×D414yescomplemented
399C2×M16—22no—
400C2×M16—22no—
401C2×M16C3×D414yescomplemented
402C22×C8C23×C311yescharacteristic
403C22×C8C23×C311yescharacteristic
404C22×C8C23×C311yescharacteristic
405C22×C8C23×C311yescharacteristic
406#127—22no—
407#127—41no—
408#124—22no—
409#124—22no—
410#124—22no—
411#124—41no—
412#124—41no—
413#124—41no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416#121—22no—
417#121—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4C23×C311yescharacteristic
420C2×C4⋊C4C23×C311yescharacteristic
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4C3×D412yes—
430C2×C42C23×C311yescharacteristic
431C2×C42C23×C311yescharacteristic
432#107—22no—
433#103—22no—
434#103—22no—
435#102—22no—
436#102—22no—
437#102—22no—
438#102—22no—
439C22⋊C8C3×D414yescomplemented
440#97—22no—
441C4×C8—22no—
442#95—22no—
443#95C3×D412yes—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—48no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—42no—
459C23×C3—42no—
460C23×C3—42no—
461C23×C3—42no—
462C23×C3—42no—
463C23×C3—42no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—42no—
468C23×C3—42no—
469C23×C3—84no—
470C23×C3—84no—
471C23×C3—88no—
472C23×C3—88no—
473C23×C3#12712yes—
474C23×C3C22×D411yescharacteristic
475C3×Q8—22no—
476C3×Q8—22no—
477C3×Q8—41no—
478C3×Q8—41no—
479C3×Q8—41no—
480C3×Q8—41no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×D4—22no—
484C3×D4—22no—
485C3×D4—22no—
486C3×D4—22no—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—48no—
490C3×D4—48no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—41no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—88no—
502C3×D4—84no—
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—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—48no—
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—42no—
525C2×C3×C4—42no—
526C2×C3×C4#12712yes—
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C22×D411yescharacteristic
530C2×C3×C4C22×D411yescharacteristic
531C2×C3×C4H(5,𝔽2)11yescharacteristic
532C2×C3×C4H(5,𝔽2)11yescharacteristic
533C3×C8—22no—
534C3×C8—22no—
535C3×C8—22no—
536C3×C8#12014yes—
537C24—21no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24—42no—
542C24—42no—
543C24—44no—
544C24—42no—
545C24—82no—
546C24C2×C3×D411yescharacteristic
547#41—28no—
548#41—44no—
549#41—44no—
550#41—44no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8C2×C3×D412yes—
563C2×D4—28no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
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—44no—
586C2×D4—44no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—44no—
591C2×D4—44no—
592C2×D4—44no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—82no—
598C2×D4—82no—
599C2×D4C2×C3×D412yes—
600C2×D4C2×C3×D412yes—
601C2×D4C2×C3×D412yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4C2×C3×D412yes—
614C22×C4C2×C3×D412yes—
615C22×C4C2×C3×D411yescharacteristic
616C22×C4C2×C3×D412yes—
617C22×C4C2×C3×D412yes—
618C22×C4C24×C311yescharacteristic
619Q16—44no—
620SD16—28no—
621SD16—28no—
622SD16—44no—
623SD16—44no—
624D8—28no—
625D8—28no—
626D8—44no—
627D8—44no—
628M16—28no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8C2×C3×D412yes—
636C2×C8C2×C3×D412yes—
637C2×C8C2×C3×D412yes—
638C2×C8C2×C3×D412yes—
639C2×C8C2×C3×D412yes—
640C2×C8C2×C3×D412yes—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—82no—
653C22⋊C4—82no—
654C22⋊C4—82no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—42no—
665C22×C3—42no—
666C22×C3—42no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—44no—
670C22×C3—816no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—82no—
678C22×C3—82no—
679C22×C3—82no—
680C22×C3—81no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—82no—
684C22×C3—82no—
685C22×C3C2×#12711yescharacteristic
686C22×C3D4211yescharacteristic
687C22×C3D4211yescharacteristic
688C22×C3#57512yes—
689C22×C3#57612yes—
690C3×C4—22no—
691C3×C4—42no—
692C3×C4—42no—
693C3×C4—42no—
694C3×C4—81no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4C2×#12011yescharacteristic
698C3×C4#53511yescharacteristic
699C3×C4D4211yescharacteristic
700C3×C4D4211yescharacteristic
701C23—22no—
702C23—22no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—48no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—42no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—84no—
727C23—84no—
728C23—88no—
729C23—88no—
730C23C3×#12712yes—
731C23C22×C3×D411yescharacteristic
732Q8—22no—
733Q8—22no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—48no—
747D4—48no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—88no—
759D4—84no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—48no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4C3×#12712yes—
784C2×C4C22×C3×D411yescharacteristic
785C2×C4C22×C3×D411yescharacteristic
786C2×C4C22×C3×D411yescharacteristic
787C2×C4C22×C3×D411yescharacteristic
788C2×C4C3×H(5,𝔽2)11yescharacteristic
789C2×C4C3×H(5,𝔽2)11yescharacteristic
790C8—22no—
791C8—22no—
792C8—22no—
793C8C3×#12014yes—
794C2×C3—42no—
795C2×C3—82no—
796C2×C3—82no—
797C2×C3—82no—
798C2×C3—161no—
799C2×C3#243311yescharacteristic
800C2×C3#315311yescharacteristic
801C2×C3#315511yescharacteristic
802C2×C3#326812yes—
803C2×C3#327312yes—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—816no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—82no—
829C22—82no—
830C22C2×C3×#12711yescharacteristic
831C22C3×D4211yescharacteristic
832C22C3×D4211yescharacteristic
833C22C3×#57512yes—
834C22C3×#57612yes—
835C4—22no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4C2×C3×#12011yescharacteristic
843C4C3×#53511yescharacteristic
844C4C3×D4211yescharacteristic
845C4C3×D4211yescharacteristic
846C3#2579311yescharacteristic, direct product factor, Sylow
847C2—42no—
848C2—82no—
849C2—82no—
850C2—82no—
851C2—161no—
852C2C3×#243311yescharacteristic
853C2C3×#315311yescharacteristic
854C2C3×#315511yescharacteristic
855C2C3×#326812yes—
856C2C3×#327312yes—
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. C22×C3×AGL(1,ℤ/8)C2semidirect
2. C2×C3×#496C2semidirect
3. C2×C3×#495C2semidirect
4. C2×C3×#468C2semidirect
5. C2×C3×#452C2semidirect
6. C2×C3×#447C2semidirect
7. C3×#2435C2semidirect
8. C3×#2431C2semidirect
9. C3×#2015C2semidirect
10. C3×#2012C2semidirect
11. C3×#2012C2semidirect
12. C3×#2011C2semidirect
13. C3×#1973C2semidirect
14. C3×#1970C2semidirect
15. C3×#1753C2semidirect
16. #25793C3direct (N × H)
22. C22×C3×Q16C22semidirect
25. C22×C3×SD16C22semidirect
26. C22×C3×SD16C22semidirect
32. C2×C3×#127C22semidirect
35. C2×C3×#124C22semidirect
43. C2×C3×#107C22semidirect
44. C2×C3×#103C22semidirect
45. C2×C3×#103C22semidirect
48. C2×C3×#102C22semidirect
49. C2×C3×#102C22semidirect
51. C2×C3×#97C22semidirect
52. C2×C3×C4×C8C22semidirect
55. C3×#391C22semidirect
58. C3×#390C22semidirect
62. C3×#336C22semidirect
63. C3×#336C22semidirect
64. C22×AGL(1,ℤ/8)C2×C3semidirect
65. C2×#496C2×C3semidirect
66. C2×#495C2×C3semidirect
67. C2×#468C2×C3semidirect
68. C2×#452C2×C3semidirect
69. C2×#447C2×C3semidirect
70. #2435C2×C3semidirect
71. #2431C2×C3semidirect
72. #2015C2×C3semidirect
73. #2012C2×C3semidirect
74. #2012C2×C3semidirect
75. #2011C2×C3semidirect
76. #1973C2×C3semidirect
77. #1970C2×C3semidirect
78. #1753C2×C3semidirect
119. C2×C3×SD16D4semidirect
131. C2×C3×D8D4semidirect
134. C2×C3×M16D4semidirect
172. C3×C22⋊C8D4semidirect
182. C22×Q16C22×C3semidirect
185. C22×SD16C22×C3semidirect
186. C22×SD16C22×C3semidirect
192. C2×#127C22×C3semidirect
195. C2×#124C22×C3semidirect
203. C2×#107C22×C3semidirect
204. C2×#103C22×C3semidirect
205. C2×#103C22×C3semidirect
208. C2×#102C22×C3semidirect
209. C2×#102C22×C3semidirect
211. C2×#97C22×C3semidirect
212. C2×C4×C8C22×C3semidirect
215. #391C22×C3semidirect
218. #390C22×C3semidirect
222. #336C22×C3semidirect
223. #336C22×C3semidirect
386. C2×SD16C3×D4semidirect
398. C2×D8C3×D4semidirect
401. C2×M16C3×D4semidirect
439. C22⋊C8C3×D4semidirect
846. C3#25793direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×AGL(1,ℤ/8)2
C2×C3×#4962
C2×C3×#4952
C2×C3×#4682
C2×C3×#4522
C2×C3×#4472
C3×#24352
C3×#24312
C3×#20152
C3×#20122
C3×#20112
C3×#19732
C3×#19702
C3×#17532
#257933