Finite Group Databasebeta

← C3×#25794 #10644401

Subgroups — C3×#25794 #10644401

Order 768.

1818 conjugacy classes of subgroups.

The subgroup lattice has 890 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×#493C211yesmaximal, characteristic, complemented
4C2×C3×#469C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic, complemented
6C2×C3×#447C211yesmaximal, characteristic, complemented
7C3×#2433C211yesmaximal, characteristic, complemented
8C3×#2431C211yesmaximal, characteristic, complemented
9C3×#2014C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#2011C211yesmaximal, characteristic, complemented
12C3×#2011C211yesmaximal, characteristic, complemented
13C3×#1972C211yesmaximal, characteristic, complemented
14C3×#1968C211yesmaximal, characteristic, complemented
15C3×#1753C211yesmaximal, characteristic, complemented
16#25794C311yesmaximal, 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×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic, complemented
25C22×C3×D8C2211yescharacteristic
26C22×C3×D8C2211yescharacteristic
27C22×C3×D8C2211yescharacteristic
28C22×C3×D8C2211yescharacteristic
29C22×C3×D8C2211yescharacteristic, complemented
30C22×C3×D8C2211yescharacteristic, complemented
31C22×C3×M16C2211yescharacteristic
32C2×C3×#127C2211yescharacteristic
33C2×C3×#127C2211yescharacteristic
34C2×C3×#127C2211yescharacteristic, complemented
35C2×C3×#124C2211yescharacteristic, complemented
36C2×C3×#121C2211yescharacteristic
37C2×C3×#121C2211yescharacteristic
38C2×C3×#120—22no—
39C3×#496—24no—
40C3×#493—24no—
41C3×#469—24no—
42C3×#449—24no—
43C3×#447—24no—
44C2×C3×#106C2211yescharacteristic, complemented
45C2×C3×#103C2211yescharacteristic, complemented
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic, complemented
49C2×C3×#102C2211yescharacteristic, complemented
50C2×C3×#102C2211yescharacteristic, complemented
51C2×C3×C22⋊C8C2211yescharacteristic
52C2×C3×#97C2211yescharacteristic, complemented
53C2×C3×C4×C8C2211yescharacteristic, complemented
54C3×#392—22no—
55C3×#392—22no—
56C3×#391C2211yescharacteristic, complemented
57C3×#390C2211yescharacteristic
58C3×#390C2211yescharacteristic
59C3×#390C2211yescharacteristic, complemented
60C3×#386—22no—
61C3×C4×C22⋊C4C2211yescharacteristic
62C3×#336C2211yescharacteristic, complemented
63C3×#336C2211yescharacteristic, complemented
64C22×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
65C2×#496C2×C311yescharacteristic, complemented
66C2×#493C2×C311yescharacteristic, complemented
67C2×#469C2×C311yescharacteristic, complemented
68C2×#449C2×C311yescharacteristic, complemented
69C2×#447C2×C311yescharacteristic, complemented
70#2433C2×C311yescharacteristic, complemented
71#2431C2×C311yescharacteristic, complemented
72#2014C2×C311yescharacteristic, complemented
73#2012C2×C311yescharacteristic, complemented
74#2011C2×C311yescharacteristic, complemented
75#2011C2×C311yescharacteristic, complemented
76#1972C2×C311yescharacteristic, complemented
77#1968C2×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×D4—22no—
88C22×C3×D4—22no—
89C22×C3×D4—21no—
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—22no—
97C22×C3×D4—22no—
98C22×C3×D4—41no—
99C22×C3×D4—41no—
100C22×C3×D4C2311yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4—21no—
106C23×C3×C4C2311yescharacteristic
107C3×AGL(1,ℤ/8)—232no—
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—41no—
116C2×C3×SD16D414yescomplemented
117C2×C3×D8—22no—
118C2×C3×D8—22no—
119C2×C3×D8—22no—
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—22no—
130C2×C3×D8—22no—
131C2×C3×D8—41no—
132C2×C3×D8—41no—
133C2×C3×D8—41no—
134C2×C3×D8D414yescomplemented
135C2×C3×M16—22no—
136C2×C3×M16—22no—
137C2×C3×M16D414yescomplemented
138C22×C3×C8C2311yescharacteristic
139C22×C3×C8C2311yescharacteristic
140C22×C3×C8C2311yescharacteristic
141C22×C3×C8C2311yescharacteristic
142C3×#127—22no—
143C3×#127—22no—
144C3×#127—22no—
145C3×#127—41no—
146C3×#127—41no—
147C3×#127—41no—
148C3×#124—22no—
149C3×#124—41no—
150C3×#121—22no—
151C3×#121—22no—
152C3×#121—22no—
153C3×#121—22no—
154C3×#120—48no—
155C2×C3×C4⋊C4C2311yescharacteristic
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C22⋊C4—21no—
158C2×C3×C22⋊C4—22no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4—22no—
161C2×C3×C22⋊C4—21no—
162C2×C3×C22⋊C4—22no—
163C2×C3×C22⋊C4D412yes—
164C2×C3×C42C2311yescharacteristic
165C2×C3×C42C2311yescharacteristic
166C3×#106—22no—
167C3×#103—22no—
168C3×#102—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—22no—
173C3×C22⋊C8D414yescomplemented
174C3×#97—22no—
175C3×C4×C8—22no—
176C3×#95—22no—
177C3×#95D412yes—
178C22×#41C22×C311yescharacteristic
179C23×D4C22×C311yescharacteristic
180C2×AGL(1,ℤ/8)—24no—
181C2×AGL(1,ℤ/8)—24no—
182C2×AGL(1,ℤ/8)—24no—
183C22×SD16C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic, complemented
186C22×D8C22×C311yescharacteristic
187C22×D8C22×C311yescharacteristic
188C22×D8C22×C311yescharacteristic
189C22×D8C22×C311yescharacteristic
190C22×D8C22×C311yescharacteristic, complemented
191C22×D8C22×C311yescharacteristic, complemented
192C22×M16C22×C311yescharacteristic
193C2×#127C22×C311yescharacteristic
194C2×#127C22×C311yescharacteristic
195C2×#127C22×C311yescharacteristic, complemented
196C2×#124C22×C311yescharacteristic, complemented
197C2×#121C22×C311yescharacteristic
198C2×#121C22×C311yescharacteristic
199C2×#120—22no—
200#496—24no—
201#493—24no—
202#469—24no—
203#449—24no—
204#447—24no—
205C2×#106C22×C311yescharacteristic, complemented
206C2×#103C22×C311yescharacteristic, complemented
207C2×#102C22×C311yescharacteristic
208C2×#102C22×C311yescharacteristic
209C2×#102C22×C311yescharacteristic, complemented
210C2×#102C22×C311yescharacteristic, complemented
211C2×#102C22×C311yescharacteristic, complemented
212C2×C22⋊C8C22×C311yescharacteristic
213C2×#97C22×C311yescharacteristic, complemented
214C2×C4×C8C22×C311yescharacteristic, complemented
215#392—22no—
216#392—22no—
217#391C22×C311yescharacteristic, complemented
218#390C22×C311yescharacteristic
219#390C22×C311yescharacteristic
220#390C22×C311yescharacteristic, complemented
221#386—22no—
222C4×C22⋊C4C22×C311yescharacteristic
223#336C22×C311yescharacteristic, complemented
224#336C22×C311yescharacteristic, complemented
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—42no—
231C24×C3—42no—
232C24×C3—44no—
233C24×C3—42no—
234C24×C3—82no—
235C24×C3C2×D411yescharacteristic
236C3×#41—28no—
237C3×#41—44no—
238C3×#41—44no—
239C3×#41—44no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8C2×D412yes—
246C2×C3×D4—28no—
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—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—44no—
275C2×C3×D4—44no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—44no—
280C2×C3×D4—44no—
281C2×C3×D4—44no—
282C2×C3×D4—44no—
283C2×C3×D4—44no—
284C2×C3×D4—42no—
285C2×C3×D4—42no—
286C2×C3×D4—44no—
287C2×C3×D4—42no—
288C2×C3×D4—42no—
289C2×C3×D4—42no—
290C2×C3×D4—44no—
291C2×C3×D4—44no—
292C2×C3×D4—82no—
293C2×C3×D4—82no—
294C2×C3×D4—82no—
295C2×C3×D4—82no—
296C2×C3×D4C2×D412yes—
297C2×C3×D4C2×D412yes—
298C2×C3×D4C2×D412yes—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—42no—
307C22×C3×C4—42no—
308C22×C3×C4—42no—
309C22×C3×C4C2×D412yes—
310C22×C3×C4C2×D411yescharacteristic
311C22×C3×C4C2×D412yes—
312C22×C3×C4C2×D412yes—
313C22×C3×C4C2×D412yes—
314C22×C3×C4C2411yescharacteristic
315C3×SD16—28no—
316C3×SD16—28no—
317C3×SD16—44no—
318C3×D8—28no—
319C3×D8—28no—
320C3×D8—44no—
321C3×D8—44no—
322C3×D8—44no—
323C3×D8—44no—
324C3×M16—28no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8C2×D412yes—
332C2×C3×C8C2×D412yes—
333C2×C3×C8C2×D412yes—
334C2×C3×C8C2×D412yes—
335C2×C3×C8C2×D412yes—
336C2×C3×C8C2×D412yes—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C22⋊C4—24no—
342C3×C22⋊C4—44no—
343C3×C22⋊C4—44no—
344C3×C22⋊C4—42no—
345C3×C22⋊C4—42no—
346C3×C22⋊C4—44no—
347C3×C22⋊C4—82no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—21no—
352C25—21no—
353C2×#41—22no—
354C2×#41—22no—
355C2×#41—22no—
356C2×#41—22no—
357C2×#41—41no—
358C2×#41—41no—
359C22×Q8C23×C311yescharacteristic
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—21no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—21no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—41no—
372C22×D4—41no—
373C22×D4C23×C311yescharacteristic
374C22×D4C23×C311yescharacteristic
375C22×D4C23×C311yescharacteristic
376C22×D4C23×C311yescharacteristic
377C22×D4C23×C311yescharacteristic
378C23×C4—21no—
379C23×C4C23×C311yescharacteristic
380AGL(1,ℤ/8)—232no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—41no—
389C2×SD16C3×D414yescomplemented
390C2×D8—22no—
391C2×D8—22no—
392C2×D8—22no—
393C2×D8—22no—
394C2×D8—22no—
395C2×D8—22no—
396C2×D8—22no—
397C2×D8—22no—
398C2×D8—22no—
399C2×D8—22no—
400C2×D8—22no—
401C2×D8—22no—
402C2×D8—22no—
403C2×D8—22no—
404C2×D8—41no—
405C2×D8—41no—
406C2×D8—41no—
407C2×D8C3×D414yescomplemented
408C2×M16—22no—
409C2×M16—22no—
410C2×M16C3×D414yescomplemented
411C22×C8C23×C311yescharacteristic
412C22×C8C23×C311yescharacteristic
413C22×C8C23×C311yescharacteristic
414C22×C8C23×C311yescharacteristic
415#127—22no—
416#127—22no—
417#127—22no—
418#127—41no—
419#127—41no—
420#127—41no—
421#124—22no—
422#124—41no—
423#121—22no—
424#121—22no—
425#121—22no—
426#121—22no—
427#120—48no—
428C2×C4⋊C4C23×C311yescharacteristic
429C2×C4⋊C4C23×C311yescharacteristic
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4C3×D412yes—
437C2×C42C23×C311yescharacteristic
438C2×C42C23×C311yescharacteristic
439#106—22no—
440#103—22no—
441#102—22no—
442#102—22no—
443#102—22no—
444#102—22no—
445#102—22no—
446C22⋊C8C3×D414yescomplemented
447#97—22no—
448C4×C8—22no—
449#95—22no—
450#95C3×D412yes—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—48no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—42no—
466C23×C3—42no—
467C23×C3—42no—
468C23×C3—42no—
469C23×C3—42no—
470C23×C3—42no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—42no—
478C23×C3—42no—
479C23×C3—42no—
480C23×C3—42no—
481C23×C3—84no—
482C23×C3—84no—
483C23×C3—88no—
484C23×C3—88no—
485C23×C3#12712yes—
486C23×C3C22×D411yescharacteristic
487C3×Q8—22no—
488C3×Q8—22no—
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—48no—
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—41no—
509C3×D4—41no—
510C3×D4—41no—
511C3×D4—41no—
512C3×D4—41no—
513C3×D4—88no—
514C3×D4—88no—
515C3×D4—88no—
516C3×D4—84no—
517C3×D4—84no—
518C2×C3×C4—22no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—48no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—42no—
536C2×C3×C4—42no—
537C2×C3×C4#12712yes—
538C2×C3×C4AGL(1,ℤ/8)14yescomplemented
539C2×C3×C4C22×D411yescharacteristic
540C2×C3×C4C22×D411yescharacteristic
541C2×C3×C4C22×D411yescharacteristic
542C2×C3×C4C22×D411yescharacteristic
543C2×C3×C4H(5,𝔽2)11yescharacteristic
544C2×C3×C4H(5,𝔽2)11yescharacteristic
545C3×C8—22no—
546C3×C8—22no—
547C3×C8—22no—
548C3×C8#12014yescomplemented
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—42no—
555C24—42no—
556C24—44no—
557C24—42no—
558C24—82no—
559C24C2×C3×D411yescharacteristic
560#41—28no—
561#41—44no—
562#41—44no—
563#41—44no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8C2×C3×D412yes—
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—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—44no—
604C2×D4—44no—
605C2×D4—44no—
606C2×D4—44no—
607C2×D4—44no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—82no—
617C2×D4—82no—
618C2×D4—82no—
619C2×D4—82no—
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—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4C2×C3×D412yes—
634C22×C4C2×C3×D411yescharacteristic
635C22×C4C2×C3×D412yes—
636C22×C4C2×C3×D412yes—
637C22×C4C2×C3×D412yes—
638C22×C4C24×C311yescharacteristic
639SD16—28no—
640SD16—28no—
641SD16—44no—
642D8—28no—
643D8—28no—
644D8—44no—
645D8—44no—
646D8—44no—
647D8—44no—
648M16—28no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8C2×C3×D412yes—
656C2×C8C2×C3×D412yes—
657C2×C8C2×C3×D412yes—
658C2×C8C2×C3×D412yes—
659C2×C8C2×C3×D412yes—
660C2×C8C2×C3×D412yes—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C22⋊C4—24no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—44no—
671C22⋊C4—82no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—21no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—44no—
685C22×C3—44no—
686C22×C3—44no—
687C22×C3—816no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—82no—
695C22×C3—82no—
696C22×C3—82no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—81no—
701C22×C3—81no—
702C22×C3—81no—
703C22×C3—82no—
704C22×C3—82no—
705C22×C3—82no—
706C22×C3—82no—
707C22×C3C2×#12711yescharacteristic
708C22×C3D4211yescharacteristic
709C22×C3D4211yescharacteristic
710C22×C3C2×AGL(1,ℤ/8)12yes—
711C22×C3#57612yes—
712C3×C4—22no—
713C3×C4—24no—
714C3×C4—42no—
715C3×C4—42no—
716C3×C4—81no—
717C3×C4—81no—
718C3×C4C2×#12011yescharacteristic
719C3×C4#53511yescharacteristic
720C3×C4D4211yescharacteristic
721C3×C4D4211yescharacteristic
722C23—22no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—48no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—88no—
755C23—88no—
756C23C3×#12712yes—
757C23C22×C3×D411yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—41no—
761Q8—41no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—48no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—88no—
785D4—88no—
786D4—88no—
787D4—84no—
788D4—84no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—48no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4C3×#12712yes—
809C2×C4C3×AGL(1,ℤ/8)14yescomplemented
810C2×C4C22×C3×D411yescharacteristic
811C2×C4C22×C3×D411yescharacteristic
812C2×C4C22×C3×D411yescharacteristic
813C2×C4C22×C3×D411yescharacteristic
814C2×C4C3×H(5,𝔽2)11yescharacteristic
815C2×C4C3×H(5,𝔽2)11yescharacteristic
816C8—22no—
817C8—22no—
818C8—22no—
819C8C3×#12014yescomplemented
820C2×C3—42no—
821C2×C3—82no—
822C2×C3—82no—
823C2×C3—82no—
824C2×C3—161no—
825C2×C3—161no—
826C2×C3#243311yescharacteristic
827C2×C3#315111yescharacteristic
828C2×C3#315511yescharacteristic
829C2×C3#326412yes—
830C2×C3#327412yes—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—816no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22C2×C3×#12711yescharacteristic
863C22C3×D4211yescharacteristic
864C22C3×D4211yescharacteristic
865C22C2×C3×AGL(1,ℤ/8)12yes—
866C22C3×#57612yes—
867C4—22no—
868C4—24no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4C2×C3×#12011yescharacteristic
874C4C3×#53511yescharacteristic
875C4C3×D4211yescharacteristic
876C4C3×D4211yescharacteristic
877C3#2579411yescharacteristic, direct product factor, Sylow
878C2—42no—
879C2—82no—
880C2—82no—
881C2—82no—
882C2—161no—
883C2—161no—
884C2C3×#243311yescharacteristic
885C2C3×#315111yescharacteristic
886C2C3×#315511yescharacteristic
887C2C3×#326412yes—
888C2C3×#327412yes—
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×#493C2semidirect
4. C2×C3×#469C2semidirect
5. C2×C3×#449C2semidirect
6. C2×C3×#447C2semidirect
7. C3×#2433C2semidirect
8. C3×#2431C2semidirect
9. C3×#2014C2semidirect
10. C3×#2012C2semidirect
11. C3×#2011C2semidirect
12. C3×#2011C2semidirect
13. C3×#1972C2semidirect
14. C3×#1968C2semidirect
15. C3×#1753C2semidirect
16. #25794C3direct (N × H)
24. C22×C3×SD16C22semidirect
29. C22×C3×D8C22semidirect
30. C22×C3×D8C22semidirect
34. C2×C3×#127C22semidirect
35. C2×C3×#124C22semidirect
44. C2×C3×#106C22semidirect
45. C2×C3×#103C22semidirect
48. C2×C3×#102C22semidirect
49. C2×C3×#102C22semidirect
50. C2×C3×#102C22semidirect
52. C2×C3×#97C22semidirect
53. C2×C3×C4×C8C22semidirect
56. C3×#391C22semidirect
59. C3×#390C22semidirect
62. C3×#336C22semidirect
63. C3×#336C22semidirect
64. C22×AGL(1,ℤ/8)C2×C3semidirect
65. C2×#496C2×C3semidirect
66. C2×#493C2×C3semidirect
67. C2×#469C2×C3semidirect
68. C2×#449C2×C3semidirect
69. C2×#447C2×C3semidirect
70. #2433C2×C3semidirect
71. #2431C2×C3semidirect
72. #2014C2×C3semidirect
73. #2012C2×C3semidirect
74. #2011C2×C3semidirect
75. #2011C2×C3semidirect
76. #1972C2×C3semidirect
77. #1968C2×C3semidirect
78. #1753C2×C3semidirect
116. C2×C3×SD16D4semidirect
134. C2×C3×D8D4semidirect
137. C2×C3×M16D4semidirect
173. C3×C22⋊C8D4semidirect
185. C22×SD16C22×C3semidirect
190. C22×D8C22×C3semidirect
191. C22×D8C22×C3semidirect
195. C2×#127C22×C3semidirect
196. C2×#124C22×C3semidirect
205. C2×#106C22×C3semidirect
206. C2×#103C22×C3semidirect
209. C2×#102C22×C3semidirect
210. C2×#102C22×C3semidirect
211. C2×#102C22×C3semidirect
213. C2×#97C22×C3semidirect
214. C2×C4×C8C22×C3semidirect
217. #391C22×C3semidirect
220. #390C22×C3semidirect
223. #336C22×C3semidirect
224. #336C22×C3semidirect
389. C2×SD16C3×D4semidirect
407. C2×D8C3×D4semidirect
410. C2×M16C3×D4semidirect
446. C22⋊C8C3×D4semidirect
538. C2×C3×C4AGL(1,ℤ/8)semidirect
548. C3×C8#120semidirect
809. C2×C4C3×AGL(1,ℤ/8)semidirect
819. C8C3×#120semidirect
877. C3#25794direct (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×#4932
C2×C3×#4692
C2×C3×#4492
C2×C3×#4472
C3×#24332
C3×#24312
C3×#20142
C3×#20122
C3×#20112
C3×#19722
C3×#19682
C3×#17532
#257943