Finite Group Databasebeta

← C3×#24234 #10642841

Subgroups — C3×#24234 #10642841

Order 768.

1440 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3500C211yesmaximal, characteristic, complemented
2C3×#3036C211yesmaximal, characteristic, complemented
3C2×C3×#454C211yesmaximal, characteristic, complemented
4C2×C3×#453C211yesmaximal, characteristic, complemented
5C3×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
6C3×#2544C211yesmaximal, characteristic, complemented
7C3×#2038C211yesmaximal, characteristic, complemented
8C3×#2037C211yesmaximal, characteristic, complemented
9C3×#2003C211yesmaximal, characteristic, complemented
10C3×#2002C211yesmaximal, characteristic, complemented
11C3×#1980C211yesmaximal, characteristic, complemented
12C3×#1967C211yesmaximal, characteristic, complemented
13C3×#1806C211yesmaximal, characteristic, complemented
14C3×#1793C211yesmaximal, characteristic, complemented
15C3×#1792C211yesmaximal, characteristic, complemented
16#24234C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×2−1+4C2211yescharacteristic
18C2×C3×H(5,𝔽2)C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
21C2×C3×AGL(1,ℤ/8)C2211yescharacteristic, complemented
22C3×#548—21no—
23C3×#548—21no—
24C3×#546—21no—
25C3×#546—21no—
26C3×#546—22no—
27C3×#546—22no—
28C3×#536—21no—
29C3×#536C2211yescharacteristic
30C3×#535—21no—
31C3×#535C2211yescharacteristic
32C3×#532—21no—
33C3×#532C2211yescharacteristic
34C2×C3×#127C2211yescharacteristic
35C2×C3×#124—21no—
36C2×C3×#124C2211yescharacteristic
37C2×C3×#124C2211yescharacteristic, complemented
38C3×C4×#41C2211yescharacteristic
39C2×C3×C4×D4C2211yescharacteristic, complemented
40C3×#463—21no—
41C3×#463—21no—
42C3×#461—21no—
43C3×#459—21no—
44C3×#454—24no—
45C3×#453—24no—
46C3×#442—21no—
47C3×#440—21no—
48C3×C4×SD16—21no—
49C3×C4×D8—21no—
50C3×#428C2211yescharacteristic, complemented
51C3×#423C2211yescharacteristic, complemented
52C2×C3×#104C2211yescharacteristic
53C2×C3×#104C2211yescharacteristic
54C2×C3×#104C2211yescharacteristic
55C2×C3×#104C2211yescharacteristic
56C2×C3×#104C2211yescharacteristic, complemented
57C2×C3×#104C2211yescharacteristic, complemented
58C3×#418C2211yescharacteristic, complemented
59C3×#417C2211yescharacteristic
60C3×#417C2211yescharacteristic
61C3×#417C2211yescharacteristic, complemented
62C2×C3×#101C2211yescharacteristic, complemented
63C2×C3×#101C2211yescharacteristic, complemented
64C2×C3×#100C2211yescharacteristic
65C2×C3×#100C2211yescharacteristic
66C3×C4×M16C2211yescharacteristic, complemented
67C3×#394—22no—
68C3×#391C2211yescharacteristic, complemented
69C3×#390C2211yescharacteristic
70C3×#386—22no—
71C3×C4×C4⋊C4C2211yescharacteristic, complemented
72C3×#339C2211yescharacteristic, complemented
73C3×#339C2211yescharacteristic, complemented
74#3500C2×C311yescharacteristic, complemented
75#3036C2×C311yescharacteristic, complemented
76C2×#454C2×C311yescharacteristic, complemented
77C2×#453C2×C311yescharacteristic, complemented
78C4×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
79#2544C2×C311yescharacteristic, complemented
80#2038C2×C311yescharacteristic, complemented
81#2037C2×C311yescharacteristic, complemented
82#2003C2×C311yescharacteristic, complemented
83#2002C2×C311yescharacteristic, complemented
84#1980C2×C311yescharacteristic, complemented
85#1967C2×C311yescharacteristic, complemented
86#1806C2×C311yescharacteristic, complemented
87#1793C2×C311yescharacteristic, complemented
88#1792C2×C311yescharacteristic, complemented
89C3×2−1+4—22no—
90C3×2−1+4—22no—
91C3×2−1+4—41no—
92C3×2−1+4—41no—
93C3×H(5,𝔽2)—22no—
94C3×H(5,𝔽2)—22no—
95C3×H(5,𝔽2)—41no—
96C3×H(5,𝔽2)—41no—
97C2×C3×#41—21no—
98C2×C3×#41—21no—
99C2×C3×#41—21no—
100C2×C3×#41—21no—
101C2×C3×#41—22no—
102C2×C3×#41C2311yescharacteristic
103C2×C3×#41C2311yescharacteristic
104C2×C3×#41C2311yescharacteristic
105C22×C3×Q8—21no—
106C22×C3×Q8—21no—
107C22×C3×Q8C2311yescharacteristic
108C22×C3×D4—22no—
109C22×C3×D4—21no—
110C22×C3×D4—21no—
111C22×C3×D4—22no—
112C22×C3×D4C2311yescharacteristic
113C22×C3×D4C2311yescharacteristic
114C23×C3×C4—21no—
115C3×AGL(1,ℤ/8)—22no—
116C3×AGL(1,ℤ/8)—22no—
117C3×AGL(1,ℤ/8)—22no—
118C3×AGL(1,ℤ/8)—41no—
119C3×AGL(1,ℤ/8)—41no—
120C3×AGL(1,ℤ/8)D414yescomplemented
121C2×C3×SD16—21no—
122C2×C3×SD16—21no—
123C2×C3×SD16—21no—
124C2×C3×D8—21no—
125C2×C3×D8—21no—
126C2×C3×D8—21no—
127C2×C3×M16C2311yescharacteristic
128C2×C3×M16C2311yescharacteristic
129C2×C3×M16C2311yescharacteristic
130C2×C3×M16C2311yescharacteristic
131C3×C4⋊Q8—21no—
132C3×C4⋊Q8D411yescharacteristic, complemented
133C3×#127—21no—
134C3×#127—22no—
135C3×#127—41no—
136C3×#127D411yescharacteristic, complemented
137C3×#124—22no—
138C3×#124—22no—
139C3×#124—21no—
140C3×#124—21no—
141C3×#124—22no—
142C3×#124—21no—
143C3×#124—21no—
144C3×#124—21no—
145C3×#124—21no—
146C3×#124—41no—
147C3×#124D411yescharacteristic, complemented
148C3×#124D411yescharacteristic, complemented
149C3×#123—22no—
150C3×#123—22no—
151C3×#123—22no—
152C3×C22⋊Q8—22no—
153C3×C22⋊Q8—22no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—21no—
156C3×#121—22no—
157C3×#121—22no—
158C3×#121—22no—
159C3×#121—22no—
160C3×#121—21no—
161C3×#121—21no—
162C3×#121—21no—
163C3×#121—21no—
164C3×#120—22no—
165C3×#120—22no—
166C3×#120—22no—
167C3×C4×Q8D411yescharacteristic, complemented
168C3×C4×Q8D411yescharacteristic, complemented
169C3×C4×D4—22no—
170C3×C4×D4—22no—
171C3×C4×D4—21no—
172C3×C4×D4—21no—
173C3×C4×D4—21no—
174C3×C4×D4—21no—
175C3×C4×D4—21no—
176C3×C4×D4—21no—
177C3×C4×D4—21no—
178C3×C4×D4—21no—
179C3×C4×D4D411yescharacteristic, complemented
180C3×C4×D4D411yescharacteristic, complemented
181C3×#117—21no—
182C3×#117C2311yescharacteristic
183C2×C3×C4⋊C4—21no—
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C22⋊C4—22no—
186C2×C3×C22⋊C4—22no—
187C2×C3×C22⋊C4—22no—
188C2×C3×C22⋊C4—21no—
189C2×C3×C22⋊C4—22no—
190C2×C3×C22⋊C4D412yes—
191C2×C3×C22⋊C4D412yes—
192C2×C3×C42—21no—
193C2×C3×C42C2311yescharacteristic
194C2×C3×C42C2311yescharacteristic
195C2×C3×C42C2311yescharacteristic
196C3×#107—21no—
197C3×#106—21no—
198C3×C4⋊C8—21no—
199C3×C4⋊C8—21no—
200C3×#104—22no—
201C3×#104—22no—
202C3×#104—22no—
203C3×#104—22no—
204C3×#104—41no—
205C3×#104—41no—
206C3×#103—21no—
207C3×#103—21no—
208C3×#103—21no—
209C3×#102—21no—
210C3×#102—21no—
211C3×#102—21no—
212C3×#102—21no—
213C3×#102—21no—
214C3×#101—22no—
215C3×#101—41no—
216C3×#100—22no—
217C3×#100—41no—
218C3×#97—21no—
219C3×C4×C8—21no—
220C3×#95—21no—
221C3×#95—22no—
222C2×2−1+4C22×C311yescharacteristic
223C2×H(5,𝔽2)C22×C311yescharacteristic
224C2×AGL(1,ℤ/8)C22×C311yescharacteristic
225C2×AGL(1,ℤ/8)C22×C311yescharacteristic
226C2×AGL(1,ℤ/8)C22×C311yescharacteristic, complemented
227#548—21no—
228#548—21no—
229#546—21no—
230#546—21no—
231#546—22no—
232#546—22no—
233#536—21no—
234#536C22×C311yescharacteristic
235#535—21no—
236#535C22×C311yescharacteristic
237#532—21no—
238#532C22×C311yescharacteristic
239C2×#127C22×C311yescharacteristic
240C2×#124—21no—
241C2×#124C22×C311yescharacteristic
242C2×#124C22×C311yescharacteristic, complemented
243C4×#41C22×C311yescharacteristic
244C2×C4×D4C22×C311yescharacteristic, complemented
245#463—21no—
246#463—21no—
247#461—21no—
248#459—21no—
249#454—24no—
250#453—24no—
251#442—21no—
252#440—21no—
253C4×SD16—21no—
254C4×D8—21no—
255#428C22×C311yescharacteristic, complemented
256#423C22×C311yescharacteristic, complemented
257C2×#104C22×C311yescharacteristic
258C2×#104C22×C311yescharacteristic
259C2×#104C22×C311yescharacteristic
260C2×#104C22×C311yescharacteristic
261C2×#104C22×C311yescharacteristic, complemented
262C2×#104C22×C311yescharacteristic, complemented
263#418C22×C311yescharacteristic, complemented
264#417C22×C311yescharacteristic
265#417C22×C311yescharacteristic
266#417C22×C311yescharacteristic, complemented
267C2×#101C22×C311yescharacteristic, complemented
268C2×#101C22×C311yescharacteristic, complemented
269C2×#100C22×C311yescharacteristic
270C2×#100C22×C311yescharacteristic
271C4×M16C22×C311yescharacteristic, complemented
272#394—22no—
273#391C22×C311yescharacteristic, complemented
274#390C22×C311yescharacteristic
275#386—22no—
276C4×C4⋊C4C22×C311yescharacteristic, complemented
277#339C22×C311yescharacteristic, complemented
278#339C22×C311yescharacteristic, complemented
279C24×C3—22no—
280C24×C3—21no—
281C24×C3C2×D412yes—
282C3×#41—21no—
283C3×#41—21no—
284C3×#41—21no—
285C3×#41—21no—
286C3×#41—21no—
287C3×#41—21no—
288C3×#41—21no—
289C3×#41—21no—
290C3×#41—21no—
291C3×#41—21no—
292C3×#41—42no—
293C3×#41—42no—
294C3×#41—44no—
295C3×#41—44no—
296C3×#41—42no—
297C3×#41—42no—
298C3×#41—42no—
299C3×#41—42no—
300C3×#41—42no—
301C3×#41—42no—
302C3×#41C2×D412yes—
303C3×#41#4112yes—
304C2×C3×Q8—22no—
305C2×C3×Q8—21no—
306C2×C3×Q8—21no—
307C2×C3×Q8—21no—
308C2×C3×Q8—21no—
309C2×C3×Q8—21no—
310C2×C3×Q8—21no—
311C2×C3×Q8—42no—
312C2×C3×Q8—42no—
313C2×C3×Q8—42no—
314C2×C3×Q8—42no—
315C2×C3×Q8C2×D411yescharacteristic
316C2×C3×Q8C2×D411yescharacteristic
317C2×C3×Q8C2×D411yescharacteristic
318C2×C3×D4—21no—
319C2×C3×D4—22no—
320C2×C3×D4—22no—
321C2×C3×D4—22no—
322C2×C3×D4—21no—
323C2×C3×D4—21no—
324C2×C3×D4—22no—
325C2×C3×D4—22no—
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—42no—
340C2×C3×D4—42no—
341C2×C3×D4—44no—
342C2×C3×D4—44no—
343C2×C3×D4—44no—
344C2×C3×D4—42no—
345C2×C3×D4—42no—
346C2×C3×D4—44no—
347C2×C3×D4—82no—
348C2×C3×D4C2×D411yescharacteristic
349C2×C3×D4C2×D411yescharacteristic
350C2×C3×D4C2×D412yes—
351C2×C3×D4C2×D411yescharacteristic
352C22×C3×C4—21no—
353C22×C3×C4—22no—
354C22×C3×C4—22no—
355C22×C3×C4—22no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—21no—
363C22×C3×C4—41no—
364C22×C3×C4—41no—
365C22×C3×C4—82no—
366C22×C3×C4C2×D412yes—
367C22×C3×C4C2×D411yescharacteristic
368C22×C3×C4C2×D411yescharacteristic
369C22×C3×C4C2411yescharacteristic
370C3×SD16—24no—
371C3×SD16—42no—
372C3×SD16—42no—
373C3×D8—24no—
374C3×D8—42no—
375C3×D8—42no—
376C3×M16—21no—
377C3×M16—21no—
378C3×M16—21no—
379C3×M16—21no—
380C3×M16—21no—
381C3×M16—21no—
382C3×M16—21no—
383C3×M16C2×D412yes—
384C2×C3×C8—21no—
385C2×C3×C8—21no—
386C2×C3×C8—21no—
387C2×C3×C8—21no—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—21no—
394C3×C4⋊C4—21no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—42no—
397C3×C4⋊C4C2×D411yescharacteristic
398C3×C4⋊C4C2×D411yescharacteristic
399C3×C22⋊C4—22no—
400C3×C22⋊C4—22no—
401C3×C22⋊C4—22no—
402C3×C22⋊C4—22no—
403C3×C22⋊C4—21no—
404C3×C22⋊C4—21no—
405C3×C22⋊C4—21no—
406C3×C22⋊C4—22no—
407C3×C22⋊C4—22no—
408C3×C22⋊C4—22no—
409C3×C22⋊C4—22no—
410C3×C22⋊C4—21no—
411C3×C22⋊C4—21no—
412C3×C22⋊C4—21no—
413C3×C22⋊C4—21no—
414C3×C22⋊C4—44no—
415C3×C22⋊C4—41no—
416C3×C22⋊C4—41no—
417C3×C22⋊C4—82no—
418C3×C42—21no—
419C3×C42—21no—
420C3×C42—21no—
421C3×C42—21no—
422C3×C42—21no—
423C3×C42—21no—
424C3×C42—21no—
425C3×C42C2×D411yescharacteristic
426C3×C42C2×D411yescharacteristic
427C3×C42C2×D411yescharacteristic
428C3×C42C2×D411yescharacteristic
4292−1+4—22no—
4302−1+4—22no—
4312−1+4—41no—
4322−1+4—41no—
433H(5,𝔽2)—22no—
434H(5,𝔽2)—22no—
435H(5,𝔽2)—41no—
436H(5,𝔽2)—41no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—22no—
442C2×#41C23×C311yescharacteristic
443C2×#41C23×C311yescharacteristic
444C2×#41C23×C311yescharacteristic
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8C23×C311yescharacteristic
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—22no—
452C22×D4C23×C311yescharacteristic
453C22×D4C23×C311yescharacteristic
454C23×C4—21no—
455AGL(1,ℤ/8)—22no—
456AGL(1,ℤ/8)—22no—
457AGL(1,ℤ/8)—22no—
458AGL(1,ℤ/8)—41no—
459AGL(1,ℤ/8)—41no—
460AGL(1,ℤ/8)C3×D414yescomplemented
461C2×SD16—21no—
462C2×SD16—21no—
463C2×SD16—21no—
464C2×D8—21no—
465C2×D8—21no—
466C2×D8—21no—
467C2×M16C23×C311yescharacteristic
468C2×M16C23×C311yescharacteristic
469C2×M16C23×C311yescharacteristic
470C2×M16C23×C311yescharacteristic
471C4⋊Q8—21no—
472C4⋊Q8C3×D411yescharacteristic, complemented
473#127—21no—
474#127—22no—
475#127—41no—
476#127C3×D411yescharacteristic, complemented
477#124—22no—
478#124—22no—
479#124—21no—
480#124—21no—
481#124—22no—
482#124—21no—
483#124—21no—
484#124—21no—
485#124—21no—
486#124—41no—
487#124C3×D411yescharacteristic, complemented
488#124C3×D411yescharacteristic, complemented
489#123—22no—
490#123—22no—
491#123—22no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#120—22no—
505#120—22no—
506#120—22no—
507C4×Q8C3×D411yescharacteristic, complemented
508C4×Q8C3×D411yescharacteristic, complemented
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4C3×D411yescharacteristic, complemented
520C4×D4C3×D411yescharacteristic, complemented
521#117—21no—
522#117C23×C311yescharacteristic
523C2×C4⋊C4—21no—
524C2×C4⋊C4C23×C311yescharacteristic
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4C3×D412yes—
531C2×C22⋊C4C3×D412yes—
532C2×C42—21no—
533C2×C42C23×C311yescharacteristic
534C2×C42C23×C311yescharacteristic
535C2×C42C23×C311yescharacteristic
536#107—21no—
537#106—21no—
538C4⋊C8—21no—
539C4⋊C8—21no—
540#104—22no—
541#104—22no—
542#104—22no—
543#104—22no—
544#104—41no—
545#104—41no—
546#103—21no—
547#103—21no—
548#103—21no—
549#102—21no—
550#102—21no—
551#102—21no—
552#102—21no—
553#102—21no—
554#101—22no—
555#101—41no—
556#100—22no—
557#100—41no—
558#97—21no—
559C4×C8—21no—
560#95—21no—
561#95—22no—
562C23×C3—21no—
563C23×C3—22no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—42no—
570C23×C3—42no—
571C23×C3—44no—
572C23×C3—42no—
573C23×C3—42no—
574C23×C3—41no—
575C23×C3—41no—
576C23×C3—82no—
577C23×C3—82no—
578C23×C3C22×D411yescharacteristic
579C3×Q8—21no—
580C3×Q8—21no—
581C3×Q8—21no—
582C3×Q8—21no—
583C3×Q8—21no—
584C3×Q8—44no—
585C3×Q8—41no—
586C3×Q8—41no—
587C3×Q8—41no—
588C3×Q8—41no—
589C3×Q8#12112yes—
590C3×D4—22no—
591C3×D4—22no—
592C3×D4—22no—
593C3×D4—21no—
594C3×D4—22no—
595C3×D4—21no—
596C3×D4—21no—
597C3×D4—21no—
598C3×D4—21no—
599C3×D4—44no—
600C3×D4—44no—
601C3×D4—44no—
602C3×D4—41no—
603C3×D4—41no—
604C3×D4—41no—
605C3×D4—41no—
606C3×D4—41no—
607C3×D4—41no—
608C3×D4—41no—
609C3×D4—41no—
610C3×D4—41no—
611C3×D4—41no—
612C3×D4—81no—
613C3×D4—81no—
614C3×D4—82no—
615C3×D4—82no—
616C3×D4—88no—
617C3×D4#12112yes—
618C2×C3×C4—21no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—22no—
626C2×C3×C4—21no—
627C2×C3×C4—22no—
628C2×C3×C4—22no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—44no—
632C2×C3×C4—44no—
633C2×C3×C4—41no—
634C2×C3×C4—44no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—41no—
640C2×C3×C4—41no—
641C2×C3×C4—42no—
642C2×C3×C4—41no—
643C2×C3×C4—41no—
644C2×C3×C4—41no—
645C2×C3×C4—81no—
646C2×C3×C4—81no—
647C2×C3×C4—82no—
648C2×C3×C4—82no—
649C2×C3×C4#12011yescharacteristic
650C2×C3×C4#12011yescharacteristic
651C2×C3×C4#12011yescharacteristic
652C2×C3×C4#12011yescharacteristic
653C2×C3×C4C22×D411yescharacteristic
654C2×C3×C4C22×D411yescharacteristic
655C2×C3×C4C22×D411yescharacteristic
656C2×C3×C4C2×#4111yescharacteristic
657C2×C3×C4H(5,𝔽2)11yescharacteristic
658C2×C3×C4H(5,𝔽2)11yescharacteristic
659C3×C8—22no—
660C3×C8—41no—
661C3×C8—41no—
662C3×C8—41no—
663C24—22no—
664C24—21no—
665C24C2×C3×D412yes—
666#41—21no—
667#41—21no—
668#41—21no—
669#41—21no—
670#41—21no—
671#41—21no—
672#41—21no—
673#41—21no—
674#41—21no—
675#41—21no—
676#41—42no—
677#41—42no—
678#41—44no—
679#41—44no—
680#41—42no—
681#41—42no—
682#41—42no—
683#41—42no—
684#41—42no—
685#41—42no—
686#41C2×C3×D412yes—
687#41C3×#4112yes—
688C2×Q8—22no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—42no—
698C2×Q8—42no—
699C2×Q8C2×C3×D411yescharacteristic
700C2×Q8C2×C3×D411yescharacteristic
701C2×Q8C2×C3×D411yescharacteristic
702C2×D4—21no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—22no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—22no—
709C2×D4—22no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—42no—
729C2×D4—42no—
730C2×D4—44no—
731C2×D4—82no—
732C2×D4C2×C3×D411yescharacteristic
733C2×D4C2×C3×D411yescharacteristic
734C2×D4C2×C3×D412yes—
735C2×D4C2×C3×D411yescharacteristic
736C22×C4—21no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—82no—
750C22×C4C2×C3×D412yes—
751C22×C4C2×C3×D411yescharacteristic
752C22×C4C2×C3×D411yescharacteristic
753C22×C4C24×C311yescharacteristic
754SD16—24no—
755SD16—42no—
756SD16—42no—
757D8—24no—
758D8—42no—
759D8—42no—
760M16—21no—
761M16—21no—
762M16—21no—
763M16—21no—
764M16—21no—
765M16—21no—
766M16—21no—
767M16C2×C3×D412yes—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C4⋊C4—22no—
773C4⋊C4—22no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—21no—
777C4⋊C4—21no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—42no—
781C4⋊C4C2×C3×D411yescharacteristic
782C4⋊C4C2×C3×D411yescharacteristic
783C22⋊C4—22no—
784C22⋊C4—22no—
785C22⋊C4—22no—
786C22⋊C4—22no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—22no—
791C22⋊C4—22no—
792C22⋊C4—22no—
793C22⋊C4—22no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—44no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—82no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—21no—
808C42—21no—
809C42C2×C3×D411yescharacteristic
810C42C2×C3×D411yescharacteristic
811C42C2×C3×D411yescharacteristic
812C42C2×C3×D411yescharacteristic
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—22no—
816C22×C3—44no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—41no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—41no—
824C22×C3—42no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—42no—
828C22×C3—41no—
829C22×C3—82no—
830C22×C3—82no—
831C22×C3—82no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3—164no—
835C22×C3C2×#12011yescharacteristic
836C22×C3D4211yescharacteristic
837C22×C3#54611yescharacteristic
838C3×C4—22no—
839C3×C4—21no—
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—21no—
843C3×C4—42no—
844C3×C4—42no—
845C3×C4—41no—
846C3×C4—41no—
847C3×C4—41no—
848C3×C4—41no—
849C3×C4—81no—
850C3×C4—81no—
851C3×C4C2×#12111yescharacteristic
852C3×C4#53511yescharacteristic
853C3×C4D4211yescharacteristic
854C3×C4#54611yescharacteristic
855C23—21no—
856C23—22no—
857C23—21no—
858C23—21no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—42no—
863C23—42no—
864C23—44no—
865C23—42no—
866C23—42no—
867C23—41no—
868C23—41no—
869C23—82no—
870C23—82no—
871C23C22×C3×D411yescharacteristic
872Q8—21no—
873Q8—21no—
874Q8—21no—
875Q8—21no—
876Q8—21no—
877Q8—44no—
878Q8—41no—
879Q8—41no—
880Q8—41no—
881Q8—41no—
882Q8C3×#12112yes—
883D4—22no—
884D4—22no—
885D4—22no—
886D4—21no—
887D4—22no—
888D4—21no—
889D4—21no—
890D4—21no—
891D4—21no—
892D4—44no—
893D4—44no—
894D4—44no—
895D4—41no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—41no—
905D4—81no—
906D4—81no—
907D4—82no—
908D4—82no—
909D4—88no—
910D4C3×#12112yes—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—41no—
927C2×C4—44no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—81no—
939C2×C4—81no—
940C2×C4—82no—
941C2×C4—82no—
942C2×C4C3×#12011yescharacteristic
943C2×C4C3×#12011yescharacteristic
944C2×C4C3×#12011yescharacteristic
945C2×C4C3×#12011yescharacteristic
946C2×C4C22×C3×D411yescharacteristic
947C2×C4C22×C3×D411yescharacteristic
948C2×C4C22×C3×D411yescharacteristic
949C2×C4C2×C3×#4111yescharacteristic
950C2×C4C3×H(5,𝔽2)11yescharacteristic
951C2×C4C3×H(5,𝔽2)11yescharacteristic
952C8—22no—
953C8—41no—
954C8—41no—
955C8—41no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—42no—
959C2×C3—81no—
960C2×C3—82no—
961C2×C3—82no—
962C2×C3—81no—
963C2×C3#240811yescharacteristic
964C2×C3#301811yescharacteristic
965C2×C3#302111yescharacteristic
966C22—21no—
967C22—21no—
968C22—22no—
969C22—44no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—42no—
975C22—42no—
976C22—41no—
977C22—42no—
978C22—41no—
979C22—41no—
980C22—42no—
981C22—41no—
982C22—82no—
983C22—82no—
984C22—82no—
985C22—81no—
986C22—81no—
987C22—164no—
988C22C2×C3×#12011yescharacteristic
989C22C3×D4211yescharacteristic
990C22C3×#54611yescharacteristic
991C4—22no—
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—41no—
1001C4—41no—
1002C4—81no—
1003C4—81no—
1004C4C2×C3×#12111yescharacteristic
1005C4C3×#53511yescharacteristic
1006C4C3×D4211yescharacteristic
1007C4C3×#54611yescharacteristic
1008C3#2423411yescharacteristic, direct product factor, Sylow
1009C2—21no—
1010C2—21no—
1011C2—42no—
1012C2—82no—
1013C2—82no—
1014C2—81no—
1015C2—81no—
1016C2C3×#240811yescharacteristic
1017C2C3×#301811yescharacteristic
1018C2C3×#302111yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#3500C2semidirect
2. C3×#3036C2semidirect
3. C2×C3×#454C2semidirect
4. C2×C3×#453C2semidirect
5. C3×C4×AGL(1,ℤ/8)C2semidirect
6. C3×#2544C2semidirect
7. C3×#2038C2semidirect
8. C3×#2037C2semidirect
9. C3×#2003C2semidirect
10. C3×#2002C2semidirect
11. C3×#1980C2semidirect
12. C3×#1967C2semidirect
13. C3×#1806C2semidirect
14. C3×#1793C2semidirect
15. C3×#1792C2semidirect
16. #24234C3direct (N × H)
21. C2×C3×AGL(1,ℤ/8)C22semidirect
37. C2×C3×#124C22semidirect
39. C2×C3×C4×D4C22semidirect
50. C3×#428C22semidirect
51. C3×#423C22semidirect
56. C2×C3×#104C22semidirect
57. C2×C3×#104C22semidirect
58. C3×#418C22semidirect
61. C3×#417C22semidirect
62. C2×C3×#101C22semidirect
63. C2×C3×#101C22semidirect
66. C3×C4×M16C22semidirect
68. C3×#391C22semidirect
71. C3×C4×C4⋊C4C22semidirect
72. C3×#339C22semidirect
73. C3×#339C22semidirect
74. #3500C2×C3semidirect
75. #3036C2×C3semidirect
76. C2×#454C2×C3semidirect
77. C2×#453C2×C3semidirect
78. C4×AGL(1,ℤ/8)C2×C3semidirect
79. #2544C2×C3semidirect
80. #2038C2×C3semidirect
81. #2037C2×C3semidirect
82. #2003C2×C3semidirect
83. #2002C2×C3semidirect
84. #1980C2×C3semidirect
85. #1967C2×C3semidirect
86. #1806C2×C3semidirect
87. #1793C2×C3semidirect
88. #1792C2×C3semidirect
120. C3×AGL(1,ℤ/8)D4semidirect
132. C3×C4⋊Q8D4semidirect
136. C3×#127D4semidirect
147. C3×#124D4semidirect
148. C3×#124D4semidirect
167. C3×C4×Q8D4semidirect
168. C3×C4×Q8D4semidirect
179. C3×C4×D4D4semidirect
180. C3×C4×D4D4semidirect
226. C2×AGL(1,ℤ/8)C22×C3semidirect
242. C2×#124C22×C3semidirect
244. C2×C4×D4C22×C3semidirect
255. #428C22×C3semidirect
256. #423C22×C3semidirect
261. C2×#104C22×C3semidirect
262. C2×#104C22×C3semidirect
263. #418C22×C3semidirect
266. #417C22×C3semidirect
267. C2×#101C22×C3semidirect
268. C2×#101C22×C3semidirect
271. C4×M16C22×C3semidirect
273. #391C22×C3semidirect
276. C4×C4⋊C4C22×C3semidirect
277. #339C22×C3semidirect
278. #339C22×C3semidirect
460. AGL(1,ℤ/8)C3×D4semidirect
472. C4⋊Q8C3×D4semidirect
476. #127C3×D4semidirect
487. #124C3×D4semidirect
488. #124C3×D4semidirect
507. C4×Q8C3×D4semidirect
508. C4×Q8C3×D4semidirect
519. C4×D4C3×D4semidirect
520. C4×D4C3×D4semidirect
1008. C3#24234direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35002
C3×#30362
C2×C3×#4542
C2×C3×#4532
C3×C4×AGL(1,ℤ/8)2
C3×#25442
C3×#20382
C3×#20372
C3×#20032
C3×#20022
C3×#19802
C3×#19672
C3×#18062
C3×#17932
C3×#17922
#242343