Finite Group Databasebeta

← C3×#24174 #10642781

Subgroups — C3×#24174 #10642781

Order 768.

1078 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3512C211yesmaximal, characteristic, complemented
2C3×#3036C211yesmaximal, characteristic, complemented
3C3×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
4C3×#2566C211yesmaximal, characteristic, complemented
5C3×#2040C211yesmaximal, characteristic, complemented
6C3×#2039C211yesmaximal, characteristic, complemented
7C3×#2006C211yesmaximal, characteristic, complemented
8C3×#2006C211yesmaximal, characteristic, complemented
9C3×#1998C211yesmaximal, characteristic, complemented
10C3×#1980C211yesmaximal, characteristic, complemented
11C3×#1883C211yesmaximal, characteristic, complemented
12C3×#1883C211yesmaximal, characteristic, complemented
13C3×#1860C211yesmaximal, characteristic, complemented
14C3×#1859C211yesmaximal, characteristic, complemented
15C3×#1806C211yesmaximal, characteristic, complemented
16#24174C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
18C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
20C3×#553—21no—
21C3×#553—21no—
22C3×#553—22no—
23C3×#553—22no—
24C3×#552—21no—
25C3×#552—21no—
26C3×#541—21no—
27C3×#540—21no—
28C3×#537C2211yescharacteristic
29C3×#537C2211yescharacteristic
30C3×#532C2211yescharacteristic
31C3×#529—21no—
32C3×#529—21no—
33C2×C3×#125C2211yescharacteristic
34C3×#520C2211yescharacteristic
35C3×#520C2211yescharacteristic
36C3×C4×#41C2211yescharacteristic
37C2×C3×C4×D4C2211yescharacteristic
38C3×#463—21no—
39C3×#463—21no—
40C3×#461—21no—
41C3×#459—21no—
42C3×#442—21no—
43C3×#440—21no—
44C3×C4×SD16—21no—
45C3×C4×D8—21no—
46C3×#428C2211yescharacteristic
47C3×#423C2211yescharacteristic
48C2×C3×#104C2211yescharacteristic
49C2×C3×#104C2211yescharacteristic
50C2×C3×#104C2211yescharacteristic
51C2×C3×#104C2211yescharacteristic
52C2×C3×#104C2211yescharacteristic
53C2×C3×#104C2211yescharacteristic
54C3×#418C2211yescharacteristic
55C3×#417C2211yescharacteristic
56C3×#417C2211yescharacteristic
57C3×#417C2211yescharacteristic
58C3×C4×M16C2211yescharacteristic
59C3×#396—22no—
60C3×#390C2211yescharacteristic
61C3×#390C2211yescharacteristic
62C3×#385—22no—
63C3×#384C2211yescharacteristic
64C3×#382C2211yescharacteristic
65C3×C4×C4⋊C4C2211yescharacteristic
66C3×#343C2211yescharacteristic
67C3×#343C2211yescharacteristic
68C3×#343C2211yescharacteristic
69C3×#343C2211yescharacteristic
70C3×#339C2211yescharacteristic
71C3×#339C2211yescharacteristic
72#3512C2×C311yescharacteristic, complemented
73#3036C2×C311yescharacteristic, complemented
74C4×AGL(1,ℤ/8)C2×C311yescharacteristic, complemented
75#2566C2×C311yescharacteristic, complemented
76#2040C2×C311yescharacteristic, complemented
77#2039C2×C311yescharacteristic, complemented
78#2006C2×C311yescharacteristic, complemented
79#2006C2×C311yescharacteristic, complemented
80#1998C2×C311yescharacteristic, complemented
81#1980C2×C311yescharacteristic, complemented
82#1883C2×C311yescharacteristic, complemented
83#1883C2×C311yescharacteristic, complemented
84#1860C2×C311yescharacteristic, complemented
85#1859C2×C311yescharacteristic, complemented
86#1806C2×C311yescharacteristic, complemented
87C2×C3×#41C2311yescharacteristic
88C2×C3×#41C2311yescharacteristic
89C2×C3×#41C2311yescharacteristic
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4—21no—
92C3×AGL(1,ℤ/8)—22no—
93C3×AGL(1,ℤ/8)—22no—
94C3×AGL(1,ℤ/8)—22no—
95C3×AGL(1,ℤ/8)—22no—
96C3×AGL(1,ℤ/8)—41no—
97C3×AGL(1,ℤ/8)—41no—
98C2×C3×SD16—21no—
99C2×C3×SD16—21no—
100C2×C3×SD16—21no—
101C2×C3×D8—21no—
102C2×C3×D8—21no—
103C2×C3×D8—21no—
104C2×C3×M16C2311yescharacteristic
105C2×C3×M16C2311yescharacteristic
106C2×C3×M16C2311yescharacteristic
107C2×C3×M16C2311yescharacteristic
108C3×C4⋊Q8D411yescharacteristic
109C3×#127D411yescharacteristic
110C3×#126—22no—
111C3×#126—22no—
112C3×#126—22no—
113C3×#126—22no—
114C3×#125—22no—
115C3×#125—22no—
116C3×#125—21no—
117C3×#125—21no—
118C3×#125—21no—
119C3×#125—21no—
120C3×#124D411yescharacteristic
121C3×#124D411yescharacteristic
122C3×#123—22no—
123C3×#123—22no—
124C3×#123—22no—
125C3×#123—22no—
126C3×C22⋊Q8—21no—
127C3×C22⋊Q8—21no—
128C3×C22⋊Q8—21no—
129C3×C22⋊Q8—21no—
130C3×#121—22no—
131C3×#121—22no—
132C3×#121—21no—
133C3×#121—21no—
134C3×#121—21no—
135C3×#121—21no—
136C3×#121—21no—
137C3×#121—21no—
138C3×#121—22no—
139C3×#121—22no—
140C3×C4×Q8—21no—
141C3×C4×Q8—21no—
142C3×C4×Q8D411yescharacteristic
143C3×C4×Q8D411yescharacteristic
144C3×C4×D4—22no—
145C3×C4×D4—22no—
146C3×C4×D4—21no—
147C3×C4×D4—21no—
148C3×C4×D4—21no—
149C3×C4×D4—21no—
150C3×C4×D4—22no—
151C3×C4×D4—22no—
152C3×C4×D4—21no—
153C3×C4×D4—21no—
154C3×C4×D4—21no—
155C3×C4×D4—21no—
156C3×C4×D4—21no—
157C3×C4×D4—21no—
158C3×C4×D4D411yescharacteristic
159C3×C4×D4D411yescharacteristic
160C3×#117—22no—
161C3×#117—22no—
162C3×#117—21no—
163C3×#117—21no—
164C3×#117—21no—
165C3×#117C2311yescharacteristic
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4—21no—
169C2×C3×C4⋊C4—22no—
170C2×C3×C4⋊C4D412yes—
171C2×C3×C4⋊C4D412yes—
172C2×C3×C4⋊C4C2311yescharacteristic
173C2×C3×C4⋊C4C2311yescharacteristic
174C2×C3×C4⋊C4C2311yescharacteristic
175C2×C3×C22⋊C4—22no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—22no—
178C2×C3×C42—21no—
179C2×C3×C42C2311yescharacteristic
180C2×C3×C42C2311yescharacteristic
181C2×C3×C42C2311yescharacteristic
182C3×#107—21no—
183C3×#106—21no—
184C3×C4⋊C8—21no—
185C3×C4⋊C8—21no—
186C3×#104—22no—
187C3×#104—22no—
188C3×#104—41no—
189C3×#104—41no—
190C3×#104—41no—
191C3×#104—41no—
192C3×#103—21no—
193C3×#103—21no—
194C3×#103—21no—
195C3×#102—21no—
196C3×#102—21no—
197C3×#102—21no—
198C3×#102—21no—
199C3×#102—21no—
200C3×#97—21no—
201C3×C4×C8—21no—
202C3×#95—21no—
203C3×#95—22no—
204C2×AGL(1,ℤ/8)C22×C311yescharacteristic
205C2×AGL(1,ℤ/8)C22×C311yescharacteristic
206C2×AGL(1,ℤ/8)C22×C311yescharacteristic
207#553—21no—
208#553—21no—
209#553—22no—
210#553—22no—
211#552—21no—
212#552—21no—
213#541—21no—
214#540—21no—
215#537C22×C311yescharacteristic
216#537C22×C311yescharacteristic
217#532C22×C311yescharacteristic
218#529—21no—
219#529—21no—
220C2×#125C22×C311yescharacteristic
221#520C22×C311yescharacteristic
222#520C22×C311yescharacteristic
223C4×#41C22×C311yescharacteristic
224C2×C4×D4C22×C311yescharacteristic
225#463—21no—
226#463—21no—
227#461—21no—
228#459—21no—
229#442—21no—
230#440—21no—
231C4×SD16—21no—
232C4×D8—21no—
233#428C22×C311yescharacteristic
234#423C22×C311yescharacteristic
235C2×#104C22×C311yescharacteristic
236C2×#104C22×C311yescharacteristic
237C2×#104C22×C311yescharacteristic
238C2×#104C22×C311yescharacteristic
239C2×#104C22×C311yescharacteristic
240C2×#104C22×C311yescharacteristic
241#418C22×C311yescharacteristic
242#417C22×C311yescharacteristic
243#417C22×C311yescharacteristic
244#417C22×C311yescharacteristic
245C4×M16C22×C311yescharacteristic
246#396—22no—
247#390C22×C311yescharacteristic
248#390C22×C311yescharacteristic
249#385—22no—
250#384C22×C311yescharacteristic
251#382C22×C311yescharacteristic
252C4×C4⋊C4C22×C311yescharacteristic
253#343C22×C311yescharacteristic
254#343C22×C311yescharacteristic
255#343C22×C311yescharacteristic
256#343C22×C311yescharacteristic
257#339C22×C311yescharacteristic
258#339C22×C311yescharacteristic
259C24×C3—21no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C3×#41—21no—
265C3×#41—21no—
266C3×#41—21no—
267C3×#41—21no—
268C3×#41—21no—
269C3×#41—21no—
270C3×#41—21no—
271C3×#41—21no—
272C2×C3×Q8C2×D411yescharacteristic
273C2×C3×Q8C2×D411yescharacteristic
274C2×C3×Q8C2×D411yescharacteristic
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—21no—
284C2×C3×D4—21no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4C2×D411yescharacteristic
288C2×C3×D4C2×D411yescharacteristic
289C2×C3×D4C2×D411yescharacteristic
290C2×C3×D4#4112yes—
291C22×C3×C4—21no—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—41no—
302C22×C3×C4—41no—
303C22×C3×C4—82no—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2×D411yescharacteristic
308C22×C3×C4C2411yescharacteristic
309C3×SD16—24no—
310C3×SD16—42no—
311C3×SD16—42no—
312C3×D8—24no—
313C3×D8—42no—
314C3×D8—42no—
315C3×M16—21no—
316C3×M16—21no—
317C3×M16—21no—
318C3×M16—21no—
319C3×M16—21no—
320C3×M16—21no—
321C3×M16—21no—
322C3×M16#4112yes—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C3×C4⋊C4—22no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—22no—
331C3×C4⋊C4—22no—
332C3×C4⋊C4—22no—
333C3×C4⋊C4—22no—
334C3×C4⋊C4—22no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—42no—
346C3×C4⋊C4—82no—
347C3×C4⋊C4C2×D411yescharacteristic
348C3×C4⋊C4C2×D411yescharacteristic
349C3×C22⋊C4—22no—
350C3×C22⋊C4—22no—
351C3×C22⋊C4—22no—
352C3×C22⋊C4—22no—
353C3×C22⋊C4—22no—
354C3×C22⋊C4—22no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—44no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—82no—
366C3×C42—22no—
367C3×C42—22no—
368C3×C42—21no—
369C3×C42—21no—
370C3×C42—21no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42C2×D411yescharacteristic
376C3×C42C2×D411yescharacteristic
377C3×C42C2×D411yescharacteristic
378C3×C42C2×D411yescharacteristic
379C2×#41C23×C311yescharacteristic
380C2×#41C23×C311yescharacteristic
381C2×#41C23×C311yescharacteristic
382C22×D4C23×C311yescharacteristic
383C23×C4—21no—
384AGL(1,ℤ/8)—22no—
385AGL(1,ℤ/8)—22no—
386AGL(1,ℤ/8)—22no—
387AGL(1,ℤ/8)—22no—
388AGL(1,ℤ/8)—41no—
389AGL(1,ℤ/8)—41no—
390C2×SD16—21no—
391C2×SD16—21no—
392C2×SD16—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×D8—21no—
396C2×M16C23×C311yescharacteristic
397C2×M16C23×C311yescharacteristic
398C2×M16C23×C311yescharacteristic
399C2×M16C23×C311yescharacteristic
400C4⋊Q8C3×D411yescharacteristic
401#127C3×D411yescharacteristic
402#126—22no—
403#126—22no—
404#126—22no—
405#126—22no—
406#125—22no—
407#125—22no—
408#125—21no—
409#125—21no—
410#125—21no—
411#125—21no—
412#124C3×D411yescharacteristic
413#124C3×D411yescharacteristic
414#123—22no—
415#123—22no—
416#123—22no—
417#123—22no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422#121—22no—
423#121—22no—
424#121—21no—
425#121—21no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—22no—
431#121—22no—
432C4×Q8—21no—
433C4×Q8—21no—
434C4×Q8C3×D411yescharacteristic
435C4×Q8C3×D411yescharacteristic
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4C3×D411yescharacteristic
451C4×D4C3×D411yescharacteristic
452#117—22no—
453#117—22no—
454#117—21no—
455#117—21no—
456#117—21no—
457#117C23×C311yescharacteristic
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4C3×D412yes—
463C2×C4⋊C4C3×D412yes—
464C2×C4⋊C4C23×C311yescharacteristic
465C2×C4⋊C4C23×C311yescharacteristic
466C2×C4⋊C4C23×C311yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C42—21no—
471C2×C42C23×C311yescharacteristic
472C2×C42C23×C311yescharacteristic
473C2×C42C23×C311yescharacteristic
474#107—21no—
475#106—21no—
476C4⋊C8—21no—
477C4⋊C8—21no—
478#104—22no—
479#104—22no—
480#104—41no—
481#104—41no—
482#104—41no—
483#104—41no—
484#103—21no—
485#103—21no—
486#103—21no—
487#102—21no—
488#102—21no—
489#102—21no—
490#102—21no—
491#102—21no—
492#97—21no—
493C4×C8—21no—
494#95—21no—
495#95—22no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—22no—
500C23×C3—42no—
501C23×C3—42no—
502C23×C3—41no—
503C23×C3—41no—
504C23×C3C22×D411yescharacteristic
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—21no—
514C3×D4—22no—
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—41no—
520C3×D4—41no—
521C3×D4—41no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—41no—
527C3×D4—81no—
528C3×D4—81no—
529C3×D4—82no—
530C3×D4—82no—
531C2×C3×C4—22no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—42no—
550C2×C3×C4—42no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—42no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—81no—
557C2×C3×C4—81no—
558C2×C3×C4—82no—
559C2×C3×C4—82no—
560C2×C3×C4—82no—
561C2×C3×C4—82no—
562C2×C3×C4#12011yescharacteristic
563C2×C3×C4#12011yescharacteristic
564C2×C3×C4#12011yescharacteristic
565C2×C3×C4#12011yescharacteristic
566C2×C3×C4C22×D411yescharacteristic
567C2×C3×C4C22×D411yescharacteristic
568C2×C3×C4C2×#4111yescharacteristic
569C2×C3×C4C2×#4111yescharacteristic
570C2×C3×C4H(5,𝔽2)11yescharacteristic
571C2×C3×C42−1+411yescharacteristic
572C3×C8—22no—
573C3×C8—41no—
574C3×C8—41no—
575C3×C8—41no—
576C24—21no—
577#41—21no—
578#41—21no—
579#41—21no—
580#41—21no—
581#41—21no—
582#41—21no—
583#41—21no—
584#41—21no—
585#41—21no—
586#41—21no—
587#41—21no—
588#41—21no—
589C2×Q8C2×C3×D411yescharacteristic
590C2×Q8C2×C3×D411yescharacteristic
591C2×Q8C2×C3×D411yescharacteristic
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4C2×C3×D411yescharacteristic
605C2×D4C2×C3×D411yescharacteristic
606C2×D4C2×C3×D411yescharacteristic
607C2×D4C3×#4112yes—
608C22×C4—21no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—82no—
621C22×C4C2×C3×D412yes—
622C22×C4C2×C3×D412yes—
623C22×C4C2×C3×D411yescharacteristic
624C22×C4C2×C3×D411yescharacteristic
625C22×C4C24×C311yescharacteristic
626SD16—24no—
627SD16—42no—
628SD16—42no—
629D8—24no—
630D8—42no—
631D8—42no—
632M16—21no—
633M16—21no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—21no—
639M16C3×#4112yes—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—42no—
663C4⋊C4—82no—
664C4⋊C4C2×C3×D411yescharacteristic
665C4⋊C4C2×C3×D411yescharacteristic
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—44no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—82no—
683C42—22no—
684C42—22no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42C2×C3×D411yescharacteristic
693C42C2×C3×D411yescharacteristic
694C42C2×C3×D411yescharacteristic
695C42C2×C3×D411yescharacteristic
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—44no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—42no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—82no—
710C22×C3—81no—
711C22×C3—81no—
712C22×C3C2×#12011yescharacteristic
713C22×C3#54811yescharacteristic
714C22×C3#55011yescharacteristic
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—42no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—41no—
723C3×C4—42no—
724C3×C4—41no—
725C3×C4—42no—
726C3×C4—41no—
727C3×C4—81no—
728C3×C4—81no—
729C3×C4#52511yescharacteristic
730C3×C4#53711yescharacteristic
731C3×C4#54611yescharacteristic
732C3×C4#54711yescharacteristic
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—42no—
738C23—42no—
739C23—41no—
740C23—41no—
741C23C22×C3×D411yescharacteristic
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—21no—
747Q8—21no—
748D4—21no—
749D4—22no—
750D4—21no—
751D4—22no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—21no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—41no—
764D4—81no—
765D4—81no—
766D4—82no—
767D4—82no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—82no—
796C2×C4—82no—
797C2×C4—82no—
798C2×C4—82no—
799C2×C4C3×#12011yescharacteristic
800C2×C4C3×#12011yescharacteristic
801C2×C4C3×#12011yescharacteristic
802C2×C4C3×#12011yescharacteristic
803C2×C4C22×C3×D411yescharacteristic
804C2×C4C22×C3×D411yescharacteristic
805C2×C4C2×C3×#4111yescharacteristic
806C2×C4C2×C3×#4111yescharacteristic
807C2×C4C3×H(5,𝔽2)11yescharacteristic
808C2×C4C3×2−1+411yescharacteristic
809C8—22no—
810C8—41no—
811C8—41no—
812C8—41no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—81no—
816C2×C3—81no—
817C2×C3—81no—
818C2×C3—82no—
819C2×C3#240711yescharacteristic
820C2×C3#301811yescharacteristic
821C2×C3#302111yescharacteristic
822C22—21no—
823C22—21no—
824C22—44no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—82no—
836C22—81no—
837C22—81no—
838C22C2×C3×#12011yescharacteristic
839C22C3×#54811yescharacteristic
840C22C3×#55011yescharacteristic
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—42no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—81no—
854C4—81no—
855C4C3×#52511yescharacteristic
856C4C3×#53711yescharacteristic
857C4C3×#54611yescharacteristic
858C4C3×#54711yescharacteristic
859C3#2417411yescharacteristic, direct product factor, Sylow
860C2—21no—
861C2—21no—
862C2—82no—
863C2—81no—
864C2—81no—
865C2—81no—
866C2C3×#240711yescharacteristic
867C2C3×#301811yescharacteristic
868C2C3×#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×#3512C2semidirect
2. C3×#3036C2semidirect
3. C3×C4×AGL(1,ℤ/8)C2semidirect
4. C3×#2566C2semidirect
5. C3×#2040C2semidirect
6. C3×#2039C2semidirect
7. C3×#2006C2semidirect
8. C3×#2006C2semidirect
9. C3×#1998C2semidirect
10. C3×#1980C2semidirect
11. C3×#1883C2semidirect
12. C3×#1883C2semidirect
13. C3×#1860C2semidirect
14. C3×#1859C2semidirect
15. C3×#1806C2semidirect
16. #24174C3direct (N × H)
72. #3512C2×C3semidirect
73. #3036C2×C3semidirect
74. C4×AGL(1,ℤ/8)C2×C3semidirect
75. #2566C2×C3semidirect
76. #2040C2×C3semidirect
77. #2039C2×C3semidirect
78. #2006C2×C3semidirect
79. #2006C2×C3semidirect
80. #1998C2×C3semidirect
81. #1980C2×C3semidirect
82. #1883C2×C3semidirect
83. #1883C2×C3semidirect
84. #1860C2×C3semidirect
85. #1859C2×C3semidirect
86. #1806C2×C3semidirect
859. C3#24174direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35122
C3×#30362
C3×C4×AGL(1,ℤ/8)2
C3×#25662
C3×#20402
C3×#20392
C3×#20062
C3×#19982
C3×#19802
C3×#18832
C3×#18602
C3×#18592
C3×#18062
#241743