Finite Group Databasebeta

← C3×#30478 #10649085

Subgroups — C3×#30478 #10649085

Order 768.

1034 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×#3154C211yesmaximal, characteristic, complemented
2C2×C3×#472C211yesmaximal, characteristic, complemented
3C3×#3063C211yesmaximal, characteristic, complemented
4C2×C3×#455C211yesmaximal, characteristic, complemented
5C3×#3012C211yesmaximal, characteristic, complemented
6C3×#3008C211yesmaximal, characteristic, complemented
7C3×#2052C211yesmaximal, characteristic, complemented
8C3×#2037C211yesmaximal, characteristic, complemented
9C3×#2019C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#2006C211yesmaximal, characteristic, complemented
12C3×#2003C211yesmaximal, characteristic, complemented
13C3×#1931C211yesmaximal, characteristic, complemented
14C3×#1929C211yesmaximal, characteristic, complemented
15C3×#1876C211yesmaximal, characteristic, complemented
16#30478C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×H(5,𝔽2)C2211yescharacteristic
18C2×C3×#137C2211yescharacteristic
19C2×C3×#137C2211yescharacteristic
20C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
21C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
22C2×C3×AGL(1,ℤ/8)C2211yescharacteristic, complemented
23C2×C3×#135C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic, complemented
25C22×C3×D8C2211yescharacteristic
26C2×C3×#131C2211yescharacteristic, complemented
27C3×#537C2211yescharacteristic
28C3×#536C2211yescharacteristic, complemented
29C3×#535C2211yescharacteristic
30C2×C3×#124C2211yescharacteristic
31C3×#497—21no—
32C3×#496—21no—
33C3×#495—21no—
34C3×#492—21no—
35C3×#472—24no—
36C3×#470—21no—
37C3×#468—21no—
38C3×#467—21no—
39C3×#465—21no—
40C3×#455—24no—
41C3×#452—21no—
42C3×#450—21no—
43C3×#449—21no—
44C3×#449—21no—
45C3×#449—21no—
46C3×#447—21no—
47C3×#447—21no—
48C3×#447—21no—
49C2×C3×#108C2211yescharacteristic, complemented
50C3×#428C2211yescharacteristic, complemented
51C2×C3×#104C2211yescharacteristic
52C2×C3×#104C2211yescharacteristic
53C2×C3×#104C2211yescharacteristic, complemented
54C3×#418C2211yescharacteristic
55C3×#417C2211yescharacteristic
56C3×#416C2211yescharacteristic
57C2×C3×#103C2211yescharacteristic, complemented
58C2×C3×#102C2211yescharacteristic
59C2×C3×#101C2211yescharacteristic, complemented
60C2×C3×#100C2211yescharacteristic
61C2×C3×#100C2211yescharacteristic, complemented
62C3×#408C2211yescharacteristic
63C3×#408C2211yescharacteristic
64C3×#405C2211yescharacteristic, complemented
65C3×#390C2211yescharacteristic, complemented
66C3×#343C2211yescharacteristic, complemented
67C3×#341C2211yescharacteristic, complemented
68C3×#339C2211yescharacteristic, complemented
69C3×#336C2211yescharacteristic, complemented
70#3154C2×C311yescharacteristic, complemented
71C2×#472C2×C311yescharacteristic, complemented
72#3063C2×C311yescharacteristic, complemented
73C2×#455C2×C311yescharacteristic, complemented
74#3012C2×C311yescharacteristic, complemented
75#3008C2×C311yescharacteristic, complemented
76#2052C2×C311yescharacteristic, complemented
77#2037C2×C311yescharacteristic, complemented
78#2019C2×C311yescharacteristic, complemented
79#2012C2×C311yescharacteristic, complemented
80#2006C2×C311yescharacteristic, complemented
81#2003C2×C311yescharacteristic, complemented
82#1931C2×C311yescharacteristic, complemented
83#1929C2×C311yescharacteristic, complemented
84#1876C2×C311yescharacteristic, complemented
85C3×H(5,𝔽2)—22no—
86C3×H(5,𝔽2)—41no—
87C3×H(5,𝔽2)—41no—
88C3×H(5,𝔽2)—41no—
89C2×C3×#41—21no—
90C2×C3×#41—21no—
91C2×C3×#41C2311yescharacteristic
92C2×C3×#41C2311yescharacteristic
93C2×C3×#41C2311yescharacteristic
94C22×C3×Q8C2311yescharacteristic
95C22×C3×D4—21no—
96C22×C3×D4—21no—
97C22×C3×D4—41no—
98C22×C3×D4C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C3×#137—22no—
101C3×#137—22no—
102C3×#137—41no—
103C3×#137—41no—
104C3×AGL(1,ℤ/8)—22no—
105C3×AGL(1,ℤ/8)—22no—
106C3×AGL(1,ℤ/8)—41no—
107C3×AGL(1,ℤ/8)—41no—
108C3×AGL(1,ℤ/8)—41no—
109C3×AGL(1,ℤ/8)—41no—
110C3×#135—41no—
111C3×#135—41no—
112C2×C3×Q16—21no—
113C2×C3×Q16—21no—
114C2×C3×Q16D411yescharacteristic
115C2×C3×SD16—21no—
116C2×C3×SD16—21no—
117C2×C3×SD16—21no—
118C2×C3×SD16—21no—
119C2×C3×SD16—21no—
120C2×C3×SD16—21no—
121C2×C3×SD16—21no—
122C2×C3×SD16—41no—
123C2×C3×SD16—41no—
124C2×C3×SD16D411yescharacteristic
125C2×C3×SD16D411yescharacteristic
126C2×C3×D8—22no—
127C2×C3×D8—21no—
128C2×C3×D8—21no—
129C2×C3×D8—21no—
130C2×C3×D8—21no—
131C2×C3×D8—21no—
132C2×C3×D8—41no—
133C2×C3×D8D411yescharacteristic
134C3×#131—22no—
135C3×#131—41no—
136C2×C3×M16—21no—
137C2×C3×M16C2311yescharacteristic
138C2×C3×M16C2311yescharacteristic
139C2×C3×M16C2311yescharacteristic
140C2×C3×M16C2311yescharacteristic
141C22×C3×C8—21no—
142C22×C3×C8C2311yescharacteristic
143C22×C3×C8C2311yescharacteristic
144C3×C4⋊Q8—21no—
145C3×#127—21no—
146C3×#124—21no—
147C3×#124—22no—
148C3×#124—21no—
149C3×#124—41no—
150C3×#123—41no—
151C3×C22⋊Q8—21no—
152C3×C22⋊Q8—21no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—21no—
155C3×#121—21no—
156C3×#121—21no—
157C3×#121—21no—
158C3×#121—21no—
159C3×#121—41no—
160C3×#120—41no—
161C3×#117C2311yescharacteristic
162C2×C3×C4⋊C4C2311yescharacteristic
163C2×C3×C22⋊C4—41no—
164C2×C3×C22⋊C4—41no—
165C2×C3×C42C2311yescharacteristic
166C3×#108—22no—
167C3×#107—21no—
168C3×#106—21no—
169C3×#104—22no—
170C3×#104—22no—
171C3×#104—41no—
172C3×#103—21no—
173C3×#103—21no—
174C3×#103—21no—
175C3×#103D411yescharacteristic
176C3×#103D411yescharacteristic
177C3×#102—21no—
178C3×#102—21no—
179C3×#102—21no—
180C3×#102—21no—
181C3×#102—21no—
182C3×#102D411yescharacteristic
183C3×#102D411yescharacteristic
184C3×#101—41no—
185C3×#100—22no—
186C3×#100D414yescomplemented
187C3×C22⋊C8—21no—
188C3×C22⋊C8—21no—
189C3×C22⋊C8—21no—
190C3×C22⋊C8—21no—
191C3×#97—21no—
192C3×C4×C8—21no—
193C2×H(5,𝔽2)C22×C311yescharacteristic
194C2×#137C22×C311yescharacteristic
195C2×#137C22×C311yescharacteristic
196C2×AGL(1,ℤ/8)C22×C311yescharacteristic
197C2×AGL(1,ℤ/8)C22×C311yescharacteristic
198C2×AGL(1,ℤ/8)C22×C311yescharacteristic, complemented
199C2×#135C22×C311yescharacteristic
200C22×SD16C22×C311yescharacteristic, complemented
201C22×D8C22×C311yescharacteristic
202C2×#131C22×C311yescharacteristic, complemented
203#537C22×C311yescharacteristic
204#536C22×C311yescharacteristic, complemented
205#535C22×C311yescharacteristic
206C2×#124C22×C311yescharacteristic
207#497—21no—
208#496—21no—
209#495—21no—
210#492—21no—
211#472—24no—
212#470—21no—
213#468—21no—
214#467—21no—
215#465—21no—
216#455—24no—
217#452—21no—
218#450—21no—
219#449—21no—
220#449—21no—
221#449—21no—
222#447—21no—
223#447—21no—
224#447—21no—
225C2×#108C22×C311yescharacteristic, complemented
226#428C22×C311yescharacteristic, complemented
227C2×#104C22×C311yescharacteristic
228C2×#104C22×C311yescharacteristic
229C2×#104C22×C311yescharacteristic, complemented
230#418C22×C311yescharacteristic
231#417C22×C311yescharacteristic
232#416C22×C311yescharacteristic
233C2×#103C22×C311yescharacteristic, complemented
234C2×#102C22×C311yescharacteristic
235C2×#101C22×C311yescharacteristic, complemented
236C2×#100C22×C311yescharacteristic
237C2×#100C22×C311yescharacteristic, complemented
238#408C22×C311yescharacteristic
239#408C22×C311yescharacteristic
240#405C22×C311yescharacteristic, complemented
241#390C22×C311yescharacteristic, complemented
242#343C22×C311yescharacteristic, complemented
243#341C22×C311yescharacteristic, complemented
244#339C22×C311yescharacteristic, complemented
245#336C22×C311yescharacteristic, complemented
246C24×C3—21no—
247C24×C3—21no—
248C24×C3—41no—
249C3×#41—21no—
250C3×#41—21no—
251C3×#41—21no—
252C3×#41—21no—
253C3×#41—21no—
254C3×#41—21no—
255C3×#41—21no—
256C3×#41—21no—
257C3×#41—21no—
258C3×#41—21no—
259C3×#41—21no—
260C3×#41—21no—
261C3×#41—42no—
262C3×#41—42no—
263C3×#41—42no—
264C3×#41—42no—
265C2×C3×Q8—21no—
266C2×C3×Q8—21no—
267C2×C3×Q8—21no—
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8C2×D411yescharacteristic
272C2×C3×Q8C2×D411yescharacteristic
273C2×C3×Q8C2×D411yescharacteristic
274C2×C3×D4—21no—
275C2×C3×D4—21no—
276C2×C3×D4—21no—
277C2×C3×D4—21no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
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×D4—21no—
288C2×C3×D4—41no—
289C2×C3×D4—41no—
290C2×C3×D4—41no—
291C2×C3×D4—41no—
292C2×C3×D4—42no—
293C2×C3×D4—42no—
294C2×C3×D4—42no—
295C2×C3×D4—42no—
296C2×C3×D4—44no—
297C2×C3×D4—44no—
298C2×C3×D4—41no—
299C2×C3×D4C2×D412yes—
300C2×C3×D4C2×D411yescharacteristic
301C2×C3×D4C2×D411yescharacteristic
302C2×C3×D4C2×D411yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—41no—
310C22×C3×C4C2411yescharacteristic
311C3×Q16—41no—
312C3×Q16—42no—
313C3×Q16—42no—
314C3×SD16—41no—
315C3×SD16—41no—
316C3×SD16—42no—
317C3×SD16—42no—
318C3×SD16—42no—
319C3×SD16—42no—
320C3×SD16—42no—
321C3×SD16—42no—
322C3×SD16—42no—
323C3×D8—41no—
324C3×D8—42no—
325C3×D8—42no—
326C3×D8—42no—
327C3×D8—42no—
328C3×D8—42no—
329C3×M16—21no—
330C3×M16—21no—
331C3×M16—21no—
332C3×M16—21no—
333C3×M16—21no—
334C3×M16—21no—
335C3×M16—42no—
336C3×M16C2×D412yes—
337C3×M16C2×D412yes—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—42no—
347C2×C3×C8C2×D411yescharacteristic
348C2×C3×C8C2×D411yescharacteristic
349C2×C3×C8C2×D411yescharacteristic
350C2×C3×C8C2×D411yescharacteristic
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—41no—
355C3×C4⋊C4—41no—
356C3×C4⋊C4C2×D411yescharacteristic
357C3×C4⋊C4C2×D411yescharacteristic
358C3×C22⋊C4—21no—
359C3×C22⋊C4—41no—
360C3×C22⋊C4—41no—
361C3×C22⋊C4—41no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—44no—
366C3×C22⋊C4—82no—
367C3×C42—21no—
368C3×C42—21no—
369C3×C42—21no—
370H(5,𝔽2)—22no—
371H(5,𝔽2)—41no—
372H(5,𝔽2)—41no—
373H(5,𝔽2)—41no—
374C2×#41—21no—
375C2×#41—21no—
376C2×#41C23×C311yescharacteristic
377C2×#41C23×C311yescharacteristic
378C2×#41C23×C311yescharacteristic
379C22×Q8C23×C311yescharacteristic
380C22×D4—21no—
381C22×D4—21no—
382C22×D4—41no—
383C22×D4C23×C311yescharacteristic
384C22×D4C23×C311yescharacteristic
385#137—22no—
386#137—22no—
387#137—41no—
388#137—41no—
389AGL(1,ℤ/8)—22no—
390AGL(1,ℤ/8)—22no—
391AGL(1,ℤ/8)—41no—
392AGL(1,ℤ/8)—41no—
393AGL(1,ℤ/8)—41no—
394AGL(1,ℤ/8)—41no—
395#135—41no—
396#135—41no—
397C2×Q16—21no—
398C2×Q16—21no—
399C2×Q16C3×D411yescharacteristic
400C2×SD16—21no—
401C2×SD16—21no—
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—21no—
405C2×SD16—21no—
406C2×SD16—21no—
407C2×SD16—41no—
408C2×SD16—41no—
409C2×SD16C3×D411yescharacteristic
410C2×SD16C3×D411yescharacteristic
411C2×D8—22no—
412C2×D8—21no—
413C2×D8—21no—
414C2×D8—21no—
415C2×D8—21no—
416C2×D8—21no—
417C2×D8—41no—
418C2×D8C3×D411yescharacteristic
419#131—22no—
420#131—41no—
421C2×M16—21no—
422C2×M16C23×C311yescharacteristic
423C2×M16C23×C311yescharacteristic
424C2×M16C23×C311yescharacteristic
425C2×M16C23×C311yescharacteristic
426C22×C8—21no—
427C22×C8C23×C311yescharacteristic
428C22×C8C23×C311yescharacteristic
429C4⋊Q8—21no—
430#127—21no—
431#124—21no—
432#124—22no—
433#124—21no—
434#124—41no—
435#123—41no—
436C22⋊Q8—21no—
437C22⋊Q8—21no—
438C22⋊Q8—21no—
439C22⋊Q8—21no—
440#121—21no—
441#121—21no—
442#121—21no—
443#121—21no—
444#121—41no—
445#120—41no—
446#117C23×C311yescharacteristic
447C2×C4⋊C4C23×C311yescharacteristic
448C2×C22⋊C4—41no—
449C2×C22⋊C4—41no—
450C2×C42C23×C311yescharacteristic
451#108—22no—
452#107—21no—
453#106—21no—
454#104—22no—
455#104—22no—
456#104—41no—
457#103—21no—
458#103—21no—
459#103—21no—
460#103C3×D411yescharacteristic
461#103C3×D411yescharacteristic
462#102—21no—
463#102—21no—
464#102—21no—
465#102—21no—
466#102—21no—
467#102C3×D411yescharacteristic
468#102C3×D411yescharacteristic
469#101—41no—
470#100—22no—
471#100C3×D414yescomplemented
472C22⋊C8—21no—
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—21no—
476#97—21no—
477C4×C8—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—22no—
482C23×C3—44no—
483C23×C3—41no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—81no—
489C23×C3—81no—
490C23×C3—81no—
491C23×C3—81no—
492C23×C3—161no—
493C23×C3—161no—
494C23×C3H(5,𝔽2)11yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—41no—
502C3×Q8—41no—
503C3×Q8—41no—
504C3×Q8—41no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—22no—
510C3×D4—22no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—44no—
514C3×D4—44no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—41no—
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—161no—
528C3×D4—161no—
529C3×D4—161no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—44no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
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—81no—
550C2×C3×C4C22×D411yescharacteristic
551C2×C3×C4C22×D411yescharacteristic
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4H(5,𝔽2)11yescharacteristic
554C2×C3×C4H(5,𝔽2)11yescharacteristic
555C2×C3×C4H(5,𝔽2)11yescharacteristic
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—22no—
561C3×C8—22no—
562C3×C8—41no—
563C3×C8—41no—
564C24—21no—
565C24—21no—
566C24—41no—
567#41—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577#41—21no—
578#41—21no—
579#41—42no—
580#41—42no—
581#41—42no—
582#41—42no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8C2×C3×D411yescharacteristic
590C2×Q8C2×C3×D411yescharacteristic
591C2×Q8C2×C3×D411yescharacteristic
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—41no—
617C2×D4C2×C3×D412yes—
618C2×D4C2×C3×D411yescharacteristic
619C2×D4C2×C3×D411yescharacteristic
620C2×D4C2×C3×D411yescharacteristic
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—41no—
628C22×C4C24×C311yescharacteristic
629Q16—41no—
630Q16—42no—
631Q16—42no—
632SD16—41no—
633SD16—41no—
634SD16—42no—
635SD16—42no—
636SD16—42no—
637SD16—42no—
638SD16—42no—
639SD16—42no—
640SD16—42no—
641D8—41no—
642D8—42no—
643D8—42no—
644D8—42no—
645D8—42no—
646D8—42no—
647M16—21no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—21no—
653M16—42no—
654M16C2×C3×D412yes—
655M16C2×C3×D412yes—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—42no—
665C2×C8C2×C3×D411yescharacteristic
666C2×C8C2×C3×D411yescharacteristic
667C2×C8C2×C3×D411yescharacteristic
668C2×C8C2×C3×D411yescharacteristic
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—41no—
672C4⋊C4—41no—
673C4⋊C4—41no—
674C4⋊C4C2×C3×D411yescharacteristic
675C4⋊C4C2×C3×D411yescharacteristic
676C22⋊C4—21no—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—41no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—44no—
684C22⋊C4—82no—
685C42—21no—
686C42—21no—
687C42—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—42no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—82no—
701C22×C3—82no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—161no—
708C22×C3—161no—
709C22×C3—164no—
710C22×C3#53511yescharacteristic
711C22×C3D4211yescharacteristic
712C22×C3#56011yescharacteristic
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—81no—
719C3×C4—81no—
720C3×C4—81no—
721C3×C4#53411yescharacteristic
722C3×C4#53511yescharacteristic
723C3×C4D4211yescharacteristic
724C3×C4D4211yescharacteristic
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—44no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—161no—
740C23—161no—
741C23C3×H(5,𝔽2)11yescharacteristic
742Q8—21no—
743Q8—21no—
744Q8—21no—
745Q8—21no—
746Q8—21no—
747Q8—21no—
748Q8—41no—
749Q8—41no—
750Q8—41no—
751Q8—41no—
752D4—21no—
753D4—21no—
754D4—21no—
755D4—21no—
756D4—22no—
757D4—22no—
758D4—21no—
759D4—21no—
760D4—44no—
761D4—44no—
762D4—41no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—161no—
775D4—161no—
776D4—161no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—44no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—81no—
797C2×C4C22×C3×D411yescharacteristic
798C2×C4C22×C3×D411yescharacteristic
799C2×C4C22×C3×D411yescharacteristic
800C2×C4C3×H(5,𝔽2)11yescharacteristic
801C2×C4C3×H(5,𝔽2)11yescharacteristic
802C2×C4C3×H(5,𝔽2)11yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—22no—
808C8—22no—
809C8—41no—
810C8—41no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—81no—
814C2×C3—81no—
815C2×C3—81no—
816C2×C3—82no—
817C2×C3—161no—
818C2×C3#266911yescharacteristic
819C2×C3#328811yescharacteristic
820C2×C3#329011yescharacteristic
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—82no—
834C22—82no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—161no—
841C22—161no—
842C22—164no—
843C22C3×#53511yescharacteristic
844C22C3×D4211yescharacteristic
845C22C3×#56011yescharacteristic
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4C3×#53411yescharacteristic
855C4C3×#53511yescharacteristic
856C4C3×D4211yescharacteristic
857C4C3×D4211yescharacteristic
858C3#3047811yescharacteristic, direct product factor, Sylow
859C2—21no—
860C2—21no—
861C2—81no—
862C2—81no—
863C2—81no—
864C2—82no—
865C2—161no—
866C2C3×#266911yescharacteristic
867C2C3×#328811yescharacteristic
868C2C3×#329011yescharacteristic
subgroupG/H
center, socleC22×C3D42
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3154C2semidirect
2. C2×C3×#472C2semidirect
3. C3×#3063C2semidirect
4. C2×C3×#455C2semidirect
5. C3×#3012C2semidirect
6. C3×#3008C2semidirect
7. C3×#2052C2semidirect
8. C3×#2037C2semidirect
9. C3×#2019C2semidirect
10. C3×#2012C2semidirect
11. C3×#2006C2semidirect
12. C3×#2003C2semidirect
13. C3×#1931C2semidirect
14. C3×#1929C2semidirect
15. C3×#1876C2semidirect
16. #30478C3direct (N × H)
22. C2×C3×AGL(1,ℤ/8)C22semidirect
24. C22×C3×SD16C22semidirect
26. C2×C3×#131C22semidirect
28. C3×#536C22semidirect
49. C2×C3×#108C22semidirect
50. C3×#428C22semidirect
53. C2×C3×#104C22semidirect
57. C2×C3×#103C22semidirect
59. C2×C3×#101C22semidirect
61. C2×C3×#100C22semidirect
64. C3×#405C22semidirect
65. C3×#390C22semidirect
66. C3×#343C22semidirect
67. C3×#341C22semidirect
68. C3×#339C22semidirect
69. C3×#336C22semidirect
70. #3154C2×C3semidirect
71. C2×#472C2×C3semidirect
72. #3063C2×C3semidirect
73. C2×#455C2×C3semidirect
74. #3012C2×C3semidirect
75. #3008C2×C3semidirect
76. #2052C2×C3semidirect
77. #2037C2×C3semidirect
78. #2019C2×C3semidirect
79. #2012C2×C3semidirect
80. #2006C2×C3semidirect
81. #2003C2×C3semidirect
82. #1931C2×C3semidirect
83. #1929C2×C3semidirect
84. #1876C2×C3semidirect
186. C3×#100D4semidirect
198. C2×AGL(1,ℤ/8)C22×C3semidirect
200. C22×SD16C22×C3semidirect
202. C2×#131C22×C3semidirect
204. #536C22×C3semidirect
225. C2×#108C22×C3semidirect
226. #428C22×C3semidirect
229. C2×#104C22×C3semidirect
233. C2×#103C22×C3semidirect
235. C2×#101C22×C3semidirect
237. C2×#100C22×C3semidirect
240. #405C22×C3semidirect
241. #390C22×C3semidirect
242. #343C22×C3semidirect
243. #341C22×C3semidirect
244. #339C22×C3semidirect
245. #336C22×C3semidirect
471. #100C3×D4semidirect
858. C3#30478direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#31542
C2×C3×#4722
C3×#30632
C2×C3×#4552
C3×#30122
C3×#30082
C3×#20522
C3×#20372
C3×#20192
C3×#20122
C3×#20062
C3×#20032
C3×#19312
C3×#19292
C3×#18762
#304783