Finite Group Databasebeta

← C3×#30480 #10649087

Subgroups — C3×#30480 #10649087

Order 768.

1058 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3154C211yesmaximal, characteristic, complemented
2C2×C3×#471C211yesmaximal, characteristic, complemented
3C3×#3062C211yesmaximal, characteristic, complemented
4C2×C3×#453C211yesmaximal, characteristic, complemented
5C3×#3012C211yesmaximal, characteristic, complemented
6C3×#3009C211yesmaximal, characteristic, complemented
7C3×#2051C211yesmaximal, characteristic, complemented
8C3×#2038C211yesmaximal, characteristic, complemented
9C3×#2019C211yesmaximal, characteristic, complemented
10C3×#2014C211yesmaximal, characteristic, complemented
11C3×#2007C211yesmaximal, characteristic, complemented
12C3×#2002C211yesmaximal, characteristic, complemented
13C3×#1931C211yesmaximal, characteristic, complemented
14C3×#1929C211yesmaximal, characteristic, complemented
15C3×#1876C211yesmaximal, characteristic, complemented
16#30480C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×H(5,𝔽2)C2211yescharacteristic
18C2×C3×#137C2211yescharacteristic
19C2×C3×#137C2211yescharacteristic, complemented
20C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
21C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
22C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
23C2×C3×#135C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic, complemented
26C2×C3×#131C2211yescharacteristic, complemented
27C3×#537C2211yescharacteristic
28C3×#536C2211yescharacteristic
29C3×#535C2211yescharacteristic, complemented
30C2×C3×#127C2211yescharacteristic
31C3×#497—21no—
32C3×#496—21no—
33C3×#495—21no—
34C3×#492—21no—
35C3×#471—24no—
36C3×#469—21no—
37C3×#468—21no—
38C3×#466—21no—
39C3×#465—21no—
40C3×#453—24no—
41C3×#452—21no—
42C3×#452—21no—
43C3×#452—21no—
44C3×#450—21no—
45C3×#450—21no—
46C3×#450—21no—
47C3×#449—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×#102C2211yescharacteristic
58C2×C3×#102C2211yescharacteristic, complemented
59C2×C3×#101C2211yescharacteristic, complemented
60C2×C3×#100C2211yescharacteristic
61C2×C3×#100C2211yescharacteristic, complemented
62C3×#408C2211yescharacteristic
63C3×#408C2211yescharacteristic
64C3×#405C2211yescharacteristic, complemented
65C3×#391C2211yescharacteristic, complemented
66C3×#343C2211yescharacteristic, complemented
67C3×#341C2211yescharacteristic, complemented
68C3×#339C2211yescharacteristic, complemented
69C3×#336C2211yescharacteristic, complemented
70#3154C2×C311yescharacteristic, complemented
71C2×#471C2×C311yescharacteristic, complemented
72#3062C2×C311yescharacteristic, complemented
73C2×#453C2×C311yescharacteristic, complemented
74#3012C2×C311yescharacteristic, complemented
75#3009C2×C311yescharacteristic, complemented
76#2051C2×C311yescharacteristic, complemented
77#2038C2×C311yescharacteristic, complemented
78#2019C2×C311yescharacteristic, complemented
79#2014C2×C311yescharacteristic, complemented
80#2007C2×C311yescharacteristic, complemented
81#2002C2×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×D4—41no—
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C3×#137—22no—
102C3×#137—41no—
103C3×#137—41no—
104C3×#137—41no—
105C3×AGL(1,ℤ/8)—22no—
106C3×AGL(1,ℤ/8)—22no—
107C3×AGL(1,ℤ/8)—22no—
108C3×AGL(1,ℤ/8)—41no—
109C3×AGL(1,ℤ/8)—41no—
110C3×AGL(1,ℤ/8)—41no—
111C3×#135—41no—
112C3×#135—41no—
113C2×C3×Q16—21no—
114C2×C3×Q16—21no—
115C2×C3×Q16D411yescharacteristic, complemented
116C2×C3×SD16—21no—
117C2×C3×SD16—21no—
118C2×C3×SD16—21no—
119C2×C3×SD16—22no—
120C2×C3×SD16—21no—
121C2×C3×SD16—21no—
122C2×C3×SD16—21no—
123C2×C3×SD16—21no—
124C2×C3×SD16—21no—
125C2×C3×SD16—21no—
126C2×C3×SD16—41no—
127C2×C3×SD16—41no—
128C2×C3×SD16—41no—
129C2×C3×SD16D411yescharacteristic, complemented
130C2×C3×SD16D411yescharacteristic, complemented
131C2×C3×D8—21no—
132C2×C3×D8—21no—
133C2×C3×D8—21no—
134C2×C3×D8D411yescharacteristic, complemented
135C3×#131—22no—
136C3×#131—41no—
137C2×C3×M16—21no—
138C2×C3×M16C2311yescharacteristic
139C2×C3×M16C2311yescharacteristic
140C2×C3×M16C2311yescharacteristic
141C2×C3×M16C2311yescharacteristic
142C22×C3×C8—21no—
143C22×C3×C8C2311yescharacteristic
144C22×C3×C8C2311yescharacteristic
145C3×C4⋊Q8—21no—
146C3×#127—22no—
147C3×#127—21no—
148C3×#127—41no—
149C3×#124—21no—
150C3×#124—21no—
151C3×#123—41no—
152C3×C22⋊Q8—21no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—21no—
156C3×#121—21no—
157C3×#121—21no—
158C3×#121—21no—
159C3×#121—21no—
160C3×#121—41no—
161C3×#120—41no—
162C3×#117C2311yescharacteristic
163C2×C3×C4⋊C4C2311yescharacteristic
164C2×C3×C42C2311yescharacteristic
165C3×#108—22no—
166C3×#107—21no—
167C3×#106—21no—
168C3×#104—22no—
169C3×#104—22no—
170C3×#104—41no—
171C3×#103—21no—
172C3×#103D411yescharacteristic, complemented
173C3×#103D411yescharacteristic, complemented
174C3×#102—21no—
175C3×#102—21no—
176C3×#102—21no—
177C3×#102—21no—
178C3×#102—21no—
179C3×#102—21no—
180C3×#102—21no—
181C3×#102D411yescharacteristic, complemented
182C3×#102D411yescharacteristic, complemented
183C3×#101—22no—
184C3×#100—41no—
185C3×#100D414yescomplemented
186C3×C22⋊C8—21no—
187C3×C22⋊C8—21no—
188C3×C22⋊C8—21no—
189C3×C22⋊C8—21no—
190C3×#97—21no—
191C3×C4×C8—21no—
192C3×#95—41no—
193C2×H(5,𝔽2)C22×C311yescharacteristic
194C2×#137C22×C311yescharacteristic
195C2×#137C22×C311yescharacteristic, complemented
196C2×AGL(1,ℤ/8)C22×C311yescharacteristic
197C2×AGL(1,ℤ/8)C22×C311yescharacteristic
198C2×AGL(1,ℤ/8)C22×C311yescharacteristic
199C2×#135C22×C311yescharacteristic
200C22×SD16C22×C311yescharacteristic
201C22×SD16C22×C311yescharacteristic, complemented
202C2×#131C22×C311yescharacteristic, complemented
203#537C22×C311yescharacteristic
204#536C22×C311yescharacteristic
205#535C22×C311yescharacteristic, complemented
206C2×#127C22×C311yescharacteristic
207#497—21no—
208#496—21no—
209#495—21no—
210#492—21no—
211#471—24no—
212#469—21no—
213#468—21no—
214#466—21no—
215#465—21no—
216#453—24no—
217#452—21no—
218#452—21no—
219#452—21no—
220#450—21no—
221#450—21no—
222#450—21no—
223#449—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×#102C22×C311yescharacteristic
234C2×#102C22×C311yescharacteristic, complemented
235C2×#101C22×C311yescharacteristic, complemented
236C2×#100C22×C311yescharacteristic
237C2×#100C22×C311yescharacteristic, complemented
238#408C22×C311yescharacteristic
239#408C22×C311yescharacteristic
240#405C22×C311yescharacteristic, complemented
241#391C22×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—44no—
299C2×C3×D4—41no—
300C2×C3×D4—82no—
301C2×C3×D4—82no—
302C2×C3×D4C2×D412yes—
303C2×C3×D4C2×D411yescharacteristic
304C2×C3×D4C2×D411yescharacteristic
305C2×C3×D4C2×D411yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—41no—
313C22×C3×C4C2411yescharacteristic
314C3×Q16—41no—
315C3×Q16—42no—
316C3×Q16—42no—
317C3×SD16—41no—
318C3×SD16—41no—
319C3×SD16—42no—
320C3×SD16—42no—
321C3×SD16—42no—
322C3×SD16—42no—
323C3×SD16—42no—
324C3×SD16—42no—
325C3×SD16—42no—
326C3×SD16—42no—
327C3×SD16—42no—
328C3×D8—41no—
329C3×D8—42no—
330C3×D8—42no—
331C3×D8—42no—
332C3×M16—21no—
333C3×M16—21no—
334C3×M16—21no—
335C3×M16—21no—
336C3×M16—21no—
337C3×M16—21no—
338C3×M16—42no—
339C3×M16C2×D412yes—
340C3×M16C2×D412yes—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—21no—
348C2×C3×C8—21no—
349C2×C3×C8—42no—
350C2×C3×C8C2×D411yescharacteristic
351C2×C3×C8C2×D411yescharacteristic
352C2×C3×C8C2×D411yescharacteristic
353C2×C3×C8C2×D411yescharacteristic
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—41no—
357C3×C4⋊C4—41no—
358C3×C4⋊C4—41no—
359C3×C4⋊C4C2×D411yescharacteristic
360C3×C4⋊C4C2×D411yescharacteristic
361C3×C22⋊C4—21no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—41no—
366C3×C22⋊C4—41no—
367C3×C22⋊C4—41no—
368C3×C42—21no—
369C3×C42—21no—
370C3×C42—21no—
371H(5,𝔽2)—22no—
372H(5,𝔽2)—41no—
373H(5,𝔽2)—41no—
374H(5,𝔽2)—41no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41C23×C311yescharacteristic
378C2×#41C23×C311yescharacteristic
379C2×#41C23×C311yescharacteristic
380C22×Q8C23×C311yescharacteristic
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—41no—
384C22×D4—41no—
385C22×D4C23×C311yescharacteristic
386C22×D4C23×C311yescharacteristic
387#137—22no—
388#137—41no—
389#137—41no—
390#137—41no—
391AGL(1,ℤ/8)—22no—
392AGL(1,ℤ/8)—22no—
393AGL(1,ℤ/8)—22no—
394AGL(1,ℤ/8)—41no—
395AGL(1,ℤ/8)—41no—
396AGL(1,ℤ/8)—41no—
397#135—41no—
398#135—41no—
399C2×Q16—21no—
400C2×Q16—21no—
401C2×Q16C3×D411yescharacteristic, complemented
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—21no—
405C2×SD16—22no—
406C2×SD16—21no—
407C2×SD16—21no—
408C2×SD16—21no—
409C2×SD16—21no—
410C2×SD16—21no—
411C2×SD16—21no—
412C2×SD16—41no—
413C2×SD16—41no—
414C2×SD16—41no—
415C2×SD16C3×D411yescharacteristic, complemented
416C2×SD16C3×D411yescharacteristic, complemented
417C2×D8—21no—
418C2×D8—21no—
419C2×D8—21no—
420C2×D8C3×D411yescharacteristic, complemented
421#131—22no—
422#131—41no—
423C2×M16—21no—
424C2×M16C23×C311yescharacteristic
425C2×M16C23×C311yescharacteristic
426C2×M16C23×C311yescharacteristic
427C2×M16C23×C311yescharacteristic
428C22×C8—21no—
429C22×C8C23×C311yescharacteristic
430C22×C8C23×C311yescharacteristic
431C4⋊Q8—21no—
432#127—22no—
433#127—21no—
434#127—41no—
435#124—21no—
436#124—21no—
437#123—41no—
438C22⋊Q8—21no—
439C22⋊Q8—21no—
440C22⋊Q8—21no—
441C22⋊Q8—21no—
442#121—21no—
443#121—21no—
444#121—21no—
445#121—21no—
446#121—41no—
447#120—41no—
448#117C23×C311yescharacteristic
449C2×C4⋊C4C23×C311yescharacteristic
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#103C3×D411yescharacteristic, complemented
459#103C3×D411yescharacteristic, complemented
460#102—21no—
461#102—21no—
462#102—21no—
463#102—21no—
464#102—21no—
465#102—21no—
466#102—21no—
467#102C3×D411yescharacteristic, complemented
468#102C3×D411yescharacteristic, complemented
469#101—22no—
470#100—41no—
471#100C3×D414yescomplemented
472C22⋊C8—21no—
473C22⋊C8—21no—
474C22⋊C8—21no—
475C22⋊C8—21no—
476#97—21no—
477C4×C8—21no—
478#95—41no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—22no—
483C23×C3—44no—
484C23×C3—41no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—81no—
490C23×C3—81no—
491C23×C3—81no—
492C23×C3—81no—
493C23×C3—161no—
494C23×C3—161no—
495C23×C3H(5,𝔽2)11yescharacteristic
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—41no—
503C3×Q8—41no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—44no—
515C3×D4—44no—
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—41no—
528C3×D4—88no—
529C3×D4—161no—
530C3×D4—161no—
531C3×D4—161no—
532C2×C3×C4—22no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—41no—
539C2×C3×C4—44no—
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—41no—
550C2×C3×C4—41no—
551C2×C3×C4—81no—
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C22×D411yescharacteristic
554C2×C3×C4C22×D411yescharacteristic
555C2×C3×C4H(5,𝔽2)11yescharacteristic
556C2×C3×C4H(5,𝔽2)11yescharacteristic
557C2×C3×C4H(5,𝔽2)11yescharacteristic
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—22no—
563C3×C8—22no—
564C3×C8—41no—
565C3×C8—41no—
566C24—21no—
567C24—21no—
568C24—41no—
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—21no—
580#41—21no—
581#41—42no—
582#41—42no—
583#41—42no—
584#41—42no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8C2×C3×D411yescharacteristic
592C2×Q8C2×C3×D411yescharacteristic
593C2×Q8C2×C3×D411yescharacteristic
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—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—44no—
619C2×D4—41no—
620C2×D4—82no—
621C2×D4—82no—
622C2×D4C2×C3×D412yes—
623C2×D4C2×C3×D411yescharacteristic
624C2×D4C2×C3×D411yescharacteristic
625C2×D4C2×C3×D411yescharacteristic
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—41no—
633C22×C4C24×C311yescharacteristic
634Q16—41no—
635Q16—42no—
636Q16—42no—
637SD16—41no—
638SD16—41no—
639SD16—42no—
640SD16—42no—
641SD16—42no—
642SD16—42no—
643SD16—42no—
644SD16—42no—
645SD16—42no—
646SD16—42no—
647SD16—42no—
648D8—41no—
649D8—42no—
650D8—42no—
651D8—42no—
652M16—21no—
653M16—21no—
654M16—21no—
655M16—21no—
656M16—21no—
657M16—21no—
658M16—42no—
659M16C2×C3×D412yes—
660M16C2×C3×D412yes—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—42no—
670C2×C8C2×C3×D411yescharacteristic
671C2×C8C2×C3×D411yescharacteristic
672C2×C8C2×C3×D411yescharacteristic
673C2×C8C2×C3×D411yescharacteristic
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—41no—
679C4⋊C4C2×C3×D411yescharacteristic
680C4⋊C4C2×C3×D411yescharacteristic
681C22⋊C4—21no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C42—21no—
689C42—21no—
690C42—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—42no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—82no—
704C22×C3—82no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—161no—
711C22×C3—161no—
712C22×C3—164no—
713C22×C3#53511yescharacteristic
714C22×C3D4211yescharacteristic
715C22×C3#56011yescharacteristic
716C3×C4—42no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—81no—
723C3×C4—81no—
724C3×C4#53411yescharacteristic
725C3×C4#53511yescharacteristic
726C3×C4D4211yescharacteristic
727C3×C4D4211yescharacteristic
728C23—21no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—44no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—81no—
739C23—81no—
740C23—81no—
741C23—81no—
742C23—161no—
743C23—161no—
744C23C3×H(5,𝔽2)11yescharacteristic
745Q8—21no—
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754Q8—41no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—21no—
761D4—22no—
762D4—22no—
763D4—44no—
764D4—44no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—88no—
778D4—161no—
779D4—161no—
780D4—161no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—41no—
788C2×C4—44no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—81no—
801C2×C4C22×C3×D411yescharacteristic
802C2×C4C22×C3×D411yescharacteristic
803C2×C4C22×C3×D411yescharacteristic
804C2×C4C3×H(5,𝔽2)11yescharacteristic
805C2×C4C3×H(5,𝔽2)11yescharacteristic
806C2×C4C3×H(5,𝔽2)11yescharacteristic
807C8—21no—
808C8—21no—
809C8—21no—
810C8—21no—
811C8—22no—
812C8—22no—
813C8—41no—
814C8—41no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—81no—
818C2×C3—81no—
819C2×C3—81no—
820C2×C3—82no—
821C2×C3—161no—
822C2×C3#266911yescharacteristic
823C2×C3#328811yescharacteristic
824C2×C3#329111yescharacteristic
825C22—21no—
826C22—21no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—82no—
838C22—82no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—161no—
845C22—161no—
846C22—164no—
847C22C3×#53511yescharacteristic
848C22C3×D4211yescharacteristic
849C22C3×#56011yescharacteristic
850C4—42no—
851C4—41no—
852C4—41no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—81no—
857C4—81no—
858C4C3×#53411yescharacteristic
859C4C3×#53511yescharacteristic
860C4C3×D4211yescharacteristic
861C4C3×D4211yescharacteristic
862C3#3048011yescharacteristic, direct product factor, Sylow
863C2—21no—
864C2—21no—
865C2—81no—
866C2—81no—
867C2—81no—
868C2—82no—
869C2—161no—
870C2C3×#266911yescharacteristic
871C2C3×#328811yescharacteristic
872C2C3×#329111yescharacteristic
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×#471C2semidirect
3. C3×#3062C2semidirect
4. C2×C3×#453C2semidirect
5. C3×#3012C2semidirect
6. C3×#3009C2semidirect
7. C3×#2051C2semidirect
8. C3×#2038C2semidirect
9. C3×#2019C2semidirect
10. C3×#2014C2semidirect
11. C3×#2007C2semidirect
12. C3×#2002C2semidirect
13. C3×#1931C2semidirect
14. C3×#1929C2semidirect
15. C3×#1876C2semidirect
16. #30480C3direct (N × H)
19. C2×C3×#137C22semidirect
25. C22×C3×SD16C22semidirect
26. C2×C3×#131C22semidirect
29. C3×#535C22semidirect
49. C2×C3×#108C22semidirect
50. C3×#428C22semidirect
53. C2×C3×#104C22semidirect
58. C2×C3×#102C22semidirect
59. C2×C3×#101C22semidirect
61. C2×C3×#100C22semidirect
64. C3×#405C22semidirect
65. C3×#391C22semidirect
66. C3×#343C22semidirect
67. C3×#341C22semidirect
68. C3×#339C22semidirect
69. C3×#336C22semidirect
70. #3154C2×C3semidirect
71. C2×#471C2×C3semidirect
72. #3062C2×C3semidirect
73. C2×#453C2×C3semidirect
74. #3012C2×C3semidirect
75. #3009C2×C3semidirect
76. #2051C2×C3semidirect
77. #2038C2×C3semidirect
78. #2019C2×C3semidirect
79. #2014C2×C3semidirect
80. #2007C2×C3semidirect
81. #2002C2×C3semidirect
82. #1931C2×C3semidirect
83. #1929C2×C3semidirect
84. #1876C2×C3semidirect
115. C2×C3×Q16D4semidirect
129. C2×C3×SD16D4semidirect
130. C2×C3×SD16D4semidirect
134. C2×C3×D8D4semidirect
172. C3×#103D4semidirect
173. C3×#103D4semidirect
181. C3×#102D4semidirect
182. C3×#102D4semidirect
185. C3×#100D4semidirect
195. C2×#137C22×C3semidirect
201. C22×SD16C22×C3semidirect
202. C2×#131C22×C3semidirect
205. #535C22×C3semidirect
225. C2×#108C22×C3semidirect
226. #428C22×C3semidirect
229. C2×#104C22×C3semidirect
234. C2×#102C22×C3semidirect
235. C2×#101C22×C3semidirect
237. C2×#100C22×C3semidirect
240. #405C22×C3semidirect
241. #391C22×C3semidirect
242. #343C22×C3semidirect
243. #341C22×C3semidirect
244. #339C22×C3semidirect
245. #336C22×C3semidirect
401. C2×Q16C3×D4semidirect
415. C2×SD16C3×D4semidirect
416. C2×SD16C3×D4semidirect
420. C2×D8C3×D4semidirect
458. #103C3×D4semidirect
459. #103C3×D4semidirect
467. #102C3×D4semidirect
468. #102C3×D4semidirect
471. #100C3×D4semidirect
862. C3#30480direct (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×#4712
C3×#30622
C2×C3×#4532
C3×#30122
C3×#30092
C3×#20512
C3×#20382
C3×#20192
C3×#20142
C3×#20072
C3×#20022
C3×#19312
C3×#19292
C3×#18762
#304803