Finite Group Databasebeta

← C3×#30476 #10649083

Subgroups — C3×#30476 #10649083

Order 768.

1082 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3155C211yesmaximal, characteristic, complemented
2C2×C3×#472C211yesmaximal, characteristic, complemented
3C3×#3062C211yesmaximal, characteristic, complemented
4C2×C3×#453C211yesmaximal, characteristic, complemented
5C3×#3012C211yesmaximal, characteristic, complemented
6C3×#3008C211yesmaximal, characteristic, complemented
7C3×#2051C211yesmaximal, characteristic, complemented
8C3×#2037C211yesmaximal, characteristic, complemented
9C3×#2018C211yesmaximal, characteristic, complemented
10C3×#2011C211yesmaximal, characteristic, complemented
11C3×#2006C211yesmaximal, characteristic, complemented
12C3×#2002C211yesmaximal, characteristic, complemented
13C3×#1931C211yesmaximal, characteristic, complemented
14C3×#1929C211yesmaximal, characteristic, complemented
15C3×#1876C211yesmaximal, characteristic, complemented
16#30476C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×H(5,𝔽2)C2211yescharacteristic
18C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
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×D8C2211yescharacteristic
25C22×C3×D8C2211yescharacteristic, complemented
26C2×C3×#131C2211yescharacteristic, complemented
27C3×#537C2211yescharacteristic
28C3×#535C2211yescharacteristic
29C3×#535C2211yescharacteristic, complemented
30C2×C3×#127C2211yescharacteristic
31C3×#496—21no—
32C3×#496—21no—
33C3×#495—21no—
34C3×#493—21no—
35C3×#472—24no—
36C3×#469—21no—
37C3×#468—21no—
38C3×#466—21no—
39C3×#465—21no—
40C3×#453—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×#102C2211yescharacteristic
58C2×C3×#102C2211yescharacteristic, complemented
59C2×C3×#100C2211yescharacteristic
60C2×C3×#100C2211yescharacteristic, complemented
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#3155C2×C311yescharacteristic, complemented
71C2×#472C2×C311yescharacteristic, complemented
72#3062C2×C311yescharacteristic, complemented
73C2×#453C2×C311yescharacteristic, complemented
74#3012C2×C311yescharacteristic, complemented
75#3008C2×C311yescharacteristic, complemented
76#2051C2×C311yescharacteristic, complemented
77#2037C2×C311yescharacteristic, complemented
78#2018C2×C311yescharacteristic, complemented
79#2011C2×C311yescharacteristic, complemented
80#2006C2×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×D4—21no—
95C22×C3×D4—21no—
96C22×C3×D4—41no—
97C22×C3×D4—41no—
98C22×C3×D4C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C3×AGL(1,ℤ/8)—22no—
102C3×AGL(1,ℤ/8)—22no—
103C3×AGL(1,ℤ/8)—22no—
104C3×AGL(1,ℤ/8)—22no—
105C3×AGL(1,ℤ/8)—41no—
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×AGL(1,ℤ/8)—41no—
111C3×#135—41no—
112C3×#135—41no—
113C2×C3×Q16D411yescharacteristic, complemented
114C2×C3×SD16—21no—
115C2×C3×SD16—21no—
116C2×C3×SD16—21no—
117C2×C3×SD16—21no—
118C2×C3×SD16—21no—
119C2×C3×SD16D411yescharacteristic, complemented
120C2×C3×SD16D411yescharacteristic, complemented
121C2×C3×D8—22no—
122C2×C3×D8—21no—
123C2×C3×D8—21no—
124C2×C3×D8—21no—
125C2×C3×D8—21no—
126C2×C3×D8—21no—
127C2×C3×D8—21no—
128C2×C3×D8—21no—
129C2×C3×D8—21no—
130C2×C3×D8—21no—
131C2×C3×D8—41no—
132C2×C3×D8—41no—
133C2×C3×D8—41no—
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×#127—22no—
146C3×#127—21no—
147C3×#127—21no—
148C3×#127—41no—
149C3×#124—21no—
150C3×#124—21no—
151C3×C22⋊Q8—21no—
152C3×C22⋊Q8—21no—
153C3×#121—21no—
154C3×#121—21no—
155C3×#121—21no—
156C3×#121—21no—
157C3×#121—21no—
158C3×#121—21no—
159C3×#121—41no—
160C3×#120—41no—
161C3×#120—41no—
162C3×#117C2311yescharacteristic
163C2×C3×C4⋊C4C2311yescharacteristic
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×#103D411yescharacteristic, complemented
174C3×#103D411yescharacteristic, complemented
175C3×#102—21no—
176C3×#102—21no—
177C3×#102—21no—
178C3×#102—21no—
179C3×#102—21no—
180C3×#102—21no—
181C3×#102—21no—
182C3×#102D411yescharacteristic, complemented
183C3×#102D411yescharacteristic, complemented
184C3×#100—22no—
185C3×#100—41no—
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×AGL(1,ℤ/8)C22×C311yescharacteristic
195C2×AGL(1,ℤ/8)C22×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×D8C22×C311yescharacteristic
201C22×D8C22×C311yescharacteristic, complemented
202C2×#131C22×C311yescharacteristic, complemented
203#537C22×C311yescharacteristic
204#535C22×C311yescharacteristic
205#535C22×C311yescharacteristic, complemented
206C2×#127C22×C311yescharacteristic
207#496—21no—
208#496—21no—
209#495—21no—
210#493—21no—
211#472—24no—
212#469—21no—
213#468—21no—
214#466—21no—
215#465—21no—
216#453—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×#102C22×C311yescharacteristic
234C2×#102C22×C311yescharacteristic, complemented
235C2×#100C22×C311yescharacteristic
236C2×#100C22×C311yescharacteristic, complemented
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—21no—
249C24×C3—41no—
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—21no—
262C3×#41—42no—
263C3×#41—42no—
264C3×#41—42no—
265C3×#41—42no—
266C2×C3×Q8C2×D411yescharacteristic
267C2×C3×Q8C2×D411yescharacteristic
268C2×C3×Q8C2×D411yescharacteristic
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—21no—
273C2×C3×D4—21no—
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—21no—
289C2×C3×D4—41no—
290C2×C3×D4—41no—
291C2×C3×D4—41no—
292C2×C3×D4—41no—
293C2×C3×D4—41no—
294C2×C3×D4—41no—
295C2×C3×D4—42no—
296C2×C3×D4—42no—
297C2×C3×D4—42no—
298C2×C3×D4—42no—
299C2×C3×D4—44no—
300C2×C3×D4—44no—
301C2×C3×D4—44no—
302C2×C3×D4—41no—
303C2×C3×D4—82no—
304C2×C3×D4—82no—
305C2×C3×D4C2×D412yes—
306C2×C3×D4C2×D411yescharacteristic
307C2×C3×D4C2×D411yescharacteristic
308C2×C3×D4C2×D411yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—41no—
315C22×C3×C4C2411yescharacteristic
316C3×Q16—41no—
317C3×SD16—41no—
318C3×SD16—41no—
319C3×SD16—42no—
320C3×SD16—42no—
321C3×SD16—42no—
322C3×SD16—42no—
323C3×SD16—42no—
324C3×D8—41no—
325C3×D8—42no—
326C3×D8—42no—
327C3×D8—42no—
328C3×D8—42no—
329C3×D8—42no—
330C3×D8—42no—
331C3×D8—42no—
332C3×D8—42no—
333C3×D8—42no—
334C3×M16—21no—
335C3×M16—21no—
336C3×M16—21no—
337C3×M16—21no—
338C3×M16—21no—
339C3×M16—21no—
340C3×M16—42no—
341C3×M16C2×D412yes—
342C3×M16C2×D412yes—
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—21no—
350C2×C3×C8—21no—
351C2×C3×C8—42no—
352C2×C3×C8C2×D411yescharacteristic
353C2×C3×C8C2×D411yescharacteristic
354C2×C3×C8C2×D411yescharacteristic
355C2×C3×C8C2×D411yescharacteristic
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
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×C22⋊C4—82no—
369C3×C42—21no—
370C3×C42—21no—
371C3×C42—21no—
372H(5,𝔽2)—22no—
373H(5,𝔽2)—41no—
374H(5,𝔽2)—41no—
375H(5,𝔽2)—41no—
376C2×#41—21no—
377C2×#41—21no—
378C2×#41C23×C311yescharacteristic
379C2×#41C23×C311yescharacteristic
380C2×#41C23×C311yescharacteristic
381C22×D4—21no—
382C22×D4—21no—
383C22×D4—41no—
384C22×D4—41no—
385C22×D4C23×C311yescharacteristic
386C22×D4C23×C311yescharacteristic
387C22×D4C23×C311yescharacteristic
388AGL(1,ℤ/8)—22no—
389AGL(1,ℤ/8)—22no—
390AGL(1,ℤ/8)—22no—
391AGL(1,ℤ/8)—22no—
392AGL(1,ℤ/8)—41no—
393AGL(1,ℤ/8)—41no—
394AGL(1,ℤ/8)—41no—
395AGL(1,ℤ/8)—41no—
396AGL(1,ℤ/8)—41no—
397AGL(1,ℤ/8)—41no—
398#135—41no—
399#135—41no—
400C2×Q16C3×D411yescharacteristic, complemented
401C2×SD16—21no—
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—21no—
405C2×SD16—21no—
406C2×SD16C3×D411yescharacteristic, complemented
407C2×SD16C3×D411yescharacteristic, complemented
408C2×D8—22no—
409C2×D8—21no—
410C2×D8—21no—
411C2×D8—21no—
412C2×D8—21no—
413C2×D8—21no—
414C2×D8—21no—
415C2×D8—21no—
416C2×D8—21no—
417C2×D8—21no—
418C2×D8—41no—
419C2×D8—41no—
420C2×D8—41no—
421C2×D8C3×D411yescharacteristic, complemented
422#131—22no—
423#131—41no—
424C2×M16—21no—
425C2×M16C23×C311yescharacteristic
426C2×M16C23×C311yescharacteristic
427C2×M16C23×C311yescharacteristic
428C2×M16C23×C311yescharacteristic
429C22×C8—21no—
430C22×C8C23×C311yescharacteristic
431C22×C8C23×C311yescharacteristic
432#127—22no—
433#127—21no—
434#127—21no—
435#127—41no—
436#124—21no—
437#124—21no—
438C22⋊Q8—21no—
439C22⋊Q8—21no—
440#121—21no—
441#121—21no—
442#121—21no—
443#121—21no—
444#121—21no—
445#121—21no—
446#121—41no—
447#120—41no—
448#120—41no—
449#117C23×C311yescharacteristic
450C2×C4⋊C4C23×C311yescharacteristic
451C2×C22⋊C4—41no—
452C2×C42C23×C311yescharacteristic
453#108—22no—
454#107—21no—
455#106—21no—
456#104—22no—
457#104—22no—
458#104—41no—
459#103—21no—
460#103C3×D411yescharacteristic, complemented
461#103C3×D411yescharacteristic, complemented
462#102—21no—
463#102—21no—
464#102—21no—
465#102—21no—
466#102—21no—
467#102—21no—
468#102—21no—
469#102C3×D411yescharacteristic, complemented
470#102C3×D411yescharacteristic, complemented
471#100—22no—
472#100—41no—
473#100C3×D414yescomplemented
474C22⋊C8—21no—
475C22⋊C8—21no—
476C22⋊C8—21no—
477C22⋊C8—21no—
478#97—21no—
479C4×C8—21no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—21no—
483C23×C3—22no—
484C23×C3—44no—
485C23×C3—41no—
486C23×C3—41no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—41no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—41no—
493C23×C3—81no—
494C23×C3—81no—
495C23×C3—81no—
496C23×C3—81no—
497C23×C3—81no—
498C23×C3—81no—
499C23×C3—161no—
500C23×C3—161no—
501C23×C3H(5,𝔽2)11yescharacteristic
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—22no—
516C3×D4—44no—
517C3×D4—44no—
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—41no—
529C3×D4—41no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—41no—
533C3×D4—41no—
534C3×D4—88no—
535C3×D4—161no—
536C3×D4—161no—
537C3×D4—161no—
538C3×D4—161no—
539C3×D4—161no—
540C2×C3×C4—22no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—41no—
547C2×C3×C4—44no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—41no—
556C2×C3×C4—81no—
557C2×C3×C4C22×D411yescharacteristic
558C2×C3×C4C22×D411yescharacteristic
559C2×C3×C4C22×D411yescharacteristic
560C2×C3×C4H(5,𝔽2)11yescharacteristic
561C2×C3×C4H(5,𝔽2)11yescharacteristic
562C2×C3×C4H(5,𝔽2)11yescharacteristic
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—22no—
568C3×C8—22no—
569C3×C8—41no—
570C3×C8—41no—
571C24—21no—
572C24—21no—
573C24—21no—
574C24—41no—
575#41—21no—
576#41—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—42no—
588#41—42no—
589#41—42no—
590#41—42no—
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—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—41no—
628C2×D4—82no—
629C2×D4—82no—
630C2×D4C2×C3×D412yes—
631C2×D4C2×C3×D411yescharacteristic
632C2×D4C2×C3×D411yescharacteristic
633C2×D4C2×C3×D411yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—41no—
640C22×C4C24×C311yescharacteristic
641Q16—41no—
642SD16—41no—
643SD16—41no—
644SD16—42no—
645SD16—42no—
646SD16—42no—
647SD16—42no—
648SD16—42no—
649D8—41no—
650D8—42no—
651D8—42no—
652D8—42no—
653D8—42no—
654D8—42no—
655D8—42no—
656D8—42no—
657D8—42no—
658D8—42no—
659M16—21no—
660M16—21no—
661M16—21no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—42no—
666M16C2×C3×D412yes—
667M16C2×C3×D412yes—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—42no—
677C2×C8C2×C3×D411yescharacteristic
678C2×C8C2×C3×D411yescharacteristic
679C2×C8C2×C3×D411yescharacteristic
680C2×C8C2×C3×D411yescharacteristic
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—41no—
684C4⋊C4C2×C3×D411yescharacteristic
685C4⋊C4C2×C3×D411yescharacteristic
686C22⋊C4—21no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—41no—
691C22⋊C4—41no—
692C22⋊C4—41no—
693C22⋊C4—82no—
694C42—21no—
695C42—21no—
696C42—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—42no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—82no—
710C22×C3—82no—
711C22×C3—82no—
712C22×C3—81no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—81no—
720C22×C3—161no—
721C22×C3—161no—
722C22×C3—161no—
723C22×C3—164no—
724C22×C3#53511yescharacteristic
725C22×C3D4211yescharacteristic
726C22×C3#56011yescharacteristic
727C3×C4—42no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4—41no—
731C3×C4—41no—
732C3×C4—41no—
733C3×C4—81no—
734C3×C4#53411yescharacteristic
735C3×C4#53511yescharacteristic
736C3×C4D4211yescharacteristic
737C3×C4D4211yescharacteristic
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—44no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—81no—
752C23—81no—
753C23—81no—
754C23—81no—
755C23—81no—
756C23—81no—
757C23—161no—
758C23—161no—
759C23C3×H(5,𝔽2)11yescharacteristic
760Q8—21no—
761Q8—21no—
762Q8—21no—
763Q8—21no—
764Q8—21no—
765Q8—21no—
766D4—21no—
767D4—21no—
768D4—21no—
769D4—21no—
770D4—22no—
771D4—21no—
772D4—21no—
773D4—22no—
774D4—44no—
775D4—44no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—88no—
793D4—161no—
794D4—161no—
795D4—161no—
796D4—161no—
797D4—161no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—41no—
805C2×C4—44no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—81no—
815C2×C4C22×C3×D411yescharacteristic
816C2×C4C22×C3×D411yescharacteristic
817C2×C4C22×C3×D411yescharacteristic
818C2×C4C3×H(5,𝔽2)11yescharacteristic
819C2×C4C3×H(5,𝔽2)11yescharacteristic
820C2×C4C3×H(5,𝔽2)11yescharacteristic
821C8—21no—
822C8—21no—
823C8—21no—
824C8—21no—
825C8—22no—
826C8—22no—
827C8—41no—
828C8—41no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—81no—
832C2×C3—81no—
833C2×C3—81no—
834C2×C3—82no—
835C2×C3—161no—
836C2×C3—161no—
837C2×C3#266911yescharacteristic
838C2×C3#328811yescharacteristic
839C2×C3#329211yescharacteristic
840C22—21no—
841C22—21no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—161no—
864C22—161no—
865C22—161no—
866C22—164no—
867C22C3×#53511yescharacteristic
868C22C3×D4211yescharacteristic
869C22C3×#56011yescharacteristic
870C4—42no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—81no—
877C4C3×#53411yescharacteristic
878C4C3×#53511yescharacteristic
879C4C3×D4211yescharacteristic
880C4C3×D4211yescharacteristic
881C3#3047611yescharacteristic, direct product factor, Sylow
882C2—21no—
883C2—21no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—82no—
888C2—161no—
889C2—161no—
890C2C3×#266911yescharacteristic
891C2C3×#328811yescharacteristic
892C2C3×#329211yescharacteristic
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×#3155C2semidirect
2. C2×C3×#472C2semidirect
3. C3×#3062C2semidirect
4. C2×C3×#453C2semidirect
5. C3×#3012C2semidirect
6. C3×#3008C2semidirect
7. C3×#2051C2semidirect
8. C3×#2037C2semidirect
9. C3×#2018C2semidirect
10. C3×#2011C2semidirect
11. C3×#2006C2semidirect
12. C3×#2002C2semidirect
13. C3×#1931C2semidirect
14. C3×#1929C2semidirect
15. C3×#1876C2semidirect
16. #30476C3direct (N × H)
22. C2×C3×AGL(1,ℤ/8)C22semidirect
25. C22×C3×D8C22semidirect
26. C2×C3×#131C22semidirect
29. C3×#535C22semidirect
49. C2×C3×#108C22semidirect
50. C3×#428C22semidirect
53. C2×C3×#104C22semidirect
58. C2×C3×#102C22semidirect
60. C2×C3×#100C22semidirect
61. C2×C3×#100C22semidirect
64. C3×#405C22semidirect
65. C3×#390C22semidirect
66. C3×#343C22semidirect
67. C3×#341C22semidirect
68. C3×#339C22semidirect
69. C3×#336C22semidirect
70. #3155C2×C3semidirect
71. C2×#472C2×C3semidirect
72. #3062C2×C3semidirect
73. C2×#453C2×C3semidirect
74. #3012C2×C3semidirect
75. #3008C2×C3semidirect
76. #2051C2×C3semidirect
77. #2037C2×C3semidirect
78. #2018C2×C3semidirect
79. #2011C2×C3semidirect
80. #2006C2×C3semidirect
81. #2002C2×C3semidirect
82. #1931C2×C3semidirect
83. #1929C2×C3semidirect
84. #1876C2×C3semidirect
113. C2×C3×Q16D4semidirect
119. C2×C3×SD16D4semidirect
120. C2×C3×SD16D4semidirect
134. C2×C3×D8D4semidirect
173. C3×#103D4semidirect
174. C3×#103D4semidirect
182. C3×#102D4semidirect
183. C3×#102D4semidirect
186. C3×#100D4semidirect
198. C2×AGL(1,ℤ/8)C22×C3semidirect
201. C22×D8C22×C3semidirect
202. C2×#131C22×C3semidirect
205. #535C22×C3semidirect
225. C2×#108C22×C3semidirect
226. #428C22×C3semidirect
229. C2×#104C22×C3semidirect
234. C2×#102C22×C3semidirect
236. C2×#100C22×C3semidirect
237. C2×#100C22×C3semidirect
240. #405C22×C3semidirect
241. #390C22×C3semidirect
242. #343C22×C3semidirect
243. #341C22×C3semidirect
244. #339C22×C3semidirect
245. #336C22×C3semidirect
400. C2×Q16C3×D4semidirect
406. C2×SD16C3×D4semidirect
407. C2×SD16C3×D4semidirect
421. C2×D8C3×D4semidirect
460. #103C3×D4semidirect
461. #103C3×D4semidirect
469. #102C3×D4semidirect
470. #102C3×D4semidirect
473. #100C3×D4semidirect
881. C3#30476direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#31552
C2×C3×#4722
C3×#30622
C2×C3×#4532
C3×#30122
C3×#30082
C3×#20512
C3×#20372
C3×#20182
C3×#20112
C3×#20062
C3×#20022
C3×#19312
C3×#19292
C3×#18762
#304763