Finite Group Databasebeta

← C3×#30417 #10649024

Subgroups — C3×#30417 #10649024

Order 768.

1086 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#468C211yesmaximal, characteristic, complemented
2C2×C3×#449C211yesmaximal, characteristic, complemented
3C3×#2537C211yesmaximal, characteristic, complemented
4C3×#2407C211yesmaximal, characteristic, complemented
5C3×#2093C211yesmaximal, characteristic, complemented
6C3×#2076C211yesmaximal, characteristic, complemented
7C3×#2072C211yesmaximal, characteristic, complemented
8C3×#2036C211yesmaximal, characteristic, complemented
9C3×#2033C211yesmaximal, characteristic, complemented
10C3×#1999C211yesmaximal, characteristic, complemented
11C3×#1895C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1877C211yesmaximal, characteristic, complemented
14C3×#1870C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#30417C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#121—21no—
23C2×C3×#121C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C3×#468—24no—
29C3×#449—24no—
30C2×C3×#107C2211yescharacteristic
31C2×C3×#107C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic
42C2×C3×C22⋊C8C2211yescharacteristic
43C3×#394—21no—
44C3×#394—21no—
45C3×#394—21no—
46C3×#392—21no—
47C3×#391C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#386—21no—
50C3×#385—21no—
51C3×#384C2211yescharacteristic
52C3×#380—21no—
53C3×#380C2211yescharacteristic
54C3×#380C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#468C2×C311yescharacteristic, complemented
63C2×#449C2×C311yescharacteristic, complemented
64#2537C2×C311yescharacteristic, complemented
65#2407C2×C311yescharacteristic, complemented
66#2093C2×C311yescharacteristic, complemented
67#2076C2×C311yescharacteristic, complemented
68#2072C2×C311yescharacteristic, complemented
69#2036C2×C311yescharacteristic, complemented
70#2033C2×C311yescharacteristic, complemented
71#1999C2×C311yescharacteristic, complemented
72#1895C2×C311yescharacteristic, complemented
73#1879C2×C311yescharacteristic, complemented
74#1877C2×C311yescharacteristic, complemented
75#1870C2×C311yescharacteristic, complemented
76#1788C2×C311yescharacteristic, complemented
77C2×C3×#41—22no—
78C2×C3×#41—22no—
79C2×C3×#41—41no—
80C2×C3×#41—41no—
81C2×C3×#41—41no—
82C2×C3×#41—41no—
83C22×C3×Q8C2311yescharacteristic
84C22×C3×D4—21no—
85C22×C3×D4—21no—
86C22×C3×D4—21no—
87C22×C3×D4—21no—
88C22×C3×D4D411yescharacteristic
89C22×C3×D4C2311yescharacteristic
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4—21no—
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C2×C3×SD16—41no—
96C2×C3×SD16—41no—
97C2×C3×SD16D414yescomplemented
98C2×C3×D8—22no—
99C2×C3×D8—22no—
100C2×C3×D8—41no—
101C2×C3×M16—22no—
102C2×C3×M16—41no—
103C2×C3×M16—41no—
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—41no—
110C3×#121—22no—
111C3×#121—22no—
112C3×#121—22no—
113C3×#121—41no—
114C3×#121—41no—
115C3×#121—41no—
116C3×#121—44no—
117C3×C4×D4—41no—
118C3×C4×D4—41no—
119C3×C4×D4—41no—
120C3×C4×D4—41no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4D411yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4D411yescharacteristic
141C2×C3×C22⋊C4D411yescharacteristic
142C2×C3×C42C2311yescharacteristic
143C3×#107—22no—
144C3×#107—41no—
145C3×#103—22no—
146C3×#103—22no—
147C3×#103—41no—
148C3×#102—22no—
149C3×#102—22no—
150C3×#102—41no—
151C3×#102—41no—
152C3×#102—41no—
153C3×C22⋊C8—22no—
154C3×C22⋊C8—41no—
155C3×C22⋊C8—41no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C22×#41C22×C311yescharacteristic
162C22×SD16C22×C311yescharacteristic
163C22×D8C22×C311yescharacteristic
164C22×M16C22×C311yescharacteristic
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×#121—21no—
167C2×#121C22×C311yescharacteristic
168C2×#121C22×C311yescharacteristic
169C2×#121C22×C311yescharacteristic
170C2×C4×D4C22×C311yescharacteristic
171C2×C4×D4C22×C311yescharacteristic
172#468—24no—
173#449—24no—
174C2×#107C22×C311yescharacteristic
175C2×#107C22×C311yescharacteristic
176C2×#103C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×#102C22×C311yescharacteristic
184C2×C22⋊C8C22×C311yescharacteristic
185C2×C22⋊C8C22×C311yescharacteristic
186C2×C22⋊C8C22×C311yescharacteristic
187#394—21no—
188#394—21no—
189#394—21no—
190#392—21no—
191#391C22×C311yescharacteristic
192#390C22×C311yescharacteristic
193#386—21no—
194#385—21no—
195#384C22×C311yescharacteristic
196#380—21no—
197#380C22×C311yescharacteristic
198#380C22×C311yescharacteristic
199#380C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#340C22×C311yescharacteristic
202#340C22×C311yescharacteristic
203#340C22×C311yescharacteristic
204#336C22×C311yescharacteristic
205#336C22×C311yescharacteristic
206C24×C3—21no—
207C24×C3—21no—
208C24×C3C2×D411yescharacteristic
209C24×C3C2×D411yescharacteristic
210C3×#41—44no—
211C3×#41—44no—
212C3×#41—44no—
213C3×#41—44no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8C2×D412yes—
220C2×C3×D4—22no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—41no—
232C2×C3×D4—41no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—42no—
241C2×C3×D4—42no—
242C2×C3×D4—81no—
243C2×C3×D4—81no—
244C2×C3×D4—81no—
245C2×C3×D4C2×D412yes—
246C2×C3×D4#4112yes—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—42no—
266C22×C3×C4—42no—
267C22×C3×C4—42no—
268C22×C3×C4—42no—
269C22×C3×C4—42no—
270C22×C3×C4—42no—
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C3×SD16—44no—
277C3×D8—44no—
278C3×M16—44no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8C2×D412yes—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—41no—
302C3×C4⋊C4—42no—
303C3×C4⋊C4—42no—
304C3×C4⋊C4—81no—
305C3×C22⋊C4—41no—
306C3×C22⋊C4—41no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—42no—
309C3×C22⋊C4—42no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—42no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—81no—
316C3×C22⋊C4—81no—
317C3×C42—21no—
318C3×C42—21no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—41no—
322C2×#41—41no—
323C2×#41—41no—
324C2×#41—41no—
325C22×Q8C23×C311yescharacteristic
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4C3×D411yescharacteristic
331C22×D4C23×C311yescharacteristic
332C22×D4C23×C311yescharacteristic
333C23×C4—21no—
334C23×C4—21no—
335C23×C4C23×C311yescharacteristic
336C23×C4C23×C311yescharacteristic
337C2×SD16—41no—
338C2×SD16—41no—
339C2×SD16C3×D414yescomplemented
340C2×D8—22no—
341C2×D8—22no—
342C2×D8—41no—
343C2×M16—22no—
344C2×M16—41no—
345C2×M16—41no—
346C22×C8C23×C311yescharacteristic
347C22×C8C23×C311yescharacteristic
348C22×C8C23×C311yescharacteristic
349C22×C8C23×C311yescharacteristic
350C22⋊Q8—22no—
351C22⋊Q8—41no—
352#121—22no—
353#121—22no—
354#121—22no—
355#121—41no—
356#121—41no—
357#121—41no—
358#121—44no—
359C4×D4—41no—
360C4×D4—41no—
361C4×D4—41no—
362C4×D4—41no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4C3×D411yescharacteristic
367C2×C4⋊C4C23×C311yescharacteristic
368C2×C4⋊C4C23×C311yescharacteristic
369C2×C4⋊C4C23×C311yescharacteristic
370C2×C4⋊C4C23×C311yescharacteristic
371C2×C4⋊C4C23×C311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4C3×D411yescharacteristic
383C2×C22⋊C4C3×D411yescharacteristic
384C2×C42C23×C311yescharacteristic
385#107—22no—
386#107—41no—
387#103—22no—
388#103—22no—
389#103—41no—
390#102—22no—
391#102—22no—
392#102—41no—
393#102—41no—
394#102—41no—
395C22⋊C8—22no—
396C22⋊C8—41no—
397C22⋊C8—41no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—21no—
408C23×C3—22no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3C22×D411yescharacteristic
432C3×Q8—22no—
433C3×Q8—22no—
434C3×Q8—41no—
435C3×Q8—41no—
436C3×D4—22no—
437C3×D4—22no—
438C3×D4—22no—
439C3×D4—22no—
440C3×D4—44no—
441C3×D4—48no—
442C3×D4—41no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4—41no—
446C3×D4—84no—
447C3×D4—84no—
448C3×D4—84no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—48no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—84no—
488C2×C3×C4AGL(1,ℤ/8)12yes—
489C2×C3×C4C22×D411yescharacteristic
490C2×C3×C4C2×#4111yescharacteristic
491C2×C3×C4H(5,𝔽2)11yescharacteristic
492C2×C3×C4H(5,𝔽2)11yescharacteristic
493C2×C3×C4H(5,𝔽2)11yescharacteristic
494C2×C3×C4H(5,𝔽2)11yescharacteristic
495C3×C8—22no—
496C3×C8—41no—
497C3×C8—41no—
498C3×C8—41no—
499C24—21no—
500C24—21no—
501C24C2×C3×D411yescharacteristic
502C24C2×C3×D411yescharacteristic
503#41—44no—
504#41—44no—
505#41—44no—
506#41—44no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8C2×C3×D412yes—
513C2×D4—22no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—81no—
536C2×D4—81no—
537C2×D4—81no—
538C2×D4C2×C3×D412yes—
539C2×D4C3×#4112yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4C2×C3×D411yescharacteristic
565C22×C4C2×C3×D411yescharacteristic
566C22×C4C2×C3×D411yescharacteristic
567C22×C4C2×C3×D411yescharacteristic
568C22×C4C24×C311yescharacteristic
569SD16—44no—
570D8—44no—
571M16—44no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8C2×C3×D412yes—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—41no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—81no—
598C22⋊C4—41no—
599C22⋊C4—41no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C42—21no—
611C42—21no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—42no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—42no—
629C22×C3—41no—
630C22×C3—42no—
631C22×C3—41no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—81no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3#53411yescharacteristic
641C22×C3D4211yescharacteristic
642C22×C3#54611yescharacteristic
643C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
644C22×C3#57511yescharacteristic
645C22×C3#57611yescharacteristic
646C22×C3#57811yescharacteristic
647C3×C4—22no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—42no—
651C3×C4—41no—
652C3×C4—81no—
653C3×C4—81no—
654C3×C4—81no—
655C3×C4—81no—
656C3×C4—81no—
657C3×C4#53411yescharacteristic
658C3×C4#53811yescharacteristic
659C3×C4#54611yescharacteristic
660C3×C4#56011yescharacteristic
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—21no—
674C23—22no—
675C23—21no—
676C23—21no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23C22×C3×D411yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—41no—
693Q8—41no—
694D4—22no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—44no—
699D4—48no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—84no—
705D4—84no—
706D4—84no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—48no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—84no—
746C2×C4C3×AGL(1,ℤ/8)12yes—
747C2×C4C22×C3×D411yescharacteristic
748C2×C4C2×C3×#4111yescharacteristic
749C2×C4C3×H(5,𝔽2)11yescharacteristic
750C2×C4C3×H(5,𝔽2)11yescharacteristic
751C2×C4C3×H(5,𝔽2)11yescharacteristic
752C2×C4C3×H(5,𝔽2)11yescharacteristic
753C8—22no—
754C8—41no—
755C8—41no—
756C8—41no—
757C2×C3—81no—
758C2×C3—81no—
759C2×C3—82no—
760C2×C3—82no—
761C2×C3#266811yescharacteristic
762C2×C3#319411yescharacteristic
763C2×C3#320311yescharacteristic
764C2×C3#326911yescharacteristic
765C2×C3#327411yescharacteristic
766C2×C3#331911yescharacteristic
767C2×C3#333011yescharacteristic
768C22—42no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—41no—
781C22—42no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22C3×#53411yescharacteristic
797C22C3×D4211yescharacteristic
798C22C3×#54611yescharacteristic
799C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
800C22C3×#57511yescharacteristic
801C22C3×#57611yescharacteristic
802C22C3×#57811yescharacteristic
803C4—22no—
804C4—41no—
805C4—41no—
806C4—42no—
807C4—41no—
808C4—81no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4—81no—
813C4C3×#53411yescharacteristic
814C4C3×#53811yescharacteristic
815C4C3×#54611yescharacteristic
816C4C3×#56011yescharacteristic
817C3#3041711yescharacteristic, direct product factor, Sylow
818C2—81no—
819C2—81no—
820C2—82no—
821C2—82no—
822C2C3×#266811yescharacteristic
823C2C3×#319411yescharacteristic
824C2C3×#320311yescharacteristic
825C2C3×#326911yescharacteristic
826C2C3×#327411yescharacteristic
827C2C3×#331911yescharacteristic
828C2C3×#333011yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#468C2semidirect
2. C2×C3×#449C2semidirect
3. C3×#2537C2semidirect
4. C3×#2407C2semidirect
5. C3×#2093C2semidirect
6. C3×#2076C2semidirect
7. C3×#2072C2semidirect
8. C3×#2036C2semidirect
9. C3×#2033C2semidirect
10. C3×#1999C2semidirect
11. C3×#1895C2semidirect
12. C3×#1879C2semidirect
13. C3×#1877C2semidirect
14. C3×#1870C2semidirect
15. C3×#1788C2semidirect
16. #30417C3direct (N × H)
62. C2×#468C2×C3semidirect
63. C2×#449C2×C3semidirect
64. #2537C2×C3semidirect
65. #2407C2×C3semidirect
66. #2093C2×C3semidirect
67. #2076C2×C3semidirect
68. #2072C2×C3semidirect
69. #2036C2×C3semidirect
70. #2033C2×C3semidirect
71. #1999C2×C3semidirect
72. #1895C2×C3semidirect
73. #1879C2×C3semidirect
74. #1877C2×C3semidirect
75. #1870C2×C3semidirect
76. #1788C2×C3semidirect
97. C2×C3×SD16D4semidirect
339. C2×SD16C3×D4semidirect
817. C3#30417direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4682
C2×C3×#4492
C3×#25372
C3×#24072
C3×#20932
C3×#20762
C3×#20722
C3×#20362
C3×#20332
C3×#19992
C3×#18952
C3×#18792
C3×#18772
C3×#18702
C3×#17882
#304173