Finite Group Databasebeta

← C3×#30413 #10649020

Subgroups — C3×#30413 #10649020

Order 768.

1058 conjugacy classes of subgroups.

The subgroup lattice has 824 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×#2535C211yesmaximal, characteristic, complemented
4C3×#2407C211yesmaximal, characteristic, complemented
5C3×#2092C211yesmaximal, characteristic, complemented
6C3×#2075C211yesmaximal, characteristic, complemented
7C3×#2074C211yesmaximal, characteristic, complemented
8C3×#2035C211yesmaximal, characteristic, complemented
9C3×#2034C211yesmaximal, 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#30413C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×#121C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C3×#468—24no—
28C3×#449—24no—
29C2×C3×#107C2211yescharacteristic
30C2×C3×#106C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic
42C3×#397—21no—
43C3×#394—21no—
44C3×#392—21no—
45C3×#392—21no—
46C3×#391C2211yescharacteristic
47C3×#390C2211yescharacteristic
48C3×#386—21no—
49C3×#386—21no—
50C3×#386—21no—
51C3×#385—21no—
52C3×#382C2211yescharacteristic
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#2535C2×C311yescharacteristic, complemented
65#2407C2×C311yescharacteristic, complemented
66#2092C2×C311yescharacteristic, complemented
67#2075C2×C311yescharacteristic, complemented
68#2074C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2034C2×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×C4×D4—41no—
117C3×C4×D4—41no—
118C3×C4×D4—41no—
119C3×C4×D4—41no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4D411yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
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⋊C4D411yescharacteristic
138C2×C3×C22⋊C4D411yescharacteristic
139C2×C3×C42C2311yescharacteristic
140C3×#107—22no—
141C3×#106—41no—
142C3×#103—22no—
143C3×#103—22no—
144C3×#103—41no—
145C3×#102—22no—
146C3×#102—22no—
147C3×#102—41no—
148C3×#102—41no—
149C3×#102—41no—
150C3×C22⋊C8—22no—
151C3×C22⋊C8—41no—
152C3×C22⋊C8—41no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C22×#41C22×C311yescharacteristic
161C22×SD16C22×C311yescharacteristic
162C22×D8C22×C311yescharacteristic
163C22×M16C22×C311yescharacteristic
164C2×C22⋊Q8C22×C311yescharacteristic
165C2×#121C22×C311yescharacteristic
166C2×#121C22×C311yescharacteristic
167C2×#121C22×C311yescharacteristic
168C2×C4×D4C22×C311yescharacteristic
169C2×C4×D4C22×C311yescharacteristic
170#468—24no—
171#449—24no—
172C2×#107C22×C311yescharacteristic
173C2×#106C22×C311yescharacteristic
174C2×#103C22×C311yescharacteristic
175C2×#103C22×C311yescharacteristic
176C2×#103C22×C311yescharacteristic
177C2×#102C22×C311yescharacteristic
178C2×#102C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×C22⋊C8C22×C311yescharacteristic
183C2×C22⋊C8C22×C311yescharacteristic
184C2×C22⋊C8C22×C311yescharacteristic
185#397—21no—
186#394—21no—
187#392—21no—
188#392—21no—
189#391C22×C311yescharacteristic
190#390C22×C311yescharacteristic
191#386—21no—
192#386—21no—
193#386—21no—
194#385—21no—
195#382C22×C311yescharacteristic
196#380C22×C311yescharacteristic
197#380C22×C311yescharacteristic
198#380C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#340C22×C311yescharacteristic
202#340C22×C311yescharacteristic
203#336C22×C311yescharacteristic
204#336C22×C311yescharacteristic
205C24×C3—21no—
206C24×C3—21no—
207C24×C3C2×D411yescharacteristic
208C24×C3C2×D411yescharacteristic
209C3×#41—44no—
210C3×#41—44no—
211C3×#41—44no—
212C3×#41—44no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8C2×D412yes—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
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—41no—
230C2×C3×D4—41no—
231C2×C3×D4—41no—
232C2×C3×D4—42no—
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—81no—
242C2×C3×D4—81no—
243C2×C3×D4—81no—
244C2×C3×D4C2×D412yes—
245C2×C3×D4#4112yes—
246C22×C3×C4—21no—
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—42no—
265C22×C3×C4—42no—
266C22×C3×C4—42no—
267C22×C3×C4—42no—
268C22×C3×C4—81no—
269C22×C3×C4—81no—
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2411yescharacteristic
275C3×SD16—44no—
276C3×D8—44no—
277C3×M16—44no—
278C2×C3×C8—21no—
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×C8C2×D412yes—
290C3×C4⋊C4—21no—
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—41no—
301C3×C4⋊C4—42no—
302C3×C22⋊C4—41no—
303C3×C22⋊C4—41no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—42no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—42no—
309C3×C22⋊C4—42no—
310C3×C22⋊C4—81no—
311C3×C22⋊C4—81no—
312C3×C22⋊C4—81no—
313C3×C22⋊C4—81no—
314C3×C42—21no—
315C3×C42—21no—
316C2×#41—22no—
317C2×#41—22no—
318C2×#41—41no—
319C2×#41—41no—
320C2×#41—41no—
321C2×#41—41no—
322C22×Q8C23×C311yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4C3×D411yescharacteristic
328C22×D4C23×C311yescharacteristic
329C22×D4C23×C311yescharacteristic
330C23×C4—21no—
331C23×C4—21no—
332C23×C4C23×C311yescharacteristic
333C23×C4C23×C311yescharacteristic
334C2×SD16—41no—
335C2×SD16—41no—
336C2×SD16C3×D414yescomplemented
337C2×D8—22no—
338C2×D8—22no—
339C2×D8—41no—
340C2×M16—22no—
341C2×M16—41no—
342C2×M16—41no—
343C22×C8C23×C311yescharacteristic
344C22×C8C23×C311yescharacteristic
345C22×C8C23×C311yescharacteristic
346C22×C8C23×C311yescharacteristic
347C22⋊Q8—22no—
348C22⋊Q8—41no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—41no—
353#121—41no—
354#121—41no—
355C4×D4—41no—
356C4×D4—41no—
357C4×D4—41no—
358C4×D4—41no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4C3×D411yescharacteristic
361C2×C4⋊C4C23×C311yescharacteristic
362C2×C4⋊C4C23×C311yescharacteristic
363C2×C4⋊C4C23×C311yescharacteristic
364C2×C4⋊C4C23×C311yescharacteristic
365C2×C4⋊C4C23×C311yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4C3×D411yescharacteristic
377C2×C22⋊C4C3×D411yescharacteristic
378C2×C42C23×C311yescharacteristic
379#107—22no—
380#106—41no—
381#103—22no—
382#103—22no—
383#103—41no—
384#102—22no—
385#102—22no—
386#102—41no—
387#102—41no—
388#102—41no—
389C22⋊C8—22no—
390C22⋊C8—41no—
391C22⋊C8—41no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—22no—
403C23×C3—21no—
404C23×C3—22no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
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×C3C22×D411yescharacteristic
428C3×Q8—22no—
429C3×Q8—22no—
430C3×Q8—41no—
431C3×Q8—41no—
432C3×D4—22no—
433C3×D4—22no—
434C3×D4—22no—
435C3×D4—22no—
436C3×D4—44no—
437C3×D4—48no—
438C3×D4—41no—
439C3×D4—41no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—84no—
443C3×D4—84no—
444C3×D4—84no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—48no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
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—84no—
485C2×C3×C4C22×D411yescharacteristic
486C2×C3×C4C2×#4111yescharacteristic
487C2×C3×C4H(5,𝔽2)11yescharacteristic
488C2×C3×C4H(5,𝔽2)11yescharacteristic
489C2×C3×C4H(5,𝔽2)11yescharacteristic
490C2×C3×C4H(5,𝔽2)11yescharacteristic
491C3×C8—22no—
492C3×C8—41no—
493C3×C8—41no—
494C3×C8—41no—
495C24—21no—
496C24—21no—
497C24C2×C3×D411yescharacteristic
498C24C2×C3×D411yescharacteristic
499#41—44no—
500#41—44no—
501#41—44no—
502#41—44no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8C2×C3×D412yes—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—81no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4C2×C3×D412yes—
535C2×D4C3×#4112yes—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
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—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4C2×C3×D411yescharacteristic
561C22×C4C2×C3×D411yescharacteristic
562C22×C4C2×C3×D411yescharacteristic
563C22×C4C2×C3×D411yescharacteristic
564C22×C4C24×C311yescharacteristic
565SD16—44no—
566D8—44no—
567M16—44no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8C2×C3×D412yes—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—41no—
591C4⋊C4—42no—
592C22⋊C4—41no—
593C22⋊C4—41no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—81no—
601C22⋊C4—81no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C42—21no—
605C42—21no—
606C22×C3—42no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—42no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—42no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—42no—
623C22×C3—41no—
624C22×C3—42no—
625C22×C3—41no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3#53411yescharacteristic
635C22×C3D4211yescharacteristic
636C22×C3#54611yescharacteristic
637C22×C3#57511yescharacteristic
638C22×C3#57511yescharacteristic
639C22×C3#57611yescharacteristic
640C22×C3#57711yescharacteristic
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—42no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—81no—
647C3×C4—81no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—81no—
651C3×C4#53411yescharacteristic
652C3×C4#53811yescharacteristic
653C3×C4#54611yescharacteristic
654C3×C4#56011yescharacteristic
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—22no—
667C23—21no—
668C23—22no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23C22×C3×D411yescharacteristic
684Q8—22no—
685Q8—22no—
686Q8—41no—
687Q8—41no—
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—48no—
693D4—44no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—48no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
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—84no—
741C2×C4C22×C3×D411yescharacteristic
742C2×C4C2×C3×#4111yescharacteristic
743C2×C4C3×H(5,𝔽2)11yescharacteristic
744C2×C4C3×H(5,𝔽2)11yescharacteristic
745C2×C4C3×H(5,𝔽2)11yescharacteristic
746C2×C4C3×H(5,𝔽2)11yescharacteristic
747C8—22no—
748C8—41no—
749C8—41no—
750C8—41no—
751C2×C3—81no—
752C2×C3—81no—
753C2×C3—82no—
754C2×C3—82no—
755C2×C3#266811yescharacteristic
756C2×C3#319711yescharacteristic
757C2×C3#319811yescharacteristic
758C2×C3#326811yescharacteristic
759C2×C3#327511yescharacteristic
760C2×C3#330711yescharacteristic
761C2×C3#332211yescharacteristic
762C22—42no—
763C22—41no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—41no—
773C22—41no—
774C22—42no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22C3×#53411yescharacteristic
791C22C3×D4211yescharacteristic
792C22C3×#54611yescharacteristic
793C22C3×#57511yescharacteristic
794C22C3×#57511yescharacteristic
795C22C3×#57611yescharacteristic
796C22C3×#57711yescharacteristic
797C4—41no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—41no—
802C4—81no—
803C4—81no—
804C4—81no—
805C4—81no—
806C4—81no—
807C4C3×#53411yescharacteristic
808C4C3×#53811yescharacteristic
809C4C3×#54611yescharacteristic
810C4C3×#56011yescharacteristic
811C3#3041311yescharacteristic, direct product factor, Sylow
812C2—81no—
813C2—81no—
814C2—82no—
815C2—82no—
816C2C3×#266811yescharacteristic
817C2C3×#319711yescharacteristic
818C2C3×#319811yescharacteristic
819C2C3×#326811yescharacteristic
820C2C3×#327511yescharacteristic
821C2C3×#330711yescharacteristic
822C2C3×#332211yescharacteristic
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×#2535C2semidirect
4. C3×#2407C2semidirect
5. C3×#2092C2semidirect
6. C3×#2075C2semidirect
7. C3×#2074C2semidirect
8. C3×#2035C2semidirect
9. C3×#2034C2semidirect
10. C3×#1999C2semidirect
11. C3×#1895C2semidirect
12. C3×#1879C2semidirect
13. C3×#1877C2semidirect
14. C3×#1870C2semidirect
15. C3×#1788C2semidirect
16. #30413C3direct (N × H)
62. C2×#468C2×C3semidirect
63. C2×#449C2×C3semidirect
64. #2535C2×C3semidirect
65. #2407C2×C3semidirect
66. #2092C2×C3semidirect
67. #2075C2×C3semidirect
68. #2074C2×C3semidirect
69. #2035C2×C3semidirect
70. #2034C2×C3semidirect
71. #1999C2×C3semidirect
72. #1895C2×C3semidirect
73. #1879C2×C3semidirect
74. #1877C2×C3semidirect
75. #1870C2×C3semidirect
76. #1788C2×C3semidirect
97. C2×C3×SD16D4semidirect
336. C2×SD16C3×D4semidirect
811. C3#30413direct (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×#25352
C3×#24072
C3×#20922
C3×#20752
C3×#20742
C3×#20352
C3×#20342
C3×#19992
C3×#18952
C3×#18792
C3×#18772
C3×#18702
C3×#17882
#304133