Finite Group Databasebeta

← C3×#24656 #10643263

Subgroups — C3×#24656 #10643263

Order 768.

986 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#463C211yesmaximal, characteristic, complemented
2C2×C3×#432C211yesmaximal, characteristic, complemented
3C3×#2850C211yesmaximal, characteristic, complemented
4C3×C4×#121C211yesmaximal, characteristic, complemented
5C3×#2035C211yesmaximal, characteristic, complemented
6C3×#2033C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8C3×#1999C211yesmaximal, characteristic
9C3×#1983C211yesmaximal, characteristic, complemented
10C3×#1973C211yesmaximal, characteristic, complemented
11C3×#1972C211yesmaximal, characteristic, complemented
12C3×#1949C211yesmaximal, characteristic, complemented
13C3×#1936C211yesmaximal, characteristic, complemented
14C3×#1935C211yesmaximal, characteristic, complemented
15C3×#1804C211yesmaximal, characteristic, complemented
16#24656C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×#124C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×C4×D4—21no—
24C2×C3×C4×D4C2211yescharacteristic
25C22×C3×C42C2211yescharacteristic
26C3×#463—24no—
27C3×#432—24no—
28C2×C3×#107C2211yescharacteristic
29C2×C3×#106C2211yescharacteristic
30C2×C3×C4⋊C8C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic
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×#97C2211yescharacteristic
43C2×C3×#97C2211yescharacteristic
44C3×#391C2211yescharacteristic
45C3×#390C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#389C2211yescharacteristic
48C3×#388—21no—
49C3×#388—21no—
50C3×#388—21no—
51C3×#386—21no—
52C3×#386—21no—
53C3×#386—21no—
54C3×#382C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×C4×C4⋊C4C2211yescharacteristic
57C3×C4×C22⋊C4—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C2×#463C2×C311yescharacteristic, complemented
63C2×#432C2×C311yescharacteristic, complemented
64#2850C2×C311yescharacteristic, complemented
65C4×#121C2×C311yescharacteristic, complemented
66#2035C2×C311yescharacteristic, complemented
67#2033C2×C311yescharacteristic, complemented
68#2000C2×C311yescharacteristic, complemented
69#1999C2×C311yescharacteristic
70#1983C2×C311yescharacteristic, complemented
71#1973C2×C311yescharacteristic, complemented
72#1972C2×C311yescharacteristic, complemented
73#1949C2×C311yescharacteristic, complemented
74#1936C2×C311yescharacteristic, complemented
75#1935C2×C311yescharacteristic, complemented
76#1804C2×C311yescharacteristic, complemented
77C22×C3×Q8C2311yescharacteristic
78C22×C3×D4—21no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4D411yescharacteristic
84C23×C3×C4D411yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C2×C3×SD16—22no—
87C2×C3×SD16—22no—
88C2×C3×SD16—41no—
89C2×C3×D8—22no—
90C2×C3×D8—22no—
91C2×C3×D8—41no—
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C3×#124—22no—
97C3×#124—22no—
98C3×C22⋊Q8—41no—
99C3×C22⋊Q8—41no—
100C3×#121—22no—
101C3×#121—22no—
102C3×#121—41no—
103C3×#121—41no—
104C3×C4×D4—22no—
105C3×C4×D4—22no—
106C3×C4×D4—44no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C42—22no—
126C2×C3×C42—22no—
127C2×C3×C42—21no—
128C2×C3×C42D411yescharacteristic
129C2×C3×C42D411yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C2×C3×C42C2311yescharacteristic
132C3×#107—41no—
133C3×#106—41no—
134C3×C4⋊C8—22no—
135C3×C4⋊C8D414yescomplemented
136C3×#103—22no—
137C3×#103—22no—
138C3×#103—41no—
139C3×#102—22no—
140C3×#102—22no—
141C3×#102—41no—
142C3×#102—41no—
143C3×#102—41no—
144C3×C22⋊C8—22no—
145C3×C22⋊C8—22no—
146C3×#97—22no—
147C3×#97—22no—
148C3×#95—21no—
149C3×#95—21no—
150C3×#95—21no—
151C3×#95—21no—
152C3×#95—21no—
153C3×#95—21no—
154C3×#95—21no—
155C22×SD16C22×C311yescharacteristic
156C22×D8C22×C311yescharacteristic
157C2×#124C22×C311yescharacteristic
158C2×C22⋊Q8C22×C311yescharacteristic
159C2×#121C22×C311yescharacteristic
160C2×#121C22×C311yescharacteristic
161C2×C4×D4—21no—
162C2×C4×D4C22×C311yescharacteristic
163C22×C42C22×C311yescharacteristic
164#463—24no—
165#432—24no—
166C2×#107C22×C311yescharacteristic
167C2×#106C22×C311yescharacteristic
168C2×C4⋊C8C22×C311yescharacteristic
169C2×C4⋊C8C22×C311yescharacteristic
170C2×#103C22×C311yescharacteristic
171C2×#103C22×C311yescharacteristic
172C2×#103C22×C311yescharacteristic
173C2×#102C22×C311yescharacteristic
174C2×#102C22×C311yescharacteristic
175C2×#102C22×C311yescharacteristic
176C2×#102C22×C311yescharacteristic
177C2×#102C22×C311yescharacteristic
178C2×C22⋊C8C22×C311yescharacteristic
179C2×C22⋊C8C22×C311yescharacteristic
180C2×#97C22×C311yescharacteristic
181C2×#97C22×C311yescharacteristic
182#391C22×C311yescharacteristic
183#390C22×C311yescharacteristic
184#390C22×C311yescharacteristic
185#389C22×C311yescharacteristic
186#388—21no—
187#388—21no—
188#388—21no—
189#386—21no—
190#386—21no—
191#386—21no—
192#382C22×C311yescharacteristic
193#380C22×C311yescharacteristic
194C4×C4⋊C4C22×C311yescharacteristic
195C4×C22⋊C4—21no—
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200C24×C3—21no—
201C24×C3—21no—
202C24×C3C2×D411yescharacteristic
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×D4—24no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—42no—
222C2×C3×D4—42no—
223C2×C3×D4—42no—
224C2×C3×D4—42no—
225C2×C3×D4—42no—
226C2×C3×D4#4112yes—
227C22×C3×C4—22no—
228C22×C3×C4—21no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—41no—
243C22×C3×C4—41no—
244C22×C3×C4—41no—
245C22×C3×C4—42no—
246C22×C3×C4—42no—
247C22×C3×C4—42no—
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2411yescharacteristic
254C3×SD16—44no—
255C3×D8—44no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8C2×D412yes—
267C2×C3×C8C2×D412yes—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—42no—
278C3×C4⋊C4—42no—
279C3×C4⋊C4#4112yes—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—42no—
282C3×C22⋊C4—42no—
283C3×C22⋊C4—42no—
284C3×C22⋊C4—42no—
285C3×C22⋊C4—42no—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4—42no—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291C3×C42—22no—
292C3×C42—22no—
293C3×C42—21no—
294C3×C42—21no—
295C3×C42—42no—
296C3×C42C2×D412yes—
297C3×C42#4112yes—
298C22×Q8C23×C311yescharacteristic
299C22×D4—21no—
300C22×D4—21no—
301C22×D4C23×C311yescharacteristic
302C22×D4C23×C311yescharacteristic
303C23×C4—21no—
304C23×C4C3×D411yescharacteristic
305C23×C4C3×D411yescharacteristic
306C23×C4C23×C311yescharacteristic
307C2×SD16—22no—
308C2×SD16—22no—
309C2×SD16—41no—
310C2×D8—22no—
311C2×D8—22no—
312C2×D8—41no—
313C22×C8C23×C311yescharacteristic
314C22×C8C23×C311yescharacteristic
315C22×C8C23×C311yescharacteristic
316C22×C8C23×C311yescharacteristic
317#124—22no—
318#124—22no—
319C22⋊Q8—41no—
320C22⋊Q8—41no—
321#121—22no—
322#121—22no—
323#121—41no—
324#121—41no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4—44no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4C23×C311yescharacteristic
331C2×C4⋊C4C23×C311yescharacteristic
332C2×C4⋊C4C23×C311yescharacteristic
333C2×C4⋊C4C23×C311yescharacteristic
334C2×C4⋊C4C23×C311yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—21no—
349C2×C42C3×D411yescharacteristic
350C2×C42C3×D411yescharacteristic
351C2×C42C23×C311yescharacteristic
352C2×C42C23×C311yescharacteristic
353#107—41no—
354#106—41no—
355C4⋊C8—22no—
356C4⋊C8C3×D414yescomplemented
357#103—22no—
358#103—22no—
359#103—41no—
360#102—22no—
361#102—22no—
362#102—41no—
363#102—41no—
364#102—41no—
365C22⋊C8—22no—
366C22⋊C8—22no—
367#97—22no—
368#97—22no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—22no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3—41no—
394C23×C3—41no—
395C23×C3—41no—
396C23×C3AGL(1,ℤ/8)12yes—
397C23×C3C22×D411yescharacteristic
398C3×Q8—41no—
399C3×Q8—41no—
400C3×Q8—41no—
401C3×Q8—41no—
402C3×D4—22no—
403C3×D4—22no—
404C3×D4—48no—
405C3×D4—41no—
406C3×D4—41no—
407C3×D4—41no—
408C3×D4—41no—
409C3×D4—41no—
410C3×D4—41no—
411C3×D4—84no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—44no—
427C2×C3×C4—44no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—84no—
450C2×C3×C4#12112yes—
451C2×C3×C4#12112yes—
452C2×C3×C4C22×D411yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4H(5,𝔽2)11yescharacteristic
457C2×C3×C4H(5,𝔽2)11yescharacteristic
458C3×C8—22no—
459C3×C8—22no—
460C3×C8—41no—
461C3×C8—41no—
462C24—21no—
463C24—21no—
464C24C2×C3×D411yescharacteristic
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×D4—24no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4C3×#4112yes—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4C2×C3×D411yescharacteristic
511C22×C4C2×C3×D411yescharacteristic
512C22×C4C2×C3×D411yescharacteristic
513C22×C4C2×C3×D411yescharacteristic
514C22×C4C2×C3×D411yescharacteristic
515C22×C4C24×C311yescharacteristic
516SD16—44no—
517D8—44no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8C2×C3×D412yes—
529C2×C8C2×C3×D412yes—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4C3×#4112yes—
542C22⋊C4—24no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C42—22no—
554C42—22no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42C2×C3×D412yes—
559C42C3×#4112yes—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—22no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—42no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3—81no—
571C22×C3—81no—
572C22×C3—81no—
573C22×C3—81no—
574C22×C3—81no—
575C22×C3—81no—
576C22×C3—81no—
577C22×C3—81no—
578C22×C3—81no—
579C22×C3—81no—
580C22×C3—81no—
581C22×C3C2×#12111yescharacteristic
582C22×C3#52511yescharacteristic
583C22×C3#53511yescharacteristic
584C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
585C22×C3#57511yescharacteristic
586C22×C3#57511yescharacteristic
587C22×C3#57511yescharacteristic
588C3×C4—22no—
589C3×C4—22no—
590C3×C4—42no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—81no—
595C3×C4—81no—
596C3×C4—81no—
597C3×C4—81no—
598C3×C4—81no—
599C3×C4#54611yescharacteristic
600C3×C4#55011yescharacteristic
601C3×C4#55311yescharacteristic
602C3×C4#55511yescharacteristic
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—22no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23C3×AGL(1,ℤ/8)12yes—
624C23C22×C3×D411yescharacteristic
625Q8—41no—
626Q8—41no—
627Q8—41no—
628Q8—41no—
629D4—22no—
630D4—22no—
631D4—48no—
632D4—41no—
633D4—41no—
634D4—41no—
635D4—41no—
636D4—41no—
637D4—41no—
638D4—84no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—44no—
654C2×C4—44no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—84no—
677C2×C4C3×#12112yes—
678C2×C4C3×#12112yes—
679C2×C4C22×C3×D411yescharacteristic
680C2×C4C2×C3×#4111yescharacteristic
681C2×C4C2×C3×#4111yescharacteristic
682C2×C4C2×C3×#4111yescharacteristic
683C2×C4C3×H(5,𝔽2)11yescharacteristic
684C2×C4C3×H(5,𝔽2)11yescharacteristic
685C8—22no—
686C8—22no—
687C8—41no—
688C8—41no—
689C2×C3—42no—
690C2×C3—82no—
691C2×C3—161no—
692C2×C3#241411yescharacteristic
693C2×C3#305411yescharacteristic
694C2×C3#305511yescharacteristic
695C2×C3#311111yescharacteristic
696C2×C3#311411yescharacteristic
697C2×C3#321311yescharacteristic
698C2×C3#321911yescharacteristic
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22C2×C3×#12111yescharacteristic
721C22C3×#52511yescharacteristic
722C22C3×#53511yescharacteristic
723C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
724C22C3×#57511yescharacteristic
725C22C3×#57511yescharacteristic
726C22C3×#57511yescharacteristic
727C4—22no—
728C4—22no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—42no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4—81no—
737C4—81no—
738C4C3×#54611yescharacteristic
739C4C3×#55011yescharacteristic
740C4C3×#55311yescharacteristic
741C4C3×#55511yescharacteristic
742C3#2465611yescharacteristic, direct product factor, Sylow
743C2—42no—
744C2—82no—
745C2—161no—
746C2C3×#241411yescharacteristic
747C2C3×#305411yescharacteristic
748C2C3×#305511yescharacteristic
749C2C3×#311111yescharacteristic
750C2C3×#311411yescharacteristic
751C2C3×#321311yescharacteristic
752C2C3×#321911yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#463C2semidirect
2. C2×C3×#432C2semidirect
3. C3×#2850C2semidirect
4. C3×C4×#121C2semidirect
5. C3×#2035C2semidirect
6. C3×#2033C2semidirect
7. C3×#2000C2semidirect
9. C3×#1983C2semidirect
10. C3×#1973C2semidirect
11. C3×#1972C2semidirect
12. C3×#1949C2semidirect
13. C3×#1936C2semidirect
14. C3×#1935C2semidirect
15. C3×#1804C2semidirect
16. #24656C3direct (N × H)
62. C2×#463C2×C3semidirect
63. C2×#432C2×C3semidirect
64. #2850C2×C3semidirect
65. C4×#121C2×C3semidirect
66. #2035C2×C3semidirect
67. #2033C2×C3semidirect
68. #2000C2×C3semidirect
70. #1983C2×C3semidirect
71. #1973C2×C3semidirect
72. #1972C2×C3semidirect
73. #1949C2×C3semidirect
74. #1936C2×C3semidirect
75. #1935C2×C3semidirect
76. #1804C2×C3semidirect
135. C3×C4⋊C8D4semidirect
356. C4⋊C8C3×D4semidirect
742. C3#24656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4632
C2×C3×#4322
C3×#28502
C3×C4×#1212
C3×#20352
C3×#20332
C3×#20002
C3×#19992
C3×#19832
C3×#19732
C3×#19722
C3×#19492
C3×#19362
C3×#19352
C3×#18042
#246563