Finite Group Databasebeta

← C2×C3×#3069 #10679075

Subgroups — C2×C3×#3069 #10679075

Order 768.

2618 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#575C211yesmaximal, characteristic
2C22×C3×#137C211yesmaximal, characteristic, complemented
3C22×C3×#137C211yesmaximal, characteristic, complemented
4C2×C3×#568C211yesmaximal, characteristic, complemented
5C3×#3069C2116yesmaximal, direct product factor
6C2×C3×#473C214yesmaximal, complemented
7C2×C3×#471C214yesmaximal, complemented
8C2×C3×#430C211yesmaximal, characteristic, complemented
9C2×C3×#413C211yesmaximal, characteristic, complemented
10C22×C3×#101C211yesmaximal, characteristic, complemented
11C2×#3069C311yesmaximal, characteristic, direct product factor, Sylow
12C22×C3×#41C2211yescharacteristic
13C22×C3×#41C2211yescharacteristic
14C23×C3×Q8C2211yescharacteristic
15C3×#575—24no—
16C3×#575C2218yes—
17C2×C3×#137—22no—
18C2×C3×#137—24no—
19C2×C3×#137—21no—
20C2×C3×#137—22no—
21C2×C3×#137—22no—
22C2×C3×#137—24no—
23C2×C3×#137C2214yes—
24C2×C3×#137C2212yes—
25C2×C3×#137C2218yescomplemented
26C2×C3×#137C2218yescomplemented
27C2×C3×AGL(1,ℤ/8)—21no—
28C2×C3×AGL(1,ℤ/8)C2212yes—
29C2×C3×#135—22no—
30C22×C3×Q16—21no—
31C22×C3×Q16C2212yescomplemented
32C22×C3×SD16—21no—
33C22×C3×SD16C2212yescomplemented
34C3×#568—24no—
35C3×#568C2218yescomplemented
36C2×C3×#131—22no—
37C2×C3×#131C2214yes—
38C22×C3×M16—22no—
39C22×C3×M16C2211yescharacteristic
40C22×C3×M16C2211yescharacteristic
41C22×C3×M16C2211yescharacteristic
42C22×C3×M16C2211yescharacteristic
43C3×#473C22132yescomplemented
44C3×#471C22132yescomplemented
45C3×#430C2218yescomplemented
46C2×C3×#108C2214yescomplemented
47C3×#413C2218yescomplemented
48C2×C3×#101C2214yescomplemented
49C2×C3×#101C2218yescomplemented
50C2×C3×#101C2212yescomplemented
51C2×C3×#100C2212yescomplemented
52C2×#575C2×C311yescharacteristic
53C22×#137C2×C311yescharacteristic, complemented
54C22×#137C2×C311yescharacteristic, complemented
55C2×#568C2×C311yescharacteristic, complemented
56#3069C2×C3116yesdirect product factor
57C2×#473C2×C314yescomplemented
58C2×#471C2×C314yescomplemented
59C2×#430C2×C311yescharacteristic, complemented
60C2×#413C2×C311yescharacteristic, complemented
61C22×#101C2×C311yescharacteristic, complemented
62C2×C3×#41—21no—
63C2×C3×#41—22no—
64C2×C3×#41—21no—
65C2×C3×#41—22no—
66C2×C3×#41—22no—
67C2×C3×#41—21no—
68C2×C3×#41—21no—
69C2×C3×#41—21no—
70C2×C3×#41—21no—
71C2×C3×#41—22no—
72C2×C3×#41—22no—
73C2×C3×#41D412yes—
74C2×C3×#41D414yes—
75C2×C3×#41C2312yes—
76C2×C3×#41C2314yes—
77C2×C3×#41C2314yes—
78C22×C3×Q8—21no—
79C22×C3×Q8—22no—
80C22×C3×Q8—21no—
81C22×C3×Q8—21no—
82C22×C3×Q8—21no—
83C22×C3×Q8—22no—
84C22×C3×Q8—21no—
85C22×C3×Q8—22no—
86C22×C3×Q8D411yescharacteristic
87C22×C3×Q8C2312yes—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×Q8C2314yes—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4D411yescharacteristic
93C22×C3×D4C2311yescharacteristic
94C23×C3×C4—21no—
95C23×C3×C4—21no—
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C3×#137—28no—
99C3×#137—216no—
100C3×#137—24no—
101C3×#137—28no—
102C3×#137—216no—
103C3×#137—216no—
104C3×#137C23116yes—
105C3×#137C2318yes—
106C3×AGL(1,ℤ/8)—24no—
107C3×AGL(1,ℤ/8)—28no—
108C3×AGL(1,ℤ/8)C2318yes—
109C3×#135—216no—
110C2×C3×Q16—24no—
111C2×C3×Q16—28no—
112C2×C3×Q16—22no—
113C2×C3×Q16—24no—
114C2×C3×Q16—24no—
115C2×C3×Q16C2318yescomplemented
116C2×C3×SD16—22no—
117C2×C3×SD16—24no—
118C2×C3×SD16—28no—
119C2×C3×SD16—22no—
120C2×C3×SD16—24no—
121C2×C3×SD16—24no—
122C2×C3×SD16C2318yescomplemented
123C2×C3×D8—22no—
124C3×#131—216no—
125C3×#131—28no—
126C3×#131C23116yes—
127C2×C3×M16—21no—
128C2×C3×M16—22no—
129C2×C3×M16—21no—
130C2×C3×M16—21no—
131C2×C3×M16—22no—
132C2×C3×M16—22no—
133C2×C3×M16—216no—
134C2×C3×M16—24no—
135C2×C3×M16D412yes—
136C2×C3×M16D412yes—
137C2×C3×M16D414yes—
138C2×C3×M16C2312yes—
139C2×C3×M16C2314yes—
140C2×C3×M16C2312yes—
141C2×C3×M16C2312yes—
142C2×C3×M16C2314yes—
143C2×C3×M16C2314yes—
144C2×C3×M16C2314yes—
145C22×C3×C8—21no—
146C22×C3×C8—21no—
147C22×C3×C8—21no—
148C22×C3×C8—24no—
149C22×C3×C8C2312yes—
150C3×#108C23116yescomplemented
151C3×#101C23116yescomplemented
152C3×#101C2318yescomplemented
153C3×#100C2318yescomplemented
154C22×#41C22×C311yescharacteristic
155C22×#41C22×C311yescharacteristic
156C23×Q8C22×C311yescharacteristic
157#575—24no—
158#575C22×C318yes—
159C2×#137—22no—
160C2×#137—24no—
161C2×#137—21no—
162C2×#137—22no—
163C2×#137—22no—
164C2×#137—24no—
165C2×#137C22×C314yes—
166C2×#137C22×C312yes—
167C2×#137C22×C318yescomplemented
168C2×#137C22×C318yescomplemented
169C2×AGL(1,ℤ/8)—21no—
170C2×AGL(1,ℤ/8)C22×C312yes—
171C2×#135—22no—
172C22×Q16—21no—
173C22×Q16C22×C312yescomplemented
174C22×SD16—21no—
175C22×SD16C22×C312yescomplemented
176#568—24no—
177#568C22×C318yescomplemented
178C2×#131—22no—
179C2×#131C22×C314yes—
180C22×M16—22no—
181C22×M16C22×C311yescharacteristic
182C22×M16C22×C311yescharacteristic
183C22×M16C22×C311yescharacteristic
184C22×M16C22×C311yescharacteristic
185#473C22×C3132yescomplemented
186#471C22×C3132yescomplemented
187#430C22×C318yescomplemented
188C2×#108C22×C314yescomplemented
189#413C22×C318yescomplemented
190C2×#101C22×C314yescomplemented
191C2×#101C22×C318yescomplemented
192C2×#101C22×C312yescomplemented
193C2×#100C22×C312yescomplemented
194C24×C3—21no—
195C24×C3—21no—
196C24×C3#4111yescharacteristic
197C3×#41—24no—
198C3×#41—24no—
199C3×#41—24no—
200C3×#41—24no—
201C3×#41—22no—
202C3×#41—24no—
203C3×#41—22no—
204C3×#41—24no—
205C3×#41—24no—
206C3×#41—24no—
207C3×#41—24no—
208C3×#41—42no—
209C3×#41—42no—
210C3×#41—42no—
211C3×#41—42no—
212C3×#41C2×D418yes—
213C3×#41C2×D414yes—
214C3×#41C2414yes—
215C2×C3×Q8—22no—
216C2×C3×Q8—21no—
217C2×C3×Q8—24no—
218C2×C3×Q8—22no—
219C2×C3×Q8—21no—
220C2×C3×Q8—24no—
221C2×C3×Q8—22no—
222C2×C3×Q8—22no—
223C2×C3×Q8—22no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—24no—
228C2×C3×Q8—24no—
229C2×C3×Q8—22no—
230C2×C3×Q8—24no—
231C2×C3×Q8—21no—
232C2×C3×Q8—42no—
233C2×C3×Q8—42no—
234C2×C3×Q8—42no—
235C2×C3×Q8—42no—
236C2×C3×Q8—42no—
237C2×C3×Q8—41no—
238C2×C3×Q8—41no—
239C2×C3×Q8C2×D412yes—
240C2×C3×Q8C2×D414yes—
241C2×C3×Q8C2414yes—
242C2×C3×Q8C2412yes—
243C2×C3×D4—24no—
244C2×C3×D4—22no—
245C2×C3×D4—24no—
246C2×C3×D4—22no—
247C2×C3×D4—24no—
248C2×C3×D4—22no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—42no—
256C2×C3×D4—41no—
257C2×C3×D4—41no—
258C2×C3×D4C2×D412yes—
259C2×C3×D4C2×D414yes—
260C2×C3×D4C2412yes—
261C22×C3×C4—21no—
262C22×C3×C4—24no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—24no—
266C22×C3×C4—21no—
267C22×C3×C4—24no—
268C22×C3×C4—22no—
269C22×C3×C4—24no—
270C22×C3×C4—42no—
271C22×C3×C4—41no—
272C22×C3×C4—41no—
273C22×C3×C4—42no—
274C22×C3×C4—41no—
275C22×C3×C4—41no—
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D412yes—
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D412yes—
282C22×C3×C4#4111yescharacteristic
283C22×C3×C4#4112yes—
284C22×C3×C4C2411yescharacteristic
285C22×C3×C4C2412yes—
286C3×Q16—216no—
287C3×Q16—28no—
288C3×Q16—216no—
289C3×SD16—28no—
290C3×SD16—216no—
291C3×SD16—28no—
292C3×SD16—216no—
293C3×D8—28no—
294C3×M16—24no—
295C3×M16—22no—
296C3×M16—24no—
297C3×M16—22no—
298C3×M16—24no—
299C3×M16—22no—
300C3×M16—216no—
301C3×M16C2×D418yes—
302C3×M16C2×D418yes—
303C3×M16C2414yes—
304C3×M16C2414yes—
305C3×M16C2414yes—
306C2×C3×C8—22no—
307C2×C3×C8—24no—
308C2×C3×C8—22no—
309C2×C3×C8—24no—
310C2×C3×C8—22no—
311C2×C3×C8—24no—
312C2×C3×C8—216no—
313C2×C3×C8C2×D414yes—
314C2×C3×C8C2×D414yes—
315C2×C3×C8C2414yes—
316C2×#41—21no—
317C2×#41—22no—
318C2×#41—21no—
319C2×#41—22no—
320C2×#41—22no—
321C2×#41—21no—
322C2×#41—21no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41C3×D412yes—
328C2×#41C3×D414yes—
329C2×#41C23×C312yes—
330C2×#41C23×C314yes—
331C2×#41C23×C314yes—
332C22×Q8—21no—
333C22×Q8—22no—
334C22×Q8—21no—
335C22×Q8—21no—
336C22×Q8—21no—
337C22×Q8—22no—
338C22×Q8—21no—
339C22×Q8—22no—
340C22×Q8C3×D411yescharacteristic
341C22×Q8C23×C312yes—
342C22×Q8C23×C311yescharacteristic
343C22×Q8C23×C314yes—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4C3×D411yescharacteristic
347C22×D4C23×C311yescharacteristic
348C23×C4—21no—
349C23×C4—21no—
350C23×C4—21no—
351C23×C4C23×C311yescharacteristic
352#137—28no—
353#137—216no—
354#137—24no—
355#137—28no—
356#137—216no—
357#137—216no—
358#137C23×C3116yes—
359#137C23×C318yes—
360AGL(1,ℤ/8)—24no—
361AGL(1,ℤ/8)—28no—
362AGL(1,ℤ/8)C23×C318yes—
363#135—216no—
364C2×Q16—24no—
365C2×Q16—28no—
366C2×Q16—22no—
367C2×Q16—24no—
368C2×Q16—24no—
369C2×Q16C23×C318yescomplemented
370C2×SD16—22no—
371C2×SD16—24no—
372C2×SD16—28no—
373C2×SD16—22no—
374C2×SD16—24no—
375C2×SD16—24no—
376C2×SD16C23×C318yescomplemented
377C2×D8—22no—
378#131—216no—
379#131—28no—
380#131C23×C3116yes—
381C2×M16—21no—
382C2×M16—22no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—22no—
386C2×M16—22no—
387C2×M16—216no—
388C2×M16—24no—
389C2×M16C3×D412yes—
390C2×M16C3×D412yes—
391C2×M16C3×D414yes—
392C2×M16C23×C312yes—
393C2×M16C23×C314yes—
394C2×M16C23×C312yes—
395C2×M16C23×C312yes—
396C2×M16C23×C314yes—
397C2×M16C23×C314yes—
398C2×M16C23×C314yes—
399C22×C8—21no—
400C22×C8—21no—
401C22×C8—21no—
402C22×C8—24no—
403C22×C8C23×C312yes—
404#108C23×C3116yescomplemented
405#101C23×C3116yescomplemented
406#101C23×C318yescomplemented
407#100C23×C318yescomplemented
408C23×C3—22no—
409C23×C3—24no—
410C23×C3—22no—
411C23×C3—42no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—82no—
415C23×C3—82no—
416C23×C3#12111yescharacteristic
417C23×C3#12111yescharacteristic
418C23×C3#12112yes—
419C23×C3C2×#4111yescharacteristic
420C23×C3C2×#4112yes—
421C3×Q8—24no—
422C3×Q8—22no—
423C3×Q8—24no—
424C3×Q8—24no—
425C3×Q8—22no—
426C3×Q8—22no—
427C3×Q8—44no—
428C3×Q8—42no—
429C3×Q8—44no—
430C3×Q8—42no—
431C3×Q8—41no—
432C3×Q8—41no—
433C3×Q8C22×D414yes—
434C3×D4—24no—
435C3×D4—28no—
436C3×D4—24no—
437C3×D4—24no—
438C3×D4—22no—
439C3×D4—22no—
440C3×D4—22no—
441C3×D4—44no—
442C3×D4—44no—
443C3×D4—41no—
444C3×D4—41no—
445C3×D4C22×D414yes—
446C2×C3×C4—24no—
447C2×C3×C4—22no—
448C2×C3×C4—28no—
449C2×C3×C4—24no—
450C2×C3×C4—24no—
451C2×C3×C4—22no—
452C2×C3×C4—24no—
453C2×C3×C4—41no—
454C2×C3×C4—44no—
455C2×C3×C4—42no—
456C2×C3×C4—44no—
457C2×C3×C4—41no—
458C2×C3×C4—42no—
459C2×C3×C4—44no—
460C2×C3×C4—44no—
461C2×C3×C4#12112yes—
462C2×C3×C4#12112yes—
463C2×C3×C4#12112yes—
464C2×C3×C4#12112yes—
465C2×C3×C4#12112yes—
466C2×C3×C4#12111yescharacteristic
467C2×C3×C4#12111yescharacteristic
468C2×C3×C4C22×D412yes—
469C2×C3×C4C22×D412yes—
470C2×C3×C4C22×D412yes—
471C2×C3×C4C22×D411yescharacteristic
472C2×C3×C4C22×D411yescharacteristic
473C2×C3×C4C22×D412yes—
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4C2×#4112yes—
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4C2511yescharacteristic
479C3×C8—24no—
480C3×C8—24no—
481C3×C8—24no—
482C3×C8C22×D418yes—
483C24—21no—
484C24—21no—
485C24C3×#4111yescharacteristic
486#41—24no—
487#41—24no—
488#41—24no—
489#41—24no—
490#41—22no—
491#41—24no—
492#41—22no—
493#41—24no—
494#41—24no—
495#41—24no—
496#41—24no—
497#41—42no—
498#41—42no—
499#41—42no—
500#41—42no—
501#41C2×C3×D418yes—
502#41C2×C3×D414yes—
503#41C24×C314yes—
504C2×Q8—21no—
505C2×Q8—22no—
506C2×Q8—24no—
507C2×Q8—22no—
508C2×Q8—21no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—24no—
512C2×Q8—22no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—24no—
517C2×Q8—24no—
518C2×Q8—22no—
519C2×Q8—24no—
520C2×Q8—21no—
521C2×Q8—41no—
522C2×Q8—42no—
523C2×Q8—41no—
524C2×Q8—42no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—42no—
528C2×Q8C2×C3×D412yes—
529C2×Q8C2×C3×D414yes—
530C2×Q8C24×C314yes—
531C2×Q8C24×C312yes—
532C2×D4—22no—
533C2×D4—24no—
534C2×D4—22no—
535C2×D4—24no—
536C2×D4—24no—
537C2×D4—21no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—42no—
547C2×D4C2×C3×D412yes—
548C2×D4C2×C3×D414yes—
549C2×D4C24×C312yes—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—42no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—42no—
565C22×C4C2×C3×D411yescharacteristic
566C22×C4C2×C3×D411yescharacteristic
567C22×C4C2×C3×D411yescharacteristic
568C22×C4C2×C3×D412yes—
569C22×C4C2×C3×D411yescharacteristic
570C22×C4C2×C3×D412yes—
571C22×C4C3×#4111yescharacteristic
572C22×C4C3×#4112yes—
573C22×C4C24×C311yescharacteristic
574C22×C4C24×C312yes—
575Q16—216no—
576Q16—28no—
577Q16—216no—
578SD16—28no—
579SD16—216no—
580SD16—28no—
581SD16—216no—
582D8—28no—
583M16—24no—
584M16—22no—
585M16—24no—
586M16—22no—
587M16—24no—
588M16—22no—
589M16—216no—
590M16C2×C3×D418yes—
591M16C2×C3×D418yes—
592M16C24×C314yes—
593M16C24×C314yes—
594M16C24×C314yes—
595C2×C8—22no—
596C2×C8—24no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—24no—
600C2×C8—24no—
601C2×C8—216no—
602C2×C8C2×C3×D414yes—
603C2×C8C2×C3×D414yes—
604C2×C8C24×C314yes—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—24no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—44no—
612C22×C3—42no—
613C22×C3—84no—
614C22×C3—82no—
615C22×C3—82no—
616C22×C3—82no—
617C22×C3C2×#12112yes—
618C22×C3C2×#12111yescharacteristic
619C22×C3C2×#12112yes—
620C22×C3C2×#12111yescharacteristic
621C22×C3C22×#4111yescharacteristic
622C3×C4—24no—
623C3×C4—42no—
624C3×C4—44no—
625C3×C4C2×#12112yes—
626C3×C4C2×#12111yescharacteristic
627C3×C4C2×#12112yes—
628C3×C4C2×#12111yescharacteristic
629C3×C4C23×D411yescharacteristic
630C3×C4C23×D411yescharacteristic
631C23—22no—
632C23—24no—
633C23—22no—
634C23—42no—
635C23—41no—
636C23—41no—
637C23—82no—
638C23—82no—
639C23C3×#12111yescharacteristic
640C23C3×#12111yescharacteristic
641C23C3×#12112yes—
642C23C2×C3×#4111yescharacteristic
643C23C2×C3×#4112yes—
644Q8—24no—
645Q8—22no—
646Q8—24no—
647Q8—24no—
648Q8—22no—
649Q8—22no—
650Q8—44no—
651Q8—42no—
652Q8—44no—
653Q8—42no—
654Q8—41no—
655Q8—41no—
656Q8C22×C3×D414yes—
657D4—24no—
658D4—24no—
659D4—28no—
660D4—22no—
661D4—22no—
662D4—24no—
663D4—22no—
664D4—44no—
665D4—44no—
666D4—41no—
667D4—41no—
668D4C22×C3×D414yes—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—28no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4C3×#12111yescharacteristic
685C2×C4C3×#12112yes—
686C2×C4C3×#12111yescharacteristic
687C2×C4C3×#12112yes—
688C2×C4C3×#12112yes—
689C2×C4C3×#12112yes—
690C2×C4C3×#12112yes—
691C2×C4C22×C3×D411yescharacteristic
692C2×C4C22×C3×D411yescharacteristic
693C2×C4C22×C3×D412yes—
694C2×C4C22×C3×D412yes—
695C2×C4C22×C3×D412yes—
696C2×C4C22×C3×D411yescharacteristic
697C2×C4C22×C3×D411yescharacteristic
698C2×C4C22×C3×D412yes—
699C2×C4C2×C3×#4112yes—
700C2×C4C2×C3×#4111yescharacteristic
701C2×C4C25×C311yescharacteristic
702C8—24no—
703C8—24no—
704C8—24no—
705C8C22×C3×D418yes—
706C2×C3—22no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—22no—
710C2×C3—44no—
711C2×C3—82no—
712C2×C3#306912yesdirect product factor
713C2×C3C22×#12111yescharacteristic
714C22—22no—
715C22—22no—
716C22—22no—
717C22—24no—
718C22—42no—
719C22—42no—
720C22—44no—
721C22—42no—
722C22—84no—
723C22—82no—
724C22—82no—
725C22—82no—
726C22C2×C3×#12112yes—
727C22C2×C3×#12111yescharacteristic
728C22C2×C3×#12112yes—
729C22C2×C3×#12111yescharacteristic
730C22C22×C3×#4111yescharacteristic
731C4—24no—
732C4—42no—
733C4—44no—
734C4C2×C3×#12112yes—
735C4C2×C3×#12111yescharacteristic
736C4C2×C3×#12112yes—
737C4C2×C3×#12111yescharacteristic
738C4C23×C3×D411yescharacteristic
739C4C23×C3×D411yescharacteristic
740C3C2×#306911yescharacteristic, direct product factor, Sylow
741C2—21no—
742C2—22no—
743C2—21no—
744C2—22no—
745C2—44no—
746C2—82no—
747C2C3×#306912yesdirect product factor
748C2C22×C3×#12111yescharacteristic
subgroupG/H
center, socleC22×C3C2×#121
commutator, Frattini, cosocleC2×C4C25×C3
prime radicalC2×C3×#575C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×#137C2semidirect
3. C22×C3×#137C2semidirect
4. C2×C3×#568C2semidirect
5. C3×#3069C2direct (N × H)
6. C2×C3×#473C2semidirect
7. C2×C3×#471C2semidirect
8. C2×C3×#430C2semidirect
9. C2×C3×#413C2semidirect
10. C22×C3×#101C2semidirect
11. C2×#3069C3direct (N × H)
25. C2×C3×#137C22semidirect
26. C2×C3×#137C22semidirect
31. C22×C3×Q16C22semidirect
33. C22×C3×SD16C22semidirect
35. C3×#568C22semidirect
43. C3×#473C22semidirect
44. C3×#471C22semidirect
45. C3×#430C22semidirect
46. C2×C3×#108C22semidirect
47. C3×#413C22semidirect
48. C2×C3×#101C22semidirect
49. C2×C3×#101C22semidirect
50. C2×C3×#101C22semidirect
51. C2×C3×#100C22semidirect
53. C22×#137C2×C3semidirect
54. C22×#137C2×C3semidirect
55. C2×#568C2×C3semidirect
56. #3069C2×C3direct (N × H)
57. C2×#473C2×C3semidirect
58. C2×#471C2×C3semidirect
59. C2×#430C2×C3semidirect
60. C2×#413C2×C3semidirect
61. C22×#101C2×C3semidirect
115. C2×C3×Q16C23semidirect
122. C2×C3×SD16C23semidirect
150. C3×#108C23semidirect
151. C3×#101C23semidirect
152. C3×#101C23semidirect
153. C3×#100C23semidirect
167. C2×#137C22×C3semidirect
168. C2×#137C22×C3semidirect
173. C22×Q16C22×C3semidirect
175. C22×SD16C22×C3semidirect
177. #568C22×C3semidirect
185. #473C22×C3semidirect
186. #471C22×C3semidirect
187. #430C22×C3semidirect
188. C2×#108C22×C3semidirect
189. #413C22×C3semidirect
190. C2×#101C22×C3semidirect
191. C2×#101C22×C3semidirect
192. C2×#101C22×C3semidirect
193. C2×#100C22×C3semidirect
369. C2×Q16C23×C3semidirect
376. C2×SD16C23×C3semidirect
404. #108C23×C3semidirect
405. #101C23×C3semidirect
406. #101C23×C3semidirect
407. #100C23×C3semidirect
712. C2×C3#3069direct (N × H)
740. C3C2×#3069direct (N × H)
747. C2C3×#3069direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5752
C22×C3×#1372
C2×C3×#5682
C3×#30692
C2×C3×#4732
C2×C3×#4712
C2×C3×#4302
C2×C3×#4132
C22×C3×#1012
C2×#30693