Finite Group Databasebeta

← C3×#30425 #10649032

Subgroups — C3×#30425 #10649032

Order 768.

1002 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#470C211yesmaximal, characteristic, complemented
2C2×C3×#452C211yesmaximal, characteristic, complemented
3C3×#2538C211yesmaximal, characteristic, complemented
4C3×#2407C211yesmaximal, characteristic
5C3×#2094C211yesmaximal, characteristic, complemented
6C3×#2077C211yesmaximal, characteristic, complemented
7C3×#2072C211yesmaximal, characteristic, complemented
8C3×#2035C211yesmaximal, characteristic, complemented
9C3×#2035C211yesmaximal, characteristic, complemented
10C3×#2000C211yesmaximal, characteristic, complemented
11C3×#1895C211yesmaximal, characteristic, complemented
12C3×#1880C211yesmaximal, characteristic, complemented
13C3×#1878C211yesmaximal, characteristic, complemented
14C3×#1870C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#30425C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C3×#470—24no—
28C3×#452—24no—
29C2×C3×#106C2211yescharacteristic
30C2×C3×#106C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic
42C3×#396—21no—
43C3×#396—21no—
44C3×#394—21no—
45C3×#392—21no—
46C3×#391C2211yescharacteristic
47C3×#390—21no—
48C3×#390C2211yescharacteristic
49C3×#389—21no—
50C3×#386—21no—
51C3×#385—21no—
52C3×#384C2211yescharacteristic
53C3×#380C2211yescharacteristic
54C3×#380C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#470C2×C311yescharacteristic, complemented
63C2×#452C2×C311yescharacteristic, complemented
64#2538C2×C311yescharacteristic, complemented
65#2407C2×C311yescharacteristic
66#2094C2×C311yescharacteristic, complemented
67#2077C2×C311yescharacteristic, complemented
68#2072C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2035C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1895C2×C311yescharacteristic, complemented
73#1880C2×C311yescharacteristic, complemented
74#1878C2×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×Q8C2311yescharacteristic
85C22×C3×D4—21no—
86C22×C3×D4—21no—
87C22×C3×D4D411yescharacteristic
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C2×C3×Q16—41no—
93C2×C3×Q16—41no—
94C2×C3×Q16D414yescomplemented
95C2×C3×SD16—22no—
96C2×C3×SD16—22no—
97C2×C3×SD16—41no—
98C2×C3×M16—22no—
99C2×C3×M16—41no—
100C2×C3×M16—41no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—41no—
109C3×C22⋊Q8—41no—
110C3×C22⋊Q8—41no—
111C3×#121—22no—
112C3×#121—41no—
113C3×C4×Q8—41no—
114C3×C4×Q8—41no—
115C3×C4×D4—41no—
116C3×C4×D4—41no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4D411yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
138C2×C3×C22⋊C4D411yescharacteristic
139C2×C3×C22⋊C4D411yescharacteristic
140C2×C3×C42—21no—
141C2×C3×C42C2311yescharacteristic
142C3×#106—22no—
143C3×#106—41no—
144C3×#103—22no—
145C3×#103—22no—
146C3×#103—22no—
147C3×#103—41no—
148C3×#103—41no—
149C3×#102—22no—
150C3×#102—41no—
151C3×#102—41no—
152C3×C22⋊C8—22no—
153C3×C22⋊C8—41no—
154C3×C22⋊C8—41no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C22×#41C22×C311yescharacteristic
161C22×Q16C22×C311yescharacteristic
162C22×SD16C22×C311yescharacteristic
163C22×M16C22×C311yescharacteristic
164C2×C22⋊Q8C22×C311yescharacteristic
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×C22⋊Q8C22×C311yescharacteristic
167C2×#121C22×C311yescharacteristic
168C2×C4×Q8C22×C311yescharacteristic
169C2×C4×D4C22×C311yescharacteristic
170#470—24no—
171#452—24no—
172C2×#106C22×C311yescharacteristic
173C2×#106C22×C311yescharacteristic
174C2×#103C22×C311yescharacteristic
175C2×#103C22×C311yescharacteristic
176C2×#103C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×C22⋊C8C22×C311yescharacteristic
183C2×C22⋊C8C22×C311yescharacteristic
184C2×C22⋊C8C22×C311yescharacteristic
185#396—21no—
186#396—21no—
187#394—21no—
188#392—21no—
189#391C22×C311yescharacteristic
190#390—21no—
191#390C22×C311yescharacteristic
192#389—21no—
193#386—21no—
194#385—21no—
195#384C22×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×C3C2×D411yescharacteristic
207C24×C3C2×D411yescharacteristic
208C3×#41—44no—
209C3×#41—44no—
210C3×#41—44no—
211C3×#41—44no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8C2×D412yes—
223C2×C3×Q8C2×D412yes—
224C2×C3×D4—22no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
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—81no—
238C2×C3×D4#4112yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
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—42no—
259C22×C3×C4—42no—
260C22×C3×C4—42no—
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C3×Q16—44no—
267C3×SD16—44no—
268C3×M16—44no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8C2×D412yes—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—41no—
292C3×C4⋊C4—42no—
293C3×C4⋊C4—42no—
294C3×C4⋊C4—42no—
295C3×C4⋊C4—42no—
296C3×C4⋊C4—42no—
297C3×C4⋊C4—81no—
298C3×C22⋊C4—41no—
299C3×C22⋊C4—41no—
300C3×C22⋊C4—42no—
301C3×C22⋊C4—42no—
302C3×C22⋊C4—42no—
303C3×C22⋊C4—42no—
304C3×C22⋊C4—42no—
305C3×C22⋊C4—81no—
306C3×C22⋊C4—81no—
307C3×C22⋊C4—81no—
308C3×C22⋊C4—81no—
309C3×C42—21no—
310C3×C42—21no—
311C3×C42—42no—
312C2×#41—22no—
313C2×#41—22no—
314C2×#41—41no—
315C2×#41—41no—
316C2×#41—41no—
317C2×#41—41no—
318C22×Q8C23×C311yescharacteristic
319C22×Q8C23×C311yescharacteristic
320C22×D4—21no—
321C22×D4—21no—
322C22×D4C3×D411yescharacteristic
323C22×D4C23×C311yescharacteristic
324C23×C4—21no—
325C23×C4C23×C311yescharacteristic
326C23×C4C23×C311yescharacteristic
327C2×Q16—41no—
328C2×Q16—41no—
329C2×Q16C3×D414yescomplemented
330C2×SD16—22no—
331C2×SD16—22no—
332C2×SD16—41no—
333C2×M16—22no—
334C2×M16—41no—
335C2×M16—41no—
336C22×C8C23×C311yescharacteristic
337C22×C8C23×C311yescharacteristic
338C22×C8C23×C311yescharacteristic
339C22×C8C23×C311yescharacteristic
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—41no—
344C22⋊Q8—41no—
345C22⋊Q8—41no—
346#121—22no—
347#121—41no—
348C4×Q8—41no—
349C4×Q8—41no—
350C4×D4—41no—
351C4×D4—41no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4C3×D411yescharacteristic
359C2×C4⋊C4C23×C311yescharacteristic
360C2×C4⋊C4C23×C311yescharacteristic
361C2×C4⋊C4C23×C311yescharacteristic
362C2×C4⋊C4C23×C311yescharacteristic
363C2×C4⋊C4C23×C311yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
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⋊C4C3×D411yescharacteristic
374C2×C22⋊C4C3×D411yescharacteristic
375C2×C42—21no—
376C2×C42C23×C311yescharacteristic
377#106—22no—
378#106—41no—
379#103—22no—
380#103—22no—
381#103—22no—
382#103—41no—
383#103—41no—
384#102—22no—
385#102—41no—
386#102—41no—
387C22⋊C8—22no—
388C22⋊C8—41no—
389C22⋊C8—41no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—22no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3C22×D411yescharacteristic
417C3×Q8—22no—
418C3×Q8—22no—
419C3×Q8—22no—
420C3×Q8—22no—
421C3×Q8—41no—
422C3×Q8—41no—
423C3×Q8—41no—
424C3×Q8—41no—
425C3×D4—22no—
426C3×D4—22no—
427C3×D4—44no—
428C3×D4—48no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—84no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—48no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
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#13712yes—
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×C3×C4H(5,𝔽2)11yescharacteristic
477C2×C3×C4H(5,𝔽2)11yescharacteristic
478C2×C3×C4H(5,𝔽2)11yescharacteristic
479C2×C3×C4H(5,𝔽2)11yescharacteristic
480C3×C8—22no—
481C3×C8—41no—
482C3×C8—41no—
483C3×C8—41no—
484C24—21no—
485C24C2×C3×D411yescharacteristic
486C24C2×C3×D411yescharacteristic
487#41—44no—
488#41—44no—
489#41—44no—
490#41—44no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8C2×C3×D412yes—
502C2×Q8C2×C3×D412yes—
503C2×D4—22no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—41no—
510C2×D4—41no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—81no—
517C2×D4C3×#4112yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4C2×C3×D411yescharacteristic
541C22×C4C2×C3×D411yescharacteristic
542C22×C4C2×C3×D411yescharacteristic
543C22×C4C2×C3×D411yescharacteristic
544C22×C4C24×C311yescharacteristic
545Q16—44no—
546SD16—44no—
547M16—44no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8C2×C3×D412yes—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—41no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—81no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C42—21no—
589C42—21no—
590C42—42no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—41no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—42no—
607C22×C3—41no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—81no—
612C22×C3#53411yescharacteristic
613C22×C3D4211yescharacteristic
614C22×C3#54611yescharacteristic
615C22×C3C2×#13711yescharacteristic
616C22×C3#57511yescharacteristic
617C22×C3#57711yescharacteristic
618C22×C3#57711yescharacteristic
619C3×C4—22no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—41no—
625C3×C4—81no—
626C3×C4—81no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4—81no—
630C3×C4#53411yescharacteristic
631C3×C4#53811yescharacteristic
632C3×C4#54611yescharacteristic
633C3×C4#56011yescharacteristic
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23C22×C3×D411yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—22no—
659Q8—22no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—41no—
664D4—22no—
665D4—22no—
666D4—44no—
667D4—48no—
668D4—41no—
669D4—41no—
670D4—84no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—48no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4C3×#13712yes—
713C2×C4C22×C3×D411yescharacteristic
714C2×C4C2×C3×#4111yescharacteristic
715C2×C4C3×H(5,𝔽2)11yescharacteristic
716C2×C4C3×H(5,𝔽2)11yescharacteristic
717C2×C4C3×H(5,𝔽2)11yescharacteristic
718C2×C4C3×H(5,𝔽2)11yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C2×C3—81no—
724C2×C3—81no—
725C2×C3—82no—
726C2×C3#266811yescharacteristic
727C2×C3#319611yescharacteristic
728C2×C3#320411yescharacteristic
729C2×C3#327111yescharacteristic
730C2×C3#327811yescharacteristic
731C2×C3#331111yescharacteristic
732C2×C3#333111yescharacteristic
733C22—42no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22C3×#53411yescharacteristic
755C22C3×D4211yescharacteristic
756C22C3×#54611yescharacteristic
757C22C2×C3×#13711yescharacteristic
758C22C3×#57511yescharacteristic
759C22C3×#57711yescharacteristic
760C22C3×#57711yescharacteristic
761C4—22no—
762C4—41no—
763C4—41no—
764C4—42no—
765C4—42no—
766C4—41no—
767C4—81no—
768C4—81no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4C3×#53411yescharacteristic
773C4C3×#53811yescharacteristic
774C4C3×#54611yescharacteristic
775C4C3×#56011yescharacteristic
776C3#3042511yescharacteristic, direct product factor, Sylow
777C2—81no—
778C2—81no—
779C2—82no—
780C2C3×#266811yescharacteristic
781C2C3×#319611yescharacteristic
782C2C3×#320411yescharacteristic
783C2C3×#327111yescharacteristic
784C2C3×#327811yescharacteristic
785C2C3×#331111yescharacteristic
786C2C3×#333111yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2407C2
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×#470C2semidirect
2. C2×C3×#452C2semidirect
3. C3×#2538C2semidirect
5. C3×#2094C2semidirect
6. C3×#2077C2semidirect
7. C3×#2072C2semidirect
8. C3×#2035C2semidirect
9. C3×#2035C2semidirect
10. C3×#2000C2semidirect
11. C3×#1895C2semidirect
12. C3×#1880C2semidirect
13. C3×#1878C2semidirect
14. C3×#1870C2semidirect
15. C3×#1788C2semidirect
16. #30425C3direct (N × H)
62. C2×#470C2×C3semidirect
63. C2×#452C2×C3semidirect
64. #2538C2×C3semidirect
66. #2094C2×C3semidirect
67. #2077C2×C3semidirect
68. #2072C2×C3semidirect
69. #2035C2×C3semidirect
70. #2035C2×C3semidirect
71. #2000C2×C3semidirect
72. #1895C2×C3semidirect
73. #1880C2×C3semidirect
74. #1878C2×C3semidirect
75. #1870C2×C3semidirect
76. #1788C2×C3semidirect
94. C2×C3×Q16D4semidirect
329. C2×Q16C3×D4semidirect
776. C3#30425direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4702
C2×C3×#4522
C3×#25382
C3×#24072
C3×#20942
C3×#20772
C3×#20722
C3×#20352
C3×#20002
C3×#18952
C3×#18802
C3×#18782
C3×#18702
C3×#17882
#304253