Finite Group Databasebeta

← C3×#23922 #10642529

Subgroups — C3×#23922 #10642529

Order 768.

1928 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic
2C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×#452C212yesmaximal, complemented
4C2×C3×#451C211yesmaximal, characteristic, complemented
5C2×C3×#448C211yesmaximal, characteristic, complemented
6C3×#2001C212yesmaximal, complemented
7C3×#2000C212yesmaximal, complemented
8C3×#1874C211yesmaximal, characteristic, complemented
9C3×#1873C212yesmaximal, complemented
10C3×#1872C211yesmaximal, characteristic, complemented
11C3×#1779C211yesmaximal, characteristic, complemented
12#23922C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic
14C23×C3×Q8C2211yescharacteristic
15C24×C3×C4C2211yescharacteristic
16C22×C3×Q16C2212yescomplemented
17C22×C3×SD16C2212yescomplemented
18C3×#525—24no—
19C3×#525—24no—
20C2×C3×#123—21no—
21C2×C3×C22⋊Q8—21no—
22C2×C3×C22⋊Q8—21no—
23C2×C3×C22⋊Q8—28no—
24C2×C3×C22⋊Q8C2212yes—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×C22⋊Q8C2212yes—
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#120—21no—
31C2×C3×C4×D4—21no—
32C2×C3×C4×D4—21no—
33C2×C3×#117C2211yescharacteristic
34C22×C3×C4⋊C4—21no—
35C22×C3×C4⋊C4C2211yescharacteristic
36C22×C3×C22⋊C4—21no—
37C3×#452—28no—
38C3×#451—24no—
39C3×#448—24no—
40C2×C3×#103C2212yescomplemented
41C2×C3×#103C2212yescomplemented
42C2×C3×#103C2212yescomplemented
43C2×C3×#102C2212yescomplemented
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C22⋊C8C2212yes—
47C2×C3×C22⋊C8C2212yes—
48C3×#340C2212yescomplemented
49C3×#340C2212yescomplemented
50C2×#525C2×C311yescharacteristic
51C22×C22⋊Q8C2×C311yescharacteristic, complemented
52C2×#452C2×C312yescomplemented
53C2×#451C2×C311yescharacteristic, complemented
54C2×#448C2×C311yescharacteristic, complemented
55#2001C2×C312yescomplemented
56#2000C2×C312yescomplemented
57#1874C2×C311yescharacteristic, complemented
58#1873C2×C312yescomplemented
59#1872C2×C311yescharacteristic, complemented
60#1779C2×C311yescharacteristic, complemented
61C25×C3D411yescharacteristic
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—24no—
65C2×C3×#41—42no—
66C22×C3×Q8—24no—
67C22×C3×Q8—21no—
68C22×C3×Q8—22no—
69C22×C3×Q8—22no—
70C22×C3×Q8—42no—
71C22×C3×Q8C2312yes—
72C22×C3×Q8C2311yescharacteristic
73C22×C3×D4—21no—
74C22×C3×D4—21no—
75C22×C3×D4—21no—
76C22×C3×D4C2311yescharacteristic
77C23×C3×C4—21no—
78C23×C3×C4—21no—
79C23×C3×C4—24no—
80C23×C3×C4—22no—
81C23×C3×C4—22no—
82C23×C3×C4—21no—
83C23×C3×C4—42no—
84C23×C3×C4D411yescharacteristic
85C23×C3×C4D411yescharacteristic
86C23×C3×C4D411yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C2×C3×Q16—24no—
91C2×C3×Q16—24no—
92C2×C3×Q16—42no—
93C2×C3×SD16—24no—
94C2×C3×SD16—24no—
95C2×C3×SD16—42no—
96C22×C3×C8C2312yes—
97C22×C3×C8C2312yes—
98C3×#123—28no—
99C3×C22⋊Q8—28no—
100C3×C22⋊Q8—28no—
101C3×C22⋊Q8—24no—
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8—24no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—24no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8D414yes—
108C3×C22⋊Q8D418yescomplemented
109C3×#121—22no—
110C3×#121—22no—
111C3×#121—22no—
112C3×#121D414yes—
113C3×#120—28no—
114C3×C4×D4—28no—
115C3×C4×D4—28no—
116C3×#117—22no—
117C3×#117—22no—
118C2×C3×C4⋊C4—28no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—24no—
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C22⋊C4—28no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
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×C42—21no—
137C3×#103—24no—
138C3×#103—24no—
139C3×#103—24no—
140C3×#102—24no—
141C3×C22⋊C8—22no—
142C3×C22⋊C8—22no—
143C3×C22⋊C8—24no—
144C3×C22⋊C8—42no—
145C22×#41C22×C311yescharacteristic
146C23×Q8C22×C311yescharacteristic
147C24×C4C22×C311yescharacteristic
148C22×Q16C22×C312yescomplemented
149C22×SD16C22×C312yescomplemented
150#525—24no—
151#525—24no—
152C2×#123—21no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—28no—
156C2×C22⋊Q8C22×C312yes—
157C2×C22⋊Q8C22×C311yescharacteristic
158C2×C22⋊Q8C22×C311yescharacteristic
159C2×C22⋊Q8C22×C312yes—
160C2×#121C22×C311yescharacteristic
161C2×#121C22×C311yescharacteristic
162C2×#120—21no—
163C2×C4×D4—21no—
164C2×C4×D4—21no—
165C2×#117C22×C311yescharacteristic
166C22×C4⋊C4—21no—
167C22×C4⋊C4C22×C311yescharacteristic
168C22×C22⋊C4—21no—
169#452—28no—
170#451—24no—
171#448—24no—
172C2×#103C22×C312yescomplemented
173C2×#103C22×C312yescomplemented
174C2×#103C22×C312yescomplemented
175C2×#102C22×C312yescomplemented
176C2×C22⋊C8C22×C311yescharacteristic
177C2×C22⋊C8C22×C312yes—
178C2×C22⋊C8C22×C311yescharacteristic
179C2×C22⋊C8C22×C312yes—
180#340C22×C312yescomplemented
181#340C22×C312yescomplemented
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—21no—
188C24×C3—41no—
189C24×C3—41no—
190C24×C3C2×D411yescharacteristic
191C24×C3C2×D411yescharacteristic
192C24×C3C2×D411yescharacteristic
193C3×#41—48no—
194C3×#41—48no—
195C2×C3×Q8—24no—
196C2×C3×Q8—22no—
197C2×C3×Q8—21no—
198C2×C3×Q8—22no—
199C2×C3×Q8—22no—
200C2×C3×Q8—22no—
201C2×C3×Q8—22no—
202C2×C3×Q8—22no—
203C2×C3×Q8—22no—
204C2×C3×Q8—48no—
205C2×C3×Q8—48no—
206C2×C3×Q8—42no—
207C2×C3×Q8—42no—
208C2×C3×Q8C2×D412yes—
209C2×C3×Q8C2×D414yes—
210C2×C3×D4—24no—
211C2×C3×D4—24no—
212C2×C3×D4—24no—
213C2×C3×D4—22no—
214C2×C3×D4—21no—
215C2×C3×D4—22no—
216C2×C3×D4—42no—
217C2×C3×D4—42no—
218C2×C3×D4—42no—
219C2×C3×D4—42no—
220C2×C3×D4—42no—
221C2×C3×D4—42no—
222C2×C3×D4C2×D412yes—
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—24no—
229C22×C3×C4—24no—
230C22×C3×C4—24no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—22no—
236C22×C3×C4—21no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—41no—
247C22×C3×C4—41no—
248C22×C3×C4—41no—
249C22×C3×C4—48no—
250C22×C3×C4—48no—
251C22×C3×C4—42no—
252C22×C3×C4—42no—
253C22×C3×C4—42no—
254C22×C3×C4—42no—
255C22×C3×C4—42no—
256C22×C3×C4—42no—
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D412yes—
261C22×C3×C4C2×D412yes—
262C22×C3×C4C2×D414yes—
263C22×C3×C4C2411yescharacteristic
264C3×Q16—48no—
265C3×SD16—48no—
266C2×C3×C8—22no—
267C2×C3×C8—22no—
268C2×C3×C8—22no—
269C2×C3×C8—22no—
270C2×C3×C8—22no—
271C2×C3×C8—22no—
272C3×C4⋊C4—24no—
273C3×C4⋊C4—28no—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—28no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4C2×D414yes—
281C3×C4⋊C4C2×D412yes—
282C3×C4⋊C4C2×D412yes—
283C3×C22⋊C4—28no—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—28no—
288C3×C22⋊C4—24no—
289C3×C22⋊C4—24no—
290C3×C42—24no—
291C25C3×D411yescharacteristic
292C2×#41—22no—
293C2×#41—22no—
294C2×#41—24no—
295C2×#41—42no—
296C22×Q8—24no—
297C22×Q8—21no—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8—42no—
301C22×Q8C23×C312yes—
302C22×Q8C23×C311yescharacteristic
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4C23×C311yescharacteristic
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4—24no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—42no—
314C23×C4C3×D411yescharacteristic
315C23×C4C3×D411yescharacteristic
316C23×C4C3×D411yescharacteristic
317C23×C4C23×C311yescharacteristic
318C23×C4C23×C311yescharacteristic
319C23×C4C23×C311yescharacteristic
320C2×Q16—24no—
321C2×Q16—24no—
322C2×Q16—42no—
323C2×SD16—24no—
324C2×SD16—24no—
325C2×SD16—42no—
326C22×C8C23×C312yes—
327C22×C8C23×C312yes—
328#123—28no—
329C22⋊Q8—28no—
330C22⋊Q8—28no—
331C22⋊Q8—24no—
332C22⋊Q8—22no—
333C22⋊Q8—24no—
334C22⋊Q8—22no—
335C22⋊Q8—24no—
336C22⋊Q8—22no—
337C22⋊Q8C3×D414yes—
338C22⋊Q8C3×D418yescomplemented
339#121—22no—
340#121—22no—
341#121—22no—
342#121C3×D414yes—
343#120—28no—
344C4×D4—28no—
345C4×D4—28no—
346#117—22no—
347#117—22no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4C23×C312yes—
356C2×C4⋊C4C23×C311yescharacteristic
357C2×C4⋊C4C23×C311yescharacteristic
358C2×C22⋊C4—28no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C42—21no—
367#103—24no—
368#103—24no—
369#103—24no—
370#102—24no—
371C22⋊C8—22no—
372C22⋊C8—22no—
373C22⋊C8—24no—
374C22⋊C8—42no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—28no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—22no—
393C23×C3—44no—
394C23×C3—44no—
395C23×C3—44no—
396C23×C3—44no—
397C23×C3—44no—
398C23×C3—44no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3#12012yes—
406C23×C3#12012yes—
407C23×C3#13512yes—
408C23×C3#13712yes—
409C23×C3#13712yes—
410C23×C3C22×D411yescharacteristic
411C3×Q8—24no—
412C3×Q8—24no—
413C3×Q8—24no—
414C3×Q8—48no—
415C3×Q8—42no—
416C3×Q8—42no—
417C3×Q8—42no—
418C3×D4—24no—
419C3×D4—48no—
420C3×D4—48no—
421C3×D4—48no—
422C3×D4—42no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—24no—
430C2×C3×C4—24no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—24no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—24no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—44no—
440C2×C3×C4—44no—
441C2×C3×C4—44no—
442C2×C3×C4—48no—
443C2×C3×C4—48no—
444C2×C3×C4—48no—
445C2×C3×C4—41no—
446C2×C3×C4—42no—
447C2×C3×C4—41no—
448C2×C3×C4—42no—
449C2×C3×C4—42no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—42no—
454C2×C3×C4—41no—
455C2×C3×C4—42no—
456C2×C3×C4—42no—
457C2×C3×C4#12012yes—
458C2×C3×C4#12012yes—
459C2×C3×C4C22×D412yes—
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C22×D411yescharacteristic
462C2×C3×C4H(5,𝔽2)12yes—
463C3×C8—42no—
464C3×C8—42no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—41no—
472C24—41no—
473C24C2×C3×D411yescharacteristic
474C24C2×C3×D411yescharacteristic
475C24C2×C3×D411yescharacteristic
476#41—48no—
477#41—48no—
478C2×Q8—24no—
479C2×Q8—22no—
480C2×Q8—21no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8C2×C3×D412yes—
492C2×Q8C2×C3×D414yes—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—24no—
496C2×D4—22no—
497C2×D4—21no—
498C2×D4—22no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4C2×C3×D412yes—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4C2×C3×D411yescharacteristic
541C22×C4C2×C3×D411yescharacteristic
542C22×C4C2×C3×D411yescharacteristic
543C22×C4C2×C3×D412yes—
544C22×C4C2×C3×D412yes—
545C22×C4C2×C3×D414yes—
546C22×C4C24×C311yescharacteristic
547Q16—48no—
548SD16—48no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C4⋊C4—24no—
556C4⋊C4—28no—
557C4⋊C4—24no—
558C4⋊C4—28no—
559C4⋊C4—24no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4C2×C3×D414yes—
564C4⋊C4C2×C3×D412yes—
565C4⋊C4C2×C3×D412yes—
566C22⋊C4—28no—
567C22⋊C4—24no—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—28no—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C42—24no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—416no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3#45214yescomplemented
603C22×C3C2×#12011yescharacteristic
604C22×C3C2×#12011yescharacteristic
605C22×C3#53411yescharacteristic
606C22×C3C2×#13511yescharacteristic
607C22×C3C2×#13711yescharacteristic
608C22×C3C2×#13711yescharacteristic
609C22×C3#57511yescharacteristic
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—41no—
613C3×C4—42no—
614C3×C4—44no—
615C3×C4—42no—
616C3×C4—44no—
617C3×C4—42no—
618C3×C4D4212yes—
619C3×C4D4212yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—28no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C3×#12012yes—
651C23C3×#12012yes—
652C23C3×#13512yes—
653C23C3×#13712yes—
654C23C3×#13712yes—
655C23C22×C3×D411yescharacteristic
656Q8—24no—
657Q8—24no—
658Q8—24no—
659Q8—48no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663D4—24no—
664D4—48no—
665D4—48no—
666D4—48no—
667D4—42no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—48no—
688C2×C4—48no—
689C2×C4—48no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4C3×#12012yes—
703C2×C4C3×#12012yes—
704C2×C4C22×C3×D412yes—
705C2×C4C22×C3×D411yescharacteristic
706C2×C4C22×C3×D411yescharacteristic
707C2×C4C3×H(5,𝔽2)12yes—
708C8—42no—
709C8—42no—
710C2×C3—24no—
711C2×C3—42no—
712C2×C3—42no—
713C2×C3—82no—
714C2×C3#240311yescharacteristic
715C2×C3C2×#45211yescharacteristic
716C2×C3#300211yescharacteristic
717C2×C3#300411yescharacteristic
718C2×C3#300711yescharacteristic
719C2×C3#319011yescharacteristic
720C2×C3#319611yescharacteristic
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—416no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22C3×#45214yescomplemented
750C22C2×C3×#12011yescharacteristic
751C22C2×C3×#12011yescharacteristic
752C22C3×#53411yescharacteristic
753C22C2×C3×#13511yescharacteristic
754C22C2×C3×#13711yescharacteristic
755C22C2×C3×#13711yescharacteristic
756C22C3×#57511yescharacteristic
757C4—22no—
758C4—22no—
759C4—41no—
760C4—42no—
761C4—44no—
762C4—42no—
763C4—44no—
764C4—42no—
765C4C3×D4212yes—
766C4C3×D4212yes—
767C3#2392211yescharacteristic, direct product factor, Sylow
768C2—24no—
769C2—42no—
770C2—42no—
771C2—82no—
772C2C3×#240311yescharacteristic
773C2C2×C3×#45211yescharacteristic
774C2C3×#300211yescharacteristic
775C2C3×#300411yescharacteristic
776C2C3×#300711yescharacteristic
777C2C3×#319011yescharacteristic
778C2C3×#319611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×C22⋊Q8C2semidirect
3. C2×C3×#452C2semidirect
4. C2×C3×#451C2semidirect
5. C2×C3×#448C2semidirect
6. C3×#2001C2semidirect
7. C3×#2000C2semidirect
8. C3×#1874C2semidirect
9. C3×#1873C2semidirect
10. C3×#1872C2semidirect
11. C3×#1779C2semidirect
12. #23922C3direct (N × H)
16. C22×C3×Q16C22semidirect
17. C22×C3×SD16C22semidirect
40. C2×C3×#103C22semidirect
41. C2×C3×#103C22semidirect
42. C2×C3×#103C22semidirect
43. C2×C3×#102C22semidirect
48. C3×#340C22semidirect
49. C3×#340C22semidirect
51. C22×C22⋊Q8C2×C3semidirect
52. C2×#452C2×C3semidirect
53. C2×#451C2×C3semidirect
54. C2×#448C2×C3semidirect
55. #2001C2×C3semidirect
56. #2000C2×C3semidirect
57. #1874C2×C3semidirect
58. #1873C2×C3semidirect
59. #1872C2×C3semidirect
60. #1779C2×C3semidirect
108. C3×C22⋊Q8D4semidirect
148. C22×Q16C22×C3semidirect
149. C22×SD16C22×C3semidirect
172. C2×#103C22×C3semidirect
173. C2×#103C22×C3semidirect
174. C2×#103C22×C3semidirect
175. C2×#102C22×C3semidirect
180. #340C22×C3semidirect
181. #340C22×C3semidirect
338. C22⋊Q8C3×D4semidirect
602. C22×C3#452semidirect
749. C22C3×#452semidirect
767. C3#23922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C22×C3×C22⋊Q82
C2×C3×#4522
C2×C3×#4512
C2×C3×#4482
C3×#20012
C3×#20002
C3×#18742
C3×#18732
C3×#18722
C3×#17792
#239223