Finite Group Databasebeta

← C3×#23583 #10642190

Subgroups — C3×#23583 #10642190

Order 768.

1178 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×#542C211yesmaximal, characteristic, complemented
2C2×C3×#442C211yesmaximal, characteristic, complemented
3C2×C3×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#2324C211yesmaximal, characteristic, complemented
5C3×#2058C211yesmaximal, characteristic, complemented
6C3×#2042C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8C3×#2034C211yesmaximal, characteristic, complemented
9C3×#2023C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#1999C211yesmaximal, characteristic
13C3×#1763C211yesmaximal, characteristic, complemented
14C3×C4×#102C211yesmaximal, characteristic, complemented
15C3×#1750C211yesmaximal, characteristic, complemented
16#23583C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C3×#542—24no—
20C3×#542—24no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#126—21no—
23C2×C3×#124—21no—
24C2×C3×#124C2211yescharacteristic
25C2×C3×#123—21no—
26C2×C3×C22⋊Q8—21no—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×#117C2211yescharacteristic
34C3×#442—24no—
35C3×C4×SD16—24no—
36C2×C3×#106C2211yescharacteristic
37C2×C3×#106C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×#97C2211yescharacteristic
49C2×C3×C4×C8C2211yescharacteristic
50C3×#390—21no—
51C3×#390C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#388—21no—
54C3×#386—21no—
55C3×#385—21no—
56C3×#380C2211yescharacteristic
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#542C2×C311yescharacteristic, complemented
65C2×#442C2×C311yescharacteristic, complemented
66C2×C4×SD16C2×C311yescharacteristic, complemented
67#2324C2×C311yescharacteristic, complemented
68#2058C2×C311yescharacteristic, complemented
69#2042C2×C311yescharacteristic, complemented
70#2035C2×C311yescharacteristic, complemented
71#2034C2×C311yescharacteristic, complemented
72#2023C2×C311yescharacteristic, complemented
73#2012C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic
76#1763C2×C311yescharacteristic, complemented
77C4×#102C2×C311yescharacteristic, complemented
78#1750C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4—21no—
87C23×C3×C4C2311yescharacteristic
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C2×C3×D8—22no—
92C2×C3×D8—22no—
93C2×C3×D8—22no—
94C22×C3×C8C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C3×C4⋊Q8—22no—
99C3×C4⋊Q8—22no—
100C3×#126—28no—
101C3×#124—28no—
102C3×#124—22no—
103C3×#124—22no—
104C3×#123—28no—
105C3×C22⋊Q8—28no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—22no—
108C3×#121—22no—
109C3×#121—22no—
110C3×#121—22no—
111C3×#121—22no—
112C3×C4×Q8—22no—
113C3×C4×Q8D414yescomplemented
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×C4×D4D414yescomplemented
118C3×#117—22no—
119C3×#117—22no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4D411yescharacteristic
125C2×C3×C4⋊C4D411yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4D411yescharacteristic
142C2×C3×C22⋊C4D411yescharacteristic
143C2×C3×C42—21no—
144C2×C3×C42—21no—
145C2×C3×C42C2311yescharacteristic
146C2×C3×C42C2311yescharacteristic
147C3×#106—22no—
148C3×#106—22no—
149C3×#103—22no—
150C3×#103—22no—
151C3×#103—22no—
152C3×#102—22no—
153C3×#102—22no—
154C3×#102—22no—
155C3×#102—22no—
156C3×#102—22no—
157C3×C22⋊C8—22no—
158C3×C22⋊C8—22no—
159C3×#97—22no—
160C3×C4×C8—22no—
161C3×#95—21no—
162C3×#95—21no—
163C3×#95—21no—
164C22×SD16C22×C311yescharacteristic
165C22×D8C22×C311yescharacteristic
166#542—24no—
167#542—24no—
168C2×C4⋊Q8C22×C311yescharacteristic
169C2×#126—21no—
170C2×#124—21no—
171C2×#124C22×C311yescharacteristic
172C2×#123—21no—
173C2×C22⋊Q8—21no—
174C2×C22⋊Q8C22×C311yescharacteristic
175C2×#121C22×C311yescharacteristic
176C2×#121C22×C311yescharacteristic
177C2×C4×Q8C22×C311yescharacteristic
178C2×C4×D4C22×C311yescharacteristic
179C2×C4×D4C22×C311yescharacteristic
180C2×#117C22×C311yescharacteristic
181#442—24no—
182C4×SD16—24no—
183C2×#106C22×C311yescharacteristic
184C2×#106C22×C311yescharacteristic
185C2×#103C22×C311yescharacteristic
186C2×#103C22×C311yescharacteristic
187C2×#103C22×C311yescharacteristic
188C2×#102C22×C311yescharacteristic
189C2×#102C22×C311yescharacteristic
190C2×#102C22×C311yescharacteristic
191C2×#102C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×C22⋊C8C22×C311yescharacteristic
194C2×C22⋊C8C22×C311yescharacteristic
195C2×#97C22×C311yescharacteristic
196C2×C4×C8C22×C311yescharacteristic
197#390—21no—
198#390C22×C311yescharacteristic
199#389C22×C311yescharacteristic
200#388—21no—
201#386—21no—
202#385—21no—
203#380C22×C311yescharacteristic
204C4×C4⋊C4C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#340C22×C311yescharacteristic
209#336C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211C24×C3—21no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C2×C3×Q8—24no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—81no—
221C2×C3×Q8—81no—
222C2×C3×Q8C2×D412yes—
223C2×C3×D4—24no—
224C2×C3×D4—24no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—81no—
236C2×C3×D4—81no—
237C2×C3×D4—81no—
238C2×C3×D4—81no—
239C2×C3×D4C2×D412yes—
240C2×C3×D4#4112yes—
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—24no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—42no—
255C22×C3×C4—81no—
256C22×C3×C4—81no—
257C22×C3×C4—81no—
258C22×C3×C4—81no—
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2411yescharacteristic
265C3×SD16—28no—
266C3×D8—28no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
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#4112yes—
278C2×C3×C8#4112yes—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—22no—
283C3×C4⋊C4—22no—
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—81no—
292C3×C4⋊C4C2×D412yes—
293C3×C4⋊C4C2×D412yes—
294C3×C4⋊C4#4112yes—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—24no—
301C3×C22⋊C4—22no—
302C3×C22⋊C4—22no—
303C3×C22⋊C4—42no—
304C3×C22⋊C4—81no—
305C3×C22⋊C4—81no—
306C3×C22⋊C4—81no—
307C3×C42—24no—
308C3×C42—21no—
309C3×C42—21no—
310C3×C42—81no—
311C3×C42C2×D412yes—
312C3×C42C2×D412yes—
313C22×Q8—21no—
314C22×Q8C23×C311yescharacteristic
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C23×C311yescharacteristic
318C22×D4C23×C311yescharacteristic
319C23×C4—21no—
320C23×C4—21no—
321C23×C4C23×C311yescharacteristic
322C2×SD16—22no—
323C2×SD16—22no—
324C2×SD16—22no—
325C2×D8—22no—
326C2×D8—22no—
327C2×D8—22no—
328C22×C8C23×C311yescharacteristic
329C22×C8C23×C311yescharacteristic
330C22×C8C23×C311yescharacteristic
331C22×C8C23×C311yescharacteristic
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334#126—28no—
335#124—28no—
336#124—22no—
337#124—22no—
338#123—28no—
339C22⋊Q8—28no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342#121—22no—
343#121—22no—
344#121—22no—
345#121—22no—
346C4×Q8—22no—
347C4×Q8C3×D414yescomplemented
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4C3×D414yescomplemented
352#117—22no—
353#117—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4C3×D411yescharacteristic
359C2×C4⋊C4C3×D411yescharacteristic
360C2×C4⋊C4C23×C311yescharacteristic
361C2×C4⋊C4C23×C311yescharacteristic
362C2×C4⋊C4C23×C311yescharacteristic
363C2×C4⋊C4C23×C311yescharacteristic
364C2×C4⋊C4C23×C311yescharacteristic
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⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4C3×D411yescharacteristic
376C2×C22⋊C4C3×D411yescharacteristic
377C2×C42—21no—
378C2×C42—21no—
379C2×C42C23×C311yescharacteristic
380C2×C42C23×C311yescharacteristic
381#106—22no—
382#106—22no—
383#103—22no—
384#103—22no—
385#103—22no—
386#102—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391C22⋊C8—22no—
392C22⋊C8—22no—
393#97—22no—
394C4×C8—22no—
395#95—21no—
396#95—21no—
397#95—21no—
398C23×C3—21no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3C22×D411yescharacteristic
420C3×Q8—22no—
421C3×Q8—22no—
422C3×Q8—41no—
423C3×Q8—41no—
424C3×Q8—84no—
425C3×D4—22no—
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—22no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—41no—
433C3×D4—84no—
434C3×D4—84no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
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—84no—
471C2×C3×C4—84no—
472C2×C3×C4#12012yes—
473C2×C3×C4#12012yes—
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478C2×C3×C4C2×#4111yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C3×C8—22no—
481C3×C8—22no—
482C3×C8—41no—
483C3×C8—41no—
484C24—21no—
485C24—21no—
486C24C2×C3×D411yescharacteristic
487C2×Q8—24no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—81no—
494C2×Q8—81no—
495C2×Q8C2×C3×D412yes—
496C2×D4—24no—
497C2×D4—24no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4—81no—
511C2×D4—81no—
512C2×D4C2×C3×D412yes—
513C2×D4C3×#4112yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4C2×C3×D411yescharacteristic
533C22×C4C2×C3×D411yescharacteristic
534C22×C4C2×C3×D411yescharacteristic
535C22×C4C2×C3×D411yescharacteristic
536C22×C4C2×C3×D411yescharacteristic
537C22×C4C24×C311yescharacteristic
538SD16—28no—
539D8—28no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8C3×#4112yes—
551C2×C8C3×#4112yes—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—81no—
565C4⋊C4C2×C3×D412yes—
566C4⋊C4C2×C3×D412yes—
567C4⋊C4C3×#4112yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—42no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C42—24no—
581C42—21no—
582C42—21no—
583C42—81no—
584C42C2×C3×D412yes—
585C42C2×C3×D412yes—
586C22×C3—41no—
587C22×C3—42no—
588C22×C3—41no—
589C22×C3—42no—
590C22×C3—41no—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—41no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3C2×#12011yescharacteristic
608C22×C3#52511yescharacteristic
609C22×C3#53211yescharacteristic
610C22×C3#57611yescharacteristic
611C22×C3#57711yescharacteristic
612C22×C3#57711yescharacteristic
613C22×C3#57711yescharacteristic
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—42no—
617C3×C4—41no—
618C3×C4—42no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4—81no—
624C3×C4—81no—
625C3×C4#52511yescharacteristic
626C3×C4#52511yescharacteristic
627C3×C4#53211yescharacteristic
628C3×C4#53211yescharacteristic
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23C22×C3×D411yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655Q8—84no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—84no—
665D4—84no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
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—84no—
702C2×C4—84no—
703C2×C4C3×#12012yes—
704C2×C4C3×#12012yes—
705C2×C4C22×C3×D411yescharacteristic
706C2×C4C22×C3×D411yescharacteristic
707C2×C4C2×C3×#4111yescharacteristic
708C2×C4C2×C3×#4111yescharacteristic
709C2×C4C2×C3×#4111yescharacteristic
710C2×C4C2×C3×#4111yescharacteristic
711C8—22no—
712C8—22no—
713C8—41no—
714C8—41no—
715C2×C3—81no—
716C2×C3—82no—
717C2×C3—82no—
718C2×C3#238811yescharacteristic
719C2×C3#301011yescharacteristic
720C2×C3#301211yescharacteristic
721C2×C3#311811yescharacteristic
722C2×C3#312511yescharacteristic
723C2×C3#317311yescharacteristic
724C2×C3#317911yescharacteristic
725C22—41no—
726C22—42no—
727C22—42no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—41no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22C2×C3×#12011yescharacteristic
747C22C3×#52511yescharacteristic
748C22C3×#53211yescharacteristic
749C22C3×#57611yescharacteristic
750C22C3×#57711yescharacteristic
751C22C3×#57711yescharacteristic
752C22C3×#57711yescharacteristic
753C4—22no—
754C4—22no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—81no—
763C4—81no—
764C4C3×#52511yescharacteristic
765C4C3×#52511yescharacteristic
766C4C3×#53211yescharacteristic
767C4C3×#53211yescharacteristic
768C3#2358311yescharacteristic, direct product factor, Sylow
769C2—81no—
770C2—82no—
771C2—82no—
772C2C3×#238811yescharacteristic
773C2C3×#301011yescharacteristic
774C2C3×#301211yescharacteristic
775C2C3×#311811yescharacteristic
776C2C3×#312511yescharacteristic
777C2C3×#317311yescharacteristic
778C2C3×#317911yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#542C2semidirect
2. C2×C3×#442C2semidirect
3. C2×C3×C4×SD16C2semidirect
4. C3×#2324C2semidirect
5. C3×#2058C2semidirect
6. C3×#2042C2semidirect
7. C3×#2035C2semidirect
8. C3×#2034C2semidirect
9. C3×#2023C2semidirect
10. C3×#2012C2semidirect
11. C3×#2000C2semidirect
13. C3×#1763C2semidirect
14. C3×C4×#102C2semidirect
15. C3×#1750C2semidirect
16. #23583C3direct (N × H)
64. C2×#542C2×C3semidirect
65. C2×#442C2×C3semidirect
66. C2×C4×SD16C2×C3semidirect
67. #2324C2×C3semidirect
68. #2058C2×C3semidirect
69. #2042C2×C3semidirect
70. #2035C2×C3semidirect
71. #2034C2×C3semidirect
72. #2023C2×C3semidirect
73. #2012C2×C3semidirect
74. #2000C2×C3semidirect
76. #1763C2×C3semidirect
77. C4×#102C2×C3semidirect
78. #1750C2×C3semidirect
113. C3×C4×Q8D4semidirect
117. C3×C4×D4D4semidirect
347. C4×Q8C3×D4semidirect
351. C4×D4C3×D4semidirect
768. C3#23583direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5422
C2×C3×#4422
C2×C3×C4×SD162
C3×#23242
C3×#20582
C3×#20422
C3×#20352
C3×#20342
C3×#20232
C3×#20122
C3×#20002
C3×#19992
C3×#17632
C3×C4×#1022
C3×#17502
#235833